Electronic structure of organic diradicals: Evaluation of the performance of coupled-cluster methods

Abstract

The performance of (i) the reduced multireference (RMR) coupled-cluster (CC) method with singles and doubles (RMR CCSD) that employs a modest-size MR CISD wave function as an external source for the most important (primary) triples and quadruples in order to account for the nondynamic correlation effects in the presence of quasidegeneracy, (ii) the RMR CCSD(T) method that adds a perturbative correction for the remaining (secondary) triples to the RMR CCSD energy, and (iii) the recently developed partially linearized MR CCSD method, which determines primary triples and quadruples using a subset of linear CC equations projected onto the corresponding higher-than-doubly excited configurations, are tested by considering the singlet-triplet splitting for several diradicals, ranging from a prototypical methylene radical to trimethylenemethane, and benzyne and pyridynium cation isomers. Both RHF and multiconfigurational self-consistent field molecular orbitals are employed. The equilibrium geometries for the lowest-lying singlet and triplet states are determined using both the density functional theory (DFT) and various CC approaches, and a comparison with both the experiment and other theoretical results, wherever available, is made. The RMR CCSD(T) results provide the most satisfactory description in all cases. The dependence of the MR diradical character on a spatial separation of radical centers, as well as the artifactual DFT geometry in the case of benzyne and pyridynium meta-isomers, is also pointed out.

Energetics of 1,n‐didehydro‐polyene diradicals and performance of reduced multireference coupled‐cluster method

“…For example, for the n = 4 trans isomer, the largest CCSD t 2 is 0. 46 These conclusions are consistent with our earlier results [4,12] which clearly indicate that, generally, when the CCSD t 2 amplitude is smaller than 0.4, the CCSD(T) energies are almost identical with the RMR CCSD(T) ones. Also, when the CCSD t 2 amplitude is greater than the above given critical value of 0.4, yet not very far from it, as in the case of trans-C 4 H 4 , the CCSD(T) results are still useful even though the errors likely exceed the chemical accuracy requirement, so that the RMR CCSD(T) method should be given a preference.…”

“…These smallest members of arynes have been studied both experimentally and theoretically. We refer the reader to a paper by Evangelista et al [3], where he can find references to an earlier work, as well as to our recent study of these [4] and related [5] diradicaloid species. Likewise, stable isomers of didehydronaphthalenes (or naphthynes) that derive from naphthalene were examined experimentally via infrared spectroscopy [6][7][8] and the presence of their less stable isomers was documented as reaction intermediates [9][10][11].…”

Studies on m-benzyne and phenol via improved virtual orbital-complete active space configuration interaction (IVO-CASCI) analytical gradient method

“…1) system showing significant diradical character. The treatment of electronic structure of m-benzyne requires special consideration [27][28][29][30][31][32][33]. The computed geometrical parameters, vibrational frequency (x) and the adiabatic singlet-triplet (ST) gap (DE ST ) via IVO-CASCI approach have been compared with the CASSCF calculations to illustrate the efficacy of the method.…”

Multireference Coupled-Cluster Methods: Recent Developments

“…), including a very demanding case of the triple-bond breaking in the nitrogen molecule [176,217] (see also [122]), but also enabled the handling of relatively large systems, such as nickel-carbonyls [218] and transition metal ion -methylene complexes [219]. Likewise, they enabled a reliable determination of the spin-multiplicity of the ground state in radicaloid systems with a small singlet-triplet splittings between the lowest-lying states, again in both small species [177,220,221] (such as CH 2 , BN, and C 2 ) and in relatively large systems, such as benzynes [178], pyridynes [222], naphthynes [223], and linear di-dehydro-polyenes [224]. Particularly remarkable turned out to be the RMR handling of a triple-bond dissociation of N 2 [176] using a 56-dimensional reference space for MR CISD (including hextuples).…”

“…However, in contrast to the latter, plMR CCSD considers only a small subset of important triples, as well as higher order amplitudes (possibly up to hextuples). Again, the remaining triples may be accounted for perturbatively, yielding plMR CCSD(T) method [114,115,178]. Although plMR methods are fully size extensive, the corresponding RMR approaches always yield superior results [115].…”