Equation of motion coupled-cluster cumulant approach for intrinsic losses in x-ray spectra

Abstract

We present a combined equation of motion coupled-cluster cumulant Green’s function approach for calculating and understanding intrinsic inelastic losses in core level x-ray absorption spectra (XAS) and x-ray photoemission spectra. The method is based on a factorization of the transition amplitude in the time domain, which leads to a convolution of an effective one-body absorption spectrum and the core-hole spectral function. The spectral function characterizes intrinsic losses in terms of shake-up excitations and satellites using a cumulant representation of the core-hole Green’s function that simplifies the interpretation. The one-body spectrum also includes orthogonality corrections that enhance the XAS at the edge.

Equation-of-Motion Coupled-Cluster Cumulant Green’s Function for Excited States and X-Ray Spectra

“…The ground state single-particle states and molecular orbitals integrals for the RT-EOM-CCS approach and the ΔSCF method were calculated from a Hartree-Fock (HF) reference, while those for the core-excited ΔSCF were derived from a spin-symmetric and occupation-constrained HF reference. The final spectra were broadened to compare with experiment as in Rehr et al, 2020 and Vila et al, 2020 with varying (1–6 eV) broadening to account for the limited basis set for the continuum; similarly XAS used constant broadening consistent with experimental broadening below and 3.5 eV above the binding energy.…”

“…Our treatment here is adapted from that in our original EOM-CC paper ( Rehr et al, 2020 ), but updated here with a more detailed treatment of the EOM discussed above. As outlined in the introduction, the contribution from a deep core level | c ⟩ to the XAS is given by the time-correlation function μ ( t ) = L ( t ) G c ( t ) in Eq.…”

“…Real-time approaches can also be advantageous as they avoid explicit calculations of eigenstates. Our treatment here exploits real-time approaches, following several recent developments: 1) Equation of motion coupled-cluster (EOM-CC) approaches for molecular systems have been formulated for the Green’s function in energy-space ( Peng and Kowalski, 2016 ; Peng and Kowalski, 2018a ), 2) An approach has also been developed ( Rehr et al, 2020 ) for calculations of many-body XAS μ ( ω ) in terms of the convolution of a one-body XAS μ 1 ( ω ) and the spectral function of the core-hole A c ( ω ) This result originates from the time-correlation approach ( Nozieres and de Dominicis, 1969 ) that was used to solve the x-ray edge-singularity problem. In this approach the time-domain XAS transition amplitude μ ( t ) is given by the factorization Here L ( t ) is an effective one-body transition amplitude and A c ( ω ) = −(1/ π )Im G c ( t ).…”

“…Real-time approaches can also be advantageous as they avoid explicit calculations of eigenstates. Our treatment here exploits real-time approaches, following several recent developments: 1) Equation of motion coupled-cluster (EOM-CC) approaches for molecular systems have been formulated for the Green's function in energy-space (Peng and Kowalski, 2016;Peng and Kowalski, 2018a), 2) An approach has also been developed (Rehr et al, 2020) for calculations of many-body XAS μ(ω) in terms of the convolution of a one-body XAS μ 1 (ω) and the spectral function of the core-hole A c (ω) μ(ω) dte −iωt μ(t) dω ′ μ 1 (ω ′ )A c (ω − ω ′ ).…”

Nonlinear response in the cumulant expansion for core-level photoemission

“…[15,47,48], the derivation of higher-order correlation functions from the Mahan-Nozières-De Dominicis (MND) or electron-boson Hamiltonians [49], or more recently with the description of nonlinear electron-boson couplings in Ref. [50], and in the equationof-motion, coupled-cluster method [51,52]. However, there is still a gap to be filled concerning the ab initio calculation of spectral functions.…”