Classical Electrostatics of Molecules in Electric Fields

Consider a molecule composed of N electric charges e (electrons and nuclei) located at positions r referenced to an arbitrary origin in space. The total 

The latter expression reduces to a familiar expression for the dipole moment in a neutral molecule consisting of two point charges, = + C nd = -C(F g. 1.1). In this case, we have +Qri+i-Q)r2=Q Ti-T2)=QR, which is the conventional expression for the dipole moment of a pair of opposite charges + Q separated by the vector R. By convention, R points toward the positive charge. For molecules characterized by electric charge distributions p(r) instead of point charges, the expressions for the molecular charge and dipole moment are superseded by 

For a point charge e located at position r under an external electrostatic potential 0(r), the energy of interaction with the potential is [1]  

For a molecule consisting of N point charges at locations r , this becomes 

The first two terms in W arise from the interaction of the molecular charge with the scalar potential 0 and the interaction of the molecular dipole moment with the electric field E, respectively. The next terms in IV are due to interactions between the various electric field gradients dEJdir j and the corresponding components [2] 

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