From: LEWYN LI (ll2150_at_columbia.edu)
Date: Wed May 31 2006 - 14:14:05 CDT
Here are my two cents. Some of it would be very similar to
what Sterling has said, but put slightly differently. Energy is a state
function, whereas work done is not i.e.
dE = q + w
where dE = change in total energy, q = heat exchange and w = work done by
the system. The heat term means that dE would not equal w unless q = 0
(= an adiabatic reaction).
Another important point is that the laws of thermodynamics deals
with ensemble of molecules. Therefore, dE can be viewed as the change in
average total energy of many, many identical molecules or systems.
Therefore, we need to be careful in applying thermodynamics to a few
single-molecule pulling simulations. For example, in a thermally
equilibrated ensemble of molecules, some molecules may have conformations
that are more reactive than others, so these molecules would have a higher
tendency to react. If a single simulation trajectory began with a
molecule in this reactive state, then any quantities you extracted from
this simulation would be severely biased by this initial state.
Note that a long equilibration will not necessarily solve this
problem. When a system is equilibrated, it just means that, over time, it
has sampled all the available states according to the Boltzmann factor.
Therefore, at any particularly moment in time, the system could fluctuate
into some rare but reactive state. Only by doing multiple simulations
with multiple initial starting conformations can we get an idea if the
single-molecule MD trajectories represent the ensemble behavior.
Of course, if we invoke the ergodic hypothesis, then we can apply
thermodynamics to single-molecule trajectories. But then we have to deal
with the daunting task of proving ergodicity ...
On Wed, 31 May 2006, Sterling Paramore wrote:
> The problem is that the total energy you calculate in MD doesn't include the
> "energy" of the thermostat. You must keep in mind that heat exchange is also
> a source of energy change. One of the first things we learn in a
> thermodynamics class is that the change in total energy of a system is equal
> to the work done on it PLUS the energy due to heat exchange with the
> environment. If you're doing NVE dynamics, then there is no "environment" to
> speak of and yes, the work done on the system will be equal to the energy
> change. However, in this case the temperature of the system will change
> (usually it will increase due to viscous heating). When you have a
> thermostat on the system (either NVT or NPT), the temperature is kept
> constant by removing the heat produced during the process. Therefore, the
> total energy change of the MD system is equal to the work done on it minus
> the heat removed from it. While it's very easy to calculate the energy
> removed as heat with a Nose-Hoover thermostat, I am not aware of how (or if)
> this can be done with a Langevin thermostat.
> Again, what do you hope to learn about your system by calculating the energy
> Pijush Ghosh wrote:
>> Dear Sterling and Li
>> Sorry to bother you again. Well, fantastic discussion so far. I completely
>> agree with what Sterling said about the fluctuation of total energy in NPT
>> ensemble particularly for a large biosystem. I have had the experience of
>> such in the past. But what I want to insist on is, purely from the of
>> mechanics viewpoint whats the flaw in going with the theory that "change
>> total energy is equal to the work done"
>> Where: change in energy is the difference in initial and final energy of
>> the whole
>> system, and,
>> wrok done is the mechanical work done in displacing the pulling SMD atom.
>> If they don't match, where the remaining energy dissipates to? Does all of
>> it goes to the thermostat system.
>> For example in one of my organic-inorganic system:
>> At vel= 0.50A/ps
>> Change in total energy: -4745 kcal/mol
>> Area under force-disp. Curve: 8142 Kcal/mol
>> Whereas at vel= 0.25A/ps
>> Change in total energy: -4626 kcal/mol
>> Area under force-disp. Curve: 2143 Kcal/mol
>> I am not quite sure how to explain this....or if at all it makes sense to
>> draw any conclusion from these numbers.
>> I will look forward for some discussion from your end.
>> I appreciate your time so much.
>> Pijush Ghosh
>> PhD Student
>> Department of Civil Engineering
>> North Dakota State University
>> Fargo. ND. 58105. USA
>> Phone: 701-231-6491(Lab)
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