# Vibrational Density Matrix Renormalization Group

## TL;DR

This paper introduces a vibrational density matrix renormalization group (vDMRG) method that efficiently computes vibrational wave functions for molecules, achieving high accuracy and scalability beyond traditional approaches.

## Contribution

The paper presents the application of DMRG to vibrational problems, enabling accurate calculations for larger molecules with many vibrational modes.

## Key findings

- High accuracy for small molecules
- Effective calculation of the sarcosyn-glycin dipeptide's vibrational spectrum
- Demonstrated convergence with basis size and DMRG parameters

## Abstract

Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. However, the unfavorable scaling and the resulting high computational cost of standard variational approaches limit their application to small molecules with only few vibrational modes. Here, we demonstrate how the density matrix renormalization group (DMRG) can be exploited to optimize vibrational wave functions (vDMRG) expressed as matrix product states. We study the convergence of these calculations with respect to the size of the local basis of each mode, the number of renormalized block states, and the number of DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for small molecules that were intensively studied in the literature. We then proceed to show that the complete fingerprint region of the sarcosyn-glycin dipeptide can be calculated with vDMRG.