def test_LS_commutation_relations():
eps = 1e-7
Re = dieke.RareEarthIon(2) # Pr
L = Re.FreeIonMatrix['L']
Lx = Re.FreeIonMatrix['Lx']
Ly = Re.FreeIonMatrix['Ly']
Lz = Re.FreeIonMatrix['Lz']
S = Re.FreeIonMatrix['S']
Sx = Re.FreeIonMatrix['Sx']
Sy = Re.FreeIonMatrix['Sy']
Sz = Re.FreeIonMatrix['Sz']
J = Re.FreeIonMatrix['J']
Jx = Lx+Sx
Jy = Ly+Sy
Jz = Lz+Sz
Lvec = [Lx,Ly,Lz]
Svec = [Sx,Sy,Sz]
for k in range(3):
for j in range(3):
assert(norm((Lvec[k]@Svec[j]-Svec[j]@Lvec[k]).A)<eps)
assert(norm((Lx@Ly-Ly@Lx-1j*Lz).A)<eps)
assert(norm((Sx@Sy-Sy@Sx-1j*Sz).A)<eps)
assert(norm((Jx@Jy-Jy@Jx-1j*Jz).A)<eps)
assert(norm((Lx@Lx + Ly@Ly + Lz@ Lz - L@(L+np.eye(Re.numstates()))).A) < eps)
assert(norm((Sx@Sx + Sy@Sy + Sz@ Sz - S@(S+np.eye(Re.numstates()))).A) < eps)
assert(norm((Jx@Jx + Jy@Jy + Jz@ Jz - J@(J+np.eye(Re.numstates()))).A) < eps)
def test_Er_LaF3():
"""
Tests that we give the same results as Carnall 1989 for Pr:LaF3
"""
#energy levels from Carnall's paper
carnall_levels = [-22, 27, 92, 176, 193, 289, 375, 420,
6612, 6637, 6686, 6699, 6732, 6771, 6830,
10300, 10314, 10336, 10351, 10365, 10405]
carnall_levels = np.array(carnall_levels)
carnall_levels = carnall_levels -np.min(carnall_levels)
nf = 11 # 11 f-electrons means we're dealing with Er
Er = dieke.RareEarthIon(nf)
cfparams = dieke.readLaF3params(nf)
# Number of levels and states
numLSJ = Er.numlevels()
numLSJmJ = Er.numstates()
# Make a free-ion Hamiltonian
H0 = np.zeros([numLSJmJ, numLSJmJ])
for k in cfparams.keys():
if k in Er.FreeIonMatrix:
H0 = H0+cfparams[k]*Er.FreeIonMatrix[k]
# Add in the crystal field terms
H = H0
for k in [2, 4, 6]:
for q in range(0, k+1):
if 'B%d%d' % (k, q) in cfparams:
if q == 0:
H = H+cfparams['B%d%d' % (k, q)]*Er.Cmatrix(k, q)
else:
Bkq = cfparams['B%d%d' % (k, q)]
Bkmq = (-1)**q*np.conj(Bkq) # B_{k,-q}
Ckq = Er.Cmatrix(k, q)
Ckmq = Er.Cmatrix(k, -q)
# See page 44, eq 3.1 of the crystal field handbook
H = H + Bkq*Ckq + Bkmq*Ckmq
# Diagonalise the result
(evals, evects) = np.linalg.eig(H)
E0 = np.min(evals)
calc_nrg_levels = np.sort(evals-E0)
calc_nrg_levels = calc_nrg_levels[::2]
print(' Jevon Carnall Difference')
for k in range(len(carnall_levels)):
print("%9.1f %9.1f %6.1f"%(np.real(calc_nrg_levels[k]),carnall_levels[k],np.real(calc_nrg_levels[k]) - carnall_levels[k]))
# Assert that they all agree within 1.1 wave number
assert(np.max(np.abs(
calc_nrg_levels[0:len(carnall_levels)]-carnall_levels))
< 1.1 )
def test_content(response):
"""Sample pytest test function with the pytest fixture as an argument."""
# from bs4 import BeautifulSoup
# assert 'GitHub' in BeautifulSoup(response.content).title.string
rare_earths = ["La", "Ce", "Pr", "Nd", "Pm", "Sm", "Eu", "Gd",
"Tb", "Dy", "Ho", "Er", "Tm", "Yb"]
for k in [2]: # range(2, 13):
print("Making matricies for %s (nf=%d)\n" % (rare_earths[k], k))
dieke.RareEarthIon(k)
def test_Pr_LaF3():
"""
Tests that we give the same results as Carnall 1989 for Pr:LaF3
"""
#energy levels from Carnall's paper
carnall_levels = [0.2, 71, 95, 138, 183, 221, 333, 444, 463,
2126, 2158, 2191, 2284, 2290, 2295, 2318,
2399, 2412,2438, 2540, 4179,4200, 4283,
4321, 4384, 4467, 4478, 4496]
carnall_levels = np.array(carnall_levels)
nf = 2 # 2 f-electrons means we're dealing with Pr
Pr = dieke.RareEarthIon(nf)
cfparams = dieke.readLaF3params(nf)
# Number of levels and states
numLSJ = Pr.numlevels()
numLSJmJ = Pr.numstates()
# Make a free-ion Hamiltonian
H0 = np.zeros([numLSJmJ, numLSJmJ])
for k in cfparams.keys():
if k in Pr.FreeIonMatrix:
H0 = H0+cfparams[k]*Pr.FreeIonMatrix[k]
# Add in the crystal field terms
H = H0
for k in [2, 4, 6]:
for q in range(0, k+1):
if 'B%d%d' % (k, q) in cfparams:
if q == 0:
H = H+cfparams['B%d%d' % (k, q)]*Pr.Cmatrix(k, q)
else:
Bkq = cfparams['B%d%d' % (k, q)]
Bkmq = (-1)**q*np.conj(Bkq) # B_{k,-q}
Ckq = Pr.Cmatrix(k, q)
Ckmq = Pr.Cmatrix(k, -q)
# See page 44, eq 3.1 of the crystal field handbook
H = H + Bkq*Ckq + Bkmq*Ckmq
# Diagonalise the result
(evals, evects) = np.linalg.eig(H)
E0 = np.min(evals)
calc_nrg_levels = np.sort(evals-E0)
# Assert that they all agree within one wave number
assert(np.max(np.abs(
calc_nrg_levels[0:len(carnall_levels)]-carnall_levels))
< 1.0 )
sebmats = pickle.load(gzip.open('f11cf_matel.p.gz', 'rb'))
nf = 11 # 2 f-electrons means we're dealing with Er
# This object contains the matricies we need for the
# calculations all in the dictionary "FreeIonMatrix"
# or via the function "Cmatrix"
#cache my version of the matrix elements to make stuff faster
try:
f = gzip.open('erbium.dat.gz', 'rb')
print("Loading Er object")
Er = pickle.load(f)
except FileNotFoundError:
print("Making Er ojbect")
Er = dieke.RareEarthIon(nf)
pickle.dump(Er, gzip.open('erbium.dat.gz', 'wb'))
#Er = dieke.RareEarthIon(nf)
#pickle.dump(Er, gzip.open('erbium.dat.gz', 'wb'))
jevmats = Er.FreeIonMatrix
# Add the crystal field matricies to my dict
for k in [2, 4, 6]:
for q in range(k + 1):
jevmats['C%d%d' % (k, q)] = Er.Cmatrix(k, q)
statedict = {}
for i in range(364):
statedict[Er.LSJmJstateLabels[i]] = i
cfparams = {'nf': 2.0, 'F2': 68878.0, 'F4': 50347.0, 'F6': 32901.0}
numLSJ = Pr.numlevels()
for operator in ['F2', 'F4', 'F6', 'ZETA']:
mat = Pr.FreeIonMatrix[operator]
print(operator)
for i in range(numLSJ):
for j in range(i, numLSJ):
if np.abs(mat[i, j]) > 1e-6:
print("<%s | %s | %s > = %f" %
(Pr.LSJlevelLabels[i], operator, Pr.LSJlevelLabels[i],
mat[i, j]))
Ce = dieke.RareEarthIon(1)
mat = Ce.Cmatrix(2, 0)
for i in range(Ce.numstates()):
for j in range(Ce.numstates()):
if np.abs(mat[i, j]) > 1e-6:
print("<%s | C20 | %s > = %f" %
(Ce.LSJmJstateLabels[i], Ce.LSJmJstateLabels[j], mat[i, j]))
# # Make an empy matrix to put the results in as well as an
# # empty matrix for the Hamiltonian
# numLSJ = Pr.numlevels()
H0 = np.zeros([numLSJ, numLSJ])
# Make the Hamiltonian, diagonalise it and work out the
# energy of the ground state
def test_ErYSO():
"""
Tests that we give the same as Sebastians calcs for ErYSO
(arXiv:1809.01058)
"""
#energy levels from Paper
seb_levels = [15, 47, 75, 130, 199, 388, 462, 508,
6522, 6560, 6583, 6640, 6777, 6833, 6867,
10206, 10236, 10267, 10339, 10381, 10398]
seb_levels = np.array(seb_levels)
nf = 11 # 11 f-electrons means we're dealing with Er
Er = dieke.RareEarthIon(nf)
# Number of levels and states
numLSJ = Er.numlevels()
numLSJmJ = Er.numstates()
cfparams = dieke.readLaF3params(nf)
cfparams['E0'] = 35503.5 #this is ignored
cfparams['ZETA'] = 2362.9
cfparams['F2'] = 96029.6
cfparams['F4'] = 67670.6
cfparams['F6'] = 53167.1
cfparams['B20'] = -149.8
cfparams['B21'] = 420.6+396.0j
cfparams['B22'] = -228.5+27.6j
cfparams['B40'] = 1131.2
cfparams['B41'] = 985.7+34.2j
cfparams['B42'] = 296.8+145.0j
cfparams['B43'] = -402.3-381.7j
cfparams['B44'] = -282.3+1114.3j
cfparams['B60'] = -263.2
cfparams['B61'] = 111.9+222.9j
cfparams['B62'] = 124.7+195.9j
cfparams['B63'] = -97.9+139.7j
cfparams['B64'] = -93.7-145.0j
cfparams['B65'] = 13.9+109.5j
cfparams['B66'] = 3.0-108.6j
cfparams['A'] = 0.005466 #this is ignored
cfparams['Q'] = 0.0716 #this is ignored
# Make a free-ion Hamiltonian
H0 = np.zeros([numLSJmJ, numLSJmJ])
for k in sorted(cfparams.keys()):
if k in Er.FreeIonMatrix:
print("Adding free ion parameter \'%s\' = %g" % (k, cfparams[k]))
H0 = H0+cfparams[k]*Er.FreeIonMatrix[k]
# Add in the crystal field terms and diagonalise the result
H = H0
for k in [2, 4, 6]:
for q in range(0, k+1):
if 'B%d%d' % (k, q) in cfparams:
if q == 0:
H = H+cfparams['B%d%d' % (k, q)]*Er.Cmatrix(k, q)
else:
Bkq = cfparams['B%d%d' % (k, q)]
Bkmq = (-1)**q*np.conj(Bkq)
Ckq = Er.Cmatrix(k, q)
Ckmq = Er.Cmatrix(k, -q)
#See page 44, eq 3.1 of the crystal field handbook
H = H + Bkq*Ckq + Bkmq*Ckmq
(evals, evects) = np.linalg.eig(H)
E0 = np.min(evals)
calc_nrg_levels = np.sort(evals-E0)
calc_nrg_levels = calc_nrg_levels[::2] # ignore every second element
E0seb = np.min(seb_levels)
seb_levels = seb_levels-E0seb
print(' Jevon Sebastian Difference')
for k in range(len(seb_levels)):
print("%9.1f %9.1f %6.1f"%(np.real(calc_nrg_levels[k]),seb_levels[k],np.real(calc_nrg_levels[k]) - seb_levels[k]))
# This isn't much of a test at the moment because there seems to be
# an issue with the free ion parameters
assert(np.max(np.abs(
calc_nrg_levels[0:len(seb_levels)]-seb_levels))
< 26.0 )
# This is more of a test because it it only looks at the ground multiplet
assert(np.max(np.abs(
calc_nrg_levels[0:8]-seb_levels[0:8]))
< 0.6 )