def sdot_integral(traj1,
traj2,
centroid=None,
Snuc=None,
e_only=False,
nuc_only=False):
"""Returns the matrix element <Psi_1 | d/dt | Psi_2>."""
if Snuc is None:
Snuc = nuclear.overlap(traj1.phase(), traj1.widths(), traj1.x(),
traj1.p(), traj2.phase(), traj2.widths(),
traj2.x(), traj2.p())
# overlap of electronic functions
Selec = elec_overlap(traj1, traj2, centroid)
# < chi | d / dx | chi'>
deldx = nuclear.deldx(Snuc, traj1.phase(), traj1.widths(), traj1.x(),
traj1.p(), traj2.phase(), traj2.widths(), traj2.x(),
traj2.p())
# < chi | d / dp | chi'>
deldp = nuclear.deldp(Snuc, traj1.phase(), traj1.widths(), traj1.x(),
traj1.p(), traj2.phase(), traj2.widths(), traj2.x(),
traj2.p())
# the nuclear contribution to the sdot matrix
sdot = (np.dot(traj2.velocity(), deldx) + np.dot(traj2.force(), deldp) +
1j * traj2.phase_dot() * Snuc) * Selec
# time-derivative of the electronic component
return sdot
def sdot_integral(t1, t2, Snuc=None):
"""Returns the matrix element <Psi_1 | d/dt | Psi_2>."""
if t1.state != t2.state:
return complex(0., 0.)
else:
if Snuc is None:
Snuc = nuclear.overlap(t1.phase(), t1.widths(), t1.x(), t1.p(),
t2.phase(), t2.widths(), t2.x(), t2.p())
t1_dx_t2 = nuclear.deldx(Snuc, t1.widths(), t1.x(), t1.p(),
t2.widths(), t2.x(), t2.p())
t1_dp_t2 = nuclear.deldp(Snuc, t1.widths(), t1.x(), t1.p(),
t2.widths(), t2.x(), t2.p())
sdot = (np.dot(t2.velocity(), t1_dx_t2) +
np.dot(t2.force(), t1_dp_t2) + 1.j * t2.phase_dot() * Snuc)
return sdot
def v_integral(t1, t2, centroid=None, Snuc=None):
"""Returns potential coupling matrix element between two trajectories."""
# if we are passed a single trajectory, this is a diagonal
# matrix element -- simply return potential energy of trajectory
if t1.label == t2.label:
# Adiabatic energy
v = t1.energy(t1.state)
# DBOC
if glbl.interface['coupling_order'] == 3:
v += t1.scalar_coup(t1.state, t2.state)
return v
if Snuc is None:
Snuc = nuclear.overlap(t1.phase(),t1.widths(),t1.x(),t1.p(),
t2.phase(),t2.widths(),t2.x(),t2.p())
# Snuc = nuclear.overlap(t1,t2)
# off-diagonal matrix element, between trajectories on the same
# state (this also requires the centroid be present)
elif t1.state == t2.state:
# Adiabatic energy
v = centroid.energy(t1.state) * Snuc
# DBOC
if glbl.interface['coupling_order'] == 3:
v += centroid.scalar_coup(t1.state, t2.state) * Snuc
return v
# [necessarily] off-diagonal matrix element between trajectories
# on different electronic states
elif t1.state != t2.state:
# Derivative coupling
fij = centroid.derivative(t1.state, t2.state)
v = 2.*np.vdot(fij, glbl.pes.kecoeff *
nuclear.deldx(Snuc,t1.widths(),t1.x(),t1.p(),
t2.widths(),t2.x(),t2.p()))
# nuclear.deldx(t1, t2, S=Snuc))
# Scalar coupling
if glbl.interface['coupling_order'] > 1:
v += centroid.scalar_coup(t1.state, t2.state) * Snuc
return v
else:
print('ERROR in v_integral -- argument disagreement')
return 0j
def sdot_integral(t1, t2, Snuc=None, e_only=False, nuc_only=False):
"""Returns the matrix element <Psi_1 | d/dt | Psi_2>."""
if t1.state != t2.state:
return 0j
else:
if Snuc is None:
Snuc = nuclear.overlap(t1.phase(),t1.widths(),t1.x(),t1.p(),
t2.phase(),t2.widths(),t2.x(),t2.p())
deldx = nuclear.deldx(Snuc,t1.widths(),t1.x(),t1.p(),
t2.widths(),t2.x(),t2.p())
deldp = nuclear.deldp(Snuc,t1.widths(),t1.x(),t1.p(),
t2.widths(),t2.x(),t2.p())
sdot = (np.dot(deldx,t2.velocity()) + np.dot(deldp,t2.force()) +
1j * t2.phase_dot() * Snuc)
return sdot
def v_integral(t1, t2, centroid=None, Snuc=None):
"""Returns potential coupling matrix element between two trajectories.
If we are passed a single trajectory, this is a diagonal matrix
element -- simply return potential energy of trajectory.
"""
if Snuc is None:
Sij = nuclear.overlap(t1.phase(),t1.widths(),t1.x(),t1.p(),
t2.phase(),t2.widths(),t2.x(),t2.p())
else:
Sij = Snuc
Sji = Sij.conjugate()
if glbl.propagate['integral_order'] > 2:
raise ValueError('Integral_order > 2 not implemented for bra_ket_averaged')
if t1.state == t2.state:
state = t1.state
# Adiabatic energy
vij = t1.energy(state) * Sij
vji = t2.energy(state) * Sji
if glbl.propagate['integral_order'] > 0:
o1_ij = nuclear.ordr1_vec(t1.widths(),t1.x(),t1.p(),
t2.widths(),t2.x(),t2.p())
o1_ji = nuclear.ordr1_vec(t2.widths(),t2.x(),t2.p(),
t1.widths(),t1.x(),t1.p())
vij += np.dot(o1_ij - t1.x()*Sij, t1.derivative(state,state))
vji += np.dot(o1_ji - t2.x()*Sji, t2.derivative(state,state))
if glbl.propagate['integral_order'] > 1:
xcen = (t1.widths()*t1.x() + t2.widths()*t2.x()) / (t1.widths()+t2.widths())
o2_ij = nuclear.ordr2_vec(t1.widths(),t1.x(),t1.p(),
t2.widths(),t2.x(),t2.p())
o2_ji = nuclear.ordr2_vec(t2.widths(),t2.x(),t2.p(),
t1.widths(),t1.x(),t1.p())
for k in range(t1.dim):
vij += 0.5*o2_ij[k]*t1.hessian(state)[k,k]
vji += 0.5*o2_ji[k]*t2.hessian(state)[k,k]
for l in range(k):
vij += 0.5 * ((2.*o1_ij[k]*o1_ij[l] -
xcen[k]*o1_ij[l] - xcen[l]*o1_ij[k] -
o1_ij[k]*t1.x()[l] - o1_ij[l]*t1.x()[k] +
(t1.x()[k]*xcen[l] + t1.x()[l]*xcen[k])*Sij) *
t1.hessian(state)[k,l])
vji += 0.5 * ((2.*o1_ji[k]*o1_ji[l] -
xcen[k]*o1_ji[l] - xcen[l]*o1_ji[k] -
o1_ji[k]*t2.x()[l] - o1_ji[l]*t2.x()[k] +
(t2.x()[k]*xcen[l] + t2.x()[l]*xcen[k])*Sji) *
t2.hessian(state)[k,l])
# [necessarily] off-diagonal matrix element between trajectories
# on different electronic states
else:
# Derivative coupling
fij = t1.derivative(t1.state, t2.state)
vij = 2.*np.vdot(t1.derivative(t1.state,t2.state), glbl.pes.kecoeff *
nuclear.deldx(Sij,t1.widths(),t1.x(),t1.p(),
t2.widths(),t2.x(),t2.p()))
vji = 2.*np.vdot(t2.derivative(t2.state,t1.state), glbl.pes.kecoeff *
nuclear.deldx(Sji,t2.widths(),t2.x(),t2.p(),
t1.widths(),t1.x(),t1.p()))
return 0.5*(vij + vji.conjugate())