I need the numeric value. Consider STP.
Please don't explain -dE/dR stuff.
You can assume that water molecules fluctuate around the equilibrium distance given by the LJ potential. If we have a harmonic approximation around this point with
U = 1/2 K (r - r_eq) ^ 2
we come up with the oscillatory solution
r = r_eq + A sin (w t)
with w = sqrt (K / m). The velocity and accelerations would be:
v = A w cos (wt)
a = -A w ^ 2 sin (wt)
Now, this way, the actual "mean" velocity and acceleration become zero. If we consider the root mean square values, we have:
v_rms = A w / sqrt (2)
a_rms = A w ^ 2 / sqrt (2) = v_rms * w
We can get an approximation of v_rms from Maxwell-Boltzmann distribution:
v_rms = sqrt (3 kT / m)
For the 12-6 Lennard-Jones, the spring constant around the equilibrium distance is:
K = [72 / 2 ^ (1/3)] * eps / sig ^ 2
For numerical values, I have used SPC water model with
sig = 0.3166 nm
eps = 0.650 kJ / mol
This will result in
a_rms = 2.79 x 10 ^ 15 m / s^2
I think this is straightforward enough and you can check the results for yourself.
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