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

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.