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

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*, <i>n</i> → 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. <i>J. Chem. Phys.</i>, <b>2008</b>, <i>128</i>, 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 <i>n</i> → 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.