def get_lindh_k(atoms, coords3d, bonds=None, angles=None, torsions=None):
if bonds is None:
bonds = list()
if angles is None:
angles = list()
if torsions is None:
torsions = list()
atoms = [a.lower() for a in atoms]
alphas = [get_lindh_alpha(a1, a2) for a1, a2 in it.combinations(atoms, 2)]
pair_cov_radii = get_pair_covalent_radii(atoms)
cdm = pdist(coords3d)
rhos = squareform(np.exp(alphas * (pair_cov_radii**2 - cdm**2)))
k_dict = {
2: 0.45, # Stretches/bonds
3: 0.15, # Bends/angles
4: 0.005, # Torsions/dihedrals
}
ks = list()
for inds in it.chain(bonds, angles, torsions):
rho_product = 1
for i in range(len(inds) - 1):
i1, i2 = inds[i:i + 2]
rho_product *= rhos[i1, i2]
ks.append(k_dict[len(inds)] * rho_product)
return ks
def fischer_guess(geom):
cdm = pdist(geom.coords3d)
pair_cov_radii = get_pair_covalent_radii(geom.atoms)
dihedrals = geom.internal.dihedrals
# For the dihedral force constants we also have to count the number
# of bonds formed with the centrals atoms of the dihedral.
central_atoms = [dh.inds[1:3] for dh in dihedrals]
bond_factor = geom.internal.bond_factor
bond_mat = squareform(cdm <= (pair_cov_radii * bond_factor))
tors_atom_bonds = dict()
for a, b in central_atoms:
# Substract 2, as we don't want the bond between a and b,
# but this bond will be in both rows of the bond_mat.
bond_sum = bond_mat[a].sum() + bond_mat[b].sum() - 2
tors_atom_bonds[(a, b)] = bond_sum
dist_mat = squareform(cdm)
pair_cov_radii_mat = squareform(pair_cov_radii)
def h_bond(bond):
a, b = bond.indices
r_ab = dist_mat[a, b]
r_ab_cov = pair_cov_radii_mat[a, b]
return 0.3601 * exp(-1.944 * (r_ab - r_ab_cov))
def h_bend(bend):
b, a, c = bend.indices
r_ab = dist_mat[a, b]
r_ac = dist_mat[a, c]
r_ab_cov = pair_cov_radii_mat[a, b]
r_ac_cov = pair_cov_radii_mat[a, c]
return (0.089 + 0.11 / (r_ab_cov * r_ac_cov)**(-0.42) *
exp(-0.44 * (r_ab + r_ac - r_ab_cov - r_ac_cov)))
def h_dihedral(dihedral):
# import pdb; pdb.set_trace()
c, a, b, d = dihedral.indices
r_ab = dist_mat[a, b]
r_ab_cov = pair_cov_radii_mat[a, b]
bond_sum = max(tors_atom_bonds[(a, b)], 0)
return (0.0015 + 14.0 * bond_sum**0.57 /
(r_ab * r_ab_cov)**4.0 * exp(-2.85 * (r_ab - r_ab_cov)))
h_funcs = {
2: h_bond,
3: h_bend,
4: h_dihedral,
}
h_diag = list()
for primitive in geom.internal.primitives:
f = h_funcs[len(primitive.indices)]
h_diag.append(f(primitive))
H = np.array(np.diagflat(h_diag))
return H
def swart_guess(geom):
pair_cov_radii = get_pair_covalent_radii(geom.atoms)
cdm = pdist(geom.coords3d)
rhos = squareform(np.exp(-cdm / pair_cov_radii + 1))
k_dict = {
2: 0.35,
3: 0.15,
4: 0.005,
}
k_diag = list()
for primitive in geom.internal.primitives:
rho_product = 1
for i in range(len(primitive.indices) - 1):
i1, i2 = primitive.indices[i:i + 2]
rho_product *= rhos[i1, i2]
k_diag.append(k_dict[len(primitive.indices)] * rho_product)
return np.diagflat(k_diag)
def lindh_guess(geom):
"""Slightly modified Lindh model hessian as described in [1].
Instead of using the tabulated r_ref,ij values from [1] we will use the
'true' covalent radii as pyberny. The tabulated r_ref,ij value for two
carbons (2nd period) is 2.87 Bohr. Carbons covalent radius is ~ 1.44 Bohr,
so 2*1.44 Bohr = 2.88 Bohr which fits nicely with the tabulate value.
If values for elements > 3rd are requested the alpha values for the 3rd
period will be (re)used.
"""
first_period = "h he".split()
def get_alpha(atom1, atom2):
if (atom1 in first_period) and (atom2 in first_period):
return 1.
elif (atom1 in first_period) or (atom2 in first_period):
return 0.3949
else:
return 0.28
atoms = [a.lower() for a in geom.atoms]
alphas = [get_alpha(a1, a2) for a1, a2 in it.combinations(atoms, 2)]
pair_cov_radii = get_pair_covalent_radii(geom.atoms)
cdm = pdist(geom.coords3d)
rhos = squareform(np.exp(alphas * (pair_cov_radii**2 - cdm**2)))
k_dict = {
2: 0.45, # Stretches/bonds
3: 0.15, # Bends/angles
4: 0.005, # Torsions/dihedrals
}
k_diag = list()
for prim_int in geom.internal.prim_internals:
rho_product = 1
for i in range(len(prim_int.inds) - 1):
i1, i2 = prim_int.inds[i:i + 2]
rho_product *= rhos[i1, i2]
k_diag.append(k_dict[len(prim_int.inds)] * rho_product)
H = np.diagflat(k_diag)
return H
def atoms_are_too_close(self, geom, factor=.7):
"""Determine if atoms are too close."""
dist_mat = pdist(geom.coords3d)
cov_rad_mat = get_pair_covalent_radii(geom.atoms)
too_close = dist_mat < factor*cov_rad_mat
return any(too_close)