Accelerating geometry optimization via Grassmann-DIIS extrapolation

Abstract

Geometry optimization in electronic structure theory requires repeated self-consistent field (SCF) calculations at every optimization step, making SCF convergence one of the primary computational bottlenecks in quantum chemistry simulations. Consequently, generating superior SCF initial guesses that reduce the number of required SCF iterations provides an effective strategy for significantly accelerating geometry optimization calculations. In this work, we develop a Grassmann extrapolation framework combined with direct inversion in the iterative subspace (G-Ext-DIIS) to generate improved density matrix initial guesses throughout geometry optimization. The proposed approach exploits the geometric structure of density matrices on the nonlinear Grassmann manifold, enabling physically consistent extrapolation while rigorously preserving the fundamental physical constraints of the density matrix. The method was systematically evaluated through calibration studies and benchmark calculations on diverse covalently bonded organic molecules and flexible noncovalent molecular clusters. Using either the overlap matrix or the core Hamiltonian matrix as the molecular descriptor, G-Ext-DIIS consistently reduces the total number of SCF iterations during geometry optimization. The performance of G-Ext-DIIS was found to be largely insensitive to the choice of density functional and basis set. For flexible cluster systems, reductions of approximately 20-30% in SCF iterations are routinely achieved, including a reduction of nearly 2000 SCF cycles for a hydroquinone clathrate cluster containing 129 atoms. Importantly, the computational overhead associated with the Grassmann extrapolation procedure is negligible compared with that of a single SCF iteration. These results demonstrate that G-Ext-DIIS provides an efficient, transferable, black-box, and computationally inexpensive strategy for accelerating geometry optimization calculations in large-scale quantum chemical simulations, making it a promising default SCF initialization scheme for future quantum chemistry software implementations.