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  • 1
    Electronic Resource
    Electronic Resource
    A Conjugate Gradient Algorithm with a Trust Region for Molecular Geometry Optimization (1995)
    Springer
    Journal of molecular modeling 1 (1995), S. 11-17 
    Details
    ISSN: 0948-5023
    Keywords: Keywords Conjugate gradient, restricted step algortihm, optimization for nonquadratic functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract An algorithm is presented for the optimization of molecular geometries and general nonquadratic functions using the nonlinear conjugate gradient method with a restricted step and restart procedure. The algorithm only requires the evaluation of the energy function and its gradient, therefor less memory storage is needed than for other conjugate gradient algorithms. Some numerical results are also presented and the efficiency and behaviour of the algorithm is compared with the standard conjugate gradient method. We also present comparisons of both conjugate gradient and variable metric methods with and without the trust region technique. One of the main conclusions of the present work is that a trust region always improves the converge of any optimization method. A sketch of the algorithm is also given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s008940050002
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  • 2
    Electronic Resource
    Electronic Resource
    New strategies to incorporate the solvent polarization in self-consistent reaction field and free-energy perturbation simulations (1995)
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 103 (1995), S. 10183-10191 
    Details
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A first-order perturbation treatment of the polarization contribution to the free energy of hydration is presented. Very simple expressions for the computation of the total electrostatic free energy of solvation, the polarization contribution, and its components (distortion and stabilization) are derived. These equations can be used with either continuum (quantum and classical) or discrete approaches. The reliability of these equations is examined by comparison with rigorous expressions derived previously within the framework of the self-consistent reaction field theory. Indeed, the suitability of the classical expressions for the distortion and stabilization terms used in the context of discrete strategies has been explored by comparison between self-consistent reaction field and molecular dynamics–free-energy perturbation results. The excellent agreement found between the two techniques allows us to envisage a procedure to account for the polarization in force field-derived methods. © 1995 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.469921
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  • 3
    Electronic Resource
    Electronic Resource
    On the automatic restricted-step rational-function-optimization method (1998)
    Springer
    Theoretical chemistry accounts 100 (1998), S. 265-274 
    Details
    ISSN: 1432-2234
    Keywords: Key words: Rational function optimization method ; Molecular geometry optimization ; Transition state geometry optimization ; Restricted step algorithm ; Augmented Hessian algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. The rational function optimization algorithm is one of the widely used methods to search stationary points on surfaces. However, one of the drawbacks of this method is the step reduction procedure to deal with the overstepping problem. We present and comment on a method such that the step obtained from the solution of the rational function equations possesses the desired correct length. The analysis and discussion of the method is mainly centered on the location and optimization of transition states.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002140050387
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  • 4
    Electronic Resource
    Electronic Resource
    Remarks on large-scale matrix diagonalization using a Lagrange–Newton–Raphson minimization in a subspace (1999)
    Springer
    Theoretical chemistry accounts 103 (1999), S. 163-166 
    Details
    ISSN: 1432-2234
    Keywords: Key words: Large-scale matrix diagonalization ; Lagrange ; Newton ; Raphson minimization ; Ritz ; Galerkin method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract. We present a matrix diagonalization method where the diagonalization is carried out through a normal Lagrange–Newton–Raphson method solved in a subspace. The subspace is generated using the correction vector that predicts the standard Lagrange–Newton–Raphson formula in the full space. Some numerical examples and the performance of the algorithm are given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s002140050527
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  • 5
    Electronic Resource
    Electronic Resource
    A geometry optimization benchmark using highly correlated wavefunctions (FCI and MRD-CI) (1995)
    Springer
    Theoretical chemistry accounts 92 (1995), S. 369-381 
    Details
    ISSN: 1432-2234
    Keywords: Geometry optimization ; FCI ; MRD-CI
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary Full configuration interaction (FCI) geometry optimizations have been performed for the X3B1, a1A1, b1B1 and c1A1 electronic states of CH2, the X2B1 and A2A1 electronic states of NH2 and the X1A′1 electronic state of BH3 using a DZP basis set. The results are compared with those obtained using the MRD-CI method at different levels of theoretical treatment. The agreement between the geometrical parameters optimized with the FCI and MRD-CI methods is very good.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01114851
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  • 6
    Electronic Resource
    Electronic Resource
    A geometry optimization benchmark using highly correlated wavefunctions (FCI and MRD-CI) (1995)
    Springer
    Theoretica chimica acta 92 (1995), S. 369-381 
    Details
    ISSN: 0040-5744
    Keywords: Key words: Geometry optimization ; FCI ; MRD-CI
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Summary.  Full configuration interaction (FCI) geometry optimizations have been performed for the X3B1, a1A1, b1B1 and c1A1 electronic states of CH2, the X2B1 and A2A1 electronic states of NH2 and the X1A′ 1 electronic state of BH3 using a DZP basis set. The results are compared with those obtained using the MRD-CI method at different levels of theoretical treatment. The agreement between the geometrical parameters optimized with the FCI and MRD-CI methods is very good.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01114851
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  • 7
    Electronic Resource
    Electronic Resource
    Another way to implement the Powell formula for updating Hessian matrices related to transition structures (1999)
    Springer
    Journal of mathematical chemistry 25 (1999), S. 85-92 
    Details
    ISSN: 1572-8897
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Mathematics
    Notes: Abstract A way to update the Hessian matrix according to the Powell formula is given. With this formula one does not need to store the full Hessian matrix at any iteration. A method to find transition structures, which is a combination of the quasi‐Newton–Raphson augmented Hessian algorithm with the proposed Powell update scheme, is also given. The diagonalization of the augmented Hessian matrix is carried out by Lanczos‐like methods. In this way, during all the optimization process, one avoids to store full matrices.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1019168013391
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  • 8
    Electronic Resource
    Electronic Resource
    On the restricted step method coupled with the augmented Hessian for the search of stationary points of any continuous function (1997)
    New York, NY : Wiley-Blackwell
    International Journal of Quantum Chemistry 62 (1997), S. 153-165 
    Details
    ISSN: 0020-7608
    Keywords: Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology
    Notes: In any optimization using the augmented Hessian technique, the step is not restricted to any length. Since the restriction of the step at each iteration is very important in order to achieve good convergence, we present a coupled method such that the augmented Hessian automatically gives both the adequate length of the step and the correct Hessian structure. The method is showed for the minima and saddle points of any order. © 1997 John Wiley & Sons, Inc.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
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    Paper (German National Licenses)
  • 9
    Electronic Resource
    Electronic Resource
    Analysis of the convergence of the general coupling operator method for one-configuration-type wave functions (1998)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 19 (1998), S. 368-376 
    Details
    ISSN: 0192-8651
    Keywords: general coupling operator ; coupling operator ; wave functions ; Chemistry ; Theoretical, Physical and Computational Chemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We comment on the convergence of the general coupling operator for all types of one-configuration or multiconfigurational wave functions that still preserve the one-configuration structure for the energy expression. The choice on the best arbitrary real and antisymmetric parameters inherent in the coupling operator methodology is discussed, giving a theoretical reason. Another type of coupling operator is defined, presented, and analyzed. Finally, we give some numerical examples related to the low-lying electronic states of a cluster model for K2NiF4 solid.   © 1998 John Wiley & Sons, Inc.   J Comput Chem 19: 368-376, 1998
    Additional Material: 2 Tab.
    Type of Medium: Electronic Resource
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  • 10
    Electronic Resource
    Electronic Resource
    Analysis of the updated Hessian matrices for locating transition structures (1995)
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 16 (1995), S. 1326-1338 
    Details
    ISSN: 0192-8651
    Keywords: Computational Chemistry and Molecular Modeling ; Biochemistry
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Chemistry and Pharmacology , Computer Science
    Notes: We present an analysis of the behavior of different updating Hessian formulas when they are used for the location and optimization of transition structures. The analysis is based on the number of iterations, the minimum of the weighted Euclidean matrix norm, and first-order perturbation theory applied to each type of Hessian correction. Finally, we give a derivation of a family of updated Hessians from the variational method proposed by Greenstadt. We conclude that the proposed family of updated Hessians is useful for the optimization of transition structures. © 1995 John Wiley & Sons, Inc.
    Additional Material: 10 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/jcc.540161103
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