Determination of effective pair interactions from the structure factor

In this work we present an efficient procedure to evaluate effective pair potentials, compatible with “experimental” structure factors, using a Monte Carlo simulation scheme. The procedure does not require the use of inverse Fourier transforms and is robust and rapidly convergent. As a test case the structure factor of liquid Selenium obtained from a Tight-Binding Molecular Dynamics simulation is inverted to obtain an effective pair potential and, as a by-product, the pair distribution function. The inversion procedure yields a pair structure in perfect agreement with the original molecular dynamics calculations and the analysis of the triplet structure and the dynamics also illustrates the limitations of the use of pair potentials in the description of liquids with strongly directional bonding, such as the covalent liquid Selenium.

Figure 1

Structure factor of liquid selenium evaluated from Fourier transformation of the results of $g\left(r\right)$ obtained in the TBMD simulation.

Figure 2

PDF for liquid Se. The solid curve represents the TBMD results, the dotted line corresponds to models A–D (see Sec. 3 and Fig. 3 for details of the models), which are indistinguishable at the scale of the figure.

Figure 3

Effective pair potentials evaluated using inversion techniques. Case A {inversion of $\mathrm{g}\left(\mathrm{r}\right)$ following the method of [13]}: continuous line. Case B $(k_{\mathit{max}}=40\mathrm{\AA })$: dashed line. Case C $(k_{\mathit{max}}=15\mathrm{\AA })$: filled circles. Case D $(k_{\mathit{max}}=10\mathrm{\AA })$: white circles. In the right frame, only Cases A and B are represented (since Cases C and D are indistinguishable from Case B at the scale of the figure).

Figure 4

Three-particle distribution function $g^{\left(3\right)}(r,s,\theta )$ calculated for $r=s=2.48\mathrm{\AA }$, nearest-neighbor distance in liquid Se.

Figure 5

Vibrational density of states for liquid Se.