Multireference coupled-cluster calculations on the energy of activation in the automerization of cyclobutadiene: Assessment of the state-specific multireference Brillouin–Wigner theory

Abstract

Automerization reaction of cyclobutadiene and its barrier height: An ab initio benchmark multireference averagequadratic coupled cluster study J. Chem. Phys. 125, 064310 (2006); 10.1063/1.2222366 Continuous transition between Brillouin-Wigner and Rayleigh-Schrödinger perturbation theory, generalized Bloch equation, and Hilbert space multireference coupled cluster Hilbert-space state-universal multireference coupled-cluster ͑MR CC͒ data on cyclobutadiene ͓A. Balková and R. J. Bartlett, J. Chem. Phys. 101, 8972 ͑1994͔͒ were used as a benchmark for testing our recently developed state-specific ͑single-root͒ multireference Brillouin-Wigner coupled-cluster ͑MR BWCC͒ theory. For the energy of activation in the automerization of cyclobutadiene ͑i.e., the energy difference between the square and rectangular structures͒ at the CCSD/͓3s2 p1d/2s͔ level of theory, our MR BWCCSD method gives the value of 6.2 kcal/mol, compared to 6.5 kcal/mol given by MR CCSD. With the cc-pVDZ and cc-pVTZ/cc-pVDZ basis sets, the MR BWCCSD activation barrier is 6.4 and 7.0 kcal/mol, respectively. The effect of the triple excitations ͓in MR CCSD͑T͔͒ and of the frozen core approximation were estimated previously to be below 0.1 kcal/mol and in the opposite direction. This shows the way of how to arrive at a more accurate automerization barrier in future calculations: extension of the basis set seems to be more important than going beyond the CCSD͑T͒ or MB BWCCSD level of the theory.

Double-hybrid density functionals: merging wavefunction and density approaches to get the best of both worlds

“…As a matter of illustration, the energy barrier for the auto-isomerization of cyclobutadiene is known to be a longstanding problem [151][152][153][154]. The interconversion between two iso-energetic (rectangular) forms passes through a (square) transition state having degenerate frontier orbitals, see Figure 5, which would thus need a multiconfigurational treatment or a more generalised treatment than that provided by current methods [155][156][157].…”

The State-Universal Multi-Reference Coupled-Cluster Theory: An Overview of Some Recent Advances

“…The direct use of the final energy expressions in CC calculations, as is done in our MMCC theory [7,[118][119][120][121][122][123] and its multi-reference extension discussed here and in Ref. 117, which may result in the introduction of unlinked terms, is also exploited in the Brillouin-Wigner MRCC method [32][33][34][35][36][37]. As in the approximate MMCC case, the Brillouin-Wigner MRCC approach is not size extensive.…”

“…In this paper, we focus on the genuine multi-reference CC (MRCC) theories, which are based on the concept of effective Hamiltonian acting in a multi-dimensional reference or model space [4,6,[8][9][10][11][12] and which use the exponential CC ansatz to parametrize the solutions of the generalized Bloch equation [8]. The state-specific (SS) MRCC methods [4,6], including the active-space CC approaches of Adamowicz, Piecuch, Bartlett, and their collaborators [13][14][15][16][17][18][19][20][21][22][23][24][25][26] and their more recent excited-state extensions [27][28][29], the SSMRCC approach of Mahapatra et al [30,31], and the highly promising Brillouin-Wigner MRCC approach [32][33][34][35][36][37], will not be discussed in this work, although the similarity of the wave function ansatz used in the genuine state-universal MRCC theory [4,6,, considered in this paper, and the form of the wave function exploited by the SSMRCC and Brillouin-Wigner MRCC approaches of Refs. 30, 31 and 32-37, respectively, should be noted.…”

Multireference Configuration Interaction Methods – An Application to the Valence Isomerism in Cyclobutadieno-p-benzoquinone and its Diprotonated Form

“…[12,13] However, this finding initiated heated debate in literature on whether the measured crystal structure corresponds to 1,3-dimethylcyclobutadiene at al. [14][15][16][17] Valence bond isomerism of cyclobutadiene has also aroused considerable interest of theoretical chemists, to mention only the most recent high level computational studies by Balkova and Bartlett, [12] Sancho-Garcia et al, [18] Shen et al, [19] Lefrancois et al, [20] and our research group. [13] We have shown that the barrier for automerization reaction of the parent CBD molecule obtained at the MR-AQCC level of theory including extrapolations to the basis set limit is 6.3 kcal mol −1 .…”

“…[13] This value is 2.2 kcal mol −1 above the two determinant TDCCSD(T) result of Balková and Bartlett. [12] The state specific multireference BrillouinWigner CC (MR BWCC) theory gives 4.5 kcal mol −1 , [18] whereas the recent block correlated coupled cluster CAS-BCCC4 method yields 6.2 kcal mol −1 . [19] Except for cyclobutadiene MR-AQCC calculations were also performed on derivatives of CBD, such as benzo [1,2:4,5]dicyclobutadiene, [21,22] and cyano substituted CBDs.…”