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Core and valence excitations in resonant X-ray spectroscopy using restricted excitation window time-dependent density functional theory
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Image of FIG. 1.
FIG. 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. 88 and 89. 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).

Image of FIG. 2.
FIG. 2.

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

Image of FIG. 3.
FIG. 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.

Image of FIG. 4.
FIG. 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.

Image of FIG. 5.
FIG. 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.

Image of FIG. 6.
FIG. 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.

Image of FIG. 7.
FIG. 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.


Generic image for table
Table I.

Shifts (in eV) for excitation energies calculated at different edges and level of theories.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Core and valence excitations in resonant X-ray spectroscopy using restricted excitation window time-dependent density functional theory