Yu. F. Pedash

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.

π-Electron hyperpolarizability of even-numbered polyenes in the complete configuration interaction method

It has been established that the second hyperpolarizability of short polyenes with 2–10 carbon atoms increases in proportion to N3.95 in the complete configuration interaction method, and in proportion to N5.97 in the restricted Hartree-Fock method.

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.

End-group internal rotation barrier in cumulenes calculated taking into account the effects of electron correlation

The internal rotation barrier of the end groups in cumulenes has been calculated taking into account the effects of electron correlation. It has been found that this barrier approaches zero as the length of the conjugated chain increases.

Nature of the excited states of dialkylamino derivatives of aromatic and heteroaromatic compounds with an annelated oxazole ring

On the basis of analysis of the electron density redistribution upon excitation, drawing on charge transfer numbers, we have considered the nature of the electronic transitions in the absorption spectra of analogs of 2,5-diphenyloxazole, in which the carbon atom at position 4 of the oxazole ring is bonded to the ortho position of the 5-phenyl fragment of the vinylene, azomethine, amide, and ester groups. We have shown that the differences in the electronic transitions of the basal molecule and the studied structural analogs are determined by the electron-donor effect of the bridging group and the degree of its conjugation with the extended π-electron system of the original molecule. The dialkylamino derivatives of the studied compounds, on the other hand, display a high degree of similarity in the electronic structure of the excited states, and the characteristics of their long-wavelength transitions, such as in the case of substitution of the 2-phenyl fragment, do not depend on the nature of the bridging group of atoms. We give a theoretical explanation of the experimentally observed increase in the intensity of the long-wavelength transitions and the efficiency of luminescence upon introduction of dialkylamino groups into the 2- and 5-phenyl fragments.

Complete configuration interaction and π-shell structure in 10-center conjugated systems

An exact π-electron calculation is presented for the ground singlet and lowest triplet states in naphthalene, azulene, and linear and cyclic decapentaene.

An Optimal Way for Computation of Non-Linear Optical Properties of Crystals and Large Conjugated Molecules within Cluster Models

Cluster models are of importance in quantum-mechanical computations of Nonlinear Optical (NLO) properties of macroscopic objects such as crystals and large conjugated molecules, since they preserve important electronic structure features, topology and symmetry of the nuclear frame. In a cluster approach the NLO properties such as polarizability (α), first (β) and second (γ) hyperpolarizability tensors are computed for a series of clusters large enough for further extrapolation of the calculated values to infinite cluster dimensions. For realistic models the most appropriate and acceptable is the finite field method, when α,β,γ are derived by differentiation of either induced dipole moment d(ɛ) or total energy E(ɛ) with respect to the intensity of a trial uniform electric field (ɛ). In this study, we apply non-finite-difference formulae of numerical differentiation with interpolating Lagrangian polynomials on regular evenand odd-point grids. Estimates of absolute errors (8) are obtained for derivatives of any order, including the number of points in the grid, the e value, the values of the higher derivatives of d(ɛ) and E(ɛ) with respect to e. Errors in α,β,γ are minimized with an optimal e that can be found a priori from model systems. Our approach is more than just a technical improvement: it yields the maximum size of a cluster that can be studied with a finite-field method. In particular, the dependence of the δ interval on the spatial length and extent of delocalization of valence electrons is established. Of special notice are the cases where the finite-field method fails due to divergence. It is found for the variational methods of quantum chemistry that other things being equal, the errors are decreased by two orders of magnitude by differentiation of E(ɛ) rather than d(ɛ), even though the order of derivative is lower by one in the latter case. New analytical expressions are presented for the higher order NLO properties of conjugated molecular systems.

Comparison of the variational and bound perturbation theories in dipole polarizability calculations of molecular complexes

For a model molecular complex, analytical expressions are obtained for the coefficients A3 and A6 of dipole polarizability expansion in a reciprocal power series of intermolecular distances in terms of the variational (VPT) and bound (BPT) Hartree-Fock perturbation theories. It is shown that A3(VPT)<A3(BPT), A6(VPT)<A6(BPT) for weak electron-electron interactions and A3(BPT)<A3(VPT), A6(BPT)<A6(VPT) for strong electron-electron interactions.

Electrical properties of the π-electron shells of polyenes, radicals, and polymethynes calculated by the full configurational interaction method

The dipole polarizability and the first and second hyperpolarizabilities of the π-shells of polyenes and polymethynes have been calculated by the full configurational interaction method. An increase in nonlinear characteristics of the polymethynes in comparison with the polyenes has been established.