Molecular Geometry and the Number of Electrons

Molecular geometry depends not only on the constituent atoms, but also on the total number of electrons. Molecules with identical formulas but with varying numbers of electrons may prefer different geometries. 

Repeat your analysis for 2-methyl-2-propyl radical and 2-methyl-2-propyl anion, and assign preferred equilibrium geometry and the energy required to distort (by 10°) away from this geometry to each. 

Compare electrostatic potential maps for planar and pyramidal forms of 2-methyl-2-propyl anion. For which is the negative charge more delocalized Is this the lower-energy structure For this case, does charge delocalization lead to stabilization Explain. 

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In addition to this influence of the molecular structure, which correlates with the number and the delocalization of -electrons, steric effects resulting from the internal molecular geometry and the nature of the substituents may play an important role in intermolecular charge transfer because of the packing of adjacent molecules in the solid 80>. For instance, the observation that the introduction... 

Table21.1 is derived largely from Table 13.2, Section 13.3. The earlier table Includes Illustrations that show how molecular structure Is related to electron-pair geometry and the number of atoms bonded to the central atom.

The application of this treatment appears to be successful in many cases, often explaining the differences between different geometries, for instance between tetranuclear species. Tetrahedral, square-planar, or butterfly metal atom arrays may be differentiated by considering the corresponding molecular orbital diagrams and the number of electrons in the system. However the benefits of such calculations do not go farther than those obtained from the analogy with boranes discussed above. 

For each molecular geometry, list the number of total electron groups, the number of bonding groups, and the number of lone pairs on the central atom. 

Use the number of electron groups, the number of lone pairs of electrons, and Table 9.2 to determine both the electron group geometry and the molecular geometry. 

The semiempirical and empirical methods have been by far the major source of the potentials used for molecular-dynamics studies. This fact stems from computational problems, which are examined next. First, the number of bielectronic molecular integrals in an ab initio calculation increases as the fourth power of the dimension of the function basis set (d4) or approximately as n4, where n represents the number of electrons—the n explosion.50,51 Second, the number of ab initio points necessary to determine (as a large table) the potential-energy surface, i.e., the number of nuclear geometries for which... 

The TEC model developed by Teo also has been successfully applied to rationalize the geometries of a large number of cluster compounds. The TEC model combines Lauher s rule with Euler s theorem and adds an adjustable parameter This parameter X is equal to the number of electron pairs present in excess of that predicted by the 18-electron rule. " X has also been interpreted in terms of the number of missing antibonding orbitals. Given a value for X, determined by the shape of the cluster, an equation predicts the electron count for a cluster. Theoretical justification of the parameter X is based largely upon the classical molecular orbital calculations performed by Hoffmann and Lipscomb via the extended Hiickel method on the corresponding polyhedral boron hydride clusters The values... 

While semiempirical models which can be applied to molecules the size of 1 and 2 are necessarily only approximate, we were searching for trends rather than absolute values. In concept, the design of semiempirical quantum mechanical models of molecular electronic structure requires the definition of the electronic wavefunction space by a basis set of atomic orbitals representing the valence shells of the atoms which constitute the molecule. A specification of quantum mechanical operators in this function space is provided by means of parameterized matrices. Specification of the number of electrons in the system completes the information necessary for a calculation of electronic energies and wavefunctions if the molecular geometry is known. The selection of the appropriate functional forms for the parameterization of matrices is based on physical intuition and analogy to exact quantum mechanics. The numerical values of the parameters are obtained by fitting to selected experimental results, typically atomic properties. 

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