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

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.