46
2 Computational Methods
In this equation, ε 0 is the permittivity of vacuum, k the Boltzmann constant and
T the absolute temperature. The dipole moment is usually given in Debye: 1 D =
3.335640952 × 10
−30 Cm.
2.19.5.2 Induced Forces (Also Known as Debye Forces)
A permanent dipole moment in one molecule induces charge displacements in the
neighboring molecules giving rise to an induced dipole moment. This process is
called polarization, and the value of the induced dipole depends on the polarizability
α which is roughly a function of the number of electrons in the polarized molecule.
The induction energy for molecule 1 with dipole moment μ 1 and polarizability α 1
and molecule 2 with dipole moment μ 2 and polarizability α 2 is
E Debye = −
1
(4πε 0 )
2
μ
2
1 α 2 + μ
2
2 α 1
r 6
(2.64)
The SI unit for the polarizability is C
2 m
2 J
−1 , but it is often expressed in Å
3 or
in units of a
3
0 (atomic units):
1 Å
3
= 1.112650×10
−40 C
2 m
2 J
−1
1 au = e
2 a
2
0
E H = 1.648777274×10
−41 C
2 m
2 J
−1
2.19.5.3 Dispersion Forces (Also Known as London Forces)
Non-polar molecules have instantaneous dipole moments due to the fluctuations of
the electron distribution. They induce a dipole moment in the neighboring molecules.
The dispersion energy of two interacting molecules 1 and 2 of polarizabilities α 1 and
α 2 is
E London = −
1
(4πε 0 )
2
I 1 I 2
I 1 + I 2
α 1 α 2
r 6
(2.65)
where I 1 and I 2 are the first ionization potentials (an ionization potential is the energy
required to remove an electron from an atom, molecule, or radical, usually measured
in eV).
Dispersion forces are usually the dominant ones of the three van der Waals forces
between atoms and molecules, with the exception of molecules that are small and
highly polar, such as water.