Simultaneous optimization of exponents, centers of Gaussian-type basis functions, and geometry with full-configuration interaction wave function: Application to the ground and excited states of hydrogen molecule

We have extended the fully variational molecular orbital (FVMO) method to the full-configuration interaction (CI) wave function (full-CI FVMO). All variational parameters in the full-CI scheme, i.e., exponents and centers in Gaussian-type function (GTF) basis set, and nuclear positions, as well as the CI coefficients, are simultaneously optimized by using their analytical gradients. We have applied the full-CI FVMO method to the ground and electronic excited states of hydrogen molecule. In the ground state, the total energy $(−1.174 015$ hartree) and the internuclear distance (1.4016 bohr) obtained by the full-CI FVMO calculation with $[8s4p2d]$ GTFs agree very well with the high-level calculation by the 249 term expansion in elliptic coordinates $(−1.174 476$ hartree and 1.4010 bohr, respectively). The excitation energies to the $Σu+1,$ $Πu1,$ $Σg+3,$ and $Πu3$ Rydberg states calculated by the full-CI FVMO method with $[8s4p2d]$ GTFs coincide with the experimental values within 52 $cm−1.$ The present result can not be obtained with the conventional basis set approach because of the fact that our full-CI FVMO calculation gives an extremely accurate wave function with a relatively small number of basis functions owing to the extension of flexibility in the variational space.