The Intricate Case of Tetramethyleneethane: A Full Configuration Interaction Quantum Monte Carlo Benchmark and Multireference Coupled Cluster Studies

Abstract

We have performed a full configuration interaction (FCI) quality benchmark calculation for the tetramethyleneethane molecule in the cc-pVTZ basis set employing a subset of complete active space second order perturbation theory, CASPT2(6,6), natural orbitals for the FCI quantum Monte Carlo calculation. The results are in an excellent agreement with the previous large scale diffusion Monte Carlo calculations by Pozun et al. and available experimental results. Our computations verified that there is a maximum on the potential energy surface (PES) of the ground singlet state (A) 45° torsional angle, and the corresponding vertical singlet-triplet energy gap is 0.01 eV. We have employed this benchmark for the assessment of the accuracy of Mukherjee's coupled clusters with up to triple excitations (MkCCSDT) and CCSD tailored by the density matrix renormalization group method (DMRG). Multireference MkCCSDT with CAS(2,2) model space, though giving good values for the singlet-triplet energy gap, is not able to properly describe the shape of the multireference singlet PES. Similarly, DMRG(24,25) is not able to correctly capture the shape of the singlet surface, due to the missing dynamic correlation. On the other hand, the DMRG-tailored CCSD method describes the shape of the ground singlet state with excellent accuracy but for the correct ordering requires computation of the zero-spin-projection component of the triplet state (B).

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

“…The estimates of Veis et al [106] are in a very good accord with the previous large-scale DMC estimations due to Jordon and corkers [108] and available experimental results. [112] Depending upon the truncation scheme employed in the MRCC calculations of Pittner et al [105] , the ST splittings for TME appears to range from −3.22 to 15.45 kcal/mol suggesting the challenge of balancing and accounting the different types of correlation effects in the singlet and nonsinglet states when employing such levels of methods.…”

“…RAS(h,p)‐SF, DMC, and LRDMC predict slightly smaller gaps of 2.44, 2.17, and 2.76 kcal/mol, while VMC, RAS(S,2h,2p)‐SF/cc‐pVTZ, and RAS(h,p)(S)‐SF/cc‐pVTZ level of calculations yield slightly higher splittings of 3.87, 3.21, and 3.04 kcal/mol. For the torsional angle of 90 ° , IVO‐SSMRPT predicts an excellent agreement with the computationally highly expensive FCIQMC energy difference between singlet and triplet states . It is worth mentioning that, at D 2d , the DMRG‐TCCSD level of calculation yields highly accurate energy gap between ground singlet and triplet state.…”

“…It should be underlined that the lack of dynamical correlation in IVO‐CASCI has a pronounced impact on the topology of the computed torsional potential surface (TPS) as already noted in earlier CASSCF vis‐a‐vis CASPT2 studies. Very recently, Pittner and coworkers pointed out that DMRG(24,25) calculations fail to generate correct shape of the singlet surface, due to explicit absence of dynamic correlation effects as it is evident from the fact that DMRG‐based TCCSD (tailored CCSD) model describes 1 [TME] energy surface with a very good accuracy if one uses the zero‐spin‐projection component . Thus, for correct description of the singlet, surface requires delicate balance between nondynamic and dynamical electronic correlations.…”

“…(B) Description of various structural forms of TME emerging from the torsion of the central carbon-carbon bond nearly degenerate (obey the Ovchinnikov's rule) that are responsible for the diradical character and hence obtaining a definite order of the singlet and triplet states of TME is not easy task. [102][103][104][105][106][107][108][109][110][111][112][113] Despite various works on TME, determination of the shape of twisting potential for the lowest energy singlet and triplet states is a challenging task as the system easily twists around the central C C bond and various methods encountered give an unbalanced account of the intricate interplay of different correlation effects in the two low-lying electronic states. Note that the singlet and triplet energy surfaces could cross one another as the twisting angle is varied.…”

“…Very recently, Pittner and coworkers pointed out that DMRG(24,25) calculations fail to generate correct shape of the singlet surface, due to explicit absence of dynamic correlation effects as it is evident from the fact that DMRG-based TCCSD (tailored CCSD) model describes 1 [TME] energy surface with a very good accuracy if one uses the zero-spin-projection component. [106] Thus, for correct description of the singlet, surface requires delicate balance between nondynamic and dynamical electronic correlations. Figure 9 revealed that the singlet twisting energy surface is much flatter than the triplet one obtained by IVO-SSMRPT method as that of other well-established calculations.…”