An improved DIIS method using a versatile residual matrix to accelerate SCF starting from a crude guess.

The minimization of the commutator of the Fock and density matrices as the error matrix in the direct inversion of the iterative subspace (CDIIS) developed by Pulay is a powerful self-consistent field (SCF) acceleration technique for the construction of optimum Fock matrix, if initiated with a fair initial guess. In this work, we present an alternative minimized error matrix to the commutator in the CDIIS, namely the residual or the gradient of the energy-functional for a Slater determinant subject to the orthonormality constraints among orbitals, representing the search for a newly improved Fock matrix in the direction of the residual in the direct inversion of the iterative subspace (RDIIS). Implemented in the computational chemistry package GAMESS, the RDIIS is compared with the standard CDIIS and the second order SCF orbital optimization (SOSCF) for tested molecules started with a crude guess.

Higher-order Rayleigh-quotient gradient effect on electron correlations.

The incomplete understanding of electron correlation is still profound due to the lack of exact solutions of the Schrödinger equation of many electron systems. In this work, we present the correlation-induced changes in the calculated many-electron systems beyond the standard residual. To locate the minimum of the Rayleigh quotient, each iteration is to seek the lowest eigenpairs in a subspace spanned by the current wave function and its gradient of the Rayleigh-quotient as well as the upcoming higher-order residual.

Tunneling lifetimes of electrons escaping from atoms under a static electric field.

The tunneling lifetime of an electron escaping from an atom is calculated using a projected Green's function method, combining with the radial potential of the atom which is obtained from density functional theory. Results of the calculated electron tunneling lifetimes in model systems such as a quantum dot are shown to be comparable with other theoretical studies. For the first time, we have obtained the tunneling lifetimes of electrons escaping from a series of atoms (He, Ne, Ar, Kr, H, Li, Na, K) under a static electric field.