摘要:

Crossed Laser and Molecular Beam Studies of Mixed Alkali Dimer : Preparation, Perturbation and Predissociation BY ERNST J. BREFORD, FRIEDRICH ENGELKE, GUNTHER ENNEN AND KARL H. MEIWES Fakultat fur Physik, Universitiit Bielefeld, D 4800 Bielefeld 1, West Germany Receiiyed 4th December, 1980 Recent developments in tunable lasers and molecular beams have enabled a major refinement in the study of molecular properties. For example, the supersonic nozzle beam preparation technique has brought the spectral resolution of measurements of homonuclear and heteronuclear alkali dimers in our laboratory down to 0.001 cm-' ( = 30 MHz). Apart from classical applications, such as accurate determination of vibrational and rotational constants, dimer concentrations and internal distributions, " selectively detected laser-induced fluorescence (SDLIF) " spectroscopy opens up pos- sibilities of studying new fundamental properties of these molecules. Thus, studies of individual rotational levels have revealed that predissociation phenomena are much more common than was earlier believed.In addition to an increased knowledge of basic molecular properties, these pheno- mena have important applications, such as the accurate determination of dissociation energies and molecular formation rates. It is also shown that crossed laser and molecular beam studies are a powerful tool for investigating perturbation effects. Although our first experimental knowledge of resonance fluorescence of excited states in atoms and molecules goes back more than seventy years,' more systematic studies did not come until the late 1960s.This is largely because modern experimental tech- niques, developed in laser physics, are necessary for studying complex spectra under high resolution. Another reason for the renaissance in optical spectroscopy during the past decade is that new research fields, such as laser chemistry, plasma physics and certain branches of physical chemistry, opened up where knowledge of involved mole- cular parameters and transition probabilities is frequently demanded. Consequently, it is worthwhile to re-examine classical spectroscopic studies in the light of what molecular-beam and laser devices can do to improve them. Under those felicitous circumstances where both can be utilized effectively, the progeny of this com- bination is a delight in that it provides some of the most detailed information on spectroscopic knowledge yet available.The introduction of laser-induced fluorescence spectroscopy in 1973 at the 55th Faraday Discussion2 by R. N. Zare and coworkers3 implied great progress in deter- mining the internal state distribution of nascent reaction products and this same tech- nique continues to provide the bulk of knowledge in this field.4 The most frequent application of the LIF data obtained in this or various other ways has been the deter- mination of molecular parameters. However, poor spectral resolution has severely limited several of these measurements, so that very few investigations have been car- ried out at a resolution better than 0.1 cm-l (f.w.h.m.).This should be compared with a resolution of ca. 0.01 cm-*, which is frequently necessary to analyse complex atomic and molecular spectra (and is about the Doppler width at room temperature). On the other hand, it has recently been possible to gradually approach another resolu- tion limit: the natural linewidth, which is < 0.001 cm-I for dipole-allowed transitions, by the introduction of supersonic nozzle beam techniques. We use the combination234 MIXED ALKALI METAL DIMERS of crossed laser and molecular beams at our laboratory especially for alkali dimers by the introduction of different types of tunable dye lasers in the visible spectral range. As an example, fig. 1 shows a small section of the electronically excited spectrum of Rb, recorded at three different spectral resolutions using crossed laser and mole- cular beams.Evidently, a 0.01 cm-' f.w.h.m. is necessary to resolve the rotational structure of the BIII,-XIC,+ band system of Rb,.5 In what follows, we describe, after a short general account, how molecular-beam r e s o l u t i o n I 0.1 c m - ' I II I 1 I I I 1 I 1 l ' l ' l ' l ' i ' l ' l FIG. 1.-Part of the excitation spectra of the Rbz B1n,-XIE: band system recorded at 1.0, 0.1 and 0.005 cm-' f.w.h.m. resolution using the crossed laser and molecular-beam technique. These spectra drastically illustrate the need for high resolution in optical spectroscopy. and spectroscopic techniques allow detailed studies in the field of heteronuclear and homonuclear alkali dimers. The scope of these new methods is now very wide and includes, besides the " classical '? determination of molecular constants, new possi- bilities of studying predissociation, dissociation energies, molecular formation rates in nozzle beams, transition moments: lifetimes and perturbations.Thus, by the in- troduction of a new technique, " selectively detected LIF '? spectroscopy (SDLIF),E . J . BREFORD, F. E N G E L K E , G . ENNEN AND K. H . MEIWES 235 much new information can be obtained justifying the name “ high-resolution spectro- scopy ” . LASER-INDUCED FLUORESCENCE-HOW I S IT DONE ? To start, we present a molecular-beam-laser set-up, which has already been des- cribed in a recent publication.6 In brief, a horizontal alkali metal beam crosses a well-collimated laser beam, as shown in fig.2. The metal dimers (Na,, Liz, NaLi, LASER DE TECTOR OVEN1 OVEN2 ‘yG& PIPE i’l NOZZLE ._+-’ TO PM POWER METER FIG. 2.-Schematic diagram of our crossed laser and molecular beam experimental set-up. K2, NaK, Rb,, . . .) are produced in different types of ovens. Separate temperature controls maintain defined pressures of the alkali metal mixture which escapes through a 0.3-0.5 mm nozzle and a skimmer or a set of slits into the excitation chamber. This is a separately pumped vacuum chamber which contains carefully constructed light baffles to avoid scattered laser and oven light, fluorescence observation flanges and a Langmuir Taylor detector (LTD). The LTD can be moved perpendicular to the molecular beam to measure the beam profile and the total beam flux.When the metal beam is on, the pressure in the excitation chamber is typically < 1.3 x Pa (<lo-‘ Torr); hence the set-up is operated as a true molecular beam, which per- mits high-resolution spectroscopic studies. The fluorescence is observed by eye to originate primarily from the volume intersected by the alkali beam and the laser. Either a scanning spectrometer or fast photon detection systems view the fluorescence through one (or two) light pipe(s) perpendicular to the beams. The light sources we use include the following commercial lasers : (a) argon-ion laser and krypton-ion laser (Spectra-Physics, model 171, fixed wavelengths), (6) nitrogen-pumped dye laser (Avco C 5000, Lambda Physik FL 1000, tunable from 7200 to 3800 A), and (c) Ar+ and Kr+ pumped dye laser (Spectra Physics, model 580, tunable from 6750 to 5700 A).236 MIXED A L K A L I METAL DIMERS L A S E R - I N D U C E D FLUORESCENCE-WHAT C A N BE LEARNED ? I f one could prepare a molecule in a few known internal (v", J " ) states, detection of excited states would be straightforward and within present capabilities.Such experiments represent an important advance in determining excited-state properties. Here we describe : 1. The first successful experiments on the heteronuclear alkali dimer NaLi in a molecular beam in Section 1 of this paper. In addition, complementary experiments are presented using a new device, the Injection Heat Pipe (LHP). 2. Under the conditions described above the (molecular) absorption linewidths are sub-Doppler close to the natural linewidth (i.e., a few MHz).Therefore, we are able to carry out high-resolution molecular spectroscopy using a single-mode dye laser for excitation. An example is presented in Section I1 illustrating the LIF recorded for the NaKBIII-XIC+ band system. The great impact of SDLIF upon beam experi- ments in the field of intramolecular energy transfer is illustrated, which in turn gives us insight into the strong perturbations. 3. Furthermore, the collision-free flow of atoms and molecules in a supersonic beam may be used to study weak and very weak predissociation processes. Once again alkali dimers (Rb2 and K2) serve as an example in Section 111. From knowledge of both the resulting molecular and atomic fluorescence we determine the molecular states responsible for the predissociation.These studies merely serve as examples of the far-reaching conclusions that can be derived from a laser-induced fluorescence spectrum obtained under collision-free con- ditions in molecular beams. RESULTS AND DISCUSSION I . PREPARATION : Na6Li AND Na7Li The NaLi molecule is the lightest heteronuclear diatomic alkali molecule and as such has been the object of a number of ab i n i t i ~ , ~ - ~ pseudopotentiallO*lt and other c a l c ~ l a t i o n s . ~ ~ - ~ ~ Experimental data concerning the electronic states of NaLi are few. As early as 1928, all possible alkali molecules MM' (M, M': Li, Na, K, Rb and Cs) had been observed experimentally16 with the exception of NaLi. However, up to 1971, despite several attempts,16*17 the NaLi molecule had not been observed, probably because of overlap with the spectra of Na, and Li,.Hessel demonstrated, for the first time, experimental observation of the Na7Li molecule by laser excitation within the B1n-XIZ+ band system." He showed that the most intense feature in the LIF of a Na + Li mixture excited by the 4965 A Ar+ laser line is a long progression of P and R doublets which lie in the region between 4950 and 5480 A. The values of the mole- cular constants obtained agree with those predicted by ab initio calculations to within loo/,. They are systematically higher than expected. We have reinvestigated the fluorescence spectrum at higher resolution using both molecular-beam techniques and the newly designed injection heat pipe (IHP).l9 We found that most of the discrepancies arise from perturbations in the excited B'II state, especially in the spectral region studied by Hessel, which resulted in an incorrect assignment of the rotational numbering of the series he observed.The new data, which include 10 different fl~orescence series in Na6Li and Na7Li and well-resolved excitation spectra ranging from 0' - 0 to u' = 20 for the excited l I I state and from v" = 0 to u" = 43 for the X'C+ ground state, allow us to obtain reliable potential-energy curves for the B and X states of NaLi, highly accurate disso-E. J . B R E F O R D , F. E N G E L K E , G. ENNEN A N D K. H. MEIWES 237 ciation energies for both the B ' n and X'C+ states, and to investigate the long-range forces between the two ground-state alkali atoms Na and Li as well as the long-range interaction between Na(32S,,,) and excited Li(22P3,,) in the n-configuration.Since the experimental conditions required to take laser-induced fluorescence spectra in a nozzle beam have been outlined above, only the features pertinent to the present investigation are discussed here. We used two types of beam ovens: (1) a double-chamber oven as described previously6 and (2) a newly designed three-chamber nozzle oven shown schematically in fig. 3. Our first experiments on NaLi nozzle POSITION OF CAPILLARY -M- FIG. 3.-Three-chamber alkali oven. A detailed description of design, construction and perform- ances is given in ref. (19). beams were performed in the simple double chamber oven. Several good beams of NaLi were obtained but running times were short and concentration quite unstable, because lithium is apparently not completely miscible with sodium.20 Then, a three- chamber oven was designed and built with separate temperature controls for each section (see fig.3) producing a high concentration of NaLi during expansion in high vacuum, with the mixing of Na and Li occurring in the front nozzle chamber. LIF is observed perpendicular to both the metal and laser beams with a photo- multiplier tube (RCA 8852, ERMA 111 photocathode) in conjunction with different filters to avoid the intense fluorescence from the Li2B-X and Na,B-X band systems excited at the same time. The signals are processed using gated detection electronics (PAR boxcar, model 162 with a model 165 plug-in preintegrator, gate width 5-15 ns). Fig.4 shows a typical fluorescence excitation spectrum when a nozzle beam of NaLi is excited in the spectral range 4650-4950 A. The band-heads of the Na'Li and Na7Li B-X band system are readily identified. Similarly, the band-heads of the Liz and Na,B-X systems, which are known precisely, can be used as a wavelength calibration. In addition, a new device based on the heat-pipe oven21*22 has been demonstrated to be extraordinarily useful in LIF studies of mixed alkali metal niolec~les.'~ It allows fluorescence studies under known, uniform and easily adjustable metal-coni- pound concentrations even for iininiscible metals which have quite different vapour pressures at a given temperature. The basic idea was to take a conventional heat pipe for the metal with the smaller vapour pressure at a given temperature and then inject continuously a small amount of the other metal vapour which is produced out- side the heat pipe in an external oven held at a different, usually lower, temperature.By adjusting the amount of vapour injected by varying the temperature of the external oven, steady-state conditions are obtained and held for many hours, The apparatus is shown schematically in fig. 5. The heat pipe consists of a stainless-steel tube with Brewster windows on both ends and a stainless-steel mesh inside which serves as a wick. The central part is heated with heater HI and the ends are positioned by cool- ing flanges C. The external injection oven 10, filled with the second metal, is heated to a different temperature by heater H3.The small-diameter injection tube is always kept at a higher temperature by heater H2 to prevent clogging. A small amount of238 MIXED A L K A L I METAL DIMERS rare gas of ca. 15 Pa pressure is added through the pump system PS to keep the win- dows free from contamination. The excitation laser beam is directed through the IHP close to the optical axis by the mirror M. The fluorescence light is collected by lens L and then focused on the entrance slit of a spectrometer-photomultiplier com- bination. We have tested this system with the alkali metals Na and Li by observing the different dimers Na,, NaLi and Li, by LIF from an Ar+laser. The fluorescence spectra I I I I I 4700 4800 4900 wavelength/A FIG. 4.-Excitation spectrum of NaLi formed in a supersonic nozzle beam from the three-chamber oven.Note the large isotopic displacements in the u’ progression with 8‘‘ = 0 of the B-X bands of NaLi. The wavelength scale is the tunable dye laser excitation wavelength. were first measured photoelectrically on a 3/4 m Spex grating spectrometer and then photographed on Kodak 103aF plates in a Jarrel-Ash 5 m Ebert spectrograph with a grating blazed at 5000 8, (1 200 lines per mm) yielding a linear dispersion of 1.50 8, per mm. For such high- quality spectra the estimated absolute uncertainty in wavelength determination of unblended lines is G0.05 cm-I and the uncertainty in relative position is G.02 cm-‘. Ar+ 5145 and 5017 A were found to excite two strong and two weak fluorescence series in Na6Li. Most of the work on Na7Li was done with the 4965, 4880 and 4765 8, lines, which give rise to six series.In searching for extremely long fluorescence series we found that Ar+ 4765 8, excites a Q series in the 15-1 band of Na7Li, which gives rise to fluorescence up to V” = 43 (Na7Li dissociates at v” = 48!). These weak lines Using 20 pm slits exposure times varied from 5 to 30 min. FIG. 5.-Schematic diagram of the injection heat-pipe (IHP). text and in ref. (19). A detailed description is given in theE . J . BREFORD, F . ENGELKE, G . E N N E N AND K . H. MEIWES 239 were measured photoelectrically and could be located with an accuracy of 0.2 A. In all, LIF spectra were studied in the region from 4500 to 7000 A. The fluorescence series of doublets which were first observed by Hessel18 were readily identified.In addition, many new fluorescence series were recorded throughout the investigated region due to Li,, Na2 and NaLi. The aim of the experiments using different isotope mixtures was to establish if a fluorescence series was due to a Na6Li or Na7Li molecule. With the exception of a few stray lines, all features could be assigned unambiguously. The first problem was to determine the rotational and vibrational quantum num- bers of each of the observed fluorescence lines. Due to the presence of important perturbations in the B state, the P and R branches have to be treated separately from the Q branch. Fortunately, the series excited by the 5145 and 5017 A Ar+ laser lines belonging to the Na6Li isotopic species do not exhibit strong perturbations.Each series is composed of P, Q and R lines. Due to the observed band-head formation at low J levels populated by inelastic collisions with the buffer gas and the presence of the Q(l) line, indicating that the upper state is indeed the B’II state, the rotational lines TABLE WAVENUM NUMBERS OF THE P AND R LINES AND COMBINATION DIFFERENCES IN THE (u’ = 1 + u”) BANDS OF THE Na’Li B’lT-X’C+ TRANSITION The experimental data are compared with Hessel’s data (in parentheses).’* In addition, absolute wavenumbers and combination differences have been calculated from molecular constants of table 2. 0 20 178.62 (20 178.62) 1 19 927.95 (19 927.93) 2 (-) 3 19 436.53 (19 436.55) 4 19 195.92 (19 195.91) 5 18 958.71 (18 958.68) 6 18 724.98 (18 724.89) 7 18 494.70 (18 494.70) 8 18 268.03 (1 8 268.04) - 20 135.10 (20 135.08) 19 884.82 (19 884.81) - (-1 19 394.20 (19 394.19) 19 153.97 (19 154.00) 18 917.18 (18 917.17) 18 683.86 (18 683.78) 18 454.07 (18 453.96) 18 227.76 (18 227.69) 43.52 43.13 (43.12) (43.54) - (-1 42.33 (42.3 6) 41.95 (41.91) 41.53 (41.51) 41.12 (41.11) 40.63 (40.74) 40.27 (40.35) 43.49 43.1 1 42.37 41.95 41.52 41.10 40.62 40.23 $0.01 (+0.01) f0.02 (0.00) (-3 -0.02 (0.00) f0.01 (0.00) - 0.02 (- 0.05) -0.01 - 0.03 (- 0.03) - (-0.10) $0.03 ($0.04) -0.02 (- 0.04) 0.00 (- 0.01) (4 f0.02 (f0.01) +0.01 ($0.04) -0.01 (- 0.02) - 0.03 (-0.11) (-0.13) - - 0.04 - 0.01 (- 0.08) were numbered unambiguously.Lower state combination differences A#‘‘ are easily obtained, but, after using the isotope relations, did not agree with those ob- tained from Hessel’s analysis of the 4965 8, series in Na7Li.18 Comparison of the observed spacings of the doublets of this series with the energy-level spacings cal- culated from Na6Li data shows that the doublets consist of R(28) and P(30) lines.In table 1 the observed doublet spacings and the separation between successive doublets o f “ Hessel’s series ” are compared with A2F”(29) values and vibrational spacings cal- culated from the Dunham coefficients, given for both isotopic species in table 2. The agreement between the observed and calculated values shown in table 1 leaves no doubt that the “ Hessel series ” results from the excitation of the J’ = 29 level of240 MIXED ALKALI METAL DIMERS Na7Li B'II. More series of doublets and singlets could be identified comparing the doublet spacing (in the case of Q line excitation the accompanying collision-induced P and R satellites were used) and the distances between lines with the measured rota- tional and vibrational spacings of the lowest few vibrational levels.Unfortunately most of the series belonging to both isotopic species, Na6Li and Na7Li, show pertur- bations and we have not been able to use all the data in determining the constants of the excited B'II state. Once the J numbering in the B-X series had been established, the next step was to determine rotational constants for the B'II state. Because it TABLE 2.-THE DUNHAM COEFFICIENTS Yik FOR THE BLn AND X'x' STATES OF Na6Li AND Na'Li, RESPECTIVELY The analysis is described in the text, and in more detail in ref.(25). Error limits are standard deviations. All quantities are in cm- '. The number in parantheses that follows a quantity is the exponent of 10 that multiplies the quantity. Na7Li, X'C+ Na6Li, X'C+ 0.25655 - 0.1 61 43 -0.6174 0.3751 -0.3131 -0.2321 - 0.2894 0.3106 -0.105 0.776 0.1 32 0.488 0.590 0.937 0.316 0.386 0.496 0.328 0.27246 - 0.18072 - 0.6897 0.423 1 -0.3732 -0.3007 - 0.449 0.3500 -0.124 - 0.928 0.287 0.751 0.691 0.995 0.274 0.328 0.541 0.433 could not be assumed that upper-state levels are unperturbed, the values of F ( J ) were determined from the frequency of the laser line(s) together with the known constants for XIC+. We assume that the upper-state rotational values are roughly represented by constants given in table 2.A good deal of rotational structure is well-resolved in different fluorescence and excitation spectra of NaLi. From these lines we deter- mined smoothed values A2F'(.J) for different u' values from which finally, with cal- culated values of Dfe, values of B: were obtained. These estimated rotational con- stants, satisfying the isotope relations are then used to calculate band origins and band-head formations of the uf t (u" = 0) bands in the B'l-I-X'C+ system for both isotopic species and thus to determine the isotope shifts in the upper state. The results are in good agreement with those from the pulsed laser excitation spectra in a nozzle beam in fig. 4. In conclusion, these results provide an indeed unambiguous vibrational numbering in the B'l-I state.The vibrational quanta of the ground state of Na7Li decrease regularly and slowly up to u" = 30 and then decrease rapidly up to un = 40 where they again decrease slowly, see fig. 6. This behaviour, which is not unusual for diatomic molecules, indi- cates the difficulties in extrapolating a series of vibrational levels. Thus, we decided to do a long-range analysis of the XIC+ state. In recent years there have been great advances in the interest and understanding of the properties of diatomic molecules in levels near dissociation. These properties are largely determined by the intermolecular potential in the neighbourhood of the outer turning points. The interaction energy between two atoms at sufficiently large inter- nuclear distance, R, neglecting rotation, can be expressed in its characteristic form V(R) = D - CC,,/R", nE .J . BREFORD, F. E N G E L K E , G . ENNEN AND K . H . MEIWES 241 36 38 40 42 44 46 U" FIG. 6.-(a) Birge-Sponer plot, vibrational term energy differences AGO,, against u", for the X'Z+ state of Na'Li measured with the 4765 A laser line excitation. (b) LeRoy-Bernstein plot,23 (AGL...)''z against u", of the values from (a). u; is the non-integer fictitious vibrational quantum number at which the molecule dissociates. where D is the energy at infinity and n and C,t are a set of integers and constants, res- pectively. The long-range intramolecular potential for ground-state NaLi has the same form as that for other state alkali dimers or that of molecular hydrogen. The highest observed levels of Na'Li lie sufficiently close to dissociation that their outer turning points lie in the region described by eqn ( l).23 This kind of analysis, described in a previous paper in more detail,24 applies well to the X'C' state of NaLi.The value of D,(NaLi, X'C') is thereby found to be D,(NaLi, X'C+) = 7068 -j= 4 cm-'. (2)242 MIXED ALKALI METAL DIMERS The data obtained from our observations of the excitation spectrum of NaLi B ' n are less suitable for evaluating long-range forces for this state. The excitation spectrum involves (1) perturbations and (2) can be followed only up to ca. 260 cm-l below the limit of the B state. Nevertheless, the long-range portion of the BlII poten- tial does provide some information, since it can be used to determine the C, constant and probably a rough ratio C6/C8.Six points of the B state RKR curve were fitted allowing the constants C6 and c, to vary. Using the values c, = 3.68 x 10' cm-' A6, c,/c6 = 65, we have calculated the long-range portion of the potential-energy curve of the B'll state. The agreement between the calculated and observed values of D - V(R) for u' 3 10 gives the dissociation energy D,(NaLi, B'II) = 1918 10 cm-'. (3) From the present investigations, molecular-beam LIF results combined with the LTF spectra from the IHP have proved to be powerful techniques in the characteriza- tion of spectra and properties of NaLi. Applying this technique, the dissociation energies of NaLi B'II and X'C+ states derived from the fluorescence spectra are reli- able to within a few wavenumbers.Ground-state constants obtained from the experiments show a gratifying agreement with ab initio and pseudopotential calcula- tions, whereas excited-state results from our studies are not in reasonable accord with theoretical values. Table 3 compiles the known theoretical and experimental values TABLE 3.-cOMPARISON OF DISSOCIATION ENERGIES De (IN C I I I - l ) FOR THE B1n AND xlx STATES OF NaLi ref. De(NaLi, X' E +) D,(NaLi, B'll) 7 9 10 11 12 13 26 this work 6777 f 320 0 7178 f 160 - 7017 & 1300 - 6936 968 9598 - 649 1 - 7364 - 7068 5 4 1918 * 10 for the dissociation energies D, for the B'II and XIC+ state of NaLi. In the near future, theoretical effort should be expended in attempting to resolve the large discre- pancies between experiment and I I . PERTURBATION: NaK B1ll-XIZ+ It is well-known that in normal excitation spectroscopy in cells or heat pipes the ultimate resolution is limited by the linewidth due to Doppler broadening.This limitation has been overcome by using Lamb-dip 2 7 9 2 8 and two-photon absorption techniques. 28-30 The disadvantage of these two methods is that -they require rather high-power tunable lasers, which are not always available in the required wavelength region. Another obvious method for reducing the linewidth and reducing the com- plexity associated with the large number of populated rovibronic states is to use a well- collimated molecular nozzle beam and to cool the sample during e~pansion.~' The disadvantage of using molecular beams is the low optical density, which makes fluorescence experiments rather difficult.On the other hand, the spectrum is freeE . J . BREFORD, F. E N G E L K E , G . E N N E N AND K . H . MEIWES 243 from interactions with other molecules, and spectroscopists are sure that novel and interesting features are due to a property of the isolated molecule. In the following we discuss the B1ll-X'Cf band system of NaK as an example where the above-mentioned sub-Doppler technique combined with the " selectively detected LIF " spectroscopy yields information that could not have been obtained from spectra of NaK in a cell. We have observed the spectrum from 5730 to 5900 A at a resolution of ca. 25 MHz and have resolved and analysed different perturbed and unperturbed vibronic bands in the region. From the correlation diagram, fig.7, it follows that the potential curves of two case ( a ) case ( c ) separated coupling coupling atoms c 3 1 + A t + b3 n 0' 0- '1 _1 0' 0- FIG. 7. -Correlation diagram for Na (32S112) and K ( 4 2 p 1 j 2 . 3 / 2 ) . The b 311i state is the most probable candidate for causing the perturbations in the NaK B'n state (see Section 11). electronic states in NaK, Bill and b311i, perturb each other, where 111-3n, perturbation is the strongest and most probable i n t e r a ~ t i o n . ~ ~ One well-known case of such a perturbation is the interaction between the D ' n and d 3 n , states in NaK, which is dis- cussed in ref. (24) in more detail. The NaK B ' n and b3n1 states are represented by a single electron configuration and the molecular orbitals for both states are identical.Due to this interaction the intensities I (B'n-X'X+) and Z'(b3FIl-X1 C+) of the(unper- turbed) transitions from these levels to the ground state (XIC+) change to the perturbed \dues Ipert(B-X) and Ilpert(b-X), respectively, in such a way that the sum Ipert(B-X) + I'pert(b-X) = I(B-X) + I'(6-X) is fulfilled for all u', J' levels. Closer analysis of the present case shows that the perturbation permits another means of detection : Whenever the two perturbing states exchange oscillatory strengths (so that the above sum is always fulfilled) then the interaction causes an increase in the b3n,-a3C+ intensities at the expense of the corresponding decrease of B-X inten- sities. Accordingly, we would expect a smaller fluorescence yield for the B-X (singlet) band system and, at the same time, the intensity I"p,r,(b3FI,-~3~+) of the perturbed transition to the lowest triplet state should increase.This effect has, in- deed, been discovered in the present precision studies of the NaK molecule. In par- ticular, the resolved rotational structure enables measurements of individual rota- tional lines. Such studies allow a determination of the variation in the mixing co- efficients of the perturbed wavefunctions as a function of rotational energy. More- over, fluorescence measurements of closelying unperturbed levels also directly yield the unperturbed parameters. A beam of NaK dimers is pro- duced by the supersonic expansion of a mixture of sodium (10 yo) and potassium (907;) from a double stainless-steel oven through a nozzle with a 0.5 mm throat diameter.The apparatus is shown schematically in fig. 2.244 MIXED A L K A L I METAL DIMERS ARGON - I ON DYE \ ;\ LASER LASER - For most of the runs, the oven body was maintained at a temperature of ca. 770 K, corresponding to a pressure of 4 kPa of the alkali mixture. A block diagram of the essential parts of the present laser frequency monitoring and regulating set-up is shown in fig. 8. The light from a commercial C.W. tunable dye laser (Spectra Physics model 580 A, pumped with the green lines of a model 171 8 W Kr+ laser) intersects the well-collimated molecular beam at an angle of 90". We use Rh-6G, which gives a single-mode output power of ca. 10 mW in the spectral region of interest. The Doppler broadening due to the finite collimation of the beam is less than the linewidth of the dye laser used.(1) The resulting fluorescence is viewed \ L 7. HE-NE LASER, STANDARD LAMP - 7 , -METER LIGHT -METER ' 1 BAFFLE i , STAB1 L I SAT I ON @+t- FIG. 8.-Single-mode dye laser frequency monitoring and calibration arrangement combined with the crossed laser and molecular-beam LIF experiment. A detailed description is given in ref. ( 5 ) . - << . STABLE REFERENCE - FABRY PEROT at right angles to both the excitation laser beam and the molecular beam with a cooled, high-efficiency photomultiplier RCA 8852 (ERMA I I t response) in conjunction with a bandpass filter. This filter opens at 7800 3 100 A and limits the response to the expected b3rI-a3C+ transitions. (2) The molecular bands of the B'17-X1C+ system are measured at the same time with an EM1 6256s photomultiplier (Sll photocathode) whose sensitivity is limited to wavelengths (6000 A.The photoelectric signals are detected with fast picoammeters (Keithley model 417) and the fluorescence spectra are displayed on a strip-chart recorder simultaneously with frequency marks from a stable Fabry-Perot etalon and with absolute frequencies from an optogalvanic calibra- tion spectrum from a hollow-cathode lamp filled with neon. This improved calibra- tion allows high-accuracy measurements. Continuous scans were performed as wide as 350 GHz. Spectral resolved LIF spectroscopy is applied to the measurement of the rotational structure of vibronic bands in the NaK B'n-X'C+ band system. Fig. 9 is a spectrum obtained for the NaK B-X (6, 0) transition.The signal-to-noise ratio is excellent. All R, Q and P lines for J < 40 are resolved and measured for the first time. As can be seen from fig. 9, considerable narrowing of the absorption has been achieved by using the nozzle beam-the Doppler width of the bulk NaK vapour is ca. 500 MHz.E. J . BREFORD, F. ENGELKE, G. ENNEN AND K. H . MEIWES 245 s Icl 1.998GHz G YH- 1 1 1 1 1 1 1 1 1 1 1 l 1 1 1 1 1 1 1 1 1 I l l l l l l l l l l l l l I I I I I I I 576.40630nrn 576.44188 nrn wavelength /nm FIG. 9.-Selectively detected LIF spectrum of NaK produced in a supersonic nozzle beam, The (6, 0) band of the B'H-X'X+ band system is shown for J d 10. The rotational lines are assigned on top, and at the bottom the frequency marks of the external Fabry-Perot interferometer are displayed.Two neon lines give absolute frequencies from an optogalvanic calibration spectrum of a hollow- cathode lamp. The linewidth of the transitions measured here is ca. 35 MHz. Triplet-triplet fluores- cence is absent and both P and R as well as Q lines appear and have the relative inten- sities expected for an unperturbed system. Thus, we conclude that this part of the B-X band system is unperturbed and molecular constants can now be obtained with- out large systematic errors. The first step in our analysis is to identify the correct v", J" and v', J' quantum numbers which are assigned to each line. This is not easy for the dense NaK mole- cular spectrum. Unfortunately the approximate values of mi, LD,X:, me)):, B: and a: for the excited B'n state from previous absorption and fluorescence e ~ p e r i m e n t s ~ ~ - ~ ~ are not very precise, while molecular constants for the ground state are well-estab- The vibrational numbering we use agrees with the vibrational numbering adopted by Loomis et aL3' and later confirmed by S i r ~ h a .~ ~ Table 4 lists these band origins and band-head positions observed. 1 ished.24,36,37 TABLE 4.-oBSERVED BAND-HEAD AND BAND-ORIGIN POSITIONS (in Cm-') OF THE NaK B'n- x'c+ BAND SYSTEM All positions are uncertain by cu. 0.005 cm-'. In addition, band-head positions from the l i t e r - a t ~ r e ~ ~ , ~ ~ are given for comparison. u', u" band-head band-origin from ref. (32) from ref. (34) 17 102.416 17 166.774 17 288.305 17 345.534 17 400.486 17 503.685 17 598.082 17 684.354 17 102.153 17 166.528 17 288.090 17 345.336 17 400.301 17 503.516 I7 957.923 17 684.221 17 102.68 17 103.4 I 7 166.20 17 167.1 17 287.3 17 345.22 17 346.1 17 399.73 17 400.1 17 502.71 17 503.0 17 597.63 17 598.2 17 683.57 17 689.7 -246 MIXED ALKALI METAL DIMERS With our completely resolved rotational lines the rotational numbering is greatly facilitated.From the vibrational and rotational analysis we have fitted molecular constants of the B'n and X'C+ states of NaK. The results in table 5 are given in the form of conventional Dunham coefficients, where we have used different vibrational bands with ca. 500 lines excited in NaK to improve them. From the potential curves for the XIC+ and B'll states of NaK constructed from these spectroscopic constants given in table 5 using the RKR method we have evaluated Franck-Condon factors for TABLE 5.-THE DUNHAM COEFFICIENTS Yir; FOR THE NaK B'n STATE CALCULATED IN THE PRESENT ANALYSIS The precision is indicated by the quoted standard error.All quantities are in ern-'. The number in parantheses that followsaquantity is the exponent of 10 that multiplies the quantity. For the calculation of line positions voo = 16 966.1 68 cm- and the X'C+ state constants from ref. (37) should be used in addition. 0.71 756 0.4388 0.7806 0.72 10 -0.1012 -0.4358 0.1354 - 0.1 2533 - 0.2288 - 0.4435 0.3548 0.635 0.144 0.134 0.433 0.243 0.879 0.120 0.498 0.146 0.410 0.362 the observed bands. Using the measured intensities and the calculated Franck-Con- don factors we are able to determine the " internal " temperature the NaK beam reaches during the expansion.We use the unperturbed bands of the 21'' = 0 progres- sion of the B-X system to obtain the rotational state distribution. The line intensi- ties are taken to be proportional to the height. Two assumptions are made: (1) the laser power is constant over a given band contour and (2) the fluorescence detector has an equal probability of collecting all photons in the band with the same efficiency. Both assumptions are reasonable given the narrow shape of the band, the calculated Franck-Condon factors and the characteristics of the photocathode. The experi- mental data have been fitted to a Boltzmann distribution yielding a rotational tempera- ture of T,,,(NaK, X I C + , U" = 0) = 55 & 7 K.(4) These rotational distributions are the same regardless of which unperturbed band in the u" = 0 progression is fitted.* Now let us come back to the perturbed bands of the NaK B-X band system. Despite rapid progress in the analysis of the electronic transitions of alkali dimers, success has been largely limited to transitions between " well-behaved " states, i.e., unperturbed systems. Certain molecular bands have defied analysis by traditional means, a situation that arises whenever extensive near-resonant interaction disrupts the regularity of the line positions. Prime examples of this behaviour are the red * At this stage it is not very meaningful to deduce a vibrational temperature for the NaK dimers, because the number of different excited vibrational levels of the ground state measured so far is not large enough within the restricted tuning range of the dye laser.E.J . BREFORD, F. ENGELKE, G . ENNEN AND K. H. MEIWES 247 A-X band system of Na2,38339 the blue C-X band systems of K2 and Rb,4°-43 and the present NaK B-X band system. We investigate these highly perturbed molecular band systems by monitoring the molecular B-X fluorescence as well as the molecular b-a fluorescence following excitation, the latter of which accounts for the evidence of perturbations in this NaK band system. Fig. 10 shows the molecular fluorescence R I , I v 14 16 Q I P , I I I 18 1 l6 12 I 14 5 8 0 . 4 4 4 9 6 n m wavelength Inm FIG. 10-The perturbed (4, 0) band of the NaK B-X selectively detected LIF obtained under the same conditions as given above in fig.9. Infrared emission, (b), is caused by perturbations due to the Observed B-Xmolecular fluores- cence, (a), is given on top, frequency marks of the external Fabry-Perot interferometer and absolute state which belongs to the K 4'Pi and Na 32S1,2 configuration. frequencies from neon lines, (c), are represented at the bottom. B-A' and b-a as a function of dye-laser excitation wavelength for the (4, O j band. Strong perturbations are manifested by the intense, irregularly spaced rotational linss and the appearance of molecular fluorescence in the triplet-triplet system. The mole- cular fluorescence line intensities are very close to proportional to the dye laser inten- sity, thus ruling out multi-photon processes.Hence it is concluded that they are pro- portional to the perturbation rate of the NaK B state. This perturbation causes the appearance of the infrared triplet-triplet emission, very similar to measurements ob- tained earlier in our laboratory by Breford and Engelke24*44 on the NaK D-X band system. Note that each v', J' level populated by the laser gives rise to B-X and b-a molecular fluorescence in a very different manner. The ratio in turn determines the magnitude of the perturbation. While detailed analysis is still in progress, preliminary results suggest that the effects can be explained by interaction of the B'II state with the b3n1 state. Allegrini et ~ 1 , ~ ~ have performed a rotational analysis on the NaK B'II state. Laser light with 5640 < A/A < 5700 populates numerous vibrational-rotational levels in the NaK Bill state resulting in complicated overlapping series of lines.Allegrini et al. did not recognize the evidence for strong perturbations in the intense irregularly spaced pro- gressions in the excitation spectra. This renders their molecular constants not useful, indeed their rotational numbering is incorrect. We established the vibrational num- bering of the upper-state levels from direct observation of the (0, 0) band at 5893 A, confirming earlier vibrational a n a l y ~ i s . ~ ~ . ~ ~ Perturbation may Next we discuss the nature of the state perturbing theB'II state.248 MIXED A L K A L I METAL DIMERS be induced by both internal (intramolecular) and external interactions. Here the important internal case is covered by selection rules first given by K r ~ n i g .~ ~ Some information about the perturbing state can be obtained from an estimation of the elec- tronic matrix elements. In our case the B ' n state of NaK interacts with a state which gives strong fluorescence in the triplet-triplet system. Following the Wigner-Witmer rules, this state can only be 3C+ or 311i. A correlation diagram for these terms, con- structed on the basis of the relationships given by M ~ l l i k e n ~ ~ is shown in fig. 7 and discussed in the next section in detail. The b3ni state would cause perturbations of both A components as observed. This presumes that the B'II state is higher in energy than the b3ni state. Indeed, strong perturbations in the lower AIC+ state appearing due to a magnetic rotation spectrum in the neighbourhood of the infrared A'C+-XC+ band system of NaK47 are caused by the interaction of the A'C+ and the b3ni state, similar to the perturbations in the red A-X band system of odium.^^,^^ Interaction of the AIC+ with the B ' n would affect only one of the A components.From the rela- tively strong perturbations of the B state we conclude that the spin-orbit interaction causes the perturbation. Consequently the only non-vanishing matrix elements are the elements between the B'II and the b3n, or the c3C+ states, respectively. The c3C+ possibility can be ruled out because such perturbations affect only one parity level not both of the same J value." Our results show clear evidence for perturbations involv- ing both e andflevels for the same value of J. Thus, we conclude that the b3n state is the only candidate for the B'n triplet perturbations.111. PREDISSOCIATION EFFECTS I N ALKALI DIMERS Different cases of predissociation effects in molecules are discussed in the litera- t ~ r e . ~ ~ * ~ ~ The last decade has seen a revival of theoretical interest in predissociation phenomena, coupled with increasing sophistication in experimental techniques. The object of our recent experimental work has been to underline further information available from selectively detected LIF measurements in molecular beams. The pur- pose of this section is to present preliminary results of the predissociation of Rb,? and Kz C'l3 states by curve crossings with hitherto unknown 3C states.Competition with radiationless transitions has earlier been observed as line broadening and intensity anomalies using classical spectroscopic tools. However, the development of tunable lasers has promised to put at the disposal of the " mole- cular beamist " new powerful instruments that will permit the performance of highly refined and sophisticated experiments not previously feasible. It is easy to show that selectively detected LIF spectroscopy is orders of magnitude more sensitive than the classical tools in tracing and studying predissociation effects, which has been one of the most important tasks in molecular spectroscopy. Thus, for instance, knowledge of these effects makes possible a correlation of the energy states in the associated atomic constituents and a careful deduction of the shape of the potential-energy curves.As a most important application, predissociation effects form the most accurate way of determining dissociation energies and hence studies of chemical bonds. In the conventional terminology, predissociation probabilities l/rpred. of the order 108-109 s-' are called weak or " forbidden ", while we have shown that selectively detected LIF spectroscopy, in principle, makes possible determinations of 1 /rpred. values as small as lo5 s-',~' corresponding to line broadening of ca. A (!) and indicating the weakest predissociation effect observed so far by us. Accordingly, we could expect to find a large number of earlier unknown predissociations using this new experimental technique. One of the first cases studied with this goal was the * The e levels of the upper state have only 'ZL character while the f levels have 'El and 'XO.E .J . BREFORD, F. E N G E L K E , G . E N N E N A N D K . H. MEIWES 249 Rb, dimer.43 For the Cln, state a drastic variation in l/rpred. was observed for all rotational levels appearing in the same way for the two A components. The informa- tion derived from the molecular and atomic fluorescence is displayed in fig. l l , where the different spectra associated with dye laser excitation and selective detection of the fluorescence light are plotted. Note that each level 19' populated by the laser gives rise to atomic fluorescence which determines the magnitude of the predissociative pertur- bations. It is concluded that predissociation of the Rb, Cln, state, mainly caused by q 7 9 4 8 A ) i 4 7 9 0 4801) wavelength/A FIG.1 1.-Summary of the Rb, C-X laser induced molecular and atomic fluorescence. The latter is caused by predissociation due to the hitherto unknown c3Z: state. Molecular fluorescence is given on top together with the vibrational numbering, the atomic fluorescence (Rb 0 2 ) is represented below. The spectra shown are not corrected for the varying laser power which is d 15 ?( in this spectral region. The laser bandwidth is measured as 0.15 & 0.03 A. radiationless transitions to an hitherto unknown c3C+ state (case c- in Mulliken's notation)49 is responsibie for the appearance of the Rb 0 2 line, whereas the Rb D1 is absent. This result gives the first definite proof that part of the excited Rb, molecules, which absorb photons in the C-X band system, will be destroyed by predissociation, forming exclusively Rb(SP,,,).Another recent predissociation study has been completed for the K, molecule. In the case of this molecule, new effects are found for higher vibrational levels u' of the Cln, state. The experimental set-up for these measurements is essentially the same as described above, see fig. 2. The selectively detected LIF experiments are performed in a similar way to the Rb, studies. In brief, the fluorescence is detected at right angles to both250 MIXED ALKALI METAL DIMERS the nozzle beam and the laser beam by two photomultipliers. The molecular bands were measured with an EM1 6256s photomultiplier (Sl 1 photocathode), whose sen- sitivity is limited to wavelengths < 6000 A.The atomic emission at 7665 and 7699 a was measured at the same time with a cooled RCA 8852 PM tube (ERMA 111 res- ponse) in conjunction with interference filters. These filters, centred at 7665 & 6 and 7698 f 6 A, limit the response to the D1 or 0 2 line of the potassium atom. The upper part of fig. 12 shows a typical excitation spectrum obtained for the J I I 1 1 I l l l l l l I I I I I J v y 13 11 9 7 5 4 2 0 I I l l I I I I I I 1 r I I d I v : o l 14 12 10 8 6 1.4 2 0 K,C-X 02 7 6 6 5 4 1 I 1 I I 4 2 0 0 4300 LLOO wavelength/A FIG. 12.-Measured predissociation etrects for different vibrational levels u’ of the K2 Cln, state from laser excitation starting at u’’ = 0 and u“ = 1. Observed molecular fluorescence is given on top, the atomic fluorescence, K 4’P-4’S, (K 02) is represented below.K D1 line emission is absent. Obviously parts of the levels are strongly influenced by hitherto unknown predissociation effects, most probably due to (a) the c3Zf state and (b) another unknown molecular state which belongs t o the K 5’s and K 4‘s configuration. K, C-X band system, detecting the blue molecular radiation, and below the spectra obtained when atomic potassium ( 0 1 or 02) line emission is measured. The dominant peaks in the spectra correspond to the band-heads of the U” = 0 progression of the K2- (C1ll,-XII:g) band system. Examination of the atomic emission of the C-Xspectrum reveals the strong appearance of 0 2 line emission from band-heads of higher vibrational numbering u’ in the D” = 0 progression.The 0 2 line emission from these bands indi- cates that higher vibrational states are predissociated and give exclusively K 42P3,2 atoms. The intensities of the peaks in the different spectra can be related to the rela- tive rates (i.e., populations) for forming K2 and K(42P3/2), respectively.E . J . BREFORD, F . ENGELKE, G . ENNEN AND K. H . MEIWES 251 It is interesting to speculate about the form of the observed predissociation pro- cesses in relating them to different potential curves. We suggest that the results can be explained by two different predissociation channels, which in detail are discussed further below. First, we discuss the possible states responsible for predissociating the K,C'II, state and forming directly K 42Pi atoms in both fine structure states.Fig. 3 of ref. (50) shows a correlation diagram showing the states of separated atoms (K in the 32S1/2 ground state, and in the excited 42P,,2 or 4'P3/2 state, respectively) first transformed into Hund's case (c) states of K, and then into Hund's case (a) states, where the order- ing follows Mulliken's rec~mmendation.~~ Selection rules for predissociation are similar to perturbations."~~~ The selection rule A S = 0 may be violated (weak pre- dissociation). This narrows the possible states for predissociating the C state to the states b31T,, A'Z,+, B'n, and c3Z;. The b3n, state would cause the appearance of both K 0 1 and 0 2 emission lines.43 Interaction of a 'II, state with a 'X: would affect only one of the A components, while interaction with a 3rIu state would predissociate both components.Since under higher resolution both P and R as well as Q lines appear and have the relative intensities that are expected for an unperturbed system51 and predissociation of the C state is relatively weak, we doubt that the A'Z; state or the b3n, state or both are responsible for the predissociation seen. Thus, we conclude that the c3C: state causes the observed predissociation in the Cln, state. So far we have concentrated our attention on predissociation which causes the appearance of K 0 2 directly. Higher vibrational states of the K2 Cln, state again only yield the K 0 2 line emission; the K D1 line emission is absent, see fig. 12. More- over, the K, C-X fluorescence disappears almost completely.Here detailed analysis is still in progress. Preliminary results suggest that these features can be explained by a different predissociating channel which forces the excited Kz molecules from the higher vibraticnal levels of the C'n, state first into a bound K2 3E state, which in turn, due to a pseudo-crossing for this 3C, [K(4s) + K (5s)l state and the predissociating c3C; [K (4s) + K (4p)], gives K 4'PP,/, emission. Consequently, one interesting fea- ture observed in these studies is the appearance of curve-crossing in the potential- energy curves of the excited 'Xi states of K, molecules leading to the dissociation fragments K (4'S1/,) + K (4'Pji2). We will test this hypothesis by detecting the K 42P3/2 population under single-mode dye-laser excitation, i.e., under higher resolu- tion, in the vicinity of the pseudocrossing.CONCLUSION We have shown that, by the laser-induced fluorescence technique in supersonic nozzle beams, combined with systematic measurements of both selectively detected molecular fluorescence as well as emission from atomic fragments over series of rovi- bronic levels of excited states of alkali dimers, it is possible to understand the impor- tant perturbation and predissociation mechanisms of these states. The predissocia- tion effects observed are similar in the case of the Rb2C'nI, state and the K2C1rI, state. This may have some applications in studying intramultiplet mixing and depolarization in atomic collision. The technique presented here appears to offer many new and exciting possibilities for molecular spectroscopy using laser excitation and nozzle beams.It has been shown in this paper how this technique can give information on small perturbing and predissociating effects. Most probably many molecular energy levels which are pre- sently believed to be stable are actually subjected to weak or very weak predissociation. It should be possible to study these effects in more detail in the near future and there-252 MIXED A L K A L I METAL DIMERS fore to go one step further in the understanding of simple molecules, especially intra- molecular energy transfer. We thank Dr. C. D. Caldwell for her valuable assistance during part of the experi- mental work and H. Rudolf for help in analysing the data. Partial support by the Deutsche Forschungsgemeinscliaft is also gratefully acknowledged.We are indebted to Prof. Dr. D. Beck for his continuous interest and support. R. W. Wood, Philos. 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ISSN:0301-7249    

DOI:10.1039/DC9817100233

出版商:RSC    

年代:1981

数据来源: RSC

摘要:

Spectroscopy in the Ionisation Continuum Vibrational Preionisation in H, Calculated by Multichannel Quantum-defect Theory BY CH. JUNGEN AND M. RAOULT Laboratoire de Photophysique Molhlaire du C.N.R.S., Universitk de Paris-Sud, 91405 Orsay, France Receiced 9th February, 198 1 Multichannel quantum-defect theory has been used to calculate the effect of vibrational-rotational preionisation on the total and partial oscillator-strength distributions and photoelectron angular distribution in H, for excitation between 800 and 750 A. The total oscillator-strength profiles ob- tained agree well with the high-resolution photoionisation data of Dehmer and Chupka. The results of these authors concerning the final vibrational state distributions obtained by exciting pre- ionisation resonances are also in excellent agreement with the present calculations.Particular atten- tion is given to Rydberg levels which preionise via Av < -1 processes. Preionisation is found to affect all partial vibrational cross-sections ol,+ near narrow Av < - 1 resonances, while near broad Av = -1 peaks only L‘ - 1 is perturbed ( v + and u are the vibrational quantum numbers of the final state and of the preionised Rydberg level, respectively). Further, it is found that peaks which preionise via Av < - 1 and fall among the higher members of a series with less vibrational energy tend to appear as “ complex ” resonances, consisting of a sharp central peak surrounded by an extensive structure of broader satellites. + 1. INTRODUCTION Molecular photoionisation cross-sections near threshold often exhibit a rich line structure consisting of peaks of variable intensity, width and shape, which appear superimposed on an otherwise smooth intensity distribution.Such resonances are the manifestation of preionisatior?, i.e. they reveal the existence of an “ indirect ” photo- ionisation process which can be envisaged as consisting of two successive steps. Absorption of a photon in the first step carries one electron into a highly excited Ryd- berg orbit and simultaneously induces some vibrational excitation if the radiative transition involves a change in molecular geometry. During subsequent collisions with the loosely bound electron the vibrationally excited residual core exchanges part or all of its vibrational energy with the clectron, allowing the latter to escape to infinity.’ It was pointed out many years ago2 that the conversion of vibrational into electronic energy should occur preferentially by exchange of a single vibrational quantum of energy.Indeed, if the vibrational motion is strictly harmonic and the quantum defect of the Rydberg electron varies linearly with internuclear distance, the selection rule Azi = _ t l for the non-radiative coupling holds ~trictly.~ One purpose of the present paper is to show that this selection rule, even when it is valid, cannot be applied without precautions to observable quantities such as photoionisation cross-sections or photoion currents. We have recently used4 multichannel quantum defect theory (MQDT)’s6 to cal- culate the profiles of several broad preionisation resonances in the photoionisation spectrum of H2, corresponding to Rydberg levels 8pa, L’, J == 1 and 8pn, u, J = 1, t Laboratoire associe a 1’Universite de Paris-Sud.254 SPECTROSCOPY IN THE IONISATION CONTINUUM which preionise through exchange of a single quantum of vibrational energy, and we have found good agreement with the high-resolution photoionisation relative cross- sections measured by Dehmer and Chupka’ for this molecule.Here we extend the calculations to a broader spectral range, and we focus in particular on the profiles of resonances npll, u, J which lie below the ionisation threshold corresponding to the vibrational state u+ = u - 1 of the ion. Near such resonances preionisation there- fore proceeds by conversion of at least two vibrational quanta and yields the ion in a final state u+ < u - 2.At the same time the absorption oscillator strength associated with the quasi-bound Rydberg level npll, u is relatively high, since the principal quantum number is relatively low (typically n < 7). > It has often been argued (as again recently in the cases of the NO and NH3 mole- c u l e ~ ) , ~ ~ ~ that such levels should not appear in the photoionisation spectrum since they are so weakly coupled to the ionisation continua that the alternative processes, fluorescence and predissociation, can compete successfully against preionisation, and in fact take over completely. The shortcoming of this argument is that it takes into consideration only one Rydberg level (or series) and one single continuum, or, in other terms, one closed and one open ionised channel.It overlooks the multichannel character of a real situation where, for example, the Rydberg levels with high n associa- ated with the closed channel u - 1 are coupled to both the continuum v - 2 and the low-n Rydberg levels u, and thereby induce preionisation. In the present paper we document this in detail on the basis of experimentally well-studied examples in the H2 spectrum. We find that interchannel coupling tends to spread the oscillator strength associated with a low-nlhigh-u Rydberg level over several Rydberg “ satellites ’’ u - 1 covering a spectral range much broader than the preionisation width of the Rydberg level npll, Our examples show further that most of the individual satellites are substantially broader than the central peak.Such a situation then, if not recog- nised, may lead to apparently conflicting experimental results, namely, when a broad resonance is seen in the photoionisation spectrum at low resolution, yet fluorescence is also observed at the same excitation wavelength, implying a level width which is orders of magnitude smaller. Only little attention has been given in the past to this aspect of molecular photoionisation. We think, however, that the appearance of such ‘‘ complex ” resonances-as we propose to call them-may become a widely observed phenomenon. A previously documented example appears in H2 right at threshold .lo Jn addition to the calculations of the total oscillator strength profile we present detailed predictions concerning the partial vibrational-rotational cross-section pro- files as well as photoelectron angular distributions.Our calculations also yield a slightly improved experimental value for the vibrational quantum AG( 1/2) of the H2+ ion. itself. 2. CALCULATIONS The calculations of total and partial integrated cross-sections (oscillator strengths) have been carried out as previously described.l0 Briefly, we suppose that the mole- cule is initially in the J” = 0 level of the XIZ:, u” = 0 ground state of H2 (para-H2 cooled to liquid-nitrogen temperature as in Dehmer and Chupka’s experiment) and that only the I = 1 partial wave, corresponding to a p electron, contributes near thres- hold.“ Fluorescence and predissociation are neglected, although some evidence for their presence will emerge below. In these circumstances the photoabsorption- photoionisation spectrum is fully characterised by the following set of parameters: (i) the ionisation potential l.P.theor = 124 417.3 cm-l of H, calculated12 includingC H .JUNGEN AND M . RAOULT 255 radiative and relativistic effects, as well as non-adiabatic corrections for the H2 ground state; (ii) the adiabatic potential-energy curve V+(R) for the H’; ion in its ’Z: ground state, which serves to generate the rotation-vibration levels E,+,N+ of the ion in the adiabatic approximation and the associated vibrational wavefunctions x:$ + (R);13 (iii) the adiabatic potential-energy curve Vx(R) of the H2 ground state, which is used to evaluate the vibrational wavefunction x$’(R) for the initial state;14 (iv) two electronic dipole transition-moment functions dA(R), A = 0 and 1 , for excita- tion from the ground state to npA Rydberg levels; (v) two quantum-defect func- tions PA(&), A = 0 and 1, which measure the net effect on the motion of the pA (A = A) photoelectron of all its interactions with the individual particles inside the core.The quantum defect functions are the key quantities in the present calculations. Their magnitudes determine where the Rydberg resonances occur with respect to those given by the Balmer formula, E = -1/(2n2). Further, their variations with internuclear distance R account for the coupling between nuclear and electronic motion which is responsible for vibrational preionisation. The functions pz(R) and pn(R) have been determined previo~sly~*’~ from accurate Rydberg line positions measured in the absorption spectrum3 of H2 for the range of electron energies of interest here.In the following we review briefly how they are used together with the other quantities listed above in order to evaluate the photoionisation oscillator strength as a function of excitation energy E. The reader who is not interested in the theoretical details or who is familiar with MQDT may at this point move directly to the beginning of section 3. 2.1. SPECTRAL DISTRIBUTION OF OSCILLATOR STRENGTH The oscillator strength for photoionisation of HZ, leaving the ion in a given rovi- brational state2 = u+, N + , can be expressed’O as a coherent superposition of dipole amplitudes D i , i = u+, N + , referring to excitation of alternative channel components which are present in the molecular wavefunction at short range with amplitude Bi.At long range by definition only the component i remains. The expression for the oscillator strength is where the dipole amplitudes are given by For a given value J of the total angular momentum, the ion rotational quantum num- ber values N + implicit in the summations over p and i are restricted to the three values N + = J 1 and N + = J for parity (- 1)” and (- 1)” + ’, respectively, owing to the fact that the photoelectron departs with 1 = 1. The corresponding experimental fact is that only two electronic Rydberg series are observed in absorption, npa and npn, of which the latter is doubly degenerate. . . .includes all channels which are open at the given total energy E, E - E, being the transition energy, while the 2 . . . includes all vibrational-rotational channels, open or closed, which are of physical importance at E. The T~ are the asymptotic eigenphase-shifts of the open- channel interaction. Their number equals that of open channels and their sum In eqn (1) the P I256 SPECTROSCOPY I N THE IONISATION CONTINUUM increases by unity each time when the energy E passes through a preionisation reson- ance. The rate of change of the phases is proportional to the lifetime of the preionised le~e1.I~ The eigenphases are related to the scattering matrix which pertains to the collision of a p electron with a rotating-vibrating ion by An explicit expression for the elements (ilp> of the unitary transformation which diagonalises the S matrix is mentioned below.The phases zp and channel mixing coefficients Bf are determined by the following homogeneous algebraic linear system which results from the application of the appro- priate boundary conditions to the molecular wavefunction at infinity and on the boundary of the core, and which hence is set up in terms of the quantum defect func- tions ,u*(R) : Here i = u+, N + , and P and Q refer to open and closed channels, respectively. The matrix elements (ilcli’) and (iJs1i’) are ( i [ c l i f ) J = ( N + / L I ) ~ (u’, N + ICAILV”, N + ’ ) ( A / N + ’ j J , with a similar expression for (ilsji’)J where cos is replaced by sin. I n the separated ion plus electron system the total energy E is shared between the two fragments accord- ing to E = I.P.+ Ei + ci where Ei are the levels of the ion. The electron energy E~ isnegative for closed channels, ci =; -1/(2v?), while it is positive for open channels where the quantity nvi in the linear system eqn (4) is replaced by -nzp. The unitary transformation which diagonalises the scattering matrix is also expressed in terms of the phases z p and coefficients Bi. The elements of the transformation matrix are Finally, the transformation matrix elements ( N + occurring in eqn (2) and (5) connect Hund’s case ( d ) with case (b) states, that is, they account for the uncoupling of I from the molecular axis occurring when the electron ranges far from the core. They are analytically known.5 The coefficients (AIJ”)” are in essence the Honl- London factors for the optical transition.They happen to be the same as the (N+[A)-’ in the present case where the angular momenta of the photon and the photoelectron are the same.’* Comparison of eqn (1) and (3) shows how MQDT treats the photoionisation pro- cess as a half-collision in which the dipole elements Di act as a source term. Note also how explicit reference to discrete states (closed channels) has been eliminated from eqn (1) and (3). It is the channel mixing coefficients Bf and phases ‘sP which by means of their rapid variation near a resonance account for preionisation. On the other hand the basic parameters p*(R) and ~ A ( R ) vary slowly, on the scale of the total energy E, since they refer to the motion of the excited electron at short range where its kinetic energy is very high.In the following we regard the quantum defects as beingC H . JUNGEN A N D M . RAOULT 257 independent of energy over the range of ca. 1 eV. On the other hand we neglect the dependences on R and A of the electronic dipole elements, but we include a slight variation with energy. We take &(R) = dn(R) = d (7) with the values d = 1.86 a.u. near threshold (804 A) and d = 1.73 a.u. near the U + = 4 limit (755 A) obtained from the measurements of Backx et aI.,16 whose low-resolution experiment did not resolve vibrational and rotational fine structure. 2.2 P H O T 0 E L EC TRON A NG U L A R D I S TR I BUT IONS The theory of photoelectron angular distributions has been discussed in detail by Dill" and has recently been adapted to the treatment of vibrational preionisation." We mention here briefly that for J" = 0 and I = 1 the asymmetry parameter relating the differential cross-section to the integrated cross-section according to (randomly oriented molecules, unpolarised light; 0 is the angle between the incoming light beam and the outgoing electron), depends solely on the geometry of the process and not on its dynamics.It is therefore independent of energy with values P = 2 for N + = J" == 0 and /? = 1/5 for N + = J" + 2 = 2. However, if the final rotational state of the ion is not resolved because of insufficient experimental resolution, the effective value pr+ observed will reflect the rotational photoelectron branching ratio according to [The integrated Po+ = 2s:P:,, + fSL,Y,*.(10) cross-section in eqn (8) and (9) is to within the factor 1.098 x 10-l6 cm2 eV equal to the oscillator strength dfldE of eqn (l).] The rotational branching ratio s, in turn, is predicted to oscillate strongly near preionisation resonances, with the result that such resonances are expected to show up conspicuously in the (partial vibrational or total) differential cross-section (oscillator strength) distribution. We predict below that most of the resonancesjust below the P + = 1 ionisation limit have preionisation widths smaller than the Doppler width (ca. 0.5 cm-' at 78 K). Yet we expect that they should give rise to dips in the spectral distribution of the asymmetry parameter PL.+ which are several wavenumbers wide and hence should be observable with conventional light sources. We have evaluated eqn (I), (9) and (10) by including between 14 and 20 rovibra- tional channels (i.e.L'+ = 0 to 6 or 9 with N + = 0 and 2). The energy was varied in steps of typically 0.02 or 0.2 cm-' near sharp resonances, and of 2 cm-l in the smoother parts of the spectrum. 3 . RESULTS We have selected two spectral regions for calculation, corresponding to excitation wavelengths near 791 and 754A, respectively. Fig. 1 is an energy-level diagram showing the Rydberg levels falling into these regions and the continua involved in the photoionisation process.258 SPECTROSCOPY I N THE IONISATION CONTINUUM 3.1 T H E REGION NEAR 791 A The first region chosen for calculation is dominated by the 7pa, u = 2, J = 1 and 5pn, v = 3, J = 1 photoionisation peaks.At this energy only the v + = 0, N + = 0 and v + = 0, N + = 2 channels are open (cf. fig. I). Fig. 2 shows the total photo- ionisation cross-section observed by Dehmer and Chupka’ between 790.7 and 791.7 A (points) along with our calculated spectrum (full line). The resonance profiles 8 o L i . I v+=o v’= 2 U v+= 3 5Pn: -7po - ( ‘16p2-+ 19p2 \ 19pO + 27p 0 \ v* = 5 v+=4 \, 27p2 -. 32p 2 36 000 32 000 * I & 2 5 . h 28 000 24 000 FIG. 1 .-Schematic illustration of vibrational-rotational preionisation in H2 (J = 1, negative parity). Continua are indicated by shading: for each given u+ of the ion H2+ there are two continua corres- ponding to rotational numbers N + Selected discrete Rydberg levels are indica- ted below the vibrational ionisation limit with which they are associated. All ionisation channels (i.e.continua plus associated Rydberg series) interact as a consequence of rotation-vibration-elec- tron coupling. calculated in this range have widths ca. one order of magnitude smaller than the ex- perimental resolution width of 0.016 A (f.w.h.m.). In order to compare the observed and calculated spectra we therefore had to convolute the calculated spectrum with a corresponding triangular apparatus function. In addition, since Dehmer and Chupka 0 and 2 of the ion.CH. JUNGEN AND M . RAOULT 259 give only the relative photoionisation cross-section curve, we must match the theoretical to the experimental spectrum at one point. This matching was done in ref. (4) at the maximum of the broad 8pa, u = 2, J = 1 peak near 788 A; the resulting scaling factor has been taken over into the present work.Table 1 contains complementary data concerning the observed and calculated peak energies, unconvoluted peak maxima and widths. energylcm- 126 450 126 400 126 350 126 300 - 19 I I I 27 I I 1 I I I I I , ' I I I I 17 I 1 I l l I 22 z 5pTc,v=3 I max. x 1/2 II J = l 1 1 6 ~ 2 , ~ =1 I I I z o p o , v = 7 1 . \7pa,v=2 , . ' . . . . . . . . . . . . . . . . . . . . . . . . , *.: ., ' . JJL. . . . . . . . . . : '. .."') ;:: :/JJ:. ~ 1: . . - I I 1 I 1 I I 1 1 I I I I I 1 I I 791.0 791.5 wavelength/A FIG. 2 . 4 ~ 7 ) (top) Observed and calculated photoionisation spectra near the G + = 1, N + = 0 thres- hold (789.836 A) in H 1 ( J = 1, J" = 0). The experimental points are from Dehmer and Chupka [ref.(7)]. The calculated spectrum is broadened to a resolution of 0.016 A to correspond to the experimental measurements. Each circle refers to the peak situated at the same wavelength in the upper part of the figure. Note the difference in the See text for further explanations. The good overall agreement between the experimental and theoretical data dis- played in fig. 2 is evident, in particular when the highly perturbed and irregular character of this portion of the spectrum is taken into account. A dominant feature are the two pronounced maxima in the distribution of the intensity among the various Rydberg peaks. These maxima are centred around the positions of the 7pa, t' = 2 and 5 p z , u = 3 lines, indicating that the high oscillator strength associated with these lines is distributed by vibration-electron (vibronic) coupling among several lines belonging to the v = 1 Rydberg series.Indeed, by arbitrarily removing the u+ = 2 (6) (bottom) Calculated preionisation widths. energy scales on the ordinate (bottom) and the abscissa (top).260 SPECTROSCOPY IN THE IONISATION CONTINUUM and 3 channels from the calculation, we have found that none of the remaining ZI = 1 lines has an intrinsic intensity of more than 0.2 eV-’ in the plot of fig. 2. Thus the present situation is somewhat complex : the photoionisation oscillator strength ori- ginates primarily from the two low-nlhigh-u interlopers, while the coupling with the u + = 0 continuum, necessary for the peaks to appear in the photoionisation spectrum, is provided by the quasi-discrete levels with u = 1 . We conclude that the enhanced TABLE EX EXCITED LEVELS OF H2 NEAR THE 0’ = 1 IONISATION THRESHOLD ( J = 1, NEGA- TIVE PARITY) : ENERGIES, PREIONISATION WIDTHS AND OSCILLATOR STRENGTHS I h D i i obs.calculated calculated calc. obs. approximate df e df’ f description &bsa Ecalc’ Eobs - Ecalc AL*(/?rnin)‘ rd (dE)rnax (dE)rnax(eff) 5 & 19p2, v - 1 126 464.8 126 27p0, I) = 1 457.1 5pn, u = 3 442.3 2 5 ~ 0 , u = 1 435.0 1 8 ~ 2 , u = 1 428.7 24p0, u = I 417.5 23p0, u = 1 401.9 17p2, u = 1 390.9 22p0, u = 1 380.8 21p0, u = 1 360.7 7p0, v = 2 355.7 16p2, v = 1 338.7 20po. u = 1 325.6 1 9 ~ 0 , = 1 304.6 26p0, u = 1 - ~~ ~ , 465.0, 457.52 446.7, 442.2, 435.2, 428.8, 417.6, 402.I 391.1, 38 1.2, 361.1, 356.5, 339.1 , 326.4, 305.1, ~ ~- 0.2 - 0.4 ( t 0 . I ) 0.3 - 0.2 -0.1 - 0.2 0.3 - 0.4 - 0.5 ( - 0.8) - 0.5 - 0.8 - 0.5 - -0.4 0.26 0.31 0.05 0.06 -0.2 0.14 1 . 1 0.09 0.10 -0.02 0.03, 0.009‘ - - ~ 0 . 9 0.008, 880 4.75 I .79 -0.08 0.030 0.7, - - - 1.1 0.35 3.2 0.65 0.59 ~ 0.5 0.15 6.1 0.53 0.45 tO.0, 0.03, 12.8 0.24 0.23 - 1.3 0.35 2.8 0.58 0.43 - 1.3 0.27 8.0 1.28 0.99 -0.5 0.12 28.6 2.07 1.19 -2.3 0.061 96.8 3.57 2.18 + 1.2 0.02, 88.0 1.15 1.15 i 0 . 9 0.29 2.0 0.35 0.40 -0.07 0.10 2.9 0.17 0.26 83 - 90 - - - 38 67 _ _ 89 - 85 - 96 - 74 - 77 - 57 - 61 71 100 - (114)[ - (153)f - ~~ ~ ~ ~ ~ ~ ~~ ~~~ ~- ~~~~ ~ a cm - I ; R(0) absorption lines from ref. (3). b cm - I ; energy of intensity maximum. c cm - l ; Av(8rnin) = E(8min) - E C ~ I C where E(8mrn) is the energy at which the asymetry parameterb” + = o has a minimum (see the text).cm - I ; preionisation width. eV - l ; intensity maximum. f eV - I ; intensity maximum after convolution with apparatus function of width (f.w.h.m.)2.6cm-l. 9 eV-’; from ref. (7) with overall normalisation as described in thetext. h %; evaluated according to u‘ (df’/dE)rnax (eff, obs) ”,, , -7 ,,>, obtained in ref. (7) from a comparison o f the photoabsorption and photoionisation o a (df/dE)max (eff. calc)’ spectra. Note: The widths r have been obtained by fitting the calculated intensity profiles by a Fano profile. The shape indexq (defined only for ‘I isolated ” resonances) is related to the peak height by (dj/dE)rnax = 3.35 x 10 -’ ( E - E,) (cm - I ) ‘.: d2 (a.u.) <v+ = O l d ’ == O>’ (4’ + I ) with d = 1.86 a.u.and <I;+ - 01 u” -= 0 > = 0.298. The factor multiplying (4’ -t- I ) is the intensity of the unperturbed vf = 0, N + = 0 and 2 continua and has the value 0.0130 eV-’. k Intensity minimum (window resonance). 1 Overlapped by J” = 1 absorption line. Rydberg lines flanking the two dominating resonances can be regarded as “ satellites ” resulting from the breakdown of the independence of the nuclear and electronic motions. The whole spectral section shown in fig. 2 can be viewed as consisting of two “ complex ” resonances characterised by a broad distribution of intensity and a rather sharp fine structure. Indeed, under low experimental resolution all the lines seen in fig. 2 fuse into two broad photoionisation peaks which have apparent widths of ca.20 cm-I, This is illustrated, for example, by the fig. 1 of the paper by Dehmer and Chupka l 8 representing a spectrum taken with a wavelength resolution of 0.08 A. If on the other hand we examine the spectrum calculated for infinite resolution (i.e., without convolution) the picture once more changes drastically. The calculated widths and peak heights are compared in table 1 with the convoluted data from fig. 2. The non-convoluted preionisation widths are also plotted as circles in fig. 2(b). It appears that the unconvoluted peak heights, along with the preionisation widths, vary from level to level according to a pattern which could not have been foreseen from the lower resolution plot. Two interesting features show up in the bottom part of fig.2. The first is that in spite of the broad spectral distribution of their oscillator strengths the interlopers with u > 1 remain very narrow themselves, owing to the weakness of the direct vibronic coupling between the u 3 2 and u = 0 channels. The second is that the widths of the zi = 1 lines, while generally being larger than those of the interlopers, show a characteristic cyclic variation with energy.CH. JUNGEN AND M . RAOULT 26 1 The origin of the second effect can be understood when one considers the structure of the electron wavefunction at short range where the interconversion of electronic and vibrational energy takes place. It is kn0wn~9~ that the vibration-electron coupl- ing is carried almost exclusively by the electronic-wavefunction component of C sym- metry since only the quantum defect j r ~ varies strongly with R.(The Il component has a nodal plane parallel to the molecular axis and is little affected by vibration.) As a consequence the preionisation widths are largest near energies where the C ampli- tude of the wavefunction near the core is largest. The decomposition of the wave- function into components of a definite value A is obtained from the channel mixing coefficients B, t, N l by the from Hund's case (d) to case (6). In fig. 2 (bottom) we have plotted the curve (A,+ ~ 1, z)z, calculated from eqn (1 1) [with coefficients B,+= 1, N i obtained by eliminat- ing all but the P + = I , N + = 0 and 2 channels from eqn (4)] and normalised accord- ing to (A,.+ ~ 1, z)z + ( A , + = l , n)2 = 1, which directly gives the C content of the mole- cular wavefunction near the core as a function of energy: it is seen that its oscillatory behaviour indeed parallels that of the calculated preionisation widths.The present data furnish a good illustration of Fano's concept of short-range or eigen- channels which are connected to the ionisation channels by a frame transformation such as described by eqn (1 1) for the angular coordinates of the excited electron. The eigen- channel functions are appropriate at short range, as in the present example where the Born-Oppenheimer classification of states is valid when the excited electron is near or inside the core. This is the case in the lowest Rydberg levels. As the energy increases and the Rydberg electron ranges progressively farther from the core, the short-range part of the molecular wavefunction begins to oscillate between the two limiting situations [case ( b ) : A = 0 or 1 ; case (d): N + = 0 or 21 with a period deter- mined by the spacing of the Rydberg series converging to the N + = 2 limit.These oscillations have been illustrated by Fano2' in an instructive figure. The present example is a prediction which remains to be tested by a sub-Doppler experiment. Returning to the line profiles of the interlopm 7pa, u = 2 and 5~27, L, = 3 we note that their small calculated preionisation widths imply lifetimes as long as 0.6 ns for Sprr, u = 3 and 0.1 ns for 7pa. 2' = 2, that is, sufficiently long that molecular fluores- cence may begin to compete.Breton et a1.2' have indeed been able to induce fluores- cence by exciting H2 near 791.41 8, ( 7 ~ 0 , u = 2). Excitation near 790.87 A ($171, u = 3) on the other hand gave a negative result: the failure of the 5pn, L' = 3 level to fluoresce, in spite of its calculated sharpness, suggests that it must be predis- sociated. The observation near 791.41 8, is one of the six known cases in H2 where fluorescence from levels with parity (- l ) J situated above the ionisation thres- hold has been seen, and it represents the only case where the fluorescing level has (approximate) C+ symmetry. [Levels having parity ( - l ) J + ' are not affected by I- uncoupling; they have pure 'Il; symmetry and are so little broadened by preionisa- tion that fluorescence can be observed in many cases].The exceptional behaviour of the 7p0, 17 = 2 level is only in part related to the weakness of the Au = 2 coupling as can be inferred from the width of 6pa, o = 2 at 797.32 A: this level falls among the widely spaced L' = 1 Rydberg levels with 17 == 8 . . . 10 and does not form a " complex " resonance. The calculation gives the substantial width r = I .2 cm-', i.e., the resonance is ca. 20 times broader than 7170, L' -= 2, in total contradiction to the rule stating that the peak widths vary along a series as (n*)-3. The experimental information available on 6pa, L' = 2 is in accordance with the present result: this262 SPECTROSCOPY IN THE IONISATION CONTINUUM energy Icm- \ i 126 450 126 400 126 350 126 300 I t I 1 1 I I I I I I I h \ t \ I 01 I I I I I I I I I 1 791.0 791.5 wavelength/A FIG.3.-Asymmetry parameter B (top) and rotational branching ratios (bottom) as functions of wavelength for the spectral range shown in fig. 2. The positions of the peak maxima seen in fig. 2 are indicated by crosses.C H . JUNGEN A N D M . RAOULT 263 level is 100% preionised' and does not fluoresce.21 Note on the other hand that 8po, u = 2 is situated above the u+ = 1 limit, preionises via A L ~ = --I and is very broad (r = 9.7 cm-I), while 5po, u = 2 lies lower than the ionisation potential. In view of the foregoing discussion we can interpret the discrepancies between the systematically too high calculated and the observed photoionisation peaks in fig. 2 as being due to our neglect of the fluorescence and dissociation channels. Table 1 lists the photoionisation efficiencies oi/oa (second last column) derived with this assumption and compares them with the available purely experimental data of Dehmer and Chupka7 (last column).oi and oa are here defined as the ionisation and absorption cross-sections integrated over each peak profile with the experimental apparatus func- tion from ref. (7). Considering the relatively crude approximations used in our evalu- ation of the dipole amplitudes Di [neglect of the R, A dependences of the functions d*(R)], we think that the deviations from 100% are probably significant only in the few cases where they exceed 20%. We note good agreement with the result of ref. (7) for 7po, u = 2, but a substantial discrepancy for 5pn, u = 3.We finally turn to the discussion of the calculated asymmetry parameter Po+ == I . This quantity, evaluated according to eqn (9) and (lo), is plotted in fig. 3 along with the related rotational branching ratios derived from the partial oscillator strength distributions. A suprising result is that the resonances which are calculated to appear with sub-Doppler widths in the integrated oscillator strength curve, are predicted to exhibit Put profiles orders of magnitude broader and hence readily measurable with the wavelength resolution of the monochromator used in ref. (7). The characteristic variation of broadness as a function of energy is again seen in fig. 3. The wavelengths corresponding to the maxima of photoionisation intensity are indicated by crosses in the figure: we see that they do not exactly coincide with the predicted minima of the P parameter.We find in fact that the corresponding energy differences, listed in table 1, in most cases are larger than the resonance widths r themselves. 3.2 IONISATION POTENTIAL OF H2 AND F I R S T V I B R A T I O N A L QUANTUM OF H; The reader may have noticed that there is a systematic smal! shift of ca. 0.01 A between the calculated and observed spectra shown in fig. 2. The origin of this shift is experimental; it arises7 from an imperfection of the wavelength drive used by Dehmer and Chupka. On the other hand, the corresponding wavenumbers entered in table 1 stem from the high-resolution photoabsorption photographic plates obtained by Herz- berg;3 they have an absolute accuracy of &0.0010 8, (50.16 cm-l). It can be seen from table I that a small systematic shift of ca.-0.3 cm-' between experiment and theory nevertheless persists, although this would not show up on the scale of fig. 2. It is quite unlikely that this shift arises from the limitation of the accuracy of the quan- tum defects used in the calculations. We estimate on the basis of the accuracy with which these have been determined47l9 and of their known variation with en erg^,^ that this source of error explains only 10% of the observed discrepancy. Other possible sources of error are the limited accuracy of the theoretical ionisation potential of H, and the fact that non-adiabatic effects in the ion H; have not been included in the rovibrational limits E,+, N + (cf.section 2). In order to check this hypothesis we have calculated several discrete R(0) lines corresponding to high Rydberg levels (n = 16 to 27) associated with the u+ = 0, N+ = 0 and 2 ionisation limits, which are free from blending by strong low nlhigh u lines [cf. fig. 1 of ref. (3)]. The results are presented in table 2: it is seen that there is again a systematic, but this time much smaller, discrepancy between experiment264 SPECTROSCOPY I N THE IONISATION CONTINUUM and theory. Adjustment of the ionisation limits on the basis of the combined data of tables 1 and 2, yields the following slightly revised observed values for the ionisa- tion potential of H2 and the first vibrational quantum of H i : I*P*OtX = 124417.2 0.2 cm-' AW2)obs = 2191.1 & 0.1 cm-l which are to be compared with the theoretical values12*22 I.P.theor = 124 417.3 cm-l A.G(1/2)theor = 2191.14 cm-'.The value of the observed ionisation potential given here is the same as in ref. (3); the uncertainty, however, is reduced by a factor of two. The present AG(1/2) value is slightly smaller than that of ref. (3) and also has a reduced uncertainty. The slight improvement is due to the more sophisticated treatment by MQDT of the strong vibronic effects in excited H2. The very weak vibronic coupling in the ion H+ itself has been calculated by Bishop22 to lower the AC(1/2) value by 0.18 cm-': this corre- TABLE 2.-EXCITED LEVELS OF Hz NEAR THE 2,' = 0 IONISATION THRESHOLD (J = 1, NEGATIVE PARITY) approximate description Eobs a E c a l c &Is - E c a l c lobs x 5 L a l c x 27p0, u = 0 26p0, u = 0 18p2, u = 0 25p0, u = 0 24p0, u = 0 23p0, u = 0 17p2, u = 0 22p0, 2, = 0 21p0, 2, = 0 unidentified 20p0, U = 0 16p2, u = 0 124 266.8 256.1 247.9 240.9 226.8 212.2 205.0d 189.7 169.9 162.0 1 55.0d 141.2 124 266.78 256.02 247.97 240.43 226.94 212.27 204.09 189.98 169.97 156.13 141.51 - 0.0 $0.1 -0.1 (+0.5) -0.1 -0.I - 0.3 -0.1 (0.9) (- 1.l)d -0.3 20 20 15 25 30 25 0 30 30 30 0 30 0.11 0.20 0.09 0.06 0.20 0.24 0.002 0.25 0.33 0.005 0.33 - cm-l; R(0) absorption line from ref. (3); * cm-*; calculated energy of discrete level; oscilla- These lines are calculated and observed very weak; the experimental values are This line is calculated weak but observed strong; it is possibly tor strength. probably less reliable in these cases.blended with an unidentified line. sponds essentially to the shift which we have found in table 1. A more accurate experimental test of the theoretical predictions for H;, such as has been possible for HD+,23 cannot be made on the basis of the present data. 3.3 THE REGION NEAR 754A The second region chosen for calculation lies almost 1 eV higher in energy than the first, near the u+ = 4 ionisation limit. In this range a total of ten vibrational- rotational ionisation channels is available for ionisation. At the same time the interactions between channels due to vi bration-electron coupling are stronger because the average kinetic energy of the nuclei is higher. The consequences areC H . JUNGEN AND M. RAOULT 265 clearly reflected by the photoionisation spectrum in this range, shown in fig.4: instead of the quasidiscrete many-line spectrum of fig. 2 we see now mostly broad continuous variations of oscillator strength density. Two resonances with 11 = 6 , 6pa and 6pz, fall into this range, and appear strongly in spite of their high vibrational quantum number, which implies Ail < -2. The 6pa peak located between the N + = 0 and N’ = 2 thresholds associated with u+ = 4 is an extreme example of a “ complex ” resonance of the type encoun- tered previously near 7pa, v = 2 and 5pz, u = 3. It is the strongly preionised Ryd- berg series np2, u = 4, represented by the strongly enhanced members IZ = 28 to 32, energy,’cm - ’ I I I I I I 1 132 800 132 600 753 0 75L 0 755.0 wavelength /A FIG. 4.-Preionisation near the u+ = 4, N + = 0 and 2 thresholds in Hz ( J 1, J” ~ 0).The observed and calculated total oscillator strengths are shown as functions of photon wavelength. The experi- mental points from Dehmer and Chupka [ref. (7)] have been shifted by -0.068 A such as to bring the observed and calculated 9pa, u ~ 5 peaks into coincidence. The calculated spectrum is broadened to a resolution of 0.016 A to correspond to the experimental measurements. which in this case provides the link with the continua. The “ complex ” 6pa reson- ance is quite broad (ca. 15 cm-’), yet the 6pa, u = 6 level intercalated between the n = 30 and 31 N + = 2 members is calculated to be quite sharp, though this may not be appreciated from the convoluted spectrum of fig. 4. The unconvoluted data showing this are summarised in table 3: the np2, u = 4 lines are broad, with widths of the order of 2 cm-l, to be compared with the Rydberg spacing of ca.10 cm-’. 6pa, u = 6 , with its width of only 0.35 cm-’, on the other hand, is a counter-example to the common rule which states that Rydberg resonances are broader, the lower their principal quantum number. More insight into the vibration-electron coupling mechanism can be gained by examining the channel mixing coefficients A , + , A or B,,?, N + [eqn (4) and (1 l)] calculated for the Rydberg levels under consideration. The data of table 3 indicate the presence of strong mixing between the closed channels, which does not involve just u = 4 and 6 but affects all vibrational components from u = 4-7. Thus it is clear that simple rules concerning vibrational preionisation cannot be verified here, and that spectroscopic assignments can be made only in terms, for example, of the largest vibrational component present in the molecular wavefunction at a given energy, or on intensity grounds.It is not surprising in this context that out of the five peaks with n < 20 seen in fig. 4 only two had previously been attributed.TABLE 3.-EXClTED LEVELS OF H2 NEAR THE 2, ' = 4 THRESHOLD ( J = 1, NEGATIVE PARITY) channel mixing coefficients for discrete level 2 9 ~ 2 , 1' =- 4 3 0 ~ 2 , 1' 4 6pu, c = 6 3 1 ~ 2 , L' : 4 32p2, L: 4 8pn, L' = 5 9pu, L' = 5 6pn, c 6 9pK, C =- 5 755.055 755.016 754.992 754.956 754.91 7 754.50 753.30 752.866 752.63 132 440.6 I32 440.8 -0.2 3.6 0.34 0.26 0.18 0.31 -0.72 -0.13 0.48 447.5 448.0 - 0.5 1.1 I .8 -0.20 -0.38 0.72 0.13 -0.48 451.7 454.I -2.4 0.35 5.7 0.12 -0.20 -0.44 0.70 0.13 -0.47 458.1 460.0 -1.9 2.2 0.71 0.34 -0.18 -0.48 0.63 0.11 -0.42 464.9 466.4 -1.5 2.6 0.30 0.55 -0.14 -0.51 0.52 0.09 0.34 5385 539.79 -1.7 13 0.11 - - 0.46 0.58 0.55 -0.08 -0.34 749 75 I .7 -3 26 0.28 - 0.79 0.49 0.10 -0.30 0.13 825.7 827.6 -1.9 0.8 2.6 - -0.21 0.96 -0.10 867.'' 867.9s - 1 12 0.11 - -0.70 0.68 -0.10 -0.12 0.10 0.14 -0.14 -0.14 -0.13 -0.10 -0.13 0.10 -0.14 0.12 -0.12 -0.1 1 -0.10 cm - I ; R(0) absorption lines from ref. (3) (unpublished). b crn - l ; calculated position of intensity maximum. f crn - I . d eV - I ; calculated intensity maximum. The unperturbed back- e Coefficients Bv+,N+ or Au+,A, eqn (4) and ( I I), calculated by eliminating the open channels from the linear calculated by eli- This line does not appear in the ground intensity (c' = 0 .. . 4, N + = 0 and 2) is calculated to be 0.092 eV -l. system eqn (4). minating the open channels from the linear system eqn (4). photoionisation spectrum due to predissociation; it has not been calculated since the linear system eqn (4) was truncated at c+ = 9. Only coefficients with absolute values greater than 0.1 are shown. f Boundary between absorption and apparent emission zones. 9 Discrete level Note: The 3p,, v = 14 R(0) line is observed in the absorption spectrum at 132 791.5 cm-'.C H . JUNGEN AND M . RAOULT 267 Fig. 5 presents calculated (unconvoluted) partial vibrational oscillator strength densities for the same region, obtained by summing over the rotational components ( d E / d f ) l m with N + = 0 and 2 where these are both open.Fig. 6 contains the vi- brational branching ratios defined as 0 . 0 4 0.00 0.08 0.06 0.00 0.08 w I . % * 5 0.00- 5 0.04 2 M + a - .z 0.8 ;3 0.4 0.0 0.8 0 . 4 0.0 L . v+= 3 ~ l ~ ' ' " 1 1 l ' l ~ l ' l ' l " ----__-- I - - max.x L v+= 4 rU I I I I ~ " l l l l ' i l , l l 753 7 54 wavelength/A 75 5 FIG. 5.-Calculated partial vibrational oscillator strength distributions for the spectral range shown in fig. 4. Near the u+ = 4, Nf = 2 limit the data have been averaged over the dense Rydberg struc- ture arising from the np2, u 4 (n > 36) Rydberg series (broken line). in terms of the partial vibrational cross-sections (oscillator-strength densities) together with the vibrational asymmetry parameters PI.+.The main features of these plots are the following. One and the same resonance can according to our predictions present268 SPECTROSCOPY I N THE IONISATION CONTINUUM quite different shapes depending on the vibrational photoelectron group selected for observation, although its width will always be the same. Notice, for example, how the 6pa, u = 6 fine-structure peak in the " complex " resonance yields essentially a Lorentzian profile (Fano profile with 141 > 1) in the u+ == 4 and 3 channels, but shows up with the shape of a dispersion curve (141 zx 1) in the u+ = 1 channel. 2.0 1 .o 0.0 I r I I I I r l , l , ' ' O t (bl ~ ~ l l l l l 7 53 7 5L waveIengthlA FIG. 6.-Calculated vibrational asymmetry parameter B (a) and vibrational branching ratios (b) as functions of photon wavelength near 753 A.The numbers u+ = 0-4 give the ordering of the various vibrational components shown. Franck-Condon values are indicated by horizontal straight lines on the left. The vibrational branching ratios near resonances deviate substantially from the Franck-Condon values (indicated by horizontal straight lines in fig. 6). The com- ponent corresponding to the least change of 11, giving the highest energetically possible final u + , is strongly enhanced at the expense of all other channels in the neighbourhood of the intense photoionisation peaks, independently of whether preionisation proceedsC H . JUNGEN AND M . RAOULT 269 with Ail = -1 or with Av := -2. Near the less intense peaks this behaviour is less pronounced although strong oscillations still occur.Dehmer and Chupka l8 have utilised the strong dependence on vibrational quantum number of the rate of reaction between H; and rare gases in order to establish which are the preferred ionisation channels in the photoionisation of H2. They studied in particular the three peaks seen at 755.0,753,3 and 752.9 A in fig. 4, and they found that the final vibrational state distributions of H f are nearly the same regardless of the vibrational quantum number of the preionised level. This conclusion is confirmed by the calculated data shown in fig. 6. Dehmer and Chupka were able to push their analysis somewhat further, by showing that there are small but systematic differences between those peaks which decay through exchange of a single vibrational quantum and those which decay through exchange of several quanta.They showed that in the second case the number of ions formed in the highest available vibrational state is ca. 15-20'x less than in the first case. These findings appear at first sight to be in contra- diction with the present fig. 6 , but they can be explained if account is taken of the pro- cedure of analysis used by Dehmer and Chupka. Their method consisted essentially in measuring peak heights in their spectra qfter subtraction of the background conti- nuum intensity. Now, as fig. 5 shows, all intensity exceeding the background near 9p0, u = 5 is picked up by the u+ = 4 channel, just as Dehmer and Chupka had assumed. On the other hand near 6 p x , u = 6 about 1/4 of the additional intensity shows up in the u+ = 3 channel and 1/40 shows up in the u+ = 2 channel, as can be inferred directly from the peak heights seen in fig.5. Somewhat more precise values, taken at the intensity maximum, are in excellent agreement with experiment: Final vibrational state distribution in photoionisation of H2 at 752.866 A (6pn, u = 6 Peak) v + - 4 u+ = 3 Zlf = 2 theoretical ((x) 82 16 2 experimental'* (%) 82 15 3. The 6pa, u = 6 " complex " resonance behaves similarly as 6pn, u = 6 in that it affects all partial cross-sections down to u+ = 0 (fig. 5). An interesting predicted feature is that in the u+ = 0 channel the only traces of preionisation are one small spike associated with 6 p , u = 6 , and two dips belonging to the 6pa, v = 6 " com- plex ".Inspection of table 3 shows that these spectral features correspond to three of the sharpest levels listed there. This suggests that IAula 1 preionisation processes are favoured near narrow resonances where the ejection of the photoelectron is de- layed substantially with respect to direct ionisation. In this way several collisions between electron and nuclei can occur before ionisation takes place, allowing the electron to pick up several quanta of vibrational energy. We finally remark that the calculated and observed peak maxima in fig. 4 all agree to within 20%. Thus we find no clear evidence for predissociation and/or fluores- cence in this range (c$ the discussion in section 3.1). The displacement of the observed with respect to the calculated 6pn, L' = 6 peak in fig.4 is an experimental artefact as evidenced by the more precise absorption data listed in table 3. The dis- placement of the intensity distribution in the 6p0, 2' = 6 " complex '' resonance on the other hand is genuine and no doubt arises from the fact that the quantum defect curve / I , , = 6, x(R) was fitted in ref. (4) on the basis of observed peak positions up to 17 = 5 only because the present u -- 6 " complex " was not assigned at the time. Further refinement of the /in 6,z(R) curve published in ref. ( 3 ) would involve values270 SPECTROSCOPY I N THE IONISATION CONTINUUM R X 4 a.u., that is, larger than the classical outer turning point of the u+ = 5 level, and adjustments of the order of 0.01 would probably be sufficient to remove the observed discrepancy.4. CONCLUSIONS In the present work we have presented a quantitative treatment of vibrational- rotational preionisation in molecular hydrogen. The power of multichannel quan- tum defect theory is evident, considering the ease with which it handles a variety of aspects of molecular preionisation. We stress that the same theory, with virtually the same molecular parameters (in particular quantum defects), has previously been applied19 with successs to the discrete level spectrum of the lowest Rydberg states of H2 with PI = 2 and 3. In these low-lying states the effects of vibration-rotation-elec- tron coupling are quite different from those encountered in the continuum, and they are commonly referred to in spectroscopic terms, as adiabatic and non-adiabatic cor- rections, A-doubling, spectral perturbations and so forth.Thus, while the observed phenomena are varied and complex (and can only partly be understood in terms of simple rules such as the " Au = -1 " selection rule), multichannel quantum defect theory is characterised by an inherent simplicity. This derives from the fact that the physics of electron-core interactions at short range is separated in the a p p r ~ a c h ~ , ~ ~ * ~ ~ from the details of electron motion at long range, where the potential field is purely Coulombic and local solutions of the Schrodinger equation are known analyti~ally.~ The overall qualitative behaviour of the quantum defect functions pA(R) from which the whole discrete and continuous spectrum emerges, can be understood simply on the basis of a correlation diagram for electron orbitals connecting the united-atom and separated-atoms limits.25 The fitting procedure or ab initio calculation, in which the quantum defects are determined, then has to deal only with the details of their evolution between the known limits.We finally point out that the formation of " complex " resonances is not restricted to vibrational-rotational preionisation, but occurs also, and possibly more typically, in electronic preionisation. The N2 spectrum near 785 A furnishes a striking ex- ample.26 Here the perturbing interloper is a low Rydberg level associated with the Nf A211,, state, and interferes with the Rydberg series converging to the N; X 2 Z c , u+ = 1 limit.27 To what degree the detailed characteristics of the " complex " re- sonance in N2 are the same as we have found in H2 is not yet known.The sharpness of the central components of the resonance " complexes ", with the simultaneous broad distribution of intensity among the " satellites ", emerges as a striking feature of molecular preionisation. A more detailed theoretical study of the conditions required for its appearance might be worthwhile. We thank Dr. D. Gauyacq (Orsay) for her help in the initial calculations. We also thank Drs. A. Giusti, S. Leach and H. Lefebvre-Brion (Orsay), and Dr. E. Miescher (Basel), for their comments on the manuscript, and Dr. A. Beswick (Orsay) for helpful discussions. ' V. H. Dibeler, R. M. Reese and M. Krauss, J. Chem. Phys., 1965, 42, 2045. R. S. Berry, J. Chem. Phys., 1966, 45, 1228; R. S. Berry and S. E. Nielsen, Phys. Rev., 1970, Al, 383, 395. G. Herzberg and Ch. Jungen, J. Mol. Spectrosc., 1972, 41, 425. M. Raoult and Ch. Jungen, J. Chem. Phys., 1981, in press. M. J. Seaton, Proc. Phys. SOC. London, 1966, 88, 801.C H . JUNGEN AND M . RAOULT 27 1 U. Fano, Phys. Reu., 1970, A2, 353. P. M. Dehmer and W. A. Chupka, J. Chem. Phys., 1976,65, 2243. J. H. D. Eland, J . Chim. Phys. Phys.-Chim. Biol., 1980, 77, 613; C. Y. Ng, B. H. Mahan and Y. T. Lee, J. Chem. Phys., 1976, 65, 1956. See, however, also the following papers for a reintepretation of the NO photoionisation spec- trum: E. Miescher, Y . T. Lee and P. Gurtler, J. Chem. Phys., 1978, 68, 2753; Y. Ono, s. H. Lin, H. F. Prest, C. Y . Ng and E. Miescher, J. Chem. Phys., 1980, 73, 4855. Note also that neither R. S. Berry [ref. (2)] nor J. N. Bardsley, Chem. Phys. Lett., 1967, 1, 229, explicitly come to this conclusion. M. Raoult, Ch. Jungen and Dan Dill, J. Chim. Phys., Phys. Chim. Biol., 1980, 77, 599. B. Jeziorski and W. Kolos, Chem. Phys. Lett., 1969, 3, 677. l3 H. Wind, J. Chem. Phys., 1965, 42, 2371; W. Kolos, Acta Phys. Acad. Hung., 1969, 27, 241 ; D. M. Bishop and R. W. Wetmore, Mol. Phys., 1973, 26, 145; 1974, 27, 279. l4 W. Kolos and L. Wolniewicz, J. Mol. Spectrosc., 1975, 54, 303. U. Fano, Lecture Notes, 1979, unpublished. l6 C . Backx, G. P. Wight and M. J. Van der Wiel, J. Phys. B, 1976, 9, 315. Dan Dill, Phys. Reu. A , 1972, 6, 160. P. M. Dehmer and W. A. Chupka, J. Chem. Phys., 1977, 66, 1972. lo Ch. Jungen and Dan Dill, J. Chem. Phys., 1980, 73, 3338. l9 Ch. Jungen and 0. Atabek, J. Chem. Phys., 1977, 66, 5584. ’O U. Fano, J. Opt. Soc. Am., 1975, 65, 979. ’’ D. M. Bishop, MoI. Phys., 1974, 28, 1397. 23 W. H. Wing, G. A. Ruff, W. E. Lamb, Jr and J. J. Spezeski, Phys. Rev. Lett., 1976, 36, 1488. 24 Dan Dill and Ch. Jungen, J. Phys. Chem., 1980, 84, 21 16. 25 R. S. Mulliken, J , Am. Chem. Soc., 1964, 86, 3183; 1966, 88, 1849; 1969, 91, 4615. ’‘ P. M. Dehmer and W. A. Chupka, 1978, unpublished results. ” A. Giusti-Suzor and H. Lefebvre-Brion, Chem. Phys. Lett., 1980, 76, 132; Abstracts of the Workshop Electron Atom and Molecule Collisions, Bielefeld, May 1980 (Plenum Press, New York), to be published. J. Breton, P. M. Guyon and M. Glass-Maujean, Phys. Rev. A , 1980, 21, 1909.

ISSN:0301-7249    

DOI:10.1039/DC9817100253

出版商:RSC    

年代:1981

数据来源: RSC

摘要:

Local and Normal Vibrational States : a Harmonically Coupled Anharmonic-oscillator Model BY M. S. CHILD AND R. T. LAWTON Theoretical Chemistry Department, University of Oxford, 1 South Parks Road, Oxford OX1 3TG Receiced 8th December, 1980 Analysis of previous calculations indicates that the observation of an irregular overtone/combina- tion spectrum implies increasingly close local-mode near-degeneracies in the higher overtone states. This behaviour is accurately reproduced by a model of two harmonically coupled anharmonic oscil- lators, when the anharmonicity parameter exceeds the coupling strength, the effect being independent of the momentum or potential origin of the coupling. The same model reproduces familiar normal- mode behaviour in the opposite limit. Applications of the model indicate local-mode behaviour for H 2 0 and CzH2 and normal mode features for CzD2 and SO2, the dominant inter-bond coupling in all cases except HzO being due to cross-terms in the kinetic-energy operator.In HzO such momentum coupling is combined with an approximately equal potential coupling contribution. 1 . INTRODUCTION Recent experimental evidence 1--5 for a bond-localised rather than a normal-co- ordinate picture of X-H stretching vibrations comes from the stability of the higher overtone bands to partial deuteration and from the decreasing overtone bandwidths with increasing excitation. Theoretical interest in a local-mode description of X-H vibrations has a longer history, the main argument until r e ~ e n t l y ~ . ~ being that poten- tial coupling between the bonds is relatively unimportant compared with a cor- rectly anharmonic description of the individual bond potentials,*- l2 The tacit assump- tion here is that the observed frequency splitting between vibrations associated with identical XH bonds is attributable to momentum (G-matrix) coupling, but the same argument could be advanced with more justice for vibrations involving heavy peri- pheral atoms and hence much stronger momentum coupling (the case of SOz is dis- cussed below).This suggests that a bond-separable potential model would not be peculiar to XH systems. Moreover, our own quantum-mechanical ' and classical studies6V1' have demonstrated a bond localisation of certain vibrational states in a sense akin to that required by the experimental observation^'-^ even in the presence of strong potential coupling between identical bonds.The purpose of this paper is to argue that localisation in this second sense is attri- butable to quenching of the interbond coupling by the anharmonicity of the individual bond potentials. To do this we offer a simple model of harmonic momentum and potential coupling between degenerate anharmonic oscillators which is shown to re- produce incipient local-mode features of observed spectra and the more obvious effects shown by our previous extensive numerical calc~lations.~ The model also goes over naturally to the familiar normal-coordinate picture in the limit of weak bond anharmonicity, and covers all intermediate cases. The present formulation covers both direct coupling between two identical bonds and indirect coupling through a third degree of freedom, but the model allows extension to any symmetrical system and could be developed to include farther anharmonic coupling terms without disturb- ing the structure of the theory.274 LOCAL A N D NORMAL VIBRATIONAL STATES - - - - - [a;' .- This theory is first set in context in section 2 below, by demonstrating the irregular nature of the overtone/combination spectra of H20 both as observed experiment- and as calculated l 9 on the Sorbie-Murrel120 potential surface. Other localis- ation characteristics found in previous c a l c ~ l a t i o n s ~ ~ ~ are also briefly reviewed.The model is then developed in section 3 and the predicted characteristics of the overtone spectrum are described in section 4.Applications to H20, C2H2, C2D2 and SO2 are given in section 5. Finally the main conclusions are summarized in section 6. 2. LOCAL-MODE CHARACTERISTICS Previous quanta1 calcdations on the stretching vibrations of the Sorbie-Murrel12" model for water have been extended to include the effect of the bending vibration19 with very Fig. 1 1 3 I s -. 4 2 3 + - 12 2 1 .,,'--- 1131 - 103 -i - - L FIG. 1.-Energy levels for the first five (vl, 0, v3) overtone manifolds of H,O. For each manifold index v = vl + v3, the figures show (a) the Morse energy levels as given by eqn (32), labelled by local mode quantum numbers [n,, nb], (6) calculated level positions designated (k) according to the symmetry under interchange of the bonds, and (c) experimental level positions labelled (vl, v2, v3) The energy zero for each manifold is the lowest Morse eigenvalue. obtained by these extended calculations, and presented in relation to the experimental level^,'^-'^ labelled by conventional quantum numbers (ul, v2, u3), and to the levels [n,, n,l implied by a separable Morse approximation for each bond, with En = (n + 3)hw - (n + &)'hxw, (fiwlhc) = 3876 cm-', (hxco/hc) = 84.4 cm-l.* taken as the lowest Morse level, measured from the zero-point energy, The origin for each manifold is E[Ou] = vhco - v(u + 1)hxo (2) where u = u, + u3 = n, + nb.to interchange of the two bonds. given manifold. gies, with equivalent wavenumber units (hoihc) and (hxo/hc). The symbols & designate the symmetry with respect The most striking feature is the marked irregularity of the level separations in any For example the intervals between successive experimental levels in f r o and hxco are ener- * In the notation adopted here, w and xw have dimensions of frequency.M .S . CHILD AND R. T . LAWTON 275 the v = 2 manifold are 49 and 195 cm-’, and the calculated disparities become pro- gressively further exaggerated until the intervals in the u = 5 manifold become 0.1, 599, 44, 274 and 224 crn-l. This pattern may be understood in terms of an increased trend towards local mode doubling of adjacent levels as the disparity between the local mode numbers [n,, n,] increases. Seen in conjunction with the Morse eigenvalues, this behaviour is plausibly attributed to a perturbation that splits the degeneracies in increasingly high order on moving down any given manifold.This indicates a pro- gressive decoupling between the stretching of the two OH bonds in the very close doublet states. A second feature, not demonstrated by our previous calculation^,^ which sup- pressed the bending vibration, is that the magnitudes of the local mode splittings in H,O are largely unaffected by the level of excitation of this bending mode, as shown in fig. 2. c nanb 23 12 13 01 02 14 1 o----;-a:-.-o : ;f I -a-0- o---- S 0 1 2 3 4 0 2 FIG. 2.-Calculated H,O local-mode splittings A = E[M,, nb+] - E[II,, n i l as a function of bending quantum number u2. Points marked by S on the u2 axis are taken from a stretching-only calculation.’ Other local-mode features of previous calculations, but not discussed in detail below are the transition from normal-coordinate to bond-coordinate selection rules as the energy increase^,^ and the spatial localisation of the wavefunction in relation to the classical trajectory relevant to the state in question.7* l2 3.HARMONICALLY COUPLED DEGENERATE ANHARMONIC OSCILLATORS D I R E C T C O U P L I N G Direct harmonic coupling between anharmonic oscillators with coordinates (qa, qb) may be represented by the Hamiltonian Hdir = HJ;: + HJil,) (3)276 with LOCAL A N D NORMAL VIBRATIONAL STATES It is assumed for simplicity that any coordinate dependence of the effective masses p and ,uab can be neglected. The extension to indirect coupling through a third coordi- nate qc is outlined below. Two simple limiting cases may be recognised, the first arising for Hi:: = 0, when the separability of H implies a doubly degenerate anharmonic oscillator spectrum, as labelled by the local mode labels [n,, n b ] in fig.1. The second limit occurs when the anharmonicity of the bond potentials V(q,,) is neglected; thus V(qv) = + kq:; v = a, b. (6) This leads to the normal-mode picture, with coordinates conventionally labelled (ql, q3) for the examples which follow, 41 = 2-'(qa + qb), q 3 = 2-'(qa - q b ) (7) and harmonic frequencies t (9) Notice for future reference that the two frequencies remain degenerate even in the presence of harmonic coupling if by chance kab P a b = k p - (10) Even the most minor anharmonic perturbation will lead back to the local-mode picture in this case, showing that the two types of harmonic interbond coupling can act in the same or in opposite senses according to the relative signs of ,&, and k a b .The model adopted for the anharmonic oscillators is such that the eigenvalues of H'O) are given by the Morse expression: E(n,, n b ) = 2 [(nv 4)hw - (11" + 3)'hwXl. (1 1) v = a,b The coupling matrix elements will, however, be approximated by means of the har- monic oscillator identities where k is the effective force constant, k = pm2, for the unperturbed motion. The corrections required for a full Morse expansion, of order (cq'w) for the lowest states, are assumed to be at most comparable with those due to inclusion of cubic and higher terms in the potential. As such, they would be required for any attempt to fit the spectrum exactly, but they are not expected to alter the qualitative picture.Eqn (12)M . S . CHILD AND R . T . LAWTON 277 and (13) carry the advantage of Anv = 1 selection rules, and simple analytical matrix elements throughout. In this approximation the only non-zero coupling matrix elements may be divided into those which couple states within the same ( v = na + nb) manifold, namely The first type are taken into account in first order, by constructing a manifold coupling matrix with diagonal elements given by eqn (1 1 ) and off-diagonal elements by eqn (14). The second type give rise to a common second-order shift for all diagonal elements in the manifold : INDIRECT COUPLING The extension to indirect coupling through a third coordinate qc is achieved by augmenting Hdir by a harmonic-oscillator Hamiltonian for the qc motion and further harmonic-coupling terms.Thus The resulting additional matrix elements are analogous to those given by eqn (14) and (15), but with the coupling strength expressed in terms of and where It is assumed in the model that the magnitude of this coupling is small compared with the energy difference (hw - hcu,) as will normally be the case when hco applies to the X-H stretching motion and w2 is an H-X-H bending frequency or a stretching frequency involving larger masses. The effect of the indirect coupling may therefore be taken into account by second-order perturbation theory. Again two types of278 LOCAL A N D NORMAL VIBRATIONAL STATES interaction may be identified. perturbed energy level First there is a second-order correction to each un- Eo(na, n b , nc) = 2 [(nV + &)hOJ - (nil + *)’hxw] + ( n c + *)hwc, (21) v = a,b namely n’ # n Secondly the second-order coupling between states Ina, n b , n,) and In, + 1, n b - 1, n,) gives rise to matrix elements within a given anharmonic manifold of the form Since eqn (22) and (23) have precisely the same dependence on the quantum num- bers n, and n b as the corresponding direct coupling terms given by eqn (17) and (14) respectively, the effects of both direct and indirect coupling can be taken account by diagonalising a single intramanifold tridiagonal matrix for each u = n, + nb level of the system.The elements of the effective harniltonian are given according to eqn ( 141, (1 71, (22) and (23) by (nay ??b, n,lHeffina, lib, ?I,> = 2 [(n, + 3)hw‘ - (Ha + 3)’hxwI + (nc + +)ti.>: Y = a,b <na + nb - 1, nclHeff\na? n b , nc> = + 1)nb13 (24) where w’ and 0); include second-order corrections to the unperturbed frequencies; w’ = w - ( a + P)’/2iiw - (-ac + pc)”h(U -+ LO,) - (-ac - p,)’/ii(w - (3,) a; = w, - 2(a, + PC)’/h(.l + w,) + 2(-a, - P,)’/ii(.> - c0,).(25) Similarly the total coupling strength parameter is given by 3, = --a + p + (‘, - P C ) ” h ( . . , - w,) - (ac + P,>”h(.., + 4. (26) Three points are worthy of notice. First the symmetry in na and n b allows an immediate factorisation of He,, into symmetric and antisymmetric parts. Thus the energy distribution in the uth manifold requires at most diagonalisation of two (u + 1)/2 dimensional matrices. Secondly both the coupling strength il and diagonal term differences are independent of the excitation state n, of the indirect coupling mode.This is consistent with the behaviour shown in fig. 2. Finally eqn (26) shows that the various contributions to ,I may act in opposite senses. In particular the case cc = /I, a, = pc = 0 corresponds to the situation envisaged in eqn (lo), where the two types of harmonic coupling cause a frequency shift without removing the zero-order de- generacy. 4. EIGENVALUE STRUCTURE OF THE OVERTONE MANIFOLD The nature of the eigenvalue spectrum for any given manifold is readily apparent from the structure of the reduced coupling matrices. These are presented below in symmetrised and antisymmetrised form for u = 1-5 using the compact notation E[n,, nb] to indicate the appropriate sum of Morse eigenvalues, and H&u) for theM.S. CHILD AND R . T. LAWTON 279 coupling matrix itself. The energy dependence on n, is suppressed, as irrelevant to the level splitting within the manifold. H'+'(l) = E[O, I] = A ; H(-'(l) = E[O, 11 - 3, (27 [ 0, da, E[2, 31 + 3A 0, dgA, E[2, 31 - 32 1 . (30) The two quantities of importance are the Morse anharmonicity parameter hxco, which determines the diagonal energy differences, and the coupling strength A. The nature of the eigenvalue spectrum depends on the ratio between them. For small (Alhxco) there is evidently a first-order splitting between the two E[O, 1 +], E[1,2*] and E[2, 3'1 levels respectively, whereas the separation between E[O, 2+] and E[O, 2-1 arises only from the second-order interaction of E[O, 2+] with E[1, 11.Similarly in the u = 3 manifold E[O, 3+] and E[O, 3-1 are separated by the difference in second-order interaction with E[1, 2'1 which are themselves split by a first-order perturbation. The level splitting E[O, 3+] - E[O, 3-1 is therefore of order (A/h~co)~. Proceeding to the general case the local-mode splitting of the [0, v] level is of order (A/hxco)". Similar considerations clearly account for the pattern of splittings in fig. 1. Turning to the opposite limit hxco<A it is readily verified that the eigenvalues of H(*)(u) fall into the sequence ~ [ o , 51, m, o 1 ECO, 51, 4%' o H'+'(5) = d%, E[1, 41, 2/%A ; H'-'(5) = dTA, E[1, 41, V'KA E = -uA, -(u - 2)A, .. . vA (31) with a regular spacing of 2A indicative of the overtone and combination bands arising from two harmonic vibrations with frequencies (co - A) and (co + A), respectively. These two limits confirm the behaviour anticipated when the model was introduced. The transition between them is conveniently followed by plotting the general eigen- values as a function of (A/xco) using the reduced notation & = [E - E(u)]/[A~ + h2X2U2]* (32) where E(u) denotes the mean energy of the 0th manifold. The form of such a dia- gram, given in fig. 3 for u = 5, shows the expected transition from doubly degenerate local modes to equally spaced harmonic energy levels, with the local-mode degeneracy persisting to higher (A/hxw> values the greater the disparity between the local-mode [n,, n,] quantum numbers.The relative order of the symmetric (+) and antisym- metric (-) levels depends on the sign of A, which is taken here to be positive. 5 . APPLICATION TO INDIVIDUAL MOLECULES In applying the theory to individual molecules our purposes are first to show that the present model can explain the main features of observed and calculated overtone spectra. Secondly we examine the extent to which the implied harmonic coupling280 LOCAL A N D NORMAL VIBRATIONAL STATES - 2 - 1 0 1 2 log,, (A lJlxa) FIG. 3.-Scaled model eigenvalues, E = (E - l?)/(h2 + Ii2x2w2),+ for the u = 5 manifold, as a function can be attributed to purely momentum coupling, since this bears on the original pro- position8-" concerning the role of potential coupling between the bonds in the mole- cule.Finally the model may be used to extrapolate from the observed spectrum, to predict the positions of hitherto unobserved bands. The four parameters required by the model are the apparent Morse oscillator con- stants co' and xw, the frequency of the indirect coupling mode, wrc, (at most one such mode is considered in each case) and the coupling strength 1. These parameters may be derived from the experimental spectrum with levels most conveniently identified by normal-coordinate labels (vl, v2, u,), u1 and v3 being taken to refer to the coupled modes and vz to the indirect mode. The structure of the matrices given by eqn (27)-(30) provides various estimates for the remaining parameters. Thus with all energies measured from the zero-point (0, 0, 0) level, it follows in the light of the correlations between normal- and local-mode labels shown in fig.1 that of log,,(h/hxco). E is the mean energy of the manifold. w: is therefore identified with co2. I? = [E(l, 0, 0) - E(0, 0, 1)]/2 = [E(3, 0, 0) - E(2, 0, 1) + E(1, 0, 2) - E(O, 0, 3)]/4 (33) and hw' - 2hxw = [E(l, 0, 0) + E(0, 0, 1)]/2 hw' - 3trxu = E(1, 0, 1)/2 ~ C O ' - 2 . 5 h x ~ = [E(2, 0, 0) + E(0, 0, 2)]/4 hw' - 4.25hxw = [E(3, 0, 1) + E(1, 0, 3 ) ] / 8 . (34) Applications of the theory based on these estimates are given for H20, C2H2, C2D, and SO, below, using the derived parameter values given in table 1 . HzO Table 2 gives a comparison between the experimental level p o s i t i o n ~ , l ~ - ~ ~ those on the Sorbie-Murrell 2o surface, including given by a new variational calculationM .S . CHILD AND R . T . LAWTON 28 1 TABLE 1 .-MODEL PARAMETER VALUES (hm'/hc)/cm-l 3876.2 3450.3 26 19.4 1271.6 (hxw/hc)/cm- 84.4 58.4 23.6 7.5 (hm',//zc)/cm- 1594.6 1974.3 1764.8 519 (A/hc)/cm- -49.5 39.0 132.9 - 105.2 both stretching and bending vibrations, and finally the levels calculated by the present model. The latter reproduce the experimental and numerical eigenvalues with stan- dard deviations of 7.5 cm-I and 6.3 cm-', the corresponding standard deviation between numerical and experimental results being 7.1 cm-'. This shows that the model performs remarkably well in reproducing the main features of the spectrum. It is also illuminating to examine the various contributions to the coupling strength 1, the momentum terms in which may be deduced from knowledge of the valence- coordinate G matrix for a symmetrical XY2 molecule with bond length Y and interbond angle p2' 1 Pi& mxl cos p, -(mXr)-l sin p G = m s l c o s p , &, -(mXr)-' sin p I -(rnXr)-I sin p, -(mXr)-' sin p, 2[mx + my(l - cos p)]/rnxmyrz where pXy denotes the X-Y reduced mass.The bond angle p in H20 is 104.5°15 from which it follows using eqn (16) and (19) TABLE 2.-EXPERIMENTAL NUMERICAL AND MODEL EIGENVALUES FOR H20 1 0 0 0 0 1 2 0 0 1 0 1 0 0 2 3 0 0 2 0 1 1 0 2 0 0 3 4 0 0 3 0 1 2 0 2 1 0 3 0 0 4 5 0 0 4 0 1 3 0 2 2 0 3 1 0 4 0 0 5 0 1 +o 0 1 -0 0 2 +o 0 2 -0 1 1 0 0 3 +o 0 3 -0 1 2 +O 1 2 -0 0 4 +o 0 4 -0 1 3 +o 1 3 -0 2 2 0 0 5 +o 0 5 -0 1 4 +o 1 4 -0 2 3 +o 2 3 -0 3 657 3 756 7 201 7 250 7 445 10 613 10 868 11 032 13 831 14 319 - - - 16 899 17 496 - 3 663 3 765 7 206 7 257 7 462 10 594 10 608 10 877 11 055 13 800 13 802 14 213 14 323 14 560 16 830 16 830 17 429 17 473 17 745 17 971 3 658 3 757 7 201 7 246 7 460 10 589 10 600 10 882 11 069 13 798 13 799 14 277 14 343 14 559 16 832 16 832 17 466 17 505 17 792 18 049 Ref.(13)-(18); ref. (19).282 LOCAL A N D NORMAL VIBRATIONAL STATES that u/hc = 28.6 cm-I and cr,/hc = 49.7 cm-', giving a direct momentum contribution of -28.6 cm-I to the total coupling strength 3Jhc = -49.5 cm-', but a negligible in- direct term of +0.63 cm-l because according to eqn (26), a, contributes to II only in second-order. Information on the division of the residual potential coupling is available by comparison between the present calculation and previous stretching-only calculation^,^ which would be fit by A/hc = -53 cm-'.The difference of +4 cm-' it therefore attributable to indirect potential coupling, leaving - 19.9 cm-' due to direcs potential coupling between the bonds. C2H2 AND C2D2 The available experimental i n f o r m a t i ~ n ~ ~ * ~ ~ - ~ ~ on the ( u ; , 0, v,) levels of acetylene and deuteroacetylene is summarised in table 3. TABLE 3.-EXPERIMENTAL AND MODEL EIGENVALUES FOR C2H2, C2D2, so2 1 0 0 0 1 + 0 0 0 1 0 1 - 0 2 0 0 0 2 + 0 1 0 1 0 2 - 0 0 0 2 1 1 0 3 0 0 0 3 + 0 2 0 1 0 3 - 0 1 0 2 1 2 + O 0 0 3 1 2 - 0 4 0 0 O 4 + O 3 0 1 0 4 - 0 2 0 2 1 3 + 0 1 0 3 1 3 - 0 0 0 4 2 2 0 5 0 0 0 5 + 0 4 0 1 0 5 - 0 3 0 2 1 4 + 0 2 0 3 1 4 - 0 1 0 4 2 3 + 0 0 0 5 2 3 - 0 3 373 3 295 6 502 6 556 6 709 9 640 9 835 12 676 - - - - - (1 5 600)d 3 373 3 295 6 511 6 550 6 706 9 636 9 625 9 976 9 831 12 615 12 617 12 910 13 001 13 192 15 484 15 484 15 951 15 914 16 350 16 153 2 705 2 439 5 097 - - - 7 734 9 794 10 348 - - - - 11 905 12 344 - - 2 705 2 439 4 854 5 097 5 388 7 463 7 244 8 047 7 735 9 608 9 801 10 055 10 351 10 684 12 111 11 946 12 628 12 347 13 297 12 946 1151 1362 2 296 2 500 2 715 3 431 3 630 4 054 4 751 5 166 - - - - 1151 1362 2 295 2 498 2 716 3 431 3 627 3 838 4 063 4 560 4 747 4 951 5 170 5 403 5 906 6 085 6 282 6 495 6 721 6 961 a Ref.(15) and (22)-(24); (0, 0, 0) band in Herzberg." ref. (15) and (24)-(26); ref. (27) and (28); assigned as (0, 0, 5)- Notice that the coupling strength II given in table 2 is now positive, thereby reversing the order of symmetric and antisymmetric levels from that in fig.1 and table 2. Se- condly ,i is larger and the anharmonicity hxw is smaller in C2D2 than in C2H2, a dif- ference that profoundly affects the relative natures of the overtone spectra. As seen in table 3 and fig. 4 the spectrum of C2H2 shows qualitatively the same local-mode doublet structure as that encountered in the case of H20. The spectrum of C2D2 on the other hand is much more " normal " in nature with an almost uniform variation in the intervals between successive levels. Part of this difference in character is due to the change in bond anharmonicity, roughly in inverse proportion to the change in C-H reduced mass as required by a strict interpretation of the model.The major change is, however, due to the greatlyM. S . CHILD AND R. T . LAWTON 283 increased coupling strength A in C2D2 arising from the relatively near resonance be- tween the stretching frequencies of the C-D and C-C bonds, the dominant contribu- tion to ;1 being indirect momentum couplifig generated by the G matrix P d , 0, -mE1 G = [o Pu,?: 3 -m;l Thus in the notation of eqn (1 S), pa, = n2,/2. It follows from eqn (19) and the values of w' in table 2 that ~ J h c = 262 and 306 cm-I in C2H2 and C2D2, respectively, but this relatively small difference is greatly exaggerated in its second-order effect, as given by eqn (26). The resulting indirect msmentum coupling contributions are 40 cm-I for (36) 1 -mE1 -inE1, PG! - !OOO I 2 3' I- 2 3- - - 22 1 i+ - 12' 13- K- 13' - - - 11 12- C2D2 22 - 2 3' - 2 3- - 12+ 13- - 14' - l1 12- 13+ - 14- -- - - FIG.4.-Calculated eigenvalues for the first five CHICD stretching overtone manifolds for C2Hz and CzD2, designated by local mode labels [n,, nb]. Short heavy lines mark available experimental levels. Energies are measured in each manifold from the lowest calculated level (see table 3). C2H2 and 197 cm-' for C2D2 after correcting the " observed " frequencies w' and co', in table 1 for the second-order shifts given in eqn (25). The corresponding values for A/hc in table 1 are 39 and 133 cm-I. This shows that the coupling in C2H2 is entirely attributable to the indirect momentum terms involving M, eqn (26). The same is al- most certainly true for C2D2, the overestimate obtained being attributable to the breakdown of second-order perturbation theory.Tn any case the substantial qualita- tive difference between the two overtone spectra is well-accounted for by the model. so2 The case of SO2 is of interest in completing the transition from local-mode beha- viour in H20 and C2H2 to an extremely regular normal-mode overtone spectrum. The very large coupling parameter A/hc = -105 cm-l would seem to dominate the very small anharmonicity (kxw/hc) = 7.53 cm-' given in table 2, but this anharmonicity is in fact required to account for the minor variations in level spacings shown in table 3. Thus the present model again gives a good fit to the experimental level positions. Finally it is readily verified by substituting the appropriate masses in the matrix284 LOCAL AND NORMAL VIBRATIONAL STATES given by eqn (41) that with the bond angle q~ = 119.3", the direct momentum coupling contribution to A/hc is -102.5 cm-I which may be compared with the full value of - 105 cm-'.We therefore have a good representation of a completely " normal " spectrum, reproduced within a bond separable potential model. 6 . SUMMARY AND CONCLUSIONS It has been argued that the observation of a markedly irregular overtone spectrum for a symmetrical molecule should be interpreted as a sign of incipient decoupling between symmetry related bond vibrations in certain states, such decoupling beiog predicted to increase with further excitation. The cause of this decoupling was shown to be strong bond anharmonicity which can in favourable cases quench any interbond coupling terms arising either from potential- or kinetic-energy terms in the Hamiltonian.Thus local-mode behaviour should not be associated with a bond- separable potential approximation. A model embodying bond anharmonicity and both direct and indirect harmonic coupling between two bonds was introduced, and applied to the stretching spectra of H20, C2H2, C2D2 and SO,. The important parameter in the model is the ratio of coupling strength to bond anharmonicity, very large and very small values of which give rise to " near-normal " and " near-local " behaviour, respectively. Of the mole- cules considered H 2 0 and C2H, lay towards the local limit, while C2D2 and SO2 showed more normal behaviour. Analysis of the origin of the interbond coupling showed that in H20 the dominant and roughly equally important mechanisms were direct potential and momentum coupling.In C2H2 and C2D2 the important term was indirect momentum coupling via the C-C stretching mode, this second-order effect being much stronger in C2D, than in C2H, due to the closer resonance between C-D and C-C vibrational frequencies. Finally in SO, direct momentum coupling between the bonds was sufficient to quench the weak bond anharmonicity, and to reproduce the experimental spectrum. Finally it should be recognised that the predicted increasingly near degeneracy with increasing excitation in the lowest local-mode progressions of H20 and C2H2 remains to be tested experimentally. Direct observation of the effect is in principle possible in the infrared overtone spectrum.of H 2 0 because both symmetric and anti- symmetric stretching modes are infrared active. The analysis is, however, compli- cated by the large rotational constants, principally due to strong Coriolis interaction, but also because the rotational envelope width (BkT)' E 100 cm-' exceeds even the predicted [03'] band origin separation by an order of magnitude. In the case of C2H2 on the other band direct information on the highly excited Eg CH stretching states would be available only from the Raman overtone spectrum. Indirect coupling cia the bending mode was relatively unimportant. The authors are grateful for discussions with and some computational assistance from Dr. L. Halonen. R. L. Swofford, M. E. Long and A. C . Albrecht, J . Cliem. Phys., 1976, 65, 179. R. L. Swofford, M. E. Long, M. S. Burberry and A. C . Albrecht, J . Clwnr. Pliys., 1977,66, 664. R. L. Swofford, M. S. Burberry, J. A. Morrell and A. C. Albrecht, J . Clienr. Pliys., 1977, 66, 5245. J. N. Perry and A. H. Zewail, Cheni. Pliys. Lett., 1979, 65, 31. R. G. Bray and M. J . Berry, J. Clretii. Pliys., 1979, 71, 4909. R. T. Lawton and M. S. Child, Mol. Plrys., 1979, 37, 1799. R. T. Lawton and M. S . Child, Mol. Pliys., 1980, 40, 773.M. S. CHILD AND R . T. LAWTON 285 See B. R. Henry, Acc. Chem. Res., 1977, 10, 207. R. Wallace, Chem. Phys., 1975, 11, 189. lo M. L. Elert, P. R. Stannard and W. M. Gelbart, J. Chem. PhyJ., 1977, 67, 5395. l1 W. M. Gelbart, P. R. Stannard and M. L. Elert, Int. J. Quant. Chem., 1978, 14, 703. l3 R. Mecke, 2. Phys., 1933, 81, 313. l4 K. Frendenberg and R. Mecke, 2. Phys., 1933, 81, 465. l5 G. Herzberg, Infrared and Raman Spectra, 1948, 74, 703. l6 0. C. Mohler and W. S. Benedict, Phys. Reit., 1948, 74, 702. R. C. Nelson and W. S. Benedict, Phys. Reu., 1948, 74, 703. l8 W. S. Benedict, Phys. Reo., 1948, 74, 1246A. l9 R. T. Lawton, D.Phil. Thesis (Oxford University, 1980). ” K. S. Sorbie and J. N. Murrell, Mol. Phys., 1975, 29, 1387. 22 E. K. Plyler, E. D. Tidwell and T. A. Wjggins, J. Opt. Soc. Am., 1963, 53, 589. 23 W. J. Lafferty and R. J. Thibault, J. Mol. Spectrosc., 1964, 14, 79. 24 H. Fast and H. L. Welsh, J. Mol. Spectrosc., 1972, 41, 203. 25 0. D. Saksena, J. Chem. Phys., 1952, 20, 95. 26 R. M. Talley and A. H. Nielson, J. Chem. Phys., 1954, 22, 2030. ’’ R. D. Shelton and A. H. Nielson, J. Chem. Phys., 1953, 21, 2178. ’’ R. D. Shelton, A. H. Neilson and W. H. Fletcher, J. Chem. Phys., 1954,22, 1731. R. T. Lawton and M. S . Child, to be published. E. B. Wilson, J. C. Decius and P. C. Cross, Molecular Vibrations (McGraw-Hill, N.Y., 1955).

ISSN:0301-7249    

DOI:10.1039/DC9817100273

出版商:RSC    

年代:1981

数据来源: RSC

摘要:

Exact Calculation of the Rotational-Vibrational Energy Levels of Triatomic Species BY 1. F. KIDD AND G. G. BALINT-KURTI School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 ITS AND M. SHAPIRO* Department of Theoretical Chemistry, Oxford University, 1 South Parks Road, Oxford OX1 3TG Receioed 22nd December, 1980 A recently proposed method for calculating the bound rotational-vibrational energy levels of triatomic molecules is applied to the Ar-HCI van der Waals complex and to the water molecule. For Ar-HCl energy levels, rotational constants and centrifugal distortion constants for several different potential-energy functions are calculated. The accuracy of the calculations is critically examined and is found to be very high. It is demonstrated that the method may be used to calculate the higher lying rotational-vibrational energy levels of the complex without either a significant loss of of accuracy or any large increase in computational effort.The complete set of rotational-vibrational energy levels is calculated for two different Ar-HCl potentials and for several different values of the total angular momentum. The coupled states or p-helicity decoupling approximation, which has been used previously in the context of molecular scattering theory, is examined and shown to yield very reliable results. This approximation greatly reduces the computational effort required to per- form calculations, especially for higher values of the total angular momentum. In the case of the water molecule we examine the use of a “ hindered-rotor ” basis set, and show that we are able to obtain a faster rate of convergence and greater accuracy for the low-lying energy levels of water with this type of basis.1. INTRODUCTION The ever increasing sophistication and accuracy of spectroscopic measurements, as is well-illustrated by the other papers presented at this Discussion, demands a con- comitant improvement in the methods used to analyse and assess experimental re- sults. In particular, it has become apparent over recent years that the traditional perturbation theoretical methods of relating the observed spectral frequencies to the potential-energy surface of the system need to be replaced by more exact procedures. Several groups have, consequently, developed and used such procedures for calculat- ing the bound rotational-vibrational energy levels for systems with predetermined potential-energy surfaces.The majority of the methods used in this context have been of the “ quantum-mechanical variational approach ” type. In these methods the total wavefunction for the system is expanded in terms of some “ basis functions ’’ and the variational method is used to determine the optimal expansion coefficients. These methods have been reviewed by Carney et al.I The “ secular equation ” method of Le Roy is also of the type just mentioned and is discussed in a review on van der Waals molecules by LeRoy and Carley.’ Some methods based on the use of semiclassical quantum theory have also been devel~ped.~.~ Israel. * Permanent address: Department of Chemical Physics, Weizmann Institute of Science, Rehovot,288 ENERGY LEVELS OF TRIATOMIC SPECIES An alternative to the " variational method " approach of determining bound state energies is provided by the close coupling method of scattering theory.In this ap- proach one of the atom-diatom distances (for a triatomic) is chosen to be a " scattering coordinate". The total wavefunction of the system is then expanded in terms of " basis functions " in all of the variables except in the " scattering coordinate ". As will be shown in more detail below, this leads to a set of coupled differential equations. The solutions of these differential equations, which obey the appropriate bound-state boundary conditions, are the bound-state rotational-vibrational wavefunctions of the system.This method of finding bound-state energy levels has been pioneered by Gordon5 and has, in particular, been applied to the Ar-HCl system by Dunker and Gordon.6 A related method, for the calculation of bound-state energy levels, has been proposed in connection with the calculation of photodissociation pr~babilities.~ This method, which has become known as the artificial channels method, has been described in detail and has been applied to the calculation of the low- lying states of the water mole~ule.~ In this paper we apply the artificial channels method to the calculation of the energy levels of the Ar-HC1 system using several different potential-energy surfaces, and also present some more accurate results than were previously available for the low-lying states of water.We demonstrate that the method is capable of yielding highly accurate results. Furthermore, it can be used to calculate the higher states of a system without the inordinate increase in computational effort which is required in a " variational approach " calculation. We also test out an approximate method, which is widely used in scattering theory where it is called the coupied states or p- helicity decoupling method, for the case of Ar-HC1 and find it to be very reliable. The approximation greatly simplifies calculations for higher total angular momentum quantum numbers. For the water molecule we examine a transformation of the basis set of angular functions to a " hindered-rotor " basis and show that we are able to realise a considerably improved convergence with number of basis functions using this type of basis.Section 3 describes the application of the method to the Ar-HC1 system. In section 4 we examine the use of the coupled states or p-helicity decoupling approximation. Some results for the water molecule using a hindered-rotor basis are presented and discussed in section 5 and we make our concluding remarks in section 6. In section 2, below, we outline the theory of the method. 2 . THEORY The coordinates used in the calculation are shown in fig. 1. The calculations are formulated in a body-fixed axis systemlo where the body-fixed z axis points along the HCl-Ar direction. The total wavefunction for the system is expanded in terms of orthonormal parity-adapted angular functions which are eigenfunctions of the square of the total angular momentum and its z component:9*11 (1) These functions are discussed briefly in ref.(9)[eqn (24)] and more extensively in a forthcoming publication, ref. (1 1). The parity quantum number p takes on the values A1 and is related to the overall parity of the wavefunction by: parity = (- l)Jp.I . F . K I D D , G . G . BALINT-KURT1 A N D M . SHAPIRO 289 J and M are the quantum numbers for the square of the total angular momentum and for its z component (referred to space-fixed axes). J. is the absolute value of the helicity quantum number and is always positive. The helicity is the quantum number for the z component of the total angular momentum referred to the body-fixed axis system. The total wavefunction for states with quantum numbers J and M and parity (- 1)p is now expanded as: where xUj(r) are the radial parts of the vibrational-rotational eigenfunctions of the diatomic (i.e., HCl for Ar-HCl and H2 for H,O).If we substitute the expansion of eqn (3) into the Schrodinger equation, and make use of the fact that functions c.m.( FIG. 1.-Space-fixed and body-fixed (21 IR) coordinate systems for Ar-HCI. O;Tp (R, P)xUj(r) form an orthonormal set, we get a set of coupled, 2nd-order differen- tial equations for the expansion coefficients (D$L(R).~*~~ The set of quantum numbers “ vjJ. ” are said to define a channel. If we abbreviate this set of quantum numbers by “ a ” the set of coupled differential equations which @a[= @:j!(R)] must obey has the general form : The radial coefficients @a must satisfy the bound-state boundary conditions at large R, i.e.: @a(R) R ~ r n 0 (5) and we note that all channels are “closed ” at large R, i.e., [ Vaa - ( E - E,)] > 0 for large R.The set of coupled differential equations, eqn (4), only possesses solutions which obey the correct boundary conditions [eqn ( 5 ) ] for special values of the energy, which correspond to the bound rotational-vibrational energy levels of the system. The coupled differential equations and the boundary conditions are of exactZy the same290 ENERGY LEVELS OF TRIATOMIC SPECIES form as those of the closed channels in a close coupling scattering calc~lation.~ It has been shown ’-’ that this similarity may be turned to our advantage by adding two artificial scattering channels, denoted by subscripts /3 and y, to the set of coupled dif- ferential equations.These channels are asymptotically open, i.e., [I”Bp - (E - 4 1 < 0 at large R. The channels p and y are not coupled directly to each other but are only coupled in a specified ’-’ non-symmetric manner via the bound-state channels or manifold. In this case it is possible to show that the Tmatrix element (i.e., the transi- tion probability amplitude) between the two artificial channels p and y possesses poles at the bound-state energies. To illustrate this point we reproduce in fig. 2 an “ energy - 2 5 - 20 - 15 -10 -5 0 energylcm- FIG. 2.-Im(T~y)/cos(Sp + 6,) plotted as a function of energy for Ar-HCl using the Vliegenthart and Rozendaal potential [ref. (15)] and jmax = 4.Calculations were performed at energy intervals of AE = 0.25 cm-’. scan ” of the T matrix element, Tpy, for Ar-HC1. The calculations depicted in the figure were carried out using a rather small basis set expansion [eqn (3)J and are conse- quently not very accurate. Such calculations are carried out to provide a first rough estimate of where the bound-state energy levels lie. In the neighbourhood of each bound-state energy (Eb) the T matrix element behaves like a first-order pole, i.e., Because we know the analytic behaviour of the T matrix elements in the vicinity of a pole we can very rapidly “ zero in ” on a pole and locate it to a very high accuracy, with only a few evaluations of the T matrix elements. The precise details of how the poles are located are described in the appendix to ref.(9).I . F . K I D D , G . G . BALINT-KURT1 AND M . SHAPIRO 29 1 THE CENTRIFUGAL DECOUPLING APPROXIMATION This approximation, which is widely used in scattering the~ry,’~-’~ where it is often called the coupled states l3 or p-helicity decoupling l4 approximation, involves the neglect of the off-diagonal elements of the operator for the square of the orbital angular momentum (i.e., L2) in the body-fixed axis system. Within the framework of this approximation the helicity quantum number becomes a “ good ” quantum number, i.e., channels of different helicities are no longer coupled together. The approximation reduces the number of channels which are coupled together and there- fore greatly simplifies the solution of the set of coupled differential equations, especi- ally for higher values of the total angular momentum. THE HINDERED-ROTOR BASIS In our calculations for the rotational-vibrational energy levels of H20 the H, fragment was treated as the diatomic (note, however, that an equilibrium separation and force constant appropriate to H2 in H20 was used for the fragment.g The basis set of angular functions [eqn (l)], in terms of which the total wavefunction is expanded, is therefore constructed from eigenfunctions of a freely rotating H2 rigid rotor [i.e., Kl(O,., y,,)].These eigenfunctions, while they do form a complete orthonormal set for the angular motion of the H2 fragment in H20, are not in any way optimal for use in such an expansion. This is because the angular motion of the H, in the water molecule is not free, but is highly hindered by the valence forces in the molecule. In an attempt to obtain a more suitable basis set for the description of the angular motion of the H2 in H,O, we have fixed the radial coordinates R and Y at their values corresponding to the equilibrium geometry of H,O.The matrix elements of the potential between the angular functions El$’” have then been evaluated. The hin- dered-rotor functions are then defined as that set of functions which diagonalise the Hamiltonian for the fixed (equilibrium) values of R and r. In general we start off with a large basis set of the original “ free-rotor ” functions, find the transformation just discussed to yield the hindered-rotor basis, and then retain only the lowest few (i.e., those corresponding to the lowest eigenvalues of the Hamiltonian) hindered- rotor basis functions. Typically we would start off with 20 free-rotor functions and retain only 7 hindered-rotor functions.3. Ar-HC1 VAN D E R WAALS COMPLEX-EXACT CALCULATIONS In keeping with other calculations on the Ar-HCl complex and also because of the nature of the available potential-energy surfaces, the HC1 was treated as a rigid rotor in the present calculations. These potentials can be split into three groups: 1. An analytic fit to an ab initio (SCF + perturbation theory) potential calculated by Vliegenthart and R0zendaa1.l~ The detailed form of this potential is given in table 1. 2. The potentials of Dunker and Gordon6 which are slightly modified forms of those previously proposed by Nielsen and Gordon (only results for potential I are discussed in the present paper).3. The IIb potential of the Holmgren, Waldman and Klemperer (HWK potential).16 In order to be able to make meaningful comparisons with other calculations it is impor- tant that all the physical constants and potential-energy parameters be the same in the calculations being compared. In table 2 we list some of the important physical con- stants and potential-energy parameters used in the present calculations. The calculations reported in this paper rely on the numerical solution of sets of coupled differential equations (see a b ~ v e ) . ~ The accuracy of the solutions we obtain Several different potentials were examined.292 ENERGY LEVELS OF TRIATOMIC SPECIES TABLE 1 .-MI initio Ar-HC1 POTENTIAL-ENERGY SURFACE OF VLIEGENTHART AND ROZEN- DAALa (REF.15) The potential has the analytic form 3 n - I V,(R) :: C,,, e-nr(R-Re) where a = 0.617 703 a.u.-’ Re = 6.912 833 a.u. C,, K/a. u . n = 1 2 3 K = O -8.730 91(-4” -5.030 03(-4) 1.111 823(-3) 1 -1.369 22(-4) -2.633 32(-4) 5.236 90(-4) 2 -6.557 3(-5) -4.279 64(--4) 4.256 38(-4) 3 - 1.226 94(-4) -1.317 88(-4) 4.817 09(-4) 5 5.823( - 6) -1.396 73(-4) 1.752 44( -4) 6 - 2.424 7( - 5) 3.838( - 6) 3.645 8 ( - 5 ) 4 1.196 2(-5) -2.733 lo(-4) 3.357 33(-4) ‘ 1 a.u. of energy = 219 475.797 cm-’. -8.730 91 (-4) for stands--8.730 91 x 1 a.u. of length = 0.529 177 x lo-’’ m. depends on the detailed method used to solve the equations. In particular it depends on how large a basis set is used to expand the overall wavefunction [eqn (3)] and on how many integration steps are used in the integration of the coupled set of differential equations.The method we use to solve the set of coupled differential equations is that of Johnson and Secrest.” In table 3 we examine the convergence of two of the bound-state energies of the Vliegenthart-Rozendaal potential with respect to : (a) increasing the number of HC1 rotational states used in the expansion of the wave- function and (6) increasing the number of integration steps used in the solution of the coupled differential equations. From the table we conclude that using j,,, = 9 (i.e., a basis of HC1 rotational states j = 0 to 9) and 300 integration steps the energy TABLE 2.-PHYSICAL CONSTANTS AND POTENTIAL-ENERGY PARAMETERS USED IN THE CALCULA- TION OF BOUND STATES OF 40Ar-H35C1 Calculations on Vliegenthart-Rozendaal potential [ref.( 1 5 ) ] a , b pR = 34 505.15 a.u. Bo = 10.594 17 cm-’. Calculations on Dunker-Gordon potential [ref. (6)] a* pR = 34 505.15 a.u. Bo = 10.440 19 cm-’ E = 140.395 66 cm-’ (= 202 K) tc = 13.50 R, = 3.930 A. Calculations on Holmgren-Waldman-Klemperer potential [ref. (1 6)] a , b pR = 34 505.15 a.u. Bo = 10.440 19 cm-’. ‘ pR is the Ar-HCl reduced mass. B, is the HCI rotational constant.I . F. KIDD, G . G . BALINT-KURT1 AND M . SHAPIRO 293 TABLE 3 .-CONVERGENCE OF TWO ROTATIONAL-VIBRATIONAL ENERGIES OF Ar-HC1 USING THE VLIEGENTHART-ROZENDAAL POTENTIAL [REF. (15)] FOR J = 0 ( a ) Convergence with size of HCI rotntiorral basis. j,,, = 4 denotes that rotational states j = 0 to j = 4 were used in the expansion of the wavefunction.Thesecalculationsused 100 integration steps over range R = 2.0 to 21.0 a.u. level/cm - high leve1,'cm-' Jmax energy of lowest energy of a 3 -95.2893 -4.9351 5 - 95.361 1 - 5.1357 7 - 95.3630 - 5.1389 9 -95.3630 - 5.1390 (b) Convergence with number of integration steps. These calculations usedj,,, = 9 and an integration range of R = 2.0 to 21.0 a.u. number of energy of lowest energy of a high integration steps level/cm-' level/cm- 1 00 - 95.3630 - 5.1390 200 -95.3436 - 4.9986 300 - 95.3430 -4.9873 400 -95.3429 -4.9854 of the lowest level is converged within 0.001 cm-l, while that of the high-lying level close to the dissociation limit is converged to within 0.02 cm-'. The calculations reported in this paper use.j,,, = 9 and 300 integration steps, unless otherwise stated.We note that quantities such as the change of energy with total angular momentum are almost certainly far more accurately predicted than is indicated by this discussion, as they will involve an almost total cancellation of errors. In order to compare the accuracy of the present calculations with results obtain- able using other methods we have performed calculations on the Dunker-Gordon potential These calculations usedj,,,, = 4 in order to provide a valid comparison with other calculations. Our results for the lowest energy level are compared with other calculations in table 4. We see that our calculations agree very well with those TABLE 4.-cOMPARISON OF DIFFERENT CALCULATIONS FOR THE LOWEST ENERGY LEVEL OF THE DUNKER-GORDON POTENTIAL^ ref.calculated energy/cm- LeRoy, Carley and Grabenstetter l 8 - 132.497 this workU - 132.495 Holmgren, Waldman and Klemperer l 6 - I3 1.71 1 upper bound - 134.066 lower bound Dunker and Gordon6 - 132.44 a These calculations usedj,,, == 4, as did the others in this table. of LeRoy et a1.l' which are the most accurate of the previously available results. A new method of Hutson and Howard19 also gives good agreement with this value. Usingj,,, = 9 we obtain an energy of --132.5015 cm-'. The energy obtained using j,,, = 4 was therefore converged within 0.007 cm-'. In table 5 we present our results for the lowest energy level of the Dunker-Gordon potential 1 for several values of the total angular momentum (again calculzted using294 ENERGY LEVELS OF TRIATOMIC SPECIES j,,, = 4).By dividing these energies by J(J + l), and finding the best straight line of E,/J(J + 1) as a function of J ( J + 1) in the least-squares sense, we can find the rotational constant and the centrifugal distortion constant of the system. In table 6 we present our calculated values of the rotational constant and of the centrifugal dis- tortion constant and compare them with other published values. From the table it can be noted that our results are in excellent agreement with those of Hutson and Howard. l9 So far we have discussed, for any given value of the total angular momentum quan- tum number J , only the lowest energy level of the system. One of the advantages of TABLE 5.-GROUND-STATE ENERGIES OF THE Ar--HCl VAN DER WAALS COMPLEX FOR A SERIES OF TOTAL ANGULAR MOMENTUM QUANTUM NUMBERS USING DUNKER-GORDON POTENTIALI [REF.(6)] present calculations Dunker and Gordon J /cm- ' /cm-' 0 - 1 3 2 . 4 9 5 4 - 1 3 2 . 4 3 6 1 - 1 3 2 . 3 8 2 4 - 1 3 2 . 3 1 5 2 - 1 3 2 . 1 5 6 6 - 1 3 2 . 0 9 2 3 - 1 3 1 . 8 1 7 8 - - 1 3 1 . 3 6 6 3 - 4 - 1 3 0 . 8 0 2 2 - 5 HCI rotational statesj = 0 to 4 were included in these calculations. the non-variational type approaches, such as the artificial channels approach here under discussion, is that it is possible to use them to calculate accurate energy levels also for the excited states of a system, without incurring too great a computational effort. In table 7 we present the results of our calculations for the complete set of energy levels of the Vliegenthart-Rozendaal potential l5 for J = 0.Also presented in the table are some variational results which Vliegenthart and Roosendaal15 have obtained by expanding the wavefunction in terms of a set of basis functions consisting of a product of 60 harmonic-oscillator functions for the radial coordinate and 20 angular functions. The agreement of the first six levels between the variational and our artificial channels calculation is very good. Vliegenthart and Rozendaal15 have also obtained similar results using smaller basis sets. For higher levels, however, the agreement between the two calculations rapidly deteriorates. In particular there are three extra levels present in our calculations which are absent from the variational TABLE 6.-cOMPARISON OF THE GROUND-STATE ROTATIONAL AND CENTRIFUGAL DISTORTION CONSTANTS FOR THE DUNKER-GORDON POTENTIAL I [REF.(6)] WITH THOSE OF PREVIOUS CAL- CULATIONS rotational constant Bo/cm- Dunker and Gordon6 Holmgren ut U I . ~ ~ this worku Hutson and Howard" 0.056 4 0 ( 1 0 ) 0.056 4 1 upper bound 0.056 48 0.056 45 centrifugal distortion constant DJ/10-6 cm-' 0 . 0 5 6 82 lower bound Dunker and Gordon6 Holmgren et U E . ~ ~ this worku Hutson and Howard" , , 0.95(50) 1.2449(7) upper bound 1 . 2 3 4 0 1 . 2 5 0 5 1.1 346( 1 6) lower These values were calculated from the values in table 5.I. F . KIDD, G . G . BALINT-KURT1 AND M . SHAPIRO 295 TABLE 7.-BOUND-STATE EIGENVALUES FOR VLIEGENTHART AND ROZENDAAL POTENTIAL [REF. (15)] J = 0 present calculations" Vliegenthart and Rozendaal /cm- /cm-' 1 2 3 4 5 6 7 8 9 10 1 1 12 1 3 14 -95.3430 - 79.1 33 1 - 68.0940 -55.3403 - 46.5935 - 35.4651 - 31.5121 - 27.5603 - 17.3462 - 16.61 30 -8.5871 -4.9873 -2.9494 - 1.3209 -95.3436 - 79.1338 - 68.0950 -55.3414 -46.5657 - 35.4631 -31.2235 - 26,9506 - 16.8857 - 11.8255 - 4.2926 (I HCl rotational statesj = 0 to 9 were used for these calculations.calculations. The variational calculations expand the Ar-HC1 dependence of the wavefunction in terms of simple harmonic-oscillator functions. It seems reasonable to suppose that this set of basis functions is not sufficiently flexible to represent the wavefunctions of states near the dissociation limit. In contrast, in the artificial channels method, the Ar-HCl dependence of the wavefunction is handled by the direct solution of the differential equations in this coordinate, and it should therefore be possible to obtain reliable energies even for levels near the dissociation threshold.We now turn our attention to the Ilb potential of Holmgren et a1.I6 (HWK poten- tial). This potential is the one which most accurately reproduces the spectroscopic data on the system. In table 8 are presented the calculated values of the lowest energy level for several different values of the total angular momentum quantum number J, calculated usingj,,, = 4. While in table 9 we compare our calculated values of the rotational constant and of the centrifugal distortion constant with those calculated by other workers for the same potential. It may be seen that our values for these " ground state " properties agree well with previously reported values.TABLE ~.-GROUND-STATE ENERGIES OF THE Ar-HCl VAN DER WAALS COMPLEX FOR A SERIES OF TOTAL ANGULAR MOMENTUM QUANTUM NUMBERS USING THE POTENTIAL OF HOLMGREN, WALDMAN AND KLEMPERER [REF. (16)] ground-s ta t e energy " J /cm-' 0 - 128.3946 1 - 128.2818 2 - 128.0562 3 -127.7179 4 - 127.2669 5 - 126.7032 HCl rotational states j = 0 to j = 4 were included for these calculations.296 ENERGY LEVELS OF TRIATOMIC SPECIES TABLE 9 .-COMPARISON OF THE ROTATIONAL AND CENTRIFUGAL DISTORTION CONSTANTS CALCULATED FROM THE POTENTIAL OF HOLMGREN, WALDMAN AND KLEMPERER [REF. (1 6)] WITH THOSE OF OTHER CALCULATIONS AND OF EXPERIMENT rotational constant &/cm - this work" Hutson and Howard l9 Holmgren, Waldman experiment 25 0.056 40 0.056 31 0.055 98 0.055 99 and Klemperer l6 centrifugal distort ion constant DJ/l 0- ' cm - this work" Hutson and Howard Holmgren, Waldman experiment 2s 6.7338 6.91 14 6.6379 6.6713 and Klemperer ~~~ a Calculated from values in table 8.In table 10 the complete set of bound-state energies for the Holmgren-Waldman- Klemperer IIb potential for total angular momentum quantum numbers J = 0 and 1 are presented. The calculated positions of the higher-lying bound-state energies clearly provide a means of testing the correctness of the proposed potential over a TABLE ~~.-ROTATIONAL-VIBRATIONAL ENERGY LEVELS (IN cm- ') OF Ar-HC1 VAN DER WAALS COMPLEX CALCULATED USING POTENTIAL-ENERGY SURFACE OF HOLMGREN, WALDMAN AND KLEMPERER [REF.(16)]" J = O J=l odd parity even parity - 128.3978 - 98.9503 -91.0337 - 70.0008 - 59.7207 - 53.4514 - 45.7516 - 33.1350 -29.3785 - 21.1 808 - 16.5351 -12.3814 -7.8191 -3.3012 - 1.01 16 - 128.2850 - 98.8392 - 92.9430 -92.9362 -90.9119 - 69.901 1 -62.9812 -62.9747 - 59.6025 - 53.3543 - 49.8262 -49.8376 -45.6550 - 34.0957 - 34.0889 - 33.0329 -29.2887 - 21.1202 - 20.1393 - 20.1751 - 16.4547 - 12.3074 - 11.3906 - 11.3196 -7.7566 -3.2535 -0.9756 a HCI rotational statesj = 0 to 9 were included for these calculations.I . F . K I D D , G . G . BALINT-KURT1 A N D M . SHAPIRO 297 wider range of coordinates than are tested by the calculation of ground-state proper- ties only. In principle, it would be possible to relate the calculated energies of the higher lying levels with the frequencies observed in the far-infrared20 and also in the near-infrared spectra of the system.21 We were, unfortunately, unable to relate our calculated energy levels with the presently available spectral data.4. APPLICATION OF THE CENTRIFUGAL DECOUPLING APPROXIMATION TO Ar-HCI As discussed in the theory section above, a common approximate technique in scattering theory is to ignore the terms which couple channels with different helicity quantum numbers (A) in the body-fixed axis system.'2-14 A similar technique has also been used in the BOARS method of Holmgren, Waldman and Klernpe~er.'~*~~ In table 11 we present results of calculations in which the centrifugal decoupling approxi- TABLE 11 ,-CALCULATED GROUND-STATE ENERGIES OF Ar-HCl COMPLEX FOR A SERIES OF TOTAL ANGULAR MOMENTUM QUANTUM NUMBERS USING THE POTENTIAL OF HOLMGREN, WALD- MAN AND KLEMPERER [REF.( 1 6)] AND THE CENTRIFUGAL DECOUPLING APPROXIMATION lowest bound-s ta te energy /cm - J jmax = 4 jmax = 9 0 - 128.3946 - 128.3978 1 - 128.2814 - 128.2846 2 - 128.0551 - 128.0583 3 - 127.7157 - 127.7188 4 - 127.263 1 - 127.2663 5 - 126.6976 - 126.7008 mation has been used to calculate the lowest energy level of the HWK potential for several values of J , using both j,,, = 4 and j,,, = 9. The use of the centrifugal- decoupling approximation greatly simplifies these calculations, especially for higher J values. Comparison of the first set of values in table 11 (thej,,, = 4 column) with table 8 gives a measure of the reliability of the centrifugal decoupling approximation.From this comparison we see that: the J = 0 result is exact, as we should expect because only A = 0 occurs even for the exact calculation in this case; the J = 1 result is in error by 0.0004 cm-' and the error increases with J to 0.0056 cm-' for J = 5. These errors are within acceptable bounds, and indeed only lead to an error of 0.0002 cm-' in the rotational constant and 5 x cm-l in the centrifugal-distortion con- stant. Comparison of the two columns of table 11 provides a check on the conver- gence of the energies with basis set. This comparison indicates that the j,,, = 4 energies are converged within 0.004 cm-l. In table 12 we list the complete set of energy levels of the HWK potential calculated using the centrifugal decoupling approximation for J = 1, 2 and 3.By comparing the J = 1 results with the exact ones given in table 10, we see that the errors caused by the centrifugal decoupling approximation for the J = 1 case are very small indeed. 5. USE OF HINDERED-ROTOR BASIS FOR CALCULATING THE ROTATIONAL-VIBRATIONAL ENERGY LEVELS OF H 2 0 The philosophy behind the hindered-rotor basis has been outlined in the theory We report below calculations in which we start off with 20 "free- section above.298 ENERGY LEVELS OF TRIATOMIC SPECIES TABLE 12.-ROTATIONAL-VIBRATIONAL ENERGY LEVELS (IN Cm- ') OF Ar-HCl VAN DER WAALS COMPLEX CALCULATED USING POTENTIAL-ENERGY SURFACE OF HOLMGREN, WALDMAN AND KLEMPERER [REF. (1 6)] AND THE CENTRIFUGAL DECOUPLING APPROXIMATION J = l J = 2 J = 3 A = O A = l A = O A = l 11=2 A = O A = 1 A = 2 - 128.2846 -92.9362 - 128.0583 -92.7019 -98.8386 -62.9747 -98.6153 -62.7505 -90.9193 -49.8376 -90.6905 -49.6093 -69.9007 -34.0889 -69.7006 -33.8846 -59.6084 -20.1751 -59.3839 - 19.9669 -53.3412 -11.3196 -53.1210 -11.1328 - 45 -6570 - 45.4677 -33.0387 -32.8461 - 29.2894 -29.1 121 - 21.0820 -20.8846 - 16.4563 - 16.2987 - 12.2980 - 12.1312 - 7.7571 - 7.6333 -3.2534 -3.1581 -0.9754 - 0.9042 -46.8464 - 127.7188 -92.3504 -46.4897 -13.8190 -98.2805 -62.4141 -13.4876 - 90.3473 - 49.2670 - 69.4006 - 33.5781 - 59.0472 - 19.6547 -52.7909 -10.8526 - 45.1838 - 32.5575 -28.8439 - 20.5890 - 16.0622 - 11.8813 - 7.4478 - 3.0157 -0.8001 HCl rotational statesj = 0 to 9 were included in these calculations.rotor " functions, for each H2 vibrational function, transform to the " hindered- rotor " rotational basis and then use only the lower lying hindered-rotor functions in solving the set of coupled differential equations. We note a difference between the present calculations and those of our previous publication' in that we have used here a much improved procedure for fitting the S~rbie-Murrell~~ H20 potential to the desired analytic form.In the improved procedure we fit the potential as a function of Y and 0 separately for each fixed value of R used in the calculations. In this way we are able to attain a fit to the potential which has a root-mean-square deviation of ca. 2 CM-' over the entire region of the potential lying within 10 000 cm" of the energy at the equilibrium geometry . In table 13 the energies of two of the levels of H20 forJ = 0 calculated using various TABLE 13.-cONVERGENCE OF 1ST AND 6TH J = 0 ENERGY LEVELS OF HzO USING " HINDERED- ROTOR " FUNCTIONS The " hindered-rotor " functions were obtained by diagonalising a Hamiltonian matrix All calculations used 7 Hz vibrational functions.evaluated using 20 " free-rotor " functions. rotational basis set calculated energy calculated energy of 1st level/cm-' of 6th level/cm-' 1 hindered-rotor function 7 9 7 9 ' 7 6 7 ) ' 7 7 ' 7 7 ' '7 7 7 7 free-ro tor functions -76 568.75 -71 723.80 -76 582.48 -71 936.07 -76 582.52 -71 949.11 -76 582.53 -71 954.09 -76 582.53 -71 956.35 -71 957.60 -76 582.53 -76 446.51 -71 887.98I . F. KIDD, G . G . BALINT-KURT1 AND M. SHAPIRO 299 numbers of “ hindered-rotor ” functions are given.It is clear from the table that when a basis set of 7 hindered-rotor levels is used the lowest level has converged to at least 0.01 cm-’ while the 6th level has converged to within ca. 1 cm-’. Also shown in the table are the results of using a basis of 7 “free-rotor” functions. For the lowest level, this basis yields inferior results to even that obtained using only a single “ hin- dered-rotor ” function, while for the 6th level 3 “ hindered-rotor ” functions give far better results than 7 “ free-rotor ” functions. TABLE 14.--CALCULATED BAND ORIGINS FOR HzO USING SORBIE-MURRELL POTENTIAL [REF. (23)] vibrational assignment this work Whitehead and 1crn-I Handy24 1cm-l 0 1 0 1589.6 0 2 0 31 35.2 1 0 0 3666.2 0 0 1 3757.9 0 3 0 4624.9 1 1 0 5226.7 0 1 1 5320.8 1590.2 3135.9 3666.6 3757.9 4624.3 5224.5 5321.4 In table 14 we present some of our calculated values for the band origins of the infrared spectrum of water and compare them with those of Whitehead and Handy.24 We see that, for these lowest levels, the agreement is extremely good.6. CONCLUSIONS The results presented in this paper demonstrate that the artificial channels method of calculating the rotational-vibrational energy levels of triatomic molecules can yield very accurate results. For the Ar-HCI van der Waals complex it is demonstrated that the use of the centrifugal decoupling approximation does not lead to a significant loss of accuracy. The method is particularly useful for calculating the higher lying rotational-vibrational energy levels of triatomic systems, especially as variational type methods are sometimes difficult to use for this purpose.The choice of basis functions in the application of the method may often be important. In section 5 we demonstrate that the use of a “hindered- rotor ” basis leads to greatly accelerated convergence properties for the energies of the low lying levels of H,O. Further work is in progress to develop suitable basis functions for accurate calculations on the higher levels of water. It does, however, greatly speed up the calculations. The authors would like to express their gratitude to Dr. J. A. Vliegenthart for providing them with his ab initio potential and his calculations of rotational-vibra- tional energy levels before publication, and for permitting them to include some of these results in the present paper.G. G. B-K. thanks the S.R.C. for a research grant and M. S. thanks the S.R.C. for a Senior Visiting Fellowship which made this colla- borative research possible. I. F. K. thanks the S.R.C. for a studentship, and we all thank the S.R.C. for provision of computer facilities on the Rutherford Laboratory computer. G. D. Carney, L. L. Sprandel and C. W. Kern, Ado. Chem. Phys., 1978, 37, 305. R. J. LeRoy and J. S. Carley, Ado. Chem. Phys., 1980, 42, 353. N. C. Handy, S. M. Colwell and W. H. Miller, Faraday Discuss. Chem. SOC., 1977, 62, 29. I. C . Percival and N. Pomphrey, Mol. Phys., 1978, 35, 649.300 ENERGY LEVELS OF TRIATOMIC SPECIES ’ R. G. Gordon, J. Chem. Phys., 1969, 51, 14; Methods Comp. Phys., 1971, 10, 81. A. M. Dunker and R. G. Gordon, J. Chem. Phys., 1976, 64, 354. M. Shapiro, J. Chem. Phys., 1972, 56, 2582. M. Shapiro and G. G. Balint-Kurti, Faraday Discuss. Chem. SOC., 1977, 62, 51. M. Shapiro and G. G. Balint-Kurti, J. Chem. Phys., 1979, 71, 1461. G. G. Balint-Kurti and M. Shapiro, Photofragmentation of Triatomic Molecules-Theory of Angular and State Distribution of Product Fragments, to be published. lo R. T. Pack, J. Chem. Phys., 1974, 60, 633. . l2 L. Eno and G. G. Balint-Kurti, Chem. Phys., 1978, 33, 435. l3 P. McGuire and D. J. Kouri, J . Chem. Phys., 1974, 60, 2488; D. J. Kouri in Atom-Molecule Collision Theory, A Guide for the Experimentalist, ed. R. B. Bernstein (Plenum Press, New York, 1979), p. 301. J. A. Vliegenthart and A. Rozendaal, personal communication. l4 M. Shapiro and M. Tamir, Chem. Phys., 1976, 13, 215. l6 S. L. Holmgren, M. Waldman and W. Klemperer, J. Chem. Phys., 1978, 69, 1661. l7 B. R. Johnson and D. Secrest, J . Chem. Phys., 1968, 48, 4682. l9 J. M. Hutson and B. J. Howard, personal communication. 2o E. W. Boom and J. van der Elsken, J. Chem. Phys., 1980, 73, 15. ” D. H. Rank, B. S. Rao and T. A. Wiggins, J. Chem. Phys., 1962,37,2511; D. H. Rank, P. Sita- ram, W. A. Glickman and T. A. Wiggins, J . Chem. Phys., 1963,39, 2673; H. Vu and B. Vodar, 2. Elektrochem., 1960, 64, 756; M. R. Atwood, H. Vu and B. Vodar, Spectrochim. Acta, Part A , 1967,23,553. R. J. LeRoy, J. S. Carley and J. E. Grabenstetter, Faraday Discuss. Chem. Soc., 1977, 62, 169. ’’ S . L. Holmgren, M. Waldman and W. Klemperer, J. Chem. Phys., 1977, 67, 4414. 23 K. S. Sorbie and J . N. Murrell, Mol. Phys., 1975, 29, 1387; 1976, 31, 905. 24 R. J. Whitehead and N. C. Handy, J. Mol. Spectrosc., 1976, 59, 459. 25 S. E. Novick, P. Davies, S. J. Harris and W. Klemperer, J. Chem. Phys., 1973, 59, 2273; S. E. Novick, K. C. Janda, S. L. Holmgren, M. Waldman and W. Klemperer, J. Chem. Phys., 1976, 65, 1114.

ISSN:0301-7249    

DOI:10.1039/DC9817100287

出版商:RSC    

年代:1981

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr. P. B. Davies (University of Cambridge) said: Dr. Evenson and his colleagues have reported that CH2 1.m.r. spectra in the F + CH, flame appear inverted, implying emission rather than absorption spectra. Some years ago we made similar observa- tions on 1.m.r. spectra of vibrationally excited OH but our experiments were incon- clusive. In our system spectra appearing on different laser lines at 78.4 and 79.1 ,urn (lasing singly or simultaneously) appeared with opposite phase in first derivative presentation. Would Dr. Evenson make any further comment on the behaviour of the CH2 spectra? Dr. K. M. Evenson (National Bureau of Standards, Boulder, Colorado) said: We have seen this same effect you mention when lines are lasing simultaneously; how- ever, using this particular line we have observed non-inverted spectra on the same scans. It is possi- ble that this originates in perturbations from the singlet state and therefore could lead to a way of measuring the singlet-triplet separation. Therefore, we believe that we have seen real stimulated emission.Dr. J. M. Brown (University of Southampton) said: In response to an informal comment by Prof. Thrush I would remark that the magnetic moment of a molecule in any particular level is composed of several contributions (electron spin, orbital angular momentum, rotation and nuclear spin) each characterized by a different set of g-factors. The complete determination of all these g-factors is a difficult task. The extent and precision of measurements in the far-i.r. 1.m.r.for a given radical are not yet sufficient t o permit such a determination. The few cases in which we have been successful in determining g-factors have incorporated data from other sources (e.g. the microwave or e.p.r. spectrum). An example is the HO, radical (J. Mol. Spectrosc., 1978, 72, 86). In the absence of such additional data, one must rely on relationships such as that due to Curl (Mol. Phys., 1955, 9, 585) to estimate the g- factors. Prof. J. A. Coxon and Mr. S. C. Foster (Dalhousie University, Halgax, Nora Scotia) said: We have recently analysed seven vibration-rotation bands (6 < u' <lo) of hydroxyl in the range 6250-8500 A. Our determinations of the u = 6, J = 5/2 f--) 7/2 intervals, 92.72 ( e t) e) and 92.87 ( f - f ) cm-' are in excellent agreement with those of Davies.We wish to point out, however, that the linear extrapolation assumed by Davies of the rotational intervals to higher vibrational levels is not reliable. Errors in the extrapolated values of table 1 of his paper vary from 0.14 cm-I for u = 7, J = 3/2 +-+ 5/2 to 1.1 1 cm-l for u = 9, J = 7/2 f-) 9/2. The error limit of 0.05 cm-' assumed by Davies for the intervals in table 1 is overly optimistic. Our measured splittings should be of considerable help in obtaining further data on hydroxyl by the laser magnetic resonance technique. J . A. Coxon and S. C. Foster, Can. J . Phys., in press.302 GENERAL DISCUSSION Dr. P. B. Davies (Uniuersify of Cambridge) said: The extrapolation of the u = 0 to 5 data shown in table 1 of our paper was a necessary approximation as a guide to the rotational transitions accessible to 1.m.r.It was not intended to imply that these would be as reliable as an accurate fitting similar to that in ref. (3). This type of data for the higher vibrational levels has recently become available (J. A. Coxon and S. C. Foster, in press) and for u = 6, J = 5/2 * 7/2 yields: . f i e * f i e flf *hf 92.72 cm-I 92.87 cm-' in excellent agreement with our 1.m.r. result (table 2). Mr. J. M. Hutson (Oxford University) said: We would like to report a new inter- molecular potential that we have obtained for the Ar * * - HCl system. Experimental information on the potential is available from (1) molecular-beam electric resonance (MBER) spectra of the Ar HCl complex, (2) pressure broadening of HCl rota- tional spectra by Ar, ( 3 ) molecular-beam total differential cross-sections, (4) second virial coefficients for Ar + HC1 mixtures.Several intermolecular potentials have previously been obtained by fitting to only one set of data, but this has not been successful : potentials derived from pressure-broadening do not fit the MBER spectra of the complex, whereas the potential derived from the MBER spectra3 fails to reproduce' the observed line-broadening. We have obtained a new potential by fitting to all these data simultane~usly,~ and a contour plot 5 . 0 of the resulting potential is shown in fig. 1. The different sets of 4 . 5 4 . d 3.5 ~~ 0 30 60 90 120 150 el" FIG. 1.-Contour plot of the fully optimised intermolecular potential for Ar - + * HCI.Contours are at 10 cm-' intervals, relative to the absolute minimum at -180.8 cm-'. data are complementary, and enable us to determine the potential reliably over a large area of configuration space. The equilibrium configuration is linear, Ar H-C1, at an Ar-HC1 centre-of-mass distance of 4.00 A, and the absolute well depth isGENERAL DISCUSSION 303 - 3 - - 4 180 10 cm-'. The barrier to internal rotation of HC1 in the complex is 68 cm-l. The only feature of the potential which is not reliably determined is the well depth near the Ar C1-H configuration, where a shallow secondary minimum (<40 cm-' relative to the 0 = 90" configuration) is not excluded by the existing data. - W. B. Neilsen and R. G. Gordon, J. Chem. Phys., 1973,58,4149. J. G. Kircz, G.J. Q. van der Peijl, J. van der Elsken and D. Frenkel, J. Chem. Phys., 1978, 69, 4606. S. L. Holmgren, M. Waldman and W. Klemperer, J. Chern. Phys., 1978, 69, 1661. ' J. M. Hutson and B. J. Howard, Mol. Phys., 1981, 43,493. Dr. C. J. Ashton and Dr. M. S. Child (Oxford University) said: The paper by Dr. Howard emphasises that rather detailed experimental evidence is now available on certain atom-diatom intermolecular potentials at low energy. We would like to remark that yet more information is to be obtained by observing " rotationally pre- dissociating " quasibound states of the van der Waals complexes (in scattering termin- ology, rotational compound-state resonances). Loosely speaking, these states are unstable because the rotational energy of the diatom, when transferred to atom- diatom translational motion, is sufficient to break up the complex.Such states have a finite lifetime and therefore a finite energy width, and these widths should depend sensitively on the anisotropy of the intermolecular potential in the region of its mini- mum and low on the repulsive wall. The published infrared spectra of the rare-gas- H2 complexes, for example, contain many lines corresponding to such quasi-bound states, and broadening assigned to rotational predissociation has now been resolved for the Ar - HD complex.2 We have recently made an accurate, relatively extensive computational study of such resonances for the realistic Ar + HCI potential surface obtained by Hutson and H o ~ a r d . ~ Close-coupled scattering calculations were carried out using the R-matrix propagator algorithm .4 5'-matrices, fully converged to three significant 0 I 50 t 4 100 150 200 scattering energy/cm- -12 -11 -10 t4 s M - -9 - 0 jo -7 FIG.2.-Widths and energies of J = 0 rotational compound state resonances for Ar + HCl up to the HCI j = 4 threshold. r denotes the f.w.h.m. width in cm-', and z the corresponding lifetimes in s. Note the logarithmic scale for r. HCI rotational thresholds are indicated by vertical lines.304 GENERAL DISCUSSION figures, were obtained for total angular momenta ( J ) of 0 and 1, at several thousand different energies up to the HC1 j = 4 rotational threshold (208.8 cm-l above the dissociation limit of the van der Waals complex). Quasibound states were identified and characterised from the energy dependence of the S-matrix eigenphase sum.5 The energies and widths of the J = 0 states are shown in fig.2. We believe this figure includes the complete resonance spectrum in the region shown, with the excep- tion of a few features which are too close to a threshold or too broad to be charac- terised. Approximate calculations in a perturbation scheme6 show that the resonances may be classified approximately into a series of progressions, each associated with a particular rotational state of HCl and supported by a diabatic potential well in the van der Waals stretching coordinate. A tentative classification is indicated in fig. 2, and the resonance energies obviously correspond roughly to one's general ideas about vibrational progressions. First the surprisingly large variation in widths and the observed trends require theoretical rationalisation.Secondly, these solidly based predictions should, we feel, provide a stimulus and a challenge for experimental work. The widths are such that there should be a real possibility of observing the narrower resonances in spectroscopy of the van der Waals complex, and the wider ones as perturbations in molecular beam differential scattering cross- sections. The significance of these results is twofold. B. J. Howard, paper at Faraday Discuss. Chem. SOC., 1981, 71, 23. A. R. W. McKellar, unpublished work. J. M. Hutson, Faruday Discuss. Chem. SOC., 1981, 71, 302; J. M. Hutson and B. J. Howard, Mol. Phys., 1981, 43, 493. E. B. Stechel, R. B. Walker and J. C . Light, J.Chem. Phys., 1978, 69, 1518. A. U. Hazi, Phys. Rev. A, 1979, 19, 820. J. M. Hutson, unpublished work; see also the comment by Hutson on the contribution of Baht-Kurti et al., Faraduy Discuss. Chem. SOC., 1981, 71, 365. Dr. Ph. BrCchignac, (Universite' de Paris-Sud, Orsay) said: This contribution aims at emphasizing the complementary nature of the spectroscopic data on the bourtd van der Waals complexes and of the collisional properties of the separate molecules, in the way in which they both give information on the intermolecular potential- energy surface. Indeed, as pointed out in Dr. Howard's paper, the spectroscopic data are mainly sensitive to the shape of the potential near the equilibrium con- figuration and cannot be extrapolated too far from it. In contrast to this, collision experiments can probe very different regions of the surface. Also, there are different kinds of collision experiments, each one being sensitive to a particular feature of the interaction.Most of the molecular-beam scattering experiments are essentially sensitive to the isotropic part of the potential-energy surface. There are a few exceptions for which rotationally inelastic transitions have been detected in a molecular and they have given information on the anisotropic part of the potential. However, such studies need very sophisticated machines, which unfortunately are not readily usable for differ- ent molecules. The energy-change which requires a crossed-beam ar- rangement and a long time-of-flight detection for rotational-energy resolution, has so far been limited to hydrogenic molecules.The sensitive laser-induced fluorescence detection technique either combined with electric quadrupole state selection3 (usable only for strongly polar molecules) or with laser-labelling state selection4 has been limited to dye-laser-absorbing molecules.GENERAL DISCUSSION 305 In comparison, the pump-and-probe kind of experiment in the bulk gas appears as a versatile and low-cost technique. The information obtained in these experiments has basically the same nature as that from pressure-broadening of rotational lines, namely the rotationally inelastic cross-sections. However, they are far more power- ful since the results are very much more detailed owing to the double state selection at preparation and at detection.The first is usually achieved by laser pumping, the second either by observing the fluorescence or by using a probe laser beam. The following few examples are selected to show that this kind of study does give information on the shape of the intermolecular potential. There have been generated data for polar molecules like HF,' Ba06 and for homonuclear diatomic molecules like 12,7 Na: and Li2.9 As one might expect in these two cases the rotationally inelastic transitions proceed mainly by Aj = 1 and A j = 2 quantum jumps, respec- tively. Moreover, the individual cross-sections are found to obey the magic Pritchard power law." This last finding is probably related to the fact that the ani- sotropic part of the potential has essentially a long-range P,(cos 0) shape and a P, (cos 0) shape, respectively.-~ ~ ~ - _ _ , . l o t a la) i 0 FIG. 3.-State-to-state rotationally inelastic cross-sections in CO-H2: 0, theory; 0, experiment ; (a) 77, (b) 293 K [from ref. (ll)].306 GENERAL DISCUSSION The case of non-polar heteronuclear molecules appears to be more interesting because it is very difficult to foresee what is the shape of the potential. Fig. 3 is a comparison of the results of an infrared-infrared double resonance experiment and fully quantum ab initio calculations for the CO-H2 couple.ll State-to-state cross-sections corresponding to an initial quantum number j = 7 are plotted against the final j going from 3 to 11, leading to a very satisfactory agreement between experi- ment and theory. At low temperatures (T = 77 K) there is a detailed balancing factor which favours the downwards transitions, but this is negligible at room tem- perature (T = 293 K) and the main result is that A j = 1 and Aj = 2 transitions have about the same cross-section.Actually this similarity in cross-sections appears to be related to the shape of the potential, as apparent from fig. 4, which shows the radial 1000 c I I I I 1 I 4 5 6 7 8 9 10 11 P (a.u.) FIG. 4.-Radial dependence of the first coefficients z ~ l ~ , ~ ~ ( p ) in the polynomial expansion of the CO-H2 potential [from ref. (12)). dependence of the coefficients u ~ ~ l , ~ ( p ) of the polynomial expansion of the CO-H, energy surface.12 The behaviour of the uolo and u020 coefficients, responsible for the Aj = 1 and Aj = 2 transitions, respectively, is about the same since the corresponding curves remain very close to one another.Can the results now be predicted when retaining the CO molecule but changing the collision partner from Hz to another CO molecule? Simple arguments, based on the small size of the dipole moment and the medium size of the quadrupole moment, would tend to favour the Aj = 2 transition. However, the experiment gives the reverse result,13 as can be seen in fig. S ( 0 ) . Both the large value of the Aj = 1 cross-section and the relatively small value of the Aj = 2 cross-section demonstrate the importance of short-range anisotropy. A PI-like and a P2-like contribution shouldGENERAL DISCUSSION o'8 c o.6[ P 0.2c P 307 0 AJ FIG. 5.-Relative values of the inelastic cross-sections as a function of the quantum jump AJ for CO-CO (0) and NO-NO (El).be present in the repulsive region to compensate the quadrupole-quadrupole inter- action by the interference effect along intermediate impact-parameter trajectories.'1 NO is another interesting non-polar diatomic molecule. Some preliminary results14 of infrared-infrared double resonance are also plotted in fig. 5 for the NO- NO collisional interaction at high J (X). Unexpectedly they look very different from the CO-CO case: the Aj = 1 cross-section is about four times less than the Aj = 2 cross-section and the Aj = 3 cross-section is relatively large (about twice that of Aj = 1). Further analysis is needed to interpret these last results in terms of intermolecular anisotropy.Efficient techniques for close-coupling dynamical calculations are now available and positive testing of energy surfaces is definitely possible from rotationally inelastic cross-sections. Owing to the recent availability of tunable infrared lasers, so con- venient for the non-polar molecules, such pump-and-probe experiments should be developed in the future. In conclusion, the spectroscopic data on van der Waals molecules appear as only one way of obtaining information on the interaction potential. W. R. Gentry and C. F. Giese, J. Chem. Phys., 1977, 67, 5389. U. Buck, F. Huisken and J. Schleusener, J. Chem. Phys., 1978, 68, 5654. B. E. Wilcomb and P. J. Dagdigian, J. Chem. Phys., 1977, 67, 3829; P. J. Dagdigian, B. E. Wilcomb and M. H. Alexander, J . Chem. Phys., 1979,71, 1670.K. Bergmann, R. Engelhardt, U. Hefter, P. Hering and J. Witt, Phys. Rev. Lett., 1978,40,1446. J. J. Hinchen and R. H. Hobbs, J . Chem. Phys., 1976, 65, 2732; B. A. Esche, R. E. Kutina, N. C. Lang, J. C. Polanyi and A. M. Rulis, Chern. Phys., 1979, 41, 183; J. A. Barnes, M. Keil. R. E. Kutina and J. C . Polanyi, J. Chem. Phys., 1980, 72, 6306. R. A. Gottscho, R. W. Field, R. Back and S. J. Silvers, J. Chem. Phys., 1980, 73, 599. S. R. Jeyes, A. J. McCaffery, M. D. Rowe and H. Kat6, Chem. PhjJs. Lett., 1977, 48, 91. T. A. Brunner, R. D. Driver, N. Smith and D. E. Pritchard, J . Chem. Phys., 1979,70,4155. Ch. Ottinger and M. Schroder, J. Phys. B, 1979, 12, 3533; Ch. Ottinger and M. Schroder, J. Phys. B, 1980, 13, 4163. lo D. E. Pritchard, N. Smith, R.D. Driver and T. A. Brunner, J. Chem. Phys., 1979,70, 2115.308 GENERAL DISCUSSION l1 Ph. Brechignac, A. Picard-Bersellini, R. Charneau and J. M. Launay, Chem. Phys., 1980, 53, l 2 D. R. Flower, J. M. Launay, E. Kochanski and J. Prissette, Chem. Phys., 1979, 37, 355. l3 Ph. Brechignac, A. Picard-Bersellini and R. Charneau, to be published. l4 Ph. Brechignac, to be published. 165. Prof. R. C. Woods (University of Winconsin) said : In his paper Prof. Winnewisser has described his laboratory work on formation of cyanoacetylene and cyano- diacetylene in electric discharges and related it to the interstellar synthesis of the cyanopolyacetylenes. We have also observed copious production of cyanoacetylene in a d.c. discharge in methane +- nitrogen mixtures, but it seems to me that the ques- tion of how these molecules are synthesized in the interstellar environment is still unanswered.The great disparity in temperature, density, etc. makes the relation between the laboratory and space synthesis rather uncertain, although the discharge results do indicate in a general way that these molecules are rather stable. The syn- thesis suggested in the quoted paper by Mitchell, Huntress and Prasad requires an extremely high rate constant for radiative association at low temperatures. Such high values have been suggested in the literature, but never measured or demonstrated, so this mechanism is highly speculative. Prof. M. Winnewisser (Giessen University) said: Indeed it is correct that the plasma chemistry results cannot claim to indicate how the cyanopolyacetylenes are synthesized in the interstellar clouds. However, I do believe that the laboratory results indicate some of the bulk properties, such as which molecules are chemical sinks and survive most easily hostile environments.The work of Mitchell, Huntress and Prasad is based on the assumption that the gas-phase formation of the cyanopoly- acetylenes is possible if the radiative association reaction of H,CN+ with C2H2 is rapid at low temperatures. Indeed no experimental proof for this assumption can be put forward; therefore, I agree with you that the proposed formation mechanism is rather speculative. Perhaps attention should be drawn to a recent paper by Cleggl concerning carbyne, a high-temperature allotrope of graphite, and cyanoacetylenes in stellar atmospheres.Clegg speculates that the long-chain structure of carbyne, which it shares with the polyacetylenes, implies some related formation process. He points to work by Bonne et a1.2 that in the soot formation zone of acetylene flames, the polyacetylenes HC4H, HC,H and HCSH were found to be very abundant. Thus, the long carbon chain type molecules seem to be rather stable under a variety of con- ditions. R. E. S. Clegg, Mon. Not. R. Astron. SOC., 1980, 191, 451. V. Bonne, K. H. Honiann and H. G. Wagner, in Tenth Symposium on Combustion (The Com- bustion Institute, Pittsburgh, 1965), p. 503. Prof. M. Winnewisser (Giessen University) said : The pivotal requirements for the detection of unstable species in a hostile environment by microwave techniques may be summarized as follows: (a) Efficient production scheme for the species in question in order to increase the particle density.This requires the optimization of the chemical and physical parameters at a minimum temperature. (6) High spectro- meter sensitivity. Optimization of all the parameters in the absorption coefficient as has been discussed beautifully by Prof. Woods. (c) Good frequency predictions either from data obtained from other branches of spectroscopy or from high-quality ab initio calculations. Even when all these requirements are met, the search for unknown species will only succeed in a narrow parameter range of the multiparameter systems in which theGENERAL DISCUSSION 309 species are produced. As a recent example of these difficulties 1 would like to men- tion the millimetre-wave detection of H,N-N-C, isocyanamide, by E.Schafer, M. Winnewisser and J. J. Christiansen in Giessen. The millimetre-wave absorption lines were only detectable at a pressure of ca. Torr in a Pyrex glass absorption cell. In a metal cell or in the presence of metals, rapid decomposition occurs pro- hibiting the observation of this transient species. Similar problems have been found in the detection of plasma-generated species such as HNC and particularly in the case of the detection of high-temperature species such as Bas. The large dipole moments of the latter species, ca. 8 D, require careful monitoring of the incident millimetre-wave power, otherwise saturation effects occur and the absorption signal is not observable if the particle density is low.Also, with respect to the other experimental parameters, only a narrow parameter range de- scribes the conditions for maximizing the absorption intensity and thus for detecting such species. Prof. R. C. Woods (Unioersity of Wisconsin) said: I agree completely with what Prof. Winnewisser has just said about the difficulty of observing transient molecules in plasmas. The intensities are usually very sensitive to the conditions and it is extremely important to try to quantify these conditions as thoroughly as possible by other techniques, as discussed in my paper, to diminish the guesswork involved in obtaining new spectra. Dr. M. Quack (Gottingen University) said: Prof. Winnewisser has discussed in his paper the cases of non-rigid (flexible, quasilinear) triatomic and polyatomic molecules, such as KCN, which are most interesting from the point of view of both chemical bonding and intramolecular time-dependent and time-independent dynamics.An interesting development in this connection is the suggestion of Yamada and Winne- wisser,' extended by Bunker and Howe,2 to quantify the degree of non-linearity and flexibility using their y-parameter. The success of this method has been beautifully illustrated by Prof. Winnewisser. I should like to comment here on certain similarities between the above-mentioned flexible molecules and the concept of a " flexible transition state ", which is of some use in chemical kinetic^.^ These analogies may help to stimulate some fruitful exchange between spectroscopists and kineticists, although the mathematical con- struct of the transitian state is not an experimental (spectroscopic) observable.Fig. 6 FIG. 6.-Coordinate system for a triatomic case. sketches the coordinate system for the simplest case of a triatomic system (although the considerations below are general). The large-amplitude motion for a typical flexible molecule would be associated with the angle p (see the cases of, say, C, and KCN in Prof. Winnewisser's paper). Two similarities arise with kinetic systems, such as in recombinations3310 GENERAL DISCUSSION or bimolecular substitutions H + F2 -+ HF + F. (4) The first similarity is fairly straightforward in that the very highly excited molecules (D+H,)* or (H20)* (these are not transition states, but rather similar to ordinary vibrationally excited molecules with the possibility of vibrational predissociation) often will show highly non-rigid behaviour independent of their position on the Yamada-Winnewisser scale at low energies.The second analogy is of a more fundamental interest. The kinetic systems con- tain two (at least) large-amplitude motions, corresponding to q and the dissociation- recombination or generally reaction coordinate q. However, in the transition-state description the slow q-motion is treated separately, by calculating energy levels of the quasi-molecule with fixed q (" clamped q-approximation '*)3 analogous to the Born- Oppenheimer approximation and from this effective potential curve, the scattering channel potentials.Although these channel potentials have a completely different physical significance, they behave computationally similar to ordinary energy levels of a polyatomic molecule. It was recognized some time ago that these " energy levels *' are not well-descri bed by the harmonic-oscillator-rigid-rotor approxima- tion, but rather by a flexible-molecule-large-amplitude approximation. A correla- tion scheme was suggested4 which connects the limits of a tight bent vibrator-rotator and completely flexible free internal-rotator-external-rotator via equations of the form Eqn (5) gives a reasonable semi-quantitative description of rotation-vibration energy levels for all degrees of flexibility, characterized by the bond extension (qe - q) and the interpolation parameter o! [for details see ref.(3) and (4)]. AppropJiate correla- tion schemes including symmetry labelling are a~ailable.~ The interpolation of eqn ( 5 ) can be related to a parametric dependence of the potential in the coordinate p upon the bond extension (q - qJ: Eqn (6b) is similar in its form to a Morse-shaped potential, but applies to barrier heights for internal r ~ t a t i o n . ~ Other potential forms that may be useful for both the interpolation of energy levels [eqn (5)] or of barriers [eqn ( 6 ) ] are, for instance, (using the general notation F for appropriate energies) I;' = Fo exp [~(x)"] F = Fo exp[ - ( ~ l x ) " ] F = Fo { l - [tanh(x/cc)]"> with x = (q - qe) 0. The parameter tc characterizes the rate of change from aGENERAL DISCUSSION 311 tight or rigid system corresponding to the energy parameter Fo at q = qe to a freely rotating non-rigid system at q = co as a function of (q - qe).Since the kinetic applications are far-removed from high-resolution spectroscopy, I had better conclude with a practical analogy arising in spectroscopically accessible flexible molecules. In a molecule such as KCN or LiCN (or even HCN) one might study the parametric dependence of the bending (internal rotational) energy levels upon the vibrational excitation in the stretching coordinate q (i.e. Li-CN). This would be similar to the parametric dependence of scattering channel energies upon q and some of the above formulae and concepts may be useful. K. Yamada and M. Winnewisser, 2. Naturforsch. Teil A , 1976, 31, 139. P. R. Bunker and D.J. Howe, J. Mol. Spectrosc., 1980, 83, 288. M. Quack, J. Phys. Chem., 1979, 83, 150. M. Quack and J. Troe, Bey. Bunsenges. Phys. Chem., 1974, 78, 240. M. Quack, Mol. Phys., 1977, 34, 477. Dr. S . Leach (Uniuersite' de Paris Sud, Orsay) said: In his paper, Prof. Woods, mentions the absence of ion vibrational satellites, indicating a low vibrational tem- perature. He suggests that there is a relaxation mechanism for vibrational excitation that is specific for ions. I believe that in some cases rather rapid radiative vibra- tional decay could occur for molecular ions, especially for high vibrational states. Infrared emission rates of low-lying vibrational levels of neutral molecules have been measured. The corresponding lifetimes are in the millisecond to second region.However, from harmonic oscillator, linear dipole moment matrix elements, the u + 1 -+ u dipole emission rates should increase approximately linearly with v , and a considerably faster increased rate could ensue when nuclear and electrical anharmoni- cities are taken into account. Furthermore, the dipole-moment derivatives with respect to nuclear displacements might be considerably greater for charged systems than for the corresponding neutral species. In a polyatomic species the radiative decay can be further enhanced by the greater number of emission channels, involving quantum- number changes in more than one mode. Arguments of this nature have been used to rationalize the possibility that for vibrationally hot chloroacetylene ground-state ions (vibrational energy ~ 2 6 700 cm-') the dipole decay rates could be as high as Direct experimental evidence of fast infrared emission decay of high vibrational levels of molecular ions is lacking at present.It is worth investigating since, as has been pointed out elsewhere,2 the existence of very rapid infrared emission for vibra- tionally hot molecular ions could have important effects in cold plasma systems and in planetary ionospheres. Furthermore, fast infrared emission of molecular ions would have to be taken into account in temperature-altitude modelling of planetary atmospheres. 104-105 s-1.1 G. Dujardin, S . Leach, G. Taieb, J. P. Maier and W. M. Gelbart, J . Chem. Phys., 1980, 73, 4987. S. Leach, G. Dujardin and G. Taieb, J. Chim. Phys., 1980, 77, 705.Prof. R. C. Woods (University of Wisconsin) said: We do not have any definite information about the mechanism for the enhanced rate of vibrational relaxation for molecular ions that is suggested by our not having observed vibrational satellites, but I agree with Dr. Leach that radiative decay may be quite fast and very important in many cases. Further experimental and theoretical work on this question would be quite useful, I think.312 GENERAL DISCUSSION Dr. T. A. Miller (Bell Laboratories, Murray Hill, New Jersey) said: Since very little is known about the cross-section for rotational and vibrational energy transfer for molecular ions, the rotational and vibrational temperature of ions in an otherwise well-characterized environment may be unknown. This is particularly true for environments such as the discharge used by Prof.Woods, since electric fields con- tinually accelerate the ions, giving them translational energy, which can be converted into internal energy by collision. As the paper makes clear, the resulting uncertainty in the ion’s temperature, particularly rotational, causes the largest errors in the calculations of the ions’ absorption coefficients and hence their detectabilities. We have recently observed laser-induced fluorescence spectra of molecular ions, e.g. N2+, CO+, cooled to ca. 100 K by collision with liquid-N,-cooled He following pro- duction by Penning ionization. There are normally no electric fields in our apparatus. However, with the addition of Stark plates, we should be able to apply known electric fields to our ions while maintaining a precise measure of their rotational and vibra- tional temperatures with the laser-induced fluorescence technique.This should provide a measure of the desired cross-sections and give more precise knowledge about the internal energy distribution of the ions in your experiments. Prof. R. C. Woods (University of Wisconsin) said : I think it would be very interest- ing if Dr. Miller could obtain some information on rotational and vibrational tem- peratures in the ground electronic state of ions in external electric fields by using his laser-induced fluorescence methods. Dr. J. M. Brown (University of Southampton) said : Could Prof. Hirota comment on: (a) the relative sensitivity of diode laser and laser magnetic resonance spectro- scopy for the study of free radicals in the mid-infrared, and (b) the apparent lack of observation of 19F hyperfine structure in the diode laser spectrum assigned to the FCO radical, in view of the large splittings expected from the study of this radical in a matrix by e.s.r.? Prof.E. Hirota (Institute for Molecular Science, Okazaki, Japan) said: I find that almost nothing is being reported on diode laser spectroscopy at this Faraday Dis- cussion. As you may well know, diode laser spectroscopy is becoming a method as powerful as laser magnetic resonance (1.m.r.) in the infrared region. Unfortunately, I have not prepared slides which give you an overview on the present status of diode laser spectroscopy in the world, but I have one slide which summarizes molecules we have investigated or we are investigating using this method.The content of this slide is reproduced in table 1 . I would like to make brief comments on some of the molecules listed here. I will pass over the diatomic molecules, since NS, CCl, CF and SF are all typical Hund’s case (a) diatomic free radicals. Among the triatomics B 0 2 is an interesting molecule; it is well-known as a species that exhibits Renner-Teller effects in its spectra. An interesting new aspect is present in the v3 band. Some time ago John Johns (N.R.C., Canada) observed electronic absorption and emission spectra of this molecule, and determined 2C3 in the ground state to be 2644 cm-l, whereas the fundamental frequency we obtained recently is 1278 cm-l. We confirmed Johns’ value of 2C3 by observing the hot band v3 = 2 +- 1.It is thus apparent that the v3 mode of B 0 2 is subject to a rather large negative an- harmonicity. We suspect that this anharmonicity is mainly due to a vibronic inter- action of the ground z211g state with the excited A””ITg state through the antisymmetric stretching v3 mode.GENERAL DISCUSSION 313 TABLE 1 .-DIODE LASER SPECTROSCOPY OF TRANSIENT MOLECULES triatomic diatomic cs so (X”-) CCl (X’rI,) CF (X’JI,) SF (X’ni) NH2 BOZ FCO H 0 2 FSO ClBO quadratomic CH3 CF3 atomic He * Ar * a NS ( X 2 n r ) v = 1 - 0 , 2 - 1 v = l - o a v = 1 - 0 v = 1 - 0 , 2 - 1 v = 1 - - 0 v = 1 - 0 , 2 - 1 v2a v1 (C=O stretch), v2 (C-F stretch) v2 (H-0-0 bend) vl (S=O stretch), v2 (S-F stretch) v1 (B-Cl stretch) v2 (out-of-plane bend) v3 (deg.C-F stretch)” V 3 , V2 f V 3 - V2, 2 V 3 - v3, Vza * Partially or tenatively assigned. There have been almost no spectroscopic investigations reported on FCO in the gas phase. We have been able to observe two bands, the C=O and C-F stretching bands, and also the v1 band of the 13C species. The band origins we observed corre- spond well with the matrix data reported by Jacox and others. The next molecule, H02, has been known as an important intermediate in oxidation reactions of hydro- carbons, and we have been able to observe and analyse the v2 band by diode laser spectroscopy and the v1 band by difference-frequency laser spectroscopy. A similar study has been carried out on two bands of FSO, i.e. v1 (S=O stretching) and v2 (C-F stretching).The ClBO molecule, which has a singlet ground state, was found by chance in the course of studying B02. The band we observed is the B-Cl stretch- ing band. We have also completed the observation of its microwave spectrum, and have confirmed the molecule to be linear. One of the most recent and perhaps most important results we obtained is a suc- cessful observation of the CH, v2 band. Prof. Herzberg reported absorption spectra of CH3 in the ultraviolet region twenty years ago. From our diode laser spectra we established the planarity of the CH, radical in the ground state unequivocally. We have found, however, that the out-of-plane vibration (the v 2 mode) has a rather large negative anharmonicity, which may again, as in B02, be ascribed to a vibrbnic interaction. Unlike CH3, CF3 is non-planar in the ground state; in our group Yamada has succeeded in assigning Q-branch transitions of its v3 band by diode laser spectro- scopy, and Endo observed and assigned two rotational transitions by microwave spectroscopy.In the course of our investigations we also observed a few atomic lines for He and Ar in metastable states. I turn now to the specific questions raised by Dr. Brown. (a) It is very difficult to estimate the sensitivity of diode laser spectroscopy, be- cause the sensitivity is very much dependent on the quality of diodes employed. In one of the most favourable cases, i.e. the CF radical, we have made a rough estimate of the minimum detectable number of CF molecules. The number we obtained is 6 x lo8 molecules ~ m - ~ , which may be compared with 3 x lo8 molecules cm-, calculated by Evenson et al.for mid-infrared laser magnetic resonance spectroscopy.314 GENERAL DISCUSSION Please note that Dr. Evenson's value applies to a typical case, whereas our number cor- responds to an optimum condition. I should, however, mention as an advantage of diode laser spectroscopy over laser magnetic resonance that in principle we can choose the strongest band of a molecule to be investigated. (b) We have not observed any hyperfine splittings, although some high-K. lines were observed to be split by spin-rotation interaction. The absence of hyperfine structures in the observed spectrum is ascribed to the following reasons: (1) both of the two bands we observed, the C=O and the C-F stretching bands, obey a-type selection rules, (2) our measurements were concentrated mainly on large N lines, because these transitions are much stronger than smaller N transitions for which hyperfine splittings are larger, (3) Zeeman modulation was necessary to be employed, especially in the 5 pm region (i.e.for the v, band) because of the presence of many interfering lines. Although Zeeman modulation is extremely useful in detecting weak paramagnetic lines, it often obscures small splittings. Prof. W. Urban (University of Bonn) said : We have been able to push the CO-laser operation with a liquid-nitrogen-cooled discharge of 75 cm active length up to the u = 36 + 35 band at 1225 cm-' (8.2 pm). There is complete coverage by laser lines up to this region since adjacent vibrational bands overlap.At these high vibrational bands the rotational constant of CO is considerably reduced, thus giving a distance of 3 cm-' for the transition within one band. The low-energy end of the v/cm-' 1225 1250 1275 1300 1325 1 I 1 I * I ~ 25 1 !ill L L L L L J 13 10 8 1 ia - 30mW I 15 7 17 6 3 6-35 35-3 4 3 4-33 3 3 - 3 2 32-31 FIG. 7.-Low-frequency region of the CO-laser system described in ref. (1). Absence of the laser line P(12) u = 32+31 is due to internal absorption by a transition in the R-branch R(4) u = 34 t 33 of the CO plasma.GENERAL DISCUSSION 31 5 CO-laser spectrum is plotted in fig. 7. Details of the laser construction and operating conditions can be taken from ref. (1). The short discharge tube can easily be used in an intracavity type 1.m.r.spectro- meter, thus opening up a new wavelength region for free-radical investigations. Our first candidate for this purpose was the HO, radical with its v2 bending mode near 7.2 pm. Fig. 8 shows a series of transitions taken with the P(12) u = 29 j- 28 laser I I I I I I I I 1 1 1 1 1 0 0.1 0.2 0.3 0 . 4 0.5 0 . 6 0.7 0.8 0.9 1.0 1 . 7 1.2 BjT preliminary assignment is in good agreement with the results of ref. (2). FIG. 8.-L.m.r. signal of HO, obtained at the laser line P(12)v = 29 + 28 at 1394.140 cm-I. line. data by Nagai and Endo.* The Our preliminary analysis is in good agreement with the previously communicated A detailed analysis of our investigations will be published As pointed out by Dr. Brkhignac, the same wavelength region as our CO-laser has been covered by a laser system of the Orsay group.4 T.X. Lin, W. Rohrbeck and W. Urban, Appl. Phys., 1981, in press. K. Nagai and Y . Endo. Insf. Mol. Sci., Annu. Reu., 1980, IIA, 13; K. Nagai, Y . Endo and E. Hirota, f. Mol. Spectrosc., in press. F. Niebuhr, A. Hinz, M. A. Gondal, W. Rohrbeck, W. Urban and J. M. Brown, to be pub- lished. P. Brechignac and J. P. Martin, IEEEJ. Quantum Electron., 1976, QE 12, 80. Dr. Ph. Brkchignac (Uniuersite' de Paris-Sud, Orsay) said: Prof. Urban has just shown that it is now possible, " by pushing the CO laser ", to perform 1.m.r. spectro- scopy in the 7-8 ,um range. He presented typical spectra of the laser lines obtained with two different gratings, in which appeared the high-lying vibrational bands up to u = 36 -+ 35 with the rotational lines J = 9-13.The purpose of this contribution is to recall that we built in our group at Orsay during the years 1974-75 CO lasers capable of such high-lying laser oscillation. These lasers were used as a tool to investigate the vibrational distribution' and the kinetics of the V-V transfer2l3 collisional processes in the highly excited vibrational states of CO. Although we did not circulate the results widely, we did report in a short paper' in 1976 the observa- tions of c.w. laser oscillation in the vibrational bands from u = 1 -+ 0 up to u = 36 + 35 [P(9)-P( 13)] (near 8.15 pm). It seems that the lasers built in Prof. Urban's group have been built according to our design5 and that they are very similar despite small differences.The Bonn lasers have a shorter active length, but also have a water-vapour-evacuated cavity and ZnSe316 GENERAL DISCUSSION windows, while we made these observations with an atmospheric optical path between the cavity reflectors and the CaF, Brewster windows (CaF, absorption is ca. 0.15 cm-l at 8.0 pm). To our knowledge there is no evidence of any new line emitted by the Bonn lasers; if there is it would not represent a significant improvement, because only the frequencies of the lines are considered.. However, it is a great pleasure for us to see actual spectroscopic measurements coming out in this spectral range, intermediate between the " usual '' CO and CO, wavelengths. Could we now urge laser spectroscopists to think differently of the liquid-nitrogen-cooled CO laser as a reliable, safe and eventually powerful instrument? Ph.Brechignac, J. P. Martin and G. Taieb, IEEE J . Quantum Electron., 1974, QE 10, 797. Ph. Brkchignac, Chem. Phys., 1978, 34, 119. Ph. Brkchignac and J . P. Martin, fEEE J . Quantum Electron., 1976, QE 12, 80. J . Puerta, W. Herrmann, G. Bourauel and W. Urban, Appl. Phys., 1979, 19, 439. ' Ph. Brkchignac, G. Taieb and F. Legay, Cltem. Phys. Lett., 1975, 36, 242. Prof. T. E. Gough (Waterloo Uniuersity) said: Since the completion of our work on the dipole moments of vibrationally excited states, two developments of note have taken place. (i) A semi-empirical model for the dipole-moment functions of hydro- gen halides in the form of Pad6 approximants has been published.' For hydrogen fluoride, this function, vibrationally averaged, yields a value of p1 identical to our experimental mean of 1.872 D.(ii) Infrared radiofrequency double-resonance spectroscopy has been used to measure poll for hydrogen cyanide as 2.976 D,2 estab- lishing pool-,uoll as 0.036 D. From ref. (21) of our contribution to these discussions pooo-polo is 0.042 D. It is clear that excitations of the normal modes of hydrogen cyanide do not produce independent contributions to the dipole moment. Replying to a comment made informally by Prof. Carrington, I confirm that our bolometers are one to two orders of magnitude less sensitive than the best commercially available devices. W Hz-3) is set by approximately equal noise contribution from the bolometer and from the molecular beam. Hence, there is, for our present purposes, no advantage to be gained by using a more sensitive, and probably more delicate, detection element.However, in the present apparatus the limit of sensitivity J. F. Ogilvie, W. R. Rodwell and R. H. Tipping, J. Chem. Phys., 1980, 73, 5221. ' J. S . Muenter, to be published. Dr. M. N. R. Ashfold (University of Oxford) said: Following on from Prof. Hirota's elegant work on the high-resolution electronic spectroscopy of the CHF radical,' I would like to draw attention to the potential of pulsed CO, laser photolysis and the process of infrared multiple photon dissociation (IRMPD) as a means of producing high instantaneous concentrations of this, and many other, triatomic carbenes.' When combined with the high sensitivity provided by laser-induced fluorescence detection methods both spectroscopic and kinetic measurements involving these species become relatively straightforward. For example, we have recently used the IRMPD of normal, and perdeuterated, acetic anhydride as a means of pre- paring the respective methylene radicals CH, and CD, in their low-lying GIAl excited electronic ~ t a t e s .~ This work has extended the previously known electronic spectro- scopy of CH2,4 and provided the first systematic measurements of the CD2(8'B1 t a"'A,) transition which, as with its CH, counterpart, is-dominated by a long progression involving excitation of the v2 bending mode in the b'B, state (see fig. 9). Similarly, we have demonstrated that the IRMPD of CH2F2 and CH2FCI provide high yields of CHF(f1A')5 and that the CO, laser photolysis of CF2CCI2 represents a good source of CCl,(f1Al).6 Again, using IRMPD as the radical source, King, Stephenson andGENERAL DISCUSSION 317 - - pR,,J-I pQl*J pF;.J-l I I I I I 5 6 4 565 566 567 568 p P pP2,J-1 Q2,J-1; Q2.J-2, I 'p;,-2 ; I I I 1 54 4 545 5& 6 547 5 4 8 5 4 9 wavelength inn1 FIG.9.-Part of the laser excitation spectrum of the CD2(g'B, - Zr'A,) transition, illustrating ( a ) the Z(0, 20, 0)-(0, 0, 0) vibronic band at ca. 565 nm and (b) the n(0, 21,O)-(O, O, 0) band near 546 nm. CD,(G'A,) was produced through the IRMPD of 5 mTorr of ['H,]acetic anhydride using the P(24) (001-100) COz laser line at 10.63 pm. The probing dye laser pulse was delayed 1 p s with respect to the peak of the photolysing COz laser pulse.coworkers have analysed the wavelength resolved fluorescence obtained following dye-laser excitation of CF,(flA,)' and CFCl (g'A')8 to specific vibronic levels in their respective first excited singlet states, and thereby provided a more extensive and de- tailed understanding of those transitions than was' previously available from conven- tional gas-phase absorption spectroscopy9 or from studies in a rare-gas matrix. loll1 The investigations briefly surveyed here provide some illustration of the impact currently being made by lRMPD as a novel source of free radicals. In certain instances the technique can offer substantial advantages over other, more conven- tional, methods of radical production such as single photon UV photolysis or chemical reaction.By the very nature of the coilisionless infrared multiple photon absorption and dissociation processes, radicals are only formed in their ground, or very low-lying electronically excited, states with, in general, a low level of internal excitation. This concentration of the radical population into a relatively few quantum states has obvi- ous advantages both in the simplification and in the signal-to-noise ratio of any sub- sequent spectroscopic investigations. In addition, the use of a low-pressure, pulsed method of formation is obviously more suitable than higher-pressure reactive meth- ods when, as exemplified by the case of singlet rneth~lene,~ the radical of interest is rapidly removed by the effect of collisions. E. Hirota, Farnday Discuss. Cliein. Soc., 1981, 71, 87.* For a review see: M. N. R. Ashfold and G. Hancock, in Gas Kinetics artd Eizergy Transfer, senior reporters R. J. Donovan and P. G. Ashmore (Specialist Periodical Report, The Royal Society of Chemistry, London, 1981), vol. 4, pp. 73-116.318 GENERAL DISCUSSION M. N. R. Ashfold, G. Hancock, G. W. Ketley and J. P. Minshull-Beech, J. Photochern., 1980, 12, 75; M. N. R. Ashfold, M. A. Fullstone, G. Hancock and G. W. Ketley, Chern. Phys., 1981, 55, 245. G. Herzberg and J. W. C. Johns, Proc. R. SOC. London, Ser. A, 1966, 265A, 107. M. N. R. Ashfold, F. Castano, G. Hancock and G. W. Ketley, Chern. Phys. Lett., 1980,73,421. M . N . R. Ashfold, G. Hancock, G. W. Ketley and S. Park, unpublished results. ’ D. S. King, P. K. Schenck and J. C. Stephenson, J.Mol. Spectrosc., 1979, 78, 1. S. E. Bialkowski, D. S. King and J. C. Stephenson, J. Chern. Phys., 1979, 71, 4010. C. W. Mathews, Can. J . Phys., 1967, 45, 2355. lo V. E. Bondybey, J. Mol. Spectrosc., 1976, 63, 164. l1 V. E. Bondybey and J. H. English, J. Mol. Spectrosc., 1977, 68, 89. Prof. R. N. Dixon (Bristol Uniuersity) said: 1 should like to make two comments on the paper by Prof. Hirota. (a) The spin-splitting in the Z3A” state of HCCI: Prof. Hirota has deduced from the second-order Zeeman shift of the perturbed levels of the J I A ” state that the Fl and F3 triplet levels must lie above the F2 level interacting with the singlet level. Consequently the spin-spin coupling constant of the 3A” state must be negative, although this constant is positive in the X3C- ground state of the isoelectronic molecule NC1.We show how this apparently unexpected result could arise from the bent equilibrium geometry of HCCI. In a diatomic (or linear polyatomic) molecule with a n2 electron configuration one contribution to the triplet splitting of the 3C- ground state is second-order spin-orbit coupling between its O+ component and the higher ‘C+ state [fig. lO(a)]. This de- O+ , ’=+ /- \ I I 0’ R I I ; Hso 1 I \ I \ I I t Ir) FIG. 10.-Contribution of second-order spin-orbit coupling to the spin-spin splitting of triplet states derived from the electronic configuration n’. (a) Linear molecules (02, NCl) where the 3C- state is the ground state; (b) bent molecules (HNO, HCCI) where the 3A’’ state is the first excited state. presses the O+ component and thus makes a positive contribution to the spin-spin coupling constant cx : where is the n-orbital spin-orbit coupling constant.In O2 this second-order termGENERAL DISCUSSION 319 is known to be comparable to the first-order spin-spin dipolar coupling,' and both terms are positive, thereby accounting for the positive value of CI. This will be the general rule for 3C- ground states. Quantum-chemical calculations have predicted that the 3C- state of HNO lies lowest for a linear geometry,' and this will also hold for HCC1. However, the equi- librium geometries of these molecules are bent. In molecular-orbital terms the singlet ground state arises from configuration interaction in bent conformations between the 'A' components of the 'A state and the 'Z+ state, the bent states being better represented as (n, a')2 and (n, a")', (i.e.2-$('A A' & 'Zf A')). The second- order spin-orbit mixing between the O f components of the 3C- state and 'Z+ state (of the linear molecule) is now shared approximately equally between the two 'A' states [fig. 10(6)]. In this limit the second-order contribution to OL will be: The Z'A', C3A" and X'A" states all dissocia.te to ground-state dissociation products and span of ca. 2 eV, whereas the B'A' state should lie much higher. Thus for geometries close to equilibrium the second term in eqn (2) will dominate over the first, so that spin-orbit coupling should give a net negative contribution to a, opposite in sign to that in 0, or NC1. Further from equilibrium the coupling will be compli- cated by the crossing of the 2 and a" potential functions and by their convergence to the same dissociation limit. This model is clearly not quantitatively accurate, but does indicate how a negative value of c( could arise in the lowest triplet state of HCC1.Furthermore, the value of CI could be large for levels with energies close to the crossing of the potential functions of the a" and 2 states. ( 6 ) Collision-induced intersystem crossing: Prof. Hirota's illustration of the 050- 000 fluorescence excitation band of HCCl shows a pronounced loss of intensity in the vicinity of the triplet-singlet perturbation which he has analysed. This is similar to the intensity anomaly described in our paper on HNO, but is much more clearly developed. This loss can be attributed to collision-induced intersystem crossing (CIISC) uia the perturbed levels, together with energy transfer into these levels from nearby unperturbed singlet levels.Prof. Hirota's detailed analysis shows that this system has a much simpler pattern of perturbations than HNO. It should therefore provide a good testing ground for the theory of ClISC in small polyatomic molecules conforming to Freed's small-molecule limit.3 We are setting up an experiment to make time-resolved measurements on this system of energy levels. K. Kayama and J. C. Baird, J. Chem. Phys., 1965, 43, 1082. P. J. Bruna, Chern. Phys., 1980, 49, 39. K. F. Freed, Adv. Chern. Phys., 1978, 42, 207. Dr. G. Duxbury (Strathclyde University) said : Tn addition to the bands described in our paper, we have recently analysed most of the v8 band, which lies in the region of 1123 cm-'.This band shows strong local perturbations, particularly for levels with K,' = 5. 1 interactions with levels of the vg/v, pair of interacting states, which have origins in the vicinity of 1060 cm-'. In the 9 pm bands, the spectrum of the parent molecule, methylamine, is still in evidence, particularly the strong Q band at 1044 cm-'. Fig. 11 shows the spectrum These can be understood as AKa =320 GENERAL DISCUSSION 130- 120 110 100 90 8 0 7 0 r - - - - - - 80 - 70 - 60- 50 - 40 - 140 130 - 130 120 - 120 110- 110 100 90 80 - 80 1 I I 1 I 140 r (d) -- - - - - - - 1 I I I I 182 184 186 180 110 x 10 of methylamine, and the result of stripping the methylamine spectrum from that of the imine.Similar methods have recently been employed by Turner et al. to obtain a " pure '' spectrum of thioformaldehyde, by stripping away the spectrum of the ethylene pro- duced in the pyrolysis.' In order to show the necessity of using the highest possible resolution when dealing with spectra of molecules such as CH,NH, in fig. 12 we show the vg QQ branch region, with the resolution' reduced by a factor of 10 from that employed in our analysis. A comparison with the same spectrum taken at maximum resolution, fig. 4 of the paper, shows that most of the rotational structure is lost, and only the sharp edges of the sub-bands remain. The lower resolution of ca. 0.06 cm-' is equivalent to that of most commercial Fourier-transform spectrometers, although one has recently been developed which possesses a resolution comparable to that used in our work.P. H. Turner, L. Halonen and I. M. Mills, J . Mol. Spectrmc., in press.GENERAL DISCUSSION 32 1 - 1343 1345 I I I I I I I I I 13A7 1349 1351 1353 wavenumberlcm - ' FIG. 12.-QQ transitions of the v6 band of CHzNH (fig.4 of our paper), with the resolution reduced to 0.06 cm-', approximately that of many commercial Fourier-transform spectrometers. Note the almost complete loss of resolved rotational structure of these transitions, particularly that of QQ(J,3) which appears to be almost linelike at this resolution. Prof. R. Back (Laboratoire de Spectrornetrie Ionique et Moleculaire, Villeurbanne) said: Duxbury et al. have clearly shown in their paper the complementary nature of the spectra obtained using the high-resolution Michelson interferometers of the Connes type when compared with the results given by laser spectrometers in the 11-2 pm region.However, interferometers may become absolutely necessary in other types of spectroscopic research with lasers. This occurs in the study of laser-induced fluores- cence (LIF) spectra when looking for new electronic states of a molecule with a Fourier-transform spectrometer (FTS). The recent development of this technique (LIF-FTS)1*2 shows that it is the most powerful technique in this respect. For instance it allowed the analysis of the b'C; states which arise from the ground-state electron configuration . . . 112 of Se, and Te2.3*4 It also led to the discovery of the 1, and 0: new lower electronic states of the I2 m~lecule.'~~ In the latter case only the high throughput of the instrument allowed the observation of the very faint lines terminating on these states.of the intensity of the main transitions and they were observed in the 1.3 pm region. R. Bacis, S. Churassy, R. W. Field, J. B. Koffend and J. Verges, J. Chern. Phys., 1980, 72, 34. J. Verges, J. d'Incan, C. Effantin, D. J. Greenwood and R. F. Barrow, J. Phys. B, 1979, 12, L 301. S . J. Prosser, R. F. Barrow, J. Verges, C. Effantin and J. d'Incan, J . Phys. B, 1980, 13, L 547. ' C. Effantin, J. d'Incan, J. Verges, M. T. Macpherson and R. F. Barrow, Chern. Phys. Left., 1980, 70, 560. S . Churassy, F. Martin, R. Bacis, J. Verges and R. W . Field, J. Chern. Phys., to be published.Their intensity was Prof. I. M. Mills (Reading University) said : I would like to comment on the nota- tion used for labelling the rovibration levels of an asymmetric top in laser Stark322 GENERAL DISCUSSION spectroscopy. Although I am making this remark specifically in relation to Dr. Duxbury's paper, my comment is actually general because the same notation is used by all workers in this field. Consider the high K, asymmetry doublets of a prolate asymmetric top with an a-axis dipole moment. In the absence of the Stark field we use the usual J K a ~ c labels, e.g. 440 and 44, for the pair of levels in fig. 13. In the presence of a Stark field v = o type (a) Q -branch transit ions [l transit ions -w 7 electric field FIG. 13.-High-K, asymmetry doublets of a prolate asymmetric top with an a-axis dipoIe moment, showing absence and presence of Stark splitting. the wavefunctions mix through the a-axis dipole, and the energy levels push apart.In practice the mixing term may be larger than the asymmetry splitting even for quite low fields, so that the perturbed wavefunctions become Sol50 mixtures of the Wang functions appropriate to the absence of a field. They should be labelled by J, k and m, where k and m are the signed components of angular momentum about the a-axis and the external field ; the energy levels and wavefunctions become indistinguishable from those of a symmetric top. In fact, however, it is customary to continue to use the Wang function labels, according to the correlation of the levels as the field is turned off.I believe this is a confusing and misleading notation, since the perturbed wavefunctions should not be associated with one of the Wang functions any more than the other. The confusion may be seen, for example, in the selection rules for type-a Q-branch transitions, which are AJ = 0, AKa = 0, AK, = 1 in the absence of a field, giving rise to 440-441 and 44L-440 transitions (upper-lower and lower-upper, see fig. 13). In the presence of a field the selection rules are AJ = 0, Ak = 0, Am = 0 or &l, giving rise to upper-upper and lower-lower transitions (see fig. 13). In terms of the Wang function labels these become 440'440 and 441-441, apparently violat- ing the selection rules (see tabIe 2 of Duxbury's paper). However, the selection rules have not really changed; it is simply that the notation is inappropriate.A possible solution would be to label the levels 4,+ and 4,- in the presence of a field, where the sign indicates that the product of k and m is positive or negative respectively, as indicated in fig. 13. A more complete labelling would have to also give the magnitude of m. Dr. A. R. W. McKellar (National Research Council of Canada, Ottawa) said Prof. Mills suggests using a " high-field " or " symmetric-top " labelling system (JK & M) for laser Stark spectra of asymmetric-top molecules, rather than the " low-field " or " asymmetric-top '' system ( J K ~ K ~ M ) which has generally been used in the literature. While appreciating the difficulties raised by the latter notation as illustrated by Prof.GENERAL DISCUSSION 323 Mills, I would suggest that comparable difficulties arise when the former notation is used at low or intermediate fields (Stark energy 5 asymmetry doubling).Further- more, in some cases even near-symmetric asymmetric tops have Stark energy-level patterns very different from a symmetric top; for example, near prolate molecules with p b > pa such as cis-HNO, and HFCO. And even in Prof. Mills’ example at high field, the levels with A4 = 0 are still best described by JXaKc. On balance I feel that labelling asymmetric top Stark energy levels by the (JKaKcM) quantum numbers with which they correlate at zero field is the more generally useful system, as long as the modifications in selection rules due to the electric field are borne in mind.Dr. G. Duxbury (Strathclyde University) said: The problem of notation referred to by Prof. Mills arises in Stark spectroscopy because the electric field mixes the levels of opposite parity, whereas in laser magnetic resonance spectroscopy the magnetic field mixes levels of the same parity, and hence the information about asymmetry splitting is still available even in the high-field limit. The result of the parity mixing in Stark spectroscopy is that for the majority of the levels the patterns cannot be distinguished from those of a symmetric top. For ex- ample, in our work on thioformaldehyde presented at this discussion only the transi- tions with K, = 1 show a resolvable asymmetry splitting. An alternative suggestion to that of Mills is that the transitions in which the effects of asymmetry splitting are negligible should be labelled as though the molecule were a symmetric rotor in a non- degenerate vibrational state, i.e., using J , K,, M.In the cases of Coriolis interaction, the differences between symmetric- and asymmetric-rotor behaviour are still apparent. Another problem which arises in the use of Stark spectroscopy for studying states in which there is considerable Coriolis mixing is that the usual selection rules cannot be used to determine the symmetry of the vibrational state. For example, where strong mixing occurs between levels of opposite parity the distinction between type-B and type-C perpendicular transitions of a near-symmetric top is lost. As an example, Turner et al.’ have recently studied the spectra of H,CS and D,CS by using a Fourier- transform spectrometer, and have been able unambiguously to determine the sym- metry of the v4 and the v6 vibrational states, which was not possible in the electric- field studies of Bedwell and Duxbury., P.H. Turner, L. Halonen and J. M. Mills, J. Mol. Spectrosc., 1981, in press. * D. J. Bedwell and G. Duxbury, J. Mol. Spectrosc., 1980, 84, 531. Prof. R. Back (Laboratoire de Spectrometrie Ionique et Moleculaire, Vilieurbanne) said: As noted by Prof. Field: “ A difficulty unique to sub-Doppler Fourier-trans- form fluorescence spectroscopy is that short- and long-term frequency or amplitude variations of the exciting laser will seriously degrade both resolution and sensitivity ”. Nevertheless, the related problems may be overcome in the following manner: The 514.5 nm single-mode line of a C.W.Ar+ laser has been locked to a sigmameter.’m2 A He-Ne laser locked on an iodine saturated absorption line is used to servo-control the sigmameter path difference. Thus the frequency of the 514.5 nm line can be fixed for several hours anywhere within the Doppler profile of the P(13)BO;(v’ = 43) - XIC,+(u’ = 0) iodine absorption line. The high-resolution Fourier-transform spectrometer records the forward and backward fluorescence from the excited hyperfine levels along the axis of the 514.5 nm exciting line. Fig. 14 and 15 show the shape of the P(13)BO: - (0’ = 43) -+ X’C; (u” = 83) fluorescence line. Since the excited molecules are velocity-selected along the detection line-of-sight, the emission frequencies are Doppler-shifted.This can be324 GENERAL DISCUSSION Q1 Q 2 a 3 a4 G wavenumberlcm- ' FIG, 14.-Spectrum of forward scattered fluorescence of the P(13) SO:(u' = 43)-+X'C,+(u" = 83) line. The 514.5 nm Ar+ exciting line is shifted 0.022 cm-' to the red of the centre-of-gravity of the absorbing line: P(13) BO:(v' = 43) <- X'E:,'(d' = 0) (this position corresponds to the al hyperfine line). The fluorescence intensity maximum is red shifted 0.009 39 cm-' from the maximum (vertical arrow) of the full Doppler profile of the line (dashed curve). At the bottom of the figure are the 21 hyperfine components of the P(13) fluorescence line which give the full Doppler profile under multi- mode excitation (G = centre of gravity of the 21 hyperfine lines). Iodine pressure 0.1 Torr, ap- paratus function f.w.h.m.= 0.003 cm-', sub-Doppler fluorescing line (h.w.h.m.) red = 0.002 31 cm-', (h.w.h.m.) violet = 0.002 40 cm-'. seen by comparing the positions of the hyperfine components (a, a2 . . .) in multimode (unshifted) and single-mode excitation (fig. 14 and 15). With a laser linewidth of (10 MHz the emission frequencies would not be Doppler-broadened in the absence of redistribution of the selected velocities. However, at an T2 pressure of 0.1 Torr, this collisional redistribution is evidenced by a broadening of the emission lines. This is displayed in the backward direction spectrum where this enlargement smooths the oscillations of the apparatus function (fig. 15). The related broadening in the for- ward direction is much narrower and the recorded spectrum is close to the apparatus function (fig. 14).The rotational relaxed lines are broader but remain sub-Doppler as has already been observed in the BaO molecule with OODR [see ref. (8) in Field's paper]. Because of the good signal-to-noise ratio, deconvolution of the observed lineshapes allow the determination of the various parameters defining the collision process: temperature of the gas, position of the exciting laser line, cross-section for velocity- changing collisions in the excited levels and parameters for rotational relaxation. The Fourier-transform spectra were obtained by J. Verges and P. Juncar (Labora- toire Aim6 Cotton, Orsay); the analyses are in progress with P. Weiss (R. W. Field'sGENERAL DISCUSSION I I I I I t 0.005 06crn-’ I I I 325 1 I I I I I \ I I I I a1 a2 a3 a4 G wavenumber/cm- ’ FIG.15.-Spectrum of backward scattered fluorescence of the P(13) BO:(u’ = 43) + X’X$(u’’ -83 line. The 514.5 nm Ar+ exciting line is 0.028 cm-’ red-shifted from the centre of gravity of the absorbing line: P(13) BO:(u’ = 43) t X’X,+(u’’ = 0). The fluorescence maximum occurs 0.005 06 cm-’ to the red of the maximum (vertical arrow) of the full Doppler profile of the line (dashed curve). At the bottom of the figure are shown the 21 hyperfine components of the P(13) line which give the full Doppler profile under 514.5 multimode excitation. (G = centre of gravity). Iodine pressure 0.1 Torr, apparatus function: f.w.h.m. = 0.0041 1 cm-’, sub-Doppler fluorescing line (h.w.h.m.) red = 0.00313 cm-’, (h.w.h.m.) violet = 0.00306 cm-’.group, M. I. T., Cambridge, Mass.) and C. Effantin, J.]d’Incan and myself (Laboratoire de Spectromktrie Ionique et Molkculaire, Villeurbanne). Thus high-resolution Fourier-transform spectroscopy may be used to perform sub-Doppler fluorescence spectroscopy of small molecules. P. Juncar and J. Pinard, Opt. Cornmiin., 1975, 14, 438. P. Juncar, ThPse de 3Pme cycle (Paris, 19763. Dr. M. Quack (University of Gottingen) said: It is unfortunately true, as Prof. Field states, that much of the current work in i.r.-multiphoton excitation and i.r.- photochemistry is of a very crude, ill-defined, alchemical nature. In a newly de- veloping field this is not unusual. It is, however, by no means characteristic of all work.I should like to mention only the beautiful work of Ashfold et al.,I who have used i.r. laser chemistry to produce radicals for spectroscopic investigations in a con- trolled and particularly suitable way. Also, on the basis of spectroscopic concepts, quantitative theoretical tools have been developed for the understanding of the dynamics of i .r.-laser photochemical experiments that are carried out under well- defined conditions.2 The mere possibility of i.r.-multiphoton excitation and its efficiency, which is now defined and known absolutely in some cases, provides an326 GENERAL DISCUSSION interesting insight into general features of the i.r. spectra of polyatomic molecules. Questions that arise and can be partly answered concern the distribution functions for energy-level spacings and transition moments and the nature of the time-inde- pendent and time-dependent wavefunctions of very highly excited polyatomic mole- cules.Although spectroscopists often “ do not like ” to think in these terms, high- resolution spectroscopy will in the future contribute precisely along these lines, in my opinion. The very stimulus from i.r. photochemistry to ask such questions in high- resolution spectroscopy helps to advance our understanding of molecular properties. M. N. R. Ashfold and G. Hancock, in Gas Kinetics and Energy Transfer (Specialist Periodical Report, The Royal Society of Chemistry, London, 1981), vol. 4. M. Quack, J. Chem. Phys., 1978,69, 1282; Ber. Bunsenges. Phys. Chem., 1979, 83, 757, 1287; 1981, 85, 318.Prof. T. E. Gough (Waterloo University) said: It has been suggested in this discus- sion that the spectroscopic advantages described in Prof. Field’s paper may only be realised for species which absorb dye-laser radiation and subsequently fluoresce. Such a view greatly underestimates the potential of laser spectroscopy. Tunable coherent radiation may be generated by diode lasers, colour-centre lasers, optical parametric oscillators, and by a variety of frequency-shifting, mixing and multiplica- tion techniques. *Furthermore, there exist many techniques which detect the occur- rence of spectroscopic transitions by indirect means. Among them one may list photoacoustic and photothermal spectroscopy, ionisation by electric fields or by secondary lasers, photodissociation and deflection of atomic beams.Such techniques, far from requiring fluorescence, are at their best when fluorescence is absent. Prof. R. C. Woods (University of Wisconsin) said: In the second sentence of his paper Prof, Field suggests the extreme desirability of lasers tunable from the r.f. to the X-ray region. Perhaps he should say from the far-infrared to the X-ray region, since in the r.f., microwave and inillimetre-wave regions, coherent, monochromatic, tunable oscillators, e.g. klystrons, are already available and play the role that tunable lasers do or would play in the shorter-wavelength regions of the spectrum. Prof. R. W. Field (M.I. T., Cambridge) said: There has been considerable discus- sion of the second sentence of my paper: “ I hope that I have avoided stressing the obvious, that lasers promise almost embarrassing resolution, precision and sensitivity, and that, if only lasers were tunable from r.f, to X-ray, laser-free spectroscopy would be obsolete.” Of course, coherent sources are not tunable from r.f.to X-ray and laser-free spectroscopy is not obsolete. I attempted to define and explore the tactical strengths df laser techniques. In certain situations (e.g. the CaO “ Orange Bands ”, Pro, CaBr and CaI), it is now possible to record, calibrate and assign a spectrum more rapidly and at a higher precision than would be possible by non-laser techniques, completely without reference to prior spectral information. On the other hand, searches over wide spectral intervals for weak transitions of transient molecules (especially those with unbound electronic ground states) are out of the reach of laser techniques, even in the Rhodamine region.My choice of the word “ passive ” in describing various one-photon spectro- scopies unintentionally under-valued the active effort invested by classical spectro- scopists in obtaining the right molecule under optimum conditions. The distinction I was trying to make involved the degree of knowledge of and control over the outcome of an adjustment in operating conditions. For example, in a pump-probe schemeGENERAL DISCUSSION 327 the combination of degree of state selectivity and range of selectable states is far beyond that achievable by the most ingenious source manipulation. The power of laser techniques stems primarily from the ability to force a molecule to jump through two hoops.Until recently, most multiple interrogation schemes have involved detection of spontaneous fluorescence. However, detectable fluores- cence is not essential, as demsnst rated by several two-colour, resonance-enhanced multiphoton ionization experiments. Prof. J. Winn (University of California) said: In his supplementary material on the rare-earth oxides, Prof. Field describes the use of crystal-field theory to aid the analysis of complex spectra arising from very many possible electronic states. A similar situation will arise in the case of transition metal diatomics, especially those of Groups IIIB-VIII. For instance, the ground-state terms of Ni correlate to 100 molecular states of Ni,. Since atomic-metal transition moments vary over 3 to 4 orders of magnitude from state to state, one must expect a similar phenomenon to occur in the molecular case.As a result, one can anticipate the following experi- mental situation. Absorption occurs readily to a particular level located in a dense manifold of levels from a variety of states. Collisions may induce a non-adiabatic transition to a state of long radiative lifetime, followed by collisional de-excitation of this long-lived state. The result is an apparently low quantum yield for fluorescence from a state which, in isolation, would fluoresce strongly. Can crystal-field theory or any allied theory be of help in predicting which states of such molecules are likely to be most isolated from nearby states of radically different radiative lifetime? Prof.R. W. Field (M.I.T., Cambridge) said: Since the material on the rare-earth oxides appears neither in my talk nor in supplementary remarks, I will first sum- marize those results and then respond to Prof. Winn's question. C. Linton, R. F. Barrow, and M. Dulick have identified all 16 of the CeO states (total degeneracy 28) that are expected to arise from the crystal-field split Ce2+ f ( s + d)a configuration. They have shown that these states are among the lowest- lying states-of CeO and that the pattern of the four R = J, molecular states is very similar to that of the four J, Ce2+ fs free-ion states. (J, is the total atomic spin plus orbital angular momentum.) Furthermore, Mr. Dulick has shown that 12 of the lowest states (0 = J, and R = J , - 1) of P r o match the Pr2+f2(3H)s free-ion states.This indicates that an 02- ' S ligand has a negligible effect on electrons inf-orbitals and that the molecule remembers how many, and which, f-orbitals are occupied. It is likely that free-ion quantum numbers (J,, parity) will be " almost good " molecular quantum numbers and that transition intensities, perturbation strengths, and hyper- fine splittings will be calculable from free-ion properties using eigenfunctions of a crystal-field effective-Hamiltonian matrix. At present it is not possible to characterize the non-forbitals or even to estimate the net charge associated with the metal ion. This is illustrated by the fact that Ce2+ f lies below fd and fs and Pr2+ f 3 lies well below f 2 d and f 2 s .The ordering of n f relative to (n + 1)d and (n + 2)p, s orbitals depends critically on charge. The effect of the crystal field on non--orbitals is too large to be treated by perturbation theory. I am unable to guess whether a zero-order picture similar to crystal-field theory could relate separated-atom electronic properties to those of covalently bound transi- tion metal diatomics. Certainly special cases will exist when the free atom states split into a group of low-lying configurations, well-separated from all higher-energy states. Another special case would be weakly bound homonuclear diatomics where the binding energy is small compared to free-atom interconfigurational energy328 GENERAL DISCUSSION separations. It is important to test many naive, zero-order, semi-empirical models, but this will require experimental determination of nearly complete molecular energy- level diagrams in the 0-2 eV region.However, even when a zero-order model successfully accounts for isolated- molecule properties, it is improbable that any simple scheme will yield useful predic- tions of propensity rules for collision-induced transitions between electronic states of radically different radiative lifetimes. The crystal-field picture will identify close- lying eigenstates of mutually mixed J, character between which collisional transfer should be facile, but these states would have similar radiative lifetimes. Every laser spectroscopist knows many examples of inexplicably efficient colli- sional transfer between electronic states.The situation for diatomic molecules, where the vibronic density of states is one per 10 cm-', is beyond imagining. Prof. R. N. Dixon (Bristol University) said: In presenting our paper I wish to extend the analysis of the two strong perturbations in the 011 vibronic level of HNO xlA" [eqn (2) and (3)]. These are two of the strongest perturbations in this state, and in view of the lack of magnetic activity might be expected to arise from 2-f electronic Coriolis interaction about the a-axis. The coupling matrix elements do not appear to have the correct J and K dependence for an interaction of this type with a single vibronic level of the 8 state. However, these levels lie only ca. 500 cm-' below the limit to H NO dissociation. In such high-lying levels of the ground state the H atom can execute a very large amplitude vibration, and the axes of the mean inverse inertial tensor become substantially rotated compared with those for lower- lying levels.' In consequence there can be a large axis-switching2 contribution to the J and K dependence of the perturbation matrix elements.In terms of the axis- switching angle 8T the matrix elements can be expanded as: (JK'(w') I H' 1 JK"(w")) 2 2 (JK'(mO') I H' I JK *(u')) (JK *(cot) I D( 8T) I JK"(w")) (1) K* where the Eulerian angles cot refer to the 2 state rotating axes, and 0" to the ;F: state axes. For non-zero OT there is no selection rule on K. It has been found possible to rationalise all the observations using an axis-switch- ing angle of ca. 12", which is also in rough agreement with a value calculated from the vibrational behaviour at this energy.The perturbations are then assigned as : 011 K = 4 Perturbed by K = 5 of a level of Z. There is no apparent K- doubling. 011 K = 3 Perturbed by K = 2 of the same level of 8. This is in accord with the depression of theflevel below the e level for each J. The pattern of rovibronic origins for this assignment is illustrated in fig. 16. This leads to the following approximate constants for the perturbing levels of the f state: A" x 7.17 cm-'; B" x 1.244 crn-'; DiK z 2.2 x cm-I (2) (3) which may be compared with the values for the lowest level of the ground state: A" - - 18.48 cm-l; & = 1.359 cm-'; D;K,o = 9.8 x cm-l. If we assume that in such a high ground state level the NO bond has an average length equal to that of free NO then the average structure is: FNH = 1.99 A; (FNo = 1.15 A, assumed); GHNo = 117".(4) This structure clearly indicates a very loosely bound H NO molecule.GENERAL DISCUSSION 329 15500 12 FIG. 16.-Rovibronic origins for the 011 level of HNO A" 'A" and the perturbing level of the 8 'A' state. Dashed lines indicate predicted levels which are too remote to interact strongly with the A" state. A more detailed analysis of these perturbations is in progress. ' R. N. Dixon, K. B. Jones, M. Noble and S. Carter, Mol. Phys., 1981,42, 455. ' J. T. Hougen and J. K. G. Watson, Can. J. Phys., 1965,43,298. Dr. D. A. Ramsay (National Research Council of Canada, Ottawa), said: Magnetic rotation spectroscopy has recently been found to provide a sensitive method for prob- ing singlet-triplet perturbations in simple polyatomic molecules.The sensibility of the method depends on the magnetic moment which arises from the triplet component of a mixed wavefunction and the transition moment which depends on the singlet component. In the last few years at Ottawa extensive investigations have been car- ried out on the singlet-triplet perturbations in the near ultraviolet bands of H2C0, HDCO and D2C0 and current work involves the first excited singlet and triplet states of H2CS. Dr. R. F. Barrow (Oxford University) said: There are two comments suggested by Dr. Gouedard's work: the first is the possibility which these experiments afford of distinguishing homogeneous and heterogeneous perturbations is potentially very valuable.The second concerns the character of the " P1, " state. The states of Se, seem to be very much like those of S2 and here calculations and experiment show that B3Z; is perturbed by a 311u state.' It is then most likely that P1, in Se, is the R = 1 com- ponent of 311u. The AX = 0 selection rule seems not to be strong: certainly in Te, the transition AO$ (3~n,)-X0,+(3Zg) is reasonably intense. It has been suggested that one of the levels populated by the krypton-ion laser line at 4131 A in *OSe, belongs to the 0: component of the 311u state., W. C. Swope, Y.-P. Lee and H. F. Schaefer, J. Chem. Phys., 1979,70,947. S . J. Prosser, R. F. Barrow, J. Verges, C. Effantin and J. d'Incan, J. Phys. B, 1980, 13, L547.330 GENERAL DISCUSSION Dr.J. M. Brown (Southampton Uniuersity) said : The alkaline earth monohalides all have the same pattern of low-lying electronic states. The ground state is 2Z+, and the first two excited states, which are very close together, are A211 and B2Z+. The molecules in these states are well-described by an ionic model, M+X- with the unpaired electron located on the alkaline earth atom. The major components of the dominant configurations for the three state are . . . (nsa)', . , . (npn)l and . . . (npa)' in order of increasing energy, although it has been shown that the halide ligand causes significant contamination by (n - 1)d orbitals. The observation of nuclear hyperfine structure provides a direct probe of the wavefunction for the unpaired electron and hence can be very informative about the detailed nature of the electronic states.Such observations involve sub-Doppler spectroscopy in the optical region. The molecules CaF, CaC1, CaI and SrF have all been studied at sub-Doppler resolution by intermodulated fluorescence; the results for CaCl and SrF are reported in the present paper. The hyperfine splittings ob- served in an electronic transition measure the difference of the hyperfine interactions for the two states. In our analysis of the 19F splittings in the B2E+-X2X+ transition of SrF, we used hyperfine parameters for the lower state from a solid state e.s.r. study in order to determine separately the parameters for the excited state. Since submitting the manuscript, we have learned of a recent study by radio frequency optical double resonance of the fine and hyperfine structure of SrF in the X2Z+ state.' Since this is a gas-phase measurement of much higher precision, it provides much more reliable parameters for the X state.We have therefore refitted our data using the double resonance values to give the results shown in table 2. The earlier assumption that the e.s.r. results were reliable was well-founded. TABLE 2.-19F HYPERFINE PARAMETERS FOR SrF XZC + 95.0 31.0 105.3 e.s.r. BZC + 14.5(16) - 54 (29) - 3.4 revised values 97.0834 30.2675 107.1726 double resonance We were unable to resolve Cl hyperfine splittings in either the A-X or the B-X systems of CaCl. This is a result of the small magnetic moment of the C1 nucleus rather than an indication of a dramatic change in the distribution of the unpaired electron spin compared with the other calcium monohalides.In the A2n-X2Z+ system of CaCl, rather striking, negative crossover signals were observed at low pressure. In the paper we developed a density matrix description of the 3-level system involved in an attempt to explain the unexpected sign of these signals [the negative sign corresponds to an increase in fluorescent intensity when the crossover condition co = ~(co, + co2) is satisfied]. The treatment was carried through to 4th order, at which stage the crossover signal was predicted to be positive. Prof. R. F. Curl of Rice University, Houston, Texas has pointed out that our model fails to take proper account of the repopulation of the ground state levels by direct fluorescence.Such a process is likely to be much more important in the visible region of the spectrum than in the infrared (where the density matrix models of these phenomena were largely developed), because of the v3 factor in the expression for the Einstein A-coefficient. It is especially important in the case of the A213-X2Z+ transition of CaCl which has much of the character of an atomic transition as dis- cussed earlier and there is very little redistribution to other vibrational levels of the ground state by fluorescence.GENERAL DISCUSSION 33 1 The direct relaxation of molecules in level 3 to levels 1 and 2 by spontaneous emission is included by replacing eqn (4b) and (4c) in the paper by = (iE/fi)P32(P$2 - pi31 - y22(pi2 - p&”) + Y22,23pj3 bil zz (iE/h)f131(h1 - p;3) - Y11)P;l - Pi\*’) + Y11,33h3 (12) (13) (see fig.3 in the paper for the labelling involved); the new terms appear last in each equation. Because the natural lifetime of the molecules in the A state is very short (ca. 30 ns), the homogeneous broadening of the transitions 31 and 32 is described by T2-I = C ~ i i , 3 3 * 1 The effects of these additional terms on the crossover signals first manifest them- selves in 5th order in the scheme summarized in fig. 6 of our paper. They allow two more routes through from p3; in 2nd order, namely pj3(2) -+ p;1(3) --f P31‘4’ + p;3‘5’ and pj3(2) --t --f p32(4) --t Pj3‘”. The calculation proceeds in the same way as described in the paper and the following expression for the population of molecules contributing to the crossover signal is obtained : This equation is to be compared with the fourth-order result, eqn (10) in the paper.We anticipate that (Y22,33/y22) ”N (711,33/Yll) = R, say* (15) The total result to fifth order is then (1 - R) times the 4th-order result given in eqn (10) and the condition for the crossover signal to be negative is R > 1 . Dr. Brichignac has pointed out that a treatment of this problem which is essentially the same as that given here has already been published by Holt.’ The paper is con- cerned with the description of similar crossover signals in the spectrum of the sodium atom. W. J. Childs, L. S . Goodman and I. Renhorn, J. Mol. Spectrosc., 1981, 87, 522. H. K. Holt, Phys. Rev. Lett., 1972, 29, 1138. Prof. R. W. Field (M.I.T., Cambridge) said: By showing a level diagram that labels the X2E+, A2n and B2X+ states of the Ca, Sr and Ba monohalides as respectively nso, npn and npo, it is suggested that the electric field due to the X- ligand causes insignificant s/p/d mixing and that the A and B states are in “ pure precession ”.Recent calculations (CaF) and experimental measurements (CaF, CaBr, CaI ; mag- netic hyperfine structure, spin-rotation constants, lambda-doubling constants and radiative lifetimes) have shown that the CaX X2X+ state is predominantly Ca+4sa, but that the CaX A213 and B2C+ states are 4p-3d mixtures. The extent of the p-d mixing is quite different in the A and B states; thus, they are not in pure pre- cession.332 GENERAL DISCUSSION When a mutually interacting, near-degenerate pair of 211 and 2Z+ electronic states have very similar potential curves, then the 211 lambda doubling constant p will be equal to the 2Z+ spin-rotation constant y.This is a consequence of the unique perturber, not the pure procession relationship. An effective I-value can be defined when one inserts the known p or y values into the pure precession equation, 2ArIBnW+ 1) y = p = Ent-EEI: ' where A , B, and Ent - Ex are, respectively, the A 2 n spin-orbit and rotational constants and the 211t - 2Z+ Av = 0 band-origin separation. For the CaX mole- cules, these are I = 1.04 (CaF), 1.12 (CaCl), 1.23 (CaBr), 1.34 (CaI), which are fortuitously close to I = 1, the value expected for a p-complex. All of the CaX B2Z+ states are shown to be almost 50% + 50% p + d mixtures, while the A211 states vary from 9% dn (CaF) to 30% dn (CaI).These results are taken from the Ph.D. thesis of Peter Bernath (M.T.T., 1980). Dr. D. L. Cooper (Oxford University) (communicated). Pure precession : In the limit of pure precession, the electronic matrix elements between the A2Z+ and X211 states of OH arise from a single electron with orbital angular momentum I, whose projection onto the molecular axis is zero in the excited state and unity in the ground state. The matrix element of L + , the raising operator for total electronic orbital angular momentum, becomes d I ( I + 1) = dr Indeed, the ab initio value' of ?.3564 is quite close to 1/z Conversely, if a matrix element of L+ is found to be close to 16 then pure pre- cession is frequently believed to be a good approximation.This is not necessarily valid. Colbourn and Wayne2 have calculated expectation values of L2 for NH and NF by expanding (92- I L ~ ~ ~ c I - ) = 2 l ( 3 ~ - IL- 13n)12 3n in which the summation extends over all 'J3 states. The values obtained were 4.32 for NH and 272.77 for NF. A large value of (L2) indicates that many states have significant contributions to the summation. In the ab initio calculation of fine structure, the pure precession hypothesis may be of use in deciding which states need to be considered. If all the vibronic matrix elements are explicitly computed, then excellent agreement is often found with experiment when interactions with only the lowest electronic states are included. This situation is best described, for example, as the X 2 n state of Li03 being uniquely perturbed by the A2Z+ state with negligible interactions with other states.As an example of a system where one state is not uniquely perturbed by another, we may cite the spin-splitting in the X2Z+ ground state of CaH:4 there are significant inter- actions with both the A211 and E211 states. Field's suggestion that pure precession is a poor approximation for the alkaline- earth halides cannot be overemphasised. The concept of pure precession is only really valid for molecules which do not deviate markedly from the united-atom limit. The approximation leads to reasonable A-doubling parameters for OH but Veseth has separated the electronic g value for this molecule into contributions from 2 X + states, 2C- states and 'A states and has found that all of these are significant.When using terms such as " pure precession " and " unique perturber " it is most important to bear in mind the particular phenomena being considered. The pureGENERAL DISCUSSION 333 precession approximation does not, in general, form a sound basis for the under- standing of molecular processes and frequently leads to erroneous results. R. K. Hinkley, J. A. Hall, T. E. H. Walker and W. G . Richards, J. Phys. B, 1972,5,204. E. A. Colbourn and F. D. Wayne, Mol. Phys., 1979, 37, 1755. D. L. Cooper and W. G . Richards, J . Chern. Phys., 1980,73,991. D. L. Cooper and W. G. Richards, J. Chem. Phys., 1980,73,3515. L. Veseth, J. Mol. Spectrosc., 1979, 77, 195. Dr. G. Duxbury (Strathclyde University) said: I wish to comment on two aspects of the relative sign of saturation signals.In the explanation presented at this Dis- cussion, Dr. Brown attributed the relative signs of the crossover signals and the Lamb dips to the effects of direct repopulation of the two lower levels from the common upper level by spontaneous emission. We have observed many three- and four-level crossover signals in the 10 ,urn spectra of a large number of molecules, and have noticed that in all cases the signs of the Lamb dips and the crossover signals are the same. Since the effects of spontaneous emission are much less important at 10 ,um compared to those in the visible region, our results support the explanation proposed by Brown for the sign change occurring in electronic spectra, It is possible to observe negative double-resonance signals in spectra taken in the 10 ,urn region if a polarisation anisotropy is induced in the sample.Fig. 17 below 2 f (0) x7.5 IAM1=2 i y J 500 1000 U E/V cm-' FIG. 17.-OODR spectrum of the QQ(13, 13) transition of l2CH3F using the 9R(32) line of a 13C1802 laser. The path length was 3 m, the total gas pressure was 50 m Torr, the modulation field 5 V cm-l and the time constant of the detection system 100 ms. The radio frequency used was 60.12 MHz. The half-wave plate was set to provide approximately equal signals of [AM\ -1 and /AM1 = 2 transitions. The polariser settings are (a) 90": accepts parallel component, (6) 80", (c) 60", ( d ) 0": accepts perpendicular component. Note the reversal in phase of the [AM1 = 1 signal from (a) to ( d ) .334 GENERAL DISCUSSION shows the ]AM1 = 1 and 2 signals observed in the QQ(13, 13) transition of the v3 band of 12CH3F using the 9R(32) line of 13C1802.It can be seen that the relative phase of the \AM/ = 1 and the /AM1 = 2 signals can be reversed by judicious choice of polari- sers. The reversal in phase of the ]AM1 = 1 signal is probably an example of polari- sation spectroscopy, where the slight handedness imparted to the medium by the partial circular polarisation in one beam causes the signal carried by the parallel polarised beam to be transmitted by the crossed polarisers. Dr. Ph. BrCchignac (Uniuersite‘ de Paris-Sud, Orsay) said: The paper presented by Brown, Milton and Steimle contains a somewhat developed section concerning the interpretation of the so-called negative signals in the cross-over resonances that they observed in the A211-X2Z+ saturation spectroscopy of CaCl.In the original written text the negative sign of these signals remained unexplained despite an apparently comprehensive density-matrix treatment of the system. The reason for that failure was the omission of some spontaneous emission terms in the treatment. These terms have now been accounted for and corrected expressions have been given by Dr. Brown during his oral presentation. The purpose of this contribution is to comment about the role that collision- induced transitions can play in the formation of the cross-over resonances in such systems. Holt derived a theoretical formulation of this problem in 1972,l following the qualitative explanation of the phenomenon given by Hansch, Shahin and Schaw- low.2 According to this formulation and to the notations defined in fig.18, the FIG. 18.--Energy-level diagram: +, radiative transitions ; -0, collision-induced transitions. normal and cross-over resonances are respectively proportional to : and where Wi - No)19ro14 (14 + r; - Aoi)/r~r; (i = 1 or 2) 1 ~ 1 0 1 2 1 ~ 2 0 1 2 C(N1 - NO)(A - A02)/Y& + “2 - NO)(Yi - Ao1)lrM. r; = Z A i , + Yi +ri i is the total rate of population loss for the molecules on level i(i = 0, 1, 2) within a particular velocity group. yi is the rate of state-changing collisions (SCC), Ti is the rate of elastic velocity-changing collisions (VCC). It follows that the normal re- sonances are always positive (smaller absorption) while the sign of the crossover resonances depends on the sign of (7; - AoJ.In the case of a long-lived ground- state, spontaneous emission from level 1 and 2 can be neglected and this term becomesGENERAL DISCUSSION 335 ( y , +Ti - Aoi). At low pressure, the collisional rate (yl + r,) can be very small and the negative crossover resonance dominated by the influence of radiative decay terms. But as the pressure is increased, the competition between radiative decay and collision-induced transitions produces first a reduction of the signal down to zero, then a change of sign. This inversion of the crossover resonance with pressure has actually been observed by Cahuzac and Damaschinij in the 330-23P components of the He atom. I would suggest the use of the pressure dependence of the crossover signals as a method for measuring collisional cross-sections.Indeed, assuming that the levels 1 and 2 have esssentially the same characteristics, the crossover to normal resonances ratio is: The low-pressure limit (CO/N) = (ri + Ti - Aoi)/(C Aoj - Aoi + YO + + Y t + rJ* i (CO/N>o = --Aoi/(C A,j - AoJ i depends only on the branching ratio for the 0 - t i transition. system its magnitude will generally be less than unity. The high-pressure limit will depend on the particular system in consideration. The VCC rates do not usually exhibit a strong level dependence. It is the same for the SCC rates if the rotational levels are mainly coupled to a bath of other rotational levels. In such a case this ratio (CO/N), will be close to 1/2.The situation can be different if the levels 0, 1, 2 are coupled to a small number of levels or even to themselves. An interesting situation, very likely for such sub-Doppler splitting, arises when a strong velocity- conserving collisional coupling between levels 1 and 2 is present. Indeed any hole burned in the level 1 velocity distribution is then efficiently transferred to level 2, thus increasing the size of the crossover signal. The upper limit for (CO/N) will be 2 in that case. It appears then that measurements of the (CO/N) ratio as a function of pressure should be a sensitive and accurate zero method to determine collisional cross-sections in the appropriate molecular systems. For a molecular (CO/N)= == (ri + ri)/(~i + Ti + YO + r o ) H.K. Holt, Phys. Rev. Lett., 1972, 29, 1138. T. W. Hansch, I. S. Shahin and A. L. Schawlow, Phys. Rev. Lett., 1971, 27, 707. Ph. Cahuzac and R. Damaschini, Opt. Commun., 1977, 20, 111. Prof. P. Gray (University ofleeds) said : Prof. Herzberg wins our admiration over and over again for his sustained attacks on problems of major importance and often of considerable difficulty. I should like to consider whether, when discussing the spectrum of ND4 and NH4 and identifying transitions as belonging to Rydberg series, it is today possible to make the thermochemistry more definite than Bernstein [ref. (9) of Herzberg’s paper] was able to in his 1963 estimates. We can construct the cycle: D(H-NH3) NH, ________+ NH3 + H I ( H ) = 13.59 eV I P(NH4) = 8.8 eV I WH4) NHZ + e - NH3 + H+ + e from which I(NH4) + P(NH4) = I(H) + D(H-NH3)336 GENERAL DISCUSSION so that I(NH,) - D(H-NH,) = I(H) - P(NH4) z 4.8 eV.Existing thermochemistry fixes the difference between the (magnitudes of the) ionization potential of ammonium and the first N-H bond strength as equal to the difference between the ionization potential of hydrogen and the proton affinity of ammonia. Any new knowledge about either I (NH,) or D,(NH4) thus provides knowledge about the other. There are several interesting and related problems such as those provided by H,O and H30+, CH4 and CH; to which Prof. Herzberg himself has opened the door; and I suppose that for some of these species, appearance-potential measurements may exist. Bernstein's own path to the problem was quite a different 0ne.l Can new bounds be set upon either? H.J. Bernstein, J. Am. Chem. SOC., 1963, 85, 484. Dr. G. Herzberg (National Research Council of Canada, Ottawa) (communicated) : At the present stage of our work we have not been able to obtain an improvement in the values for the ionization potential or dissociation energy of NH,. It is to be hoped that once the observed transitions have been unambiguously identified and higher Rydberg transitions have been obtained an improved value of the ionization potential will be determined. Dr. S. Leach and Dr. C. Cossart-Magos (Uniuersite' de Paris-Sud, Orsay) said: We have been studying the Jahn-Teller effect in gas-phase halogenobenzene ions for the last few years.14 Our experimental technique differs from that of the Bell group.We obtain emission spectra of the cations, using as source a relatively low-voltage d.c. discharge through the flowing parent species, with a transverse magnetic field applied to spatially concentrate the ions and create a high source brilliance.' In this way, the visible-region emission spectra of a series of eight fluorobenzene ions C6FnH+6-,, (n = 2-6),'-, including the Jahn-Teller species C,'F:,2 sym-C,F+,H-t 2 9 3 and sym-C6F3D3+ ,, and one chlorobenzene Jahn-Teller species, sym-C6C1,H3f, have been photographed with resolutions up to 200000. As we shall remark later, the relatively high temperature (ca. 300 K) of our source is useful in that it enables us populate upper-state hot levels which are critical for Jahn-Teller analysis.A cri- terion of usefulness of such a source is that the rotational contour feature separations should be less than sequence band intervals. This is true, e.g. in the case of the sym- trifluorobenzene ion but less so in the case of C,F,+. The ground states of the D3h and D6h ions are orbitally doubly degenerate and are expected to exhibit Jahn-Teller inherent instabilities at their nuclear configuration of maximum symmetry. Coupling with appropriate non-totally symmetric vibra- tions removes the electronic degeneracy and is able to bring the system to sets of equivalent nuclear configurations of lesser symmetry but of lower potential energy. The Jahn-Teller vibronic levels are specified as follows: vN, the radial quantum number of the two-dimensional harmonic oscillator corresponding to the Nth Jahn- Teller mode; I the vibrational angular momentum quantum number; j = I 3, the vibronic quantum number.u and 1 are useful but not good quantum numbers; j is a good quantum number in the linear-coupling approximation but ceases to be so if quadratic coupling exists. To identify the Jahn-Teller inducing vibrations, it is necessary to carry out vibronic analysis of the emission spectra. The question therefore arises as to the assignment, in terms of normal modes, of the observed ground-state vibrationalGENERAL DISCUSSION 337 TABLE Z.-JAHN-TELLER EFFECT IN THE GROUND STATE OF 1,3,5-C6FSH3+ PRINCIPAL IN- DUCING MODE PARAMETER VALUES OBTAINED FROM A SERIES OF MODEL CALCULATIONS USED TO FIT OBSERVED SPECTRA. D and 4 are, respectively, the linear and quadratic dimensionless coupling constants; o = zero-order harmonic frequency; EJT is the energy of the minimum [= Do] in the linear coupling approximation or minima [= (1 + 4y)DoI6 in the linear + quadratic coupling approximation.Values in brackets are implicit from data given by the authors. o6 E;= D6 /cm-' q6" /cm-' model references authors 0.100 484 - 48 single-mode (I), (2) linear 0.120 483 - 58 three-mode ( 5 ) Orsay (6,7,8) linear group ~~ 0.118 478 0.006 58 single-mode (6) linear quadratic 0.111 480 0.004 54 + (1 1) 0.107 482 - (52) single-mode ( 1 2) linear ~~ 0.80 475 0.0035 380 Three-mode (13) Bell linear group + quadratic 0.73 (479) (0.0035)? 350 four-mode (14) " The quadratic coupling constant q is as defined in ref. (5) and (6).The Bell group definesI3 a corresponding constant K (= 2q). TABLE 3.-FREQUENCIES, RELATIVE INT_ENSITIES AND ASSIGNMENTS OF BANDS IN THE 0: f 230 Cm-' REGION OF THE B2/f"2-X2E" TRANSITION OF 1 ,3,5-C6F3H: emission (gas-phase) LIFEX (gas-phase) Orsay group Bell group -~ frequencyrelative approximate assignment" approximate assignment" to 0: band/cm-' relative relative intensity intensity X = 1l(azu); x, Y = unassigned sequences. frequencies. i.r. and Raman spectroscopy. information from vibrational spectroscopy is mostly lacking. For neutral species this is readily possible through prior knowledge of In the case of aromatic free radicals* and ions, such In responding to this338 GENERAL DISCUSSION problem in the past, we have developed the method of isodynamic molecules which, in the case of the fluorobenzene cations, takes the form of first correlating the modes and frequencies of C6FnH6-,, (n = 0-6) neutral fluorobenzenes, and then correlating the neutral frequencies with the observed ion frequencies.2 Such correlations are justifiable for the following reasons: (1) although the force field changes with suc- cessive fluorine substitutions, the dominant effect in determining this field is that of the carbon ring (this also enables us to use a single notation (Wilson, benzene) for the mode numbering, thus facilitating comparison between the results for the various C6FnH6-,, species studied); (2) going from the neutral parent to the ion corresponds to removal of only one of six 71 electrons on the carbon ring, implying that the ring force field will change little, so that the neutral and ion species will be quasi-isodynamic.Our explicit isodynamic molecule approach was also used implicitly by the Bell group but restricted to comparing each ion/parent molecule fundamental frequency. The Bell group used the Herzberg-Mulliken mode notation, thus giving a different numbering for modes having analogous dynamics, but in the present Faraday Dis- cussion paper by Sears et al., the convenience of a common labelling is recognized. In our studies, the ion spectrum analysed in greatest detail is that of sym-trifluoro- benzene. Our formal isodynamic molecule correlations enabled us to assign four of the e' modes (6-9) and to identify the features peculiar to Jahn-Teller effects absent in the less symmetrical C6FnH6-,,+ ion_s.The relatively high temperature in our dis- charge source enabled us to populate B2A2" upper-state vibrational levels so that we observed vibronic transitions to levels j > 3 in the2 2E" ground state. We emphasize strongly that these are key levels to identify for Jahn-Teller analysis. In the linear- coupling approximation, selection rules show that access to these levels can only occur in emission by transitions from u' 3 1 upper state levels. In assigning our observed bands we used the linear coupling model reviewed by Longuet-Higgins,'O which we extended to include multimode interactions and/or quadratic coupling6 effects. The Bell group used essentially the same progression of models, with results initially in agreement with our own (table 2) but later results differ from ours concerning the values of particular dimensionless linear coupling constants D,.The basic reason for this lies in a difference between the Bell group and our group in assignment of one key band, 6::$/2 in our notation, which involves a transition from u' = 1, I' = 1 to t" = 1, j = 3/2 of mode 6 (mode 13 in the Bell group notation). (Note that for the analogous chlorine compound, 1 ,3,5-C6C1,H$, both groups agree on the assignment of the 6!;il2 band and derive similar values of the mode 6 linear coupling ~ o n s t a n t . ) ~ * ' ~ The effects of multimode interactions on energy levels is only marked if the coup- ling constants are large. Indeed our analysis of the 1 ,3,5-C6F,H$ emission spectrum, which gave low D, values, was little modified by three-mode calculation^,^ whereas that of the Bell group, with the much larger D, value resulting from their 6:::;2 assignment coupled with a high given value of D for mode 7 (mode 9 in the Bell group notation), was much more sensitive to multimode interactions. For our three-mode calculations it was sufficient to diagonalize a 143 x 143 matrix, whereas the Bell group was obliged to diagonalize matrices of dimension ca.7000 in order to get acceptable accuracy for calculated eigenvalues below 1000 cm- l . Because of the critical nature of identification of the j = 3/2 level of mode 6, a comparison of those aspects of the spectra and analysis of the two groups relating to this question is called for. We first consider the origin band region of the $A;-i2E" transition in 1,3,5- C6F3H3+.There is an apparent discrepancy in the gas-phase frequency of the principal peak of the 0," band: we find 21 868.9 cm-1p'*2 whereas the Bell group have variously reported 21 862 cm-'9I5 21 865 cm-' l6 and, most recently, 21 855 crn-'9'' We againGENERAL DISCUSSION 339 find the value 21 868.9 cm-' in further high-resolution studies; our value has been recently confirmed by Tuckett's observations of the fluorescence spectrum of 1,3,5- C6F3H3+ excited by an electron gun in a supersonic jet.18 In comparing the low-temperature, gas-phase, laser-induced fluorescence spec- trum of Bondybey et aI.17 with our discharge spectrum, we find a very similar struc- ture in the 0; band region, including rotational peaks and sequence bands; the differ- ences in relative intensities of features of the two spectra are as expected from the different temperatures.When we go to frequencies higher than the 0; band and its accompanying satellites, the first bands of any intensity are a group of five in the 0; + 80 cm-I region. We have observed a pair of bands at +67.5 cm-' and +82.1 cm-' which we have as- signed to the quadratically split A; and A; components of the 6:;i/2 band. These are accompanied by the expected sequence bands at 74.1 cm-' and 89.3 cm-', respectively. Only one other band is observed in this region, at 0; + 71.9 a n - ' ; it fits perfectly the assignment 1i6i;i/2. The intensities of the 6:::,2 ( A : , A,") pair of bands are the same, as is expected to be the case from the selection rules.The same is true for the pair of close-lying sequence bands. A band was found at 0; 4- 82 cm-' by Bondybey and Miller in a low-resolution, laser-induced fluorescence excitation (LI FEX) gas- phase study15 but was not assigned. Its apparent width covers the entire region of the five bands discussed above. No feature was found in this region in the LIFEX spectrum in a 4 K Ne matrix,12 which is consistent with our interpretation of the bands in the 00, $ 80 cm-I region as hot bands. However, observations in this spectral region were not reported by the Bell group either in their laser-induced gas-phase wavelength-resolved fluorescence studies l6 or in their unrelaxed emission observations in a Ne matrix." There ensues a critical absence of information for further testing our assignments of the 6!;i/z features.We discuss now the 6:::/2 assignment of the Bell group. The corresponding fea- tures are in the 0; + 230 cm-' region. Four bands are observed in this region in the cooled gas-phase LIFEX spectrum of Bondybey et a/." Although the individual frequencies were not reported, we are able to give their values (table 3), with respect to the 0; band, by direct comparison of the Bell published spectrum with the bands in this region on the microdensitometer tracing of our high-resolution discharge emission spectrum." Since the frequencies of the actual pair of bands assigned to the A;, A: components of 6::i,2 were not given by the Bell group (only their frequency difference, 12 cm-l was reported), we assume that they must be associated with the pair of strong- est bands at +226 cm-' and $238 cm-', even if these bands, which should have the same strength if they are 6{::/2 components, do differ in intensity.However, as Bondybey et a / . remark,17 laser-induced fluorescence-excitation intensities are un- reliable. One argument of the Bell group against our assignments in this region is that the Ne matrix LIFEX spectrum shows no band in the $230 cm-' region, which it might be expected to do if our assignment 9A::12 is correct. We counter this argument with the following two remarks. First, the corresponding 9!;Yl2 band in the Ne matrix LIF spectrum is weak; it might be difficult to observe the 9& band by LIFEX since the observed relative intensities are sensitive to laser power variation and also depend critically on efficient vibrational relaxation to the zero vibrational level of the state.That the latter is not always rapid in a Ne matrix is evident from other results of the Bell group, in particular on LIFEX of C6F2 in a Ne matrix." The second point, more important in our eyes, is that in the Ne matrix absorption spectra, where the defects of LIFEX are not present, an absorption band in the 0; 4- 230 cm-'region is indeed observed [at ca +218 cm-I as can be seen in fig. 1, trace (a), of ref. (17)]. B2A340 GENERAL DISCUSSION 9' 11' Furthermore, it is rather stronger than the very weak band at +324 cm-' which is where the Bell group now assign the 9h;:,2 transition (vi4 in their notation) (the Bell group originally agreed with assigning vi4 to the 230 cm-l band).l5 The basis of the present Bell assignment is the observation of a weak band at 327 cm-l in the Ne matrix LTFEX spectrum" and in the cooled gas-phase spectrum." (We also observe a very weak band at this frequency in our discharge emissim spectrum' which could possibly be assigned to the 16; transition.)" An apparently more serious argument in favour of the Bell group's interpretation concerns observations of unrelaxed emission in the +230 cm-l region, assigned to the A:, A'; components of 6:::,2, after pumping the 6'9' level at $481 cm-' in a Ne matrix. However, according to our assignments, the resulting term scheme (fig. 19) 9' 11' A: 0' ii2 14' 1 7 ' 00 500 0 FIG. 19.-Levels involved in- interyetations of bands in the 0; $- 80 cm-I and 0; + 230 cm-' regions of the 1,3,5-CbF3H3+ BZA;-X2E" transition.Corresponding levels in the two different mode- numbering schemes are linked by thin lines. (a) Orsay group (gas-phase emission); (h) Bell group (gas-phase LIFEX). would allow the observations to be compatible with the following: excitation to the 6'9' level at 481 cm-', followed by rapid vibrational relaxation to the only two lower- lying levels able to radiate to ground-state levels, i.e. 9'3l 11' and 9 1 e 1 . The resultingGENERAL DISCUSSION 341 transitions 9& 11: and 9$,,2 would, on our assignments, correspond to the observed bands. (The 7 cm-' gas-phase separation is expected to become ca. 12 cm-' in the Ne matrix: in the latter it is known that 211v'- 2 4 , = 26 cm-1*12 so that the two above bands would be separated by 1/2 of this value.) If our 6::$/2 assignments are correct one might then expect that pumping the 6l.l level would also lead to observa- tion of unrelaxed emission at 0; + 67.5 cm-' and 0: + 82.1 cm-'.Unfortunately the Bell group have published no observations in this spectral region in these particular experiments. There are two, more general, arguments used to support the Bell group's analysis. One is the good agreement between calculated and experimental relative band in- tensities, whereas with our coupling-constant values the relative intensities in a Jahn- Teller progression fall off faster than observed. [Some possible reasons for this are given in ref. (2), (5) and (6).] A second point is that, in general, the value of the linear coupling constant of the equivalent of mode 6 is of the same order of magnitude are arguments of some weight, in themselves they are insufficient as conclusive proof of the correctness of the Bell group analysis of 1,3,5-C6F3Hi.We feel that further experiments are required in order to decide conclusively between the interpretation of the two groups. Some of these experiments have been mentioned in the above remarks. In particular we have recently obtained a new higher-resolution gas-discharge emission spectrum of 1 ,3,5-C6F3D$, the analysis of which should highlight any inconsistencies in that of 1,3,5-C6F3H:. Finally, we note that both in our own work and in that of the Bell group there is far more experimental information on mode 6 than on the other Jahn-Teller modes.In fact, because of this lack of data, analysis involving modes other than mode 6 tends to use some of these other modes as very pliable parameters; furthermore, when the D, values are high, fitting levels above 1000 cm-l with the same degree of accuracy as those below 1000 cm-l becomes a herculean, and so far unachieved, task. This adds a further note of caution regarding present day analyses of Jahn-Teller effects in halogenobenzene cations. Further work is called for in this respect. in the species C6F6+, I ,3,5-C6F3H:, 1,3,5-C6C13H: and C6CI3F: .I4 Although these Others have already been done and are in the course of analysis. C. Cossart-Magos, D. Cossart and S. Leach, J . Cheni. Phys., 1978, 69, 4313.C. Cossart-Magos, D. Cossart and S. Leach, Mol. Phys., 1979, 37, 793. C. Cossart-Magos, D. Cossart and S. Leach, Cheni. Phys., 1979, 41, 345. C. Cossart-Magos, D. Cossart and S. Leach, Chem. Phys., 1979, 41, 363. C. Cossart-Magos and S. Leach, Cheni. Phys., 1980, 48, 329. C. Cossart-Magos and S. Leach, Chem. Phys., 1980, 48, 349. D. Cossart, J . Chim. Phys., 1979, 76, 1045. S. Leach, J. Phys. Paris, 1967, 28, C.3, 134. New York, 1961), p. 429. a C. Cossart-Magos and S. Leach, J. Chem. Phys., 1972, 56, 1534; 1976, 64, 4006. lo H. C. Longuet-Higgins, Aduarzces in Spectroscopy I/, ed. H. W. Thompson (Interscience, l1 C. Cossart-Magos, D. Cossart and S. Leach, manuscript in preparation. l2 V. E. Bondybey, T. A. Miller and J. H. English, J. Chern. Phys., 1979, 71, 1088. l3 T.Sears, T. A. Miller and V. E. Bondybey, J. Chem. Phys., 1979,72, 6070. l4 T. J. Sears, T. A. Miller and V. E. Bondybey, Faraday Discuss. Chem. Soc., 1981, 71, 175. Is V. E. Bondybey and T. A. Miller, J . Cheni. Phys., 1979, 70, 138. l6 T. Sears, T. A. Miller and V. E. Bondybey, J . Chem. Phys., 1980, 72, 6749. l7 V. E. Bondybey, T. J. Sears, J. H. English and T. A. Miller, J . Cheni. Phys., 1980, 73, 2063. la R. P. Tuckett, Cheni. Phys., 1981, 58, 151. l9 V. E. Bondybey, T. A. Miller and J. H. English, Pliys. Rer. Left., 1980, 44, 1344. Dr. T. A. Miller (Bell Laboratories, Murray Hill, NeM1 Jersey) (communicated): In response to the comment by Drs. Leach and Cossart-Magos, it is appropriate first342 GENERAL DISCUSSION to put the matter into perspective. Our paper summarizes the results of the analysis of roughly 500 vibronic transitions of four symmetrical molecular ions, C6F3H:, C6F2, C6C13H,+ and C6F3C1;, and of their isotopic variants.Although the data of the Orsay group are overall considerably less extensive than ours, where the data overlap there appears to be good agreement in interpretation between the two groups for the latter three species. Only for three transitions of C6F& involving the modes ~ 1 ? ( 9 ’ and v13(6) (we give the Orsay notation in parenthesis) does a serious disagreement exist. Unfortunately, the assignment of these few transitions is of key importance for interpreting the Jahn-Teller effect in this ion. The Comment by Drs. Leach and Cossart-Magos would seem to suggest that our assignment for C6H3F3+ results in some inconsistencies, or leaves some transitions without satisfactory assignment.In reality, our model provides a remarkably self- consistent and complete description, not only of our own data obtained by a variety of different techiques, but also of the Orsay discharge spectrum. Our model not only provides satisfactory assignments for virtually all of the ca. 150 transitions observed (most of them by several different techniques), but the same parameters which predict correctly the level positions also reproduce remarkably well the observed relative intensities. Our model also explains quite adequately the changes in the spectrum as the temperature is varied from 300 to 77 K, and eventually to the 4 K neon matrix, and is further supported by reasonable and consistent isotopic shifts of the individual vibronic transitions. As the comment itself notes, the analysis also leads to a reassuring similarity in the Jahn-Teller distortion parameters for all four of these closely related halogenobenzene cations.The interpretation of Leach and Cossart-Magos, on the other hand, while perhaps providing assignment for most of the transitions observed in their high-temperature discharge leaves many “ loose ends ” and needs tortuous and cumbersome arguments to rationalize a variety of different experimental observations. There are basically only three bands which the Bell Laboratories and Orsay groups assign differently. Two of these bands are referred to in the Orsay comment as 0; + 80 cm-’ and 0; + 230 cm-’.For simplicity, we will continue to use these designations. However, we will discuss structure in these bands and note that in different experiments the exact positions of these bands, and especially their substructure, varies slightly as a result of differing resolution, environments, and experimental error. A third band, important to our arguments, is at 0; + 327 cm-’. It is worthwhile to note at the beginning that there is no argument about the existence of any of these bands. They are present in high- temperature (300 K and above) spectra taken in our laboratory4v5 and at Or~ay.’-~ It is only the assignments of these bands by the two groups that differ. The Orsay group assigns the 0; + 80 cm-’ structure to an emission transition u’ = 1 of mode 13 (6) in the excited state to the C” = 1, j = 3/2, ~ 1 3 , level of the ground state, i.e.13::i12 (6;;i12). (There is some other structure in the emission band which they assign to sequence transitions, which is irrelevant for the present arguments.) The band at 0; + 230 cm-’ is assigned by the Orsay group to the transition between the vibrationless level of the ground state and the u’ = 1 level of v14 in the excited state, i.e. 14,$ (9;). Orsay also assigns in this region the 14; 17: (9; 11 {) sequence band which depending upon the experiment’s resolution may or may not be resolved. These assignments lead to the Orsay energy level diagram depicted on the left of fig. 19. In our assignment, both the 0; + 80 cm-I and the 0; + 230 cm-’ transitions are due to hot bands.The band at 0; + 230 cm-’ in the room temperature spectra is a transition between the LI” = 1, j = 3/2, vI3 ground-state level and the u’ = 1 , vI3 upper-state level, i.e., 13::312 (6j;&2). As for the weak band at 0; + 80 cm”, we Let us now clearly state the points of disagreement.GENERAL DISCUSSION 343 believe it arises from the transition between ~ ' ~ 3 , u" = 1 , j = 3/2, and u = 1 of the excited-state mode 14 (9), i.e. 13A:!,2 14; (6!;3,2 9 3 which our Jahn-Teller intensity calculations predict to be weak but observable. There is also a weak line at 0; + 327 cm-' (observed by both groups) which we assign to the transition 14; (93. These assignments lead to the Bell energy-level scheme depicted on the right-hand side of fig. 19. As mentioned earlier, the choice between the above two sets of assignments based upon high temperature alone is not straightforward.Nor is any real guidance offered by the two theoretical papers6 of the Orsay group as they offer no new data. However, the two sets of assignments make very different predictions for the low- temperature appearance of the laser-excitation spectra. Thus, to resolve the argu- ment, we have performed Ne matrix experiments7.' at 4 K and gas-phase experi- ment~~*'* at liquid N2 temperature. Leach and Cossart-Magos claim a useful feature of their source is that it produces emission from " hot " vibrationally excited levels. It is, however, well known that in a discharge source the distribution of vibrationally excited levels is poorly known.We, on the other hand, have obtained'' the desired emission from excited vibrational levels in a cold source by selective laser excitation of specific levels. It is the weight of these recent, extensive experimental data which " force " us to adopt the present " Bell energy-level scheme ". Looking back at the two energy-level schemes, we note that in a laser-excitation experiment, the 08 + 80 cm-' and 0; + 230 cm-' bands are " hot bands " according to the Bell scheme, while the 0; + 327 cm-' is not. The Orsay analysis requires that the 0; + 230 cm-I band be a cold band originating in the ground-state vibra- tionless level, although it may, like all the other transitions, have " hot-band " se- quence structure built upon it. We now list the specific points, as determined by our more recent experiments, that we believe support the Bell Laboratories energy-level scheme and make the Orsay scheme highly unlikely. (1) Laser-excitation spectra' at liquid-nitrogen temperature show the 0: + 80 cm-' and 0; + 230 cm-' bands decreasing in intensity compared with the 0: band and in a ratio consistent with the lower level being ca.250 cm-' above the vibrationless level as implied by the Bell Laboratories scheme. On the other hand, the 0; + 327 cm-I band does not decrease in relative intensity. Extremely precise relative in- tensity measurements are precluded by the different sequence structure in these bands; however, the difference between hot and cold bands is clear. (2) Laser-excitation spectra' in a Ne matrix at 4 K do not show any band at 0; + 230 cm-' (or 0; + 80 cm-') but do show the 14; (9;) transition at 0; + 327 cm-l as predicted by the Bell energy-level diagram.With the available signal-to-noise ratio a band at the 0; + 230 cm-' position would have to have been 50 x weaker not to be observed. Leach and Cossart-Magos rationalize this observation by the " slow vibrational relaxation " of this level in the matrix. We have studied several hundred transitions of substituted benzene cations in Ne matrices, and never has " slow vibrational relaxation " prevented the observation in the matrix of any other transition seen in the gas phase. Moreover, a simple consideration of the dynamics make such an argument unlikely. To escape observation in the Ne matrix excitation spectrum, vibrational relaxation would have, very conservatively estimated, to be at least a factor of 20 slower than the radiative lifetime, corresponding to a vibrational relaxa- tion lifetime of ca.1 i t s . The longest lifetime observed' for any vibrationally excited level of the fluorobenzene cations was ca. 55 ps, leaving us with a " safety factor " of > 104.344 GENERAL DISCUSSION Finally, Leach and Cossart-Magos try to find support (which is critical to their argument) for the 0," + 230 cm-' being a cold band, in our matrix absorption spec- trum of C,F3H3+. There is a very weak band appearing in this spectrum at 0; + 218 cm-' but it, as well as several much stronger bands at larger lower energies, are due to inhomogeneous broadening and site effects, as noted in ref.(9). While this may not be clear from considering a single published spectrum [fig. 1 of ref. (9)] out of context, it is quite unambiguously established by careful examination of the close to 100 absorption, fluorescence, and laser-excitation spectra taken in our laboratory. In carrying out our spectral assignments, the existence and identity of each important band was checked and double-checked against possible matrix perturbation and site effects. (3) To combine the advantages of low sample temperature with emission from vibrationally excited upper-state levels, we have performed several experiments pump- ing selectively specific levels.'o In one case we have excited the 13; (63 transition by the laser and resolved spectrally the emission. Obviously, one would expect the bulk of the re-emission to occur into the vI3, U" = 1, j = 3/2 and 1/2 levels (our Jahn-Teller calculationsll predict the emission into the j = 3/2 level to be most intense).Indeed, by nearly an order of magnitude, the strongest fluorescence band (other than at the laser wavelength where scatter makes interpretation difficult) is located 250 cm-' to the red of the laser, precisely at the position predicted by the Bell energy level scheme." On the other hand, the Orsay energy-level scheme re- quires re-emission at 80 cm-' red of the laser as is stated in their comment. Contrary to their statements, we did make observations in this region and foucd no bands. Although our sensitivity in this wavelength region is lowered owing to the proximity of scattered laser radiation, an emission band at the laser frequency -80 cm-' as strong as the observed emission at the laser frequency -250 cm-' could easily have been detected.In another selective-excitation experiment we tuned the laser frequency to the 0," + 230 cm-' band. As we believe this is a hot band originating in an excited vibrational level, we could expect to see emission back to the vibrationless level of the ground state, ca. 230 cm-I blue of the laser. Again, this expectation was clearly realized. We may note that in our model, excitation at either 0," + 230 cm-' or 0," + 410 cm-' populates the same upper-state level, 13.' Indeed, for both excitation wavelengths, identical re-emission spectra are observed. (4) Very similar selective excitation experiments were performed8 in the Ne matrix, where selective short-time-interval gates immediately following the laser pulse allowed us to record spectra from the less than 0.1 "/o of the fluorescence which emanated from the initially excited, unrelaxed vibrational level.Again, excitation of the 13; (63 transition resulted in emission predominantly to a level ca. 250 cm-' above the vibrationless one, where our scheme, of course, places the u" = 1, j = 3/2, v13(6) level. The higher resolution of the matrix experiment shows that this transition is a doublet separated by ca. 12 cm-I, which we have attributed to quadratic Jahn- Teller splitting of the j = 3/2, a; and a; vibronic levels.' Significantly this same 12 cm-l doubling appears in our low-temperature high-resolution gas-phase excitation spectra' on the 0: + 230 cm-I band, just as it should since our scheme maintains these transitions involve the common v13, u" = 1, j = 3/2 level.Finally, we note that our previously published' assignment of the 0," + 80 cm-' transition also shows it to involve this same ~13, U" = 1 , j = 3/2 level. The fact that the Orsay group observes (see their comment) a doublet splitting of ca. 12 cm-l in the 0: + 80 cm-' band simply strengthens our conviction about the correctness of our assignment,GENERAL DISCUSSION 345 Having adopted our energy-level scheme on the basis of the experimental evidence alone, we have proceeded to perform the quantum-mechanical analysis 11* l 2 required to extract meaningful physical information from those energy levels.In the com- ment of Leach and Cossart-Magos, it has been remarked that our analysis has “ obliged (us) to diagonalize matrices of dimension ca. 7000 in order to get acceptable accuracy . . . , ” while they found that “ it was sufficient to diagonalize a 143 x 143 matrix ”. It is well to point out that the increase in computational complexity is solely the result of the values of the linear Jahn-Teller distortion parameter, D, needed to describe our experimental energy-level scheme. There can be no question but that ours is the rigorous approach. However, it is just as important to emphasize that our approach does not result in any additional ambiguity in the analysis. Given our computational power, the eigenvalues of a 7000 x 7000 matrix are as well- determined as those of a 143 x 143.Most importantly, our approach does not introduce additional variables into the problem above those in the analysis of Leach and Cossart-Magos. [The only exception to this statement is the additional two parameters describing the 4th mode for which Leach and Cossart-Magos obtain no information. These two additional parameters do not, contrary to the assertion of the comment, make the analysis more “ pliable ”. The parameters for the 3 common modes do not change very significantly for C6F3H: between the 3 and 4 mode analyses -compare our paper and ref. (1 l).] The results of the Jahn-Teller analysis on our energy-level scheme are very much more consistent and physically understandable than those based upon the Orsay energy-level scheme as is indicated by the following examples.have pointed out, the present multi-mode Jahn-Teller analyses explain the frequencies of all the observed Jahn- Teller lines and all the measured intensities. Even Leach and Cossart-Magos point out that their (presumably correct) Jahn-Teller analysis of their energy-level scheme clearly fails to predict correctly the intensities of many of the observed transi- tions. (2) As our present paper points out, there is a very pleasing consistency among all the parameters obtained from our Jahn-Teller analysis for all four of the ions con- sidered. This is to be expected as the Jahn-Teller effect is basically caused by the “ hole ” in the n system of the benzene ring. For instance, in our analysis the linear Jahn-Teller distortion constant D for the ring bending mode 13(6) is 0.68 for C6FZ and 0.73 for C6F3H3+ while for the chlorinated compounds it drops slightly to 0.62 for C6C13H3+ and 0.60 for C6C13F$.This slight drop upon chlorination is consistent with the intuitive idea that the cloud will be slightly more delocalized on the C1 atoms than the F, thus slightly decreasing the strength of the hole’s interaction with the ring itself. On the other hand, the Orsay group’s analyses6i13 for C6Cl3H; finds a D for mode 13(6) of 0.45, as compared to their value of D = 0.11 for C6F3H:. We cannot understand an increase of a factor of 4 or more in goingI2 from C6F3H: to C6C13H3+. (In the case of C6C13H:, there is no real controversy between our D value of 0.62 and the Orsay group’s 0.45. The line assignments and frequencies are essentially the same; we simply have more observations and have used our more rigorous multi-mode analysis, which causes the parameter D to increase.In fair- ness, the Orsay group also claims that their C6CI,H3+ spectrum could be explained by a D ~ 0 . 2 0 and a quadratic constant nearly an order of magnitude larger than for C,F3H3+. However, our data do not support the latter analysis nor could we under- stand the large change in the quadratic constant.) ( 3 ) The Orsay group promotes an “ isodynamic molecule ” approach for assign- (1) As our present paper and previous346 GENERAL DISCUSSION ing vibrational frequencies, arguing in their comment that " going from the neutral molecule to the ion corresponds to removal of only one of six .n electrons on the carbon ring, implying that the force field will change little .. .". Indeed, we have found a striking similarity between the vibrational frequencies in both states of a number of ions and the corresponding neutrals. For example, we have compared the non-Jahn-Teller perturbed fundamental frequencies of sym-C,F,H,+ and C6C13H3+, 1 ,2,3,4-C6H2F,+, 1 ,2,3,5-C,H2F,+, C6HFz and 1 ,2,4,5-C6H2F,+ for both the ground and excited ionic states with the parent neutral ground-state f~equencies.~~'~ We find an average change (increase or decrease) of ca. 3% for some 72 transitions. Accepting the Orsay assignments gives a vibrational frequency for ~14'(9) of 230 cm-l, compared with a frequency for the parent neutral of 326 cm-', which constitutes an increase of 42%.In view of the constancy of the in-plane vibrational frequencies in all these related species, we find such a change highly improbable. On the other hand, our assignment yields a v14'(9) value of 327 cm-', nearly identical with the parent. Overall, we feel that on the basis of the totality of experimental observations, the lack of any experimental observations at Orsay or elsewhere contrary to our model, and the general consistency of the results of the Bell Laboratories interpretation that the arguments for the " Bell energy-level scheme " are extremely strong. While we wish to maintain an open mind, we feel at this stage that little productive can be accomplished by continued investigations. While an assignment in a complicated problem like this is rarely " beyond any doubt ", our present assignment is, we be- lieve, beyond reasonable doubt.C. Cossart-Magos, D. Cossart and S. Leach, J , Chem. Phys., 1978, 69, 4313. C. Cossart-Magos, D. Cossart and S. Leach, Chern. Phys., 1979, 41, 345. T. A. Miller and V. E. Bondybey, Chem. Phys. Lett., 1978, 58, 454. V. E. Bondybey and T. A. Miller, J. Chenz. Phys., 1979, 70, 138. C. Cossart-Magos and S. Leach, Chem. Phys., 1980, 48, 329 and 349. V. E. Bondybey, T. A. Miller and J. H. English, Phys. Reu. Lett., 1980, 44, 1344. V. E. Bondybey, T. J. Sears, J. H. English and T. A. Miller, J. Chem. Phys., 1980, 73, 2063. ' C. Cossart-Magos, D. Cossart and S. Leach, Mol. Phys., 1979, 37, 793. ' V. E. Bondybey, T. A. Miller and J. H. English, J. Chem. Phys., 1979, 71, 1088.lo T. Sears, T. A. Miller and V. E. Bondybey, J . Chem. Phys., 1980, 72, 6749. l1 T. Sears, T. A. Miller and V. E. Bondybey, J. Chern. Phys., 1980, 72, 6070. '' T. Sears, T. A. Miller and V. E. Bondybey, J . Chem. Phys., 1981, 74, 3240. l3 C. Cossart-Magos, D. Cossart and S. Leach, Chem. Phys., 1979, 41, 363. l4 V. E. Bondybey, J. H. English and T. A. Miller, J. Mol. Spectrosc., 1980, 81, 455. Dr. J. H. D. Eland ( O ~ f o r d University) said: Has Dr. Maier observed emission from excited fragment ions by any of his techniques? It would be interesting to study such emissions by the coincidence method, to identify the molecular ion states which decompose to excited products. Dr. J. P. Maier (Basel University) said: We have not observed emission from excited fragment ions but neither have we searched for these specifically.In my opinion the best way of setting about this would be to preselect suitable parent- fragment ion candidates on thermodynamic considerations and then first apply a technique such as the photoion-photon coincidence one mentioned in the following remark by Dr. Leach. The advantage of the latter approach is that one can then identify the mass of the charged emitting carrier although the internal energy/state is not specified. However, one can then apply the photoelectron-photon coincidence technique to locate the molecular ion states which yield the excited fragment ions.GENERAL DISCUSSION 347 Dr. S. Leach (Uniuersite‘ de Paris-Sud, Orsay) said: One of the problems in mole- cular-ion spectroscopy is identification of the species responsible for observed emis- sion.A technique which we have used to this end involves photoion-fluorescence photon coincidence (PIFCO) measurements in which the emitted photons are monitored in delayed coincidence with mass-selected photoions.1*2 We have used this method in order rapidly to discover whether a particular ion emits, and to determine the spectral regions of such emission. Once these facts are ascertained, special emission sources have been devised and operated under conditions so as to maximalise the ion emission intensity, thus permitting high-resolution s t u d i e ~ . ~ . ~ Besides this function as a scout for molecular-ion emission, the PIFCO technique has been used extensively for studies of radiationless transitions in molecular ions, the probes being two quantities which can be determined using this method, namely ion fluorescence temporal decay characteristics and fluorescence quantum yield.2 A particular use of the PIFCO technique provides an answer to a question raised by Dr.Eland who asked Dr. Maier whether one observes not only parent-ion emission but also emission from fragment ions formed in a primary process. However, Dr. Maier’s very useful complementary technique of monitoring emitted photons at the same time as energy-selected electrons cannot immediately distinguish between parent- and fragment-ion emitters if formation of both types of species is possible at ion energies corresponding to a particular electron kinetic energy monitored. Using the PIFCO technique, Dr.Gerald Dujardin and 1 have studied the radiative and dissociative relaxation processes in V.U.V. photoexcited SO,? Line photo- excitation sources in the range 10.2-21.2 eV were used to produce excited electronic states of SO2 and/or SO,+ whose first ionization potential is at 12.3 eV. PIFCO measurements showed that SO; states in the 16 eV region fluoresce within a 175-370 nm detection window, with a quantum yield qF(c2Bz + b 2 A , ) z 6 x The fluorescence lifetime is < 10 ns, the emission being in competition with predissociation. The products of predissociation of excited states of SO; were identified by their time- of-flight mass spectra and/or dispersed optical emission. With He I excitation (21.22 eV), SO+(A2n-X211) emission was observed over the spectral range 250-630 nm, with a measured lifetime of T~ = 2.4 0.4 ,us and a fluorescence efficiency qF(SO+, A2n-X211) z 6 x (qF is the ratio of the total number of fluorescence photons emitted to the total number of parent plus fragment photoions produced ever a given time interval). The SO+ A2n state is produced by predissociation of the F2Al state of SOT, as has been confirmed by studies using the Orsay synchrotron radiation source, monitoring coincidences between SO + (A’II-X’II) fluorescence photons and threshold photoelectrons corresponding to formation of the SO+ F(’A,) state6 at 20.3 eV.The emission of SO,’ falls within the same spectral region as that of SO+ (and of SO). It will be probably difficult to identify the dispersed SO,’- emission spectrum, since our measurements indicate that the fluorescence efficiency of SO+ fragment emission is ca.300 times greater than that of SO;. Whether SO,+ fluoresces has been the subject of a number of controversial spectro- scopic studies. Our results support the view of Tsuji et al.7 that the rather intense emission in the 300-500 nm range, produced by a He+, He(23S) + SO2 flowing after- glow reaction, were incorrectly assigned to the SO,’ parent The recent analysis by Tsuji et al.7 reassigns the observed spectrum to the SO+ A2n-X2n transition. In my opinion, further work is required to ascertain whether all of the bands reassigned by these authors are indeed due to SO+, although some of them certainly are, as has been shown by high resolution results obtained in our laboratory by Daniel Cossart.’O348 GENERAL DISCUSSION J. H.D. Eland, M. Devoret and S. Leach, Chem. Phys. Lett., 1976, 43, 97. S. Leach, G. Dujardin and G. Taieb, J. Chim. Phys., 1980, 77, 705. D. Cossart, J . Chim. Phys., 1979, 76, 1045. D. Cossart, J. Chim. Phys., 1981, 78, in press. G. Dujardin and S. Leach, J. Chem. Phys., A81, 75, in press. G. Dujardin, 0. Dutuit, T. Covers, P-M. Guyon and S. Leach, unpublished results. ' M. Tsuji, C. Yamagiwa, M. Endoh and Y. Nishimura, Chem. Phys. Lett., 1980, 73, 407. ' K. T. Wu and A. J. Yencha, Can. J. Phys., 1977, 55, 767. M. Tsuji, H. Fukutome, K. Tsuji and Y . Nishimira, Int. J . Mass Spectrom. Ion Phys., 1978,28.257. D. Cossart, unpublished results; see following remark. Manuscript in preparation. Dr. S.Leach (and Dr. D. Cossart) (Universite' de Paris-Sud, Orsay) (partly communicated) : Dr. Cossart has shown that SO+ ion emission spectra are preferentially excited in microwave or spatially confined discharges through flowing He + SO2 mixtures. In the 2700-5000 8, region many SO and S, bands were observed, but four red-degraded, double-headed bands (4009-4077, 41 94-4270, 4412-449 1 and 4653-4747 A) differ clearly from the spectra of these neutral species. The A-doubling seen for many lines, as well as the apparent B f - B" z 0.15 cm-l rotational constant differences are consistent with an assignment of these four bands to SO+, A211-X211 (0, 6-9) follow- ing the vibrational numbering of Tsuji et al.' However, the interval between sub- band heads varies between 400 and 425 cm-', which suggests that the upper vibra- tional level is not the same for all the bands and that the vibrational assignment should be revised.Spin-orbit perturbations expected between A211 (v 3 2) and 4C- levels could be responsible for anomalies in intensities and vibrational structure in the A2n- X 2 n transition. I n the 5000-9000 A region, Dr. Cossart has observed five new bands, showing four violet-degraded heads which have been classified in a Deslandres table. They have been assigned to the (3-0,O) and (1, 1) bands of the previously unknown 4C--411 system of SO+, consistent with the photoelectron data of Dyke et aL2 Rotational analysis is in progress on the unperturbed bands. The (3,O) band is clearly perturbed; the branch degradation sense is reversed between the 4C--4115,2 and 4C-4111,2 sub-bands.Apparent rotational constants for each 411 sub-band agree quite well with the interval of about 65 cm-' between sub- band heads using a second-order perturbation formula (BQ - Bn-l= -22B2/A in the Hund's case a basis set of an inverted 411 state) relating these apparent rota- tional constants to the true rotational and spin-orbit constants B and A . M. Tsuji, C. Yamagiwa, M. Endoh and Y. Nishimura, Chetn. Phys. Lett., 1980, 73, 407. J. M. Dyke, L. Golob, N. Jonathan, A. Morris, M. Okuda and D. J. Smith, J . Chem. Soc., Faraduy Trans. 2, 1974, 70, 1818. Dr. S. Leach (UniuersitP de Paris-Sud, Orsay) said : The order of the first excited 2C+ and 211 states varies among the 15 valence electron molecules; e.g.the 2C+ state is below the excited 211 in N20f but above in OCS+. Although there is not much quantitative data, it appears likely that the relative oscillator strengths of the 2C+- g2rI and 'l--f2II transitions also vary among the members of this isovalent group. HCCS is a 15 valence-electron species and should therefore exhibit in the visible-u.v. region a 2Cf-211 as well as a 211-2n transition. The transient absorption spectrum in the 3770-4170 8, region was tentatively assigned by Krishnamachari and Ramsay to the 211-g211 transition. Are there any indications of a 2C+-211 electronic transi- tion for HCCS? Is it expected, or found, to be at a higher or a lower energy than the 21-1-211 transition? Can one say anything about the relative oscillator strengths of these two transitions in HCCS?GENERAL DISCUSSION 349 Dr.S. N. L. G. Krishnamachari and Dr. D. A. Ramsay (National Research Council of Canada, Ottawa) said: We have not obtained any definite evidence for a ’C+- ’II electronic transition up to the present, although there are many weak unidentified bands, especially at shorter wavelengths. Since the strongest bands are definitely of the type ’KI-’n, the predicted 2E+-2rI transition must presumably be weaker. Dr. K. Evenson (National Bureau oJ’ Standards, Boulder) said: The rotational constant looks a little small for far infrared laser magnetic resonance. However, cross-stack transitions might be possible; therefore, do you know what the spin- orbit splitting is? Dr. S. L. N. G. Krishnamachari and Dr. D.A. Ramsay (National Research Council of Canada, Ottawa) said: We have no information concerning the magnitude of the spin-orbit coupling constant A” from the present work, but a value could be obtained if the predicted 2C+-211 transition could be found. Dr. R. F. Barrow (Oxford University) said: Is it possible to use the values of the centrifugal distortion constants to derive the absolute J-numbering, or are they not sufficiently well-determined ? Dr. S. L. N. G. Krishnamachari and Dr. D. A. Ramsay (National Research Council of Canada, Ottau3a) said : The centrifugal distortion constants are not sufficiently well-determined to give any reliable guidance concerning the absolute J-numbering. Dr. S. Leach (UniuersitP c k Paris-Sud, Orsay) said: Perturbation analysis of the spectra of diatomic molecules is usually carried out on the basis of interactions between two zero-order levels of different electronic states.This is the case in the results on SnO presented by Clyne and Heaven. However, in the case of CS, which is isovalent to SnO so that the two species should have similar term manifolds, Cossart and Berge- man’ have found it necessary to introduce interactions between more than two simul- taneously interacting levels in their study of the perturbations involving the A’II state. For example, in analysing the A’rI-X’*Z+ 0,O band, a I5 x 15 matrix was diagonal- ized, involving levels of 3C+, 3 C - , ’A and 3Fl states. Multiple interactions were also considered by Field in the isovalent case of CO,’ but here the diminished spin-orbit coupling leads to a smaller number of interacting levels being involved.In Si0,3 the increased spatial separation of the n and 0 outer orbitals gives rise to reduced spin-orbit interactions, so that singlet-triplet transitions become essentially forbidden in this case. 1 would like to ask Dr. Clyne if in the detailed perturbation analysis of the SnO bands, at present underway, it has been necessary to introduce multi-level perturbations as in the case of CS. D. Cossart and T. Bergeman, J . Cliem. Phys., 1976, 65, 5462; T. Bergeman and D. Cossart, J. Mol. Spectrosc., 1981, 87, 119. R. W. Field, A. Lagerqvist and J. Renhorn, Phys. SCI.., 1976, 14, 298. ’ R. W. Field, B. S. Wicke, J. D. Simmonds and S. G. Tilford, J. Mol. Spectrosc., 1972,44, 383. Dr.M. A. A. Clyne (Queen Marl? College, London) said: At the present time, there is considerably less knowledge of the potential energy functions of states of SnO than of states of CO, CS and SiO. Continuation of the present work on SnO is intended to remedy this situation. In the meanwhile, it is not possible definitely to exclude the possibility of interactions in SnO involving more than two states.3 50 GENERAL DISCUSSION Prof. R. W. Field (M.I.T., Cambridge) said: For various reasons, laser techniques are well-suited for detecting and providing rotational assignments of “ extra lines ” near perturbations. These lines can provide crucial information about the perturbation, often of greater value than that from main lines. Careful searches for extra lines should always be made and, when found, their frequencies should be reported.At an intermediate stage of a perturbation analysis, it is often useful to prepare a graphical display of the energy levels derived from the assigned lines. One of the most straightforward of such displays is a reduced term-value plot: E,, - Beslimated J(J + 1) against J(J + 1). The advantage of such a plot is that it displays the per- turbation effects clearly. Each plotted point is derived from one assigned line, not from complicated sums and differences of lines. When lines are missing or only tentatively assigned, the more complex graphical presentations can be confusing. The preliminary values of band origins and rotational constants obtained from such plots are probably not necessary as initial values for a proper least-squares deperturba- tion.Adequate initial estimates may usually be made by inspection from the reduced term-value plot. Dr. M. A. A. Clyne (Queen Mary College, London) said: One particularly interest- ing aspect of the detection of perturbations by laser-induced fluorescence is lifetime determinations. ‘ A relatively weak perturbation, not sufficient to show as a detect- able shift in the relevant molecular energy level, should be clearly apparent as an abnormal lifetime when the upper (d, J’) state is excited. Of course, in such studies, it is necessary to use nearly collision-free conditions, in order to eliminate rotational energy transfer. Investigations of this type on SnO are planned in the near future. The excited B311(O+) states of the interhalogens (e.g.BrF, 1F)’ and halogens (e.g. I,, Br,, Cl,)’ provide interesting examples where perturbations or predissociations are clearly seen from lifetime abnormalities, whilst no detectable shifts in the corres- ponding molecular energy levels are observed. Regarding the presentation of data in perturbation analysis, Field’s suggested procedure would appear to be simpler than that adopted in our paper. It is quite similar to that used in fig. 7(a) of our paper, however. M. A. A. Clyne and I. S. McDermid, J. Chem. Soc. Faraday Trans 2., 1978, 74, 1376, 1644. M. A. A. Clyne and M. C. Heaven, J. Chem. SOC. Faraday Trans 2., 1978, 74, 1992. Prof. R. W. Field (M.I.T., Cambridge) said: Laser excitation spectra are generally recorded as two (or more) simultaneous channels of information: the un- known spectrum and calibration markers (Fabry-Perot fringes, I, or Te, spectra).The signal-to-noise ratio, particularly in the calibration channel, is likely to be ex- tremely high. One is obligated to calibrate the unknown spectrum at a precision limited only by the quality of the unknown spectrum, not by the frequency calibration channel. An upper bound on the uncertainty is giveti by the line f.w.h.m. divided by the signal-to-noise ratio and degraded by uncertainties about lineshapes and possi- bilities of unsuspected blends. It is not uncommon that a blend-free, hyperfine- free, Doppler-limited (0.02 cm- f.w. h.m.) spectrum warrants relative precision of Such precision, although prob- ably routinely available over < l cm-I intervals, cannot be obtained by trusting the linearity of a pressure read-out or the constancy of a Fabry-Perot free spectral range.Careful consistency checks must be performed so that laser spectroscopists know what their limiting precision is and how to define it as a function of the width of a spanned frequency interval. Unfortunately, spectrum-quality-limited precision cm-’, which corresponds to a few parts in lo9.GENERAL DISCUSSION 35 1 means many decimals; but, if the precision becomes routine, it is available and can be taken for granted until the electronic structural picture demands it. Prof. T. E. Gough (Waterloo University) said: While it is, of course, important that experimental laser spectroscopists produce data at the highest level of precision offered by their techniques, it is equally important that this precision not be over- stated.The quantity full-width-half-maximum (f.w.h.m. divided by signal-to-noise ratio) has gained acceptance as being indicative of the precision available from an experiment. However, this precision will often be degraded by inferior scanning characteristics of a laser, and by systematic effects such as pressure shifts. Further- more, should the observed transition contain unresolved structure, it will be necessary to have independent information concerning the details of this structure before the structure-free line position can be known. Dr. M. A. A. Clyne (Queen Mary College, London) said: In principle, it is clearly desirable that the accuracy and precision of frequency measurements in the calibra- tion of spectra should exceed the available spectral resolution.In practice, this ideal may not be achieved, at least in an initial phase of a new investigation. It may be considered to be desirable to conduct an initial survey, before attempting the most accurate possible measurements. Accurate frequency calibration of scannable lasers involves the satisfaction of a number of criteria, including the achievement of linearity of the scanning system, usually involving etalons. Use of a pressure-scanning laser is desirable, since the refractive indices of most scan gases are accurately linear with pressure, and pressure transducers with linearity to better than 0.S'x are available. The effect of temperature variations on such a pressure-scanned laser should be minimized by use of a massive enclosure for the scanning assembly.The linearity of a scanning laser can readily be investigated with one or more confocal interferometers, as was done in the present work. However, the stability of available confocal interferometers provides a limit to the accuracy of such measurements. Prof. R. Back (Laboratoire de Syectrometrie Ionique et Moleculaire, Villeurbanne) said: The spectral resolution of measurements obtained in Dr. Engelke's group of the order of 0.001 cm-I (= 30 MHz) is approaching the natural linewidth for the alkali dimer transitions observed. But a 30 MHz resolution is not a limit imposed by the Doppler width of a supersonic beam. We are currently using an I 2 supersonic beam for high-resolution spectroscopic studies.Our residual linewidth, of the order of 1 MHz, is not due to the Doppler width of the molecular beam ( < I MHz) or the natural lifetime (<0.1 MHz), but is limited by the exciting laser. These supersonic molecular beams are extremely powerful tools when used in spectrosopic studies. One reason is the high throughput of molecules along the axis of the nozzle. Thus very small residual Doppler widths may be obtained without a great loss of beam density. For example, thanks to a high signal-to-noise ratio, we have observed 220 hyperfine components belonging to nine iodine BO,+-XlC,+ lines excited by the 501.7 nm Ar+ laser line.' A number of these lines could not be ob- served using the usual sub-Doppler spectroscopic techniques such as saturated ab- sorption.With these data we have been able to determine the evolution of the hyperfine structure as the levels approach the dissociation limit of the iodine BO,+ state. We have even determined hyperfine structure parameters for one level352 GENERAL DISCUSSION above the rotationless dissociation limit. The results give surprisingly good agree- ment with theoretical magnetic hyperfine interaction predictions. Another interesting point is the control one has over the populations of the rovi- brational levels of the XII=,+ ground state. Population variations may be obtained by modifying the gas pressure, the size of the nozzle and the temperature in the exit region. Since rotational relaxation is by far more efficient than vibrational relaxa- tion in the expansion process, significant populations in higher vibrational levels of the ground state may be produced with low rotational temperatures.This is useful to excite BO,+ vibrational levels that are inaccessible, due to poor Franck-Condon factors, from room-temperature population distributions. ' J. P. Pique, F. Hartmann, R. Back and S. Churassy, Opt. Commun., 1981, 36, 354. Dr. F. Engelke (Bielefeld University) said : Not having a Fabry-Perot interfero- meter of sufficiently small free spectral range, it is impossible for us to give an exact value for the highest resolution we can obtain with the present experimental arrange- ment. It was possible for us, however, to evaluate the performance of the setup for a similar arrangement in which the dye-laser system was employed for optically pump- ing lithium atoms.For an excitation wavelength II = 6.7 x lo-' cm, the Doppler shift v = vO/A is 2 x lo3 19 MHz. With 8 = 0.004 rad, based on a collimation ratio of 100, the resultant Doppler broadening is Av < 20 MHz. To approach Prof. Bacis's value of <1 MHz a collimation ratio of ca. 1000 is necessary, a good value for molecular beams. The natural linewidth is 5.9 MHz in the case of lithium, based on the spontaneous transi- tion probability A = 3.72 x lo7 s-l quoted in ref. (1). The laser was stabilized to a width of ca. 1 MHz for the optical pumping experiment. We calculated a width of 25 MHz, which is consistent with our ability to fully resolve the hyperfine splitting of the 6Li 2P1,2 state, which is 26.2 MHz.In our alkali dimer experiments presented at this discussion, the resolution is less, as the laser system is not stabilized but is allowed to scan freely. These atoms had a thermal velocity v = 2 x lo5 cm s-l. ' W. L. Wiese, M. W. Smith and B. M . Glennon, Afomic Transition Probabilities, vol. 1, Hydrogen through Neon (U.S. Dept. o f Commerce, N.B.S., Washington, D.C., 1966). Dr. F. Engelke, Mr. H. Hage (Bielefeld University) and Prof. C. D. Caldwell (Yale University, New Haven) said: A particularly intriguing perturbation is that between the A'C: and b3H, states of Na,. Mulliken' postulated that a 311- manifold lies near the A'C: state. Carroll2 suggested that the perturbing state is a b3110u. No direct observations of optical transitions between the 311u and the ground state, XIC,+, have been made since this is a " forbidden " singlet-triplet transition.High- resolution absorption studies of A-X have been carried out by Kusch and H e ~ s e l . ~ These, together with the high-resolution modulated population spectroscopy of Kaminsky et aL4 and the earlier magnetic-rotation stu~iies,~ have shown that there are indeed strong perturbations in the A T , + . Through laser-induced fluorescence (LIF) in a supersonic beam of sodium, we have directly observed intercombination bands of the b311,-X1C9+ system in Na,. These observations indicate that the perturbations of AIC,+ are caused by the b3110u, b3r11, and b3n2, states. The information derived from the rotationally assigned perturbed main ( A - X ) and " extra " (b-X) lines is displayed in fig.20. The term energies, T, associated with different u(A) and u(b) levels are plotted against J ( J + 1). Neglecting 6-A interaction effects, term values associated with a given vibrational level should fall on a straight353 GENERAL DISCUSSION lbooo ___ L - 5- -- 3--- --- _+-- 40 45 50 55 .----.?--2O 25 30 35 __-- 1 --- __-- -_-- 0--- , , , I I , , , , l j l line with slope B, and intercept T,, where B and T are, respectively, the rotational constant and rotationless term energy. The crossing diagram shown in fig. 20 permits the observed intercombination (" extra ") lines to be grouped into common vibrational levels of the perturbing b3&, b3111, and b3r12, states. Since parity is rigorously a good quantum number for perturbations and the '2: state possesses only e-parity levels, we observe only the e levels of b3n,.The matrix elements for perturbations of a 'C,+ state by an intermediate Hund's case " a-b " 311u state are largest for the nominal 3110u substate, smaller and J de- pendent for 3111u, and even smaller (often undetectable except at high J values) for 3112u, perturbations are detected in our case, see fig. 20; this identification is consistent with a regular 313,, state with A , w7.8 cm-l. It is evident that all of the important information about the b313, states is obtainable directly from fig. 20. We have used a model perturbation Hamiltonian matrix and least-squares fit the eigenvalues of this matrix to the observed term energies.6 Thus, we derive highly precise information for these states.In addition to Te(b3110,-X1C,+) = 13 670.1 1 cm-', the following constants are the most important ones for the b3JIOu substate: we = 152.76 cm-', coexe3 = 0.44 cm-I, Be = 0.147 cm-', Re = 3.159 A and D, = 1.220 eV. RKR potential curves have been constructed and calculated overlaps (&A) give evidence that the only acceptable vibrational numbering within the 311u states is the one presented in fig, 20. The above set of preliminary values of the Na, b3n, molecu- lar constants permits various pseudopotential '.* and ab initio9 calculations to be rigorously tested so that we can judge how reliable are present theoretical estimates. R. S. Mulliken, Rev. Mod. Phys., 1932, 4, 16. P. Kusch and M. M. Hessel, J. Chem. Phys., 1975, 63, 4087.' T. Carroll, Phys. Rev., 1937, 52, 822.354 GENERAL DISCUSSION M. E. Kaminsky, R. T. Hawkins, F. V. Kowalski and A. L. Schawlow, Phys. Rev. Lett., 1976, 36, 671. W. R. Fredrickson and C. R. Stannard, Phys. Reo., 1933,44, 632. F. Engelke, H. Hage and C. D. Caldwell, Chem. Phys., 1981, submitted for publication. A. C . Roach, J. Mol. Spectrosc., 1972, 42, 27. D. D. Konowalow, M. E. Rosenkrantz and M. L. Olson, J. Chem, Phys., 1980, 72, 2612. ' 3. N. Bardsley, B. R. Junker and D. W. Norcross, Chern. Phys. Lett., 1976, 37, 502. Dr. M. S . Child (Oxford University) said: Dr. Engelke referred during his pre- sentation to the earlier observation' of structured continuum D1n --+ a3C emission by the molecule NaK, which goes over at short wavelengths to a discrete spectrum giving rise to an RKR curve for the shallow van der Waal's potential for the a3C state.2 1 wonder whether Dr.Engelke can comment on the perturbations in the D1l3 state, because Dr. H. Essen, Prof. R. J. Le Roy and I have developed a new semi-classi- cal method3 for direct recovery of' repulsive curves from structural continuum spectra, and the results appear inconsistent with the above observations. This method requires knowledge of the peak positions in the spectrum, the potential curve for the emitting state, and an assignment of the emitting vibrational level, which was taken on energetic grounds as u' = 12 of the D'II state. As a test of the reliability of the resulting a3C curve, represented by the solid line in fig. 21, the continuum emission spectrum was calculated numerically; the agreement between calculated and experimental peak positions is seen to be excellent.We also find that I E i3' -14000 -15000 -14000 c -160001 -16000l 1 I I I I 3.0 4.0 5.0 v4 I <nIP 10 I RIA FIG. 21.-Potential curves for the D'Il --f a3C emission spectrum of NaK. The new inversion method yields the continuous (-) n3C curve; the dashed (- - -) curve is obtained by the continuum reflection approximation; and the dot-dashed (-.---) curve shows the repulsive branch of the cr3C RKR curve.' The panel to the left shows an exactly calculated spectrum derived from the a3C curve in relation to the experimental peak positions, marked by arrows.GENERAL DISCUSSION 3 55 application of the simple reflection approximation based on the same upper-state assignment yields the markedly different (dashed) curve.Thus the reflection approximation would be seriously unreliable for this system. On the other hand, our recovered a3C repulsive curve does not connect with the repulsive branch of the RKR a3Z weakly bound potential. The most likely source of this discrepancy seems to us to be the D"Il(u' = 12) upper-state assignment, because the presence of the perturbations indicates a nearby triplet state. Is there any prospect of analysis of these perturbations to provide information on a possible emitting vibrational level with triplet character? E. J. Breford and F. Engelke, Ciiem. Phys. Lett., 1978, 53, 282. E. J. Breford and F . Engelke, J. Chem. PAYS., 1979, 71, 1994. G. Herzberg, Spectra of Diatomic Molecules (Van Nostrand, New York, 1950).' H. Essen, R. J. Le Roy and M. S. Child, to be published. Dr. F. Engelke (Bielefeld Uniuersity) said: Dr. Child (because of an incorrect assumption we made in our first presentation of D1H-a3C+ emission by NaK') assumes the potential curve of the perturbed excited state, which causes the radiative transition to the a3C+ state, to be almost identical with that of the D1n state. How- ever, as shown in the analysis of the discrete spectrum2-4 this assumption is inconsis- tent with the observed equilibrium internuclear distance of the lower state and the outer turning point of the excited Dill state. Analysis of the fluorescence spectra of the transitions to the a3X+ state determines the molecular constants of the a3C+ state; we have constructed the potential curve in the bound region by the RKR method.2 It has not been necessary so far to distinguish explicitly the D1n and the d 3 n , states or to assume them to be closely parallel.The spin-orbit interaction for the strong perturbation between the and 3n states has been discussed; the radiative transition to the a3C+ state occurs following a radiation excitation to the d 3 n , state. As shown recently by Katb and Noda4 the observed and calculated intensity distribu- tion for the discrete spectrum and the bound-continuum transition depends strongly on the vibrational-rotational level of the d3n, state. Following their analysis the mixing of the two unperturbed wavefunctions v(D1Il) and t,~('Il~) occurs at the pseudocrossing of the potential curves of the and the 311i states near the left turning point of the D1n, u' = 12 level.The eigenfunctions of the perturbed states are linear combinations and The wavefunctions w('n) and t , ~ ( ~ I l ~ ) are functions of intermolecular distance R. The right turning point is determined from the calculated intensities of discrete fluorescence lines compared with the observed ones. The vibrational quantum number is identified to be 13. The preliminary molecular constants of the potential curve of the d3n, state are LL), = 64 cm-', D, = 1960 cm-I and Re = 4.19 A, respec- tively. However, more extensive work on different perturbed levels is necessary to de- termine the potential energy curve(s) and perturbing interaction precisely. Dr.Child's calculation determines the continuum part of the a3C+ potential-energy curve. We believe that use of the molecular constants given above is essential to analyse the observed spectra. w1 = Gly('n) -I- G ~ , M ( ~ ~ A t , ~ 2 = - - 2 v / ( W + Gt,~(~nd. E. J. Breford and F. Engelke, Chem. Phys. Lett., 1978, 53, 282. E. J. Breford and F. Engelke, J. Chen?. Phys., 1979, 71, 1994. D. Eisel, D. Zevgolis and W. Demtroder, J. Chem. Phys., 1979, 71, 2005. H. Kat6 and C. Noda, J. Chern. Phys., 1980, 73, 4940.356 GENERAL DISCUSSION Prof. R. W. Field (M.I.T., Cambridge) said: When a perturbed level is viewed as a mixture of vibrational eigenstates of two diabatic potentials certain of its properties are a weighted average of those of basis states 1 and 2, others appear to be purely those of state 1, and still others, those of state 2.The mixing coefficients C are independent of internuclear distance R. For the particular case of a nominal level, perturbed by only one vibrational level of 3111, undergoing an electric dipole transition to a pure 3C lower-lying state, the relevant vibrational wave- function for calculation of Franck-Condon factors is that of the 311 state, regardless of the size of the mixing coefficient. If, however, the lower state is contaminated by a singlet perturber or the upper state contains a significant admixture of several vi- brational levels of the 311 perturber, then calculation of vibrational intensity factors becomes very complicated. All components can contribute in proportion to their mixing coefficient squared, and all spin-allowed transition amplitudes can interfere through cross-terms.In no case, however, is a weighted average of the vibrational wavefunctions of the contributing vibrational basis functions appropriate. vJperturbed = CIVI(~; R)xI~,(R) + C2~2(r; R)x~V~(R) Dr. F. Engelke (Bielefeld University) said: In addition to the strong emission features in the green region due to the D1ll-XIC+ band system of NaK, weaker transitions appear in the red region between 625 and 720 nm for different laser lines including 467.5,'-3 488, 496.5, 501.7 and 514.5 nm.495 On closer examination, most of these features are observed to have regularfy spaced maxima and minima of the oscillatory structure associated with bound-continuum emission and often look like an admixture of the singlet vibrational level to the triplet vibrational level.As Prof. Field pointed out it is necessary that the lower a3C+ state is contaminated by a singlet perturber (XiC+). 3C+-1Z* perturbations occur if a nearby 311 (or In or 3Cc-) state perturbs both u 3C+ and X'Z+. Such perturbations are weak and rarely ob- served. During this discussion we present such a perturbation analysis between A'C: and b3nU states of Na2.6 If we consider that the states involved in spectroscopic studies of heteronuclear alkali dimer do not have gerade or ungerade parity, it is possible that the perturbations equivalent to the observed Na, A'C; - b3H, may ad- mix X'C+, a3C+ and b311 character into the lowest triplet state of NaK; however, in homonuclear alkali dimers, mixing of X 'CJ zjia b 3171, and a 'Zcf is strongly for- bidden by the u t[+ g selection rule for perturbations.E. J. Breford and F. Engelke, Chenr. Phys. Left., 1978, 53, 282. E. J. Breford and F. Engelke, J . Chent. Phys., 1979, 71, 1994. D. Eisel, D. Zevgolis and W. Demtroder, J. Chern. Phys., 1979, 71, 2005. M. M. Hessel and S, Giraud-Cotton, NaK Revisited: The Ground '1;+ and D'II States, preprint. E. J . Breford, Thesis (Universitat Bielefeld, 1981). F. Engelke, H. Hage and C. D. Caldwell, Faraday Discuss. Chern. SOC, 1981, 71, 352. Prof. J. Winn (University of Culifornia) said: It is known from molecular-beam electric resonance studies' that the ground states of the mixed alkali dimers have surprisingly large dipole moments (e.g. NaLi, 0.47 D ; KNa, 2.76 D; CsNa, 4.75 D).This means that the diatomic potential-energy curve must change shape rather dramatically from R-6 behaviour at very long range to something quite different at intermediate to short distances. It would be very instructive to know over what region of R this ionic character becomes manifest. Can Dr. Engelke tell from his ground-state analyses at what distance the R-6 behaviour ceases and the ionic be- haviour dominates the shape of the potential curve? P. J . Dagdigian, J. Graff and L. Wharton, J . Chent. Pliys., 1971, 55, 4980; P. J. Dagdigian and L. Wharton, J. Chem. Phys., 1972, 57, 1487.GENERAL DISCUSSION 357 Dr. F. Engelke (Bielefeld Uniuersity) said: We have determined some rotational constants of mixed alkali dimer from laser-induced fluorescence (LIF) spectra and give them in table 4 below.Using data from molecular-beam electric and mag- TABLE 4.-DIPOLE MOMENTS (D) FOR SELECTED MIXED ALKALI DIMER MM' MM' Cro21Bo Bo/cm - P O D Bo/cm-' POIaD ref. (1) and (3) ref. (1) and (3) ref. (1) and (3) this work this work 23Na7Li (2.7740 & 0.004) x 0.394 0.463 0.3764 0.4525 ( 5 ) 39K7Li (2.267 f 0.002) x 0.265 3.45 0.2638 3.447 (3) s5Rb7Li (3.964 i- 0.004) x 0.218 4.00 39K23Na (3.966 f 0.004) x 0.0968 2.76 0.09499 2.735 (2) - - a o uncertainty in parentheses. netic-resonance studies the dipole moments deduced, are given in the last column of table 4. Effective utilization of the long-range analysis4 requires a knowledge of the absolute vibrational-rotational numbering near dissociation.LI F spectra are observed for this region and correct vibrational-rotational numbering is achieved by utilizing asymptotic formulas for vibrational and rotational energies near dissociation for NaK and KLi; in addition for NaLi isotopic shift formulae' are used. These techniques allow determination of c6 and, roughly, cs/cb. The results obtained from these fits show that the dominant R-6 behaviour in all cases ceases at a distance R ;L 2.5 Re where Re is the equilibrium distance of the ground state. Unfortunately there are no experimental data available for homonuclear alkali dimer molecules to study long-range forces. It is possible that mixed alkali dimer potential curves in the ground state as well as in excited 'C+ states have observably different shapes from those of the homonuclear dimer due to the ionic character of the bond.However, more extensive work on high-lying vibrational-rotational levels in ground states of homonuclear a1 kali dimer are necessary to determine their long-range interaction and potential-energy curves precisely. P. J. Dagdigian, J. Graff and L. Wharton, J . Cliein. Phys., 1971, 55, 4980. R. A. Brooks, C. H . Anderson and N. F. Ramsey, J . Chem. Pliys., 1972, 56, 5193. P. J. Dagdigian and L. Wharton, J . Chertz. Pliys., 1972, 57, 1487. R. J. LeRoy and R. B. Bernstein, J . Cheni. Phys., 1970, 52, 3869. Burlington House, London, 1973), vol. I . ' R. J. LeRoy, in Molecular Spectroscopy (Specialist Periodical Report, The Chemical Society, Dr. D. L. Cooper (Oxford University) said: Can Dr. Engelke obtain any informa- tion from his experiments concerning the magnitude of the perturbations between the various electronic states, and concerning the shapes of the interacting potentials ? Dr.F. Engelke (Bielefeld University) said : We have experimentally demonstrated the assignment of perturbations in the D'n state of NaK' and in the A'C: state of Na,.'p3 In both cases the perturbing state was shown to be 311, for which the molecu- lar constants are determined and given during this Discussion. The possible states responsible for perturbing the NaLi B'II state are 311, 3C+ and 'C+. Interaction of a 'C+ state with a I l l state would affect only one of the A components, while interaction with 311 or 3C+ would perturb both components. Because P and R lines are per- turbed, whereas Q lines appear to have the position and relative intensities that are expected for an unperturbed system, we conclude that a 'C+ state is responsible for358 GENERAL DISCUSSION causing the perturbation seen.However, more extensive work on the perturbed energy levels is necessary to test this hypothesis, to determine the spectroscopic constants and to calculate the potential energy curves involved precisely. Ab initio calculations in mixed alkali dimers have indicated that the lowest Ill state lies sig- nificantly above the first excited 'C+ state (A%+), thus, perturbations are probably due to the second excited 'C+ state (CIC+). E. J. Breford and F. Engelke, J. Chem. Phys., 1979, 71, 1994. F. Engelke, H. Hage and C. D. Caldwell, Faraday Discuss.Chem. Soc., 1981, 71, 352. ' F. Engelke, H. Hage and C. D. Caldwell, Chem. Phys., 1981, submitted for publication. Dr. J. H. D. Eland (Oxford University) (communicated): From Dr. Jungen's results on H2 it is clear that perturbations allow vibrational autoionization with almost any Av; nevertheless the smallest changes in v still predominate in the branching ratios, and large Av produce narrow peaks. Is it therefore correct to expect that in cases where neutral predissociation is relatively strong, as in NO, resonances requir- ing Av < - 1 for autoionization will tend to be predissociated? Dr. Ch. Jungen (Universite' Paris-Sud, Orsay) (communicated) : This depends on whether predissociation is weak or strong. In the case of H2 where predissociation is a weak process (arising from the same rotation-vibration-electron coupling which is also responsible for the rotational-vibrational preionisation) Dr. Eland's remark is certainly correct, as shown by the discussion given in section 3.1 of our paper (cf.in particular the last two columns of table 1). Here of course molecular fluorescence is an additional successful competitor in the de-excitation process. On the other hand, I do not think that Dr. Eland's remark applies to the case of NO where predissociation is much stronger (it arises here from an electrostatic mixing of Rydberg and non- Rydberg electron configurations which is absent in the ungerade states of H2). In fact, A. Giusti in our laboratory has recently been able to show' that in NO the Rydberg-non-Rydberg interaction dominates to the extent that it is responsible not only for the (strong) predissociation but also induces the (weak) preionisation, as an indirect process whereby a Rydberg level becomes coupled to the ionisation continuum via the dissociative channel.Under these circumstances the magnitude of Av is of no importance whatsoever. A. Giusti and Ch. Jungen, in preparation; cf. also A. Giusti, J. Phys. B, 1980, 13, 3867. Prof. T. E. Gough (Waterloo University) said: I address Drs. Child and Quack. It has been suggested that, at high levels of vibrational excitation, the infrared spectrum of a molecule will show either line-broadening or additional structure not adequately described by a normal-mode approach. Can one estimate how large a molecule must be before such effects are observable using sub-Doppler resolution infrared spectroscopy around 3500 cm-l? Dr.G. Duxbury (Strathclyde University) said: The circumstances in which the local-mode approximation is valid are similar to those described by Hershbach and Laurie' in their treatment of the inertia defect in molecules. Hershbach and Laurie defined two coupling regimes, that of " dominant coupling " and of " uniform coup- ling ". Water, which is a good example of " local-mode " behaviour is classified as an example of " dominant coupling ", where t12 z 0 and tZ3 z 1 , and where the hydrogen atoms move almost parallel to the bonds for cul and co3 and perpendicular for m2. SO2 on the other hand belongs to the " uniform coupling" limit, which is where the present authors find the normal mode model to be more applicable.D. Hershbach and V. W. Laurie, J. Chem. Phys., 1964, 40, 3142.GENERAL DISCUSSION 3 59 Dr. M. Quack (University of Giittingen) said : I shall confine my remarks to certain dynamical consequences of the model of local vibrations discussed in the paper of Child and Lawt0n.l The situation presented by Dr. Child is briefly as follows: In polyatomic molecules containing two equal bonds, such as H20, SOz, C2H2 etc., certain vibrational eigenstates appear in nearly degenerate pairs (I shall omit in the following some symmetry considerations that would be useful in addition). A linear superposition of two such states corresponds to a wavefunction, which is largely localized in one bond. This time-dependent state is a local vibrational state.The excitation is transferred to the other bond during a time interval (2/2) = h/2AE, where AE is the splitting of the nearly degenerate pair of eigenstates. The time dependence is periodic with period z. The splitting decreases with vibrational excitation, indicating an increasing validity of the local vibrational description. For instance, for H,O a corresponding increase of z from 0.5 ps at v = 1 to ca. 30 ns at u = 8 has been found.' On time-scales short compared with this an initially local- ized vibrational excitation would remain in one bond or local mode. The model of Child and Lawton appears to be consistent and appears to fit well the experimental data which they quote, It certainly is an interesting addition to the ordinary treatment of norniul ztibrutional states of polyatomic molecules [see also ref.(2) and (3)J However, in general the view of an increasingly long-lived local bond excitation at high energies in polyatomic molecules is in conflict with our present understanding of the time-dependent dynamics of highly excited polyatomic niole- c~iles.'~ As an example, 1 might mention the recombination, say, of a hydrogen atom with a methyl radical M H + CH3 --f (CHJ* -+ CH4. Clearly, initially only one hydrogen is " locally excited " with respect to the frame. If the transfer of this local excitation to other vibrations in the highly vibrationally excited complex CHq* were slow (nanosecond time-scale, see above), the recombina- tion of a polyatomic molecule, eqn (l), would be qualitatively similar in its pressure dependence to the recombination of diatomic molecules (say H + H + M, etc.), since essentially, on the time-scales of interest, only one bond would be involved.This is known not to be the case.5 Therefore, although the long-lived local state description appears to work well for the cases treated by Child and Lawton, other concepts may be required at still higher vibrational excitation and larger vibrational densities of states in polyatomic molecules quite generally. I shall put forward here as a constructive suggestion the concept of the global vibrational state and point out some of the spectroscopic and dynamical consequences, which are under current investigation in our This discussion may help to resolve some of the difficulties which arise when one tries to describe highly ex- cited polyatomic molecules by either normal or local vibrational states.Instead of discussing the specific interactions between subsets of nearly degenerate zero-order states of two or more local vibrations with equal frequency, I shall concentrate here first on the interaction of zero-order states of one high frequency (local or normal) vibrational state Iu,O, 0, . . .} with all overtone and combination states of the low- frequency vibrations 10, x, y , . . .} in a polyatomic molecule. Subject to realistic assumptions about non-local, anharmonic, vibrational or generally rovibrational couplings, it can be shown' that if the average spacing 6 between these states becomes smaller than a certain value, one will get a global interaction and mixing among many nearly degenerate states.As an example I may mention the case of the C-H vibration in (CF3)3C-H, where the average vibrational spacings are 6 = cm-' for v = 1 and 6 = lov9 cm-' for u = 2, subject to symmetry conditions for360 GENERAL DISCUSSION allowed couplings, which do not change the orders of magnitude.6 With such close spacings of background states the situation becomes fairly similar (not identical) to radiationless electronic transition^,^ predissociation1° or preionization." Fig. 22 -10 - 5 0 5 10 (a - wo)/V FIG. 22.-Model spectrum arising from the interaction of one optically active (local or normal) vibrational state with many optically inactive background states (equal couplings, equal spacings).v = 6. shows the resulting many-line spectrum if one assumes equal coupling Y of the high- frequency vibrational state to all background states (equal spacing 6). One has a Lorentzian envelope of width r. The width corresponds to an initial exponential decay of local excitation with a rate coefficient k = l/zd =r/ti (experimentally, the local excitation might be produced by a coherent, short light pulse). The underlying assumptions are not quite realistic, but the model can be solved by closed expressions.' A more realistic assumption would use irregular coupling matrix elements (some large IVI, some small IVI, with irregular phase factors or signs, since the background states are of a very different nature). A typical resulting many-line spectrum is shown in fig.23. This looks very L -15 -10 (0 -coo)/ V FIG. 23.-As fig. 22, but from diagonalizing a hamiltonian with irregularly distributed coupling matrix elements. different from the artificial fig. 22, yet the initial decay of a local vibrational excitation is essentially the same. This is shown in fig. 24 [pn is the population of a local state with pn(0) = 1 and pn = c,cX, diagonal element of the density matrix in the basis of local states]. At longer times, the irregular spectrum leads to larger fluctuationsGENERAL DISCUSSION 36 1 but not to the pronounced recurrence, occurring for the regular spectrum at Vt = 2n (the recurrence of probability would be complete for an infinite, regular m ~ d e l ) . ~ The physically relevant result is the initial decay, since with many coupled states any recovery of probability of the initial " local " state is quite negligible.Experimentally, we have found for molecules in the series C,F,X,-H vibrational band-widths of the order of a few cm-I for the fundamental and up to tens of cm-' for overtones of the 1 . 0 7 I Vf FIG. 24.-Time-dependent population of an initially populated local state for the two spectra in fig. 22 (regular) and fig. 23 (irregular): (a) irregular, (b) regular. C-H local vibration, which is essentially also a normal vibration in these molecules.6 Although part of the experimental structure is " inhomogeneous " [see ref. (6) for proper definitions], temperature-dependent studies indicate a substantial " homo- geneous " contribution, i.e. lifetimes of local vibrational states of picoseconds and less (but not nanoseconds and more at high excitations).This is also consistent with more difficult to interpret findings for high overtone absorptions in benzene.I2 The view of vibrational i.r.-absorption band structures of possibly fairly large width (instead of one vibrational state and rotational fine structure only) has been advanced for polyatomic molecules in particular in connection with unimolecular reactions induced by monochromatic infrared radiation.13 The coarse and fine structures of these band systems are of crucial importance for the dynamics of i.r.-laser excitation of polyatomic molecules. Fig. 25 shows a model spectrum for a situation which is more directly related to - 10 - 5 I 5 to (0 - ~ 0 , ) i V FIG. 25.-Spectrum arising from the interaction of two local states (degenerate in zero order) with many background states (optically inactive).362 GENERAL DISCUSSION the paper of Child and Lawton.Two local vibrational states (fundamentals or overtones) are very weakly coupled with each other, but also coupled to many back- ground states of low frequency vibrations. One may think of a molecule H-CX2- (chain)-CY,-H or similar. The spectrum does not look qualitatively different from the previous ones: in particular there is no prominent doublet structure corre- sponding to the degenerate zero-order local states. Furthermore, the corresponding time dependence is characterized again by a fast initial exponential decay of a local state. This does, of course, not imply fast transfer of excitation to the other local state.In fact, such a transfer is negligible on practical time-scales. The question may arise, whether the coupling between one local state and the majority of other vibrational states of very high density is so weak that it is completely negligible. This might then invalidate the above considerations. Whereas a com- plete, realistic model treatment of intramolecular couplings in polyatomic molecules will be given elsewhere,8 I may illustrate in a simple manner, which kind of mechani- cal global couplings can arise. The initial local state may be weakly coupled to a small subset one of states, but not to any further subsets of states. Nevertheless the states in subset one will be coupled to subset two and so forth.This then gives rise to the spectrum shown in fig. 26 and again the same fast initial decay of a local excitation (a - %)/V FIG. 26.-Spectrum of eigenstates and intensities arising from the coupling model as indicated in the figure and discussed in the text. as shown in fig. 24. similar results.8 Many further coupling schemes have been investigated with I now briefly consider the nature of the various " states " discussed above. (1) The eigenstates of the (ro)vibrational hamiltonian correspond to the individual sharp lines in the spectra shown. They are time-independent, subject to their natural lifetime and width with respect to spontaneous emission. The wavefunctions are different for every eigenstate but on the whole globally distributed over the entire molecule.We may therefore call these states global vibrational states (including rotation one has global rovibrational states, restricted by angular-momentum selec- tion rules). One might be tempted to think of ergodicity in this context, but this temptation should be resisted. I should also stress that the lines in the spectra are not all equally intense, the large majority is quite weak, and they are not equally spaced. The eigenstates are not similar in nature but they are all global, of a non-localized nature.GENERAL DISCUSSJON 363 ( 2 ) A local vibrational state can be created (in a “ thought-experiment ” or in reality) as a time-dependent superposition state of finite energy bandwidth (amplitude of vibration localized in one bond at t = 0). I conjecture that this local state will decay in general quickly (picoseconds in highly excited molecules).The same would be true for a normal vibrational state somehow created at t = 0. In that sense normal and local states do exist but are short-lived. (3) One may further consider the states of large-energy band-width created in (2) but at times long compared to the decay times of the local or normal excitations. Averaged over some time interval (time coarse-graining) the probability density of such a state will again be globally distributed over the entire molecule. The same is true for a statistical mixture of finite energy bandwidth (diagonal density matrix, energy coarse-graining). These states may still be termed (coarse-grained) global vibrational states and are best treated by the methods of statistical mechanics.8 Table 5 gives a summary of the predictions of the two different views concerning TABLE 5.-cONCEPTS FOR VIBRATIONAL STATES (BEYOND NORMAL VIBRATIONS) observable local vibrational states global vibrational states spectral structure (energy resolved) ~ ~~~~ pairs of states, whose energy band system of many vibra- separation decreases with tional lines-envelope has a vibrational energy to very large width at all energies, small values often increasing with energy vibrational amplitude and quasi-irreversible decay of any derived observables between local states, period T initial local excitation ( T ~ (time resolved) lurge, >ns, at high energies small, ps, at high energies) periodic transfer of cxcitation range of applicability (con- some small, symmetric mole- all large polyatomic molecules jectured, to be tested ex- cules at low and moderate at moderate and high energies, perimen tal ly) energies some small molecules (all at high energies?) the “ local ” and the “ global ” states.The experimental truth could, in principle, fairly easily be established by very high-resolution spectroscopy. It turns out that there is surprisingly little definite evidence, so far, to establish the limits of applica- bility of either view. A recent high-resolution study of perturbations in the C-H fundamental of fluoroform indicates that global behaviour may start at energies as low as 3000 cm-’ even in such a small molecule under certain circumstances.’ Partly anticipating the interesting question (concerning line broadening) raised by Prof. Gough, I should point out that the observation of sharp rotational fine structure does not contradict fast relaxation of a local state.Of course, the individual rovibrational eigenstates do not relax without external perturbations, but their wave- function is global rather than local. Below the onset of the radiative or dissociative continuum, global coupling manifests itself not by line-broadening but by the appear- ance of additional lines, most of which will be weak. For instance, it has been estab- lished by Herzberg and coworkers long that molecules such as fluoroform and methylacetylene show rotational fine-structure in the high overtones of the C-H vibration in the photographic infrared. In more recent lower-resolution experiments by other authors, sometimes “ broadening ” has been invoked.This is a miscon- ception as long as the states are discrete. However, the possible role of a number364 GENERAL DISCUSSION of weak and very weak additional lines (required by the global description) still needs full elucidation even for the above mentioned, well-studied molecules, in my opinion. At very high energies, when radiative widths are large compared with energy separa- tions, or in the dissociation continuum, the concept of the time independent eigen- state of an isolated molecule loses its usefulness, whereas the time-dependent global state discussed under paragraph (3) above remains a useful concept, particularly for dynamical considerations. Nevertheless, the most intriguing questions in connection with high-resolution spectroscopy occur in the discrete spectrum, and the technique discussed in the papers of Gough et al.'' may, indeed, be one of those best suited owing to the low temperatures in the beams and the correspondingly simplified rota- tional structure.Even for molecules such as (CF3)3CH it may then become possible to go beyond the coarse bandshapes and resolve individual lines. M. S. Child and R. T. Lawton, Faraday Discuss. Chem. SOC., 1981,71, 273; R. T. Lawton and M. S. Child, Mol. Phys., 1980, 40, 773, Nuovo Cimento B, 198 I , 63, 262. ' B. R. Henry and W. Siebrand, J. Chem. Phys., 1968, 49, 5369; B. R. Henry, Acc. Chem. Res., 1977, 10, 20. R. Mecke, 2. Phys. Chem., 1932, B17, 1 . M. Quack in Moleculur Structure and Energy Scrambling, ed.J. Hinze (Plenum Press, New York, 1981); Nuovo Cimento B, 1981, 63, 358. J. Trrae, in Physical Chemistry, an Advanced Treatise, ed. W. Jost (Academic Press, New York, 1975), vol. 68. H. R. Dubal and M. Quack, Chem. Phys. Lett., 1980,72, 342. H. R. Dubal and M. Quack, Chem. Phys. Lett., 1981, 80, 439. M. Quack, to be published. M. Bixon and J. Jortner, J. Chem. Phys., 1968, 48, 715. vol 111. lo G. Herzberg, Molecular Spectru and Molecular Structure (Van Nostrand, New York, 1966) l1 Ch. Jungen and M. Raoult, Faraday Discuss, Chem. Soc., 1981, 71, 253. l2 R. G. Bray and M. J. Berry, J. Chem. Phys., 1979, 71, 4909. l3 M. Quack, J. Chem. Phys., 1978, 69, 1282. l4 G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, New York, 1945), l5 H.J. Bernstein and G. Herzberg, J. Chem. Phys., 1948, 16, 30. l6 T. E. Gough, R. E. Miller and G. Scoles, Faraday Discuss. Chem. SOC., 1981, 71, 77; Appl. vol. 11. Phys. Lett., 1977, 30, 338. Prof. I. M. Mills (Reading University) said: I would like to draw attention to the formal analogy between the local-mode matrix for a particular value of the total vibrational quantum number v = u1 + u3 = n, + n b in the water molecule, and the asymmetric-top rotational energy level matrix for a particular value of J. The local-mode doublets arise in a similar way to the asymmetry doublets of an asym- metric top, the harmonic coupling terms in the local-mode problem playing the role of the asymmetry coupling terms in the rotational problem. Thus, for example, in the right hand column of Child and Lawton's fig.1, for v = 5, the Ena, n b ] = [2, 31 and [3, 21 states are directly coupled by cross-terms in the F and G matrices and are split in first order into + and - states, but the [1, 41 and [0, 51 pairs show smaller split- tings in successively higher order of perturbation theory (third-order and fifth-order, respectively), since the coupling of each pair occurs indirectly through the other states with ZI == 5. This is analogous to the splitting of asymmetry doublets for K, = 1, 3 and 5 for J = 5 of an asymmetric top, which would split in successively higher order in a perturbation treatment. The analogy can be followed through the detailed structure of the hamiltonian matrices. This would seem to suggest that if the Lawton and Child model is successful in fitting the experimental data, then the important coupling between local modeGENERAL DISCUSSION 365 doublets is through the other local mode H-stretching levels of the same total u, and not through the dense array of vibrational states in the same region of the energy spectrum associated with other vibrational degrees of freedom in the molecule. Dr.M. S. Child (Oxford University) (coniniunicated): Dr. Quack has rightly drawn attention to possible complexities arising from very high states of excitation in small molecules and from a high density of states in larger systems. He has also usefully emphasised that knowledge of the spectrum provides insight into the intra- molecular kinetics following preparation of a non-stationary state.Perhaps I can comment on two of his observations in relation to the possible observation of local-made degeneracy as discussed in our paper. The central point in our discussion, which has also been mentioned by Prof. Mills, is that the coupling between two equivalent X-H bonds, either directly or through the agency of other modes can be quenched in its effect on the highly excited local-mode states by the bond anharmonicity. Our conclusion was that the interbond coupling must be large compared with this anharmonicity in order to disturb the local-mode picture. It is therefore important to try to assess the physical origin and the magnitude of this coupling in any counter-examples. The first case considered by Dr. Quack is the newly formed CH, molecule follow- ing H atom/CH3 radical recombination and here one can visualise strong coupling between the new CH bond vibration and the umbrella and rotational motions of the CH3 fragment, which could easily dominate the bond anharmonicity.We have here what would be described in classical terms as an irregular or stochastic motion, which is qualitatively quite different from that obtaining at the lower energies for which our model is designed. It is not easy to assess in advance, however, at which energy the stochastic behaviour will predominate for any given molecule. The second relevant case cited by Dr. Quack is illustrated in fig. 25, showing two degenerate states irregularly coupled to a dense manifold. Here the strong coupling to certain of the manifold states would constitute Fermi resonances, which could dis- turb the local mode picture.The difference between local motions in C,H, and normal motions in C2D2 is attributed in our paper to a similar effect-the CC stretch- ing frequency being much closer to the CD than the CH frequency. This is a case of two fundamentals in close resonance and the interbond coupling may be expected to decrease markedly for resonances between the XH fundamental and the first overtone of a lower-frequency mode, and even more markedly for coupling with the second, third and higher overtones. I therefore remain to be convinced that the presence of a dense manifold per se is of any relevance to the observation of our pre- dicted local-mode degeneracy ; the predominant couplings are expected to involve modes with frequencies of the same order of magnitudes as the XH vibrations, and it is the density of these states which is really relevant.Mr. J. M. Hutson (Oxford University) said: Drs. Kidd, Baht-Kurti and Shapiro have performed calculations of the excited states of the Ar HC1 complex on two different potential surfaces ; the potential of Holmgren, Waldman and Klemperer is the more realistic of these. Their computational method gives very accurate bound-state energies, but does not provide quantum numbers for the levels, so that it is difficult to relate their calculations to spectroscopic data. We have performed approximate calculations on the same potential, using an extension of our corrected Born-Oppenheimer method., Our results are not as accurate as those of Kidd et a/., but they do allow us to assign quantum numbers to the energy levels shown in tables 10 and 12 of their paper.366 GENERAL DISCUSSION Complexes such as Ar HC1 exhibit wide-amplitude bending motion, and their energy levels are characterised by three approximate quantum numbers, in addition to the total angular momentum J . These are a bending quantum number b, which correlates in the isotropic limit with the HCl rotational quantum number j ; the stretching quantum number for the van der Waals bond v ; and the body-fixed projec- tion of J, A (or K). Our assignment of the energy levels obtained by Kidd et ul. is as shown in fig. 27. 0 d ' -50 6 G - 100 v = l - v = 3 - 5- 1- 1- L- 2- 2- 3- 0- 0- 0- 1- 1- 2- b = O 1 2 b = l 2 b = 2 A= 0 A = 1 A= 2 FIG. 27.-Energy-level scheme and assignment of quantum numbers for Ar HCl. The energy levels are taken from the paper by Kidd et al. (this Discussion). Splittings due to changes in rota- tional quantum number J are not shown; for a given J , only levels with ;1 d J occur. The J = 0 levels may be separated into three sets corresponding to b = 0, 1 and 2, each being a progression in the van der Waals stretching quantum number v , and each tending to its own dissociation limit. Similar levels appear again for J > 0, shifted by BJ(J+ l), but additional levels also appear because d can take values O < d < J . It is now possible to make predictions of spectroscopically observable transitions in the far-infrared spectrum of the Ar HC1 molecule. The most intense transi- tions are expected to be those following the propensity rules: AA = 0, -&I A b = f l AV = 0 with the rotational selection rule AJ = -&l for parallel bands (Ad = 0) and AJ = 0, & 1 for perpendicular bands (AA. = & 1). The most intense bands originating in the ground vibrational state should thus occur with band origins at 35.5 cm-I (perpendi- cular band) and 37.4 cm-' (parallel band) for this potential. The existing spectra of Boom and van der Elsken3 are at low resolution, but do indeed show peaks in thisGENERAL DISCUSSION 367 region. High-resolution spectra of the Ar HC1 complex in this region would provide important new information on the intermolecular potential, since the energy levels are sensitive to parts of the potential surface which are not probed by the existing data. S . L,. Holmgren, M. Waldman and W. Klemperer, J. Chem. Phys., 1978, 69, 1661. J. M. Hutson and B. J. Howard, Mol. Phys., 1980, 41, 1123. E. W. Boom and J. van .der Elsken, J. Chem. Phys., 1980,73, 15. Dr. G. Duxbury (Strathclyde Uniuersity) said: I would like to comment on the inter-relation between the methods currently used for calculating the vibration- rotation and vibronic energy levels of small polyatomic molecules. Kidd et al. have used a scattering theoretical approach which relies on the use of the analytical basis functions which are appropriate over a large part of coordinate space. Thus one way of viewing the function of their scattering coordinate, with respect to which the differential equations are set up, is to build some anharmonic flexibility into the system. The coupled channels in this method are labelled by the quantum numbers appropriate to the analytical wavefunction used, e.g. u j l . An alternative way of treating a system was developed by Dixon and Duxbury1v2 and by Jungen and Merer3 in connection with molecules such as NH, in which there is both vibronic interaction and large amplitude vibration. This approach can be viewed as something intermediate between scattering theory and a matrix diagonalisa- tion approach. In molecules such as NH2 the usual Born-Oppenheimer separation of the electronic and vibrational motion is not valid, so that the total wavefunction must include a linear combination of two products of electronic and nuclear motion. l~ W e + ( r e , rn)X+(rn) + ve-(re, rn)X-(rn)- (1) In a triatomic molecule with a large amplitude bending coordinate p, the supplement to the interbond angle, substitution of eqn (1) into the Schrodinger equation and integrating over the electronic coordinates then gives rise to two coupled differential equations for the nuclear wavefunction x+ (p) : where Hb(p) is the kinetic energy operator, U& includes the potential function and the " a-axis rotation ", and HE + is the coupling function. In order to transform the problem into one of only two coupled channels, the original Hamiltonian was partitioned so that the effects of overall rotation labelled by J , which would lead to four coupled channels, are neglected in the initial step. The effects of molecular asymmetry, which introduces terms coupling channels which differ in K by &2 are also neglected at this stage. This approximation has been justified in the non-degenerate problem by Bunker and Stone.4 The remaining two coupled differential equations can then be decoupled by a method which involves removing the potential part of the coupling at each value of p , leaving the remaining kinetic perturbation to be evaluated by a matrix diagonalisation method. The initial equations are then solved by direct numerical integration of the one-dimensional Schrodinger equations of the uncoupled problems. The final perturbation matrix elements are then easily evaluated from the numerical wavefunctions. The problems with the application of the scattering theory method are that it relies on more information to construct the potential energy surface than is often available, as for example is the case in NH2, that it does not easily allow separability368 GENERAL DISCUSSION to be applied when a particular limiting case is reached, and that for molecules such as water the choice of the z-coordinate is not a very helpful one for anything other than the J = 0 levels. The decoupling used in the NH2 problem was successful since it preserved informa- tion about K, the projection o i the total angular momentum along the a-molecular axis, which is parallel to the H-H direction at equilibrium. The method can therefore be compared with the use of the centrifugal decoupling approximation. The choice of a molecule fixed z axis perpendicular to the H-H distance is a poor one in water for states where the average geometry is close to that at equilibrium, or for those in which large symmetrical distortions occur. This is because this par- ticular choice of z axis corresponds to the b-intermediate molecular axis, and hence does not correlate with either the prolate or oblate limiting symmetric top axes of H20. This makes it difficult to correlate the quantum numbers used in the scattering approach with those commonly used by molecular spectroscopists. The final point that can be made about symmetrical molecules such as water is that as Child and Lawton have shown, the bending and the stretching are effectively decoupled even up to vibrational energies of ca. 18 000 cm-l. This implies that for molecules of this type the separation into a large-amplitude bending problem and a stretching problem may be more appropriate over even high vibrational levels in the bound part of the potential surface. In asymmetrical molecules such as HCCl or HNO where there is both strong vibronic interaction and considerable coupling between different vibrational modes, it is likely that a variant of the scattering-theory approach may be more fruitful than the methods described in this comment. l T. Barrow, R. N. Dixon and G. Duxbury, Mol. Phys., 1974,27, 1217. G. Duxbury and R. N. Dixon, Mol. Phys., 1971,1981,43,255. Ch. Jungen and A. J. Merer, Mol. Phys., 1980, 40, 1. P. R. Bunker and J. M. R. Stone, J. Mol. Spectrosc., 1972, 41, 310.

ISSN:0301-7249    

DOI:10.1039/DC9817100301

出版商:RSC    

年代:1981

数据来源: RSC

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ADDITIONAL REMARKS The replies to Professor Winnewisser’s questions were received too late for in- corporation in sequence. Prof. M. Winnewisser (Giessen University) said : In his Introductory Lecture Dr. Evenson described the mixing of laser frequencies with the output frequencies of microwave oscillators. Could he comment on the construction of these mixers, the impedance matching, frequency range and sensitivity: in short, could he reveal some of his trade secrets? Dr. K. M. Evenson (National Bureau of Standards, Boulder, Colorado) (communicated) : These are the tungsten-nickel diodes which we use to measure laser frequencies. They are probably the world’s highest speed detectors, and will generate useful beats up to ca. 12 harmonics and up to frequencies corresponding to wavelengths of 2 pm or so.Two useful references are: K. M. Evenson, D. A. Jennings, F. R. Petersen and J. S. Wells, Laser Spectroscopy I11 (Springer, New York, 1977) and A. Sanchez, C. F. Davis Jr, K. C. Liu and A. Javan, J. Appl. Phys., 1978, 49, 5270. Prof. M. Winnewisser (Giessen University) said : Millimetre waves and HCCS would make a good combination. Could you comment on the molecular stability in hostile environments? What is the lowest lying bending mode? Dr. S. L. N. G. Krishnamachari and Dr. D. A. Ramsay (National Research Council of Canada) said: Our only experience of the stability of HCCS is under the conditions described in the paper for which the lifetime is < 100 ps. The lowest-lying bending mode is presumably the CCS bending vibration, which in the 213 ground state has three components, zC+, 2C- and 2A. At present we do not have any values for this ground-state frequency or for the Renner-Teller splittings.

ISSN:0301-7249    

DOI:10.1039/DC9817100369

出版商:RSC    

年代:1981

数据来源: RSC

摘要:

INDEX OF NAMES* Ashfold, M. N. R. 316 Ashton, C. J. 303 Bacis, R. 321, 323, 351 Balint-Kurti, G. G. 287 Barrow, R. F. 329, 349 Bondybey, V. E. 175 BrCchignac, Ph. 304, 315, 334 Breford, E. J. 233 Brown, J. M. 151, 301, 312, 330 Caldwell, C. D. 352 Child, M. S. 273, 303, 354, 365 Clyne, M. A. A. 213, 349, 350, 351 Cooper, D. L. 332, 357 Cossart, D. 348 Cossart-Magos, C. 336 Coxon, J. A. 301 Davies, P. B. 15, 301, 302 Delhoume, M. 125 Dixon, R. N. 125, 318, 328 Duxbury, G. 97, 319, 323, 333, 358, 367 Eland, J. H. D. 346, 358 Engelke, F. 233, 352, 354, 355, 356, 357 Ennen, G. 233 Evenson, K. M. 7, 301, 349, 369 Field, R. W. 111, 326, 327, 331, 350, 356 Foster, S. C. 301 Gouedard, G. 143 Gough, T. E. 77, 316, 326, 351, 358 Gray, P. 335 Griemann, F. J. 191 Hack, W. 15 Hage, H. 352 Heaven, M. C. 213 Herzberg, G. 165, 336 Hirota, E. 87, 312 Howard, B. J. 23 Hutson, J. M. 302, 365 Jungen, Ch. 253, 358 Kato, H. 97 Kidd, I. F. 287 Krishnamachari, S. L. N. G. 205, 349, 369 Lawton, R. T. 273 Leach, S. 31 1, 336, 347, 348, 349 Lehmann, J. C. 143 Le Lerre, M. L. 97 Mahan, B. H. 191 Maier, J. P. 181, 346 Marthaler, 0. 181 McKellar, A. R. W. 63, 322 Meiwes, K. H. 233 Miller, R. E. 77 Miller, T. A. 175, 312, 341 Mills, I. M. 321, 364 Milton, D. J. 151 Misev, L. 181 Noble, M. 125 O’Keefe, A. 191 Quack, M. 309, 325, 359 Ramsay, D. A. 205, 329, 349, 369 Raoult, M. 253 Scoles, G. 77 Sears, T. J. 175 Shapiro, M. 287 Steimle, T. C. 151 Taylor, C. A. 125 Thommen, F. 181 Urban, W. 314 Wagner, H. Gg. 15 Winn, J. S. 191, 327, 356 Winnewisser, M. 31, 308, 309, 369 Woods, R. C. 57, 308, 309, 31 1, 312, 326 * The page numbers in heavy type indicate papers submitted for discussion.

ISSN:0301-7249    

DOI:10.1039/DC9817100370

出版商:RSC    

年代:1981

数据来源: RSC

摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY/FARADAY DISCUSSIONS OF THE CHEMICAL SOCIETY Date Subject 1907 1907 1910 191 1 1912 1913 1913 1913 1914 1914 1915 1916 1916 1917 1917 1917 1918 1918 1918 1918 1919 1919 1920 1920 1920 1920 1921 1921 1921 1921 1922 1922 1923 1923 1923 1923 1923 1924 1924 1924 1924 1924 1925 1925 1926 1926 1927 1927 1927 1928 1929 1929 1929 1930 1931 1932 1932 Osmotic Pressure Hydrates in Solution The Constitution of Water High Temperature Work Magnetic Properties of Alloys Colloids and their Viscosity The Corrosion of Iron and Steel The Passivity of Metals Optical Rotatory Power The Hardening of Metals The Transformation of Pure Iron Methods and Appliances for the Attainment of High Temperatures in a Laboratory Refractory Materials Training and Work of the Chemical Engineer Osmotic Pressure Pyrometers and Pyrometry The Setting of Cements and Plasters Electrical Furnaces Co-ordination of Scientific Publication The Occlusion of Gases by Metals The Present Position of the Theory of Ionization The Examination of Materials by X-Rays The Microscope: Its Design, Construction and Applications Basic Slags: Their Production and Utilization in Agriculture Physics and Chemistry of Colloids Electrodeposition and Electroplating Capillarity The Failure of Metals under Internal and Prolonged Stress Physico-Chemical Problems Relating to the Soil Catalysis with special reference to Newer Theories of Chemical Action Some Properties of Powders with special reference to Grading by Elutria- The Generation and Utilization of Cold Alloys Resistant to Corrosion The Physical Chemistry of the Photographic Process The Electronic Theory of Valency Electrode Reactions and Equilibria Atmospheric Corrosion.First Report Investigation on Oppau Ammonium Sulphate-Nitrate Fluxes and Slags in Metal Melting and Working Physical and Physico-Chemical Problems relating to Textile Fibres The Physical Chemistry of Igneous Rock Formation Base Exchange in Soils The Physical Chemistry of Steel-Making Processes Photochemical Reactions in Liquids and Gases Explosive Reactions in Gaseous Media Physical Phenomena at Interfaces, with special reference to Molecular Atmospheric Corrosion. Second Report The Theory of Strong Electrolytes Cohesion and Related Problems Homogeneous Catalysis Crystal Structure and Chemical Constitution Atmospheric Corrosion of Metals.Third Report Molecular Spectra and MolecuIar Structure Colloid Science Applied to Biology Photochemical Processes The Adsorption of Gases by Solids The Colloid Aspect of Textile Materials tion Orientation Volume Trans. 3* 3* 6* 7" 8* 9* 9* 9* 10* 10" 11* 12" 12* 13* 13* 13* 14* 14* 14* 14* 15* 15* 16* 16" 16" 16" 17" 17" 17" 17* 18* 18 19" 19 19* 19 19* 20 * 20 * 20* 20* 20 * 21 * 21 22 22 23 * 23 * 24 24 25 * 25 * 26 * 26 27 28 293'72 Date 1933 1933 1934 1934 1935 1935 1936 1936 1937 1937 1938 1938 1939 1939 1940 1941 1941 1942 1943 1944 1945 1945 1946 1946 1947 1947 1947 1947 1948 1948 1949 1949 1949 1950 1950 1950 1950 1951 1951 1952 1952 1952 1953 1953 1954 1954 1955 1955 I956 1956 1957 1958 1957 1958 1959 1959 1960 1960 1961 1961 1962 1962 1963 GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Subject Liquid Crystals and Anisotropic Melts Free Radicals Dipole Moments Colloidal Electrolytes The Structure of Metallic Coatings, Films and Surfaces The Phenomena of Polymerization and Condensation Disperse Systems in Gases : Dust, Smoke and Fog Structure and Molecular Forces in (a) Pure Liquids, and (b) Solutions The Properties and Functions of Membranes, Natural and Artificial Reaction Kinetics Chemical Reactions Involving Solids Luminescence Hydrocarbon Chemistry The Electrical Double Layer (owing to the outbreak of war the meeting The Hydrogen Bond The Oil-Water Interface The Mechanism and Chemical Kinetics of Organic Reactions in Liquid The Structure and Reactions of Rubber Modes of Drug Action Molecular Weight and Molecular Weight Distribution in High Polymers (Joint Meeting with the Plastics Group, Society of Chemical Industry) The Application of Infra-red Spectra to Chemical Problems Oxidation Dielectrics Swelling and Shrinking Electrode Processes The Labile Molecule Surface Chemistry (Jointly with the Societe de Chimie Physique at Colloidal Electrolytes and Solutions The Interaction of Water and Porous Materials The Physical Chemistry of Process Metallurgy Crystal Growth Lipo-Proteins Chromatographic Analysis Heterogeneous Catalysis Physico-chemical Properties and Behaviour of Nuclear Acids Spectroscopy and Molecular Structure and Optical Methods of Investi- gating Cell Structure Electrical Double Layer Hydrocarbons The size and shape Factor in Colloidal Systems Radiation Chemistry The Physical Chemistry of Proteins The Reactivity of Free Radicals The Equilibrium Properties of Solutions on Non-Electrolytes The Physical Chemistry of Dyeing and Tanning The Study of Fast Reactions Coagulation and Flocculation Microwave and Radio-Frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions Configurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents The Physical Chemistry of Aerosols Radiation Effects in Inorganic Solids The Structure and Properties of Ionic Melts Inelastic Collisions of Atoms and Simple Molecules High Resolution Nuclear Magnetic Resonance The Structure of Electronicallv-Excited SDecies in the Gas-Phase was abandoned, but the papers were printed in the Transactions) Systems Bordeaux) Published by Butterworths Scientific Publications, Ltd 1963 Fundamental Processes in Radiation Chemistry Volume 29 * 30 30 31 * 31 * 32* 32* 33* 33* 34* 34* 35* 35* 35* 36* 37* 37 * 38 39 40 * 41 * 42 * 42 A 42 B Disc. 1* 2 Trans.43* Disc. 3 4* 5 6 7 8* Trans. 46' Disc. 9 Trans. 47 Disc. 10 1 1 12* 13 14 15 16" 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 * 34 35 36Date 1964 1964 1965 1965 1966 1966 1967 1967 1968 1968 1969 1969 1970 1970 1971 1971 1972 1972 1973 1973 1974 1974 1975 1975 1976 1977 1977 1977 1978 1978 1979 1979 1980 1980 1981 GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Subject Chemical Reactions in the Atmosphere Dislocations in Solids The Kinetics of Proton Transfer Processes Intermolecular Forces The Role of the Adsorbed State in Heterogeneous Catalysis Colloid Stability in Aqueous and Non-Aqueous Media The Structure and Properties of Liquids Molecular Dynamics of the Chemical Reactions of Gases Electrode Reactions of Organic Compounds Homogeneous Catalysis with Special Reference to Hydrogenation and Bonding in Metallo-Organic Compounds Motions in Molecular Crystals Polymer Solutions The Vitreous State Electrical Conduction in Organic Solids Surface Chemistry of Oxides Reactions of Small Molecules in Excited States The Photoelectron Spectroscopy of Molecules Molecular Beam Scattering Intermediates in Electrochemical Reactions Gels and Gelling Processes Photo-effects in Adsorbed Species Physical Adsorption in Condensed Phases Electron Spectroscopy of Solids and Surfaces Precipitation Potential Energy Surfaces Radiation Effects in Liquids and Solids lon-Ion and Ion-Solvent Interactions Colloid Stability Structure and Motion in Molecular Liquids Kinetics of State Selected Species Organization of Macronlolecules in the Condensed Phase Phase Transitions in Molecular Solids Photoelectrochemistry High Resolution Spectroscopy Oxidation 373 Volume 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 * 66 67 68 69 70 71 * Not atlailable; for mrrcirt irgbrmn fion on prices, etc, of available volumes, please contact the Mnrketitig Oficer, Royal Society of Chemistry, Birrlington House, London WI V OBN statitrg Izihetlicr or not you are a meniber of the S0ciet.y.

ISSN:0301-7249    

DOI:10.1039/DC9817100371

出版商:RSC    

年代:1981

数据来源: RSC