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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of mathematical chemistry 15 (1994), S. 109-113 
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract 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.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 15 (1994), S. 747-751 
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: 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. © 1994 by John Wiley & Sons, Inc.
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 19 (1998), S. 1877-1886 
    ISSN: 0192-8651
    Keywords: update formula ; optimization method ; molecular geometry optimization ; ab initio calculations ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: 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
    Additional Material: 4 Tab.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 18 (1997), S. 1200-1210 
    ISSN: 0192-8651
    Keywords: basis set ; Gaussian-type function ; Hartree-Fock energy ; Ab initio calculations ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: 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. © 1997 John Wiley & Sons, Inc.   J Comput Chem 18: 1200-1210
    Additional Material: 16 Tab.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 19 (1998), S. 94-101 
    ISSN: 0192-8651
    Keywords: Dunham method ; rovibrational energy levels ; rovibrational Schrödinger equation ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: 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
    Additional Material: 6 Tab.
    Type of Medium: Electronic Resource
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