# n‑Mode Quantized Anharmonic Vibronic Hamiltonians for Matrix Product State Dynamics

## TL;DR

This paper introduces a new method for modeling vibronic dynamics using quantized Hamiltonians and matrix product states to accurately simulate photochemical processes.

## Contribution

The novel n-mode quantization of vibronic Hamiltonian terms and a tailored matrix product state architecture for vibronic wave functions.

## Key findings

- The n-mode quantization enables accurate modeling of anharmonic effects and nonadiabatic couplings in vibronic systems.
- The new matrix product state architecture improves the encoding of vibronic wave functions for quantum dynamics simulations.
- The approach successfully calculates the excited-state dynamics of maleimide with high accuracy.

## Abstract

Theoretical predictions of photochemical processes are
essential
for interpreting and understanding spectral features. Reliable quantum
dynamics calculations of vibronic systems require precise modeling
of anharmonic effects in the potential energy surfaces and off-diagonal
nonadiabatic coupling terms. In this work, we present the n-mode quantization of all vibronic Hamiltonian terms comprised
of general high-dimensional model representations. We expand the existing
vibrational DMRG formalism by applying the n-mode
quantization to all potential energy surfaces entering the Hamiltonian
as well as to all off-diagonal coupling terms. This is accompanied
by the introduction of a novel matrix product state architecture employing
tailored local site operators, which allow an effective encoding of
the vibronic wave function in a tensor-train format. This results
in a second-quantized framework for accurate vibronic calculations
employing the density matrix renormalization group algorithm. We demonstrate
the accuracy and reliability of this approach by calculating the excited-state
quantum dynamics of maleimide. We analyze convergence and the choice
of parameters of the underlying time-dependent density matrix renormalization
group algorithm for the n-mode vibronic Hamiltonian,
demonstrating that it enables accurate calculations of complex photochemical
dynamics.