Valence shell theory

As mentioned above, HMO theory is not used much any more except to illustrate the principles involved in MO theory. However, a variation of HMO theory, extended Huckel theory (EHT), was introduced by Roald Hof nann in 1963 [10]. EHT is a one-electron theory just Hke HMO theory. It is, however, three-dimensional. The AOs used now correspond to a minimal basis set (the minimum number of AOs necessary to accommodate the electrons of the neutral atom and retain spherical symmetry) for the valence shell of the element. This means, for instance, for carbon a 2s-, and three 2p-orbitals (2p, 2p, 2p ). Because EHT deals with three-dimensional structures, we need better approximations for the Huckel matrix than... 

Valence shell electron pair repulsion theory, 1, 564 Valence tautomerism photochromic processes and, 1, 387 y-Valerolactone, o -allyl-a -2-(pyrido[2,3-6]-imidazolyl)-synthesis, 5, 637 Validamycin A as fungicide, 1, 194 Valinomycin... 

Thus the orbitals and r electrons lie in the outermost part of the valence shell of ethane. They should play a critical role in determining the chemical properties of the molecule. Some theories have ascribed the barrier to internal rotation to these orbitals. It should be noted that the existence of r electrons in ethane is not a novelty, and was first pointed out by Mullikcn in 1935. 

Valence shell electron pair repulsion theory, 1,32-39 effective bond length ratios, 1.34 halogenium species, 3, 312 noble gas compounds, 3,312 repulsion energy coefficient, 1, 33 Valency... 

The Lewis structures encountered in Chapter 2 are two-dimensional representations of the links between atoms—their connectivity—and except in the simplest cases do not depict the arrangement of atoms in space. The valence-shell electron-pair repulsion model (VSEPR model) extends Lewis s theory of bonding to account for molecular shapes by adding rules that account for bond angles. The model starts from the idea that because electrons repel one another, the shapes of simple molecules correspond to arrangements in which pairs of bonding electrons lie as far apart as possible. Specifically ... 

In valence-bond theory, we assume that bonds form when unpaired electrons in valence-shell atomic orbitals pair the atomic orbitals overlap end to end to form cr-bonds or side by side to form ir-bonds. 

In this section we start, as in valence-bond theory, with a simple molecule, H2, and in the following sections extend the same principles to more complex molecules and solids. In every case, molecular orbitals are built by adding together—the technical term is superimposing—atomic orbitals belonging to the valence shells of the atoms in the molecule. For example, a molecular orbital for Fi2 is... 

Now that we know how to determine hybridization states, we need to know the geometry of each of the three hybridization states. One simple theory explains it all. This theory is called the valence shell electron pair repulsion theory (VSEPR). Stated simply, all orbitals containing electrons in the outermost shell (the valence shell) want to get as far apart from each other as possible. This one simple idea is all you need to predict the geometry around an atom. First, let s apply the theory to the three types of hybridized orbitals. 

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

This theory appears not to involve adjustable parameters (other than the nuclear radius parameters that were taken from the literature). In particular, it was criticized that the calibration approach involved a slope that is too high by about a factor of two. However, in actual calculations with the linear response approach, it was found that the slope of the correlation line between theory and experiment (dependent on the quantum chemical method) is close to 0.5. Thus, it also requires a scaling factor of about 2 in order to reach quantitative agreement with experiment. The standard deviations between the calibration and linear response approaches are comparable thus indicating that the major error in both approaches still stems from errors in the description of the bonding that is responsible for the actual valence shell electron distribution. 

In one respect the valence shell electron-pair repulsion theory is no better (and no worse) than other theories of molecular structure. Predictions can only be made when the constitution is known, i.e. when it is already known which and how many atoms are joined... 

To derive the values of the coefficients at, Ph y, and 8i so that the bond energy is maximized and the correct molecular structure results, the mutual interactions between the electrons have to be considered. This requires a great deal of computational expenditure. However, in a qualitative manner the interactions can be estimated rather well that is exactly what the valence shell electron-pair repulsion theory accomplishes. 

Redress can be obtained by the electron localization function (ELF). It decomposes the electron density spatially into regions that correspond to the notion of electron pairs, and its results are compatible with the valence shell electron-pair repulsion theory. An electron has a certain electron density p, (x, y, z) at a site x, y, z this can be calculated with quantum mechanics. Take a small, spherical volume element AV around this site. The product nY(x, y, z) = p, (x, y, z)AV corresponds to the number of electrons in this volume element. For a given number of electrons the size of the sphere AV adapts itself to the electron density. For this given number of electrons one can calculate the probability w(x, y, z) of finding a second electron with the same spin within this very volume element. According to the Pauli principle this electron must belong to another electron pair. The electron localization function is defined with the aid of this probability ... 

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. 

For Li—F, the quantal ionic interaction can be qualitatively pictured in terms of the donor-acceptor interaction between a filled 2pf. orbital of the anion and the vacant 2su orbital of the cation. However, ionic-bond formation is accompanied by continuous changes in orbital hybridization and atomic charges whose magnitude can be estimated by the perturbation theory of donor-acceptor interactions. These changes affect not only the attractive interactions between filled and unfilled orbitals, but also the opposing filled—filled orbital interactions (steric repulsions) as the ionic valence shells begin to overlap. 

In the spirit of elementary bonding theories, we expect that the dominant contributions to h,(A) come only from the first summation, consisting (for an s/p-block atom) simply of the four contributions (s, px, pv, p-) from the valence shell. At this level, the hybrid can be written simply as (dropping the atom label throughout)... 

Due to the simplicity and the ability to explain the spectroscopic and excited state properties, the MO theory in addition to easy adaptability for modern computers has gained tremendous popularity among chemists. The concept of directed valence, based on the principle of maximum overlap and valence shell electron pair repulsion theory (VSEPR), has successfully explained the molecular geometries and bonding in polyatomic molecules. 

---