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