diff --git a/src/grogu_magn/magnetism.py b/src/grogu_magn/magnetism.py
index 38a3e14..289cc55 100644
--- a/src/grogu_magn/magnetism.py
+++ b/src/grogu_magn/magnetism.py
@@ -70,7 +70,10 @@ def calculate_exchange_tensor(pair):
     D[2] = np.mean([energies[2, 1], -energies[2, 2]])
 
     J_iso = np.trace(J) / 3
-    J_S = (J - J_iso * np.eye(3)).flatten()
+    # based on the grogu output pdf
+    # traceless symmetric exchange matrix:
+    # Jxx, Jyy, Jxy, Jxz, Jyz
+    J_S = np.array([J[0, 0] - J_iso, J[1, 1] - J_iso, J[0, 1], J[0, 2], J[1, 2]])
 
     return J_iso, J_S, D, J