content_image/384217.jpg content_image/384224.jpg content_image/384227.jpg
fluids, figure 4(b). 

For monatomic systems at relatively low densities ( ρ$_{a}$ = 0 . 375 − 0 . 480), the real space kernels are affected considerably by the functional form chosen to fit the re- ciprocal space kernel, figure 5. For instance, the equally weighted two-term Gaussian function, figure 5(a), dis- torts the real space kernels and predicts a noticeably higher η ( y = 0) value. As we increase the density, the dis- crepancy between Gaussian functions, as well as between Gaussian and Lorentzian-type functions, only partially reduces, figure 5(b,d). The width of the kernel for WCA fluids at low density is roughly 2-4 atomic diameters. 

In figures 6(a) and 6(b) we compare the unnormalized kernel data in y space extracted from four-term Gaussian and Lorentzian-type functional forms for all the simu- lated systems. Despite the fact that the difference be- tween the reciprocal kernels is less than 4%, figure 2(d) (e.g. chlorine - dashed line), the kernels for the corre- sponding systems in real space look noticeably different (figure 6(a) and figure 6(b)), for all the systems (e.g. chlo- rine - dashed dotted line). However, the zero wave-vector viscosities obtained from both functional forms are very close, with less than 2% error. 

We can determine the zero wave-vector viscosities η$_{0}$ = η ( k = 0 , ω = 0) by integrating the real space kernel over y , and thus test our numerical analysis. The zero wave- vector viscosity η$_{0}$ obtained by a Gaussian function η$_{G}$ ( y ) 

<img src='content_image/384217.jpg'>

<img src='content_image/384224.jpg'>

is 

<img src='content_image/384227.jpg'>

Since the general analytical expression for η$_{L}$ ( y ) does not exist [20] we evaluate the integral numerically and present the results from all functional forms in Table IV. A comparison of the viscosities in Table IV with the sim- ulated zero frequency zero wave-vector shear viscosities given in Table II shows an integration error of less than 3%. This confirms the accuracy of our numerical analysis techniques. 

It is of interest to discuss the real space viscosity ker- nels for monatomic and diatomic systems from a struc- tural point of view. For this purpose we define a struc- 

