Method of molecular orbitals

A convenient orbital method for describing eleetron motion in moleeules is the method of molecular orbitals. Molecular orbitals are defined and calculated in the same way as atomic orbitals and they display similar wave-like properties. The main difference between molecular and atomic orbitals is that molecular orbitals are not confined to a single atom. The crests and troughs in an atomic orbital are confined to a region close to the atomic nucleus (typieally within 1-2 A). The electrons in a molecule, on the other hand, do not stick to a single atom, and are free to move all around the molecule. Consequendy, the crests and troughs in a molecular orbital are usually spread over several atoms. 

The wave functions just described are one-electron wave functions, but the H2 molecule has two electrons to be dealt with. In the methods of molecular orbital theory, a wave function for the... 

A method of molecular-orbital calculations, also referred to as the self-consistent field method (SCF), to characterize the bonding in unsaturated and aromatic molecules while neglecting electron-electron repulsion. The method has been extended to all valence electrons. 

It is interesting to note that the method of molecular orbitals leads to identical results, but by a rather different route. In this method we consider first the set of orbitals on the atoms surrounding the central atom. If this set consists of orbitals symmetrical about the line joining each external atom to the central atom, then these external orbitals form a basis for a representation of the symmetry group which is identical with the o- representation. The reduction of this representation then corresponds to the resonance of these external orbitals among themselves. The formation of molecular orbitals then takes place by the interaction between these reduced external orbitals and the orbitals of the central atom. This interaction can only take place, however, between orbitals belonging to the same representation. Hence, to obtain a set of molecular orbitals equal in number to the... 

R. S. Mulliken, Electronic structures of polyatomic molecules and valence. VI. On the method of molecular orbitals, Journal of Chemical Physics 3 (1935) 375-378. 

Nevertheless we must point out that in regard to the problem of orientation Hiickel limited his calculations to the inductive effects. In 1935, Pauling with G. Wheland, and some months later after Bonino s paper, published a paper, in which turned his attention to the problem of orientation in aromatic molecules using the method of molecular orbitals. (See G.W. Wheland and L. Pauling, A quantum mechanical discussion of orientation of substituents in aro-... 

The basic idea at the foundations of the method of molecular orbitals consists, as is well known, of constructing the wave function of a poly-electronic system as a suitable combination of individual one-electron wave functions. 

Yu. A. Kruglyak, V. S. Kvakush, and G. G. Dyadyusha, Methods of Calculation for Quantum Chemistry, No. 1 Calculation of Pi-Electron Structures of Molecules by the Simple Methods of Molecular Orbitals, Naukova Dumka, Kiev, 1967. 

These are called the method of molecular orbitals and the method of valence bond combinations. 

The method of molecular orbitals is of great value for quantitative discussions, especially of molecules containing heteroatoms. 

The LCAO MO method. The method of molecular orbitals (MO) dominates in modern quantum chemistry. The main idea of the method is that the electrons in a molecule are accommodated in definite MOs just as in an atoni they... 

The failure of crystal field theory and VB theory to explain the spectrochemical series stimulated the development of ligand field theory, which applies qualitative methods of molecular orbital theory to describe the bonding and structure of coordination complexes. The terms ligand field theory and molecular orbital theory are often used interchangeably in inorganic chemistry today. 

Lennard-Jones, J.E. (1937) The electronic structure of some polyenes and aromatic molecules. I. The nature of the links by the method of molecular orbitals. Proc. R. Soc. London Ser. A, 158, 280-296. 

Since the first quantum mechanical calculation of phenol performed in 1967 using the CNDO/2 method" , the phenol geometry was considered at a variety of computational levels "" ranging from the HE to the MP2 method of molecular orbital theory and density functional theory (DFT) employed with several basis sets, mainly of the split valence type as, e.g. 6-31G(d,p) and 6-31- -G(d,p). These computational results are summarized in Tables 1-3 and Figure 4. It seems noteworthy that the semi-empirical geometries listed in Table 1 are rather close to the experimental observations. Also, to complete the theoretical picture of the phenol molecule, its theoretical inertia moments calculated at the B3LYP/6-31- -G(d,p) level are equal to 320.14639, 692.63671 and 1012.78307 a.u. 

Having outlined the way in which the method of molecular orbitals, either in the simple form or in the more sophisticated form developed by Roothaan, may be applied in principle to the ground states of closed shell molecules, we may now turn to the more recent developments which have borne fruit in relation to experimental measurements. 

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