Molecular dynamics test of the Brownian description of Na+ motion in water

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Abstract
The autocorrelation function of the velocity of an infinitely dilute Na+ ion in aqueous solution, and the autocorrelation function of the force exerted on a stationary Na+ under the same conditions are evaluated by molecular dynamics calculations. The results are used to test the accuracy of Brownian motion assumptions which are basic to hydrodynamic models of ion dynamics in solution. The self-diffusion coefficient of the Na+ ion predicted by Brownian motion theory is (0.65±0.1)×10−5cm2/s. This value is about 60% greater than the one obtained for the proper dynamics of the finite mass ion, (0.4±0.1)×10−5cm2/s. The numerically correct velocity autocorrelation function is nonexponential, and the autocorrelation of the force on the stationary ion does not decay faster than the ion velocity autocorrelation function. Motivated by previous hydrodynamic modeling of friction kernels, we examine the approximation in which the memory function for the velocity autocorrelation function is identified with the autocorrelation function of the force on the stationary ion. The overall agreement between this approximation for the velocity autocorrelation function and the numerically correct answer is quite good.

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