Reference Energies for Cyclobutadiene: Automerization and Excited States

Abstract

Cyclobutadiene is a well-known playground for theoretical chemists and is particularly suitable to test ground- and excited-state methods. Indeed, due to its high spatial symmetry, especially at the D 4h square geometry but also in the D 2h rectangular arrangement, the ground and excited states of cyclobutadiene exhibit multiconfigurational characters and single-reference methods, such as standard adiabatic time-dependent density-functional theory (TD-DFT) or standard equation-of-motion coupled cluster (EOM-CC), are notoriously known to struggle in such situations. In this work, using a large panel of methods and basis sets, we provide an extensive computational study of the automerization barrier (defined as the difference between the square and rectangular ground-state energies) and the vertical excitation energies at D 2h and D 4h equilibrium structures. In particular, selected configuration interaction (SCI), multireference perturbation theory (CASSCF, CASPT2, and NEVPT2), and coupled-cluster (CCSD, CC3, CCSDT, CC4, and CCSDTQ) calculations are performed. The spin-flip formalism, which is known to provide a qualitatively correct description of these diradical states, is also tested within TD-DFT (combined with numerous exchange-correlation functionals) and the algebraic diagrammatic construction [ADC(2)-s, ADC(2)-x, and ADC(3)]. A theoretical best estimate is defined for the automerization barrier and for each vertical transition energy.

Advances in Parallel Heat Bath Configuration Interaction

“…Methods that approximate the FCI energy are especially useful for approaching strongly correlated problems. Therefore high quality activation barriers and gaps are computed for the cyclobutadiene automerization, which are consistent with prior CCSDTQ 53 calculations. Additionally, FCI extrapolations are obtained to compute the electron correlation from the Fe�O valence space along with N lone-pairs in [FeO(NH 3 ) 5 ] 2+ .…”

“…To further test the capabilities of the new HCI implementation, HCI is applied to the automerization of cyclobutadiene, ,,− a well-known strongly correlated system. The reaction begins and ends at a D 2 h geometry, and proceeds through a D 4 h transition state that has a low-lying triplet electronic state.…”

“…Using the two extrapolation schemes, the relative energies change only slightly, with the largest change being 0.22 kcal mol –1 (see Table ). Prior studies computed the ”theoretical best estimate” for the singlet–triplet gaps of the D 2 h and D 4 h geometries and singlet barrier at the CCSDTQ/aug-cc-pVTZ level of theory . These quantities are shown in Table alongside the CI extrapolation energies.…”

“…Prior studies computed the "theoretical best estimate" for the singlet−triplet gaps of the D 2h and D 4h geometries and singlet barrier at the CCSDTQ/aug-cc-pVTZ level of theory. 53 These quantities are shown in Table 5 alongside the CI extrapolation energies. Some discrepancy arises from the difference in basis, though the largest relative energy difference is relatively small at 1.15 kcal mol −1 .…”

“…The singlet and triplet gaps in the cyclobutadiene automerization reaction were also studied with HCI. D 2 h and D 4 h geometries for cyclobutadiene were taken from a prior coupled-cluster study . The HCI calculations included all valence electrons and were performed with the cc-pVTZ basis set resulting in a FCI space of (20e,172o).…”