Ab Initio MCSCF Study on the Pseudo-Jahn−Teller Distortion from Planarity in Cycloheptatriene, Heptalene, and Heptafulvalene

Variation from closed-shell to open shell electronic structures in oligothiophene bis(dioxolene) complexes

A series of oligothiophene bis(dioxolene) complexes, SQ-Thn-SQ (SQ = S = ½TpCum,MeZnII(3-tert-butyl-orthosemiquinonate); TpCum,Me = tris(5-cumenyl-3-methylpyrazolyl)borate anion) have been synthesized, structurally characterized, and studied as a function of the number of thiophene bridging units, n (n = 0-3) using a combination of variable-temperature (VT) electronic absorption and EPR spectroscopies, and VT magnetic susceptibility measurements. The thiophene bridge bond lengths determined by X-ray crystallography display dramatic differences across the SQ-Thn-SQ series. Bridge bond deviation values (Σ|Δi|) display a progressive change in the nature of the bridge fragment bonding as the number of thiophene groups increases, with quinoidal bridge character for n = 1 (SQ-Th-SQ) and biradical character with "aromatic" bridge bond lengths for n = 3 (SQ-Th3-SQ). Remarkably, for n = 2 (SQ-Th2-SQ) the nature of the bridge fragment is intermediate between quinoid and biradical aromatic, which we describe as having open-shell character as opposed to biradicaloid since the open-shell biradical configuration does not have the correct symmetry to mix with the quinoidal ground-state configuration. This bridge bonding character is reflected in the energies of the lowest lying open-shell states for these three molecules. The SQ-Th-SQ molecule is diamagnetic at all temperatures studied, and we provide evidence for SQ-SQ antiferromagnetic exchange coupling and population of triplet states in SQ-Th2-SQ and SQ-Th3-SQ, with JSQ-SQ(ave) = -279 cm-1 (VT EPR/electronic absorption/magnetic susceptibility) and JSQ-SQ = -117 cm-1 (VT EPR/electronic absorption/magnetic susceptibility), respectively. The results have been interpreted in the context of state configurational mixing within a simplified 4-electron, 3-orbital model that explicitly contains contributions of a bridge fragment. Variable-temperature spectroscopic- and magnetic susceptibility data are consistent with two low-lying open-shell states for SQ-Th3-SQ, but three low-lying states (one closed-shell and two open-shell) for SQ-Th2-SQ. This model provides a simple symmetry-based framework to understand the continuum of electronic and geometric structures of this class of molecules as a function of the number of thiophene units in the bridge.

Do Antarafacial Cycloadditions Occur? Cycloaddition of Heptafulvalene with Tetracyanoethylene

The cycloaddition of heptafulvalene (1) with tetracyanoethylene (TCNE) was previously described as an example of an antarafacial cycloaddition, a [π¹⁴ _a +π² _s ] process that afforded only the trans cycloadduct by virtue of the edge-to-face approach of TCNE, facilitated by the S shape of 1. The reaction has been investigated in depth and found not to be a concerted antarafacial process. At low temperature, the reaction is observed to give a mixture of cis and trans cycloadducts as well as a [4+2] cycloadduct. The mixture of products is converted to the trans cycloadduct by equilibration upon warming to room temperature. Studies with diethyl 2,3-dicyanofumarate and -maleate confirmed the formation of cis cycloadducts. DFT studies at the M06-2X/6-311+G(2d,p) SCRF=acetone level of theory show that the originally proposed edge-to-face approach of TCNE to 1 is highly disfavored, whereas a stepwise mechanism involving the addition of TCNE at C2 to form a zwitterion followed by collapse at either C2' or C7' is energetically accessible. The Diels-Alder adduct is also formed in a stepwise reaction by competitive addition of TCNE at C4 of 1. These studies suggest that edge-to-face interactions are prohibitive in even the most favorable cases.

Multiconfiguration Self-Consistent Field Study on Formonitrile Imine and N-Substituted Nitrile Imines HCN2-R: Energy Component Analysis of the Pseudo-Jahn-Teller Effect

Stable geometrical structures for formonitrile imine (1) and N-substituted nitrile imines HCN₂-R (R = Li, BeH, BH₂, CH₃, CN, CCH, C₆H₅, NH₂, OH, and F) (2-11) were examined by using the multiconfiguration self-consistent-field (MCSCF) method followed by second-order configuration interaction (SOCI) calculations and second-order multiconfiguration quasi-degenerate perturbation theory (MCQDPT2) calculations, together with the aug-cc-pVTZ basis sets. The results show that 1 suffers a pseudo-Jahn-Teller (JT) distortion from a linear C_∞v structure to a C₁ structure via a planar bent C_s structure. Each of the others is found to undergo pseudo-JT distortion from a symmetrical structure to a planar bent C_s structure for 2, 3, and 7 and to a C₁ structure for 4, 5, 6, 8, 9, 10, and 11. At the stationary structures of 1-11, the structural characteristics were briefly discussed in terms of allenic and propargylic. To elucidate the nature of pseudo-JT distortions, energy component analyses were carried out at the MCSCF+SOCI level of theory at all of the stationary structures for the relevant molecules. In most of the molecules examined, pseudo-JT stabilizations were classified into two groups, one in which the stability arises from a lowering of the energy of the attractive term V_en and the other in which the stability results from a lowering of the energy of the repulsive terms V_nn and V_ee. In addition to the above two groups, it was also found that the following three groups are responsible for the pseudo-JT stabilizations in a certain stage of the structural changes. Namely, one is a lowering of the energy of the term V_ee observed in 6, another is a lowering of the energy of the terms V_ee and V_en observed in 9-11, and the other is a lowering of the energy of the terms V_en and V_nn observed in 10. These energetic behaviors were accounted in terms of an elongation or a contraction of the molecular skeleton, a migration of electrons from one part of the molecule to other parts, and the combined effects arising from these two factors.

Numerical Estimation of the Pseudo-Jahn-Teller Effect Using Nonadiabatic Coupling Integrals in Monocyclic and Bicyclic Conjugated Molecules

The pseudo-Jahn-Teller (pJT) effect in monocyclic and bicyclic conjugated molecules was investigated by using the state-averaged multiconfiguration self-consistent field (MCSCF) method, together with the 6-31G(d,p) basis sets. Following the perturbation theory, the force constant along a normal mode Q is given by the sum of the classical force constant and the vibronic contribution (VC) resulting from the interaction of the ground state with excited states. The latter is given as the sum of individual contributions arising from vibronic interactions between the ground state and excited states. In the present work, each VC was calculated on the basis of nonadiabatic coupling (NAC) integrals. Furthermore, the classical force constant was estimated by taking advantage of the VC and the force constant obtained by vibrational analyses. For pentalene and heptalene, the present method seems to overestimate the VC in absolute value because of the small energy gap between the ground state and the lowest excited state. However, we are confident that the VC and the classical force constant for the other molecules are reasonable in magnitude in comparison with available literature information. Thus, it is proved that the present method is applicable and useful for numerical estimation of pJT effect.