An approximation strategy to compute accurate initial density matrices for repeated self-consistent field calculations at different geometries

Molecular Physics, vol. 118

Abstract

É. Polacka, A. Mikhalevb, G. Dussona, B. Stammb & F. Lipparinic* a Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université Bourgogne Franche-Comté, Besançon, Franceb Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germanyc Dipartimento di Chimica e Chimica Industriale, Univeristà di Pisa, Pisa, ItalyCONTACT F. Lipparini filippo.lipparini@unipi.it Dipartimento di Chimica e Chimica Industriale, Univeristà di Pisa, Via G. Moruzzi 13, Pisa I-56124, ItalyABSTRACTRepeated computations on the same molecular system, but with different geometries, are often performed in quantum chemistry, for instance, in ab-initio molecular dynamics simulations or geometry optimisations. While many efficient strategies exist to provide a good guess for the self-consistent field procedure, little is known on how to efficiently exploit the abundance of information generated during the many computations. In this article, we present a strategy to provide an accurate initial guess for the density matrix, expanded in a set of localised basis functions, within the self-consistent field iterations for parametrised Hartree–Fock problems where the nuclear coordinates are changed along with a few user-specified collective variables, such as the molecule's normal modes. Our approach is based on an offline-stage where the Hartree–Fock eigenvalue problem is solved for some particular parameter values and an online-stage where the initial guess is computed very efficiently for any new parameter value. The method allows nonlinear approximations of density matrices, which belong to a non-linear manifold that is isomorphic to the Grassmann manifold, by mapping such a manifold onto the tangent space. Numerical tests on different amino acids show promising initial results.GRAPHICAL ABSTRACT

Authors 5

1. Étienne Polack

   Centre National de la Recherche Scientifique · Université Bourgogne Franche-Comté · Laboratoire de Mathématiques de Besançon

   Affiliation as printed

   Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université Bourgogne Franche-Comté, Besançon, France

2. Aleksandr Mikhalev Aachen Center for Computational Engineering Science

   RWTH Aachen University

   Affiliation as printed

   Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany

3. Geneviève Dusson

   Centre National de la Recherche Scientifique · Université Bourgogne Franche-Comté · Laboratoire de Mathématiques de Besançon

   Affiliation as printed

   Laboratoire de Mathématiques de Besançon, UMR CNRS 6623, Université Bourgogne Franche-Comté, Besançon, France

4. Benjamin Stamm Aachen Center for Computational Engineering Science

   RWTH Aachen University

   Affiliation as printed

   Center for Computational Engineering Science, RWTH Aachen University, Aachen, Germany

5. Filippo Lipparini corresponding

   University of Pisa

   Affiliation as printed

   Dipartimento di Chimica e Chimica Industriale, Univeristà di Pisa, Pisa, Italy

   Dipartimento di Chimica e Chimica Industriale (Lungarno Pacinotti, 43 - 56126 Pisa - Italy)