The effect of approximating some molecular integrals in coupled-cluster calculations: fundamental frequencies and rovibrational spectroscopic constants for isotopologues of cyclopropenylidene

Abstract

The effect of approximating the three- and four-virtual molecular orbital integrals in single and double coupled-cluster theory including a perturbational correction for connected triple excitations [CCSD(T)] is investigated for the calculation of higher-order properties, specifically the calculation of a molecular quartic force field and spectroscopic constants. The approach was proposed previously, but investigated for only second- and lower-order properties. It is shown that the conclusions reached previously are essentially unchanged on moving to higher-order properties. That is, approximating the selected integrals has essentially no effect on the accuracy of CCSD(T) calculations, and the error due to approximating integrals is much smaller than the residual error due to one-particle basis set deficiencies. The advantage of this approach is that it significantly reduces the amount of data needed to perform CCSD(T) calculations, thereby reducing computational requirements associated with input/output operations and message passing in massively parallel, distributed memory algorithms. These savings are particularly important for large basis set calculations where the reduction in data can be as high as three orders of magnitude for ∼1000 unoccupied molecular orbitals. The approach was tested by computing the quartic force field, vibrational frequencies, and spectroscopic constants of cyclopropenylidene and isotopologues. Comparison of our best results with available experimental data shows excellent agreement between theory and experiment. It is hoped that the theoretical spectroscopic data presented herein for cyclopropenylidene and isotopologues is useful in the interpretation of future laboratory experiments and astronomical observations.

Keywords:

• coupled-cluster theory
• approximate integrals
• cyclopropenylidene
• anharmonic analysis
• fundamental vibrational frequencies

Acknowledgements

This paper is dedicated to Professor Henry F. Schaefer, III in celebration of his 65th birthday, and in honor of his significant research accomplishments and service to the field of theoretical and computational chemistry over many years. In addition, TJL thanks Professor Schaefer for the guidance and tremendous help he has graciously given over the last 26 years. XH acknowledges the support by an appointment to the NASA Postdoctoral Program at the Ames Research Center, administered by Oak Ridge Associated Universities through a contract with NASA. Support from the Spitzer Space Telescope GO program (Cycle 4) is gratefully acknowledged. CED gratefully acknowledges support under NASA Contract #NNA04BC25C to ELORET Corporation. Professor Martin Head-Gordon is thanked for spirited and helpful discussions.