Aqueous solution computations

We performed Car-Parrinello molecular dynamics simulations of the following solutions: (a) HCl in water, (b) CH$_3$Cl in water and (c) both HCl and CH$_3$Cl in water. For reference, a CP-PAW calculation of a pure water sample of 32 H$_2$O molecules per unit cell was also done (d). All simulations were performed in a periodic system with the cubic unit cell containing one of each type of solute molecules (HCl or CH$_3$Cl or both) and 32 water molecules. The box sizes were: 9.9684, 10.1450, 10.2463 and 9.8650 Å for samples (a), (b), (c) and (d), respectively, yielding the experimental density of the solution at $T=300$ K. The simulations of sample (c), the reactants in water, yield the central result of the present work. It involved the calculation of the free energy barrier for the CH$_3$Cl + Cl$^-$ reaction in water by a series of constrained CP-PAW runs at different values of the reaction coordinate (eqn 3.2). The starting configuration of the first run was created from a previous run of CH$_3$Cl in water, sample (b), at $T=300$ K. A sphere-shaped cavity of radius 2 Å was created near the CH$_3$Cl molecule, in which HCl$^\prime$ ( $R_{\rm HCl^\prime}= 1.10$ Å) was placed at a distance from CH$_3$Cl equal to $R_{\rm CCl^\prime}= 4.00$ Å and with an angle $\angle_{HCl^{\prime}C} = 180^{\circ}$. With the angle $\angle_{\rm ClCCl^\prime} = 176^{\circ}$ and the C-Cl distance in CH$_3$Cl $R_{\rm CCl}= 1.871$ Ry and the C-Cl distance in CH$_3$Cl $R_{\rm CCl}= 1.871$ Å, this corresponds to a value for our reaction coordinate in this initial snapshot of $\xi = 0.31848$. This value was constrained and equilibration was performed at $T=300$ K until there was no longer a drift in the constraint force and the potential energy $E\left[\rho\right]$. Then a production run of 3-5 ps. was performed to collect statistics. After each production run, the constraint was moved to the next reaction coordinate value in a number of steps large enough to keep the induced atomic velocities very small compared to their average velocities at $T=300$ K (typically 1000-2000 steps). This was again followed by equilibration and mean force sampling. Equilibrations took typically 1.5-3 ps.