Enthalpy difference between conformations of normal alkanes: effects of basis set and chain length on intramolecular basis set superposition error

Abstract

The quantum chemistry of conformation equilibrium is a field where great accuracy (better than 100 cal mol⁻¹) is needed because the energy difference between molecular conformers rarely exceeds 1000–3000 cal mol⁻¹. The conformation equilibrium of straight-chain (normal) alkanes is of particular interest and importance for modern chemistry. In this paper, an extra error source for high-quality ab initio (first principles) and DFT calculations of the conformation equilibrium of normal alkanes, namely the intramolecular basis set superposition error (BSSE), is discussed. In contrast to out-of-plane vibrations in benzene molecules, diffuse functions on carbon and hydrogen atoms were found to greatly reduce the relative BSSE of n-alkanes. The corrections due to the intramolecular BSSE were found to be almost identical for the MP2, MP4, and CCSD(T) levels of theory. Their cancelation is expected when CCSD(T)/CBS (CBS, complete basis set) energies are evaluated by addition schemes. For larger normal alkanes (N > 12), the magnitude of the BSSE correction was found to be up to three times larger than the relative stability of the conformer; in this case, the basis set superposition error led to a two orders of magnitude difference in conformer abundance. No error cancelation due to the basis set superposition was found. A comparison with amino acid, peptide, and protein data was provided.

Keywords:

• basis set superposition error (BSSE)
• normal alkane (n-alkane)
• intermolecular interactions (van der Waals forces)
• stereochemistry
• counterpoise
• binding energies

Acknowledgements

E. Lomakina is acknowledged for her help with manuscript preparation. I. Samoilenko is acknowledged for his computational assistance (software and hardware). This study was partly supported by a special grant from the Ministry of Defense of the Russian Federation.