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.

Density Functional Theory for Electronic Excited States

“…161 Similar truncations of the excitation manifold can be used to access core-excited states. [162][163][164][165] There is significant interest in core excitations in contemporary quantum chemistry, [164][165][166][167][168][169] driven by the recent availability of tabletop laser sources with femtosecond time resolution. [170][171][172][173][174] However, core-to-valence excitations lie embedded in an ionization continuum and, at a practical level, lie above all of the valence-excited states, such that the use of iterative eigensolvers is prohibitively expensive if the spectrum must be computed starting from the lowest excitation energies.…”

“…This section focuses on the use of TDKS simulations to obtain broadband spectra. Within the electric dipole approximation (which is also invoked in LR-TDDFT insofar as oscillator strengths are proportional to transition dipole matrix elements), the absorption spectrum corresponds to the dipole strength function 163,459 S(ω) = 4πω 3c Im α xx (ω) + α yy (ω) + α zz (ω) (81) where for example…”

“…52,462 Using this approach, spectra that are well-converged (with respect to LR-TDDFT results) can be obtained in < 10 fs of time propagation and rough spectra can be obtained with as little as 3-5 fs. 163 The time step ∆t dictates the spectral window that can be accessed, via the usual time-energy 466 along with LR-and RT-TDDFT calculations using a cluster model Si5O16H12 of the bulk material (as shown), with modified hydrogen charges to enforce charge neutrality. 467 The spectrum labeled "RT-TDDFT + iΓ" includes phenomenological lifetime parameters for the virtual orbitals.…”

High harmonic spectra computed using time-dependent Kohn-Sham theory with Gaussian orbitals and a complex absorbing potential

“…Our implementation of the CAP is similar to that used by Schlegel and coworkers to study strong-field ionization dynamics, [57][58][59][60][61] and which we have previously used to compute broadband x-ray absorption spectra. 25 The real-space CAP function W CAP (r) is constructed from a set of overlapping, atom-centered spherical potentials, each of which is zero within a cutoff radius r 0 then rises quadratically with curvature η. Explicitly, these functions are…”

“…12,22 This approach is often called "real-time" TDDFT, 23 although we prefer the term time-dependent Kohn-Sham (TDKS) theory. 24,25 In practice, however, there are significant questions as to whether existing * herbert@chemistry.ohio-state.edu exchange-correlation functionals that invoke the adiabatic approximation are up to the task, 12,23 although improving the description of the derivative discontinuity improves the description of ionization, even within the adiabatic approximation. 26 In the present work, we examine the HHG phenomenon in a simple test case, H 2 molecule, using an atom-centered Gaussian representation of the Kohn-Sham orbitals.…”