Complete vs Restricted Active Space Perturbation Theory Calculation of the Cr₂ Potential Energy Surface

Abstract

In this paper, we calculate the potential energy surface (PES) and the spectroscopic constants of the chromium dimer using the recently developed restricted active space second-order perturbation (RASPT2) method. This approach is benchmarked against available experimental measurements and the complete active space second-order perturbation theory (CASPT2), which is nowadays established as one of the most accurate theoretical models available. Dissociation energies, vibrational frequencies, and bond distances are computed at the RASPT2 level using several reference spaces. The major advantage of the RASPT2 method is that with a limited number of configuration state functions, it can reproduce well the equilibrium bond length and the vibrational frequency of the Cr dimer. On the other hand, the PES is well described only at short distances, while at large distances, it compares very poorly with the CASPT2. The dissociation energy is also ill-behaved, but its value can be largely improved using a simple workaround that we explain in the text. In the paper, we also address the effect of the Ionization Potential Electron Affinity (IPEA) shift (a parameter introduced in the zeroth-order Hamiltonian in the CASPT2 method to include the effect of two-electron terms) and show how its default value of 0.25 is not suitable for a proper description of the PES and of the spectroscopic parameters and must be changed to a more sound value of 0.45.

Systematic Expansion of Active Spaces beyond the CASSCF Limit: A GASSCF/SplitGAS Benchmark Study

“…Table 7 reports the ligand-field and charge-transfer excitations of [CuCl 4 ] 2− obtained with the different methods discussed in this study. CASPT2 (11,11) energies are in good agreement with the experimental values 85 for the first two ligand-field states (1 2 B 1g , 1 2 B 2g /1 2 B 3g ). The GASSCF-4(11,11)-0e0eN ex e partition (N ex = 0 or 1, vide inf ra) is based on symmetry considerations: MOs belonging to the same irrep form a separate subspace (Figure 2).…”

“…Article 7(11,11)//(33,37) excitation energy for this state is similar to the one obtained at the CASSCF (11,11) level of theory, whereas the CASPT2 (11,11) value is about 2 eV lower (see the discussion in the next section). No experimental value is available.…”

“…For simplicity, this level of theory is referred to as GASSCF-4(11,11)-0e0eN ex e (N ex = 0 or 1). No significant deviations (≥0.01 eV) from those obtained with the parent CASSCF- (11,11) level (Table 7) occur, and the size of the CI expansion is reduced by almost 75%. It should be noted that both CASSCF and GASSCF densities predict a 0.82 ground-state spin population for Cu, whereas the experimental value is 0.62.…”

“…86 Two different P spaces were employed in the SplitGAS calculations. In the first case, the full CAS (11,11) forms the P space. The Q space is composed of single holes created in the 3p orbitals of the four chlorine atoms and double particles in the 15 lowest virtual orbitals, which are split in 5 subspaces.…”

“…The SplitGAS- Figure 2. Four subspaces (GAS1(2,2), GAS2(2,2), GAS3(2,2), and GAS4(5,5)) used in the GASSCF-4 (11,11) calculations for [CuCl 4 ] 2− . Single electron excitations from GAS1, GAS2, or GAS3 to GAS4 are allowed for the 1 2 B 1g , 1 2 B 2g , and 1 2 B 3g excited states, respectively.…”