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 fixeddimensional 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.

$\mathbb{i}$CAS: Imposed Automatic Selection and Localization of Complete Active Spaces

“…(3) The CAS can be maintained the same for all geometries, which is of vital importance for the scanning of potential energy surfaces. (4) Further combined with the iterative vector interaction (iVI) approach 89,90 for directly accessing interior roots of the CI eigenvalue problem, the CASSCF calculation can be dictated to converge to a predesignated chare/spin configuration composed of some special motifs (e.g., metal valence d/f orbitals, atomic core orbitals or aromatic rings), a point that is to be investigated in future though.…”

SOiCI and iCISO: Combining iterative configuration interaction with spin-orbit coupling in two ways

“…The above ranking procedure expands the reference P 0 to P 1 , which is diagonalized by the iterative vector interaction (iVI) approach [147,148]. Those CSFs of coefficients smaller in absolute value than C min are then pruned away, leading to P. The procedure is iterated until P and P 0 are sufficiently similar in compositions.…”

Relativistic four-component linear damped response TDDFT for electronic absorption and circular dichroism calculations

“…The frequency-dependent susceptibility is real or complex, depending on whether the solutions of standard (γ = 0) or damped response equation (Eqs. (17) and (16), respectively) were used in Eq. (34).…”

“…The popularity of this approach for a wide range of systems is also due to efficient algorithms available for solving this equation. [12][13][14][15][16][17] However, since eigenvalue calculations normally proceed from the lowest excitation energy and the computational cost increases with the number of eigenvalues, its applications in high-frequency spectral regions and regions with high density-of-states remain challenging and require a development of special techniques. 15,16,18,19 Moreover, due to its perturbative nature, the response eigenvalue equation requires the evaluation of the derivatives of DFT exchangecorrelation potentials (so-called kernels) that must be formulated carefully, particularly in relativistic multi-component theories with spin-orbit coupling.…”

“…[12][13][14][15][16][17] However, since eigenvalue calculations normally proceed from the lowest excitation energy and the computational cost increases with the number of eigenvalues, its applications in high-frequency spectral regions and regions with high density-of-states remain challenging and require a development of special techniques. 15,16,18,19 Moreover, due to its perturbative nature, the response eigenvalue equation requires the evaluation of the derivatives of DFT exchangecorrelation potentials (so-called kernels) that must be formulated carefully, particularly in relativistic multi-component theories with spin-orbit coupling. 17,[20][21][22] Relativistic implementations of the response eigenvalue equations have been reported at the 4c level of theory for closed-shell 20,23,24 as well as open-shell systems 17 , X2C level of theory 22,[25][26][27] , scalar zerothorder regular approximation (ZORA) 28,29 and spin-orbit ZORA 30 , and recently reviewed by Liu and Xiao.…”