Units for the series expansion "charge - dipole - alpha - beta - gamma" are as follows:

Charge: positrons (Charge on a fluoride ion is "-1", on a sodium cation is "+1")

Dipole: Debye

Polarizability (alpha): Cubic atomic units and cubic Angstroms. 1 au^{3}
= (0.529)^{3} Angstroms^{3}

First hyperpolarizability (beta): ESU or atomic units (atomic units)^{5}
and (Angstroms)^{5}. The description given by
D. Kanis, M. Ratner and T. Marks, Chem.
Rev. vol 94, pg 239 (1994), is as follows:

"The units for molecular hyperpolarizabilities can be somewhat complicated. Most contributions quote
β
in either atomic or esu units. Dimensional analysis of the quadratic
hyperpolarizability indicates that is possesses the units of dipole moment^{3}/energy^{2},
or in atomic units:

β
= e^{3}a_{o}^{3}/E_{h}^{2}

where a_{o} is the Bohr radius
and E_{h} is the ionization energy of hydrogen (a Hartree). Substituting
E_{h} (Hartree) =e^{2}/a_{o}

β
= e^{3}a_{o}^{3}/(e^{2}/a_{o})^{2
}= a_{o}^{5}/e

in esu units; the second-order
response is given as cm^{5}statcoulomb^{-1} which is identical
to cm^{5}esu^{-1}. Sometimes these units are simply
referred to as esu. The conversion factor between atomic units and esu is
as follows:

1 atomic unit = (a_{o}^{5}/e)
(0.529 x 10^{-8}cm/a_{o})^{5}(e/4.803 x 10^{-10}esu)
or

1 atomic unit =8.641 x
10^{-33} cm^{5}.esu^{-1}

in SI units, 1 atomic
unit =3.206 x 10^{-53} C^{3}m^{3}J^{-2} and 1
= 2.693 x 10^{20} cm^{5}esu^{-1}."

(In earlier MOPACs, the
quantity "4.803" was not used, therefore until December 2003 the value in cm^{5}esu^{-1}
was too large by a factor of 4.803).

Second hyperpolarizability (gamma): Esu.