The theory of molecular structure determined by the gradient vector field of the charge density ρ identifies the set of atomic interactions present in a molecule. The interactions so defined are characterized in terms of the properties of the Laplacian of the charge density ∇2ρ(r). A scalar field is concentrated in those regions of space where its Laplacian is negative and depleted in those where it is positive. An expression derived from the quantum mechanical stress tensor relates the sign of the Laplacian of ρ to the relative magnitudes of the local contributions of the potential and kinetic energy densities to their virial theorem averages. By obtaining a map of those regions where ∇2ρ(r) 0. The mechanics are characterized by the relatively large value of the kinetic energy, particularly the component parallel to the interaction line. In the closed‐shell interactions, the regions of dominant potential energy contributions are separately localized within the boundaries of each of the interacting atoms or molecules. In the shared interactions, a region of low potential energy is contiguous over the basins of both of the interacting atoms. The problem of further classifying a given interaction as belonging to a bound or unbound state of a system is also considered, first from the electrostatic point of view wherein the regions of charge concentration as determined by the Laplacian of ρ are related to the forces acting on the nuclei. This is followed by and linked to a discussion of the energetics of interactions in terms of the regions of dominant potential and kinetic energy contributions to the virial as again determined by the Laplacian of ρ. The properties of the Laplacian of the electronic charge thus yield a unified view of atomic interactions, one which incorporates the understandings afforded by both the Hellmann–Feynman and virial theorems.

The structures of ethylene oxide, cyclopropane, and related molecules

The characterization of atomic interactions

Theory of Orientation and Stereoselection

Moebius-Hueckel concept in organic chemistry. Application of organic molecules and reactions

Among the cyclic compounds of carbon, cyclopropane and its derivatives are outstanding by virtue of their unusual structural, spectroscopic, and chemical properties. The cyclopropane ring more closely resembles the CC double bond than the cyclobutane ring: it is a small ring with “double bond character”. Cyclopropyl and vinyl groups interact with neighbouring π-electron systems and p-electron centers; both cyclopropane derivatives and olefins form metal complexes, and add strong acids, halogens, and ozone; they both undergo catalytic hydrogenation and cycloadditions. While distinct differences in reactivity do exist–the double bond usually being more reactive than the three-membered ring–there are no fundamental differences in behavior.–Although cyclopropane derivatives have been known for more than 90 years, intensive studies have been limited to the past 25 years. The development of carbene chemistry has rendered cyclopropane derivatives far more readily accessible. In recent years, the synthetic potential of the small-ring function has been increasingly exploited. A considerable number of newly developed methods utilizing this approach clearly demonstrates that the reactivity of the cyclopropene ring, like that of the CC double bond, qualify it as a “functional carbon group”. This development is in full swing; we may therefore justifiably devote considerable effort to the study of cyclopropane chemistry.

Bonding Properties of Cyclopropane and Their Chemical Consequences

The conformations, relative stabilities, and electronic distribution of a sample of the more important carbonium ions and positively charged hypothetical transition states are examined. The species studied include the methyl, ethyl, isopropyl, tertiary butyl, and higher alkyl carbonium ions; protonated ethylene, acetylene, benzene, cyclopropane; the cyclopropyl, cyclobutyl, cyclopentyl, cyclohexyl carbinyl, allyl, and benzyl cations; the carbonium ions based on norbornane, norbornene, norbornadiene. Significant charge delocalization for a classical carbonium ion geometry is observed—the extent of this phenomenon is wider than anticipated. For the alkyl carbonium ions it is shown that the order of stabilities may be obtained from a calculation in which the polarity of the C–H bond is C—–H+. Protonated ethylene and acetylene show local minima for a symmetrical complex, but with rearrangement to an unsymmetrical cation favored. Protonated cyclopropane prefers an unsymmetrical three‐center bonded structure, protonated benzene stabilizes in the familiar benzenium. The orientation of the empty carbonium p orbital with respect to other π‐type orbitals determines the conformation in cyclopropyl carbinyl, benzyl, and allyl. The peculiar nature of the cyclopropane electron distribution is studied. The carbonium ions based on the bicyclo[2.2.1]‐heptane structure show some nonclassical features; confirming experimental conclusions, the unusual 7‐norbornadienyl cation is calculated to prefer an unsymmetrical geometry. Difficulties in applying the extended Huckel theory to charged species make some of the conclusions from the calculations less certain.

The structures of ethylene oxide, cyclopropane, and related molecules

Citations

The characterization of atomic interactions

Theory of Orientation and Stereoselection

Moebius-Hueckel concept in organic chemistry. Application of organic molecules and reactions

Bonding Properties of Cyclopropane and Their Chemical Consequences

Extended Hückel Theory. IV. Carbonium Ions

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Bonding Properties of Cyclopropane and Their Chemical Consequences