-type
axial ligands allow such modeling. Some type of complexes also can be modeled within the Hückel approach.
In particular, the porphyrin-type complexes with -type
axial ligands allow such modeling.
Let us assume for certainty that the porphyrin ring is in the xy-plane. Its -system
consists of the pz-AOs. The metal atom is in the coordinate system
origin. Metal dxz and dyz orbitals can overlap with the
ring -system. The same AOs can
also interact with the axial ligand -systems:
Because of the asymmetry of the dxz and dyz orbitals the overlap (and the resonance integrals) depend on the orientation the ring atoms relative to the orbitals:
The dependence is the following:
Here 
is the angle between the orientation to the atom a and the x-axis.
The axial ligand -orbitals
rotate with the rotation of the axial ligand plane orientation:
The dependence is the following:
In the program the central atom is treated as two atoms (Mxz, Myz) with 
M = -0.2 and 
M-N = -0.3.
Number of -electrons
In the Hückel approach only the d-electrons
interact with the -system of
the ligands. As an example let us consider the Fe3+ ion. This
is the d 5 system. The energy structure for the high spin
state (S = 5/2 ) is
It means that the high spin Fe3+ ion contributes two electrons to
the -system.
The energy structure for the low spin ion (S = 1/2) is
In this case the ion contributes three electrons to the -system
of a complex.
The Hückel method is approximate and the coulomb and the resonance parameters are actually empirical fitting parameters. The table for hetero-atoms contains the "average" parameters. The parameters can be adjusted and modified in order to describe specific properties and values.
The Hückel method cannot automatically reproduce the correct multiplicity of a complex. The transition metal parameters should be adjusted so that they describe not only the the correct (at least qualitatively) values but also the system total spin.
1. H. H. Greenwood, Computing Methods in Quantum Organic Chemistry, Wiley-Interscience, NY, 1972.
ŠNikolai V. Shokhirev, F. Aann Walker 2003