# Accurate and Affordable Vibrational Spectra of Large Molecules: Primary, Auxiliary, and Spectator Modes in a Perturb-then-Diagonalize Framework

## TL;DR

This paper introduces a new computational method to accurately calculate vibrational spectra of large molecules at lower cost.

## Contribution

A novel perturb-then-diagonalize framework partitions normal modes to efficiently compute anharmonic vibrational spectra.

## Key findings

- The method partitions normal modes into primary, auxiliary, and spectator classes for efficient computation.
- Accurate anharmonic contributions are included for primary modes while avoiding expensive Hessian evaluations.
- Case studies show robustness and accuracy across various molecular systems including biomolecules.

## Abstract

Vibrational spectra
convey a wealth of structural and dynamical
information; however, their reliable assignment and interpretation
often benefit from the integration of complementary spectroscopic
techniques and require the support of accurate quantum chemical calculations.
The harmonic approximation is frequently insufficient for quantitative
spectroscopy, while fully anharmonic treatments rapidly become computationally
prohibitive for large and flexible molecular systems, in particular,
for biomolecules. In this framework, we introduce a general perturb-then-diagonalize
approach that relies on a three-class partitioning of normal modes
into primary, auxiliary, and spectator subsets and combines numerical
strategies based on analytical Hessians and analytical gradients.
Accurate anharmonic contributions are explicitly included for the
modes of primary interest, while the influence of external modes is
accounted for through finite differences of analytical gradients,
avoiding the much more expensive evaluation of Hessians. Several case
studies demonstrate the robustness, ease of use, and accuracy of the
proposed approach across a broad range of molecular systems, including
situations in which vibrational and rotational spectroscopic data
provide complementary information. When combined with a dual-level
strategy in which accurate methods are employed for harmonic terms
and less expensive methods for anharmonic contributions, the present
framework enables vibrational spectra of near-spectroscopic accuracy
for biomolecules and other chemically rich systems. More complex environments
can be addressed by coupling the method with multilayer approaches.