RI-GW.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# RI GW\n",
    "\n",
    "## Abstract \n",
    "\n",
    "Here we present a reference implementation of a GW class with the option of applying resolution-of-identity (JK with Coulomb metric, available for both self-energy and W) as well as SPA approximation when evaluating W. The class will be further extended to incorporate GW@DFT and spin polarization.\n",
    "\n",
    "1. Bruneval, F., Rangel, T., Hamed, S. M., Shao, M., Yang, C., & Neaton, J. B. (2016). molgw 1: Many-body perturbation theory software for atoms, molecules, and clusters. Computer Physics Communications, 208, 149–161. https://doi.org/10.1016/J.CPC.2016.06.019\n",
    "\n",
    "2. van Setten, M. J., Weigend, F., & Evers, F. (2013). The GW -Method for Quantum Chemistry Applications: Theory and Implementation. Journal of Chemical Theory and Computation, 9(1), 232–246. https://doi.org/10.1021/ct300648t"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import psi4\n",
    "import numpy as np\n",
    "import scipy as sp\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "SCF energy is   -76.0033540582\n"
     ]
    }
   ],
   "source": [
    "h2o = psi4.geometry(\"\"\"O   0.000000000000  -0.143225816552   0.000000000000 \n",
    "                       H   1.638036840407   1.136548822547  -0.000000000000\n",
    "                       H  -1.638036840407   1.136548822547  -0.000000000000\n",
    "                       symmetry c1\n",
    "                       units bohr\n",
    "\"\"\")\n",
    "\n",
    "psi4.set_options({'basis': 'aug-cc-pvdz', 'd_convergence' : 1e-7,'scf_type' : 'direct'})\n",
    "#psi4.set_options({'basis': 'aug-cc-pvdz', 'd_convergence' : 1e-7,'scf_type' : 'df', 'ints_tolerance' : 1.0E-10})\n",
    "\n",
    "\n",
    "psi4.set_memory('2 GB')\n",
    "psi4.set_output_file('h2o_accpvdz_rigw.out')\n",
    "\n",
    "# Get the SCF wavefunction & energies\n",
    "scf_e, scf_wfn = psi4.energy('hf', return_wfn=True)\n",
    "\n",
    "print(\"SCF energy is %16.10f\" % scf_e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# GW implementation will be folded into a standalone class that uses molecule and wave function data from Psi4\n",
    "\n",
    "class GW:\n",
    "    \n",
    "    def __init__(self, wfn, mol, gw_par):\n",
    "        \n",
    "        # wfn - Psi4 w.f. object from SCF calculation\n",
    "        # mol - Psi4 molecule object\n",
    "        # gw_par - is a dictionary with GW calculation parameters\n",
    "        #          such as the number of states or the number of \n",
    "        #          omega sampling points\n",
    "        \n",
    "        self.scf_wfn = wfn\n",
    "        self.mol = mol\n",
    "        \n",
    "        self._init_sys_params() # sets some basic system parameters\n",
    "        \n",
    "        # Determine if we are doing RI\n",
    "        \n",
    "        self.do_ri = True if not 'do_ri' in gw_par.keys() else gw_par['do_ri']\n",
    "        \n",
    "        if self.do_ri:\n",
    "            self._gen_ri_ints()     # generates integrals for RI-GW and\n",
    "            # RI integrals are now available in self.nmR\n",
    "        else:\n",
    "            self._transform_eri()\n",
    "            \n",
    "        #self._calculate_W(gw_par) # this will produce RPA excitation energies and X + Y\n",
    "        self._calculate_W_SPA(gw_par) # this will produce RPA excitation energies and X + Y\n",
    "        \n",
    "        # set GW calculation parameters\n",
    "        \n",
    "        # parameters of the self-energy calculation\n",
    "        nomega_sigma =  501 if not 'nomega_sigma' in gw_par.keys() else gw_par['nomega_sigma']\n",
    "        step_sigma = 0.01 if not 'step_sigma' in gw_par.keys() else  gw_par['step_sigma']\n",
    "        \n",
    "        # Quasi-particle states \n",
    "        self.no_qp = self.nocc if not 'no_qp' in gw_par.keys() else gw_par['no_qp'] # Number of hole states \n",
    "        self.nv_qp = 0 if not 'nv_qp' in gw_par.keys() else gw_par['nv_qp']             # Number of particle states\n",
    "        self.eta = 1e-3  # Default eta value as recommended by F. Bruneval\n",
    "        \n",
    "        # Quick sanity check\n",
    "        \n",
    "        assert self.no_qp <= self.nocc and self.nv_qp <= self.nvir\n",
    "\n",
    "        # create an array of sampling frequencies similar to MolGW\n",
    "\n",
    "        nomega_grid = nomega_sigma // 2 # note this is a truncation (aka integer) division\n",
    "        omega_grid = np.array(range(-nomega_grid, nomega_grid + 1)) * step_sigma\n",
    "        \n",
    "        # sampling energies for all the states so we could calculate the self-energy matrix (broadcasting)\n",
    "\n",
    "        omega_grid_all = omega_grid + self.eps[self.nocc - self.no_qp:self.nocc + self.nv_qp].reshape((-1, 1))\n",
    "        assert omega_grid_all.shape == (self.no_qp + self.nv_qp, 2*nomega_grid + 1)\n",
    "        \n",
    "        Sigma_c_grid = self._calculate_iGW(omega_grid_all) # self-energy matrix\n",
    "        \n",
    "        # Apply solvers; Similar to MolGW - linear & graphic solutions\n",
    "\n",
    "        print(\"Performing one-shot G0W0\")\n",
    "        \n",
    "        qp_molgw_lin_ = np.zeros(self.no_qp + self.nv_qp)\n",
    "\n",
    "        # Calculate pole strengths by performing numerical derivative on the omega grid\n",
    "\n",
    "        zz = np.real(Sigma_c_grid[:, nomega_grid + 1] - Sigma_c_grid[:, nomega_grid - 1]) / (omega_grid[nomega_grid + 1] - omega_grid[nomega_grid - 1])\n",
    "        zz = 1. / (1. - zz)\n",
    "        zz[zz <= 0.0] = 0.0\n",
    "        zz[zz >= 1.0] = 1.0\n",
    "        \n",
    "        qp_molgw_lin_ = self.eps[self.nocc - self.no_qp:self.nocc + self.nv_qp] + zz * np.real(Sigma_c_grid[:, nomega_grid])\n",
    "        \n",
    "        print(\"Perfoming graphic solution of the inverse Dyson equation\")\n",
    "\n",
    "        # both rhs and lhs of the QP equation have been calculated above\n",
    "        \n",
    "        qp_molgw_graph_ = np.copy(self.eps[self.nocc - self.no_qp:self.nocc + self.nv_qp])\n",
    "        zz_graph = np.zeros(self.no_qp + self.nv_qp)\n",
    "        \n",
    "        for state in range(self.no_qp + self.nv_qp):\n",
    "            z , e = self._find_fixed_point(omega_grid_all[state], np.real(Sigma_c_grid[state, :]) + self.eps[state + self.nocc - self.no_qp])\n",
    "            if z[0] < 1e-6:\n",
    "                print(\"Graphical solver failed for state %d\" % (state + 1))\n",
    "            # Do nothing since the array cell already contains HF orbital energy\n",
    "            else:\n",
    "                qp_molgw_graph_[state] = e[0]\n",
    "                zz_graph[state] = z[0]\n",
    "                \n",
    "        self.zz = np.copy(zz)\n",
    "        self.qp_molgw_lin_ = np.copy(qp_molgw_lin_)\n",
    "        self.qp_molgw_graph_ = np.copy(qp_molgw_graph_)\n",
    "                \n",
    "        print(\"Done!\")\n",
    "        \n",
    "    def print_summary(self):\n",
    "        \n",
    "        Ha2eV = 27.21138505\n",
    "        \n",
    "        print(\"E^lin, eV  E^graph, eV  Z \")\n",
    "        for i in range(self.no_qp + self.nv_qp):\n",
    "            print(\"%13.6f  %13.6f  %13.6f\" % (self.qp_molgw_lin_[i]*Ha2eV, self.qp_molgw_graph_[i]*Ha2eV, self.zz[i]))\n",
    "    \n",
    "                \n",
    "    def _init_sys_params(self):\n",
    "        \n",
    "        self.nocc = self.scf_wfn.nalpha()\n",
    "        self.nbf = self.scf_wfn.nmo()\n",
    "        self.nvir = self.nbf - self.nocc\n",
    "        self.C = self.scf_wfn.Ca()\n",
    "        \n",
    "        self.Cocc = self.scf_wfn.Ca_subset(\"AO\", \"OCC\")\n",
    "        self.Cvirt = self.scf_wfn.Ca_subset(\"AO\", \"VIR\")\n",
    "        \n",
    "        self.eps = np.asarray(self.scf_wfn.epsilon_a())\n",
    "        \n",
    "        # print a quick summary\n",
    "        print(\"Number of basis functions: \", self.nbf)\n",
    "        print(\"occ/virt: %d/%d\" % (self.nocc, self.nvir))\n",
    "    \n",
    "    def _transform_eri(self):\n",
    "        \n",
    "        Co = self.Cocc\n",
    "        C = self.C\n",
    "        \n",
    "        mints = psi4.core.MintsHelper(self.scf_wfn.basisset())\n",
    "        self.MO = np.asarray(mints.mo_eri(Co, C, C, C))\n",
    "        \n",
    "    def _gen_ri_ints(self):\n",
    "        \n",
    "        # MO coefficients\n",
    "        C = np.asarray(self.C)\n",
    "        \n",
    "        # Extract basis set from the wfn object\n",
    "        orb = self.scf_wfn.basisset()\n",
    "        \n",
    "        # Build auxiliary basis set\n",
    "        aux = psi4.core.BasisSet.build(self.mol, \"DF_BASIS_SCF\", \"\", \"JKFIT\", orb.name())\n",
    "        \n",
    "        # From Psi4 doc as of March, 2019 (http://www.psicode.org/psi4manual/1.2/psi4api.html#psi4.core.BasisSet.zero_ao_basis_set): \n",
    "        # Returns a BasisSet object that actually has a single s-function at \n",
    "        # the origin with an exponent of 0.0 and contraction of 1.0.\n",
    "        zero_bas = psi4.core.BasisSet.zero_ao_basis_set()\n",
    "        \n",
    "        # Create a MintsHelper Instance\n",
    "        mints = psi4.core.MintsHelper(orb)\n",
    "\n",
    "        # Build (pq|P) raw 3-index ERIs, dimension (nbf, nbf, Naux, 1)\n",
    "        pqP = mints.ao_eri(orb, orb, aux, zero_bas)\n",
    "\n",
    "        # Build and invert the metric\n",
    "        metric = mints.ao_eri(zero_bas, aux, zero_bas, aux)\n",
    "        metric.power(-0.5, 1.e-14)\n",
    "        \n",
    "        # Remove the dimensions of size 1\n",
    "        pqP = np.squeeze(pqP)\n",
    "        metric = np.squeeze(metric)\n",
    "\n",
    "        # Transform (pq|P) to obtain (nm|P) in molecular orbital basis\n",
    "        nmP = np.einsum(\"pn, qm, pqR-> nmR\", C, C, pqP)\n",
    "        \n",
    "        # Contract with the inverse square root of the metric tensor\n",
    "        self.nmR = np.einsum( \"nmP, PR-> nmR\", nmP, metric)\n",
    "        \n",
    "        print(\"Auxiliary basis set has been generated!\")\n",
    "        print(\"Number of auxiliary basis functions: \", self.nmR.shape[2])\n",
    "    \n",
    "    \n",
    "    def _calculate_W_SPA(self, gw_par):\n",
    "        # spa_onset - is the orbital # starting from which SPA will be employed, \n",
    "        # i.e. spa_onset - 1 is the index of the last virtual active in \n",
    "        # RPA calculation\n",
    "        \n",
    "        spa_onset = self.nbf if not 'spa_onset' in gw_par.keys() else gw_par['spa_onset']\n",
    "        spa_alpha = 1.5 if not 'spa_alpha' in gw_par.keys() else gw_par['spa_alpha']\n",
    "        \n",
    "        assert (spa_onset >= self.nocc) and (spa_alpha >= 0.0)\n",
    "        \n",
    "        nocc = self.nocc\n",
    "        nvir = self.nvir\n",
    "        nbf = self.nbf\n",
    "        \n",
    "        if spa_onset < nbf:\n",
    "            # The actual number of virtual orbitals is reduced\n",
    "            nvir = spa_onset  - nocc # if spa_onset is nocc (i.e. LUMO) => there is no virtual orbitals in the RPA\n",
    "        else:\n",
    "            spa_onset = nbf # for extra safety so that nothing fails if spa_onset is too large; the last virtual is nbf - 1 \n",
    "            \n",
    "        print(\"Number of virtual orbitals in RPA: %d\" % (nvir))\n",
    "        \n",
    "        # Diagonal \\epsilon_a - \\epsilon_i\n",
    "        eps_diag = self.eps[nocc:nocc + nvir].reshape(-1, 1) - self.eps[:nocc]\n",
    "        assert eps_diag.shape == (nvir, nocc)\n",
    "        \n",
    "        # Diagonal orbital difference matrix for SPA\n",
    "        eps_spa_diag = self.eps[spa_onset:].reshape(-1, 1) - self.eps[:nocc]\n",
    "        assert eps_spa_diag.shape == (nbf - nvir - nocc, nocc)\n",
    "        \n",
    "        # A^{+} + B^{+}\n",
    "        ApB = np.zeros((nocc, nvir, nocc, nvir))\n",
    "        ApB_spa_diag = np.zeros((nocc, nbf - nvir - nocc))\n",
    "        if self.do_ri:\n",
    "            ApB = np.einsum(\"ij,ab,ai -> iajb\", np.eye(nocc), np.eye(nvir), eps_diag) + 4. * np.einsum(\"iaQ, jbQ->iajb\", self.nmR[:nocc, nocc:nocc+nvir], self.nmR[:nocc, nocc:nocc+nvir])\n",
    "        else:\n",
    "            ApB = np.einsum(\"ij,ab,ai -> iajb\", np.eye(nocc), np.eye(nvir), eps_diag) + 4. * self.MO[:nocc, nocc:nocc + nvir, :nocc, nocc:nocc + nvir ]\n",
    "            \n",
    "        if spa_onset < nbf:\n",
    "            # calculate ApB_spa_diag\n",
    "            if self.do_ri:\n",
    "                ApB_spa_diag = spa_alpha * ( eps_spa_diag.T + 4. * np.einsum(\"iaQ, iaQ->ia\", self.nmR[:nocc, spa_onset:], self.nmR[:nocc, spa_onset:]))\n",
    "            else:\n",
    "                ApB_spa_diag = spa_alpha * (eps_spa_diag.T + 4. * np.einsum(\"iaia->ia\", self.MO[:nocc, spa_onset:, :nocc, spa_onset: ])) # not sure if this is 100% correct\n",
    "                    \n",
    "                \n",
    "        ApB = ApB.reshape((nocc*nvir, nocc*nvir)) \n",
    "        # since nD numpy arrays have C-style memroy layout the occupied orbital inedex changes slower than the virtual one\n",
    "\n",
    "        # Diagonal of  A^{+} - B^{+}\n",
    "        AmB_diag = eps_diag.T.reshape((1, -1))\n",
    "        AmB_diag = np.diag(AmB_diag[0,:])\n",
    "        \n",
    "        # Reshape the ApB_spa_diag as well\n",
    "        AmB_spa_diag = spa_alpha * eps_spa_diag.T.reshape((1, -1))\n",
    "        #AmB_spa_diag = np.diag(AmB_spa_diag[0,:])\n",
    "        ApB_spa_diag = ApB_spa_diag.reshape((1, -1))\n",
    "        \n",
    "\n",
    "        # Form C matrix (RPA eigenvalue problem)\n",
    "        C_ = np.einsum(\"ij,jk,kl->il\", np.sqrt(AmB_diag), ApB, np.sqrt(AmB_diag))\n",
    "        \n",
    "        # Solve for the excitation energies and calculate X + Y eigenvectors\n",
    "        \n",
    "        omega2, Z = np.linalg.eigh(C_)\n",
    "        self.omega_s = np.sqrt(omega2)\n",
    "        self.xpy = np.einsum(\"ij,jk,kl->il\", np.sqrt(AmB_diag), Z, np.diag(1./np.sqrt(self.omega_s)))\n",
    "        \n",
    "        if spa_onset < nbf:\n",
    "            omega_s_spa = np.sqrt(ApB_spa_diag * AmB_spa_diag)\n",
    "            #print(omega_s_spa.shape)\n",
    "            #print(np.sqrt(np.diag(AmB_spa_diag[0,:])).shape)\n",
    "            #print(np.eye(nocc * (nbf - nocc - nvir)).shape)\n",
    "            #print(np.diag(1./np.sqrt(omega_s_spa)).shape)\n",
    "            xpy_spa = np.einsum(\"ij,jk,kl->il\", np.sqrt(np.diag(AmB_spa_diag[0,:])), np.eye(nocc * (nbf - nocc - nvir)), np.diag(1./np.sqrt(omega_s_spa[0,:])))\n",
    "            # The trickiest part is the eigenvectors since the index spaces should be \n",
    "            # aligned; Here we need to do the following:\n",
    "            # 1. Stretch xpy array such that its shape = (nocc * (nbf - nocc), nocc * (nbf - nocc))\n",
    "            # 2. Copy the eigenvectors adding 0 in place of excitations excluded via SPA\n",
    "            # 3. Add an apropriate number of xpy_spa padding them with zero at the indexes corresponding\n",
    "            #    to excitations excluded from SPA\n",
    "            \n",
    "            xpy_tmp = np.zeros((nocc * (nbf - nocc), nocc * (nbf - nocc)))\n",
    "            \n",
    "            # Merge non-SPA eigenvectors first\n",
    "            \n",
    "            nvir_spa = nbf - nocc - nvir\n",
    "            \n",
    "            for i in range(len(self.omega_s)):\n",
    "                for j in range(nocc):\n",
    "                    xpy_tmp[j * (nbf - nocc) : j * (nbf - nocc) + nvir , i] = self.xpy[j * nvir: (j+1) * nvir, i] \n",
    "                    \n",
    "            # Now merge SPA vectors\n",
    "            \n",
    "            for i in range(len(omega_s_spa)):\n",
    "                for j in range(nocc):\n",
    "                    xpy_tmp[ j * (nbf - nocc) + nvir : (j + 1) * (nbf - nocc)  , i + len(self.omega_s)] = xpy_spa[j * nvir_spa: (j+1) * nvir_spa, i] \n",
    "                    \n",
    "            # Replace xpy with xpy_tmp and update the list of excitation energies accordingly\n",
    "            \n",
    "            self.xpy = np.copy(xpy_tmp)\n",
    "            self.omega_s = np.hstack((self.omega_s, omega_s_spa[0,:]))\n",
    "\n",
    "        \n",
    "    def _calculate_W(self, gw_par):\n",
    "        \n",
    "                \n",
    "        nocc = self.nocc\n",
    "        nvir = self.nvir\n",
    "        \n",
    "        # Diagonal \\epsilon_a - \\epsilon_i\n",
    "        eps_diag = self.eps[nocc:].reshape(-1, 1) - self.eps[:nocc]\n",
    "        assert eps_diag.shape == (nvir, nocc)\n",
    "        \n",
    "        # A^{+} + B^{+}\n",
    "        ApB = np.zeros((nocc, nvir, nocc, nvir))\n",
    "        if self.do_ri:\n",
    "            ApB = np.einsum(\"ij,ab,ai -> iajb\", np.eye(nocc), np.eye(nvir), eps_diag) + 4. * np.einsum(\"iaQ, jbQ->iajb\", self.nmR[:nocc, nocc:], self.nmR[:nocc, nocc:])\n",
    "        else:\n",
    "            ApB = np.einsum(\"ij,ab,ai -> iajb\", np.eye(nocc), np.eye(nvir), eps_diag) + 4. * self.MO[:nocc, nocc:, :nocc, nocc: ]\n",
    "        \n",
    "                  \n",
    "        \n",
    "        ApB = ApB.reshape((nocc*nvir, nocc*nvir)) \n",
    "        # since nD numpy arrays have C-style memroy layout the occupied orbital inedex changes slower than the virtual one\n",
    "\n",
    "        # Diagonal of  A^{+} - B^{+}\n",
    "        AmB_diag = eps_diag.T.reshape((1, -1))\n",
    "        AmB_diag = np.diag(AmB_diag[0,:])\n",
    "\n",
    "        assert AmB_diag.shape == ApB.shape\n",
    "\n",
    "        # Form C matrix (as one usually does when solving RPA eigenvalue problem)\n",
    "        C_ = np.einsum(\"ij,jk,kl->il\", np.sqrt(AmB_diag), ApB, np.sqrt(AmB_diag))\n",
    "        \n",
    "        # Solve for the excitation energies and calculate X + Y eigenvectors\n",
    "        \n",
    "        omega2, Z = np.linalg.eigh(C_)\n",
    "        self.omega_s = np.sqrt(omega2)\n",
    "        self.xpy = np.einsum(\"ij,jk,kl->il\", np.sqrt(AmB_diag), Z, np.diag(1./np.sqrt(self.omega_s)))\n",
    "        \n",
    "    def _calculate_iGW(self, omega_grid_all):\n",
    "        \n",
    "        nocc = self.nocc\n",
    "        nvir = self.nvir\n",
    "        eps = self.eps\n",
    "        \n",
    "        no_qp = self.no_qp\n",
    "        nv_qp = self.nv_qp\n",
    "        nbf = self.nbf\n",
    "        \n",
    "        # Self-energy denominators; those are of two kinds\n",
    "\n",
    "        Dis = -eps[:nocc].reshape((-1, 1)) + self.omega_s\n",
    "        Das = -eps[nocc:].reshape((-1, 1)) - self.omega_s \n",
    "        \n",
    "        # Omega tensors; This will be refactored to improve memory efficiency\n",
    "        i_rtia = np.zeros((nbf,nbf, nocc, nvir))\n",
    "        if self.do_ri:\n",
    "            i_rtia = np.einsum(\"iaQ, rtQ ->rtia\", self.nmR[:nocc, nocc:, :], self.nmR) \n",
    "            i_rtia = i_rtia.reshape((nbf, nbf, nocc*nvir))\n",
    "        else:\n",
    "            i_rtia = np.einsum(\"iart->rtia\", self.MO[:,nocc:,:,:]) \n",
    "            i_rtia = i_rtia.reshape((nbf, nbf, nocc*nvir))\n",
    "            \n",
    "        omega_rts = np.sqrt(2.) * np.einsum(\"rtk, ks->rts\", i_rtia, self.xpy)\n",
    "        \n",
    "        #Calculate denominators\n",
    "        \n",
    "        Dis_ = Dis + omega_grid_all.reshape((no_qp + nv_qp, omega_grid_all.shape[1], 1, 1)) - 1.j*self.eta\n",
    "        Das_ = Das + omega_grid_all.reshape((no_qp + nv_qp, omega_grid_all.shape[1], 1, 1)) + 1.j*self.eta\n",
    "\n",
    "        # self-energy matrix (with the shape (no_qp + nv_qp, 2*nomega_grid + 1))\n",
    "\n",
    "        # Contribution due to occupied orbitals (note that the shape of the structure of the denominator array is not optimal)\n",
    "        Sigma_c_grid = np.einsum(\"kis, klis, kis->kl\", omega_rts[nocc - no_qp:nocc + nv_qp,:nocc,:], 1./Dis_, omega_rts[nocc - no_qp:nocc + nv_qp,:nocc,:])\n",
    "        # Contribution due to virtuals\n",
    "        Sigma_c_grid +=  np.einsum(\"kas, klas, kas->kl\", omega_rts[nocc - no_qp:nocc + nv_qp,nocc:,:], 1./Das_, omega_rts[nocc - no_qp:nocc + nv_qp,nocc:,:])\n",
    " \n",
    "        \n",
    "        return Sigma_c_grid\n",
    "    \n",
    "    \n",
    "    def _find_fixed_point(self, lhs, rhs):\n",
    "        # This function returns an array of fixed points and correspoinding pole strengths\n",
    "        # Its application can be vectorized using strandard NumPy np.vectorize\n",
    "    \n",
    "        assert lhs.shape == rhs.shape\n",
    "    \n",
    "        # Maximum number of fixed points (same as in MolGW)\n",
    "        nfp_max = 4\n",
    "    \n",
    "        # Pole strength threshold\n",
    "        pthresh = 1e-5\n",
    "    \n",
    "        # Arrays of f.p. energies and  Z\n",
    "        zfp = np.zeros(nfp_max)\n",
    "        zfp[:] = -1.0\n",
    "        efp = np.zeros(nfp_max)\n",
    "    \n",
    "        # Auxiliary index array\n",
    "        idx = np.arange(nfp_max)\n",
    "    \n",
    "        n = len(lhs)\n",
    "        ifixed = 0\n",
    "        g = rhs - lhs\n",
    "    \n",
    "        # loop over grid points excluding the last one\n",
    "    \n",
    "        for i in range(n - 1):\n",
    "            if g[i] * g[i + 1] < 0.0:\n",
    "                #print(\"Fixed point found betwenn %13.6f and %13.6f eV! \" % (lhs[i] * Ha2eV, lhs[i+1] * Ha2eV))\n",
    "                z_zero = 1. / ( 1. - ( g[i+1] - g[i] ) / ( lhs[i+1] - lhs[i] ) )\n",
    "                if z_zero < pthresh:\n",
    "                    continue\n",
    "                # Do some bookkeeping; the code looks ugly but that is exactly what F.Bruneval has in MolGW package\n",
    "            \n",
    "                if z_zero > zfp[-1]:\n",
    "                    jfixed = np.min(idx[z_zero > zfp])\n",
    "                    zfp[jfixed + 1:] = zfp[jfixed:nfp_max - 1]\n",
    "                    efp[jfixed + 1:] = efp[jfixed:nfp_max - 1]\n",
    "                    zfp[jfixed] = z_zero\n",
    "                    # Perfom linear interpolation to find the root\n",
    "                    zeta = (g[i + 1] - g[i]) / (lhs[i + 1] - lhs[i])\n",
    "                    efp[jfixed] = lhs[i] - g[i] / zeta\n",
    "    \n",
    "        #print(\"Graphical solver concluded operation\")\n",
    "        return (zfp, efp)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "E^lin, eV  E^graph, eV  Z \n",
      "  -548.539374    -547.986942       0.794502\n",
      "   -32.344115     -31.106137       0.651707\n",
      "   -17.199686     -17.199453       0.938071\n",
      "   -14.246618     -14.245208       0.928771\n",
      "   -12.060278     -12.056027       0.921941\n",
      "     0.718180       0.718175       0.994145\n"
     ]
    }
   ],
   "source": [
    "# Quick test for the GW class\n",
    "\n",
    "gw_par = {'no_qp' : 5, 'nv_qp' : 1, 'nomega_sigma' : 501, 'step_sigma' : 0.01, 'do_ri' : False}\n",
    "\n",
    "gw_h2o_accpvdz = GW(scf_wfn, h2o, gw_par)\n",
    "gw_h2o_accpvdz.print_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Auxiliary basis set has been generated!\n",
      "Number of auxiliary basis functions:  150\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "E^lin, eV  E^graph, eV  Z \n",
      "  -548.539289    -547.986854       0.794502\n",
      "   -32.343877     -31.105740       0.651667\n",
      "   -17.198599     -17.198365       0.938078\n",
      "   -14.245902     -14.244489       0.928775\n",
      "   -12.059619     -12.055365       0.921945\n",
      "     0.718147       0.718143       0.994143\n"
     ]
    }
   ],
   "source": [
    "gw_par = {'no_qp' : 5, 'nv_qp' : 1, 'nomega_sigma' : 501, 'step_sigma' : 0.01, 'do_ri' : True}\n",
    "\n",
    "rigw_h2o_accpvdz = GW(scf_wfn, h2o, gw_par)\n",
    "rigw_h2o_accpvdz.print_summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 2\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "E^lin, eV  E^graph, eV  Z \n",
      "  -559.330154    -559.326189       0.943804\n",
      "   -35.092657     -35.108317       0.736476\n",
      "   -17.457153     -17.457130       0.988255\n",
      "   -14.989264     -14.989221       0.985092\n",
      "   -13.319399     -13.319324       0.983257\n",
      "     0.864673       0.864673       0.999210\n"
     ]
    }
   ],
   "source": [
    "# GW class with the new SPA-enabled calculate_W method (SPA will be enabled starting from orbital #7 (LUMO + 2))\n",
    "\n",
    "gw_par = {'no_qp' : 5, 'nv_qp' : 1, 'nomega_sigma' : 501, 'step_sigma' : 0.01, 'do_ri' : False, 'spa_onset' : 7}\n",
    "\n",
    "gw_h2o_accpvdz = GW(scf_wfn, h2o, gw_par)\n",
    "gw_h2o_accpvdz.print_summary()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "```\n",
    "   1   -560.533646    -0.000000    15.096607     0.794502  -548.539363  -547.986931\n",
    "   2    -35.249771    -0.000000     4.458541     0.651707   -32.344109   -31.106131\n",
    "   3    -17.621318    -0.000000     0.449470     0.938071   -17.199683   -17.199450\n",
    "   4    -15.211273    -0.000000     1.038641     0.928771   -14.246613   -14.245203\n",
    "   5    -13.614305    -0.000000     1.685604     0.921941   -12.060277   -12.056026\n",
    "   6      0.873198    -0.000000    -0.155930     0.994145     0.718181     0.718176\n",
    "\n",
    "```\n",
    "\n",
    "```\n",
    "   WITH SPA (2 virtuals in RPA)\n",
    "   1   -560.533646    -0.000000     1.269277     0.943812  -559.335688  -559.331759\n",
    "   2    -35.249771    -0.000000     0.213172     0.736479   -35.092774   -35.108421\n",
    "   3    -17.621318    -0.000000     0.166196     0.988255   -17.457074   -17.457051\n",
    "   4    -15.211273    -0.000000     0.225294     0.985092   -14.989337   -14.989294\n",
    "   5    -13.614305    -0.000000     0.300034     0.983257   -13.319294   -13.319219\n",
    "   6      0.873198    -0.000000    -0.008534     0.999210     0.864670     0.864670\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 0\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 1\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 2\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 3\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 4\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 5\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 6\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 7\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 8\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 9\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 10\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 11\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 12\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 13\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 14\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 15\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 16\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 17\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 18\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 19\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 20\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 21\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 22\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 23\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 24\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 25\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 26\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 27\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 28\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 29\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 30\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 31\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 32\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 33\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 34\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n",
      "Number of basis functions:  41\n",
      "occ/virt: 5/36\n",
      "Number of virtual orbitals in RPA: 35\n",
      "Performing one-shot G0W0\n",
      "Perfoming graphic solution of the inverse Dyson equation\n",
      "Done!\n"
     ]
    }
   ],
   "source": [
    "# Convergence test for water (noRI; SPA as specified below)\n",
    "global_gw_par = {'no_qp' : 5, 'nv_qp' : 10, 'nomega_sigma' : 501, 'step_sigma' : 0.01, 'do_ri' : False}\n",
    "ilumo = 5 # Water has five occ. orbitals\n",
    "ilastvir = 40 # for aug-cc-pvdz\n",
    "qp_en = np.zeros((global_gw_par['no_qp'] + global_gw_par['nv_qp'], 36))\n",
    "\n",
    "for i in range(ilumo, ilastvir+1):\n",
    "    global_gw_par['spa_onset'] = i\n",
    "    gw_h2o = GW(scf_wfn, h2o, global_gw_par)\n",
    "    qp_en[:, i - ilumo] = gw_h2o.qp_molgw_graph_\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f9387d0e668>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Ha2eV = 27.21138505\n",
    "\n",
    "x = np.asarray(range(ilumo, ilastvir + 1))\n",
    "for state in range(7, global_gw_par['no_qp'] + global_gw_par['nv_qp']):\n",
    "    plt.plot(x + 1, Ha2eV * qp_en[state, :], 'o-', label='state '+str(state + 1) )\n",
    "    \n",
    "plt.xlabel('SPA onset (counting from 1)')\n",
    "plt.ylabel('BE, eV')\n",
    "plt.legend()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f93875eaf98>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Some error convergence analysis\n",
    "\n",
    "qp_en_err = (qp_en.T - qp_en[:,-1].T).T\n",
    "x = np.asarray(range(ilumo, ilastvir + 1))\n",
    "for state in range(5, global_gw_par['no_qp'] + global_gw_par['nv_qp']):\n",
    "    plt.plot(x + 1, Ha2eV * qp_en_err[state, :], 'o-', label='state '+str(state + 1) )\n",
    "    \n",
    "plt.xlabel('SPA onset (counting from 1)')\n",
    "plt.ylabel('BE Error, eV')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f9387518a90>"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
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     "output_type": "display_data"
    }
   ],
   "source": [
    "# Error analysis for occupied states\n",
    "\n",
    "for state in range(0, 5):\n",
    "    plt.plot(x + 1, Ha2eV * qp_en_err[state, :], 'o-', label='state '+str(state + 1) )\n",
    "    \n",
    "plt.xlabel('SPA onset (counting from 1)')\n",
    "plt.ylabel('BE Error (occupied), eV')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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