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By Pople J., Beveridge D.

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For example, such a transformation might mix the three orbitals 2px, 2py, and 2pz, or the five 3d functions. A particularly important transformation of this kind is rotation of the cartesian axes used to define the atomic orbitals. 2. Transformations which mix any atomic orbitals on the same atom. If different azimuthal quantum numbers l are involved, the resulting orbitals 4>: are usually known as atomic hybrid orbitals. For a carbon atom, for example, the four atomic orbitals 2s, 2px, 2py, 2pz may be replaced by four Sp3 hybrids along tetrahedral directions.

1'12- 1 X P'! ""la (1)a(1)y"l(2){3(2) . } d-': l d-': 2 . 82) SELF·CONSISTENT FIELD MOLECULAR ORBITAL THEORY APPROXIMATE MOLECULAR ORBITAL THEORY 5Z wavefunction is superior. On the other hand, it can be shown that the unrestricted wavefunction is not generally an eigenfunction of the spin operator 8 2. Thus, if p - q = 1, the unrestricted single determinant does not describe a pure doublet state, but has "contaminating" components of other multiplicities [12]. However, it is still an eigenfunction of 8 z , the total spin component in the z direction, with eigenvalue p - q.

These conclusions are valid over a wider range of comparisons as reported in the original publication. In addition, fairly good agreement was obtained in a similar comparison for HCN using the fJ parameters selected for diatomic molecules. This provides some check on the use of diatomic calibration for the application of the theory to larger polyatomic systems. A number of detailed studies of polyatomic molecules using the CNDO/l method were reported in Ref. [3J. However, these will not be described here as improved versions of the techniques are now available.

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Aproximate Molecular Orbital Theory by Pople J., Beveridge D.


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