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orbitals.py
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orbitals.py
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import concurrent.futures
import numpy as np
from scipy.spatial import distance_matrix
from scipy.special import factorial2
from AaronTools import addlogger
from AaronTools.const import ELEMENTS, UNIT, VDW_RADII, BONDI_RADII
from AaronTools.utils.utils import lebedev_sphere, gauss_legendre_grid
@addlogger
class Orbitals:
"""
stores functions for the shells in a basis set
for evaluation at arbitrary points
attributes:
* basis_functions - list(len=n_shell) of lists(len=n_prim_per_shell)
of functions
function takes the arguments:
* r2 - float array like, squared distance from the
shell's center to each point being evaluated
* x, y, and z - float or array like, distance from the shell's
center to the point(s) being evaluated along
the x axis
* mo_coeffs - list(len=funcs_per_shell), MO coefficients
for the functions in this shell (e.g. 3
coefficients for the p shell); order
might depend on input file format
for example, FCHK files will be px, py, pz
ORCA files will be pz, px, py
* funcs_per_shell - list(len=n_shell), number of basis functions for
each shell
* alpha_coefficients - array(shape=(n_mos, n_mos)), coefficients of
molecular orbitals for alpha electrons
* beta_coefficients - same as alpha_coefficients for beta electrons
* shell_coords - array(shape=(n_shells, 3)), coordinates of each shell
in Angstroms
* shell_types - list(str, len=n_shell), type of each shell (e.g. s,
p, sp, 5d, 6d...)
* n_shell - number of shells
* n_prim_per_shell - list(len=n_shell), number of primitives per shell
* n_mos - number of molecular orbitals
* exponents - array, exponents for primitives in Eh
each shell
* alpha_nrgs - array(len=n_mos), energy of alpha MO's
* beta_nrgs - array(len=n_mos), energy of beta MO's
* contraction_coeff - array, contraction coefficients for each primitive
in each shell
* n_alpha - int, number of alpha electrons
* n_beta - int, number of beta electrons
"""
LOG = None
def __init__(self, filereader):
if filereader["file_type"] == "fchk":
self._load_fchk_data(filereader)
self.fmt = "fchk"
elif filereader["file_type"] == "out":
self._load_orca_out_data(filereader)
self.fmt = "orca"
elif filereader["file_type"] == "47" or filereader["file_type"] == "31":
self._load_nbo_data(filereader)
self.fmt = "nbo"
else:
raise NotImplementedError(
"cannot load orbital info from %s files" % filereader["file_type"]
)
def _load_fchk_data(self, filereader):
self.alpha_occupancies = None
self.beta_occupancies = None
if "Coordinates of each shell" in filereader.keys():
self.shell_coords = np.reshape(
filereader["Coordinates of each shell"],
(len(filereader["Shell types"]), 3),
)
else:
center_coords = []
for ndx in filereader["Shell to atom map"]:
center_coords.append(filereader["atoms"][ndx - 1].coords)
self.center_coords = np.array(center_coords)
self.shell_coords *= UNIT.BOHR_TO_ANG
self.contraction_coeff = filereader["Contraction coefficients"]
try:
self.sp_contraction_coeff = filereader["P(S=P) Contraction coefficients"]
except (KeyError, AttributeError):
self.sp_contraction_coeff = None
self.exponents = filereader["Primitive exponents"]
self.n_prim_per_shell = filereader["Number of primitives per shell"]
self.alpha_nrgs = filereader["Alpha Orbital Energies"]
self.beta_nrgs = None
if "Beta Orbital Energies" in filereader.keys():
self.beta_nrgs = filereader["Beta Orbital Energies"]
self.funcs_per_shell = []
def gau_norm(a, l):
"""
normalization for gaussian primitives that depends on
the exponential (a) and the total angular momentum (l)
"""
t1 = np.sqrt((2 * a) ** (l + 3 / 2)) / (np.pi ** (3.0 / 4))
t2 = np.sqrt(2 ** l / max(factorial2(2 * l - 1), 1))
return t1 * t2
# get functions for norm of s, p, 5d, and 7f
s_norm = lambda a, l=0: gau_norm(a, l)
p_norm = lambda a, l=1: gau_norm(a, l)
d_norm = lambda a, l=2: gau_norm(a, l)
f_norm = lambda a, l=3: gau_norm(a, l)
g_norm = lambda a, l=4: gau_norm(a, l)
h_norm = lambda a, l=5: gau_norm(a, l)
i_norm = lambda a, l=6: gau_norm(a, l)
self.basis_functions = list()
self.n_mos = 0
self.shell_types = []
shell_i = 0
for n_prim, shell in zip(
self.n_prim_per_shell,
filereader["Shell types"],
):
exponents = self.exponents[shell_i : shell_i + n_prim]
con_coeff = self.contraction_coeff[shell_i : shell_i + n_prim]
if shell == 0:
# s functions
self.shell_types.append("s")
self.n_mos += 1
self.funcs_per_shell.append(1)
norms = s_norm(exponents)
if n_prim > 1:
def s_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeff=con_coeff, norms=norms
):
e_r2 = np.exp(np.outer(-alpha, r2))
return mo_coeffs[0] * np.dot(con_coeff * norms, e_r2)
else:
def s_shell(
r2, x, y, z, mo_coeff,
alpha=exponents, con_coeff=con_coeff, norms=norms
):
e_r2 = np.exp(-alpha * r2)
return mo_coeff * con_coeff * norms * e_r2
self.basis_functions.append(s_shell)
elif shell == 1:
# p functions
self.shell_types.append("p")
self.n_mos += 3
self.funcs_per_shell.append(3)
norms = p_norm(exponents)
if n_prim > 1:
def p_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeff=con_coeff, norms=norms
):
e_r2 = np.exp(np.outer(-alpha, r2))
s_val = np.dot(con_coeff * norms, e_r2)
res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
res += mo_coeffs[0] * x
if mo_coeffs[1] != 0:
res += mo_coeffs[1] * y
if mo_coeffs[2] != 0:
res += mo_coeffs[2] * z
return res * s_val
else:
def p_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeff=con_coeff, norms=norms
):
e_r2 = np.exp(-alpha * r2)
s_val = con_coeff * norms * e_r2
res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
res += mo_coeffs[0] * x
if mo_coeffs[1] != 0:
res += mo_coeffs[1] * y
if mo_coeffs[2] != 0:
res += mo_coeffs[2] * z
return res * s_val
self.basis_functions.append(p_shell)
elif shell == -1:
# s=p functions
self.shell_types.append("sp")
self.n_mos += 4
self.funcs_per_shell.append(4)
norm_s = s_norm(exponents)
norm_p = p_norm(exponents)
sp_coeff = filereader["P(S=P) Contraction coefficients"][shell_i: shell_i + n_prim]
if n_prim > 1:
def sp_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents,
s_coeff=con_coeff,
p_coeff=sp_coeff,
s_norms=norm_s,
p_norms=norm_p,
):
e_r2 = np.exp(np.outer(-alpha, r2))
sp_val_s = np.dot(s_coeff * s_norms, e_r2)
sp_val_p = np.dot(p_coeff * p_norms, e_r2)
s_res = np.zeros(len(r2))
p_res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
s_res += mo_coeffs[0]
if mo_coeffs[1] != 0:
p_res += mo_coeffs[1] * x
if mo_coeffs[2] != 0:
p_res += mo_coeffs[2] * y
if mo_coeffs[3] != 0:
p_res += mo_coeffs[3] * z
return s_res * sp_val_s + p_res * sp_val_p
else:
def sp_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents,
s_coeff=con_coeff,
p_coeff=sp_coeff,
s_norms=norm_s,
p_norms=norm_p,
):
e_r2 = np.exp(-alpha * r2)
sp_val_s = s_coeff * s_norms * e_r2
sp_val_p = p_coeff * p_norms * e_r2
s_res = np.zeros(len(r2))
p_res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
s_res += mo_coeffs[0]
if mo_coeffs[1] != 0:
p_res += mo_coeffs[1] * x
if mo_coeffs[2] != 0:
p_res += mo_coeffs[2] * y
if mo_coeffs[3] != 0:
p_res += mo_coeffs[3] * z
return s_res * sp_val_s + p_res * sp_val_p
self.basis_functions.append(sp_shell)
elif shell == 2:
# cartesian d functions
self.shell_types.append("6d")
self.n_mos += 6
self.funcs_per_shell.append(6)
norms = d_norm(exponents)
if n_prim > 1:
def d_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeff=con_coeff, norms=norms
):
e_r2 = np.exp(np.outer(-alpha, r2))
s_val = np.dot(con_coeff * norms, e_r2)
res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
xx = x ** 2
res += mo_coeffs[0] * xx
if mo_coeffs[1] != 0:
yy = y ** 2
res += mo_coeffs[1] * yy
if mo_coeffs[2] != 0:
zz = z ** 2
res += mo_coeffs[2] * zz
if mo_coeffs[3] != 0:
xy = np.sqrt(3) * x * y
res += mo_coeffs[3] * xy
if mo_coeffs[4] != 0:
xz = np.sqrt(3) * x * z
res += mo_coeffs[4] * xz
if mo_coeffs[5] != 0:
yz = np.sqrt(3) * y * z
res += mo_coeffs[5] * yz
return res * s_val
else:
def d_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeff=con_coeff, norms=norms
):
e_r2 = np.exp(-alpha * r2)
s_val = con_coeff * norms * e_r2
res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
xx = x ** 2
res += mo_coeffs[0] * xx
if mo_coeffs[1] != 0:
yy = y ** 2
res += mo_coeffs[1] * yy
if mo_coeffs[2] != 0:
zz = z ** 2
res += mo_coeffs[2] * zz
if mo_coeffs[3] != 0:
xy = np.sqrt(3) * x * y
res += mo_coeffs[3] * xy
if mo_coeffs[4] != 0:
xz = np.sqrt(3) * x * z
res += mo_coeffs[4] * xz
if mo_coeffs[5] != 0:
yz = np.sqrt(3) * y * z
res += mo_coeffs[5] * yz
return res * s_val
self.basis_functions.append(d_shell)
elif shell == -2:
# pure d functions
self.shell_types.append("5d")
self.n_mos += 5
self.funcs_per_shell.append(5)
norms = d_norm(exponents)
if n_prim > 1:
def d_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeff=con_coeff, norms=norms
):
e_r2 = np.exp(np.outer(-alpha, r2))
s_val = np.dot(con_coeff * norms, e_r2)
res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
z2r2 = 0.5 * (3 * z ** 2 - r2)
res += mo_coeffs[0] * z2r2
if mo_coeffs[1] != 0:
xz = np.sqrt(3) * x * z
res += mo_coeffs[1] * xz
if mo_coeffs[2] != 0:
yz = np.sqrt(3) * y * z
res += mo_coeffs[2] * yz
if mo_coeffs[3] != 0:
x2y2 = np.sqrt(3) * (x ** 2 - y ** 2) / 2
res += mo_coeffs[3] * x2y2
if mo_coeffs[4] != 0:
xy = np.sqrt(3) * x * y
res += mo_coeffs[4] * xy
return res * s_val
else:
def d_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeff=con_coeff, norms=norms
):
e_r2 = np.exp(-alpha * r2)
s_val = con_coeff * norms * e_r2
res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
z2r2 = 0.5 * (3 * z ** 2 - r2)
res += mo_coeffs[0] * z2r2
if mo_coeffs[1] != 0:
xz = np.sqrt(3) * x * z
res += mo_coeffs[1] * xz
if mo_coeffs[2] != 0:
yz = np.sqrt(3) * y * z
res += mo_coeffs[2] * yz
if mo_coeffs[3] != 0:
x2y2 = np.sqrt(3) * (x ** 2 - y ** 2) / 2
res += mo_coeffs[3] * x2y2
if mo_coeffs[4] != 0:
xy = np.sqrt(3) * x * y
res += mo_coeffs[4] * xy
return res * s_val
self.basis_functions.append(d_shell)
elif shell == 3:
# 10f functions
self.shell_types.append("10f")
self.n_mos += 10
self.funcs_per_shell.append(10)
norms = f_norm(exponents)
def f_shell(
r2,
x,
y,
z,
mo_coeffs,
alpha=exponents,
con_coeff=con_coeff,
norms=norms,
):
e_r2 = np.exp(np.outer(-alpha, r2))
s_val = np.dot(con_coeff * norms, e_r2)
res = np.zeros(len(r2))
# ** 3 takes ~6x longer than x * x * x or x ** 2 * x
if mo_coeffs[0] != 0:
xxx = x * x * x
res += mo_coeffs[0] * xxx
if mo_coeffs[1] != 0:
yyy = y * y * y
res += mo_coeffs[1] * yyy
if mo_coeffs[2] != 0:
zzz = z * z * z
res += mo_coeffs[2] * zzz
if mo_coeffs[3] != 0:
xyy = np.sqrt(5) * x * y ** 2
res += mo_coeffs[3] * xyy
if mo_coeffs[4] != 0:
xxy = np.sqrt(5) * x ** 2 * y
res += mo_coeffs[4] * xxy
if mo_coeffs[5] != 0:
xxz = np.sqrt(5) * x ** 2 * z
res += mo_coeffs[5] * xxz
if mo_coeffs[6] != 0:
xzz = np.sqrt(5) * x * z ** 2
res += mo_coeffs[6] * xzz
if mo_coeffs[7] != 0:
yzz = np.sqrt(5) * y * z ** 2
res += mo_coeffs[7] * yzz
if mo_coeffs[8] != 0:
yyz = np.sqrt(5) * y ** 2 * z
res += mo_coeffs[8] * yyz
if mo_coeffs[9] != 0:
xyz = np.sqrt(15) * x * y * z
res += mo_coeffs[9] * xyz
return res * s_val
self.basis_functions.append(f_shell)
elif shell == -3:
# pure f functions
self.shell_types.append("7f")
self.n_mos += 7
self.funcs_per_shell.append(7)
norms = f_norm(exponents)
def f_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeff=con_coeff, norms=norms
):
e_r2 = np.exp(np.outer(-alpha, r2))
s_val = np.dot(con_coeff * norms, e_r2)
res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
z3zr2 = z * (5 * z ** 2 - 3 * r2) / 2
res += mo_coeffs[0] * z3zr2
if mo_coeffs[1] != 0:
xz2xr2 = np.sqrt(3) * x * (5 * z ** 2 - r2) / (2 * np.sqrt(2))
res += mo_coeffs[1] * xz2xr2
if mo_coeffs[2] != 0:
yz2yr2 = np.sqrt(3) * y * (5 * z ** 2 - r2) / (2 * np.sqrt(2))
res += mo_coeffs[2] * yz2yr2
if mo_coeffs[3] != 0:
x2zr2z = np.sqrt(15) * z * (x ** 2 - y ** 2) / 2
res += mo_coeffs[3] * x2zr2z
if mo_coeffs[4] != 0:
xyz = np.sqrt(15) * x * y * z
res += mo_coeffs[4] * xyz
if mo_coeffs[5] != 0:
x3r2x = np.sqrt(5) * x * (x ** 2 - 3 * y ** 2) / (2 * np.sqrt(2))
res += mo_coeffs[5] * x3r2x
if mo_coeffs[6] != 0:
x2yy3 = np.sqrt(5) * y * (3 * x ** 2 - y ** 2) / (2 * np.sqrt(2))
res += mo_coeffs[6] * x2yy3
return res * s_val
self.basis_functions.append(f_shell)
# elif shell == 4:
elif False:
# TODO: validate these - order might be wrong
self.shell_types.append("15g")
self.n_mos += 15
self.funcs_per_shell.append(15)
norms = g_norm(exponents)
def g_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeffs=con_coeff, norms=norms
):
e_r2 = np.exp(np.outer(-alpha, r2))
s_val = np.dot(con_coeff * norms, e_r2)
res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
x4 = (x ** 2) ** 2
res += mo_coeffs[0] * x4
if mo_coeffs[1] != 0:
x3y = (x ** 3) * x * y
res += mo_coeffs[1] * x3y
if mo_coeffs[2] != 0:
x3z = (x ** 3) * x * z
res += mo_coeffs[2] * x3z
if mo_coeffs[3] != 0:
x2y2 = (x ** 2) * (y ** 2)
res += mo_coeffs[3] * x2y2
if mo_coeffs[4] != 0:
x2yz = (x ** 2) * y * z
res += mo_coeffs[4] * x2yz
if mo_coeffs[5] != 0:
x2z2 = (x ** 2) * (z ** 2)
res += mo_coeffs[5] * x2z2
if mo_coeffs[6] != 0:
xy3 = x * y * y ** 2
res += mo_coeffs[6] * xy3
if mo_coeffs[7] != 0:
xy2z = x * z * y ** 2
res += mo_coeffs[7] * xy2z
if mo_coeffs[8] != 0:
xyz2 = x * y * z ** 2
res += mo_coeffs[8] * xyz2
if mo_coeffs[9] != 0:
xz3 = x * z * z ** 2
res += mo_coeffs[9] * xz3
if mo_coeffs[10] != 0:
y4 = (y ** 2) ** 2
res += mo_coeffs[10] * y4
if mo_coeffs[11] != 0:
y3z = (y ** 2) * y * z
res += mo_coeffs[11] * y3z
if mo_coeffs[12] != 0:
y2z2 = (y * z) ** 2
res += mo_coeffs[12] * y2z2
if mo_coeffs[13] != 0:
yz3 = y * z * z ** 2
res += mo_coeffs[13] * yz3
if mo_coeffs[14] != 0:
z4 = (z ** 2) ** 2
res += mo_coeffs[14] * z4
return res * s_val
self.basis_functions.append(g_shell)
elif shell == -4:
self.shell_types.append("9g")
self.n_mos += 9
self.funcs_per_shell.append(9)
norms = g_norm(exponents)
def g_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeffs=con_coeff, norms=norms
):
e_r2 = np.exp(np.outer(-alpha, r2))
s_val = np.dot(con_coeff * norms, e_r2)
res = np.zeros(len(r2))
if mo_coeffs[0] != 0:
z4 = (35 * (z ** 4) - 30 * (r2 * z ** 2) + 3 * r2 ** 2) / 8
res += mo_coeffs[0] * z4
if mo_coeffs[1] != 0:
z3x = np.sqrt(10) * (x * z * (7 * z ** 2 - 3 * r2)) / 4
res += mo_coeffs[1] * z3x
if mo_coeffs[2] != 0:
z3y = np.sqrt(10) * (y * z * (7 * z ** 2 - 3 * r2)) / 4
res += mo_coeffs[2] * z3y
if mo_coeffs[3] != 0:
z2x2y2 = np.sqrt(5) * (x ** 2 - y ** 2) * (7 * z ** 2 - r2) / 4
res += mo_coeffs[3] * z2x2y2
if mo_coeffs[4] != 0:
z2xy = np.sqrt(5) * x * y * (7 * z ** 2 - r2) / 2
res += mo_coeffs[4] * z2xy
if mo_coeffs[5] != 0:
zx3 = np.sqrt(70) * x * z * (x ** 2 - 3 * y ** 2) / 4
res += mo_coeffs[5] * zx3
if mo_coeffs[6] != 0:
zy3 = np.sqrt(70) * z * y * (3 * x ** 2 - y ** 2) / 4
res += mo_coeffs[6] * zy3
if mo_coeffs[7] != 0:
x2 = x ** 2
y2 = y ** 2
x4y4 = np.sqrt(35) * (x2 * (x2 - 3 * y2) - y2 * (3 * x2 - y2)) / 8
res += mo_coeffs[7] * x4y4
if mo_coeffs[8] != 0:
xyx2y2 = np.sqrt(35) * x * y * (x ** 2 - y ** 2) / 2
res += mo_coeffs[8] * xyx2y2
return res * s_val
self.basis_functions.append(g_shell)
elif shell == -5:
self.shell_types.append("11h")
self.n_mos += 11
self.funcs_per_shell.append(11)
norms = h_norm(exponents)
def h_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeffs=con_coeff, norms=norms
):
e_r2 = np.exp(np.outer(-alpha, r2))
s_val = np.dot(con_coeff * norms, e_r2)
res = np.zeros(len(r2))
z2 = z ** 2
if mo_coeffs[0] != 0:
z5z3r2zr4 = z * (63 * z2 ** 2 - 70 * z2 * r2 + 15 * r2 ** 2) / 8
res += mo_coeffs[0] * z5z3r2zr4
if mo_coeffs[1] != 0:
xz4xz2r2xr4 = np.sqrt(15) * x * (21 * z2 ** 2 - 14 * z2 * r2 + r2 ** 2) / 8
res += mo_coeffs[1] * xz4xz2r2xr4
if mo_coeffs[2] != 0:
yz4yz2r2yr4 = np.sqrt(15) * y * (21 * z2 ** 2 - 14 * z2 * r2 + r2 ** 2) / 8
res += mo_coeffs[2] * yz4yz2r2yr4
if mo_coeffs[3] != 0:
x2y3z3zr2 = np.sqrt(105) * (x ** 2 - y ** 2) * (3 * z2 - r2) * z / 4
res += mo_coeffs[3] * x2y3z3zr2
if mo_coeffs[4] != 0:
xyz3zr2 = np.sqrt(105) * x * y * z * (3 * z2 - r2) / 2
res += mo_coeffs[4] * xyz3zr2
if mo_coeffs[5] != 0:
xx2y2z2r2 = 35 * x * (x ** 2 - 3 * y ** 2) * (9 * z2 - r2) / (8 * np.sqrt(70))
res += mo_coeffs[5] * xx2y2z2r2
if mo_coeffs[6] != 0:
yx2y2z2r2 = 35 * y * (3 * x ** 2 - y ** 2) * (9 * z2 - r2) / (8 * np.sqrt(70))
res += mo_coeffs[6] * yx2y2z2r2
if mo_coeffs[7] != 0:
zx4x2y2y4 = 105 * z * ((x ** 2) ** 2 - 6 * (x * y) ** 2 + (y ** 2) ** 2) / (8 * np.sqrt(35))
res += mo_coeffs[7] * zx4x2y2y4
if mo_coeffs[8] != 0:
zx3yxy3 = 105 * x * y * z * (4 * x ** 2 - 4 * y ** 2) / (8 * np.sqrt(35))
res += mo_coeffs[8] * zx3yxy3
if mo_coeffs[9] != 0:
xx4y2x2y4 = 21 * x * ((x ** 2) ** 2 - 10 * (x * y) ** 2 + 5 * (y ** 2) ** 2) / (8 * np.sqrt(14))
res += mo_coeffs[9] * xx4y2x2y4
if mo_coeffs[10] != 0:
yx4y2x2y4 = 21 * y * (5 * (x ** 2) ** 2 - 10 * (x * y) ** 2 + (y ** 2) ** 2) / (8 * np.sqrt(14))
res += mo_coeffs[10] * yx4y2x2y4
return res * s_val
self.basis_functions.append(h_shell)
elif shell == -6:
self.shell_types.append("13i")
self.n_mos += 13
self.funcs_per_shell.append(13)
norms = i_norm(exponents)
def i_shell(
r2, x, y, z, mo_coeffs,
alpha=exponents, con_coeffs=con_coeff, norms=norms
):
e_r2 = np.exp(np.outer(-alpha, r2))
s_val = np.dot(con_coeff * norms, e_r2)
res = np.zeros(len(r2))
z2 = z ** 2
if mo_coeffs[0] != 0:
z6z4r2z2r4r6 = (231 * z2 * z2 ** 2 - 315 * z2 ** 2 * r2 + 105 * z2 * r2 ** 2 - 5 * r2 * r2 ** 2) / 16
res += mo_coeffs[0] * z6z4r2z2r4r6
if mo_coeffs[1] != 0:
xz5z3r2zr4 = np.sqrt(21) * x * z * (33 * z2 ** 2 - 30 * z2 * r2 + 5 * r2 ** 2) / 8
res += mo_coeffs[1] * xz5z3r2zr4
if mo_coeffs[2] != 0:
yz5z3r2zr4 = np.sqrt(21) * y * z * (33 * z2 ** 2 - 30 * z2 * r2 + 5 * r2 ** 2) / 8
res += mo_coeffs[2] * yz5z3r2zr4
if mo_coeffs[3] != 0:
x2y2z4z2r2r3 = 105 * (x ** 2 - y ** 2) * (33 * z2 ** 2 - 18 * z2 * r2 + r2 ** 2) / (16 * np.sqrt(210))
res += mo_coeffs[3] * x2y2z4z2r2r3
if mo_coeffs[4] != 0:
xyz4z2r2r4 = 105 * x * y * (33 * z2 ** 2 - 18 * z2 * r2 + r2 ** 2) / (8 * np.sqrt(210))
res += mo_coeffs[4] * xyz4z2r2r4
if mo_coeffs[5] != 0:
xx2y2z3zr2 = 105 * x * z * (x ** 2 - 3 * y ** 2) * (11 * z2 - 3 * r2) / (8 * np.sqrt(210))
res += mo_coeffs[5] * xx2y2z3zr2
if mo_coeffs[6] != 0:
yx2y2z3zr2 = 105 * y * z * (3 * x ** 2 - y ** 2) * (11 * z2 - 3 * r2) / (8 * np.sqrt(210))
res += mo_coeffs[6] * yx2y2z3zr2
if mo_coeffs[7] != 0:
x4x2y2y4z2r2 = np.sqrt(63) * ((x ** 2) ** 2 - 6 * (x * y) ** 2 + (y ** 2) ** 2) * (11 * z2 - r2) / 16
res += mo_coeffs[7] * x4x2y2y4z2r2
if mo_coeffs[8] != 0:
xyx2y2z2r2 = np.sqrt(63) * x * y * (x ** 2 - y ** 2) * (11 * z2 - r2) / 4
res += mo_coeffs[8] * xyx2y2z2r2
if mo_coeffs[9] != 0:
xzx4x2y2y4 = 231 * x * z * ((x ** 2) ** 2 - 10 * (x * y) ** 2 + 5 * (y ** 2) ** 2) / (8 * np.sqrt(154))
res += mo_coeffs[9] * xzx4x2y2y4
if mo_coeffs[10] != 0:
yzx4x2y2y4 = 231 * y * z * (5 * (x ** 2) ** 2 - 10 * (x * y) ** 2 + (y ** 2) ** 2) / (8 * np.sqrt(154))
res += mo_coeffs[10] * yzx4x2y2y4
if mo_coeffs[11] != 0:
x6x4y2x2y4y6 = 231 * ((x * x ** 2) ** 2 - 15 * (x ** 2 * y) ** 2 + 15 * (x * y ** 2) ** 2 - (y * y ** 2) ** 2) / (16 * np.sqrt(462))
res += mo_coeffs[11] * x6x4y2x2y4y6
if mo_coeffs[12] != 0:
yx5x3y3xy5 = 231 * x * y * (6 * (x ** 2) ** 2 - 20 * (x * y) ** 2 + 6 * (y ** 2) ** 2) / (16 * np.sqrt(462))
res += mo_coeffs[12] * yx5x3y3xy5
return res * s_val
self.basis_functions.append(i_shell)
else:
self.LOG.warning("cannot parse shell with type %i" % shell)
shell_i += n_prim
self.alpha_coefficients = np.reshape(
filereader["Alpha MO coefficients"],
(self.n_mos, self.n_mos),
)
if "Beta MO coefficients" in filereader.keys():
self.beta_coefficients = np.reshape(
filereader["Beta MO coefficients"],
(self.n_mos, self.n_mos),
)
else:
self.beta_coefficients = None
self.n_alpha = filereader["Number of alpha electrons"]
if "Number of beta electrons" in filereader:
self.n_beta = filereader["Number of beta electrons"]
def _load_nbo_data(self, filereader):
self.alpha_occupancies = None
self.beta_occupancies = None
self.basis_functions = []
self.exponents = np.array(filereader["exponents"])
self.alpha_coefficients = np.array(filereader["alpha_coefficients"])
self.beta_coefficients = None
self.shell_coords = []
self.funcs_per_shell = []
self.start_ndx = []
self.shell_types = []
self.n_shell = len(filereader["n_prim_per_shell"])
self.momentum_label = filereader["momentum_label"]
self.coeffs_by_type = dict()
for x in ["s", "p", "d", "f", "g"]:
try:
key = "%s_coeff" % x
self.coeffs_by_type[key] = filereader[key]
except (KeyError, AttributeError):
pass
self.alpha_nrgs = [0 for x in self.alpha_coefficients]
self.n_mos = len(self.alpha_coefficients)
self.n_alpha = 0
self.n_beta = 0
self.beta_nrgs = None
label_i = 0
# NBO includes normalization constant with the contraction coefficient
# so we don't have a gau_norm function like gaussian or orca
for n_prim, n_funcs, shell_i in zip(
filereader["n_prim_per_shell"],
filereader["funcs_per_shell"],
filereader["start_ndx"],
):
shell_i -= 1
exponents = self.exponents[shell_i: shell_i + n_prim]
shell_funcs = []
con_coeffs = []
shell_type = []
self.funcs_per_shell.append(n_funcs)
self.start_ndx.append(shell_i)
self.shell_coords.append(
filereader.atoms[filereader["shell_to_atom"][label_i] - 1].coords
)
for i in range(0, n_funcs):
shell = filereader["momentum_label"][label_i]
label_i += 1
# XXX: each function is treated as a different
# shell because NBO allows them to be in any order
# I think that technically means the functions in
# the d shell for example don't need to be next
# to each other
if shell < 100:
shell_type.append("s")
# s - shell can be 1 or 51
con_coeff = filereader["s_coeff"][shell_i: shell_i + n_prim]
con_coeffs.append(con_coeff)
def s_shell(
r2, x, y, z, s_val
):
return s_val
shell_funcs.append(s_shell)
elif shell < 200:
# p - shell can be 101, 102, 103, 151, 152, 153
con_coeff = filereader["p_coeff"][shell_i: shell_i + n_prim]
con_coeffs.append(con_coeff)
if shell == 101 or shell == 151:
shell_type.append("px")
def px_shell(
r2, x, y, z, s_val
):
return s_val * x
shell_funcs.append(px_shell)
elif shell == 102 or shell == 152:
shell_type.append("py")
def py_shell(
r2, x, y, z, s_val
):
return s_val * y
shell_funcs.append(py_shell)
elif shell == 103 or shell == 153:
shell_type.append("pz")
def pz_shell(
r2, x, y, z, s_val
):
return s_val * z
shell_funcs.append(pz_shell)
elif shell < 300:
con_coeff = filereader["d_coeff"][shell_i: shell_i + n_prim]
con_coeffs.append(con_coeff)
if shell == 201:
shell_type.append("dxx")
def dxx_shell(
r2, x, y, z, s_val
):
return s_val * x * x
shell_funcs.append(dxx_shell)
elif shell == 202:
shell_type.append("dxy")
def dxy_shell(
r2, x, y, z, s_val
):
return s_val * x * y
shell_funcs.append(dxy_shell)
elif shell == 203:
shell_type.append("dxz")
def dxz_shell(
r2, x, y, z, s_val
):
return s_val * x * z
shell_funcs.append(dxz_shell)
elif shell == 204:
shell_type.append("dyy")
def dyy_shell(
r2, x, y, z, s_val
):
return s_val * y * y
shell_funcs.append(dyy_shell)
elif shell == 205:
shell_type.append("dyz")
def dyz_shell(
r2, x, y, z, s_val
):
return s_val * y * z
shell_funcs.append(dyz_shell)
elif shell == 206:
shell_type.append("dzz")
def dzz_shell(
r2, x, y, z, s_val
):
return s_val * z * z
shell_funcs.append(dzz_shell)
elif shell == 251:
shell_type.append("5dxy")
def dxy_shell(
r2, x, y, z, s_val
):
return np.sqrt(3) * s_val * x * y
shell_funcs.append(dxy_shell)
elif shell == 252:
shell_type.append("5dxz")
def dxz_shell(
r2, x, y, z, s_val
):
return np.sqrt(3) * s_val * x * z
shell_funcs.append(dxz_shell)
elif shell == 253:
shell_type.append("5dyz")
def dyz_shell(
r2, x, y, z, s_val
):
return np.sqrt(3) * s_val * y * z
shell_funcs.append(dyz_shell)
elif shell == 254:
shell_type.append("5dx2-y2")
def dx2y2_shell(
r2, x, y, z, s_val
):
return np.sqrt(3) * s_val * (x ** 2 - y ** 2) / 2
shell_funcs.append(dx2y2_shell)
elif shell == 255:
shell_type.append("5dz2")
def dz2_shell(
r2, x, y, z, s_val
):
return (3 * z ** 2 - r2) * s_val / 2
shell_funcs.append(dz2_shell)
elif shell < 400:
con_coeff = filereader["f_coeff"][shell_i: shell_i + n_prim]
con_coeffs.append(con_coeff)
if shell == 301:
shell_type.append("fxxx")
def fxxx_shell(
r2, x, y, z, s_val
):
return s_val * x * x * x
shell_funcs.append(fxxx_shell)
if shell == 302:
shell_type.append("fxxy")
def fxxy_shell(
r2, x, y, z, s_val
):
return s_val * x * x * y
shell_funcs.append(fxxy_shell)
if shell == 303:
shell_type.append("fxxz")
def fxxz_shell(
r2, x, y, z, s_val
):
return s_val * x * x * z
shell_funcs.append(fxxz_shell)
if shell == 304:
shell_type.append("fxyy")
def fxyy_shell(
r2, x, y, z, s_val
):
return s_val * x * y * y
shell_funcs.append(fxyy_shell)
if shell == 305:
shell_type.append("fxyz")
def fxyz_shell(
r2, x, y, z, s_val
):
return s_val * x * y * z
shell_funcs.append(fxyz_shell)
if shell == 306:
shell_type.append("fxzz")
def fxzz_shell(
r2, x, y, z, s_val
):
return s_val * x * z * z
shell_funcs.append(fxzz_shell)
if shell == 307:
shell_type.append("fyyy")
def fyyy_shell(
r2, x, y, z, s_val
):
return s_val * y * y * y
shell_funcs.append(fyyy_shell)
if shell == 308:
shell_type.append("fyyz")
def fyyz_shell(
r2, x, y, z, s_val
):
return s_val * y * y * z
shell_funcs.append(fyyz_shell)
if shell == 309:
shell_type.append("fyzz")
def fyzz_shell(
r2, x, y, z, s_val
):
return s_val * y * z * z
shell_funcs.append(fyzz_shell)
if shell == 310:
shell_type.append("fzzz")
def fzzz_shell(
r2, x, y, z, s_val
):
return s_val * z * z * z
shell_funcs.append(fzzz_shell)
if shell == 351:
shell_type.append("7fz3-zr2")
def fz3zr2_shell(
r2, x, y, z, s_val
):
return s_val * z * (5 * z ** 2 - 3 * r2) / 2
shell_funcs.append(fz3zr2_shell)
if shell == 352:
shell_type.append("7fxz2-xr2")
def fxz2xr2_shell(
r2, x, y, z, s_val
):
return np.sqrt(3) * s_val * x * (5 * z ** 2 - r2) / (2 * np.sqrt(2))
shell_funcs.append(fxz2xr2_shell)
if shell == 353:
shell_type.append("7fyz2-yr2")
def fyz2yr2_shell(
r2, x, y, z, s_val
):
return s_val * y * (5 * z ** 2 - r2) / (2 * np.sqrt(2))
shell_funcs.append(fyz2yr2_shell)
if shell == 354:
shell_type.append("7fzx2-zy2")
def fzx2zy2_shell(
r2, x, y, z, s_val
):
return np.sqrt(15) * s_val * z * (x ** 2 - y ** 2) / 2
shell_funcs.append(fzx2zy2_shell)
if shell == 355:
shell_type.append("7fxyz")
def fxyz_shell(
r2, x, y, z, s_val
):
return np.sqrt(15) * s_val * x * y * z
shell_funcs.append(fxyz_shell)
if shell == 356:
shell_type.append("7fx3-xy2")
def fx3xy2_shell(
r2, x, y, z, s_val
):
return np.sqrt(5) * s_val * x * (x ** 2 - 3 * y ** 2) / (2 * np.sqrt(2))
shell_funcs.append(fx3xy2_shell)
if shell == 357:
shell_type.append("7fyx2-y3")
def fyx2y3_shell(
r2, x, y, z, s_val
):
return np.sqrt(5) * s_val * y * (3 * x ** 2 - y ** 2) / (2 * np.sqrt(2))
shell_funcs.append(fyx2y3_shell)
elif shell < 500:
# I can't tell what NBO does with g orbitals
# I don't have any reference to compare to
self.LOG.warning(
"g shell results have not been verified for NBO\n"
"any LCAO's may be invalid"
)
con_coeff = filereader["g_coeff"][shell_i: shell_i + n_prim]
con_coeffs.append(con_coeff)
if shell == 401:
shell_type.append("gxxxx")
def gxxxx_shell(
r2, x, y, z, s_val
):
return s_val * x * x * x * x