Juxtaposing the fourth order vibrational operator perturbation theory CVPT(4) and the adaptive VCI (A-VCI): Accuracy, vibrational resonances and polyads of C2H4 and C2D4

Abstract

Ab initio prediction of anharmonic vibrational spectra produces an increasing computational overhead for larger molecules, requesting a balance between an accuracy and resources. Two complementary fundamental quantum mechanical approaches, the perturbative and variational, have various strong and weak features, depending on a specific target problem. The vibrational perturbation theory (VPT) treats weak couplings and strong resonances separately, relying on somewhat artificial criteria. In contrast, the more precise but computationally intense variational configuration interaction (VCI) method treats all couplings in universal manner. The active ongoing development of approaches to solving vibrational problems requires an update of comparative benchmarks, helping to choose the best theoretical tools for a particular target. In this work, the performance of two particular modern implementations of these methods was juxtaposed: the second and fourth order operator canonical perturbation theory CVPT(2,4) and a recently proposed adaptive vibrational configuration interaction method (A-VCI). Two practically important C₂H₄ and C₂D₄ molecules and an accurate CCSD(T)/cc-pVQZ four-body sextic normal mode PES were employed for benchmarking. The comprehensive picture of vibrational resonances and the polyad quantum number was revealed in the form: $P\left[C_2{H}_4\right]=4({\nu }_1+{\nu }_5+{\nu }_9+{\nu }_{11})+2({\nu }_2+{\nu }_3+{\nu }_6+{\nu }_{12})+{\nu }_4+{\nu }_7+{\nu }_8+{\nu }_{10}$. A new quadratic resonance criterion $X_j=|V_j^2/\left({\sum }_k(n_k-m_k){\omega }_k\right)|$ is proposed and its efficiency in elucidating polyad structures is demonstrated. A striking observation was made that CVPT(2) often produces better predictions of fundamental frequencies (e.g., RMSD for C₂H₄ fundamentals is 2.7 cm⁻¹, and for C₂D₄ is 1.9 cm⁻¹), while CVPT(4) demonstrates an excellent level of correlation with A-VCI results for both fundamentals and two-quanta states.