The need for quantum-mechanical treatment of capacitance and related properties of nanoelectrodes

Capacitance and other properties of large metal clusters proposed for use as nanoelectrodes in complex molecular-electronic devices, or as cores of the monolayer-passivated nanoparticles studied by Murray (J. Phys. Chem. B 1999, 103, 9996), are discussed using atomistic formalisms based on classical electrostatics as well as INDO electronic structure theory. Using classical electrostatics, both finite-size and atomicity effects are found to be important for properties such as the surface charge distribution but unimportant for other properties such as the electric field profile between electrodes. The INDO and classical atomistic charge distributions are found to be strikingly different, with both departing from textbook expectations based on theorems of classical continuum electrostatics such as Gauss' law. For linear chains of metallic atoms, ab initio full configuration interaction as well as density-functional (DFT) calculations validate the INDO/S picture in which both positively and negatively charged atoms appear within a chain of net positive charge, contrary to the classical treatment that permits only distribution of the net charge. Examination of the form of the INDO/S Hamiltonian reveals that a key aspect of the failure of classical atomistic electrostatics arises from its treatment of self-energy (the energy required to store a finite charge in the finite atomic volume). Exchange operators present in the quantum approaches halve the classical self-energy contributions, facilitating charging. Even the requirement that atomic charges be distributed across the width of a surface atomic plane is found to significantly modify the classical self-energy and hence induce large short-range deviations from standard capacitance relationships. For large clusters, the INDO/S results are shown to depict qualitatively reasonable properties by comparison with published DFT calculations. INDO/S may prove an efficient computational scheme,for the study of a wide range of nanoparticle electronic properties: here, we deduce the voltage differential arising from the cluster to cluster charge-transfer state.