Convergence Acceleration Techniques for Non-Hermitian SCF Problems

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 nonHermitian 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. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem 109: 2564–2571, 2009