Page 140 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

MOLECULAR ORBITAL ELECTRONEGATIVITY AS ELECTRON CHEMICAL POTENTIAL 125

in an iterative MO-LCAO scheme using as an AO basis maximum localization hybrids
[12], Hoffman’s atomic parameters [13], and Cusachs’ expression [14] for the off-
diagonal elements of the Hamiltonian . Since this is just an illustration of the
numerical aspects of the equations given above, we need not justify further the scheme
used. The special features which make the present example especially suited for our
purpose include the fact that in the case of the system the MO occupation numbers
must be given the values 2, 1.5, 0 (in the order of increasing orbital energies) in
order to ensure the equivalence between the two degenerate systems of our linear
molecule. This feature is especially important since of eqn 28 is the sum of
terms containing as factors the differences between MO occupation numbers
This fact implies that only MO's with different occupation numbers play a role in
the terms by which eqn 38 differs from the simpler form 39.

Table 1: Source data and for the average system of FeCO
a. Overlap matrix for one system of FeCO

1.0000 0.2783 0
0.2783 1.0000 0.2414
0 0.2414 1.0000

b. Ham. matrix (eV) with correction at convergence
-9.6177 -2.2081 0
-2.2081 -10.9490 -2.7811
0 -2.7811 -12.6638
c. Eigenvalues (italics, eV) and Löwdin charge bond-order matrix

-12.7349 -11.4723 -9.4836
0.7671 0.5442 -0.0530
0.5442 -0.2747 0.0418
-0.0530 0.0418 -0.4924

d. Derivative of P with respect to and diagonal elements of (italics)
0.2087 -0.4060 -0.0689
-0.4060 0.7583 0.1859
-0.0689 0.1859 -0.0281
0.1502 0.8355 0.0142

The source matrices (for the sequence Fe C 0) are presented in Table 1 together with
the resulting derivative of the Löwdin population matrix P. The electronegativities
derived from the complete expression 38 and from the approximate expression 39 are
-7.1690 eV and -7.3582 eV, respectively, thus suggesting that even in the unfavourable