A nonorthogonal state-interaction approach for matrix product state wave functions

TL;DR

This paper introduces a nonorthogonal state-interaction method for matrix product state wave functions, enabling calculation of transition and spin-orbit couplings between states sharing the same orbital basis.

Contribution

It develops a novel approach to transform MPS wave functions from nonorthogonal to biorthonormal bases, facilitating state interaction calculations.

Findings

Enables calculation of transition matrix elements between arbitrary states.

Allows for spin-orbit coupling computations within MPS framework.

Extends traditional wave-function transformation techniques to MPS wave functions.

Abstract

We present a state-interaction approach for matrix product state (MPS) wave functions in a nonorthogonal molecular orbital basis. Our approach allows us to calculate for example transition and spin-orbit coupling matrix elements between arbitrary electronic states provided that they share the same one-electron basis functions and active orbital space, respectively. The key element is the transformation of the MPS wave functions of different states from a nonorthogonal to a biorthonormal molecular orbital basis representation exploiting a sequence of non-unitary transformations following a proposal by Malmqvist (Int. J. Quantum Chem. 30, 479 (1986)). This is well-known for traditional wave-function parametrizations but has not yet been exploited for MPS wave functions.