Broadband X-Ray Absorption Spectra from Time-Dependent Kohn-Sham Calculations

Abstract

We present a protocol for calculation of K-edge x-ray absorption spectra using time-dependent Kohn-Sham (TDKS) calculations, also known as "real-time" time-dependent density functional theory (TDDFT). In principle, the entire absorption spectrum (at all wavelengths) can be computed via Fourier transform of the time-dependent dipole moment function, following a perturbation of the ground-state density and propagation of time-dependent Kohn-Sham molecular orbitals. In practice, very short time steps are required to obtain an accurate spectrum, which increases the cost, but the use of Pade approximants significantly reduces the length of time propagation that is required. Spectra that are well converged with respect to the corresponding linear-response (LR-)TDDFT result can be obtained with < 10 fs of propagation time. Use of complex absorbing potentials helps to remove artifacts at high energies that otherwise result from the use of a finite atom-centered Gaussian basis set. Benchmark results, comparing TDKS to LR-TDDFT, are presented for several small molecules at the carbon and oxygen K-edges, demonstrating good agreement with experiment without the need for specialized basis sets. Whereas LR-TDDFT is a reasonable approach to obtain the near-edge structure, that approach requires hundreds of states and quickly becomes cost prohibitive for large systems, even when the core\slash valence separation approximation is used to remove most of the occupied states from the excitation manifold. We demonstrate the cost-effective TDKS approach by application to a copper dithiolene complex, where binding of a ligand is detectable via shifts in the sulfur K-edge.

Time-Dependent Density Functional Theory for X-ray Absorption Spectra: Comparing the Real-Time Approach to Linear Response

“…The appearance of bound → continuum peaks can be avoided in TDKS simulations via ad hoc replacement of positive (unbound) SCF eigenvalues with complex-valued eigenvalues in the MO representation of P ( t ). , This transformation has the effect of imposing a finite lifetime to any excitation that involves unbound MOs, and that lifetime can be rendered arbitrarily short by the appropriate choice of the imaginary part of the eigenvalue. An alternative might be to introduce a complex absorbing potential. , Both methods have some arbitrary parameters that must be adjusted, potentially on a case-by-case basis, so we do not pursue these methods here. Instead, we turned to dipole filtering as a diagnostic to understand the origins of the features in a TDKS spectrum.…”

“…Alternatively, one might imagine that a complex absorbing potential could be used as a form of open-system boundary condition, in order to suppress the intensity from what are presumably very diffuse excitations. Although this may be explored further in future work, our preliminary experiments with absorbing potentials continued to afford spectra with pre-edge artifacts …”