From 42462303ad00467f51d65ccb13ed3eb3fc7ca4a1 Mon Sep 17 00:00:00 2001
From: = <valerachuiko@gmail.com>
Date: Thu, 21 Aug 2025 16:53:07 -0400
Subject: [PATCH 1/4] fix antisymmetrization

---
 examples/molkit.ipynb        | 74 ++++++++++++++++++++++--------------
 moha/molkit/hamiltonians.py  |  6 ++-
 moha/molkit/utils/spinops.py | 18 ++++++---
 3 files changed, 62 insertions(+), 36 deletions(-)

diff --git a/examples/molkit.ipynb b/examples/molkit.ipynb
index dfe756d..1b22376 100644
--- a/examples/molkit.ipynb
+++ b/examples/molkit.ipynb
@@ -26,15 +26,15 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "<moha.molkit.hamiltonians.MolHam object at 0x7e5f1d197560>\n"
+      "<moha.molkit.hamiltonians.MolHam object at 0x7fb2f0ea4be0>\n"
      ]
     },
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/workspaces/ModelHamiltonian/moha/molkit/hamiltonians.py:179: UserWarning: Duplicate entries in the FCIDUMP file are ignored\n",
-      "  data = load_fcidump(open(path, 'r'))\n"
+      "/Users/valeriichuiko/Desktop/projects/ModelHamiltonian/moha/molkit/hamiltonians.py:177: UserWarning: Duplicate entries in the FCIDUMP file are ignored\n",
+      "  data = load_fcidump(open(path))\n"
      ]
     }
    ],
@@ -42,6 +42,7 @@
     "import numpy as np\n",
     "from moha import HamHeisenberg\n",
     "from moha.molkit.hamiltonians import MolHam\n",
+    "from moha.molkit.utils.tools import to_geminal\n",
     "\n",
     "# load a hamiltonian from the fcidump file\n",
     "hami = MolHam()\n",
@@ -644,9 +645,33 @@
    "cell_type": "code",
    "execution_count": 3,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Elements 0, 1, 0, 1 and 1, 0, 0, 1 of aaaa part:\n",
+      " 0.07723439239467665 -0.07723439239467664\n",
+      "--------------------\n",
+      "Elements 0, 1, 0, 1 and 1, 0, 0, 1 of abab part:\n",
+      " 0.3187342023639616 0.1642654175746083\n",
+      "--------------------\n",
+      "Elements 0, 0, 1, 1 for aaaa and abab parts:\n",
+      " 0.0 0.1642654175746083\n"
+     ]
+    }
+   ],
    "source": [
-    "hami.antisymmetrize()"
+    "hami.antisymmetrize()\n",
+    "hami.two_body_spin[0, 1, 0, 1]\n",
+    "two_body_aaaa = hami.get_spin_blocks()['aaaa']\n",
+    "two_body_abab = hami.get_spin_blocks()['abab']\n",
+    "\n",
+    "print(\"Elements 0, 1, 0, 1 and 1, 0, 0, 1 of aaaa part:\\n\", two_body_aaaa[0, 1, 0, 1], two_body_aaaa[1, 0, 0, 1])\n",
+    "print(\"--\"*10)\n",
+    "print(\"Elements 0, 1, 0, 1 and 1, 0, 0, 1 of abab part:\\n\", two_body_abab[0, 1, 0, 1], two_body_abab[1, 0, 0, 1])\n",
+    "print(\"--\"*10)\n",
+    "print(\"Elements 0, 0, 1, 1 for aaaa and abab parts:\\n\", two_body_aaaa[0, 0, 1, 1], two_body_abab[0, 0, 1, 1])"
    ]
   },
   {
@@ -666,21 +691,9 @@
    "cell_type": "code",
    "execution_count": 4,
    "metadata": {},
-   "outputs": [
-    {
-     "ename": "AttributeError",
-     "evalue": "'MolHam' object has no attribute 'to_geminal'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
-      "\u001b[31mAttributeError\u001b[39m                            Traceback (most recent call last)",
-      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[4]\u001b[39m\u001b[32m, line 1\u001b[39m\n\u001b[32m----> \u001b[39m\u001b[32m1\u001b[39m geminal = \u001b[43mhami\u001b[49m\u001b[43m.\u001b[49m\u001b[43mto_geminal\u001b[49m(two_body_spin, \u001b[38;5;28mtype\u001b[39m=\u001b[33m'\u001b[39m\u001b[33mh2\u001b[39m\u001b[33m'\u001b[39m)\n",
-      "\u001b[31mAttributeError\u001b[39m: 'MolHam' object has no attribute 'to_geminal'"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
-    "geminal = hami.to_geminal(two_body_spin, type='h2')"
+    "geminal = to_geminal(two_body_spin, type='h2')"
    ]
   },
   {
@@ -705,7 +718,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -732,7 +745,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 6,
    "metadata": {},
    "outputs": [
     {
@@ -763,15 +776,16 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 7,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "E_spin-orbital : -4.121211958837992\n",
-      "E_geminal      : -4.121211958837991\n"
+      "E_spin-orbital : -3.0622781536522004\n",
+      "E_geminal      : -3.0622781536522012\n",
+      "FCI energy     : -3.062278153652201\n"
      ]
     }
    ],
@@ -787,7 +801,7 @@
     "N_ELEC, norb  = 4, hami.n_spatial\n",
     "\n",
     "# Perform Full CI calculation\n",
-    "e_fci, ci_vec = fci.direct_spin1.kernel(h1, h2, norb, N_ELEC, ecore=core_energy)\n",
+    "e_fci, ci_vec = fci.direct_spin1.kernel(h1, np.einsum('pqrs -> prqs', h2), norb, N_ELEC, ecore=core_energy, tol=1e-12)\n",
     "rdm1s, rdm2s = fci.direct_spin1.make_rdm12s(ci_vec, norb, N_ELEC)\n",
     "\n",
     "# construct 2-rdm\n",
@@ -815,16 +829,18 @@
     "# Energy from geminal formulation\n",
     "E_gem = np.einsum('pq,pq', H_gem, rdm_gem)\n",
     "\n",
-    "# Print the energies from both formulations\n",
+    "# Print the energies from all formulations\n",
     "print(\"E_spin-orbital :\", E_spin)\n",
     "print(\"E_geminal      :\", E_gem)\n",
-    "assert np.allclose(E_spin, E_gem), \"Energies do not match!\""
+    "print(\"FCI energy     :\", e_fci - core_energy)\n",
+    "assert np.allclose(E_spin, E_gem), \"Energies do not match!\"\n",
+    "assert np.allclose(E_spin, e_fci - core_energy), \"Energies do not match!\""
    ]
   }
  ],
  "metadata": {
   "kernelspec": {
-   "display_name": "Python 3",
+   "display_name": "base",
    "language": "python",
    "name": "python3"
   },
@@ -838,7 +854,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.12.1"
+   "version": "3.9.7"
   }
  },
  "nbformat": 4,
diff --git a/moha/molkit/hamiltonians.py b/moha/molkit/hamiltonians.py
index 1d1df5c..5c21121 100644
--- a/moha/molkit/hamiltonians.py
+++ b/moha/molkit/hamiltonians.py
@@ -42,7 +42,10 @@ def __init__(self, one_body=None, two_body=None, zero_body=0):
 
     def antisymmetrize(self):
         """Apply proper antisymmetrization to two-electron integrals."""
-        self.two_body = antisymmetrize_two_body(self.two_body, inplace=True)
+        if not hasattr(self, "two_body_spin"):
+            raise RuntimeError(
+                "Call .spinize_H() first to compute spin-orbital form.")
+        self.two_body_spin = antisymmetrize_two_body(self.two_body_spin, inplace=True)
 
     def get_spin_blocks(self):
         """Return the main spin blocks of the two-body spin-orbital tensor.
@@ -152,6 +155,7 @@ def to_reduced(self, n_elec):
         ``MolHam`` instance.
         """
         h_spin, V_spin = self.spinize_H()
+        self.antisymmetrize()
 
         h_upscaled = upscale_one_body(h_spin, n_elec)
 
diff --git a/moha/molkit/utils/spinops.py b/moha/molkit/utils/spinops.py
index 0f38f2f..14dcf67 100644
--- a/moha/molkit/utils/spinops.py
+++ b/moha/molkit/utils/spinops.py
@@ -55,14 +55,20 @@ def antisymmetrize_two_body(
     n = nspin // 2      # number of spatial orbitals
 
     # αααα block
-    aa = tensor[:n, :n, :n, :n]
-    aa -= np.swapaxes(aa, 2, 3)
-    aa *= 0.5
+    aa = tensor[:n, :n, :n, :n].copy()
+    aa = aa - np.einsum('pqrs->qprs', aa) - np.einsum('pqrs->pqsr', aa) +\
+             np.einsum('pqrs->rspq', aa) - np.einsum('pqrs->srpq', aa) - np.einsum('pqrs->rsqp', aa) +\
+             np.einsum('pqrs->qpsr', aa) + np.einsum('pqrs->srqp', aa)
 
     # ββββ block
-    bb = tensor[n:, n:, n:, n:]
-    bb -= np.swapaxes(bb, 2, 3)
-    bb *= 0.5
+    bb = tensor[n:, n:, n:, n:].copy()
+    bb = bb - np.einsum('pqrs->qprs', bb) - np.einsum('pqrs->pqsr', bb) +\
+                np.einsum('pqrs->rspq', bb) - np.einsum('pqrs->srpq', bb) - np.einsum('pqrs->rsqp', bb) +\
+                np.einsum('pqrs->qpsr', bb) + np.einsum('pqrs->srqp', bb)
+
+
+    tensor[:n, :n, :n, :n] = aa / 8
+    tensor[n:, n:, n:, n:] = bb / 8
 
     return tensor
 

From 71f9e2ba2a6b2cadaf6e236d5fb56aef203654e5 Mon Sep 17 00:00:00 2001
From: = <valerachuiko@gmail.com>
Date: Fri, 22 Aug 2025 13:30:20 -0400
Subject: [PATCH 2/4] fix style

---
 docs/molham.rst              |   8 +
 examples/molkit.ipynb        | 559 +----------------------------------
 moha/molkit/hamiltonians.py  |   1 -
 moha/molkit/utils/spinops.py |  41 ++-
 moha/molkit/utils/tools.py   |   4 +-
 website/_toc.yml             |   1 +
 6 files changed, 39 insertions(+), 575 deletions(-)
 create mode 100644 docs/molham.rst

diff --git a/docs/molham.rst b/docs/molham.rst
new file mode 100644
index 0000000..d51428c
--- /dev/null
+++ b/docs/molham.rst
@@ -0,0 +1,8 @@
+Molecular Hamiltonian
+=====================
+MolHam class
+-----------------
+... autoclass:: moha.molkit.hamiltonians.MolHam
+    :members:
+
+    .. automethod:: __init__
\ No newline at end of file
diff --git a/examples/molkit.ipynb b/examples/molkit.ipynb
index 1b22376..cfd32cd 100644
--- a/examples/molkit.ipynb
+++ b/examples/molkit.ipynb
@@ -26,14 +26,14 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "<moha.molkit.hamiltonians.MolHam object at 0x7fb2f0ea4be0>\n"
+      "<moha.molkit.hamiltonians.MolHam object at 0x7f7a91a24130>\n"
      ]
     },
     {
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/Users/valeriichuiko/Desktop/projects/ModelHamiltonian/moha/molkit/hamiltonians.py:177: UserWarning: Duplicate entries in the FCIDUMP file are ignored\n",
+      "/Users/valeriichuiko/Desktop/projects/ModelHamiltonian/moha/molkit/hamiltonians.py:176: UserWarning: Duplicate entries in the FCIDUMP file are ignored\n",
       "  data = load_fcidump(open(path))\n"
      ]
     }
@@ -79,554 +79,17 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "One-body integrals (spin basis):\n",
-      " [[-1.13831275e+00  4.44089210e-16  9.23269847e-02  8.32667268e-17\n",
-      "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      " [ 4.44089210e-16 -1.04621069e+00  2.77555756e-16  7.41183629e-02\n",
-      "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      " [ 9.23269847e-02  2.77555756e-16 -9.82637700e-01 -1.38777878e-16\n",
-      "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      " [ 8.32667268e-17  7.41183629e-02 -1.38777878e-16 -9.72184231e-01\n",
-      "   0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00]\n",
-      " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
-      "  -1.13831275e+00  4.44089210e-16  9.23269847e-02  8.32667268e-17]\n",
-      " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
-      "   4.44089210e-16 -1.04621069e+00  2.77555756e-16  7.41183629e-02]\n",
-      " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
-      "   9.23269847e-02  2.77555756e-16 -9.82637700e-01 -1.38777878e-16]\n",
-      " [ 0.00000000e+00  0.00000000e+00  0.00000000e+00  0.00000000e+00\n",
-      "   8.32667268e-17  7.41183629e-02 -1.38777878e-16 -9.72184231e-01]]\n",
-      "Two-body integrals (spin basis):\n",
-      " [[[[ 3.49974212e-01 -2.91433544e-16 -5.76085753e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-2.91433544e-16  1.64265418e-01 -6.24500451e-17 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-5.76085753e-02 -6.24500451e-17  1.27619481e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[-2.91433544e-16  3.18734202e-01 -1.31838984e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 1.64265418e-01  1.38777878e-17  6.98132857e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-6.24500451e-17  1.75474384e-02  1.66533454e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[-5.76085753e-02 -1.31838984e-16  3.22024071e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-6.24500451e-17  6.98132857e-02  2.08166817e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 1.27619481e-01  1.66533454e-16  1.81604262e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  ...\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  3.18734202e-01\n",
-      "    -1.31838984e-16 -5.99199501e-02]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.38777878e-17\n",
-      "     6.98132857e-02  8.32667268e-17]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.75474384e-02\n",
-      "     1.66533454e-16  1.29061413e-01]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ... -1.31838984e-16\n",
-      "     3.22024071e-01 -2.08166817e-17]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  6.98132857e-02\n",
-      "     2.08166817e-16  1.68393804e-01]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.66533454e-16\n",
-      "     1.81604262e-02 -3.74700271e-16]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ... -5.99199501e-02\n",
-      "    -2.08166817e-17  3.62156186e-01]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  8.32667268e-17\n",
-      "     1.68393804e-01 -4.99600361e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.29061413e-01\n",
-      "    -3.74700271e-16 -6.01544349e-02]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]]\n",
-      "\n",
-      "\n",
-      " [[[-2.91433544e-16  1.64265418e-01 -6.24500451e-17 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 3.18734202e-01  1.38777878e-17  1.75474384e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-1.31838984e-16  6.98132857e-02  1.66533454e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 1.64265418e-01  1.38777878e-17  6.98132857e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 1.38777878e-17  3.32316870e-01  1.66533454e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 6.98132857e-02  1.66533454e-16  1.46071836e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[-6.24500451e-17  6.98132857e-02  2.08166817e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 1.75474384e-02  1.66533454e-16  3.35356211e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 1.66533454e-16  1.46071836e-01 -1.11022302e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  ...\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.38777878e-17\n",
-      "     6.98132857e-02  8.32667268e-17]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  3.32316870e-01\n",
-      "     1.66533454e-16  1.52359077e-02]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.66533454e-16\n",
-      "     1.46071836e-01  4.85722573e-17]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  6.98132857e-02\n",
-      "     2.08166817e-16  1.68393804e-01]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.66533454e-16\n",
-      "     3.35356211e-01  1.31838984e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.46071836e-01\n",
-      "    -1.11022302e-16  7.29178274e-02]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
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-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  8.32667268e-17\n",
-      "     1.68393804e-01 -4.99600361e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.52359077e-02\n",
-      "     1.31838984e-16  3.30604577e-01]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  4.85722573e-17\n",
-      "     7.29178274e-02 -3.05311332e-16]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
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-      "     0.00000000e+00  0.00000000e+00]]]\n",
-      "\n",
-      "\n",
-      " [[[-5.76085753e-02 -6.24500451e-17  1.27619481e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-1.31838984e-16  6.98132857e-02  1.66533454e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 3.22024071e-01  2.08166817e-16  1.81604262e-02 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
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-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[-6.24500451e-17  1.75474384e-02  1.66533454e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 6.98132857e-02  1.66533454e-16  1.46071836e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 2.08166817e-16  3.35356211e-01 -1.11022302e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 1.27619481e-01  1.66533454e-16  1.81604262e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 1.66533454e-16  1.46071836e-01 -1.11022302e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 1.81604262e-02 -1.11022302e-16  3.42057681e-01 ...  0.00000000e+00\n",
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-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
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-      "\n",
-      "  ...\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.75474384e-02\n",
-      "     1.66533454e-16  1.29061413e-01]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.66533454e-16\n",
-      "     1.46071836e-01  4.85722573e-17]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  3.35356211e-01\n",
-      "    -1.11022302e-16  1.78424099e-02]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
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-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.66533454e-16\n",
-      "     1.81604262e-02 -3.74700271e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.46071836e-01\n",
-      "    -1.11022302e-16  7.29178274e-02]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ... -1.11022302e-16\n",
-      "     3.42057681e-01  2.84494650e-16]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
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-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.29061413e-01\n",
-      "    -3.74700271e-16 -6.01544349e-02]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  4.85722573e-17\n",
-      "     7.29178274e-02 -3.05311332e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.78424099e-02\n",
-      "     2.84494650e-16  3.35192040e-01]\n",
-      "   ...\n",
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-      "     0.00000000e+00  0.00000000e+00]]]\n",
-      "\n",
-      "\n",
-      " ...\n",
-      "\n",
-      "\n",
-      " [[[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "   ...\n",
-      "   [ 3.18734202e-01  1.38777878e-17  1.75474384e-02 ...  0.00000000e+00\n",
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-      "   [-1.31838984e-16  6.98132857e-02  1.66533454e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-5.99199501e-02  8.32667268e-17  1.29061413e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "   ...\n",
-      "   [ 1.38777878e-17  3.32316870e-01  1.66533454e-16 ...  0.00000000e+00\n",
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-      "   [ 6.98132857e-02  1.66533454e-16  1.46071836e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 8.32667268e-17  1.52359077e-02  4.85722573e-17 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "   ...\n",
-      "   [ 1.75474384e-02  1.66533454e-16  3.35356211e-01 ...  0.00000000e+00\n",
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-      "   [ 1.66533454e-16  1.46071836e-01 -1.11022302e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
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-      "\n",
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-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  3.32316870e-01\n",
-      "     1.66533454e-16  1.52359077e-02]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.66533454e-16\n",
-      "     1.46071836e-01  4.85722573e-17]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.52359077e-02\n",
-      "     4.85722573e-17  1.32179395e-01]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
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-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.66533454e-16\n",
-      "     3.35356211e-01  1.31838984e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.46071836e-01\n",
-      "    -1.11022302e-16  7.29178274e-02]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  4.85722573e-17\n",
-      "     1.78424099e-02 -2.49800181e-16]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.52359077e-02\n",
-      "     1.31838984e-16  3.30604577e-01]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  4.85722573e-17\n",
-      "     7.29178274e-02 -3.05311332e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.32179395e-01\n",
-      "    -2.49800181e-16 -6.33638455e-02]]]\n",
-      "\n",
-      "\n",
-      " [[[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
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-      "   ...\n",
-      "   [-1.31838984e-16  6.98132857e-02  1.66533454e-16 ...  0.00000000e+00\n",
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-      "   [ 3.22024071e-01  2.08166817e-16  1.81604262e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
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-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
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-      "   ...\n",
-      "   [ 6.98132857e-02  1.66533454e-16  1.46071836e-01 ...  0.00000000e+00\n",
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-      "   [ 2.08166817e-16  3.35356211e-01 -1.11022302e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 1.68393804e-01  1.31838984e-16  7.29178274e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
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-      "   ...\n",
-      "   [ 1.66533454e-16  1.46071836e-01 -1.11022302e-16 ...  0.00000000e+00\n",
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-      "   [ 1.81604262e-02 -1.11022302e-16  3.42057681e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-3.74700271e-16  7.29178274e-02  2.84494650e-16 ...  0.00000000e+00\n",
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-      "\n",
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-      "\n",
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-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.66533454e-16\n",
-      "     1.46071836e-01  4.85722573e-17]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  3.35356211e-01\n",
-      "    -1.11022302e-16  1.78424099e-02]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.31838984e-16\n",
-      "     7.29178274e-02 -2.49800181e-16]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.46071836e-01\n",
-      "    -1.11022302e-16  7.29178274e-02]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ... -1.11022302e-16\n",
-      "     3.42057681e-01  2.84494650e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  7.29178274e-02\n",
-      "     2.84494650e-16  1.75364226e-01]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  4.85722573e-17\n",
-      "     7.29178274e-02 -3.05311332e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.78424099e-02\n",
-      "     2.84494650e-16  3.35192040e-01]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ... -2.49800181e-16\n",
-      "     1.75364226e-01 -2.49800181e-16]]]\n",
-      "\n",
-      "\n",
-      " [[[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [-5.99199501e-02  8.32667268e-17  1.29061413e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-2.08166817e-17  1.68393804e-01 -3.74700271e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 3.62156186e-01 -4.99600361e-16 -6.01544349e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 8.32667268e-17  1.52359077e-02  4.85722573e-17 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 1.68393804e-01  1.31838984e-16  7.29178274e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-4.99600361e-16  3.30604577e-01 -3.05311332e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 1.29061413e-01  4.85722573e-17  1.78424099e-02 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-3.74700271e-16  7.29178274e-02  2.84494650e-16 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [-6.01544349e-02 -3.05311332e-16  3.35192040e-01 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]]\n",
-      "\n",
-      "  ...\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.52359077e-02\n",
-      "     4.85722573e-17  1.32179395e-01]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.31838984e-16\n",
-      "     7.29178274e-02 -2.49800181e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  3.30604577e-01\n",
-      "    -3.05311332e-16 -6.33638455e-02]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  4.85722573e-17\n",
-      "     1.78424099e-02 -2.49800181e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  7.29178274e-02\n",
-      "     2.84494650e-16  1.75364226e-01]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ... -3.05311332e-16\n",
-      "     3.35192040e-01 -2.49800181e-16]]\n",
-      "\n",
-      "  [[ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  0.00000000e+00\n",
-      "     0.00000000e+00  0.00000000e+00]\n",
-      "   ...\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ...  1.32179395e-01\n",
-      "    -2.49800181e-16 -6.33638455e-02]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ... -2.49800181e-16\n",
-      "     1.75364226e-01 -2.49800181e-16]\n",
-      "   [ 0.00000000e+00  0.00000000e+00  0.00000000e+00 ... -6.33638455e-02\n",
-      "    -2.49800181e-16  3.79154904e-01]]]]\n"
+      "Shape of one-body integrals (spin basis):\n",
+      " (8, 8)\n",
+      "Shape of two-body integrals (spin basis):\n",
+      " (8, 8, 8, 8)\n"
      ]
     }
    ],
    "source": [
     "one_body_spin, two_body_spin = hami.spinize_H()\n",
-    "print(\"One-body integrals (spin basis):\\n\", one_body_spin)\n",
-    "print(\"Two-body integrals (spin basis):\\n\", two_body_spin)"
+    "print(\"Shape of one-body integrals (spin basis):\\n\", one_body_spin.shape)\n",
+    "print(\"Shape of two-body integrals (spin basis):\\n\", two_body_spin.shape)"
    ]
   },
   {
@@ -651,7 +114,7 @@
      "output_type": "stream",
      "text": [
       "Elements 0, 1, 0, 1 and 1, 0, 0, 1 of aaaa part:\n",
-      " 0.07723439239467665 -0.07723439239467664\n",
+      " 0.1544687847893533 -0.1544687847893533\n",
       "--------------------\n",
       "Elements 0, 1, 0, 1 and 1, 0, 0, 1 of abab part:\n",
       " 0.3187342023639616 0.1642654175746083\n",
@@ -680,8 +143,8 @@
    "source": [
     "### 4. Converting the Two-Body Term to the Geminal Basis\n",
     "\n",
-    "The `to_geminal` method converts the two-body term from the spin-orbital basis to the geminal basis.  \n",
-    "You can specify the type of two-body term: `'rdm2'` (two-body reduced density matrix) or `'h2'` (two-body Hamiltonian).\n",
+    "The `to_geminal` function in the utils module converts the two-body term from the spin-orbital basis to the geminal basis.  \n",
+    "You can specify the type of two-body term: `'h2'` (Hamiltonian) ; we also added conversion to the geminal basis for reduced density matrices: `'rdm2'`.\n",
     "\n",
     "The Hamiltonian in the geminal basis is obtained by the following formula:\n",
     "$V_{A B} =\\frac{1}{2}\\left(V_{p q r s}-V_{q p r s}-V_{p q r s}+V_{qprs}\\right)$\n"
diff --git a/moha/molkit/hamiltonians.py b/moha/molkit/hamiltonians.py
index 5c21121..785f17f 100644
--- a/moha/molkit/hamiltonians.py
+++ b/moha/molkit/hamiltonians.py
@@ -155,7 +155,6 @@ def to_reduced(self, n_elec):
         ``MolHam`` instance.
         """
         h_spin, V_spin = self.spinize_H()
-        self.antisymmetrize()
 
         h_upscaled = upscale_one_body(h_spin, n_elec)
 
diff --git a/moha/molkit/utils/spinops.py b/moha/molkit/utils/spinops.py
index 14dcf67..5ecd13c 100644
--- a/moha/molkit/utils/spinops.py
+++ b/moha/molkit/utils/spinops.py
@@ -20,7 +20,7 @@ def antisymmetrize_two_body(
     Returns
     -------
     np.ndarray
-        Antisymmetrised tensor obeying
+        Antisymmetrised tensor obeys
 
         .. math::
 
@@ -32,18 +32,27 @@ def antisymmetrize_two_body(
 
     Notes
     -----
-    The operation applied is
+    https://vergil.chemistry.gatech.edu/static/content/permsymm.pdf
+
+    The input tensor obbeys the following 8-fold symmetry
 
     .. math::
 
-        V^{\\sigma\\sigma\\sigma\\sigma}_{pqrs}
-            \\;\\;\\leftarrow\\;\\;
-            \\tfrac12\\,\\bigl(V^{\\sigma\\sigma\\sigma\\sigma}_{pqrs}
-                              -V^{\\sigma\\sigma\\sigma\\sigma}_{pqsr}\\bigr),
+        V_{ijkl} = V_{jilk}
+                 = V_{klij}
+                 = V_{lkji}
+                 = V_{kjjl}
+                 = V_{lijk}
+                 = V_{ilkj}
+                 = V_{jklj}
+
+    The operation applied is
 
-    for ``σ = α`` and ``σ = β``.  All other spin sectors are returned
-    untouched.
+    .. math::
+        \langle i j \| k l\rangle=\langle i j \mid k l\rangle-\langle i j \mid l k\rangle
 
+    Keep in mind, that such operation produces terms of the form
+    abba, baab, that are not present in the original tensor.
     """
     if not inplace:
         tensor = tensor.copy()
@@ -54,21 +63,7 @@ def antisymmetrize_two_body(
 
     n = nspin // 2      # number of spatial orbitals
 
-    # αααα block
-    aa = tensor[:n, :n, :n, :n].copy()
-    aa = aa - np.einsum('pqrs->qprs', aa) - np.einsum('pqrs->pqsr', aa) +\
-             np.einsum('pqrs->rspq', aa) - np.einsum('pqrs->srpq', aa) - np.einsum('pqrs->rsqp', aa) +\
-             np.einsum('pqrs->qpsr', aa) + np.einsum('pqrs->srqp', aa)
-
-    # ββββ block
-    bb = tensor[n:, n:, n:, n:].copy()
-    bb = bb - np.einsum('pqrs->qprs', bb) - np.einsum('pqrs->pqsr', bb) +\
-                np.einsum('pqrs->rspq', bb) - np.einsum('pqrs->srpq', bb) - np.einsum('pqrs->rsqp', bb) +\
-                np.einsum('pqrs->qpsr', bb) + np.einsum('pqrs->srqp', bb)
-
-
-    tensor[:n, :n, :n, :n] = aa / 8
-    tensor[n:, n:, n:, n:] = bb / 8
+    tensor = tensor - np.einsum('pqrs->pqsr', tensor)
 
     return tensor
 
diff --git a/moha/molkit/utils/tools.py b/moha/molkit/utils/tools.py
index fad250f..a06211d 100644
--- a/moha/molkit/utils/tools.py
+++ b/moha/molkit/utils/tools.py
@@ -55,16 +55,14 @@ def to_geminal(two_body=None, type='h2'):
                 for s in range(r + 1, n):
                     if type == 'rdm2':
                         two_body_gem.append(
-                            0.5 * 4 * two_body[p, q, r, s]
+                            two_body[p, q, r, s]
                         )
                     elif type == 'h2':
                         two_body_gem.append(
-                            0.5 * (
                                 two_body[p, q, r, s]
                                 - two_body[q, p, r, s]
                                 - two_body[p, q, s, r]
                                 + two_body[q, p, s, r]
-                            )
                         )
 
     n_gem = n * (n - 1) // 2
diff --git a/website/_toc.yml b/website/_toc.yml
index efd8511..b236314 100644
--- a/website/_toc.yml
+++ b/website/_toc.yml
@@ -12,6 +12,7 @@ parts:
       - file: examples/mohagpt.ipynb
       - file: examples/gui.ipynb
       - file: examples/RG.ipynb
+      - file: examples/molkit.ipynb
       
     - caption: API
       chapters:

From 8c0a4d1be2f5a46e3c0d1bd51d932eece0bfcd0a Mon Sep 17 00:00:00 2001
From: = <valerachuiko@gmail.com>
Date: Fri, 22 Aug 2025 13:31:09 -0400
Subject: [PATCH 3/4] fix style

---
 moha/molkit/utils/tests/__init__.py     |  1 -
 moha/molkit/utils/tests/test_spinops.py |  0
 moha/test/test_molham.py                | 70 +++++++++++++++++++++++++
 3 files changed, 70 insertions(+), 1 deletion(-)
 delete mode 100644 moha/molkit/utils/tests/__init__.py
 delete mode 100644 moha/molkit/utils/tests/test_spinops.py
 create mode 100644 moha/test/test_molham.py

diff --git a/moha/molkit/utils/tests/__init__.py b/moha/molkit/utils/tests/__init__.py
deleted file mode 100644
index 4befe01..0000000
--- a/moha/molkit/utils/tests/__init__.py
+++ /dev/null
@@ -1 +0,0 @@
-r"""Tests Molkit Module."""
diff --git a/moha/molkit/utils/tests/test_spinops.py b/moha/molkit/utils/tests/test_spinops.py
deleted file mode 100644
index e69de29..0000000
diff --git a/moha/test/test_molham.py b/moha/test/test_molham.py
new file mode 100644
index 0000000..ac8f1ba
--- /dev/null
+++ b/moha/test/test_molham.py
@@ -0,0 +1,70 @@
+"""Testing the MolHam class."""
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal
+from moha.molkit import utils
+from moha.molkit.hamiltonians import MolHam
+
+
+def test_antisymmetrize():
+    """Test antisymmetrization of two-electron integrals."""
+    one_body = np.eye(2)
+    two_body = np.zeros((2, 2, 2, 2))
+    two_body[0, 0, 1, 1] = 1.0
+    two_body[1, 1, 0, 0] = 1.0
+
+    mol_ham = MolHam(one_body=one_body, two_body=two_body)
+    mol_ham.spinize_H()
+    mol_ham.antisymmetrize()
+
+    expected_two_body_aa = np.zeros((2, 2, 2, 2))
+    expected_two_body_aa[0, 0, 1, 1] = 1
+    expected_two_body_aa[1, 1, 0, 0] = 1
+    expected_two_body_aa[0, 1, 0, 1] = 0
+    expected_two_body_aa[1, 0, 1, 0] = 0
+
+    assert_allclose(mol_ham.two_body[:2, :2, :2, :2], expected_two_body_aa)
+
+def test_to_geminal():
+    """Test conversion to geminal basis."""
+    n_orb = 4
+    two_body = np.zeros((2, 2, 2, 2))
+    two_body[0, 0, 1, 1] = 1.0
+    two_body[1, 1, 0, 0] = 1.0
+    two_body[1, 0, 0, 1] = 1.0
+    two_body[0, 1, 1, 0] = 1.0
+
+    geminal_true = np.array([
+        [-2.0]
+    ])
+    geminal = utils.tools.to_geminal(two_body, type='h2')
+    assert_equal(geminal.shape, (1, 1))
+    assert_allclose(geminal, geminal_true)
+
+
+def test_to_reduced_ham():
+    """Test conversion to reduced Hamiltonian."""
+    n_orb = 2
+    one_body = np.eye(n_orb)
+    two_body = np.zeros((n_orb, n_orb, n_orb, n_orb))
+    two_body[0, 0, 1, 1] = 1.0
+    two_body[1, 1, 0, 0] = 1.0
+
+    mol_ham = MolHam(one_body=one_body, two_body=two_body)
+    reduced_ham = mol_ham.to_reduced(n_elec=2)
+
+
+    # sum over the spin-orbital indices
+    reduced_ham = reduced_ham[:2, :2, :2, :2] +\
+                  reduced_ham[2:, 2:, 2:, 2:] +\
+                  reduced_ham[:2, 2:, :2, 2:] +\
+                  reduced_ham[2:, :2, 2:, :2]
+    reduced_ham *= 0.25
+
+    reduced_ham_true = 0.5 * two_body
+    reduced_ham_true[0, 0, 0, 0] = 1
+    reduced_ham_true[1, 1, 1, 1] = 1
+    reduced_ham_true[0, 1, 0, 1] = 1
+    reduced_ham_true[1, 0, 1, 0] = 1
+
+    assert_allclose(reduced_ham, reduced_ham_true)
\ No newline at end of file

From c93792c9c7dbfdc571e9f49c8d3d64a9d8874e1e Mon Sep 17 00:00:00 2001
From: = <valerachuiko@gmail.com>
Date: Fri, 22 Aug 2025 13:37:56 -0400
Subject: [PATCH 4/4] fix style

---
 moha/molkit/hamiltonians.py  |  3 ++-
 moha/molkit/utils/spinops.py |  3 ++-
 moha/test/test_molham.py     | 10 +++++-----
 3 files changed, 9 insertions(+), 7 deletions(-)

diff --git a/moha/molkit/hamiltonians.py b/moha/molkit/hamiltonians.py
index 785f17f..db314eb 100644
--- a/moha/molkit/hamiltonians.py
+++ b/moha/molkit/hamiltonians.py
@@ -45,7 +45,8 @@ def antisymmetrize(self):
         if not hasattr(self, "two_body_spin"):
             raise RuntimeError(
                 "Call .spinize_H() first to compute spin-orbital form.")
-        self.two_body_spin = antisymmetrize_two_body(self.two_body_spin, inplace=True)
+        self.two_body_spin = antisymmetrize_two_body(self.two_body_spin,
+                                                     inplace=True)
 
     def get_spin_blocks(self):
         """Return the main spin blocks of the two-body spin-orbital tensor.
diff --git a/moha/molkit/utils/spinops.py b/moha/molkit/utils/spinops.py
index 5ecd13c..c4de044 100644
--- a/moha/molkit/utils/spinops.py
+++ b/moha/molkit/utils/spinops.py
@@ -49,7 +49,8 @@ def antisymmetrize_two_body(
     The operation applied is
 
     .. math::
-        \langle i j \| k l\rangle=\langle i j \mid k l\rangle-\langle i j \mid l k\rangle
+        \langle ij\| kl\rangle=
+        \langle ij\mid kl\rangle-\langle ij\mid lk\rangle
 
     Keep in mind, that such operation produces terms of the form
     abba, baab, that are not present in the original tensor.
diff --git a/moha/test/test_molham.py b/moha/test/test_molham.py
index ac8f1ba..e65255a 100644
--- a/moha/test/test_molham.py
+++ b/moha/test/test_molham.py
@@ -25,6 +25,7 @@ def test_antisymmetrize():
 
     assert_allclose(mol_ham.two_body[:2, :2, :2, :2], expected_two_body_aa)
 
+
 def test_to_geminal():
     """Test conversion to geminal basis."""
     n_orb = 4
@@ -53,12 +54,11 @@ def test_to_reduced_ham():
     mol_ham = MolHam(one_body=one_body, two_body=two_body)
     reduced_ham = mol_ham.to_reduced(n_elec=2)
 
-
     # sum over the spin-orbital indices
     reduced_ham = reduced_ham[:2, :2, :2, :2] +\
-                  reduced_ham[2:, 2:, 2:, 2:] +\
-                  reduced_ham[:2, 2:, :2, 2:] +\
-                  reduced_ham[2:, :2, 2:, :2]
+        reduced_ham[2:, 2:, 2:, 2:] +\
+        reduced_ham[:2, 2:, :2, 2:] +\
+        reduced_ham[2:, :2, 2:, :2]
     reduced_ham *= 0.25
 
     reduced_ham_true = 0.5 * two_body
@@ -67,4 +67,4 @@ def test_to_reduced_ham():
     reduced_ham_true[0, 1, 0, 1] = 1
     reduced_ham_true[1, 0, 1, 0] = 1
 
-    assert_allclose(reduced_ham, reduced_ham_true)
\ No newline at end of file
+    assert_allclose(reduced_ham, reduced_ham_true)