CHAPTER 1
Part I
PHYSICAL ASPECTS OF PHOTOCHEMISTRY
1
Spectroscopic and Theoretical Aspects
Introduction
The subjects discussed in this chapter are classified under the headings of molecular orbital calculations, spectra, theories of non-radiative transitions, and theories of chemical reactions. The first section is a very brief report on methods of calculations, and the results of such calculations applied to particular molecules, particularly when these include properties and energy levels of excited states. In the second section, attention is confined to articles discussing strictly spectroscopic aspects of the subject, and in particular absorption, fluorescence, and phosphorescence spectra where detailed assignments are discussed. Articles which contain in addition extensive measurements of luminescence quantum yields and decay times are discussed in Chapters 3 and 4. Among the theories of chemical reactions, a section on CIDNP studies is included. The section on e.s.r. studies, on the other hand, has been retained in Chapter 3.
The discussion in the whole of Part I refers almost exclusively to organic molecules. Theoretical and spectroscopic properties of inorganic molecules, including species such as H2O, OH, H3O, etc., will be found in Part II.
2 Molecular Orbital Calculations
Brief mention will first be made of methods in MO calculations. A method of rapid geometry optimization for semi-empirical MO calculations has been given, and a formula given for the rapid calculation of integrals of Gaussian functions. A derivation of extended Hartree–Fock equations and relations for supermatrices in Hartree–Fock–Roothan equations have been given, and the use of general spin orbitals in the projected Hartree–Fock method has been discussed. The applicability of the Roothan–Bagus procedure has been commented upon, the fundamentals of an orthonormal basis set MO theory have been given,' a perturbation treatment of virtual orbitals in SCF theory has been described, and a least-squares solution of the Schrödinger equation by a Monte Carlo method outlined. Application of the theory of symmetric groups for the energy of n-electron systems gives a lower bound for the eigenvalues, and an upper bound to excited-state energies of atomic species can be obtained using Hall's variational principle. Upper and lower bounds to second-order perturbation energies are also discussed for atomic species, and a variational lower bound to the overlap for excited states of the helium atom has been obtained. Ellipsoidal limits for the ground and excited states of H2+ have been calculated.
Halthen transform functions for the excited states of two-electron atoms have been presented, and SCF calculations for the excited state 3P wavefunctions of atoms have been performed. The reasons for differences in energy between singlet and triplet states in helium have been outlined. The Messmer and Rayleigh–Ritz variational methods for excited-state wavefunctions of hydrogen have been compared, and the use of the James wavefunction for the ground state of H2+ has been reported. Ab initio LCAO–MO calculations on H2, LiH, and Li2 have been shown to yield near HF energies, and similar calculations have been carried out on the He2 system. The bonding properties of some diatomic MO's and centrifugal distortion in the spin–orbit coupling of triplet states of light diatomic molecules have been described.
Properties of the [??]2π and [??]2Σ+ states of NO, including energies, have been calculated using a large Slater-like basis set, and good agreement with experimental values was found.
The ground state and the five lowest excited states of NO2, have been investigated. It was found that, of various methods of including configuration interaction, better results were obtained when configurations of each symmetry and spin species were formed from the SCF orbitals of the lowest state of that species. With a basis set of 33 Gaussian-type orbitals, up to 180 configurations were included at three values of the bond angle to obtain potential-energy curves of the six states. The calculations were then repeated at the equilibrium geometry of the ground state using 72 Gaussian-type orbitals contracted to 39 basis functions. Oscillator strengths of the allowed and forbidden transitions were obtained, and these are shown in Table 1.
The excitation energies, potential-energy surfaces, and oscillator strengths computed in the previous paper have been discussed in light of experimentally reported spectroscopic data, namely absorption, fluorescence, chemiluminescence, predissociation, photolysis, and the absence of phosphorecence. It was proposed that the main components of the visible spectrum are due to the transitions 2B1<- 2A1 and 2B2<- with the 2B2 state being responsible for the observed fluorescence emission.
Generalized valence-bond (GVB) and GVB with configuration interaction (CI) calculations on the low-lying states of methylene have been carried out. Results are indicated in Figure 1. The 1A1 state is found to lie 0.5 eV above that of the 3B1 ground state, and an additional 1B1 state is seen to lie 1.40eV above the 1A1 state. Similar calculations on ozone yielded the results shown in Table 2. The geometry and dissociation energy of He have been calculated. A theoretical study of the ground state of carbon trioxide has been carried out.
Theoretical calculations have been reported for the ground and first excited states of NH2. A contracted Gaussian basis of four s, two p, and one d functions is centred on the nitrogen atom, while for hydrogen two s and one p functions are used. Both SCF and multiconfiguration first-order wavefunctions have been computed, the latter using the iterative natural-orbit method. For the 2B1 state the SCF, CI, and experimental geometries are θ = 105.4°, r = 1.019 Å; θ = 102.7°, r = 1.055 Å; θ = 103.3 [+ or -] 0.5, r = 1.024 [+ or -] 0.005 Å. The analogous results for the 2A1 state are θ = 141.9°, r = 0.997 Å; θ = 144.7°, r = 1.010 Å; θ = 144 [+ or -] 5°, r = 0.97 — 1.00 Å. For the upper 2A1 state the barrier to linearity is 1370 cm-1 in the SCF approximation, 1030 cm-1 from the correlated wavefunctions, and 770 [+ or -] 100 cm-1 experimentally. The 2B1-2A1 splitting Te is predicted to be 12 800 cm-1 (SCF) and 14 500 cm-1 (CI), whereas the experimental value is thought to be ~ 11 000 cm-1.
The excimer states, selection rules, and oscillator strengths in co-operative optical transitions in the oxygen dimer, O4, have been calculated. An extension of an SCF open-shell theory in the CNDO approximation has improved convergence and gives more reliable geometries for excited electronic states. The method has been applied to H2CO, HCN, and CH2CO. A generalization of Dewar's half-electron method for calculating energies of open-shell electronic states has been presented, and an approximate MO method has been tested against the exact non-empirical SCF–MO result for different definitions of the gross orbital population and differing contributing terms in the total energy expression for BH3CO, H2CO, H2CCO, and HFCO.
A comparative study of the Random Phase Approximation, HF, and Single Excited CI methods of computing excitation properties of H2O, H2CO, CH2N2, and HCOOH has shown that the RPA method has no advantages, and several disadvantages, compared with SECI methods when static rather than dynamic properties are computed. This seems to be generally true for low-lying non-Rydberg molecular and atomic states. A similar study reports the calculation of vertical transition energies using minimal and extended basis sets both with and without configuration inter- action between singly excited states. The separate effects of extending the basis set and including CI were examined, and an evaluation of the overall performance at each level was made by comparing calculated results with experimental values. Minimal basis calculations with limited CI were found to describe adequately n -> π* transition energies. Although triplet π -> π* energies are reasonably described at this level, an extended basis set is necessary to obtain even a moderate approximation to singlet π -> π* energies. Results for the molecules studied are shown in Tables 3 and 4. A study of the ππ* state of formaldehyde using CI theory, and the effect of higher excited configurations on charge-density calculations in ground and excited states of acrolein, have been reported.
A theoretical calculation on the electronic excited states of biacetyl has appeared recently. The orbitals in this molecule are shown in Figure 2. In first order, the electronic properties of biacetyl follow from a consideration of the n,π one-electron LCAO MO's. In zeroth order, the n-orbitals on the different oxygen atoms are of the same energy and thus the orbitals can be represented by a symmetric linear combination (ag) and an antisymmetric linear combination (bu). By interaction with each other and with the σ,σ*-orbitals they will split. The π-orbitals are split by the conjugation across the central C-C bond.
The two possibilities are (i) large n+-n- splitting, (ii) small n+-n- splitting. The difference in energy between the first and second symmetry-allowed absorption bands is always
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The photoelectron spectrum of biacetyl shows a first IP at 9.55 eV, a second at 11.46eV, and a third at 13.0 eV. The separation between the first and second bands is 1.9 eV. For glyoxal (C2H2 O2) this separation is 1.6 eV and has been interpreted as the direct energy-difference of the two n+ and n- orbitals. For biacetyl, this interpretation has the important consequence that [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] must be small since the sum of n+-n- and π4-π 3 separations is 1.7 eV. The small value for [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] means that there is almost no π-conjugation over the central C — C bond of biacetyl. This interpretation then is in favour of a normal single-bond C — C stretching frequency. Figure 3(A) gives the electronic state scheme for biacetyl following from this assignment of the orbitals.
If n+-n- is small, the difference between the two first IP's must be due to the n+-π2 splitting. The u.v. spectrum then gives about 1.7 eV for the π4 -π3, splitting. The first band in the photoelectron spectrum would be due to both n levels, in agreement with its diffusivity, which is not found in the higher ionization bands. This difference is much more pronounced in glyoxal, but the torsional motions of the Me groups in biacetyl may partly obscure the difference. In this interpretation the central C — C bond has partial double-bond character, in agreement with the C — C stretching frequency of 1285 cm-1. The bond length of 1.46–1.48 Å, measured by electron diffraction, also indicates a degree of double-bond character.
The second ionization band in the photoelectron spectrum is found at 11.46 eV, which in this interpretation yields 1.9 eV for the n[+ or -]-π2 separation. From the u.v. spectra, one finds 2.4 eV for the difference between the n[+ or -] -> π3 and the π2 ->π3 absorptions, which at least gives better agreement than the value of 3.4 eV as found from the first interpretation. The consequences for the electronic states on the basis of this assignment of the transitions are given in Figure 3(B). The nature of the intersystem process in this molecule was also discussed.
A ring-puckering potential function for 1,3-propiolactone has been formulated, and appropriate non-bonding orbitals for describing photo-physical properties in benzaldehyde have been discussed. Semi-empirical MO calculations with CI on saturated molecules, and unparameterized LO calculations for saturated hydrocarbons have been carried out. SCF with CI calculations on the low-lying states of ethylene have been shown to lead to an improvement in estimation of vertical transition energies from the closed-shell ground state to open-shell excited states compared with the SCF treatment, which underestimates these energies by about 1 eV. Semi-empirical MO–CI calculations on excited states in unsaturated molecules have been discussed. The bond exciton model applied to alkenes leads to the results shown in Table 5 for transition wavelengths and oscillator strengths. The electronic structures of trans- and cis-isomers of halogenoethylenes revealed by the closed-shell SCF–MO method have been reported.
Ab initio calculations on the structure of allene in the ground 1A1 and excited states have been reported, and similar calculations on buta-1,3-diene show that inclusion of interactions between σ- and π-electrons in excited electronic states causes appreciable lowering of the energies of the excited states which are predominantly of π-character, but agreement with experiment is still poor. The CNDO/2 method does not correctly predict barriers to rotation and conformations in buta-1,3-diene, benzaldehyde, biphenyl, and 2,2'-difluorobiphenyl The paramagnetic properties and lower excited states of long molecules with conjugated bonds have been reported.
It has been pointed out that the Pariser–Parr–Pople (PPP) semi-empirical theory of π-electron systems, as well as the more approximate Hückel theory and the more general Hoffman and Pople treatments of all the valence electrons, have been of great use in explaining, correlating, and predicting the structure, reactivity, and other physical properties of molecules containing π-electron systems. A fundamental problem in quantum chemistry is to explain why these theories work so well. The simplest explanations of PPP theory argue that it is a semi-empirical version of HF theory where the parameters are chosen by comparison with experimental quantities, i.e. the real world. However, the fundamental point is that HF theory can lead to predictions which are extremely far from reality. If the PPP theory were simply an approximation to HF theory, it could not provide results which are significantly better than HF theory when comparison is made with experiments. Thus, the justification for the PPP theory must lie in more fundamental considerations. A derivation of the exact π-electron Hamiltonian has been shown to be generally consistent with its customarily assumed form, which thus accounts for the success of the PPP method.
The use of the HMO method for studying the electronic structure and properties of molecules in excited states has been proposed, and HMO–SCF calculations on singlet–triplet transitions in conjugated hydrocarbons and their derivatives have been carried out. Cyclo-octatetraene has been studied by the ab initio SCF–LCAO–MO method. Charge distributions in the ground states of aromatic hydrocarbons and their perfluoro-analogues, determined by ESCA, and the conformational stabilities and charge distributions in the ground states of monosubstituted benzenes, determined by ab initio MO theory, have been reported. Some problems in the π-electron model of benzene, the effect of semi-empirical parameters on the triplet energy levels and triplet-triplet absorption in benzene, SCF–MO calculations on the electronic structure and spectra of some mono-and di-substituted benzenes, electron correlation in excited states of substituted benzenes, an SCF–CI–MO study of trans-monohydroxy-azobenzene in its ground and excited states, and an interpretation of the lower IP's of benzene have been described.
