def GetGdirAngle(coords1, coords2, coords3, r_21=None, r_23=None):
"""Calculate direction of energy gradients between bond angle 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.
r_21 (float): Distance between atom2 and atom1 (default None).
r_23 (float): Distance between atom2 and atom3 (default None).
Returns:
gdir1 (float*), gdir2 (float*), gdir3 (float*): vectors in the direction of
max increasing bond angle.
"""
if r_21 is not None:
r_21 = geomcalc.GetRij(coords2, coords1)
if r_23 is not None:
r_23 = geomcalc.GetRij(coords2, coords3)
u_21 = geomcalc.GetUij(coords2, coords1, r_21)
u_23 = geomcalc.GetUij(coords2, coords3, r_23)
cp = geomcalc.GetUcp(u_21, u_23)
gdir1 = geomcalc.GetUcp(u_21, cp) / r_21
gdir3 = geomcalc.GetUcp(cp, u_23) / r_23
gdir2 = -1.0 * (gdir1 + gdir3)
return gdir1, gdir2, gdir3
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 GetEBoundI(k_box, bound, coords, origin, boundtype):
"""Calculate simulation boundary energy of an atom.
Args:
k_box (float): Spring constant [kcal/(mol*A^2)] of boundary.
bound (float): Distance from origin [Angstrom] of boundary.
coords (float*): Array of cartesian coordinates [Angstrom] of atom.
origin (float*): Array of cartesian coordiantes [Angstrom] of origin of
simulation.
boundtype (str): 'cube' or 'sphere', type of boundary condition.
Returns:
e_bound_i (float): Boundary energy [kcal/mol] of atom.
"""
e_bound_i = 0.0
if (boundtype == 'cube'):
for j in range(const.NUMDIM):
scale = 1.0 if (abs(coords[j] - origin[j]) >= bound) else 0.0
e_bound_i += (scale * k_box *
(abs(coords[j] - origin[j]) - bound)**2)
elif (boundtype == 'sphere'):
r_io = geomcalc.GetRij(origin, coords)
u_io = geomcalc.GetUij(origin, coords)
scale = 1.0 if (r_io >= bound) else 0.0
e_bound_i += scale * k_box * (r_io - bound)**2
return e_bound_i
def GetGNonbonded(g_vdw, g_elst, atoms, nonints, dielectric):
"""Calculate non-bonded energy gradients between all nonbonded atom pairs.
Computes van der waals and electrostatic energy gradient [kcal/(mol*A)]
components between all pairs of non-bonded atoms in a system.
Args:
g_vdw (float**): Nx3 array of molecule's van der waals gradients.
g_elst (float**): Nx3 array of molecule's electrostatic gradients.
atoms (mmlib.molecule.Atom*): Array of molecule's Atom objects.
nonints (set(int, int)): Set of atomic index pairs of atoms without
nonbonded interactions due to covalent (near-)ajecency.
dielectric (float): Dielectric constant of molecule.
"""
g_vdw.fill(0.0)
g_elst.fill(0.0)
for i, j in itertools.combinations(range(len(atoms)), 2):
if (i, j) in nonints:
continue
atom1, atom2 = atoms[i], atoms[j]
r_ij = geomcalc.GetRij(atom1.coords, atom2.coords)
dir1, dir2 = GetGDirInter(atom1.coords, atom2.coords, r_ij)
eps_ij = atom1.sreps * atom2.sreps
ro_ij = atom1.ro + atom2.ro
g_elst_mag = GetGMagElstIJ(r_ij, atom1.charge, atom2.charge, dielectric)
g_vdw_mag = GetGMagVdwIJ(r_ij, eps_ij, ro_ij)
g_vdw[i] += g_vdw_mag * dir1
g_vdw[j] += g_vdw_mag * dir2
g_elst[i] += g_elst_mag * dir1
g_elst[j] += g_elst_mag * dir2
def GetGNonbonded(mol):
"""Calculate vdw and elst energy gradients for all nonbonded atom pairs.
Args:
mol (mmlib.molecule.Molecule): Molecule object with associated Atom
objects with geometry and parameter data.
"""
mol.g_nonbonded.fill(0.0)
mol.g_vdw.fill(0.0)
mol.g_elst.fill(0.0)
for i in range(mol.n_atoms):
at1 = mol.atoms[i]
for j in range(i + 1, mol.n_atoms):
if not j in mol.nonints[i]:
at2 = mol.atoms[j]
r_ij = geomcalc.GetRij(at1.coords, at2.coords)
dir1, dir2 = GetGdirInter(at1.coords, at2.coords, r_ij)
eps_ij = at1.sreps * at2.sreps
ro_ij = at1.ro + at2.ro
g_elst = GetGElstIJ(r_ij, at1.charge, at2.charge,
mol.dielectric)
g_vdw = GetGVdwIJ(r_ij, eps_ij, ro_ij)
mol.g_vdw[i] += g_vdw * dir1
mol.g_vdw[j] += g_vdw * dir2
mol.g_elst[i] += g_elst * dir1
mol.g_elst[j] += g_elst * dir2
def GetGBoundI(k_box, bound, coord, origin, boundtype):
"""Calculate energy gradient magnitude of boundary energy.
Args:
k_box (float): Spring constant [kcal/(mol*A^2)] of boundary.
bound (float): Distance from origin [Angstrom] of boundary.
coords (float*): Array of cartesian coordinates [Angstrom] of atom.
origin (float*): Array of cartesian coordiantes [Angstrom] of origin of
simulation.
boundtype (str): 'cube' or 'sphere', type of boundary condition.
Returns:
g_bound_i (float): Magnitude of energy gradient [kcal/(mol*A)].
"""
g_bound_i = numpy.zeros(const.NUMDIM)
if boundtype == 'cube':
for j in range(const.NUMDIM):
sign = 1.0 if (coord[j] - origin[j]) <= 0.0 else -1.0
scale = 1.0 if abs(coord[j] - origin[j]) >= bound else 0.0
g_bound_i[j] = (-2.0 * sign * scale * k_box *
(abs(coord[j]) - bound))
elif boundtype == 'sphere':
r_io = geomcalc.GetRij(origin, coord)
u_io = geomcalc.GetUij(origin, coord)
scale = 1.0 if r_io >= bound else 0.0
g_bound_i = 2.0 * scale * k_box * (r_io - bound) * u_io
return g_bound_i
def GetENonbonded(atoms, nonints, dielectric):
"""Calculate non-bonded interaction energy between all atoms.
Computes van der waals and electrostatic energy [kcal/mol] components
between all pairs of non-bonded atoms in a system.
Args:
atoms (mmlib.molecule.Atom*): Array of Atom objects containing Cartesian
coordinates and molecular mechanics parameters.
nonints (set(int, int)): Set of atomic index pairs of atoms without
nonbonded interactions due to covalent (near-)adjacency.
dielectric (float): Dielectric constant of molecule.
Returns:
e_vdw (float): Van der waals energy [kcal/mol] of molecule.
e_elst (float): Electrostatic energy [kcal/mol] of molecule.
"""
e_vdw, e_elst = 0.0, 0.0
for i, j in itertools.combinations(range(len(atoms)), 2):
if (i, j) in nonints:
continue
at1, at2 = atoms[i], atoms[j]
r_ij = geomcalc.GetRij(at1.coords, at2.coords)
eps_ij = at1.sreps * at2.sreps
ro_ij = at1.ro + at2.ro
e_elst += GetEElstIJ(r_ij, at1.charge, at2.charge, dielectric)
e_vdw += GetEVdwIJ(r_ij, eps_ij, ro_ij)
return e_vdw, e_elst
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.
"""
if r_12 is not None:
r_12 = geomcalc.GetRij(coords1, coords2)
if r_23 is not None:
r_23 = geomcalc.GetRij(coords2, coords3)
if r_34 is not None:
r_34 = geomcalc.GetRij(coords3, coords4)
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 UpdateBonds(bonds):
"""Update all bond lengths [Angstrom] within a molecule object.
Args:
bonds (mmlib.molecule.Bond*): Array of molecule's Bond objects.
"""
for bond in mol.bonds:
c1 = mol.atoms[bond.at1].coords
c2 = mol.atoms[bond.at2].coords
bond.r_ij = geomcalc.GetRij(c1, c2)
mol.bond_graph[bond.at1][bond.at2] = bond.r_ij
mol.bond_graph[bond.at2][bond.at1] = bond.r_ij
def UpdateBonds(mol):
"""Update all bond lengths [Angstrom] within a molecule object.
Args:
mol (mmlib.molecule.Molecule): Molecule object with bond data.
"""
for p in range(mol.n_bonds):
b = mol.bonds[p]
c1 = mol.atoms[b.at1].coords
c2 = mol.atoms[b.at2].coords
b.r_ij = geomcalc.GetRij(c1, c2)
mol.bond_graph[b.at1][b.at2] = b.r_ij
mol.bond_graph[b.at2][b.at1] = b.r_ij
def UpdateBonds(bonds, atoms, bond_graph):
"""Update all bond lengths [Angstrom] within a molecule object.
Args:
bonds (mmlib.molecule.Bond*): Array of molecule's Bond objects.
atoms (mmlib.molecule.Atom*): Array of molecule's Atom objects.
bond_graph (int:(int:float)): Dictionary of bond connectivity.
"""
for bond in bonds:
c1 = atoms[bond.at1].coords
c2 = atoms[bond.at2].coords
bond.r_ij = geomcalc.GetRij(c1, c2)
bond_graph[bond.at1][bond.at2] = bond.r_ij
bond_graph[bond.at2][bond.at1] = bond.r_ij
def GetBondFromPrm(record, atoms):
"""Parses bond record into a Bond object.
Args:
record (str*): Array of strings from line of prm file.
atoms (mmlib.molecule.Atom*): Array of molecule's Atom objects.
Returns:
bond (mmlib.molecule.Bond): Bond object with attributes from record.
"""
at1, at2 = (x - 1 for x in map(int, record[1:3]))
k_b, r_eq = tuple(map(float, record[3:5]))
c1, c2 = (atoms[i].coords for i in (at1, at2))
r_ij = geomcalc.GetRij(c1, c2)
return molecule.Bond(at1, at2, r_ij, r_eq, k_b)
def _GetBond(mol, record):
"""Parse bond record into a bond object and append to molecule.
Appends mmlib.molecule.Bond object to mmlib.molecule.Molecule object. Contents
of bond object include (int) 2 atomic indices, (float) spring constant
[kcal/(mol*A^2)], (float) equilibrium bond length [Angstrom], (float) bond
length [Angstrom].
Args:
mol (mmlib.molecule.Molecule): Molecule to append bond.
record (str*): Array of strings from line of prm file.
"""
at1, at2 = [x-1 for x in list(map(int, record[1:3]))]
k_b, r_eq = list(map(float, record[3:5]))
c1, c2 = [mol.atoms[i].coords for i in [at1, at2]]
r_ij = geomcalc.GetRij(c1, c2)
bond = molecule.Bond(at1, at2, r_ij, r_eq, k_b)
mol.bonds.append(bond)
mol.bond_graph[at1][at2] = r_ij
mol.bond_graph[at2][at1] = r_ij
def GetBonds(records, atoms):
"""Parses bond records into an array of Bond objects.
Args:
records (str**): 2d array of strings from lines of prm file.
atoms (mmlib.molecule.Atom*): Array of molecule's Atom objects.
Returns:
bonds (mmlib.molecule.Bond*): Array of Bond objects with parameters from
records.
"""
bonds = []
for record in records:
if not record[0].upper() == 'BOND':
continue
at1, at2 = [x - 1 for x in list(map(int, record[1:3]))]
k_b, r_eq = list(map(float, record[3:5]))
c1, c2 = [atoms[i].coords for i in [at1, at2]]
r_ij = geomcalc.GetRij(c1, c2)
bonds.append(molecule.Bond(at1, at2, r_ij, r_eq, k_b))
return bonds
def GetENonbonded(mol):
"""Calculate non-bonded interaction energy between all atoms.
Computes van der waals and electrostatic energy [kcal/mol] components
between all pairs of non-bonded atoms in a system.
Args:
mol (mmlib.molecule.Molecule): Molecule object with Atom objects containing
cartesian coordinates and molecular mechanics parameters
"""
mol.e_nonbonded, mol.e_vdw, mol.e_elst = 0.0, 0.0, 0.0
for i in range(mol.n_atoms):
at1 = mol.atoms[i]
for j in range(i + 1, mol.n_atoms):
if not j in mol.nonints[i]:
at2 = mol.atoms[j]
r_ij = geomcalc.GetRij(at1.coords, at2.coords)
eps_ij = at1.sreps * at2.sreps
ro_ij = at1.ro + at2.ro
mol.e_elst += GetEElstIJ(r_ij, at1.charge, at2.charge,
mol.dielectric)
mol.e_vdw += GetEVdwIJ(r_ij, eps_ij, ro_ij)
def testUnitLength(self):
"""Asserts unit length for points one distance unit apart."""
params = ORIGIN, NEGATIVE_UNIT_X
self.assertAlmostEqual(geomcalc.GetRij(*params), 1.0)
def testSamePoint(self):
"""Asserts zero distance between identical points."""
params = ARBITRARY_XYZ1, ARBITRARY_XYZ1
self.assertAlmostEqual(geomcalc.GetRij(*params), 0.0)
def testOnAxisX(self):
"""Asserts correct value for points separated along x-axis."""
params = POSITIVE_ARBITRARY_X, NEGATIVE_ARBITRARY_X
self.assertAlmostEqual(geomcalc.GetRij(*params), 12.3099410)
def testOnAxisY(self):
"""Asserts correct value for points separated along y-axis."""
params = NEGATIVE_ARBITRARY_Y, POSITIVE_ARBITRARY_Y
self.assertAlmostEqual(geomcalc.GetRij(*params), 12.2413450)
def testReflexive(self):
"""Asserts same value for inverted order of inputs."""
params = ARBITRARY_XYZ2, ARBITRARY_XYZ1
self.assertAlmostEqual(geomcalc.GetRij(*params), 12.1693138)
def testArbitrary(self):
"""Asserts correct distance between arbitrary points in 3d space."""
params = ARBITRARY_XYZ1, ARBITRARY_XYZ2
self.assertAlmostEqual(geomcalc.GetRij(*params), 12.1693138)
def testOnAxisZ(self):
"""Asserts correct value for points separated along z-axis."""
params = POSITIVE_ARBITRARY_Z, NEGATIVE_ARBITRARY_Z
self.assertAlmostEqual(geomcalc.GetRij(*params), 12.6247660)
