CHAPTER 1
Part I
PHYSICAL ASPECTS OF PHOTOCHEMISTRY
1
Spectroscopic and Theoretical Aspects
BY D. PHILLIPS
1 Introduction
The format for presentation of this section is as in previous years. Attempts have been made this year to reduce the length of the volume, so although coverage of significant new work is believed to be complete, detailed discussion of individual papers is more selective.
2 MO Calculations
All papers discussed under this section are concerned with calculations of energy levels and transition energies. A criterion for Gaussian approximations of Slater-type orbitals, multi-configuration SCF theory for excited states, spin-restricted open-shell SCF theory, and complex MO's in the extended HF scheme have been presented. A one-electron model has been used with some success to predict singlet- and triplet-state energy differences in helium and carbon monoxide, results being within 15% of observed values. The method thus permits reasonable estimation of triplet levels from more easily observed singlet levels. Experimental energy levels of helium have also been compared with values calculated using a method of autocorrelation fields. Theoretical transition probabilities for electronic transitions in beryllium, first-row neutral and singly and doubly ionized atoms, and for the SiI 3s23p23P-3s5p33 D0 isoelectronic sequence in PII, ClIV, CaVII, and FeXIII have been obtained and compared with experimental values.
The use of the CNDO method in spectroscopy has been illustrated with respect to doublet states, and electronic quadrupole moments of excited states have been computed. A simple new function which can be used to represent the intermolecular pair potential energy of the noble gases has been proposed, and this can be compared with the excited state Ar + Xe (3P1) potential obtained from solvent shifts of the vacuum-u.v. spectrum of xenon in gaseous argon. Recent experiments involving microwave optical magnetic resonance induced by electrons (MOMRIE) on the d(3p)3IIu states of ortho- and para-H2 and -D2 have revealed discrepancies in measured fine-structure parameters, which are inexplicable in terms of the Born–Oppenheimer approximation. A general theory which can account for the observations has been presented.
SCF wavefunctions and energies for valence states and excited states of carbon and nitrogen have been discussed, and the momentum distribution in the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [??] Σu+ states have been presented graphically and the results discussed. An exact numerical method for reducing eigenvalues of diatomic molecules to molecular parameters has been described for triplet states, particularly for those with Λ ≥ 2, such as the [??]3Δg and [??]3Φu states of N2 Dipole moments, induced dipole moments, and quadrupole moments for the [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [??]2Σ + states of CH have been calculated from accurate ab initio wavefunctions and potential curves. The oscillator strength for the [??]1Σ+ -> [??]2Π system in CH+ has been calculated as 0.001 (excitation energy 2.50 eV) by the equations of motion method. CI calculations on NO [??]2Π and [??]2Σ+ have been carried out but, at least for the [??]2Σ+ state, serious discrepancies were found between the theoretical and experimental values for the dipole moment and quadrupole coupling constant. Spectroscopic constants for the eight lowest electronic states of the NO+ ion have been tabulated. Several calculations on the iodine molecule potential curves, including analysis of the long-range RKR potential of the B3ΠOu+ state have been carried out. Unexpected effects concerning perturbations of the latter state have been discussed.
A number of papers presented during the past year have been concerned with calculations on triatomic species, and several of these have dealt with ozone. Thus ab initio SCF–CI calculations have shown that the ππ* singlet state of ozone has an unsymmetrical equilibrium geometry, with one long and one short O — O bond, and similar behaviour was proposed for the SO2 molecule. Theoretical evidence for strongly bent excited states of ozone has also been given by the same group. A comparison of INDO and ab initio methods for the corrected wavefunctions of ground and excited states of ozone has been carried out, and theoretical evidence for bound excited states of ozone has been presented. This indicates that the 3B2, 3A2, 1A2 and B1 states have binding energies of 0.4, 0.3, 0.1, and 0.0 eV, respectively, with respect to ground-state O2 and O. These results could be of importance if experiment verifies the existence of bound upper states, since ozone is of great importance in the upper atmosphere. Non-empirical SCF calculations have also been carried out on the open and closed forms of ozone.
Walsh's rules relating to the bond angles in BH2, CH2, NH2, and H2O have been shown to have significant quantitative validity. MINDO/3 calculations on the electronic states of methylene have been performed, and results in agreement with the most recent ab initio calculations obtained, namely that the excited singlet–triplet separation is small, being 8.7, 9.2, and experimentally 8 — 9 kcal mol-1.
Extensive CI calculations on CO2 have provided an accurate description of the excited states which have been in some cases mis-assigned by experimentalists. Thus the states with vertical excitation energies of 7.35, 8.38, 11.07, and 11.53 eV have been assigned to the ground state to 3Σu+, 1Δu, 1Σ+, and 1Πu states, respectively. Ab initio calculations on CO2, principally concerned with the ground-state vibrational frequencies, have also been carried out. MC SCF calculations on H2O have shown that the 3B1 state is unbound with respect to dissociation to H(2S) + OH(2Π) and O(3P) and H2(1Σg+), and thus the assignment of the absorption band at 4.5 eV to the transition to the 3B1 state is probably in error. Franck–Condon calculations and transition moments for the 3B1 -1A1 transition in SO2 have been presented.
Calculations on hydrocarbons have been concerned principally with π-electron systems, although ab initio calculations of some low-lying electronic states of methane, localized orbital methods in other saturated hydrocarbons, and other semi-empirical SCF calculations on hydrocarbons have been the subjects of reports in the past year. For π-electron systems Huckel theory is often employed, and it has been shown that the use of the theory to define resonance energy in Dewar's terms is justified. A correlation of HMO energies with π-ionization potentials has been found and an SCF determination of ion and neutral-molecule wave-functions in a theory of electron affinities and ionization potentials reported. Ground-state properties of acetylene, ethylene, and benzene have been calculated by two methods, a description of the σ and π-orbitals of ethylene has been given, and DC SCF calculations on the barrier to rotation of the ground state of this molecule have been reported. Pyramidal distortions which may stabilize the triplet ππ* state of ethylene have been investigated using ab initio MO calculations; these are illustrated below.
In structure (1) (C2v symmetry) the methylene groups are flapped in the same direction, resulting in the non-bonding electrons being cis with respect to each other. In (2) (C2h symmetry) the methylene groups are flapped in opposite directions, resulting in a trans orientation of the non-bonding electrons. In (3) (C2 symmetry) the methylene groups are twisted 90° and then flapped. The flap angle is defined as the angle between the carbon–carbon axis and the HCH angle bisector, and is assumed in the calculations to be equal at both carbon atoms for any given conformation. Using a minimal basis set, the stabilization energies are 5.1 kcal mol-1 for a cis-flapped configuration, 3.6 kcal mol-1 for a trans-flapped configuration, and 0.8 kcal mol-1 for the twisted flapped conformation. The stabilization energies became much smaller (1.3, 0.7, and 0.0 kcal mol-1, respectively) when a double zeta basis set is used. CNDO calculations of transition energies of allene give values in reasonable agreement with experiment. Extensive SCF–CI calculations on low-lying π-electron states of trans-butadiene have been carried out, giving good agreement with electron impact data for the triplet states and at 3Bu and 3Ag at 3.45 and 5.04 eV, respectively, but agreement is not as good for corresponding singlet states. The linear relationship between the energies of the S0-S1 and S0-T1 absorption transitions of conjugated polyenes predicted by Hückel theory, the application of RPA theory to excited states of linear polyenes, the computed energies, oscillator strengths, and polarization directions for the low-energy transitions in eight 6π-electron molecules of C3 symmetry, and the improvement in calculated triplet-excitation energies by using screened potentials in π-electron systems such as linear polyenes and benzenoid and non-benzenoid hydrocarbons have all been the subjects of recent reports.
Extensive semi-empirical calculations on the potential energy surfaces of trans-stilbene as a function of two internal co-ordinates, namely the rotation angle about the central double bond and the twisting angle about the exocyclic single bonds, have been reported. The results are of great interest since the exact mechanism of the observed direct trans-cis isomerization process is the subject of some debate, both singlet and triplet states being held responsible by different groups. The calculations show that the barrier to rotation about the central bond in the first excited singlet state is 35 kcal mol-1, which is much greater than the observed activation energy (2 — 3 kcal mol-1). The calculations thus favour the triplet mechanism. Electronic overlap population as a measure of reactivity in electrocyclic reactions has been discussed with reference to stilbene and its analogues, and good correlation with experiment found. A semi-empirical calculation of resonance energies in some alternant hydrocarbons has been reported.
Ab initio valence-bond calculations on ground-state benzene have shown that the Kekulé structures alone can account for chemical stability and reactivity, a result which may modify existing concepts of resonance. Ab initio extensive CI calculations have also been carried out on benzene, and results showed that in the and 1B2u (S1) and 1B1u (S2 states the π*-orbital was valence-like whereas in the 1E1u (S3) state the π*-orbital was diffuse. All three of the corresponding triplet states were valence-like. The lowest 1E2g and 3E2g states were also valence-like and had computed energies of 8.62 eV and 7.28 eV, respectively. No other low-lying valence states (such as S5 or T5) of E2g symmetry were found, in contrast with results of semi-empirical calculations, and thus assignments of observed spectral bands to transitions involving such states must be questioned. Assignments of the electronic transitions of benzene based on calculations of the equations of motion type have been made, and an interpretation offered of the ionization transitions of benzene in the 9.2 — 13 eV range. SCF–CI calculations on the triplet-state energies of benzene, naphthalene, anthracene, pyrene, chrysene, and coronene have yielded results in agreement with experiment, but assignments differ from those given earlier by other workers.
A theoretical study of electrophilic substitution in ground-state fluorobenzene has shown the fluorine substituent to be para-directing, in accord with experiment. Extended HMO calculations have also been performed on some homo-substituted fluorobenzenes. π-Electron calculations on disubstituted benzenes using the MIM and PP methods can be compared with CNDO–CI studies on the ground and excited states of fluorobenzenes and p-difluorobenzene. Other SCF calculations have been carried out on the di- and tri-homosubstituted benzenes using F, Cl, OH, NH2, and CH3 as substituents, and computed singlet-excitation energies and transition oscillator strengths were tabulated. Much work has been done in the past on the correlation of substituent constants, usually in the form of Hammett σ values with u.v. absorption frequencies and to some extent with intensities, but a recent article has shown that the simple relationships claimed are for the most part spurious. Good correlations are found, however, where the substituent is not part of the chromophoric group and also for the excitations of some monosubstituted benzenes.
Excited-state polarizabilities for some condensed aromatic molecules including anthracene, tetracene, pyrene, chrysene, and 1,2:5,6-dibenzanthracene have been calculated, good agreement with experiment being found. The normal co-ordinates and vibrational frequencies in the S1 (1B2u), S2(1B1u), and T1 (3B1u) states of naphthalene have been evaluated and vibronic intensity distributions in the absorption spectra obtained. Configuration analysis of naphthalenes, α- and β-naphthols, and α- and β-naphthylamines has shown that the two strong absorption bands of α-substituted naphthalenes which appear in the place of the Bb band of naphthalene result from a mixing of the B3u+ (Bb) and Ag- states. The influence of different choices of atomic and molecular wavefunctions on calculated triplet Davydov splitting in aromatic crystals has been studied, and a comparison of photoselection studies on anthracene and its derivatives and PPP–SCF calculations made. A simple expression has been presented for the calculation of aromatic stabilization of annulenes, based on HMO calculations.
There have been several calculations on molecules containing hetero-atoms. Ab initio SCF calculations on 1,1-dihydrodiazine, H2N=N, show that the molecule has a triplet ground state (3A2), which might have interesting chemical consequences in that cheletropic cleavage would give rise to a biradical species. Similar calculations have been carried out on the aminotrenes H2NN, CH3HNN, FHNN, and HCOHNN in the lowest singlet and triplet states, and again it was found that the optimum geometry triplet is slightly more stable than the optimum geometry singlet in all cases. Clearly the involvement of the triplet state in chemical reactions must be considered in the light of these findings. The lower electronic states of nitrate, nitrate ion, nitromethane, nitramide, nitric acid, and nitrate esters have been discussed. Molecular energy levels of the azines have also been calculated on an ab initio basis. Ab initio calculations on the azabenzenes pyridine, pyridazine, pyrimidine, pyrazine, sym-triazine, and sym-tetrazine that have been reported were motivated principally in order to understand the photoelectron spectra. There have been several reports concerned with the triplet energies, oscillator strengths for the S0 -T1 transition, ionization potentials, and dipole moments of pyridine,* pyrazine, pyrimidine, pyridazine, 3-cyanopyridine, and 4-cyanopyridine, quinoline, isoquinoline, and a series of diazanaphthalenes, and other azanaphthalenes. The work reported in ref. 91 is of interest since it was motivated by a direct challenge from a laboratory of experimentalists (Professor M. Kasha) for theoretical results to be published in advance of the experimental data, thus providing a real test of the validity of the calculations. It will be of interest to compare results quoted in ref. 91 with experimental data when they become available. Minimal basis set SCF calculations on the ground and excited states of carbazole (and the ground state of trinitrofluorenone) have been reported. Carbazole is the largest molecule for which excited-state wavefunctions have been reported to date.
