Page 219 - Adsorbents fundamentals and applications

204 π-COMPLEXATION SORBENTS AND APPLICATIONS

DFT electron correlation, with parameters adjusted to provide the best fit with
specific experimental data. The dynamic interaction between electrons is theoreti-
cally included by these density functional methods. This gives these methods the
benefit of including electron–electron correlation for a computational expense
similar to HF, giving DFT methods the major advantage of low computational
cost compared to accuracy (Hohenberg and Kohn, 1964; Kohn and Sham, 1965;
Parr and Yang, 1989; Foresman and Frisch, 1996).

8.2.4. Ab Initio Methods
Quantum mechanics provides a potential method for the complete description
of the electronic properties of molecular systems, their structures, physical and
chemical properties, and reactivities. Unlike semi-empirical methods, ab initio
methods use no experimental parameters in their computations; they are based
solely on the laws of quantum mechanics — the first principles referred to in
the name ab initio (Foresman and Frisch, 1996). The computational difficulties
encountered in the general case, as well as the magnitude of extraneous infor-
mation generated by multi-electron wave functions, have been overcome by the
development of entire conceptual frameworks, new computational methods, and
more powerful computational machines. Progress in molecular orbital calcula-
tion has made it possible to make reliable predictions of molecular structures,
relative energies, potential surfaces, vibrational properties, reactivities, reaction
mechanisms, and so on. An increasing number of molecular orbital computer pro-
grams have become available, for example, Gaussian, GAMESS and AMPAC.
Among all programs, Gaussian is most popular and has been applied success-
fully in many fields. It provides high-quality quantitative predictions for a broad
range of systems. Gaussian 98 can handle jobs of more than 100 atoms on
supercomputer systems.
Different ab initio methods can be characterized by their treatment of elec-
tron–electron interactions, that is, electron correlation. The first practical ab initio
method was the HF method, which treats each electron as if it exists in a uni-
form field made from the total charge and space occupied by the other electrons.
This treatment is only an approximation to the interactions between electrons
as point charges in a dynamic system and excludes the contribution of excited
electronic configurations. This neglect of electron correlation can lead to sig-
nificant errors in determining thermochemical properties. It was theorized that
the electron correlation was a perturbation of the wave function known as the
Møller/Plesset perturbation (MP) theory, so the MP theory could be applied to
the HF wave function to include the electron correlation. As more perturbations
are made to the system, more electron correlation is included. These methods are
denoted as MP2, MP3, and MP4. Another method is to calculate the energy of
the system when electrons are moved into vacant orbitals, such as the QCISDT
(quadratic configuration interaction with all single and double excitations and
perturbative inclusion of triple excitations) method, which improves energy val-
ues but at greater computational costs (Clark, 1985; Hehre et al., 1986; Foresman
and Frisch, 1996).