Core and valence excitations in resonant X-ray spectroscopy using restricted excitation window time-dependent density functional theory

Abstract

We report simulations of X-ray absorption near edge structure (XANES), resonant inelastic X-ray scattering (RIXS) and 1D stimulated X-ray Raman spectroscopy (SXRS) signals of cysteine at the oxygen, nitrogen, and sulfur K and L(2,3) edges. Comparison of the simulated XANES signals with experiment shows that the restricted window time-dependent density functional theory is more accurate and computationally less expensive than the static exchange method. Simulated RIXS and 1D SXRS signals give some insights into the correlation of different excitations in the molecule.

Figure 1

Calculated XANES spectra of cysteine taken at the nitrogen, oxygen, and sulfur K-edges (solid red traces), from either the REW-TDDFT (top) or STEX (bottom) level of theory, compared with experimental spectra (solid blue traces) adapted from Refs. and . In plotting the calculated absorption, the stick spectrum (black lines) is convoluted with a Lorentzian function with an energy-dependent linewidth, Γ_e, whose value is given by the dashed green trace (the same Γ_e is used for both REW-TDDFT and STEX).

Figure 2

Calculated UV absorption spectrum of cysteine from TDDFT. The same active valence excitations contribute to the Raman signals shown below.

Figure 3

Calculated RIXS signal at the nitrogen K-edge, oxygen K-edge, sulfur K-edge, and sulfur L-edge from cysteine. The excitation frequency ω₁ is given with respect to the K-edge frequency.

Figure 4

Hermitian and anti-Hermitian parts of the effective isotropic polarizabilities (Eq. 14) for the four pulses used in our simulations, in arbitrary units. The Hermitian part is purely real, while the anti-Hermitian part is purely imaginary.

Figure 5

1D SXRS spectra from cysteine with the two pulses polarized at the magic angle. The pulses are Gaussian, with bandwidth 14 eV, FWHM. The center frequency of the pulses is set to the core edge frequency for a given atom. Spectra in the same row share a common pump pulse, while spectra in the same column share a common probe pulse.

Figure 6

(Top row) The N1s/O1s (solid traces) and O1s/N1s (dashed traces) signals, shown as the real (left), imaginary (middle), and modulus (right) of the Fourier transform signal. As shown in the text, differences between these signals are related to the complex valued polarizability when the pulses are near resonance with multiple core transitions. The real and imaginary FT signals are both mixtures of dispersive and Lorentzian lineshapes. (Bottom row) The left and middle panels show the imaginary and real parts of the FT difference spectra. Unlike the top row, here the imaginary part is purely absorptive and the real part purely dispersive. The right panel shows both the modulus of the difference signal (solid trace), and the difference of the modulus signals (dashed trace). Peaks for which the solid trace is large in value, but the dashed trace is not, indicate that the two signals have similar magnitude for a given peak but have a large phase difference. Peaks for which the two traces are similar in magnitude indicate that the phase and amplitude for that peak are different for the two pulse configurations.

Figure 7

Difference 1D-SXRS spectra for the six possible two-color combinations considered here. The top middle panel, for example, shows the modulus of the difference between the N1s/S1s and S1s/N1s signals as the solid trace, and the difference between the moduli of the N1s/S1s and S1s/N1s signals as the dashed trace.