def graphene(n1,n2,R,height=5.0):
"""
Construct graphene lattice, multiply the primitive cell
n1 x n2 times in corresponding directions.
.-----.
/ /
/ X / a2
/ /
X----->
a1
"""
from hotbit import Atoms
if not isinstance(R,float): R=R[0]
a1=vec([R*np.cos(pi/6)*2,0.,0.])
a2=0.5*a1 + vec([0.,1.5*R,0.])
#assert n2%2==0
r=[]
for i1 in range(n1):
for i2 in range(n2):
corner = i1*a1+i2*a2
r.append(corner)
r.append(corner+a1+vec([0.0,R,0.0]))
cell=[[n1*a1[0], 0, 0],[n2*a2[0],n2*a2[1],0],[0,0,10]]
atoms=Atoms('C'*len(r),positions=r,cell=cell)
atoms.center(vacuum=height/2,axis=2)
atoms.set_pbc((True,True,False))
return atoms
def compare_trajectory(self, i_traj, calc, tables, i_par):
"""
Calculate the energies for the frames in the trajectory
and plot them.
"""
frames = []
energies = []
trajectory = PickleTrajectory(self.trajectories[i_traj])
for i, image in enumerate(trajectory):
e_tb = None
try:
atoms = Atoms(image)
c = copy(calc)
c.tables = tables
atoms.set_calculator(c)
e_tb = atoms.get_potential_energy()
except Exception as ex:
print(ex, file=self.txt)
if e_tb != None:
energies.append(e_tb)
frames.append(i)
delta_E = self.norm_to_isolated_atoms(trajectory[0])
for i in range(len(energies)):
energies[i] += delta_E
self.plot(frames, energies, i_traj, tables, i_par)
def append_dimer(self,
weight,
calc,
R,
comment=None,
label='dimer',
color=None):
"""
Use dimer bond length in fitting.
parameters:
===========
weight: fitting weight
calc: Hotbit calculator used in calculation
(remember Gamma-point and charge)
R: dimer bond length (Angstroms)
comment: fitting comment for par-file (replaced by label if None)
label: plotting label (replaced by comment if None)
color: plotting color
"""
if comment == None: comment = label
self.r_dimer = R
atoms = Atoms([self.sym1, self.sym2], [(0, 0, 0), (R, 0, 0)],
pbc=False)
atoms.center(vacuum=5)
color = self._get_color(color)
self.append_scalable_system(weight,
calc,
atoms,
comment=comment,
label=label,
color=color)
def chiral_nanotube(n, m, R=1.42, element='C'):
"""
Construct a nanotube with a chiral container.
parameters:
===========
n,m: chiral indices
R: bond length
element: element type
"""
from hotbit import Atoms
a = np.sqrt(3) * R
a1 = np.array([a, 0, 0])
a2 = np.array([0.5 * a, -1.5 * R, 0])
rl = []
shift = (a / 2, -0.5 * R, 0)
for i in range(n):
origin = i * a1
rl.append(origin)
rl.append(origin + shift)
for j in range(m):
origin = (n - 1) * a1 + (j + 1) * a1
rl.append(origin)
rl.append(origin + shift)
atoms = Atoms()
C = n * a1 + m * a2
Cn = np.linalg.norm(C)
T = np.array([C[1], -C[0], 0])
t = T / np.linalg.norm(T)
radius = Cn / (2 * pi)
atoms = Atoms()
for r in rl:
phi = np.dot(r, C) / Cn**2 * 2 * pi
atoms += Atom(
element,
(radius * np.cos(phi), radius * np.sin(phi), np.dot(r, t)))
atoms = Atoms(atoms, container='Chiral')
height = np.abs(np.dot(a1 - a2, t))
angle = -np.dot(a1 - a2, C) / Cn**2 * 2 * pi
atoms.set_container(angle=angle, height=height)
data = nanotube_data(n, m, R)
T, Ntot = data['T'], 2 * data['hexagons_per_cell']
data['height'] = height
data['twist'] = angle
atoms.data = data
return atoms
def setup_bending(atoms, angle, radius, rotation=0.0, physical=True):
"""
Prepare a bending setup for a tube or slab.
Tube should be originally periodic in z-direction with
the correct cell, and optionally periodic in y-direction.
Then atoms are set up for bending with hotbit.Wedge class
with bending wrt. z-axis, and optionally periodic along
z-axis.
Atoms are first rotated pi/2 around -x-axis, then
rotated an angle 'rotation' around y-axis, then
transformed the distance 'radius' towards x-axis.
The atoms are further adjusted for the wedge angle 'angle'.
'physical' tells if the angle should be 2*pi/integer.
"""
a = atoms.copy()
a.rotate('-x', np.pi / 2)
L = a.get_cell().diagonal()
if abs(L.prod() - a.get_volume()) > 1E-10:
raise AssertionError('Cell should be orthorhombic.')
pbc = a.get_pbc()
if not pbc[2] or pbc[0]:
raise AssertionError(
'Should be periodic in z-direction and not periodic in x-direction'
)
r = a.get_positions()
if np.any(r[:, 1] < 0): # index 1 is correct here
raise AssertionError('For bending, all atoms should be above xy-plane')
# move and adjust
a.rotate('y', rotation)
for i in range(len(a)):
x, y = r[i, 0:2]
R = x + radius
phi = y * angle / L[2]
r[i, 0] = R * np.cos(phi)
r[i, 1] = R * np.sin(phi)
a.set_positions(r)
a = Atoms(a, container='Wedge')
a.set_container(angle=angle, height=L[1], pbcz=pbc[1], physical=physical)
return a
def append_dimer(self,weight,calc,R,comment=None,label='dimer',color=None):
"""
Use dimer bond length in fitting.
parameters:
===========
weight: fitting weight
calc: Hotbit calculator used in calculation
(remember Gamma-point and charge)
R: dimer bond length (Angstroms)
comment: fitting comment for par-file (replaced by label if None)
label: plotting label (replaced by comment if None)
color: plotting color
"""
if comment==None: comment=label
self.r_dimer = R
atoms = Atoms([self.sym1,self.sym2],[(0,0,0),(R,0,0)],pbc=False)
atoms.center(vacuum=5)
color = self._get_color(color)
self.append_scalable_system(weight,calc,atoms,comment=comment,label=label,color=color)
def setup_bending(atoms,angle,radius,rotation=0.0,physical=True):
"""
Prepare a bending setup for a tube or slab.
Tube should be originally periodic in z-direction with
the correct cell, and optionally periodic in y-direction.
Then atoms are set up for bending with hotbit.Wedge class
with bending wrt. z-axis, and optionally periodic along
z-axis.
Atoms are first rotated pi/2 around -x-axis, then
rotated an angle 'rotation' around y-axis, then
transformed the distance 'radius' towards x-axis.
The atoms are further adjusted for the wedge angle 'angle'.
'physical' tells if the angle should be 2*pi/integer.
"""
a = atoms.copy()
a.rotate('-x',np.pi/2)
L = a.get_cell().diagonal()
if abs(L.prod()-a.get_volume())>1E-10:
raise AssertionError('Cell should be orthorhombic.')
pbc = a.get_pbc()
if not pbc[2] or pbc[0]:
raise AssertionError('Should be periodic in z-direction and not periodic in x-direction')
r = a.get_positions()
if np.any( r[:,1]<0 ): # index 1 is correct here
raise AssertionError('For bending, all atoms should be above xy-plane')
# move and adjust
a.rotate('y',rotation)
for i in range(len(a)):
x,y = r[i,0:2]
R = x + radius
phi = y*angle/L[2]
r[i,0] = R*np.cos(phi)
r[i,1] = R*np.sin(phi)
a.set_positions(r)
a = Atoms(a,container='Wedge')
a.set_container(angle=angle,height=L[1],pbcz=pbc[1],physical=physical)
return a
def compare_trajectory(self, i_traj, calc, tables, i_par):
"""
Calculate the energies for the frames in the trajectory
and plot them.
"""
frames = []
energies = []
trajectory = PickleTrajectory(self.trajectories[i_traj])
for i, image in enumerate(trajectory):
e_tb = None
try:
atoms = Atoms(image)
c = copy(calc)
c.tables = tables
atoms.set_calculator(c)
e_tb = atoms.get_potential_energy()
except Exception, ex:
print>>self.txt, ex
if e_tb != None:
energies.append(e_tb)
frames.append(i)
def compare_trajectory(self, i_traj, calc, tables, i_par):
"""
Calculate the energies for the frames in the trajectory
and plot them.
"""
frames = []
energies = []
trajectory = PickleTrajectory(self.trajectories[i_traj])
for i, image in enumerate(trajectory):
e_tb = None
try:
atoms = Atoms(image)
c = copy(calc)
c.tables = tables
atoms.set_calculator(c)
e_tb = atoms.get_potential_energy()
except Exception, ex:
print >> self.txt, ex
if e_tb != None:
energies.append(e_tb)
frames.append(i)
def graphene(n1, n2, R, height=5.0):
"""
Construct graphene lattice, multiply the primitive cell
n1 x n2 times in corresponding directions.
.-----.
/ /
/ X / a2
/ /
X----->
a1
"""
from hotbit import Atoms
if not isinstance(R, float): R = R[0]
a1 = vec([R * np.cos(pi / 6) * 2, 0., 0.])
a2 = 0.5 * a1 + vec([0., 1.5 * R, 0.])
#assert n2%2==0
r = []
for i1 in range(n1):
for i2 in range(n2):
corner = i1 * a1 + i2 * a2
r.append(corner)
r.append(corner + a1 + vec([0.0, R, 0.0]))
cell = [[n1 * a1[0], 0, 0], [n2 * a2[0], n2 * a2[1], 0], [0, 0, 10]]
atoms = Atoms('C' * len(r), positions=r, cell=cell)
atoms.center(vacuum=height / 2, axis=2)
atoms.set_pbc((True, True, False))
return atoms
def chiral_nanotube(n,m,R=1.42,element='C'):
"""
Construct a nanotube with a chiral container.
parameters:
===========
n,m: chiral indices
R: bond length
element: element type
"""
from hotbit import Atoms
a = np.sqrt(3)*R
a1 = np.array([a,0,0])
a2 = np.array([0.5*a,-1.5*R,0])
rl = []
shift = (a/2,-0.5*R,0)
for i in range(n):
origin = i*a1
rl.append( origin )
rl.append( origin+shift )
for j in range(m):
origin = (n-1)*a1 + (j+1)*a1
rl.append( origin )
rl.append( origin + shift )
atoms = Atoms()
C = n*a1 + m*a2
Cn = np.linalg.norm(C)
T = np.array([C[1],-C[0],0])
t = T/np.linalg.norm(T)
radius = Cn/(2*pi)
atoms = Atoms()
for r in rl:
phi = np.dot(r,C)/Cn**2 * 2*pi
atoms += Atom( element,(radius*np.cos(phi),radius*np.sin(phi),np.dot(r,t)) )
atoms = Atoms(atoms,container='Chiral')
height = np.abs( np.dot(a1-a2,t) )
angle = -np.dot(a1-a2,C)/Cn**2 * 2*pi
atoms.set_container(angle=angle,height=height)
data = nanotube_data(n,m,R)
T, Ntot = data['T'],2*data['hexagons_per_cell']
data['height']=height
data['twist']=angle
atoms.data = data
return atoms
def get_isolated_energies(self, trajs, par):
"""
Return the energies of an isolated atoms.
"""
elements = []
energies = {}
for t in trajs:
traj = PickleTrajectory(t)
for atom in traj[0]:
if not atom.symbol in elements:
elements.append(atom.symbol)
el1, el2 = par.split("_")[0:2]
for el in elements:
ss = "%s%s" % (el, el)
if el1 == el2 and el1 == el:
tables = {ss:par, 'rest':'default'}
calc = Hotbit(SCC=True, tables=tables)
else:
calc = Hotbit(SCC=True)
atoms = Atoms(ss, ((0,0,0),(200,0,0)))
atoms.center(vacuum=100)
atoms.set_calculator(calc)
energies[el] = atoms.get_potential_energy() / 2
return energies
def get_isolated_energies(self, trajs, par):
"""
Return the energies of an isolated atoms.
"""
elements = []
energies = {}
for t in trajs:
traj = PickleTrajectory(t)
for atom in traj[0]:
if not atom.symbol in elements:
elements.append(atom.symbol)
el1, el2 = par.split("_")[0:2]
for el in elements:
ss = "%s%s" % (el, el)
if el1 == el2 and el1 == el:
tables = {ss:par, 'rest':'default'}
calc = Hotbit(SCC=True, tables=tables)
else:
calc = Hotbit(SCC=True)
atoms = Atoms(ss, ((0,0,0),(200,0,0)))
atoms.center(vacuum=100)
atoms.set_calculator(calc)
energies[el] = atoms.get_potential_energy() / 2
return energies
def nanotube(n, m, R=1.42, length=1, element='C'):
'''
Create a nanotube around z-axis.
parameters:
-----------
n,m: chiral indices
R: nearest neighbor distance
length: number of unit cells
element: element symbol
'''
from hotbit import Atoms
at = Atoms(pbc=(False, False, True))
sq3 = sqrt(3.0)
a0 = R
gcn = gcd(n, m)
a1 = np.array([sq3 / 2, 0.5]) * a0 * sq3
a2 = np.array([sq3 / 2, -0.5]) * a0 * sq3
h = float(float(n) - float(m)) / float(3 * gcn)
if h - int(h) == 0.0:
RR = 3
else:
RR = 1
c = n * a1 + m * a2
abs_c = sqrt(dot(c, c))
a = (-(2 * m + n) * a1 + (2 * n + m) * a2) / (gcn * RR)
abs_a = sqrt(dot(a, a))
eps = 0.01
b = [[1. / 3 - eps, 1. / 3 - eps], [2. / 3 - eps, 2. / 3 - eps]]
nxy = max(n, m) + 100
eps = 0.00001
for x in xrange(-nxy, nxy):
for y in xrange(-nxy, nxy):
for b1, b2 in b:
p = (x + b1) * a1 + (y + b2) * a2
abs_p = sqrt(dot(p, p))
sa = dot(p, a) / (abs_a**2)
sc = dot(p, c) / (abs_c**2)
if sa >= 0 and sa < 1 - eps and sc >= 0 and sc < 1 - eps:
r = (cos(2 * pi * sc) * abs_c / (2 * pi),
sin(2 * pi * sc) * abs_c / (2 * pi), sa * abs_a)
at += Atom(element, r)
at.set_cell((2 * abs_c / (2 * pi), 2 * abs_c / (2 * pi), length * abs_a))
b = at.copy()
for i in range(length - 1):
b.translate((0.0, 0.0, abs_a))
for j in b:
at += j
at.center(axis=2)
rcm = at.get_center_of_mass()
at.translate((-rcm[0], -rcm[1], 0))
at.set_pbc((False, False, True))
at.data = nanotube_data(n, m)
return at
def nanotube(n,m,R=1.42,length=1,element='C'):
'''
Create a nanotube around z-axis.
parameters:
-----------
n,m: chiral indices
R: nearest neighbor distance
length: number of unit cells
element: element symbol
'''
from hotbit import Atoms
at = Atoms( pbc = ( False, False, True ) )
sq3 = sqrt(3.0)
a0 = R
gcn = gcd(n, m)
a1 = np.array( [ sq3/2, 0.5 ] ) * a0 * sq3
a2 = np.array( [ sq3/2, -0.5 ] ) * a0 * sq3
h = float(float(n)-float(m))/float(3*gcn)
if h-int(h) == 0.0:
RR = 3
else:
RR = 1
c = n*a1 + m*a2
abs_c = sqrt(dot(c, c))
a = ( -(2*m+n)*a1 + (2*n+m)*a2 )/(gcn*RR)
abs_a = sqrt(dot(a, a))
eps = 0.01
b = [ [ 1./3-eps, 1./3-eps ], [ 2./3-eps, 2./3-eps ] ]
nxy = max(n, m)+100
eps = 0.00001
for x in xrange(-nxy, nxy):
for y in xrange(-nxy, nxy):
for b1, b2 in b:
p = (x+b1)*a1 + (y+b2)*a2
abs_p = sqrt(dot(p, p))
sa = dot(p, a)/(abs_a**2)
sc = dot(p, c)/(abs_c**2)
if sa >= 0 and sa < 1-eps and sc >= 0 and sc < 1-eps:
r = ( cos(2*pi*sc)*abs_c/(2*pi), sin(2*pi*sc)*abs_c/(2*pi), sa*abs_a )
at += Atom( element, r )
at.set_cell( ( 2*abs_c/(2*pi), 2*abs_c/(2*pi), length*abs_a ) )
b = at.copy()
for i in range(length-1):
b.translate( ( 0.0, 0.0, abs_a ) )
for j in b:
at += j
at.center(axis=2)
rcm = at.get_center_of_mass()
at.translate( (-rcm[0],-rcm[1],0) )
at.set_pbc((False,False,True))
at.data = nanotube_data(n,m)
return at