General Linear-Expansion Shooting Techniques Based on Minimization of Intra-Iteration Errors

Preceded by our previous papers on linear-expansion shooting techniquesLinear-expansion shooting techniques (LIST) (LIST) [Y. A. Wang, C. Y. Yam, Y. K. Chen, and G. H. Chen, J. Chem. Phys. 134, 241103 (2011); Y. K. Chen and Y. A. Wang, J. Chem. Theory Comput. 7, 3045–3048 (2011)] in which the direct approaches (LISTdLISTd and LISTbLISTb) and the indirect approach (LISTiLISTi) were proposed to accelerate the self-consistent field (SCF) convergenceSCF convergence, we have developed a series of new LISTLinear-expansion shooting techniques (LIST) methods (including LISTrLISTr, fDIISFDIIS, and LISTfLISTf) based on minimization of intra-iterationIntra-iteration errors. These new LISTLinear-expansion shooting techniques (LIST) methods are competitive and often superior to the existing LISTiLISTi and LISTbLISTb methods. Furthermore, based on a minimal error sampling algorithm (MESA)Minimal error sampling algorithm (MESA), a variable length scheme (VLS)Variable length scheme (VLS), and the technique of alleviation of linear dependence in asymmetric system via transposition (ALDAST)Alleviation of linear dependence in asymmetric system via transposition (ALDAST), a combination of these LISTLinear-expansion shooting techniques (LIST) methods together with Pulay’s direct inversion in the iterative subspace (DIIS)Direct inversion in the iterative subspace (DIIS)  method significantly decrease the number of SCF iterationsSCF iteration necessary to reach SCF convergenceSCF convergence for virtually all systems we have studied, with only a trivial increase in computational cost.