A. V. Luzanov

Dipole polarizability in π systems in complete configuration interaction

Electron polarizabilities α have been calculated for the π shells in certain conjugated hydrocarbons on the basis of complete configuration interaction. The calculations have been based on the wave-operator method (Teor. Éksp. Khim., 25, No. 1, 1 (1989)). In a polyene series, α increases nonadditively with the chain length, but not as sharply as MO calculations predict. Results are compared for singlet and triplet states in π systems with various types of topology.

Restricted Hartree-Fock method for open shells; Self-consistency and Koopmans' theorem

Numerical solution of the restricted Hartree-Fock (RHF) equations for radicals is achieved by iteration, where Koopmans theorem is applied to a freely varied closed shell. The procedure exhibits good convergence, characteristic of the unrestricted Hartree-Fock (UHF) method. They present a comparative discussion of the ..pi..-electron properties of long polyene-radicals and aromatic radicals, obtained by the RHF and UHF methods.

Interpretation of multiconfigurational states in the wave-operator method

We discuss methods of analyzing arbitrary wave functions, such as those for the total configuration interaction. We introduce the collectivity number as an invariant characteristic of the multiconfigurational character of the state. We determine the maximum value of the collectivity which can occur in the dissociative state. It is shown that in conjugated systems the weights of the valence structure of different ionic characters (polarities) approximately follow a binomial distribution. The ionic and covalent character indices of an atom are defined and a connection is established between these indices and the spin correlation functions, for which a sum rule is found.

Superoperator method for calculating configuration interaction, including doubly excited configurations

A superoperator algorithm that had been proposed previously [Teor. Éksp. Khim.,11, No. 1, 3 (1975)] for taking all doubly excited configurations into account has been worked out in detail for singlet states and has been realized numerically in theab initio version of STO-4G. The method does not require the construction of the configuration interaction matrix. This matrix is replaced by superoperators, which are rules for the transformation of the variational parameters, “stacked,” in a transition-type matrix. Calculations have been performed for small molecules of the second period, and also for linear chains of hydrogen atoms (for h14, 1275 configurations were taken into account), for which additivity of the correlation energy is observed in the approximation that was used.

Spin-orbit coupling of ππ*-states of aromatic molecules in zero differential overlap approximation

It has been shown that, in the standard π-scheme using a 2pz-AO basis and the principle of zero differential overlap, there are nonzero three-center contributions of one-electron spin-orbit coupling (SOC). Systematic calculations have been performed on the π-channel of SOC for condensed and heteroaromatic molecules. Prohibition rules in alternant hydrocarbons make it possible to ignore, in the firstorder approximation, SOC between states with identical alternant parity. It has been shown that SOC of π-states in systems with a chain structure is an order of magnitude smaller than in analogous condensed systems. A breakdown of alternant character in heterosubstitution usually reduces the SOC effect.

Comparison of variational and coupled perturbation theories in semiempirical calculations on molecular polarizability

One can calculate the molecular dipole polarizability when the ground state is described by self-consistent Hartree-Fock orbitals by using the two most rigorous perturbation theory schemes: self-consistent perturbation theory SCPT and variational perturbation theory VPT. A major difference between SCPT and VPT is that the Coulomb interaction is incorporated in different ways into the wave function for the perturbed state. They therefore have to consider which theory is preferable for calculating the interaction between the electron shell of a molecule and an electric field. This practical aspect is of particular significance of or the -electron and valence approximations, where the semiempirical parameters as it were inexplicitly include the electron correlation, and so far there have been no rigorous criteria on the relationship between the calculated polarizabilities in VPT and SCPT. The purpose of this study is to compare the polarizabilities in the valency approximation (CNDO/2 and CNDO/C and to compare (VPT) with (SCPT) for the extended -electron systems of polyenes.