From owner-chemistry@ccl.net Fri Nov 4 12:41:01 2005 From: "Patrick Senet Patrick.Senet**u-bourgogne.fr" To: CCL Subject: CCL: Dipole moment calculation from non-zero charge distribution Message-Id: <-29881-051104121710-10518-N7CdpzYbA2BowA1QP3ZusQ[a]server.ccl.net> X-Original-From: "Patrick Senet" Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset="iso-8859-1" Date: Fri, 4 Nov 2005 18:17:05 +0100 MIME-Version: 1.0 Sent to CCL by: "Patrick Senet" [Patrick.Senet]=[u-bourgogne.fr] > I guess the second moment definition as integral over charge times position > vector would be a better/more general definition. But what makes > these definitions equivalent or allows to expand from one to the other ? > (The first definition a priori breaking down for charged species) > Dear Marc Baaden, Yes indeed, the most general definition of multipole moments came from the expansion of the electric potential of a charge density (confined in a sphere of large radius) in spherical harmonics. The dipole moment is defined by the integral of r*density in all cases. For two opposite point charges represented by Dirac Delta functions you recover the > pair of electric charges of equal magnitude but opposite polarity [..]" An electrostatic theorem tells you that the lowest nonvanishing multipole moment of any charge distribution is independent of the choice of the coordinates but all higher multipole moments are not in general translationaly invariant. In other words, a charged system has a dipole depending on the choice of coordinates. For two opposite charges, the monopole vanishes and the dipole is invariant. Best regards, Patrick Senet Prof. Patrick Senet Théorie de la matière condensée CNRS-UMR 5027, LPUB, Univ. de Bourgogne 9 Avenue Alain Savary - BP 47870 F-21078 Dijon Cedex Tel: 03 80 39 5922 Fax:03 80 39 6024 psenet(0)u-bourgogne.fr http://www;u-bourgogne.fr/LPUB