Mid-infrared Laser Magnetic Resonance Spectroscopy BY A. ROBERT W. MCKELLAR Herzberg Institute of Astrophysics, National Research Council of Canada, Ottawa, Ontario, Canada K1A OR6 Received 10th December, 1980 The development of laser magnetic resonance (1.m.r.) spectroscopy with CO (h = 5-7 pm) and C02 (A = 9-1 1 pm) laser sources originally lagged behind the application of this technique in the far- infrared region. However, during the past five years, mid-infrared 1.m.r. has been extensively used to study vibration-rotation and electronic spectra of a large number of atoms, diatomic molecules and triatomic molecules. It has allowed the study of many unstable free radicals that could not be detected by more conventional infrared techniques. This paper presents a brief review of these developments with an emphasis on recent work.Some new analyses of already published mid-in- frared 1.m.r. data are also presented. These are made possible by newly available measurements of isotopic C02 laser frequencies and improved ground vibrational state data, and they result in improved molecular parameters for the following molecules: HCO(v2), H02(v3), D02(v2), PH2(v2) and ND2(v3. During the last ten years much of the increase in our understanding of the structure and properties of short-lived molecules has come from the application of laser magnetic resonance (1.m.r.) spectroscopy to the study of rotational spectra in the far-infrared. The technique was developed in 1968 by Evenson et al.,' and first used to study a transient species, OH, in 1970.2 In one sense, the effect of far-infrared 1.m.r.was to extend to higher frequencies earlier gas-phase electron paramagnetic resonance (e.p.r.) studies of free radicals. The extension to still higher frequencies may be ac- complished using COz (9-1 1 pm) and CO (5-7 pm) lasers in an 1.m.r. apparatus, and in this case molecular vibration-rotation transitions become accessible. The exploita- tion of the 1.m.r. technique in the mid-infrared region has lagged behind the far-infra- red, but in the last five years it too has been applied to an increasing number of atoms and molecules. Reviews of far-infrared 1.m.r. have been given by Davies and Evenson3 and by Evenson et aL4 A general comparision of the technique as applied in the far- and mid-infrared regions is given in table 1, which also lists the species studied to date.The stable and nearly stable paramagnetic molecules 02, NO, NO2, NF2 and C10, have all been studied, but the real value of 1.m.r. clearly lies in studying unstable free radicals which are generally difficult to detect by other means, especially in the infrared region. The essential features of an 1.m.r. spectrometer are illustrated schematically in fig. 1 (a), which shows an experimental configuration with the absorption cell located out- side the laser cavity. Fixed-frequency laser radiation is directed through a free- radical absorption cell located in a magnetic field and then monitored by a detector. The field is swept, and an absorption line of the sample gas that happens to be Zeeman- tuned through the laser frequency results in a decrease in detected laser power.In practice, a small modulation at 0.1-100 kHz is added to the magnetic field using coils (not shown) near the cell, and the change in transmitted laser power is recorded as a first derivative signal by processing the detector output in a phase-sensitive amplifier. A detailed analysis of the observed spectrum requires, of course, a detailed knowledge of the Zeeman effect in the atom or molecule studied.64 M I D - I . R . LASER MAGNETIC RESONANCE SPECTROSCOPY TABLE 1 .-COMPARISON OF FAR- AND MID-INFRARED LASER MAGNETIC RESONANCE far-infrared 1. m.r. mid-infrared 1.m.r. sensit iu it y Probably higher. Evenson et 0 1 . ~ Evenson et aL4 estimate 3 x 108 estimate 5 x lo7 molecule ~ r n - ~ .molecule crnP3. These estimates, however, are very dependent on the particular molecule. The sensitivity achieved in practice also depends on the refinement of the apparatus. resolution Typical Doppler widths: 0.5-20 Typical Doppler widths: 40-1 50 MHz. Pressure broadening: 2- MHz. Pressure broadening: 2- 20 MHz. Lamb dips can be 20 MHz. Lamb dips are gener- seen in some cases where pres- ally easier to detect, though this sure broadening is less than is very dependent on the strength Doppler broadening. of absorption. practical wavelength limits 10-250 cni-'. Can be extended CO, laser: 875-11 10 cm-I (lower beyond these limits. frequencies available from 14C1602). CO laser: 1450-2000 cm- (can be extended). Higher frequencies are available using HF, DF, etc.lasers, but exten- sions are more likely to come using tunable lasers and Zeeman modulation. experimental Probably more difficult. For Probably easier, especially in CO, dficulty optically pumped system, both laser region. Detector is less pump (CO,) and far4.r. lasers expensive. Magnet can be smal- are required. ler thanks to shorter wavelength. information in Ground vibrational state para- Ground and excited vibrational spectrum meters. state parameters. dificulty of Depends very much on the na- Analysis is similar but probably anaLysis ture of the molecule and whether more difficult, because: (1) the previous information is available resolution is generally lower ow- on it. ing to greater Doppler width and (2) more parameters are required to describe the spectrum, in parti- cular the vibrational band origin.One advantage is that low-J transitions are more easily seen (they tend to be at too low a fre- quency in the far-Lr.). atom\.and 0, C, 02, OH, NO,, NO, CH, C1, Hg*, He*, NO, NO2, NF2, HCO, CH30, CH2F, SH, SD, DO,, SeH, SeD, FO, ClO, BrO, SeH, CH2, C2H, CF, CO*, 02*, SD, C102, SeO, NSe, SO, SO*, N2H, HBr+, DBr', CH20H, OD CH3, CH30( ?), FCO(?), NCO molecules studied HO2, DO2, NHI, PH2, NH, PH, HCO,DCO,NH2,ND2,PH2,HOz,A. R . W. MCKELLAR 65 Fig. l(b) illustrates the alternate arrangement of an 1.m.r. spectrometer with intra- cavity absorption cell. Placing the cell inside the laser cavity results in a gain in sensitivity due to multipassing of the laser radiation. A further sensitivity gain may also arise from the interaction between the absorbing medium and the non-linear-gain medium of the laser; this effect is especially important for optically pumped far- infrared lasers.Another benefit of the int-racavity configuration is that it favours the I DETECTOR LASER DJ %, >n \AB SOR PT I ON I I CELL ( b ) DETECTOR I I-. LASER GAI I ~ LASER CAVITY ! FIG. 1 .-Schematic representation of an 1.m.r. spectrometer with (a) absorption cell located outside the laser cavity, and (b) intracavity location of absorption cell. Both arrangements have been widely used for mid-infrared l.m,r., but (b) has generally been used in the far-infared region. observation of saturation dips because it ensures perfect alignment of counterpropaga- ting laser radiation and gives higher power densities in the absorption cell.This is especially important in the mid-infrared region, where Doppler widths are greater and the high resolution of saturation spectroscopy is needed more. A transverse magnetic field as given by an ordinary iron-core electromagnet is implied in fig. 1, but it is also possible to use a solenoid in an 1.m.r. spectrometer. However, the application of solenoids has been limited to date because of the difficulty of achieving high fields with conventional solenoids and the experimental complications of superconducting mag- nets. In the first part of the present paper, the development of 1.m.r. spectroscopy using CO, and CO laser sources is briefly reviewed with an emphasis on recent develop- ments. The second part of the paper is devoted to an examination and reanalysis of already published 1.m.r. results on the HCO, HO,, DO2, PH, and ND, radicals.T H E D E V E L O P M E N T OF M I D - I N F R A R E D L . M . R . The first molecule to be observed in the mid-infrared region by 1.m.r. spectroscopy was NO, which is the species most accessible to the technique because of its stability and the location of its fundamental band in a favourable region for CO laser operation (5. 3 pm). In 1972, Kaldor et aL5 published spectra which exploited a close coinci- dence (ca. 780 MHz) between the R(1.5) line of NO and a CO laser line at 1884.35 cm-'. The spectrum, which appeared in the 0.6-7 kG region, was proposed as a sen- sitive means of monitoring atmospheric NO concentration. A similar observation66 MID-I.R.LASER MAGNETIC RESONANCE SPECTROSCOPY was also published in 1972 by Bonczyk and Ultee,6 and subsequently Bonczyk mea- sured the pressure broadening of the NO transition7 and built a compact 1.m.r. appara- tus specifically for trace NO detection.' It appears, however, that the proposal to use 1.m.r. as a sensitive pollution detector has not been seriously adopted. NO spectra were also observed by Zeiger et aL9 using a superconducting solenoid with fields up to 50 kG, and by Bridges and Burkhardt,'O who used the optoacoustic tech- nique to detect the absorption of CO laser radiation by placing a spectrophone in the NO cell in the magnetic field. The above studies utilized the original 1884.35 cm-l laser line, except for that of Zeiger et al., who used a laser line at 1876.31 cm" to observe the Q(1.5) and Q(2.5) NO transitions. More spectroscopically oriented 1.m.r.studies of the NO fundamental band were later made by Hakuta and Uehara," who measured spectra using three other CO laser lines, and by Dale et a1.,12 who detected spectra of 14N1'0, 15N160 and I4NI7O in natural abundance, as well as the 2 t 1 hot band and 2111/2 t ,I-I3/2 satellite band of l4NI6O. Dale et al. also observed one transition within the ,Ill/, substate of l4NI6O; all the previous 1.m.r. spectra involved the more magnetically tunable , I I 3 / 2 state. This latter work', was the first in which the absorption cell was placed inside the laser cavity for mid-infrared l.m.r., though this is almost universal practice with far-infra- red 1.m.r. Thus Dale et al.were able to observe saturation (inverse Lamb) dips and resolve hyperfine and A-doubling splittings as small as 2.7 MHz. A second stable molecule, NOz, was also studied using the CO laser by Freund et al.13 in 1975. They obtained zero-field frequencies and spin splittings for two I4NO, and six lSNO, transitions in the v3 band, and derived some lSNO2 spectroscopic con- stants. A more detailed 1.m.r. study of the v3 band of NO, is certainly possible, but has not been performed, probably because, in contrast to unstable free radicals, NO, can be studied easily by more conventional techniques. The first use of 1.m.r. with a CO, laser was made around 1975 in the Soviet Union by Broude et aI.,I4 who studied the semi-stable radical NF, which occurs in the gaseous state in equilibrium with N2F4.They observed 1.m.r. signals on 20 laser lines in both the 9.4 and 10.4 pm CO, bands. However, they were limited by their solenoid electro- magnet to fields below 500 G, and did not give any assignments or analysis of their results. In a later paper (Gershenzon et al.") the kinetics of the N2F4 + 2NF, reac- tion were explored using 1.m.r. to measure the NF, concentrations, the first applica- tion of mid-infrared 1.m.r. to chemical kinetics. However, the Soviet group has not published any further spectroscopic results. In 1976, the first 1.m.r. spectroscopy of an atom was reported by Dagenais et a1.16 They observed the ground-state fine-structure transition (,P1,, +- 2P3,2) in atomic chlorine using a 13C1602 laser line at 882.287 cm-'.The next year, Johns et al.17 observed a similar transition in an excited atomic state, 6s6p 3P1 t 3P0 in the mercury atom. The C1 transition was relatively easy to detect, and was studiedI6 using a small (6 cm) electromagnet and an extracavity absorption cell; it has also recently been detected using a tunable diode laser.l8 However, the Hg transition was more difficult to detect because of the problem of producing sufficient excited metastable 3P0 atoms. In this case, the intracavity CO laser spectrometer, also used', for NO, was employed. Following the observations of the C1 and Hg spectra, analogous fine-structure spectra have been observed in the ~ x y g e n ' ~ * ~ ~ and carbon,' atoms using far-infrared 1.m.r. A rather different sort of atomic 1.m.r.spectroscopy with a CO, laser has been reported by Rosenbluh et al.,,-,' These authors have measured Rydberg transitions in excited helium atoms using a very high field (140 kG) 1.m.r. apparatus in which the absorption of 10 pm CO, photons was detected in the optical region by a change in However, they did not attempt a full-scale analysis.A . R. W. MCKELLAR 67 atomic luminescence. This double-resonance technique was more sensitive than the direct detection of the absorbed infrared photons. They also observed a novel line- shape which was the result of a motional Stark effect experienced by the atoms moving in the intense magnetic field, and which in principle provided sub-Doppler resolution. The application of mid-infrared 1.m.r. to the study of transient molecular species began in 1977 with the report by Brown et of the detection of NH, and HCO in the 5 pm CO laser region.They observed three transitions of the v, (bending) fundamen- tal band of NHz and three in the v3 (C-0 stretch) fundamental band of HCO, but did not give detailed assignments. Complete analyses of these 1.m.r. spectra have recently been published by Kawaguchi et al.27 for NH, and Brown et a1.28 for HCO. The first detailed analysis of the rotation-vibration 1.m.r. spectrum of an unstable molecule was made by Riggin et al.29 for the v, (bending) fundamental band of HCO around 9.25 pm. They observed and assigned ca. 90 discrete HCO resonances on 17 different CO, laser lines between 1069 and 1101 cm-', and fitted these to obtain the band origin, rotational constants, centrifugal distortion constants and spin-rotation constants.The analysis was greatly aided by the slightly earlier work of Landsberg et al.30 who had studied the same band using the technique of laser Stark spectroscopy. This technique is very similar to l.m.r., with an electric field and the Stark effect taking the place of the magnetic field and Zeeman effect. However, laser Stark spectroscopy is generally a much less appropriate technique for short-lived free radicals. There are two reasons for this: first, it is necessary to use quite low gas pressures ( 5 20 mTorr) to avoid electrical breakdown, and this limits the practical sensitivity which may be obtained; secondly, the Stark technique does not automatically discriminate against non-paramagnetic molecules (as does l.m.r.), and this may result in serious spectral interference by unwanted species. The work of Landsberg et aL30 on HCO was all the more notable because of these difficulties in applying laser Stark spectroscopy to free radicals.In addition to the 5 pm CO laser spectra already menti~ned,,~.,~ some weak transi- tions in the v, band of NH, have also been detected3' in the 9 pm CO, laser region. A number of other triatomic free radicals have now been studied by mid-infrared l.m.r., including HO, (v3, ca. 1098 ~ m - ' ) , ~ , DO, (v2, ca. 1020 cm-1),33 PH, (v,, ca. 1102 ~ m - ' ) , ~ ~ ND, (v,, ca. 1109 ~ m - 9 , ~ ~ and DCO (vl, ca. 1910 cm-'; and v3, ca. 1795 ~ m - 9 . ~ ~ For two of these, DO2 and DCO, the analysis involved a Coriolis interaction between two nearby vibrational states.In the case of DO,, only one of the states could be ob- served by 1.m.r. and the properties of the other were inferred from their effect on the observed spectrum, whereas in the case of DCO, both states were observed in the 1.m.r. spectrum. Another triatomic radical, the semi-stable species ClO,, has exhibited a new type of 1.m.r. spectrum in studies by Hakuta and Uehara.37-40 It has usually been con- sidered that molecules with small spin-rotation interactions will give 1.m.r. spectra only at relatively low magnetic fields, because high fields decouple the electron spin from the molecular rotation, with a resulting loss of electric dipole transition intensity for fast-tuning transitions. However, high-field spectra were observed3' in the v1 band of C10, (ca. 946 cm-') in spite of its small spin-rotation interaction, and Uehara and Hakuta assigned these spectra to transitions induced by avoided crossings be- tween Zeeman levels having the same value of MJ but differing by one in N .This type of transition offers a new means to study molecules which might otherwise be inac- cessible to the 1.m.r. techniques, though it may be difficult to apply to new molecules about which little is known since the assignment of observed spectra is not easy, even for the relatively well-known C10,. A considerable number of short-lived diatomic free radicals have also been studied68 MID-I.R. LASER MAGNETIC RESONANCE SPECTROSCOPY by mid-infrared 1.m.r. The 1-0 band (ca. 11 15 cm-l) of the metastable a 'A excited electronic state of SO was detected by Yamada et aL4' The same authors also studied4, the 1-0 and 2-1 bands of the X3C- ground state of SO, which occur in the same spectral region. They produced SO by reacting OCS with 0 atoms, and found that the addition of CF, to the oxygen discharge enhanced the production of the SO ground state and diminished production of the a*A state.The closely related mole- cule SeO has recently been studied by Hakuta and U e h a ~ a , ~ ~ who observed and analysed the 1-0 bands of 4 of the Se isotopic species of SeO in the 11 pm CO, laser region. Among diatomic radicals with ,l-I ground electronic states, vibration-rotation transitions have been observed by 1.m.r. for FO (1-0 band, ca 1033 ~ m - ' ) , ~ ~ C10 (2-0 band, ca.1670 ~ m - ' ) , ~ ~ SD (1-0 band, ca. 1885 cm-1),46-47 and NSe (1-0 band, ca. 945 ~ m - ' ) . ~ ' Especially notable here was the detection of FO, which had not previously been observed by spectroscopic means in the gas phase. It was pro- duced simply by a microwave discharge in CF4, the oxygen atoms coming from the erosion of the quartz discharge tube, and gave remarkably strong spectra with pro- minent saturation dips and 19F hyperfine s t r ~ c t u r e . ~ ~ The above diatomics were observed by means of rotation-vibration transitions within the '113/, component. The electronic transition between the 21t3/2 and 2111,2 components may also happen to lie in the mid-infrared, and such a spectrum was in fact observed in SeH by Brown et aZ.49 using 1.m.r.in the 5.7 prn CO laser region. The transitions they observed were of magnetic dipole origin with the exception of one weak electric dipole line, and their analysis yielded a direct determination of the spin-orbit splitting, A = -1764.019 cm-l. Very recently, a similar study of SeD has been c~mpleted,'~ and a combination of the SeH and SeD results determines some further fundamental parameters for this molecule. A similar 2111/2 t 'II3/, spectrum has recently been observed by McKellar" for BrO in the 10.3 pm region. In this case, the spectrum consisted entirely of mag- netic dipole transitions, and extensive hyperfine, A-doubling and isotopic structure was observed. The spin-orbit splitting was determined to be A = -967.983 cm-l for 79Br0 and -967.998 cm-' for "BrO, and a number of rotational, hyperfine, A-doubling and Zeeman parameters were also determined.Some recent and as yet unpublished work using mid-infrared 1.m.r. also deserves to be mentioned. The group at the Institute for Molecular Science in Okazaki (Amano et al.)', has been studying infrared-optical double resonance in NH,. Their spectrometer resembles a conventional CO, 1.m.r. apparatus, but visible radiation from a tunable C.W. dye laser is introduced into the absorption cell as well as the 10 pm CO, laser radiation. The change in intensity of the visible fluorescence of NH, due to the presence of the infrared radiation is monitored while the magnetic field is swept. The resulting signals effectively give 1.m.r. spectra of vibration-rotation transitions within the 2, 2A1 excited electronic state of NH,; for example, the 2,' t 2, transition of the (0, 10,O) t (0,9,0) vibrational band has been observed.Jn other unpublished work, the group at the University of Southampton has been studying the 1-0 vibrational transition of Sen in the ,113/, state (v, z 1677 cm-') and the v3 (antisymmetric stretch) band of the linear radical NCO. This latter molecule is interesting because it exhibits strong vibronic interactions, but these also complicate the observed spectrum. Around 1977 the same Southampton group also observed the 1.m.r. spectrum of an unknown species in the 5.4 pm region.53 This " mystery molecule " could be pro- duced, for example, by discharging mixtures of CF, + CO or SF, + CO, and possible candidates were ground-state FCO, or electronically excited CF, or F2C0.How- ever, very little was known about these molecules, and there were various arguments against each one. Very recently, Nagai et aZ.54 have measured the v, (ca. 1862 crn-')A . R. W. MCKELLAR 69 and v, (ca. 1026 cm-') bands of FCO using a tunable diode laser, and using their molecular parameters it is now possible to calculate the expected v1 band 1.m.r. spec- trum. Preliminary indications are that FCO may indeed be the 5.4 pm mystery mole- cule. Unassigned spectra have also been observed in the 9.5 pm region by G. W. Hills using a discharge in CF,. Though the conditions required for this spectrum seemed somewhat different from those for the 5.4 pm mystery spectrum, there were also many similarities, and it was considered possible that both were due to the same species (0 atoms were available for the 9.5 pm spectrum from the erosion of the quartz discharge tube). However, it now seems that the parallel (a-type) component of v2 of FCO measured by Nagai et al.54 is not the source of the 9.5 pm 1.m.r.spectrum unless very high values of N and K are involved. It is still possible that the perpendicular (b-type) component of this band, which was too weak to be observed by diode laser,54 could be responsible, but perhaps more likely that the spectrum is due to another species, such as excited triplet state CF,. The symmetric rotor free-radical CH30 is one of the most interesting molecules to be studied and analysed by far-infrared l.m.r.55*56 Now that its rotational spectrum is understood thanks to the beautiful work of Russell and R a d f ~ r d , ~ ~ a search for rotation-vibration spectra is of some interest.Such a search has begun at N.R.C.,57 and some weak spectra have been observed in the 975 to 1020 cm-I region. The pro- duction scheme, mixing CH30H with the products of a discharge in CF, + He, was the same as used for CH,O by Radford. The spectra observed are not due to HO, or HCO, and are unlikely to be due to CH,OH, which Radford has found to be more I I magnetic field/kG FIG. 2.-L.m.r. spectrum, possibly owing to CH30, observed with perpendicular polarization using the 1zC1602 R(20) laser line at 978.930 cm-'. The free-radical source was methanol mixed with the products of a microwave discharge in CF4 + He.The two traces are simply repetitions of the same scan; on close examination, some of the structure that at first seems to be noise is actually due to real spectral features.70 MID-I.R. LASER MAGNETIC RESONANCE SPECTROSCOPY difficult to produce than CH30. However, there is no proof that the 10 pm spectra are really CH30 apart from the production scheme used. An example of an observed " CH30 " spectrum is shown in fig. 2, which was recorded with perpendicular polariz- ation using the 12C'60, R(20) laser line at 975.930 cm-'. There is considerable noise in the two traces of fig. 2, in spite of their having been recorded with a 3 s time constant and a very slow scan rate. The poor signal-to-noise ratio is a reflection of the weak- ness of the absorption, but on close examination of these and other traces of the same region, some of the " noise " is seen to be a dense succession of real overlapping fea- tures.Approximately similar spectra have been observed on a number of other laser lines between 975 and 1020 cm-l, though there are relatively few features as sharp and isolated as the prominent line near 3 kG in fig. 2. There is no evidence for any par- ticularly strong or simple 1.m.r. spectra in the region of 1015 cm-', which is thought from visible laser excited fluorescence meas~rements~~ to be the v3 (C-0 stretch) fre- quency of CH30. None of the spectra observed to date invite even an attempt at analysis; clearly it is necessary either to increase the signal-to-noise ratio considerably, or to find more spectra with isolated and easily measurable lines. In any event, analysis of CH30 spectra would not be easy, because the rotational structure is itself very complicateds6 and there may be a number of vibrational bands (some degenerate) in the 10 ,urn region.NEW FITS O F L . M . R . SPECTRA OF HCO, H02, D02, PH2 A N D ND, The reanalysis of already published results in molecular spectroscopy may generally seem to be a sterile pastime. Nevertheless, such a re-fitting of data is reported here for 5 triatomic free radicals that have been studied at N.R.C. by mid-infrared 1.m.r. during the past 4 years: HCO ( u ~ ) , ~ ~ HO, ( v J , ~ , DO, ( v , ) ~ ~ PH, (u,),~~ and ND, (u,).~~ There are three recent developments that make this effort worthwhile: (1) Most im- portantly, new improved measurements of isotopic CO, laser frequencies have become available59 which differ from the best previous values by up to 70 MHz (this is most important for HO,, PH2, and ND,).(2) New information on the ground vibrational states of some of the molecules has become available (this is most important for HCO, DO2, and PH,). (3) A sign error has been discovered in the computer program ori- ginally used to fit these spectra. The error involved the relative sign of the isotropic and anisotropic parts of the Zeeman matrix element connecting the Fl and F, levels of a given ( N , K,, K,) state, and had only a small effect at worst, being most important for HO, and DO,. In the following paragraphs, the results of new analyses of these previously reported spectra are given; for more complete information, the reader is also referred to the original HCO The new measurements of Freed et ~ 1 .~ ~ change the frequencies of laser lines used to the v, band of HCO by only small amounts ((7 MHz), and this molecule was unaffected by the sign error, because it was originally analysed using a simpler com- puter program. However, much better parameters for the ground vibrational state of HCO are now available60 from analyses of e.p.r. and far-infrared 1.m.r. spectra.61 In particular, the A rotational constant and the quadratic centrifugal distortion con- stants are now well-known. The results of the new fit of the HCO v, band data of Johns et aZ.29 are shown in table 2. The ground-state parameters were all fixed at the values of Brown60v61 and 9 excited-state parameters were varied, as compared with 13 ground- and excited-state parameters varied in the original fit.29 The new Zeeman calculation included the effects of the anisotropic g-tensor and AN = &I mixingA .R . W. MCKELLAR 71 approximated in a way previously described32 (these effects are small for HCO because of its relatively small spin-rotation interaction). The r.m.s. deviation of the fit was 25 MHz, slightly worse than the original29 20 MHz, but still well within the expected experimental error. The parameters of the ( Z J ~ Z J ~ V ~ ) = (010) excited state given in TABLE 2.-MOLECULAR PARAMETERS FOR HCO (IN Cm-') parameter ground (000) state" excited (010) state VO A B C A K lo6 A N lo5 A N K 104 6 , 1 0 7 t j N &a, lo4 Ebb 103 &,, 103 AL 24.329 01 1.494 045 1.398 576 0.030 683 1.50 3.919 1.93 3.656 0.387 752 6.324 - 6.861 - 1.643 1080.762 l(3) 26.574 98( 15) 1.500 256(53) 1.392 562(79) 0.049 561 (1 7) 3.22( 106) - 0.20(46) C C 0.475 93(50) C C - 3.160(62) From a fit to microwave, e.p.r.and 1.m.r. data.60.61 Present results, from a fit to 1.m.r. data Uncertainties in parentheses are la from the least-squares fit, in units of the last Rotational g-factors were also fixed at of Johns et quoted digit. the following values6' for both states: g;a Parameters fixed at the ground-state value. -0.0039; gp'b = 0; g,'" = -0.000 07. table 2 are changed from the previous determinati~n,,~ and should be more reliable thanks to the improved laser frequencies, ground-state parameters and Zeeman cal- culation.HO, The best parameters for the ground vibrational state of HO, (Barnes et aZ.)62 remain the same as those assumed by Johns, McKellar and Riggin32 in their analysis of the v3 band, except for slightly refined values of I , , and cbb due to Brown and Sears.63 However, the new laser-frequency measurements have a large effect for this molecule. Lines of the R-branch of the 9.2 pm band of 12C180, above 1100 cm-' are the most changed of the news9 measurements, and more than one third of the H02 data was obtained with these laser lines. The most changed of the frequencies used is that of R(44) at 1109.880 crn-l, which has moved up by ca. 70 MHz. The sign error also has a significant effect in this case, since HO, has the largest spin-rotation interaction of the molecules considered here, and hence the largest anisotropic electron g-factor effects.The parameters resulting from the new fit to the HO, v3 band data of Johns et aL3' are given in table 3. The r.m.s. deviation of the new fit was 19 MHz, as com- pared in the 26 MHz in the original fit; there were 12 parameters varied in each case. One pleasing aspect of the new results is that the values obtained for SE, and E:, are much closer to their ground-state values. DO2 The v2 band 1.m.r. spectrum of DOz at ca. 1020 cm-' was studied by M ~ K e l l a r , ~ ~ who found it necessary to include in the analysis the effects of the Coriolis interaction72 M I D - I . R . LASER MAGNETIC RESONANCE SPECTROSCOPY between the observed (010) vibrational state and the (001) state which lies about 100 cm-I higher in energy.Thus the v 2 analysis yielded a few effective v3 parameters even though this band was not directly observed. Only one microwave transition had been measured for the ground state of DOz, so a number of ground-state parameters were also varied and determined from the mid-infrared results.33 The laser frequen- cies used in the original analysis are little changed, but now accurate ground-state constants are available from the study of the far-infrared 1.m.r. spectrum of DO2 made TABLE 3.---MOLECULAR PARAMETERS OF H 0 2 (IN Cm-') parameter ground (000) state" excited (001) stateh VO A B C 104 A~ 104 los 6, 107 an: 104 E,, 104 A; lo6 Ajv &a, lo2 Ebb 20.356 560 1.118 0356 1.056 3188 4.124 1.155 3.893 6.71 1 -2.33 -1.653 516 - 1.409 6 2.88 7.61 1097.625 8( 1) 20.309 080( 50) 1.105 532(37) 1.042 649(38) 4.152 2(69) I .306( 29) 2.3 5( 65) 8.1(84) C -1.711 65(26) - 1.4200( 98) 2.9( 12) 7.3 1 (33) a From Barnes ef a/.,62 except for Ebb from Brown and Sears.63 Converted to the A-reduced Uncertainties in parentheses Parameter fixed at the ground- Sextic centrifugal distortion parameters and rotational g-factors were also fixed to the form.65 Present results, from a fit to the 1.m.r.data of Johns et are la from the least-squares fit, in units of the last quoted digit. state value. values of Barnes et ~ 1 . ~ ' recently by Barnes et af.64 The ground-state constants that could be determined from the mid-infrared analysis33 are in remarkably good agreement with the new64 values, but they can now be held fixed at more accurate values.And less well-known para- meters (e.g., A" and A:) that had previously to be fixed are now known much better. The results of the new fit to the DO2 v2 band 1.m.r. data33 are shown in table 4, which also lists the ground-state parameters of Barnes er af.,64 converted from the S-reduced to the A-reduced form of the asymmetric rotor Hamiltonian.6s The r.m.s. deviation of the fit was improved to ca. 19 MHz from the value of 24 MHz. There are fairly large changes in A' and A; between the old33 and new (table 4) fits, but this is simply a reflection of the newly assumed ground-state parameters. Only the dif- ferences A' - A'' and A; - A: are well-determined since vz is an a-type band (A& = 0) and these are little changed.The altered A values do, however, have an important secondary effect on the calculations, since they affect the relative positions of the (OlO), K, and (OOl), K, - 1 levels which are in Coriolis interaction. This is probably the reason that the effective value of vj inferred from the new calculation is ca. 1 cm-l higher than the previous value. PH2 At the time of the study of the v2 band of PH, by Hills and M ~ K e l l a r , ~ ~ some far- infrared 1.m.r. measurements on one ground-state rotational transition were also available.66 These two sets of 1.m.r. data were combined in a fit in which all the neces-A . R. W. MCKELLAR 73 TABLE 4.-MOLECULAR PARAMETERS FOR DO1 (IN Cm-') parameter ground (000) statea excited (010) stateb 11.194 508 1.055 982 8 0.961 059 2 1.281 8.304 3.612 5.17 0.253 -0.905 486 - 1.3077 2.03 2.97 1020.161 5(2) 11.431 885(42) 1.056 796(68) 0.955 891(67) 1.639 4(21) 8.83(23) 4.43(73) 5.2( 15) C -0.946 74(21) - 1.399(30) 3.2(29) 2.7 1 ( 1 6) Coriolis parameters 1121.35(3) 0.680 29(96) -0.013 4(18)d +0.008 5(59)e a From Barnes et u I ., ~ ~ converted to the A-reduced form.65 Present results, from a fit to the 1.m.r. data of M ~ K e l l a r . ~ ~ Uncertainties in parentheses are lo from the least-squares fit, in units of the last quoted digit. Rotational g-factors were also fixed to the values of Barnes et ~ 7 1 . ~ ~ d A s = 8(001) - 8(000); 8 = (B t C)/2. AEaa = E,, (001) - ~ ~ ~ ( 0 0 0 ) . sary ground- and excited-state parameters (25 in all) were determined.Since then, further far-infrared 1.m.r. measurements have been reported by Davies et al. ; 67 these involve 8 more rotational transitions which may now be added to a combined fit. The newly CO, laser frequencies alter one line used for PH, by ca. 40 MHz Parameters fixed at the ground-state value. All other (001) state parameters were fixed at their (000) state values. TABLE 5.-MOLECULAR PARAMETERS FOR PH2 (IN Cm-') parameter ground (000) statea excited (010) state" VO A B C lo3 AK lo3 ANK 104 A~ 104 aK 104 6, Eaa lo2 Ebb 104 E , , 104 ~k 9.132 45(8) 8.084 37( 11) 4.214 40(8) 2.821 O(54) 5.477(25) 2.524(19) - 1.758 O(74) - 1.048(27) -0.281 41(37) - 8.1 20( 24) -7.5(18) 1.62(20) 1 101.908 6(2) 9.432 87( 16) 8.252 70(13) 4.154 51(6) 3.358(26) 6.3 33(49) 2.91 9(23) -2.071(17) - 0.44(70) -0.303 60(63) - 8.81 8(35) 0.6( 17) 3.07(70) a All parameters determined in the present fit to the data of Davies et a1.66*67 and Hills and Mc- Kellar.34 Uncertainties are la from the least-squares fit, in units of the last quoted digit.Rota- tional g-factors were fixed at the following estimated values (see text) for both states: g;" = -0.000 94; g,"b = -0.00027; g:' = 0.74 MID-I.R. LASER MAGNETIC RESONANCE SPECTROSCOPY and the rest by 2 MHz or less; the above-mentioned sign error has very little effect for this molecule. 1 . m .r. data on PH2 are shown in table 5. All the data were equally weighted in the fit, and rotational g- factors were fixed at values (see table 5) estimated using a simple approximate rela- tion6’ for the electronic contribution to g , .The r.m.s. deviations resulting from the fit were 21 MHz for the v, band data34 and 14 MHz for the rotational data.66*67 The uncertainties in 24 out of the 25 parameters (table 5 ) are less than those in the earlier fit,34 and for many ground-state parameters the improvement is quite large. This is, of course, mostly due to the newly included ground-state data.67 In their analysis of the PH2 ground state, Davies et ~ 1 . ~ ’ fitted their own measure- m e n t ~ ~ ~ ~ ~ ~ plus the calculated ground-state term values from the v, band The latter were given a reduced weight (0.01), but were still required because the far- infrared data were insufficient for a good determination of all the parameters. It might thus be thought that the present results (table 5) and would be very similar, since all the same data contributed to each fit.However, this is not the case: the present results are to be preferred since all the original measurements were directly fitted. Fitting a mixture of measured lines and calculated term values was convenient, but failed to make best use of the available data. (There remains, however, an area of legitimate argument as to the best relative weights for the mid- and far-infrared mea- surements.) The quoted parameter uncertainties (converted to la) are generally lower in Davies et ~ 1 . ~ ~ than here, but this is likely an artifact of their fit (i.e., by fitting cal- culated term values one could even achieve zero apparent uncertainties). The results of the new fit to the ND2 The v2 band measurements of Hills and M ~ K e l l a r ~ ~ remain the only available high- resolution data for ND2.The new C02 laser frequencies result in significant changes (25 to 50 MHz) for three of the laser lines used in the original study. The results of the new fit to the ND, v2 band data are shown in table 6; this fit differs from the pre- vious in the assumed laser frequencies and in that the rotational g-factors were TABLE 6.-MOLECULAR PARAMETERS FOR ND2 (IN Cm-’) parameter ground (000) statea excited (010) statea b’0 A B C 103 AK lo3 ANK lo4 AN 1 0 4 6, 1 0 5 H~ 104 8 N Eaa Ebb Ecc 1 0 4 A; 13.344 18(30) 6.490 62( 11) 4.287 03(14) 6.707(35) 2.339(41) 0.59(26) 1.878(26) 1.55(15) -0.979( 13) - 0.1 70 49(29) -0.021 65(26) 0.000 21 1.34( 12) 1108.749 3(6) 14.234 96(18) 6.552 23(9) 4.237 39(12) 9.544(30) 2.982(28) 5.60( 16) 1.261 (16) 2.9 1 (29) - 1.366 2(80) -0.203 14(56) -0.024 09(23) - 0.0005 2.44(39) a Determined from a fit to the data of Hills and M ~ K e l l a r .~ ~ Uncertainties in parentheses are la from the least-squares fit, in units of the last quoted digit. Rotational g-factors were fixed at the following estimated values: g:a = -0.0024; g:b = -0.000 30; giC = -0.0000. be cc was fixed at values estimated from NH2.”A . R. W. MCKELLAR 75 fixed at approximate calculated6’ values instead of at zero. The r.m.s. deviation of the fit improved to 34 MHz from the previous 40 MHz. There were corresponding improvements in the uncertainties of the 25 parameters varied, but all remained within la of their previous3s values.CONCLUSTON In the past 5 years, mid-infrared 1.m.r. has yielded a remarkable amount of infor- mation on vibration-rotation and spin-orbit spectra of unstable molecules. In most cases, these results could not have been obtained by other, more conventional, in- frared spectroscopic techniques. We can anticipate a continuation of new results in this field during the coming years. However, the pace of developments may be somewhat slowed, since many of the better-known free radicals expected to absorb in the accessible (5-7 and 9-1 1.3 pm) regions have now been observed. As for lesser- known free radicals, l.m.r., especially of vibration-rotation bands, is a difficult way to obtain the first knowledge (at least for polyatomics) because the Zeeman effect must be analysed as well as the zero-field spectrum.Of course, it may be the only available technique, and remarkable successes are possible as illustrated by the case of CH,OS6 in the far-infrared. Tunable lasers are another factor in the development of infrared spectroscopy of high sensitivity and resolution. A prominent example of this is the great progress made by Hirota68 and co-workers at the Institute for Molecular Science with the appli- cation of semiconductor diode lasers to free radical spectroscopy. 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