ab initio molecular dynamics (DFT/MD)

Ab initio molecular dynamics uses DFT to calculate the forces between the atoms at each time step. While computationally expensive, prohibiting simulations longer than a few ps, DFT/MD can be directly applied to any system that DFT can describe.

Transmission of hydrogen through graphene

Neutral atom transmission through a graphene target can be simulated with DFT/MD. However, note that TDDFT/MD is required to account for electronic stopping (Ref. 1).

The following script simulates the impact of a hydrogen atom with an initial velocity corresponding to a kinetic energy of 40 keV, transmitting through the center of a hexagon in a graphene target. The impact point in this case is the center of a carbon hexagon, but this can be modified by changing the x-y position of the H atom (projpos).

In a realistic calculation, one should consider the choice of the XC functional, and verify the convergence of the results with respect to the grid spacing, timestep and k-points. Here, less accurate parameters are used so that the calculation can be run on 4-8 CPU cores.

import ase.units as units
from ase import Atoms
from ase.build import graphene
from ase.io import Trajectory
from ase.md.verlet import VelocityVerlet
from gpaw import GPAW
from gpaw.utilities import h2gpts

name = 'graphene_h'

# 5 x 5 supercell of graphene
a = 2.45
gra = graphene(a=a, size=(5, 5, 1), vacuum=10)
gra.center()

# Starting position of the projectile with an impact point at the
# center of a hexagon.
# Set mass to one atomic mass unit to avoid isotope average.
atoms = gra + Atoms('H', masses=[1.0])
d = a / 3**0.5
atoms.positions[-1] = atoms.positions[22] + (0, d, 5)
atoms.pbc = (True, True, True)

calc = GPAW(gpts=h2gpts(0.2, gra.get_cell(), idiv=8),
            nbands=110,
            xc='LDA',
            txt=f'{name}_gs.txt')

atoms.calc = calc
atoms.get_potential_energy()

# Moving to the MD part
ekin = 100  # kinetic energy of the ion (in eV)
timestep = 0.1  # timestep in fs

# Filename for saving trajectory
ekin_str = '_ek' + str(int(ekin / 1000)) + 'keV'
strbody = name + ekin_str
traj_file = f'{name}_ek_{ekin}.traj'

# Integrator for the equations of motion, timestep depends on system
dyn = VelocityVerlet(atoms, timestep * units.fs)

# Saving the positions of all atoms after every time step
with Trajectory(traj_file, 'w', atoms) as traj:
    dyn.attach(traj.write, interval=1)

    # Running one timestep before impact
    dyn.run(1)

    # Giving the target atom a kinetic energy of ene in the -z direction
    atoms[-1].momentum[2] = -(2 * ekin * atoms[-1].mass)**0.5

    # Running the simulation for 80 timesteps
    dyn.run(80)

References

1

C. Brand, M. Debiossac, T. Susi, F. Aguillon, J. Kotakoski, P. Roncin, M. Arndt, “Coherent diffraction of hydrogen through the 246 pm lattice of graphene”, New J. Phys. 21, 033004 (2019).