Molecular-orbital calculations cyclopropanes

The relative importance of a and r contributions to the overall bonding is unclear, but several different combinations of relative strengths lead to limiting case models. When there are 2 electrons in the forward (T-bond and 2 electrons in the ir-backbond, there are 2 bonding electrons for each metal-carbon bond. This is mathematically equivalent to 2tr-bonds and a metallocyclopropane structure (72). This model does not necessitate strict sp3 hybridization at the carbon atoms. Molecular orbital calculations for cyclopropane (15) indicate that the C—C bonds have higher carbon atom p character than do the C—H bonds. Thus, the metallocyclopropane model allows it interactions with substituent groups on the olefin (68). 

In order to understand these and related differences between cyclopropane and other carbocycles, it is helpful first to consider the results of theoretical calculations. It is now possible to obtain high quality wave functions for cyclopropane and related molecules via ab initio molecular orbital calculations. The most satisfactory way in which to examine these wave functions is by calculating the charge densities. It must be remembered that the molecular orbitals themselves are just convenient functions for solving the Schroedinger wave equation ... 

A number of SCF molecular orbital calculations for cyclopropane have been reported, among them those of Skancke, Kochanski and Lehn ", Kao and Radom, Hase and colleaguesBasch and colleagues Collins and Gallup and von Niessen and colleagues the most accurate appear to be those of Skancke (Table 1). 

TABLE 1. Energies of the molecular orbitals of cyclopropane E (in eV) calculated by the SCF method, together with their irreducible representations in the Dajj point group and the vertical ionization energies / (in eV) derived from the He(I) photoelectron spectra of the vapour... 

The interaction of the bent banana bonds of the classical Coulson-Mofiit valence bond model of cyclopropane which uses methane-like sp hybrids and joins three units to form the alicyclic ring imply a resonance energy in cyclopropane of 69 kcalmol" Modern molecular orbital calculations (STO-3G) support an electron rich n system and an electron deficient cr-system for cyclopropane. 

The apparent discrepancy in assignment of structure to the protonated cyclopropanes from the experiments described above could be resolved if corner-protonated and edge-protonated ions were in fact very close in energy and if the preference for one or other then depended on substituents. As it happens, this is exactly the picture that emerges from molecular orbital calculations on protonated cyclopropane. While early calculations seemed to favor the corner-protonated structure later ones involving extensive electron... 

The PE spectrum of cyclobutane (69) exhibits (Fig. 18) two close lying intense bands at 10.7 and 11.3 eV, followed by a weak but clearly separated band at 12.5 eV and another broad band at 13.39 eV. The first two bands have been assigned as due to a Jahn-Teller split of the Eu state The split encountered (0.6 eV) is similar to the one found in the PE spectrum of cyclopropane. The third band is assigned to the state according to a comparison between a molecular orbital calculation... 

The results of experimental observations and molecular orbital calculations indicate that many carbenes have a nonlinear triplet ground state. Exceptions are the dihalocarbenes and carbenes with oxygen, nitrogen or sulfiar atoms attached to the bivalent carbon, all of which are singlets. The singlet and triplet states of a carbene do not necessarily show the same chemical behaviour. For example, addition of singlet carbenes to olelinic double bonds to form cyclopropane derivatives is more stereoselective than addition of triplet carbenes. 

In conclusion, most of the evidence and molecular orbital calculations (see p. 27) support the view that cyclopropylcarbinyl cations have a bisected conformation that is stabilized because of the increased p-character of the bent C—C cyclopropane bonds which increases greatly their C—C hyperconjugative ability. The most important evidence that has been interpreted as arguing against this formulation is the NMR spectra of the cyclopropylmethyl cation itself, and hence there must be certain reservations about the < bove conclusion concerning this ion. It must also be... 

The molecular orbitals of cyclopropane from an ah initio calculation. The letters correspond to the lettering from Figure 14.21. 

MINDO/3 calculations relative to cyclopropane and cyclopropene show that the two highest molecular orbitals for silacyclopropane and silacyclopropene are destabilized. As a result, silacyclopropane and silacyclopropene are predicted to be more reactive toward electrophiles than their carbon analogues <79JCS(P1)443>. 

Although cyclopropanes are far less reactive than alkenes, they can be opened by various electrophiles including protic acids, bromine, chlorine, mercury(II) salts and acetyl chloride. The ring-cleavage processes of cyclopropanes by electrophiles were studied with the aid of ab initio molecular orbital and other calculations. Early studies assumed that traditional... 

Figure 2. MNDO calculations of potential precursors for intramolecular [2n+2a] cycloaddition. Molecular orbitals ( t of the double bond and e -Walsh orbital of the cyclopropane) have been plotted with PERGRA. ...

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