HB Potential by Gaussian Functions

Recognizing the fact that the hydrogen bond occurs only along four directions pointing to the vertices of a regular tetrahedron, we can use the four unit vectors introduced in Section 6.2 (see Fig. 6.2) to construct a HB potential function. This we denote by C/hb(Xi, Xg), so that the full effective pair potential is a superposition of three terms 

Construction of a HB Potential Function Based on the Bjerrum Mode for Water 

The hydrogen bond potential in this case consists of the 16 Coulom-bic interactions between the pairs of point charges situated on different molecules, which can be written as 

In the construction of the total pair potential, we need not take an additional term for the dipole-dipole interaction, as in (6.14). However, in order to avoid divergence of the potential function when two charges of opposite signs come very close to each other, we use a switching function S(i i2) which serves to suppress this possibility by switching off the HB potential at close distances. The specific function S R chosen by Ben-Naim and Stillinger (1972) is 

Note that the value of ly = 0.19 is slightly larger than the value of 77 = 0.17 chosen by Bjerrum to reproduce the dipole moment of a free water molecule. The combined potential function is thus 

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