Resonance theory - polyatomic case

The VB method was developed by Linus Pauling under the name of theory of resonance. 

Linus Carl Pauling (1901-1994), American physicist and chemist, in the years 1931-1964 professor at the Calitbmia Institute of Technology in Pasadena, in 1967-1969 professor at the University of California, San Diego, from 1969-1974 professor at the Starrfbrd University. Me received the 1954 Nobel prize for his research into the nature of the chemical bond and its application to the efucidsrSon of the structure of complex substanced . In 1962 he received the Nobel peace prize. His major achievements are the development of fhe fhe-ory of chemical bond, i.a., the VB method (also called resonance theory), and determining fhe 

The method can be applied to all molecules, although a particularly useful field of applications of resonance theory can be found in the organic chemistry of aromatic systems. For example, the total electronic wave function of the benzene molecule is presented as a linear combination of resonance structures  

The first two structures are famous Kekule structures, the next three are Dewar structures, the sixth is an example of the possible mixed covalent-ionic structures. From these graphs, we may deduce which atomic orbitals (out of the 2p, orbital of carbon atoms, z is perpendicular to the plane of the benzene ring) takes part in the covalent bond (of the tt type). As far as the mathematical form of the bi structure is concerned, we can write it as the antisymmetrized (cf. anti mmetrization operator, p. 986) product of three Heitler-London functions (involving the proper pairs oflpz carbon atomic orbitals), the first for electrons 1,2, the second for electrons 3,4, and the third for 5,6. Within the functions d /, the ionic structures can 

In fact, the problem is connected to the Ritz method and to expansion into the complete set of functions, i.e. a purely mathematical problem. Although it may seem very strange to students (fortunately), many people were threatened for supporting the theory of resonance. Scientists serving the totalitarian regime decided to attack eq. (10.20). How, was this possible The Stalinists did not like the idea that the sum of fictitious structures can describe reality . Wait a second If some artificial functions could interfere with reality then socialist realism may lose to abstraction, a kolkhoz (collective farm) member to an intellectual, Lysenkoism to Mendelism, goulags to the idea of freedom, and you are on the brink of disaster. 

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However, the calculation of resonance Raman profiles by file direct use of the KHD equation is so difficult in the case of polyatomic molecules due to the sum of a great number of intermediate states, even using the A term or using the great order terms B, C, and D of Albrecht theory. In a polyatomic molecule with N atoms, there will be 3N—6 normal modes, and the Iv) term is an abbreviate notation used for the vibrational quantum number set of all modes, that is, IV1V2V3.. Each possible combination of the v, vibra-... 

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