Orbitals. The LCAO Method

The molecular orbital method assumes that the properties of Ha might be calculated through consideration of the two nuclei surrounded by a single molecular orbital represented by molecule containing one electron. Thus, 

These equations are not formidable the trouble comes in the form of H and j olecule them to calcu- 

A serious notational problem arises with regard to the atomic wave functions. Various authors have used ( , X, etc. We shall use X but with no conviction that this is the best or wisest choice. 

We shall treat ci and C2 as parameters for which we shall wish to determine values ili will be used for Jmclecule and Xi and X2 will be used for the respective atomic orbitals. E will be found in terms of ci and Cz and the energies of the atomic orbitals, and to do this we start with 

In the last equation E is obtained in a form such that the coordinate problem is greatly simplified. Substituting cjXi + C2X2 for 4 we have 

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This highly successful qualitative model parallels the most convenient quantum mechanical approach to molecular orbitals the method of linear combination of atomic orbitals (LCAO). We have assumed that the shapes and dispositions of bond orbitals are related, in a simple way to the shapes and dispositions of atomic orbitals. The LCAO method makes the same assumption mathematically to... 

In the procedure outlined we have used a linear combination of atomic orbitals as the trial wave function. This procedure is known as the LCAO method or as the LCAO "MO method, the latter designation meaning that we have constructed a molecular orbital (MO) as a linear combination of atomic orbitals. The LCAO method is frequently employed,-but unless additional terms are added the agreement with experiment is never very close. 

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