On the effectiveness of CCSD(T) complete basis set extrapolations for atomization energies

Abstract

The leading cause of error in standard coupled cluster theory calculations of thermodynamic properties such as atomization energies and heats of formation originates with the truncation of the one-particle basis set expansion. Unfortunately, the use of finite basis sets is currently a computational necessity. Even with basis sets of quadruple zeta quality, errors can easily exceed 8 kcal/mol in small molecules, rendering the results of little practical use. Attempts to address this serious problem have led to a wide variety of proposals for simple complete basis set extrapolation formulas that exploit the regularity in the correlation consistent sequence of basis sets. This study explores the effectiveness of six formulas for reproducing the complete basis set limit. The W4 approach was also examined, although in lesser detail. Reference atomization energies were obtained from standard coupled-cluster singles, doubles, and perturbative triples (CCSD(T)) calculations involving basis sets of 6ζ or better quality for a collection of 141 molecules. In addition, a subset of 51 atomization energies was treated with explicitly correlated CCSD(T)-F12b calculations and very large basis sets. Of the formulas considered, all proved reliable at reducing the one-particle expansion error. Even the least effective formulas cut the error in the raw values by more than half, a feat requiring a much larger basis set without the aid of extrapolation. The most effective formulas cut the mean absolute deviation by a further factor of two. Careful examination of the complete body of statistics failed to reveal a single choice that out performed the others for all basis set combinations and all classes of molecules.

Wave Function and Density Functional Theory Studies of Dihydrogen Complexes

“…The results show that, as it may be expected, QCISD(T) calculations are very close to CCSD(T) ones, with average differences of the order of 0.06 kcal/mol. This error is close to the expected accuracy of CCSD(T) calculations [8,103,110]. Thus, the two methods can be considered equally accurate from the practical point of view.…”

“…Such energies can be considered accurate within 1% or ∼0.05 kcal/mol with respect to the true CBS limit [101][102][103] All DFT calculations were performed using the def2-TZVPP basis set [104,105]. The choice of this basis set was dictated by the fact that we wanted to test DFT methods in conditions resembling those used in real applications, where usually very large basis sets are not employed.…”

Gaussian basis sets for molecular applications

“…A review of extrapolation procedures is beyond the scope of the current work, and interested readers are referred to Ref. [37] and references therein.…”

Communication: Convergence of anharmonic infrared intensities of hydrogen fluoride in traditional and explicitly correlated coupled cluster calculations

“…[1][2][3][4][5][6] On the other hand, it has been observed that molecular properties, such as infrared vibrational frequencies and dipole moments, do not necessarily converge smoothly in traditional calculations. [7][8][9][10] The basis set convergence of properties is especially poor in non-augmented cc-p(C)VXZ basis sets.…”