A comparison of accelerators for direct energy minimization in electronic structure calculations

Abstract

Abstract:We compare three different methods for direct energy minimization in electronic structure calculations where the gradient of the energy functional with respect to the molecular orbitals is available. These methods make use of the preconditioned gradient to increase robustness. An orbital transformation is used to ensure that the orthogonality constraint on the orbitals remains satisfied when using standard minimization methods. In addition, we propose an adaptive scheme for estimating the curvature of the energy functional to increase the performance of a line search free quasi-Newton method. We show that the performance of all methods is similar when robustness of the methods is ensured. We compare three different methods for direct energy minimization in electronic structure calculations where the gradient of the energy functional with respect to the molecular orbitals is available. These methods make use of the preconditioned gradient to increase robustness. An orbital transformation is used to ensure that the orthogonality constraint on the orbitals remains satisfied when using standard minimization methods. In addition, we propose an adaptive scheme for estimating the curvature of the energy functional to increase the performance of a line search free quasi-Newton method. We show that the performance of all methods is similar when robustness of the methods is ensured.

Variational calculations of excited states via direct optimization of the orbitals in DFT

“…Despite the fact that DO has long been known to be an alternative to SCF for energy minimization 39,83,84 , DO calculations of saddle points have so far been considered to be too difficult, due to the risk of variational collapse. Here, a DO method for converging to single-determinant DFT excited states is presented.…”

Direct Minimization for Ensemble Electronic Structure Calculations

“…We base our method on Broyden's second or bad update to construct the approximate inverse Hessian, G k , of f at X k . While Broyden's second update does not construct a symmetric approximation, or ensure that the approximation is positive definite it is a robust choice for electronic structure calculations [16,1,2]. However, we must take into account that our vectors are actually R m×n matrices, which will lead to a method identical to the generalized Broyden update.…”

“…When secant conditions are enforced we can use σ to control the influence of G 0 compared to the information gained from the secant conditions. In general, the information gained from these is reliable, and therefore σ should be small [1,2]. To construct the search direction we use…”

“…Instead we represent it as a low rank update. Details on recursive or low rank implementation of G k can be found in [12,19,1,2].…”

“…In practice X is often represented by a discretization that requires a generalization of the orthonormality constraint (2). The generalized constraint is…”