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For simplicity of notation let us consider the energy of the surface as depending on only one coordinate, u: E surf tot (u) =K u2 /2 (terms not depending on u are omitted). In presence of the adatom, E A/surf tot (u) =K u2 /2-Fu, which is minimized for u= ū ≡F/K (the coordinate after structural optimization), where it takes the value - F2 /2K. Not allowing relaxation would result in the energy E A/surf-frozen tot ≡ E A/surf tot (0) =0, hence, Erelax ≡ E A/surf tot (0) - E A/surf tot (ū) = F2 /2K. Similarly, the energy of the deformed surface is E surf-def tot ≡ E surf tot (ū) = F2 /2K, which results in Edef ≡ E surf tot (ū) - E surf tot (0) = F2 /2K.
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For simplicity of notation let us consider the energy of the surface as depending on only one coordinate, u: E surf tot (u) =K u2 /2 (terms not depending on u are omitted). In presence of the adatom, E A/surf tot (u) =K u2 /2-Fu, which is minimized for u= ū ≡F/K (the coordinate after structural optimization), where it takes the value - F2 /2K. Not allowing relaxation would result in the energy E A/surf-frozen tot ≡ E A/surf tot (0) =0, hence, Erelax ≡ E A/surf tot (0) - E A/surf tot (ū) = F2 /2K. Similarly, the energy of the deformed surface is E surf-def tot ≡ E surf tot (ū) = F2 /2K, which results in Edef ≡ E surf tot (ū) - E surf tot (0) = F2 /2K.
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