Molecular geometry orbital

In our treatment of molecular systems we first show how to determine the energy for a given iva efunction, and then demonstrate how to calculate the wavefunction for a specific nuclear geometry. In the most popular kind of quantum mechanical calculations performed on molecules each molecular spin orbital is expressed as a linear combination of atomic orhilals (the LCAO approach ). Thus each molecular orbital can be written as a summation of the following form ... 

The primary reason for interest in extended Huckel today is because the method is general enough to use for all the elements in the periodic table. This is not an extremely accurate or sophisticated method however, it is still used for inorganic modeling due to the scarcity of full periodic table methods with reasonable CPU time requirements. Another current use is for computing band structures, which are extremely computation-intensive calculations. Because of this, extended Huckel is often the method of choice for band structure calculations. It is also a very convenient way to view orbital symmetry. It is known to be fairly poor at predicting molecular geometries. 

Practically all CNDO calculations are actually performed using the CNDO/ 2 method, which is an improved parameterization over the original CNDO/1 method. There is a CNDO/S method that is parameterized to reproduce electronic spectra. The CNDO/S method does yield improved prediction of excitation energies, but at the expense of the poorer prediction of molecular geometry. There have also been extensions of the CNDO/2 method to include elements with occupied d orbitals. These techniques have not seen widespread use due to the limited accuracy of results. 

Extended Hiickel gives a qualitative view of the valence orbitals. The formulation of extended Hiickel is such that it is only applicable to the valence orbitals. The method reproduces the correct symmetry properties for the valence orbitals. Energetics, such as band gaps, are sometimes reasonable and other times reproduce trends better than absolute values. Extended Hiickel tends to be more useful for examining orbital symmetry and energy than for predicting molecular geometries. It is the method of choice for many band structure calculations due to the very computation-intensive nature of those calculations. 

Structural studies show allene to be nonplanar As Figure 10 7 illustrates the plane of one HCH unit is perpendicular to the plane of the other Figure 10 7 also portrays the reason for the molecular geometry of allene The 2p orbital of each of the terminal car bons overlaps with a different 2p orbital of the central carbon Because the 2p orbitals of the central carbon are perpendicular to each other the perpendicular nature of the two HCH units follows naturally... 

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 major features of molecular geometry can be predicted on the basis of a quite simple principle—electron-pair repulsion. This principle is the essence of the valence-shell electron-pair repulsion (VSEPR) model, first suggested by N. V. Sidgwick and H. M. Powell in 1940. It was developed and expanded later by R. J. Gillespie and R. S. Nyholm. According to the VSEPR model, the valence electron pairs surrounding an atom repel one another. Consequently, the orbitals containing those electron pairs are oriented to be as far apart as possible. 

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. 

Octet rule The principle that bonded atoms (except H) tend to have a share in eight valence electrons, 166-171 exceptions to, 172-176 molecular geometry and, 181t molecular orbitals and, 650 Octyl acetate, 596t Open-pit copper mine, 540 Oppenheimer, J. Robert, 523 Optical isomer Isomer which rotates the... 

References for the molecular geometries used in generating the drawings are given in Section IV. 1. Effort was made to make these as up-to-date as possible. For this reason the geometry references are not always the same as those used to determine the ab initio orbital energies. 

The following is a list of references for the molecular geometries and orbital energies used in constructing the drawings of Chapter III. The ordering of the molecules is the same as in Chapter III. 

Methylenecyclopropane, 48, 194 bond lengths, 38 rotational barrier, 38 Methylenimine, 83 MINDO A 54 Molecular geometries, 287 Molecular orbitals, 57, see also individual molecules... 

We are now ready to account for the bonding in methane. In the promoted, hybridized atom each of the electrons in the four sp3 hybrid orbitals can pair with an electron in a hydrogen ls-orbital. Their overlapping orbitals form four o-bonds that point toward the corners of a tetrahedron (Fig. 3.14). The valence-bond description is now consistent with experimental data on molecular geometry. 

Non-cyclic interactions of two and three orbitals are described in the preceding chapters of this volume. We describe here cyclic interactions of three or more orbitals (Scheme 1). In 1982, cyclic orbital interaction was found in non-cyclic conjugation [15]. Interactions of bonds in molecules contain cyclic interactions of bond (bonding and antibonding) orbitals even if the molecular geometry is non-cyclic. The cyclic... 

At this stage, we wish to emphasize that a point (molecular geometry) on a conical intersection hyperline has a well-defined electronic structure (illustrated in Figure 9.6 or Eq. 9.2 with T = 0) and a well-defined geometry. Of course, the four electrons in four Is orbitals shown in Figure 9.6 is a very simple example, but we believe it is useful in order to be able to appreciate the generality of the conical intersection construct. In more complex systems, the conical intersection hyperline concept persists, but the rationalization may be less obvious. 

Andzelm, J., Wimmer, E., 1992, Density Functional Gaussian-Type-Orbital Approach to Molecular Geometries, Vibrations, and Reaction Energies , J. Chem. Phys., 96, 1280. 

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