Localized impurity states in the Hartree-Fock,LCAO approximation. I.

One-electron energies and wave functions for deep trap impurity electrons in a crystal are calculated by the Hartree-Fock, single determinant method. The interactions arising from a many-electron single determinant crystal wave function, with automatic inclusion of exchange effects, are those which determine the one-electron functions and energies. The crystal plus impurity system has no translational symmetry and hence the Bloch theorem is not applicable for the solution of the essentially infinite Hartree-Fock eigenvalue matrix. Thus we develop a technique in which the Hamiltonian and overlap matrices are written in terms of bordered matrices, with the interaction of the impurity functions with the rest of the crystal environment contained in the bordering rows and columns. The resulting secular equation explicitly includes the effects of orthogonalization of the entire basis set, including the impurity functions. This technique could be used in an iterative calculation of the electronic structure of a small number of electrons, assuming that the rest of the electrons in the environment are fixed according to an initial estimate.     

Localized states in a simple cubic crystal via the next-nearest neighbor approximation

The energy spectrum of localized states in a simple cubic crystal is analysed, using the next-nearest neighbor approximation. The main distinguishing feature between the nearest and next-nearest neighbor approximation is the energy distribution of the localized states. Contrary to the tight-binding approximation, a non-symmetric distribution is found for clean surfaces, and split energy bands are found for surfaces completely covered by adsorbed atoms.     

Computer program for calculating electronic excited states in the valence approximation of the unrestricted Hartree-Fock method

State University, Khar'kov. Translated from Zhurnal Strukturnoi Khimii, Vol. 31, No. 1, pp. 160–161, January–February, 1990.     

The electronic structures of biradicals in the unrestricted Hartree-Fock approximation

The electronic structures of biradicals are investigated by the unrestricted Hartree-Fock (UHF) method and explained in terms of spin density wave (SDW) orbitals. The biradical characters are calculated by the use of the occupation numbers of the natural orbitals in the SDW configuration. The results are wholly compatible with those of other methods of calculation.     

Spectral density analysis of nuclear spin—spin coupling: II. Hartree-Fock LCAO studies for homonuclear coupling constants

A spectral density function has been calculated for the indirect nuclear spin—spin coupling constant for homonuclear coupling. The ground state wavefunction is obtained with a normal ab-initio calculation. The sum over states approach for calculating the reduced coupling constant K is replaced by an integration over a spectral density function where the integration variable is the orbital exponent of a “scanning molecular orbital”. This results in a stable method for calculating K with reasonable accuracy. The spectral density function also gives information about which excited states give important contributions to K.Furthermore a residual spectral density function is defined that can be used as a test for the completeness of a set of virtual orbitals in a sum over states calculation.     

Half-projected and projected Hartree-Fock calculations for singlet ground states. II. Lithium hydride

The half-projected Hartree–Fock function (HPHF ) for singlet states is defined as a linear combination of two Slater determinants which contains only spin eigenstates with even spin quantum numbers. The possible uses of such an approach for determining molecular properties are investigated computing the potential energy curve, binding energy, force constant, and dipole moment variation corresponding to the lithium hydride ground state. Full projected and restricted Hartree–Fock calculations (PHF and RHF ) are performed simultaneously for comparison purposes. It is found that the HPHF model yields very satisfactory results, very close to those of the PHF scheme. Both models predict properly the molecular behavior as a function of nuclear separation, whereas the RHF one fails. A discussion is given in terms of configuration equivalents. It is concluded that the HPHF scheme seems to be useful for determining molecular properties specially in the case of large systems in which the more sophisticated methods are unmanageable.     

Two-photon absorption in the relativistic four-component Hartree-Fock approximation

A first implementation of the single residue of the quadratic response function in the four-component Hartree-Fock approximation is presented. The implementation is based on a Kramers paired molecular orbital basis and takes full advantage of time and spatial symmetry reductions in a quaternion formulation-in analogy with the previous work on the quadratic response function [J. Chem. Phys. 121, 6145 (2004)]. Sample calculations are given in terms of the monochromatic and coherent two-photon absorption cross sections in the noble gases. The relativistic two-photon selection rule DeltaJ = {0,+/-2} allows for nonrelativistically spin-forbidden transitions, and, even in neon, strong two-photon absorption is shown to occur for the X (1)S(0)-->2 (3)P(2) transition. It is argued that relevant comparisons between nonrelativistic and relativistic calculations must be performed at the level of integrated absorption cross sections.     

Localized states in polymeric molecules. II. Applications to chemical and biological processes

We present a simple real space method, based on the Green's function formalism, which is convenient for the calculation of the electronic structure of polymers with broken translational symmetry. The method is applied to the study of a model Hamiltonian which may describe conformational modifications of polymeric molecules. The possible role of localized states in chemical and biophysical processes is discussed.This work has been partially supported by the Brazilian Agencies FINEP and CNPq.     

Quadratic response functions in the time-dependent four-component Hartree-Fock approximation

The second-order response function has been implemented in the time-dependent four-component Hartree-Fock approximation. The implementation is atomic orbital direct and formulated in terms of Fock-type matrices. It employs a quaternion symmetry scheme that provides maximum computational efficiency with consideration made to time-reversal and spatial symmetries. Calculations are presented for the electric dipole first-order hyperpolarizabilities of CsAg and CsAu in the second-harmonic generation optical process beta(-2omega;omega,omega). It is shown that relativistic corrections to property values are substantial in these cases--the orientationally averaged hyperpolarizabilities in the static limit beta(0;0,0) are overestimated in nonrelativistic calculations by 18% and 66% for CsAg and CsAu, respectively. The dispersion displays anomalies in the band gap region due to one- and two-photon resonances with nonrelativistically spin-forbidden states. Although weakly absorbing these states inflict divergences in the quadratic response function, since the response theoretical approach which is used adopts the infinite excited-state lifetime approximation. This fact calls for caution in applications where knowledge of the exact positioning of all excited states in the spectrum is unknown.     

A multiconfigurational time-dependent Hartree-Fock method for excited electronic states. II. Coulomb interaction effects in single conjugated polymer chains

Conjugated polymers have attracted considerable attention in the last few decades due to their potential for optoelectronic applications. A key step that needs optimisation is charge carrier separation following photoexcitation. To understand better the dynamics of the exciton prior to charge separation, we have performed simulations of the formation and dynamics of localised excitations in single conjugated polymer strands. We use a nonadiabatic molecular dynamics method which allows for the coupled evolution of the nuclear degrees of freedom and of multiconfigurational electronic wavefunctions. We show the relaxation of electron-hole pairs to form excitons and oppositely charged polaron pairs and discuss the modifications to the relaxation process predicted by the inclusion of the Coulomb interaction between the carriers. The issue of charge photogeneration in conjugated polymers in dilute solution is also addressed.     

DFT-based chemical reactivity indices in the Hartree-Fock method. II. Fukui function, chemical potential, and hardness

A derivation of the density-functional-theory- (DFT) based reactivity indices in the ensemble unrestricted Hartree-Fock (eUHF) method is presented. The comparison between the properties of the reactivity indices evaluated in one and two sets of spin-orbital approach of the eUHF and hyper-unrestricted Hartree-Fock (UHF) methods are shown. All approaches give similar Fukui function irrespective of methodology used, but significantly differ for the global indices, containing important chemical information, and so their interpretation in terms of DFT- based indices can be questionable. The calculation scheme for the indices using the first- and second-order coupled perturbed eHF equations is proposed. A method for the identification of the spinorbitals involved in the change of the total number of electrons is included. The illustrative examples (water and hydrogen cyanide) show that the ground-state (GS) properties of the (Z +/- 1)-electron systems can be predicted from the GS properties of the Z-electron systems with an accuracy comparable with the UHF calculations. The relaxation effect, important for the HCN system in which a change in the symmetry of the highest-occupied spin-orbital occurs, is effectively predicted.     

The d-electron states of iron group impurity atoms in silicon

The question of the relative arrangement of the crystalline terms is considered, within the framework of crystal field theory, as a function of the location of the impurity atom in the silicon. The results of the corresponding calculations are found to agree with the experimental data.