Adaptive Regularized Self-Consistent Field Iteration with Exact Hessian for Electronic Structure Calculation

The self-consistent field (SCF) iteration has been used ubiquitously for solving the Kohn-Sham (KS) equation or the minimization of the KS total energy functional with respect to orthogonality constraints in electronic structure calculations. Although SCF with heuristics such as charge mixing often works remarkably well on many problems, it is well known that its convergence can be unpredictable and there is no general theoretical analysis on their performance. We regularize the SCF iteration and establish rigorous global convergence to the first-order optimality conditions. The Hessian of the total energy functional is further exploited. By adding the part of the Hessian which is not considered in SCF, our methods can always achieve a high accurate solution on problems for which SCF fails and even exhibit quadratic or superlinear convergence on most test problems in the KSSOLV toolbox under the Matlab environment.