Convergence Acceleration Techniques for Non-Hermitian SCF Problems

摘要

Conventional convergence acceleration techniques for the SCF procedure like the direct inversion in the iterative subspace and the level-shifting can not be applied in the general case of non-Hermitian Fock operators. The commutator of the Fock matrix and the density matrix do not vanish upon convergence of non-Hermitian SCF equations and hence the usual error vector choice is not applicable. In this work we describe in detail the implementation of these convergence acceleration techniques for the non-Hermitian case. We focus in particular in the solution of the CHA-SCF equations (arising from the application of the chemical Hamiltonian approach at the Hartree-Fock level of theory), but it can be generalized to any non-Hermitian SCF problem. It is shown that a general commutation relationship combining the right and left eigenvectors of the Fock matrix is appropriate as error vector. In a similar fashion, level-shifting techniques of the virtual orbitals can be easily implemented as well.