Core-Excited States and X-ray Absorption Spectra from Multireference Algebraic Diagrammatic Construction Theory

Abstract

We report the development and benchmark of multireference algebraic diagrammatic construction theory (MR-ADC) for the simulations of core-excited states and X-ray absorption spectra (XAS). Our work features an implementation that incorporates core-valence separation into the strict and extended second-order MR-ADC approximations (MR-ADC(2) and MR-ADC(2)-X), providing efficient access to high-energy excited states without including inner-shell orbitals in the active space. Benchmark results on a set of small molecules indicate that at equilibrium geometries, the accuracy of MR-ADC is similar to that of single-reference ADC theory when static correlation effects are not important. In this case, MR-ADC(2)-X performs similarly to single- and multireference coupled cluster methods in reproducing the experimental XAS peak spacings. We demonstrate the potential of MR-ADC for chemical systems with multiconfigurational electronic structure by calculating the K-edge XAS spectrum of the ozone molecule with a multireference character in its ground electronic state and the dissociation curve of core-excited molecular nitrogen. For ozone, the MR-ADC results agree well with the data from experimental and previous multireference studies of ozone XAS, in contrast to the results of single-reference methods, which underestimate relative peak energies and intensities. The MR-ADC methods also predict the correct shape of the core-excited nitrogen potential energy curve, and are in good agreement with accurate calculations using driven similarity renormalization group approaches. These findings suggest that MR-ADC(2) and MR-ADC(2)-X are promising methods for the XAS simulations of multireference systems and pave the way for their efficient computer implementation and applications.

Predicting the X-ray Absorption Spectrum of Ozone with Single Configuration State Functions

“…ROKS/SCAN with VS, therefore, yields a semiquantitative description of the experimental O 3 XAS profile. The single geometry FC approach with ROKS also yields a relatively similar spectrum, though the 1s(O T ) → 7a 1 transition is visible as a distinct shoulder instead of the asymmetric skew observed in the experiment and predicted by VS. At least to our perception, the level of agreement surpasses what was achieved with uniform broadening at a single geometry in prior studies utilizing explicitly multireference methods. − We also find that the PBE, BLYP, PBE0, and B3LYP functionals yield similar quality spectra in conjunction with ROKS, albeit with some minor differences in peak positions (as shown in the Supporting Information). This indicates that the good performance of ROKS/SCAN was not fortuitous, and reasonable results can likely be expected of other well-behaved density functional approximations.…”

“…Some of these studies ,, also noted the challenges of modeling the spectrum with related single reference methods like second-order ADC or EOM-CC singles and doubles (EOM-CCSD) . Computed spectra in refs − utilize uniform broadening of “stick” spectra computed at the equilibrium geometry, thereby neglecting all nuclear quantum effects. However, this “single-geometry” approach makes it quite difficult to properly gauge the relative accuracy of different methods via comparison with experiment, especially because bound and dissociative states have quite distinct intrinsic broadening .…”

“…O 3 , therefore, has been used to examine the performance of linear-response complete active space self-consistent field (LR-CASSCF), multistate restricted active space second-order perturbation theory (MS-RASPT2), driven similarity renormalization group multireference perturbation theory (DSRG-MRPT), and multireference ADC in predicting XAS. Some of these studies ,, also noted the challenges of modeling the spectrum with related single reference methods like second-order ADC or EOM-CC singles and doubles (EOM-CCSD) . Computed spectra in refs − utilize uniform broadening of “stick” spectra computed at the equilibrium geometry, thereby neglecting all nuclear quantum effects.…”

Time-Dependent Density Functional Theory for X-ray Absorption Spectra: Comparing the Real-Time Approach to Linear Response

“…This is supported by both theoretical analysis and empirical timing data when the LR-TDDFT calculation is performed using a CVS-style active-space approximation that excludes most of the occupied MOs. Therefore, we suggest that the utility of the TDKS approach for core-level spectroscopy may lie in the fact that it obviates the need to invoke a CVS approximation, which is (by contrast) ubiquitous in LR-TDDFT and other eigenvalue-based approaches to core-level spectroscopy. − At least within the realm of DFT, TDKS simulations may therefore provide benchmarks to assess the accuracy of active-space approximations, which remain relatively untested for XAS at elemental L- and M-edges. This will require careful processing of the TDKS data in order to avoid contamination by continuum artifacts; the tools to facilitate this are now in place.…”

“…By inclusion of only a few core orbitals along with the full virtual space, core-to-valence excitations appear as the lowest-energy states in the spectrum. In many-body theory, this active-space approximation is known as “core/valence separation” (CVS), ,− whereas in LR-TDDFT it has also been called a “restricted excitation window”. , It amounts to freezing most of the occupied MOs.…”