Corrections to the configurational energy

We assume the confined fluid to be homogeneous represented by a constant density p [see Eq. (4.20)]. 

Assuming now the radius r to be sufficiently large, we may approximate the relevant interaction potentials by their attractive contributions only [see Eq. (5.24)], that is 

Wc insert Eq. (5.30) into Eq. (5.29), cairy out the integration over p, and obtain 

The remaining two integrations can be carried out with the help of tabulated integrals (141). One finally arrives at 

as configuratipns n— 1 and n in the second step of the GCEMC-adapted Metropolis algorithm differ in N = N -i 1, we obtain from the previous expression 

It is customary to relate (ri) and i i.r2) to the pair correlation function g(ri,r2) via Elq. (4.17). To proceed we introduce two key assump-tioas, nanudy 

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In a bulk fluid, similar considerations may be used to derive an expression for cut-off corrections to the configurational energy. U.sing in this case a cutoff sphere rather than a cylinder gives rise to... 

However, these results do not immediately carry over to the problems of interest here where (while PBCs are the norm) the ensembles are frequently open or constant pressure, and the systems do not fit in to the lattice model framework. Even in the apparently simple case of crystalline solids in NVT, the free translation of the center of mass introduces /-dependent phase space factors in the configurational integral which manifest themselves as additional finite-size corrections to the free energy these may not yet be fully understood [58, 97]. If one adopts the traditional stance, then, one is typically faced with having to make extrapolations of the free-energy densities in each of the two phases, without a secure understanding of the underlying form (jf . ..) of the corrections involved. 

The model described allows the ions of the first n layers at the free j 100 J face of a hemScrystal with sodium chloride structure to relax in a direction normal to the face and to be polarized by the electric field in the surface region. The equilibrium configuration is determined by minimizing the energy of the system. Numerical results for sodium chloride are presented for the five cases 1 n < 5. A value of —107.4 erg cm.-2 is estimated for the total correction to the surface energy of this material due to surface distortion. 

Corrections to the Reorganizational Energy Terms that Result from D/A Configurational Mixing... 

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