Accurate and efficient calculation of excited vibrational states from quartic potential energy surfaces

Abstract

Vibrational anharmonicity and resonances frequently complicate assignment of vibrational spectra. In order to analyse such spectra, these effects can be calculated from ab initio quartic potential energy surfaces (PESs) using second-order vibrational theory with resonances (VPT2 + K). This study compares the accuracies of using the cc-pVTZ basis set, the aug-cc-pVQZ basis set, and a hybrid approach that uses the cc-pVTZ basis set for the equilibrium geometry and quadratic force constants and the aug-cc-pVQZ basis set for the cubic and quartic force constants. Quartic PESs are computed using these basis sets for H₂O, H₂CO, HFCO, SCCl₂, and their deuterated analogs with the CCSD(T) method. The computed PESs are assessed by comparing experimentally determined and theoretically calculated spectroscopic constants. The average absolute difference (⟨|error|⟩) between theoretical and experimental zero-point energy-corrected harmonic frequencies () decreases by 54.7% when the hybrid approach is used instead of the cc-pVTZ basis, but decreases by only an additional 2.3% when the aug-cc-pVQZ basis is used. The computed PESs are also assessed by comparing predicted and observed vibrational energy states. The weighted average root-mean-square (RMS) difference between predicted and observed vibrational energy levels decreases by 42.3% when the hybrid approach is used instead of cc-pVTZ, but decreases by only an additional 4.0% when aug-cc-pVQZ is used. These results demonstrate that calculations performed using the hybrid basis set approach, which have a substantially lower computational cost, are comparable in accuracy to those performed using the aug-cc-pVQZ basis set.

Keywords:

• vibrational
• anharmonic
• resonances
• quartic
• spectroscopy

Acknowledgements

The authors are indebted to Professor Peter R. Taylor for the inspiration and guidance he has provided to the field of accurate chemical computation and specifically for his suggestion of using a hybrid basis set to improve computational efficiency and his advocacy of computer clusters for performing scientific calculations. We wish to thank Kristin K. Ellsworth for her insightful analysis of H₂CO, HDCO, and D₂CO spectra. We also thank Michael L. Poublon for maintenance of the Hope College computer clusters, on which all computations mentioned in this work were performed. This work was supported by the Arnold and Mabel Beckman Foundation, the Dreyfus Foundation, and National Science Foundation grants CHE-0520704 and CHE-0624602.