aplrt
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Equilibration, Intramolecular/Hamiltonian energy
I was wondering if someone here could help with the physical interpretation of my data. I have performed a molecular dynamics simulation and
calculated/plotted the intramolecular energy and the Hamiltonian energy (total energy including my 'heatbath') during the equilibration stage. Why is
the Hamiltonian energy decreasing over time, whereas the intramolecular energy is increasing ? I was told that this has something to do with the total
energy remaining constant, but I couldn't fully grasp the explanation.
Also, what happens if the intramolecular potential energy is 'too small' or 'too large' ?
Thanks for any help.
[Edited on 24-11-2010 by aplrt]
[Edited on 24-11-2010 by aplrt]
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watson.fawkes
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Quote: Originally posted by aplrt  | | I was wondering if someone here could help with the physical interpretation of my data. I have performed a molecular dynamics simulation and
calculated/plotted the intramolecular energy and the Hamiltonian energy (total energy including my 'heatbath') during the equilibration stage. Why is
the Hamiltonian energy decreasing over time, whereas the intramolecular energy is increasing ? I was told that this has something to do with the total
energy remaining constant, but I couldn't fully grasp the explanation. |
There's barely enough information to
say much anything at all here, really, except a few generalities.
One thing is immediately obvious to me, though. If you have a heat bath, it's not part of your Hamiltonian function. A heat bath is a term of art for
a constant temperature reservoir that can source or sink arbitrary amounts of heat energy. Its energy is not bounded. Each value of the Hamiltonian is
bounded; that's what it means to be a function. So your heat bath is not represented in that function.
With that problem out of the way, if your Hamiltonian function is decreasing, that means that the system is losing energy to its environment. In other
words, your reaction is exothermic. Non-constant Hamiltonians are typical for non-adiabatic processes.
If your intramolecular energy is increasing, it means that your enthalpy is increasing, assuming constant pressure and volume, not that I should
really assume that, given that you didn't say anything about either.
Now it's mighty unusual to have both enthalpy increase and an exotherm if you start at the equilibrium temperature, which leads me to believe that
your reactants are starting effectively above that temperature, or in some other non-generic initial condition you haven't stated.
I'm giving you the benefit of the doubt that the simulation is sound in the first place. This may well be overgenerous, given how little you've said
about it.
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aplrt
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Thank you for your reply. Unfortunately it was not of much help, as I had apparently not described the simulation well enough. I had omitted the
information as I was hoping for a general relation, but here goes.
The simulation is not of a reaction, it was simply a simulation of water molecules, with an initial configuration that I've gradually relaxed through
equilibration. This was a microcanonical ensemble (i.e. fixed NVE), where I have also held the temperature constant by velocity scaling followed by
the Nosé-Hoover method in the second equilibration step (which is the one of relevance to this question).
This is what I have been told: "Remember that the Hamiltonian is the total energy of the system including the 'heat bath' ".
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watson.fawkes
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| Quote: Originally posted by aplrt | | This is what I have been told: "Remember that the Hamiltonian is the total energy of the system including the 'heat bath' ". |
Then you'll have to explain what's going on, because it makes no mathematical sense. It might be something in the software itself.
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aplrt
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I assume it has to do with the software - this is actually the only 'definition' of the Hamiltonian mentioned in the instructions. If we say like
this, ignoring what they have named it, the Hamiltonian in the software is the "total energy of all particles and the heat bath". I have been asked to
describe how the Hamiltonian is behaving during equilibration, I can see that it's decreasing and would like to know why (taking into account that the
intramolecular energy is increasing). In the very vague explanation I was given, the atoms are initially vibrating with a low energy. The
'temperature' of the vibration increases due to the input from the kinetic energy, resulting in that other degrees of freedom in the system should
decrease in temperature over time in order to maintain constant energy. I'm not even sure if this explanation is accurate, but does it make sense ?
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watson.fawkes
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| Quote: Originally posted by aplrt | | I assume it has to do with the software - this is actually the only 'definition' of the Hamiltonian mentioned in the instructions. If we say like
this, ignoring what they have named it, the Hamiltonian in the software is the "total energy of all particles and the heat bath".
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I can't really help you. There is no such thing as the total energy of a heat bath. I don't know what this
software is actually doing, nor what they think they mean by their Alice in Humptyland terms.
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