Large-scale relativistic complete active space self-consistent field with robust convergence

TL;DR

This paper introduces a robust, efficient algorithm for relativistic CASSCF calculations using density fitting, significantly improving stability and convergence speed, and enabling practical calculations with complex interactions and external magnetic fields.

Contribution

The authors develop a second-order orbital update scheme with an iterative augmented Hessian for relativistic CASSCF, enhancing stability and efficiency over previous methods.

Findings

Algorithm achieves quadratic convergence.

Efficiently handles Gaunt and Breit interactions.

Applicable to systems with external magnetic fields.

Abstract

We report an efficient algorithm using density fitting for the relativistic complete active space self-consistent field (CASSCF) method, which is significantly more stable than the algorithm previously reported by one of the authors [J. E. Bates and T. Shiozaki, J. Chem. Phys. 142, 044112 (2015)]. Our algorithm is based on the second-order orbital update scheme with an iterative augmented Hessian procedure, in which the density-fitted orbital Hessian is directly contracted to the trial vectors. Using this scheme, each microiteration is made less time consuming than one Dirac-Hartree-Fock iteration, and macroiterations converge quadratically. In addition, we show that the CASSCF calculations with the Gaunt and full Breit interactions can be efficiently performed by means of approximate orbital Hessians computed with the Dirac-Coulomb Hamiltonian. It is demonstrated that our algorithm can also be applied to systems under an external magnetic field, for which all of the molecular integrals are computed using gauge-including atomic orbitals.