To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning's hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to improvements comparable to or even better than those obtained by increasing the cardinal number in the used basis set by one. However, BSE alone is insufficient to improve agreement with experiment, even after additional consideration of inner-shell correlation and quadruple-excitation effects (mean error and standard deviation with extrapolation are -0.014 and 0.047 pm in comparison with mean error and standard deviation of -0.002 and 0.036 pm without extrapolation). Improvement is obtained only when other contributions of similar magnitude as the BSE contributions (e.g., pentuple-excitation effects and relativistic effects) are also considered. A rather large discrepancy (of the order of a few tenths of a picometer) is observed for the F(2) molecule indicating an enhanced basis-set requirement for the various contributions in this case.

No abstract

A statistical analysis of the accuracy of theoretically predicted rotational constants is presented based on the data for a total of 16 molecules and 97 isotopologues. Special focus is given on the treatment of electron correlation by using coupled-cluster methods up to quadruple excitations, core correlation, basis-set effects, zero-point vibrational corrections, and the electronic contribution to the rotational constants. The high accuracy achieved in the present investigation is demonstrated by the fact that at our best theoretical level, termed as CCSD(T)cc-pV infinity Z+Delta core+DeltaT+DeltaQ+DeltaB vib+DeltaB el, the mean absolute error is 0.04% and the standard deviation is 0.07% in comparison with the available experimental data. The importance of higher excitations, core correlation, and zero-point vibrational effects is emphasized, while the electronic contribution is found to be less important.

Benchmark, frozen-core CCSD(T) equilibrium harmonic vibrational frequencies of 12 closed-shell and five open-shell molecules are computed to within 1 cm-1 of the basis set limit using the explicitly correlated CCSD(T)-R12 method. The convergence of the standard CCSD(T) method with the one-particle basis sets of Dunning and co-workers is examined and found to be slow, with mean and maximum absolute errors of 1.3 and 3.5 cm-1 remaining at the cc-pV6Z level. Finite basis set effects do not appear to introduce systematic errors in equilibrium harmonic frequencies, and mean absolute errors reduce by a factor of 2 for each basis set cardinal number increment. The convergence of individual equilibrium harmonic frequencies is not guaranteed to be monotonic due to the associated shift in the equilibrium structure. The inclusion of computed scalar relativistic effects and previously available corrections for core-valence correlation and higher-order excitations in the cluster operator results in an agreement with experimentally derived harmonic frequencies of 0.1, 0.3, and -0.4 cm-1 for HF, N2, and CO, respectively. F2 continues to present a challenge to computational chemistry with an error of 3.2 cm-1, primarily resulting from the high basis set dependence of the quadruples contribution.

A spin-adapted coupled-cluster (SA-CC) scheme based on the additional consideration of spin constraints is proposed for the quantum chemical treatment of high-spin open-shell cases. Its computational feasibility is demonstrated via a pilot implementation within the singles and doubles approximation. Test calculations indicate that the suggested SA-CC scheme provides results of similar accuracy as the more traditional schemes without spin adaptation.