Author Topic: Green-Kubo or autocorrelation function of velocity  (Read 5331 times)

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Offline payam

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Green-Kubo or autocorrelation function of velocity
« on: November 7, 2016, 05:11 »
Hello ATK-Classical users,
I have a question and any response will be help.
Is there any tutorial  showing how to calculate thermal conductivity using Green-Kubo method?
Does anyone know how to calculate the autocorrelation function of velocity in a MD run?
Thanks in advance.

Best regards,
Payam

Offline Petr Khomyakov

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Re: Green-Kubo or autocorrelation function of velocity
« Reply #1 on: November 7, 2016, 09:29 »
You may find an example of how to calculate the thermal conductance in ATK at http://docs.quantumwise.com/tutorials/thermoelectrics_cnt_isotope/thermoelectrics_cnt_isotope.html.

Regarding the velocity autocorrelation function, have a look at the usage example in the reference manual, http://docs.quantumwise.com/manuals/Types/VelocityAutocorrelation/VelocityAutocorrelation.html.

Offline payam

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Re: Green-Kubo or autocorrelation function of velocity
« Reply #2 on: November 7, 2016, 18:18 »
Thank you Petr.
As I noticed, the calculation of thermal conductance in that example is based on NEGF and not Green-Kubo method.
velocity autocorrelation function is available through menu of MD analyzer.
Do you know how to calculate the heat capacity after a MD simulation? Do you know an example by ATK?
Thanks again.

Best regards,
Payam

Offline Petr Khomyakov

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Re: Green-Kubo or autocorrelation function of velocity
« Reply #3 on: November 7, 2016, 20:57 »
To calculate the heat capacity from the MD simulations, you may adopt, for example, the procedure discussed in PHYSICAL REVIEW B 72, 132204 2005. It might also be useful to take a look at the following post http://quantumwise.com/forum/index.php?topic=3359.msg15378#msg15378.

Offline payam

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Re: Green-Kubo or autocorrelation function of velocity
« Reply #4 on: November 8, 2016, 15:24 »
Thank you Petr for your response.
BR,
Payam

Offline Julian Schneider

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Re: Green-Kubo or autocorrelation function of velocity
« Reply #5 on: November 11, 2016, 15:06 »
Just as an additional comment, we currently don't support calculating thermal conductivity via the Green-Kubo approach, because we don't have the atom resolved potential energy implemented. That might be something to be included in the next release. As an alternative to NEGF, you can use Non-equilibrium MD simulations, often called the "direct method", see http://docs.quantumwise.com/tutorials/interfacial_thermal_conductance/interfacial_thermal_conductance.html.

The constant volume heat capacity can be calculated from MD, assuming that the system behaves purely harmonic, by calculating the vibrational density of states from the VelocityAutocorrelation MD analysis object (http://docs.quantumwise.com/manuals/Types/VelocityAutocorrelation/VelocityAutocorrelation.html#velocityautocorrelation-c), and then integrating over the VDOS to get the heat capacity as shown in the attached script.
To get reliable results, it is important that you carefully equilibrate the system (using NVT Nose Hoover) and that you run the actual MD simulation in NVE with a small log interval of around 10 and I would recommend a smaller time step than normal, e.g. 0.5 fs. You typically don't need to run the simulation very long, 40 000 steps is normally enough. Check in the MD-Analyzer that the vibrational density of states looks reasonable (use Velocity Autocorrelation and the "Show vibrational DOS" checkbox).
For a non-harmonic system, you can use the approach in the paper, mentioned  by Petr, by running an MD simulation and very slowly increasing the temperature. The slope of the energy-temperature curve will give you the heat capacity.
« Last Edit: November 11, 2016, 15:22 by Julian Schneider »

Offline payam

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Re: Green-Kubo or autocorrelation function of velocity
« Reply #6 on: November 16, 2016, 18:57 »
Thank you very much Julian for your informative response.

Best regards,
Payam