Essentials of Computational Chemistry

140 5 SEMIEMPIRICAL IMPLEMENTATIONS OF MO THEORY
The G and L values may be regarded as free parameters, but in practice they can be estimated
from spectroscopic data. When the atomic valence orbitals include d and f functions, the
number of unique integrals increases considerably, and the estimation of appropriate values
from spectroscopy becomes considerably more complicated.
One effect of the greater flexibility inherent in the INDO scheme is that valence bond
angles are predicted with much greater accuracy than is the case for CNDO. Nevertheless,
overall molecular geometries predicted from INDO tend to be rather poor (although preliminary
efforts to address this problem have been reported by Da Motta Neto and Zerner 2001).
However, if a good molecular geometry is available from some other source (ideally experiment)
the INDO method has considerable potential for modeling the UV/Vis spectroscopy
of the compound because of its better treatment of one-center electronic interactions.
Ridley and Zerner (1973) first described a careful parameterization of INDO specifically
for spectroscopic problems, and designated that model INDO/S. Over the course of many
years, Zerner and co-workers extended the model to most of the elements in the periodic table,
including the lanthanides (Kotzian, Rösch, and Zerner 1992), although few available modern
codes appear to include parameters for elements having f electrons, possibly because of
challenges associated with accounting for relativistic effects, especially spin–orbit coupling,
which cannot be ignored when such heavy atoms are involved. Table 5.1 lists the energetic
separations between various electronic states for three cases studied by INDO/S, ranging from
the organic molecule pyridine, to the transition metal complex Cr(H2O)6 3+ , to the metalloenzyme
oxyhemocyanin which has a bimetallic Cu2O2 core ligated by enzyme histidine
residues. Even just the ligated core of the latter system is daunting in size, but the simplifications
intrinsic in semiempirical MO theory render it tractable. All of the geometries used
Table 5.1 Relative state energies (units of 1000 cm −1 ) as computed by the INDO/S model
System (ground state) State (transition) INDO/S prediction Experiment
Pyridine ( 1 A1) a 1 B1 (n → π ∗ ) 34.7 35.0
1 B2 (π → π ∗ ) 38.6 38.4
1 A2 (n → π ∗ ) 43.9 –
1 A1 (π → π ∗ ) 49.7 49.8
1 A1 (π → π ∗ ) 56.9 55.0
Cr(H2O)6 3+ ( 4 A1g) b 4 T2g (t → e) 12.4 12.4
4 T1g (t → e) 17.5 18.5
2 T1g (t → t) 13.2 13.1
2 Eg (t → t) 13.6 13.1
Oxyhemocyanin c d→d 15.0 14.3–15.0
π →SOMO 17.8 17.5–18.1
π →SOMO 18.3 17.5–18.1
π ∗ → π ∗ 25.3 23.5–23.6
π →SOMO 36.3 29.4–30.4
a Ridley, J. E. and Zerner, M. C. 1973. Theor. Chim. Acta, 32, 111.
b Anderson, W. P., Edwards, W. D., and Zerner, M. C. 1986. Inorg. Chem., 25, 2728.
c Estiú, G. L. and Zerner, M. C. 1999. J. Am. Chem. Soc. 121, 1893.