Excitation Energies of UO₂²⁺, NUO⁺, and NUN Based on Equation-of-Motion Coupled-Cluster Theory with Spin–Orbit Coupling

Abstract

Obtaining reliable excitation energies of the isoelectronic series, UO, NUO, and UN, is a challenge in quantum chemistry calculations due to importance of electron correlation and spin-orbit coupling (SOC). Vertical spin-free and spin-orbit coupled excitation energies of these molecules are calculated in this work using equation-of-motion coupled-cluster approach at the CC singles and doubles level (EOM-CCSD). SOC is included in post-SCF calculations and this treatment has been shown to provide SOC effects with high accuracy for heavy elements. Excitation energies for UO with the present approach are in good agreement with previous results using linear response CCSD, multiconfiguration perturbation theory (CASPT2), and multireference configuration interaction (MRCI). As for NUO and UN, excitation energies with CASPT2 from two previous calculations differ significantly and the present results usually lie between these two sets of CASPT2 results. On the other hand, excitation energies with intermediate Hamiltonian Fock space CC method (IHFSCC) are generally too small compared with our results. This work provides new estimates on excitation energies of these molecules and it could be helpful in investigating spectroscopic and luminescence properties of larger uranium complexes.

Equation-of-motion coupled-cluster theory based on the 4-component Dirac–Coulomb(–Gaunt) Hamiltonian. Energies for single electron detachment, attachment, and electronically excited states

“…While in the aforementioned works and elsewhere in the literature 43,[50][51][52] one can see that approximate treatments of SOC such as in the AMF approximation can yield rather accurate excitation energies even for heavier species up to and including iodine, the situation is not as clear cut for heavier elements 80 , and therefore for 5d, 5f, 6p elements and beyond it may be preferable to rely on approaches based on 4C Hamiltonians (that is, the Dirac-Coulomb (DC), Dirac-Coulomb-Gaunt (DCG) or Dirac-Coulomb-Breit (DCB) Hamiltonians), or on X2C approaches but using a molecular mean-field 84 (MMF) approach, which have been shown to yield results largely indistinguishable from their 4C counterparts 55 .…”

“…The appealing features of EOM-CC have made it an extremely popular method for light element systems, and its popularity is growing for heavier species as attested by the number of recent reports in the literature of EOM-CC implementations that take into account relativistic effects. Though some of the latter are based on solving the four-component (4C) Dirac equation for atomic and molecular systems [69][70][71][72][73] and therefore account rigorously for scalar relativistic (SR) effects and spin-orbit coupling (SOC), for reasons of computational efficiency most of them [74][75][76][77][78][79][80][81][82] have been devised in a more approximate framework where SOC is treated to within different degrees of approximation e.g. starting from the spin-free exact two-component (sfX2C) Hamiltonian and including SOC via atomic mean-field (AMF) integrals 83 or perturbatively.…”

Relativistic coupled‐cluster and equation‐of‐motion coupled‐cluster methods

“…EOM‐CCSD calculations using two schemes discussed in Sections 2.3.1 and 2.3.2 to enhance the computational efficiency, that is, the spin‐orbit effective core potential (SOECP) calculations using scalar orbitals 272 and the X2CAMF calculations using AO‐based algorithms, 273 yield similar results, as shown in Table 4. They are also similar to the SO‐CASPT2 results for this system.…”

“…They are also similar to the SO‐CASPT2 results for this system. However, this agreement between SO‐CASPT2 and SO‐EOM‐CCSD results is molecule specific, since the corresponding SOECP‐EOM‐CCSD results for the excitation energies of the closely related UN 2 molecule differ substantially from those of SO‐CASPT2 272 . Therefore, importantly, it is the inclusion of triple excitations using the EOM‐CCSD(T)(a)* 31 method that offers a reliable estimate of the accuracy of the EOM‐CC results 273 .…”

“…Here we use the bare uranyl ion [O-U-O] 2+ as an example. It turns out to be a challenging task for relativistic quantum-chemical calculations [266][267][268][269][270][271][272] to obtain accurate excitation energies for this system. As shown in Table 4, computational results obtained from complete active space second-order perturbation theory with perturbative treatment of spin-orbit coupling (SO-CASTP2) 266 and the Dirac-Coulomb intermediate Hamiltonian Fock space coupled-cluster (DC-IHFSCC) 271 calculations differ by more than 0.5 eV for these excitation energies.…”