Construction of Correlation Diagrams between the States of a Reacting System Using HMO Theory
'
A simple method to construct orbital correlation diagrams war reported in a recent article in this .Journal. This kind of diagram is very useful to indicate iuto which product nwlecular orbital each reactant molecular orbital is converted iri undergoing a chemical transformation. Although the employed technique has enjoyed considerable pedagogical success in overcoming same difficulties concerning 5)-mmetry concepts, it is possible and desirable to carry the method a step further in order to obtain an even better understanding of this kind of problem The extension is very simple and only requires the student to manage elemental symmetry concepts which aro by now a standard lopic in those physical organic chemistry courses which includemolecular orbital theory in their syllabus. The employment of orbital correlation diagram iscorrect as far as it goes, and leads t o a satisfying insight into the decision as to whether agiven concerted reaction isorbitally "allowed or "forbidden." But t o think exclusively in terms of the way in which the one-electron orbitals are populated Le., configurations) does not directly provide a satisfactory basis for describing and underfitanding the electronic structure of molecules and electronic transitions. Orbitals and electron configurations are in themselves fictional. These conceptual devices arise from the approximatiou MO-LCAO. It is the states arising out of ulectron configurations which are real, su wave functions to be genuine must describe states and not individual orhilals or configurations. The method consists in drawing correlation diagrams for states, not for orbitals, and seeing if a given state to state process is inhibited or not by a substantial energy barrier.'The crucial feature to note in the construction of state correlation diagrams is that the noncrossing rule%must be applied. This rule states that energies corresponding to slates whose wave functions are the basis for the same irreducible representation of the molecular point group do not cross. Thc symmetry of electronic states is determined fmmn the symmetries of the mcupied orbitals and the state energies are obtained summing up the respective orbitals energies. These orbitals energies are calculated following an identical previous procedure.' so that no additional effurt is needed from the computational point uf view. It must be noted that in the absence oiay~nmetrythe molecule belungs to the point gruup CI and the crossing of states is no longer possible for any case so states should bc correlated only in ascending order of energies. In a supplement to this note, the construction of the state correlation diagrams far various chemical reactions is shown in a step-by-step manner. The supplement may be obtained upon request from one of the authors (E.A.C.). 'Dalton, J. C., and Friedrich, L. E., J. CHEM. EDUC., 52,721 (1975). 'Longuet-Higgins, H.C., and Abrahamson, E. W., J. Amrr. C h e m Soc., 87,2045 (1965). "Teller, E.,J.Phys. Chrm., 41, LO9 (1937). Instituto de Investigaciones ~ i s i c o q u i m a c a s l'rurirar y Aplxadas Sucumal4. C u d l a dr. C o r r r o lfi IrUll La I'lala. Arycnlina
338 / Journal of Chemical Education
Roberto A. Mor6 Eduardo A. Castro
