High electric fields affect the diffusion dynamics of atoms on a metal surface, causing biased surface diffusion that possibly leads to the growth of intensively field emitting protrusions and consequent vacuum breakdown (VBD). The scientific understanding of this process, as well as other fundamental VBD initiation mechanisms, is far from complete. Here we investigate the exact atomic behaviour of metal surfaces exposed to extremely high electric fields using density functional theory (DFT). Previous theories describe the field-surface dynamics in terms of the effective dipole moments and polarizability of surface atoms, disregarding higher-order (hyperpolarizability) terms. The validity of this approximation has been evaluated only for electric fields up to 3 GV/m, due to computational limitations of the plane-wave DFT basis used in previous works. In this work, we test the validity of this approximation for a much wider field range, relevant for VBD and field emission (FE), using Cu nanoparticles as our test structures. We find that although such high fields can change the entire structure of Cu nanoparticles, their energetics are described very precisely by the permanent dipole moment and polarizability terms. Thus, we show that neglecting the hyperpolarizability terms is valid even for field values that exceeds the range that is relevant for intense FE and VBD. This work lays a solid foundation for further developing atomic-level simulation models for electric field-induced surface diffusion on metal surfaces and its effects on protrusion growth and VBD initiation.