Ab Initio Wavenumber Accurate Spectroscopy: ¹CH₂ and HCN Vibrational Levels on Automatically Generated IMLS Potential Energy Surfaces


We report here calculated J = 0 vibrational frequencies for ¹CH₂ and HCN with root-mean-square error relative to available measurements of 2.0 cm-1 and 3.2 cm-1, respectively. These results are obtained with DVR calculations with a dense grid on ab initio potential energy surfaces (PESs). The ab initio electronic structure calculations employed are Davidson-corrected MRCI calculations with double-, triple-, and quadruple-ζ basis sets extrapolated to the complete basis set (CBS) limit. In the ¹CH₂ case, Full CI tests of the Davidson correction at small basis set levels lead to a scaling of the correction with the bend angle that can be profitably applied at the CBS limit. Core-valence corrections are added derived from CCSD(T) calculations with and without frozen cores. Relativistic and non-Born−Oppenheimer corrections are available for HCN and were applied. CBS limit CCSD(T) and CASPT2 calculations with the same basis sets were also tried for HCN. The CCSD(T) results are noticeably less accurate than the MRCI results while the CASPT2 results are much poorer. The PESs were generated automatically using the local interpolative moving least-squares method (L-IMLS). A general triatomic code is described where the L-IMLS method is interfaced with several common electronic structure packages. All PESs were computed with this code running in parallel on eight processors. The L-IMLS method provides global and local fitting error measures important in automatically growing the PES from initial ab initio seed points. The reliability of this approach was tested for ¹CH₂ by comparing DVR-calculated vibrational levels on an L-IMLS ab initio surface with levels generated by an explicit ab initio calculation at each DVR grid point. For all levels (200) below 20 000 cm-1, the mean unsigned difference between the levels of these two calculations was 0.1 cm-1, consistent with the L-IMLS estimated mean unsigned fitting error of 0.3 cm-1. All L-IMLS PESs used in this work have comparable mean unsigned fitting errors, implying that fitting errors have a negligible role in the final errors of the computed vibrational levels with experiment. Less than 500 ab initio calculations of the energy and gradients are required to achieve this level of accuracy.



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