Orbital-based direct inversion in the iterative subspace for the generalized valence bond method

We present an algorithm that is a new combination of the direct inversion in the iterative subspace (DIIS) and the generalized valence bond (GVB) methods. The proposed algorithm is based on applying the DIIS directly to the orbitals updated via the GVB scheme as opposed to the conventional approach of applying DIIS to a series of composite Fock matrices (CFMs). The new method results in GVB convergence in situations where the CFM-based GVB-DIIS cannot be applied at all, e.g., when the original GVB method diverges. When both the new and the conventional methods converge, the former achieves the same reduction in the number of self-consistent field (SCF) iterations as the latter, but using considerably less storage and DIIS-related CPU time. Also, the orbital-based GVB-DIIS is less sensitive to the proximity of an initial guess to the exact wave function, and it does not depend on empirical criteria used in the CFM-based GVB-DIIS. Finally, the orbital-based DIIS formulation is not limited to GVB; it can be easily incorporated into any SCF approach that involves an iterative updating of the orbitals, such as, e.g., multiconfiguration SCF or Kohn-Sham density-functional theory.