Biomedical Engineering Reference
In-Depth Information
electronegativity of a specific orbital in a given valence state. You will understand that
I am introducing quantum mechanical concepts before we have finished our discussion of
techniques based on classical mechanics; just bear with me.
In the abstract of their paper, Gasteiger and Marsili (1980) state:
Amethod is presented for the rapid calculation of atomic charges in σ -bonded and nonconjug-
ated π systems. Atoms are characterized by their orbital electronegativities. In the calculation,
only the connectivities of the atoms are considered. Thus only the topology of a molecule is
of importance. Through an iterative procedure partial equalization of orbital electronegativity
is obtained. Excellent correlations of the atomic charges with core electron binding energies
and with acidity constants are observed.
These authors decided to relate the electronegativity of orbital ν on atom
i
(χ
i
,ν
)tothe
total charge
Q
i
on atom
i
as a quadratic
χ
i
,ν
=
a
i
,ν
+
b
i
,ν
Q
i
+
c
i
,ν
Q
i
(6.2)
The three unknowns
a
,
b
and
c
were determined from values used at the time for orbital
ionization energies and affinities. Typical values are listed in Table 6.1.
Table 6.1
Parameters needed to calculate electronegativity
Atom
Hybridization
a
b
c
H
7.17
6.24
−
0.56
sp
3
C
7.98
9.18
1.88
sp
2
8.79
9.32
1.51
sp
1
10.39
9.45
0.73
The calculation is iterative; starting from a reference structure where all the atoms carry
zero charge, electric charge is permitted to flow from the less to the more electronegat-
ive atoms. The electronegativity of an atom decreases as it accumulates electric charge,
according to the formula, and in the next iteration less charge will flow until eventually the
electronegativity of each (charged) atom is equalized. At this point the flow of charge stops.
Molecular mechanics is of course a classical treatment, and orbitals do not appear. The
key equation is therefore written in terms of the atoms overall rather than in terms of orbital
contributions:
χ
i
=
a
i
+
b
i
Q
i
+
c
i
Q
i
(6.3)
Atom electronegativities are adjusted at each iteration using the calculated charges, until
self-consistency is achieved. Figure 6.5 shows typical results for phenylanine. Notice the
negative charges on oxygen and the positive charge on nitrogen. Charges calculated in this
way depend only on the atomic connectivity and not on the molecular geometry.
6.4.2 Polarizabilities
I introduced you to polarizabilities in Chapter 2, when we discussed the theory of inter-
molecular forces. The experimental determination of a molecular polarizability is far
from straightforward, especially if the molecule has little or no symmetry. The classical
experimental route to the mean polarizability <α> is via the refractive index or relative
