摘要:

DISCUSSIONS OF THE FARADAY SOCIETY No. 35, 1963 THE STRUCTURE OF ELECTRONICALLY EXCITED SPECIES IN THE GAS-PHASE THE FARADAY SOCIETY Agents f o r the Society’s Publications: The Aberdeen University Press Ltd. Farmers Hall Aberdeen scotland@ The Faraday Society and Contributors, 1963 PUBLISHED . . . . 1963 PRINTED IN GREAT BRITAIN AT THE UNIVERSITY PRESS ABERDEENA GENERAL DISCUSSION ON THE STRUCTURE OF ELECTRONICALLY EXCITED SPECIES IN THE GAS-PHASE 2nd and 3rd April, 1963 A GENERAL DISCUSSION on The Structure of Electronically-Excited Species in the Gas Phase was held at Queen’s College, University of St. Andrews, Dundee, on the 2nd and 3rd April, 1963. The President, Prof. A. R. Ubbelohde, C.B.E., M.A., D.Sc., F.R.S., was in the Chair and about 135 members and others were present.Among the visitors from overseas were the following: Mr. F. A. Baker (Switzerland), Mr. U. Bonne (Germany), Dr. J. Colpa (Netherlands), Prof. J. B. Coon (U.S.A.), Dr. M. Daniels (Puerto Rico), Dr. D. W. Davies (Netherlands), Dr. E. de Boer (Netherlands), Dr. A. E. Douglas (Canada), Prof. D. A. DOWS, (U.S.A.), Dr. H. R. Gersmann (Netherlands), Dr. Y. Haven (Netherlands), Dr. and Mme. H. Hering (France), Dr. G. Herzberg (Canada), Mr. M. Horani (France), Dr. J. C. Lorquet (Belgium), Dr. E. L. Mackor (Netherlands), Prof. B. H. Mahan (U.S.A.), Prof. L. J. Oosterhoff (Netherlands), Prof. H. B. Palmer (U.S.A.), Dr. L. M. Raff (U.S.A.), Dr. D. A. Ramsay (Canada), Prof. and Mrs. B. Rosen (Belgium), Prof. R. M. Rosenberg (U.S.A.), Mme. J. Rostas (France), Prof.P. S. Skell (U.S.A.), Dr. B. R. Stein (Germany), Dr. G. Szasz (Switzerland), Miss J. A. van der Hoek (Netherlands), Dr. J. H. van der Waals (Netherlands), Dr. G. A. J. Voetelink (U. S . A.) . . .. .A GENERAL DISCUSSION ON THE STRUCTURE OF ELECTRONICALLY EXCITED SPECIES IN THE GAS-PHASE 2nd and 3rd April, 1963 A GENERAL DISCUSSION on The Structure of Electronically-Excited Species in the Gas Phase was held at Queen’s College, University of St. Andrews, Dundee, on the 2nd and 3rd April, 1963. The President, Prof. A. R. Ubbelohde, C.B.E., M.A., D.Sc., F.R.S., was in the Chair and about 135 members and others were present. Among the visitors from overseas were the following: Mr. F. A. Baker (Switzerland), Mr. U. Bonne (Germany), Dr. J. Colpa (Netherlands), Prof. J.B. Coon (U.S.A.), Dr. M. Daniels (Puerto Rico), Dr. D. W. Davies (Netherlands), Dr. E. de Boer (Netherlands), Dr. A. E. Douglas (Canada), Prof. D. A. DOWS, (U.S.A.), Dr. H. R. Gersmann (Netherlands), Dr. Y. Haven (Netherlands), Dr. and Mme. H. Hering (France), Dr. G. Herzberg (Canada), Mr. M. Horani (France), Dr. J. C. Lorquet (Belgium), Dr. E. L. Mackor (Netherlands), Prof. B. H. Mahan (U.S.A.), Prof. L. J. Oosterhoff (Netherlands), Prof. H. B. Palmer (U.S.A.), Dr. L. M. Raff (U.S.A.), Dr. D. A. Ramsay (Canada), Prof. and Mrs. B. Rosen (Belgium), Prof. R. M. Rosenberg (U.S.A.), Mme. J. Rostas (France), Prof. P. S. Skell (U.S.A.), Dr. B. R. Stein (Germany), Dr. G. Szasz (Switzerland), Miss J. A. van der Hoek (Netherlands), Dr. J. H. van der Waals (Netherlands), Dr. G.A. J. Voetelink (U. S . A.) . . .. .CONTENTS PAGE Twelfth Spiers Memorial Lecture-Determination of the Structures of Simple Poly- atomic Molecules and Radicals in Electronically Excited States. By G. Herzberg . . 7 Electron-Impact Spectroscopy. By Aaron Kuppermann and L. M. Roff. . . 30 Circular Dichroism of Dissymmetric ap-Unsaturated Ketones. By R. E. Ballard, S. F. Mason and G. W. Vane . . 43 Dipole Moments and Polarizabilities of Electronically Excited Molecules Through the Kerr Effect. By A. D. Buckingham and David A. Dows . . 48 Wave Functions of Excited States. By J. W. Linnett and 0. Sovers . . 58 Angular Correlation Diagrams for AH2-Type Molecules. By C . A. Coulson and A. H. Neilson . . 71 Intersection of Potential Energy Surfaces in Polyatomic Molecules. By G.Herzberg and H. C. Longuet-Higgins . . 77 Stereochemistry of Hydrocarbon Ions. By J. C. Lorquet . . 83 Electronic Absorption Spectra of HCO and DCO Radicals. By J. W. C. Johns, S. H. Priddle and D. A. Ramsay . . 90 Carbon Monoxide Flame Bands. By R. N. Dixon . . 105 Spectrum of the C3 Molecule. By L. Gausset, G. Herzberg, A. Lagerqvist and B. Rosen . . 113 Evidence for a Double-Minimum Potential in an Excited State of C102. By J. B. Coon, F. A. Cesani and C. M. Loyd . . 118 Absorption Spectrum of Sulphur Dioxide in the Vacuum Ultra-violet. andB. Rosen . . 124 Rotational Analysis of Bands of the 3800A System of SO2. . 127 Absorption Spectrum of Chlorine Dioxide in the Vacuum Ultra-violet. By C . M. Electronic Structure and Spectrum of the HC02 Radical.By T. E. Peacock, Rias- ur-Rahman, D. H. Sleeman and E. S. G. Tuckley . . 144 Absorption Spectra of the Hydrides, Deuterides and Halides of Group 5 Elements. By C. M. Humphries, A. D. Walsh and P. A. Warsop . . 148 Electronically Excited States of Ammonia. By A. E. Douglas . . 158 The 38208, Band System of Propynol. By J. C. D. Brand, J. H. CalIomon and J. K. G. Watson . . 175 Near-Ultra-violet Spectrum of Propenal. By J. C . D. Brand and D. G. Williamson 184 By I. Dubois By A. J. Merer . Humphries, A. D. Walsh and P. A. Warsop . 137 Polarization and Assignment of the 3700 8, Absorption Spectrum of the Tropyl Radical. By B. A. Thrush and J. Vapour. By K. K. Innes and L. E. Giddings, Jr. . 5 Spectrum of 7,4-Diazine . 192 J. Zwolenik . . 1966 CONTENTS PAGE Ionization and Dissociation Energies of the Hydrides and Fluorides of the First Row Elements in Relation to their Electronic Structures. By W. C. Price, T. R. Passmore and D. M. Roessler . . 201 GENERAL DrscussroN.-~r. J. €3. van der Walls, Dr. E. L. Mackor, Prof. A. D. Walsh, Dr. S. F. Mason, Dr. E. Charney, Prof. C. A. Coulson, Dr. J. W. Linnett, Dr. D. W. Davies, Mr. D. M. Hirst, Dr. A. H. Neilson, Dr. H. H. Greenwood, Dr. A. E. Douglas, Dr. G. Herzberg, Dr. J. C. Lorquet, Dr. I. M. Mills, Dr. B. A. Thrush, Dr. R. N. Dixon, Dr. J. C. Brand, Prof. P. S. Skell, Dr. J. K. G. Watson, Mr. A. J. Merer, Dr. T. E. Peacock, Dr. J. L. Duncan, Prof. W. C. Price, Dr. T. R. Passmore, Dr. J. M. Hollas, Prof. K. K. Innes, Dr. D. M. Roessler 212 Author Index . . . . . 240

ISSN:0366-9033    

DOI:10.1039/DF9633500001

出版商:RSC    

年代:1963

数据来源: RSC

摘要:

TWELFTH SPIERS MEMORIAL LECTURE Determination of the Structures of Simple Polyatomic Molecules and Radicals in Electronically Excited States BY G. HERZBERG Division of Pure Physics National Research Council Ottawa Ontario Canada A. INTRODUCTION I am greatly honoured by the request of the Council of the Faraday Society to present the Twelfth Spiers Memorial Lecture and I am most grateful to them for giving me this opportunity of discussing a subject in which my collaborators and I have been interested for many years. Mr. Spiers I understand was the person mainly responsible for developing the kind of discussion for which the Faraday Society is now known throughout the world. The last Discussion that Mr. Spiers organized before his death was the one in Oxford in 1925 on Photochemistry.It had a lasting effect on the future development of spectroscopy because it gave us the Franck-Condon principle. The first Faraday Society Discussion that I attended as a young post-doctorate fellow was the Bristol discussion on Molecular Spectroscopy and Molecular Struc-ture in 1929 which took place within a year of the First Spiers Memorial Lecture given by Sir Oliver Lodge. I still remember vividly the great impression that this Discussion made on me. This meeting concluded a period of rapid development in our understanding of the electronic spectra of diatomic molecules At the same time it marked the beginning of the rapid advances that have been made in the study of infra-red and Raman spectra of polyatomic molecules of their vibrational and rotational structure and therefore of their force fields and geometrical struc-tures.After the last war through the development of microwave spectroscopy, great strides were made with regard to geometrical structures and this subject formed a prominent part of the Cambridge Discussion of the Faraday Society in 1950. While a good deal of important work was done before 1950 on electronic spectra of polyatomic molecules and while some of the basic theory was developed in the 1930s these spectra were then not in the centre of attention. It is only since about 1950 that detailed applications of the theory have been made and new theoretical developments have taken place. The study of electronic spectra is our only source of information about the structure of polyatomic molecules in their excited states the topic of this Discussion.For free radicals electronic spectra supply the only means of information even about their ground states since infra-red Raman and microwave spectra of free radicals have not yet been obtained. Progress in the study of electronic spectra of polyatomic molecules has been relatively slow because even now there are many gaps in our theoretical knowledge which impede progress toward the understanding of the structure of excited states of even very simple molecules. Apart from that progress is retarded by the com-plexities of the observed spectra produced by well-known effects and the consequent large amount of labour required for the analysis. 8 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES In this lecture I should like to summarize some of the results that have been ob-tained in the last 10 to 15 years and to explain some of the difficulties that have been encountered pointing out both those that have been solved and those that still await solution by further theoretical developments.B. SIMPLE (ALLOWED) ELECTRONIC TRANSITIONS In the simplest case the absorption spectrum of a polyatomic molecule should be very similar to that of a diatomic molecule except for the complication introduced by the presence of several normal vibrations and for non-linear molecules the greater complication of the rotational structure. As is well known in an allowed electronic transition almost exclusively the totally symmetric vibrations are excited. For non-totally symmetric vibrations we have the selection rule Ava = 0 +2 +4 .. ., but the transitions with Aua = +2 +4 are extremely weak unless there is a verylarge change (by a factor 2 or more) in frequency in the transition from upper to lower state. When only one totally symmetric vibration exists as in linear XY2 molecules then as for diatomic molecules only one single progression of bands is expected in absorption at low temperature. When two (or more) totally symmetric vibrations exist each band of the first progression (in v1 say) is the starting point of a new progression (in v2) and so on. This soon leads to quite a complicated pattern unless the internuclear distances change very little in which case according to the Franck-Condon principle the 0-0 band is very much stronger than all others.Such a situation is often encountered in Rydberg transitions when the geometry of the ion deviates little from that of the neutral molecule. Conversely, the observation of clear Rydberg series of bands allows the conclusion that the geometry of the molecule in the upper states (and therefore in the ion) is very similar to that of the ground state. The rotational structure in these simple cases is closely similar to that of corres-ponding infra-red bands except that the difference between the rotational constants in the upper and lower states may be larger. By corresponding infra-red bands we mean here bands for which the direction of the vibrational transition moment in the infra-red spectrum is the same as that of the electronic transition moment in the ultra-violet spectrum since it is this direction of the dipole moment which deter-mines the rotational selection rules and therefore the band structure.Thus bands of X-Z II-Z . . . electronic transitions of linear molecules have the same structure as E-E II-X . . . vibrational bands in the infra-red; bands of Al-Al and E-Al electronic transitions of C3u molecules would have the same structure as 11 and 1. infra-red bands. It must however be remembered that band types can arise in electronic spectra which cannot arise in infra-red spectra simply because appropriate vibrations do not exist. Unfortunately examples of such simple spectra are not very plentiful for several reasons (i) in many cases the geometry of the molecule in the excited state is not the same as that in the ground state ; (ii) vibronic interactions often introduce com-plications ; (iii) all too frequently predissociation blurs the rotational structure and sometimes even the vibrational structure of electronic transitions ; and (iv) many simple transitions lie in the vacuum ultra-violet where the available resolution is insufficient to resolve them.The last reason applies particularly to Rydberg transitions which are likely to be of the simple type when the ion has the same geometrical structure as the neutral molecule. Nevertheless a few examples of such simple electronic transitions are known. Almost all well-known linear molecules like HCN C2H2 C02 CS2 etc. hav G . HERZBERG 9 first and second excited states in which the molecule is not linear and therefore the corresponding spectra are not simple while in the Rydberg series which are ob-served either predissociation blots out the rotational structure (as in the first Rydberg transitions of HCN and C2H2) or the attainable resolution is not sufficient (as for C02 and CS2).An exception is the absorption band of C2H2 (and C2D2) in the region 1250 A reproduced in fig. 1. Here we have a single strong band with a simple fine structure (having a single P Q and R branch). Since the lower state is 1Ei, the upper state must clearly be In,. This band is the second member of one of Price’s Rydberg series. Another very similar band at shorter wave lengths is un-doubtedly the 1-0 band in the totally symmetric C=C stretching vibration of the same electronic transition.Even in this simple spectrum complications arise as soon as hot bands are considered (see below). Another example of a simple spectrum of a linear molecule is the 3C-3E transition of CH2 CHD and CD2 at 1415A. Only a single strong band has been observed in each case. The lines are very broad and hardly recognizable for CH2, but for CHD and CD2 the typical X-X structure is clearly visible and in CD2 an intensity alternation is observed. In my Bakerian lecture 1 I have shown that in all probability this is a triplet transition; but in spite of renewed efforts the triplet structure has not yet been resolved. It appears that the two examples given are the only ones of simple well-resolved electronic transitions of linear molecules known at present. The situation is no better for (genuine) symmetric top molecules.While there are several simple spectra whose fine structure has not been resolved there appear to be only two or three with a resolved fine structure. Fig. 2 shows one of these, a 11 band of CD3 at 1410 A which shows a simple P Q and R branch. The Kstructure is only partially resolved. There are a number of asymmetric top molecules for which “ simple ” spectra have been found. The most nearly symmetric case seems to be the spectrum of the HNCN radical recently observed by Warsop and myself? It consists of a single typical 1 band at 3440 A entirely similar to the usual 1. infra-red band of a sym-metric top molecule. The partially resolved Q branches of the sub-bands are very nearly equidistant (having half the spacing in the deuterated molecule) and the P and R branches are rather well resolved and readily analyzed.The fairly large K-type doublings in the sub-bands involving K’ = 1 or K” = 1 show that the mole-cule is really an asymmetric top and that the transition moment is _L to the plane of the molecule. The three heavier atoms are nearly on a straight line but the H (or D) atom is off that line at an angle of 11 6.5” in the lower and 120.6” in the upper state. The N-N distance is 2.471 and 2 - 4 4 respectively. Another spectrum of this type is the red spectrum of HNO first studied by Dalby 3 and more recently in greater detail by Ramsay and his collaborators.4 The sub-bands in each band are clearly resolved and the K-type doubling is visible up to K = 3 indicating a much less symmetric top than HNCN.The geometrical struc-ture of the molecule in the two electronic states is shown in fig. 3. A number of other vibrational transitions in addition to the 0 4 band has been found and has yielded all three vibrational frequencies in both the upper and lower state. The rotational structure of the bands shows that the transition is electronically A”-A’ (or A’-”’) i.e. the transition moment is perpendicular to the plane of the molecule. A similar simple electronic transition gives rise to the system of near ultra-violet bands of propynal analyzed by Brand Callomon and Watson 5 and reported at this meeting. But complications arise because of the presence of forbidden components of the dipole moment. The spectrum of NO2 near 2400A recently analyzed i 10 STRUCTURES OF SIMPLE POLYATOMIC STRUCTURES detail by Ritchie Walsh and Warsop 6 also belongs to this group.But the visible NO2 bands which one would expect to correspond to a simple electronic transition have thus far defied all attempts at analysis even though they lie in a very con-venient spectral region and at least above 4000& do not suffer broadening by predissociation. Finally a " simple " spectrum of a strongly asymmetric top should be mentioned : the 1240A band of H20 and the similar band of D20 recently analyzed by Johns.7 Even though in H20 the lines of higher J are strongly broadened by predissociation, it was possible to obtain an unambiguous analysis because the ground state rotational levels were known. Fig. 4 shows the result.N UPPER STATE 0 N LOWER STATE J H FIG. 3.-Geometrical structure known electronic 0 of HNO in its two states. As expected from the predominant 0 H H 0 H H FIG. 4.-Geometrical structure of H20 in the upper 1B1 state of the 1240 8 band as compared with that in the ground state. intensity of the 0-0 band there is only a slight change of angle and of 0-H distance in the excited state compared to the ground state. The transition is electron-ically of the type 1B1-1A1 (i.e. the transition moment is _L to the plane of the molecule) a type that does not occur in the infra-red. C. COMPLICATIONS O F THE SPECTRUM BY CHANGE OF SHAPE OF THE MOLECULE Perhaps the most important and frequent complication in electronic spectra arises when the molecule has a different symmetry in the excited state from that in the ground state (or lower state).In a way this is a trivial complication and certainly the easiest to take into account once it has been established that such a change occurs; but this is often beset with difficulties. A change of shape can be established either by a study of the vibrational or of the rotational structure or both. (a) VIBRATIONAL STRUCTURE When the equilibrium positions of the nuclei in two electronic states of a given molecule have different symmetry the vibrational selection rules in the transitio G. HERZBERG 11 between these two states are determined only by the symmetry elements that are common to the two equilibrium positions. Therefore these selection rules will be less restrictive than when the symmetry is the same.All those vibrations will be counted as totally symmetric which are symmetric with respect to the common symmetry elements and they may therefore be excited strongly in the transition. Thus in a transition of an XY2 molecule from a state in which it is linear (and symmetric) to a state in which it is bent there are two totally symmetric vibrations, that is two progressions (rather than one) that can occur strongly. In particular, the bending vibration which in a linear-linear transition is restricted to A212 = 0, 2 +4 . . . with ADZ = 0 by far the strongest will now occur in a long progression with consecutive A212 values and with an intensity maximum at the wave number corresponding to the initial conformation.In this way the first case of a change of shape in the near ultra-violet bands of CS2 was recognized by Mulliken.8 In the same way the non-linearity in the first excited states of HCN and C2H2 was first suspected. Such conclusions from the vibrational structure alone are however somewhat dangerous since they presume a knowledge of the type of vibration corresponding to an observed progression. It is often difficult to be quite certain of such an assignment. Similarly if a non-linear molecule is planar in one state but non-planar in another, there will be long progressions of the out-of-plane vibration in the transition be-tween these two states. Such progressions are very prominent in the two first ultra-violet absorption systems of NH3 one consisting of 11 bands and the other of 1 bands and this observation seems to show that NH3 is planar in the upper states of these bands.This is in contrast to the situation in CH3 which is planar in both its ground state and most of its excited states and for which therefore only a single prominent band is observed in each electronic transition. Of course we must guard against the possibility that the long progression observed is one in a totally symmetric vibration whose frequency has changed greatly in going from one to the other electronic state. However for planar-non-planar transitions, there is a very simple and definite way of establishing the character of the vibration, if there is a noticeable inversion doubling in the non-planar state. In that case as shown by fig. 5 only one component of the inversion doublet can combine with a given vibrational level in the planar configuration and for successive vibrational levels of the planar state it will be alternately the upper and the lower inversion doublet component.Therefore a " staggering " results in the progression corresponding to the out-of-plane bending vibration in the planar state. In this way Walsh and Warsop 9 first established the planarity of the first excited state of NH3. Here the inversion doubling in the vibrationless ground state is too small to be detected in the ultra-violet spectrum but the hot bands coming from the state in which the bending vibration is singly excited show a clear case of this staggering since the inversion doubling of this state amounts to about 30 cm-1.A case of a planar molecule which has a non-planar equilibrium configuration in its first excited state is the H2CO molecule. The interpretation of the " hot " bands of the near ultra-violet absorption system of this molecule remained a puzzle until Walsh 10 and Brand 11 recognized that the molecule is non-planar in the excited state and that the " hot " bands go to the other inversion doublet component (other than the one involved in the main bands). (b) ROTATIONAL STRUCTURE Very definite information about a change of shape of a molecule in an electronic transition comes from a detailed study of the rotational structure. Consider agai 12 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES an electronic transition of a linear molecule from its ground state to an excited state in which the molecule is bent.Usually in this excited state the molecule has still one fairly small moment of inertia; in other words it is a nearly symmetric top molecule in which the rotational quantum number K is approximately defined. We have a coarse rotational structure corresponding to the various values of K, and a finer structure corresponding to the various values of J for each given K and AK. Since in the ground state the quantum number I the analogue of K is zero and since the selection rule AK = 0 1 must apply we can reach from the lowest level of the ground state only the K = 0 and K = 1 levels of the upper state as shown in fig. 6. v + 4 3 + 2 -1 -+ 0 -2 I + + -T 0 FIG. 5.Vibrational energy Ievels for a planar-non-planar transition.K FIG. 6.-Vibrational levels and K rotational levels in a bent-linear transition. The broken vertical lines represent transitions with AK = 0 the full vertical lines transitions with A K = fl. Let us consider first the case in which AK = & 1 which applies when the transi-tion moment is at right-angles to the plane of the molecule in the upper state. Then only the K = 1 levels in the upper state will be reached from the lowest vibrational level of the ground state and we obtain a progression of main bands of the II-X type. Such progressions are for example observed in the first absorption systems of HCN and C2H2 mentioned earlier. At first sight the bands look exactly like those of a linear-linear transition. There is however one difference.Since the molecule in the upper state is really an asymmetric top there will be a large K-type doubling whose magnitude is in general much larger than the A-type doubling o G . HERZBERG 13 electronic origin in a linear molecule. Moreover the magnitude of the doubling will be larger for the deuterated species than for the ordinary molecule while elec-tronic A-type doubling should be independent of isotopic substitution. In the spectra of HCN and C2H2 such a large K-type doubling which increases substan-tially with deuterium substitution has actually been found as illustrated by fig. 7, which shows the doubling observed in one of the vibrational levels of the a state of HCN and DCN. 20 15 4 I g 10 5 0 FIG. 7.-Combination defects in the (020)1-00” 0 bands of HCN and DCN as a function of J(J+ l> The combination defect for a given J is the sum of the K-type doublings for the levels J and J+ 1.Even if the J structure is not sufficiently resolved to determine the magnitude of the K-type doubling or if no isotopes can be investigated it is possible to get very definite information about the absence or presence of a change of shape when the coarse structure of “ h o t ” bands is investigated. If the linear molecule is vibrating in its ground state with one quantum of the bending vibration we have I = 1 and therefore still assuming AK = 1 we reach in the upper state K = 0 and 2 (see fig. 6). In other words the “ hot ” band consists of two sub-bands, one of the type X-Il and the other of the type A-II.The separation of these two sub-bands is given by 4(A’-B‘) and may be relatively large depending on the magnitude of the angle of bending in the excited state. At any rate there will be a double progression of “ hot ” bands (rather than a single one) corresponding to each progression of main bands. Moreover since the upper states of the “ hot ’’ bands have K values different from that of the main bands (K = I) there will be a combination defect between the separations of the “ h o t ” bands from the cor-responding main bands and the infra-red or Raman frequency corresponding to the bending vibration (see fig. 6). Both these points a double series of “ hot ” bands and a combination defect have been found in the first ultra-violet absorption systems of HCN and C2H2.Conversely these observations show even without consider-ation of the J structure that the transition moment is perpendicular to the plane of the (bent) molecule that is that the transition is lA’’-JX+ for HCN and Au-lXi for C2Hz 14 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES A similar situation arises when the transition moment is parallel to the figure axis of the molecule that is when AK = 0. This is the case in the near ultra-violet bands of CS2. Here there is only a single progression of " hot " bands for a given lower vibrational level which is of the type H-II or A-A etc. depending on the 2 value of the lower state. The K-type doubling in the upper state is recognized by the presence of two heads in each of these " hot " bands and again there is a com-bination defect between the vibrational intervals obtained from the separation of " hot " bands and corresponding main bands on the one hand and those obtained from the infra-red or Raman spectrum on the other.In a planar molecule the transition moment can only be either parallel or per-pendicular to the plane of the molecule. If it is perpendicular to the plane and if the top axis is in the plane a pure _L band results. But if the transition moment is in the plane it will in general for an unsymmetrical molecule have a component parallel as well as perpendicular to the top axis resulting in a hybrid band. This is observed in the 1500 A system of HCN shown in fig. 8. Here each main band has two sub-bands corresponding to K = 0 and 1 of the upper state (see fig.6), one having only one head the other having two heads. For the " hot '' bands in which one quantum of the bending vibration is excited in the lower state there arc now three sub-bands corresponding to K = 0 1 2 that is there are sub-bands of the C-II II-IT and A-II type. Here even though the J structure has not been resolved on account of predissociation the K structure and in particular the triple nature of the progression of" hot " bands shows unambiguously that the molecule is non-linear in the excited state and that the electronic transition is of the type 1A'-1~+. If the molecule is bent in the lower state but linear in the excited state we obtain again a progression in the bending vibration. However in this case each of the bands consists of a number of sub-bands corresponding to different values of K but with the restriction introduced by the fact that in the upper state the even numbered vibrational levels of the bending vibration have only even I values while the odd numbered vibrational levels have only odd 2 values.1 for example the first sub-band in successive members of the progression is alter-nately of the type C-II and l3-Z Such an alternation has been observed for HCO NH2 and CH2 confirming that the molecules are linear in the upper non-linear in the lower states of the respective band systems. In XY3 molecules a change of shape from planar to non-planar can be unambig-uously recognized if the rotational structure is resolved sufficiently so that the presence or absence of an intensity alternation in the sub-bands with K = 0 can be ascertained.As is well known for planar XY3 there is an alternation of statistical weights in the K = 0 levels of a non-degenerate state for even and odd J. This alternation is in the ratio 1 0 if the nuclear spin of the Y atoms is I = 0 ; it is 0 I for I = + and 10 1 for I = 1. It is reversed when the vibronic wave function is antisymmetric with respect to the plane of the molecule. On the other hand there is no alternation of weights when the molecule is non-planar or expressed differently, there are always two sets of levels with opposite alternation (corresponding to a symmetric and an antisymmetric vibronic wave function) nearly coinciding with each other. Their slight separation is the inversion doubling. As a consequence of the alternation of statistical weights for the planar conformation there is an in-tensity alternation (or alternate missing lines for I = 0 and +) in the K = 0 sub-bands of any 11 band of both a planar-planar and a planar-non-planar transition." * Even for a non-planar -non-planar transition an intensity alternation would occur if the in-version doubling were resolved in at least one of the two states.But there would then be always two bands with opposite intensity alternation close together. Thus for AK G. HERZBERG 15 But for a planar-planar transition the intensity alternation is the same in all bands of a progression (Av = 0 2 4 . . .) while for a planar-non-planar transition the intensity alternation alternates in sign in a progression in the out-of-plane bending vibration (Av = 0 1 2 3) for even v the lines with even J for odd v the lines with odd J are weak or missing; or conversely for even va the lines with odd J and for odd v the lines with even J are weak or missing depending on the sym-metry type of the electronic state with planar equilibrium conformation (and on the statistics of the nuclei).Such an alternation of the intensity alternation was found by Douglas 12 in the 2000A bands of KD3 thus confirming the conclusion from the vibrational analysis of Walsh and Warsop 9 that in the upper state the molecule is planar. For CD3 the presence of an intensity alternation for the K = 0 sub-band of a 11 band showed that at least in one of the two states involved the molecule must be planar and, since here no progression in the out-of-plane bending vibration is observed it was concluded that the molecule is planar in both states.Unfortunately here the absence of an alternation of the intensity alternation could not be established. For 1 bands (E-A transitions) the situation is similar except that the intensity alternation is now in the K’ = 1 tK” = 0 sub-band. Again for a planar-non-planar transition unlike a planar-planar transition there will be an alternation in the sign of the intensity alternation in a progression in the out-of-plane-bending vibration. At the same time the sign of the combination defect between P R and Q branches will alternate if the I-type doubling in the E state is not negligible. Both the alternation in the sign of the intensity alternation and that of the combination defect have been found in the 1600A bands of NH3 by Douglas and Hollas.13 I shall not deal here with the question why in certain cases a change of shape takes place and not in others.As is well known the Walsh diagrams in which the energies of the various orbitals are plotted against the angle or any other suitable variable, have proved to be very useful for an understanding of these changes and in the hands of Walsh 14 have led to a number of predictions which were later on strikingly confirmed for example for HCO NH2 and others. Coulson and Neilson 15 will tell us more about these correlation diagrams. D. VIBRONIC INTERACTIONS I N DEGENERATE ELECTRONIC STATES A very important complication in the electronic spectra of polyatomic mole-cules is introduced by the fact that in polyatomic molecules unlike diatomic mole-cules the interaction of vibration and electronic motion may lead to splittings of electronic degeneracies.This is because in (symmetric) polyatomic molecules (unlike diatomic molecules) there are non-totally symmetric vibrations which take the molecule to unsymmetrical conformations in which the reason for the degeneracy (in general the presence of a more than twofold axis of symmetry) no longer exists. (a) LINEAR MOLECULES In linear molecules degenerate electronic states are of the type IT A . . . just as for diatomic molecules. Let us recall some of the methods by means of which one can establish whether or not a given electronic state of a diatomic molecule is degenerate and what its type is.All of them involve a closer study of the rotational structure of the observed bands. 1 or AJ = 0, - +1 (or for multiplet states in Hund’s case b AN = k 1 or AN = +1 0) tell us (i) The selection rules followed in the observed branches AJ 16 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES immediately whether one (or both) of the two combining states is degenerate (Le., not a Z state). If no Q branch is present the transition must be of the type E-E; if there is a strong Q branch it must be of the type Z-ll ll-Z ll-A . . . and if there is a weak Q branch it must be of the type II-ll A-A . . Often even incomplete resolution allows one to decide whether a Q branch is present and therefore whether or not one of the two states (or both) is degenerate.Thus in the previous example of the 1250A C2H2 band (fig. I) since we know that the ground state is 1Z the observation of a strong Q branch in addition to P and R immediately shows that the upper electronic state is Ill,. (ii) One way of distinguishing Z-II from II-Z or ll-A . . . transitions is by means of the missing lines near the band origin since J>A. However this method is even less practical in linear polyatomic molecules than in diatomic molecules since the region near the band origin is less often sufficiently resolved. (iii) The interaction of rotation and electronic motion in a degenerate state pro-duces a splitting (A-type doubling) which varies as J(J+l) for II states and as J2(J+1)2 for A states. It is in general very much smaller for the latter.Thus, it is possible to distinguish II A . . . states and to say whether in a given transition it is the upper or the lower state that is degenerate. In the 1250A C2H2 band a A-doubling is found through a combination defect between P R and Q branches [increasing proportionally to J(J+l)] and confirms that the upper state is a II state. (iv) If the resultant electron spin S is different from zero spin orbit coupling will produce a splitting of IT A . . . states even for zero rotation which except for the lightest molecules (Hz He2 . . .) is easily recognizable. For X states on the other hand the splitting is much smaller since it depends mainly on the interaction of the spin with the rotation of the molecule. (For 3Z states a spin-spin interaction may add a term that is independent of rotation.) All these methods are applicable to linear polyatomic as well as to diatomic molecules.But for the former an additional method arises connected with vibronic interaction. (v) As already mentioned on account of vibrational-electronic interaction the excitation of a bending vibration produces a splitting first discussed by Teller 16 and Renner 17 and here called Renner-Teller splitting. The existence of this splitting may be used to recognize the degeneracy of a given electronic state of a linear molecule even if the rotational structure is not resolved. On the other hand it leads to a considerable complication of the spectrum. It is easy to see that there must be a splitting of all vibrational levels in a degenerate electronic state except those in which none of the bending vibrations are excited.If for example in a II electronic state of a linear XY2 molecule the bending vibration v2 is singly excited there is a vibrational angular momentum t = 1 about the axis which must be combined with the electronic angular momentum A = 1. This can be done either by having the two angular momentum vectors parallel or antiparallel leading to a vibronic A state (resulting from and 2) and a pair of vibronic Z+ X- states (resulting from 2 and Z). Fig. 9 (centre) shows the number and type of states resulting from the first few vibrational levels of the bending vibrations in ll electronic states of linear XY;! and X2Y2 molecules. In order to predict what the relative separations of the various component levels are it is necessary to consider the potential energy of the system as a function of the angle of bending.This was first done by Rennerl7 for II states of XY2 mole-cules. It is clear that with increasing angle the potential function will show an increasing splitting as shown in fig. 10a. In fact we obtain in a first approximatio FIG. 1.-Absorption spectrum of C2H2 and C2Dz near 1250 8 obtained in the 4th order of a 3 m grating. For each molecule three spectrograms taken at different pressures (0.001 0.003 and 0.010 mm at 1 m path) are reproduced. FIG. 2.-Absorption band of CD3 near 1410 A. [To face page 1 FIG. 8 . y - X system of HCN after Herzberg and hnes (unpublished). The bottom part shows an enlargement of the region between the first three main bands showing the sub-band structure.[See page 14 1732.1 0-0 I I - I % n FIG. 17.-Sections of the absorption spectrum of CF31 under high resolutions howing intensity in V6 and probable Jahn-Teller splitting in a 1-1 band in V6 G . HERZBERG 17 two parabolic potential curves with the same position of their minima. However, the energy levels of the system are not simply the levels of two independent harmonic oscillators. Fig. 9 at right shows the predicted energy levels for small Renner-Teller splitting. Fig. 11 shows the predicted variation of the energy of the C ll A * n 0 2+ n c n FIG. 9.-Vibrational levels of a bending vibration in a Z and a 27 state of a linear molecule. At the right the Renner-Teller splitting is plotted to scale for E = 0-2.V I0 1 (b) FIG. lO.-Potential functions in a I? state of a linear molecule for small and large vibronic interaction. The abscissa is the bending angle. vibronic levels with increasing vibronic coupling. It is seen that while for small interaction the levels are symmetrically placed about the zero-approximation posi-tions for large interaction their positions become quite unsymmetrical so much so that eventually it is no longer clear to which zero-approximation level a given vibronic level belongs 18 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES In a lII-lZ electronic transition observed in absorption at low temperature, the Renner-Teller splittings are not expected to be prominent since the transitions with Aua # 0 are usually very weak (unless there is a very large change of the fre-quency of a non-totally symmetric vibration).But in hot bands this splitting be-comes immediately apparent. Fig. 12 shows an energy level diagram giving the 0 4 1-1 and 2-2 bands of a III-lC electronic transition. It is seen that the 1-1 transition will consist of three component bands the 2-2 transition of five. I I t 0 2 0.4 0 6 c n A FIG. 11.-Variation of energy of C II A vibronic levels with Renner parameter c in a II electronic state of a linear molecule. Up to now no definite predictions about the relative intensities of these bands have been made. The 4050 group of C3 represents a III-lC transition and does show evidence of some of these component bands of 1-1 and 2-2 vibrational transitions as will be shown in the paper by Gausset Lagerqvist Rosen and myself.18 Another example of such a splitting of the hot bands can be seen in the 1E-1C transition of C2H2 (C2D2) discussed earlier.Here since there are two low-frequency bending vibrations two triads of 1-1 bands are expected. In C2H2 three hot bands in C2D2 five are visible in fig. 1. A more detaiIed assignment is not possible at present since no theoretical guide exists with regard to the relative splittings in the 1-1 bands of v4 and v g nor with regard to the relative intensities. Unfortunately these hot bands are not sufficiently resolved to distinguish A-II from Zf-II on the basis of their rotational structure. Actually the first case in which a small Renner-Teller splitting was recognized was in the 2C-2II transition of NCO at 4400A by Dixon.19 Here all three com-ponents of the 1-1 band have been found that is 2II--2C+ 2II-2A and 2II-TZ-.The magnitude of the Renner-Teller splitting in this case is approximately 100 cm-1 in a bending frequency of 533 cm-1. There is a further complication by the spin splitting but on the other hand this splitting helps in distinguishing 2II-2Z from 2II-2A transitions. Hougen 20 has developed theoretical formulae for the mag-nitude of the doublet splitting in the various vibronic levels. The most striking result is that the 2C+ and 2C- vibronic levels of the 2II electronic state have a very large splitting constant y of the same order as the B value. The observed value for the splitting constant agrees very well with that predicted from Hougen's formulae on the basis of the observed Renner parameter.An interesting observation in NCO is the appearance of the 1 4 band in the bending vibration. This band is of the type II-IT which in a 2Z-l-I electronic transition with a perpendicular transition moment would be rigorously forbidden. Its occurrence in NCO cannot be ascribed to Renner-Teller interactions but mus G . HERZBERG 19 be produced by the fact that there is a 2 I I electronic state near the upper 2Z+ state of this transition so that the 1 - 0 band of the %--XI transition can borrow intensity from the 2 I I - 4 - I transition. Another example of Renner-Teller splittings in a 2E-2II transition has been found by Johns 21 for BO2. This molecule shows in addition entirely similar effects 2 in a 2II-n electronic transition.In this case also the agreement of the observed doublet splittings and Hougen’s theory is very gratifying. One interesting peculiarity of a 2II-H transition is that vibronic transitions of the type 2Z-Z occur and indeed that on account of the large spin splitting in these 2Z states both 2E+-2X+ and 2Z-2Z+ transitions occur. The + and - character of the Z states loses its meaning when the splitting is large. The 222 states then behave more like 3 states. Hougen22 has also considered the Renner-Teller splittings in triplet tran-sitions. It is possible that the band system2.23 at 3286A probably due to NCN represents such a transition but this remains to be established. If the Renner-Teller interaction be-comes very large the minimum of the lower of the two potential functions may no longer occur at 4 = 0 but at some other value of the bending angle.In other words we have a splitting of a degenerate electronic state of a linear molecule into one state with linear equili-brium position and another state with 1 $+ V 2 ~ I I l l I ‘n 0 n c-A s+ n I1 I I 1 $+ FIG. 12.-Energy level diagram for hot bands in v2 of a linear triatomic molecule. bent equilibrium position. Such a situation was first recognized by Dressler and Ramsay24 for NH2 and has more recently also been found for the singlet system of CH2 (Herzberg and Johns 25). The potential functions in such a case are qualitatively given in fig. lob. The vibrational energy levels in the state with linear equilibrium configuration are not the same as those of a non-degenerate state.Pople and Longuet-Higgins 26 have carried out calculations of the effect of the vibronic interaction on the vibrational levels and very good agreement with the observed levels in NH2 has been found. The main effect consists in a large splitting of the levels with given 212 but different l values. (b) NON-LINEAR MOLECULES The degeneracy of electronic states of non-linear molecules can be recognized by similar criteria as in linear molecules. (i) It is now the selection rule for K that establishes whether a certain transition is of the 11 or 1 type that is whether the transition is of the type A-A B-A, B-B or E-A E-B (or possibly E-E). If an observed band clearly follows the selection rule AK = & 1 and if the ground state of the molecule is of type A then we know immediately that the excited state must be of type E.On the other hand 20 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES if AK = 0 is observed and if the ground state is of type A then we know immediately that the excited state must be non-degenerate also that is must be of type A or B. While this rule seems very simple here is a complication arising from point (ii) which at least under insufficient resolution can give a band the appearance of a 11 band and vice versa. (ii) The rotation of the molecule about the figure axis because of Jirst-order Coriolis interaction produces an increasing splitting of the electronic degeneracy with increasing K similar to the splitting of degenerate vibrational levels observed in the infra-red.The magnitude of this splitting is given by 4cJK or 45&K for a prolate or oblate top respectively. If such a splitting is observed it would immedi-ately establish the degeneracy of the electronic state. The Coriolis parameter ce may have a value between - 1 and + 1. Often it is close to + 1. In that case the levels with K+l of one component Lie close to the levels with K-1 of the other component and since the selection rule for a _L band is such that the former levels combine in the P branch (in K) the latter in the R branch with those of the lower state a band of the appearance of a 11 band may result. (iii) If the total spin is not 0 we may expect large multiplet splittings in degenerate electronic states. These will be discussed in a little more detail in the next section.(iv) The interaction of vibration and electronic motion will lead to splittings of the higher vibrational levels of degenerate vibrations and the observations of such split-tings would represent unambiguous evidence for the degeneracy of a given electronic state and for the occurrence of such vibronic interactions even if the rotational structure is not resolved. Jahn and Teller 27 have shown that in a degenerate electronic state there is always at least one normal co-ordinate on which the potential energy depends linearly near the symmetrical conformation. As a consequence the symmetrical conformation is unstable; a potential minimum if it exists at all occurs for an unsymmetrical position of the nuclei.As an example fig. 13 gives a qualitative diagram of the potential function in a molecule with a threefold axis. For example for the motion of the I nucleus in CH31 there are three potential minima which are symmetrically placed around the symmetry axis but there is no potential minimum on the axis. The potential function still has the C3v symmetry but any one equilibrium position of the nuclei does not have this symmetry. The question of what the energy levels are for such a Jahn-Teller distorted potential function (dynamic Jahn-Teller effect) has been considered in detail by Longuet-Higgins Opik Pryce and Sack,28 by Moffitt and Liehr 29 and Moffitt and Thorson.30 Qualitatively we can see by forming direct products what the number and type of vibronic states is in a given degenerate electronic state.This is shown for a simple case in fig. 14 (centre). If one quantum of a degenerate vibration is excited in the degenerate electronic state we obtain three vibronic levels of types A1 A2 and E, and more levels for the higher levels of this vibration as shown in fig. 14. We call the splitting between the three levels A1 A2 and E the Jahn-Teller splitting. (Without vibronic interaction they would coincide.) It should be noted that the lowest vibra-tional level in the degenerate electronic state is not split. I t remains degenerate. The other splittings increase as a function of the depth of the “ moat ” below the central peak of the potential function but not in a simple way. At the right in fig. 14 the levels are given for D = 0.1 where Do2 is the depth of the moat.In fig. 15 the levels for D = 0.5 are compared with those of D = 0-1. In this figure the levels are separated according to the value of Longuet-Higgins’31 quantum number j which takes the values 14-3 where I = 0 u-2 . . . 1 or 0. In the approximation considered by Longuet-Higgins et ~ 2 . 2 8 the potential function is simplified to hav G. HERZBERG 21 FIG. 13.Xontour lines of the potential surface of a Jahn-Teller distorted C30 molecule. 9 E I E FIG. 14.-Vibrational levels of a degenerate vibration in an A1 and E electronic state of a C3" molecule. At the right the Jab-Teller splitting is plotted to scale for D = 0.1 22 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES rotational symmetry about the axis that is the minima are neglected.As a con-sequence the A1 and A2 levels are not split. In an actual molecule when the minima are not negligible the splitting between A1 and A2 is likely to be large (Hougen 32). Experimental evidence for vibronic interactions and Jahn-Teller splittings in non-linear polyatomic molecules is as yet very incomplete. It may be obtained in one of the following four ways. I I - \ \ L I (a) In an allowed electronic transition the 1 - 4 and 0-1 bands in a degenerate bending vibration are forbidden (Herzberg and Teller 1 6 ) . In an Al-Al transition they can only occur with the forbidden (1) dipole component and therefore will occur only if there is a nearby E-Al transition from which intensity can be borrowed. However in an E-Al electronic transition there are E-Al or E-E vibronic com-ponents of the 1 - 4 or 0-1 transitions respectively (see fig.16) which may occur with an intensity that depends on the magnitude of the vibronic interaction (without borrowing intensity from another electronic transition). Indeed Child 33 has shown that the intensity ratio Z(l-O)/Z(O--O) = D where D is the Jahn-Teller parameter introduced earlier. Thus in principle this parameter can be determined experimentally and therefore the presence of Jahn-Teller instability established. The difficulty lies of course in the correct identification of the 1-0 band. That of the 0-1 band is easier since the frequency of the bending vibration in the lower state may be known from infra-red work. (6) The identification of the 1-4 and 0-1 bands and therefore the presence of Jahn-Teller interaction can be made much more definite if the K structure of these bands can be resolved.The spacing of the Q branches in a band is given (both in the infra-red and the ultra-violet) by 2[A(1- Ceff) -B] if the change of A and B in going from the upper to the lower state is neglected. It was first shown by Mulliken and Teller 34 that in the E vibronic component of the v = 1 state of a de-generate electronic state the effective value of the Coriolis parameter is Serf = -(Ce+Cv). Thus if re is close to 1 and cv is positive the spacing of the Q branches in the 1 4 band will be more than twice what it would be without Coriolis splittings [when it is 2(A-B)] in contrast to the 0 4 band (and other bands involving totally symmetric vibrations only) for which cer r= re = 1 and for which therefore th G .HERZBERG 23 spacing is very small (-2B) giving an appearance of a 11 band. A result similar to that for the 1-0 band is found for the 0-1 band. In this way Mulliken and Teller were able to account for the long-known anomalous spacings in some of the I I I weaker bands in the first discrete absorp-tion system of CH3I (Scheibe Povenz and Linstrom 35) and at the same time estab-lished that the main bands which look like 11 bands are actually 1_ bands (Cexl), that is that the upper electronic state is an E state. The presence of the 1 4 bands (both in v5 and v6) together with the anomalous spacing clearly shows the presence of Jahn-Teller interaction in this E state.A very similar situation has recently been found for the corresponding absorption system of CF3I. Fig. 17a shows one of the weak bands that exhibits the characteristic intensity alternation and me anomalously large spacing which proves that here also the upper state is an E electronic state and Jahn-Teller inter-action is present. ( c ) As previously mentioned the rota-tional levels with K = 1 in a degenerate vibronic state are split into two sets on account of Coriolis interaction.36 While one of these sets consists of doubly de-generate rotational levels the other con-sists of A1 A2 pairs alternating with A2 A1 pairs for even and odd Jvalues. Child 37 has shown that these pairs are split in a degenerate electronic state on account of E I I I I I I 0 1 ‘ I ! I E i; E I I FIG.16.-Energy level diagram for vibronic transitions in an E- A1 electronic transition of a C3“ molecule. vibronic (Jahn-Teller) interaction. We shall call this splitting j-type doubling. It is analogous to the I-type doubling produced in degenerate vibrational levels of non-degenerate electronic states on account of corio!is interaction with a nearby non-degenerate vibration (Garing Nielsen and Rao 38). However if the AlA2 doubling is large in vibrational levels of a degenerate electronic state when degener-ate vibrations are not excited one can be fairly certain that it isj-type doubling, i.e. that vibronic interaction is present. Douglas and Hollas 13 have observed a large A1A2 doubling in the main progression of the 1600 A bands of NH3 which they have shown to represent an E”-AI transition the molecule being planar in the excited state.The main progression corresponds to the excitation of the (non-degenerate) out-of-plane bending vibration. No degenerate vibration is excited. It is therefore likely that the main part of the observed splitting is caused by vibronic interaction. However part of it may also be caused by Coriolis interaction with the nearby A; electronic state (see Douglas 12). (d) The most clear-cut proof of Jahn-Teller interaction would of course be the direct determination of the Jahn-Teller splitting by actual observation of transitions to the different vibronic sub-levels of a given vibrational level of a degenerate electronic state. From fig.16 it is immediately clear that this can only be done through the observation‘of hot bands of the type 1-1 (or 2-2) in the degenerat 24 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES vibration. For the I 4 transition only one component band is possible (E-A); for the 2-0 transition even though there are two E vibronic levels in the upper state again only one E-A transition is possible because the other is forbidden by the selection rule for j (which is j’-Z” = ++). On the other hand for the 1-1 transition three component bands are expected all of the I_ type viz. E-E A2-E and AI-E (entirely analogous to the three component bands of a 1-1 transition of a linear molecule in a II-Z electronic transition see fig. 12); for a 2-2 transi-tion four component bands are expected.As far as I know there is at present only one case in which two component bands of 1-1 transitions have been assigned with considerable probability namely in CF31. Here the lowest degenerate vibration has a frequency of only 265 cm-1 and thus hot bands involving it are relatively strong. The difficulty is that hot bands of other vibrations also appear. But it seems very probable that the two bands marked in the spectrogram fig. 17b are such component bands. Similar band pairs occur associated with other main bands. The splitting of about 8 cm-1 fits in with that expected from the parameter D evaluated from the intensity ratio of the 1 - 0 and 0 4 bands. However here it is assumed that the A1 A2 splitting is small. It may also be that the two observed bands correspond to A1-E and A2-E and that E-E has not been observed.Unfortunately just as for linear molecules no theoretical guide is as yet available for the relative intensities of the component bands. This lack is even more serious for an interpretation of the 2-2 group of transitions where clearly several com-ponents are observed. E. SPIN-ORBIT INTERACTION If the resultant spin in an electronic state is different from zero further com-plications of the spectrum are introduced through the effects of spin-orbit interaction. (a) LINEAR MOLECULES The effects of spin-orbit interaction are fairly well understood for linear mole-cules since they can in the main be taken over from diatomic molecules. Up to now, only doublet transitions have been studied in any detail. For example the spectra of NCO B02 CO; mentioned earlier show fairly large doublings in the zII states, which as long as no bending vibrations are excited follow the usual Hill and Van Vleck formulae.Similarly in 2X electronic states the doublet splitting increases linearly with the rotational quantum number N. As aIready mentioned the com-plications that arise on account of vibronic interactions when bending vibrations are excited have been studied theoretically in detail by Hougen 20 and his formulae do represent the experimental data in a very satisfactory way. Triplet states and states of higher multiplicities have not yet been investigated in detail since no examples have as yet been sufficiently analyzed. (b) NON-LINEAR MOLECULES Theoretical and experimental information about multiplet splittings in non-linear molecules is rather scarce.It is to be expected that non-degenerate electronic states behave like E states of linear molecules that is that the multiplet splitting is small or zero for zero rotation and rises very slowly with increasing rotation. Henderson 39 has developed general formulae for this splitting. Dressler and Ramsay 24 have observed doublet splittings in the 2B1 ground state of NH2. These are presented in fig. 18 as a function of J for various K values. The theoretical curves assuming a symmetric top approximation are also included. It is seen tha G . HERZBERG 25 the agreement is only moderately good. DiGiorgio and Robinson 40 have studied the triplet splitting in the first excited 3A2 state of H2CO (in which the molecule is non-planar) and in this Discussion Merer 4 1 interprets the 3800 A system of SO2 as a 3B1- 1Al transition and determines the splitting constants in the 3B1 state.As mentioned earlier in its first excited state the CS2 molecule is not linear. Douglas42 has found Zeeman splittings of the band lines which can only be ac-counted for by assuming that the excited state is a triplet state (3B2). Yet in spite of considerable effort Douglas has not been able to find any indication of a triplet splitting without a magnetic field. An explanation for the absence of observable triplet splittings in this case is not obvious. N FIG. 18.4bserved and calculated doublet splittings in the 2B1 ground state of NH2. Dr. Verma and I have recently studied the absorption spectra of HSiCl and HSiBr in the 4000A region.Well-resolved bands have been observed which show that in both upper and lower state the molecule is bent. The rotational constant A is very much larger than B and C and therefore the molecule is extremely close to a symmetric top. Sub-bands with AK = 0 & 1 and f 2 appear very distinctly. The simultaneous occurrence of sub-bands with AK = 1 and AK = 0 could be easily understood if the bands were hybrid bands. However there is some rather strong evidence from the J structure that the bands are pure 1_ bands with the transition moment at right-angles to the plane of the molecule and therefore only the sub-bands with AK = f 1 should appear. The occurrence of sub-bands with AK = k 2 is at first sight even more puzzling.They certainly cannot be accounted for by the slight asymmetry of the molecule. However an explanation for the occurrence of sub-bands with both AK = 0 and AK = f 2 can be given under the assumption that the transition is between a triplet and a singlet state. It is well known that in diatomic molecules 3A-1C transitions can occur on account of spin-orbit coupling or more generally triplet-singlet transitions wit 26 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES AA = &2 can occur and are indeed found to have the same order of intensity as triplet-singlet transitions with AA = +1 or 0. To the quantum number A cor-responds K in the symmetric top case. We are thus led to the conjecture that in triplet-singlet transitions of symmetric top molecules we may have AK = 52 & 1 0, irrespective of whether the transition is of the 11 or I_ type.Just as in diatomic molecules spin-orbit coupling mixes states of different A and S (e.g. 3A with In), so in symmetric top molecules it mixes states of different K and S (e.g. K = 4 with K = 3 K = 3 with K = 2 etc.) and for this reason transitions with unorthodox AK values can occur. A more detailed development by Hougen43 has confirmed these qualitative considerations. Therefore if we assume that the observed HSiCl and HSiBr band systems represent triplet-singlet transitions more specifically 3A”-lA’ we can immediately understand why AK = f 2 and 0 sub-bands occur in addition to AK = f 1. It is fairly easy to see that in planar CzU molecules like S 0 2 the overall symmetry rules (+ t-) - A+l+B) do not allow even as well odd AK values for a given triplet-singlet transition.Rather for 11 bands only AK = 0 +2 and for _L bands only AK = + 1 can occur. The latter alternative is in agreement with the assump-tions made by Merer 41 in his analysis of the 3800 On the other hand in a planar molecule of point group C2h if it is a prolate top, both AK = 0 +2 and AK = fi 1 are allowed by symmetry in a triplet-singlet transition. An example I believe is provided by the near ultra-violet absorption bands of acetylene which are well known to represent a transition from the ground state in which the molecule is linear to an excited state in which it has C2h Symmetry. Among the main bands which follow the selection rule AK = 1 both Ingold and King44 and Innes 45 found definite evidence for weak transitions with AK = 0 and +2 which they were unable to explain.These transitions indeed cannot be accounted for on the basis of the selection rules as long as it is assumed that the transition is a singlet-singlet transition. The presence of these AK = 0 +2 transitions must be considered as strong evidence that the upper state is a triplet state. It is true that no triplet splitting has been observed but that is also true for the absorption spectrum of CS2 which on the basis of Zeeman investigations has definitely been shown by Douglas to be a triplet-singlet transition. It may be noted that if in the excited state the CzHz molecule had CzP) symmetry the AK = 0, rfr2 transitions could not occur in a triplet-singlet transition but only AK = Finally I believe that the observation of Innes and Giddings 46 to be presented at this Discussion that in the 3700 A system of pyrazine transitions with AK = fi:2 occur together with AK = 0 shows contrary to the conclusions drawn by Innes and Giddings that the upper state is a triplet state * and that it is not necessary to assume this system to represent a quadrupole transition.Transitions with AK = & 1 are in this case forbidden by the overall symmetry rules as one can easily show. For a further study of all these cases of triplet-singlet transitions it would of course be very desirable to have more precise theoretical predictions about the relative intensities of the various branches. system of SOz. 1. (C) LARGE SPIN-ORBIT INTERACTION When the spin-orbit interaction is very large there will be splittings into a number of sub-states.In order to classify these sub-states we have to “ multiply ” the species of the orbital function with that of the (molecule fixed) spin function which for half-integral spin leads us to the use of the so-called extended or double * see discussion p. 192 G . HERZBERG 27 point groups.* In a molecule of point group C3v for example the spin function for S = 3 belongs to the representation Ez while the spin function for S = 1 belongs to A2+E. Therefore the overall electronic wave function in a 2A1 electronic state is of species E5. In a 2E electronic state we have a splitting into two states of species E+ amd E+. On the other hand in a 3A1 electronic state we find a splitting into an A2 and E state while in a 3E state we have a splitting into four states Al, 4 E and E.These results are summarized in table 1. TABLE SPECIES OF SPIN FUNCTIONS AND OVERALL EIGENFUNCTIONS IN C3” MOLECULES S spin function over a1 1 function E E+ + E$ 1E 0 A1 3 2E 3E 1 A2+E E+A1+A2$.E As an illustration let us consider the ground state of the CH31+ ion. Since here one electron is missing from an e orbital the ground state is 2E which since spin-orbit interaction is large splits into the two states E+ and Eg (corresponding to ZIT+ and 2II+ in the linear case). From the ultra-violet spectrum we know that the splitting is about 5000 cm-1 and the two states E+ and E; must be considered as separate states. A similar situation arises for the C2H5I-t ion except that here, since the symmetry is only Cs the two component states have the same species namely, E*.If we combine a ma1 electron (or in double group notation a nseg electron) with the ground state E+ of the CH31+ ion we obtain the resulting states of neutral CH31 by forming the direct product of E+ x E+ which yields A1 +A2+E. In other words, there will be three Rydberg series of states of the types mentioned. If on the other hand we combine nsal with the Es component of the CH3I+ ion we obtain from the direct product two E states for each value of n that is two Rydberg series of states of type E. Another way of looking at this situation is to consider directly the configuration ef(nsa1) of the neutral CH3I molecule.This is immediately seen to give the two states 1E and 3E. For large spin-orbit coupling since the spin function has symmetry &+E the 3E state splits into A1 A2 E and E while the 1E state simply becomes E and thus we see that we get the same five states as by starting out from the two component states of the CH3I+ ion. (In the linear case the five states just men-tioned correspond to 3ITo+ 3IIo- 3 I T 1 3II2 and 1 I I l . ) The first discrete excited states of CH3I fit in with this prediction in a very striking manner. Two states called B and C separated by about 5000 cm-1 have been known for a long time and have always been interpreted as belonging to the two series limits. Recently in a re-investigation of the ultra-violet absorption spectrum of CH31 by Dunn and myself, it has been found that there is a third electronic state overlapping the B state and by means of the observed values this third state can be definitely identified as the third expected E state which corresponds to the 3 I I 2 component in the linear case.*The designation of the degenerate species in these extended point groups has not yet been We use here a designation (related to that of Jahn 47) which will be used in vol. 111 standardized. of Molecular Spectra and Molecular Structure 28 STRUCTURES OF SIMPLE POLYATOMIC MOLECULES Thus all three E states arising from the configuration e3(nsal) heve been found in the expected relative order. Fig. 19 shows in an energy level diagram the predicted and observed states. The transition from the ground state to the A2 state is of course forbidden the transition to the A1 state is probably mixed up with the C state but has not yet been recognized.c m-I predicted observed 156000 I 52000 I 3E -I/--- c E t50000 I L FIG. 19.-Predicted and observed excited states of CH3I. F. CONCLUSION It was not possible in this lecture to touch upon more than a small section of the work that has been done in the field of electronic spectra of polyatomic mole-cules and the information obtained from them on excited electronic states. Other speakers in this Discussion will emphasize many other important points. It is clear from the programme that many different lines of attack are being actively pursued and that the whole field is in a healthy state of development which promises much new knowledge and understanding in the future.I should like to conclude by summarizing those points arising from the preceding discussion in which our present theoretical knowledge is weak and further theoretical developments could help greatly in the interpretation of observed electronic spectra. (i) We do not know what relative intensities to expect in a II-C or E-A elec-tronic transition for the component bands of a 1-1 transition in a degenerate vibration. (ii) We know nothing about the relative magnitudes of Renner-Teller splittings for the two bending vibrations of linear X2Y2 (e.g. in acetylene). (iii) We have very little information about the splitting between A1 and A2 component levels in the groups of levels arising from Jahn-Teller interaction in degenerate electronic states of non-linear molecules.(iv) We do not know what relative intensities to expect for the various Rydberg series of a molecule. Such knowledge would greatly aid in assigning observed series. (v) We do not understand the great difference of intensity between different triplet-singlet transitions (cf. HSiCl and C4H4N2) nor the smallness of the observed triplet (or doublet) splittings. (vi) We have no reliable guide for the relative intensities of various branches in triplet-singlet transitions. Such a guide would be of great help in the assignment of observed fine structures. I am indebted to Dr. A. E. Douglas J. T. Hougen and B. P. StoicheE for critical comments on the manuscript of this paper G . HERZBERG 29 1 Herzberg Proc. Roy.Soc. A 1961 262 291. 2 Herzberg and Warsop Can. J. Physics 1963 41,286. 3 Dalby Can. J. Physics 1958 36 1336. 4Bancroft Hollas and Ramsay Can. J. Physics 1962 40 322 ; Ramsay and Stamper to be 5 Brand Callomon and Watson Disc. Faraday SOC. 1963. 6 Ritchie Walsh and Warsop Proc. Roy. SOC. A 1962,266,257. 7 Johns Can. J. Physics 1963 41 209. 8 Mulliken Physic. Rev. 1941 60 506. 9,Walsh and Warsop Trans. Faraday SOC. 1961 57 345. 10 Walsh J. Chem. SOC. 1953,2306. 11 Brand J. Chem. SOC. 1956 858. 12 Douglas Disc. Faraday SOC. 1963. 13 Douglas and Hollas Can. J. Physics 1961,39,479. 14 Walsh J. Chem. Soc. 1953,2260. 15 Coulson and Neilson Disc. Faradby SOC. 1963. 16 Herzberg and Teller 2. physik. Chem. 1933,21,410. 17 Renner 2. Physik 1934,92 172. 18 Gausset Herzberg Lagerqvist and Rosen Disc. Faraduy SOC. 1963. 19Dixon Phil. Trans. A 1960 252 165. 20 Hougen J. Chem. Physics 1962 36 519. 21 Johns Can. J. Physics 1961 39 1738. 22 Hougen J. Chem. Physics 1962 36 1874. 23 Jennings and Linnett Trans. Faraday Suc. 1960 46 1737. 24 Dressler and Ramsay Phil. Trans. A 1959,251 553. 25 Herzberg and Johns to be published. 26 Pople and Longuet-Higgins Mol. Physics 1958,1 372. 27 Jahn and Teller Pyuc. Roy. SOC. A 1937 161 220. 28 Longuet-Higgins Opik Pryce and Sack Proc. Roy. SOC. A 1958,244,l. 29 Moffitt and Liehr Physic. Rev. 1957 106 1201. 30 Moffitt and Thorson Cofl. Int. C.N.R.S. 1958 82 141. 31 Longuet-Higgins Adv. Spectr. 1961 2 429. 32 Hougen J. Chem. Physics 1963,38 1167. 33 Child M. S. private communication. 34 Mulliken and Teller Physic. Rev. 1942 61 283. 35 Scheibe Povenz and Linstrom 2. physik. Chem. B 1933,20,283. 36 Herzberg Molecular Spectra and Molecular Structure vol. I1 @. Van Nostrand Co. 1945). 37 Child Mol. Physics 1962 5 391. 38 Garing Nielsen and Rao J. Mol. Spectr. 1959 3 496. 39 Henderson Physic. Rev. 1955 100 723. 40 DiGiorgio and Robinson J. Chem. Physics 1959,31,1678. 41 Merer Disc. Faraday SOC. 1963. 42 Douglas Can. J. Physics 1958 36 147. 43 Hougen to be published. 44 Ingold and King J. Chem. Sac. 1953,2702. 45 Innes J. Chem. Physics 1954 22 863. 46 Innes and Giddings Disc. Faraday SOC. 1963. 47 Jahn Proc. Roy. SOC. A 1938,164 117. published

ISSN:0366-9033    

DOI:10.1039/DF9633500007

出版商:RSC    

年代:1963

数据来源: RSC

摘要:

Electron-Impact Spectroscopy * BY &ON KUPPERMANN-~ AND L. M. RAFF$ Noyes Chemical Laboratory, University of Illinois, Urbana, Ill., U.S.A. Received 29th January, 1963 A spectrometer has been devised for determining electronic energy levels of molecules by in- elastic scattering of low-energy electrons. It permits the detection of optically forbidden electronic transitions as clearly as optically allowed ones in a routine manner. The spectrometer has been used to obtain excitation spectra for helium, argon, hydrogen and ethylene. For the first three of these substances, the spectra agree with previous experiments. For ethylene, in addition to optically allowed transitions, two forbidden ones occur at about 4-6 and 6-5eV. Variation of peak heights with incident electron beam energy suggest that the first corresponds to a triplet state but that the second does not.Franck and Hertz1 used the measurement of energy losses of electron swarms in atomic gases as a means of determining the lowest excitation energies of those gases. However, such electron-impact techniques have not been used to any ap- preciable extent for the determination of electronic energy levels of molecules. The reasons are : first, because electrons can produce rotational and vibrational excitation of the ground electronic states of molecules, it is not possible to use ex- perimental techniques in which the electrons build up energy slowly between collisions if one wishes to determine the electronic levels of those molecules. Therefore, one must use single-scattering electron beam techniques, which require more elaborate set-ups.Secondly, because of the relatively simple optical techniques which permit great accuracy in the determination of photon energies, optical spectroscopy pro- vides a simpler method of much higher resolution for the measurement of electronic transitions in atoms and molecules. The development of metal high vacuum techniques and of electronic circuitry have simplified the construction and operation of single-scattering electron-impact spectrometers. In addition, there exists an extremely powerful reason for using low-energy electron impact as a spectroscopic tool. This is the difference in the selection rules for excitation of electronic energy levels of atoms and molecules by photons and by electrons.Practically all electronic transitions are allowed when low-energy electrons are used.2 They include transitions which are spin-forbidden and/or symmetry-forbidden when photons are used. Therefore, low-energy electron- impact spectroscopy provides in principle a technique which permits determination of such optically forbidden electronic transitions, as well as optically allowed ones. In addition, transition energies above 11 eV, which are difficult to deal with optically, can be easily studied with electron-impact techniques. The inelastic scattering of low-energy electrons by molecules has been experi- mentally studied by a number of researchers. The molecules studied include hydrogen,3 oxygen,4 nitrogen,s carbon monoxide 6 and carbon dioxide.6 However, most studies were directed either to the measurement of scattering cross-sections or to the determination of the appearance potentials of assorted ions.Studies aimed mainly at the determination of electronic energy levels in molecules were relatively scarce. * Supported in part by funds from the U.S. Atomic Energy Commission. present address: Gates and Crellin Lab. of Chem., California Inst. of Technology, Pasadena. present address: Dept. of Chem., Columbia University, New York. 30A. KUPPERMANN A N D L. M. RAFF 31 There have been two important recent studies; first, Lassettre and his students 7 have constructed an electron-impact spectrometer with which they have made accurate measurements of differential scattering cross-sections in several atoms and molecules.However, they have worked mainly with electrons whose incident energy was between 400 and 600 eV. In this region the Born approximation 8 is valid, and transitions involving change of spin multiplicity are forbidden. There- fore, in those experiments Lassettre does not see such transitions. However, in measurements made with incident energies below 100 eV, forbidden transitions were observed.7 Secondly, Schulz 9 has used a low-energy electron impact method for determining electronic transitions in H2 and H20. The energy of the incident beam is scanned, and the electrons which lose all but a small energy (usually about 0.3 eV) are trapped in a potential well and detected. This method, which also permits the observation of optically forbidden transitions, is further discussed later.In this paper we describe the use of a low-energy electron-impact spectrometer in which optically forbidden electronic transitions in molecules can usually be detected as clearly and easily as optically allowed ones.10 Spectra for He, Ar, H2 and C2H4 are given and discussed. DESIGN AND CONSTRUCTION OF APPARATUS The design and construction of the spectrometer is based in part on the apparatus used by Arnot and Baines 11 to measure collision cross-sections of electrons with mercury atoms. Our version consists essentially of two differentially pumped high-vacuum chambers, an electron gun chamber, and a collision chamber, connected through a 1.5 mm diam. pin- hole. A beam of approximately mono-energetic electrons is produced in the gun chamber and enters the collision chamber through that pinhole.There the electrons undergo collisions with the molecules being studied, and the energy losses of electrons scattered away from the direction of the incident beam are determined by a retardation potential method. Details of the design and construction of the apperatus are given elsewhere,lZ but a summarized description is given below. VACUUM SYSTEMS Fig. 1 shows a schematic diagram of the apparatus and its associated circuitry. The gun and collision chambers are represented respectively by the regions to the left and right of electrode E5. Each of these chambers is separately pumped by a 300 l./sec oil diffusion pump. The gun and collision chamber pumps are backed respectively by a 33*41./min and a 140l./min mechanical pump.Each of the diffusion pumps is separated from the corresponding chamber by a trap, which can hold about 3 1. of liquid nitrogen, and a 5.1 cm gate valve, which uses neoprene O-ring gaskets. The gas to be studied is admitted to the collision chamber through a set of high vacuum needle valves, which permit a fine adjust- ment of the pressure in that chamber. All electron scattering measurements are made under dynamic conditions, the gas flowing through the collision chamber. Since the two chambers are connected only by a 1.5 mm diam. pinhole, good differential pumping can be maintained. In general, the pressure within the gun chamber can be maintained at about 1/50 of that in the collision chamber when the pressure in the latter is of the order of 10-4 mm Hg.The pressures were read by calibrated ionization gauge tubes and circuits. The electron gun and collision chambers are made of 6-03 cm ext. diam. brass tubes, with a wall thickness of 1.66 mm. They are closed at the ends by flanges made of non- magnetic stainless steel through which electrical leads pass via glass to metal seals. The two chambers are mechanically joined by a double flange of the same steel, on which elec- trode E5 is mounted. This electrode is insulated from that flange by a flat quartz ring, represented in fig. 1 by the two hatched rectangles close to Eg. Electrode E5 contains the pinhole which connects the two chambers. All gaskets in the chambers are of 0.76 mm diam. gold wire, and all materials used are resistant to temperatures of about 350°C.The two chambers can be baked at that temperature by an external oven which can be placed32 ELECTRON-IMPACT SPECTROSCOPY around them. After baking the chambers for 24 h at about 300°C, with the pumps on and no gas flowing through the system, the pressure in each of them was usually about 3x 10-7 mm Hg. ELECTRON GUN The electron gun consists of an oxide cathode heated by a tungsten filament and of five electrodes, represented by El . . . E5 in fig. 1. The oxide coating of the cathode has the shape of a circular disc with 3 mm diam. This cathode is usually operated at 1000°K. Electrode El, which is made of inconel, is mounted directly in front of the cathode and has a 5 mm dim, centre hole. It is usually operated at potentials 40-65 V positive with respect to the cathode.This results in a total emission of 3 to 5 mA. ,2 CM, SH 1 [ T R e c o r d e r FIG. 1 .-Schematic diagram of apparatus and circuitry. Electrodes E2, E3 and E4 are made of 0.80 nun thick inconel discs, 47.6 m in diam. Their centre holes have diameters of 0 5 , 1.0 and 0.5 mm respectively. The spacing be- tween Ei and Ei+l (i = 1,2,3) is 1.5 mm. Electrodes Ez, E3 and E4 are usually operated as an Einzel lens with Ez and E4 equipotentiai and E3 negative with respect to the other two, The voltage difference between Es and the cathode is positive and determines the energy with which the e€ectron beam enters the collision chamber. Usually, E2 and E4 are oper- ated at the same potential as Es. The potential on E3 is chosen so as to minimize the ratio of background current (current reaching collector SC) to beam current within the collision chamber.Electrode E5 is 5-7 m away from E4 and is made of a 0.25 mm thick gold disc mounted by means of an epoxy resin to a 2.5 cm dim. quartz disc, 1.6 m thick, which contains a 1 2 5 m hole in its centre. The electron beam passes from the gun chamber into the scattering chamber through the 1.5 mm diam. pinhole on E5. COLLISION CHAMBER In the collision chamber there are several grids and collectors. First, there is the grid GI. I t s a cylinder made of tantalum gauze woven from 0.076 mm dim. wires with 19.7A. KUPPERMANN A N D L. M. RAFP 33 wireslcm. This furnishes a transparency of 72 %. The diameter of G1 is 12.5 mm and its length 25 mm. The end of G1 away from E5 is closed by a piece of tungsten gauze of 92 % transparency containing 39.4 wireslcm.Grid G1 is operated at the same potential as E5. Therefore, the space enclosed by GI and E5 is free of electric fields. It is also made free of about 90 % of the earth’s magnetic field by the use of two pairs of Helmholtz coils. The collisions between electrons and molecules take place in this region. Four mm beyond the termination of GI there is another grid GIA also made of the 92 % transparency tungsten. This grid serves a dual purpose. First, during the oper- ation of the spectrometer, it is set at the same potential as GI, whereas the beam collector BC which follows it is set at a higher potential. Grid GIA thus prevents electric field pene- tration into the field-free region enclosed by GI and E5.Secondly, it may be used to energy- analyze the electron beam. After GIA there is a beam collector BC, made of brass and shaped internally as a conical Faraday cage to provide multiple internal reflections of the incident electrons in order to decrease the background current. To decrease further the chance of reflection of electrons back into the collision chamber, a holding voltage of 50 V is applied between BC and GIA. This voltage was crucial in order that a sufficiently low background current be reached. Surrounding GI is another cylindrical grid G2. It is made of the same tantalum gauze as GI. Its diameter is 30 mm and its length 57 mm. Its purpose is to repel any positive ions which are formed by ionizing collisions between the electrons and the molecules under study.To this end it is placed at a potential 10 V positive with respect to GI. Since positive ions would be formed with low kinetic energy, the repelling field thus produced is sufficient to prevent these positive ions from reaching the scattered electron collector SC. Around G2 there is a third cylindrical grid G3 also made of the same tantalum gauze as GI and G2. Its diameter is 45 mm and its length 71 mm. At the beginning of an experiment it is placed at a potential negative with respect to the cathode so that none of the scattered electrons has sufficient energy to pass through it and reach SC. The potential difference between G3 and the cathode is then gradually increased. This decreases the repelling field between G2 and G3 which scattered electrons have to overcome to reach SC.Eventually elastically scattered electrons can overcome this field and reach SC, which produces a sudden rise in the current 1 to that collector. As the repelling field is further decreased, electrons having lost energy to the molecules being studied can now reach SC with additional sudden rises in the current to this collector. If at a potential difference of I E I volts between G3 and the cathode there is a sudden rise in I (as determined by a maximum in the derivative d1/d I E I against I E I curve), this corresponds to a molecular transition energy of E = 1 E 1 eV after corrections for background and contact potential are made. Surrounding G3 is the scattered electron collector SC. It is made of tantalum foil 0.025 mm thick. Its diameter is 54 mm and its length 83 mm.It is surrounded by a shield SH of the same material whose diameter and length are 73 mm and 95 mm respec- tively. A constant holding potential of 40 to 50 V is applied between G3 and SC to avoid electron reflection or secondary electron emission from SC. All grids and collectors in the collision chamber are covered with a coating of platinum black formed by electrodeposition. Its purpose is to minimize the reflection of electrons off these surfaces. ELECTRICAL CIRCUITS Part of the circuitry employed is indicated in fig. 1. The potentials on electrodes E2, E3, E4 and Eg, on grids G1 and GIA and G2, on the shield and on the beam collector are applied relative to the cathode by circuits consisting each of two 90 V dry cells connected across a 300 kQ, ten turn, helical resistor.A switching arrangement allows any of these circuits to be connected to an electrometer, which is provided with 8 linear current ranges from 1 x 10-3 through 1 x 10-11 A full-scale deflection. The response time of the electro- meter can be varied from 0.1 to 30 sec. This electrometer is floating at the cathode potential, and its output is connected to a strip chart recorder. The beam current IB reaching the beam collector is continuously recorded. The potential on El, relative to the cathode, is B34 ELECTRON-IMPACT SPECTROSCOPY applied by a regulated power supply having a voltage stability of 0.1 % and a ripple of less than 3 mV r.m.s. The use of a power supply on this electrode is convenient since the currents reaching El are of the order of mA and would cause a rapid decay of dry cells. The variable potential on G3 relative to the cathode is applied by a high-stability power supply having a drift of 0.01 %/h and a ripple of 500pV r.m.s. or less.The potential between SC and G3 is applied by the same type of circuit as that between GI and the cathode. The power to the cathode heater is obtained from a 110 V d.c. generator and a 720 0 resistor in series with it. The current I reaching SC is measured with a vibrating reed electrometer, which permits current readings by meter deflection down to 10-14 A full-scale. It is connected to a strip chart recorder on which I is registered as a function of E. All potentials are measured by an accurate digital voltmeter capable of measuring d.c.potential differences between 0.1 and 500 V to within 0.05 %. GENERAL BEHAVlOUR OF THE APPARATUS By adjustment of the several potentials it was possible to obtain a scattered current to beam current ratio, I/IB, in the absence of gas in the collision chamber, ranging from about 4x 10-2 at beam energies of 30 eV down to 1 . 6 ~ 10-4 at beam energies of 75 eV for E = 13 eV. The beam current was about 4x 10-7 A in this range. These ratios were sufficiently small for the increase in I produced by the introduction of about 10-4 mm Hg of gas into the collision chamber to be adequate for gathering spectra. These ratios were achieved with the help of a one-quarter gauss axial magnetic field from a small horseshoe permanent magnet placed outside the gun chamber so as to minimize I/IB in the absence of gas.At beam energies below 25 eV this ratio became too high to permit impact spectra to be obtained. With about 10-4 mm Hg of test gas in the collision chamber, the variation of I with the holding voltage between G3 and SC showed a plateau for values of 40 V and above. All spectral measurements were made in this plateau region. Also, the variation of I with the positive ion repelling field between G2 and GI was determined and showed a plateau when G2 was made 6 V or more positive with respect to GI. Spectra were usually obtained with this potential difference equal to 10 V. The current I due to gas phase scattering (the difference in the value of I with gas present and absent from the collision chamber, all other conditions being the same) was propor- tional to the beam current IB and to the gas pressurep in the collision chamber, up to pres- sures of about 1 p Hg.Above this pressure, the curve of I against p showed a downward curvature, as expected from the onset of double scattering. All spectra were gathered in the range for which the gas phase signal was proportional to both pressure and beam current, which satisfies the conditions for observing only single scattering events. The procedure followed in obtaining the excitation spectra was the following. After the instrument was baked out and pumped down, a background curve of I against E was obtained with no gas in the collisional chamber, Curve B of fig. 2 represents a portion of one such curve.Then, the gas was admitted to the collision chamber through the needle valves of the inlet system. The flow rate was regulated to produce a steady-state pressure in that chamber in the proportionality region discussed above. This pressure was usually around 5 x 10-4 mm Hg. Then another curve of I against E was taken. The beam current IB was simultaneously measured and adjusted to its initial value when necessary, which was very seldom. Curve A of fig. 2 represents a portion of such a curve for helium. Then, the background was subtracted to give the part of I due to gas-phase scattering and a smooth curve drawn through these difference points. In fig. 2 this is represented by curve C, which shows the sudden rises mentioned previously. Then, closely and equally spaced ordinates were read off this curve and used as input data for a digital computer programme which computed its derivative numerically using a sixth degree polynomial fitted to seven successive points of the curve. The derivative curve was then plotted.The one corres- ponding to fig. 2 is given in fig. 3. The vertical line in the left-hand side corner of this figure, and in all other excitation spectra figures reported here, represents the scatter in the derivative produced by the scatter in the reading of the ordinates from the smoothed .A . KUPPERMANN A N D L. M. RAFF 35 FIG. 2.-Variation of scattered electron current Z with energy loss E for helium. Curve A : gas phase signal plus back- ground ; curve B : background, shifted upwards by 1 .6 4 ~ 10-9 A ; curve C: gas phase signal only, shifted upwards by 0.81 x 10-9 A. Incident electron beam energy, 50 eV ; ion gauge reading, 5.9 x 10-4 mm Hg; IB = 4.0 x 10-7 A. E/eV 1 I I I I I I I 19.5 21.0 zot I I 2 3 - 1 24.6 I I FIG. 3.-Excitation spectrum of helium; same conditions as for fig. 2. 25 5 20 EIeV36 ELECTRON-IMPACT SPECTROSCOPY difference curves of type B. It thus represents a lower limit to the error in the ordinates in those spectra. The horizontal scale of the derivative curve was then displaced to make the observed ionization energy fit the known value from optical or mass spectrometric experiments. No such correction was necessary for fig. 3. Usually this contact potential energy correction was 0.1-0.2 eV. This value is surprisingly low and probably attributable to the use of tantalum in the collision chamber grids and collectors.EXCITATION SPECTRA OF HELIUM, ARGON AND HYDROGEN Electron impact spectra for helium were obtained using a research grade quality of this gas furnished by the Linde Company and reported to be 99-99 % pure. It was used without further purification. Fig. 3 shows a spectrum for energy losses between 18 and 26 eV obtained using a beam energy of 50 eV and a gas pressure corresponding to an ion gauge reading of 5.9 x 10-4 mm Hg. Fig. 4 shows a similar spectrum for a 25 eV electron beam and an ion gauge reading of 2.7 x 10-4 mm Hg. 5 19.8 LO8 228 24.6 i r I I I I f I I I 22 24 Ol I 20 E/eV i FIG. 4.-Excitation spectrum of helium ; incident electron beam energy, 25 eV; ion gauge reading, 2 7 x 10-4 ~ll~ll Hg; IB = 1.0 x 10-7 A.The numbers at the top of those figures are the energies at which the maxima in the spectra were observed. The lowest electronic transition energies for helium,l3 from the ground 11s state, are 19-82 eV (DS), 20.61 eV (21S), 20.96 eV (23P)? 21.22 eV (2lP), 22-92 eV (31s) and 23.08 eV (31P). Higher energy states are so close together that they show up as a continuum between 22-8 eV and 24.6 eV in fig. 4. This is due to impact spectrum line broadening produced by the thermal energy spread of the incident electron beam and the fact that electrons scattered with the same energy in directions forming different angles with the undeflected electron beam have different components of the energy in the direction of the retardation fieldA. KUPPERMANN AND L.M. RAFF 37 between G2 and G3 which is essentially perpendicular to the incident beam. The optical ionization potential of helium 13 is 24.58 eV, whereas the values obtained from fig. 3 and 4 before correcting for contact potential, are 24.6 eV and 24.4 eV, respectively. Comparison of the transition energies obtained from fig. 3 and 4 with each other and with the optical values indicates that the resolution and ac- curacy of the instrument are about + eV and Q eV, respectively. The resolution is consistent with a thermal spread of 0-3 eV expected 14 from an oxide-coated cathode operated at about 1000°K. The estimated accuracy is consistent with almost all transition energies reported in this paper. The transitions to the 21s (20-61 eV), 21P (20.96 eV) and 21P (21.22 eV) states show up in our impact spectra as a single line peaking at 21.0 eV in fig.3 and 20-8 eV in fig. 4, in excellent agree- ment with the optical data within the estimated accuracy and resolution. In both helium spectra, the transition to the 23s state, although spin-forbidden in optical spectra, is very strong. This contrasts sharply with the spectra obtained by Lassettre,7 using incident electron energies between 400 eV and 600 eV, who did not observe this transition. The reason for this behaviour is that at these high energies the Born approximation is valid and it furnishes spin-multiplicity selection rules identical to those of optical transitions. However, at the lower energies we employed (25 eV and 50 ev), exchange scattering 1s can occur and singlet to triplet transitions are permitted.The ordinates in our impact spectra are roughly proportional (over a certain range of scattering angles) to a partially integrated differential collision cross-section. The ratio of the peak heights of two transitions should be, qualitatively, approxim- ately equal to the ratio of the total collision cross-sections for these transitions. In spite of the very approximate nature of this equality and of the relatively large error in the ordinates of our spectra, it seems significant that in going from an incident beam energy of 25 eV (fig. 4) to one of 50 eV (fig. 3) the ratio of the in- tensities of the 19.8 and 23 eV transitions changes very little. The calculations of Bates et aE.16, 17 would have predicted a sharp decrease in this ratio.In any case, the empirical observation is that the l2S-+23S spin-forbidden transition can be easily detected in our instrument even when the incident electron beam energy is 30 eV above the excitation energy. Spectra for argon were obtained using research grade quality gas furnished by the Linde Company and reported to be 99.995 % pure. This gas was used without further purification. One of the argon spectra obtained with a 50eV electron beam is given in fig. 5. The lowest excited states of argon13 are a triplet and a singlet which are at 11-6 eV and 11.8 eV respectively above the ground state. The measured peak at 12-2 eV is not in good agreement with these values. In other argon impact spectra the measured value was 11.9 eV, in better agreement. The next set of argon levels lies between 12.9 and 13.25 eV, with which the second peak of fig.5, at 12-9 eV, agrees. Finally, the rest of the argon levels, up to ionization, are too close together to be resolved in our instrument. It is seen from fig. 5 that the peak corresponding to elastic scattering has a maxi- mum at about 2.2 eV rather than at 0 eV. This type of shift was observed in every impact spectrum obtained with our apparatus. At first, it might seem due to con- tact potentials. However, the contact potential correction to the energy scale determined by the ionization potential was usually never more than about 0.2 eV and made all excitation energies agree well with the optical ones. Moreover, since the electron beam energy is not changed during the gathering of a spectrum (contrary to the determination of an ionization efficiency curve in mass spectrometry), vari- ations in the incident beam energy are not the explanation.The cause of this elastic38 ELECTRON-IMPACT SPECTROSCOPY EIeV Fro. %-Excitation spectrum of argon; incident electron beam energy, 50 eV; ion gauge reading, 64 x 30-4 mm Hg; IB = 4.7 x 10-7 A. I EIeV gauge reading, 2x 10-4 mm Hg; IB = 2.3 x 10-7 A. FIG. 6.-Excitation spectrum of molecular hydrogen; incident electron beam energy, 150 eV; ionA . KUPPERMANN A N D L. M. RAFF 39 peak shift is not clearly understood at present. However, the spectra obtained for helium, argon and hydrogen (see next paragraph) clearly show that only the elastic peak has this shift, and that the electronic excitation energies are not affected by its existence.Research grade hydrogen, also supplied by the Linde Company and reported as being 99.9 % pure was used without further purification to obtain the impact spectrum of hydrogen given in fig. 6 for a 60eV incident beam. The excitations are represented by bands which are much broader than in the rare-gas impact spectra. 1 1 RIA FIG. 7.-Potential energy curves for molecular hydrogen. This is a consequence of the variation of electronic energy with internuclear distance and of the fact that in the range of electron energies used in these experiments the Franck-Condon principle is obeyed.18 According to it, transitions from the ground state must occur vertically within the shaded area of fig.7. This figure contains the potential energy curves for the ground state and several electronically excited states of molecular hydrogen.18-20 The four bands observed in fig. 6 are in good agreement with those which one would predict a priori from fig. 7. The band whose maximum lies at 9-2 eV corresponds to the transition l l ~ ~ - + l 3 ~ ~ . Thus, a singlet to triplet molecular transition is clearly observed with a beam energy about 50 eV above the excitation energy. EXCITATION SPECTRA OF ETHYLENE The ethylene, furnished by The Matheson Company and reported as being 99.5 mole % pure, was used without further purification. Spectra were obtained at 40 eV, 50 eV, and 75 eV incident electron beam energies and are given in fig. 8, 940 ELECTRON-IMPACT SPECTROSCOPY and 10, respectively.The vacuum ultra-violet spectrum of ethylene shows an ab- sorption maximum at 7.66 eV corresponding to the V c N band of the n-electron system,21 onsets of 7.1 eV, 8.2 eV, 8.65 eV for three R t N Rydberg series,22 and an ionization potential of 10.45 eV.22 In fig. 8 and 9 the contact potential corrections were determined as usual from the ionization potential. The bands peaking at 7.7 and 8-8 eV are in good agreement with the optical values just mentioned. In fig. 10 the contact potential correction was determined from the V t N optical transi- tion energy 21 because the ionization potential in this particular spectrum seemed to be in large error. In all these three figures the elastic peak occurs at 2.1 eV.1 1 1 I I I I I I I I 1 . E/eV FIG. 8.Excitation spectrum of ethylene; incident electron beam energy, 40 eV O ions gauge reading, 2 x 10-4 mm Hg; IB = 1.6 x 10-7 A. From fig. 8 and 9 a low-lying transition energy with an average value of 4-6 eV is obtained. This is in good agreement with the optically forbidden value of 4.6 eV obtained by Evans in optical absorption spectra using the oxygen-intensification technique 23 and assigned to a vertical T c N transition of the n electron system3 24 The peak at about 6.5 eV in fig. 8, 9 and 10, is in good agreement with an optically forbidden transition energy of 6.4 eV obtained indirectly by Potts.25 He measured forbidden band transition energies in optical absorption spectra of several methyl- ethylenes, cyclohexene, and I-hexene, taken at room temperature and at liquid- nitrogen temperature.He had assigned this energy to the T c N transition, but after Evans’ experiments it was tentatively re-assigned by Mulliken 24 to a Rydberg triplet state. Comparison of the 4.6 eV peak intensities with the 7.7 eV ones in fig. 8-10 shows that it decreases with increasing incident beam energy, becoming a shoulder in the elastic peak when this energy reaches 75 eV. This is expected for spin-forbidden transitions 2 and is consistent with Evans’ assignment. A similar comparison be- tween the 6-5 eV and 7.7 eV peak intensities shows that their ratio does not decrease to any significant extent in the 40 eV to 75 eV range of incident electron energies used, suggesting that the 6.5 peak, although optically forbidden, does not correspondA .KUPPERMANN AKD L. M. RAFF 41 to a singlet-triplet transition? Recently, Berry 26 has ascribed it to a transition ana- logous to the n+n* one of formaldehyde.27 Such assignment would be consistent with the intensity dependence described above. 40 30 - % 2- * d I 2 20- G = u 1 W b ---- 0 2 4 6 a 10 EIeV FIG. 9.Excitation spectrum of ethylene; incident electron beam energy, 50 eV; ion gauge reading, 3.8 x lO-4mm Hg; I~=2.6x 10-7 amp. - I I I I 1 t I I I I I 6.6 7.7 90 11.3 - - - - FIG. In the electron-trap method used by Schulz 9 for observing electronic excitation energies in atoms and molecules, all excitations are determined with electrons whose energies are slightly (usually 0.3 eV) above the excitation energies.Therefore,42 ELECTRON-IMPACT SPECTROSCOPY this otherwise excellent method does not permit one to obtain the additional informa- tion which results from observing the variation of peak intensities with incident electron beam energy over a wide range of the latter. CONCLUSIONS Our results indicate that low-energy electron-impact spectroscopy can be a very useful tool to help elucidate the electronic structure of molecules, specially their low-lying optically-forbidden electronic states. Not only can such states be easily located, but it seems to be possible to distinguish between spin-forbidden and sym- metry-forbidden transitions by observing the variation of peak intensities with in- cident electron beam energy. Improvement in accuracy and resolution can be expected. Since the spectrometer can be operated at 350°C, and since a vapour pressure of 10-4 mm Hg is sufficient for an impact spectrum to be obtained, a large number of molecules can be studied by this technique. The authors wish to thank Dr. Siao-fang Sun for his participation in the early stages of the development of the spectrometer here reported. 1 Franck and Hertz, Verh. dtsh. physik. Ges., 1914, 16, 457; Physik. Z., 1916, 17, 409. 2 Massey and Burhop, Electronic and Zonic Zmpact Phenomena (Oxford University Press, London, 3 Jones and Whiddingon, Phil. Mag., 1928, 6, 889. 4 Glockler and Wilson, J. Amer. Chem. SOC., 1932, 54,4544. 5 Rudberg, Proc. Roy. SOC. A , 1930, 129,629. 6 Rudberg, Proc. Roy. SOC. A , 1931, 130, 182. 7 Lassettre, Radiation Res., 1959, suppl., 1, 530, and a series of Ph.D. Diss. and of U.S. Air Force reports mentioned in this reference. 8 ref. (2), pp. 137-139. 9 Schulz, Physic. Rev., 1958, 112,150; J. Chem. Physics, 1960,33, 1661. 1952), pp. 141-146. 10 Kuppermann and Raff, J. Chem. Physics, 1962,37,2497. 11 k n o t and Baines, Proc. Roy. SOC. A , 1935, 151, 256. 12 Raff, L. M., Ph.D. Thesis (University of Illinois, Urbana, 1962). 13 Moore, Atomic Energy Levels (Nat. Bur. Stand. circ. 467, 1949), vol. I. 14 Spangenberg, Vacuum Tubes (McGraw-Hill, New York, 1948), pp. 25-26. 15 Oppenheimer, Physic. Rev., 1928, 32, 361. 16 Bates, Fundaminsky, Leech and Massey, Phil. Trans. A , 1950, 243, 11 7. 17 ref. (2), pp. 159-60. 18 ref. (2), pp. 221, 230. 19 Kolos and Roothaan, Rev. Mod. Physics, 1960, 32, 219. 20 Tanaka, Sci. Papers Znst. Physic. Chem. Res. Tokyo, 1944, 42, 49. 21 Wilkinson and Mulliken, J. Chem. Physics, 1955, 23, 1895. 22 Price and Tutte, Proc. Roy. Suc. A , 1940, 174, 207. 23 Evans, J. Chem. SOC., 1960, 1735. 24 Mulliken, J. Chem. Physics, 1960, 33, 1596. 25 Potts, J. Chem. Physics, 1955, 23, 65. 26 Berry, J. Chem. Physics, 1963, 38, 1934. 27 Mason, Mol. Physics, 1962, 5, 343.

ISSN:0366-9033    

DOI:10.1039/DF9633500030

出版商:RSC    

年代:1963

数据来源: RSC

摘要:

Circular Dichroism of Dissymmetric up-Unsaturated Ketones BY R. E. BALLARD, S . F. MASON AND G. W. VANE Chemistry Dept., University of Exeter Received 11th April, 1963 A number of dissymmetric a&unsaturated ketones have been found to give a circular dichroism absorption which changes sign in the frequency region of the long wavelength absorption band. From a study of the variation of the circular dichroism with temperature the phenomenon is shown to be due to rotational isomerism in conformationally-labile monocyclic ketones. The rotational isomers of (-)-carvone are identified, and the enthalpy difference between the isomers is evaluated. A possible vibrational origin of the phenomenon in conformationally-rigid ketones is discussed. A number of steroidal ap-unsaturated ketones have been found to give in the 3000-4000 A region associated with the carbonyl n+n* transition a circular di- chroism absorption which changes sign as the progression in the upper-state car- bony1 stretching vibrational mode moves to higher quantum numbers.ll 2 In the light of the one-electron theory of optical rotatory power,3 this observation indicates that electronic transitions occur from at least two main nuclear configurations of the electronic ground state, one giving the positive and the other the negative circular dichroism. The two nuclear configurations may arise either from the two turning points of a vibration excited in the electronic ground state, or from different conformations or rotational isomers of the molecule in the ground state.The temperature vari- ation of the circular dichroism distinguishes between these two possibilities.On lowering the temperature, the areas of both the positive and the negative circular dichroism bands should decrease on the vibrational turning-point hypothesis, since the population of molecules vibrationally excited in the electronic ground state is reduced, whereas, if rotational isomerism obtains, the circular dichroism band area of one sign should decrease whilst that of the opposite sign should increase, owing to the shift in the equilibrium between the conformations. In generaI, the steroids are fixed in one particular conformation,4 owing to the condensed system of cyclohexane rings in the chair form, so that the vibrational origin of the two nuclear configurations appears, at first sight, to be the more probable.If the vibrational mechanism obtains, the turning-point nuclear con- figurations giving, respectively, the positive and the negative circular dichroism ab- sorption may be identified in a dissymmetric ketone with a known absolute stereo- chemistry, and the particular configuration associated with the larger transition probability would indicate the likely structure of the upper electronic state resulting from the n+n* transition of the ketone. In the present work these possibilities have been investigated, using monocyclic terpenoid ketones, which are less complex and more volatile than the steroids studied previously.l.2 The measurement of the absorption and the circular di- chroism spectra in the vapour phase and in paraffin hydrocarbon solutions is reported for two ap-unsaturated dissymmetric ketones with known 5 absolute stereochemistry, namely, (-)-camone (I) and (-)-8-methoxycarvotanacetone (11).4344 CIRCULAR D I C HRO I S M 0 F U p - U N S A T UR A T ED KE T 0 NE S Both compounds give, in the wavelength region of the n+n* transition centred at 3500A, a circular dichroism absorption which undergoes a change of sign as the progression in the upper-state carbonyl-stretching vibrational mode (v N 1200 cm-1) moves to higher quantum numbers, and, in the region of the n+n* transition of the @unsaturated ketone chromophore near 2350 A, a positive circular dichroism band which is very weak in relation to the intensity of the unpolarized absorption At low temperatures the band area of the positive circular dichroism absorption is enhanced, whilst that of the negative circular dichroism is decreased (fig.1). Thus the change in the sign of the circular dichroism given by (I) and (11) in the 3000- 4000A region is due primarily to rotational isomerism, and it is concluded either (fig* 1)- FIG. the 40 30 20 10 1 I 3500 30'00 2iOO A (A) 1 .-The absorption -.-.-.- and the circular dichroism ~ of (-)-camone (I), and circular dichroism - - - - of (-)-8-methoxycarvotanacetone (11) in methylcyclohexane solution at 290"K, and the circular dichroism - - - - of (-)-carvone (I) at 195°K. that the phenomenon has a different origin in terpenoid and steroid @unsaturated ketones or, more probably, that the steroid ketones are conformationally more labile than is commonly supposed.From the known 5 absolute stereochemistry of (-)-carvone (I) and the observed variation in the circular dichroism of the compound with respect to temperature (fig. 1) it is possible to deduce the nuclear configurations of the two rotational isomers in equilibrium and the enthalpy difference AH between them. The area of a circular dichroism band given by a dissymmetric compound measures the rotational strength of the electronic transition responsible for the absorption of radiation in the wavelength region considered. The rotational strengthR. E . BALLARD, S . F. MASON A N D G . W. VANE 45 R represents 3 the scalar product of the electric, p , and the magnetic, p, dipole moments of the transition, (1) where 8 is the angle between the directions of the two moments.The angle-depend- ency of the rotational strength allows the formulation of rules which connect a particular structural configuration with a given sign of the optical rotatory power. The diene 6 and aP-unsaturated ketone 7 rules associate a positive Cotton effect in the wavelength region of the lowest-energy 71-+71* transition with the non-planar configuration which gives the chromophore the form of a right-handed helix, and the octant rule 8 relates in detail the structural dissymmetry of an optically active ketone to the sign of the rotatory power of the 3000A absorption. Tn a dissymmetric ketone, the nodal planes of the oxygen 2p, lone-pair orbital and the carbonyl antibonding 71% orbital (111) divide the molecular environment of the carbonyl group into eight spatial regions, of which the four rear octants in the -z hemisphere are generally the more important.A group or atom, other than fluorine, placed in the upper-left or the lower-right rear octant (LV), relative to an observer viewing the molecule in the -z direction (111), gives the ketone a positive rotational strength at 3000 A, whereas the corresponding substitution in the upper- right or lower-left rear octant (IV) confers a negative rotatory power upon the ketone in that wavelength region. R = pp cos 0, 7 fy 7 $-.ye 6 IT 0 0 r The positive circular dichroism band at 2350A in the spectrum of (-)-carvone (I) indicates, from the chirality rule 7 for ap-unsaturated ketones, that the carbonyl group and the 1,Zvinyl group of (I) form a segment of a right-handed helix in the dominant rotational isomer.The ap-unsaturated carbonyl chromopliore of (I) assumes the form of a right-handed helix when the 4-propenyl group has an equatorial conformation relative to the cyclohexenone ring (V), whereas the chromophore adopts the form of a left-handed helix if the 4-propenyl group has the axial conformation (VI). The octant rule 8 suggests that the axial isomer (VI) should have a strong nega- tive rotational strength at 3500& and that the equatorial isomer (V) should have only a moderate positive rotational strength in the same wavelength region, so that46 CIRCULAR DICHROISM OF QP-UNSATURATED KETONES the circular dichroism spectra of (I) and (11) measured at room temperature are consistent with an equilibrium mixture consisting predominantly of the equatorial isomer (V) and only a small percentage of the thermodynamically less stable axial isomer (VI).o=c The variation in the circular dichroism absorption with temperature gives the enthalpy difference AH between the two rotational isomers. At the absolute temperature T, the differential decadic molar extinction coefficient for left and right circularly polarized light, (Ae = el-er), is given by AeT = Aem + ( A E ~ - A E ~ ) tanh (AH/2RT), (2) where Ae, and ALEO are, respectively, the limiting high- and low-temperature values of the circular dichroism. On fitting the observed circular dichroism absorptions at different temperatures to eqn. (2) it is found that the enthalpy difference between the rotational isomers, (V) and (VI), of (-)-camone (I) is 2-0 kcal mole-1.This estimate is sensitive to the values of the circular dichroism observed at low temperature, and there is the possibility that an equilibrium composition at higher temperatures is frozen-in on cooling. However, the equilibration of the rotational isomers of (-)-cawone (I) is probably fast at the lowest temperature studied (195"K), since the rate constant for the chair-chair interconversion of cyclohexane 9 is 52.5 sec-1 at 206°K. Moreover, the enthalpy difference between the axial and the equa- torial isomers of methylcyclohexane in the chair form 10 has the comparable value of 1-8 kcal mole-1. Relative to the corresponding equatorial isomers, the axial isomers of methylcyclohexane and (-)-carvone (I) are probably destabilized, owing to steric compression, to a similar degree, for although the propenyl group is larger than the methyl group there are, in the isomer (VI), no axial hydrogen atoms on the same side of the ring as the propenyl group, the carbon atom at the 2- and the 6- position of (-)-carvone (I) being trigonal.EXPERIMENTAL MATE~UALs.--(-)-8-Methoxycar~0tanacetone (11) was prepared from (-)-carvone (I), obtained commercially, according to the directions of Buchi and Erickson,ll as modified by Djerassi et al.12R . E. BALLARD, S . F. MASON AND G . W. VANE 47 SPECTRA.-Absorption spectra were measured with an Optica grating spectrophoto- meter, and the circular dichroism spectra with an instrument constructed in these labor- atories 13 and with a Jouan Dichrograph.The spectra were measured in the vapour phase, and in isopentane, methylcyclohexane, and ethanol solution, using a silica dewar flask fitted with an optical cell for measurements over the temperature range, 195-500°K. The authors wish to thank the Royal Society, Messrs. Albright and Wilson Ltd., and the Imperial Chemical Industries Ltd., for the components used to construct the circular dicliroism spectrophotometer, and the D.S.I.R. for the provision of a Jouan Dichrograph. 1 Velluz and Legrand, Angew. Chem., 1961,73, 603. 2 Mason and Vane, unpublished observations. 3 Mason, Quart. Rev., 1963,17,20. 4 Fieser and Fieser, Steroids (Chapman and Hall, London, 1959). 5 Birch, Ann. Reports, 1950, 47, 190. 6 Moscowitz, Charney, Weiss and Ziffer, J. Amer. Chem. SOC., 1961, 83,4661. 7 Djerassi, Records, Bunnenberg, Mislow and Moscowitz, J. Amer. Chem. Soc., 1962, 84, 870. * Moffitt, Woodward, Moscowitz, Klyne and Djerassi, J. Amer. Chem. SOC., 1961, 83, 2771. 9 Jensen, Noyce, Sederholm and Berlin, J. Amer. Chem. SOC., 1962, 84, 386. 10 Hall, Trans. Faraday Soc., 1959, 55, 1319. 11 Buchi and Erickson, J. Amer. Chem. SOC., 1954, 76, 3493. 12 Djerassi, Osiecki and Eisenbraun, J. Amer. Chem. Soc., 1961, 83,4433. 13 Mason, Mol. Physics, 1962, 5, 343.

ISSN:0366-9033    

DOI:10.1039/DF9633500043

出版商:RSC    

年代:1963

数据来源: RSC

摘要:

Dipole Moments and Polarizabilities of Electronically Excited Molecules Through the Kerr Effect BY A. D. BUCKINGHAM AND DAVID A. DOWS* Inorganic Chemistry Laboratory, University of Oxford Received 14th January, 1963 Formulae are derived for the Kerr constant of a diatomic gas for frequencies close to those corresponding to electronic transitions. The magnitude of the Kerr constant is proportional to the square of the transition dipole moment and is determined by the dipole moments and polar- izabilities of the relevant electronic states. Close to an absorption line, the rapidly changing Kerr effect may be a million times that for transparent regions of the spectrum. Transitions which are normally forbidden, but which become allowed in the electric field, should also be associated with strong Kerr dispersion.The dispersion of the Kerr effect would seem to offer better possi- bilities than the straightforward Stark effect for measuring the dipole moment and the polarizability of an electronically excited molecule, and may also provide a means of obtaining accurate transition moments. The dipole moment p is one of the very few observables depending solely on an unperturbed molecular wave function. The expectation value (Yi [ p, 1 Y,) of the one-electron operator pz = xeizi is therefore a potentially useful test of the accuracy of approximate wave functions Yn. Dipole moments are accurately known for the ground states of molecules through dielectric constant measurements and through Stark splittings of pure rotational spectra ; for some diatomic molecules (particularly the alkali halides) the slight dependence of p on the vibrational quantum number II has been determined by molecular beam techniques1 However, little is known of the dipole moments of electronically excited molecules ; the explanation of this is that the obvious method of measurement, the Stark effect in electronic spectroscopy, has not yet yielded positive results.The splittings for reasonable field strengths (about 100 e.s.u. = 30 kV cm-1) are very small by ultra-violet and infra-red standards ; for X-X transitions, they may be about 10-2 cm-1 for dipolar molecules (p # 0) and 10-5 cm-1 for non-dipolar molecules. For Il or A states there is a first-order Stark effect in dipolar molecules (provided the Stark splitting is large compared to the A-type doubling) and the splittings may be about 10-1 cm-1.The difficulties of measuring Stark splittings have been discussed by Herzberg.2 Recently, Kopelman and Klemperer 3 showed that earlier failures to detect Stark splittings in the spectra of CO and CO+ indicate that the dipole moments of the appropriate states are less than about 0.1 x 10-18 e.s.u. Another experiment dependent upon the interaction of molecules with an electric field is the electro-optical Kerr effect. It has been shown 49 5 how measurements of the Kerr constant in the vicinity of absorption bands would isolate the con- tribution of the relevant excited state to the induced anisotropy in the refractive index. Since the Kerr effect largely depends on the partial orientation of molecules, its dispersion should also be a convenient tool for determining the polarization of the i * National Science Foundation Senior Postdoctoral Fellow ; permanent address : Department of Chemistry, University of Southern California, Los Angela 7, California.48A. D. BUCKINGHAM AND D. A. DOWS 49 transit.ion with respect to molecule-fixed axes, and hence the symmetry of the excited state. In this paper the theory of the dispersion of the Kerr constant is developed and the potentialities of the experiment for yielding information about excited state dipole moments, electric polarizabilities and transition moments, are assessed. The observable in Kerr's experiment is the phase difference 6 between the electric vector components parallel and perpendicular to an electric field I; = F'z in a beam of light, initially plane polarized at 45" to F, after it has travelled a distance I in the medium in the field.If nx and nz are the refractive indices in the X and 2 directions, where v is the frequency of the light in cm-1, Nn the mean number of molecules in unit volume in the state Yn, and the molecular polarizability tensor (rctJn is 6 hcv;' = Writ- Wn is the energy difference between the n'th and nth eigenstates, and the sum is over all states n ' f n . The frequencies and wave functions in eqn. (3) are those applicable to the molecule in the presence of F . (ntq)$ = -(nr,)Et is the contribution of the n'th excited state to (neq)n. Eqn. (2) and (3) show that there is a strong dispersion of the Kerr constant in the vicinity of the resonant frequency v:', and that for v nearly equal to v::, 6 is domin- ated by the transition Yn+-Yn (provided the population Nn is not negligible).The awkward summation in eqn. (3) is effectively eliminated, and each excited state's contribution to 6 is isolated. The well-known theory of the Kerr effect treats the rotation of the molecules classically and leads to a temperature dependent 6. However, when rotational structure is observed, it is not permissible to use classical mechanics, and the effects of F on the particular states involved must be considered. Actually P splits the degeneracy of the magnetic states, but as these splittings cannot usually be resolved, 6 is determined by the weighted average over all the M states : where z and z' are the internal quantum numbers and JKM and J'K'M' the rotational quantum numbers.Eqn. (2) can be written where the summation in ( 5 ) is over all transitions Ynp+-Yn. It is convenient to distinguish the internal quantum numbers 'I: and the rotational quantum numbers JKM so that Y,. and Yn become Y(z'J'K'M') and Y(zJKM). Then, for frequencies v nearly equal to v:'iK', the phase difference 6 is a sum over all M and M' : and this is the basic equation of the full quantum theory of the Kerr effect.50 POLARIZABILITIES OF ELECTRONICALLY EXCITED MOLECULES Z-Z TRANSITIONS For a linear rotating molecule, the hamiltonian for the interaction of a particular (7) internal state z with the static field F can be written H' = - PLF cos 8 - *(a 11 - al)F2((3 C O S ~ 0 - 3) - ~(CX 11 + 2a,)F2, or, if the internal state undergoes a transition, N' = -pzFZ, ( 7 4 where all and aL are the static polarizabilities parallel and perpendicular to the axis of the molecule in the state z, and 8 the angle between this axis and F.The perturbed energies and wave functions are, to second order in F, +2a,)F2, (8) J 2 + J - 3 M 2 wTJM = wTJ+F2(2J-1)(2J+3) <z"J"M I H' I z J M ) Y $k = Y , j M - C' Y , " j " M + f "J" hcv:jJ'' 1 (z"J"A4 I H' I T J M ) ~ (9) - C' 2 2 T"J" 2 ~ T J M - 2r"J" (vrJ The relevant matrix elements are given in ref. (4), and the full formula for the con- tribution of transitions YT8p--YfJ to S is q;J' = 8n2 IvN, F2 J 2 + J - 3 M 2 ( I l 2 hc(2J + 1) 2. (1 - kT (25 - 1)(2J + 3) 2 hcBJ(J + 1) 3 2hcB'J'(J' + 1)- 3 J 2 + J - 3 M 2 - In the absence of F, there is a selection rule restricting transitions to the P and R branches, with J' = J - 1 and J' = J+ 1.However, the field perturbs the rotational wave functions, and Kerr dispersion should also be detectable in Q, 0 and S branches where J' = J, J - 2 and J+2. For the R(J- 1) and P(J) lines, [L vo-v -kL][.-J+%]] v,+v (I2)A. D. BUCKINGHAM AND D. A. DOWS 51 where - 1 P‘2 P’ 2 (a 11 - al)’J(J + 1) A j = u p [ { 20hc hcB’(2J - l)-hcB(2J+ 1) ) - s ( z J - l ) (‘11 -alV(J-1)}], (13) (2J+ 1) PP‘ 1- P’’ { 8J3 -2J2 - 1GJ + 3 B j = ( j + i ) 120h2~2B’2 J(J+ 1)(2J-1)2 30h2c2BB’j+ (14) 8J3+2J2-16J-3 CXII -a,)’J(J-l) (a], -al)J(J+ 1 ) -- J(J - 1)(2J + 1)2 }-((1OhcBr(2J- 1)2 lOhcB(2J + 1)2 ~ For the induced S(J-2) and O(J) lines, And for the induced Q(J) lines II-I: TRANSITIONS If AfO, the hamiltonian (7) produces a perturbed energy proportional to the first power of P provided pf‘ is much greater than the A-type doubling energy.* For a JJ state pFM p2F2 J 2 - M 2 K,J,K= I,M - W,J,K=I - J(J+ ~ l)+={J(ZJ- 1)(2J+ 1) ( I - $ ) - ( J + I ) ~ - M ~ 1 (CX 11 - ctl)F2(J2 + J - 3M2) (J + 1)(2J + 1)(2J + 3)(’ -m)} - - 3(2J - 1)(2J + 3) * A-type doubling in the lowest J-states, which contribute most of the Kerr dispersion, is generally much smaller than the values of pF which can easily be obtained (ref.(2), p. 254). An exception may occur for the hydrides.52 In Il-E transitions, the full expression for 6:yK=l is complicated by the large number of terms. However, the first-order term in eqn.(21) provides the leading term in 6, which is proportional to (vg-v)-3. The other terms in 6 are pro- portional to (vg -v)-2 and (vg -v)-I and hence normally less important for frequencies close to V O . POLARIZABILITIES OF ELECTRONICALLY EXCITED MOLECULES The leading term is given by and for the Q(J), R(J- 1) and P(J) lines, If the molecules are non-dipolar, the formulae are simpler, and complete ex- pressions for the Q(J), R(J- 1) and P(J) lines are [& vo-v + v,+v L][. - J f %I}> (28) where (J+ 1) (a11 -a,)'(J-1)(J2+3J- 1) - (a11 - [ B'J2(2J - 1)2 E j = ~ lOhcA. D . BUCKINGHAM A N D D. A. DOWS 53 NON-ROTATING MOLECULES In solids, to a first approximation, the rotation of molecules is suppressed and only internal states (electronic and vibrational) can be excited.However, the dipole p can still interact with F, and for a fixed configuration in which the molecular axis makes an angle 8 with F, The leading contribution to 6 near vg is wqq = w, - p~ cos e - +(all - cos2 e - 3) - $(a,, + 2 a , ) ~ ~ . (32) where L(n, E ) = (n2+2)2(E+2)2/81n, (34) approximately represents the effects of long-range interactions on the local field acting on a molecule in a medium of refractive index n and static dielectric constant E ; for a dilute gas L(n, E ) = 1. If the molecule is non-dipolar, INDUCED INTERNAL TRANSITIONS If (z I p I 7') = 0, the transition z ' - ~ is forbidden when F = 0, but the per- turbation of eqn. (7a) can induce a transition probability proportional to F2. If p = p' = (z I p I z'} = 0, there are induced Z-X transitions (e.g., lZg--lCg transi- tions in homonuclear diatomic molecules) with Q, 0 and S branches, and with Kerr dispersions 8 5 5 2 = where (393 and (a): = +(ccII + 2aL):, and z is parallel to the inter-nuclear axis of the molecule. '' Transition polarizabilities " (~II): and (al):' may make small contributions to 6 when (z I p I z'} # 0.DISCUSSION All the above dispersion formulae have been derived on the assumption that the line-width is negligible. In practice 6 would not go to +a as v goes through54 POLARIZABILITIES OF ELECTRONICALLY EXCITED MOLECULES VO. If the absorption line is approximately Lorentzian in shape, with a width at half maximum height of 2A, then (vo-v)-1 must be replaced by (v~-v)/[(v~-v)~+ A2]. The shapes of ((vo-v)/[(vo--v)~+ A2])a near vo for n = 1, 2, and 3 are shown in fig.1. The magnitude of the contributions of the different rotational levels to S generally decreases rapidly as J increases since the perturbation to the more rapidly rotating states is small. For large J values in X-X and If-C transitions, 6 is proportional to J-2 when p#O ; however, in non-dipolar molecules, 6 is proportional to J". In addition the population N,, varies with J. FIG. 1.-Shapes of {(vo-v)/[(vo -v)2+ A2]}n. Except for large J, or else at very low temperatures, the term in (kT)-1, arising from the influence of the field on the populations of the different M states, is negligible. This temperature-dependent orientation normally dominates the Kerr constant of polar fluids in the visible. The well-known term (all - aL)p2/k2T2 in the classical Kerr constant is replaced, in the II-Z case, by (z I p I ~')2p'2/h3~3(vo-v)3, so that the Kerr constant should be greatly enhanced for VWVO ; in X-X transitions, the corresponding factor is (z I p ~')2p2/h3~3B(vo-v)2, which, for (VO-v) = 5 cm-1, is about 106 times the classical expression. Hence very large, and therefore easily detectable, Kerr effects should be obtainable in the vicinity of the absorption bands of polar gases.As an illustration of the magnitude, shape and complexity of the Kerr effect in a vibronic band, fig. 2 shows 6 for a X-X transition calculated with the following constants : p' = p = 10-18 e.s.u., B' = B = 5 cm-1, A = lcm-1,vo = 3 x 104 cm-1, (z I p I T') = 10-18 e.s.u., T = 300"K, I = 1 cm, and p = 0.02 atm.6, in radians, is very large. In this calculation, only the dipolar terms in AJ and BJ were considered for the P and R lines ; terms in the polarizabilities and in kT are negligible. The electric field-induced Q-branch is a prominent feature of the Kerr dis- persion. From the inequality in magnitude of the two peaks at a given R- or P- branch line, the BJ terms (in (vo-v)-~) are seen to be significant. The inequality of the two peaks arises because the BJ term (like the induced Q-branch term) is ofA. D. BUCKINGHAM AND D. A. DOWS 55 odd symmetry about the line centre, and thus contributes in opposite senses to the two peaks arising from the AJ term. Fig. 2 shows a pattern of Kerr dispersion which is antisymmetric about the band origin. This situation arises because the dipole moments and rotational constants of the two electronic states were taken to be equal.Fig. 3 shows the effect of changing p‘ to 2 x 10-18 e.s.u., all other parameters being held constant. The distortion of the Kerr dispersion is remarkable ; the P(1) line has nearly disappeared, all P-branch lines have changed sign, the Q-branch intensity has more than doubled, and the R(1) line has quintupled in intensity. m 0.04-- 0.02,- b Y -0.02 -- It 10) I FIG. 2.-Kerr effect dispersion in a vibronic band. Parameters are given in the text ; 6 is in radians. The magnitude of the Kerr effect near the rotational lines (6 - 0.1 radian for the conditions specified) indicates the feasibility of measurements ; phase differences as small as 10-7 are detectable.7 The polarizability contribution is normally negligible in polar molecules, being about 10-3 of the dipolar term, but in non- polar molecules it should be measurable.The different frequency dependence of the A J and (BJ+ CJ/kT) contributions to 6 permits each to be evaluated. Thus the sum and difference of 6 at the turning points (I VO-v I = A) gives AJ and (BJ+ CJIkT). At the turning points the sample is ab- sorbing light with one-half its maximum absorptivity, and if the sample is too concentrated it will not be possible to measure 6 at these points.* Also, for narrow lines the turning points will not be resolved. It should, however, still be possible to separate the contributions to 6 by addition and subtraction at larger differences from the line centre.For Z-Z transitions, it is possible to determine the dipole moment of the excited state by relative measurements only. The ratio of the AJ terms for cor- responding lines (e.g., R(J- 1) and P(J)) is given by Aj (2J- l ) ~ -(2J+ 1)~‘ A - j ( 2 J + l ) ~ - ( 2 J - l ) ~ ” -- = * For the parameters used in fig. 2, a pressure reduction of perhaps 100-fold would be necessary before the turning points could be measured.where u = p2/B and uf = p’2/B’. Thus, if p, B and B’ are known, p’ is determined from a relative measurement of the AJ factors.* This dependence of the R(J- l)/P(J) ratio on p’ and p is illustrated by comparing fig. 2 with fig. 3, where only p’ has changed. When p’ has been obtained by these relative measurements, the absolute value of 6 determines (z I p I z’), the transition moment for the vibronic band.Oel t R(O1 I R I I ) I FIG. 3.-Kerr effect dispersion in a vibronic band. Parameters are given in the text. The transition moment is thus obtainable from Kerr measurements on X-X bands. However, formulae (23)-(25) for II-X transitions do not allow independent determination of p’ and (z I p IT’); it seems probable, though, that the terms in (vo-v)-2 and (vo-v)-~ might make both accessible, as in X-X transitions. The leading term in the Kerr dispersion formulae for a Z+lI transition, on the other hand, involves only the ground state dipole moment and (z I p I z’) ; the transition moment, therefore, comes from the leading term, and p’ from the other terms. The transition moment (z I p I 7’) corresponds to a vibronic state change, i.e., it is approximately given by the product of the electronic transition moment and the vibrational overlap integral.The Kerr dispersion, which involves electric dipole matrix elements only, is intimately related to the intensity of the electronic transition, and should be smaller by several orders of magnitude for, say, a spin-forbidden transition. However, the amount of sample in the path may in those cases be increased (in principle) by the same factor without absorbing too much light. Thus, Kerr dispersion at forbidden transition frequencies should also be investigated. The exceptionally large phase shifts predicted by this theory suggest that relatively small amounts of sample are necessary for the measurements. It may be possible, therefore, to investigate molecules obtainable only at high temperatures or in reacting systems.Equations for the Kerr dispersion in the vicinity of vibration-rotation bands in the infra-red region have been given before.4 If, in the above equations, p’ is * Implicit in this statement is the assumption that the line widths for R(J-1) and P(J) are the same, which is probably the case.A. D. BUCKINGHAM AND D. A . DOWS 57 put equal to p, and B' equal to B, the vibration-rotation formulae are obtained; * they are complete, and include the small l/kT terms not given in the previous paper. The transition moment (z I p I z'} to be used for the infra-red bands is that con- n'ecting two vibrational states of the ground electronic state ; due to the low intensity of vibrational transitions, the Kerr dispersion will be considerably less than for electronic transitions.If the permanent dipole moment p is substituted for (z I p I TI), and allowance made for the population of excited rotational states, the R and S branch equations then apply to the pure rotational spectrum, and the Kerr dispersion may be of the same order of magnitude there as in the infra-red. Fig. 2 is appropriate to a vibration-rotation band, except that (z I p I Q2, and therefore the scale for 6, would have to be reduced by about three orders of magnitude. In the vibration-rotation region the Kerr dispersion should be closely antisymmetric about the band origin. While the results of this paper concern diatomic molecules only, the extension to polyatomics should involve no fundamentally different principles. Since the selection of stable gaseous diatomics with transitions from the ground state occurring in reasonable spectral regions is limited, it is probable that such extension will soon be necessary. Financial assistance from the D.S.I.R., in the form of a special research grant, * In the earlier work 4 the equation for the Kerr dispersion near the R(J) line was given with is gratefully acknowledged. the wrong sign. 1 Kusch and Hughes, Handbuch der Physik, Band XXXVII/l (Springer-Verlag, Berlin, 1959), p. 1. 2 Herzberg, Spectra of Diatomic Molecules (Van Nostrand, New York, 1950), p. 307. 3 Kopelman and Klemperer, J. Chem. Physics, 1962, 36, 1693. 4 Buckingham, Proc. Roy. Soc. A , 1962, 267,271. 5 Charney and Halford, J. Chem. Physics, 1958, 29, 221. 6 Eyring, Walter and Kimball, Quantum Chemistry (Wiley, New York, 1944), p. 121. 7 Badoz, J. phys. radium, 1956,17, 143A.

ISSN:0366-9033    

DOI:10.1039/DF9633500048

出版商:RSC    

年代:1963

数据来源: RSC

摘要:

Wave Functions of Excited States Ally1 Cation, Radical and Anion BY J. W. LINNETT AND 0. SOVERS Inorganic Chemistry Laboratory, Oxford Received 8th January, 1963 Various types of wave functions for the 2, 3 and 4 electrons in the r-orbitals of the allyl cation, radical and anion have been tested and their performance compared. For the cation all nine states whose wave functions can be constructed from the 2pa atomic orbitals on the carbon atoms have been studied, but for the radical only the four 2Az states and for the anion only the four 1Al states have been examined. Full configuration interaction treatments (CI) had been published. The results obtained using a number of approximate functions (molecular orbital, valence-bond and non-pairing) were compared with these (full CI).The non-pairing method gives the best overall agreement with the full CI treatment as judged from calculated energies, overlaps with the CI functions, and charge distribution. The simple non-pairing functions for the different states also required little mixing with one another to achieve orthogonality. " Correlation error " in the calculation of electronic energies is reduced if electrons of opposite spin occupy spatially separated orbitals. Two methods have been used for molecules ; (i) in orbital molecular (MO) theory, " alternant " orbitals,l and (ii) on the lines of valence-bond (VB) theory, spatially separated bond-orbitals ; the " non-pairing " (NP) functions of Hirst and Linnett.2 One object of using different orbitals for electrons of different spin is to remove, with a simple function, a large part of the correlation error for singlet states.Another is to eliminate some of the lack of balance in calculating singlet-triplet separations. Both (i) and (ii) have an advantage over configuration interaction (CI) of giving simply visualizable wave functions. The present object is to see whether the NP method,l which gave good results for the ground states of the n-systems of the allyl cation, radical and anion, may be extended to excited states. Because a complete CI treatment can reasonably be carried out for these 2, 3 and 4-electron n-systems, a necessary requirement for any NP scheme must be simplicity. The main problems are (i) choosing bond orbitals for the excited states and (ii) making the wave functions orthogonal among them- selves; these are not encountered in the MO scheme.If such difficulties can be overcome simply, and if the results resemble those of the complete CI treatment more closely than do those of the MO calculation, it may be preferable to describe excited states in this way. CALCULATIONS The method and notation of Hirst and Linnett 2 will be used for the 2,3 and 4 n-electrons. Full CI results for all states are given by them; our calculations will be compared with this " best " treatment, and with other approximate methods, using the following criteria : (a) energy ; (b) overlap of the trial function with the corresponding " best " one ; (c) charge distribution : bond orders and charge densities ; (d) distribution of the total energy between core-attraction and inter-electron repulsion energies.The last two are much more sensitive tests than (a) and (b). 58J . W . LINNETT AND 0. SOVERS 59 CATJON STATES Let a, b and c be the 2p orbitals on the three atoms, b being the central one. In the ground state, one electron is placed in the bond orbital which is a linear combination of a and b, while the other is in one formed from b and c. A variable parameter k may be introduced in two ways : As in ref. (2) these represent determinants. Combinations of these with equivalent deter- minants must be used to satisfy symmetry and spin requirements. This was done in ref. (2) and the following functions were obtained: aSym = (ka+b, b+kc) or = (a+kb, b+kc). and where and As in ref. (2), the a spin function is associated with the first term and the /3 spin function with the second.(Superscripts (+) have been omitted.) For minimum energy, k = 1.41 for Qym, and 3.97 for mSt. The latter gives a better energy and overlap.2 Six simple n-electron 1Al trial functions can be constructed for the ground and excited states of C3HC if two-centre bonding (B) and antibonding (A) orbitals are used. These are BIB, BB/, A/B, AB/, A/A and AA/. In this notation, A/B represents one anti-bonding orbital using a and 6, and one bonding one using b and c, this determinant being combined with all other equivalent ones to satisfy symmetry and spin requirements : AA/ represents two anti-bonding orbitals on the same pair of centres. Of the above six, only four can be linearly independent, and the most suitable four must be chosen. Then the constants k and k' in bonding and anti-bonding orbitals must be selected.Hirst and Linnett 2 examined BB/ as an approximation for the ground state ; it can be eliminated because it overlaps BIB too greatly. Hence A/B is selected for the first excited state. The two upper ones must be mainly ionic. For this reason A/A is omitted and AB/ and AA/ are retained. The four trial functions B/B, A/B, AB/ and AA/ will be denoted by I q ) in which q = 1,2,3,4. The above set of four simple functions may also be derived from a consideration of the MO configurations. The ground configuration, I MOI), is : I MOI) = (a+kb+c, a+kb+c), = (a++kb, +kb+c)+(+kb+c, a+$kb) (a++% a++kb)+(+kb+c, +kb+c). The first two determinants correspond to BIB, and the last two to BB/, i.e., Similarly, it can be shown for excited states that I MOI) = I BIB) + I BB/).I MOII) = I A/B)+ 1 I MOm> = I A/B) - I D/) 1 MOlv) = I AIA)+I Here I A/B) and I AB/) are combinations of four determinants of the types (a-+kb, +kb+ c) and (a-+kb, a++kb) respectively ; 1 A/A) and I AA/) are combinations of two determinants of the types (a-+kb, +kb- c) and (a-$kb, a-+kb) respectively. The Np function for the ground state is the MO configuration with I BBh dropped; this eliminates the ionic terms on the end atoms. Similarly, if 1 AB/) is dropped from60 WAVE FUNCTIONS OF EXCITED STATES I MOII), these terms are eliminated. The elimination of I A/B) and I A/A) from I MOIJI) and I MOJV) increases the weight of these ionic terms for the two upper states.The constants k and k’ in B- and A-orbitals must now be chosen. For simplicity it is desirable to retain k the same for all B-orbitals in all states. For convenience, the value that minimizes the energy in the ground state will be used. The constant k’ is likewise the same for all states, and is chosen so that k’a- b is orthogonal to a+ kb. This gives k’ = (k+Sab/l+k&), where S,b is the ab overlap. In writing down the state wave functions the symmetric form or the staggered form may be used. Further, two staggered forms (st’, st”) are possible for A/B, AB/ and AA/. In one, the bonding orbital is the one weighted more heavily on the end atom; in the other form, it is the one weighted more heavily on the central atom; the antibonding orbitals are orthogonal to the other bonding orbital in A/B, and to the same bonding orbital in AB/ and AA/.Table 10 in the appendix gives the coefficients Cqj of the basic $j in the functions 4 14) = c CqjI $j>. j = 1 The two lowest states have no contribution from $3 and the two highest states none from $2. Mutually orthogonal wave functions I I), I II), 1 111) and I IV), must now be formed from the 14). The simplest way would be to identify 1 1) with I I), 12) with III} etc., k and k’ being adjusted to achieve orthogonality. However, with only two constants this cannot be achieved between all members of the set and so this approach must be abandoned. Therefore k and k’ were kept the same throughout, as stated above, and orthogonality was obtained as follows.Function I I) was chosen to be NI I l), NI being a normalization constant. For I 11), enough of 1 I) was mixed with I 2) to make the mixture orthogonal to I I). On this basis : A similar procedure is used to make I 111) orthogonal to both I I) and I II), i.e., The function I IV) is formed in the same manner. The method can be summarized as follows. The NP state functions 1 P) (P = I, 11, 111, IV) are given in terms of the basic NP configurations I q) (q = 1, 2, 3,4) by 111) = XI([ 2)-(2 10 11)). I 111) = NIIdI 3)- (3 I 11) I 11)- (3 I 1) I 0). where This is the Schmidt orthogonalization process (these functions are not normalized). The four states may be visualized with reasonable approximation, as single NP config- urations 1 q ) only, if the weights of the admixed functions are small.The main object of this work is to provide accurate descriptions of the excited states within an orbital framework. This is not possible in the CI scheme. To pick the worst example, the CI function for 111 is given in terms of MO configurations by In the simple MO description it was just I MOIII) ; with complete C1, I MOII) and I MOT”) separately outweigh 1 MOIIT) and all simplicity of description is lost. To measure the extent of admixture of lower configurations to the one considered, a quantity, wp, is used. This is given by I 111) = -0.020 I M01)-0°.675 1 MOu)+ 0.471 1 MO111)+0.568 I MOrv). The coefficient of 1 p ) in I P) is unity. The overall admixture w for all four states is taken as the average : IV - . w = * C w p . P = IJ .W. LINNETT AND 0. SOVERS 61 If wtO.1, a good description of the four 1Al states is given by the original NP configur- ations BIB, A/B, AB/, AAI. In contrast, WIII for state I11 in terms of MO configurations, considered above, would be 3.50 (or 1-35 if the levels I1 and I11 are considered to cross over) and the average w for all four states is 1.35 (or 0.84). The hope is that, for many systems as well as allyl, the present procedure will turn out to be preferable to the MO and CI treatments in giving better energies and charge distributions than MOs, while retaining simplicity in having much smaller admixtures of NP configurations (lower w ) than of MO configurations in the CI scheme. Several NP calculations were made for each allyl species. The first involved no para- meters, i.e., k = k’ = 1.When parameters k and k’ are introduced, the configurations p can be chosen in various ways : symmetric (sym) and two staggered (st’, st”). Further, the following configurations were taken as the starting point : the two lower states as st’ and the upper two as st”. This scheme, (st’“t’’), is found to be the best. A further calculation was made, using the above orthogonalization procedure, which may be regarded as the VB analogue, the basic four configurations for the cation being $1, $2, $4, $3, in that order of energy. If the three MOs are a+kb+c, a-c and a-kb+c, k must equal 2/2(1+S,,) for the four configurations to be orthogonal (Sac is the ac overlap integral). A two parameter set of MOs can also be used: a+kb+c, a-c, a-k’bfc, where k’ = 2(1+kSab+S&,k+2Sd) for orthogonality.The energies and charge distributions in this scheme ( k f k’ and k chosen to minimize the energy for the ground state) are practically identical with those of the Huckel scheme. Configuration interaction mixing is also calculated in terms of the two parameter MO configurations for the cation, radical and anion. For judging the functions, the average deviation from 1 of the overlap with the best functions 0 = $XU - Sd, P and the average difference from the best energies, will be used. Table 1 gives the results for w, Q and E for the various treatments of the four 1Al states of the cation. TABLE VALUES OF w, Q AND E OF THE k parameters method - - CI MO 1-56 1.389 VB NP 1 1 NP (st”) 3.974 2.083 NP (st’+ st”) 3.974 2.083 - - NP (sym) 1 -409 1 -222 (in eV) FOR THE FOUR 1Al STATES CATION W I3 e 0.79 (MO) 0 0 0 0-229 2.78 0.124 0.089 0.86 0.247 0.145 1 -46 0.235 0-142 1 -49 0.407 0.252 2-45 0.056 0.009 0.10 MO configurations which have the great advantage of an unambiguous orbital descrip- tion, differ considerably, however, from the best functions (average overlap only 0-771).The VB and simplest NP schemes showed improved overlaps and energies, but use 12 % and 25 % admixture of lower states respectively. The NP (sym) scheme is worse than the VB on all counts, though it gives a better description of the ground state.2 The NP (st”) is the worst of all because, in first excited (A/B) state, it puts too much ionic character on62 WAVE FUNCTIONS OF EXCITED STATES the central atom (ie., gives too much weight to $4).The NP (st’) scheme reverses the energies of levels 111 and IV because it gives$4 too much weight in IV. Because NP (st’) is better for state I1 and NP (st”) is better for state IVY the NP (st’+ st”) gives the best results : an average of only 6 % for admixture of lower states and an average overlap of 0.991. This best sequence of NP (st‘) and NP (st”) states is obtained by the following logical procedure. The best NP(st) wave function for the ground state is constructed. Then the overlap of the two A/B functions NP (st’) and NP (st”) with the GS function are tested ; the results are 0-23 and 0-55 respectively. Because the overlap of the NP(st’) is less it is chosen as the basis for the second (first excited) state.For the third (AB/) state, NP (st’) gives overlaps of 0.83 and 0.19 with the first and second states while NP (st”) gives 0.32 and 0.16. Therefore NP (st”) is chosen as the basis for the third state. By a similar argument NP (st”) is chosen for the highest (MI) state (overlaps of 0-18, 0.09 and 0.07 compared with 0-27, 0-32 and 0-86 for NP (st‘)). The energy for a given state may be divided into W12, the expectation value of the sum of all the inter-electron repulsions (just e2lt-12 for the cation). The core energy W1 will be taken as the difference between the energy of the state (Ep-2Wzp for the cation) and the repulsion energy.2 Table 2 gives the ratio - W12/W1 for all four 1Al states, calculated by the various treatments. TABLE 2.xALCULATED VALUES OF - w12/W1 FOR THE FOUR lAl STATES OF THE CATION (I, 11, 111, IV) CI 0.242 0.267 0.49 1 0.604 MO 0-286 0.435 0-385 0.470 VB 0-249 0.199 0.50 1 0.603 NP 0.276 0.333 0.51 1 0.462 NP (sym) 0.244 0.333 0.537 0.473 NP (st’+ st”) 0.258 0.232 0.49 1 0.61 1 method I I1 I11 IV As expected MO functions make - W12/W1 too large for the two lower states (too little electron correlation) and too small for the two upper states.The orthogonalized VB scheme makes the ratio too small for state 11. Of the three NP methods (st’+st”) is the best and this gives good results. The charge distribution will now be examined. The diagonal elements of the one- particle density matrix are : P where x and s represent space and spin co-ordinates and integration is carried out over the co-ordinates of electron 2.The integral of this over the spin of electron 1 gives the diagonal elements of the spin less density matrixp(x1 I XI). It is p = C,,(ab+ bc)+C,,ac+C,(aa+cc)+C,bb, where c a b , etc., are certain coefficients and a, b and c are functions of the position of electron 1. The quantities cab and C,, are bond orders. Charge densities in the bond regions are then given by S&CUb(Pab) and S,cC,c(pac), and on the atoms by c&,) and CbfPb). The sum, Table 3 lists the charge densitiesp for all four states. The “ deviation” is the sum of the differences from the C1 charge distribution. The table shows that there are large shifts of calculated charges when configurations are allowed to interact ; differences are especially large in states I1 and IV. The NP (st’+st”) functions give much the best charge distribution of the approximate treatments though NP(sym) is much the best for the ground state.The NP (st’+ st”) functions for the four states are represented diagrammatically in fig. 1 which gives some data about each. 2pab + p a + 2pu+pb, equals 2.J . W. LINNETT AND 0. SOVERS 63 TABLE 3.-cHARGE DENSITIES IN UNITS OF THE ELECTRONIC CHARGE FOR FOUR lAl STATES OF THE CATION method STATE I CI MO VB NP NP (st’+ st”) CI MO VB NP NP (syni) NP (st’+ st“) NP (sym) STATE I1 STATE III CI MO VB NP NP (SYm) NP (st’ + st”) STATE IV CI MO VB NP NP (st‘+ st”) NP (sym) P CI energy NP energy overlap wp % Pob 0.24 0.27 0.12 0.24 0.24 0.24 -0.10 0 -0.13 -0.12 - 0.09 -0.12 - 0.26 -0.15 - 0.28 - 0.02 - 0.03 - 0.28 - 0.33 - 0.56 -0.16 - 0.55 - 0.56 - 0.29 I - 30.396 - 30.200 0.988 0 Pac 0.03 0-03 0.03 0.0 1 0.02 0.02 - 0.01 - 0.08 0.00 0.0 1 0.00 0.00 0.0 0.04 0.0 1 - 0.04 - 0.03 0.0 1 0.03 0.06 0.01 0.07 0.06 0.02 I1 CH~--OCH~CH~ CH~-CH~CH~ C H ~ ~ ~ C H - C H ~ CH;-CH-CH~ - 0 - 0 - -22.785 - 22.839 0984 5.3 Pa 0.4 1 0.3 3 0.43 0.29 0.43 0-32 0.82 1 *04 1.06 0-61 0.57 0.95 0.45 0.55 0.14 0.95 0.95 0.42 1 -02 0.78 1.08 0-86 0.75 1.01 P b 0.67 0.79 0.89 0.93 0.65 0.87 0-56 0 0.13 1 no2 1.05 0.33 1.62 1.15 2-28 0.18 0.18 1.71 0.60 1.51 0.16 1 *32 1.58 0.55 111 - 16.247 - 16.313 0996 12.7 deviation - 0.34 0.50 0.52 0.07 0.39 - 1-27 0-98 0.94 1-02 0.54 - 0.93 1.33 2.96 2.93 0.20 - 1.88 0.92 1-52 2.0 1 0.16 IV - 10.460 -10.541 0.997 4.6 FIG.1.-Diagrammatic representation of the NP functions used for the four 1A1 states of the cation.Also listed are the CI and NP calculated energies, the CI/NP overlap and wp for each NP function. (Electrons of one spin are represented by o and of the other by x. If the orbital occupied is an antibonding one a bar is placed over the o or x ; otherwise the orbital occupied is a bonding one. The o or x is placed in the bond nearer to the carbon atom whose 2p7r atomic orbital makes the bigger contribution to the two centre orbital.)64 WAVE FUNCTIONS OF EXCITED STATES STATES There are two 1B2 states, and only functions based on electrons occupying orbitals in the same bond (BB/, AB/, AA/) can have this symmetry. The lower state is BB/ and the function is The value of k (5.92) which minimizes the energy gives the exact CI function.The upper state is AA/ and the function is (k’a- b, k’a- b)- (k‘c- b, k’c- b). If k‘ is chosen so that k’a- b is orthogonal to a+ kb, its value is 2-43. It is then found that to make the upper state orthogonal with the lower state 1.3 % of the latter must be mixed with the above upper state function. It becomes then the CI function exactly. (a+ kb, a+ kb)- (c+ kb, c+ kb). 3& STATES There are two 3B2 states, and only functions based on electrons occupying orbitals in different bonds can have this symmetry ; BIB and A/A will be used. The functions are : BIB : (a+ kb, kb+ c)- (c+ kb, kb+a), A/A : (k’a- b, b- k’c)-(b- k’c, k’a- b). The value of k to minimize the energy of the lower state is 0.807, and that of k’ to make a+ kb orthogonal to b- k’c is 0.882.To make the above upper state function orthogonal to that for the lower one, 12 % of the latter must be mixed with it. 3A1 STATES This state is B/A and any function of this type reproduces the CI function exactly. RADICAL With three electrons the following difficulties arise. There are more orbitals than electrons so that the way they are occupied is uncertain and also, because the electrons are all in different orbitals more than one spin combination is allowed. Nevertheless, reason- able choices of bond orbitals and spin assignments give good approximation to 2A2 wave functions of the ally1 radical. 2A2 STATES The best NP function for the GS of the radical is a resonance hybrid of d H 2 CH-CcH2 and its mirror image.2 The function is made up of determinants of the type (a, a f k b b+kc).The radical GS is related to the cation GS by putting the third electon in the, 2pn atomic orbital on the end atom. For energy minimization k = 3.58 which is en- couragingly close to the value for the cation (3-97). This suggests that the three excited states might be formed from those for the cation by adding an electron to the end atom. Thus the second state would be described by a combination of (a, a+ kb, k’b- c) with other equivalent determinants. The third state would be made up of determinants such as (a, b f k c , k’b-c) and the top state from ones such as (a, k’b-c, k’b-c). Table 11 in the appendix gives of the basic @js (see ref. (2)) in the NP configurations 1 1> to 14). This scheme will be called NP’. This procedure is unsatisfactory because in I 3) and I 4), @4 ((a, a, b)+ (b, c, c)) should have considerable weight.The alternative for I 3) and 1 4) is to add the third electron to A/B and A/A giving I 3) as a combination of determinants like (a, k’c-b, a+kb) and I 4) as a combination of ones like (a, k’a-b, k’b-c). The coefficients in these two functions are also given in table 11. This scheme will be called NP”. Of the various spin arrangements, the one taken is the projection of that which alter- nates apa along the molecule 2 (i.e. (afh-+aap-+pcca)). The use of other combinations would complicate the method. As with the cation, k = 3.58 for all states and k’ is also constant and is chosen in the same way. Table 4 gives the results for w, Q and E for the various methods.J .W. LINNETT AND 0. SOVERS 65 TABLE VALUES OF w, cr AND E (in eV) FOR THE FOUR 2A2 STATES OF THB RADICAL CI - L 0*396(MO) - I parameters k k' method W d e MO 1 -52 1.406 0 0.143 0-96 VB - 0 0.126 0.136 1 -42 NP' 3.584 1 ~990 0.404 0.059 0.63 NP' 3.584 1.990 0.004 0.034 0.3 3 Configuration interaction does not involve as much mixing of states as for the cation but it is still 40 %. Likewise the average overlap of the simple MO functions with the CI functions is only 0.857. This amount of mixing is still too high for the CI description to be regarded as a satisfactorily visualizable one. The orthogonalized VB method gives poor results for the radical. Also the value of w for the NP' functions is much too large. On the other hand, for the NP" functions this is very small indeed and the energies and overlaps are most satisfactory.Because the overlap is 0.999 for the GS and the energy is only in error by 0.01 eV, the values of Q and E for the other three states are 0.045 and 0.43 eV respectively. The values of - W I ~ / Wl for the radical are given in table 5. (Here FV1 = Ep-3 Wzp- W12.) All treatments give similar values for this ratio except that the MO method makes it too high for the GS and too low for the highest. TABLE 5.-cALCULATED VALUES OF - w12/w1 FOR THE FOUR 2A2 STATES OF THE RADICAL (I, II, III, IV) method r II III IV CI 0.470 0.670 0.656 0-786 MO 0.514 0.66 1 0-665 0.734 VB 0.462 0.690 0.656 0.747 NP' 0.469 0.677 0.652 0.772 NP" 0.469 0.677 0.649 0.780 Charge and spin densities were calculated for the radical.The following expression was obtained : p = (C$)u2 + Ci{)p2){a b + bc) + (Cz)ci2 + C$b2)ac + (C$)ci2 + CiB)p2)(aa + cc) 3- where the constants C are functions of &b, Sac and of the coefficients of the basic wave functions. The charge densities are defined as : (CP)a2 + C p p ) b b , in the pob = Sab( cz) + c:;)) ; pa = c f ) + c:'); pac = Sue( cg + @); p b = cp + cp. Spin densities p' were calculated assigning negative signs to the p components, e.g. p; = Cf)- Cf). Defined in this way, 2p&-tp&-2pa+pb = 3, and 2pAb+pA,+2pi+p; = 1. Table 6 gives the results (those for NP' are omitted as they are worse in all cases than those for NP"). For the radical, the results obtained with the different treatments are much more similar to one another. The NP" results are, however, the best except for state IV.The NP" functions for the four 2A2 states are represented diagrammatically in fig. 2 which gives some data about each. ANION lA1 STATES If we consider the following six morbitals along the allyl system: a, kafb, a+kb, kb+c, b+kc, c, the NP function for the GS of the allyl anion can be constructed from C66 WAVE FUNCTIONS OF EXCITED STATES TABLE 6.rHARGE ( p ) AND SPIN (p') DENSITIES IN ELECTRONIC UNITS FOR THE 2A2 STATES OF THE RADICAL method STATE I CI MO VB NP'' STATE II CI MO VB NP" STATE III CI MO VB NP" STATE IV CI MO VB NP" 0.19 -0.01 0.90 0.83 - -0.01 -0.02 0.64 -0.24 - 0.27 -0.01 0.86 0.77 0.30 0 -0.04 0.52 0 0.52 0.06 -0.01 0.97 0.94 0.51 -0.02 -0.01 0.68 -0.31 0.18 0.19 -0.01 0.91 0.80 0.05 -0.01 -0.02 0.64 -0.24 0.00 -0.15 -0.02 0.84 1.64 - -0.20 -0.02 0.55 0.32 - -0.15 0.00 1.07 1.15 0.97 0 -0.04 0.52 0 0.80 -0.21 -0.03 0.62 2.21 1.14 -0.08 -0.03 0.56 0.08 0.51 -0.20 -0.02 0.74 1.94 0.60 -019 -0.01 0.56 0.27 0.10 -0.14 0.02 1.31 0.66 - 0.13 0.00 0.25 0.25 - -0.15 0.00 1.07 1.15 1.01 -0.15 0.04 0-20 0.77 1-22 -0.22 0.04 1.59 0.22 1.18 0.07 -0.04 0.48 -0.07 0.94 -0.21 0.03 1.46 0.46 0.65 0.14 -0.02 0.40 -0.05 0.64 -0.49 0.02 1.25 1.47 - -0.02 -0.04 0.33 0.43 - -0.56 0.02 1.29 1.53 0.28 0 -0.04 0.52 0 0.85 -0.23 0.01 1.11 1.23 1.05 -0.07 -0.00 0.04 1.07 1.36 -0.39 0.01 1.19 1-40 0.40 -0.04 -0.02 0.17 0.75 0.73 those of the cation by filling the " holes " and omitting the electrons from the latter.For the symmetric function this gives (a, a+kb, kb+ c, b) and for energy minimization k = 1.60 (cf.1-41 for the cation). For the staggered function this gives (a, a+kb, b+kc, c) and k = 4.33 (cf. 3-97 for the cation). For the anion the NP symmetric functions for states P I I1 HI IV 0 - - CH2XCHLCHz CI energy - 28.914 - 16.422 - 15.972 - 8.943 NP energy -28.904 -16.144 - 15.608 -9.595 wp % 0 0 2 0-5 0 9 overlap 0.999 0965 0946 0.953 FIG. 2.-Diagrammatic representation of the NP functions used for the four 1A2 states of the radical. Also listed are the CI and NP calculated energies, the CI/NP overlap and wp for each NP function. For symbolism see fig. 1. IT, I11 and IV are (a, a+ kb, b- k'c, c), (a, a, kb+ c, b- k'c) and (a, a, b- k'c, b- k'c) respec- tively, equivalent functions being included in all cases to achieve symmetry.The spins associated with the orbitals are in the order a, p, a, p, and the combination that is the pro- jection of this is used. For the Np staggered functions the following were used for 11,J . W. LINNETT AND 0. SOVERS 67 111, and IV: (a, n+kb, k’c-c, c), (a, a, b+kc, k‘b+c) and (a, a, k‘b-c, k‘b-c). The coefficients of the $j of Hirst and Linnett 2 are given in table 12 in the appendix. The NP staggered scheme is derived from NP (st’) for the cation. Those derived from NP (st”) and NP (st’+ st”) give poor results. Table 7 gives the results for the various functions applied TABLE ST VALUES OF w, CT AND E (ineV) FOR THE FOUR 1.41 STATES OF THE RADICAL W parameters k k‘ method U a CI - - 0.763 (MO) 0 0 MO 1 -48 1 -424 0 0.222 2.74 VB - - 0.123 0.105 0.97 NF ( S Y d 1.599 1.313 0-254 0.124 1 -25 NP (st) 4.325 2.158 0.055 0.020 0.23 to the anion.The general performance of the NP (st’) is better than that of the NP (sym) function, though the latter is better for the GS. For the NP (st’) functions the mean energy deviation calculated is about a twelfth of that obtained using MO functions. If the MO functions are mixed in the CI functions w is 0.763, while for the NP (st‘) functions it is less than a twelfth of this. The ratio - W I ~ / W ~ for all four 1.41 states, calculated using the various methods, is listed in table 8. With the cation and the radical, W12 was the increase in energy due to TABLE 8.-CALCULATED VALUES OF - w121Wi FOR THE FOUR ‘A1 STATES OF THE ANION (I, II, m, W ) method I1 I11 IV CI 0.794 0.899 1.01 1 -09 MO 0-8 10 0.960 0.97 1.06 VB 0.8 14 0,893 1.00 1 *07 Np bym) 0.799 0-907 1.03 1.06 NP (st) 0.797 0.895 1.01 1.09 inter-electron repulsion on bringing the three separated parts together to form the molecules.In the anion, because of the presence of four electrons, W12 is greater than this increase by an amount equal to the inter-electron repulsion energy in the fragment containing two electrons. As before, the MO scheme gives too high a repulsion in the lower states and too low a repulsion in the two upper ones. The VB scheme is better for the excited states, but it gives a poor value for the ratio for the GS. The NP(st’) method gives ratios which are closest to those obtained using CI. The charge densities, defined as before, are given in table 9. The NP (st’) scheme gives the best overall results but the NP(sym) method is better for states I and 11.Probably the most successful NP procedure would be to use symmetric functions for the lower two states and staggered ones for the upper two. However, this would not provide a uniform set as the values of k and k’ would have to be different in I and I1 from those in I11 and IV. The NP (st’) functions are shown graphically in fig. 3, together with some relevant data. DISCUSSION The results of the approximate methods have been compared throughout with those obtained using full CI. The reason for doing this is that the latter gives the best result obtainable when similar restrictions are placed on the wave functions (constructed from 2pn: atomic orbitals) and the Hamiltonian. Any agreement with experiment obtained with an approximate method which is not also obtained using fuli CI would necessarily be fortuitous.68 WAVE FUNCTIONS OF EXCITED STATES TABLE CHARGE DENS^ IN UNITS OF THE ELECXRONXC CHARGE FOR THE lAl STATES OF THE ANION method STATE I CI MO VB NP ( S Y d NP (st') CI NO VB NP (Sym) NP (st') STATE II STATE m CI MO VB NP (st') NP (SYm) STATE IV CI MO VB Np ( S Y d NP (st') P CI energy NP energy overlap wp % Pub 0.22 0.27 0-12 0.19 0-23 - 0.23 - 0.30 - 0.28 -0.12 - 0.26 - 0.30 -0.15 - 0.28 - 0.22 - 0.33 - 0.44 - 0.56 - 0.30 - 0.56 - 0.39 I - 14.506 - 14054 0975 0 Pao Pa - 0.05 1.33 - 0.05 1.39 - 0.05 1-47 - 0.04 1.33 - 0.05 1.46 0.02 1.36 0.09 1.1 1 0.01 1.14 0.0 1 1-57 0.01 1 *22 0.02 1-79 - 0.04 1 -59 0.01 2.14 0.03 1.17 0.01 1 -90 -0.01 1 *42 - 0.02 1.79 0.00 1.15 - 0.02 1.83 0,oo 1.30 11 EHz-kH-CHz OX EH~X~Z'OZCH~ - x X E H z - C H ~ C H ~ - EH2-CH%H2 X X - - 6.48 1 - 6.760 0-973 4 5 P b 0-95 0.75 0.89 1.00 0.66 1.73 2.30 2-28 1.20 2.07 1.00 1.15 0.28 2.06 0.84 2.06 1.56 2.30 1.49 2-17 I11 dev - 0.42 0-54 0.12 0.57 - 1.28 1.10 1.18 0.69 - 0.9 1 1.47 2.47 0.45 - 1 -49 1.07 1.64 0.46 IV + 0.475 + 5.748 +0.477 f5.573 0.986 0988 12.9 4.6 FIG.3.-Diagrammatic representation of the NP functions used for the four 1A1 states of the anion. Also listed are the CI and NP calculated energies, the CI/NP overIap and wp for each NP function. For symbolism see fig. 1. The MO method has the great advantages that the basic set of orbitals is con- structed easily, that it takes account of symmetry straightforwardly and that the wave function for any state is orthogonal to those of all other states (w = 0).For many applications these advantages may outweigh all others. However, when configuration interaction is applied, the simplicity of representation and of visual-J . W. LINNETT AND 0. SOVERS 69 ization is largely lost. These calculations have shown that, with an NP scheme based entirely on uniform sets of two-centre bonding and anti-bonding orbitals, it is possible to obtain energies for the ground and excited states which are very much closer to those obtained with full CI (see fig. 4). The mean improvement for the 1Al states of the cation is 28-fold, for the 2A2 states of the radical is 3-fold and for the 1A1 states of the anion is 12-fold.This is achieved using consistent schemes and orthogonalized wave functions which involve only 5+ %, 3 % and 54 %, ,-* - .. - CATtON RADICAL MO C1 NP MO CI NP -.- .-.. --.-.- -__...-- ---- --- -.. -. . . - - MO CI NP ANION FIG. 4.--Comparison of energy levels calculated using (i) a simple MO treatment, (ii) a full CI treatment, and (iii) the best NP treatment, for the 1A1 states of the ions and the 2Az states of the radical. respectively, of admixture of other states to achieve orthogonality. An orthogonal- ization procedure could have been adopted which modified all states equally (rather than 11, 111 and IV successively) but this would have been much more lengthy and difficult though it would have reduced the above percentages. The calculations here do not, of course, give the highest excited states that exist because the treatments are restricted to combinations of 2p71 orbitals. However, the inclusion of 3p or 3d orbitals might be expected to lead to combinations with NP functions similar to those with CI functions because they resemble them closely. The VB method is found to give quite good results for the cation and anion, both of which involve an even number of electrons. We wish to thank the National Science Foundation for a Fellowship to 0. S., the Royal Society and Imperial Chemical Industries for calculating machines and D. M. Hirst and others for their help. 1 Lowdin, Symp. MuZecuZar Physics (Maruzen, Tokyo, Japan, 1953), p. 13 ; Physic. Reu., 1955, 97, 1509. Pauncz, de Heer and Lowdin, J. Chem. Physics, 1962, 36, 2247, 2257. de Heer, J. Chem. Physics, 1962, 37, 2080; P a w , J. Chem. Physics, 1962, 37, 2739. 2 Hirst and Linnett, J. G e m . Suc., 1962, 1035, 3844.70 WAVE FUNCTIONS OF EXCITED STATES APPENDIX TABLE lO.-COEFFICIENTS OF $j IN EXPRESSIONS FOR THE THREE NP FUNCTIONS FOR THE CATION: Syln, St' AND St" 4 SYm 1 2 3 4 st' 1 2 3 4 St" 1 2 3 4 k 1 - kk' 1 - kk' - k' l+k2 k-k' kk'- 1 - k' l+k2 k- k' kk'- 1 - k' 1 2k 0 0 2k - 2kk' 0 0 2k 2 0 0 c93 0 0 2k 1 0 0 - 2k 1 0 0 2k' k'2 c94 2k2 - 4k' - 4k' 2k'2 4k 4 4k' 2k'2 4k 4kk' - 4k 2 TABLE COEFFICIENTS OF t,hj IN EXPRESSIONS FOR THE TWO Np FUN~IONS FOR THE 4 c91 =92 c93 cq4 1 2k2 3k 3k 3 2 2k 3 - 3kk' - 3k' 3 2kk'- 1 - 3k 3k' 0 4 - 3k' 3 3k'2 0 RADICAL: NP' AND NP" NP' NP" 1 2 3 4 2k2 3k 3k 3 2k 3 - 3kk' - 3k' - 2k 3kk' -3 3k' 2 - 3k' - 3k' 3k'2 TABLE 12.-cOEFFICIENTS OF +j IN EXPRESSIONS FOR THE TWO NP FUNCTIONS FOR THE ANION: SYm AND St' 4 c4.1 %2 cq3 cq4 1 k - k2 2 0 2 kk'- 1 2k 4k' 0 3 kk'- 1 0 4k' - 2k 4 - k' 0 2k'2 1 1 l f k 2 - 2k 4k 0 2 k- k' 2kk' 4 0 3 kk'- 1 0 - 4k 2k' 4 - k' 0 2 k'2 SYm s t'

ISSN:0366-9033    

DOI:10.1039/DF9633500058

出版商:RSC    

年代:1963

数据来源: RSC

摘要:

Angular Correlation Diagrams for AH,-type molecules BY C. A. COULSON AND A. H. NEILSON* Mathematical Jnstitute, 10 Parks Road, Oxford Received 10th January, 1963 A study is made of the theoretical basis of Walsh’s rules for discussing the equilibrium shapes of polyatomic molecules in ground and excited states. The particular series AH2 is considered, and detailed numerical calculations are made for H20. It is shown that the use of ionization potentials in Walsh’s correlation diagrams may lead to erroneous conclusions, and the importance of the nuclear repulsion energy is emphasized. A scheme of partitioning the total electronic energy in such a way that the total energy is additive with respect to certain defined orbital energies, is described, and illustrated. It is now almost ten years since Walsh 1 published his stimulating series of correlation diagrams for molecules of different symmetries.These diagrams have been widely used for interpreting the change in shape of a molecule when any given electronic excitation takes place. A particular example, with which we shall be much concerned in this paper, is the series of molecules AH2. The water molecule H20 is the best-known member of this series, but in drawing the correlation diagram (fig. 1, reproduced from ref. (1)) it is assumed that by a suitable change of scale all molecules of this kind are included on the one diagram. An example, taken from Walsh’s paper, will serve to show the use of this diagram, and also introduce us to our main problem, which is to understand what is being represented in curves such as those in fig.1 (the curve involving only the 1s orbital of A has been omitted). In the ground state of the radical NH2 there is one electron in the (lbl) orbitaf, and an allowed long-wavelength transition should be described by the formula (lal)2(2al)2(lb2)2(3al)z(lbl), ~ B I t(la1)2(2a1)2(1b2>2(3al)(l61)2, %. This excitation involves the transfer of an electron from the “ steep ” curve (3al) to the almost horizontal curve ( l b l ) . We remove an electron from an orbital where it is trying to reduce the HNH angle and put it in an orbital where it hardly influences the angle. So in the excited 2A1 state the valence angle should be increased. Arguments of this kind are satisfying on account of their simplicity. But before we can make them, we must first know how to plot the correlation diagrams on which the argument depends.This means that we must know what the ordinate represents. In Walsh’s papers, and in most others in which use is made of these diagrams, the ordinate is described as the binding energy of the individual orbital. This is usually interpreted to be the ionization potential. First, the essential idea implied in these curves is that of a one-electron model, in which we can speak unequivocally of the energy of each electron, and consider how this energy varies with valence angle. But it is not satisfactory to use the ionization potential as this energy. This is because we are concerned with the total molecular energy, and this is far from being the same as the sum of all the ionization potentials.Such a sum includes all inter- electron Coulomb and exchange interactions twice, and since these energies vary Some comments are necessary. * present address : Chemistry Department, The University, Glasgow. 7172 CORRELATION DIAGRAMS considerably with angle we may be led into serious error if we count each of them twice. A further point arises-that if we are concerned with variations in valence angle, we must add to the sum of the individual electronic energies the sum of all the nucleus-nucleus Coulomb repulsions. In the usual application of Walsh's diagram no reference is made to this, even though, as we shall see later, this inter- nuclear Coulomb repulsion curve is quite steep. Some of these points are illustrated in our previous example of NH2. Let us consider two valence angles a and fl (acfl).The energy difference between the lower orbital (3al) and the upper orbital (lbl) is less at p than at a. But in going from a to /3 we also change all the other electronic energies and the nuclear repulsions. 90" 1 80° bond angle (a) FIG. 1. I 90" I bond angle (a) Fro. 2. OC Without considering all of these we can say almost nothing about any likely change in valence angle in the excitation process involved. In an extreme case, dealing with an ionization process rather than an excitation, and in which the nuclear repulsions curve fell more steeply than the correlation curve for the electron being removed, it would be possible for a naive use of the correlation diagram to predict a change in valence angle in the opposite direction to the true one.An attempt has recently been made by Schmidtke and Preuss2 to provide a wave-mechanical basis for the curves in fig. 1. They replaced the true complete Hamiltonian by a pseudo-Hamiltonian, in which all the rl2-terms had been deleted, and an effective nuclear charge ZA replaced the true nuclear charge on the central atom A. In this way all Coulomb and exchange terms disappear ; the total energy is just the sum of the separate one-electron energies: but of course the nuclear repulsion energy must be added as an additional factor when discussing possible changes in valence angle due to excitation or ionization. There is, unfortunately,C . A. COULSON AND A. H. NIELSON 73 some doubt as to the appropriate ZA to use (Schmidtke and Preuss favour ZA = 4.5 for HzO, though this value would clearly be most inappropriate for the K-shell electrons of the oxygen atom).But there is a fairly close parallel between the resulting curves (fig. 2) and those originally proposed by Walsh and reproduced in fig. 1. However, our fundamental objections remain with any one-electron model where the Coulomb and exchange energies are neglected, or an attempt is made to com- pensate for them by an appropriate pseudo-Hamiltonian. It therefore seemed desirable to see whether a treatment of this problem could be presented, which in- cluded Coulomb and exchange energies, and at the same time had an additive (or nearly additive) character. Such a treatment will be attempted in what follows.In the process of developing the theory we shall be able to state more explicitly what is really being plotted as ordinate in these correlation diagrams. We shall agree with Schmidtke and Preuss that it is very far from being the ionization potential ; but, unlike them, in some situations we shall be able to specify it more completely. ONE-ELECTRON ENERGIES Consider a molecule with 2n electrons occupying the n molecular orbitals $1, 4 2 , . . &. We suppose these functions to be orthonormal. If these 4i are the lowest lying orbitals then the ground state is represented symbolically by q5:& . . .q5$ The complete Hamiltonian may be written in the form In where H(i) is the core Hamiltonian for electron i, VN is the internuclear Coulomb repulsion and rtj is the distance between electrons i and j.It is well known that the energy of the state considered may be expressed as where Et is the core energy for orbital &? given by Ei = 1 + r ( 1 ) ~ ( 1 ~ i ( 1 ) d z l , and where J and K are the familiar Coulomb and exchange integrals between the molecular orbitals 4i and $ j . In (2), every summation is over all i a n d j in the range 1 ton. If we accept the validity of Koopmans’ theorem, then the ionization potential of the molecular orbitalq5t is -EZ, where is the molecular-orbital energy. It is immediately clear from (2) and (3) that if we make the sum of all ionization potentials, by writing Q = 2CEi (4) then 8‘ differs from the total energy E in two respects-first, by counting the Coulomb and exchange terms twice, and secondly, by omitting the nuclear energy term VN.These two matters show why in drawing correlation diagrams it is not correct to plot ionization potentials. But of course we cannot plot the core energies either. If we want to have some quantity associated with the separate orbitals and which is truly additive, then we74 CORRELATION DIAGRAMS may obtain such a quantity by partitioning the energy * in the form E = 2&+ V,, where ( 5 ) = &(Ei + ~ i ) (7) If we now draw curves showing how each ea varies with the valence angle a, and then include the nuclear energy V', we should find a minimum of E at the equilibrium value of a. Further, each separate curve tells us the influence of the appropriate molecular orbital, in the presence of the other orbitals, in trying to open or close the valence angle.CALCULATIONS In order to show how ei(a) depends on a for a particular molecule, we have used the molecular orbitals for H20 as determined by Ellison and Shull,3 who made Roothaan-type self-consistent 1.c.a.o. calcu1ations.t Each molecular orbital 4i is given in terms of known atomic orbitals, and so all the required Coulomb and exchange integrals may be found. A matrix formulation appeared to be the most convenient, and the whole calculation was programmed for the Oxford University Mercury computer. Fig. 3 shows the variation with bond angle a of each ei(a), and should be com- pared with fig. 4 which shows the variation of the calculated ionization potentials -&&(a). The curves are labelled by the symmetry of the m.o.'s and the la1 curve has been omitted in both cases since the m.0.is composed almost entirely of the oxygen 1s orbital. By comparison of fig. I and fig. 4 it can be seen that the calculated ionization potentials and Walsh's binding energies are very similar, both in relative value and in their variation with bond angle.$ Comparison with the partitioned energies ei, however, shows that ei and E$ have entirely different angular variation for most orbitals? and that they do not even lie in the same order. In fig. 3 the ( 3 4 level has much the greatest angular variation, with a minimum at a = 180". The nuclear repulsion energy V N ( ~ ) also has its minimum at 180". On our present interpretation these are the two factors largely responsible for increasing the bond angle from 90".But if we use the ionization potential diagrams in fig. 4 it is only the (lb2) orbital which tends to open out this angle. The difficulty in using either the Walsh diagram (fig. 1) or the Schmidtke-Preuss diagram (fig. 2) is that, as they stand, they both give no expectation that the equilibrium angle is greater than 90". We have made some simple calculations (see table) using the same numerical values as Schmidtke-Preuss : they indicate that without explicit inclusion of the nuclear repulsion VN the total energy is a minimum at (or below) a = 90". When it is included, the energy minimum is close to a = 150". The corresponding value obtained from the values in fig. 3 is much nearer the experiment, being approximately 120". Similarly? a simple summation of calculated ionization potentials from fig.4 leads to a valence angle smaller than 90". * Since completing this manuscript we have noticed that Jsrgensen 8 has referred to this par- titioning in a recent book, but without any numerical applications. t In this connection it should be stated that we used both the coefficients and the integrals of Ellison and Shull, despite the fact that certain minor numerical mistakes in their work have been pointed out and corrected by McWeeny and Ohno.4 We have adopted this procedure because the errors are not large, and this facilitates comparison with Ellison and Shull's numerical work. The chief difference is that whereas the (21) curve in Walsh's diagram falls with increasing valence angle, the calculated (2al) curve rises.C. A.COULSON AND A . H. NIELSON 75 TABLE I.-SCHMIDTKE-PREUSS ENERGIES IN H20 (in eV) bond angle a 90" 1 20° 150" 1 80" total electronic energy 2 x 4 - 865.40 - 864.92 - 86443 - 864.14 2ZEjf VN - 614.34 -615.81 -616.22 -616.19 It is instructive to consider in more detail the essential difference between Walsh's energies in fig. 1, or the calculated ionization potentials in fig. 4, and our partitioned energies in fig. 3. As stated earlier this is the totally different behaviour of (3al). The core energy Ez. varies much more for this orbital-a change of over z a -Eat bond angle (a) FIG. 3. ? 52 - l o b - - 30 I bond angle (a) FIG. 4. 16.1 eV as the valence angle changes from 90 to 180O-than for any of the other orbitals. (The corresponding variations for the core energies of (1 al), (Zal), (I bz) and (lbl) are 0.1, 1.3, 10.0 and 0-0 eV respectively. The explanation of the greater variation for (3al) is the large contribution of the oxygen 2pa orbital; this has a large angular variation of the energy, unlike, for example, the Is that dominates (lal) or the 2s that dominates (2al).Table 2 shows these variations numerically.) TABLE 2.4ORE ENERGIES (-Ej) IN H20 (in ev) valence angIe a 90" 1 00" 105" 1100 120. 180" (1 ad 899.03 899.01 898.99 898.99 898.96 898-91 ( 2 4 214.12 21 3.73 213.72 213-56 213-73 212.86 (3~1) 188.45 192.19 193.32 194.08 196.75 204.60 (1bl) 204.60 for all angles W2) 167.57 165-48 164-77 163.85 161.84 157-5576 CORRELATION DIAGRAMS Now the value of c(J33-+K3J varies in the opposite direction by 9.79 eV. In the ionization potential, eqn.(3) shows that this sum occurs with a factor 2, but in the partitioned energy in (6) it occurs once. In (3) the variation of the Coulomb and exchange terms exceeds the variation of core energy ; in (6) it does not. This gives rise to the difference in slope of the two curves. Since the variation with angle of the Coulomb and exchange energy is important, it is interesting to show its precise value, and compare it with the sum of the ion- ization potentials (-2&), the sum of the core energies (- 2CEi) and the sum of the partitioned energies (- 2Zei = E- VN). Table 3 records these three quantities, and-in the third row-the value of 2C(&i-e$) = C(2Jij-Kij). In the range con- sidered this latter quantity varies more than any of the others except for the sum of the ionization potentials.It suggests that an absolute calculation of a valence angle by methods of this kind is by no means easy. This is, of course, precisely what has been found by Ellison and Shull and others. i i. j TABLE VA VARIOUS ENERGY SUMS IN H20 (inev) valence angle a goo looo 105" I loo 1200 180" - 2ZEi 1278.40 1275.52 1274.30 1274.54 127242 1262.66 - 2Zei 23 12-97 23 12.77 23 12-55 23 12.36 23 12.28 2309.84 2C(~i- ei) 1034.57 1037.25 1038-25 1037.82 1039.46 1047.18 - 2CEi 3347-53 3350.00 3350.79 3350.16 3351.74 3357.02 If it can be assumed that similar variations to those shown in fig. 3 will be found for all AH2 molecules, the importance of the nuclear repulsion term V' becomes apparent.For example, molecules of this type with four valence electrons are linear: yet both fig. 3 and fig. 4 would lead to an angle of approximately 90". It seems unwise, however, to pursue this argument since it would also predict a linear singlet CH2, and in any case the variation of the &i from the data of Krauss and Padgett 5 is entirely different from that shown in fig. 4 for H2O. It is probable that slightly different results from those shown in fig. 3 and 4 would result from improved molecular wavefunctions. But it is unlikely that our main conclusions would be materially affected. In order to test the generality of these results for H20 we are in process of ex- tending them to an AH3 system (e.g., H3O+), for which comparable s.c.f.6 and pseudo- Hamiltonian calculations 7 already exist. It is hoped to present the results of such calculations later. The chief drawback to the use of our partitioned energies ei is that they represent the influence of the orbital 4i in the presence of the other orbitals. If the number of these other orbitals changes, as by ionization or excitation, then the ei will also change. Perhaps, however, their general type of variation may not be much affected. We are now investigating this possibility. One of us (A. €3. N.) wishes to acknowledge the award of a Senior D.S.I.R. Fellowship, during the tenure of which part of the present work was performed. 1 Walsh, J. Chem. SOC., 1953, 2260, and following papers. 2 Schmidtke and Preuss, Z. Nuturforsch., 1961, 16a, 790. 3 Ellison and Shull, J. Chem. Physics, 1955, 23, 2348. 4 McWeeny and Ohno, Proc. Roy. SOC. A, 1960, 255, 367. 5 Krauss and Padgett, J. Chem. Physics, 1960, 32, 189. 6 Grahn, Arkiu Fysik, 1961, 19, 147. 7 Schmidtke, 2. Nuturforsch., 1962, 17u, 121. 8 Jsrgensen, Orbituls in Atoms and MoZecules (Academic Press, New York, 1962), p. 5.

ISSN:0366-9033    

DOI:10.1039/DF9633500071

出版商:RSC    

年代:1963

数据来源: RSC

摘要:

Intersection of Potential Energy Surfaces in Polyatomic Molecules BY G. HERZBERG * AND H. C. LONGUET-HIGGINS t Received 28th January, 1963 It is shown that in polyatomic systems the conical intersections described by Teller 4 will occur not only where demanded by symmetry but also in certain non-symmetrical systems. Other kinds of intersection are also described, and it is suggested that “ near-intersections ” are likely to be as important in polyatomic as in diatomic systems. 1. INTRODUCTION In diatomic molecules the potential energy curves of two states will only inter- sect if the states differ in symmetry or in some other essential characteristic.1-3 However, an analogous statement is not true of polyatomic systems : 4 two potential energy surfaces of a polyatomic molecule can in principle intersect even if they belong to states of the same symmetry and spin multiplicity.This sentence leaves open the question whether such intersections ever occur in polyatomic systems. We have therefore tried to find some examples of intersections between states of the same species, and this paper presents some miscellaneous results. 2. GENERAL CONSIDERATIONS We first outline Teller’s analysis of the case in which one may neglect the spin terms in the electronic Hamiltonian, so that the electronic wave function may always be taken in real form. We imagine, following von Neumann and Wigner,3 that all but two of the solutions of the electronic wave equation have been found, and that q11 and q 2 are any two functions which, together with the found solutions, constitute a complete orthonormal set.Then it must be possible to express each of the two remaining electronic wave functions in the form where, in an obvious notation, $ = c1q1 +c2q2, (2.1) all quantities in this equation being real. independent conditions, namely, and this requires the existence of at least two independently variable nuclear co- ordinates. In a diatomic molecule there is only one variable co-ordinate-the interatomic distance-so the non-crossing rule follows; but in a system of three or more atoms there are enough degrees of freedom for the rule to break down. * National Research Council, Ottawa, Canada. p University Chemical Laboratory, Cambridge. 77 In order that (2.2) shall have degenerate solutions it is necessary to satisfy two (2.3) Hll = H229 H,A= H21) = 0,78 POTENTIAL ENERGY SURFACES Following Teller we denote the two independent co-ordinates by x and y , and take the origin at the point where Hl1 = H22 and Hl2 = 0.The secular equations may then be cast in the form : W+h,x-E, zy c1 [ZY, W+h,x-E][c,l = O or W+(m+k)x-E, Zy ly, where m = +(hi + hz), k = 3(h1- h2). The eigenvalues are E = W + mx ,/(k2x2 + 12y2), and this is the equation of a double cone with vertex at the origin. This result was obtained by Teller,4 but he did not draw attention to the following property of the wave function near the origin. Define an angle 6 by the equations kx = R cos 8, l y = R sin 8, (2.7 where R = J(k2x2+ Z2y2)>0. Taking the lower root of (2.5), namely, we deduce that on the lower sheet of the energy surface the coefficients c1 and c2 satisfy E = W-tmx-R, (2.9) R+R cos 8, R sin R sin 8, R+R cos It follows that c1 -sin8 cosB-1 c2 1+cos 8 sin 8 -=-=-- - -tan 30.(2.10) (2.11) Hence, if t,b is to be real, like ~1 and q 2 , we must have c1 = sin $9, c2 = -cos 30, (2.12) or c1 = -sin $8, c2 = cos 38. (2.13) In either case, as we move round the origin keeping R constant and allowing 6 to increase from 0 to 27r, both c1 and cz change sign, and so does t,b. This result is a generalization of one which has been proved 5 in connection with the Jahn-Teller effect, 6 where one also encounters a conically self-intersecting potential surface. It shows that a conically self-intersecting potential surface has a different topolo- gical character from a pair of distinct surfaces which happen to meet at a point.Indeed, if an electronic wave function changes sign when we move round a closed loop in configuration space, we can conclude that somewhere inside the loop there must be a singular point at which the wave function is degenerate; in other words, there must be a genuine conical intersection, leading to an upper or lower sheet of the surface, as the case may be. 3. THREE HYDROGEN-LIKE ATOMS A useful illustration of the above generalizations is a system of three hydrogen atoms near the vertices of an equilateral triangle. If the internuclear distancesG . HERZBERG AND H. C. LONGUET-HIGGINS 79 are a, b and c, a convenient set of internal co-ordinates are x = (b+c-2a)/J6, Y = J2 and z = (a + b+ c)/J3. (3.1) According to both the valence-bond theory and the molecular orbital theory, the ground state is of species 2E‘ in the D3h configuration.It therefore exhibits the Jahn-Teller effect,6 and for given z the surface E(x, y ) is a double cone with vertex at the origin. It may be argued that this example does not really contravene the non-crossing rule, because the degeneracy arises from symmetry; but we can use it for constructing a non-trivial example, in the following way. Let (PA be the valence-bond wave function for a situation in which the electron on A has spin “ up ” and the electrons on B and C are spin-paired ; let c p ~ and cpc be similarly defined, so that (This is a standard result of the simple valence-bond theory.) We now take the system round a continuous loop in (x, y ) space, starting with B close to C and A far away (see fig.1). From the arguments of Q 2 the wave function must have changed sign on completion of the loop ; in fact it evolves as shown in fig. 1 : V A + ~ P B + ( P C = 0. (3.2) A A A A A A ,/ J3 B---C B-C - (PA ,A, / J3 B-C B---C B C B C B C - cpB \ A \\\ J3 VA-YB -(PB+VC VC-V-A (PC FIG. 1. SDA We have now confirmed the change of sign required by the general arguments of $2. However, the valence-bond theory requires the wave function to evolve in this way even when the atoms A, B and C are not chemically identical; they might, for example, be atoms of Li, Na and K respectively. The conical intersection implied by the London-Eyring formula 77 8 must therefore be a real one unless, which is most unlikely, the theory is qualitatively in error as to the way in which the sign of the wave function is affected by taking the system round the cycle depicted in fig.1. We conclude that in a triangular system of three hydrogen-like atoms the lowest doublet state is linked with an excited doublet by a conical intersection even when all three atoms are dissimilar. Both states are symmetric with respect to the mole- cular plane (species ZA’), so in this case at least symmetry cannot be held responsible for the existence of the intersection! E = Q * JCHJAB- Jd2 + H J B c - Jcd2 + ~ ( J c A - J,4d21 (3.3) 4. OTHER TRIATOMIC SYSTEMS In linear molecules all the electronic states are orbitally degenerate except the C states, but this degeneracy is removed when the molecule is bent.9 For example, a ll state of a linear molecule splits into one state which is symmetric and another which is antisymmetric about the plane of the bent molecule.It is therefore not unusual to find that the ground state of a bent molecule is adiabatically correlated with an excited state of different symmetry, obtained by straightening the molecule80 POTENTIAL ENERGY SURFACES out and bending it again in a different plane. We might speak of a “glancing intersection ” between the potential functions of the two states. It is also possible, however, for an A’ (or A”) state of the bent molecule to be adiabatically linked to another A’ (or A”) state, through a conical intersection in the linear configuration. An example is provided by HNO, which we now consider briefly.Bancroft, Hollas and Ramsay 10 have shown that the ground state of HNO is of species 1A’, symmetric with respect to the molecular plane. When the molecule is straightened out, this state will pass adiabatically into the lowest singlet state of the linear molecule ; analogy with the isoelectronic molecule 0 2 strongly suggests that the lowest singlet state of linear HNO is a 1A state. If the H atom is now pulled away along the NO axis, the adiabatic correlation rules imply that the products are a 2s hydrogen atom and a 2A NO molecule. But the ground state of NO is 2lI not 2A, so the linear dissociation curve must somewhere cross the In curve for H(2S)++O(zII), at a point P, say. 2 ‘d FIG. 2. We now consider what happens when we take the HNO molecule at the point P and bend it out of a straight line.The resulting perturbation is necessarily sym- metric with respect to the plane of bending; it can mix together the A’ components of the In and 1A states, or their A” components, but cannot mix the A‘ component of one with the A” component of the other. Restricting attention to the A‘ com- ponents, and denoting the bending co-ordinate by y , we arrive at a situation of exactly the type described in $2 ; the states 401 and cp2 are the A’ components of the 1l-I and 1A states, and x is an in-line co-ordinate measured from the point P. If we extend the potential energy functions for the linear situation by introducing y as a co-ordinate perpendicular to the plane of the paper, we can depict the resulting conical intersection in the manner shown in fig.2 (which is not intended to be drawn to scale). This diagram shows that there is no difficulty in forming HNO adiabatically from H and NO in their ground states, provided that the H atom does not approach the NO molecule along its axis. 5. NEAR-INTERSECTIONS So far we have considered only genuine intersections, such as the conical inter- sections described by Teller or the glancing intersections associated with the RennerG . HERZBERG AND H . C. LONGUET-HIGGINS 81 effect. But almost equally important are " near-intersections " where two potential surfaces nearly meet and only just avoid crossing because of a weak interaction at the point of closest approach. Near-intersections of this kind are well known in diatomic molecules ; a classic example is the near-intersection between the lowest " ionic " and " covalent '' states of an alkali halide molecule.In NaCl, for example, this occurs at a rather large interatomic distance, at which the resonance integral for electron transfer between the two atoms is very small. In essence, the small- ness of H12 is due to the considerable difference in electron distribution between 'pl and cp2. We shall now examine briefly a somewhat analogous case in a poly- atomic system. Douglas 11 has recently studied in detail the strong first ultra-violet absorption system of NH3, whose upper state is 12 a 1Ai state of the planar molecule (sym- metry group D3h). In molecular orbital terms this state results from exciting one of the unshared a:2p electrons of planar NH3 to the Rydberg orbital 3sa;.The absorption system shows strong signs of predissociation, but in the first few members of the main vibrational progression of ND3 rotational structure is clearly discernible. Now it seems likely that the predissociation of excited NH3 is produced by inter- action with a state arising from a hydrogen atom and an NH2 radical in their ground states. We therefore consider the approach of an H atom to an NH2 radical to form a planar NH3 molecule. The ground state of NH2 is 2 8 1 , antisymmetric with respect to the plane of the bent radical. There are two electrons in the non-bonding hybrid orbital on the N atom, and these will impede the approach of the third H atom. The singlet state formed by the combination of H(2S) and NH@Br) should therefore be repulsive, at least in the early stages of formation.But this state has the same multiplicity and symmetry (with respect to the group CzV) as the observed 1A[; state of NH3. Why, then, is the interaction between these two states so weak that the latter is only predissociated and not completely disrupted by the former? The answer, possibly, is that although the two states have the same symmetry and multiplicity, a substantial electronic rearrangement is needed to convert one into the other: the electron on the approaching H atom must be transferred to a Rydberg 3s orbital on the NH2 radical before the lone pair on the N atom can form a satisfactory bond to the H nucleus. It seems likely, therefore, that the matrix element H12 between the observed 1A'; state of NH3 and the singlet state arising from H(2S) + NHz(2Bl) is very small, so that the potential surfaces for these two states, while not actually intersecting, approach so closely that all the usual conditions are satisfied for a predissociated absorption spectrum.6. GENERAL CONCLUSIONS Our conclusions are somewhat diverse, like the facts of molecular spectroscopy. First, the conical intersections described by Teller 4 will occur not only in situations where symmetry demands them, but in asymmetrical systems such as a set of three dissimilar hydrogen-like atoms. This follows from the fact that conical intersections differ topologically from accidental meetings of potential surfaces, and cannot be " abolished " by making infinitesimal changes in the electronic Hamiltonian. Secondly, in non-linear triatomic molecules two states of the same species are sometimes connected through a conical intersection occurring in the linear con- figuration; this kind of situation is likely to occur in many cases of interest. Lastly, narrowly avoided crossings may well be as important in polyatomic as in diatomic systems; their occurrence has nothing to do with symmetry, but is due to a substantial difference in electronic character between the two states involved.82 POTENTIAL ENERGY SURFACES We are indebted to Dr. A. E. Douglas for kindly allowing us to quote his unpub- lished results. 1 Hund, 2. Physik., 1927, 40, 742. 2 Franck and Haber, Berliner Akademieberichte XIII, 193 1. 3 von Neuinann and Wigner, Physik. Z., 1927, 30,467. 4 Teller, J. Physic. Qern., 1937, 41, 109. 5 Longuet-Higgins, Opik, Pryce and Sack, Proc. Roy. Soc. A , 1958,244, 1. 6 Jahn and Teller, Proc. Roy. SOC. A, 1937, 161, 220. 7 London, 2. Elektrochem., 1929, 35, 522. 8 Glasstone, Laidler and Eyring, The Theory of Rate Processes (McGraw-Hill, New York, 1941). 9 Renner, 2. Physik, 1934, 92, 172. 10 Bancroft, Hollas and Ramsay, Can. J. Physics, 1962, 40, 377. 11 Douglas, this discussion. 12 Walsh and Worsop, Trans. Faraday SOC., 1961,57, 345.

ISSN:0366-9033    

DOI:10.1039/DF9633500077

出版商:RSC    

年代:1963

数据来源: RSC

摘要:

S tereochemistry of Hydrocarbon Ions Bridged Structure of C2Hi BY J. C. LORQUET Centre de Spectromitrie de Masse, Institut de Chimie Gtntrale, Universitk de Li&ge, Li&ge (Belgium) Received 15th January, 1963 The geometrical structure of A2H6 molecules has been studied by the correlation diagram method. Molecules containing 12 valency electrons (B2H6, C2Hg+) should belong to theD2h group, and assume the bridged configuration characteristic of electron-deficient molecules. Molecules containing 14 valency electrons (C2H6) should belong to the D3 group and have an ethane-like structure. The potential energy hypersurface of the C Z H ~ ion (13 valency electrons) in its ground state has probably two shallow minima, corresponding to the D3 and D2h configurations, and separated by a low activation energy.The CzH; ion is thus expected to have an easily deformed structure. This explains the great ease with which the hydrogen atoms are shuffled in the ethane ion, as shown by the mass spectra of the deuterated ethanes. Other alkane ions (particularly C3H,') are also briefly considered. A2H6 molecules can assume two nuclear configurations. First, there is the configuration taken by ethane in its ground state (D3d symmetry) (fig. l), and secondly, the bridged structure characteristic of diborane ( D ~ A or Vd symmetry) (fig. 2). This bridged configuration is known to be characteristic of electron-deficient molecules.1 For each of these forms, several values of the HAH angle are possible. The purpose of this note is to determine, by the correlation diagram method introduced by Walsh,2 the most stable configuration as a function of the number of electrons in the different molecular orbitals.Let us first examine the D3d configuration. D3d CON FI G UR AT I 0 N The molecular orbitals characterizing a H3AAH3 molecule in the D3d configur- ation are most easily obtained by combining those of two AH3 groups. AH3 molecules may assume two configurations : a planar one (D3h) and a pyramidal one (C3J. Walsh has given the form of the molecular orbitals in the two con- figurations.2 From the a1 orbitals of each AH3, we obtain two orbitals of A2Hs which possess the labels alg and azU. When the HAH angle is go", their expression is : a l g - . (z~-Zz,)+(h,+h,+h,+hq+h5+hs), a t , . . . ( Z , + Z B ) + ( l Z i + h z + h g - h h q - h 5 - k 6 ) .When the HAH angle is equal to 120", their expression is : a l g . . . ( S ~ + S g ) + ( h l + h 2 + h 3 + h q + h 5 + t 2 6 ) y a2U. . (S~-~g)+(hl+h2+h3-h4-hS-h6). (SA designates the 2s atomic orbital of atom A; XA, YA, ZA designate respectively, the 2ps, 2p, and 2pz atomic orbitals of A ; hly h 2 . . ., are the 1s orbitals of the hydrogen atoms, 1, 2, . . .). Walsh's first stability criterion indicates that these orbitals become more tightly bound as the HAH angle increases. a384 STEREOCHEMISTRY OF IONS The expression of the two doubly degenerate orbitals is obtained by a similar procedure. It does not depend on the value of the HAH angle. Since these orbitals are antibonding between the H atoms, they become more tightly bound as the HAH angle increases.6 t I 0 , i I 0 * I k f " FIG. 1.-Structure of the D3d configuration. i e Y FIG. 2.-Structure of the D2h configuration. The orbital bonding the A atoms is formed by the in-phase interaction of the lone-pair orbitals of each AH3 group. Its expression is (SA+SB) when the HAH angle is equal to 90", and (ZA-ZB) when this angle has a value of 120". It becomes less and less tightly bound as the HAH angle increases.J. C . LORQUET 85 The order of the energies of these orbitals has been obtained by Hall 3 for ethane (LHCH = 109"). The correlation diagram is given in fig. 3. The ethane molecule has 14 valency electrons. According to the diagram, it should have a HCH angle intermediate between 90 and 120" ; the experimental value is 109".(a 1,>2(a 2u)2(eu)4(e,)4(a1 g)2- 1 l o j 90" I09 120° D3d FIG. 3.-Correlation diagram for the D3d configuration. D2h c o NFI G UR A T I ON The electronic structure of diborane is very similar to that of ethylene.4-5 The form of the molecular orbitals of diborane can thus be obtained by taking sums and differences of the molecular orbitals of two AH2 groups as outlined by Walsh,2 and then adding the adequate symmetry orbital corresponding to the bridge hydrogens hl and h4 (i.e., adding (hl +h4) to a1 orbitals, and (hl - h4) to the b3u orbital). The expression of the alg and the bl, orbitals can be obtained by taking linear combinations of the a1 orbital of each AH2 group. When the HAH angle is 90", their expression is : alg ( Z ~ - Z g ) + ( h 2 + h 3 + h 5 + h 6 ) - ( h i + ~ ~ 4 ) bl, .. . (ZA+Z,)+(h, +h3-h5 - h 6 ) . For an HAH angle of 180" : a l , . . (sA+sg)+(h2+h3+h5+h6)+(hl+h4) b l , . - ( ~ ~ - S g ) + ( h 2 + h 3 - J ~ s - h 6 ) .86 STEREOCHEMISTRY OF IONS According to Walsh's first criterion, these orbitals become more tightly bound as the HAH angle increases. The expression of the bZu and b3g orbitals is obtained similarly from the b2 orbitals of each AH2. Their expression does not depend on the value of the HAH angle. b 2 u - (y*+y,)+(hz-h3+hg-h6) b,, * ' (Y,-Yy,)+(h,-h3-hs+h6). Since they are both antibonding between the H atoms, they become more tightly bound as the HAH angle increases. The expression of the other alg orbital is (SA +sg) + (hl + h4) when the HAH angle is go", and (ZA - ~ g ) - ( h l + h4) when the HAH angle is 180".It becomes less and less tightly bound as the HAH angle in- creases. The bridge orbital is & in type. Its expression is ( x A + x B ) + ( ~ I - ~ ~ ) and it does not depend on the value of the HAH angle. Finally, we shall also con- sider the lowest antibonding orbital. Its expression is ( x A - x ~ ) and it is b2g in type. The order of the energies of the molecular orbitals of ethylene and diborane is about the same, except that the bridge orbital b3u must be strongly stabilized by the two bridge hydrogens.6 Such a stabilization is also expected for the two alg orbitals, although to a smaller extent. We shall thus adopt the following order for diborane : This order agrees with that obtained from s.c.f. calculations for ethylene 7 and di- borane.8 The correlation diagram is given in fig.4. The diborane molecule in its ground state, containing 12 valency electrons, has to have its two outermost electrons in the ag orbital. Its HBH angle is therefore expected to have a value intermediate between 90 and 180" ; this angle is known experimentally to be about 120". In the first excited state of diborane, the orbitals a, and bZg are both singly occupied. One would expect the HBH angle to be intermediate between 120 and 180". (ag)2(b1u)2(b3u)2(b2u)2((b3g)2(a~)2(bZ8)0 STEREOCHEMISTRY OF THE C2Hz ION The occurrence of rearrangement phenomena was mentioned repeatedly in the study of the mass spectra of deuterated ethanes.9 For example, CH3CD3 gives normal fragmentary ions CH: and CD$, but also rearrangement ions CH2D+ and CHD?.It must be admitted that, before the rupture of the C-C bond takes place, the molecule undergoes a complete modification of structure which shuffles the hydrogen atoms. This phenomenon could be explained by the occurrence of a bridged structure for the C2Ht ion. A similar suggestion was already made by Walsh 10 for the C2Ht ion, and by Rosenstock et aZ.11 for the C3H7+ ion. Since this problem implies a comparison of the relative stability of the two configurations D3d and D2h, we must now establish a correlation diagram between these two structures. The intermediate state (fig. 5) belongs to the symmetry group C2h. From the character tables of the groups D3d, D2h and C2ho a one-by-one correspondence between the orbitals in these three forms can be obtained (table 1).We shall now consider each orbital individually, and discuss its binding energy in each configuration. The expression of the lowest alg-ag orbital is similar in both configurations, first, when the HCH angle is equal to go", and secondly, when it is equal to 120" for the D3d configuration, and to 180" for the D2h configuration. However, in order to take into account the stabilization effect due to the bridge hydrogens mentioned before, we have assumed that the binding energy was a little greater in the D2h configuration. This is not the case for the azu-blU orbital;J . C. LORQUET 87 its binding energy will thus be the same in the two configurations, first when the HCH angle is equal to 90", and secondly, when this angle is equal to 120" for the D3d configuration and to 180" for the D2h form.The b3u orbital is strongly stabil- ized with respect to the eu orbital by the two bridge hydrogens. This is not the r' I I Y '2h FIG. 5.-Structure of the transition state (Czh). case for the e,- bzu orbital, whose binding energy will be the same in both config- urations for equal values of the HCH angle. The other component of the e, orbital corresponds to the antibonding bZg orbital of the D2h configuration: its binding energy must be much smaller in the bridged configuration. Finally, the C-C Q orbital (alg) should have the same binding energy in both configurations when the TABLE 1 .-CORRESPONDENCE BETWEEN THE MOLECULAR ORBITALS OF THE D3d, C2h AND D2h CONFIGURATIONS 03.: C7h Dzh U l g .. . "g . . f Clg azU . . . b, . . . bl, . . . a, . . . b2, . . . b , . . . 63, . . . ag . . . h2g . . . bg . . . b j g HCH angle is equal to go", or when it is equal to 120" in the D 3 d configuration, and to 180" in the D2h configuration. However, we shall again assume a slight stabilization for the bridged structure. The two diagrams reproduced on fig. 3 and 4 have been drawn according to the above discussion. They are thus directly comparable. Let us now consider the C2Hz ion (13 valency electrons) in its ground state. If this ion assumes the configuration D3d, the orbital alg is occupied by only one electron. The value of the HCH angle should then be intermediate between 120 and 109". Let us assume about 115". If the ion belongs to the symmetry group D2h, the outermost electron will be in the bzg orbital.The HCH angle should then have the same value (120") as that observed in diborane. Fig. 6 represents a new correlation diagram between the configurations D2h and &d, in which the binding energies of the orbitals for the D2h configuration have been taken in fig. 4 for a value of 120" of the HCH angle, while those of the D3d configuration have been inter- polated in fig. 3 for a value of 115". An " avoided crossing " case occurs for the88 STEREOCHEMISTRY OF IONS /--- _._---- . . . . . . . ;>:. *.* -----_ __ --__ --.- 1 -. I .s eg A 2 M ba other hand, the orbitals eg-ag and alg-bzg, the latter being occupied only cnce. Although the bridged configuration might seem some- what favoured, it is difficult to arrive at a definite conclusion since the curves of the diagram are drawn in a purely qualitative a9 way.The situation is similar to the CH3 b3 radical and the NHf ion which are thought to be pyramida1,z but where the potential APPLICATKON TO HIGHER HYDROCARBON IONS Hydrogen atom migrations are known to occur in practically all ionized hydro- carbons. It is therefore tempting to explain these rearrangements by bridged structures characteristic of electron-deficient molecules. We might expect struc- tures analogous to that of diborane, where one (or more) " normal " hydrogen atoms would be replaced by alkyl groups. For the C3Hg ion, another possibility appears more likely. The compound B4H10. 2NH3 is known to have an ionic structure [BH~(NH~)~]+[B~Hs]-, where B3Hg, which is isoelectronic to CsH$+, exists as an independent entity.12 By analogy with CzH;, we might expect the potential energy hypersurface of the C3HS ion in its ground state to have two shallow minima : m s B 3.a2u 049 assumes an easily deformed configuration. The two forms D3d and D2h have probably similar energies, and are separated by a low potential barrier. When ethane is ionized by electrons of energy approaching that of the threshold, the Franck-Condon principle probably determines the structure assumed by the ion. But when the energy of the biu A \J . C. LORQUET 89 one corresponding to the neutral molecule (with slightly modified internuclear distances and angles), and a cyclic configuration characterized by two three-centre bonds, and analogous to that of B3Hg and C3Hif (fig.7). H H BH2 FIG. 7.ftructure of the B3Hg ion. The consideration of this possibility might help to visualize and to understand the nature of the activated complexes postulated by Kropf et al. in their statistical calculation of the mass spectrum of propane.13 The author is indebted to Prof. L. DOr for his interest in this work. He also wishes to thank the Fonds National de la Recherche Scientifique of Belgium, for a position of Charg6 de Recherches. 1 Longuet-Higgins, Quart. Rev., 1957, 11, 121. 2 Walsh, J. Chern. Soc., 1953, 2260. 3 Hall, Proc. Roy. SOC. A , 1951,205,541. 4 Pitzer, J. Amer. Chem. Soc., 1945, 67, 1126. 5 Mulliken, Chem. Rev., 1947, 41, 207. 6 Longuet-Higgins, Calcul des Fonctions d'Onde Mole'culuire (ed. du C.N.R.S., Paris, 1958), p. 93. 7Berthod, Compt. rend., 1959, 249, 1354; Ann. Chim., 1961, 285. * Yamazaki, J. Chem. Physics, 1957, 27, 1401. 9 Schissler, Thompson and Turkevich, Disc. Faruday SOC., 1951, 10, 46. Quinn and Mohler, J. Res. Nat. Bur. Stand. A, 1961, 65,93. Stief and Ausloos, J. Chem. Physics, 1962, 36, 2904. 10 Walsh, J. Chem. Soc., 1947, 89. 11 Rosenstock, Wahrhaftig and Eyring, The Mass Spectra of Large Molecules, II. The Applica- 12 Peters and Nordman, J. Amer. Chem. SOC., 1960, 82, 57. 13Kropf, Eyring, Wahrhaftig and Eyring, J. Chem. Physics, 1960, 32, 149. Eyring and tion of Absolute Rate Theory (University of Utah, Salt Lake City, 1952), p. 17. Wahrhaftig, J. Chem. Physics, 1961, 34, 23.

ISSN:0366-9033    

DOI:10.1039/DF9633500083

出版商:RSC    

年代:1963

数据来源: RSC

摘要:

Electronic Absorption Spectra of HCO and DCO Radicals BY J. W. C. JOHNS,* (Miss) S. H. PRIDDLE t AND D. A. RAMSAY Division of Pure Physics, National Research Council, Ottawa, Canada Received 15th January, 1963 The long wavelength absorption bands of HCO and DCO have been observed with much greater intensity than in the earlier work of Herzberg and Ramsay. Rotational and vibrational analyses of 22 new bands have been carried out and new molecular constants obtained. The numbering of the bands in the principal progression (0, 05, O)--(O, 0,O) has been revised so that the C vibronic levels now correspond to odd values of the quantum number 0;. Analysis of the rotational envelopes of some of the diffuse bands has been carried out. The “ ll-bands ’’ are found to be staggered to lower frequencies relative to the “ 22-bands ’’ and fairly large C-A and T T - 4 splittings are also found.These splittings are roughly quadratic in K, i.e., v$ = vo-GK2, where G-15 cm-1 for HCO and -10 cm-1 for DCO. The magnitudes of these splittings are consistent with those calculated from the theory of Pople and Longuet-Higgins assum- ing that the molecule exhibits a Renner effect. A short discussion of dissociation and predissoci- ation is given. The long wavelength absorption system (7500-4500& of the HCO free radical was first studied by Ramsay,l and Herzberg and Ramsay.2 The electronic transi- tion was found to invdve the ground state in which the molecule is bent (LHCO = 119” 30’) and a low-lying excited state in which the molecule has a linear equilibrium configuration.The spectrum consists principally of a long progression of bands (0, u;, O ) t ( O , 0, 0) involving the bending vibration vi in the excited state. Alter- nate bands in the progression are sharp while the others are difuse. The sharp bands involve the K” = 1 rotational levels of the ground state of the molecule which approximates very closely to a symmetric top, and the K‘ = 0 levels of the excited state. The sharp levels in the excited state are therefore Z vibronic levels. Since the vibrational numbering of the bands was not definitely established by Herzberg and Ramsay, it was not possible to state unambiguously whether the Z vibronic levels are &ectronic X &ibrational, nelectronic X nvibrational Or higher pro- ducts. From the rotational selection rules, however, it was found that the transition moment lies in a direction perpendicular to the molecular plane, hence the bands are vibronicaZZy either X+tA”, or X-cA’.Herzberg and Ramsay gave reasons for assigning the spectrum to a 2Z++-2Af’ electronic transition, but this conclusion was at variance with the predictions of Walsh 3 who from molecular orbital argu- ments concluded that the electronic transition should be 2A” t 2 A ’ . Ramsay 4 later pointed out that if the two combining states are derived from a common 2lI state as is implied by the predictions of Walsh, then the upper state (in which the molecule has a linear equilibrium configuration) is in effect only “ half a rll-state ”, which will be denoted by the symbol 2A”lI. The transition may there- fore be written 2A”n - 2A’.Under these circumstances, the levels associated with the bending vibration of the molecule in the upper state would be expected to show large vibronic splittings (cf. NH2, Dressler and Ramsay 5) due to the effects of elec- tronic-vibrational interaction (Renner effect). * N.R.C. Postdoctorate Fellow 1959-61. -f N.R.C. Summer Research Student 1962. 90J. W. C. JOHNS, S. H. PRIDDLE AND D. A . RAMSAY 91 Unfortunately, for HCO and DCO most of the levels of the excited state are diffuse and no rotational analysis is possible, except for the X vibronic levels. A careful study of the rotational envelopes of the diffuse bands in the present work, however, has permitted the location of several ll, A and iD vibronic levels with an accuracy of a few cm-1.Fairly large vibronic splittings (up to - 100 cm-1) have been ob- served and the origins of the various vibronic bands fit the usual quadratic formula vf = VO- GK2, where G - 15 cm-1 for HCO and G- 10 cm-1 for DCO. The mag- nitudes of these splittings are in moderately good agreement with those calculated from the theory developed by Pople and Longuet-Higgins6 for NH2. Another consequence of the present work is that the principal progressions (0, 05, 0)-(0, 0, 0) for HCO and DCO have been extended to lower quantum numbers so that it is now possible to determine unambiguously the vibrational numbering of the bands. It is found that the I: vibronic levels correspond to odd values of the quantum number vi, and the earlier values of 04 given by Herzberg and Ramsay should be reduced by one.These results leave no doubt that the I: vibronic levels are derived from nelectronic x nvibrational levels, and that the electronic transition may be written 2A”II - 2A’. The recent electron spin resonance measurements of Adrian, Cochran and Bowers 7 provide independent evidence that the ground state is a 2A’ state and not a 2A” state. EXPERIMENTAL The new bands of HCO and DCO were observed during the flash photolysis of CH3CHO and CD3CDO in the manner described by Herzberg and Ramsay. Since weaker bands were sought in the present work, longer absorption paths were used together with flash lamps which were both brighter and shorter in duration. The essential features of the apparatus are as follows : Absorption tube : length 2 m.No. of traversals of the multiple reflection mirror system-up to 32. Photolysis lamps: two 1-m flash lamps in series, fired by two 300pF condenser banks Source lamp : 3 mm int. diam. quartz capillary lamp, fired by a 2 pF condenser charged Time delay - 30 psec. Pressure of acetaldehyde : 50 mm Hg. Spectrograph : 21 ft concave grating ; Eastman Kodak 1-0, I-F and hypersensitized I-N plates. Reference spectrum : provided by iron hollow cathode lamp. charged to f7 kV ; flash duration - 30 psec. to 15 kV ; flash duration - 10 psec. The sharp bands were measured using a photoelectric comparator while measurements of the diffuse bands were taken from microphotometer traces of the bands.92 ABSORPTION SPECTRA OF HCO AND DCO of some of the bands investigated in the earlier work have been appreciably ex- tended and some new band heads observed.The band-head measurements for all the sharp bands of HCO and DCO are summarized in table 1. The vacuum wavenumbers and assignments of the rotational lines are given in a separate publication.8 TABLE BAND HEADS FOR THE SHARP BANDS OF HCO AND DCO HCO DCO &$ir) Y (vac.) int. 8573 3 11660.9 w 8561 -9 11 676.5 8235.5 12139.2 vw 8224.4 . 121 55-6 7560.9 13222-3 m 7551.6 13238.5 7310.7 1367409 vvw 7301.8 13691.4 6774.1 14758.0 s 6766.3 14774.9 6138.0 16287-5 5643.7 17714 17693 vvw 3 5650-3 5624.0 1777601 5574.95 17932.4 m 5570.1 17948'1 5538.0 18052 18036 vvw 3 5542.8 5511.5 18138.7 w 5505.8 18157.5 5201.0 19221.8 s 5195-6 19241.6 5152-5 19402.8 m 5148.1 19419.2 5123.3 19513.2 w 5119.0 19529.6 5105.9 19579.7 vw 5100.3 19601.4 4838.3 20662.8 m 4833.3 20684.0 4795.0 20849.1 w 4791.0 2Q866.6 4769.6 20966-2 vw 4761-2 20997 4757.0 21016 4527.7 22080.2 w 4523.2 22101.9 4488.7 22271.8 vw 4485.0 22290.5 4459.8 22397 22416 vvw 3 4463-6 * overlapped by emission line: I (m-q 3 "R) 3 3 3 $1 3 g} $1 9 3 3 3 3 * * 3 vvw 9 3 3- 6144.7 16269.6 vs 5629-9 17757'3 vs weak, vvw-very very weak.assignment 1 (air) Y (vac.) int. (A) (an-') (0, 390)- 8129'8 12297'0 w (0, 0, 0) 8123'2 12307.1 (0, 1, 0) 7879.5 12687.6 (0, 0, 0) 7386'2 13535'0 (0, 1, 0) 7194'6 13895.5 (0, 0, 0) 67803 14744'1 (0, 0, 0) 6273'3 15936'3 (0, 0, 1) 5842'4 171 11 -5 (0, 0, 0) 5738'3 17421-8 (1, 790)- 5475.9 18256.8 s (0, 0, 0) 5471.9 18270'0 (0, 9, 1)- 5454.6 18328.1 w (0, 0, 0) 5451'4 18338.9 (0, 1, 0) 5385.0 18564-8 (0, 0, 0) 5149'9 19412-6 (0, 0, 0) 5130.1 19487-5 (0, 0, 0) 5076.5 19693.1 (0, 15, 0)- 4870.8 205246 m (0, 1, 0) 4867-2 20540.0 (0, 0, 0) 4848.4 20619.8 (0, 0, 0) 4806-6 20799 (0, 0, 0) 4616-5 21655-4 (0, 1, 0) 4598.7 21739.1 vvw (0, 5,O)- - (0, 5, 0)- 7391.8 13524.7 m (0, 7, 0)- 7199'7 13885'7 vw (0, 7, 0)- 6785-5 14733'2 m (0, 9, 0)- 6277.9 15924.5 s (0, 11, 1)- 5846.7 17098.9 vs (0, 11, 0)- 5742'5 37409.3 vw (0, 13, 0)- 5389.0 18551'2 vw (0, 13, 0)- 5153'6 19398'6 m (1, 9, 0)- 5133'1 19476.1 w (0, 11, 1)- 5080.6 19677.2 vw (0, 15, 0)- 4851.2 20607.9 w (1, 11, 0)- 4809.4 20787 vvw (0, 13, 1)- 4620.8 21635.0 vw (0, 17,O)- 46020 21723.6 vw (0, 17,O)- (0, 0, 0) (1, 13,O)- (0, 030) (0, 15, 1)- ( O , O , O ) rs-very strong, s-strong, m-medium, w-we assignment :ak, vw-very5406.1 A I 5656.9 a I 5432-5 a 1 T Ql-2 T Rl-* 5673.1 A I b i Ql-2 1 RI-2 I QI-0 I 4 - 0 FIG.1.-Diffuse bands of HCO and DCO photographed using the second order of a 21-ft. concave grating spectrograph; (a) (0, 12, 0)-(0, 0, 0) band of HCO, (b) (0, 14, O)-(O, 0, 0) band of DCO. The reference spectrum is provided by an iron hollow cathode lamp. [To face page 93.J . W. C . JOHNS, S. H. PRIDDLE AND D. A . RAMSAY 93 Improved observations have been made on the diffuse bands. Reproductions of the (0, 12, O)--(O, 0, 0) band of HCO and of the (0, 14, 0)-(0, 0,O) band of DCO are given in fig, 1. Each diffuse band shows four distinct features which may be identified with the intensity maxima of the R- and @branches of the K’ = I t K” = 0 and K‘ = 1i-K‘’ = 2 sub-bands.Microphotometer curves of these bands are given in fig. 2 and 3a. Two further weak maxima were found at the long wave- length end of the DCO “ &band ’’ and were assigned to the intensity maxima of. QI-0 t50 +25 1/, -25 -50 -75 -100 -125 -I50 -175 FIG. 2.-Observed and calculated rotational envelopes for the (0, 12,O)-(O, O, 0) II-band of HCO. The top curve is an original microphotometer curve of the band shown in fig. la. The lower curves are calculated rotational envelopes for this band, assuming a triangular line width function and half-intensity line widths of (a) 10 cm-1, (b) 20 cm-1 and (c) 30 cm-1. the K’ = 3cK” = 2 and K’ = 3 c K ” = 4 sub-bands of the corresponding “ SD- band”. The former intensity maximum can be seen in fig.3a. A microphoto- meter curve of the (0, 15, 0)-(0, 0, 0) band of DCO is given in fig. 3c. In addition to the sharp rotational structure of the “ C-band ”, the intensity maxima of the K’ = 2 t K ” = 1 and K’ = 2 c K ” = 3 sub-bands of the “ A-band ” are clearly visible. Measurements on the intensity maxima of the various diffuse bands of HCO and DCO and their assignments are given in table 2. In addition to the sharp bands and the diffuse bands described above, the experiments gave definite evidence for an absorption continuum in the region from approximately 5000 to 7000A. The intensity of absorption of this continuum was approximately 50 in the strongest region. . .. ..94 ABSORPTION SPECTRA OF HCO AND DCO ANALYSIS SHARP BANDS Rotational constants and vibrational quanta for the upper state X levels of HCO and DCO were obtained by the method of combination differences, viz., R*(J- 1) - R(J- 1) = Q*(J) - Q(J) = P*(J+ 1) - P(J+ 1) = G*(v) - G(v) + (B* - B)J(J+ 1) - (D* - D)J2(J+ 1)2.(1) Quantities marked with an asterisk refer to a new band while the other quantities refer to a previously analyzed band. The left-hand side of eqn. (1) was plotted I I I I 1 17700 Vb50 V600 17550 17500 I 1 1 18250 18200 18150 l8lOO FIG. 3.4bserved and calculated rotational envelopes for some diffuse bands of DCO: (a) original microphotometer curve of the (0,14,0)-(0,0,0) band, showing the 11-band and part of the @-band; (b) calculated rotational envelope for the JI-band, assuming a triangular line width function and a half-intensity line width of 16 cm-1; (c) original microphotometer curve of the (0, 15,0)--(0,0,0) band showing the sharp X-band and the diffuse A-band. against J(J+1) for each new band and the various sets of points were found to lie on straight lines.The values for (D* - 0) may thus be neglected and values for AG and AB were determined from the intercepts and slopes of the straight lines.J . W. C. JOHNS, S . H. PRIDDLE A N D D . A. RAMSAY 95 TABLE 2.-INTENSITY MAXIMA FOR THE DIFFUSE BANDS OF HCO AND DCO HCO DCO assignment ir (air) Y (vac.) (A> ( a - 1 ) A (air) v (vac.) assignment (A) (cm-1) 6482.2 15422.6 Ql-2 (0, 8, 0)- 63222 15813 Q2-1 (0, 11, 0)- 6181.1 16174 ( 0 7 9, 0)- 6043.7 16505 6057.2* 16542 16948 6168.1 16208 5906.4 5874.1 5863.2 17051 5645 17709 (0, 11, 0)- 5755 5638 17732 56941- 5432-5 18402.4 5673.1 17622.1 Q1-21 54244 18430.1 (0, 12, 0)- 5665.0 17647.5 R1 2 (0, 14, 0)- 5406.1 18492.3 Ql-0 (0, 0, 0) 5656.9 17672-6 Qi-o 1 (0, b, 0) 5398-3* 18519.2 Rl-0 5648-1 17700.1 R1-o J 5213.7 19175 Q2-1 (0, 13, 0)- 5525 18094 (0, 0, 0) 5491 18207 5395 18530 5353 18677 5325.0 18774.1 531 7.4 5312.5 6449.7 15500.2 Qi-o } (0, 0, 0) ( 0 7 0, 0) 53043* 18847.4 R1-o * shoulder.These numbers are less certain. Since the present method of determination yields more accurate values for AB and AD than the method used by Herzberg and Ramsay, the earlier measurements were re-evaluated by the present procedure. Bands of the principal progression (0, u;, O)--(O, 0, 0) were referred to the (0, 9, 0)-(0, 0, 0) band of HCO or to the (0,13,0)-(0, 0, 0) band of DCO as standards and the effective band origins, voefi., and B’ values are listed in table 3.Other bands were referred to appropriate standards as indicated in table 4 in which the values for AG and AB are also given. TABLE 3 .-EFFECTIVE BAND ORIGINS AND UPPER-STATE ROTATIONAL CONSTANTS FOR THE HCO AND DCO BANDS HCO DCO band voeff* ( a - 9 B’ (cm-1) yoeff. ( c m 3 B’ (cm-1) 11661.06f0.05 13222.37 f0.04 14758.02 f0-04 16269.59 17757031 f0.03 19221.77 &Om05 20662.80 f0-06 22080.30 f0.06 1.3436 f0-0005 1-3476 f0.0003 1.3517 f0.0003 1-3565 1.3619 310-0003 1-3673 f0.0006 1.3729 f0*0006 1-3782 f0.0010 12297.17 f0.05 13524.77 f0.06 14733.27 f0.05 15924.62 50.05 17098.87 18256.86 f0.05 19398.75 f0.05 20524.73 50.06 21635.12fO-10 1.1 11 1 f0.0005 1*115Ort0~0005 1.1212 f0.0005 1 * 1270 f O.OOO5 1.1348 1.1408 f0-0005 1.1481 f0.0005 1 * 1 572 k O.OOO8 1.1657 f0.0010 All errors refer to errors obtained from combination difference plots, using the (0, 9, O)-(O, 0, 0) band as the standard band for HCO and the (0, 13, O)--(O, 0, 0) band as the standard band for DCO.The values quoted for the standard bands are taken from Herzberg and Ramsay (1955).bimds TABLE (1.-vIBRATIONAL MTERVALS HCO AG (cm-1) u (cm-1) 3174.55 f0.06 3 133.39 f0-05 3091.93 h0.08 3050.15 f0.08 1756.00 50.05 1745.57 f0.10 1083.00 f0.08 a; = Om74 &O*OOO6 a; = 0.0068 f0-0004 a; = 0.0064 &040008 a; = 0-0059 f0.0008 a; = 0.01 15 f010005 a; = 0,0123 &0*0010 afRW = 04033 f0.0006 C I ~ " = - O*Oo24 fO.OOO6 AND @-VALUES FOR HCO AND DCO DCO bands AG (cm-1) a (cm-1) (1, 11, 0)-(0, 0, 0) 2403.62jz0.05 a; = 0.0061 f0-0005 (1, 13, 0)-(0, 0, 0) 2377-33f0.05 a; = 0.0062f0*0005 (0, 11, w-0, 0, 0) 1 (0, 1 3 , 0 ) ~ 0 , 0 , 0 ) 1 (0, 15, w-0, 0,O) 1 (1, 15,O)-(O, O, 0) 2351*16f0.08 ai = 0*0042f0*0008 (1, 17,0)-(0, 0, 0) 2325.03 f0.05 ai = 0.0050 50-0005 (0, 17,0)40, OYO)J.W. C. JOHNS, S. H . PRIDDLE AND D. A. RAMSAY 97 The rotational constants were fitted to the equation : using the method of least squares 9 to determine the coefficients of (uj+ 1). The values for the constants are given in table 5. To obtain the value of Bi for DCO it was assumed that the value for a; is the same as for HCO. This assumption is TABLE 5.-MOLECULAR CONSTANTS FOR HCO AND DCO state constant HCO DCO units xzo3 Too0 Y52 Y222 cm-1 cm-1 cm-1 cm-1 cm-1 cm-1 A A cm-1 cm-1 cm-1 cm-1 cm-1 cm-1 cm-1 cm-1 cm-1 assuming the same value for a3 as for HCO; b assumed value; C from Teller-RedIich product rule.questionable, since for HCN and DCN the corresponding a-values differ by -35 % (Douglas and Sharmalo). From the rotational constants Bz for HCO and DCO, the equilibrium bond lengths r:(CH) and rk(C0) were calculated. The following values were obtained : r:(CH) = 1.044&0*03 A, r:(CO) = 1.1866 +0*008 A. The rather low value for r:(C€€) is probably due mainly to inaccuracies in the deter- mination of Bi for DCO caused by the moderately long extrapolation of the &, "i.0 values and the assumption of the value for a;. A closer estimate of the CO bond length can probably be obtained by using the HCO data alone, assuming an ap- propriate value for r;(C€€).Since the excited state of HCO is very similar to the ground state of HCN both in vibration frequencies and electronic structure,4 we shall assume that r;(CH) = 1.065+_0-01 A (cf. Douglas and Sharma lo), whence r:(CO) = I -1 82 & 0.002 A. D98 ABSORPTION SPECTRA OF HCO AND DCO The effective band origins listed in table 3 and the vibrational intervals given in table 4 were fitted to the equation : It should be noted that Tieff = T& constants and for Tho are given in table 5. The values for the vibrational The effective rotational constants a;R*’ and ~$2‘‘ and the vibrational frequency for the bending vibrational level of the ground state were obtained from the combination relations : R(J) - R’(J) = P(J) - P*(J) = v2 ” -aZpR’’ J ( J + l ) , (4) ( 5 ) Q(J) - Q*(J) = V; - a y J ( J + 1), where quantities marked with an asterisk refer to a “ hot ” band originating in the level u;‘ = 1 and the corresponding unmarked quantities refer to a band originating in the ground state.The left-hand-sides of these equations were plotted against J(J+ 1) and values for a:R.‘, ctf” and vg were readily deduced (see table 4). A very weak band was found underlying the P-branch of the (0, 11, o)-(o, 0, 0) band of HCO and might be due to HC13O in natural abundance; but a calculation of the expected isotope shift gives a value of 75 5 cm-1 whereas the observed shift is -63 cm-1. A more reasonable assignment for this band is that it is a ‘‘ hot ” band (0, 11, 1)-(0, 0, l), originating in the ui’ = 1 level of the ground state.From the difference between the frequencies of the bands (0,ll , l)---(O, 0, 0) and (0, 11 , 1)- (0, 0, 1) we find v;I = 1820-2 cm-1. This value is smaller than the value (1860 cm-1) quoted by Ewing, Thompson and Pimentel 11 on the basis of matrix studies in the infra-red. DIFFUSE BANDS The band origins for the diffuse bands were determined by fitting calculated rotational envelopes to the observed band contours. Since the rotational selection rules are AK = f 1, AJ = 0, & 1, the “ II-bands ” consist of two sub-bands, viz., K‘ = l+K” = 0 and K‘ = 1 t K ” = 2, each sub-band consisting of a P, Q and R-branch. The sub-band origins are separated by 4(A” -I?’), i.e., by N 84 cm-1 for HCO and -50 cm-1 for DCO.The calculated rotational structures for the (0, 12, O)--(O, 0, 0) band of HCO and the (0, 14, O)--(O, 0, 0) band of DCO are shown in fig. 2 and 3b respectively. The following approximations were made: (a) the B values for the II-levels were obtained by interpolating between those for the C.-levels, (b) the K-splittings of the IT-levels were neglected, (c) the Honl-London formulae (Herzberg 12) were used for the line intensities, and (d) the rotational temperature was taken as 50°C, the temperature of the absorption tube during the experiment. The ground-state energy levels were calculated by substituting the A” , B” and C” values given by Herzberg and Ramsay into the expressions derived by P0l0.13 The band envelopes were calculated by assuming a triangular line shape function and various values for the half-intensity line width, Avt.Three curves are shown in fig. 2 for different values of Ava, viz., 10,20 and 30 cm-1. The agreement between the experimental band envelope and the theoretical contour calculated with Av) = 20 cm-f leaves no doubt as to the correct assignment of this band. Furthermore,J . W. C . JOHNS, S. H. PRIDDLE AND D. A. RAMSAY 99 since the shape of the calculated envelope varies appreciably as Avt changes, we may obtain a fairly reliable estimate for the half intensity line width, viz., Avt = 20 + 3 cm-1. In a similar way the calculated rotational envelope for the (0, 14, 0)- (0, 0, 0) band of DCO fits well with the experimental curve if we assume that Avt = 16+ 3 cm-1 (see fig.3a and 3b). The band origins for the various II-bands of HCO and DCO were determined by finding the best fit of the calculated envelopes to the experimental curves. The values are given in the second column of table 6. TABLE 6.-sUB-BAND ORIGINS AND G-VALUES FOR HCO AND DCO sub-band origin (cm-1) 15537.7 15511 f 5 16269.6 16181 f8 17037.4 17023 f 3 17757.3 17716 f5 18513.5 18498 f 3 19221.8 19182 f8 15924.5 (C) 15820f8 (A) 16526.2 (L‘ C ”) 16514f5 (n) 17098.9 (C) 1705815 (A) 17692.3 (“ E ”) 17682f2 (n) 17692.3 (“ I: ”) 17579f10 (@) 18256.8 (C) 18216f5 (A) 18842.2 (“ C ”) 1883064 (n) 18842.2 (“ C ”) 18737i-10 (a) G(o bs.) G(calc.) (cm-1) (cm-1) 26.1 1 2 12.2 f5 10.2 f l - 2 10s3 k 2 1 2-6 i- 1.1 10.2 f 1.2 12.2 f 4 11.7 f 1.1 17-2 15.7 14.4 13-2 13.2 12.2 11.3 11.3 The origins of the hypothetical “ C ” sub-bands are given relative to the J = 0, K = 0 level of the ground state.The origins of the other Z sub-bands are taken from table 3 and have not been corrected by the term (A”--S”). The A-bands likewise consist of two sub-bands, viz., K’ = 2-K” = 1 and K’ = 2 t K ” = 3 separated by - 167 cm-1 for HCO and -99 cm-1 for DCO. Both sub-bands have been observed for DCO but only the stronger sub-band, viz., K’ = 2 c K ” = 1 has been identified for HCO. The rotational contours were calculated in the same way as for the II-bands and rotational line widths of -20 cm-1 were assumed. The experimental band contours are less well-defined than those for the n-bands, especially as the K‘ = 2 t K ‘ = 1 sub-bands are overlapped by100 ABSORPTION SPECTRA OF HCO A N D DCO parts of the Z-bands (see fig.3c). Nevertheless, the observed and calculated con- tours could be fitted with an accuracy of - 10 cm-1 and values for the origins of the A-bands obtained (see table 6). No HCO bands with K‘>2 could be positively identified but assignments for two @-bands of DCO are given in table 2. DISCUSSION VIBRATIONAL NUMBERING All three upper state frequencies for HCO are now known, together with the ground-state frequencies v y and v;. The only unknown frequency is thus the ground- state C-H stretching frequency vi‘. For DCO, only two upper-state frequencies, v; and vi. are known but the third frequency may be calculated using the Teller-Redlich product rule,l4 viz., Since this equation is valid for zero-order frequencies, and the anharmonic corrections for the v1 vibrations are large, the experimental values for v;(CH) and v; (CD) were corrected using the anharmonic constants determined for the HCN and DCN molecules (Douglas and Sharma 10).From the above equation we then obtain v;(DCO) = 1713 cm-1. For the ground state of DCO, only the bending frequency v;‘ is known. The Teller-Redlich product rule gives the relation If we assume that (u;’(DCO) -o;’(HCO), then a value for mi’( DCO) may be calculated from eqn. (7) if we assume a value for o;’(HCO). Provided that the difference coj’(HC0) -(uy(DCO) is small (<lo0 cm-I), the sum +[m;‘(DCO) +co;’(DCO)] is approximately constant (t 10 cm-1) and is dependent only on the value assumed for coi’(HC0) in eqn.(7). Thus, in calculating the zero-point energies for HCO and DCO in their ground and excited states, there is in effect only one unknown frequency, viz., coi’(HC0). We can now discuss the vibrational numbering for the principal progressions (0, u;, O)--(O, 0, 0) of HCO and DCO. If each progression is extrapolated to its zero band, then the difference in the frequencies of the two (000)-(000) bands must be consistent with the difference in the zero-point energies for the two molecules. It is necessary to consider only two alternatives, viz., Tioo = 8489 cm-1 for HCO and 8523 cm-1 for DCO as given by Herzberg and Ramsay, or Tioo = 9294 cm-1 for HCO and 9161 cm-1 for DCO as preferred in the present paper. According to the former assignment T~oo(HCO)-T&o(DCO) = -34 cm-1 while for the latter assignment T600(HCO) - Tim(DCO) = + 133 cm-1.Since all the relevant fre- quencies are known or are related to w;’(CH), we can use the two possible assignments to calculate the corresponding values for (ui’(C€€). On the basis of the Herzberg and Ramsay assignment we find co;’(CH)-4000 cm-1 which is clearly too large. For the revised assignment we find co;’(CH) -2700 cm-1 which is quite acceptable. To estimate the error in this determination we need to consider the various errors involved in the extrapolation of the principal progressions and in the neglect of the contributions from some of the anharmonic terms, which together are probably -10 cm-1. We then find that (u;’(CH),= 2700+100 cm-1. A value for 7’; may now be calculated to be 8690+ 50 cxn-1.J . W.C . JOHNS, S. H. PRIDDLE AND D . A. RAMSAY 101 The vibrational numbering thus shows that the upper state is derived from a n and not a X- or A-electronic state. Further confirmation of this conclusion is afforded by the vibronic structure discussed in the following section. : I I I I I I I VIBRONIC STRUCTURE A schematic diagram of part of the DCO spectrum is given in fig. 4. Two points are worthy of note. First, the II-bands are staggered to lower frequencies with respect to the E-bands. Second, in a group of levels with the same value of u;, L I I I I I I I I I the levels with higher K are found at lower frequencies and the separations between the levels are roughly quadratic in K, i.e., Thus the Z-A and II-4 splittings are equal to 4G and 8G respectively, while the staggering of the Il-bands with respect to the X-bands is equal to G.The experi- mental values of G for HCO and DCO are given in column 4 of table 6 . V: = V O - GK2. (8) FIG. 5.-Potential curves for the upper and lower states of HCO and DCO. r represents the normal co-ordinate for the bending vibration. We now calculate the vibronic structure expected if the observed splittings are due to electronic-vibrational interaction, is., to the Renner effect. We assume that the potential curves are of the form shown in fig. 5, and use the theory developed102 ABSORPTION SPECTRA OF HCO AND DCO by Pople and Longuet-Higgins.6 Following these authors we denote the upper potential curve by U+ = 3r2+hr4 and the lower curve by U- = (+-f)rZ+gr4, where f>$, g>O, and r is the normal co-ordinate associated with the bending vibra- tion.According to their theory, the energy levels of the upper state for small values of K (i.e., K<u2) are given by The quantity h is determined from the anharmonicity of the upper state while f and g are determined from the height of the barrier (8690 cm-1) valency angle (119" 30') in the ground state. For HCO and DCO we find Comparing eqn. (8) and (9), f = 1.515, 9 = 0.025, h = -0.0026. Evaluating this equation we find that G(theor.) = (:20:: -- 3.8) for HCO, and G(theor.) = ( tz4:y - - 3.0) for DCO. The theoretical values for G are given in column 5 of table 6. The experimental values are, on the whole, slightly smaller than the theoretical values, and show a trend towards lower values at higher values of 0;.The variation of G (obs.) with u;, however, is by no means regular and the irregularities are probably caused by resonances with the higher vibrational levels of the ground state. Such resonances can affect all of the levels of the excited state except the I: levels. These results are very similar to those which have been found for NH2 and ND2 (Dressler and Ramsay,s Eaton, Johns and Ramsay 15). The general agreement between theory and experiment, both in magnitude and sign, leaves little doubt that the observed vibronic splittings are due to the Renner effect. To be more rigorous, it is necessary to show that the K-dependence of the energy levels is greater than that given in the equation (Pople and Longuet-Higgins), which would be obtained in the absence of a Renner effect.Indeed, the observed K-dependence is roughly ten times greater in magnitude and opposite in sign to that given by eqn. (13). Hence we may conclude that HCO furnishes another example of the Renner effect, similar to that which was first established for NH2. An interesting point which arises is that there should be no (0, 0, 0) level in the excited state (see Dressler and Ramsay) ; the first level should be the (0, 1, 0) &level. It would be very difficult, however, to verify this point in absorption studies, because of the adverse Franck-Condon factor and the low frequency of the transition (-9000 cm-1). E + ( u ~ , K) = ((v, + l)++h[3(V2 + 1)2 - K 2 ] ) ~ 2 , (13) PREDISSOCIATION The observation of the (0, 3, O)--(O, 0,O) and (0, 5,O)-(O, O, 0) E-bands at high dispersion, but not of the (0,4,0)-(0,0,0) n-band, indicates that the (0,4,0)J .W. C . JOHNS, S. H . PRIDDLE AND D. A. RAMSAY 103 II-level is diffuse. Since this level is the lowest level which has been shown to be diffuse,” the dissociation energy of the molecule must be less than the energy of the (0, 4, 0) II-level, i.e., Do(HC0) < 12400 cm-1 (< 35.4 kcal/mole, < 1-54 ev). This value, which is an upper limit, is slightly lower than the limit given by Herzberg and Ramsay, but is still higher than the current chemical values of - 13 kcal/mole or -28 kcal/mole (see discussion by Cottrell 16). A correlation diagram showing the observed states of HCO and their probable dissociation productsis given in fig.6. cm-’ I There are no states of the products-between k ca I /mole H+CO *s +311 \ 40 000 20 000 200 I 5 0 I00 5 0 0 FIG. 6.-Correlation diagram between HCO and its dissociation products H+CO. Since the value for the dissociation energy of HCO is still in doubt, both sides of the diagram have been plotted relative to the same arbitrary zero level. the ground-state combination H(2S) + CO(lX+) and the combination H(2S) + CO(3II) at 48687 cm-1 ( G 139.2 kcal/mole, = 6.03 ev). The ground-state combination gives rise to a single state with species 2X+ or 2A’, depending on whether the molecule is linear or non-linear. This state is probably repulsive and accounts for the ob- served predissociation. The two known stable states of HCO presumably “want to dissociate ” into H(2S)+CO(W), though the problem of the crossing or the non- crossing of these potential surfaces with the repulsive potential surface needs to be considered.? While a complete discussion cannot be given at this time, two important points emerge.First, all the observed upper state levels except the X-levels are strongly predissociated. The probability of predissociation does not appear to depend strongly on the K-value (contrast the predissociation in HCN, Herzberg * The (0, 3, 0)-(0, 0, 0) A-band lies just beyond the limit of the present observations. t Teller 17 has shown that for a polyatomic molecule two potential surfaces of the same symmetry may cross in a special type of “ conical intersection ”. This behaviour is in marked contrast to that found in diatomic molecules where an “ avoided crossing ” results.104 ABSORPTION SPECTRA OF HCO AND DCO and Innes 18) since the rotational line widths in both the II- and A-levels for HCO and DCO are -20 cm-1.From the uncertainty relation Av (cm-1) = 1/2zcz, we deduce that the lifetime of the molecule in the excited state is -2.7 x 10-13 sec, which corresponds to the period of -27 C-H stretching vibrations. The second point concerns the E-levels which are sharp at low J-values and are presumably not predissociated. This sharpness can be understood if the C-levels are antisym- metric with respect to the molecular plane (Z- or A”) since the state formed from H(%S)+CO(lZ+) is symmetric (Z+ or A’), and symmetric states do not predissociate antisymmetric states.A breakdown of this selection rule, however, may be caused by the coupling of rotation to the vibronic motions of the molecule. Indeed, in the E-bands there is evidence that the rotational lines are slightly diffuse at the highest J-values observed (J- 15-20). Some slight broadening or doubling might be ex- pected due to the effects of spin uncoupling, but the widths of some of the lines at high J-values appear to be too great to be explained on this basis. A final point concerns the continuum which has been observed in the same region as the main absorption bands. This continuum might be due to the overlapping of numerous of the higher sub-bands. An estimation of intensities, however, suggests that the continuum is probably too strong to be explained on this basis. An alter- native mechanism which is more plausible, is that the continuum is due to a direct transition from the ground state to the repulsive 2Z+ (or 2A’) state. We wish to acknowledge the valuable assistance of Mr. W. Goetz with some of the experimental work. 1 Ramsay, J. Chem. Physics, 1953,21,960. 2 Herzberg and Ramsay, Proc. Roy. SOC. A, 1955,233,34. 3 Walsh, J. Chem. SOC., 1953,2292. 4 Ramsay, Adv. Spectroscopy (Interscience Publishers, New York and London, vol. 1, 1959), 5 Dressler and Ramsay, Phil. Trans., A, 1959, 251, 553. 6 Pople and Longuet-Higgins, MoZ. Physics, 1958, 1, 372. 7 Adrian, Cochran and Bowers, J. Chem. Physics, 1962, 36, 1661. 8 Johns, Priddle and Ramsay, to be published. 9 Birge, Rev. Mod. Physics, 1947, 19, 298. p. 29 ff. 10 Douglas and Sharma, J. Chem. Physics, 1953, 21,448. 11 Ewing, Thompson and Pimentel, J. Chem. Physics, 1960,32,927. 12 Herzberg, Infra-red and Ramun Spectra of PoIyatomic Molecules (Van Nostrand Co., Inc. 13 Polo, Can. J. Physics, 1957, 35, 880. 14 ref. (12), p. 231 ff. 15 Eaton, Johns and Ramsay, to be published. 16 Cottrell, The Strengths of Chemical Bonds (Butterworths Scientific Publications, London, 17 Teller, J. Physic. Chem., 1937, 41, 109. 18 Herzberg and fnnes, Can. J. Physics, 1957, 35, 842. New York, 1945), p. 426. 2nd ed. 1958), p. 185.

ISSN:0366-9033    

DOI:10.1039/DF9633500090

出版商:RSC    

年代:1963

数据来源: RSC