The available quantitatively reliable methods require higher computational costs than the DFT method [18]. Although quantum see more Monte Carlo methods [19–23] can be applied to molecular and crystal systems and show good quantitative reliability where extremely high-accuracy calculations are required, difficulties

in calculating forces for optimizing atomic configurations are a considerable disadvantage and inhibit this method from becoming a standard molecular dynamics calculation technique. Configuration interaction (CI), coupled cluster, and Møller-Plesset second-order perturbation methods, each of which use a linear combination of orthogonalized Slater determinants (SDs) as many-electron wave functions, are standard

computational techniques in quantum chemistry by which highly accurate results are obtained [24], despite suffering from basis set superposition and basis set incompleteness errors. The full CI calculation can perform an exact electron–electron correlation energy calculation in a space given by an arbitrary basis set. However, it is only applicable for small Ro 61-8048 mw molecules with modest basis sets PSI-7977 since the required number of SDs grows explosively on the order of the factorial of the number of basis. The required number of SDs in order to determine ground-state energies can be drastically decreased by employing nonorthogonal SDs as a basis set. The resonating Hartree-Fock method proposed by Fukutome utilizes nonorthogonal SDs, and many noteworthy results have been reported [25–30]. Also, Imada and co-workers [31–33]

and Kojo and Hirose [34, 35] employed nonorthogonal SDs in path integral renormalization group calculations. Goto and co-workers developed the direct energy minimization method using nonorthogonal SDs [36–39] based on the real-space finite-difference formalism [40, 41]. In these previous studies, steepest descent directions and acceleration parameters are calculated to update one-electron wave functions on the basis Rolziracetam of a variational principle [25–30, 36–39]. Although the steepest descent direction guarantees a secure approach to the ground state, a more effective updating process might be performed in a multi-direction search. In the present study, a calculation algorithm showing an arbitrary set of linearly independent correction vectors is employed to optimize one-electron wave functions with Gaussian basis sets. Since the dimension of the search space depends on the number of linearly independent correction vectors, a sufficient number of correction vectors ensure effective optimization, and the iterative updating of all the one-electron wave functions leads to smooth convergence to the ground states.