Modeling L2,3-edge X-ray absorption spectroscopy with linear response exact two-component relativistic time-dependent density functional theory

Abstract

X-ray absorption spectroscopy (XAS) is a powerful tool that can provide physical insights into element-specific chemical processes and reactivities. Although relativistic time-dependent density functional theory (TDDFT) has been previously applied to model the L-edge region in XAS, there has not been a more comprehensive study of the choices of basis sets and density functional kernels available for variational relativistic excited state methods. In this work, we introduce the implementation of the generalized preconditioned locally harmonic residual algorithm to solve the complex-valued relativistic TDDFT for modeling the L-edge X-ray absorption spectra. We investigate the L2,3-edge spectra of a series of molecular complexes using relativistic linear response TDDFT with a hybrid iterative diagonalization algorithm. A systematic error analysis was carried out with a focus on the energetics, intensities, and magnitude of L2–L3 splitting compared to experiments. Additionally, the results from relativistic TDDFT calculations are compared to those computed using other theoretical methods, and the multideterminantal effects on the L-edge XAS were investigated.

Natural transition orbitals for complex two‐component excited state calculations

“…The two‐component generalized NTOs was implemented in a locally modified version of the development version of Gaussian and applied to some small molecular clusters using the X2C‐TDDFT method . Once orbitals are obtained, a further complication associated with the two‐component, complex orbitals encountered in both relativistic and nonrelativistic two‐component theories is the need to reduce the dimensionality for visualization since the orbitals may include both α and β spin components.…”

“…The construction and visualization of NTOs is most useful in molecular species, where more complicated combinations of orbitals are present. One practical example of the use of two‐component relativistic TDDFT is in the calculation of L‐edge X‐ray spectra . Due to the presence of spin‐orbit coupling in the 2 p manifold, the main features in the X‐ray absorption near‐edge structure (XANES) region are split into two groups known as L 2 and L 3 .…”

Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory

“… 59 , 60 Applications of relativistic LR-TDDFT with variational SO interactions and focused on XAS have been reported at the level of the two-component zeroth-order regular approximation (ZORA) Hamiltonian 61 as well as the X2C Hamiltonian. 62 …”

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

“…variational SO interaction includes absorption spectra in valence [32][33][34] and X-ray regions 19 , excited-state zero-field splittings, 27 and phosphorescence lifetimes [35][36][37] .…”

“…[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.…”