I've come across many papers performing ab initio MD (Carr-Parinello or Born-Oppenheimmer) simulations of water that use the deuterium mass for hydrogen. And they state that this helps improve convergence. I haven't seen a derivation for it and I'm not able to come up with an intuitive reason for why this might be. I would greatly appreciate some insights.

Here's an example of a paper that does so (I'm linking this because it doesn't seem to need institutional credentials to access): https://www.spiedigitallibrary.org/journals/Journal-of-Photonics-for-Energy/volume-1/issue-1/016002/iAb-initio-i-modeling-of-water-semiconductor-interfaces-for-photocatalytic/10.1117/1.3625563.full?SSO=1



1 Answer 1


My intuitive reason is based on the need for time-scale separation between the evolution of the electronic degrees of freedom and the nuclear motion.

The electrons are given fictitious "masses" for the evolution of the quantum degrees of freedom, and are typically maintained in their ground state by a low-temperature thermostat. The nuclei move around at speeds consistent with the physically desired temperature (e.g. ambient temperature). This means that, technically, the system is not at equilibrium. However, energy flow between the two subsystems is kept under control if their natural timescales are sufficiently different: usually called "adiabaticity".

Giving the lightest nuclei an inflated mass is a simple way of slowing them down. It is used to allow a longer timestep in purely classical MD; but here I think that it also makes it easier to give the electrons a correspondingly higher mass, without compromising the adiabaticity, and hence use a longer timestep in the quantum part of the calculation (which is the expensive part).

  • $\begingroup$ Ah okay, that makes a lot of sense. I've a quick follow up question. I've seen the deuterium mass used in Born-Oppenheimer ab initio MD as well where there is no need for a fictitious electron mass unlike Car-Parrinello MD. But is it right for me to conclude that simulating deuterium instead of hydrogen allows for a longer time step just as in classical MD? Thank you! $\endgroup$
    – user34801
    Oct 5, 2018 at 21:34
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    $\begingroup$ I'm not a real expert, but I would think that the numerical minimisation algorithm used in BO simulations at each step would benefit in a similar way by slowing down the fastest nuclei. Actually, I think that Marx and Hutter's book Ab initio molecular dynamics, basic theory and advanced methods discusses CP vs BO, from the viewpoint of permitting a long time step; for water I believe that it is a balance between different factors. Might be worth looking there. $\endgroup$
    – user197851
    Oct 5, 2018 at 21:47

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