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First-principles calculation of electrical forces among nanospheres in a uniform applied electric field

We present a unified framework for a first-principles calculation of the electric force acting on dielectric or metallic nanospheres suspended in a dielectric host and subject to a uniform external electric field. This framework is based on the spectral representation of the local electric field in a composite medium. The quasi-static (or "surface-plasmon") eigenstates of a cluster of spheres are first calculated, numerically. Then those are used to calculate the force on any sphere as the gradient of the total electrostatic energy with respect to the position of that sphere. This approach is applicable even when the spheres are very closely spaced, and even when they are metallic: No infinities ever appear. The forces are not limited to dipole-dipole forces. Moreover, the force acting on any sphere is not a simple sum of two-body forces: When the inter-sphere gaps are small, complicated many-body forces appear. This is due to the fact that, when a sphere center is displaced slightly, the electric polarization of all the other spheres is changed. Consequently, the total electrical energy is changed in a way that cannot be represented as a sum of two-body energy changes. Explicit calculations of these forces for a few selected sphere clusters are presented. The results are quite different from what is obtained in the dipole approximation.