Polarizability volumes calculated using NDDO methods are too low by about 30%. By applying atomic corrections, this error can be reduced to about 1.5%. The form of the atomic correction used is:
P(corrected) = a +C1P + SiCi
where i runs over all atoms in the molecule, P is the uncorrected polarizability volume, and a, C1, and Ci are constants.
Constants are available for the elements H, C, N, O, F, Cl, Br, and I, only. The correction is applied automatically when either POLAR or STATIC is used, and is available for MNDO, AM1, PM3, and PM6, only.
As an example, the PM3 polarizability for dichloromethane, CH2Cl2, is 3.31 A3, and the experimental value is 6.48 A3. To convert the calculated polarizability to the corrected value, the following PM3 constants are used:
a = 0.28759, C1 = 0.246502, CH = 0.178581, CC = 1.24273, CCl = 1.8556.
The conversion equation is thus:
P(corrected) = 0.28759 + 0.246502x3.31 + (2x0.178581 + 1.24273 + 2x1.8556) = 6.41A3.
The error is thus reduced from 49% to 1%.
Constants are not available for other elements, but if only one such atom is present in a molecule, the error resulting from the absence of a correction is minor. Thus if the polarizability of chlorophyll is calculated, the atomic contribution due to the single magnesium atom will not be included in the corrected polarizability. This will introduce an error, but in most cases the error will be quite small.
For normal organic compounds, the average error in polarizability should be less than 2%.