def Fdual(j_data_opt, j_data_spplus, j_data_spminus, grid_par=-6):
qc_opt = read.convert_json(j_data_opt)
qc_spplus = read.convert_json(j_data_spplus)
qc_spminus = read.convert_json(j_data_spminus)
X, Y, Z = _init_ORB_grid(qc_opt, grid_par=grid_par)
dx, dy, dz = (X[10, 0, 0] - X[9, 0, 0]), (Y[0, 10, 0] -
Y[0, 9, 0]), (Z[0, 0, 10] -
Z[0, 0, 9])
d3r = dx * dy * dz
rho_opt = core.rho_compute(qc_opt, numproc=6)
rho_spplus = core.rho_compute(qc_spplus, numproc=6)
rho_spminus = core.rho_compute(qc_spminus, numproc=6)
delta_rho_plus = np.subtract(rho_spplus, rho_opt)
delta_rho_minus = np.subtract(rho_opt, rho_spminus)
delta_rho_2 = np.subtract(delta_rho_plus, delta_rho_minus)
print "Rho : ", np.sum(rho_opt) * d3r, "(", np.min(
rho_opt), " ... ", np.max(rho_opt), ")"
print "d : ", dx, dy, dz
print "P0 : ", X[0, 0, 0], Y[0, 0, 0], Z[0, 0, 0]
print "P1 : ", X[-1, 0, 0], Y[0, -1, 0], Z[0, 0, -1]
P = np.array([X, Y, Z])
return delta_rho_2, X, Y, Z
def Fukui(j_data_opt, j_data_sp, label=None, grid_par=-6):
u"""Calculates the density differences/Fukui functions of the molecule.
** Parameters **
j_data_opt : dict
Data on the optimized molecule, as deserialized from the scanlog format.
j_data_sp : dict
Data on the optimized molecule, as deserialized from the scanlog format.
grid_par : int, optional
Governs the grid to be used for voxel data.
- If positive, it indicates the number of points in all 3 dimensions.
- If zero, it indicates the default number of points (80).
- If negative, it indicates the resolution, in Á^-1.
** Returns **
rho : numpy.ndarray
The voxels containing the scalar values of the density.
V : numpy.ndarray
The voxels containing the scalar values of the potential.
X, Y, Z : numpy.ndarray
Meshgrids (as generated by numpy.mgrid), required for placing the voxels contained in rho and V.
"""
qc_opt = read.convert_json(j_data_opt)
qc_sp = read.convert_json(j_data_sp)
X, Y, Z = _init_ORB_grid(qc_opt, grid_par=grid_par)
dx, dy, dz = (X[10, 0, 0] - X[9, 0, 0]), (Y[0, 10, 0] -
Y[0, 9, 0]), (Z[0, 0, 10] -
Z[0, 0, 9])
d3r = dx * dy * dz
rho_opt = core.rho_compute(qc_opt, numproc=6)
rho_sp = core.rho_compute(qc_sp, numproc=6)
## Calculation of the delta rho
if label == 'plus':
delta_rho = np.subtract(rho_sp, rho_opt)
elif label == 'minus':
delta_rho = np.subtract(rho_opt, rho_sp)
print "Rho : ", np.sum(rho_opt) * d3r, "(", np.min(
rho_opt), " ... ", np.max(rho_opt), ")"
print "d : ", dx, dy, dz
print "P0 : ", X[0, 0, 0], Y[0, 0, 0], Z[0, 0, 0]
print "P1 : ", X[-1, 0, 0], Y[0, -1, 0], Z[0, 0, -1]
P = np.array([X, Y, Z])
return delta_rho, X, Y, Z
def MO(j_data, MO_list, grid_par=-6):
u"""Calculates the voxels representing the requested molecular orbitals of a molecule.
** Parameters **
j_data : dict
Data on the molecule, deserialized from the scanlog format.
MO_list : list(str) or list(int)
A list containing either:
- integers designating the molecular orbitals (starting from 1)
- strings designating the molecular orbitals either through:
- keywords (e.g. "h**o", "lumo")
- ranges (e.g. "h**o-1:lumo+2")
- symmetries (e.g. "5.A")
grid_par : int, optional
Governs the grid to be used for the voxels.
- If positive, it indicates the number of points in all 3 dimensions.
- If zero, it indicates the default number of points (80).
- If negative, it indicates the resolution, in (A.U.)^-1.
** Returns **
out : list(numpy.ndarray)
List of numpy.ndarrays, each one containing the values of the probability amplitude of a single molecular orbital at each voxel of the grid.
X, Y, Z : numpy.ndarray
Meshgrids (as generated by numpy.mgrid) required for positioning the voxel values contained in out.
"""
## Prepare data for ORBKIT
qc = read.convert_json(j_data, all_mo=True)
X, Y, Z = _init_ORB_grid(qc, grid_par=grid_par)
## Get list of orbitals
qc.mo_spec = read.mo_select(qc.mo_spec, MO_list)["mo_spec"]
## Calculate
out = core.rho_compute(qc, calc_mo=True, numproc=6)
return out, X, Y, Z
def Potential(j_data, grid_par=-6):
u"""Calculates the electric potential difference for the molecule.
** Parameters **
j_data : dict
Data on the molecule, as deserialized from the scanlog format.
grid_par : int, optional
Governs the grid to be used for voxel data.
- If positive, it indicates the number of points in all 3 dimensions.
- If zero, it indicates the default number of points (80).
- If negative, it indicates the resolution, in Á^-1.
** Returns **
rho : numpy.ndarray
The voxels containing the scalar values of the density.
V : numpy.ndarray
The voxels containing the scalar values of the potential.
X, Y, Z : numpy.ndarray
Meshgrids (as generated by numpy.mgrid), required for placing the voxels contained in rho and V.
"""
qc = read.convert_json(j_data)
X, Y, Z = _init_ORB_grid(qc, grid_par=grid_par)
dx, dy, dz = (X[10, 0, 0] - X[9, 0, 0]), (Y[0, 10, 0] -
Y[0, 9, 0]), (Z[0, 0, 10] -
Z[0, 0, 9])
d3r = dx * dy * dz
rho = core.rho_compute(qc, numproc=6)
print "Rho : ", np.sum(rho) * d3r, "(", np.min(rho), " ... ", np.max(
rho), ")"
print "d : ", dx, dy, dz
print "P0 : ", X[0, 0, 0], Y[0, 0, 0], Z[0, 0, 0]
print "P1 : ", X[-1, 0, 0], Y[0, -1, 0], Z[0, 0, -1]
P = np.array([X, Y, Z])
## The potential can be separated into two terms
## V_n, the contribution from nuclear charges (positive)
V_n = np.zeros(rho.shape)
for i in range(len(qc.geo_spec)):
## This currently works by:
## 1. reshaping the atom position triplet to the shape of the meshgrids
## 2. calculating the norm accross the three dimensions
## 3. propagating the meshgrid shape to the charge
R = np.linalg.norm(P - qc.geo_spec[i].reshape((3, 1, 1, 1)), axis=0)
R[R < 0.005] = np.inf
N_i = float(qc.geo_info[i, -1]) / R
V_n += N_i
print "V_n (", qc.geo_info[i, 0], qc.geo_info[i, -1], ") : (", np.min(
N_i), ", ", np.max(N_i), ") (", np.argwhere(N_i > 250).size, ")"
TIx, TIy, TIz = rho.shape
Tx, Ty, Tz = X[-1, 0,
0] - X[0, 0, 0], Y[0, -1,
0] - Y[0, 0, 0], Z[0, 0, -1] - Z[0, 0, 0]
## V_r, the contribution from the electron density (negative)
## To avoid calculating the full volume integral,
## we consider rho as a kernel and apply it to
## the grid of inverse distances as though it
## were an image
## 1. Accumulate local potential
V_e = np.ones(rho.shape) * rho
## Reverse rho, so that it is traversed in the
## same direction as the image matrix
rho_r = rho[::-1, ::-1, ::-1].copy()
## 2. Extend grid
X_, Y_, Z_ = np.mgrid[dx * (1 - TIx):dx * TIx:dx,
dy * (1 - TIy):dy * TIy:dy,
dz * (1 - TIz):dz * TIz:dz]
print P.shape
## 3. Calculate distance grid
D = np.linalg.norm(np.array([0, 0, 0]).reshape(
(3, 1, 1, 1)) - np.array([X_, Y_, Z_]),
axis=0)
D[TIx - 1, TIy - 1, TIz - 1] = np.inf
R = 1 / D
## 4. Convolute
for i in xrange(TIx):
ie = i + TIx
for j in xrange(TIy):
je = j + TIy
for k in xrange(TIz):
V_e[i, j, k] += (rho_r * R[i:ie, j:je, k:k + TIz]).sum()
#from scipy import signal as sg
#V_e += sg.fftconvolve(R, rho, "valid")
V_e *= d3r
return rho, V_n - V_e, X, Y, Z