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#!/usr/bin/env python
# coding: utf-8
from pyscf import gto
import numpy as np
delta_E = 1.0e-8 # Energy convergence criterion
delta_P = 1.0e-8 # Density matrix convergence criterion
MAXITER = 100 # Maximum number of SCF Iterations
def build_hc(T_e: np.array, V_ne: np.array) -> np.array:
return T_e+V_ne
def build_ortho_mat(S: np.array) -> np.array:
s, U = np.linalg.eig(S)
L = np.diag(np.power(s, -0.5))
X = np.dot(U,(np.dot(L,np.transpose(U))))
return X
def build_fock_prime(F: np.array, X: np.array) -> np.array:
Fp=np.dot(np.transpose(X),np.dot(F,X))
return Fp
def eigensort(eigenvalues: np.array, eigenvectors: np.array) -> (np.array, np.array):
eigenvectors = eigenvectors[:,eigenvalues.argsort()]
eigenvalues = np.sort(eigenvalues)
return eigenvalues, eigenvectors
def solve_eigenvalue(Fp: np.array, X: np.array) -> (np.array, np.array):
e, Cp = np.linalg.eigh(Fp)
e, Cp = eigensort(e, Cp)
C = np.dot(np.transpose(X),Cp)
return e, C
def build_density(C: np.array, NAO: int, NEL: int) -> np.array:
P = np.zeros((NAO, NAO))
for i in range(len(C)):
for j in range(len(C)):
for m in range(int(NEL/2)): #Number of occupied orbitals
P[i][j] += C[i][m] * C[j][m]
return P
def electronic_energy(P: np.array, Hc: np.array, F: np.array, NAO: int) -> float:
E = 0
for u in range(NAO):
for v in range(NAO):
E += P[u][v] * (Hc[u][v] + F[u][v])
return E
def build_new_fock(Hc: np.array, P: np.array, J: np.array, NAO: int) -> np.array:
F = np.copy(Hc)
for u in range(NAO):
for v in range(NAO):
for l in range(NAO):
for s in range(NAO):
F[u][v] += P[l][s] * ((2 * J[u][v][l][s]) - J[u][l][v][s])
return F
def compute_rmsd(P0: np.array, P1: np.array) -> float:
rmsd = 0
for u in range(len(P0)):
for v in range(len(P0[u])):
rmsd += (P1[u][v] - P0[u][v])**2
return np.sqrt(rmsd)
def scf(Hc: np.array, X: np.array, J: np.array, E_nuc: float, NAO: int, NEL: int) -> dict:
Fp_0 = build_fock_prime(Hc, X)
e_0,C_0 = solve_eigenvalue(Fp_0, X)
P_0 = build_density(C_0, NAO, NEL)
E_el_0 = electronic_energy(P_0, Hc, Hc, NAO)
E_tot_0 = E_el_0 + E_nuc
this_scf = {
"tot_energies": [E_tot_0],
"orb_eigenvalues": [e_0],
}
# SCF loop
for i in range(1,MAXITER+1):
F = build_new_fock(Hc, P_0, J, NAO)
Fp = build_fock_prime(F, X)
e, C = solve_eigenvalue(Fp, X)
P = build_density(C, NAO, NEL)
E_el = electronic_energy(P, Hc, F, NAO)
E_tot = E_el + E_nuc
this_scf["tot_energies"].append(E_tot)
this_scf["orb_eigenvalues"].append(e)
if np.abs(E_el-E_el_0)<delta_E:
print("E_el converged after: "+str(i)+" Iterations.")
print()
this_scf["iterations"] = i
break
E_el_0 = E_el
if compute_rmsd(P_0,P)<delta_P:
print("P converged after: "+str(i)+" Iterations.")
print()
this_scf["iterations"] = i
break
P_0 = np.copy(P)
print(" Final RHF results")
print(" -----------------")
print()
print("Total SCF energy = "+str(E_tot))
print()
print(" Final eigenvalues")
print(" -----------------")
print()
for i in range(len(e)):
print(str(i+1)+" "+str(e[i]))
this_scf["tot_energies"] = np.array(this_scf["tot_energies"])
this_scf["orb_eigenvalues"] = np.array(this_scf["orb_eigenvalues"])
return this_scf