Structural elements on reconstructed Si and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mtext>Ge</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>110</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>surfaces

We present ab initio studies of possible reconstruction elements on Si and $\text{Ge}(110)$ surfaces. Using $2\ifmmode\times\else\texttimes\fi{}2$, $3\ifmmode\times\else\texttimes\fi{}2$, and $6\ifmmode\times\else\texttimes\fi{}2$ unit cells we optimize models with buckled atomic chains, dimers, different adatom distributions, and interstitial atoms which may exist on the larger $\text{Si}(110)16\ifmmode\times\else\texttimes\fi{}2$ or $\text{Ge}(110)16\ifmmode\times\else\texttimes\fi{}2∕c(8\ifmmode\times\else\texttimes\fi{}10)$ surface reconstructions. We show that adatom reconstructions gain energy. Only the adatom model which seemingly leaves no dangling bonds cannot occur on Si and $\text{Ge}(110)$ surfaces. An adatom-rest atom electron transfer mechanism is more favorable. An adatom-tetramer-interstitial $3\ifmmode\times\else\texttimes\fi{}2$ model also stabilizes the Si and Ge surfaces and leads to a semiconducting behavior (at least for Si). Simulated scanning tunneling microscopy (STM) images of empty states of this reconstruction look like the pentagon structures observed on $\text{Si}(110)16\ifmmode\times\else\texttimes\fi{}2$. A $6\ifmmode\times\else\texttimes\fi{}2$ reconstruction with five-membered adclusters is energetically completely unfavorable, though it also reproduces the empty-state pentagonlike STM images.