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. As a result, the RDIIS stably and efficiently performs the SCF convergence acceleration. Furthermore, the RDIIS is considerably independent on the subspace size with the concentrated linear coefficients accounting proportionally for the Fock matrices close to the current iteration.

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. Consequently, as the upcoming errors can be introduced and circumvented with the search in the higher-order residual, a concomitant improved performance in terms of number of iterations, convergence rate, and total elapsed time is very significant. The correlation energy components obtained with the original residual are corrected with the higher-order residual application, satisfying the correlation virial theorem with much improved accuracy. The comparison with the original residual, the higher-order residual significantly improves the electron binding, favoring the localization of electrons' distribution, revealed with the increasing peak of the distribution and correlation function and the reduced interelectron distance and its angle.

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. Dependent on both the barrier width/height and the bound strength of the ground state electron, the calculated tunneling lifetime under a static electric field spans from femtosecond level to picosecond level, consistent with the attosecond-level results in experiments using a time-dependent external field.