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This page describes interaction potentials supported by pyOZ, together with the description of their properties and possible pecularities in their handling.

potential:

derivative: infinite at the discontinuity, zero otherwise; special treatment needed

parameters: hard sphere diameters σ

Very simple potential with complicated treatment due to the discontinuity at the hard sphere diameter. It is worth recalling, that a Fourier series of a function converges at a place of discontinuity to the value half way between the left and right neighborhood ε of the discontinuity σ. Then

Please note that for even in case of discrete functions, this is **not** the average of values at previous and next discretization point-only the infinitesimal neighborhood of the discontinuity has to be taken into account!

derivative:

parameters: particle charges , relative permittivity (dielectric constant) of the solvent (material)

Interaction between charged particles. Due to its long-ranged character, its treatment is complicated (discrete Fourier transform of a long-ranged function is not an easy task since this function doesn’t vanish at integration limits). See the article related to the Ng-renormalization for some information about how this problem can be solved.

When we convert the potential to the units of kT, we can write

where is the so called **Bjerrum length**-separation where Coulombic interaction is of thermal strength (kT). It follows from the previous text, that it is defined as

Charge-induced dipole interaction (CD)

potential:

derivative:

This potential corresponds to the interaction of a charge with induced dipole, represented by the value of the polarizabity . In pyOZ, the so-called excess polarizabilities are used. As all potentials of the type , the evaluation of the derivative is very easy and straightforward.

derivative:

parameters: potential well depth , separation where the potential is zero

This potential is frequently used as an approximation for the description of **van der Waals (dispersion) forces**. The repulsion part has no theoretical justification (it should be exponential, instead), but the attractive part describes the dispersion relatively well.

Normally, only ϵ and σ values for interaction between the same type of particles are given. The cross-parameters are calculated using the so-called combination rules. In practice (and in pyOZ as well), the arithmetic or geometric averages are used. In the so called **Lorentz-Berthelot rules**, geometric average is used for ϵ and arithmetic average for σ.

LJ potential provides analytical solution of the Ornstein-Zernike equation when Percus-Yevick closure is used.

Potential of mean force (PMF)

Potential read in from an external file, coming e.g., from a MD simulation of a pair of particles (“infinite dilution”) – the force between these particles is measured and converted into a potential). Derivative of this potential has to be calculated numerically.

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