Multireference perturbation theory with improved virtual orbitals for radicals: More degeneracies, more problems

Abstract

IVO‐SSMRPT is an affordable and accurate type of state‐specific multireference perturbation (SSMRPT) theory that adds dynamic correlation energy to improved virtual orbital (IVO) complete active space configuration interaction (CASCI) wave functions using a single‐root parametrization of multi‐root Hilbert‐space ansatz. We applied it to many chemically important di‐ and tri‐radicals to analyze the geometries and electronic properties of spectroscopic interest for both closed‐ and open‐shell singlet‐ and nonsinglet ground as well as excited states. We observed that IVO‐SSMRPT identifies optimized geometries, splitting between multiplets and frequencies for several radicals that are similar to those displayed by current generation state‐of‐the‐art methods but with admiringly decreased computational effort. This study illustrates the importance of having an accurate treatment of both nondynamical and dynamical correlation effects when examining multiradical species. Chemically and spectroscopically relevant answers can be obtained using our computationally tractable method. Our method will be a serviceable avenue for portraying open‐shell interactions in other radicals.

sp2 Carbon Stable Radicals

“…Many computational schemes has been suggested in this way. A most recent review [4], presented by Chattopadhyay's team, gives quite complete description of the CI branch modern state of art and supplies readers with many valuable references.…”

“…It should be noted that the spin contaminations of both states, ∆Ŝ 2 sg and ∆Ŝ 2 tr , as well as the total numbers of effectively unpaired electrons, N Dsg and N Dtr , are considerable and practically the same. The spin-triplet near-degeneracy, which is typical for polyradicoloids with double C=C bonds [23,24], greatly complicates the description of open-shell electronic states [4,21,22], and a proper computational technique has been still absent. Therefore, we will have to limit ourselves to the available capabilities and hold a discussion of the question posed in terms of the UHF consideration of the singlet state.…”

Single-Root Multireference Brillouin–Wigner Perturbative Approach to Excitation Energies

“…According to Hund’s rule, the ground state of TMM is a triplet ( 3 A′ 2 , D 3 h symmetry) as four π electrons are distributed over the four π-type molecular orbitals (MOs), two ( e ′) of which are exactly degenerate in the D 3 h framework, which is also supported by both electron paramagnetic resonance (EPR) and IR experimental results 125 − 128 and previous established theoretical investigations. 68 − 70 , 94 − 96 , 129 − 132 The first closed-shell 1 1 A 1 and the open-shell 1 1 B 2 singlets (similar to the N and V states of ethylene, respectively) are exactly degenerate in D 3 h geometry. However, owing to the Jahn–Teller effect, their degeneracy at the D 3 h geometry is lifted in lower C 2 v symmetry and both states have a manifestly MR biradical character.…”

“…However, as shown earlier, the RS-based SSMRPT method with the IVO-CASC(2,2) reference function correctly identifies the location of both the singlet states relative to the 3 B 2 TMM. 132 To illustrate the sensitivity of the estimates for VEE to the methodologies employed for geometry optimization, IVO-BWMRPT values at SF-DFT/6-31G* geometries have been compared with those at IVO-CASCI 133 geometries. The vertical energy gaps so obtained by the IVO-BWMRPT method with different geometries are in proximity because the differences yielded are at most 0.04 eV.…”

“… 134 − 136 These benzyne isomers have been scrutinized theoretically using various established ab initio methods. 68 , 93 , 94 , 132 , 137 − 147 The lowest excited state of the benzynes is a triplet state [ 3 B 2 in ortho - and meta -benzynes and 3 B 1u in p -benzyne]. As the energy gap between the frontier orbitals decreases in the ortho → meta → para sequence, the MR nature of the closed-shell ground state increases in the same direction.…”