In our paper “A nonequilibrium molecular-dynamics method for thermal conductivities based on thermal noise” [T. Terao and F. Müller-Plathe, J. Chem. Phys. 122, 081103 (2005)], hereafter referred to as $I$, we have presented a way of setting up a nonequilibrium situation in a molecular-dynamics simulation by using the thermal noise from the pair-potential truncation as a uniform heat source and the thermostat as the heat sink. If the cooling action of the thermostat is confined to a control volume (a slab-shaped subregion of the system) a parabolic temperature profile results from the solution of Fourier’s equation [Eq. (2) of $I$], from whose curvature the thermal conductivity can be extracted [Eq. (6) of $I$]. In the form presented in $I$, the algorithm violates the conservation of linear momentum. The present comment describes a modification, which ensures momentum conservation, and shows that neglecting momentum conservation, although dangerous in principle, did not have an appreciable adverse effect on the thermal conductivity of water presented in $I$.

In $I$, the Berendsen thermostat was employed. In order to localize its action, only the atoms in the control volume were used to calculate the actual temperature and only their velocities were rescaled in response to the deviation of the actual temperature from the target value. This algorithm does not conserve the total momentum of the system. (In contrast, the usual uniform scaling of *all* atomic velocities by a thermostat does conserve the total momentum, provided the latter is zero. In practical simulations, it is periodically reset to zero to counteract numerical round off.) In $I$, rescaling was applied to only a subset of the atoms, whose collective momentum $P$ was initially not zero. Hence, the collective momentum was also rescaled $P\u2032=\lambda P$. Since the algorithm did not manipulate the momenta of the remaining atoms outside the control volume, an artificial change of the system’s total momentum resulted.

This can be easily avoided by subtracting, at each step, the momentum change $\Delta P\u2261P\u2032\u2212P$ from the atoms in the control volume,

Here, $vi$ is the final velocity of atom $i$, which is one of the $N$ atoms in the control volume; $vi\u2032$ is its velocity after rescaling; and $M$ is the sum of atomic masses within the control volume. In this way, the collective momentum of the atoms in the control volume, and hence the total momentum of the system, is unchanged.

With this modification of the algorithm, we have repeated the calculation of the thermal conductivity of simple point-charge extended (SPC∕E) water under otherwise exactly the same conditions as in $I$. The resulting thermal conductivity is $0.85\xb10.07Wm\u22121K\u22121$, which is within the error margin of the value without momentum conservation of $0.81\xb10.07Wm\u22121K\u22121$ given in $I$. The calculated parabolic temperature profiles also agree to within their respective error bars (not shown). Ignoring the requirement of momentum conservation apparently did not have an adverse effect on the temperature profile or the thermal conductivity for the water system we studied. Without further investigations, we would not like to generalize this finding to other systems. We may, however, speculate why momentum nonconservation had such a small effect. If the system’s total momentum is not conserved, one would expect the entire system to diffuse around between the times when the total momentum is reset to zero (every $0.5ps$). Its motion parallel to the direction of the temperature profile and the heat flux should then blur the temperature profile and lead to a less well-defined thermal conductivity. It appears that the total momentum has been reset frequently enough, so the additional error on the temperature profile due to the motion of the entire system was small compared to the statistical error present anyway. Or, in other words, the heat transport is so much faster than the system’s translation that a stationary temperature profile can establish itself even if the fluid as a whole moves a little.