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A critical advance in the technique of low-energy electron diffraction is presented and shown to enable determining detailed structures of nanomaterials, based on experimental methods that already exist or have been proposed. Our new cluster approach speeds up the computation to scale as n logn, rather than the current n3 or n2, with n the number of atoms, for example. Applications are illustrated for C60 molecules adsorbed on a Cu(111) surface, with and without coadsorbed metal atoms, exhibiting sensitivity to important structural features such as buckyball size and deformation.

No abstract

To enable the determination of detailed structures of nanomaterials, we extend the theory of low-energy electron diffraction ͑LEED͒ to become more efficient for complex and disordered systems. Our new cluster approach speeds up the computation to scale as n log n, rather than the current n 3 or n 2 , with n the number of atoms, for example, making nanostructures accessible. Experimental methods to measure LEED data already exist or have been proposed. Potential application to ordered nanoparticles are illustrated here for C 60 molecules adsorbed on a Cu͑111͒ surface, with and without coadsorbed metal atoms, as well as for adsorbed carbon nanotubes. These demonstrate sensitivity to important structural features such as size and deformation of the nanostructures.

To enable the determination of detailed structures of nanomaterials, we have previously made the theory of low-energy electron diffraction (LEED) much more efficient for complex and disordered systems, calling it NanoLEED: our cluster approach speeds up the computation to scale as , rather than the standard or , with n the number of atoms, for example. Strong multiple scattering may occasionally cause poor convergence: this is solved here by treating all scattering within subclusters of a few atoms (e.g. a SiH n n log 3 n 2 n 3 group) with accurate matrix inversion. For the structure determination of complex nanostructures, an efficient search method is also essential: for that purpose a modified version of tensor LEED is here adapted to nanostructures, and called NanoTensorLEED.