Alexander V. Mitin

Calculation of rovibrational energy levels of diatomic molecules by Dunham method with potential obtained from ab initio calculations

A numerical algorithm of the Dunham method for the solution of the rovibrational Schrödinger equation is proposed. It uses a new quasi‐Hermitian method of constructing the optimal approximate polynomial for the tabularly defined potential curve of a diatomic molecule obtained from an ab initio calculation. In this method the optimal polynomial approximates the potential curve and its derivatives, but it uses only information about the potential curve for its construction. This property of the new method arises from analysis of a spectral representation of the optimal polynomial to determine how well it approximates the potential curve and its derivatives. Appropriate derivatives of the potential curve, needed in the Dunham method, are calculated by recurrence relations. Comparison with the finite‐difference method shows that the precision of both methods is similar, while the Dunham method is hundreds of times faster. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 94–101, 1998

Accurate small split-valence 3-21SP and 4-22SP basis sets for the first-row atoms

Abstract Split-valence Gaussian 3-21SP and 4-22SP basis sets are presented for the ground states of the first-row elements of the Periodic Table. The total energies of the atoms calculated with the new basis sets are significantly lower than those obtained with the well-known 3-21G and 4-31G basis sets. This is the consequence of the fact that the 3-21G and 4-31G basis sets do not correspond to the global minimum of the energy functional in the Hartree-Fock approximation. It is also shown that the 4–22 contraction scheme better corresponds to the solution structure of the Hartree-Fock equations with uncontracted 8s4p basis sets, and therefore permits one to obtain lower total energies than with the 4–31 contraction scheme. The proposed basis sets are tested by performing geometry optimizations and calculating the normal frequencies for the LiH, BeH 2 , BH 3 , CH 4 , NH 3 , OH 2 , and FH molecules within the Hartree-Fock approximation.

Iterative methods for the calculation of a few of the lowest eigenvalues and corresponding eigenvectors of the AX = lBX equation with real symmetric matrices of large dimension

New methods for the iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of a generalized eigenvalue problem are proposed. These methods use only multiplication of the A and B matrices on a vector.

Accurate atomic Gaussian basis functions for second‐row atoms: Small split‐valence 3‐21SP and 4‐22SP basis sets

Small split‐valence Gaussian 3‐21SP and 4‐22SP basis sets, previously reported for the first‐row atoms [Chem. Phys. Lett., 229, 151 (1996)], have been extended for the second‐row elements of the Periodic Table. The total energies of the ground states of the second‐row atoms calculated with the new basis sets are significantly lower than those obtained with the well‐known 3‐21G (J. Am. Chem. Soc., 104, 2797 (1982)] and 4‐31G [J. Chem. Phys., 56, 5255 (1972)] basis sets. This is because, as first noted in our previous work for first‐row atoms, that the 3‐21G and 4‐31G basis sets only correspond to a local minimum of the Hartree–Fock energy functional, which is relatively far from its global minimum. The proposed basis sets have been tested by performing geometry optimizations and calculations of normal frequencies in the harmonic approximation of some diatomic and polyatomic molecules at the Hartree–Fock level.

Effect of vortex dynamics on the transport properties of granular YBa2Cu3O7−δ with reduced Josephson junctions

Abstract The granular single-phase samples of YBa 2 Cu 3 O 7−δ with the reduced Josephson coupling energy E J ≤ kT cg ( T cg is a critical temperature inside granules) demonstrates a strong dependence of a voltage U ( T , H ) on thermomagnetic history at temperatures T ≤ 60 K and magnetic fields H > 40 A/m, if even a passing current J does not exceed 5 A/cm 2 . A correspondence between the temperature dependences of the voltage U ( T ) and the sample magnetization M ( T ), as well as relaxation behavior of U ( T ) and remarkable memory effects were studied at T ≤ 50 K. The majority of results can be explained on the basis of the Josephson medium models, which should be completed by consideration of the quantum tunneling of vortices.

Accurate atomic Gaussian basis functions for first-row atoms. Part 1. Contracted basis sets derived from 9s5p primitives

Abstract Contracted Gaussian basis sets (9s5p/5s3p), (9s5p/5s2p), (9s5p/4s2p), (9s5p/3s2p) and (10s5p/4s2p), (10s5p/3s2p) are presented for the ground states of the first-two atoms of the periodic table. The primitive basis (10s5p) is derived from a (9s5p) Gaussian basis by doubling one s-type function. A two-step procedure is applied for the construction of all basis sets reported. The atomic total energy is first optimized in the SCF approximation with respect to atomic exponential parameters and then with respect to the contraction coefficients. The energy functional is determined with a maximal error of less than 1.0 × 10−8 Eh in both cases. The basis sets are further tested by performing geometry optimizations of the LiH, BeH2, BH3, CH4, NH3, OH2 and FH molecules at the Hartree-Fock level.

Use of symmetric rank-one Hessian update in molecular geometry optimization

The use of the symmetric rank‐one Hessian update and the Broyden–Fletcher–Goldfarb–Shano (BFGS) update formula are considered in an ab initio molecular geometry optimization algorithm. It is noted that the symmetric rank‐one Hessian update has an advantage when compared with the BFGS update formula and this advantage must be more evident in the optimization of molecular geometry, because the total energy surface is a near‐quadratic function with a small nonlinearity close to a minimum point. The results obtained in geometry optimization of a test group of molecules support this proposal and show that the use of the symmetric rank‐one Hessian update formula permits reduction of the number of energy and gradient evaluations needed to locate a minimum on the energy surface. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1877–1886, 1998

Linear extrapolation in iterative methods

The application of extrapolation methods in an iterative process of general type is investigated. It is shown that extrapolation methods are obtained by two successive approximations from the formula defining an iterative process. The first approximation gives the general formula for extrapolation methods, while particular examples are obtained from this formula by introducing different approximations for the operator defining the iterative process.