Page 221 - Adsorbents fundamentals and applications

206 π-COMPLEXATION SORBENTS AND APPLICATIONS

the physicochemical properties of molecules. The use of effective core potentials
(ECP) has been a notable success in the molecular orbital calculations involv-
ing transition metals. Hence this method has been particularly useful for studies
on π-complexation sorbents. ECP is simply a group of potential functions that
replace the inner shell electrons and orbitals that are normally assumed to have
minor effects on the formation of chemical bonds. Calculations of the valence
electrons using ECP can be performed at a fraction of the computational cost that
is required for an all-electron calculation, while the overall quality of computa-
tion does not differ much. In addition, the relativistic mass-velocity and Darwin
terms, which are derived from all-electron relativistic HF calculations, are implic-
itly incorporated into the relativistic effective core potentials for heavier elements
(Z> 36). Combined with the use of reliable basis sets, it appears to be a very
powerful and economical method for dealing with molecules containing heavy
transition metals. Recently, Hay and co-workers have shown that effective core
potentials can be used reliably in density functional computations as well. The
LanL2DZ basis set is a double-zeta basis set containing effective core poten-
tial representations of electrons near the nuclei for post-third row atoms. The
reliability of this basis set has been confirmed by the accuracy of calculation
results compared with experimental data as well as those from a more expensive
all-electron basis set (Hay and Wadt, 1985; Gordon and Cundari, 1996).

8.2.7. Model Chemistry and Molecular Systems
Concepts of model chemistry and molecular system are required for ab initio
molecular orbital calculation. Model chemistry refers to all theoretical aspects of
calculation, whereas the molecular system refers to the molecules to be studied.
Model chemistry encompasses two elements: method + basis set, where method
and basis set deal with Hamiltonian operator and wave function in the Schr¨ odinger
equation, respectively. Many methods and basis sets are available in the commer-
cial ab initio molecular orbital calculation packages. The suitable combination of
methods and basis set, as well as the selection of calculation level, is very important
for a systematic calculation of a studied system. The higher the model chemistry,
the more accurate the results. However, a highest model chemistry is to be avoided
since the computational cost will increase with calculation level logarithmically.
Using the minimal computational resources to achieve accurate enough results is a
challenge for ab initio molecular orbital calculation (Foresman and Frisch, 1996).
Molecular system refers to the correct combination of atoms. The ab initio
molecular orbital calculation is developed strictly for isolated molecules. There-
fore, the correct extraction of a finite model from the infinite solid phase and
the saturation of the boundaries of the model are crucial steps for calculations.
Reviews on the application of ab initio molecular orbital calculation to the het-
erogeneous gas-solid systems are available (Sauer, 1989).
A suitable model chemistry may work well for a selected molecular system,
but not for another. Therefore, there is a general procedure and criterion for
the selection of model chemistry and molecular system. Usually, one selects a