By Pople J., Beveridge D.
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A lower limit on 0 will, of course, be imposed by the details of the computational equipment used. A third possibility is to examine the change in the calculated electronic energy. If this differs by less than some specified amount ti. in successive cycles, the cyclic process can be stopped. APPROXIMATE MOLECULAR ORBITAL THEORIES 73 We now turn to the comparison of the CNDOjl theory with ab initio minimal basis calculations for small molecules. As mentioned above, this is used to calibrate the bonding parameters thO.
Let us suppose that the original set 4>1' is a set of s, p, d, . . atomic orbitals centered on the various nuclei in the molecule. : ~ APPROXIMATE MOLECULAR ORBITAL THEORIES I Jl where the elements of the Fock matrix FI" are now given by FI'I' I: ,r ! I I: t' ! I ! which have the same principal and azimuthal quantum numbers nand l. 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.
Lowest eigenvalues of Fl'v). The density matrix PI'V is calculated from the coefficients of the occupied molecular orbitals and then used to form a new Fock matrix Fl'v. Diagonalization of the Fl'v matrix then leads to a new set of coefficients cl';' Steps 2, 3, and 4 are repeated until self-consistency is achieved. This may be done by comparing coefficients, but this is' not altogether satisfactory, since these are not uniquely defined if the Fock matrix has degenerate eigenvalues (as in molecules with n-fold rotation axes where n is greater than 2).