CHAPTER 1
Spectroscopic and Theoretical Aspects
BY D. PHILLIPS
1 Introduction
The format for this chapter is as in previous years, with the exception that phosphorescence–microwave resonance experiments are also discussed here. For reasons of economy of space, only scant attention is paid to the early section on energy-level calculations. As before, discussion in this chapter is confined exclusively to organic molecules.
2 Molecular Orbital Calculations
Several methods continue to be developed for the estimation of excited- state energy levels and geometries, and the oscillator strengths of transitions. Improved basis functions for ab initio calculations on large molecules have been given, and the use of unrestricted Hartree–Fock (HF) theory in considering orbital energy crossing has been commented upon. Extended HF theory applied to excited electronic states has been described. The greatest single source of error in calculations on systems containing two or more electrons is the systematic neglect of correlation between electrons having antiparallel spins. Methods by which electron correlation can be included in calculations on large molecules have been discussed, and the method has been applied to benzene and linear polyenes. The effects of electron correlations on radiative transition-matrix elements have been investigated, and calculations show that use of a modified HF operator drastically reduces the number of effective electronic configurations. Electron-correlation effects on electron-density calculations in excited electronic states of molecular species have also been described. The inclusion of electron correlation in calculations corrects for the inadequacies of the independent-particle approximation. Because of the basic importance of electron pairs in chemical binding, it is appealing to attempt to incorporate correlation effects by replacing single-electron orbitals in the independent-particle approach by electronic pair functions, termed 'geminals'. The theory of the geminal approach has been given, and applications have been mentioned.
Theoretical studies of the kind outlined in this section, in which molecular excitation energies and oscillator strengths are determined, can be of great value in assisting the interpretation of experimentally observed spectra and in predicting the photophysical and photochemical behaviour of molecules not yet studied experimentally. A recent paper has pointed out that since it is excitation energies and oscillator strengths which are of principal interest to those studying photoeffects, the conventional theoretical approach utilizing the calculation of wavefunctions and of energies of individual states is wasteful in that much of the information contained in the individual wavefunctions is of no interest. Moreover, the excitation energy in this procedure is derived as the relatively small difference between energies of two states, and large errors can be introduced. To overcome these difficulties, an energy-shift theory 7 has been developed which permits direct calculation of molecular electronic excitation spectra. The formalism for this approach has been presented, but it has not yet been applied to particular molecules.
Electrostatic force theory has been used to predict the shape of ground- and excited-state molecules, and the use of molecular symmetry in SCF calculations has been discussed. Valence-electron-only calculations of electronic structures have been outlined and basic formulae given for the one-electron perturbation calculation of molecular Rydberg excited states. A method for the characterization of excited stationary states has been described, and a theoretical study of transitions from the first excited singlet states of molecules to higher singlet states has been made. These were semi-empirical PPP calculations on benzene, naphthalene, phenanthrene, pyrene, benzanthracene, benzpyrene, triphenylene, and azulene. In all cases the most intense transition, the 1Lb ->1Kb, was found to be near to the 3La ->3Ka transition in the triplet spectrum. Since excited singlet state absorption spectroscopy has become possible recently, these results are of great interest. Table 1 shows selected data from this paper compared with experimental values.
It has been shown recently that SCF MO calculations with limited configuration interaction can yield good descriptions of the equilibrium geometries of low-lying excited states of molecular species. Molecules studied in this way include acetylene, HCN, FCN, formaldehyde, F2CO, HCF, HNO, and FNO.
The dipole moments of excited states of molecules are important indicators of chemical behaviour, and attention has been focused recently on differences in dipole moments in excited singlet and triplet states of several molecules. Three principles were outlined which permit rationalization of the magnitudes of the singlet (μS) and triplet (μT) dipole moments:
(1) The two active electrons are more separated in the triplet state than in the singlet.
(2) If the two active MOs (singly occupied and normalized) are designated u and v, where possible the more tightly bound orbital (u) will differ least in singlet and triplet states, so that differences in μ are revealed by differences in (v) rather than in (u).
(3) If the shapes of singlet and triplet states differ, a proper comparison must allow for an appropriate change in valence angles.
The principles above were applied to the radical NH and the molecules CO, formaldehyde, methylene, azulene, BeO, and CaO. With the exception of the last two molecules, the guiding principles provided an adequate explanation of results, although difficulties arise with the larger molecules. In the cases of BeO and CaO the extensive configuration interaction in these molecules prevents the use of the simple rules outlined above. A theoretical study of pK values of excited states using a pair-density matrix has been reported.
Theoretical calculations on energy levels, oscillator strengths, etc. of individual species will now be briefly outlined. The binding energies for clusters of atomic triplet hydrogen have been calculated and the exact evaluation of energies of ground states and singly excited states of some atoms has been effected. Upper and lower bounds to excited states of two-electron atoms have been given, and a theoretical approach has been derived for calculation of energies and widths of resonant auto-ionizing states in many-electron atoms. The variation method has also been used to calculate atom photo-ionization probability. Calculations have been performed on the metastable 5S02 states in atomic carbon and oxygen, and results for the lifetimes of these states are τO = 192 μs and τC = 176 ms. The former result is in good agreement with an experimental value of 185 ± 10 μs.
Singlet-triplet correction in the fine structure of two-electron ions has been discussed. Calculations of oscillator strength for the lowest Σ -> Π transition in CO and N2 using both Tamm–Dancoff and random-phase approximations gave only qualitative agreement with experiment. 27 Methylene is a molecular species of considerable photochemical importance, and the effect of singlet-d-polarization on singlet-triplet energy separations in this molecule has been described. These ab initio calculations indicate that the 1A1-3B1 energy separation is 11.0 ± 2 kcal mol-1 in excellent agreement with the value of 0.50 eV from generalized valence bond calculations, and supporting the viewpoint from kinetic data that the energy gap must be at least 8 kcal mol-1 rather than the 2 kcal mol-1 supposed earlier. A corrected f value for the 3A2-3B1 transition in methylene has been given recently as 1.4 × 10-2. The reactions of methylene have also been the subject of some theoretical work. In the earlier paper it was shown that the inclusion of d-orbital polarization effects modifies the reaction paths for singlet addition to double bonds and enhances the electrophilic nature of singlet methylene. This is because the [MATHEMATICAL EXPRESSION OMITTED] orbitals polarize the empty p-orbital perpendicular to the molecular plane away from the C–H bonds, and presumably towards the attracted double bond; furthermore, the [MATHEMATICAL EXPRESSION OMITTED] orbital allows a path-dependent shape change in the methylene lone pair and in the charge in the H–C–H region, providing optimum accommodation to electron repulsion between CH2 and the double bond. The failure of CH2 to insert into a carbon–carbon single bond can also be explained on this basis. Thus electron repulsion for all directions of approach prevents the methylene from getting near enough to insert, in contrast to insertion into C–H, where electron repulsion around the H atom is low, and also to ylide formation, where paths exist for avoiding excess repulsion. The interaction of singlet methylene with ethylene has been the subject of a further theoretical study.
Keten is frequently used as a photochemical source of singlet and triplet methylene, and ab initio calculations on the low-energy electronic states of this interesting molecule have recently been carried out. The conclusions reached in this study were that the two low-energy bands seen in the keten absorption spectrum arise from 1A1 ->3A" (3A2) and 1A1 ->1A" (1A2) excitations, although the transitions are not analogous to those observed in formaldehyde. In the 3A" and 1A" states keten has a planar molecular Cs symmetry in which the C–O bond is strongly bent in the molecular plane and the C–C and C–O bonds are lengthened. The lowest triplet state of keten (3A' in point group Cs) is characterized by a very long C–C bond, which for large C–C distances is the state of lowest energy in keten. The relaxed 3A' state cannot be formed directly by absorption from the ground state because of the large change in geometry. Either the 3A' or 3A" states of keten may dissociate to give CH2(3B1) and CO, and the 1A" may yield CH2(1B1) and CO. The results of this study may be compared with those from another recent theoretical investigation.
The equations of motion method has been applied to the excited electronic states of N2, CO, and C2H4. MO SCF calculations on isocyanates have been carried out, and ab initio calculations on the ground, 3nπ*, and 3ππ* states of thioformaldehyde have been performed. In saturated dialkyl sulphides the three lowest-lying electronic transitions of the C–S–C chromophore occur at 240, 220, and 200 nm. These bands have been assigned by means of calculations as electric-dipole-forbidden b1 ->b*2, electric-dipole-allowed b1 ->a*1, and atom-like b1 -> 3d transitions, respectively. The energies of electronic states of methane and its halogeno-derivatives have been computed using MO methods.
Simplified non-empirical calculations on the Rydberg ns and npσ series of ethylene for n = 3, 4, 5, and 6 have yielded results in agreement with experiments. The Rydberg character and effects of electron correlation in π–π* transitions of ethylene have been discussed. Open-shell multi-configuration SCF calculations on the lowest energy 1ππ* state of planar ethylene and other ππ* states have been performed. Calculations on the transition state in radical addition to ethylene have also been reported.
Methods of formulation and parametrization for the potential surfaces of ground and excited states of conjugated molecules have been laid down, and a comparison has been made of several expansions in the calculation of static electric dipole π-polarizability of conjugated molecules in ground and first excited singlet states using perturbation theory. Methods of construction of zeroth-order wavefunctions for planar conjugated systems have been described which permit calculations to be made on excited states. The vibrational structure of electronic transitions in conjugated molecules has been investigated.
Perturbation method and non-empirical calculations on the electronic spectrum of buta-1,3-diene have been carried out. (In the latter study, agreement with experiment is found only on inclusion of diffuse 3p and 3s orbitals in the CI.) Two triplet states of buta-1,3-diene have been observed at 3.2 and 4.9 eV by electron impact and these were identified with the 3Bu and 3Ag states. Theoretical states studies of singlet–triplet and triplet–triplet spectra have been extended to conjugated aromatic hydrocarbons. A correlation has been drawn between the geometry of the ground state and photochemical processes occurring in the case of polymethylhexatrienes. MO calculations on the electronic structure of trans-1-phenylprop-1-ene and its anion radical and other olefins and their radical cations have been reported.
The effects of electron correlation have again been considered with respect to the benzene molecule in ground and low-lying electronic states, and criteria for the success of the separated-pair model include free localizability of geminals. Semi-empirical π-electron theory has shown that for benzene the following ordering of the excited singlet states in terms of energy is to be preferred : 1B1u< 1E1u< 1E2g. This does not correspond with other calculations, and the new ordering is as a result of inclusion of configuration interaction and multicentre corrections in the semi-empirical theory. The results would also appear to cast doubt upon the assignment of the lowest triplet state of benzene as 3B1u, although the assignment can be taken as correct if the 3B1u state is of distorted geometry. An unexpected geometry for ground-state benzene results from calculations using the extended Hückel approximation, casting doubt on the validity of the method, and the Green's function method has also been used to estimate energy levels of the lower excited electronic states of benzene. Changes in bond length in a variety of 1,4-substituted benzenes in the excited singlet states with the F, Cl, OH, and NH2 substituent have been estimated, and this information might prove useful in analysis of absorption band contours. The work has recently been extended to 1,2- and 1,3-difluorobenzenes, and similar studies have also been reported recently.
