Sigma-scaled RPA.ipynb

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   "source": [
    "# Sigma-scaled RPA\n",
    "\n",
    "**Author:** Egor Trushin  \n",
    "**Date created:** 10/12/2021  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard RPA calcualtion for CO\n",
    "\n",
    "```\n",
    "memory,4000,m  \n",
    "gthresh,twoint=1d-20,energy=1d-10,orbital=1d-8  \n",
    "basis={  \n",
    "default,aug-cc-pwCVQZ  \n",
    "set,ri\n",
    "default,aug-cc-pwCVQZ/mp2fit  \n",
    "}\n",
    "\n",
    "symmetry,nosym  \n",
    "angstrom  \n",
    "geometry={  \n",
    "2  \n",
    "\n",
    "C        0.000000    0.000000   -0.646514 \n",
    "O        0.000000    0.000000    0.484886  \n",
    "}  \n",
    "\n",
    "charge=0  \n",
    "\n",
    "spin=0  \n",
    "\n",
    "grid,name=neese,neese_index=6  \n",
    "\n",
    "df-ks,pbe,df_basis=aug-cc-pwCV5Z/mp2fit,maxit=200  \n",
    "{cfit,basis_coul=aug-cc-pwCV5Z/mp2fit,basis_exch=aug-cc-pwCV5Z/mp2fit}  \n",
    "\n",
    "user,rirpa,orb=2100.2,nquad=50,rpa=1,\\  \n",
    "charge=1,homo=0,\\  \n",
    "dfit=1,direct=1,\\  \n",
    "thr_overlap_ri=1d-10,thr_fai_ri=1d-10  \n",
    "```\n",
    "\n",
    "This gives:\n",
    "\n",
    "correlation energy =         -0.802657418904"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sigma-scaled RPA calcualtion for CO\n",
    "Note that Nodefile is required for this calculation\n",
    "\n",
    "```\n",
    "memory,4000,m  \n",
    "gthresh,twoint=1d-20,energy=1d-10,orbital=1d-8  \n",
    "basis={  \n",
    "default,aug-cc-pwCVQZ  \n",
    "set,ri\n",
    "default,aug-cc-pwCVQZ/mp2fit  \n",
    "}\n",
    "\n",
    "symmetry,nosym  \n",
    "angstrom  \n",
    "geometry={  \n",
    "2  \n",
    "\n",
    "C        0.000000    0.000000   -0.646514 \n",
    "O        0.000000    0.000000    0.484886  \n",
    "}  \n",
    "\n",
    "charge=0  \n",
    "\n",
    "spin=0  \n",
    "\n",
    "grid,name=neese,neese_index=6  \n",
    "\n",
    "df-ks,pbe,df_basis=aug-cc-pwCV5Z/mp2fit,maxit=200  \n",
    "{cfit,basis_coul=aug-cc-pwCV5Z/mp2fit,basis_exch=aug-cc-pwCV5Z/mp2fit}  \n",
    "\n",
    "user,rirpa,orb=2100.2,nquad=50,rpa=1,\\  \n",
    "charge=1,homo=0,\\  \n",
    "dfit=1,direct=1,\\  \n",
    "thr_overlap_ri=1d-10,thr_fai_ri=1d-10,\\  \n",
    "sigma_scale=1,\\\n",
    "vc_scal=1d0  \n",
    "```\n",
    "\n",
    "This gives:\n",
    "\n",
    "correlation energy =         -0.694102192073"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Standard RPA calcualtion for Al\n",
    "\n",
    "```\n",
    "memory,4000,m  \n",
    "gthresh,twoint=1d-20,energy=1d-10,orbital=1d-8  \n",
    "basis={  \n",
    "default,aug-cc-pwCVQZ  \n",
    "set,ri  \n",
    "default,aug-cc-pwCVQZ/mp2fit  \n",
    "}\n",
    "\n",
    "symmetry,nosym  \n",
    "angstrom  \n",
    "geometry={  \n",
    "1  \n",
    "\n",
    "Al 0.0 0.0 0.0  \n",
    "}  \n",
    "\n",
    "charge=0  \n",
    "\n",
    "spin=1  \n",
    "\n",
    "grid,name=neese,neese_index=6  \n",
    "\n",
    "df-uks,pbe,df_basis=aug-cc-pwCV5Z/mp2fit,maxit=200  \n",
    "{cfit,basis_coul=aug-cc-pwCV5Z/mp2fit,basis_exch=aug-cc-pwCV5Z/mp2fit}  \n",
    "\n",
    "user,urirpa,orb=2200.2,nquad=50,rpa=1,\\  \n",
    "charge=3,homo=0,\\  \n",
    "dfit=1,direct=1,\\  \n",
    "thr_overlap_ri=1d-10,thr_fai_ri=1d-10 \n",
    "```\n",
    "\n",
    "This gives:\n",
    "\n",
    "correlation energy =         -0.622966103914"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sigma-scaled RPA calcualtion for Al\n",
    "Note that Nodefile is required for this calculation\n",
    "\n",
    "```\n",
    "memory,4000,m  \n",
    "gthresh,twoint=1d-20,energy=1d-10,orbital=1d-8  \n",
    "basis={  \n",
    "default,aug-cc-pwCVQZ  \n",
    "set,ri  \n",
    "default,aug-cc-pwCVQZ/mp2fit  \n",
    "}\n",
    "\n",
    "symmetry,nosym  \n",
    "angstrom  \n",
    "geometry={  \n",
    "1  \n",
    "\n",
    "Al 0.0 0.0 0.0  \n",
    "}  \n",
    "\n",
    "charge=0  \n",
    "\n",
    "spin=1  \n",
    "\n",
    "grid,name=neese,neese_index=6  \n",
    "\n",
    "df-uks,pbe,df_basis=aug-cc-pwCV5Z/mp2fit,maxit=200  \n",
    "{cfit,basis_coul=aug-cc-pwCV5Z/mp2fit,basis_exch=aug-cc-pwCV5Z/mp2fit}  \n",
    "\n",
    "user,urirpa,orb=2200.2,nquad=50,rpa=1,\\  \n",
    "urirpa_mode=3,\\ ! this is required to use sigma-scaling in spin-polarized calculations  \n",
    "charge=3,homo=0,\\  \n",
    "dfit=1,direct=1,\\  \n",
    "thr_overlap_ri=1d-10,thr_fai_ri=1d-10,\\  \n",
    "sigma_scale=1,\\  \n",
    "vc_scal=1d0\n",
    "```\n",
    "\n",
    "This gives:\n",
    "\n",
    "correlation energy =         -0.546128215459"
   ]
  },
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