# Evaluation of Approximate Fourth-Order N‑Electron Valence Perturbation Theory (NEVPT4(SD)) for the Excited States of Organic Molecules

## TL;DR

This paper evaluates a new computational method for calculating excited states in organic molecules and finds it to be highly accurate and efficient.

## Contribution

The study introduces and validates an approximate fourth-order N-electron valence perturbation theory (NEVPT4(SD)) for excited state calculations.

## Key findings

- NEVPT4(SD) outperforms lower-order NEVPT and CASPT2 methods for singlet and triplet excitations.
- n → π* transitions are slightly overestimated, while π → π* transitions are slightly underestimated.
- NEVPT4(SD) has a narrow error distribution and is computationally more affordable than higher-order multireference methods.

## Abstract

In this work, we assess the accuracy of the approximate
fourth-order
N-electron valence perturbation theory (NEVPT4­(SD)) methodology for
computing excited states of organic molecules. The well-established
Thiel benchmark set was employed, comprising 225 vertical excitations
spanning π → π*, n → π*,
and σ → π* transition types. A state-specific canonicalization
procedure was applied, enabling a direct comparison with CC3 reference
data reported by Schreiber et al. J. Chem. Phys., 2008, 128, 134110. For both singlet and triplet
excitations, NEVPT4­(SD) systematically outperforms lower-order NEVPT
variants, as well as previously reported complete active space second-order
perturbation theory (CASPT2) results. A detailed analysis of the singlet
excitations reveals that n → π* transitions
have a slight tendency to be overestimated (by about 0.1 eV), while
π → π* excitations tend to be slightly underestimated
(by −0.04 eV). While this shift persists across all NEVPT perturbation
orders, its magnitude decreases with higher-order treatments. Across
the entire test set, NEVPT4­(SD) has a very narrow error distribution
with a peak very close to 0. Thus, this study demonstrates the robustness
and high accuracy of NEVPT4­(SD) for vertical excitation energies,
highlighting its clear advantages over lower-order perturbative approaches
while remaining computationally much more affordable than other multireference
correlation approaches that proceed beyond second-order perturbation
theory.