An approximation strategy to compute accurate initial density matrices for repeated self-consistent field calculations at different geometries
Étienne Polack, Aleksandr Mikhalev, Geneviève Dusson, Benjamin Stamm, Filippo Lipparini
Abstract
Repeated 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.