Fewest Switches Surface Hopping

Python implementation of Tully's Fewest Switches Surface Hopping (FSSH) for model problems including a propagator and an implementation of Tully's model problems described in Tully, J.C. J. Chem. Phys. (1990) 93 1061. The current implementation is limited to one-dimensional potentials with two electronic states.

Contents

• fssh.py --- FSSH implementation. The FSSH class within fssh.py should be used to run sets of scattering simulations using FSSH.
• tullymodels.py --- Implementation of three models described in Tully's 1990 JCP: TullySimpleAvoidedCrossing, TullyDualAvoidedCrossing, TullyExtendedCouplingReflection.
• surfaces.py --- script to print potential energy surfaces of the models

Requirements

• numpy
• scipy

FSSH

Sets of simulations are run using the FSSH class. A FSSH object must be instantiated by passing a model object. All other options are passed as keyword arguments to the constructor. For example:

import fssh
import tullymodels as models

simple_model = models.SimpleAvoidedCrossing()
simulator = fssh.FSSH(simple_model, position = -5.0, momentum = 2.0)
results = simulator.compute()

print "Probability of reflection on the ground state: %12.f" % results[0]
print "Probability of transmission on the ground state: %12.f" % results[1]
print "Probability of reflection on the excited state: %12.f" % results[2]
print "Probability of transmission on the excited state: %12.f" % results[3]

will run a series of scattering simulations in parallel with a particle starting at -5.0 a.u. and travelling with an initial momentum of 2.0 a.u.

Options

• initial_state - specify how the initial electronic state is chosen
  • "ground" (default) - start on the ground state
• mass - particle mass (default: 2000 a.u.)
• position - initial position (default: -5.0 a.u.)
• momentum - initial momentum (default: 2.0 a.u.)
• initial_time - starting value of time variable (default: 0.0 a.u.)
• dt - timestep (default: abs(0.05 / velocity)))
• total_time - total simulation length (default: 2 * abs(position/velocity))
• samples - number of trajectories to run (default: 2000)
• propagator - method used to propagate electronic wavefunction
  • "exponential" (default) - apply exponentiated Hamiltonian via diagonalization
  • "ode" - scipy's ODE integrator
• nprocs - number of processes over which to parallelize trajectories (default: number of CPUs available)
• outcome_type - how to count statistics at the end of a trajectory
  • "state" (default) - use the state attribute of the simulation only
  • "populations" - use the diagonals of the density matrix

Models

The model provided to the FSSH class needs to have three functions implemented:

• V(self, x) --- returns (ndim,ndim)-shaped numpy array containing the Hamiltonian matrix at position x
• dV(self, x) --- returns (ndim,ndim,1)-shaped numpy array containing the gradient of the Hamiltonian matrix at position x
• dim(self) --- returns the number of states in the model (only 2 is supported)

In all cases, the input x ought to be a numpy array with 1 element.

The file tullymodels.py implements the three models in Tully's original paper. They are:

• TullySimpleAvoidedCrossing
• TullyDualAvoidedCrossing
• TullyExtendedCouplingReflection

Surfaces

Scans of the surfaces can be printed using the surfaces.py script. For usage, call

python surfaces.py -h

Notes

• In it's current form, FSSH will definitely break for more than two electronic states.
• This package is written to take advantage of doxygen!