Transition States for the Dimerization of 1,3-Cyclohexadiene: A DFT, CASPT2, and CBS-QB3 Quantum Mechanical Investigation

Ess, Daniel H.; Hayden, Amy E.; Klärner, Frank‐Gerrit; Houk, K. N.

doi:10.1021/jo8011804

“…Accurate predictions of the singlet-triplet (ST) energy gaps remains a challenge for conventional density-functional theory because of the multireference nature of the singlet state. 12,13 Therefore, most computational studies involving singlet diradicals utilize ab initio multireference methods, such as complete active space self-consistent field (CASSCF), [14][15][16] complete active space with second-order perturbation theory, 17,18 or multireference coupled cluster theory. 19,20 Unfortunately, all these multireference ab initio methods are extremely computationally demanding for large systems.…”

Section: Introductionmentioning

confidence: 99%

Variational fractional-spin density-functional theory for diradicals

Peng¹,

Hu²,

Devarajan³

et al. 2012

The Journal of Chemical Physics

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Accurate computation of singlet-triplet energy gaps of diradicals remains a challenging problem in density-functional theory (DFT). In this work, we propose a variational extension of our previous work [D. H. Ess, E. R. Johnson, X. Q. Hu, and W. T. Yang, J. Phys. Chem. A 115, 76 (2011)], which applied fractional-spin density-functional theory (FS-DFT) to diradicals. The original FS-DFT approach assumed equal spin-orbital occupancies of 0.5 α-spin and 0.5 β-spin for the two degenerate, or nearly degenerate, frontier orbitals. In contrast, the variational approach (VFS-DFT) optimizes the total energy of a singlet diradical with respect to the frontier-orbital occupation numbers, based on a full configuration-interaction picture. It is found that the optimal occupation numbers are exactly 0.5 α-spin and 0.5 β-spin for diradicals such as O(2), where the frontier orbitals belong to the same multidimensional irreducible representation, and VFS-DFT reduces to FS-DFT for these cases. However, for diradicals where the frontier orbitals do not belong to the same irreducible representation, the optimal occupation numbers can vary between 0 and 1. Furthermore, analysis of CH(2) by VFS-DFT and FS-DFT captures the (1)A(1) and (1)B(1) states, respectively. Finally, because of the static correlation error in commonly used density functional approximations, both VFS-DFT and FS-DFT calculations significantly overestimate the singlet-triplet energy gaps for disjoint diradicals, such as cyclobutadiene, in which the frontier orbitals are confined to separate atomic centers.

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“…In 2008, Ess et al calculated the TS structures and reaction pathways for the dimerization of 1,3-cyclohexadiene in the gas-phase. 28 Calculations at B3LYP, CASPT2 and CBS-QB3 levels show that the computed reaction barriers for the concerted [4+2]cycloadditions, concerted [6+4]-ene reactions, and the stepwise additions (Figure 3) are within 5 kcal/mol. This small difference is consistent with the difference in experimental !…”

Section: Concerted [4+2]-ene Pathwaysmentioning

confidence: 97%

High-pressure reaction profiles and activation volumes of 1,3-cyclohexadiene dimerizations computed by the extreme pressure-polarizable continuum model (XP-PCM)

Chen

¹

,

Houk

²

,

Cammi

³

2021

Preprint

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0

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Quantum chemical calculations are reported for the thermal dimerizations of 1,3-cyclohexadiene at 1 atm and high pressures up to 6 GPa. Previous experiments [Klärner et al. Angew. Chem. Int. Ed. 1986, 25, 108], based on measured activation energies and activation volumes, suggested concerted mechanisms for the formation of the endo [4+2] cycloadduct and a [6+4]-ene adduct, and stepwise mechanisms for the formation of the exo [4+2] cycloadduct and two [2+2] cycloadducts. Computed activation enthalpies (ωB97XD, CCSD(T) and SC-NEVPT2) of plausible dimerization pathways at 1 atm agree well with the experiment activation energies and the values from previous calculations [Ess et al. J. Org. Chem. 2008, 73, 7586]. High-pressure reaction profiles, computed by the recently-developed extreme pressure-polarizable continuum model (XP-PCM), show that the reduction of reaction barrier is more profound in concerted reactions than in stepwise reactions, which is rationalized on the basis of the volume profiles of different mechanisms. A clear shift of the transition state towards the reactant by high pressure is revealed for the [6+4]-ene reaction by the calculations. The computed activation volumes by XP-PCM agree excellently with the experimental values, confirming the existence of competing mechanisms in the thermal dimerizations of 1,3-cyclohexadiene.

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“…The symmetry-allowed [4+2] cycloadducts and the [6+4]-ene adduct could, in principle, be formed through either a concerted or stepwise mechanism, whereas the symmetry-forbidden [2+2] cycloadducts are usually expected to be formed via a stepwise mechanism under thermal conditions (Figure 3). 26,28 The main difference between the concerted and stepwise mechanisms, in terms of activation volume, is that two bonds are formed at once in a concerted mechanism and only one bond is initially formed in a stepwise mechanism, so that the concerted transition state (TS) structure is usually more compact than the stepwise TS structure. Therefore, the concerted reaction usually has a more negative activation volume than a stepwise reaction.…”

Section: Introductionmentioning

confidence: 99%

High-pressure reaction profiles and activation volumes of 1,3-cyclohexadiene dimerizations computed by the extreme pressure-polarizable continuum model (XP-PCM)

Chen

¹

,

Houk

²

,

Cammi

³

2021

Preprint

Self Cite

0

View full text Add to dashboard Cite

Quantum chemical calculations are reported for the thermal dimerizations of 1,3-cyclohexadiene at 1 atm and high pressures up to 6 GPa. Previous experiments [Klärner et al. Angew. Chem. Int. Ed. 1986, 25, 108], based on measured activation energies and activation volumes, suggested concerted mechanisms for the formation of the endo [4+2] cycloadduct and a [6+4]-ene adduct, and stepwise mechanisms for the formation of the exo [4+2] cycloadduct and two [2+2] cycloadducts. Computed activation enthalpies (ωB97XD, CCSD(T) and SC-NEVPT2) of plausible dimerization pathways at 1 atm agree well with the experiment activation energies and the values from previous calculations [Ess et al. J. Org. Chem. 2008, 73, 7586]. High-pressure reaction profiles, computed by the recently-developed extreme pressure-polarizable continuum model (XP-PCM), show that the reduction of reaction barrier is more profound in concerted reactions than in stepwise reactions, which is rationalized on the basis of the volume profiles of different mechanisms. A clear shift of the transition state towards the reactant by high pressure is revealed for the [6+4]-ene reaction by the calculations. The computed activation volumes by XP-PCM agree excellently with the experimental values, confirming the existence of competing mechanisms in the thermal dimerizations of 1,3-cyclohexadiene.

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Transition States for the Dimerization of 1,3-Cyclohexadiene: A DFT, CASPT2, and CBS-QB3 Quantum Mechanical Investigation

Cited by 32 publications

References 76 publications

Variational fractional-spin density-functional theory for diradicals

Variational fractional-spin density-functional theory for diradicals

High-pressure reaction profiles and activation volumes of 1,3-cyclohexadiene dimerizations computed by the extreme pressure-polarizable continuum model (XP-PCM)

High-pressure reaction profiles and activation volumes of 1,3-cyclohexadiene dimerizations computed by the extreme pressure-polarizable continuum model (XP-PCM)

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