Table 1 Three-dimensional diffusion coefficients, Dshort and Dlong (in Å2/ps), obtained from linear fits to the MSD in the short (0 ≤ t < t*) and long (t* < t) time ranges, respectively

From: Multi-proton dynamics near membrane-water interface

Simulation (proton)

t*, ps

Dshort

Dlong

1b (\({{{\rm{H}}}}_{a}^{+}\))

5.6

3.4

13.2

2a (\({{{\rm{H}}}}_{b}^{+}\))

2.1

3.8

10.8

2b (\({{{\rm{H}}}}_{b}^{+}\))

5.1

1.28

2.08

3a (\({{{\rm{H}}}}_{c}^{+}\))

6.0

1.62

6.62

3b (\({{{\rm{H}}}}_{c}^{+}\))

4.5

1.46

2.60

pure water (H+)

10.0

0.86

–

  1. The result for an excess proton in pure water (Supplementary Fig. 2) is given in the last row. It is close to the experimental value of 0.93 Å2/ps20, supporting the use of DFTB3 for proton diffusion.
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