The reaction field method is used in molecular simulations to simulate the effect of long-range dipole-dipole interactions for simulations with periodic boundary conditions. Around each molecule there is a 'cavity' or sphere within which the Coulomb interactions are treated explicitly. Outside of this cavity the medium is assumed to have a uniform dielectric constant. The molecule induces polarization in this media which in turn creates a reaction field, sometimes called the Onsager reaction field. Although Onsager's name is often attached to the technique, because he considered such a geometry in his theory of the dielectric constant, the method was first introduced by Barker and Watts in 1973. The effective pairwise potential becomes:
U A B = q A q B [ 1 r A B + ( ε R F − 1 ) r A B 2 ( 2 ε R F + 1 ) r c 3 ] {\displaystyle U_{AB}=q_{A}q_{B}\left[{\frac {1}{r_{AB}}}+{\frac {(\varepsilon _{RF}-1)r_{AB}^{2}}{(2\varepsilon _{RF}+1)r_{c}^{3}}}\right]}
where r c {\displaystyle r_{c}} is the cut-off radius. The reaction field in the center of the cavity is given by :
E R F = 2 ( ε R F − 1 ) 2 ε R F + 1 M → r c 3 {\displaystyle E_{RF}={\frac {2(\varepsilon _{RF}-1)}{2\varepsilon _{RF}+1}}{\frac {\vec {M}}{r_{c}^{3}}}}
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