Step 6 - Fix the Water Molecule Geometry

There is a hint in the structure factors for the H₂O sample (particularly the G(r)), that the intramolecular geometry of our off-the-shelf forcefield is not quite consistent with the real world. This is made clearly obvious if you look at the G(r) for the D₂O sample:

Go to the   G(r) / Neutron S(Q)   tab

Click on the “D2O” NeutronSQ module and select the Output button

Click the Total G(r) button on the “H2O” NeutronSQ module’s output page

Simulated (black), Fourier-transformed from simulated F(Q) (green), and experimental (red) G(r) for the equilibrated water (D₂O) simulation

Clearly we have a mismatch between the experimental (red) and simulated (green) peak positions at around 1 Å (related to the O-H bond) and 1.7 Å (related to the H-O-H angle). It is usually necessary to adjust the geometry of your species a little in order to be consistent with the experimentally-measured data, and in the present case we are lucky that we only have two parameters to adjust!

Here we are modifying the intramolecular terms based on comparison of the D₂O data, but bear in mind that liquid water is amongst the systems most sensitive to isotopic substitution since all hydrogens are hydroxyl hydrogens, and subject to exchange as well as strong hydrogen bonding. As such, the differences in intramolecular geometry between H₂O and D₂O are measurable.^[1]

Since we set up our simulation to use intramolecular master terms (via the Add Forcefield Terms… wizard) we can modify those to directly affect our water molecule’s geometry. For the O–H bond it is quite straightforward to read of the true distance (0.976 Å) from the reference g(r). The angle distance requires a touch more trigonometry but, given knowledge of the correct O–H distance, we can work out that the corresponding equilibrium angle we require is 107.134 °.

First of all, let’s stop the simulation from running:

Simulation ⇨ Stop

…or…

Esc

And now let’s make the changes to our intramolecular terms:

Go to the   Forcefield   tab and find the Master Terms tab

In the Bonds section, change the equilibrium bond length (’eq’) of the HW-OW bond term from 1.0 to 0.976 Å

In the Angles section the equilibrium angle (’eq’) of the HW-OW-HW angle term from 113.24 to 107.134 °

Now run the simulation for a little longer to let the species adjust to their new geometry:

Ctrl-R

You should see a marked improvement in the comparison of the D₂O total G(r) and structure factor.

Simulated (black), Fourier-transformed from simulated F(Q) (green), and experimental (red) G(r) for the equilibrated water (D₂O) simulation with adjusted intramolecular parameters

The change in the G(r) will not be instant as the majority of the evolution of the system is from the MolShake module which does not change the intramolecular geometry. Only the MD module will affect the intramolecular geometry. Also, the g(r) calculated by the GR are averaged over five calculations by default.

It’s also worth checking the other two samples, where the same kind of improvement should be noticeable (if a little less prominent).

References

1. Quantum Differences between Heavy and Light Water, A. K. Soper and C. J. Benmore, Phys. Rev. Lett. 101, 065502 (2008).

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