Simultaneous Optimization of GTF Exponents and Their Centers with Fully Variational Treatment of Hartree-Fock Molecular Orbital Calculation

摘要

We have proposed the fully variational molecular orbital (FVMO) method by which all parameters in the molecular orbitals are optimized under the variational principle. According to the fully variational treatment within the Hartree-Fock approximation, exponents and centers in the Gaussian-type function (GTF) basis set are determined simultaneously, as well as the linear combination of atomic orbital (LCAO) coefficients. The FVMO method gives the lowest energy under the variational principle, improves the flexibility of wave function drastically, and raises the ab initio (nonempirical) feature. In the calculation of the adiabatic potential for HeH~+, the electron movement for dissociation limitation is smoothly expressed due to full optimization of GTF centers and exponents under a condition that satisfies the Hellmann-Feynman and virial theorems. Properties such as dipole and polarizability of the hydrogen and helium atoms and the LiH molecule are in good agreement with the numerical Hartree-Fock values, even if only s type GTFs are used. We have also applied the FVMO method to H_2O and CH_4 molecules.