Energies and structures in biradical chemistry from the parametric two-electron reduced-density matrix method: applications to the benzene and cyclobutadiene biradicals

Abstract

The treatment of biradical chemistry presents a challenge for electronic structure theory, especially single-reference methods, as it requires the description of varying degrees and kinds of electron correlation. In this work we assess the ability of the parametric two-electron reduced-density matrix (p2-RDM) method to describe biradical chemistry through application to the benzene and cyclobutadiene biradicals. The relative energy of o- and m-benzynes predicted by the p2-RDM method is consistent with Wenthold et al.'s experimental determinations, while the more difficult relative energy prediction of the more multi-referenced p-benzyne is within 1.4 kcal mol(-1) of the experimental value [P. G. Wenthold et al., J. Am. Chem. Soc., 1998, 120, 5279], which is significantly better than traditional single-reference methods. We observe that the degree of multireference correlation in the biradicals depends upon the distance between their radical centers, with the largest radical separation displaying the largest degree of multireference correlation. In addition to relative and absolute electronic energies, we report molecular geometries, natural orbitals, and natural-orbital occupations for the benzene and cyclobutadiene biradicals.

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

“…per the analysis based natural-orbital occupation numbers within the framework of p2-RDM and MCSCF descriptions. [89] Our IVO-SSMRPT calculations predict an energy ordering of o < p, a result consistent with preexisting theoretical results as well as with experimental determinations. Although our ΔE S − T value provided by IVO-SSMRPT(2,2) is smaller than the predicted range, the IVO-SSMRPT result o-benzyne moves toward the database values with an increase in the dimension of CAS used in the construction of reference space.…”

“…Concerning o ‐benzyne, Mk‐MRCCSD method suggests the C1─C2 distance to be about 0.15 Å longer in the lowest triplet state than in the singlet ground state, whereas for p ‐benzyne the C1─C4 bond length reduces by about 0.07 Å in the triplet state compared to the ground state . For the o‐ and p ‐benzynes, the IVO‐SSMRPT method's geometrical data predictions agree most closely with that of the CR‐CC, CCSD(T), and p2‐RDM (parametric two‐electron reduced‐density matrix) level of formalisms . For o ‐benzyne system, the distance between the radical centers is suggested to be 1.267, 1.273, 1.260, and 1.277 Å by the CCSD, CR‐CC, CCSD(T), and p2‐RDM (two‐electron reduced‐density matrix) approaches, respectively .…”

“…This elongating effect is most pronounced in the CR‐CC and CCSD calculations, which suggests radical center separations of 2.746 and 2.750 Å and C2─C3 bond distances of 1.455 and 1.460 Å, respectively, compared to the IVO‐SSMRPT forecasts of 2.707 and 1.446 Å. It is worth noting the corresponding values due to p2‐RDM estimations are 2.699 and 1.421 Å …”

“…In the case of the ground singlet state of the o and p ‐benzynes, the value of t 2 amplitude for the most important doubly excited configuration in CCSD/cc‐pVTZ calculations are, respectively, 0.152, and 0.41 which are good indicators of both the diradical character and of the MR nature of the state. Moreover, unlike o ‐benzyne, p ‐benzyne is seen to be highly MR as per the analysis based natural‐orbital occupation numbers within the framework of p2‐RDM and MCSCF descriptions …”

“…[85] For the o-and p-benzynes, the IVO-SSMRPT method's geometrical data predictions agree most closely with that of the CR-CC, CCSD(T), and p2-RDM (parametric two-electron reduced-density matrix) level of formalisms. [89] For obenzyne system, the distance between the radical centers is suggested to be 1.267, 1.273, 1.260, and 1.277 Å by the CCSD, CR-CC, CCSD(T), and p2-RDM (two-electron reduced-density matrix) approaches, respectively. [89] In this context, the IVO-SSMRPT prediction (of 1.2624 Å)…”