Topology of energy hypersurfaces

Some of the basic notions of chemistry, associated with an energy function of several variables, are shown to be of topological character. Properties of potential energy hypersurfaces, structural relations, models for interconversion processes and transformations between such models suggest a topological theory (reaction topology) for the analysis of potential energy hypersurfaces. By introducing appropriate topologies into the nuclear configuration spaceR and equivalent topologies on the energy hypersurfaceE, rigorous definitions are given for fundamental chemical concepts such asmolecular structure andreaction mechanism. These definitions are based on the properties of the expectation value of energy, a quantum mechanical observable. Topologies based on curvature, structural and energetic relations of the energy hypersurface are proposed for a theoretical interpretation of molecular processes.     

New global constraints on electronic energy hypersurfaces

Improved global energy bounds — valid for the entire electronic energy hypersurfaces of a variety of polyatomic molecular systems — are proposed. The new constraints are applicable to a larger class of molecules and are tighter than the constraints proposed earlier. The new global bounds are easily applicable using readily available energy values of atoms and atom-ions. The actual evaluation of these constraints typically involves only “back-of-the-envelope” calculations, providing both upper and lower bounds for a complete energy hypersurface, even for very large molecules. Such global energy bounds are of some importance in theoretical studies of chemical reactions and conformational changes. The proposed bounds are likely to find some practical applications in computer-based quantum-chemical synthesis planning, using multidimensional potential surfaces.     

Symmetry and periodicity of potential surfaces: a test for multicenter interactions

Symmetry and periodicity of potential energy surfaces of chemical reactions and conformational changes are determined by the symmetry properties of the nuclear frameworks of all possible nuclear configurations of the given overall stoichiometry. For example, a mirror plane of a nuclear configuration implies a mirror plane of the potential surface (or that of the potential energy hypersurface in higher dimensions), and a local rotational symmetry of substituents implies a translational symmetry, that is, periodicity of the potential surface, if the latter is defined in terms of the usual bond length/bond angle internal coordinates. Such symmetry relations on potential surfaces are rather trivial consequences of molecular symmetry properties; however, when taken collectively for entire domains of nuclear configurations, they lead to nontrivial conclusions. Whereas symmetry properties and energy contents of individual conformations can be studied locally within limited domains of the potential surface, a global analysis of the potential surface may reveal significantly more. In this note, some consequences of the above approach are explored, and a simple test is proposed for the detection and evaluation of the importance of multicenter interactions in conformers related to one another by bond rotations.Dedicated to Professor J. Koutecký on the occasion of his 65th birthday     

A general formulation of the “quantum chemical le Chatelier principle”

Regularities observed in the variations of calculated energy components, for example, those of electronic and nuclear repulsion energies in the analysis of conformational changes and in studies of the propagation of basis set errors in ab initio calculations, are found to be related to the variational principle and to the boundedness of energy expectation value functionals. These relations are analogous to the le Chatelier principle of equilibrium thermodynamics, and may be formulated as a general “compensation principle” for two sets of general parameters of the molecular total energy functional.     

Validity of the Hammond postulate and constraints on general one-dimensional reaction barriers

The Hammond postulate is a useful, qualitative tool that interrelates structural similarities between reactants, transition structures, and products with the exo- or endothermicity of reactions. It applies to most chemical reactions, although several exceptions are known. In this study the following problem is addressed: is it possible to formulate conditions for the validity of the quantitative Hammond postulate in terms of simple physical quantities characteristic to the molecules involved? A detailed analysis is given for the conditions of validity of the postulate, in terms of bounds on the internal forces and force constants of nuclear arrangements encountered along a reaction path. We have determined a broad class of constraints on barrier shapes that must be satisfied in order to obtain a critical situation that violates the Hammond postulate: a reactant-like transition structure (“transition state”) for endothermic reactions, and a product-like one for exothermic reactions. The general constraints are formulated in terms of physically meaningful quantities: (i) energy differences, (ii) restrictions on slopes (e.g., an upper bound on internal forces), and (iii) restrictions on curvatures (e.g., upper bounds on force constants) along potential curves.     

Multicomponent QM study on the reaction of HOSO + NO2 with H2O: Nuclear quantum effect on structure and reaction energy profile

The hydrogen transfer reaction in the reaction of HOSO + NO₂ with and without H₂O have been investigated using multicomponent quantum-mechanics method, which can directly take nuclear quantum effect (NQE) of light nuclei into account. For the case of the reaction without H₂O, our calculation reveals that the reaction leading to trans-HONO is preferred. For the reaction with H₂O, water-non-mediated and water-mediated (hydrogen-relay) hydrogen transfer mechanism are investigated. The NQE of hydrogen nucleus lowers the relative energy of the stationary point structures and reduces the activation barrier of the reactions. The largest stabilization is found in the transition state structure of the hydrogen-relay type reaction. H/D isotope effects for the reactions are also analyzed. In particular, H/D isotope effect on the activation barrier is analyzed in detail with the aid of the active strain model.     

Principe,possibilites et applications de l'analyse par activation aux photons gamma

The various photonuclear reactions suitable for analytical purposes, their specificity and their performances are reviewed. The influence of the experimental irradiation conditions on the theoretical detection limits permitted and on the relative importance of competitive nuclear reactions liable to interfere is examined, with special reference to the determination of carbon, nitrogen and oxygen. It is shown that these parasitic effects of nuclear origin may be eliminated by the choice of the maximum irradiation energy. Examples are given of applications relative to trace determinations of lights elements, especially carbon, nitrogen, and oxygen, in metals or semi-conductors and to instrumental multi-element analyses of biological materials, atmospheric sampling filters and above all agricultural products.

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Conférence plénière prononcée dans le cadre du: 5th Symposium on the Recent Development in Activation Analysis, Oxford (GB), 17–21 Juillet 1978.     

Critical level topology of energy hypersurfaces

Topologies are introduced into the nuclear configuration space R of molecular systems, based upon equipotential contour hypersurfaces on the otential energy hypersurface E. Critical level topologies T _fc and T _fc, based upon the number and distribution of various critical points of E, are of particular importance, since they represent convenient yet rigorous mathematical models for relations between elementary reaction mechanisms, and for relations between open sets of nuclear geometries which are classically accessible at a given total energy.     

Analyse conformationnelle a l'aide de la notation des angles de torsion-VIII: Interpretation conformationnelle de la reaction de substitution nucleophile(SN2) dans la serie des cycles petits et moyens

Taking geometric constraints into account, involved at the carbon atom undergoing configurational inversion in S_N2 displacement reactions of cyclic compounds, the conformational course of the reaction can be analysed. This method allows a rationalization of the relative rates of S_N2 reactions of isomeric compounds in the cyclohexane, cyclohexene, cyclopentane, and cyclopentene series. Conformational factors involved in the displacement reaction, which may orient it towards either S_N2 or S_N2' type of reaction are discussed.     

The Photoisomerization of cis-Stilbene Does Not Follow the Minimum Energy Path

Thermal activation is not required for barrier crossing reactions in the photoisomerization of cis-stilbene, as demonstrated by computer simulations. The activation is achieved by using the excess energy from the photoexcitation. Moreover, the reaction proceeds with large energy transfers but small conformational changes. The reaction pathway is influenced by these effects and also by the solvent.     

Electron transfer reactions between the superoxide ion and quinones

The electron transfer reactions of the superoxide ion with benzoquinone, trimethylbenzoquinone, and menadione in dimethylformamide were studied. A procedure of the determination of the relative rate constants of these reactions was developed; the reaction of O? ₂ with butyl bromide was chosen as a standard one. The relative rate constants measured at 20,°, 35°, and 50°C were slightly dependent on the quinone structure. The relationship between the free energy ΔF*of the electron transfer reactions and the standard free energy ΔF^o was discussed. This relationship is proposed as ΔF* = αΔF^o + β, where the proportionality coefficient α is equal to 0.04–0.11 for exothermal reactions and to 0.90–0.96 for endothermal reactions.     

Discrete spatial symmetries: Redundant coordinates and search for stationary points in reduced spaces

Given the invariance of an N-body system under discrete operations of reflection, inversion, a rotation by 2π/n, and the corresponding relations among the derivatives of energy, we have constructed through an invertible transformation a set of active and redundant coordinates. Movement along the active coordinates preserves all symmetry relations. We show that algorithms for locating stationary points or for calculating reaction paths are exactly separable in these active and redundant coordinates. We further show that this formalism is equally applicable when equations of constraints among coordinates are specified for the movement of particles. This includes geometrical constraints on bond lengths, angles, substituent group internal rotations, etc. This formalism enhances the efficiency since (laborious) cartesian derivatives need to be calculated only for the active variables and that the problem is reduced in term of m(?3N) variables. We apply this procedure to obtain the equilibrium geometry of H₂O molecule within the subspace of C_2v symmetry configurations ab initio derivatives.     

Fitting multiple datasets in kinetics: n‐butane + OH → products

Offsets due to systematic calibration errors are a common feature of the literature on temperature‐dependent rate constants. We present a formalism for dealing with these offsets within the context of least‐squares fitting, using a priori parameter constraints based on the estimated accuracy of individual studies. This methodology not only eliminates biases caused by calibration errors, it also ensures that the metric used to compare different studies is their accuracy, not their precision. Consequently, studies with single measurements at room temperature can be meaningfully compared with studies comprising dozens of measurements spanning a wide temperature range. We apply this procedure to the complete literature dataset for two reactions: OH + propane and OH + n‐butane, after first presenting new data for OH + n‐butane spanning the temperature range 180–300 K and extending the low‐temperature limit of the literature by 50 K. There is outstanding agreement among a very large set of studies, including relative measurements of the propane:n‐butane rate constant ratio. We present new reduced transition state theory fits for each reaction that accurately reproduce the observed rate constants between 180 and 1000 K, and argue that these two reactions are the optimal reference reactions for many relative rate studies. © 2004 Wiley Periodicals, Inc. Int J Chem Kinet 36: 259–272, 2004     

Morphology-Dependent Stability of Complex Metal Hydrides and Their Intermediates Using First-Principles Calculations

Complex light metal hydrides are promising candidates for efficient, compact solid-state hydrogen storage. (De)hydrogenation of these materials often proceeds via multiple reaction intermediates, the energetics of which determine reversibility and kinetics. At the solid-state reaction front, molecular-level chemistry eventually drives the formation of bulk product phases. Therefore, a better understanding of realistic (de)hydrogenation behavior requires considering possible reaction products along all stages of morphological evolution, from molecular to bulk crystalline. Here, we use first-principles calculations to explore the interplay between intermediate morphology and reaction pathways. Employing representative complex metal hydride systems, we investigate the relative energetics of three distinct morphological stages that can be expressed by intermediates during solid-state reactions: i) dispersed molecules; ii) clustered molecular chains; and iii) condensed-phase crystals. Our results verify that the effective reaction energy landscape strongly depends on the morphological features and associated chemical environment, offering a possible explanation for observed discrepancies between X-ray diffraction and nuclear magnetic resonance measurements. Our theoretical understanding also provides physical and chemical insight into phase nucleation kinetics upon (de)hydrogenation of complex metal hydrides.     

The importance of four-membered NHCs in stabilizing Breslow intermediates on benzoin condensation pathway

N-heterocyclic carbenes (NHCs) have been established to be effective organocatalysts for facilitating the benzoin condensation and many other reactions. These reactions involve the formation of a Breslow intermediate (BI), which exhibits umpolung chemistry. To facilitate organocatalysis, several new cyclic carbenes are being introduced, four-membered NHCs are of special interest. Whether these NHCs can exhibit catalytic influence or not, can be evaluated by exploring the potential energy surface (PES) of the benzoin condensation reaction. Quantum chemical analysis has been carried out to compare the PES of these four-membered NHCs with that of standard five-membered NHCs to explore their catalytic ability. The barrier for the first step of the reaction for the formation of BI is comparable in all the cases. But the barrier for the second step of the reaction leading to the benzoin formation from BI is estimated to be very high for the four membered NHCs. These results indicate that the probability of identifying and isolating the BI is very high in comparison to the completion of benzoin condensation reaction in the case of the four-membered NHCs.     

Coordination properties of zinc 5,15-di(<Emphasis Type="Italic">ortho</Emphasis>-aminophenyl)octaalkylporphyrin in reactions with mono- an dibasic nitrogen bases

The coordination properties of zinc 5,15-di(ortho-aminophenyl)octaalkylporphyrin in reactions with mono- and dibasic nitrogen bases in benzene are studied by means of computational modeling and spectrophotometric titration. The stability of molecular zinc porphyrinate complexes in solution is estimated and their structure is determined. The correlation between the coordination properties of the compound under investigation and electronic and conformational factors of the macrocycle is established. The base nature is shown to affect the stability of zinc porphyrinate complexes. The correlations between the calculated σ bond energy of the zinc atom with the nitrogen atom of the base (E _b) and the equilibrium constant of the axial coordination reaction are obtained. It is demonstrated that the reaction is accompanied by an increase in steric hindrance and a change in the type of deformation of the porphyrin ligand.