CCL: Dipole moment calculation from non-zero charge distribution

 Sent to CCL by: "Patrick Senet" [Patrick.Senet(a)]
 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
 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
 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.
 Quant. Chem. 101 (2005),  535-542.)
 ----- Original Message -----
 > From: "Marc Baaden baaden;;"
 To: "Senet, Patrick, Cnrs Umr 5027 "
 Sent: Friday, November 04, 2005 11:22 AM
 Subject: CCL: Dipole moment calculation from non-zero charge distribution
 > Sent to CCL by: "Marc  Baaden" [baaden^^^]
 > Dear CCL readers,
 > 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.
 > Thanks in advance,
 > Marc Baaden
 > 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
 >  mailto:baaden
 _      -
 >  FAX: +33 15841 5026  -  Tel: +33 15841 5176  ou  +33 609 843217>