Comparison between set initial temperature and temperature calculated from velocities

[mto‏]

Dear cp2k users,

I wanted to conduct a comparison and performed ab initio molecular dynamics (MD) simulations with an imposed initial temperature of 300 K. I then calculated the temperature from the velocities at the 0th step, but this value was 297K, which does not match with the temperature I set. I calculated the latter temperature (297K) from '0step_velocities.xyz' which is attached on this message. Both of them must be the same because the 0th step velocities are determined by the initial temperature. (The equation I used: 1/2m*v^2 = 3/2kb*T )

Does anyone know why there is a difference in temperatures? 

Thank you in advance,

Matsuo

[Marcella Iannuzzi‏]

Hi 

Are you sure that you considered the correct number of degrees of freedom?

Regards

Marcella

[松尾拓郎‏]

Hi Marcella,

Thank you for your response.

Yes, I believe I have.

I calculated the temperature of the system by using the following method.

1. Temperatures of each atom at 0th step were calculated with 1/2*m*v^2 = 3/2*kb*T, here the value of 'm' is mass in atomic mass units (amu).
   mass: 28.0855 (Si), 15.9994 (O), 12.0107 (C)
   amu = 1.660538782E-27 kg
   mSi = amu*28.0855 kg, mO = amu*15.9994 kg, mC = amu*12.0107 kg
   v^2 = (vx^2 + vy^2 + vz^2)*10^10 (m/s)^2
   kb = 1.3806504E-23 m^2*kg*s^-2*K^-1
   
2. 0th step temperature (T_all) is calculated 
   I have 32 Si, 64 O and 4 C, so I calculated the temperature of each individual atom and determined the average T
   T_Si_k = mSi*v^2/(3*kb)
   T_O_k =  mO*v^2/(3*kb)
   T_C_k =  mC*v^2/(3*kb) (k represents the ID of the atom.)
   T_all = (T_Si_1 + T_Si_2 + ... +T_Si_32 + T_O_1 + T_O_2 + ... + T_O_64 + T_C_1 + T_C_2 + ... T_C_4) / (32 + 64 + 4)

Is this what you were referring to when you suggested looking at the degrees of freedom?

Regards

Matsuo

2022年6月10日(金) 1:04 Marcella Iannuzzi <marci...@gmail.com>:

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[Marcella Iannuzzi‏]

What about the translational and rotational degrees of freedom?

Kind regards

Marcella

[松尾拓郎‏]

Marcella,

Are you referring to the cp2k section ROTATIONAL_INFO ?

If so, I was afraid I didn't consider the section.

Here is my simulation output on calculation of degrees of freedom.

 DOF| Calculation of degrees of freedom
 DOF| Number of atoms                                                        100
 DOF| Number of intramolecular constraints                           0
 DOF| Number of intermolecular constraints                           0
 DOF| Invariants (translations + rotations)                               3
 DOF| Degrees of freedom                                                     297

The number of the translational and rotational degrees of freedom seem to be  3×(100-1) = 297, 0×(100-0) = 0.

I calculated the temperature considering the number of translational degrees of freedom (3) '1/2*m*v^2 = 3/2*kb*T'.

However I didn't consider the number of rotational degrees of freedom because it seemed to be 0.

Kind regards

Matsuo

2022年6月11日(土) 16:21 Marcella Iannuzzi <marci...@gmail.com>:

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[Marcella Iannuzzi‏]

No need to consider any cp2k section

I suppose that to calculate the temperature you summed up the kinetic energies  and then divided by the number of degrees of freedom. 

The question is whether you divided by the correct number of DoF, i.e., 297 according to the output you sent. 

Regards

Marcella

[松尾拓郎‏]

Hi Marcella,

Thank you for your reply.

I understand your intention of dividing by the correct number of DoF.

I found that when I calculated with (T_Si_1 + T_Si_2 + ... +T_Si_32 + T_O_1 + T_O_2 + ... + T_O_64 + T_C_1 + T_C_2 + ... T_C_4)/100 times the ratio of DoF (300/297), I was able to get the same temperature as the cp2k output.

I didn't consider the translational DoF of the cell which is 3.
It became clear that the number 300 was DoF including the translational DoF of the cell and the number 297 = 300 - 3.

Thank you very much for your help!

Kind regards
Matsuo

2022年6月13日(月) 16:05 Marcella Iannuzzi <marci...@gmail.com>:

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