Performance of Delta-Coupled-Cluster Methods for Calculations of Core-Ionization Energies of First-Row Elements

Abstract

A thorough study of the performance of delta-coupled-cluster (ΔCC) methods for calculations of core-ionization energies for elements of the first long row of the periodic table is reported. Inspired by the core–valence separation (CVS) scheme in response theories, a simple CVS scheme of excluding the vacant core orbital from the CC treatment has been adopted to solve the convergence problem of the CC equations for core-ionized states. Dynamic correlation effects have been shown to make important contributions to the computed core-ionization energies, especially to chemical shifts of these quantities. The maximum absolute error (MaxAE) and standard deviation (SD) of delta-Hartree–Fock results for chemical shifts of core-ionization energies with respect to the corresponding experimental values amount to more than 1.7 and 0.6 eV, respectively. In contrast, the inclusion of electron correlation in ΔCC singles and doubles augmented with a noniterative triples correction [ΔCCSD­(T)] method significantly reduces the corresponding deviations to around 0.3 and 0.1 eV. With the consideration of basis set effects and the corrections to the CVS approximation, ΔCCSD­(T) has been shown to provide highly accurate results for absolute values of core-ionization energies, with a MaxAE of 0.22 eV and SD of 0.13 eV. To further demonstrate the usefulness of ΔCCSD­(T), calculations of carbon K-edge ionization energies of ethyl trifluoroacetate, a molecule of significant interest to the study of X-ray spectroscopy and dynamics, are reported.

Excited states via coupled cluster theory without equation-of-motion methods: Seeking higher roots with application to doubly excited states and double core hole states

“…Core-ionized states are another class of excited state that can be effectively handled by ∆CC methods. In fact, this was noted in the literature several times [39][40][41][42] What we will focus in this work is the use of ∆CCSD(T) for double core hole (DCH) states. Following the prescription by Zheng and Cheng for SCH states, we first obtain an (N −2) electron reference state and freeze two unoccupied core orbitals for numerical stability.…”

Coupled-cluster techniques for computational chemistry: The CFOUR program package

“…377 The convergence problem of CC equations for core-ionized states due to coupling to valence continuum states can be handled using a generalization of the CVS scheme. 374 Favorable accuracy has been obtained for CVS-∆CC results of core ionization energies, with CVS-∆CCSD(T) providing results as accurate as CVS-EOM-CCSDTQ, as shown in Table VIII.…”

“…states. An alternative option for computing core ionization energies using ∆CC methods 374,376 has also been implemented in CFOUR and will be available in the next release. ∆CC methods perform separate HF and CC calculations for the neutral molecule and the core-ionized state.…”

“…TABLE XI. Maximum absolute deviations (MAD) and standard deviations (SD) of CVS-EOM-CC373 and CVS-∆CC374 results from experimental values for chemical shifts of twenty-one 1s ionization energies of C, N, O, F in fourteen molecules (in eV).…”

Generalized single excitation configuration interaction: an investigation into the impact of the inclusion of non-orthogonality on the calculation of core-excited states

“…Early methods used multiple scattering X α 5 and transition potential calculations 6 , but since then ab-initio quantum methods have dominated the field. Currently, the common methods used for core excitations are time-dependent density functional theory (TDDFT) [7][8][9][10][11][12] , ∆-SCF and ∆-DFT 13 , equation of motion coupled-cluster methods [14][15][16][17][18][19][20][21][22][23][24] , algebraic diagrammatic construction (ADC) methods [25][26][27][28][29][30][31] , and configuration interaction singles (CIS) [32][33][34] . The general benefits and pitfalls of all these methods have been discussed elsewhere 8,17,30 , but we would like to focus on multi-state, spin-pure, wavefunction-based methods that are cheaper than ADC and CC methods.…”