def GetGDirTorsion(coords1, coords2, coords3, coords4, r_12=None, r_23=None,
r_34=None):
"""Calculate direction of energy gradients between torsion atoms.
Args:
coords1 (float*): 3 cartesian coordinates [Angstrom] of atom1.
coords2 (float*): 3 cartesian coordinates [Angstrom] of atom2.
coords3 (float*): 3 cartesian coordinates [Angstrom] of atom3.
coords4 (float*): 3 cartesian coordinates [Angstrom] of atom4.
r_12 (float): Distance between atom1 and atom2 (default None).
r_23 (float): Distance between atom2 and atom3 (default None).
r_34 (float): Distance between atom3 and atom4 (default None).
Returns:
gdir1 (float*), gdir2 (float*), gdir3 (float*), gdir4 (float*): Vectors in
the direction of max increasing torsion angle.
"""
u_21 = geomcalc.GetUij(coords2, coords1, r_12)
u_34 = geomcalc.GetUij(coords3, coords4, r_34)
u_23 = geomcalc.GetUij(coords2, coords3, r_23)
u_32 = -1.0 * u_23
a_123 = geomcalc.GetAijk(coords1, coords2, coords3, r_12, r_23)
a_432 = geomcalc.GetAijk(coords4, coords3, coords2, r_34, r_23)
s_123 = math.sin(const.DEG2RAD * a_123)
s_432 = math.sin(const.DEG2RAD * a_432)
c_123 = math.cos(const.DEG2RAD * a_123)
c_432 = math.cos(const.DEG2RAD * a_432)
gdir1 = geomcalc.GetUcp(u_21, u_23) / (r_12*s_123)
gdir4 = geomcalc.GetUcp(u_34, u_32) / (r_34*s_432)
gdir2 = (r_12/r_23*c_123 - 1.0)*gdir1 - (r_34/r_23*c_432)*gdir4
gdir3 = (r_34/r_23*c_432 - 1.0)*gdir4 - (r_12/r_23*c_123)*gdir1
return gdir1, gdir2, gdir3, gdir4
def GetAngles(mol):
"""Determine bond angle atom triplets from bond graph and get parameters.
Search bond graph for bond angle triplets, and parameter tables for mm
parameters. Use to create a new Angle object and append to Molecule.
Count as angle if ij and jk are bonded in triplet ijk.
Args:
mol (mmlib.molecule.Molecule): Molecule object with bond graph of
atom pairs within covalent radius cutoff threshold.
"""
for j in range(mol.n_atoms):
at2 = mol.atoms[j]
for i in mol.bond_graph[j].keys():
at1 = mol.atoms[i]
r_ij = mol.bond_graph[i][j]
for k in mol.bond_graph[j].keys():
if i >= k:
continue
at3 = mol.atoms[k]
r_jk = mol.bond_graph[j][k]
a_ijk = geomcalc.GetAijk(at1.coords, at2.coords, at3.coords,
r_ij, r_jk)
k_a, a_eq = param.GetAngleParam(at1.type_, at2.type_,
at3.type_)
if k_a > 0.0:
mol.angles.append(molecule.Angle(i, j, k, a_ijk, a_eq,
k_a))
mol.angles = sorted(mol.angles, key=lambda a: a.at3)
mol.angles = sorted(mol.angles, key=lambda a: a.at2)
mol.angles = sorted(mol.angles, key=lambda a: a.at1)
mol.n_angles = len(mol.angles)
def GetAngles(atoms, bond_graph):
"""Determine bond angle atom triplets from bond graph and get parameters.
Search bond graph for bond angle triplets, and parameter tables for mm
parameters. Use to create a new Angle object and append to Molecule.
Count as angle if ij and jk are bonded in triplet ijk.
Args:
atoms (mmlib.molecule.Atom*): Array of molecule's Atom objects.
bond_graph (int:(int:float)): Dictionary of bond connectivity.
Returns:
angles (mmlib.molecule.Angle*): Array of molecule's Angle objects.
"""
angles = []
for j, at2 in enumerate(atoms):
for i, k in itertools.combinations(bond_graph[j], 2):
if i > k:
continue
at1, at3 = atoms[i], atoms[k]
a_ijk = geomcalc.GetAijk(at1.coords, at2.coords, at3.coords)
k_a, a_eq = param.GetAngleParam(at1.type_, at2.type_, at3.type_)
if k_a:
angles.append(molecule.Angle(i, j, k, k_a, a_eq, a_ijk))
angles.sort(key=lambda a: (a.at1, a.at2, a.at3))
return angles
def UpdateAngles(angles):
"""Update all bond angles [degrees] within a molecule object.
Args:
angles (mmlib.molecule.Angle*): Array of molecule's Angle objects.
"""
for angle in mol.angles:
r12 = mol.bond_graph[angle.at1][angle.at2]
r23 = mol.bond_graph[angle.at2][angle.at3]
c1 = mol.atoms[angle.at1].coords
c2 = mol.atoms[angle.at2].coords
c3 = mol.atoms[angle.at3].coords
angle.a_ijk = geomcalc.GetAijk(c1, c2, c3, r12, r23)
def UpdateAngles(mol):
"""Update all bond angles [degrees] within a molecule object.
Args:
mol (mmlib.molecule.Molecule): Molecule object with angle data.
"""
for p in range(mol.n_angles):
a = mol.angles[p]
r12 = mol.bond_graph[a.at1][a.at2]
r23 = mol.bond_graph[a.at2][a.at3]
c1 = mol.atoms[a.at1].coords
c2 = mol.atoms[a.at2].coords
c3 = mol.atoms[a.at3].coords
a.a_ijk = geomcalc.GetAijk(c1, c2, c3, r12, r23)
def UpdateAngles(angles, atoms, bond_graph):
"""Update all bond angles [degrees] within a molecule object.
Args:
angles (mmlib.molecule.Angle*): Array of molecule's Angle objects.
atoms (mmlib.molecule.Atom*): Array of molecule's Atom objects.
bond_graph (int:(int:float)): Dictionary of bond connectivity.
"""
for angle in angles:
r12 = bond_graph[angle.at1][angle.at2]
r23 = bond_graph[angle.at2][angle.at3]
c1 = atoms[angle.at1].coords
c2 = atoms[angle.at2].coords
c3 = atoms[angle.at3].coords
angle.a_ijk = geomcalc.GetAijk(c1, c2, c3, r12, r23)
def GetAngleFromPrm(record, atoms):
"""Parses angle record into an Angle object.
Args:
record (str*): Array of strings from line of prm file.
atoms (mmlib.molecule.Atom*): Array of molecule's Atom objects.
Returns:
angle (mmlib.molecule.Angle): Angle object with attributes from record.
"""
at1, at2, at3 = (x - 1 for x in (map(int, record[1:4])))
k_a, a_eq = tuple(map(float, record[4:6]))
c1, c2, c3 = (atoms[i].coords for i in (at1, at2, at3))
a_ijk = geomcalc.GetAijk(c1, c2, c3)
return molecule.Angle(at1, at2, at3, a_ijk, a_eq, k_a)
def GetGdirOutofplane(coords1,
coords2,
coords3,
coords4,
oop,
r_31=None,
r_32=None,
r_34=None):
"""Calculate direction of energy gradients between outofplane atoms.
Args:
coords1 (float*): 3 cartesian coordinates [Angstrom] of atom1.
coords2 (float*): 3 cartesian coordinates [Angstrom] of atom2.
coords3 (float*): 3 cartesian coordinates [Angstrom] of atom3.
coords4 (float*): 3 cartesian coordinates [Angstrom] of atom4.
oop (float): Out-of-plane angles bewteen atoms 1, 2, 3, and 4.
r_31 (float): Distance between atom3 and atom1 (default None).
r_32 (float): Distance between atom3 and atom2 (default None).
r_34 (float): Distance between atom3 and atom4 (default None).
Returns:
gdir1 (float*), gdir2 (float*), gdir3 (float*), gdir4 (float*): Vectors in
the direction of max increasing outofplane angle.
"""
if r_31 is not None:
r_31 = geomcalc.GetRij(coords3, coords1)
if r_32 is not None:
r_32 = geomcalc.GetRij(coords3, coords2)
if r_34 is not None:
r_34 = geomcalc.GetRij(coords3, coords4)
u_31 = geomcalc.GetUij(coords3, coords1, r_31)
u_32 = geomcalc.GetUij(coords3, coords2, r_32)
u_34 = geomcalc.GetUij(coords3, coords4, r_34)
cp_3234 = geomcalc.GetCp(u_32, u_34)
cp_3431 = geomcalc.GetCp(u_34, u_31)
cp_3132 = geomcalc.GetCp(u_31, u_32)
a_132 = geomcalc.GetAijk(coords1, coords3, coords2)
s_132 = math.sin(const.DEG2RAD * a_132)
c_132 = math.cos(const.DEG2RAD * a_132)
c_oop = math.cos(const.DEG2RAD * oop)
t_oop = math.tan(const.DEG2RAD * oop)
gdir1 = ((1.0 / r_31) * (cp_3234 / (c_oop * s_132) - (t_oop / s_132**2) *
(u_31 - c_132 * u_32)))
gdir2 = ((1.0 / r_32) * (cp_3431 / (c_oop * s_132) - (t_oop / s_132**2) *
(u_32 - c_132 * u_31)))
gdir4 = ((1.0 / r_34) * (cp_3132 / (c_oop * s_132) - (t_oop * u_34)))
gdir3 = -1.0 * (gdir1 + gdir2 + gdir4)
return gdir1, gdir2, gdir3, gdir4
def _GetAngle(mol, record):
"""Parse angle record into an angle object and append to molecule.
Appends mmlib.molecule.Angle object to mmlib.molecule.Molecule object.
Contents of angle object include (int) 3 atomic indices, (float) spring
constant [kcal/(mol*radian^2)], (float) equilibrium bond angle [degrees], and
(float) bond angle [degrees].
Args:
mol (mmlib.molecule.Molecule): Molecule to append angle.
record (str*): Array of strings from line of prm file.
"""
at1, at2, at3 = [x-1 for x in list(map(int, record[1:4]))]
k_a, a_eq = list(map(float, record[4:6]))
c1, c2, c3 = [mol.atoms[i].coords for i in [at1, at2, at3]]
a_ijk = geomcalc.GetAijk(c1, c2, c3)
angle = molecule.Angle(at1, at2, at3, a_ijk, a_eq, k_a)
mol.angles.append(angle)
def GetAngles(records, atoms):
"""Parses angle records into an array of Angle objects.
Args:
records (str**): 2d array of strings from lines of prm file.
atom (mmlib.molecule.Atom*): Array of molecule's Atom objects.
Returns:
angles (mmlib.molecule.Angle): Array of Angle objects with parameters from
records.
"""
angles = []
for record in records:
if not record[0].upper() == 'ANGLE':
continue
at1, at2, at3 = [x - 1 for x in list(map(int, record[1:4]))]
k_a, a_eq = list(map(float, record[4:6]))
c1, c2, c3 = [atoms[i].coords for i in [at1, at2, at3]]
a_ijk = geomcalc.GetAijk(c1, c2, c3)
angles.append(molecule.Angle(at1, at2, at3, a_ijk, a_eq, k_a))
return angles
def testZeroAngle(self):
"""Asserts zero angle between identical vectors."""
params = ORIGIN, NEGATIVE_UNIT_Z, ORIGIN
self.assertAlmostEqual(geomcalc.GetAijk(*params), 0.0)
def testStraightAngle(self):
"""Asserts 180 degree angle between oppositie vectors."""
params = POSITIVE_UNIT_Z, ORIGIN, NEGATIVE_UNIT_Z
self.assertAlmostEqual(geomcalc.GetAijk(*params), 180.0)
def testReflexive(self):
"""Asserts same value when inverting the order of points."""
params = ARBITRARY_XYZ4, ARBITRARY_XYZ3, ARBITRARY_XYZ2
self.assertAlmostEqual(geomcalc.GetAijk(*params), 97.75040394)
def testRightAngle(self):
"""Asserts ninety degree angle between orthogonal vectors."""
params = POSITIVE_UNIT_X, ORIGIN, POSITIVE_UNIT_Y
self.assertAlmostEqual(geomcalc.GetAijk(*params), 90.0)
def testArbitraryObtuse(self):
"""Asserts correct value between arbitrary obtuse 3d points."""
params = ARBITRARY_XYZ2, ARBITRARY_XYZ3, ARBITRARY_XYZ4
self.assertAlmostEqual(geomcalc.GetAijk(*params), 97.75040394)
def testArbitraryAcute(self):
"""Asserts correct value between arbitrary acute 3d points."""
params = ARBITRARY_XYZ1, ARBITRARY_XYZ2, ARBITRARY_XYZ3
self.assertAlmostEqual(geomcalc.GetAijk(*params), 82.37365716)
def testInPlaneYZ(self):
"""Asserts correct value within the yz-plane."""
params = ARBITRARY_YZ1, ARBITRARY_YZ2, ARBITRARY_YZ3
self.assertAlmostEqual(geomcalc.GetAijk(*params), 23.05201986)
def testInPlaneXZ(self):
"""Asserts correct value within the xz-plane."""
params = ARBITRARY_XZ1, ARBITRARY_XZ2, ARBITRARY_XZ3
self.assertAlmostEqual(geomcalc.GetAijk(*params), 42.14774907)
def testInPlaneXY(self):
"""Asserts correct value within the xy-plane."""
params = ARBITRARY_XY1, ARBITRARY_XY2, ARBITRARY_XY3
self.assertAlmostEqual(geomcalc.GetAijk(*params), 29.07348364)
