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.     

Criteria for pericyclic and pseudopericyclic character of electrocyclization of (Z)-1,2,4,6-heptatetraene and (2Z)-2,4,5-hexatriene-1-imine

The electrocyclic reaction mechanisms of (Z)-1,2,4,6-heptatetraene and (2Z)-2,4,5-hexatriene-1-imine were studied by ab initio MO methods. The activation energy barrier height of the electrocyclic reaction of (Z)-1,2,4,6-heptatetraene is extremely a low energy barrier of 8.58 kcal/mol by a MRMP method. The activation energy barrier height of the electrocyclic ring closure of the trans-type of (2Z)-2,4,5-hexatriene-1-imine is lower by 3.18 kcal/mol than that of (Z)-1,2,4,6-heptatetraene. These low energy barriers come from some orbital interactions relating to allene group. For the reaction of (Z)-1,2,4,6-heptatetraene, the interactions of the vertical and side π orbitals of the allene group with another terminal π orbital are important at the transition state. The interaction of the vertical π orbital of allene group with a lone pair orbital of N atom is dominant at the transition state of the reaction of the trans-type of (2Z)-2,4,5- hexatriene-1-imine. The electrocyclic mechanism of the cis-type of (2Z)-2,4,5-hexatriene-1-imine was also discussed. Contribution of the Mark S. Gordon 65th Birthday Festschrift issue.     

Ab initio study of the pathways and barriers of tricyclo[4.1.0.0(2,7)]heptene isomerization

The thermal isomerization of tricyclo[4.1.0.0(2,7)]heptene has been studied using computational chemistry with structures determined at the MCSCF level and energies at the MRMP2 level. Both the allowed conrotatory and forbidden disrotatory pathways have been elucidated resulting in cycloheptatriene isomers. Four reaction channels are available for the conrotatory pathway depending on which bond breaks first in the bicyclobutane moiety leading to enantiomeric pairs of (E,Z,Z)-1,3,5-cycloheptatriene and (Z,E,Z)-1,3,5-cycloheptatriene intermediates. The activation barrier is calculated to be 31.3 kcal·mol?1 for two channels and 37.5 kcal·mol?1 for the other two. The lower activation barrier leading to the (E,Z,Z)-1,3,5-cycloheptatriene enantiomeric pair is proposed to be due to resonance within the transition state. The same behavior was observed for the disrotatory pathway with activation barriers of 42.0 kcal·mol?1 and 55.1 kcal·mol?1 for the two channels, again with one transition state resonance stabilized. The barriers for trans double bond rotation of the intermediate cycloheptatrienes are determined to be 17.1 and 17.4 kcal·mol?1, about 5 kcal·mol?1 more than that for the seven carbon diene (E,Z)-1,3-cycloheptadiene. The electrocyclic ring closure of the trans cycloheptatrienes have been modeled and barriers determined to be 11.1 and 11.9 kcal·mol?1 for the formation of bicyclo[3.2.0]hepta-2,6-diene. This structure was previously reported as the end product for thermolysis of the parent tricyclo[4.1.0.0(2,7)]heptene. The thermodynamically more stable cycloheptatriene can be formed from bicyclo[3.2.0]hepta-2,6-diene through a two step process with a calculated pseudo first-order barrier of 36.4 kcal·mol?1. The trans-cycloheptatrienes reported herein are the first characterization of a small seven-membered ring triene with a trans double bond.     

Thermal isomerization of tricyclo[4.1.0.0(2,7)]heptane and bicyclo[3.2.0]hept-6-ene through the (E,Z)-1,3-cycloheptadiene intermediate

The thermal isomerization of tricyclo[4.1.0.0(2,7)]heptane and bicyclo[3.2.0]hept-6-ene was studied using ab initio methods at the multiconfiguration self-consistent field level. The lowest-energy pathway for thermolysis of both structures proceeds through the (E,Z)-1,3-cycloheptadiene intermediate. Ten transition states were located, which connect these three structures to the final product, (Z,Z)-1,3-cycloheptadiene. Three reaction channels were investigated, which included the conrotatory and disrotatory ring opening of tricyclo[4.1.0.0(2,7)]heptane and bicyclo[3.2.0]hept-6-ene and trans double bond rotation of (E,Z)-1,3-cycloheptadiene. The activation barrier for the conrotatory ring opening of tricyclo[4.1.0.0(2,7)]heptane to (E,Z)-1,3-cycloheptadiene was found to be 40 kcal mol(-1), while the disrotatory pathway to (Z,Z)-1,3-cyclohetpadiene was calculated to be 55 kcal mol(-1). The thermolysis of bicyclo[3.2.0]hept-6-ene via a conrotatory pathway to (E,Z)-1,3-cycloheptadiene had a 35 kcal mol(-1) barrier, while the disrotatory pathway to (Z,Z)-1,3-cyclohetpadiene had a barrier of 48 kcal mol(-1). The barrier for the isomerization of (E,Z)-1,3-cycloheptadiene to bicyclo[3.2.0]hept-6-ene was found to be 12 kcal mol(-1), while that directly to (Z,Z)-1,3-cycloheptadiene was 20 kcal mol(-1).     

Theoretical study of the electrocyclic ring closure of hydroxypentadienyl cations

At the 6-311G* level of theory, DFT methods predict that the rearrangement of 1,4-dihydroxy-5-methylpentadienyl cation 1 (R = Me) to protonated trans-3-hydroxy-2-methylcyclopent-4-en-1-one 2, an intermediate step in the Piancatelli reaction or rearrangement of furfuryl carbinols to trans-2-alkyl(aryl)-3-hydroxycyclopent-4-en-1-one, is a concerted electrocyclic process. Energetic, magnetic, and stereochemical criteria are consistent with a conrotatory electrocyclic ring closure of the most stable out,out-1 isomer to afford trans-2. Although the out,in-1 isomer is thermodynamically destabilized by 6.84 kcal mol(-1), the activation energy for its cyclization is slightly lower (5.29 kcal mol(-1) versus 5.95 kcal mol(-1)). The cyclization of the isomers of 1 with the C1-hydroxy group inwards showed considerably higher activation energies than their outwards counterparts. in,out-1, although close in energy to out,out-1 (difference of 1.57 kcal mol(-1)) required about 10 kcal mol(-1) more to reach the corresponding transition structure. The value measured for the activation energy of in,in-1 (17.32 kcal mol(-1)) eliminates the alternative conrotatory electrocyclization of this isomer to provide trans-2. Geometric scrambling by isomerization of the terminal C1--C2 bond of 1 is also unlikely to compete with electrocyclization. The possibility to interpret the 1-->2 reaction as a nonpericyclic cationic cyclization was also examined through NBO analysis, and the study of bond lengths and atomic charges. It was found that the 1-->2 concerted rearrangement benefits from charge separation at the cyclization termini, an effect not observed in related concerted electrocyclic processes, such as the classical Nazarov reaction 3-->4 or the cyclization of the isomeric 2-hydroxypentadienyl cation 5.     

An ab initio MO study of allene episulfide, cyclopropanethione and thioxyallyl

The electronic structures of allene episulfide, cyclopropanethione and thioxyallyl were examined by ab initio MO calculations and were compared with those of the corresponding oxygen compounds, allene oxide, cyclopropanone and oxyallyl. The difference in reactivities of allene episulfide and allene oxide was also speculatively estimated from the calculated electronic structures. The lowest singlet state of thioxyallyl was predicted to be the B₂ state, which corresponds to the σ, π-diradical. A small activation energy is required for the cyclization of the B₂ state to give allene episulfide. The A₁ singlet state lies 11 kcal mol⁻¹ higher than the B₂ singlet state and undergoes the disrotatory rotation of methylene groups to give cyclopropanethione with no activation energy.     

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.     

Strongly correlated mechanisms of a photoexcited radical reaction from the anti-Hermitian contracted Schrödinger equation

Photoexcited radical reactions are critical to processes in both nature and materials, and yet they can be challenging for electronic structure methods due to the presence of strong electron correlation. Reduced-density-matrix (RDM) methods, based on solving the anti-Hermitian contracted Schro?dinger equation (ACSE) for the two-electron RDM (2-RDM), are examined for studying the strongly correlated mechanisms of these reactions with application to the electrocyclic interconversion of allyl and cyclopropyl radicals. We combine recent extensions of the ACSE to excited states [G. Gidofalvi and D. A. Mazziotti, Phys. Rev. A 80, 022507 (2009)] and arbitrary spin states [A. E. Rothman, J. J. Foley IV, and D. A. Mazziotti, Phys. Rev. A 80, 052508 (2009)]. The ACSE predicts that the ground-state ring closure of the allyl radical has a high 52.5 kcal/mol activation energy that is consistent with experimental data, while the closure of an excited allyl radical can occur by disrotatory and conrotatory pathways whose transition states are essentially barrierless. Comparisons are made with multireference second- and third-order perturbation theories and multireference configuration interaction. While predicted energy differences do not vary greatly between methods, the ACSE appears to improve these differences when they involve a strongly and a weakly correlated radical by capturing a greater share of single-reference correlation that increases the stability of the weakly correlated radicals. For example, the ACSE predicts a -39.6 kcal/mol conversion of the excited allyl radical to the ground-state cyclopropyl radical in comparison to the -32.6 to -37.3 kcal/mol conversions predicted by multireference methods. In addition, the ACSE reduces the computational scaling with the number of strongly correlated orbitals from exponential (traditional multireference methods) to quadratic. Computed ground- and excited-state 2-RDMs are nearly N-representable.     

The cis-hexatriene electrocyclization : Attempted calculation of the transition state geometry

A model has been developed to permit calculation of the energy changes associated with the electrocyclic reaction of cis-hexatriene to 1,3-cyclohexadiene. A novel method for solving the problems associated with calculations of the pi system energy and the energy of the forming single bond as the terminal carbons undergo rehybridization was developed. The result permits calculation of the total energy in terms of contributions from the forming sigma bond, the pi system, non-bonded interactions and bond energy changes resulting from rehybridization. The angle of rotation θ about the C₂C₃ and C₄C₅ bonds was used as an approximation to the reaction coordinate. Surprisingly the plot of energy vs θ showed no maximum for either the disrotatory or the conrotatory stereopath. Failure to produce a transition state was attributed to problems with assignment of a reasonable kcal equivalent to the Hückel gb, and an artificial device was proposed to solve the problem. The geometry of the disrotatory transition state achieved in this manner suggests that non-bonded interactions between hydrogens on the terminal carbon are not serious, but the dihedral angle between the p-orbitals at C₂C₃ (and C₄C₅) leads to a significant degree of isolation of C₂ and C₅ from the remainder of the pi system.     

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.     

Carboranes and baskets from reaction of B4H10 with allene

The reaction of the boron hydride B4H10 with allene was studied at the CCSD(T)/6-311+G(d)//MP2/6-31G(d) level. The mechanism is surprisingly complex with 44 transition states and several branching points located. The four carboranes and one basket that have been observed experimentally are all connected by pathways that have very similar free energies of activation. In addition, two new structures, a basket (2,4-(CH2CH2CH2)B4H8, 5a) and a "classical" structure (1,4-(Me2C)bisdiborane, 7), which might be obtained from the B4H10 + C3H4 reaction under the right conditions (hot/cold, quenched, etc.) have been identified. The first branch point in the reaction is the competition between H2 elimination from B4H10 (DeltaG(298 K) = 32.2 kcal/mol) and the hydroboration of allene by B4H10 (DeltaG(298 K) = 31.3 kcal/mol). The next branch point in the hydroboration mechanism controls the formation of 2,4-(MeCHCH2)B4H8 (1) (DeltaG(298 K) = 31.5 kcal/mol) and arachno-1,2/arachno-1,3-Me2-1-CB4H7 (8 and 8a) (DeltaG(298 K) = 34.3 kcal/mol). Another branch point in the H2-elimination mechanism controls the formation of 1-Me-2,5-micro-CH2-1-CB4H7 (29) (DeltaG(298 K) = 0.1 kcal/mol) and 2,5-micro-CHMe-1-CB4H7 (25/26) (DeltaG(298 K) = 7.3 kcal/mol). Formation of 2-Me-2,3-C2B4H7, a carborane observed in the reaction of methylacetylene with B4H10, is calculated to be blocked by a high barrier for H2 elimination. All free energies are relative to B4H10 + allene. An interesting reaction step discovered is the "reverse hydroboration step" in which a hydrogen atom is transferred from carbon back to boron, which allows a CH hydrogen to shuttle between the terminal and central carbon of allene.     

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.     

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.     

Incorporation of an allene unit into alpha-pinene: generation of the cyclic allene 2,7,7-trimethylbicyclo[4.1.1]octa-2,3-diene and its dimerization

The reaction of etheral methyllithium with 3,3-dibromo-2,7,7-trimethyl-tricyclo[4.1.1.0(2,4)]octane (2) was investigated. The generated carbene 12 undergoes intramolecular C-H insertion to provide the tetracyclic hydrocarbon 3 and the bicyclic allene 15, which undergoes [2+2] cyclodimerization. The structures of the formed allene dimers 16, 17, and 18 were elucidated by spectral means. The activation barriers for all possible C-H insertion products 3, 13, and 14 and the allene 15 were investigated by using density functional theory computations at the B3LYP/6-31G(d) level. It was found that the activation barriers for the formation of 3 and 15 (6.2 and 6.3 kcal mol(-1)) are much lower than that for the insertion products 13 and 14 (17.5 and 12.6 kcal mol(-1)), respectively. This prediction was completely in agreement with our experimental results.     

The protonation of allene and some heteroallenes, a computational study

Protonation of allene and seven heteroallenes, X = Y = Z, at the terminal and central positions has been studied computationally at the MP2/6-311+G**, B3LYP/6-31+G**, and G3 levels. In all but one case protonation at a terminal position is preferred thermodynamically. The exception is allene, where protonation at C2 giving allyl cation prevails by about 10 kcal/mol over end-protonation, which gives the 2-propenyl cation. In the heteroallenes, protonation at a terminal carbon is strongly favored, activated by electron donation from the other terminal atom. Transition states for identity proton-transfer reactions were found for 10 of the "end-to-end" proton transfers. When the transfer termini are heteroatoms these processes are barrier free. We found no first-order saddle point structures for "center-to-center" proton transfers. An estimate of DeltaH++ for an identity center-to-center proton transfer could be made only for the reaction between the allyl cation and allene; it is approximately 22 kcal/mol higher than DeltaH++ for the end-to-end proton transfer between the 2-propenyl cation and allene. First-order saddle points for the proton transfer from H3S+ to both C1 and C2 of allene were found. The difference in activation enthalpies is 9.9 kcal/mol favoring protonation at C1 in spite of the thermodynamic disadvantage. We infer that protonation of X = Y = Z at central atoms passes through transition states much like primary carbenium (nitrenium, oxenium) cations, poorly conjugated with the attached vinylic or heterovinylic group. Several other processes following upon center protonation were studied and are discussed in the text, special attention being given to comparison of open and cyclic isomers.     

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     

2-Alkylidenesulfol-3-enes by (regio- and) stereoselective cheletropic addition of SO2 to (di)vinylallenes

[reaction: see text] The cheletropic addition of SO(2) to divinylallenes is regioselective, taking place at the most substituted vinylallene and at the E unit if vinyl groups of opposite geometry are competing. Diastereofacial differentiation results from the approach of the reagent from the less-substituted direction of the allene and from the concomitant disrotatory movement of the termini of the vinylallene to afford the sterically more congested 2-alkylidenesulfol-3-ene isomer. DFT computations confirm the regio- and the stereoselectivity of these cheletropic additions.