Clarification on converting GPUMD heat current (eV^(3/2) amu^(-1/2)) to physical heat flux (W/m²) in NEMD

[ashwanikushwaha1210-dev]

Title: Clarification on converting GPUMD heat current (eV^(3/2) amu^(-1/2)) to physical heat flux (W/m²) in NEMD

Hi everyone,

I am performing NEMD simulations using GPUMD on a layered thermoelectric system (Bi₂Te₃/Sb₂Te₃) with spatial binning (13 bins along the transport direction). I am using outputs where the heat current components (JP and JK) are reported in units of:

eV^(3/2) amu^(-1/2)

I would like to confirm the correct procedure to convert these quantities into physical heat flux (W/m²).

---

My understanding so far

From GPUMD output:

• The heat current is given per bin as:

  • JPx, JPy, JPz (potential contribution)
  • JKx, JKy, JKz (kinetic contribution)

• Total heat current per bin:

  Jx = JPx + JKx

• Units:

  eV^(3/2) amu^(-1/2), which corresponds to:

  energy × velocity

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Conversion approach I am using

1. Convert to SI units:

   1 eV = 1.602 × 10⁻¹⁹ J
   1 amu = 1.6605 × 10⁻²⁷ kg

   This gives:

   √(eV/amu) ≈ 9.79 × 10³ m/s

   So:

   1 (eV^(3/2) amu^(-1/2)) ≈ 1.57 × 10⁻¹⁵ W

---

2. Convert to heat flux:

   J (W/m²) = (J_GPUMD × 1.57 × 10⁻¹⁵) / V

   where V is the bin volume in m³.

   In my case:

   V ≈ 2.52 × 10⁻²⁵ m³ (per bin)

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⚠️ Issue I am facing

I computed heat flux using two different approaches:

(1) Energy exchange method (Ein / Eout)

Using:

Q = (Ein − Eout) / 2

and converting to W/m² using cross-sectional area, I get:

👉 Heat flux ≈ 4.72 × 10⁸ W/m²

This seems physically reasonable.

---

(2) Heat current method (JP + JK)

From bin-averaged values (steady state, bins 4–10):

⟨Jx⟩ ≈ −5.179633 (eV^(3/2) amu^(-1/2))

After conversion using volume normalization:

👉 Heat flux ≈ −1.62 × 10⁻⁴ W/m²

---

❗ Problem

There is a huge discrepancy (~10¹² difference) between the two methods:

• Ein/Eout → ~10⁸ W/m²
• JP + JK → ~10⁻⁴ W/m²

---

Questions / Clarifications

1. Is dividing by bin volume the correct normalization to obtain heat flux (W/m²) from JP + JK?

2. Should the normalization instead use cross-sectional area rather than volume?

3. For NEMD simulations in GPUMD, is it recommended to:

   • use JP + JK (microscopic heat current), or
   • rely on Ein/Eout (energy exchange method)?

4. When using spatial bins, is averaging over central bins (e.g., bins 4–10) the correct approach?

5. Could this discrepancy indicate that JP + JK is not directly comparable to macroscopic heat flux in NEMD, or that an additional normalization factor is missing?

---

Goal

Ultimately, I want to compute thermal conductivity using:

κ = J / (dT/dx)

So I want to ensure that the heat flux J is computed correctly and consistently with GPUMD conventions.

---

Any clarification or guidance would be greatly appreciated.

Thanks in advance!

plot2_thermostat_energies.pdf
plot1_temperature_profile.pdf

[brucefan1983]

The results do not look normal to me. jk should be essentially zero in solids.

[ashwani12-cmd]

This is my run.in file

potential ./nep_y2026_m02_d13_h00_m46_s49_generation300000.txt 0

AUTO-SIZED NEMD SETUP

Material : BiSbTe20

Transport : X

Supercell : 228 x 12 x 3

N_BINS : 11

Sb fraction : 20%

Seed : 1

Source group: 1

Sink group : 13

SHC group : 7

L_transport : 100.10 nm

Atoms : 123120

minimize fire 1.0e-5 100000 1
ensemble nve
time_step 0
dump_xyz -1 0 1 relaxed.xyz
run 1

velocity 300
time_step 1
ensemble npt_ber 300 300 100 0.0 0.0 0.0 0.0 0.0 0.0 56.6 56.6 10.8 8.4 8.4 20.8 1000
dump_thermo 1000
run 1000000

fix 0
ensemble heat_lan 300 100 20 1 13
compute 0 10 100 temperature jp jk
compute_shc 2 250 0 1000 50.0 group 0 7
dump_thermo 1000
run 5000000

The material is Sb2Te3.

Link for compute.out file

https://drive.google.com/file/d/13XoI-SlQHNZ-gicRnRbx-2yYfXalfMYK/view?usp=sharing

[ashwani12-cmd]

[brucefan1983]

I am not sure where the problem is, but you can use dump_xyz to check the trajectory to see if it is normal. Also check the temperature and pressure/box. I think you don't need the flexible cell NPT in the equilibration stage.