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Potential energy surfaces are the central concept in understanding the assembly of molecules; atoms form molecules via covalent bonds with structures defined by the stationary points of the surfaces. Similarly, dispersion interactions give Lennard-Jones potentials that describe atomic clusters and liquids. The formation of molecules and clusters can follow various pathways depending on the initial conditions and the potentials. Here we show that analogous mechanistic effects occur in light-mediated self-organization of metal nanoparticles; atoms are replaced by silver nanoparticles that are arranged by electrodynamic (that is, optical trapping and optical binding) interactions. We demonstrate this concept using simple Gaussian optical fields and the formation of stable clusters with various two-dimensional (2D) and three-dimensional (3D) geometries. The formation of specific clusters is 'path-dependent'; the particle motions follow an electrodynamic potential energy surface. This work paves the way for rational design of photonic clusters with combinations of imposed beam shapes, gradients and optical binding interactions.

Potential energy surfaces and reaction pathways for light-mediated self-organization of metal nanoparticle clusters