Relativistic Core-Valence-Separated Molecular Mean-Field Exact-Two-Component Equation-of-Motion Coupled Cluster Theory: Applications to L-edge X-ray Absorption Spectroscopy

TL;DR

This work develops a fully relativistic core-valence-separated equation-of-motion CCSD method within the molecular mean-field X2C framework (CVS-DCB-X2C-EOM-CCSD) to predict L-edge X-ray absorption spectra. By solving the Dirac–Coulomb–Breit problem and projecting onto a two-component space, the approach incorporates scalar and spin–orbit relativistic effects and restricts excitations to core-like configurations, enabling accurate predictions of peak energies, splittings, and intensities across first-row transition-metal complexes. Against experimental data and relativistic TDDFT benchmarks, the method shows improved accuracy in energy shifts and spectral shapes, with basis-set recontraction proving robust. Limitations remain in high-density regions where higher-order (triples and beyond) correlation and more complete basis sets are needed, guiding future extensions toward even more reliable core-excitation spectroscopy.

Abstract

L-edge X-ray absorption spectra for first-row transition metal complexes are obtained from relativistic equation-of-motion singles and doubles coupled-cluster (EOM-CCSD) calculations that make use of the core-valence separation (CVS) scheme, with scalar and spin--orbit relativistic effects modeled within the molecular mean-field exact two-component (X2C) framework. By incorporating relativistic effects variationally at the Dirac--Coulomb--Breit (DCB) reference level, this method delivers accurate predictions of L-edge features, including energy shifts, intensity ratios, and fine-structure splittings, across a range of molecular systems. Benchmarking against perturbative spin--orbit treatments and relativistic TDDFT highlights the superior performance and robustness of the CVS-DCB-X2C-EOM-CCSD approach, including the reliability of basis set recontraction schemes. While limitations remain in describing high-density spectral regions, our results establish CVS-DCB-X2C-EOM-CCSD as a powerful and broadly applicable tool for relativistic core-excitation spectroscopy.

Figures (5)

• Figure 1: Comparison of the experimental L$_{2,3}$-edge spectra of Argon with theoretical spectra computed using CVS-BP-SO-EOM-CC and CVS-DCB-X2C-EOM-CC methods. The second and third panels display spectra computed with the uncontracted 6-311(2+,+)G(p,d) basis set, supplemented by Rydberg-type functions as outlined in Ref. Coriani20_8314, while the fourth panel presents results obtained using the contracted version of the same basis. The applied energy shifts are as follows: CVS-BP-SO-EOM: $+$0.7 eV, CVS-DCB-X2C-EOM with the uncontracted basis: $-$0.6 eV, and CVS-DCB-X2C-EOM with the contracted basis: $-$0.9 eV. The CVS-BP-SO-EOM-CC results have been reproduced from Ref. Coriani20_8314. The experimental spectrum is taken from Ref. Oshio68_1303.
• Figure 2: Comparison of L$_{2,3}$-edge spectra of SiCl$_{4}$ computed with two variants of CVS-X2C-EOM-CC using x2c-TZVPall-2c basis. Also shown in the first panel is the experimental spectrumTse87_33. The 1e-X2C-TDDFT spectrum in the second panel obtained with the B3LYP functional and aug-cc-pVTZ basis has been reproduced from Ref. Li18_1998. The applied energy shifts are as follows: 1e-X2C-B3LYP: $+$6 eV, CVS-DCB-X2C-EOM: $-$0.6 eV, and 1e-X2C-EOM: $-$0.7 eV. The experimental spectrum is taken from Ref. Tse87_33
• Figure 3: Comparison of the L$_{2,3}$-edge spectra of TiCl$_{4}$ computed using 1e-X2C-TDDFT and CVS-DCB-X2C-EOM-CC with the x2c-TZVPall-2c basis set, alongside the experimental spectrum in the uppermost panel (reproduced from Ref. Hitchcock93_1632). The 1e-X2C-TDDFT spectrum in the second panel obtained with the B3LYP functional and aug-cc-pVTZ basis has been reproduced from Ref. Li18_1998. The applied energy shifts are as follows: 1e-X2C-B3LYP: $+$9.5 eV, CVS-1e-X2C-EOM-CC:$-$2.9 eV, and CVS-DCB-X2C-EOM-CC: $-$2.7 eV.
• Figure 4: The computed L$_{2,3}$-edge spectra of VOCl$_{3}$ with 1e-X2C-TDDFT and DCB-X2C-EOM-CC using x2c-TZVPall-2c basis, compared to the experimental spectrum (reproduced from Ref. Prince09_2914). The 1e-X2C-TDDFT spectrum in the second panel obtained with the B3LYP functional and aug-cc-pVTZ basis has been reproduced from Ref. Li19_234103. The applied energy shifts are as follows: 1e-X2C-B3LYP: $+$4.3 eV, and DCB-X2C-EOM: $-$3.0 eV.
• Figure 5: Comparison of L$_{2,3}$-edge spectra of CrO$_{2}$Cl$_{2}$ computed with 1e-X2C-TDDFT and DCB-X2C-EOM-CC using x2c-TZVPall-2c basis, alongside the experimental spectrum in the uppermost panel (reproduced from Ref. Prince09_2914). The 1e-X2C-TDDFT spectrum in the second panel obtained with the B3LYP functional and aug-cc-pVTZ basis has been reproduced from Ref. Li18_1998. The applied energy shifts are as follows: X2C-B3LYP: $+$8 eV, and DCB-X2C-EOM: $-$3.8 eV.