Four-component relativistic time-dependent density-functional theory using a stable noncollinear DFT ansatz applicable to both closed- and open-shell systems

Abstract

We present a formulation of relativistic linear response time-dependent density functional theory for calculation of electronic excitation energies in the framework of the four-component Dirac-Coulomb Hamiltonian. This approach is based on the noncollinear ansatz originally developed by Scalmani and Frisch [J. Chem. Theory Comp. 8, 2193 (2012)], and improves upon past treatment of the limit cases in which the spin density approaches zero. As a result of these improvements, the presented approach is capable of treating both closed-and open-shell reference states. Robust convergence of the Davidson-Olsen eigenproblem algorithm for open-shell reference states was achieved through the use of a solver which considers both left and right eigenvectors. The applicability of the present methodology on both closed-and open-shell reference states is demonstrated on calculations of low-lying excitation energies for Group 3 atomic systems (Sc 3+-Ac 3+) with non-degenerate ground states, as well as for Group 11 atomic systems (Cu-Rg) and octahedral actinide complexes (PaCl 2− 6 , UCl − 6 , and NpF 6) with effective doublet ground states. Major developments in the field of relativistic LR-TDDFT methods featuring variational inclusion of SOC began with the independent works of Gao et al. 29 in the four-component framework, and Wang and Ziegler 30 in the two-component framework. Both works combine noncollinear DFT theory with the ALDA approximation.

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

“…We have presented a detailed derivation and implementation of relativistic four-component Combined with our earlier work, 17,52 the ReSpect program now possesses three distinct TDDFT approaches (real-time TDDFT, response eigenvalue equation and damped…”

“…(M = Fe, Ru, Os) calculating their polarizabilities, electron absorption, electronic circular dichroism (ECD) and optical rotatory dispersion (ORD) spectra, the latter two constituting the first 4c relativistic linear damped response ECD and ORD spectra presented in the literature. Together with developments described in earlier works 17,52 it endows our program package ReSpect 58 with all three TDDFT approaches outlined above. Therefore, the users may choose the most suitable method for the chemical problem at hand within a single program.…”

“…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.…”

“…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. 31 The scope of applications of relativistic linear response TDDFT with 2 This is the author's peer reviewed, accepted manuscript.…”