# partial force in virial

Hello everyone

According to the reference of compute pressure command (Thompson et al. 2009), the virial term could be calculated with eq.25 (the atom form:

W=sum_n sum_i(r_in.F’_in)[i=1:N]
in which the “F’in is not the total force on an atom but rather the partial force”. But, I could not see in the corresponding section of manual mentioning that the forces are “partial”. (W=sum_i(r_i.f_i) [i=1:N’)]

could anyone explain this discrepancy for me please?

best regards

Hello everyone

According to the reference of compute pressure command (Thompson et al.
2009), the virial term could be calculated with eq.25 (the atom form:
W=sum_n sum_i(r_in.F'_in)[i=1:N]
in which the "F'in is not the total force on an atom but rather the
partial force". But, I could not see in the corresponding section of manual
mentioning that the forces are "partial". (W=sum_i(r_i.f_i) [i=1:N')]

​the LAMMPS manual has over 2000 pages. would you mind being a little more
precise than "the corresponding section"?​

​axel.​

Hi

Sorry for that. I mean the manual section for compute pressure command (http://lammps.sandia.gov/doc/compute_pressure.html) where it is written:

P=NkBT/V+sum_i_N’(r_i.f_i)

“where r_i and f_i are the position and force vector of atom i”. It seems that fi is the “total force” on atom i.

while in the reference paper (Thompson, Plimpton, Mattson, J Chem Phys, 131, 154107 (2009)) it is told:
P=NkBT/V+/3V (1)

and
W(rN)=sum_n(sum_i_1_N(r_in.F’in)) (25)

"F’in is not the total force on an atom but rather the partial force ".

Is the lammps method of calculating pressure according to eq.25? If yes, why the forces are total in the manual and partial in the paper?
thanks for any help to solve my confusion.

Regards

Hi

Sorry for that. I mean the manual section for compute pressure command (
LAMMPS Molecular Dynamics Simulator) where it is written:

P=NkBT/V+sum_i_N'(r_i.f_i)
"where r_i and f_i are the position and *force vector of atom i*". It
seems that fi is the "total force" on atom i.

while in the reference paper (Thompson, Plimpton, Mattson, J Chem Phys,
131, 154107 (2009)) it is told:
P=NkBT/V+<W>/3V (1)
and
W(rN)=sum_n(sum_i_1_N(r_in.F'in)) (25)
"*F'in is not the total force* on an atom but rather the partial force ".

Is the lammps method of calculating pressure according to eq.25? If yes,
why the forces are total in the manual and partial in the paper?
thanks for any help to solve my confusion.

​both are correct and LAMMPS can do both. which is used depends on the
individual potentials in use.
for "simple" and pairwise additive potentials, and when you only want the
global stress tensor/pressure, the sums over the individual contributions
reduce into F dot r for the summed force.
for per-atom stress/pressure and not-so-simple potentials, individual
contributions are tallied.

axel.