iVI-TD-DFT: An iterative vector interaction method for exterior/interior roots of TD-DFT

Abstract

The recently proposed iterative vector interaction (iVI) method for large Hermitian eigenvalue problems (Huang et al., J. Comput. Chem. 2017, 38, 2481) is extended to generalized eigenvalue problems, HC = SCE, with the metric S being either positive definite or not. Although, it works with a fixed-dimensional search subspace, iVI can converge quickly and monotonically from above to the exact exterior/interior roots. The algorithms are further specialized to nonrelativistic and relativistic time-dependent density functional theories (TD-DFT) by taking the orbital Hessian as the metric (i.e., the inverse TD-DFT eigenvalue problem) and incorporating explicitly the paired structure into the trial vectors. The efficacy of iVI-TD-DFT is demonstrated by various examples. © 2018 Wiley Periodicals, Inc.