Molecule molecular orbital theory applied

Molecular orbital theory applied to the polyatomic molecules BH3, NH3 and CH4... 

This discrepancy between experiment and theory (and many others) can be explained in terms of an alternative model of covalent bonding, the molecular orbital (MO) approach. Molecular orbital theory treats bonds in terms of orbitals characteristic of the molecule as a whole. To apply this approach, we carry out three basic operations. 

To illustrate molecular orbital theory, we apply it to the diatomic molecules of the elements in the first two periods of the periodic table. 

When the Hartree-Fock method is applied to molecules, molecular orbitals are used instead of atomic orbitals. To construct the molecular orbitals, one widely used approximation is LCAO (linear combinations of atomic orbitals). According to molecular orbital theory, the total wave function of the system is written as a combination of molecular orbitals, spin functions describing electrons in terms of spin j(a) or — j p). 

Some aspects of the bonding in molecules are explained by a model called molecular orbital theory. In an analogous manner to that used for atomic orbitals, the quantum mechanical model applied to molecules allows only certain energy states of an electron to exist. These quantised energy states are described by using specific wavefunctions called molecular orbitals. 

The contents of this chapter are fundamental in the applications of molecular orbital theory to bond lengths, bond angles and molecular shapes, which are discussed in Chapters 3-6. This chapter introduces the principles of group theory and its application to problems of molecular symmetry. The application of molecular orbital theory to a molecule is simplified enormously by the knowledge of the symmetry of the molecule and the group theoretical rules that apply. 

The symmetry concepts of Chapter 2 and those of molecular orbital theory were applied to the construction of molecular orbitals for a range of diatomic molecules. 

Throughout the book, theoretical concepts and experimental evidence are integrated An introductory chapter summarizes the principles on which the Periodic Table is established and describes the periodicity of various atomic properties which are relevant to chemical bonding. Symmetry and group theory are introduced to serve as the basis of all molecular orbital treatments of molecules. This basis is then applied to a variety of covalent molecules with discussions of bond lengths and angles and hence molecular shapes. Extensive comparisons of valence bond theory and VSEPR theory with molecular orbital theory are included Metallic bonding is related to electrical conduction and semi-conduction. 

Two theoretical approaches for calculating NMR chemical shift of polymers and its application to structural characterization have been described. One is that model molecules such as dimer, trimer, etc., as a local structure of polymer chains, are in the calculation by combining quantum chemistry and statistical mechanics. This approach has been applied to polymer systems in the solution, amorphous and solid states. Another approach is to employ the tight-binding molecular orbital theory to describe the NMR chemical shift and electronic structure of infinite polymer chains with periodic structure. This approach has been applied to polymer systems in the solid state. These approaches have been successfully applied to structural characterization of polymers... 

Strictly, frontier orbital theory applies only to bimolecular processes. Therefore, in uni-molecular reactions and/or in structural problems, the molecule is formally split into two fragments, the recombination of which is treated as a bimolecular reaction. However, this ingenious artifice is a rather crude approximation, to be used with caution. 

In this section, we first discuss the bonding in two linear triatomic molecules BeH2 with only a bonds and C02 with both a and n bonds. Then we go on to treat other polyatomic molecules with the hybridization theory. Next we discuss the derivation of a self-consistent set of covalent radii for the atoms. Finally, we study the bonding and reactivity of conjugated polyenes by applying Hiickel molecular orbital theory. 

As mentioned previously in Chapter 3, when we treat the bonding of a molecule by applying molecular orbital theory, we need to solve the secular determinant... 

Molecular orbital theory explains much about molecules. It can tell a chemist how far apart the atoms are, the angles of the bonds between them, and the energy of the bond. But applying molecular orbital theory requires the manipulation of its constituent atoms complicated wave functions, a cumbersome process requiring sophisticated numerical computations. That s why two easier, but less rigorous, methods for getting at the arrangements of atoms in a molecule have been developed. 

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