The proper description of electrified metal/solution interfaces, as they occur in electrochemical systems, is a key component for simulating the unique features of electrocatalytic reactions using electronic structure calculations. While in standard solid state (plane wave, periodic boundary conditions) density functional theory (DFT) calculations several models for describing electrochemical environments exist, for cluster models in a quantum chemistry approach (atomic orbital basis, finite system) this is not straightforward. In this work, two different approaches for the theoretical description of electrified interfaces of nanoparticles, the constant charge and the constant potential model, are discussed. Different schemes for describing electrochemical reactions including solvation models are tested for a consistent description of the electrochemical potential and the local chemical behavior for finite structures. The different schemes and models are investigated for the oxygen reduction reaction (ORR) on a hemispherical cuboctahedral platinum nanoparticle.