The calculation of molecular geometrical properties in the Hellmann—Feynman approximation

Abstract

The ab initio calculation of molecular geometrical properties in the Hellmann—Feynman approximation is discussed in which the atomic orbitals are fixed at the positions of the nuclei at the reference geometry, thereby avoiding the calculation of derivatives of the molecular integrals with respect to the positions of the atomic orbitals. For the molecular gradient, the molecular Hessian, and the molecular dipole gradient, the convergence of the calculated properties is studied for a large number of basis sets at the Hartree—Fock level and at the CCSD(T)-R12 level. In the Hellmann—Feynman approximation, it is found to be necessary to impose explicitly rotational and translational invariance. Although small basis sets perform poorly in the Hellmann—Feynman approximation (compared with the standard approach where the atomic orbitals are moving with the displaced nuclei), satisfactory convergence is obtained for geometries and harmonic frequencies (to within 1% of the standard approximation) with the larger of the correlation-consistent core—valence cc-pCVXZ basis sets. For the infrared intensities, the agreement with the standard approach is still poor (only within 15% for the largest correlation-consistent basis). The best results are obtained with an R12 basis previously developed for the calculation of energies in the explicitly correlated R12 approximation. In this basis, the geometrical parameters and harmonic frequencies are within 0.5% of the standard approach and the infrared intensities within 5%, suggesting that the Hellmann—Feynman approximation may be useful for applications at the highly accurate MP2-R12, CCSD-R12, and CCSD(T)-R12 levels of theory.