Reviews in Computational Chemistry Volume 18

Table 1 Polarizability Parameters for Atoms
Polarizability (A˚ 3
)
——————————————————————————————
Atom Applequist et al. a Tholeb Experimental or ab initioc H (alkane) 0.135 0.514 0.667
H (alcohol) 0.135 — —
H (aldehyde) 0.167 — —
H (amide) 0.161 — —
C (alkane) 0.878 1.405 1.76
C (carbonyl) 0.616 — —
N (amide) 0.530 1.105 1.10
N (nitrile) 0.52 — —
O (alcohol) 0.465 0.862 0.802
O (ether) 0.465 — —
O (carbonyl) 0.434 — —
F 0.32 — 0.557
Cl 1.91 — 2.18
Br 2.88 — 3.05
I 4.69 — 5.35
a Ref. 39.
b Ref. 41
c Ref. 42.
Alternatively, the polarization catastrophe can be avoided by screening
(attenuating) the dipole–dipole interaction at small distances. 41 As with the
screening of the static field, screening of the dipole–dipole interaction can be
physically interpreted as correcting for the fact that the electronic distribution
is not well represented by point charges and dipoles at small distances. 39,41,43
Mathematically, screening avoids the singularities such as those in Eqs. [15]
and [16]. The Thole procedure for screening is to introduce a scaling distance
sij ¼ 1:662ðaiajÞ 1=6 . This results in a charge density radius of 1.662 A˚ , for
example, between atoms with a polarizability of 1 A˚ 3 . The dipole field
tensor is thus changed to
0
1
Tij ¼ð4v 3
3v 4 Þ 1 3
I v4
r3 r5 Polarizable Point Dipoles 95
x2 xy xz
@
A ½17Š
yx y 2 yz
zx zy z 2
where v ¼ r=sij. Tij is unchanged if r is greater than sij. Thole’s polarizability
parameters, together with the scale factor 1.662, were selected to optimize the
molecular polarizabilities for a set of 16 molecules (Table 1). Unlike Applequist,
Thole assigns only one polarizability per atom independent of its valence
state and does not assign polarizabilities to halide atoms. The Thole parameters
are closer to the experimental and ab initio polarizabilities. 42 Although
the atomic polarizabilities of Applequist and Thole are different, the resulting