diff --git a/test.ipynb b/test.ipynb
index 13cd8fe..8500f99 100644
--- a/test.ipynb
+++ b/test.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -11,23 +11,16 @@
        "'0.14.3'"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "import os\n",
     "from tqdm import tqdm\n",
     "from sys import getsizeof\n",
     "from timeit import default_timer as timer\n",
     "\n",
-    "os.environ[\"OMP_NUM_THREADS\"] = \"1\"  # export OMP_NUM_THREADS=4\n",
-    "os.environ[\"OPENBLAS_NUM_THREADS\"] = \"1\"  # export OPENBLAS_NUM_THREADS=4\n",
-    "os.environ[\"MKL_NUM_THREADS\"] = \"1\"  # export MKL_NUM_THREADS=6\n",
-    "os.environ[\"VECLIB_MAXIMUM_THREADS\"] = \"1\"  # export VECLIB_MAXIMUM_THREADS=4\n",
-    "os.environ[\"NUMEXPR_NUM_THREADS\"] = \"1\"  # export NUMEXPR_NUM_THREADS=6\n",
-    "\n",
     "import numpy as np\n",
     "import sisl\n",
     "from src.grogu_magn.useful import *\n",
@@ -47,18 +40,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "dat = sisl.io.siesta.eigSileSiesta(\n",
-    "    \"/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.EIG\"\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -67,18 +49,21 @@
        "-12.806878959999999"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
+    "dat = sisl.io.siesta.eigSileSiesta(\n",
+    "    \"/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.EIG\"\n",
+    ")\n",
     "dat.read_data().min()"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": null,
    "metadata": {},
    "outputs": [
     {
@@ -87,9 +72,9 @@
      "text": [
       "================================================================================================================================================================\n",
       "Input file: \n",
-      "Not yet specified.\n",
+      "/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf\n",
       "Output file: \n",
-      "test.pickle\n",
+      "Fe3GeTe2.pickle\n",
       "Number of nodes in the parallel cluster:  1\n",
       "================================================================================================================================================================\n",
       "Cell [Ang]: \n",
@@ -105,26 +90,26 @@
       "[0 0 1]  --»  [array([1, 0, 0]), array([0, 1, 0])]\n",
       "================================================================================================================================================================\n",
       "Parameters for the contour integral:\n",
-      "Number of k points:  20\n",
+      "Number of k points:  100\n",
       "k point directions:  xy\n",
       "Ebot:  -13\n",
-      "Eset:  600\n",
+      "Eset:  60\n",
       "Esetp:  10000\n",
       "================================================================================================================================================================\n",
-      "Setup done. Elapsed time: 198.668371833 s\n",
+      "Setup done. Elapsed time: 291.062782833 s\n",
       "================================================================================================================================================================\n"
      ]
     }
    ],
    "source": [
-    "# this cell mimicks an input file\n",
-    "fdf = sisl.get_sile(\n",
+    "################################################################################\n",
+    "#################################### INPUT #####################################\n",
+    "################################################################################\n",
+    "path = (\n",
     "    \"/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf\"\n",
-    ")  # ./Jij_for_Marci_6p45ang/CrBr.fdf\n",
+    ")\n",
+    "outfile = \"Fe3GeTe2\"\n",
     "\n",
-    "outfile = \"test\"\n",
-    "if not outfile.endswith(\".pickle\"):\n",
-    "    outfile += \".pickle\"\n",
     "# this information needs to be given at the input!!\n",
     "scf_xcf_orientation = np.array([0, 0, 1])  # z\n",
     "# list of reference directions for around which we calculate the derivatives\n",
@@ -136,52 +121,38 @@
     "    dict(o=np.array([0, 1, 0]), vw=[np.array([1, 0, 0]), np.array([0, 0, 1])]),\n",
     "    dict(o=np.array([0, 0, 1]), vw=[np.array([1, 0, 0]), np.array([0, 1, 0])]),\n",
     "]\n",
-    "\n",
-    "\n",
-    "# human readable definition of magnetic entities ./lat3_791/Fe3GeTe2.fdf\n",
     "magnetic_entities = [\n",
     "    dict(atom=3, l=2),\n",
     "    dict(atom=4, l=2),\n",
     "    dict(atom=5, l=2),\n",
     "]\n",
-    "# pair information ./lat3_791/Fe3GeTe2.fdf\n",
-    "pairs = [\n",
-    "    # isotropic should be -82 meV\n",
-    "    dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])),\n",
-    "    dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),\n",
-    "    dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),\n",
-    "]\n",
-    "\n",
-    "\"\"\"\n",
-    "# human readable definition of magnetic entities ./Jij_for_Marci_6p45ang/CrBr.fdf\n",
-    "magnetic_entities = [\n",
-    "    dict(atom=0, l=2),\n",
-    "    dict(atom=1, l=2),\n",
-    "    dict(atom=2, l=2),\n",
-    "]\n",
-    "# pair information ./Jij_for_Marci_6p45ang/CrBr.fdf\n",
     "pairs = [\n",
     "    dict(ai=0, aj=1, Ruc=np.array([0, 0, 0])),\n",
     "    dict(ai=0, aj=2, Ruc=np.array([0, 0, 0])),\n",
     "    dict(ai=1, aj=2, Ruc=np.array([0, 0, 0])),\n",
     "    dict(ai=0, aj=1, Ruc=np.array([1, 0, 0])),\n",
     "    dict(ai=0, aj=2, Ruc=np.array([1, 0, 0])),\n",
+    "    dict(ai=1, aj=2, Ruc=np.array([1, 0, 0])),\n",
     "    dict(ai=0, aj=1, Ruc=np.array([-1, 0, 0])),\n",
     "    dict(ai=0, aj=2, Ruc=np.array([-1, 0, 0])),\n",
+    "    dict(ai=1, aj=2, Ruc=np.array([-1, 0, 0])),\n",
     "    dict(ai=0, aj=1, Ruc=np.array([0, 1, 0])),\n",
     "    dict(ai=0, aj=2, Ruc=np.array([0, 1, 0])),\n",
-    "    dict(ai=0, aj=1, Ruc=np.array([0, 1, 0])),\n",
-    "    dict(ai=0, aj=2, Ruc=np.array([0, 1, 0])),\n",
+    "    dict(ai=1, aj=2, Ruc=np.array([0, 1, 0])),\n",
+    "    dict(ai=0, aj=1, Ruc=np.array([0, -1, 0])),\n",
+    "    dict(ai=0, aj=2, Ruc=np.array([0, -1, 0])),\n",
+    "    dict(ai=1, aj=2, Ruc=np.array([0, -1, 0])),\n",
     "]\n",
-    "\"\"\"\n",
     "\n",
     "# Brilloun zone sampling and Green function contour integral\n",
-    "kset = 20\n",
+    "kset = 10\n",
     "kdirs = \"xy\"\n",
     "ebot = -13\n",
-    "eset = 600\n",
+    "eset = 60\n",
     "esetp = 10000\n",
-    "\n",
+    "################################################################################\n",
+    "#################################### INPUT #####################################\n",
+    "################################################################################\n",
     "\n",
     "# MPI parameters\n",
     "comm = MPI.COMM_WORLD\n",
@@ -189,8 +160,12 @@
     "rank = comm.Get_rank()\n",
     "root_node = 0\n",
     "\n",
+    "# rename outfile\n",
+    "if not outfile.endswith(\".pickle\"):\n",
+    "    outfile += \".pickle\"\n",
+    "\n",
     "simulation_parameters = dict(\n",
-    "    path=\"Not yet specified.\",\n",
+    "    path=path,\n",
     "    outpath=outfile,\n",
     "    scf_xcf_orientation=scf_xcf_orientation,\n",
     "    ref_xcf_orientations=ref_xcf_orientations,\n",
@@ -203,6 +178,8 @@
     ")\n",
     "\n",
     "# digestion of the input\n",
+    "# read sile\n",
+    "fdf = sisl.get_sile(path)\n",
     "# read in hamiltonian\n",
     "dh = fdf.read_hamiltonian()\n",
     "simulation_parameters[\"cell\"] = fdf.read_geometry().cell\n",
@@ -221,7 +198,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
@@ -294,14 +271,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 24,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Hamiltonian and exchange field rotated. Elapsed time: 199.591100666 s\n",
+      "Hamiltonian and exchange field rotated. Elapsed time: 292.32726 s\n",
       "================================================================================================================================================================\n"
      ]
     }
@@ -403,14 +380,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Site and pair dictionaries created. Elapsed time: 199.638437125 s\n",
+      "Site and pair dictionaries created. Elapsed time: 292.347581791 s\n",
       "================================================================================================================================================================\n"
      ]
     }
@@ -518,21 +495,22 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 26,
    "metadata": {},
    "outputs": [
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "k loop:   0%|          | 0/400 [00:00<?, ?it/s]"
+      "k loop:   0%|          | 0/100 [00:37<?, ?it/s]\n",
+      "k loop:   0%|          | 0/10000 [00:00<?, ?it/s]"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "k set created. Elapsed time: 199.64839675 s\n",
+      "k set created. Elapsed time: 292.813134416 s\n",
       "================================================================================================================================================================\n"
      ]
     }
@@ -553,14 +531,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Rotations done perpendicular to quantization axis. Elapsed time: 199.979076 s\n",
+      "Rotations done perpendicular to quantization axis. Elapsed time: 135.307556041 s\n",
       "================================================================================================================================================================\n"
      ]
     }
@@ -616,7 +594,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -624,15 +602,15 @@
      "output_type": "stream",
      "text": [
       "Starting matrix inversions\n",
-      "Total number of k points: 400\n",
-      "Number of energy samples per k point: 600\n",
+      "Total number of k points: 100\n",
+      "Number of energy samples per k point: 60\n",
       "Total number of directions: 3\n",
-      "Total number of matrix inversions: 720000\n",
+      "Total number of matrix inversions: 18000\n",
       "The shape of the Hamiltonian and the Greens function is 84x84=7056\n",
       "Memory taken by a single Hamiltonian is: 0.015625 KB\n",
       "Expected memory usage per matrix inversion: 0.5 KB\n",
-      "Expected memory usage per k point for parallel inversion: 900.0 KB\n",
-      "Expected memory usage on root node: 351.5625 MB\n",
+      "Expected memory usage per k point for parallel inversion: 90.0 KB\n",
+      "Expected memory usage on root node: 8.7890625 MB\n",
       "================================================================================================================================================================\n"
      ]
     },
@@ -640,14 +618,14 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "k loop: 100%|██████████| 400/400 [2:12:33<00:00, 19.88s/it]    "
+      "k loop: 100%|██████████| 100/100 [00:35<00:00,  2.82it/s]"
      ]
     },
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Calculated Greens functions. Elapsed time: 1375.51451525 s\n",
+      "Calculated Greens functions. Elapsed time: 170.554620458 s\n",
       "================================================================================================================================================================\n"
      ]
     },
@@ -751,7 +729,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 10,
    "metadata": {},
    "outputs": [
     {
@@ -764,9 +742,9 @@
       "##################################################################### GROGU OUTPUT #############################################################################\n",
       "================================================================================================================================================================\n",
       "Input file: \n",
-      "Not yet specified.\n",
+      "/Users/danielpozsar/Downloads/nojij/Fe3GeTe2/monolayer/soc/lat3_791/Fe3GeTe2.fdf\n",
       "Output file: \n",
-      "test.pickle\n",
+      "Fe3GeTe2.pickle\n",
       "Number of nodes in the parallel cluster:  1\n",
       "================================================================================================================================================================\n",
       "Cell [Ang]: \n",
@@ -782,10 +760,10 @@
       "[0 0 1]  --»  [array([1, 0, 0]), array([0, 1, 0])]\n",
       "================================================================================================================================================================\n",
       "Parameters for the contour integral:\n",
-      "Number of k points:  20\n",
+      "Number of k points:  10\n",
       "k point directions:  xy\n",
       "Ebot:  -13\n",
-      "Eset:  600\n",
+      "Eset:  60\n",
       "Esetp:  10000\n",
       "================================================================================================================================================================\n",
       "Atomic information: \n",
@@ -804,68 +782,294 @@
       "Magnetic entity1        Magnetic entity2       [i  j  k]       d [Ang]\n",
       "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
       "[3]Fe(2)        [4]Fe(2)        [0 0 0]        d [Ang] Not yet.\n",
-      "Isotropic:  -61.575578560021754\n",
-      "DMI:  [-9.32925576e-01 -6.69311832e-04 -1.27860983e-06]\n",
-      "Symmetric-anisotropy:  [ 3.27134566e-01 -2.18826996e-06  1.11817934e-06 -2.18826996e-06\n",
-      "  2.93842716e+00 -2.84299672e-05  1.11817934e-06 -2.84299672e-05\n",
-      " -3.26556173e+00]\n",
+      "Isotropic:  -37.10407661401345\n",
+      "DMI:  [-3.49488624e-01  2.55729732e-04 -2.76782696e-07]\n",
+      "Symmetric-anisotropy:  [ 1.17610396e+00 -2.12018279e-05 -1.68775278e-06 -2.12018279e-05\n",
+      "  1.26217741e+00 -6.17661677e-07 -1.68775278e-06 -6.17661677e-07\n",
+      " -2.43828137e+00]\n",
+      "J:  [-3.59279727e+01 -2.12018279e-05 -1.68775278e-06 -2.12018279e-05\n",
+      " -3.58418992e+01 -6.17661677e-07 -1.68775278e-06 -6.17661677e-07\n",
+      " -3.95423580e+01]\n",
       "Energies for debugging: \n",
-      "array([[-6.21988435e-02, -9.32897146e-04,  9.32954006e-04,\n",
-      "        -6.14460702e-02],\n",
-      "       [-6.74834371e-02,  6.68193653e-07, -6.70430011e-07,\n",
-      "        -6.66686592e-02],\n",
-      "       [-5.58282326e-02,  9.09660134e-10,  3.46687979e-09,\n",
-      "        -5.58282288e-02]])\n",
+      "array([[-3.94549786e-02, -3.49488006e-04,  3.49489241e-04,\n",
+      "        -3.91968963e-02],\n",
+      "       [-3.96297374e-02, -2.54041979e-07,  2.57417485e-07,\n",
+      "        -3.93690691e-02],\n",
+      "       [-3.24869021e-02,  2.09250452e-08,  2.14786106e-08,\n",
+      "        -3.24868762e-02]])\n",
       "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
-      "array([-0.06666866, -0.05582823, -0.06219884])\n",
+      "array([-0.03936907, -0.0324869 , -0.03945498])\n",
       "Test J_xx = E(y,z) = E(z,y)\n",
-      "-0.06666865917296813 -0.055828228814894104\n",
+      "-0.0393690691402239 -0.03248687617162827\n",
       "\n",
       "[3]Fe(2)        [5]Fe(2)        [0 0 0]        d [Ang] Not yet.\n",
-      "Isotropic:  -60.54611612367399\n",
-      "DMI:  [ 3.78484434e+00 -6.14206310e+00  1.63244853e-04]\n",
-      "Symmetric-anisotropy:  [ 0.20562843  0.07121269 -0.0931207   0.07121269  0.01213322 -0.04251871\n",
-      " -0.0931207  -0.04251871 -0.21776164]\n",
+      "Isotropic:  -65.61259672738467\n",
+      "DMI:  [ 3.55875363e+00 -6.14764701e+00  2.16400609e-05]\n",
+      "Symmetric-anisotropy:  [-0.0859418   0.03699169 -0.10152731  0.03699169 -0.29085831 -0.04979059\n",
+      " -0.10152731 -0.04979059  0.37680011]\n",
+      "J:  [-6.56985385e+01  3.69916940e-02 -1.01527307e-01  3.69916940e-02\n",
+      " -6.59034550e+01 -4.97905921e-02 -1.01527307e-01 -4.97905921e-02\n",
+      " -6.52357966e+01]\n",
       "Energies for debugging: \n",
-      "array([[-6.08734388e-02,  3.82736305e-03, -3.74232563e-03,\n",
-      "        -6.11763023e-02],\n",
-      "       [-6.06543168e-02,  6.23518381e-03, -6.04894240e-03,\n",
-      "        -6.08718006e-02],\n",
-      "       [-5.98916636e-02, -7.10494409e-05, -7.13759306e-05,\n",
-      "        -5.98091748e-02]])\n",
+      "array([[-6.53628254e-02,  3.60854422e-03, -3.50896304e-03,\n",
+      "        -6.58406049e-02],\n",
+      "       [-6.51087679e-02,  6.24917432e-03, -6.04611971e-03,\n",
+      "        -6.54738265e-02],\n",
+      "       [-6.59663052e-02, -3.69700539e-05, -3.70133340e-05,\n",
+      "        -6.59232506e-02]])\n",
       "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
-      "array([-0.0608718 , -0.05989166, -0.06087344])\n",
+      "array([-0.06547383, -0.06596631, -0.06536283])\n",
       "Test J_xx = E(y,z) = E(z,y)\n",
-      "-0.06087180064052234 -0.05980917475210674\n",
+      "-0.06547382649599318 -0.06592325055847004\n",
       "\n",
       "[4]Fe(2)        [5]Fe(2)        [0 0 0]        d [Ang] Not yet.\n",
-      "Isotropic:  -60.54211382677383\n",
-      "DMI:  [-3.79969677e+00  6.15441158e+00  1.64058302e-04]\n",
-      "Symmetric-anisotropy:  [ 0.20695438  0.07120989  0.08986466  0.07120989  0.00574537  0.03644448\n",
-      "  0.08986466  0.03644448 -0.21269975]\n",
+      "Isotropic:  -65.61291582804701\n",
+      "DMI:  [-3.57656657e+00  6.16370250e+00  1.72769889e-05]\n",
+      "Symmetric-anisotropy:  [-0.08507475  0.03698984  0.09551784  0.03698984 -0.29208857  0.04348767\n",
+      "  0.09551784  0.04348767  0.37716332]\n",
+      "J:  [-6.56979906e+01  3.69898372e-02  9.55178378e-02  3.69898372e-02\n",
+      " -6.59050044e+01  4.34876702e-02  9.55178378e-02  4.34876702e-02\n",
+      " -6.52357525e+01]\n",
+      "Energies for debugging: \n",
+      "array([[-6.53645241e-02, -3.62005424e-03,  3.53307890e-03,\n",
+      "        -6.58436843e-02],\n",
+      "       [-6.51069809e-02, -6.25922034e-03,  6.06818466e-03,\n",
+      "        -6.54727085e-02],\n",
+      "       [-6.59663245e-02, -3.69725603e-05, -3.70071142e-05,\n",
+      "        -6.59232727e-02]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.06547271, -0.06596632, -0.06536452])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.0654727084967254 -0.0659232726509173\n",
+      "\n",
+      "[3]Fe(2)        [4]Fe(2)        [1 0 0]        d [Ang] Not yet.\n",
+      "Isotropic:  -1.0251660485588765\n",
+      "DMI:  [5.56147340e-01 3.31683446e-04 6.04521494e-06]\n",
+      "Symmetric-anisotropy:  [-9.32615331e-01 -3.84767890e-05  1.75789862e-05 -3.84767890e-05\n",
+      "  3.05904797e-02  3.50989682e-05  1.75789862e-05  3.50989682e-05\n",
+      "  9.02024851e-01]\n",
+      "J:  [-1.95778138e+00 -3.84767890e-05  1.75789862e-05 -3.84767890e-05\n",
+      " -9.94575569e-01  3.50989682e-05  1.75789862e-05  3.50989682e-05\n",
+      " -1.23141198e-01]\n",
+      "Energies for debugging: \n",
+      "array([[ 4.97965048e-04,  5.56112241e-04, -5.56182439e-04,\n",
+      "         8.57005683e-04],\n",
+      "       [-7.44247443e-04, -3.49262432e-07,  3.14104460e-07,\n",
+      "        -8.04849198e-04],\n",
+      "       [-2.84615682e-03,  4.45220039e-08,  3.24315741e-08,\n",
+      "        -3.11071356e-03]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.00080485, -0.00284616,  0.00049797])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.0008048491979002433 -0.003110713560414389\n",
+      "\n",
+      "[3]Fe(2)        [5]Fe(2)        [1 0 0]        d [Ang] Not yet.\n",
+      "Isotropic:  -3.861520076312661\n",
+      "DMI:  [-3.85977504 -2.52369277 -4.22692922]\n",
+      "Symmetric-anisotropy:  [ 0.28001794 -0.01136935  0.01587327 -0.01136935 -0.12598869  0.05899784\n",
+      "  0.01587327  0.05899784 -0.15402925]\n",
+      "J:  [-3.58150213 -0.01136935  0.01587327 -0.01136935 -3.98750877  0.05899784\n",
+      "  0.01587327  0.05899784 -4.01554933]\n",
+      "Energies for debugging: \n",
+      "array([[-0.00437283, -0.00391877,  0.00380078, -0.0044349 ],\n",
+      "       [-0.00365826,  0.00250782, -0.00253957, -0.00358946],\n",
+      "       [-0.00354012, -0.00421556,  0.0042383 , -0.00357354]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.00358946, -0.00354012, -0.00437283])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.003589463621997051 -0.003573540645545602\n",
+      "\n",
+      "[4]Fe(2)        [5]Fe(2)        [1 0 0]        d [Ang] Not yet.\n",
+      "Isotropic:  -4.458620479895359\n",
+      "DMI:  [-4.33083787 -5.9385644  -4.22684544]\n",
+      "Symmetric-anisotropy:  [ 0.07272859 -0.01136933 -0.06310261 -0.01136933  0.39785991 -0.00993305\n",
+      " -0.06310261 -0.00993305 -0.4705885 ]\n",
+      "J:  [-4.38589189 -0.01136933 -0.06310261 -0.01136933 -4.06076057 -0.00993305\n",
+      " -0.06310261 -0.00993305 -4.92920898]\n",
+      "Energies for debugging: \n",
+      "array([[-0.00452019, -0.0043209 ,  0.00434077, -0.0045815 ],\n",
+      "       [-0.00533823,  0.00600167, -0.00587546, -0.00519834],\n",
+      "       [-0.00354003, -0.00421548,  0.00423821, -0.00357345]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.00519834, -0.00354003, -0.00452019])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.005198338074976103 -0.0035734456953877562\n",
+      "\n",
+      "[3]Fe(2)        [4]Fe(2)        [-1  0  0]        d [Ang] Not yet.\n",
+      "Isotropic:  -0.6592236155327585\n",
+      "DMI:  [ 5.59127613e-01  3.58728563e-05 -2.86086982e-06]\n",
+      "Symmetric-anisotropy:  [-6.83716963e-01 -1.51898472e-05  5.53583253e-05 -1.51898472e-05\n",
+      "  1.41032214e-01 -2.42119712e-05  5.53583253e-05 -2.42119712e-05\n",
+      "  5.42684748e-01]\n",
+      "J:  [-1.34294058e+00 -1.51898472e-05  5.53583253e-05 -1.51898472e-05\n",
+      " -5.18191401e-01 -2.42119712e-05  5.53583253e-05 -2.42119712e-05\n",
+      " -1.16538867e-01]\n",
+      "Energies for debugging: \n",
+      "array([[ 5.05733178e-04,  5.59151825e-04, -5.59103401e-04,\n",
+      "         8.53125820e-04],\n",
+      "       [-7.38810912e-04, -9.12311817e-08, -1.94854690e-08,\n",
+      "        -7.84577563e-04],\n",
+      "       [-1.88950862e-03,  1.23289774e-08,  1.80507170e-08,\n",
+      "        -1.90130359e-03]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.00078458, -0.00188951,  0.00050573])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.0007845775626293201 -0.0019013035936397693\n",
+      "\n",
+      "[3]Fe(2)        [5]Fe(2)        [-1  0  0]        d [Ang] Not yet.\n",
+      "Isotropic:  -5.329274876444571\n",
+      "DMI:  [4.32561582 5.93073478 4.17207926]\n",
+      "Symmetric-anisotropy:  [-0.2835386  -0.01607429  0.06200728 -0.01607429 -0.10548755  0.01356167\n",
+      "  0.06200728  0.01356167  0.38902615]\n",
+      "J:  [-5.61281347 -0.01607429  0.06200728 -0.01607429 -5.43476243  0.01356167\n",
+      "  0.06200728  0.01356167 -4.94024873]\n",
+      "Energies for debugging: \n",
+      "array([[-0.00454026,  0.00431205, -0.00433918, -0.00458051],\n",
+      "       [-0.00534024, -0.00599274,  0.00586873, -0.00521439],\n",
+      "       [-0.00628902,  0.00418815, -0.004156  , -0.00601124]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.00521439, -0.00628902, -0.00454026])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.005214386566508839 -0.006011240381521584\n",
+      "\n",
+      "[4]Fe(2)        [5]Fe(2)        [-1  0  0]        d [Ang] Not yet.\n",
+      "Isotropic:  -4.725061132133376\n",
+      "DMI:  [3.8792295  2.52874087 4.17199723]\n",
+      "Symmetric-anisotropy:  [-0.07053775 -0.01607386 -0.01391118 -0.01607386 -0.64500259 -0.04924493\n",
+      " -0.01391118 -0.04924493  0.71554034]\n",
+      "J:  [-4.79559888 -0.01607386 -0.01391118 -0.01607386 -5.37006372 -0.04924493\n",
+      " -0.01391118 -0.04924493 -4.00952079]\n",
+      "Energies for debugging: \n",
+      "array([[-0.00436494,  0.00392847, -0.00382998, -0.00445121],\n",
+      "       [-0.0036541 , -0.00251483,  0.00254265, -0.00358006],\n",
+      "       [-0.00628891,  0.00418807, -0.00415592, -0.00601114]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.00358006, -0.00628891, -0.00436494])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.0035800556270865367 -0.006011142134174699\n",
+      "\n",
+      "[3]Fe(2)        [4]Fe(2)        [0 1 0]        d [Ang] Not yet.\n",
+      "Isotropic:  -1.0496996447984108\n",
+      "DMI:  [-1.97020604e-01  3.93326251e-01 -7.99021874e-06]\n",
+      "Symmetric-anisotropy:  [-0.20217197  0.11453163 -0.03920952  0.11453163 -0.68803384 -0.03787685\n",
+      " -0.03920952 -0.03787685  0.8902058 ]\n",
+      "J:  [-1.25187161  0.11453163 -0.03920952  0.11453163 -1.73773348 -0.03787685\n",
+      " -0.03920952 -0.03787685 -0.15949384]\n",
+      "Energies for debugging: \n",
+      "array([[-0.00047568, -0.00015914,  0.0002349 , -0.00043124],\n",
+      "       [ 0.00015669, -0.00035412,  0.00043254,  0.00040814],\n",
+      "       [-0.00304422, -0.00011454, -0.00011452, -0.00291188]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([ 0.00040814, -0.00304422, -0.00047568])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "0.0004081381450225469 -0.002911881367375347\n",
+      "\n",
+      "[3]Fe(2)        [5]Fe(2)        [0 1 0]        d [Ang] Not yet.\n",
+      "Isotropic:  -1.6451863500909631\n",
+      "DMI:  [ 0.24862131 -0.06829953 -0.0003067 ]\n",
+      "Symmetric-anisotropy:  [-0.17839237 -0.07756692 -0.00999969 -0.07756692 -0.01604251  0.00447534\n",
+      " -0.00999969  0.00447534  0.19443488]\n",
+      "J:  [-1.82357872 -0.07756692 -0.00999969 -0.07756692 -1.66122887  0.00447534\n",
+      " -0.00999969  0.00447534 -1.45075147]\n",
+      "Energies for debugging: \n",
+      "array([[-1.33932568e-03,  2.44145966e-04, -2.53096646e-04,\n",
+      "        -1.15417279e-03],\n",
+      "       [-1.56217725e-03,  7.82992297e-05, -5.82998403e-05,\n",
+      "        -1.38940645e-03],\n",
+      "       [-2.16828494e-03,  7.72602195e-05,  7.78736263e-05,\n",
+      "        -2.25775098e-03]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.00138941, -0.00216828, -0.00133933])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.001389406450933013 -0.0022577509836049143\n",
+      "\n",
+      "[4]Fe(2)        [5]Fe(2)        [0 1 0]        d [Ang] Not yet.\n",
+      "Isotropic:  -1.925466529428356\n",
+      "DMI:  [ 5.35912969e-01 -3.81240204e-01 -3.13285724e-04]\n",
+      "Symmetric-anisotropy:  [-0.05397076 -0.07756762  0.06269827 -0.07756762  0.02186579  0.0475358\n",
+      "  0.06269827  0.0475358   0.03210497]\n",
+      "J:  [-1.97943729 -0.07756762  0.06269827 -0.07756762 -1.90360074  0.0475358\n",
+      "  0.06269827  0.0475358  -1.89336156]\n",
+      "Energies for debugging: \n",
+      "array([[-1.87844392e-03,  4.88377165e-04, -5.83448773e-04,\n",
+      "        -1.63886730e-03],\n",
+      "       [-1.90827920e-03,  3.18541935e-04, -4.43938473e-04,\n",
+      "        -1.70107327e-03],\n",
+      "       [-2.16833418e-03,  7.72543295e-05,  7.78809009e-05,\n",
+      "        -2.25780130e-03]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.00170107, -0.00216833, -0.00187844])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.0017010732733817554 -0.0022578013038436714\n",
+      "\n",
+      "[3]Fe(2)        [4]Fe(2)        [ 0 -1  0]        d [Ang] Not yet.\n",
+      "Isotropic:  -0.68223039919425\n",
+      "DMI:  [-1.89525393e-01  3.91001992e-01  1.58428064e-05]\n",
+      "Symmetric-anisotropy:  [-0.05823148  0.00509602  0.02845826  0.00509602 -0.47544519  0.02675952\n",
+      "  0.02845826  0.02675952  0.53367667]\n",
+      "J:  [-0.74046188  0.00509602  0.02845826  0.00509602 -1.15767559  0.02675952\n",
+      "  0.02845826  0.02675952 -0.14855373]\n",
+      "Energies for debugging: \n",
+      "array([[-4.64649982e-04, -2.16284909e-04,  1.62765877e-04,\n",
+      "        -4.17183456e-04],\n",
+      "       [ 1.67542528e-04, -4.19460248e-04,  3.62543736e-04,\n",
+      "         4.11325899e-04],\n",
+      "       [-1.89816773e-03, -5.08017987e-06, -5.11186549e-06,\n",
+      "        -1.89224965e-03]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([ 0.00041133, -0.00189817, -0.00046465])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "0.0004113258993876115 -0.0018922496544738186\n",
+      "\n",
+      "[3]Fe(2)        [5]Fe(2)        [ 0 -1  0]        d [Ang] Not yet.\n",
+      "Isotropic:  -1.3572259825150497\n",
+      "DMI:  [-5.38839939e-01  3.89611153e-01  8.70420696e-05]\n",
+      "Symmetric-anisotropy:  [ 0.26558549  0.01373365 -0.05609544  0.01373365  0.28408137 -0.04203485\n",
+      " -0.05609544 -0.04203485 -0.54966686]\n",
+      "J:  [-1.09164049  0.01373365 -0.05609544  0.01373365 -1.07314461 -0.04203485\n",
+      " -0.05609544 -0.04203485 -1.90689284]\n",
+      "Energies for debugging: \n",
+      "array([[-1.89490240e-03, -4.96805090e-04,  5.80874787e-04,\n",
+      "        -1.64794979e-03],\n",
+      "       [-1.91888329e-03, -3.33515713e-04,  4.45706592e-04,\n",
+      "        -1.70084474e-03],\n",
+      "       [-4.98339441e-04, -1.36466118e-05, -1.38206959e-05,\n",
+      "        -4.82436238e-04]])\n",
+      "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
+      "array([-0.00170084, -0.00049834, -0.0018949 ])\n",
+      "Test J_xx = E(y,z) = E(z,y)\n",
+      "-0.001700844742244848 -0.00048243623752327756\n",
+      "\n",
+      "[4]Fe(2)        [5]Fe(2)        [ 0 -1  0]        d [Ang] Not yet.\n",
+      "Isotropic:  -1.0714146881035242\n",
+      "DMI:  [-2.39958377e-01  5.49853449e-02  9.53349954e-05]\n",
+      "Symmetric-anisotropy:  [ 0.13849155  0.0137361   0.01047494  0.0137361   0.24743038 -0.00279692\n",
+      "  0.01047494 -0.00279692 -0.38592192]\n",
+      "J:  [-0.93292314  0.0137361   0.01047494  0.0137361  -0.82398431 -0.00279692\n",
+      "  0.01047494 -0.00279692 -1.45733661]\n",
       "Energies for debugging: \n",
-      "array([[-6.08700078e-02, -3.83614125e-03,  3.76325229e-03,\n",
-      "        -6.11810143e-02],\n",
-      "       [-6.06396194e-02, -6.24427624e-03,  6.06454692e-03,\n",
-      "        -6.08610806e-02],\n",
-      "       [-5.98917226e-02, -7.10458351e-05, -7.13739518e-05,\n",
-      "        -5.98092383e-02]])\n",
+      "array([[-1.34446326e-03, -2.37161457e-04,  2.42755297e-04,\n",
+      "        -1.14953629e-03],\n",
+      "       [-1.57020997e-03, -6.54602885e-05,  4.45104012e-05,\n",
+      "        -1.38331981e-03],\n",
+      "       [-4.98432325e-04, -1.36407658e-05, -1.38314358e-05,\n",
+      "        -4.82526480e-04]])\n",
       "J_ii for debugging: (check if this is the same as in calculate_exchange_tensor)\n",
-      "array([-0.06086108, -0.05989172, -0.06087001])\n",
+      "array([-0.00138332, -0.00049843, -0.00134446])\n",
       "Test J_xx = E(y,z) = E(z,y)\n",
-      "-0.06086108060807331 -0.059809238286325714\n",
+      "-0.001383319805189735 -0.0004825264795417615\n",
       "\n",
       "================================================================================================================================================================\n",
       "Runtime information: \n",
-      "Total runtime: 1177.247012041 s\n",
+      "Total runtime: 36.825569167000026 s\n",
       "----------------------------------------------------------------------------------------------------------------------------------------------------------------\n",
-      "Initial setup: 0.12478720800001497 s\n",
-      "Hamiltonian conversion and XC field extraction: 0.923 s\n",
-      "Pair and site datastructure creatrions: 0.047 s\n",
-      "k set cration and distribution: 0.010 s\n",
-      "Rotating XC potential: 0.331 s\n",
-      "Greens function inversion: 1175.535 s\n",
-      "Calculate energies and magnetic components: 0.276 s\n"
+      "Initial setup: 0.20532049999999913 s\n",
+      "Hamiltonian conversion and XC field extraction: 0.972 s\n",
+      "Pair and site datastructure creatrions: 0.027 s\n",
+      "k set cration and distribution: 0.027 s\n",
+      "Rotating XC potential: 0.255 s\n",
+      "Greens function inversion: 35.247 s\n",
+      "Calculate energies and magnetic components: 0.092 s\n"
      ]
     }
    ],
@@ -915,10 +1119,11 @@
     "\n",
     "    # calculate magnetic parameters\n",
     "    for pair in pairs:\n",
-    "        J_iso, J_S, D = calculate_exchange_tensor(pair)\n",
+    "        J_iso, J_S, D, J = calculate_exchange_tensor(pair)\n",
     "        pair[\"J_iso\"] = J_iso * sisl.unit_convert(\"eV\", \"meV\")\n",
     "        pair[\"J_S\"] = J_S * sisl.unit_convert(\"eV\", \"meV\")\n",
     "        pair[\"D\"] = D * sisl.unit_convert(\"eV\", \"meV\")\n",
+    "        pair[\"J\"] = J * sisl.unit_convert(\"eV\", \"meV\")\n",
     "\n",
     "    print(\"Magnetic parameters calculated.\")\n",
     "\n",
@@ -956,7 +1161,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -964,7 +1169,7 @@
      "evalue": "invalid syntax (1445642317.py, line 1)",
      "output_type": "error",
      "traceback": [
-      "\u001b[0;36m  Cell \u001b[0;32mIn[35], line 1\u001b[0;36m\u001b[0m\n\u001b[0;31m    Magnetic entities integrated.\u001b[0m\n\u001b[0m             ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
+      "\u001b[0;36m  Cell \u001b[0;32mIn[11], line 1\u001b[0;36m\u001b[0m\n\u001b[0;31m    Magnetic entities integrated.\u001b[0m\n\u001b[0m             ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
      ]
     }
    ],
@@ -1074,16 +1279,7 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {},
-   "outputs": [
-    {
-     "ename": "SyntaxError",
-     "evalue": "invalid syntax (3012513526.py, line 1)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;36m  Cell \u001b[0;32mIn[13], line 1\u001b[0;36m\u001b[0m\n\u001b[0;31m    Magnetic entities integrated.\u001b[0m\n\u001b[0m             ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "Magnetic entities integrated.\n",
     "Pairs integrated.\n",