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Molecules align in molecular overlayers for photodimerization reactions that would be disfavored in solution.

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The application and performance of conceptual and qualitative theories and quantitative quantum mechanical methods to the study of mechanism, reactivity, and selectivity of 1,3-dipolar and Diels–Alder cycloadditions are reviewed. This review emphasizes the application of conceptual density functional theory (DFT) for predicting reactivity and regioselectivity, and highly accurate quantum mechanical methods for predicting barrier heights and reaction energetics. Applications of computations to solvation effects, metal and organocatalysis, are also described.

Naturally radical: The microwave-induced rearrangement of sceptrin to natural products ageliferin and nagelamide E results in approximately the same ratio as they are isolated from natural sources. Computational investigations show that the vinylcyclobutane–cyclohexene rearrangement occurs via diradical intermediates and support the involvement of this rearrangement in the biosynthesis of the natural products.

Natürlich radikal: Die Mikrowellen-induzierte Umlagerung von Sceptrin in die Naturstoffe Ageliferin und Nagelamid E liefert die Verbindungen etwa im gleichen Verhältnis, wie sie aus natürlichen Quellen isoliert werden. Nach Berechnungen verläuft die Vinylcyclobutan-Cyclohexen-Umlagerung über Diradikalintermediate, und es spricht alles dafür, dass diese Umlagerung auch an der Biosynthese der Naturstoffe beteiligt ist.

Ursache und Allgemeingültigkeit des Halogeneffekts in Diels-Alder-Reaktionen wurden mit hoch präzisen CBS-QB3-Rechnungen untersucht. Ein Halogensubstituent erhöht die Exergonie einer Cycloaddition und senkt ihre Aktivierungsbarriere. Dieses Verhalten beruht darauf, dass die Bindung des elektronegativen Halogensubstituenten an ein höher alkyliertes, elektropositiveres Kohlenstoffgerüst energetisch begünstigt ist.

The reactions of hydrazoic acid (HN₃) with ethene, acetylene, formaldimine (H₂CNH), and HCN were explored with the high-accuracy CBS-QB3 method, as well as with the B3LYP and mPW1K density functionals. CBS-QB3 predicts that the activation energies for the reactions of hydrazoic acid with ethylene, acetylene, formaldimine, and HCN have remarkably similar activation enthalpies of 19.0, 19.0, 21.6, and 25.2 kcal/mol, respectively. The reactions are calculated to have reaction enthalpies of −21.5 for triazoline formation from ethene, and −63.7 kcal/mol for formation of the aromatic triazole from acetylene. The reaction to form tetrazoline from formaldimine has a reaction enthalpy of −8 kcal/mol (ΔG_rxn=+5.6 kcal/mol), and the formation of tetrazole from HCN has a reaction enthalpy of −23.0 kcal/mol. The trends in the energetics of these processes are rationalized by differences in σ-bond energies in the transition states and adducts, and the energy required to distort hydrazoic acid to its transition-state geometry. The density functionals predict activation enthalpies that are in relatively good agreement with CBS-QB3, the results differing from CBS-QB3 results by ca. 1–2 kcal/mol. Significant errors are revealed for mPW1K in predicting the reaction enthalpies for all reactions.

Deuterium-Markierungsexperimente belegen, dass das Methylenbicycloalken 1 stereoselektiv zu 3 umlagert, obwohl intermediär das stabilisierte Diradikal 2 auftritt. Ein theoretisches Modell auf der Grundlage von Rechnungen erklärt die beobachteten Produktverhältnisse. Die Stereoselektivität bei den [3,3]-(Neben-)Produkten legt eine ungewöhnliche Gabelung der Reaktionstrajektorien nach dem Übergangszustand der ersten Bindungsspaltung nahe.

Explaining the experiment: The transition states for a concerted asymmetric allylation (see scheme) were studied by theoretical methods. The apical attack of the aldehyde oxygen atom on Si accompanied by minimization of electrostatic repulsion in the trigonal-bipyramidal transition state leads to high stereoselectivity.

Deuterium labeling experiments on the rearrangement of methylenebicycloalkene 1 to 3 show stereoselectivity despite the intermediacy of a stabilized diradical structure 2. A theoretical model built from computational studies explains the observed product ratios. Stereoselectivity among [3,3] (minor) products implicates an unusual bifurcation of reaction trajectories after the initial bond-breaking transition state.

Das Experiment erklärt: Die Übergangszustände einer konzertierten asymmetrischen Allylierung (siehe Schema) wurden mit theoretischen Methoden untersucht. Der apikale Angriff des Aldehyd-Sauerstoffatoms auf Si, begleitet von einer Minimierung der elektrostatischen Abstoßung im trigonal-bipyramidalen Übergangszustand, führt zu hoher Stereoselektivität.

The transition structures for MacMillan's alkylations of N-methylpyrrole by aldehydes catalyzed by chiral amine salts were explored with B3LYP/6-31G(d) density functional theory. These results provide an explanation of the enantioselectivities observed with these two catalysts.

Methanoprolines are found to be catalysts for the Hajos–Parrish–Eder–Sauer–Wiechert reaction.^[1]cis-4,5-Methanoproline exhibits catalytic ability similar to proline (86% yield, 93% ee), whereas the trans-4,5-methanoproline is less selective (67% yield, 83% ee) and shows less acceleration. The reaction was also studied with hybrid density functional theory (B3LYP). The nearly planar cis-4,5-methanoproline amine better reflects the planar iminium of the transition states than the pyramidalized trans-4,5-methanoproline. This difference in conformation is responsible for the observed higher enantioselectivity and enhanced catalytic behavior of the cis-4,5-methanoproline.

A variety of 1,1,4,4-tetraal kynylbutatrienes and 1,4-dialkynylbutatrienes was synthezized by dimerization of the corresponding gem-dibromoolefins. Both ¹H and ¹³C NMR spectroscopy indicated that the di- and tetraalkynylated butatrienes are formed as a mixture of cis and trans isomers. Variable temperature NMR studies evidenced a facile cis–trans isomerization, thus preventing the separation of these isomers by gravity or high-performance liquid chromatography (HPLC). For 1,1,4,4-tetraalkynylbutatrienes, the activation barrier ΔG^≠ was measured by magnetization transfer to be around 20 kcal mol⁻¹, in the range of the barrier for internal rotation about a peptide bond. Unlike the tetraalkynylated [3]cumulenes, 1,4-dialkynylbutatrienes are more difficult to isomerize and could, in one case, be obtained isomerically pure. Based on experimental data, the rotational barrier ΔG^≠ for 1,4-dialkynylbutatrienes is estimated to be around 25 kcal mol⁻¹. The hypothesis of a stabilizing effect of the four alkynyl substituents on the proposed but-2-yne-1,4-diyl singlet diradical transition state of this cis–trans isomerization is further supported by a computational study.

A comparison of previously proposed models of the CC bond-forming step of the title reaction with density functional methods indicate that the most favored one involves an enamine intermediate undergoing a concerted aldol cyclization with proton transfer from the proline carboxylic acid group (see structure). This step is equal in energy to the intramolecular deprotonation leading to the enamine, and both are partially rate-determining steps.

Three constitutionally isomeric bis(naphthylmethyl)ammonium ions, in which the two naphthyl groups are substituted 1) both at their 1-positions, 2) one at its 1-position and the other at its 2-position, and 3) both at their 2-positions, have been investigated separately in solution for their propensities to undergo spontaneous self-assembly with three different [24]crown-8 derivatives, namely, pyrido[24]crown-8 (P24C8), dipyrido[24]crown-8 (DP24C8) and dibenzo[24]crown-8 (DB24C8), in turn to form [2]pseudorotaxanes. The strengths of the 1:1 complexes depend on the composition of the secondary dialkylammonium ions and on the nature of the crown ether hosts; generally, as far as the guest cation is concerned, the 1/1- and 2/2-isomers form stronger complexes, as indicated by stability constant measurements, than the 1/2-isomer and, as far as the crown ethers are concerned, the more flexible P24C8 is a much more efficient host than either DP24C8 or DB24C8. The rates of formation of the [2]pseudorotaxanes are fast (i.e., taking no more than a few minutes) in solution with the exception of one case, that is, in which the crown ether host is DB24C8 and the guest cation is the 1/1-isomer, when it can take upwards of one month for the complexation–decomplexation equilibrium to be established at room temperature. In all cases, the equilibrium between complexed and uncomplexed species is slow on the NMR timescale, allowing the determination of stability constants to be made readily using the single-point method. X-ray crystallography and molecular modeling have been used to gain insight into ground and transition state interactions, respectively, in some of the [2]pseudorotaxanes. The relative stabilities of the three [2]pseudorotaxanes formed by each guest cation in the presence of the three crown ether hosts were also evaluated in solution by competition experiments that were monitored by ¹H NMR spectroscopy. By and large the results of the competition experiments could be predicted on the basis of the derived stability constants for the individual [2]pseudorotaxanes.

Ein Vergleich von bekannten Modellen für den C-C-verknüpfenden Schritt der Titelreaktion mithilfe von Dichtefunktional-Methoden zeigt, dass der günstigste Weg eine Enamin-Zwischenstufe einschließt, deren Aldolcyclisierung unter Protonenübertragung von der Carboxygruppe des Prolins konzertiert verläuft (siehe Bild). Dieser Schritt und die intramolekulare Deprotonierung, die zum Enamin führt, sind energetisch ähnlich, sodass beide die Reaktionsgeschwindigkeit bestimmen.

Because only then a relatively rapid agostic-assisted hydrogen shift can help to form the product. This is the answer to the question in the title and it results from a computational analysis of the catalytic cycle shown and its alternatives for dimerization, tetramerization, and higher oligomerization.

Figures of eight correlate with corrolates: The surprising formation of the spirodicorrole dinickel complex 1, the first spirodiporphyrin as a metal complex, is the result of the varied chemistry of the “figure-eight” cyclooctapyrrole octaphyrin-(1.1.1.0.1.1.1.0). The conversion of the cyclooctapyrrole into 1 is brought about by a sequence of oxidation and a nickel(II) acetate induced cascade of rearrangement reactions. In structural respects, 1 stands out because of the orthogonal arrangement of the two nickelcorrolate chromophores linked through a common spiro carbon atom.

The affinities of hosts—ranging from small synthetic cavitands to large proteins—for organic molecules are well documented. The average association constants for the binding of organic molecules by cyclodextrins, synthetic hosts, and albumins in water, as well as of catalytic antibodies or enzymes for substrates are 10^3.5±2.5 M⁻¹. Binding affinities are elevated to 10^8±2 M⁻¹ for the complexation of transition states and biological antigens by antibodies or inhibitors by enzymes, and to 10^16±4 M⁻¹ for transition states with enzymes. The origins of the distributions of association constants observed for the broad range of host–guest systems are explored in this Review, and typical approaches to compute and analyze host–guest binding in solution are discussed. In many classes of complexes a rough correlation is found between the binding affinity and the surface area that is buried upon complexation. Enzymes transcend this effect and achieve transition-state binding much greater than is expected from the surface areas.

Denn nur dann kann eine relativ schnelle, durch agostische Wechselwirkung unterstützte Wasserstoffverschiebung die Produktbildung unterstützen. Das ist die Antwort auf die Frage im Titel, und sie folgt aus einer theoretischen Analyse des gezeigten Katalysezyklus sowie seiner Alternativen für die Dimerisierung, Tetramerisierung und höhere Oligomerisierung.

Die überraschende Bildung des ersten Spirodiporphyrins in Form eines Metallkomplexes, des Spirodicorrol-Dinickelkomplexes 1, ist ein Ergebnis der vielseitigen Chemie des „Figure-Eight“-Cyclooctapyrrols Octaphyrin-(1.1.1.0.1.1.1.0). Die Umwandlung des Cyclooctapyrrols in 1 beruht auf einer Folge von Oxidation und einer durch Nickel(II)-acetat ausgelösten Umlagerungskaskade. Hervorstechendes strukturelles Merkmal von 1 ist die Orthogonalität der über ein gemeinsames Spirozentrum verknüpften Nickelcorrolat-Chromophore.

Die Affinitäten von Wirten – ausgehend von kleinen synthetischen Cavitanten bis hin zu großen Proteinen – für organische Moleküle sind gut dokumentiert. Die mittleren Assoziationskonstanten für die Bindung organischer Moleküle durch Cyclodextrine, synthetische Wirte und Albumine in Wasser sowie von katalytischen Antikörpern oder Enzymen für Substrate betragen im Allgemeinen 10^3.5±2.5 M⁻¹. Die Bindungsaffinitäten steigen bei der Komplexierung von Übergangszuständen und biologischen Antigenen durch Antikörper oder von Enzymen durch Inhibitoren auf 10^8±2 M⁻¹ und auf 10^16±4 M⁻¹ für Enzym-Übergangszustands-Komplexe. Die Gründe für die unterschiedlichen Stabilitäten dieser Wirt-Gast-Systeme sollen hier untersucht werden, und wir beschreiben Ansätze zur computergestützten Analyse der Wirt-Gast-Komplexbildung in Lösung. Bei vielen Komplexklassen besteht eine ungefähre Korrelation der Bindungsaffinität mit der Größe der Oberfläche, die bei der Komplexierung vergraben wird. Enzyme folgen dieser Korrelation nicht, sondern binden Übergangszustände sehr viel stärker als es anhand der Oberfläche zu erwarten wäre.

The potential role of “H–vinyl” conical intersections in a photochemical process known as the hula twist has been evaluated. The H–vinyl conical intersections of butadiene are explored with complete active space self-consistent field calculations, and proposals about the geometries involved in the hula-twist mechanism are discussed and contrasted with the conventional one-bond flip mechanism of cis–trans isomerization.

Theoretical studies of stereoselectivity have been carried out with B3LYP and MP2 calculations. The high endo selectivity of hetero-Diels–Alder reactions of ortho-xylylenes with acetaldehydes is shown to result from attractive CH–π interactions between alkyl groups of the aldehyde and the aromatic ring in the transition states of the reaction. For the hetero-Diels–Alder reactions of ortho-xylylenes with benzaldehyde, the stereoselectivity is shown to be mainly governed by the attractive π–π interactions between the phenyl rings of the benzaldehyde and the ortho-xylylene. MP2 calculations are necessary to reproduce the stabilizing dispersion interactions.

The mechanisms of [3s,5s]-sigmatropic shifts of octa-1,3,7-triene and 7-methylenenona-1,3,8-triene have been elaborated using B3LYP and BPW91 density functional theory and CASPT2 methods. These orbital symmetry forbidden rearrangements are stepwise, involving diradical intermediates. A comparison with several [3,3]-sigmatropic shifts of substituted hexadienes and of [5,5]-sigmatropic shifts that are allowed, but nevertheless follow stepwise paths, shows that the activation barrier for the disallowed [3,5] shift is significantly larger than that for the stepwise reactions that are orbital symmetry allowed. Cyclic diradicals that have an aromatic circuit of electrons including the two radical centers and conjugated π or σ bonds are stabilized as compared to cyclic diradicals with an antiaromatic circuit of electrons. This applies to the transition states leading to and from the diradicals and influences the activation energies of stepwise sigmatropic shifts. The magnitudes of these effects are small but will have a significant influence on the rates of competing processes. This series of calculations has been used to assess the relative capabilities of the two functionals. We find that BPW91 underestimates the endothermicity of diradical formation and the barrier to diradical formation whereas B3LYP overestimates these quantities.

The mystery of proficiency remains: The recently solved crystal structures of free orotidine monophosphate decarboxylase (ODCase) and of the enzyme in complex with inhibitors reveal unusual structural features. However, despite the similarities among the structures, several startling new mechanisms of action have been proposed to explain how ODCase achieves its spectacular catalytic proficiency in catalyzing the decarboxylation of OMP (1) to UMP (2). R = ribose 5′-monophosphate.

Peracids prefer to attack syn to an alkyl group as shown by the most stable transition state for the epoxidation of 3-methylcyclohexene (see section of transition state). Computational and experimental evidence explain the origin of this effect and how it might be exploited in synthesis.

Das Titelbild zeigt den Vorgang der Wasserstoff- und Heliuminsertion/abgabe, der erstmals mit einem offenen Fullerenderivat (im Hintergrund angedeutet) gelang. Die experimentelle Aktivierungsbarriere für die Heliumdekomplexierung konnte bestimmt werden; sie ist sehr gut mit dem berechneten Wert (Dichtefunktionaltheorie) in Einklang. Die Barriere für die Komplexierung/Dekomplexierung von H₂ ist interessanterweise fast doppelt so groß wie die bei Helium, wie das Energiediagramm im Vordergrund illustriert. Der Grund für den Unterschied ist die größere, gestreckte Oberfläche von H₂, das stärkere van-der-Waals-Wechselwirkungen im Übergangszustand eingeht als Helium, obwohl beide Atome denselben Radius haben. Mehr über diesen Prozess erfahren Sie in dem Beitrag von Rubin, Houk, Saunders, Cross et al. auf S. 1591 ff.

Persäuren greifen bevorzugt syn zu einer Alkylgruppe an, wie der stabilste Übergangszustand (siehe Ausschnitt) für die Epoxidierung von 3-Methylcyclohexen zeigt. Rechnergestützte und experimentelle Befunde erklären den Ursprung dieses Effekts, was eine gezielte Anwendung in der Synthese ermöglichen sollte.

Antibody 1E9 is a protein catalyst for the Diels–Alder reaction between tetrachlorothiophene dioxide and N-ethylmaleimide. Quantum mechanical calculations have been employed to study the 1E9-catalyzed Diels–Alder reaction in the gas phase. The transition states and intermediates were all determined at the B3LYP/6-31G*//HF/6-31G* level. The cycloaddition step is predicted to be rate-determining, and the endo reaction pathway is strongly favored. Binding of the reactants and the transition states to antibody 1E9 was investigated by docking and molecular dynamics simulations. The linear interaction energy (LIE) method was adopted to estimate the free energy barrier of the 1E9-catalyzed Diels–Alder reaction. The catalytic efficiency of antibody 1E9 is achieved by enthalpic stabilization of the transition state, near-perfect shape complementarity of the hydrophobic binding site for the transition state, and a strategically placed hydrogen-bonding interaction.

The cover picture shows the active site of the catalytic antibody 1E9, which promotes the bimolecular Diels–Alder reaction between tetrachlorothiophene dioxide and N-ethylmaleimide. Docking and molecular dynamics simulations of the reactant complex (green) and the endo-transition state (yellow) bound at the antibody active site illustrate the excellent shape complementarity between ligand and protein. Residues Trp H50 and Asn H35, which interact with the dienophile through π-stacking and hydrogen bonding, respectively, are seen at the bottom of the active site beneath the transparent protein surface. More about shape complementarity, binding site dynamics, and transition state stabilization can be found in the theoretical study by K. N. Houk, D. Hilvert et al. on p. 255 ff. (The cover image was produced by Kinya Hotta.)

Abstract

Theoretical modeling of the dynamics of complexation and decomplexation of guest molecules by container molecules reveals that gating has a critical influence on the ease of formation and stability of host-guest complexes. Hosts equipped with gates can form very stable complexes with a variety of guests under readily achievable conditions. Gating involves conformational processes of the host molecule that alter the size of the portals through which guest molecules pass. “French door” and “sliding door” mechanisms of gate opening are identified.