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.     

Understanding the Woodward-Hoffmann rules by using changes in electron density

The Woodward-Hoffmann rules for pericyclic reactions are explained entirely in terms of directly observable physical properties of molecules (specifically changes in electron density) without any recourse to model-dependent concepts, such as orbitals and aromaticity. This results in a fundamental explanation of how the physics of molecular interactions gives rise to the chemistry of pericyclic reactions. This construction removes one of the key outstanding problems in the qualitative density-functional theory of chemical reactivity (the so-called conceptual DFT). One innovation in this paper is that the link between molecular-orbital theory and conceptual DFT is treated very explicitly, revealing how molecular-orbital theory can be used to provide "back-of-the-envelope" approximations to the reactivity indicators of conceptual DFT.     

Electron reorganization in chemical reactions: Pair population analysis along concerted reaction path of allowed and forbidden pericyclic reactions

The recently proposed pair population analysis was applied to the study of electron reorganization in the course of chemical reactions. The studied reactions involved a series of pericyclic reactions, both forbidden and allowed, and attention was devoted mainly to the evaluation of the specific differences between the allowed reactions and the forbidden ones. It was demonstrated that while the mechanism of allowed reactions can be visualized as a simple cyclic shift of the bonds the electron reorganization in forbidden reactions is much more complex and involves the considerable changes in the character of the wave function during the process. © 1997 John Wiley & Sons, Inc.     

Carbenes and Nitrenes: Recent Developments in Fundamental Chemistry

Carbenes and nitrenes can exist in both singlet and triplet states, sometimes equally stable and interconverting either thermally or photochemically. Many carbene and nitrene reactions proceed via tunneling at low temperatures. Numerous singlet and triplet states have been characterized spectroscopically, and a detailed understanding of the chemical and physical properties of carbenes and nitrenes is emerging. There has been significant progress in the direct observation of carbenes, nitrenes, and many other reactive intermediates in recent years through the application of matrix photolysis and flash vacuum pyrolysis linked with matrix isolation at cryogenic temperatures. Our understanding of singlet and triplet states has improved through the interplay of spectroscopy and computations. Bistable carbenes and nitrenes as well as many examples of tunneling have been discovered and numerous rearrangements and fragmentations have been documented. The correlation of the zero‐field splitting parameter D with calculated spin densities on nitrenes and carbenes is discussed. This Minireview gives an overview of some of these developments.     

Density functional theory study of the styrylbenzoquinoline dyad and the related dibenzoquinolylcyclobutane formed in the [2 + 2] photocycloaddition reaction

The structure and electronic properties of the biphotochromic dyad with two styrylbenzo[f]quinoline photochromes, as well as the corresponding cyclobutane with two benzo[f]quinoline (BQ) substituents, are studied by DFT at the M06-2X/6-31G* level, the cyclobutane being a product of the [2 + 2] photocycloaddition (PCA) reaction of the dyad. According to calculations, the dyad forms π-stacked folded conformers, which, when excited, can form excimers that are precursors of cyclobutane. TD DFT calculations and natural transition orbital (NTO) analysis indicated that the lowest singlet excited S₁ state in the dyad is localized on the SBQ photochrome, including the ethylene group that undergoes PCA. Thus, the conditions for concerted electrocyclic reactions are satisfied, and the direct PCA follows the Woodward–Hoffmann rules. In contrast, in cyclobutane, the S₁ state is localized on the BQ substituent rather than on the cyclobutane core. Therefore, the reverse ring-opening (retro-PCA) reaction cannot follow the Woodward-Hoffmann rules and inevitably involves a step of excitation energy transfer from BQ to cyclobutane, which means the predissociation mechanism.     

Electrocyclic Ring Opening Reactions of Ethylene Oxides

Substituents capable of stabilizing negative charge endow ethylene oxides with the ability to undergo electrocyclic ring opening at the CC bond; heating or irradiation generates small equilibrium concentrations of carbonyl ylides which can engage in 1,3-dipolar cycloadditions. Apart from the normal conrotatory mode of ring opening, predicted by the Woodward-Hoffmann rules, the disrotatory process, forbidden by orbital symmetry, also appears to occur in the case of α-cyano-cis-stilbene oxide. Kinetic studies on α-cyano-trans -and -cis-stilbene oxide permit construction of the energy profile for electrocyclic ring opening to give the stereoisomeric carbonyl ylides and for their recyclization and rotation.     

Exploring two-state reactivity pathways in the cycloaddition reactions of triplet methylene

Spin forbidden 1,2-cycloadditions of triplet methylene to alkenes have been theoretically studied as an example of the two-state reactivity paradigm in organic chemistry. The cycloadditions of triplet methylene to ethylene and the (E)- and (Z)-2-butene isomers show spin inversion after the transition state and therefore with no effect on the reaction rate. A local analysis shows that while triplet methylene addition to alkenes leading to the formation of a biradical intermediate is driven by spin polarization, the ring closure step to yield cyclopropane is a pericyclic process. We have found that at the regions in the potential energy surface where the spin crossover is likely to occur, the spin potential in the direction of increasing spin multiplicity, mu(+)(s), tends to equalize the one in the direction of decreasing spin multiplicity, mu(-)(s). This equalization facilitates the spin transfer process driven by changes in the spin density of the system.     

Fate of diradicals in the caldera: stereochemistry of thermal stereomutation and ring enlargement in cis- and trans-1-cyano-2(E)-propenylcyclopropanes

This study of thermally induced stereomutation and ring enlargement in both (-)-trans-1-cyano-2(E)-propenylcyclopropane [(-)-trans-1] and (+)-cis-1-cyano-2(E)-propenylcyclopropane [(+)-cis-1] to cyclopentenes definitively contraindicates the usefulness of Woodward-Hoffmann rules of orbital symmetry as a theoretical basis for predicting the stereochemistry of the products. From both diastereomers, the same (+)-trans-4-cyano-3-methylcyclopentene [(+)-trans-2] is the major product among the four diastereomeric products, "allowed" and formally the result of a single internal rotation of the cyano-bearing carbon atom from (-)-trans-1, "forbidden" and the result of zero internal rotations from (+)-cis-1. Stereomutation and ring enlargement are discussed in detail in terms of rotational propensity, thermodynamic preference, and the possible role of diradicals in transit and diradicals as intermediates in a caldera.     

Aromaticity changes along the reaction coordinate connecting the cyclobutadiene dimer to cubane and the benzene dimer to hexaprismane

Aromaticity and reactivity are two deeply connected concepts. Most of the thermally allowed cycloadditions take place through aromatic transition states, while transition states of thermally forbidden reactions are usually less aromatic, if at all. In this work, we perform a numerical experiment to discuss the change of aromaticity that occurs along the reaction paths that connect two antiaromatic units of cyclobutadiene to form cubane and two aromatic rings of benzene to yield hexaprismane. It is found that the aromaticity profile along the reaction coordinate of the [4+4] cycloaddition of two antiaromatic cyclobutadiene molecules goes through an aromatic highest energy point and finishes to an antiaromatic cubane species. Up to our knowledge, this represents the first example of a theoretically and thermally forbidden reaction path that goes through an intermediate aromatic region. In contrast, the aromaticity profile in the [6+6] cycloaddition of two aromatic benzene rings show a slow steady decrease of aromaticity from reactants to the highest energy point and from this to the final hexaprismane molecule a plunge of aromaticity is observed. In both systems, the main change of aromaticity occurs abruptly near the highest energy point, when the distance between the centers of the two rings is about 2.2 Å.     

Forward and backward pericyclic photochemical reactions have intermediates in common, yet cyclobutenes break the rules.

Photochemical pericyclic reactions are believed to proceed via a so-called pericyclic minimum on the lowest excited potential surface (S(1)), which is common to both the forward and backward reactions. Such a common intermediate has never been directly detected. The photointerconversion of 1,3-butadiene and cyclobutene is the prevailing prototype for such reactions, yet only diene ring closure proceeds with the stereospecificity that the Woodward-Hoffmann rules predict. This contrast seems to exclude a common intermediate. Using ultrafast spectroscopy, we show that the excited states of two cyclobutene/diene isomeric pairs are linked by not one, but by two common minima, p* and ct*. Starting from the diene side (cyclohepta-1,3-diene and cycloocta-1,3-diene), electrocyclic ring closure passes via the pericyclic minimum p*, whereas ct* is mainly responsible for cis-trans isomerization. Starting from the corresponding cyclobutenes (bicyclo[3.2.0]heptene-6 and bicyclo[4.2.0]octene-7), the forbidden isomer is formed from ct*. The path branches at the first (S(2)/S(1)) conical intersection towards p* and ct*. The fact that the energetically unfavorable ct* path can compete is ascribed to a dynamic effect: the momentum in C=C twist direction, acquired--such as in other olefins--in the Franck-Condon region of the cyclobutenes.     

Spin–orbit coupling in the intersystem crossing of the ring-opened oxirane biradical

The intersystem crossing (ISC ) between the lowest triplet and singlet states occurring in the reaction of atomic oxygen with ethylene was studied. The importance of spin–orbit coupling (SOC ) in oxirane biradicals (?R′R″—CRR*—?) is stressed through calculations where the spin–orbit matrix elements over the full Breit–Pauli SOC operator has been obtained in the singlet–triplet crossing region. The calculations are performed with a multiconfigurational linear response approach, in which the spin–orbit couplings are obtained from triplet response functions using differently correlated singlet-reference-state wave functions. Computational results confirm earlier semiempirical predictions of the spin–orbit coupling as an important mechanism behind the ring opening of oxiranes and addition of oxygen O(³P) atoms to alkenes. © 1995 John Wiley & Sons, Inc.     

Mechanism of ligand photodissociation in photoactivable [Ru(bpy)2L2]2+ complexes: a density functional theory study

A series of four photodissociable Ru polypyridyl complexes of general formula [Ru(bpy)2L2](2+), where bpy = 2,2'-bipyridine and L = 4-aminopyridine (1), pyridine (2), butylamine (3), and gamma-aminobutyric acid (4), was studied by density functional theory (DFT) and time-dependent density functional theory (TDDFT). DFT calculations (B3LYP/LanL2DZ) were able to predict and elucidate singlet and triplet excited-state properties of 1-4 and describe the photodissociation mechanism of one monodentate ligand. All derivatives display a Ru --> bpy metal-to-ligand charge transfer (MLCT) absorption band in the visible spectrum and a corresponding emitting triplet (3)MLCT state (Ru --> bpy). 1-4 have three singlet metal-centered (MC) states 0.4 eV above the major (1)MLCT states. The energy gap between the MC states and lower-energy MLCT states is significantly diminished by intersystem crossing and consequent triplet formation. Relaxed potential energy surface scans along the Ru-L stretching coordinate were performed on singlet and triplet excited states for all derivatives employing DFT and TDDFT. Excited-state evolution along the reaction coordinate allowed identification and characterization of the triplet state responsible for the photodissociation process in 1-4; moreover, calculation showed that no singlet state is able to cause dissociation of monodentate ligands. Two antibonding MC orbitals contribute to the (3)MC state responsible for the release of one of the two monodentate ligands in each complex. Comparison of theoretical triplet excited-state energy diagrams from TDDFT and unrestricted Kohn-Sham data reveals the experimental photodissociation yields as well as other structural and spectroscopic features.     

Pattern of separatrices and intrinsic reaction coordinates for degenerate thermal rearrangements

A structurally stable model of the standard adiabatic gradient field of the potential energy surface for certain pericyclic reactions is derived.These reactions are not subjected to the principles of orbital isomerism or to the Woodward-Hoffmann rules.Use is made of a principle established by Ariel Fernández and Oktay Sinanolu which precludes direct meta-IRC connections between transition states.It is shown that Jahn-Teller isomers of the singlet biradicals involved in the process are not interconvertible since the biradical configuration is not a transition state but a critical point with Hessian matrix with two negative eigenvalues.The topological features of the PES obtained by combinatorial methods are in full agreement with earlier results obtained from MINDO calculations.     

Graph-theoretic study of certain interstellar reactions

Certain interstellar reactions have been studied through the graph-theoretic method using a Fortran-77 program. A plausible mechanism has been proposed for the reactions. The criterion of the conversion of edge to loop and vice versa proposed by the Bratislava group [Theor. Chim. Acta 79 , 65 (1991)] has been given a reasonable chemical insight. In the reaction scheme the nucleophilic/electrophilic/carbene (singlet, triplet) or biradical loops have been generated by the fragmentation of reactant. Subsequently, Pearson's hard and soft acids bases (HSAB) theory and frontier orbital (FO) theory have been applied to explain the reaction mechanism. Few possible reactions of the interstellar and circumstellar molecules have been investigated with illustrations involving carbene intermediate and Woodward-Hoffmann rule. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 62: 495–508, 1997     

Triplet organometallic reactivity under ambient conditions: an ultrafast UV pump/IR probe study.

The reactivity of triplet 16-electron organometallic species has been studied in room-temperature solution using femtosecond UV pump IR probe spectroscopy. Specifically, the Si-H bond-activation reaction of photogenerated triplet Fe(CO)(4) and triplet CpCo(CO) with triethylsilane has been characterized and compared to the known singlet species CpRh(CO). The intermediates observed were studied using density functional theory (DFT) as well as ab initio quantum chemical calculations. The triplet organometallics have a greater overall reactivity than singlet species due to a change in the Si-H activation mechanism, which is due to the fact that triplet intermediates coordinate weakly at best with the ethyl groups of triethylsilane. Consequently, the triplet species do not become trapped in alkyl-solvated intermediate states. The experimental results are compared to the theoretical calculations, which qualitatively reproduce the trends in the data.     

Magnetic properties of cationic tungsten(IV) half sandwich compounds: experimental and theoretical study of a solvent and ligand stabilized singlet ground state leading to a thermally induced singlet-triplet spin state interconversion

A series of novel neutral tungsten(III) and cationic tungsten(IV) complexes with disubstituted 4,4'-R,R-2,2'-bipyridyl (R(2)-bpy) ligands of the type [CpW(R(2)-bpy)Cl(2)](n+) (n = 0,1) were prepared and characterized by X-ray crystallography. Susceptibility measurements of the tungsten(IV) complexes revealed an intrinsic paramagnetism of these compounds and evidenced different magnetic properties of the dimethylamino and methyl (R = NMe(2), Me) substituted tungsten(IV) compounds in solution and in the solid state. In dichloromethane solution, singlet ground states with thermally populated triplet states were observed, whereas triplet (R = Me) and singlet ground states (R = NMe(2)) were observed in the solid state. Using both experimental and theoretical techniques (DFT) allowed to establish solvation and ligand effects to account for the different magnetic behavior. Thermodynamic parameters were derived for the spin equlibria in solution by fits of the temperature dependent (1)H NMR shifts to the Van Vleck equation and were found to be in excellent agreement with the DFT calculations.     

Electron correlation in pericyclic reactivity: A similarity approach

The recently proposed topological approach to chemical reactivity in terms of the secondorder similarity index was applied to the detailed analysis of correlation effects in pericyclic reactivity. This analysis implies that (i) the electron correlation is generally more important in forbidden reactions than in the allowed ones; (ii) in contributing to the discrimination between the allowed and forbidden reactions, the Fermi correlation acts in parallel with the Coulomb one; and (iii) the so-called multibond reactions are more sensitive to electron correlation than are the electrocyclic ones.