Molecular Orbital Theory Polyatomics

In all of the examples thus far, we have applied a localized version of the LCAO-MO method, where the MOs were derived by taking linear combinations of the AO wavefunctions of only two of the atoms in the molecule. In other words, the electrons that occupied these MOs were localized between two nuclei, just as they were in VBT. However, MOT does not restrict us to this arrangement. The alternative is a delocalized approach, where the electrons are not forced a priori to be localized between specific nuclei in the molecule. While the delocalized approach is more consistent with the observed electronic spectra and PES data of molecules, it is also inherently less intuitive because our minds have been trained to think of the electrons in chemical bonds as always occurring between just two nuclei. Therefore, we need to discard any preconceived notions of chemical bonding and retrain our brains into thinking about the bonding in molecules from a more holistic perspective. 

The following is a general strategy for the development of the MO diagram for polyatomic molecules having identical ligands on the central atom  

On the left-hand side of the MO diagram, order the valence AOs for the central atom according to their energies and list the IRRs that correspond with those AOs in the point group of the molecule. 

On the right-hand side of the MO diagram, order the AOs of the ligands. 

Use the different sets of AOs on the ligands as basis sets to generate reducible representations known as symmetry-adapted linear combinations (SALCs). Any basis function that is unchanged by a given symmetry operation will contribute I to the character, any basis function that transforms into the opposite of itself will contribute — I, and any basis function that is transformed into a basis function on a different li d will be an off-diagonal element and contribute 0 to the character. 

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Hurley, A. C., Lennard-Jones, J., and Pople, J. A., Proc. Roy. Soc. [London) A220, 446, The molecular orbital theory of chemical valency XVI. A theory of paired electrons in polyatomic molecules." Use of two-electron functions T fa, x5) as a basis. 

The molecular orbital theory of polyatomic molecules follows the same principles as those outlined for diatomic molecules, but the molecular orbitals spread over all the atoms in the molecule. An electron pair in a bonding orbital helps to bind together the whole molecule, not just an individual pair of atoms. The energies of molecular orbitals in polyatomic molecules can be studied experimentally by using ultraviolet and visible spectroscopy (see Major Technique 2, following this chapter). 

According to molecular orbital theory, the delocalization of electrons in a polyatomic molecule spreads the bonding effects of electrons over the entire Energy molecule. 

Use molecular orbital theory to describe bonding in polyatomic molecules such as the benzene molecule, Section 3.12. 

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. 

Orbitals) (CO) are expressed as a linear combination of atomic orbitals (LCAO) or similar local functions. There is an obvious parallelism with the traditional Molecular Orbital Theory see Molecular Orbital Theory) developed by chemists, in which the wavefimctions describing the motion of an electron in the molecule (i.e. the Molecular Orbitals) (MO) are also expressed as a LCAOs. As a matter of fact, the first orbital describing the motion of an electron in a polyatomic system was written by Bloch in 1928 and it was a CO. Hence, MO theory finds its roots in solid-state physics. 

Dynamics calculations of reaction rates by semiempirical molecular orbital theory. POLYRATE for chemical reaction rates of polyatomics. POLYMOL for wavefunctions of polymers. HONDO for ab initio calculations. RIAS for configuration interaction wavefunctions of atoms. FCI for full configuration interaction wavefunctions. MOLSIMIL-88 for molecular similarity based on CNDO-like approximation. JETNET for artificial neural network calculations. More than 1350 other programs most written in FORTRAN for physics and physical chemistry. 

Molecular Orbital Theory II. Polyatomic Moiecules and Solids 171... 

Molecular Orbital Theory II Polyatomic Molecules and Solids... 

This shows no unpaired electrons, so it predicts that O2 is diamagnetic. Experiments show, however, that O2 is paramagnetic therefore, it has unpaired electrons. Thus, the valence bond structure is inconsistent with experiment and cannot be accepted as a description of the bonding. Molecular orbital theory accounts for the fact that O2 has two unpaired electrons. This ability of MO theory to explain the paramagnetism of O2 gave it credibility as a major theory of bonding. We shall develop some of the ideas of MO theory and apply them to some molecules and polyatomic ions. 

Since the valence bond theory is insufficient to explain the structure and behavior of polyatomic molecules, the molecular orbital theory was developed. In this theory, it is accepted that electrons in a polyatomic molecule should not be regarded as belonging to particular bonds but should be treated as spreading throughout the entire molecule every electron contributes to the strength of every bond. A molecular orbital is considered to be a linear combination of all the atomic orbitals of all the atoms in the molecule. Quantum... 

The molecular orbital theory is one of the two approximate theories which have been used to investigate the electronic structures of atoms and molecules. This theory, like its counterpart, the valence bond theory, was advanced very soon after the advent of wave mechanics twenty-five years ago, but it is only in recent years that the molecular orbital theory has come into general use for describing not only the ground states, but also the excited states of polyatomic molecules.7 ... 

Molecular-orbital theory, especially Hiickel theory (1931) and its extensions, is by now widely appreciated by chemists in all areas of research and teaching. This was not always so. Actually, the method of linear combinations of atomic orbitals was used by Bloch in 1928 for wave functions in crystals. Molecular wave-functions were introduced by Mulliken (1928), Hund (1928), Herzberg (1929) and Lennard-Jones (1929) for diatomic molecules, and the extensions to polyatomic molecules followed quickly thereafter. 

The quantum mechanical procedure for calculating the electronic structure and physical properties of polyatomic molecules has been developed by the use of a powerful tool, the molecular orbital theory proposed by Hund and Mulliken. The theory has been applied to large molecules with considerable vigor. However, because of the difficulty of carrying out all the molecular integral calculations involved, various approximations have been used. 

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

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