Forces in BOMD calculations

[Dmitrii Nikolaev]

Dear collegues,

I am running the Born-Oppenheimer molecular dynamics, and I notice that the sum of the forces on all atoms of my molecule is non-zero. However, as I understand for the NVE ensemble the total force should be zero? What is the reason for this force? 

Thank you in advance,

Dmitrii

[Thomas Kühne]

Dear Dmitrii, 

in principle you are obviously right. However, due to the fact that in a numerical calculation the 

number of particles is finite and typically small, the sum of all forces is fluctuating. If everything 

else is correct, the effect is expected to vanish with increasing system size. You can fix the center 

of mass by setting COMVEL_TOL to 0, but in general this is should not be necessary and if so 

likely points to a source of systematic bias in your calculations. 

Greetings, 

Thomas

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==============================

Thomas D. Kühne

Dynamics of Condensed Matter

Chair of Theoretical Chemistry

University of Paderborn

Warburger Str. 100

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Germany

tdku...@mail.upb.de

+49/(0)5251/60-5726

[Lucas Lodeiro]

Hi,

In the case of BO framework, the forces calculated with Hellmann-Feynman theorem have some instabilities, due to the theorem requires that <d\phi|\phi> = 0 = <\phi|d\phi>. In most cases this terms are very small, but requires a very accurate convergence of energy and the wfc to ensure a completely negligible value.

Then the real forces are equal <dH> + E<d\phi|\phi>.

if <d\phi|\phi> is not negligible, you are avoiding a part of the real forces and the summation  of them must not be 0.

This in the theory. The implementation of this, uses no infinite numbers and some noise are in the numerical evaluation, another thing to no cancel completely.

The important thing with this issue is if you are using and NVE system, the total energy (kinetic + potential) must be the conserved quantity, not in a perfect numeral way, but the oscillations must be small and without a biased direction, if the average (along the fluctuations) total energy is incrementing or decreasing you have problems in the forces application, either in the force calculation (more accurate scf cycles) or a too big time step integrator.

--

[Dmitrii Nikolaev]

Thank you very much! 

My energy is not shifting, and the forces are fluctuating around 20 kcal/(mol*A) -- 0.016 Ht/Bohr. Is it ok? 

On Thursday, April 9, 2020 at 3:06:17 AM UTC+3, Lucas Lodeiro wrote:

Hi,

In the case of BO framework, the forces calculated with Hellmann-Feynman theorem have some instabilities, due to the theorem requires that <d\phi|\phi> = 0 = <\phi|d\phi>. In most cases this terms are very small, but requires a very accurate convergence of energy and the wfc to ensure a completely negligible value.

Then the real forces are equal <dH> + E<d\phi|\phi>.

if <d\phi|\phi> is not negligible, you are avoiding a part of the real forces and the summation  of them must not be 0.

This in the theory. The implementation of this, uses no infinite numbers and some noise are in the numerical evaluation, another thing to no cancel completely.

The important thing with this issue is if you are using and NVE system, the total energy (kinetic + potential) must be the conserved quantity, not in a perfect numeral way, but the oscillations must be small and without a biased direction, if the average (along the fluctuations) total energy is incrementing or decreasing you have problems in the forces application, either in the force calculation (more accurate scf cycles) or a too big time step integrator.

El mié., 8 abr. 2020 a las 13:59, Dmitrii Nikolaev (<dmitrii....@gmail.com>) escribió:

Dear collegues,

I am running the Born-Oppenheimer molecular dynamics, and I notice that the sum of the forces on all atoms of my molecule is non-zero. However, as I understand for the NVE ensemble the total force should be zero? What is the reason for this force? 

Thank you in advance,

Dmitrii

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[Lucas Lodeiro]

I do not know about the forces number. I general I see the total energy fluctuation per atom, and compare this quantity with the convergence criteria related with cutoff. They would be similar.

Also, the fluctuations are related with the number of atoms in your simulation. A fluctuation of 0.02 Ry in a H2 molecule is not negligible, but this fluctuation in a 2000 atoms cell is very small (per atom this will be: 0.01 Ry/atom and 0.00001Ry/atom).

About the non zero total forces, I check the quality of it seeing the center of mass (COM) coordinates and their movement, if the forces all 100% ok, the COM does not move, and little movement is due to non vanishing total forces.

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[Vladimir Rybkin]

Dear all!

I general remark: the forces in CP2K are NOT the Hellmann-Feynman ones. That stems from the fact that CP2K uses position-dependent basis functions (Gaussians). So, the Pulay force is never zero even in theory as soon is basis is incomplete (it is never complete in mathimatical sense with Guassians).

Yours,

Vladimir

четверг, 9 апреля 2020 г., 14:39:33 UTC+2 пользователь Dmitrii Nikolaev написал: