# Diffusion coefficients of benzene isotopologues in water

## Description

Isotope fractionation induced by the diffusion of benzene in water was investigated through non-equilibrium molecular dynamics simulations in order to verify its negligible impact on the variability on the variability of compound-specific isotope signatures in the context of underground natural gas storage in aquifers. Data presented in Table S1 show the influence of applying various external forces to the reference benzene molecule (mass=78.11) on the determination of diffusion coefficients, validating the external field - non-equilibrium molecular dynamics (EF-NEMD) methodology for a range of applied forces below 1 kcal/mol/ang. The dataset includes results the applied field (kcal/mol/ang), simulated time (ns), the velocity of the center of mass of benzene relative to water (vcm, ang/fs) with 1 standard deviation (1sd), the diffusion coefficient obtained from this simulation under periodic boundary conditions (D_PBC in m2/s) with associated 1sd, diffusion coefficients corrected for the periodic boundary conditions (D_0 in m2/s) with associated 1sd, diffusion coefficients corrected for the underestimated water viscosity in spc/e model (D_corr in m2/s) with associated 1sd, as well as the computed temperature of benzene (T_benzene in K) with associated 1sd and of water (T_water in K) with associated 1sd. Table S2 presents diffusion coefficients obtained for different benzene isotopologues from the linear regression between vcm and applied force from four distinct simulations performed with fields of 0.25, 0.50, 0.75 and 1.00 kcal/mol/ang. The dataset includes the isotopologue set with the type of substitution made (x denotes the mass substitution), the value of x, total isotopologue mass (amu), simulation time (ns), and diffusion coefficients obtained under periodic boundary conditions (D_PBC), corrected for periodic boundary conditions (D_0) and corrected for the underestimated viscosity of spc/e model (D_corr), all with associated 1sd uncertainty. The dataset includes a single result obtained from an equilibrium molecular dynamics simulation for reference benzene (mass=78.11 amu) calculated using the Green-Kubo method, integrating the velocity autocorrelation function with tau=3ps.

## Files

## Steps to reproduce

All simulations were conducted with the open source molecular dynamics code. We used the Packmol package to generate a simulation box, of cubic shape, containing 1500 water molecules and one single benzene molecule for approaching infinite dilution. Non-bonded interactions were described by the 6 – 12 Lennard-Jones potential function with a cutoff radius of 11 Å. Additional coulombic pairwise interactions were implemented with a similar cutoff radius of 11 Å. Long-range coulombic interactions were computed with the particle-particle particle mesh solver. Periodic boundary conditions (PBC) were applied in all directions. Liquid water model characteristics (σ, ε, q, molecular structure) follow the extended single point charge (SPC/E) model. The benzene molecule was constructed using the OPLS-AA force field parameters. Geometric mixing rules were used to compute non-bonded interactions between benzene and water atoms. We then used this initial system to run Equilibrium Molecular Dynamics (EMD) and External Field - Non Equilibrium Molecular Dynamics (EF-NEMD) simulations. For these simulations, the Nose-Hover thermostat was only applied to water molecules, so as not to disturb the dynamics of the diffusing benzene molecule. The EF-NEMD methodology was implemented by affecting a constant force to the benzene molecule over the course of the simulation and a corresponding opposite force to water molecules in order to avoid any drift of the system. Diffusion coefficients were calculated from the mean velocity of benzene molecules relative to water.