Orbital topology. III. Orbital mapping of unsymmetrical molecules. A survey of the thermal ring opening of isoelectronically substituted cyclobutenes and benzocyclobutenes

Orbital mapping analysis based on CNDO /2 molecular orbitals has been used to survey the thermal ring-opening isomerizations of cyclobutenes and benzocyclobutenes. Isoelectronic substitutions within the molecular framework of cyclobutene (e.g., CH₂ replaced by CH^?, OH⁺, NH, NH₂⁺) result in ground-state orbital correlations via both conrotatory and disrotatory pathways in several cases, in contrast to the parent hydrocarbon conrotatory stereochemistry. The results substantiate the heteroatom effects previously revealed by orbital mapping for the disrotatory thermal isomerizations of isoelectronic Dewar benzenes. Qualitative patterns, such as nodal shifts in the butadiene π orbital, are discussed in relation to the mapping correlations. The isoelectronic benzocyclobutenes give ground-state orbital correlations via conrotatory pathways only, which suggests that delocalization may reduce the heteroatom perturbation.     

Non-adiabatic coupling constants for the disrotatory and conrotatory isomerization paths between butadiene and cyclobutene

The S₁S₀ non-adiabtic coupling constants were calculated for the disrotatory and conrotatory paths of the isomerization reaction between butadiene and cyclobutene. The calculated non-adiabatic coupling terms showed clearly the difference between the non-adiabatic interactions of the two reaction processes, and they correlate well with the Woodward-Hoffman rule.     

A theoretical study of cyclohexyne addition to carbonyl-Cα bonds: allowed and forbidden electrocyclic and nonpericyclic ring-openings of strained cyclobutenes

The mechanism of cyclohexyne insertion into a C(O)-C(α) bond of cyclic ketones, explored experimentally by the Carreira group, has been investigated using density functional theory. B3LYP and M06-2X calculations were performed in both gas phase and THF (CPCM, UAKS radii). The reaction proceeds through a stepwise [2 + 2] cycloaddition of cyclohexyne to the enolate, followed by three disparate ring-opening possibilities of the cyclobutene alkoxide to give the product: (1) thermally allowed conrotatory electrocyclic ring-opening, (2) thermally forbidden disrotatory electrocyclic ring-opening, or (3) nonpericyclic C-C bond cleavage. Our computational results for the model alkoxide and potassium alkoxide systems show that the thermally allowed electrocyclic ring-opening pathway is favored by less than 1 kcal/mol. In more complex systems containing a potassium alkoxide (e-f), the barrier of the allowed conrotatory ring-opening is disfavored by 4-8 kcal/mol. This suggests that the thermodynamically more stable disrotatory product can be formed directly through a "forbidden" pathway. Analysis of geometrical parameters and atomic charges throughout the ring-opening pathways provides evidence for a nonpericyclic C-C bond cleavage, rather than a thermally forbidden disrotatory ring-opening. A true forbidden disrotatory ring-opening transition structure was computed for the cyclobutene alcohol; however, it was 19 kcal/mol higher in energy than the allowed conrotatory transition structure. An alternate mechanism in which the disrotatory product forms via isomerization of the conrotatory product was also explored for the alkoxide and potassium alkoxide systems.     

Altering the allowed/forbidden gap in cyclobutene electrocyclic reactions: experimental and theoretical evaluations of the effect of planarity constraints

The allowed conrotatory cyclobutene ring-opening has a distinctly nonplanar carbon skeleton. Classic experiments by Brauman and Archie, and by Freedman et al., placed the allowed/forbidden gap at greater than 15 kcal/mol. Wolfgang Roth proposed that a system forced to planarity might have a smaller preference for the conrotatory mode than unconstrained systems. Such systems have now been studied theoretically and experimentally, and results that confirm Roth's postulate are presented here. The experiments were performed in Bochum, and the calculations were carried out in Osaka and Los Angeles. As the cyclobutene ring-opening transition structure approaches planarity, the energy gap between allowed conrotatory and the forbidden disrotatory pathways decreases. For the ring-opening of a cyclobutene fused to norbornene, the energy gap between the forbidden and the allowed transition state is only 4.1 kcal/mol by CASSCF and 8.0 kcal/mol by CAS-MP2 as compared to 13.4 and 19.2 kcal/mol, respectively, for the parent cyclobutene. Experimental studies of 3,4-dimethylcyclobutenes fused to various ring systems are reported, and a trend is found toward a reduced allowed/forbidden gap as the planarity of the cyclobutene is enforced.     

Theoretical studies on the electrocyclic reactions of bis(allene) and vinylallene. Role of allene group

The reaction mechanisms of the electrocyclic ring closure of bis(allene) and vinylallene were studied by ab initio MO methods. The conrotatory and disrotatory pathways of the electrocyclic reactions from bis(allene) to bis(methylene)cyclobutene were determined by a CASSCF method. The transition state on the conrotatory pathway is 26.8 kcal/mol above bis(allene) and about 23 kcal/mol lower than that on the disrotatory pathway at a MRMP calculation level. The activation energy on the conrotatory pathway is lower by 23 kcal/mol than that of the electrocyclic reaction of butadiene. This lower energy barrier comes from the interactions of the "side pi orbitals" of the allene group. The interaction of the "vertical pi orbitals" of the allene group is predominant at the early stage of the reaction. The activation energy of the electrocyclic reaction of vinylallene is about 8.5 kcal/mol higher than that on the conrotatory pathway of bis(allene).     

Computational and Experimental Evidence of Two Competing Thermal Electrocyclization Pathways for Vinylheptafulvene

The thermal electrocyclic ring‐closure reaction of vinylheptafulvene (VHF) to form dihydroazulene (DHA) is elucidated herein by using DFT and ¹H NMR spectroscopy. Two different transition states were found computationally; one corresponds to a disrotatory pathway, which is allowed according to the Woodward–Hoffmann selection rules, whereas the other corresponds to a conrotatory pathway. The conrotatory pathway is found to be zwitterionic in the transition state, whereas the disrotatory transition state varies in zwitterionic character depending on solvent and substituents in the molecular framework. The conrotatory and disrotatory transition states are found to have similar energy and their relative stability varies with solvent polarity and functionalization at the C1 position. To support these findings, we chemically ring‐opened diastereomerically pure 1‐(benzothiazol‐2‐yl)‐DHA to give the VHF form, then subsequently thermally reconverted the VHF to DHA in a range of solvents with various polarities. We found that, depending on solvent polarity, different ratios of anti‐ and syn‐diastereoisomers of DHA were formed in a systematic manner, which supports the existence of two distinct thermal ring‐closure pathways for VHF.     

Should the Woodward–Hoffmann Rules be Applied to Mechanochemical Reactions?

Since decades, pericyclic reactions have been well‐understood by means of the Woodward–Hoffmann rules and their classification as thermally or photochemically “allowed” or “forbidden”. Recently, stunning results on such reactions subject to mechanochemical activation by external forces instead of heat or light have revealed reaction pathways at sufficiently large forces, which are not expected from the Woodward–Hoffmann rules. This led to the much reiterated idea that the “Woodward–Hoffmann rules are broken in mechanochemistry”. Here, by studying ring‐opening of cyclopropane, we show that the electronic structure underlying the dis‐ and conrotatory pathways, which are greatly distorted upon applying forces to an extent that eventually the “thermally forbidden” process becomes “mechanochemically allowed”, does not change along both pathways. It is rather the mechanical work that lowers the activation barrier of the thermally forbidden conrotatory process relative to the disrotatory one at large forces.     

Electrocyclic ring opening of cis-bicyclo[m.n.0]alkenes: the anti-Woodward-Hoffmann quest

The dubbed anti-Woodward-Hoffmann ring-opening reaction of cis-bicyclo[4.2.0]oct-7-ene to yield cis,cis-cycloocta-1,3-diene has been intensively studied with robust, high-level computational methods. This reaction has been found to proceed through a conrotatory allowed pathway to afford cis,trans-cycloocta-1,3-diene followed by E to Z isomerization, instead of a disrotatory forbidden pathway, as suggested. Computational calculations of kinetic isotope effects are consistent with this interpretation and the experimental values. The study of lower bicyclic homologues with [3.2.0], [2.2.0] and [2.1.0] skeletons indicates the feasibility of a mechanistic change towards the anti-Woodward-Hoffmann disrotatory path. This is clearly favored for the ring opening of the highly strained cis-bicyclo[2.1.0]pent-2-ene and is highly competitive with the conrotatory path for cis-bicyclo[2.2.0]hex-2-ene. Therefore, the rearrangement of the smallest bicyclic cyclobutene is predicted computationally to be an anti-Woodward-Hoffmann disrotatory electrocyclic ring-opening reaction.     

Conservation of Orbital Symmetry can be Circumvented in Mechanically Induced Reactions

In first‐principles molecular dynamics simulations of the mechanically induced ring‐opening of substituted benzocyclobutene we observe both con‐ and disrotatory ring‐opening reactions. We show that this finding does not contradict the fundamental principle that the orbitals develop continuously in time. However, it constitutes an exception from the principle of the conservation of orbital symmetry and thus is indeed an exception from the Woodward–Hoffmann rules. In contrast, the ring‐opening of unsubstituted cyclobutene proceeds in a conrotatory fashion. This shows that the breaking of the Woodward–Hoffmann rules is significantly facilitated by the substituents.     

The ring opening of cyclopropylidene to allene: global features of the reaction surface

Summary The global features of the groundstate ring opening of cyclopropylidene to allene are studied by means ofab-initio FORS MCSCF calculations based on a minimal AO basis set. The energy surface is completely mapped out in terms of three reaction coordinates, namely the CCC ring-opening angle and two angles describing the rotations of the CH₂ groups. For each choice of these three variables, the twelve remaining internal coordinates are optimized by energy minimization. In the initial phase of the reaction, as the CCC angle opens, the CH₂ groups rotate in a disrotatory manner, maintainingC _s symmetry. This uphill reaction path leads to a transition region which occurs early, for a CCC angle of about 84°. In this transition region the reaction path branches into two pathways which are each others' mirror images. The system exhibits thus abifurcating transition region. Passed this region, the two pathways are overall conrotatory in character. However, these downhill reaction paths to the products are poorly defined because, from a CCC opening angle of about 90° on,the CH ₂ groups can rotate freely and isoenergetically in a synchronized, cogwheel-like manner and this disrotatory motion can mix unpredictably with the conrotatory downhill motion. There is no preference for any one of the two reaction pathways yielding the two stereoisomers of allene and the reaction is thereforenonstereospecific with respect to the numbered hydrogen atoms. The global surface is documented by means of contour maps representing slices corresponding to constant CCC angles. The bifurcating transition region is mapped in detail.Operated for the U.S. Department of Energy by Iowa State University under Contract No. 7405-ENG-82. This work was supported by the office of Basic Energy Sciences     

Orbital topology. I. A basic topological model for chemical systems,an orbital mapping technique,and analyses of model,thermal electrocyclic reactions

A topological model which provides a unifying framework for chemical reactions and molecular structure is proposed. Such basic concepts as overlap, orthogonality, reaction continuity, reaction reversibility, and orbital correspondence are incorporated into the model in a logical fashion. A chemical reaction pathway is regarded as a function that transforms a reactant topological space into its equivalent product space. The unique character usually ascribed to reactants, products, and their wavefunctions is superfluous. The model also allows considerable approximation of the wavefunctions and the reaction pathway without affecting the overall result. A simple orbital mapping technique consistent with the model which traces the transformation of orbitals using intermolecular overlaps of the orbitals is also proposed. The suitability of a given pathway (“allowed” or “forbidden”) can be deduced explicitly without invoking symmetry (or other) rules and without resorting to detailed calculation of reaction energy surfaces. The validity of the mapping procedure has been confirmed by several thermal electrocyclic reactions: the ring-opening isomerizations of substituted cyclopropyl cations, cyclopropyl anion, cyclopropanone, cyclobutene, benzocyclobutene, Dewar benzenes, and 1,3-cyclohexadiene. Orbital mapping with EHT and CNDO/2 MOs correctly predicts the reaction stereochemistry (conrotatory or disrotatory) in every case.     

Perturbing π-clouds with Substituents to Study the Effects on Reaction Dynamics of gauche-1,3-Butadiene to Bicyclobutane Electrocyclization

The conical intersection (CI) governs the ultra-fast relaxation of excited states in a radiationless manner and are observed mainly in photochemical processes. In the current work, we investigated the effects of substituents on the reaction dynamics for the conversion of gauche-1,3-butadiene to bicyclobutane via photochemical electrocyclization. We incorporated both electron withdrawing (−F) and donating (−CH₃) groups in the conjugated system. In our study, we optimized the minimum energy conical intersection (MECI) geometries using the multi-configurational state-averaged CASSCF approach, whereas, to study the ground state reaction pathways for the substituted derivatives, dispersion corrected, B3LYP-D3 functional was used. The non-adiabatic surface hopping molecular dynamics simulations were performed to observe the behaviour of electronic states involved throughout the photoconversion process. The results obtained from the multi-reference second-order perturbation correction of energy at the XMS-CASPT2 level of theory, topography analysis, and non-adiabatic dynamics suggest that the −CH₃ substituted derivatives can undergo faster thermal conversion to the product in the ground state with a smaller activation energy barrier compared to −F substituted derivative. Our study also reveals that the GBUT to BIBUT conversion follows both conrotatory and disrotatory pathways, whereas, on substitution with −F or −CH₃, the conversion proceeds via the conrotatory pathway.     

Mechanochemistry on the Müller–Brown surface by Newton trajectories

Chemical processes which suffer the application of mechanical force are theoretically described by effective potential energy surface (PES). We worked out (W. Quapp, J. M. Bofill, Theor. Chem. Acc. 2016, 135, 113) that the changes due to the force for the minimums and for the saddle points can be described by Newton trajectories (NT) of the original PES. If the force is so high that the saddle point disappears into a shoulder then the mechanochemical action is fulfilled: the pulling force breaks down the reaction barrier. The point is named barrier breakdown point. Different families of NTs form corridors on the original PES which describe qualitative different actions of the force. The border regions of such corridors are governed by the valley‐ridge inflection points (VRI) of the surface. Here, we discuss all this on the basis of the well‐known Müller–Brown surface, and we describe a new kind of NT‐corridor.     

Natural orbitals of s-cis-butadiene and their relation to photochemical cyclization

Natural orbitals of the three lowest single states of s-cis-butadiene are calculated by CNDO/S. Under the disrotatory closure of s-cis-butadiene to cyclobutene, the 2 ¹A₁ natural orbitals are correlated differently from that described by the usual orbital diagram. The natural orbital correlations account for the main features of the potential surface.     

Theoretical investigation of the conrotatory ring opening of cyclobutene and 1, 2-dihydro-1, 2-diazacyclobutadienes with ab initio and density functional Gaussian-type-orbital approach

The theoretical study of the thermally allowed conrotatory opening of cyclobutene (1) and cis- (2) and trans-1,2-dihydro-1,2-diazacyclobutadiene (3) were performed with ab initio and density functional calculations. The reactants and the transition states were fully optimized by using the 6-31 + G** basis set with RHF , MP2 , SVWN , and BLYP methods. The calculated activation barriers for the ring opening of 1 with both MP2 and SVWN incorporating ZPVF correction give extraordinary agreement with the experimental value. The predicted activation energies for 2 and 3 are lower than in the case of the cyclobutene ring opening. Of the two 1,2-dihydro-1,2-diazacyclobutadiene isomers, the trans isomer has a lower activation barrier. The structural and energy differences and the trend among these compounds are interpreted in terms of orbital overlap and steric interactions in the course of the conrotatory ring opening. © 1995 John Wiley & Sons, Inc.     

Reaction rates in a theory of mechanochemical pathways

If one applies mechanical stress to a molecule in a defined direction then one generates a new, effective potential energy surface (PES). Changes for minima and saddle points (SP) by the stress are described by Newton trajectories on the original PES (Quapp and Bofill, Theor. Chem. Acc. 2016, 135, 113). The barrier of a reaction fully breaks down for the maximal value of the norm of the gradient of the PES along a pulling Newton trajectory. This point is named barrier breakdown point (BBP). Depending on the pulling direction, different reaction pathways can be enforced. If the exit SP of the chosen pulling direction is not the lowest SP of the reactant valley, on the original PES, then the SPs must change their role anywhere: in this case the curve of the log(rate) over the pulling force of a forward reaction can show a deviation from the normal concave curvature. We discuss simple, two‐dimensional examples for this model to understand more deeply the mechanochemistry of molecular systems under a mechanical stress. © 2016 Wiley Periodicals, Inc.     

The Electrocyclic Cyclopropyl-Allyl Rearrangement. Preliminary communication

MINDO-2 SCF calculations indicate that ring-opening of cyclopropyl radical (I) to allyl radical (II) is more favourable via a disrotatory reaction path, the calculated activation energy being ～30 kcal/mole. (For conrotatory opening the activation energy was found to be ～44 kcal/mole.) The two critical motions of the nuclei during the transformation are found to be strongly decoupled, i.e. rupture of the CH₂βCH₂ bond precedes rotation of the CH₂ groups. As predicted by qualitative theories both ring-opening modes are unfavourable since they involve a change in electronic ground-state symmetry between I and II. The preferred ring-opening mode is discussed qualitatively in terms of Evans' principle.     

Conformational distortions from local symmetry in cyclic and acyclic compounds: Crystallographic data analysis of C3CZCC3 fragments (Z = C,P, Si,N, S,O).

The local conformational symmetry distortions of C₃CZCC₃ fragments versus standard reference are analyzed in a conformational φ₁, φ₂ mean torsion angle space. Local distortions induced by strain are interpreted as resulting from a conrotatory (φ₁ x φ₂ > 0 quadrants 1 and 3) or a disrotatory relaxation process (φ₁ x φ₂ < 0 quadrants 2 and 4). Impressive sectorization of acyclic fragments in quadrants 1 and 3 and cyclic ones (6 atom cycles) in quadrants 2 and 4 is reported.     

A DFT study of the [4+2] cycloadditions of conjugated ketenes (vinylketene, imidoylketene and formylketene) with formaldimine. The pericyclic or pseudopericyclic character from magnetic properties

A comprehensive B3LYP/6-31+G^∗ study of the nature of the [4+2] cycloadditions of conjugated ketenes, vinylketene, imidoylketene and formylketene, with formaldimine was conducted. For each reaction, the complete pathway was determined and changes in different magnetic properties (magnetic susceptibility, χ, magnetic susceptibility anisotropy, χ_anis, and the nucleus-independent chemical shift, NICS) were monitored along the reaction profile with a view to estimate the aromatization associated to the process. We have also applied the ACID (anisotropy of the current-induced density) method with the same purpose. The deep analysis of the results indicates the existence of both disrotatory and conrotatory pericyclic paths for the cyclization step of the cycloaddition of vinylketene with formaldimine and the pseudopericyclic character of reactions with imidoylketene and formylketene.