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

Economical quasi-Newton unitary optimization of electronic orbitals

We present an efficient quasi-Newton orbital solver optimized to reduce the number of gradient evaluations and other computational steps of comparable cost. The solver optimizes orthogonal orbitals by sequences of unitary rotations generated by the (preconditioned) limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm equipped with trust-region step restriction. The low-rank structure of the L-BFGS inverse Hessian is exploited when solving the trust-region problem. The efficiency of the proposed "Quasi-Newton Unitary Optimization with Trust-Region" (QUOTR) solver 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.

Robust ΔSCF calculations with direct energy functional minimization methods and STEP for molecules and materials

The direct energy functional minimization method using the orbital transformation (OT) scheme in the program package CP2K has been employed for Δ self-consistent field (ΔSCF) calculations. The OT method for non-uniform molecular orbitals occupations allows us to apply the ΔSCF method for various kinds of molecules and periodic systems. Vertical excitation energies of heteroaromatic molecules and condensed phase systems, such as solvated ethylene and solvated uracil obeying periodic boundary conditions, are reported using the ΔSCF method. In addition, a Re-phosphate molecule attached to the surface of anatase (TiO₂) has been investigated. Additionally, we have implemented a recently proposed state-targeted energy projection ΔSCF algorithm [K. Carter-Fenk and J. M. Herbert, J. Chem. Theory Comput. 16(8), 5067-5082 (2020)] for diagonalization based SCF in CP2K. It is found that the OT scheme provides a smooth and robust SCF convergence for all investigated excitation energies and (non-)periodic systems.

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

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

A direct optimization method for obtaining excited electronic states using density functionals is presented.

Non-linear eigensolver-based alternative to traditional SCF methods

The self-consistent procedure in electronic structure calculations is revisited using a highly efficient and robust algorithm for solving the non-linear eigenvector problem, i.e., H({ψ})ψ = Eψ. This new scheme is derived from a generalization of the FEAST eigenvalue algorithm to account for the non-linearity of the Hamiltonian with the occupied eigenvectors. Using a series of numerical examples and the density functional theory-Kohn/Sham model, it will be shown that our approach can outperform the traditional SCF mixing-scheme techniques by providing a higher converge rate, convergence to the correct solution regardless of the choice of the initial guess, and a significant reduction of the eigenvalue solve time in simulations.