Relativistic EOM-CCSD for Core-Excited and Core-Ionized State Energies Based on the Four-Component Dirac–Coulomb(−Gaunt) Hamiltonian

Abstract

We report an implementation of the core−valence separation approach to the four-component relativistic Hamiltonian-based equation-of-motion coupled-cluster with singles and doubles theory (CVS-EOM-CCSD) for the calculation of relativistic core-ionization potentials and core-excitation energies. With this implementation, which is capable of exploiting double group symmetry, we investigate the effects of the different CVS-EOM-CCSD variants and the use of different Hamiltonians based on the exact two-component (X2C) framework on the energies of different core-ionized and -excited states in halogen-(CH 3 I, HX, and X − , X = Cl−At) and xenon-containing (Xe, XeF 2 ) species. Our results show that the X2C molecular mean-field approach [Sikkema, J.; et al. J. Chem. Phys. 2009, 131, 124116], based on four-component Dirac−Coulomb mean-field calculations ( 2 DC M ), is capable of providing core excitations and ionization energies that are nearly indistinguishable from the reference four-component energies for up to and including fifth-row elements. We observe that two-electron integrals over the small-component basis sets lead to non-negligible contributions to core binding energies for the K and L edges for atoms such as iodine or astatine and that the approach based on Dirac−Coulomb−Gaunt mean-field calculations ( 2 DCG M ) are significantly more accurate than X2C calculations for which screened two-electron spin−orbit interactions are included via atomic mean-field integrals.

Electronic spectra of ytterbium fluoride from relativistic electronic structure calculations

“… 47 Among the different X2C flavors, we can distinguish two main strategies for the decoupling, which is performed based on: (i) the one-electron Dirac Hamiltonian prior to the mean-field step, 54,57 and for which two-electron spin–orbit contributions due to the untransformed two-electron potential are included via atomic mean-field contributions calculated with the AMFI code 41,58,59 (X2C-AMFI); (ii) after a converged 4-component mean-field calculation on atoms 52,53,56 or molecules 55 ( 2 DC M ). Recent benchmarks show that 2 DC M calculations closely reproduce equivalent 4-component ones for valence 60 or core 61 states.…”

Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory

“… 15 − 18 The relativistic effects are significant even in light (third row) elements, highlighting the need for a relativistic description also in these cases, 18 where perturbative treatment of SO coupling can yield accurate spectra, 19 and increase in importance for heavier elements. 20 In K-edge spectra originating from excitations from 1s 1/2 orbitals, only the scalar relativistic corrections have nonzero contributions and result in a constant shift of K-edge signals. In this case, one-component scalar relativistic Hamiltonians are convenient and sufficient for describing this XAS edge.…”

“… 21 Further spin-related contributions can be accounted for by the inclusion of the Gaunt term that has been shown to contribute to the energy shifts of core orbitals. 20 , 23 …”

Electronic Spectra of Ytterbium Fluoride from Relativistic Electronic Structure Calculations

“…47 Among the different X2C flavors, we can distinguish two main strategies for the decoupling, which is performed based on : (i) the oneelectron Dirac Hamiltonian prior to the meanfield step, 54,57 and for which two-electron spinorbit contributions due to the untransformed two-electron potential are included via atomic mean-field contributions calculated with the AMFI code 41,58,59 (X2C-AMFI); (ii) after a converged 4-component mean-field calculation on atoms 52,53,56 or molecules 55 ( 2 DC M ). Recent benchmarks show that 2 DC M calculations closely reproduce equivalent 4-component ones for valence 60 or core 61 states.…”