Economical Quasi-Newton Self Consistent Field Solver

TL;DR

This paper introduces QUOTR, a quasi-Newton method for self-consistent field calculations that reduces gradient evaluations by leveraging low-rank Hessian structures and trust-region techniques, improving efficiency over traditional methods.

Contribution

The paper develops a novel quasi-Newton orbital solver, QUOTR, that enhances SCF convergence efficiency by exploiting low-rank Hessian structures and trust-region strategies, outperforming existing methods.

Findings

QUOTR reduces the number of gradient evaluations.

QUOTR outperforms standard Roothaan-Hall and DIIS methods.

The method is effective for Hartree-Fock and Kohn-Sham calculations.

Abstract

We present an efficient quasi-Newton orbital solver optimized to reduce the number of gradient (Fock matrix) evaluations. The solver optimizes orthogonal orbitals by sequences of unitary rotations generated by the (preconditioned) limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm incorporating trust-region step restriction. Low-rank structure of the inverse (approximate) Hessian is exploited not only in L-BFGS but also when solving the trust-region problem. The efficiency of the proposed ``Quasi-Newton Unitary Optimization with Trust-Region'' (QUOTR) method is compared to that of the standard Roothaan-Hall approach accelerated by the Direct Inversion of Iterative Subspace (DIIS), and other exact and approximate Newton solvers for mean-field (Hartree-Fock and Kohn-Sham) problems.