def get_surface(lepsgui):
"""Get Vmat (potential) for a given set of parameters"""
lepsgui.get_params()
#Check if params have changed. If not, no need to recalculate
if lepsgui.old_params == lepsgui.params and not lepsgui._firstrun:
return
resl = 0.02 #Resolution
lepsgui._firstrun = False
#Get grid
lepsgui.Grid_X = np.arange(lepsgui.params.mina, lepsgui.params.maxa, resl)
lepsgui.Grid_Y = np.arange(lepsgui.params.minb, lepsgui.params.maxb, resl)
lepsgui.Vmat = np.zeros((len(lepsgui.Grid_Y), len(lepsgui.Grid_X)))
#Calculate potential for each gridpoint
for drabcount, drab in enumerate(lepsgui.Grid_X):
lepsgui.Current_Separations[0] = drab
for drbccount, drbc in enumerate(lepsgui.Grid_Y):
lepsgui.Current_Separations[1] = drbc
V = lepspoint(np.deg2rad(lepsgui.theta),
lepsgui.params.Dissociation_energies,
lepsgui.params.Reqs,
lepsgui.params.Morse_Parameters,
lepsgui.params.surface_param,
lepsgui.Current_Separations,
lepsgui.Current_First_derivative,
lepsgui.Current_Hessian,
derivative=0)
lepsgui.Vmat[drbccount, drabcount] = V
lepsgui.old_params = lepsgui.params
def get_surface(self):
"""Get Vmat (potential) for a given set of parameters"""
self.get_params()
#Check if params have changed. If not, no need to recalculate
new_params = [self.a, self.b, self.c, self.theta]
if self.old_params == new_params and not self._firstrun:
return
resl = 0.02 #Resolution
grad = 0 #Gradient calc type (0 = energy)
self._firstrun = False
#Get grid
self.x = np.arange(self.mina, self.maxa, resl)
self.y = np.arange(self.minb, self.maxb, resl)
self.Vmat = np.zeros((len(self.y), len(self.x)))
#Calculate potential for each gridpoint
for drabcount, drab in enumerate(self.x):
for drbccount, drbc in enumerate(self.y):
V = lepspoint(drab, drbc, np.deg2rad(self.theta), self.Drab,
self.Drbc, self.Drac, self.Brab, self.Brbc,
self.Brac, self.lrab, self.lrbc, self.lrac,
self.H, grad)
self.Vmat[drbccount, drabcount] = V
self.old_params = new_params
def get_first(lepsgui):
"""1 step of trajectory to get geometry properties"""
lepsgui._read_entries()
lepsgui.get_params()
lepsgui.current_potential_energy = lepspoint(
np.deg2rad(lepsgui.theta), lepsgui.params.Dissociation_energies,
lepsgui.params.Reqs, lepsgui.params.Morse_Parameters,
lepsgui.params.surface_param, lepsgui.Current_Separations,
lepsgui.Current_First_derivative, lepsgui.Current_Hessian, 2)
lepsgui.theta, lepsgui.current_kinetic_energy = lepnorm(
np.deg2rad(lepsgui.theta), lepsgui.Current_Separations,
lepsgui.Current_First_derivative, lepsgui.Current_Hessian,
lepsgui.Current_Velocities, lepsgui.Current_Accelerations,
lepsgui.params.Masses, lepsgui.params.Reduced_masses, lepsgui.dt,
False)
def get_first(self):
"""1 step of trajectory to get geometry properties"""
self._read_entries()
self.get_params()
dt = self.dt
ma = self.ma
mb = self.mb
mc = self.mc
mab = self.mab
mbc = self.mbc
Drab = self.Drab
Drbc = self.Drbc
Drac = self.Drac
lrab = self.lrab
lrbc = self.lrbc
lrac = self.lrac
Brab = self.Brab
Brbc = self.Brbc
Brac = self.Brac
xrabi = self.xrabi
xrbci = self.xrbci
prabi = self.prabi
prbci = self.prbci
thetai = np.deg2rad(self.theta)
vrabi = prabi / mab
vrbci = prbci / mbc
vraci = 0
grad = 2
ti = 0
Vrinti,Frabi,Frbci,Fraci,hr1r1i,hr1r2i,hr1r3i,hr2r2i,hr2r3i,hr3r3i = lepspoint(xrabi,xrbci,thetai,Drab,Drbc,Drac,Brab,Brbc,Brac,lrab,lrbc,lrac,self.H,grad)
xrabf,xrbcf,xracf,thetaf,vrabf,vrbcf,vracf,tf,arabi,arbci,araci,Ktoti = lepnorm(xrabi,xrbci,thetai,Frabi,Frbci,Fraci,vrabi,vrbci,vraci,hr1r1i,hr1r2i,hr1r3i,hr2r2i,hr2r3i,hr3r3i,ma,mb,mc,ti,dt,False)
return Vrinti,Frabi,Frbci,Fraci,hr1r1i,hr1r2i,hr1r3i,hr2r2i,hr2r3i,hr3r3i,xrabf,xrbcf,xracf,thetaf,vrabf,vrbcf,vracf,tf,arabi,arbci,araci,Ktoti
def get_trajectory(lepsgui):
"""Get dynamics, MEP or optimisation"""
dt = lepsgui.dt #Time step
lepsgui.current_time = 0
thetai = np.deg2rad(lepsgui.theta) #Collision Angle
grad = 2 #Calculating gradients and Hessian
lepsgui.get_arrays()
lepsgui.Animation_Positions = []
lepsgui.append_animation_position()
#Initial Velocity
lepsgui.Current_Velocities = lepsgui.Current_Momenta / lepsgui.params.Reduced_masses
lepsgui.Trajectory_Velocities = []
#Initialise outputs
lepsgui.Trajectory_times = []
lepsgui.Trajectory_Separations = []
lepsgui.Trajectory_Velocities = []
lepsgui.Trajectory_Momenta = []
lepsgui.Trajectory_Accelerations = []
lepsgui.Trajectory_First_derivatives = []
lepsgui.Trajectory_Hessians = []
lepsgui.Potential_Energies = []
lepsgui.Kinetic_Energies = []
lepsgui.Potential_Energies = []
lepsgui.Total_Energies = []
#Initial conditions
lepsgui.current_potential_energy = lepspoint(
thetai, lepsgui.params.Dissociation_energies, lepsgui.params.Reqs,
lepsgui.params.Morse_Parameters, lepsgui.params.surface_param,
lepsgui.Current_Separations, lepsgui.Current_First_derivative,
lepsgui.Current_Hessian, grad)
lepsgui.add_trajectory_step()
#Flag to stop appending to output in case of a crash
terminate = False
for itcounter in range(lepsgui.steps):
if lepsgui.calc_type != "Dynamics":
lepsgui.Current_Velocities = np.zeros((3))
#Get current potential, forces, and Hessian
lepsgui.current_potential_energy = lepspoint(
thetai, lepsgui.params.Dissociation_energies, lepsgui.params.Reqs,
lepsgui.params.Morse_Parameters, lepsgui.params.surface_param,
lepsgui.Current_Separations, lepsgui.Current_First_derivative,
lepsgui.Current_Hessian, grad)
if lepsgui.calc_type in ["Opt Min",
"Opt TS"]: #Optimisation calculations
#Diagonalise Hessian
eigenvalues, eigenvectors = np.linalg.eig(lepsgui.Current_Hessian)
#Eigenvalue test
neg_eig_i = [i for i, eig in enumerate(eigenvalues) if eig < -0.01]
if len(neg_eig_i) == 0 and lepsgui.calc_type == "Opt TS":
msgbox.showinfo("Eigenvalues Info",
"No negative eigenvalues at this geometry")
terminate = True
elif len(neg_eig_i) == 1 and lepsgui.calc_type == "Opt Min":
msgbox.showerror(
"Eigenvalues Error",
"Too many negative eigenvalues at this geometry")
terminate = True
elif len(neg_eig_i) > 1:
msgbox.showerror(
"Eigenvalues Error",
"Too many negative eigenvalues at this geometry")
terminate = True
#Optimiser
Displacements = np.array([0., 0., 0.])
for mode in range(len(eigenvalues)):
e_val = eigenvalues[mode]
e_vec = eigenvectors[mode]
disp = np.dot(
np.dot((e_vec.T), lepsgui.Current_First_derivative),
e_vec) / e_val
Displacements += disp
lepsgui.Current_Separations += Displacements
#xrabf = xrabi + disps[0]
#xrbcf = xrbci + disps[1]
#xracf = ((xrabf ** 2) + (xrbcf ** 2) - 2 * xrabf * xrbcf * np.cos(thetai)) ** 0.5
else: #Dynamics/MEP
try:
lepsgui.theta, lepsgui.current_kinetic_energy = lepnorm(
lepsgui.theta, lepsgui.Current_Separations,
lepsgui.Current_First_derivative, lepsgui.Current_Hessian,
lepsgui.Current_Velocities, lepsgui.Current_Accelerations,
lepsgui.params.Masses, lepsgui.params.Reduced_masses,
lepsgui.dt, False)
lepsgui.current_time += lepsgui.dt
except LinAlgError:
msgbox.showerror(
"Surface Error",
"Energy could not be evaulated at step {}. Steps truncated"
.format(itcounter + 1))
terminate = True
if lepsgui.Current_Separations[
0] > lepsgui.lim or lepsgui.Current_Separations[
1] > lepsgui.lim: #Stop calc if distance lim is exceeded
msgbox.showerror(
"Surface Error",
"Surface Limits exceeded at step {}. Steps truncated".format(
itcounter + 1))
terminate = True
if lepsgui.calc_type != "Dynamics":
lepsgui.Current_Velocities = np.zeros((3))
if itcounter != lepsgui.steps - 1 and not terminate:
#As above
lepsgui.append_animation_position()
### Maybe not necessary
#Get A-C Velocity
r0 = np.linalg.norm(lepsgui.Trajectory_Separations[-1][2] -
lepsgui.Trajectory_Separations[-1][0])
r1 = np.linalg.norm(lepsgui.Current_Separations[2] -
lepsgui.Current_Separations[0])
vrac = (r1 - r0) / dt
lepsgui.add_trajectory_step()
if terminate:
break
def get_trajectory(self):
"""Get dynamics, MEP or optimisation"""
itlimit = self.steps #Max number of steps
dt = self.dt #Time step
ti = 0 #Initial time variable
tf = 0 #Final time variable
ma = self.ma #Mass of A
mb = self.mb #Mass of B
mc = self.mc #Mass of C
mab = self.mab #Reduced mass of AB
mbc = self.mbc #Reduced mass of BC
Drab = self.Drab
Drbc = self.Drbc
Drac = self.Drac
lrab = self.lrab
lrbc = self.lrbc
lrac = self.lrac
Brab = self.Brab
Brbc = self.Brbc
Brac = self.Brac
thetai = np.deg2rad(self.theta) #Collision Angle
grad = 2 #Calculating gradients and Hessian
xrabi = self.xrabi #Initial AB separation
xrbci = self.xrbci #Initial BC separation
xraci = (
(xrabi**2) + (xrbci**2) -
2 * xrabi * xrbci * np.cos(thetai))**0.5 #Initial AC separation
prabi = self.prabi #Initial AB momentum
prbci = self.prbci #Initial BC momentum
vrabi = prabi / mab #Initial AB Velocity
vrbci = prbci / mbc #Initial BC Velocity
#Positions of A, B and C relative to B
a = np.array([-xrabi, 0.])
b = np.array([0., 0.])
c = np.array([-np.cos(thetai) * xrbci, np.sin(thetai) * xrbci])
#Get centre of mass
com = (a * ma + b * mb + c * mc) / (ma + mb + mc)
com = np.real(com)
#Translate to centre of mass (for animation)
a -= com
b -= com
c -= com
self.ra = [a]
self.rb = [b]
self.rc = [c]
#Initial AC Velocity
va = (a - self.ra[-1]) / dt
vc = (c - self.rc[-1]) / dt
vraci = np.linalg.norm(va + vc)
#Initialise outputs
self.xrab = [xrabi]
self.xrbc = [xrbci]
self.xrac = [xraci]
self.vrab = [vrabi]
self.vrbc = [vrbci]
self.vrac = [vraci]
self.t = [ti]
self.Vrint = Vrint = []
self.Ktot = Ktot = []
self.Frab = Frab = []
self.Frbc = Frbc = []
self.Frac = Frac = []
self.arab = arab = []
self.arbc = arbc = []
self.arac = arac = []
self.etot = etot = []
self.hr1r1 = hr1r1 = []
self.hr1r2 = hr1r2 = []
self.hr1r3 = hr1r3 = []
self.hr2r2 = hr2r2 = []
self.hr2r3 = hr2r3 = []
self.hr3r3 = hr3r3 = []
#Flag to stop appending to output in case of a crash
terminate = False
for itcounter in range(itlimit):
if self.calc_type != "Dynamics":
vrabi = 0
vrbci = 0
vraci = 0
#Get current potential, forces, and Hessian
Vrinti, Frabi, Frbci, Fraci, hr1r1i, hr1r2i, hr1r3i, hr2r2i, hr2r3i, hr3r3i = lepspoint(
xrabi, xrbci, thetai, Drab, Drbc, Drac, Brab, Brbc, Brac, lrab,
lrbc, lrac, self.H, grad)
Vrint.append(Vrinti)
Frab.append(Frabi)
Frbc.append(Frbci)
Frac.append(Fraci)
hr1r1.append(hr1r1i)
hr1r2.append(hr1r2i)
hr1r3.append(hr1r3i)
hr2r2.append(hr2r2i)
hr2r3.append(hr2r3i)
hr3r3.append(hr3r3i)
if self.calc_type in ["Opt Min",
"Opt TS"]: #Optimisation calculations
#Diagonalise Hessian
hessian = np.array([[hr1r1i, hr1r2i, hr1r3i],
[hr1r2i, hr2r2i, hr2r3i],
[hr1r3i, hr2r3i, hr3r3i]])
eigenvalues, eigenvectors = np.linalg.eig(hessian)
#Get forces for opt calculation
forces = np.array([Frabi, Frbci, Fraci])
#Eigenvalue test
neg_eig_i = [
i for i, eig in enumerate(eigenvalues) if eig < -0.01
]
if len(neg_eig_i) == 0 and self.calc_type == "Opt TS":
msgbox.showinfo(
"Eigenvalues Info",
"No negative eigenvalues at this geometry")
terminate = True
elif len(neg_eig_i) == 1 and self.calc_type == "Opt Min":
msgbox.showerror(
"Eigenvalues Error",
"Too many negative eigenvalues at this geometry")
terminate = True
elif len(neg_eig_i) > 1:
msgbox.showerror(
"Eigenvalues Error",
"Too many negative eigenvalues at this geometry")
terminate = True
#Optimiser
disps = np.array([0., 0., 0.])
for mode in range(len(eigenvalues)):
e_val = eigenvalues[mode]
e_vec = eigenvectors[mode]
disp = np.dot(np.dot((e_vec.T), forces), e_vec) / e_val
disps += disp
xrabf = xrabi + disps[0]
xrbcf = xrbci + disps[1]
xracf = ((xrabf**2) + (xrbcf**2) -
2 * xrabf * xrbcf * np.cos(thetai))**0.5
arabi = 0
arbci = 0
araci = 0
thetaf = thetai
vrabf = 0
vrbcf = 0
vracf = 0
Ktoti = 0
tf += dt
else: #Dynamics/MEP
try:
xrabf, xrbcf, xracf, thetaf, vrabf, vrbcf, vracf, tf, arabi, arbci, araci, Ktoti = lepnorm(
xrabi, xrbci, thetai, Frabi, Frbci, Fraci, vrabi,
vrbci, vraci, hr1r1i, hr1r2i, hr1r3i, hr2r2i, hr2r3i,
hr3r3i, ma, mb, mc, ti, dt, self.calc_type == "MEP")
except LinAlgError:
msgbox.showerror(
"Surface Error",
"Energy could not be evaulated at step {}. Steps truncated"
.format(itcounter + 1))
terminate = True
if xrabf > self.lim or xrbcf > self.lim: #Stop calc if distance lim is exceeded
msgbox.showerror(
"Surface Error",
"Surface Limits exceeded at step {}. Steps truncated".
format(itcounter + 1))
terminate = True
arab.append(arabi)
arbc.append(arbci)
arac.append(araci)
Ktot.append(Ktoti)
#Total energy
etot.append(Vrint[itcounter] + Ktot[itcounter])
if itcounter != itlimit - 1 and not terminate:
#As above
a = np.array([-xrabf, 0.])
b = np.array([0., 0.])
c = np.array([-np.cos(thetaf) * xrbcf, np.sin(thetaf) * xrbcf])
com = (a * ma + b * mb + c * mc) / (ma + mb + mc)
com = np.real(com)
a -= com
b -= com
c -= com
#Get A-C Velocity
r0 = np.linalg.norm(self.rc[-1] - self.ra[-1])
r1 = np.linalg.norm(c - a)
vrac = (r1 - r0) / dt
self.ra.append(a) #A Pos
self.rb.append(b) #B Pos
self.rc.append(c) #C Pos
self.xrab.append(xrabf) #A-B Distance
self.xrbc.append(xrbcf) #B-C Distance
self.xrac.append(xracf) #A-C Distance
if self.calc_type == "Dynamics":
self.vrab.append(vrabf) #A-B Velocity
self.vrbc.append(vrbcf) #B-C Velocity
self.vrac.append(vrac) #A-C Velocity
else:
self.vrab.append(0.) #A-B Velocity
self.vrbc.append(0.) #B-C Velocity
self.vrac.append(0.) #A-C Velocity
self.t.append(tf) #Time
xrabi = xrabf
xrbci = xrbcf
xraci = xracf
vrabi = vrabf
vrbci = vrbcf
vraci = vracf
ti = tf
if terminate:
break