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

The ab initio calculation of molecular geometrical properties in the Hellma nn-Feynman approximation is discussed in which the atomic orbitals are fixe d at the positions of the nuclei at the reference geometry, thereby avoidin g the calculation of derivatives of the molecular integrals with respect to the positions of the atomic orbitals. For the molecular gradient, the mole cular Hessian, and the molecular dipole gradient, the convergence of the ca lculated properties is studied for a large number of basis sets at the Hart ree-Fock level and at the CCSD(T)-R12 level. In the Hellmann-Feynman approx imation, it is found to be necessary to impose explicitly rotational and tr anslational invariance. Although small basis sets perform poorly in the Hel lmann-Feynman approximation (compared with the standard approach where the atomic orbitals are moving with the displaced nuclei), satisfactory converg ence is obtained for geometries and harmonic frequencies (to within 1% of t he standard approximation) with the larger of the correlation-consistent co re-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 ba sis 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 infr ared intensities within 5%, suggesting that the Hellmann-Feynman approximat ion may be useful for applications at the highly accurate MP2-R12, CCSD-R12 , and CCSD(T)-R12 levels of theory.