Molecular Orbital Theory of Bonding

This theory endeavors to describe the molecule by a method intrinsically similar to that used for obtaining atomic orbitals but considering multicenter wave functions. Thus this approach consists of finding the best functions for describing the state of one electron in a field formed by the totality of the nuclei placed in their equilibrium positions. These monoelectronic molecular wave functions may be obtained according to the MO-theory by a linear combination of atomic orbitals (LCAO). 

The hydrogen molecule ion, H2, with two nuclei and one electron is the most simple imaginable molecular system. It can be considered as a prototype for homonuclear biatomic molecules just as hydrogen atom is for atoms in general. 

According to MO-theory, the wave function for the system H2 may be formulated as a linear combination of two hydrogen atomic orbitals Is. The meaning of these two LCAO-MOs can be appreciated in both analytical and pictorial descriptions illustrated in Fig. 1.10. The electron density distribution associated to the orbital i/ ab shows that the charge concentration between the nuclei is indeed greater than the simple sum of contributions of two separate orbitals since (i/ a + + b- That results in binding the nuclei together. 

The energies of i/r ab and i/ b relative to that of an isolated hydrogen atom are shown in Fig. 1.11. 

The nature of the state described by ab and b may also be visualized in the plot of the potential energy of the system H2 as a function of the internuclear distance shown in Fig. 1.12. Only when the electron is in the state described by 

The basic idea is simple next to each nucleus, the most representative terms are those who correspond to the smallest nucleus-electron distances, so the total Hamiltonian is a little different respecting that of the isolated atom. Therefore the wave-functions which describe the electrons around each atom of bonding, called atomic orbitals, represent approximate local solutions of the Schrodinger s equation in molecule accordingly, one will seareh for the molecular function, called molecular orbital, as a linear combination of the atomie orbitals, or hybridized, of various atoms getting into the molecule (Huekel, 1934 Coulson, 1938, 1952 Hall, 1950 Griffith Orgel, 1957 Jensen, 1999 Lieker, 2004). 

Resuming, the ehemieal bond whieh may be formed between two atoms A and B is eonsidered as the resulted MO/the wave-function by composition of the two atomie orbitals q and q which by overlap-ping/superposition constitute the bond 

The quantum energy of chemical bonding will be thus successively written 

With these one may unfold the variational principle for the chemical bonding energy respecting the atomic contributions, respectively as  

From where worth noting that for J, = one regains the previous VB 

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B-68MI20400 R. L. Flurry, Jr. Molecular Orbital Theories of Bonding in Organic Molecules ,... 

Molecular Orbital Theory of the Electronic Structure of Organic Compounds V Molecular Orbital Theory of Bond Separation W. J. Hehre, R. Ditchfield, L. Random and J. A. Pople Journal of the American Chemical Society 92 (1970) 4796... 

The key ideas of the molecular orbital theory of bonding can be summarized as follows ... 

The simple molecular orbital theory of bonding in homonuclear diatomic molecules can be used to estimate the electron affinities of clusters. In these cases, there can be different geometries. The Cn clusters have been studied most extensively. In the case of the triatomic molecules, there are now two distances and one angle that... 

Molecular Orbital Theory of the Electronic Structure of Organic Compounds V Molecular Orbital Theory of Bond Separation... 

Let us use the above ideas to make deductions about the detailed mechanisms of some important reactions of transition metal organometallic compounds. Most of these have molecules of very low S5unmetry and group theoretic rules are of little help. Nevertheless, the molecular orbital theory of bonding is well developed in these compounds (Cotton Schlafer and Gliemann 35b)). 

Sources for further reading include references cited below as well as (a) Flurry, R. L., Jr. Molecular Orbital Theories of Bonding in Organic Molecules Marcel Dekker New York, 1968 (b) Salem, L. Electrons in Chemical Reactions First Principles John Wiley Sons New York, 1982 (c) Coulson, C. A. Streitwieser, A., Jr. Dictionary of n-Electron Calculations W. H. Freeman and Co. San Francisco, 1965 see especially reference 8 (d) Wiberg, K. B. Physical Organic Chemistry John Wiley Sons New York, 1964 (e) Zimmerman, H. E. Quantum Mechanics for Organic Chemists Academic Press New York, 1975. 

A. B. Sannigrahi and Tapas Kar, "Molecular Orbital Theory of Bond Order arxl ValetKy," y. Chetn. Educ, Vol. 65,1988, 674-676. 

The special properties of a metal result from its delocalized bonding, in which bonding electrons are spread over a number of atoms. In this section, we will look first at the electron-sea model of a metal and then at the molecular orbital theory of bonding in metals. 

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