Induced multipole moment method

The inclusion of coherent states of the radiation field in the formalism describing opfically induced forces is most conveniently carried out within the induced multipole moment method delineated in Section 5. Instead of number sfafes n(fc, 2.)) = (k)), coherent states a= =) are defined... 

An alternative approach to the evaluation of fhe resulfs obfained in the previous section, and one that provides additional physical insight into the manifestation of the process, is through the coupling of induced multipole moments [51-53]. This method also enables results for energy shifts to be obtained with considerably reduced computational effort, as will be shown in what follows. 

These expressions are only correct for wave functions that obey the Hellmann-Feynman theorem. Flowever, these expressions have been used for other methods, where they serve as a reasonable approximation. Methods that rigorously obey the Flellmann-Feynman theorem are SCF, MCSCF, and Full CF The change in energy from nonlinear effects is due to a change in the electron density, which creates an induced dipole moment and, to a lesser extent, induced higher-order multipoles. 

Higher-order multipole moments enhance the forces between particles at short distances and their neglect is extremely questionable, especially if fine effects are looked at, as for instance the ground-state properties of close-packed lattice structures [244,246-251] or the viscosity To go beyond the point dipole approximation Klingenberg and co-workers [ 173,252] developed an empirical force expression for the interaction between two dielectric spheres in a uniform external field from the munerical solution of Laplace s equation [253]. Recently, Yu and co-workers [254,255] proposed a computationally efficient (approximate) dipole-induced-dipole model based on a multiple image method which accounts partially for multipolar interactions. 

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