Abstract
The atomic geometry on the $\ensuremath{\alpha}\text{\ensuremath{-}}\mathrm{Sn}(001)(2\ifmmode\times\else\texttimes\fi{}1)$ surface have been studied by applying the ab initio pseudopotential method. Using the relaxed geometry, we studied atomic vibrations on this surface by employing two different theoretical methods: a linear response approach based on the density functional theory, and an adiabatic bond-charge model. The results from the two methods compare well with each other. Using the present results, together with previously obtained results for the $(001)(2\ifmmode\times\else\texttimes\fi{}1)$ surface of C, Si, and Ge, we have established a few interesting trends across IV(001) surfaces: correlation between dimer length and dimer tilt; correlation between dimer tilt and its strength; and variation of dimer twist phonon mode with the reduced mass and lattice constant.
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