Regularization method and molecular integrals with singular exponential functions

The regularization principle, which is based on the concept of linearly independent singular functions, makes it possible to calculate many important types of molecular matrix elements arising in the variational LCAO-MO-SCF scheme. This is done using a direct approach that employs reduction of these elements to finite sums of convergent and divergent one-electron integrals. A universal algorithm is developed to calculate two-center one-electron molecular integrals involving both singular and ordinary Slater functions. The numerical stability of the algorithms and the accuracy of the integral calculation are analyzed, and numerical estimates are given. V. I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Struktunoi Khimii, Vol. 35, No. 2, pp. 3–11, March–April, 1994. Translated by L. Chernomorskaya     

Integral invariants for high-symmetry open-shell molecules

A method for calculating the energies of electronic states arising from a degenerate open shellγ ^N in terms of integral invariants H^k(γ,γ) is presented. The calculation proceeds from expansions for the electron repulsion integrals 〈mm/nn〉 on degenerate orbitals ofγ symmetry in terms of H^k(γ,γ). The energies of states for theγ ^N electronic configurations with dimγ≤3 (e^N and t^N configurations) are tabulated. Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 2, pp. 183–195, March–April, 1998. This work was supported by RFFR grants No. 96-03-01167 and 96-03-34035.     

Novel methods for calculating the fine vibronic spectra of polyatomic molecules

Novel approximate methods for calculating the vibrational structure of the electronic spectra of polyatomic molecules—a method for the direct calculation of the overlap integrals of vibrational wave functions for the electronic states involved in a transition and a variational method for the solution of the vibrational problem for the excited states—are discussed. The methods are based on the consideration of the displacement and entanglement of normal coordinates, the quasiorthogonality of the Dushinsky transformation, and the classification of the states by total vibrational quantum numbers. Matrix perturbation theory is employed. It is shown that the accuracy of these methods compares well with the accuracy of the available “exact” techniques (the errors are ∼1 cm⁻¹ for frequency and 10% for relative intensity). At the same time, calculations by the new methods are performed more than two orders of magnitude faster than by the previously known methods. K. A. Timiryazev Agricultural Academy, Moscow. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 2, pp. 217–230, March–April, 1995. Translated by I. Izvekova     

Improved method for calculating vibronic spectra of complex molecules

The previously suggested approximate method for calculating the overlap integrals of vibrational wave functions is considerably improved for the purpose of maximally accurate calculation of excitation-induced mixing of normal coordinates. A general formula is obtained for all types of overlap integrals as a finite power series of the potential surface shift parameters; the coefficients are derivatives of the corresponding generating Junctions represented as polynomials of the shift vector elements of the normal coordinates and the mixing matrix. The spectra of model molecules of decatetraene and tetra- and hexadecaheptaene were calculated using the expressions derived in this work and a semiempirical parametric method for determination of excitation-induced changes in the potential surface of molecules. The calculations confirmed the high efficiency of both the parametric method and the new technique. Translated fromZhumal Strukturnoi Khimii, Vol. 38, No. 2, pp. 240–247, March–April, 1997.     

Asymptotic formulas for Coulomb and hybrid integrals with slater type functions

Asymptotic expressions are obtained for two-center Coulomb and hybrid integrals with Slater functions. Results of numerical test of these expressions are presented. The use of asymptotic formulas in LCAO-MO calculations of electronic molecular structure substantially reduces the computation time. V.I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 2, pp. 12–15, March–April, 1994. Translated by L. Chernomorskaya     

Semiempirical calculation of two-electron integrals using bipolar expansion of the Ohno potential

Bipolar expansion of the Ohno potential as a method of calculating two-center Coulomb integrals that appear in the NDDO approximation is generalized to one-center two-electron integrals. A unified semiempirical scheme is suggested for estimating two-electron interactions in molecules. This scheme can be readily extended to arbitrary Slater basis sets (including the s,p,d-orbitals) and involves no a priori data on the valent states of atoms. In this work, the scheme is employed to extend the semiempirical PM3 method to the s,p,d-basis set. The efficiency of the method is proven by test calculations of 24 chromium compounds (π-complexes, carbonyls, isocyanides, etc.). Scientific Research Institute of Chemistry at N. I. Lobachevskii Nizhnii Novgorod State University. Translated fromZhurnal Struktumoi Khimii, Vol. 36, No. 4, pp. 593–599, July–August, 1995. Translated by I. Izvekova.     

Integral invariants for high-symmetry open-shell molecules.

A numerical procedure for expanding electron repulsion integrals 〈mm|nn〉 on degenerate molecular orbitals of γ symmetry (γ=e, t, g, h) into integral invariants (reduced matrix elements) H^k(γ, γ) is suggested. The latter are analogous in their sense to Slater-Condon parameters F^k(l, l) for atoms with an electronic configuration l^N. The method is applicable to nonlinear molecules of arbitrary symmetries, including “not readily reducible” groups. G. K. Boreskov Institute of Catalysis, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 39, No. 1, pp. 3–17, January–February, 1998. This work was supported by RFFR grants No. 96-03-01167 and 96-03-34035.     

Parametric method for calculating the vibronic spectra of complex molecules. Diphenylpolyenes

The absorption and fluorescence spectra of diphenylpolyenes (diphenylbutadiene, diphenylhexatriene, diphenyloctatetraene, and 1,6-di(4′-methylphenyl)-1,3,5-hexatriene) are calculated by a recently proposed parametric method using the fragmentation approach for designing molecular models. The parameters of the^H>C=molecular fragment (derivatives of the Coulomb and resonance integrals with respect to internal coordinates in the HAO basis set) obtained in calculation for polyenes were transferred to the molecular models of diphenylpolyenes without changes (∂H_e/∂q⁽⁰⁾=0.055 and ∂²H_e/∂q _k ⁽⁰⁾ ∂q _l ⁽⁰⁾ =0.1 au). The theoretical spectra are sufficiently adequate to quantitatively and qualitatively reproduce the main features of the vibrational structure of the experimental absorption and fluorescence spectra, and the parameters of the models of the potential surfaces of the excited states of diphenylpolyenes are consistent with the previous estimations. It is shown that this method allows predictive calculations of the vibronic spectra of complex molecules and the developed parametrization posesses all needed properties: locality, transferability, invariance to minor changes in electron density, ranking according to magnitude, small number of parameters for molecular fragments, etc. K. A. Timiryazev Moscow Agricultural Academy. Translated fromZhurnal Struktumoi Khimii, Vol. 37, No. 6, pp. 1040–1049, November–December, 1996. Translated by I. Izvekova     

Double exchange in polynuclear mixed-valence clusters

A method for calculating the energies of the tunnel states of mixed-valence, clusters is proposed. It is based on the secondary quantization technique and allows one to obtain analytical expressions for all matrix elements that appear in double exchange theory as well as to determine the microstructures of the parameters of this theory. The energy spectra of trimeric systems are calculated with allowance made for the three-center transfer integrals, and the magnetic properties of these systems are investigated. Moldova State University. Translated fromZhurnal Struktumoi Khimii, Vol. 36, No. 4, pp. 644–653, July–August, 1995. Translated by I. Izvekova     

A modified MNDO procedure for calculating the heats of formation of organic anions

A modification of the MNDO method is suggested based on the relation ζ_A=ζ_A ⁰(1 + ϰ_AQ_A) for Slater parameters that takes into account the dependence of overlap integrals and the MNDO parameters (expressed via these integrals) on atomic charges Q_A. The core parameters U_μμ include corrections for nonorthogonality of basis functions of atoms in a molecule. For free atoms, the parameters were determined from the condition of reproducible electron affinities. The method is advantageous for calculating the heats of formation of anions, particularly those with the charge concentrated on one atom. Institute of Chemical Kinetics and Combustion, Siberian Branch, Russian Academy of Sciences. Translated fromZhurnal Strukturnoi Khimii, Vol. 35, No. 1, pp. 3–11, January-February, 1994. Translated by O. Kharlamova     

Expansion Formulae for Two-center Integer and Noninteger <Emphasis Type="Italic">n</Emphasis> STO Charge Densities and their Use in Evaluation of Multi-center Integrals

Using complete orthonormal sets of Ψ^α-exponential type orbitals (Ψ^α-ETOs, α =1, 0, −1, −2, ...) introduced by the author, the series expansion formulae are derived for the two-center integer and noninteger n STO (ISTO and NISTO) charge densities in terms of integer n STOs at a third center. The expansion coefficients occurring in these relations are presented through the two-center overlap integrals between STOs with integer and noninteger principal quantum numbers. The general formulae obtained for the STO charge densities are utilized for the evaluation of two-center Coulomb and hybrid integrals of NISTOs appearing in the Hartee–Fock–Roothaan approximation. The final results are expressed in terms of both the overlap integrals and the one-center basic integrals over integer n STOs. It should be noted that the result for the multi-center multielectron integrals with two-center noninteger n STO charge densities presented in this paper were not appeared in our past publications.     

Calculation of two-center two-electron integrals in the slaters,p,d-basis set for the Ono electron-electron potential

This paper deals with the problems of extending semiempirical MNDO methods to compounds with d-elements. The problem is solved by estimating two-center two-electron integrals (TTI) with the Ono potential modeling interaction between two electrons in a molecule. A scheme for calculating TTI is suggested which uses the expansion of the Ono potential in a series of pairwise products of spherical harmonics centered on two atoms in the molecule. The scheme is stable and efficient for calculations in arbitrary Slater basis sets (including the s,p,d-basis set) and seems to be useful for development of NDDO methods. Scientific Research Institute of Chemistry at N. I. Lobachevskii Nizhnii Novgorod State University. Translated fromZhurnul Strukturnoi Khimii Vol. 35, No. 4, pp. 24–27, July–August, 1994. Translated by L. Smolina     

New Method for calculating effective charges on atoms in molecules, clusters, and solids

A procedure for calculating effective charges on atoms in an arbitrary polyatomic system has been developed on the basis of the one-electron DV cluster method. Effective charges are calculated as three-dimensional integrals of electron density over the space around atomic nuclei in the object under investigation. An original procedure is suggested to assign the charge density to a particular center at every point of space. Translated fromZhurnal Struktumoi Khimii, vol. 39, no. 6, pp. 1134–1140, November–December, 1998.     

Indo calculation of electronic spectra for transition metal complexes in the extended approximation of singly excited configurations

Semiempirical INDO-E/S calculations of [RuX₆]^q (X=NH₃, q=+2, +3; X=CN⁻, q=−4, −3) complexes are performed to demonstrate that the MO relaxation in the electronically excited state can be taken into account by introducing certain double excitations into the configuration interaction matrix; the principles of selection of the excitations are discussed. The calculation results are compared with the experimental electronic absorption spectra. St. Petersburg State University. Translated fromZhurnal Struktumoi Khimii, Vol. 37, No. 2, pp. 195–205, March–April, 1996. Translated by I. Izvekova     

Fragment calculation of electronic structures of polyatomic molecules in the ground state. I. A method of intermediate fragment

A method is proposed for fragment calculation of electronic structures of polyatomic molecules in the ground state. The wave function of a molecule in the ground state in single-determinantal representation of a closed shell is employed. The concise formulation allows efficient calculation of the electronic structures of polyatomic molecules taking into account possible charge transfer between interacting molecular fragments. V.I. Vernadskii Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences. Translated fromZhurnal Struktumoi Khimii, Vol. 36, No. 3, pp. 387–394, May–June, 1995. Translated by I. Izvekova     

Spectrum of states in icosahedral structures of the electronic configuration gn (N = 1–7). 1. Invariant expansion for integrals and energies

The energy spectrum of the states that appear in structures of icosahedral (I,I_h symmetry with open electronic shells g^N (dim g = 4; N = 1–7) is reported. The energies are obtained in terms of integral invariants (reduced matrix elements of electron-electron interaction) H^k (g, g). The latter are analogs of the Slater-Condon parameters F^k(l,l) for atoms with the l^N electronic configuration. A similar representation is proposed for the integrals mm’≨’) of electron-electron interaction on the 4-fold degenerate g orbitals in the “standard” representation. The relation between the terms of the g^N(I,I_h) configuration and the parent states of the orthogonal group O⁺(4) is discussed. Translated fromZhurnal Strukturnoi Khimii, Vol. 38, No. 1, pp. 3–13, January–February, 1997.     

Calculation of interaction potentials for excited alkali atom-mercury atom systems. the K*-Hg interaction

Interatomic potentials for the systems alkali atom (in the ground and excited states)-mercury atom are calculated by the effective potential method using a polarization potential obtained from calculation of most important polarization diagrams of perturbation theory in the Thomas-Fermi approximation. The results are used to calculate the quasimolecular terms of the A−Hg systems, where A=Na, K. Some values of the interaction potential parameters are published for the first time. The results obtained in this work are compared with the available experimental and theoretical data. Odessa Institute of Hydrometeorology. Translated fromZhurnal Strukturnoi Khimii, Vol. 36, No. 4, pp. 608–614, July–August, 1995. Translated by I. Izvekova     

Effect of interatomic interactions on the electronic structure of solid solutions NbxTa1-xC

The electronic structure of cubic carbide alloys Nb_xTa_1-xC is investigated by X-ray emission spectroscopy. The tendencies of variation of the electronic spectrum and interatomic interactions in the ternary phases are discussed using the results of the self-consistent LMTO-ASA calculation. Translated fromZhurnal Struktumoi Khimii, Vol. 39, No. 6, pp. 1088–1092, November–December, 1998.     

Methods of correcting the results of quantitative analyses in X-ray photoelectron spectroscopy

A method of reducing the error of component concentration calculation of a multicomponent system is proposed. The method is based on an iteration technique using tabulated sensitivity coefficients of elements and one standard sample. Translated fromZhurnal Struktumoi Khimii, Vol. 39, No. 6, pp. 1151–1153, November–December, 1998.     

Use of addition theorems in evaluation of multicenter nuclear-attraction and electron-repulsion integrals with integer and noninteger n Slater-type orbitals

Multicenter integrals appearing in the Hartree–Fock–Roothaan equations for molecules are calculated using different kinds of series expansion formulas obtained from the expansions of integer and noninteger n Slater-type orbitals, in terms of Ψ ^α -exponential-type orbitals (where α=1, 0, –1, –2,...) at a displaced center, that form complete orthonormal sets and are represented by linear combinations of integer n Slater-type orbitals. The convergence of these series is tested by calculating concrete cases. The accuracy of the results is quite high for quantum numbers, screening constants, and location of orbitals. Received: 13 February 2002 / Accepted: 11 March 2002 / Published online: 4 July 2002