Molecular geometry theory

One of molecular orbital theories early successes came m 1931 when Erich Huckel dis covered an interesting pattern m the tt orbital energy levels of benzene cyclobutadiene and cyclooctatetraene By limiting his analysis to monocyclic conjugated polyenes and restricting the structures to planar geometries Huckel found that whether a hydrocarbon of this type was aromatic depended on its number of tt electrons He set forth what we now call Huckel s rule... 

Energy, geometry, dipole moment, and the electrostatic potential all have a clear relation to experimental values. Calculated atomic charges are a different matter. There are various ways to define atomic charges. HyperChem uses Mulliken atomic charges, which are commonly used in Molecular Orbital theory. These quantities have only an approximate relation to experiment their values are sensitive to the basis set and to the method of calculation. 

Another approach to calculating molecular geometry and energy is based on density functional theory (DFT). DFT focuses on the electron cloud corresponding to a molecule. The energy of a molecule is uniquely specified by the electron density functional. The calculation involves the construction of an expression for the electron density. The energy of the system is then expressed as... 

The shapes of the monomeric molecules of the Group 2 halides (gas phase or matrix isolation) pose some interesting problems for those who are content with simple theories of bonding and molecular geometry. Thus, as expected on the basis of either sp hybridization or the... 

Let s now look at an ab initio CIS calculation on pyridine. As a routine first step, I optimized the molecular geometry (yet to be discussed) at the HF/6-31G level of theory. It is interesting to examine the ab initio orbital configuration (Figure 11.3). 

The carbon parameters ac and /3cc are normally just denoted a and (3, and are rarely assigned numerical values. Simple Hiickel theory thus only considers the connectivity of the TT-atoms, there is no information about the molecular geometry entering the calculation (e.g. whether some bonds are shorter or longer than others, or differences in bond angles). 

We said in Section 1.5 that chemists use two models for describing covalent bonds valence bond theory and molecular orbital theory. Having now seen the valence bond approach, which uses hybrid atomic orbitals to account for geometry and assumes the overlap of atomic orbitals to account for electron sharing, let s look briefly at the molecular orbital approach to bonding. We ll return to the topic in Chapters 14 and 15 for a more in-depth discussion. 

In Chapter 7, we used valence bond theory to explain bonding in molecules. It accounts, at least qualitatively, for the stability of the covalent bond in terms of the overlap of atomic orbitals. By invoking hybridization, valence bond theory can account for the molecular geometries predicted by electron-pair repulsion. Where Lewis structures are inadequate, as in S02, the concept of resonance allows us to explain the observed properties. 

Experimentally, the molecular geometry has been determined by X-ray analysis for several larger radicals. These data indicate, in agreement with the theory, that bond alternation characteristic in many reduced and oxidized closed-shell forms is diminished in radical ions. Precise crystallographic data are available for 4,4 -A/s(dimethylamino)diphenylamine radical cation (87, 88), N,N -diphenyl-p-phenylenediamine radical cation (89), and Wiirster s blue (90). 

Resonance theory [15] contains essentially three assumptions beyond those of the valence bond method. Perhaps the most serious assumption is the contention that only unexcited canonical forms, non-polar valence bond structures or classical structures need be considered. Less serious, but no more than intuitive, is the proposition that the molecular geometry will take on that expected for the average of the classical structures. This is extended to the measurement of stability being greater the greater the number of classical structures. These concepts are still widely used in chemistry in very qualitative ways. 

The E-state is based solely on atom connectivity information obtained from the molecular graph, without any input from the molecular geometry or sophisticated quantum calculations. We start this chapter with a brief presentation of the relevant notions of graph theory and continue with the definitions of a couple of important graph matrices. Then the molecular connectivity indices are mentioned... 

The other approach to molecular geometry is the valence shell electron-pair repulsion (VSEPR) theory. This theory holds that... 

Andzelm and Wimmer, 1992, published one of the first comprehensive studies on the performance of approximate density functional theory in which optimized molecular geometries were reported. These authors computed the geometries of several organic species containing the atoms C, N, O, H, and F at the local SVWN level, using a polarized double-zeta basis set optimized for LDA computations. Some trends have been discerned... 

Before discussing the AIM theory, we describe in Chapters 4 and 5 two simple models, the valence shell electron pair (VSEPR) model and the ligand close-packing (LCP) model of molecular geometry. These models are based on a simple qualitative picture of the electron distribution in a molecule, particularly as it influenced by the Pauli principle. 

St.-Amant, A., W. D. Cornell, P. Kollman, and T. A. Halgren. 1995. Calculation of Molecular Geometries, Relative Conformation Energies, Dipole Moments, and Molecular Electrostatic Potential Fitted Charges of Small Organic Molecules of Biochemical Interest by Density Functional Theory. J. Comp. Chem. 16, 1483. 

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