Simulating X-ray absorption spectra with complete active space self-consistent field linear response methods

In this work, two approaches for simulating X-ray absorption (XA) spectra with the complete active space self-consistent field (CASSCF) linear response (LR) method are introduced. The first approach employs the well-known core-valence separation (CVS) approximation, which is predominantly used by many other electronic structure methods for simulating X-ray spectra. The second ansatz uses the harmonic Davidson algorithm for finding interior eigenvalues that lie close to a target excitation energy shift and virtually solves a shifted-and-inverted (S&I) generalized eigenvalue problem. LR-CASSCF K-edge transition energies are systematically blueshifted though have consistently smaller errors than those of the CAS or restricted active space (RAS) configuration interaction (CI) methods. For simple molecules at which the core hole can only be created at a single site, the state-specific RASSCF or n-electron valence second-order perturbation theory/RASCI gave more accurate principal K-edge excitation energies. If the core hole can be created at multiple sites, the LR-CASSCF approaches perform much better than RASSCF. Moreover, we observed that the LR-CASSCF variants were the only MR methods discussed here that predicted correctly the order of O K-edge features in the ozone molecule and the permanganate ion. The peak separation of edge features in ozone was as accurate as with equation-of-motion coupled cluster singles and doubles. The error of the CVS approximation turned out to be very system dependent and in some cases amounted up to 1.0 eV for the K-edge excitation energies. Those CVS errors are still acceptable if one considers the observed deviation from the experimental reference by 5-11 eV. The deviations made in the XAS intensities were even more pronounced. CVS and the full S&I oscillator strengths could differ even by a factor of 2.8. Since the S&I approach is at least as efficient as the LR-CASSCF method for valence excitations, future endeavors to improve the accuracy by accounting for dynamic correlation could be built on top of the full S&I approach.

Automated summary

Two approaches for simulating X-ray absorption spectra with the LR-CASSCF method are introduced in this work. The LR-CASSCF K-edge transition energies are systematically blueshifted but have smaller errors than CAS or RAS-CI methods. LR-CASSCF approaches perform better than RASSCF when core holes can be created at multiple sites.