Second-Order Self-Consistent-Field Density-Matrix Renormalization Group

TL;DR

This paper introduces a second-order, quadratically convergent DMRG-SCF method using matrix-product states, enabling efficient and accurate optimization of molecular orbitals and wave functions in quantum chemistry.

Contribution

It develops a novel DMRG-SCF algorithm that achieves quadratic convergence by directly minimizing a second-order energy expression with simultaneous optimization.

Findings

Quadratic convergence typically within two to four cycles.

Energy convergence surpasses previous methods.

Efficient optimization of molecular orbitals and wave functions.

Abstract

We present a matrix-product state (MPS)-based quadratically convergent density-matrix renormalization group self-consistent-field (DMRG-SCF) approach. Following a proposal by Werner and Knowles (JCP 82, 5053, (1985)), our DMRG-SCF algorithm is based on a direct minimization of an energy expression which is correct to second-order with respect to changes in the molecular orbital basis. We exploit a simultaneous optimization of the MPS wave function and molecular orbitals in order to achieve quadratic convergence. In contrast to previously reported (augmented Hessian) Newton-Raphson and super-configuration-interaction algorithms for DMRG-SCF, energy convergence beyond a quadratic scaling is possible in our ansatz. Discarding the set of redundant active-active orbital rotations, the DMRG-SCF energy converges typically within two to four cycles of the self-consistent procedure