Communications: Intramolecular basis set superposition error as a measure of basis set incompleteness: Can one reach the basis set limit without extrapolation?

Abstract

One of only two error sources in the solution of the electronic Schrodinger equation is addressed: The basis set convergence (incompleteness) error (BSIE). The results of ab initio (first principles) correlated methods, for which the Moller-Plesset second order perturbation theory (MP2) was chosen as an example, were extrapolated to the complete basis set (CBS) limit using a Dunning-type basis set series. Basis sets as large as cc-pV5Z and cc-pV6Z were used. A representative molecular set that included nitrogen (N(2)), acetylene (C(2)H(2)), ethylene (C(2)H(4)), carbon dioxide (CO(2)), water (H(2)O), ammonia (NH(3)), hydrogen cyanide (HCN), and ethanol (C(2)H(5)OH) molecules was used for the calculations. The intramolecular basis set superposition error (BSSE) was found to be correlated with BSIE, meaning that intramolecular BSSE can be used as a measure of basis set incompleteness. The BSIE dependence on BSSE could be qualitatively approximated (+/-25%) by a power-law dependence: BSIE = AxBSSE(p), where log(10)(A) = 1.45+/-0.21 and p = 1.27+/-0.09. This leads to the fact that CBS values at the MP2 theory level can be obtained using only one energy value and the corresponding intermolecular BSSE. The same power-law dependence was confirmed for all of the molecular systems studied. The universality of the BSIE versus BSSE dependence presented was checked using Pople-type basis sets. Even the results obtained with 6-311G, 6-311G(**), and 6-311G(2df,2pd) basis sets were found to be nicely described by the same (universal) power law. Benchmark studies of nitrogen and acetylene contraction (compaction) showed that BSIE can be decreased by up to 83% (at the cc-pVTZ level) using the CBS-BSSE strategy described. The presented BSIE versus BSSE dependence can greatly aid in obtaining CBS results for large molecular systems of chemical or biological interest.