Orbital exponent optimization with the analytical gradient method for molecular self-consistent-field wave functions

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Abstract
We have applied the energy gradient technique to optimize the orbital exponents of primitive Gaussian-type functions for some simple molecules including first-row elements, starting from the exponent values of the Huzinaga–Dunning basis functions. It is found that the change of the exponents clearly shows the better description of chemical bonds compared to the atomic exponents, while the energy gain due to the exponent optimization is very small. We can, however, confirm that the values of the orbital exponents optimized in atoms give extremely good description of the molecular wave functions. The scaling factor for a hydrogen atom in a molecular environment and the effect of the polarization functions for a hydrogen atom are also discussed.