Collective Excitations of Dipolar Systems

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Abstract
A system of neutral molecules having permanent electric dipole moments should exhibit self-sustained longitudinal polarization waves analogous to the plasma vibrations of an electron gas. To study these long-wavelength collective modes (dipolar plasmons), we adapt some techniques successful in many-electron problems to systems whose Hamiltonians include kinetic energy both of center-of-mass and of rotational motion, the interaction between rigid dipoles, and short-range interactions which we need not specify in detail. A canonical transformation plus a random-phase approximation (RPA) is used to display the collective modes explicitly in the Hamiltonian, and it is shown that the ground state of the system is adequately described in the RPA. The dipolar plasmon frequency so found is also obtained by linearizing equations of motion for Fourier components of the polarization charge density, and is affected statistically by short-range forces through a constant factor. Linear dielectric response theory yields a simple exact sum rule and, in a self-consistent-field approximation, a dielectric function in which dynamical effects of short-range forces can be retained. The classical dielectric function for linear and spherical rotators is evaluated in closed form when short-range forces are neglected. Its static limit is the Onsager expression for rigid dipoles, and it vanishes at the dipolar plasmon frequency.