# Approximate analytical gradients and nonadiabatic couplings for the state-average density matrix renormalization group self-consistent field method

## TL;DR

This paper introduces an approximate method for calculating analytical gradients and nonadiabatic couplings within the state-average DMRG-SCF framework, enabling accurate and efficient simulations of complex electronic states.

## Contribution

It develops a new approach to compute gradients and couplings in DMRG-SCF using a single-site MPS Lagrange multiplier, avoiding sweep procedures and closely following the SA-CASSCF formalism.

## Key findings

- Successfully applied to optimize a conical intersection in 1,2-dioxetanone.
- Reproduces SA-CASSCF results with arbitrary accuracy.
- Provides a computationally efficient scheme for nonadiabatic dynamics simulations.

## Abstract

We present an approximate scheme for analytical gradients and nonadiabatic couplings for calculating state-average density matrix renormalization group self-consistent-field wavefunction. Our formalism follows closely the state-average complete active space self-consistent-field (SA-CASSCF) \emph{ansatz}, which employs a Lagrangian, and the corresponding Lagrange multipliers are obtained from a solution of the coupled-perturbed CASSCF (CP-CASSCF) equations. We introduce a definition of the matrix product state (MPS) Lagrange multipliers based on a single-site tensor in a mixed-canonical form of the MPS, such that a sweep procedure is avoided in the solution of the CP-CASSCF equations. We apply our implementation to the optimization of a conical intersection in 1,2-dioxetanone, where we are able to fully reproduce the SA-CASSCF result up to arbitrary accuracy.