Application to Alkali Halides - Lammps - Sandia National Laboratories

Embedded Ion Method (EIM)E=12N∑iN∑N( rij) + ∑ Ei( q i i)φ ,σiji= 1 j=ii=11system total energyEi12( q σ ) = q ⋅σ*i, i i iembedding energy at ii= N∑j=iji( )q iη rcharge on atom i1ijiNσi= ∑qj⋅ϕijj= i 1( r )electrical potential (in voltage) at iijE=12⎧⎛⎞ ⎡⎛⎞ ⎤⎪⎫⎜⎜⎥ ⎬= ⎪⎩ ⎝⎟ ⎠ ⎢⎣⎝⎟ ⎠ ⎥⎦⎪ ⎭N iNN iNiNjN⎪∑∑φ( ) + ∑⎨⎜∑( ) ⎟⋅∑ ⎢⎜∑( ) ⎟ijrijηjirijηkjrjk⋅ϕ( rij)i= 1 j i1i= 1 j=i1j= i1 k=j1*when ϕ ij (r) ~ r -1 , the embedding energy reduces toCoulomb interactions between i and its neighbors:Ei12i N( qi,σi) = ∑j=i1q ⋅ qirijj4