## Developing a Hartree-Fock program, the simple Python program

	""" Star HF-iterations, preparing variables and density matrix """

""" Coefficients for setting up density matrix, assuming only one along the diagonals """
C = np.eye(spOrbitals) # HF coefficients
DensityMatrix = np.zeros([spOrbitals,spOrbitals])
for gamma in range(spOrbitals):
for delta in range(spOrbitals):
sum = 0.0
for i in range(Nparticles):
sum += C[gamma][i]*C[delta][i]
DensityMatrix[gamma][delta] = Decimal(sum)
maxHFiter = 100
epsilon =  1.0e-10
difference = 1.0
hf_count = 0
oldenergies = np.zeros(spOrbitals)
newenergies = np.zeros(spOrbitals)
while hf_count < maxHFiter and difference > epsilon:
print "############### Iteration %i ###############" % hf_count
HFmatrix = np.zeros([spOrbitals,spOrbitals])
for alpha in range(spOrbitals):
for beta in range(spOrbitals):
"""  If tests for three-dimensional systems, including isospin conservation """
if l[alpha] != l[beta] and j[alpha] != j[beta] and mj[alpha] != mj[beta] and tz[alpha] != tz[beta]: continue
"""  Setting up the Fock matrix using the density matrix and antisymmetrized NN interaction in m-scheme """
sumFockTerm = 0.0
for gamma in range(spOrbitals):
for delta in range(spOrbitals):
if (mj[alpha]+mj[gamma]) != (mj[beta]+mj[delta]) and (tz[alpha]+tz[gamma]) != (tz[beta]+tz[delta]): continue
sumFockTerm += DensityMatrix[gamma][delta]*nninteraction[alpha][gamma][beta][delta]
HFmatrix[alpha][beta] = Decimal(sumFockTerm)
"""  Adding the one-body term, here plain harmonic oscillator """
if beta == alpha:   HFmatrix[alpha][alpha] += singleparticleH[alpha]
spenergies, C = np.linalg.eigh(HFmatrix)
""" Setting up new density matrix in m-scheme """
DensityMatrix = np.zeros([spOrbitals,spOrbitals])
for gamma in range(spOrbitals):
for delta in range(spOrbitals):
sum = 0.0
for i in range(Nparticles):
sum += C[gamma][i]*C[delta][i]
DensityMatrix[gamma][delta] = Decimal(sum)
newenergies = spenergies
""" Brute force computation of difference between previous and new sp HF energies """
sum =0.0
for i in range(spOrbitals):
sum += (abs(newenergies[i]-oldenergies[i]))/spOrbitals
difference = sum
oldenergies = newenergies
print "Single-particle energies, ordering may have changed "
for i in range(spOrbitals):
print('{0:4d}  {1:.4f}'.format(i, Decimal(oldenergies[i])))
hf_count += 1