GetOptEpsilon(pots, eps_old, r1, eps_min=0, eps_max=0, npoints=100, mcmfile=None)

Calculates optimal value of the dielectric permittivity which provides fastest decay of short-range intermolecular potential tales according to the procedure described in: A.A.Mirzoev and A.P.Lyubatsev, Phys.Chem.Chem.Phys., 13, 5722-5727 (2011) DOI: 10.1039/C0CP02397C.

Briefly, the procedure to obtain values of the dielectric permittivity providing fastest decay of short-range potentials set with distance consists in the following. First, we introduce a numerical criteria of a short range potential deviation from zero at large distances:

$$W(U_{sr}^{ij}(r))=\intop_{r_{1}}^{r_{2}}\bigl\vert r^{2}(U_{sr}^{ij}(r))\bigr\vert dr$$ (3)

where $r^{2}$ factor implies a higher weight of larger distances, $r_{1}$ and $r_{2}$ are the lower and upper boundaries of the range of distances defining the tail (the $r_2$ value is taken as the cut-off of RDFs and tabulated effective potentials). The absolute value in the equation is used in order to deal with possible oscillations of the short range part of the potential. From eq. , one can write for the short-range part of the potential:

$$W(U_{sr}^{ij}(r))=\intop_{r_{1}}^{r_{2}}\bigl\vert r^{2}(U_{tot}^{ij}(r)-\frac{q_{i}q_{j}}{4\pi\varepsilon_{0}\varepsilon r})\bigr\vert dr$$ (4)

Assume we define the long-range Coulombic potential using another value of permittivity $\varepsilon^{\star}$. This, according to , introduces a new short-range potential as:

$$U_{sr}^{\star\, ij}=U_{sr}^{ij}(r)+\frac{q_{i}q_{j}}{4\pi\varepsilon_{0}r}(\frac{1}{\varepsilon}-\frac{1}{\varepsilon^{\star}})$$ (5)

Now we shell find the optimal $\varepsilon^{\star}$, which produces the fastest decay of all three short range potentials according to criteria defined by eq. . We minimize the sum:

$$W(system)=\sum_{i,j}{W(U_{sr}^{\star\, ij}(r))}=\sum_{i,j}{[U_{sr... ...}}{4\pi\varepsilon_{0}r}(\frac{1}{\varepsilon}-\frac{1}{\varepsilon^{\star}})]}$$ (6)

by varying $\varepsilon^{\star}$. The optimal value of $\varepsilon^{\star}$ can be considered as effective dielectric permittivity corresponding to the given thermodynamic conditions (temperature, concentration).

pots*

- set of potentials to analyze (mandatory argument) NB! The dielectric permittivity value calculation only takes intermolecular potentials into account skipping bonding potentials.

eps_old*

- dielectric permittivity used in inverse MC calculation (mandatory argument)

r1*

- distance where tail range begins, Å(mandatory argument)

eps_min, eps_max

- range of values for the search of $\epsilon_{opt}$ (optional argument). By default eps_min=0, eps_max=2*eps_old

npoints

- number of points in a mesh to be used for the search, e.g. accuracy of the search is equal to $\frac{\epsilon_{max}-\epsilon_{min}}{npoints}$

mcmfile

- molecular description file (or list of files) providing charges for bead/CG-atom types. Required if the potential was read from [RDFnPOT].pot file rather than from MagiC core [.out]log file.

Example:
eps_opt = MT.GetOptEpsilon(pots, eps_old=70.0, r1=15, eps_min=50,
eps_max=100, mcmfile='dmpc.mcm')