  The onset of distortion in one-dimensional monatomic chains with partially
filled valence bands is considered to be well-established by the Peierls
theorem, which associates the distortion with the formation of a band gap and a
subsequent gain in energy. Employing modern total energy methods on the test
cases of lithium, sodium and carbon chains, we reveal that the distortion is
not universal, but conditional upon the balance between distorting and
stabilizing forces. Furthermore, in all systems studied, the electrostatic
interactions between the electrons and ions act as the main driving force for
distortion, rather than the electron band lowering at the Fermi level as is
commonly believed. The main stabilizing force which drives the chains toward
their symmetric arrangement is derived from the electronic kinetic energy. Both
forces are affected by the external conditions, e.g. stress, and consequently
the instability of one-dimensional nanowires is conditional upon them. This
brings a new perspective to the field of one-dimensional metals, and may shed
new light on the distortion of more complex structures.
