Deciphering the interplay of different electronic and vibrational structure theory parameters for the computation of anharmonic molecular vibrations

Computation of accurate yet efficient quantum anharmonic spectra is a major challenge, particularly for large molecules where it significantly relies on the careful choice of different parameters. This study systematically assesses the accuracies of the anharmonic potential energy surfaces attained from the interplay of four crucial parameters, controlled by electronic and vibrational structure theories. Each pivotal parameter is further classified into three hierarchical levels. From wave function-based quantum chemical methods (M), HF, MP2 and CCSD(T) were chosen along with cc-pVDZ, cc-pVTZ, and cc-pVQZ electronic basis sets (B) from electronic structure theories. Furthermore, from the vibrational structural theory, the order of coupling (C) up to third order (<i>i.e.</i>, 1-, 2- and 3-mode) along with 8, 12 and 16 grid points (G) per normal mode are examined. A structured amalgam across each level for all four parameters results in 81 possible combinations, which are systematically analysed in the framework of the vibrational self-consistent field method and its second-order perturbation corrections variant along with the vibrational configurational interaction method. For each parameter, inner benchmarking is carried out to assess the extents of red/blue shifts in peak positions as each parameter moves from its lower to higher level. Furthermore, internal benchmarking is conducted with respect to the highest combination, as a reference framework. Subsequently, a statistical error analysis for a set of small molecules (18 vibrational modes) against the highest combination is performed and the experimental data are analysed for fundamentals, excited states and intensities. This quantitative study shows that typically a combination of CCSD(T)/cc-pVTZ along with 2-mode coupling and 12 grids per normal mode, provides converged results for fundamentals with mean absolute deviation ∼7-13 cm^-1 and ∼11-15 cm^-1 with respect to the largest combination and experiment, respectively, and is more than 99% hardware efficient for small to medium-sized molecules. For larger systems, similar combinations with the MP2 method are a more realistic choice for efficient balance between accuracy and CPU time. To further validate the inferences, an extended error analysis for 45 vibrational modes is also carried out for a few selected combinations, yielding similar results. The impact and the convergence pattern across each level of all four parameters typically adhere to the sequence: M ⋙ C ≫ B > G.