Simplified State Interaction for Matrix Product State Wave Functions.

Leon Freitag,Stefan Knecht,Alberto Baiardi,Leticia González

doi:10.1021/acs.jctc.1c00674

Abstract

We present an approximation to the state-interaction approach for matrix product state (MPS) wave functions (MPSSI) in a nonorthogonal molecular orbital basis, first presented by Knecht et al. [J. Chem. Theory Comput.,2016, 28, 5881], that allows for a significant reduction of the computational cost without significantly compromising its accuracy. The approximation is well-suited if the molecular orbital basis is close to orthogonality, and its reliability may be estimated a priori with a single numerical parameter. For an example of a platinum azide complex, our approximation offers up to 63-fold reduction in computational time compared to the original method for wave function overlaps and spin–orbit couplings, while still maintaining numerical accuracy.

Highlights

Accurate calculations of many photochemical processes can be a daunting task
We demonstrate the effectiveness of these approximations by means of MPSSI calculations of wave function overlaps and spin−orbit couplings for a medium-sized transition-metal complex
The compression scheme may become less efficient in more complex cases, such as for calculating transition properties between orbitals obtained for different excited states calculated at different nuclear geometries

Summary

INTRODUCTION

Accurate calculations of many photochemical processes can be a daunting task. Excited states are often governed by strong electron correlation effects and many close-lying excited states, where multiconfigurational electronic structure methods[1,2] are indispensable. In the CASSCF paradigm, and with DMRG-SCF, excited states are usually calculated with a state-average ansatz, where a single orthonormal set of molecular orbitals (MOs) is optimized to provide a balanced representation of several states This allows for a straightforward calculation of transition densities and moments that are required to compute properties such as oscillator strengths, magnetic properties, or spin−orbit couplings. State-averaging is not always possible or desired: (i) the individual state characters differ too much for an average set of orbitals to yield an adequate description; (ii) state-averaging, for example, between different spin multiplicities, is not supported by the computer implementation of the method, or (iii) a single molecular set of orbitals is not possible at all The latter problem is encountered, for instance, when calculating the overlap between wave functions that are associated with different molecular structures to monitor the change in the character of the electronic wave function, as described in ref 19. We demonstrate the effectiveness of these approximations by means of MPSSI calculations of wave function overlaps and spin−orbit couplings for a medium-sized transition-metal complex

THEORY

NUMERICAL EXAMPLES

Performance of MPSSI Approximation on Wave

CONCLUSIONS

Findings

■ REFERENCES