# Density-scaling exponents and virial potential-energy correlation coefficients for the (2n,n) Lennard-Jones system

## TL;DR

This study explores the relationship between the density-scaling exponent and virial potential-energy correlation coefficient in generalized Lennard-Jones systems across various dimensions and parameters, revealing a linear relation at low densities and a transition near high correlation values.

## Contribution

It establishes a roughly linear relation between the density-scaling exponent and the correlation coefficient for generalized Lennard-Jones systems, extending understanding across multiple dimensions and parameters.

## Key findings

- Linear relation $oxed{ ext{γ}
oughly 3nR/d}$ at low densities.
- Transition in $ ext{γ}$ versus $R$ plot around $R
oughly 0.9$.
- As $R
ightarrow 1$, $ ext{γ}
ightarrow 2n/d$, indicating dominance of repulsive interactions.

## Abstract

This paper investigates the relation between the density-scaling exponent $\gamma$ and the virial potential-energy correlation coefficient $R$ at several thermodynamic state points in three dimensions for the generalized $(2n,n)$ Lennard-Jones (LJ) system for $n=4, 9, 12, 18$, as well as for the standard $n=6$ LJ system in two, three, and four dimensions. The state points studied include many low-density states at which the virial potential-energy correlations are not strong. For these state points we find the roughly linear relation $\gamma\cong 3nR/d$ in $d$ dimensions. This result is discussed in light of the approximate "extended inverse power law" description of generalized LJ potentials [N. P. Bailey et al., J. Chem. Phys. 129, 184508 (2008)]. In the plot of $\gamma$ versus $R$ there is in all cases a transition around $R\approx 0.9$, above which $\gamma$ starts to decrease as $R$ approaches unity. This is consistent with the fact that $\gamma\rightarrow 2n/d$ for $R\rightarrow 1$, a limit that is approached at high densities and/or temperatures at which the repulsive $r^{-2n}$ term dominates the physics.