Frozen-Phonon Total-Energy Determination of Structural Surface Phase Transitions: W(001)

The prototypical W(001) structural phase transition is investigated by all-electron, frozen-phonon, total-energy calculations. The strong coupling between surface states and the ${\overline{M}}_5$ phonons plays a decisive role in favoring the reconstructed $c(2\mathrm{}\times 2)$ structure with a lateral $〈110〉$ zig-zag displacement of 0.18±0.01 Å (in excellent agreement with experiment) and no interlayer relaxation. The transition from the (1 × 1) into the $c(2\mathrm{}\times 2)$ phase proceeds over a very flat region of the energy hypersurface and suppresses the relaxation.