Page 223 - Adsorbents fundamentals and applications

208 π-COMPLEXATION SORBENTS AND APPLICATIONS

introduced in 1983 (Glendening et al., 1995). The NBO method transforms a
given wave function for the whole molecular structure into localized forms corre-
sponding to one-center and two-center elements. The NBO method encompasses
sequential calculations for natural atomic orbitals (NAO), natural hybrid orbitals
(NHO), NBOs, and natural localized molecular orbitals (NLMO). It performs
population analysis and energetic analysis that pertain to localized wave function
properties. It is very sensitive for calculating localized weak interactions, such
as charge transfer, hydrogen bonding, and weak chemisorption. Therefore, NBO
is the preferred method for population analysis in studying adsorption systems
involving weak adsorbate–adsorbent interactions (Mulliken and Ermler, 1977;
Frisch et al., 1998).

8.2.9. Adsorption Bond Energy Calculation
Geometry optimization is the first step in all calculations. Calculations for all
other parameters such as charges, orbital populations, and energies are all based
on the geometrically optimized system. In geometry optimization, the geome-
try is adjusted until a stationary point on the potential surface is found, which
means the structure reaches energy minimum. All adsorbate–adsorbent systems
are subjected to geometry optimization first at the STO-3G level followed by
the 3-21G or G-311G level (Chen and Yang, 1996; Huang et al., 1999a and
1999b). The bond lengths calculated by the 3-21G basis set deviates from exper-
imental values by only 1.7% (e.g., by 0.016 for a 0.95 hydrogen bond). After
geometry optimization, a number of higher-level basis sets, all including elec-
tron correlation, with NBO calculations are performed to obtain information such
as energies, atomic charges, and orbital populations (occupancies) based on the
same geometry-optimized system. Typically, energy and NBO calculations are
performed on the B3LYP/3-21+G** level (Huang et al., 1999).
The energy of adsorption, E ads , is calculated by using the optimized geome-
tries by:
(8.7)
E ads = E adsorbate + E adsorbent − E adsorbent–adsorbate
where E adsorbate and E adsorbent are, respectively, the total energies of the adsorbate
molecule and the bare adsorbent model, and E adsorbent–adsorbate is the total energy of
the adsorbate/adsorbent system. A higher E ads corresponds to a stronger adsorption.
The energies calculated by using different basis sets can vary widely. However,
it needs to be stressed that the relative values are meaningful when comparing
different sorbates/sorbents as long as the same basis set is used.

8.3. NATURE OF π-COMPLEXATION BONDING

The nature of π-complexation bonding between the adsorbate and adsorbent
has been studied for a number of systems, including C 2 H 4 /Ag halides and
C 2 H 4 /Ag-zeolite (Chen and Yang, 1996); C 2 H 4 /CuCl, C 2 H 4 /AgCl, CO/CuCl,
and CO/AgCl (Huang, 1999a); C 2 H 2 /Ni halides (Huang and Yang, 1999),