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Modeling core-level excitations with variationally optimized reduced-density matrices and the extended random phase

Elvis Maradzike1, A Eugene DePrince1

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Area of Science:

  • Quantum Chemistry
  • Computational Spectroscopy
  • Electronic Structure Theory

Background:

  • Ground-state one- and two-electron reduced-density matrices (RDMs) contain information for excited state calculations.
  • The variational 2-RDM (v2RDM) approach is limited to the lowest energy state of a given spin symmetry.
  • Extended random phase approximation (ERPA) offers a framework to describe excitations from v2RDM states.

Purpose of the Study:

  • To assess the utility of ERPA for predicting near-edge features in x-ray absorption spectroscopy.
  • To evaluate ERPA when the 2-RDM is derived from a ground-state v2RDM-driven complete active space self-consistent field (CASSCF) computation.
  • To establish conditions for ERPA excitation operators for accurate core-level excitation descriptions.

Main Methods:

  • Utilized ground-state v2RDM-driven CASSCF computations to obtain 2-RDMs.
  • Derived a class of 'killer conditions' for the CASSCF-specific ERPA excitation operator.
  • Employed the core-valence separation (CVS) scheme to obtain an operator fulfilling these conditions.

Main Results:

  • Demonstrated that a reliable description of core-level excitations necessitates an excitation operator meeting specific conditions.
  • The CASSCF/CVS-ERPA framework yielded absolute excitation energies slightly more accurate than standard random phase approximation (RPA).
  • CVS-ERPA showed comparable accuracy to RPA for predicting the relative positions of near-edge features.

Conclusions:

  • The CASSCF/CVS-ERPA method is a viable approach for calculating core-level excitations.
  • It serves as a reasonable starting point for treating core-level excitations using variationally optimized 2-RDMs.
  • While absolute energies are slightly improved, relative feature positions are similar to standard RPA.