Analysis and comparison of CVS-ADC approaches up to third order for the calculation of core-excited states

Abstract

The extended second order algebraic-diagrammatic construction (ADC(2)-x) scheme for the polarization operator in combination with core-valence separation (CVS) approximation is well known to be a powerful quantum chemical method for the calculation of core-excited states and the description of X-ray absorption spectra. For the first time, the implementation and results of the third order approach CVS-ADC(3) are reported. Therefore, the CVS approximation has been applied to the ADC(3) working equations and the resulting terms have been implemented efficiently in the adcman program. By treating the α and β spins separately from each other, the unrestricted variant CVS-UADC(3) for the treatment of open-shell systems has been implemented as well. The performance and accuracy of the CVS-ADC(3) method are demonstrated with respect to a set of small and middle-sized organic molecules. Therefore, the results obtained at the CVS-ADC(3) level are compared with CVS-ADC(2)-x values as well as experimental data by calculating complete basis set limits. The influence of basis sets is further investigated by employing a large set of different basis sets. Besides the accuracy of core-excitation energies and oscillator strengths, the importance of cartesian basis functions and the treatment of orbital relaxation effects are analyzed in this work as well as computational timings. It turns out that at the CVS-ADC(3) level, the results are not further improved compared to CVS-ADC(2)-x and experimental data, because the fortuitous error compensation inherent in the CVS-ADC(2)-x approach is broken. While CVS-ADC(3) overestimates the core excitation energies on average by 0.61% ± 0.31%, CVS-ADC(2)-x provides an averaged underestimation of -0.22% ± 0.12%. Eventually, the best agreement with experiments can be achieved using the CVS-ADC(2)-x method in combination with a diffuse cartesian basis set at least at the triple-ζ level.

Statistical analysis of electronic excitation processes: Spatial location, compactness, charge transfer, and electron-hole correlation

“…However, the double‐excitation character is stronger than for the valence‐excited states. This is in accordance with previous investigations that demonstrated typical amounts of doubly excited amplitudes between 20% and 30% for core‐excited states . The R eh and COV values are not presented in Table as these are always 0.000.…”

“…The cytosine molecule was optimized at the MP2/SV(P) level and excitation energies were computed at the ADC(2)/aug‐cc‐pVDZ level . Core excitations of cytosine were calculated at the ADC(2)‐x level in combination with the core‐valence separation (CVS) approximation using the Cartesian 6D/10F version of the 6‐311++G** basis set, a combination which has been shown to provide accurate results when compared to experimental data …”

Communication: X-ray absorption spectra and core-ionization potentials within a core-valence separated coupled cluster framework

“…The interest in accurate ab initio procedures to compute spectroscopic parameters related to X-ray absorption and ionization has significantly grown over the past five years, [1][2][3][4][5][6][7][8][9][10] concurrently with the advances on the experimental side, in particular the advent of third-generation synchrotron radiation sources for the measurement of high-quality X-ray absorption spectra, and the ongoing development of fourth-generation synchrotron facilities (e.g., free-electron lasers) and their perspective opportunities for novel experimental studies on the interaction of matter and X-ray radiation.…”

Kohn-Sham density functional theory calculations of non-resonant and resonant x-ray emission spectroscopy

“…[16][17][18][19][20][21] X-ray absorption spectra can also be computed using time-dependent density functional theory (TDDFT) [22][23][24][25][26] as a) E-mail: nick.besley@nottingham.ac.uk well as wavefunction based methods that include electron correlation. [27][28][29][30] It is well established that TDDFT with standard exchange-correlation functionals underestimates core excitation energies, and this has been associated with the self-interaction present with approximate exchange functionals. [31][32][33][34][35][36][37][38] More recently it has been demonstrated that accurate core excitation energies can be computed using TDDFT with short-range corrected (SRC) functionals, which have a large fraction of Hartree-Fock (HF) in the short range.…”