Potential energy, operator for

The Hamiltonian of the Coulomb term involves electrostatic potential energy operator for the interaction of all electrons and nuclei of donors with those of acceptors. The electrostatic potential can be expanded into multipole terms of the type... 

For an isolated atom, the potential energy operator for the Coulombic forces is a homogeneous function of degree — 1 and in this case one has... 

A force operator for particle k, — V, is the classical force exerted on this particle by all the particles in the system. Correspondingly, one may eonsider the virial of this force, r F , to be the potential energy operator for the particle since, according to eqn (6.51), the sum of such operators for all the particles in the system yields the potential energy operator V. 

In Eq. (6), Te(r) is the kinetic energy operator for the electrons and V(r,Q) is the total potential energy operator for the system. The collection of electron coordinates is denoted by r and the collection of normal coordinates for the MLg cluster is denoted by Q. Expanding V(r,Q) in the normal coordinates Q about the equilibrium nuclear configuration of the MLg cluster, we may write... 

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