Structure and Electron-density Distribution

The structure of 1 has been redetermined recently by different methods (Table 1). The agreement with the results of an earlier ED study20 is quite good. 

T ABLE 1. Structural parameters of cyclopropane (1) from experiment and ab initio calculations (re) 

FIGURE 2. Dynamic filtered deformation electron-density distribution of cyclopropane (1). Sections (a) in the ring plane and (b) in the crystallographic mirror plane, perpendicular to the ring plane. Contours are at 0.05 e A 3 intervals, dashed lines represent negative areas. Reproduced by permission of the International Union of Crystallography from Reference 23b 

Unexpectedly, the ring strain30 31 in 1,116 kJ mol 1, is about the same as in cyclobutane, 110 kJ mol 1. So it is interesting to compare their geometric parameters. 

The carbon-carbon bond is shorter in 1 than in the other cycloalkanes the bond length has a maximum in cyclobutane with increasing ring size32. A similar variation of C—O and C—S bond lengths is observed in the analogous heterocyclic molecules33 34. 

As 1 is a nonpolar symmetric top with symmetry, it should have no pure rotational spectrum, but it acquires a small dipole moment by partial isotopic substitution or through centrifugal distortion. In recent analyses of gas-phase data, rotational constants from earlier IR and Raman spectroscopic studies, and those for cyclopropane-1,1- /2 and for an excited state of the v, C—C stretching vibration were utilized Anharmonicity constants for the C—C and C—H bonds were determined in both works. It is the parameters, then from the equilibrium structure, that can be derived and compared from both the ED and the MW data by appropriate vibrational corrections. Variations due to different representations of molecular geometry are of the same magnitude as stated uncertainties. The parameters from experiment agree satisfactorily with the results of high-level theoretical calculations (Table 1). 

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G.J.H. Vannes, A. Vos, Single-crystal structures and electron density distributions of ethane, ethylene and acetylene. I. Single-crystal X-ray structure determinations of two modifications of ethane. Acta Cryst. B 34, 1947-1956 (1978)... 

Nijveldt and Vos determined by a careful analysis of XD data, the structure and electron-density distribution of 1 (at 94 K), bicyclopropyl and vinylcyclopropane. Figure 2 shows sections of the electron-density map of 1. The molecule lies at a mirror plane in the orthorhombic Cmclx crystal the plane bisects the C2—Cl—C2 angle. Some deviation from the ideal symmetry is apparent in the density map and in differences between inde-... 

The structure and electron-density distribution of two derivatives 207 and 208 have been determined at 81 K by The symmetry of the propellane part is close to Z>3h in both... 

I Higashi, T Ito. Structure and electronic density distribution of icosahedral B12 compounds. In H Werheit, ed. Proceedings of the 9th International Symposium on Boron, Borides and Related Compounds, University of Duisburg, Duisburg, 1987, p 41. 

In different molecules each term can exhibit differently depending on structure and electron density distribution as well as syntheses, temperature, experimental methods, etc. 

Intercalation of cations into a framework of titanium dioxide is a process of wide interest. This is due to the electrochromic properties associated with the process (a clear blue coloration results from the intercalation) and to the system s charge storage capabilities (facilitated by the reversibility of the process) and thus the potential application in rocking-chair batteries. We have studied alkali-metal intercalation and ion diffusion in the Ti02 anatase and spinel crystals by theoretical methods ranging from condensed-phase ab initio to semiempirical computations [65, 66]. Structure relaxation, electron-density distribution, electron transfer, diffusion paths and activation energies of the ion intercalation process were modeled. 

Stevens, E. D. Analyses of electronic structure from electron density distributions of transition metal complexes. In Electron Distributions and the Chemical Bond. (Eds., Coppens, P., and Hall, M. B.) pp. 331-349. Plenum New York, London (1982). 

Attempts have been made to correlate this behavior with the ring sizes and average T-O-T angles present in zeolites of different topologies [300]. However, the observed frequency dependencies were not fairly uniform. In particular, for A-type zeolites a trend reversed to that for faujasites has been observed by changing the nsi/n i ratio systematically [290]. Hence, the frequency shifts obviously arise from different effects of structural changes, altered nature of normal modes, and electron density distribution and from combinations of these effects. Instead of the band shift observed for aliunimun-rich samples, for highly dealuminated faujasites the band width of the most prominent peak was discovered to reflect the aliuninum content at low levels [295]. 

Gibbs GV, Hill FC, Boisen MB, Downs RT (1998) Power law relationships between bond length, bond strength and electron density distributions. Phys Chem Min 25 585-590 Gibson AS, Lafemina JP (1997) Structure of Mineral Surfaces In Physics and Chemistry of Mineral Surfaces. PV Brady (ed) p 1-62... 

Computational chemistry is now a standard part of chemical research. One major application is in pharmaceutical chemistry, where the likely pharmacological activity of a molecule can be assessed computationally from its shape and electron density distribution before expensive clinical trials are started. Commercial software is now widely available for calculating the electronic structures of molecules and displaying the results graphically. All such calculations work within the Born-Oppenheimer approximation and express the molecular orbitals as linear combinations of atomic orbitals. 

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