def mcmc_step(box, width, r_cut, r_skin, update_nblist):
# kb = 1.38064852*10**(-13) # N*Å/K (Boltzmann constant)
positions_trial = [np.zeros(box.dimension) for i in range(len(box.positions))]
trial_step = width * np.random.randn(*np.asarray(positions_trial).shape)/4 #randn -> std norm. dist, divide by 4 to keep results mostly within (-0.5, 0.5)
for i in range(len(positions_trial)):
positions_trial[i] = pbc.enforce_pbc(box.positions[i] + trial_step[i], box.size)
particles_trial = [system.Particle(positions_trial[i], box.particles[i].charge,
box.particles[i].sigmaLJ, box.particles[i].epsilonLJ) for i in range(len(box.particles))] # set trial particle list with trial positions
if update_nblist:
particles_trial = neighbourlist.verlet_neighbourlist(particles_trial, r_cut, r_skin) # update neighbourlist for trial positions
else:
for i in range(len(particles_trial)):
particles_trial[i].neighbourlist = box.particles[i].neighbourlist
LJpotential_trial = lennardjones.LJ_potential(particles_trial, r_cut, r_skin)
with warnings.catch_warnings():
warnings.simplefilter("ignore")
acceptance_prob = min(1.0, np.exp(-(LJpotential_trial - box.LJpotential)/box.temp)) # note: potential is actually potential/kb
# if (box_trial.LJpotential>box.LJpotential):
# print("increase = " + repr(box_trial.LJpotential-box.LJpotential))
# print("acceptance prob. = " + repr(acceptance_prob))
# if update_nblist:
# print(acceptance_prob)
if np.random.rand() < acceptance_prob:
return positions_trial, True, trial_step, acceptance_prob # Return True for accepted trial step return trial_step and acceptance_prob to use in unit testing
return box.positions, False, trial_step, acceptance_prob # return False for rejected trial step (no need to update box object)
def mcmc_step(box, width, r_cut, r_skin, update_nblist, kb=0.008314462175):
'''Executes single step of the MCMC simulation (see mcmc below).
NB: Currently only using LJ potential.
Arguments:
box (Box): the system/box object
width (float): approximate maximum size (change in individual coordinate) of each mcmc step
r_cut (float): cut-off radius for LJ neighbourlist computation
r_skin (float): size of skin-reigon for LJ neighbourlist computation
kb (float): boltzmann constant. Default is given in kJ/(mol*K). Can be provided in different units if desired (will result in different units for the potential and distances...)
Returns:
box.positions (numpy array): the updated (if trial step was accepted) array of positions of the particles in the system
_ (Bool): an unnamed boolean which relays whether or not the trial step was accepted
'''
positions_trial = np.zeros((len(box.particles), box.dimension))
trial_step = width * np.random.randn(
*positions_trial.shape
) / 4 #randn -> std norm. dist, divide by 4 to keep output mostly within (-0.5, 0.5)
for i in range(len(positions_trial)):
positions_trial[i] = pbc.enforce_pbc_coordinates(
box.positions[i] + trial_step[i], box.size)
if update_nblist:
nblist_trial = neighbourlist.verlet_neighbourlist(
positions_trial, r_cut, r_skin,
box.size) # update neighbourlist for trial positions
else:
nblist_trial = np.array(box.LJneighbourlists)
LJpotential_trial = lennardjones.LJ_potential(positions_trial,
nblist_trial, box.sigmas,
box.epsilons, r_cut, r_skin,
box.size)
with warnings.catch_warnings(
): # suppress warnings for possibly large arguments of the exponential function
warnings.simplefilter("ignore")
acceptance_prob = min(
1.0,
np.exp(-(LJpotential_trial - box.LJpotential) / (kb * box.temp)))
if np.random.rand() < acceptance_prob:
return positions_trial, True # Return True for accepted trial step
return box.positions, False
def Ewald_energy(positions,q,r_c,r_s,boxsize):
'''
arguments:
positions (numpy array): particles' positions
q(numpy array): the chage value
r_c (float): cutoff radius for Ewald
r_s (float): cutoff radius for Ewald
box(numpy array):the box length in each dimension
'''
r_cut = r_c + r_s
EWald_neighbourlists = neighbourlist.verlet_neighbourlist(positions, r_c, r_s, box)
unit_convert = (1.602119892525e-19)**2/(4*np.pi*(10**(-10)))/(8.854187817e-12) /1000/128 * 6.022140857 * 10e23 #(kJ/mol)
Ewald_short = Ewald_short_energy(positions,EWald_neighbourlists, q,r_cut,box) * unit_convert
Ewald_long = Ewald_long_energy(positions,q,r_cut,box) * unit_convert
Ewald_self = Ewald_self_energy(positions,q,r_cut) * unit_convert
return Ewald_short + Ewald_long - Ewald_self
def compute_LJneighbourlist(
self, r_cut, r_skin
): # computes the (LJ) neighbourlists for the particles in the system
self.LJneighbourlists = neighbourlist.verlet_neighbourlist(
self.positions, r_cut, r_skin, self.size)
for i in range(len(positions)):
Ewald_self += Ewald_self_energy_ij(q[i],r_cut)
return Ewald_self
q = np.ones(128)
for i in range(128):
if types[i] == 'Cl-' :
q[i] = -1 #* 1.602119892525e-19
else:
q[i] = 1 #* 1.602119892525e-19
#pool = ThreadPoolExecutor(max_workers=2)
r_cut = min(box)/2
EWald_neighbourlists = neighbourlist.verlet_neighbourlist(positions, r_cut, 0, box)
#print(EWald_neighbourlists)
unit_convert = (1.602119892525e-19)**2/(4*np.pi*(10**(-10)))/(8.854187817e-12) /1000/128 * 6.022140857 * 10e23
short = Ewald_short_energy(positions,EWald_neighbourlists, q, r_cut,box) * unit_convert
l = Ewald_long_energy(positions,q,r_cut,box) * unit_convert
s = Ewald_self_energy(positions,q,r_cut) * unit_convert
print("\rWith cutoff radius = half of the box length")
print("The Ewald short range energy:",short,"\t(kJ/mol)")
print("The Ewald long range energy:",l,"\t(kJ/mol)")
print("The Ewald self energy:",s ,"\t(kJ/mol)")
print("The total Ewald energy:",short+l-s,"(kJ/mol)")
def compute_LJneighbourlist(self, r_cut, r_skin):
self.particles = neighbourlist.verlet_neighbourlist(
self.particles, r_cut, r_skin)