Coupled-cluster response theory for near-edge x-ray-absorption fine structure of atoms and molecules

Based on an asymmetric Lanczos-chain subspace algorithm, damped coupled cluster linear response functions have been implemented for the hierarchy of coupled cluster (CC) models including CC with single excitations (CCS), CC2, CC with single and double excitations (CCSD), and CCSD with noniterative triple corrected excitation energies CCSDR(3). This work is a first step toward the extension of these theoretical electronic structure methods of well-established high accuracy in UV-vis absorption spectroscopies to applications concerned with x-ray radiation. From the imaginary part of the linear response function, the near $K$-edge x-ray absorption spectra of neon, water, and carbon monoxide are determined and compared with experiment. Results at the CCSD level show relative peak intensities in good agreement with experiment with discrepancies in transition energies due to incomplete treatment of electronic relaxation and correlation that amount to 1–2 eV. With inclusion of triple excitations, errors in energetics are less than 0.9 eV and thereby capturing 90$\%$, 95$\%$, and 98$\%$ of the relaxation-correlation energies for C, O, and Ne, respectively.

Figure 1

X-ray absorption spectra for neon as obtained with CC response theory and compared against experiment [41]. The results are aligned against the first given experimental peak, and the corresponding shift is given below the model label for both nonrelativistic (NR) and relativistic (REL) calculations. The NR and REL calculations [CCSD and CCSDR(3)] have the same spectral profile to within the thickness of the line. The theoretical absorption cross section is given in atomic units, whereas arbitrary units are adopted in the case of the experiment.

Figure 2

X-ray absorption spectra for water as obtained with CC response theory and compared against experiment [42]. The contribution from the different components of the dipole operator are indicated for the CCSD spectrum. For other details, see caption of Fig. 1.

Figure 3

X-ray absorption spectra for carbon monoxide as obtained with CC response theory and compared against experiment [43, 44]. The contribution from the different components of the dipole operator are indicated for the CCSD spectrum. For other details, see caption of Fig. 1.