def get_norm_cgto(ang_number,exponents,coefs_shell):
"""Gets the norms of contracted GTOs in a shell."""
from math import sqrt,pow
from BioNanoLEGO.DenseMatrix import asmatrix,empty
# Threshold of the norms
NORM_THRESHOLD = 1e-17
# Gets the number of contractions
num_contrs = len(coefs_shell)
# Gets the number of primitives
num_prims = len(exponents)
# Initializes the norms of contracted GTOs
norm_cgto = [0]*num_contrs
# Sets the power
expnt_power = float(ang_number)+1.5
# Sets up the matrix of radical overlap between two primitive GTOs
rad_overlap = asmatrix(empty((num_prims,num_prims)))
for iprim in xrange(num_prims):
for jprim in xrange(num_prims):
rad_overlap[iprim,jprim] = \
pow(2*sqrt(exponents[iprim]*exponents[jprim])/ \
(exponents[iprim]+exponents[jprim]),expnt_power)
# Gets the norms of contracted GTOs
for icontr in xrange(num_contrs):
coeff_matrix = asmatrix(coefs_shell[icontr])
norm_cgto[icontr] = sqrt((coeff_matrix*rad_overlap*coeff_matrix.transpose())[0,0])
if norm_cgto[icontr] < NORM_THRESHOLD:
raise ZeroDivisionError("Norm '%f' of CGTO '%d' is smaller than the threshold '%f'!" \
% (norm_cgto[icontr],icontr,NORM_THRESHOLD))
return norm_cgto
def getOneInt(self,other,operator,**options):
"""Calculates the integral of an one-electron operator.
other: Basis sets of ket.
molecule: Molecule class defined in Molecule.py.
operator: One-electron operator, function object, see Gen1Int.py for example.
"""
from BioNanoLEGO.DenseMatrix import empty,asmatrix
# Parallelize here, using dynamic parallelization
# MASTER sends first initial jobs to all SLAVES, SLAVES do the job,
# and send the results back, MASTER receives the result from one SLAVE,
# does some computations (like reduce the number of working nodes),
# and sends new job to it with job_tag and increases the number of
# working nodes, or sends terminator_tag.
# Sets up the integral matrix, using row-major order
one_int = asmatrix(empty((self.num_basis_functions,other.num_basis_functions)))
#from Parallel import mpi
for idx_bra in xrange(self.num_shells):
# Indices of basis functions in bra-shell
strt_row = self.idx_shell[idx_bra]+1
end_row = self.idx_shell[idx_bra+1]
for idx_ket in xrange(other.num_shells):
# Indices of basis functions in ket-shell
strt_col = other.idx_shell[idx_ket]+1
end_col = other.idx_shell[idx_ket+1]
def getInertiaTensor(self):
"""Gets the moment of inertia tensor."""
from BioNanoLEGO.DenseMatrix import zeros, asmatrix
self.inertia_tensor = asmatrix(zeros((3, 3)), "d")
for atom in self.atoms:
atom_mass = atom.getAtomcMass()
x, y, z = atom.getCoords()
x2, y2, z2 = x * x, y * y, z * z
self.inertia_tensor[0, 0] += atom_mass * (y2 + z2)
self.inertia_tensor[1, 1] += atom_mass * (x2 + z2)
self.inertia_tensor[2, 2] += atom_mass * (x2 + y2)
self.inertia_tensor[0, 1] -= atom_mass * x * y
self.inertia_tensor[1, 0] = self.inertia_tensor[0, 1]
self.inertia_tensor[0, 2] -= atom_mass * x * z
self.inertia_tensor[2, 0] = self.inertia_tensor[0, 2]
self.inertia_tensor[1, 2] -= atom_mass * y * z
self.inertia_tensor[2, 1] = self.inertia_tensor[1, 2]
return
def __init__(self, name="molecule", atom_list=[], **options):
"""Creates a molecule.
name: The name of the molecule. Default is 'molecule'.
atom_list: A list of (atomic_symbol or atomic_number,(x,y,z)) of the molecule.
Default is [].
isotope_list: A list of isotope selection (atom_index,isotope), where the
atom index starts from 0. Default is the most abundant isotope.
unit: Length unit for the coordinates. Default is Bohr.
charge: The charge of the molecule. Default is 0.
multiplicity: The spin multiplicity of the molecule. Default is 1.
inertial_coord: Transforms the molecule to inertial coordinates, i.e.,
translating to let the center of mass be zero origin, and rotating
so that the moment of inertia tensor becomes a diagonal matrix.
Default is making such transformation.
"""
from BioNanoLEGO.Element import get_atomic_symbol, get_atomic_number
from BioNanoLEGO.DenseMatrix import asmatrix, zeros, eigh, diag
self.name = name
# Default is no pseudopotential
self.pseudopotential = False
unit = options.get("unit", "bohr")
unit = unit.lower()[:4]
if unit not in DEFINED_UNITS:
raise ValueError("Unknown length unit '%s'!" % unit)
self.charge = int(options.get("charge", 0))
self.multiplicity = int(options.get("multiplicity", 1))
inertial_coord = options.get("inertial_coord", True)
# Gets the user specified isotope selections
isotope_list = options.get("isotope_list", [])
# Initializes atoms
self.atoms = []
self.num_electrons = -int(self.charge)
if atom_list:
self.num_atoms = int(len(atom_list))
# Sets up the isotope selections
isotopes = [None] * self.num_atoms
for atom_idx, isotope in isotope_list:
isotopes[atom_idx] = int(isotope)
# Sets up the atoms
atom_idx = int(0)
for atomic_number, coords in atom_list:
if unit == "angs":
coords = angs_to_bhor(coords[0], coords[1], coords[2])
# The atomic symbol is given
if type(atomic_number) == type(""):
atom_name = atomic_number
atomic_number = get_atomic_number(atom_name)
# The atomic number is given
elif type(atomic_number) == type(0):
atom_name = get_atomic_symbol(atomic_number)
else:
raise TypeError("Atomic symbol or atomic number is expected for atom '%d'!" % atom_idx)
new_atom = Atom(atom_idx, atom_name, atomic_number, isotopes[atom_idx], coords)
self.atoms.append(new_atom)
self.num_electrons += new_atom.getNumElectrons()
atom_idx += 1
# Dumps coordinates
print "Coordinates: "
for atom in self.atoms:
print atom.getCoords()
# Gets the center of mass
self.getCentMass()
if inertial_coord:
print "Translating to center of mass: ", self.cent_of_mass
self.translate(-self.cent_of_mass)
self.cent_of_mass = zeros((3), "d")
# Gets the moment of inertia tensor
self.getInertiaTensor()
if inertial_coord:
E, U = eigh(self.inertia_tensor)
print "Rotation matrix: ", U
self.rotate(U)
self.inertia_tensor = asmatrix(diag(E))
print "New moment of inertia tensor: ", self.inertia_tensor
print "New coordinates: "
for atom in self.atoms:
print atom.getCoords()
else:
self.num_atoms = int(0)
return
