Orbital exponent optimization for molecular self-consistent-field wave functions including the polarization function

We have applied the analytical energy gradient method with respect to the orbital exponents for molecular self-consistent-field wave functions including the polarization functions. The gradients for Gaussian-type functions in Huzinaga–Dunning's double zeta basis set with and without polarization functions were compared for some hydrides of the first-row elements. The changes in the gradients caused by the polarization functions were observed. It was found that the polarization functions on hydrogen play a role in reducing the gradients produced in the absence of these functions. Although optimization of the exponents gives results depending on the molecules, the total energies as well as the dipole moments are insensitive to the exponent values. We could confirm that the exponents for Gaussian functions in the standard double zeta plus polarization basis set work adequately by coupling with the variational parameters for the simple hydrides even if they have gradients in the molecules. Keywords: orbital exponent, Gaussian-type functions, analytical energy gradient, molecular SCF wave function, polarization function.