# CCL: Dipole moment calculation from non-zero charge distribution

• From: "Patrick Senet" <Patrick.Senet{}u-bourgogne.fr>
• Subject: CCL: Dipole moment calculation from non-zero charge distribution
• Date: Fri, 4 Nov 2005 12:56:17 +0100

``` Sent to CCL by: "Patrick Senet" [Patrick.Senet(a)u-bourgogne.fr]
Hi,
In fact the dipole of a charged system depends on the choice of the origin
of the coordinates. In other words, the dipole is not translation invariant.
The formula to compute the dipole in your case with fixed charges is indeed
simply
P=sum(over all atoms K) Q(K) R(K)
where Q(K) is the charge of atom K, R(K) its position.
You can defined now a molecular dipole by adding and substracting any vector
U:
P=sum(over all atoms K) Q(K) (R(K)-U) + U sum(over all atoms K) Q(K),
The first sum is invariant by translation of the molecule, the second
depends on the net charge of the molecule. The choice of U is arbitrary ! A
convenient choice in MD is the center of mass (or geometrical center), then
you can define a molecular dipole as the first term. By setting the origin
at the mass center the second term vanishes.
Hope this help,
Patrick Senet
(We used this recently in "A DFT study of polarisabilities and dipole
moments of water clusters", M. Yang, P. Senet and C. Van Alsenoy, Int. J.
of
Quant. Chem. 101 (2005),  535-542.)
----- Original Message -----
<owner-chemistry---ccl.net>
To: "Senet, Patrick, Cnrs Umr 5027 "
<patrick.senet---u-bourgogne.fr>
Sent: Friday, November 04, 2005 11:22 AM
Subject: CCL: Dipole moment calculation from non-zero charge distribution
>
>
> I am looking for a formular/recipe to calculate the dipole moment
> for a charged molecule. In that case my guess is that you first
> have to "factor out"/remove the monopole, but I couldn't find a
> precise formula for this case.
>
> In one textbook the dipole moment is simply given as the integral
> over r*p(r) where r is the position of the charge and p(r) the charge
> density at r. But for a charge distribution with net charge, this does not
> correspond to a separation of equal amounts of positive and negative
> charge ...
>
> .. as a naive suggestion, I could imagine calculating the geometrical
> centre of all negative charge and of all positive charge, remove the
> monopole charge from those and then calculate the dipole moment for this.
> But I would like confirmation (maybe even a reference or textbook) that
> explicitly handles this case.
>
>
> NB: maybe I should add that this is for a classic (molecular mechanics)
>     model of a protein with fixed point charges. The protein is charged
>     due to the protonation states of its ionizable residues.
>
>     Also in this context, is there a software package that can take a
>     charge distribution (ideally a PDB file with charges in the last
>     column) and calculate monopole + dipole + octapole + hexadecapole
>     moments for this ?
> --
>  Dr. Marc Baaden  - Institut de Biologie Physico-Chimique, Paris