What equation does HOOMD-blue use to calculate the pressure tensor for rigid body system?

[miaoblah]

Recently, I discovered that computing the pressure tensor in rigid‐body molecular dynamics is a subtle problem. In my literature search, I found the paper Pressure in Rigid Body Molecular Dynamics (DOI: 10.1016/j.commatsci.2019.109430), which derives only the isotropic pressure. However, it is essential to obtain the full pressure tensor for me, including its off‐diagonal components.

Could you please clarify the exact formula you employ to compute each component of the pressure tensor in a rigid‐body system?

[joaander]

You can find the implementation of the correction term here:

hoomd-blue/hoomd/md/ForceComposite.cc

Lines 823 to 829 in 29e7820

	// subtract intra-body virial prt
	h_virial.data[0 * m_virial_pitch + central_idx] += virialxx - f.x * dr_space.x;
	h_virial.data[1 * m_virial_pitch + central_idx] += virialxy - f.x * dr_space.y;
	h_virial.data[2 * m_virial_pitch + central_idx] += virialxz - f.x * dr_space.z;
	h_virial.data[3 * m_virial_pitch + central_idx] += virialyy - f.y * dr_space.y;
	h_virial.data[4 * m_virial_pitch + central_idx] += virialyz - f.y * dr_space.z;
	h_virial.data[5 * m_virial_pitch + central_idx] += virialzz - f.z * dr_space.z;

It is exactly equation 24 from that paper, except it preserves the full tensor.

[miaoblah]

Thank you for the explanation—the code is exactly the part that confused me. If you write Eq. (24) as tensor form, it really is the tensor product of
1. the vector from the rigid‐body centre to each constituent site, and
2. the force on that site.
Since those two vectors aren’t generally parallel, the resulting matrix is not symmetric. However, I only found calculation of “upper‐triangle” components (xx, xy, xz, yy, yz, zz). I think I might make mistakes somewhere.