NEO CCSD doi:10.1021/acs.jctc.8b01120

neo_cc.ipynb

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   "cell_type": "markdown",
   "id": "c7770cc0-e946-4c6b-b41c-f311ef962bcc",
   "metadata": {},
   "source": [
    "# Load"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "485b1cc0-750d-4a8d-9a2a-5ab19284c55b",
   "metadata": {},
   "outputs": [],
   "source": [
    "import wicked as w\n",
    "from IPython.display import display, Math, Latex\n",
    "\n",
    "def latex(expr):\n",
    "    \"\"\"Function to render any object that has a member latex() function\"\"\"\n",
    "    display(Math(expr.latex()))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4658c1e7-d76b-420f-a43d-ef624d94d717",
   "metadata": {},
   "source": [
    "# Defining orbital spaces"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "bc41a20e-9c92-4030-bbe6-d0c7740799d3",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "osi = w.osi()\n",
    "print(str(osi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2740f6ac-52d8-4a8b-a542-bf428fcae5d0",
   "metadata": {},
   "outputs": [],
   "source": [
    "w.reset_space()\n",
    "# e\n",
    "w.add_space(\"o\", \"fermion\", \"occupied\", ['i','j','k','l'])\n",
    "w.add_space(\"v\", \"fermion\", \"unoccupied\", ['a','b','c','d'])\n",
    "# p\n",
    "w.add_space(\"p\", \"fermion\", \"occupied\", ['I','J','K','L'])\n",
    "w.add_space(\"b\", \"fermion\", \"unoccupied\", ['A','B','C','D'])\n",
    "wt = w.WickTheorem()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "07196caa-6322-487b-bbae-990a3d1bac38",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "space label: o\n",
      "field type: fermion\n",
      "space type: occupied\n",
      "indices: [i,j,k,l]\n",
      "\n",
      "space label: v\n",
      "field type: fermion\n",
      "space type: unoccupied\n",
      "indices: [a,b,c,d]\n",
      "\n",
      "space label: p\n",
      "field type: fermion\n",
      "space type: occupied\n",
      "indices: [I,J,K,L]\n",
      "\n",
      "space label: b\n",
      "field type: fermion\n",
      "space type: unoccupied\n",
      "indices: [A,B,C,D]\n"
     ]
    }
   ],
   "source": [
    "osi = w.osi()\n",
    "print(str(osi))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a6ed1114-1ced-40b9-826e-3ad02af8f4b1",
   "metadata": {},
   "source": [
    "# Operators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "ba169410-3b72-4f04-8a02-bd2290f6feed",
   "metadata": {},
   "outputs": [],
   "source": [
    "E0 = w.op(\"E_0\",[\"\"])\n",
    "F_ee = w.utils.gen_op('f',1,'ov','ov')\n",
    "F_pp = w.op(\"f\",['p+ p']) + w.op(\"f\",['p+ b']) + w.op(\"f\",['b+ p']) + w.op(\"f\",['b+ b'])\n",
    "V_ee = w.utils.gen_op('v',2,'ov','ov')\n",
    "V_pp = w.utils.gen_op('v',2,'pb','pb')\n",
    "#V_ep = need to define, can't use gen_op bc no exchange\n",
    "#V_ep = w.utils.gen_op('v',2,'ov','pb') <- can't do this\n",
    "V_ep = \\\n",
    "w.op(\"v\",['v+ b+ o p']) + \\\n",
    "w.op(\"v\",['o+ p+ v b']) + \\\n",
    "w.op(\"v\",['p+ v+ b o']) "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80d72311-b8bd-4dfc-abce-bc8adbfd6e03",
   "metadata": {},
   "source": [
    "# CCSD E equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "94de7b76-e529-4969-b6f1-bb945a817bf4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle + {E_{0}}^{}_{} \\\\ \n",
       "+ {f}^{a}_{i} {t}^{i}_{a} \\\\ \n",
       "+ {f}^{A}_{I} {t}^{I}_{A} \\\\ \n",
       "+\\frac{1}{2} {t}^{i}_{a} {t}^{j}_{b} {v}^{a b}_{i j} \\\\ \n",
       "+\\frac{1}{4} {t}^{i j}_{a b} {v}^{a b}_{i j} \\\\ \n",
       "- {t}^{i I}_{a A} {v}^{a A}_{i I} \\\\ \n",
       "- {t}^{I}_{A} {t}^{i}_{a} {v}^{a A}_{i I} \\\\ \n",
       "+\\frac{1}{2} {t}^{I}_{A} {t}^{J}_{B} {v}^{A B}_{I J} \\\\ \n",
       "+\\frac{1}{4} {t}^{I J}_{A B} {v}^{A B}_{I J}$"
      ],
      "text/plain": [
       "<IPython.core.display.Math object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "H = E0 + F_ee + F_pp + V_ee + V_pp - V_ep\n",
    "T = w.op(\"t\",[\"v+ o\", \"b+ p\",\"v+ v+ o o\",\"b+ b+ p p\",\"v+ b+ o p\"])\n",
    "Hbar = w.bch_series(H,T,2)\n",
    "expr = wt.contract(Hbar,0,0)\n",
    "expr\n",
    "latex(expr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8c1cc449-8b1e-4434-accd-13eff42a1a76",
   "metadata": {},
   "outputs": [],
   "source": [
    "# This expression should match S3 of doi:10.1021/acs.jctc.8b01120"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f5ffef6c-8250-401e-8f79-d57089747a8e",
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   "outputs": [],
   "source": []
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Reproducing NEO-CCSD E expression with fevangelista wicked

Reproducing NEO-CCSD E expression with fevangelista/wicked