Note
Go to the end to download the full example code.
Molecular dynamics#
Note
These examples can be run without asap3 installed. In that case,
ASE’s Python implementation of the EMT calculator can be used instead, but it
is much slower.
Goal#
In this tutorial, we will learn how to perform basic molecular dynamics (MD) simulations using ASE.
The key objectives are:
Understand how to set up a crystal structure (Cu atoms on an FCC lattice).
Initialize velocities from Maxwell–Boltzmann distribution corresponding to a chosen temperature.
Integrate Newton’s equations of motion using Velocity-Verlet algorithm and we monitor the temperature using Langevin thermostat.
Monitor and analyze thermodynamic quantities (potential energy, kinetic energy, total energy, temperature).
Save trajectories and visualize atomic motion with ASE’s GUI.
Explore MD in different scenarios: - Constant energy MD (NVE ensemble) - Constant temperature MD (NVT ensemble) - Isolated nanoparticle simulations
By the end of this tutorial, you should be able to set up your own MD simulations, monitor energy conservation, and visualize system evolution.
Part 1: Basic Molecular Dynamics Simulation#
We start by creating a copper crystal, assigning random velocities corresponding to Maxwell Boltzmann Distribution at 300 K, and running dynamics in the NVE ensemble (constant energy).
import matplotlib.pyplot as plt
import numpy as np
# choose one of the following implementations of EMT:
# included in ase
# from ase.calculators.emt import EMT
# faster performance
from asap3 import EMT
from ase import units
from ase.cluster.cubic import FaceCenteredCubic as ClusterFCC
from ase.io.trajectory import Trajectory
from ase.lattice.cubic import FaceCenteredCubic as LatticeFCC
from ase.md.langevin import Langevin # for later NPT simulations
from ase.md.velocitydistribution import (
MaxwellBoltzmannDistribution,
Stationary,
ZeroRotation,
)
from ase.md.verlet import VelocityVerlet
from ase.optimize import QuasiNewton
from ase.visualize.plot import plot_atoms
# Set up initial positions of Cu atoms on Fcc crystal lattice
size = 10
atoms = LatticeFCC(
directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
symbol='Cu',
size=(size, size, size),
pbc=True,
)
Before setting up the MD simulation, we take a look at the initial structure:
fig, ax = plt.subplots(figsize=(5, 5))
plot_atoms(atoms, ax, rotation=('45x,45y,0z'), show_unit_cell=2, radii=0.75)
ax.set_axis_off()
plt.tight_layout()
plt.show()
Now let’s run the MD simulation and monitor the kinetic and potential energy of the whole system:
# Describe the interatomic interactions with the Effective Medium Theory (EMT)
atoms.calc = EMT()
# Set the initial velocities corresponding to T=300K from Maxwell Boltzmann
# Distribution
MaxwellBoltzmannDistribution(atoms, temperature_K=300)
# We use Velocity Verlet algorithm to integrate the Newton's equations.
timestep_fs = 5
dyn = VelocityVerlet(atoms, timestep_fs * units.fs) # 5 fs time step.
def printenergy(a):
"""
Function to print the thermodynamical properties i.e potential energy,
kinetic energy and total energy
"""
epot = a.get_potential_energy()
ekin = a.get_kinetic_energy()
temp = a.get_temperature()
print(
f'Energy per atom: Epot ={epot:6.3f}eV Ekin = {ekin:.3f}eV '
f'(T={temp:.3f}K) Etot = {epot + ekin:.3f}eV'
)
# Now run the dynamics
print('running a NVE simulation of fcc Cu')
printenergy(atoms)
# init lists to for energy vs time data
time_ps, epot, ekin = [], [], []
mdind = 0
steps_per_block = 10
for i in range(20):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the energies of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
epot.append(atoms.get_potential_energy())
ekin.append(atoms.get_kinetic_energy())
etot = np.array(epot) + np.array(ekin)
# Plot energies vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, epot, label='Potential energy')
ax.plot(time_ps, ekin, label='Kinetic energy')
ax.plot(time_ps, etot, label='Total energy')
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Energy (eV)')
ax.legend(loc='best')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
running a NVE simulation of fcc Cu
Energy per atom: Epot =-2.405eV Ekin = 155.990eV (T=301.699K) Etot = 153.586eV
Energy per atom: Epot =117.612eV Ekin = 36.771eV (T=71.119K) Etot = 154.383eV
Energy per atom: Epot =80.354eV Ekin = 73.906eV (T=142.941K) Etot = 154.261eV
Energy per atom: Epot =70.690eV Ekin = 83.398eV (T=161.299K) Etot = 154.088eV
Energy per atom: Epot =68.927eV Ekin = 85.109eV (T=164.607K) Etot = 154.035eV
Energy per atom: Epot =81.301eV Ekin = 72.910eV (T=141.014K) Etot = 154.211eV
Energy per atom: Epot =79.889eV Ekin = 74.313eV (T=143.729K) Etot = 154.203eV
Energy per atom: Epot =73.000eV Ekin = 81.097eV (T=156.849K) Etot = 154.097eV
Energy per atom: Epot =71.301eV Ekin = 82.794eV (T=160.132K) Etot = 154.096eV
Energy per atom: Epot =80.667eV Ekin = 73.526eV (T=142.206K) Etot = 154.194eV
Energy per atom: Epot =75.445eV Ekin = 78.702eV (T=152.217K) Etot = 154.147eV
Energy per atom: Epot =75.317eV Ekin = 78.815eV (T=152.435K) Etot = 154.132eV
Energy per atom: Epot =76.275eV Ekin = 77.868eV (T=150.603K) Etot = 154.143eV
Energy per atom: Epot =76.388eV Ekin = 77.756eV (T=150.388K) Etot = 154.144eV
Energy per atom: Epot =75.892eV Ekin = 78.259eV (T=151.360K) Etot = 154.151eV
Energy per atom: Epot =75.564eV Ekin = 78.590eV (T=152.000K) Etot = 154.154eV
Energy per atom: Epot =75.202eV Ekin = 78.933eV (T=152.663K) Etot = 154.135eV
Energy per atom: Epot =77.682eV Ekin = 76.468eV (T=147.895K) Etot = 154.150eV
Energy per atom: Epot =75.599eV Ekin = 78.555eV (T=151.932K) Etot = 154.154eV
Energy per atom: Epot =75.037eV Ekin = 79.096eV (T=152.979K) Etot = 154.134eV
Energy per atom: Epot =78.337eV Ekin = 75.821eV (T=146.644K) Etot = 154.158eV
Note how the total energy is conserved, but the kinetic energy quickly drops to half the expected value. Why?
What you learned here:
How to set up a basic MD run.
How to monitor the energy over time.
That total energy is approximately conserved in NVE simulations, what is the error in total energy?
Exercise: Tune the time step from 5fs to 10fs and 50fs, what changes do you observe in total energy?
Part 2: Constant temperature MD#
In many cases, you want to control temperature (NVT ensemble). This
can be done using a thermostat, like – in this tutorial – Langevin
thermostat.
Compared to the previous example, we replace the line
dyn = VelocityVerlet(...) with
where T is the desired temperature in Kelvin. For that we also imported
the Langevin in the beginning.
The Langevin dynamics will then slowly adjust the total energy of the system so the temperature approaches the desired one.
As a slightly less boring example, let us use this to melt a chunk of
copper by starting the simulation without any momentum of the atoms
(no kinetic energy), and with a desired temperature above the melting
point. We will also save information about the atoms in a trajectory
file called moldyn3.traj.
Note
It is recommended to use the asap3 implementation of the EMT
calculator here, because its performance benefits over the ase
implementation.
size = 10
T = 1500 # Kelvin
# Set up a crystal
atoms = LatticeFCC(
directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
symbol='Cu',
size=(size, size, size),
pbc=False,
)
# Describe the interatomic interactions with the Effective Medium Theory
atoms.calc = EMT()
# We want to run MD with constant energy using the Langevin algorithm
# with a time step of 5 fs, the temperature T and the friction
# coefficient to 0.02 atomic units.
timestep_fs = 5
dyn = Langevin(
atoms, timestep=timestep_fs * units.fs, temperature_K=T, friction=0.02
)
# We also want to save the positions of all atoms after every 100th time step.
traj = Trajectory('fccCu_NPT.traj', 'w', atoms)
# Now run the dynamics
print('running a NVT simulation of fcc Cu')
printenergy(atoms)
time_ps, temperature = [], []
mdind = 0
steps_per_block = 10
for i in range(200):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the temperature of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
temperature.append(atoms.get_temperature())
# Plot temperatures vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, temperature)
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Temperature (K)')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
running a NVT simulation of fcc Cu
Energy per atom: Epot =540.816eV Ekin = 0.000eV (T=0.000K) Etot = 540.816eV
Energy per atom: Epot =602.664eV Ekin = 83.010eV (T=160.548K) Etot = 685.674eV
Energy per atom: Epot =675.712eV Ekin = 142.958eV (T=276.493K) Etot = 818.670eV
Energy per atom: Epot =730.121eV Ekin = 204.969eV (T=396.428K) Etot = 935.090eV
Energy per atom: Epot =786.855eV Ekin = 255.866eV (T=494.867K) Etot = 1042.721eV
Energy per atom: Epot =833.528eV Ekin = 301.395eV (T=582.923K) Etot = 1134.922eV
Energy per atom: Epot =879.575eV Ekin = 340.692eV (T=658.928K) Etot = 1220.267eV
Energy per atom: Epot =929.504eV Ekin = 376.938eV (T=729.030K) Etot = 1306.442eV
Energy per atom: Epot =964.705eV Ekin = 412.777eV (T=798.347K) Etot = 1377.482eV
Energy per atom: Epot =1001.891eV Ekin = 442.168eV (T=855.192K) Etot = 1444.059eV
Energy per atom: Epot =1043.745eV Ekin = 458.694eV (T=887.154K) Etot = 1502.439eV
Energy per atom: Epot =1068.004eV Ekin = 493.755eV (T=954.966K) Etot = 1561.759eV
Energy per atom: Epot =1101.671eV Ekin = 512.123eV (T=990.490K) Etot = 1613.794eV
Energy per atom: Epot =1136.493eV Ekin = 527.726eV (T=1020.669K) Etot = 1664.219eV
Energy per atom: Epot =1165.568eV Ekin = 545.145eV (T=1054.358K) Etot = 1710.713eV
Energy per atom: Epot =1184.908eV Ekin = 564.409eV (T=1091.616K) Etot = 1749.317eV
Energy per atom: Epot =1220.035eV Ekin = 570.542eV (T=1103.477K) Etot = 1790.576eV
Energy per atom: Epot =1242.073eV Ekin = 584.556eV (T=1130.582K) Etot = 1826.629eV
Energy per atom: Epot =1272.755eV Ekin = 576.914eV (T=1115.803K) Etot = 1849.670eV
Energy per atom: Epot =1292.536eV Ekin = 595.682eV (T=1152.102K) Etot = 1888.218eV
Energy per atom: Epot =1335.466eV Ekin = 592.693eV (T=1146.319K) Etot = 1928.159eV
Energy per atom: Epot =1350.246eV Ekin = 613.423eV (T=1186.414K) Etot = 1963.669eV
Energy per atom: Epot =1367.738eV Ekin = 626.668eV (T=1212.031K) Etot = 1994.407eV
Energy per atom: Epot =1383.501eV Ekin = 643.886eV (T=1245.331K) Etot = 2027.386eV
Energy per atom: Epot =1408.808eV Ekin = 646.262eV (T=1249.927K) Etot = 2055.070eV
Energy per atom: Epot =1411.631eV Ekin = 666.742eV (T=1289.538K) Etot = 2078.374eV
Energy per atom: Epot =1430.742eV Ekin = 667.857eV (T=1291.693K) Etot = 2098.599eV
Energy per atom: Epot =1437.873eV Ekin = 686.423eV (T=1327.601K) Etot = 2124.296eV
Energy per atom: Epot =1464.153eV Ekin = 679.274eV (T=1313.774K) Etot = 2143.427eV
Energy per atom: Epot =1478.407eV Ekin = 674.367eV (T=1304.284K) Etot = 2152.774eV
Energy per atom: Epot =1494.823eV Ekin = 668.243eV (T=1292.440K) Etot = 2163.066eV
Energy per atom: Epot =1503.539eV Ekin = 683.461eV (T=1321.873K) Etot = 2187.000eV
Energy per atom: Epot =1517.767eV Ekin = 685.568eV (T=1325.949K) Etot = 2203.335eV
Energy per atom: Epot =1517.026eV Ekin = 702.239eV (T=1358.191K) Etot = 2219.265eV
Energy per atom: Epot =1532.512eV Ekin = 695.841eV (T=1345.818K) Etot = 2228.353eV
Energy per atom: Epot =1546.018eV Ekin = 696.272eV (T=1346.651K) Etot = 2242.290eV
Energy per atom: Epot =1540.516eV Ekin = 720.773eV (T=1394.037K) Etot = 2261.289eV
Energy per atom: Epot =1567.739eV Ekin = 707.382eV (T=1368.138K) Etot = 2275.121eV
Energy per atom: Epot =1580.714eV Ekin = 707.537eV (T=1368.439K) Etot = 2288.252eV
Energy per atom: Epot =1592.670eV Ekin = 707.571eV (T=1368.504K) Etot = 2300.241eV
Energy per atom: Epot =1611.813eV Ekin = 700.072eV (T=1354.000K) Etot = 2311.885eV
Energy per atom: Epot =1605.187eV Ekin = 709.588eV (T=1372.405K) Etot = 2314.775eV
Energy per atom: Epot =1630.789eV Ekin = 695.641eV (T=1345.431K) Etot = 2326.430eV
Energy per atom: Epot =1627.057eV Ekin = 713.039eV (T=1379.079K) Etot = 2340.096eV
Energy per atom: Epot =1632.616eV Ekin = 721.197eV (T=1394.858K) Etot = 2353.813eV
Energy per atom: Epot =1644.361eV Ekin = 722.072eV (T=1396.550K) Etot = 2366.433eV
Energy per atom: Epot =1655.982eV Ekin = 724.206eV (T=1400.677K) Etot = 2380.188eV
Energy per atom: Epot =1664.848eV Ekin = 723.532eV (T=1399.375K) Etot = 2388.380eV
Energy per atom: Epot =1678.166eV Ekin = 722.837eV (T=1398.029K) Etot = 2401.003eV
Energy per atom: Epot =1687.496eV Ekin = 730.879eV (T=1413.584K) Etot = 2418.375eV
Energy per atom: Epot =1695.633eV Ekin = 732.186eV (T=1416.111K) Etot = 2427.819eV
Energy per atom: Epot =1708.629eV Ekin = 732.556eV (T=1416.827K) Etot = 2441.185eV
Energy per atom: Epot =1713.750eV Ekin = 733.601eV (T=1418.848K) Etot = 2447.351eV
Energy per atom: Epot =1736.711eV Ekin = 718.283eV (T=1389.221K) Etot = 2454.993eV
Energy per atom: Epot =1735.765eV Ekin = 725.261eV (T=1402.717K) Etot = 2461.026eV
Energy per atom: Epot =1739.090eV Ekin = 725.122eV (T=1402.449K) Etot = 2464.212eV
Energy per atom: Epot =1731.544eV Ekin = 728.346eV (T=1408.685K) Etot = 2459.890eV
Energy per atom: Epot =1760.607eV Ekin = 709.819eV (T=1372.853K) Etot = 2470.426eV
Energy per atom: Epot =1751.095eV Ekin = 728.800eV (T=1409.562K) Etot = 2479.894eV
Energy per atom: Epot =1752.313eV Ekin = 731.620eV (T=1415.016K) Etot = 2483.933eV
Energy per atom: Epot =1774.127eV Ekin = 732.110eV (T=1415.964K) Etot = 2506.237eV
Energy per atom: Epot =1771.829eV Ekin = 745.320eV (T=1441.514K) Etot = 2517.149eV
Energy per atom: Epot =1782.472eV Ekin = 741.084eV (T=1433.322K) Etot = 2523.556eV
Energy per atom: Epot =1785.296eV Ekin = 737.607eV (T=1426.596K) Etot = 2522.903eV
Energy per atom: Epot =1779.987eV Ekin = 752.521eV (T=1455.442K) Etot = 2532.509eV
Energy per atom: Epot =1797.617eV Ekin = 730.256eV (T=1412.379K) Etot = 2527.873eV
Energy per atom: Epot =1801.898eV Ekin = 738.977eV (T=1429.247K) Etot = 2540.875eV
Energy per atom: Epot =1818.161eV Ekin = 727.652eV (T=1407.343K) Etot = 2545.813eV
Energy per atom: Epot =1824.539eV Ekin = 731.824eV (T=1415.411K) Etot = 2556.363eV
Energy per atom: Epot =1828.631eV Ekin = 739.787eV (T=1430.812K) Etot = 2568.417eV
Energy per atom: Epot =1840.439eV Ekin = 737.075eV (T=1425.567K) Etot = 2577.514eV
Energy per atom: Epot =1846.630eV Ekin = 736.005eV (T=1423.498K) Etot = 2582.636eV
Energy per atom: Epot =1847.909eV Ekin = 739.967eV (T=1431.161K) Etot = 2587.877eV
Energy per atom: Epot =1843.718eV Ekin = 756.317eV (T=1462.783K) Etot = 2600.035eV
Energy per atom: Epot =1853.485eV Ekin = 749.630eV (T=1449.850K) Etot = 2603.116eV
Energy per atom: Epot =1869.961eV Ekin = 741.588eV (T=1434.295K) Etot = 2611.549eV
Energy per atom: Epot =1872.888eV Ekin = 734.010eV (T=1419.640K) Etot = 2606.898eV
Energy per atom: Epot =1863.439eV Ekin = 759.585eV (T=1469.103K) Etot = 2623.024eV
Energy per atom: Epot =1870.991eV Ekin = 752.641eV (T=1455.674K) Etot = 2623.633eV
Energy per atom: Epot =1881.970eV Ekin = 748.198eV (T=1447.081K) Etot = 2630.169eV
Energy per atom: Epot =1897.370eV Ekin = 732.715eV (T=1417.134K) Etot = 2630.085eV
Energy per atom: Epot =1901.099eV Ekin = 737.482eV (T=1426.354K) Etot = 2638.581eV
Energy per atom: Epot =1897.992eV Ekin = 745.215eV (T=1441.310K) Etot = 2643.206eV
Energy per atom: Epot =1895.418eV Ekin = 750.573eV (T=1451.673K) Etot = 2645.990eV
Energy per atom: Epot =1909.845eV Ekin = 744.973eV (T=1440.843K) Etot = 2654.819eV
Energy per atom: Epot =1918.434eV Ekin = 743.765eV (T=1438.506K) Etot = 2662.199eV
Energy per atom: Epot =1909.903eV Ekin = 757.077eV (T=1464.254K) Etot = 2666.980eV
Energy per atom: Epot =1914.251eV Ekin = 757.325eV (T=1464.733K) Etot = 2671.576eV
Energy per atom: Epot =1935.260eV Ekin = 744.600eV (T=1440.121K) Etot = 2679.860eV
Energy per atom: Epot =1925.690eV Ekin = 760.442eV (T=1470.762K) Etot = 2686.132eV
Energy per atom: Epot =1928.956eV Ekin = 767.801eV (T=1484.993K) Etot = 2696.757eV
Energy per atom: Epot =1943.116eV Ekin = 756.959eV (T=1464.025K) Etot = 2700.076eV
Energy per atom: Epot =1930.988eV Ekin = 766.584eV (T=1482.639K) Etot = 2697.572eV
Energy per atom: Epot =1936.586eV Ekin = 767.785eV (T=1484.963K) Etot = 2704.371eV
Energy per atom: Epot =1939.065eV Ekin = 765.402eV (T=1480.354K) Etot = 2704.467eV
Energy per atom: Epot =1953.623eV Ekin = 750.296eV (T=1451.138K) Etot = 2703.919eV
Energy per atom: Epot =1945.782eV Ekin = 766.855eV (T=1483.164K) Etot = 2712.637eV
Energy per atom: Epot =1967.671eV Ekin = 754.790eV (T=1459.830K) Etot = 2722.461eV
Energy per atom: Epot =1960.099eV Ekin = 753.996eV (T=1458.294K) Etot = 2714.095eV
Energy per atom: Epot =1964.539eV Ekin = 747.248eV (T=1445.243K) Etot = 2711.788eV
Energy per atom: Epot =1969.580eV Ekin = 747.279eV (T=1445.303K) Etot = 2716.859eV
Energy per atom: Epot =1958.784eV Ekin = 757.230eV (T=1464.550K) Etot = 2716.014eV
Energy per atom: Epot =1966.581eV Ekin = 757.178eV (T=1464.449K) Etot = 2723.760eV
Energy per atom: Epot =1963.890eV Ekin = 769.370eV (T=1488.029K) Etot = 2733.260eV
Energy per atom: Epot =1960.373eV Ekin = 776.290eV (T=1501.413K) Etot = 2736.663eV
Energy per atom: Epot =1962.162eV Ekin = 774.323eV (T=1497.608K) Etot = 2736.485eV
Energy per atom: Epot =1974.816eV Ekin = 753.014eV (T=1456.394K) Etot = 2727.830eV
Energy per atom: Epot =1961.455eV Ekin = 767.790eV (T=1484.973K) Etot = 2729.245eV
Energy per atom: Epot =1970.444eV Ekin = 764.407eV (T=1478.430K) Etot = 2734.851eV
Energy per atom: Epot =1969.523eV Ekin = 762.629eV (T=1474.991K) Etot = 2732.152eV
Energy per atom: Epot =1969.468eV Ekin = 761.223eV (T=1472.272K) Etot = 2730.691eV
Energy per atom: Epot =1968.549eV Ekin = 758.226eV (T=1466.475K) Etot = 2726.775eV
Energy per atom: Epot =1969.685eV Ekin = 766.550eV (T=1482.575K) Etot = 2736.235eV
Energy per atom: Epot =1977.416eV Ekin = 766.983eV (T=1483.412K) Etot = 2744.399eV
Energy per atom: Epot =1985.118eV Ekin = 761.176eV (T=1472.181K) Etot = 2746.294eV
Energy per atom: Epot =1989.663eV Ekin = 766.847eV (T=1483.149K) Etot = 2756.510eV
Energy per atom: Epot =1997.639eV Ekin = 761.994eV (T=1473.762K) Etot = 2759.633eV
Energy per atom: Epot =2000.903eV Ekin = 764.471eV (T=1478.553K) Etot = 2765.373eV
Energy per atom: Epot =1994.035eV Ekin = 775.450eV (T=1499.788K) Etot = 2769.485eV
Energy per atom: Epot =1993.176eV Ekin = 780.378eV (T=1509.318K) Etot = 2773.553eV
Energy per atom: Epot =2006.255eV Ekin = 776.477eV (T=1501.774K) Etot = 2782.732eV
Energy per atom: Epot =2010.808eV Ekin = 774.414eV (T=1497.785K) Etot = 2785.222eV
Energy per atom: Epot =2017.437eV Ekin = 755.899eV (T=1461.974K) Etot = 2773.336eV
Energy per atom: Epot =2009.443eV Ekin = 769.499eV (T=1488.278K) Etot = 2778.942eV
Energy per atom: Epot =2019.764eV Ekin = 764.856eV (T=1479.298K) Etot = 2784.620eV
Energy per atom: Epot =2004.739eV Ekin = 779.669eV (T=1507.947K) Etot = 2784.408eV
Energy per atom: Epot =2019.704eV Ekin = 775.024eV (T=1498.963K) Etot = 2794.727eV
Energy per atom: Epot =2013.062eV Ekin = 775.101eV (T=1499.112K) Etot = 2788.163eV
Energy per atom: Epot =2016.672eV Ekin = 774.906eV (T=1498.737K) Etot = 2791.579eV
Energy per atom: Epot =2018.650eV Ekin = 783.436eV (T=1515.234K) Etot = 2802.086eV
Energy per atom: Epot =2016.301eV Ekin = 783.072eV (T=1514.530K) Etot = 2799.373eV
Energy per atom: Epot =2022.759eV Ekin = 782.373eV (T=1513.177K) Etot = 2805.132eV
Energy per atom: Epot =2022.592eV Ekin = 788.921eV (T=1525.842K) Etot = 2811.513eV
Energy per atom: Epot =2015.247eV Ekin = 782.614eV (T=1513.644K) Etot = 2797.861eV
Energy per atom: Epot =2021.949eV Ekin = 766.444eV (T=1482.369K) Etot = 2788.393eV
Energy per atom: Epot =2016.882eV Ekin = 775.264eV (T=1499.428K) Etot = 2792.146eV
Energy per atom: Epot =2011.373eV Ekin = 786.604eV (T=1521.361K) Etot = 2797.977eV
Energy per atom: Epot =2010.606eV Ekin = 776.505eV (T=1501.827K) Etot = 2787.110eV
Energy per atom: Epot =2012.196eV Ekin = 772.060eV (T=1493.232K) Etot = 2784.256eV
Energy per atom: Epot =2002.211eV Ekin = 782.186eV (T=1512.815K) Etot = 2784.397eV
Energy per atom: Epot =2009.760eV Ekin = 779.345eV (T=1507.321K) Etot = 2789.105eV
Energy per atom: Epot =2015.052eV Ekin = 781.234eV (T=1510.974K) Etot = 2796.286eV
Energy per atom: Epot =2018.461eV Ekin = 776.887eV (T=1502.567K) Etot = 2795.348eV
Energy per atom: Epot =2008.967eV Ekin = 785.691eV (T=1519.594K) Etot = 2794.658eV
Energy per atom: Epot =2013.510eV Ekin = 773.577eV (T=1496.166K) Etot = 2787.087eV
Energy per atom: Epot =2026.731eV Ekin = 757.949eV (T=1465.940K) Etot = 2784.680eV
Energy per atom: Epot =2024.258eV Ekin = 763.814eV (T=1477.282K) Etot = 2788.072eV
Energy per atom: Epot =2034.183eV Ekin = 765.823eV (T=1481.169K) Etot = 2800.006eV
Energy per atom: Epot =2035.593eV Ekin = 763.115eV (T=1475.931K) Etot = 2798.709eV
Energy per atom: Epot =2027.792eV Ekin = 769.223eV (T=1487.744K) Etot = 2797.014eV
Energy per atom: Epot =2035.046eV Ekin = 756.233eV (T=1462.621K) Etot = 2791.279eV
Energy per atom: Epot =2015.687eV Ekin = 782.542eV (T=1513.503K) Etot = 2798.229eV
Energy per atom: Epot =2027.528eV Ekin = 778.655eV (T=1505.987K) Etot = 2806.183eV
Energy per atom: Epot =2023.811eV Ekin = 778.037eV (T=1504.791K) Etot = 2801.848eV
Energy per atom: Epot =2020.691eV Ekin = 777.075eV (T=1502.930K) Etot = 2797.766eV
Energy per atom: Epot =2019.444eV Ekin = 781.418eV (T=1511.330K) Etot = 2800.862eV
Energy per atom: Epot =2025.810eV Ekin = 770.390eV (T=1490.000K) Etot = 2796.200eV
Energy per atom: Epot =2027.554eV Ekin = 770.457eV (T=1490.131K) Etot = 2798.011eV
Energy per atom: Epot =2021.864eV Ekin = 773.683eV (T=1496.370K) Etot = 2795.547eV
Energy per atom: Epot =2018.450eV Ekin = 771.521eV (T=1492.188K) Etot = 2789.971eV
Energy per atom: Epot =2017.541eV Ekin = 767.699eV (T=1484.796K) Etot = 2785.239eV
Energy per atom: Epot =2011.714eV Ekin = 763.845eV (T=1477.343K) Etot = 2775.559eV
Energy per atom: Epot =2021.568eV Ekin = 765.097eV (T=1479.765K) Etot = 2786.666eV
Energy per atom: Epot =2006.260eV Ekin = 779.070eV (T=1506.790K) Etot = 2785.331eV
Energy per atom: Epot =2017.747eV Ekin = 769.192eV (T=1487.684K) Etot = 2786.939eV
Energy per atom: Epot =2007.179eV Ekin = 785.809eV (T=1519.824K) Etot = 2792.989eV
Energy per atom: Epot =2000.350eV Ekin = 784.536eV (T=1517.361K) Etot = 2784.886eV
Energy per atom: Epot =2009.657eV Ekin = 773.810eV (T=1496.616K) Etot = 2783.467eV
Energy per atom: Epot =1999.496eV Ekin = 781.701eV (T=1511.877K) Etot = 2781.197eV
Energy per atom: Epot =1994.020eV Ekin = 791.004eV (T=1529.871K) Etot = 2785.024eV
Energy per atom: Epot =2013.736eV Ekin = 762.950eV (T=1475.612K) Etot = 2776.686eV
Energy per atom: Epot =1992.392eV Ekin = 780.121eV (T=1508.823K) Etot = 2772.513eV
Energy per atom: Epot =1992.170eV Ekin = 776.824eV (T=1502.446K) Etot = 2768.994eV
Energy per atom: Epot =2003.361eV Ekin = 773.332eV (T=1495.691K) Etot = 2776.693eV
Energy per atom: Epot =2000.174eV Ekin = 777.301eV (T=1503.368K) Etot = 2777.475eV
Energy per atom: Epot =2005.908eV Ekin = 776.472eV (T=1501.765K) Etot = 2782.380eV
Energy per atom: Epot =2000.392eV Ekin = 789.440eV (T=1526.846K) Etot = 2789.832eV
Energy per atom: Epot =2007.757eV Ekin = 782.662eV (T=1513.736K) Etot = 2790.419eV
Energy per atom: Epot =2021.604eV Ekin = 762.555eV (T=1474.848K) Etot = 2784.160eV
Energy per atom: Epot =2018.940eV Ekin = 762.189eV (T=1474.140K) Etot = 2781.129eV
Energy per atom: Epot =1997.825eV Ekin = 787.821eV (T=1523.714K) Etot = 2785.646eV
Energy per atom: Epot =2005.400eV Ekin = 772.052eV (T=1493.217K) Etot = 2777.453eV
Energy per atom: Epot =2013.577eV Ekin = 752.046eV (T=1454.523K) Etot = 2765.623eV
Energy per atom: Epot =1990.391eV Ekin = 779.178eV (T=1506.998K) Etot = 2769.569eV
Energy per atom: Epot =1999.493eV Ekin = 771.355eV (T=1491.868K) Etot = 2770.848eV
Energy per atom: Epot =2013.058eV Ekin = 759.487eV (T=1468.913K) Etot = 2772.545eV
Energy per atom: Epot =2004.132eV Ekin = 772.836eV (T=1494.732K) Etot = 2776.968eV
Energy per atom: Epot =2008.577eV Ekin = 766.150eV (T=1481.800K) Etot = 2774.727eV
Energy per atom: Epot =2006.222eV Ekin = 759.057eV (T=1468.082K) Etot = 2765.278eV
Energy per atom: Epot =1994.264eV Ekin = 783.089eV (T=1514.562K) Etot = 2777.353eV
Energy per atom: Epot =2001.667eV Ekin = 772.768eV (T=1494.601K) Etot = 2774.435eV
Energy per atom: Epot =2002.348eV Ekin = 780.979eV (T=1510.482K) Etot = 2783.327eV
Energy per atom: Epot =2002.363eV Ekin = 777.376eV (T=1503.513K) Etot = 2779.739eV
Energy per atom: Epot =2007.675eV Ekin = 772.238eV (T=1493.575K) Etot = 2779.913eV
Energy per atom: Epot =2003.083eV Ekin = 769.449eV (T=1488.182K) Etot = 2772.532eV
Energy per atom: Epot =1998.618eV Ekin = 763.828eV (T=1477.310K) Etot = 2762.446eV
Energy per atom: Epot =1996.600eV Ekin = 765.468eV (T=1480.482K) Etot = 2762.069eV
Energy per atom: Epot =1990.454eV Ekin = 774.691eV (T=1498.320K) Etot = 2765.145eV
Energy per atom: Epot =1986.105eV Ekin = 778.449eV (T=1505.589K) Etot = 2764.554eV
Energy per atom: Epot =2002.900eV Ekin = 759.461eV (T=1468.863K) Etot = 2762.361eV
Energy per atom: Epot =1994.934eV Ekin = 767.930eV (T=1485.244K) Etot = 2762.864eV
After running the simulation, you can study the result with the command
ase gui fccCu_NPT.traj
Try plotting the kinetic energy. Like in the temperature vs time plot you will not see a well-defined melting point due to finite size effects (including surface melting), but you will probably see an almost flat region where the inside of the system melts. The outermost layers melt at a lower temperature.
Note
The Langevin dynamics will by default keep the position and momentum of the center of mass unperturbed. This is another improvement over just setting momenta corresponding to a temperature, as we did before.
Part 3: Isolated particle MD#
When simulating isolated particles with MD, it is sometimes preferable to set random momenta corresponding to a specific temperature and let the system evolve freely. With a relatively high temperature, the is however a risk that the collection of atoms will drift out of the simulation box because the randomized momenta gave the center of mass a small but non-zero velocity too.
Let us see what happens when we propagate a nanoparticle:
size = 4
atoms = ClusterFCC(
'Cu',
surfaces=[[1, 0, 0], [1, 1, 0], [1, 1, 1]],
layers=(size, size, size),
vacuum=4,
)
# asap3 requires a non-zero cell even if pbc are not applied
atoms.cell = [40] * 3
atoms.set_pbc(False) # isolated cluster (explicit, for clarity)
# Describe the interatomic interactions with the Effective Medium Theory
atoms.calc = EMT()
# Quick relaxation of the cluster
qn = QuasiNewton(atoms)
qn.run(fmax=0.001, steps=10)
# Set the momenta corresponding to T=1200 K
MaxwellBoltzmannDistribution(atoms, temperature_K=1200)
Stationary(atoms) # zero linear momentum
ZeroRotation(atoms) # zero angular momentum
# Run MD using the Velocity Verlet algorithm and save trajectory
dyn = VelocityVerlet(atoms, 5 * units.fs, trajectory='nanoparticleCu_NVE.traj')
print('running a NVE simulation of a Cu nanoparticle')
printenergy(atoms)
steps_per_block = 10
for i in range(200):
dyn.run(steps_per_block)
printenergy(atoms)
Step[ FC] Time Energy fmax
BFGSLineSearch: 0[ 0] 13:42:08 43.457006 1.0818
BFGSLineSearch: 1[ 1] 13:42:08 42.347659 0.2273
BFGSLineSearch: 2[ 2] 13:42:08 42.108454 0.1349
BFGSLineSearch: 3[ 3] 13:42:08 41.964817 0.1138
BFGSLineSearch: 4[ 4] 13:42:08 41.924933 0.0683
BFGSLineSearch: 5[ 5] 13:42:08 41.915346 0.0225
BFGSLineSearch: 6[ 6] 13:42:08 41.914920 0.0059
BFGSLineSearch: 7[ 7] 13:42:08 41.914872 0.0023
BFGSLineSearch: 8[ 9] 13:42:08 41.914855 0.0023
BFGSLineSearch: 9[ 10] 13:42:08 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 14.357eV (T=1194.277K) Etot = 56.271eV
Energy per atom: Epot =51.002eV Ekin = 5.323eV (T=442.813K) Etot = 56.325eV
Energy per atom: Epot =50.679eV Ekin = 5.649eV (T=469.900K) Etot = 56.328eV
Energy per atom: Epot =50.366eV Ekin = 5.956eV (T=495.445K) Etot = 56.321eV
Energy per atom: Epot =49.895eV Ekin = 6.422eV (T=534.254K) Etot = 56.317eV
Energy per atom: Epot =48.750eV Ekin = 7.562eV (T=629.068K) Etot = 56.312eV
Energy per atom: Epot =49.182eV Ekin = 7.137eV (T=593.670K) Etot = 56.318eV
Energy per atom: Epot =49.153eV Ekin = 7.164eV (T=595.965K) Etot = 56.317eV
Energy per atom: Epot =49.095eV Ekin = 7.219eV (T=600.488K) Etot = 56.313eV
Energy per atom: Epot =51.003eV Ekin = 5.326eV (T=443.029K) Etot = 56.329eV
Energy per atom: Epot =49.713eV Ekin = 6.609eV (T=549.799K) Etot = 56.322eV
Energy per atom: Epot =49.755eV Ekin = 6.564eV (T=546.042K) Etot = 56.319eV
Energy per atom: Epot =49.991eV Ekin = 6.333eV (T=526.811K) Etot = 56.324eV
Energy per atom: Epot =49.318eV Ekin = 7.003eV (T=582.542K) Etot = 56.321eV
Energy per atom: Epot =48.895eV Ekin = 7.420eV (T=617.235K) Etot = 56.315eV
Energy per atom: Epot =49.705eV Ekin = 6.616eV (T=550.372K) Etot = 56.321eV
Energy per atom: Epot =49.932eV Ekin = 6.389eV (T=531.509K) Etot = 56.321eV
Energy per atom: Epot =49.495eV Ekin = 6.819eV (T=567.252K) Etot = 56.314eV
Energy per atom: Epot =49.606eV Ekin = 6.711eV (T=558.232K) Etot = 56.317eV
Energy per atom: Epot =50.214eV Ekin = 6.112eV (T=508.465K) Etot = 56.326eV
Energy per atom: Epot =49.627eV Ekin = 6.699eV (T=557.239K) Etot = 56.326eV
Energy per atom: Epot =49.370eV Ekin = 6.953eV (T=578.364K) Etot = 56.323eV
Energy per atom: Epot =49.559eV Ekin = 6.763eV (T=562.616K) Etot = 56.322eV
Energy per atom: Epot =49.812eV Ekin = 6.509eV (T=541.455K) Etot = 56.321eV
Energy per atom: Epot =49.874eV Ekin = 6.445eV (T=536.113K) Etot = 56.319eV
Energy per atom: Epot =49.541eV Ekin = 6.780eV (T=564.038K) Etot = 56.321eV
Energy per atom: Epot =49.970eV Ekin = 6.355eV (T=528.642K) Etot = 56.325eV
Energy per atom: Epot =49.379eV Ekin = 6.939eV (T=577.232K) Etot = 56.318eV
Energy per atom: Epot =49.741eV Ekin = 6.583eV (T=547.577K) Etot = 56.324eV
Energy per atom: Epot =49.754eV Ekin = 6.570eV (T=546.550K) Etot = 56.324eV
Energy per atom: Epot =50.568eV Ekin = 5.758eV (T=478.949K) Etot = 56.326eV
Energy per atom: Epot =49.523eV Ekin = 6.796eV (T=565.339K) Etot = 56.319eV
Energy per atom: Epot =50.126eV Ekin = 6.195eV (T=515.380K) Etot = 56.322eV
Energy per atom: Epot =49.208eV Ekin = 7.106eV (T=591.139K) Etot = 56.314eV
Energy per atom: Epot =49.178eV Ekin = 7.140eV (T=593.917K) Etot = 56.317eV
Energy per atom: Epot =49.382eV Ekin = 6.943eV (T=577.528K) Etot = 56.325eV
Energy per atom: Epot =49.673eV Ekin = 6.652eV (T=553.354K) Etot = 56.325eV
Energy per atom: Epot =49.241eV Ekin = 7.076eV (T=588.605K) Etot = 56.317eV
Energy per atom: Epot =49.294eV Ekin = 7.024eV (T=584.267K) Etot = 56.317eV
Energy per atom: Epot =48.876eV Ekin = 7.447eV (T=619.457K) Etot = 56.322eV
Energy per atom: Epot =50.379eV Ekin = 5.949eV (T=494.856K) Etot = 56.328eV
Energy per atom: Epot =49.363eV Ekin = 6.952eV (T=578.295K) Etot = 56.315eV
Energy per atom: Epot =48.857eV Ekin = 7.454eV (T=620.110K) Etot = 56.312eV
Energy per atom: Epot =50.048eV Ekin = 6.274eV (T=521.885K) Etot = 56.321eV
Energy per atom: Epot =49.587eV Ekin = 6.738eV (T=560.482K) Etot = 56.324eV
Energy per atom: Epot =49.338eV Ekin = 6.988eV (T=581.267K) Etot = 56.326eV
Energy per atom: Epot =50.329eV Ekin = 5.999eV (T=499.055K) Etot = 56.328eV
Energy per atom: Epot =48.930eV Ekin = 7.389eV (T=614.647K) Etot = 56.319eV
Energy per atom: Epot =49.440eV Ekin = 6.882eV (T=572.503K) Etot = 56.322eV
Energy per atom: Epot =48.663eV Ekin = 7.654eV (T=636.725K) Etot = 56.318eV
Energy per atom: Epot =49.559eV Ekin = 6.763eV (T=562.596K) Etot = 56.322eV
Energy per atom: Epot =49.507eV Ekin = 6.813eV (T=566.721K) Etot = 56.319eV
Energy per atom: Epot =49.444eV Ekin = 6.872eV (T=571.658K) Etot = 56.316eV
Energy per atom: Epot =49.890eV Ekin = 6.430eV (T=534.867K) Etot = 56.320eV
Energy per atom: Epot =49.423eV Ekin = 6.893eV (T=573.422K) Etot = 56.316eV
Energy per atom: Epot =49.366eV Ekin = 6.948eV (T=577.971K) Etot = 56.314eV
Energy per atom: Epot =49.128eV Ekin = 7.191eV (T=598.158K) Etot = 56.319eV
Energy per atom: Epot =49.625eV Ekin = 6.699eV (T=557.255K) Etot = 56.324eV
Energy per atom: Epot =49.587eV Ekin = 6.736eV (T=560.337K) Etot = 56.323eV
Energy per atom: Epot =49.560eV Ekin = 6.760eV (T=562.331K) Etot = 56.320eV
Energy per atom: Epot =49.420eV Ekin = 6.899eV (T=573.922K) Etot = 56.319eV
Energy per atom: Epot =48.624eV Ekin = 7.693eV (T=639.922K) Etot = 56.317eV
Energy per atom: Epot =50.109eV Ekin = 6.211eV (T=516.631K) Etot = 56.320eV
Energy per atom: Epot =48.746eV Ekin = 7.566eV (T=629.399K) Etot = 56.312eV
Energy per atom: Epot =49.769eV Ekin = 6.554eV (T=545.210K) Etot = 56.323eV
Energy per atom: Epot =49.530eV Ekin = 6.791eV (T=564.952K) Etot = 56.321eV
Energy per atom: Epot =49.165eV Ekin = 7.155eV (T=595.183K) Etot = 56.320eV
Energy per atom: Epot =49.476eV Ekin = 6.845eV (T=569.391K) Etot = 56.321eV
Energy per atom: Epot =48.939eV Ekin = 7.378eV (T=613.779K) Etot = 56.318eV
Energy per atom: Epot =50.360eV Ekin = 5.967eV (T=496.404K) Etot = 56.327eV
Energy per atom: Epot =49.168eV Ekin = 7.153eV (T=594.999K) Etot = 56.320eV
Energy per atom: Epot =49.702eV Ekin = 6.621eV (T=550.764K) Etot = 56.323eV
Energy per atom: Epot =49.864eV Ekin = 6.457eV (T=537.116K) Etot = 56.321eV
Energy per atom: Epot =50.230eV Ekin = 6.098eV (T=507.300K) Etot = 56.329eV
Energy per atom: Epot =49.348eV Ekin = 6.972eV (T=580.015K) Etot = 56.321eV
Energy per atom: Epot =48.957eV Ekin = 7.359eV (T=612.173K) Etot = 56.316eV
Energy per atom: Epot =49.584eV Ekin = 6.738eV (T=560.552K) Etot = 56.323eV
Energy per atom: Epot =49.330eV Ekin = 6.990eV (T=581.496K) Etot = 56.320eV
Energy per atom: Epot =49.836eV Ekin = 6.484eV (T=539.415K) Etot = 56.321eV
Energy per atom: Epot =49.584eV Ekin = 6.738eV (T=560.515K) Etot = 56.322eV
Energy per atom: Epot =49.308eV Ekin = 7.016eV (T=583.622K) Etot = 56.323eV
Energy per atom: Epot =49.404eV Ekin = 6.915eV (T=575.250K) Etot = 56.319eV
Energy per atom: Epot =49.902eV Ekin = 6.416eV (T=533.760K) Etot = 56.318eV
Energy per atom: Epot =48.612eV Ekin = 7.700eV (T=640.510K) Etot = 56.312eV
Energy per atom: Epot =48.829eV Ekin = 7.486eV (T=622.732K) Etot = 56.315eV
Energy per atom: Epot =49.700eV Ekin = 6.621eV (T=550.737K) Etot = 56.320eV
Energy per atom: Epot =49.945eV Ekin = 6.379eV (T=530.670K) Etot = 56.324eV
Energy per atom: Epot =49.528eV Ekin = 6.793eV (T=565.068K) Etot = 56.321eV
Energy per atom: Epot =48.688eV Ekin = 7.625eV (T=634.310K) Etot = 56.313eV
Energy per atom: Epot =49.091eV Ekin = 7.226eV (T=601.073K) Etot = 56.316eV
Energy per atom: Epot =49.326eV Ekin = 6.996eV (T=581.975K) Etot = 56.322eV
Energy per atom: Epot =48.986eV Ekin = 7.339eV (T=610.473K) Etot = 56.325eV
Energy per atom: Epot =50.314eV Ekin = 6.015eV (T=500.332K) Etot = 56.328eV
Energy per atom: Epot =49.159eV Ekin = 7.158eV (T=595.421K) Etot = 56.317eV
Energy per atom: Epot =49.384eV Ekin = 6.932eV (T=576.656K) Etot = 56.317eV
Energy per atom: Epot =50.240eV Ekin = 6.082eV (T=505.914K) Etot = 56.322eV
Energy per atom: Epot =49.378eV Ekin = 6.944eV (T=577.651K) Etot = 56.322eV
Energy per atom: Epot =49.257eV Ekin = 7.064eV (T=587.632K) Etot = 56.321eV
Energy per atom: Epot =50.275eV Ekin = 6.046eV (T=502.927K) Etot = 56.321eV
Energy per atom: Epot =48.794eV Ekin = 7.520eV (T=625.571K) Etot = 56.314eV
Energy per atom: Epot =49.442eV Ekin = 6.879eV (T=572.206K) Etot = 56.320eV
Energy per atom: Epot =48.653eV Ekin = 7.663eV (T=637.490K) Etot = 56.317eV
Energy per atom: Epot =49.755eV Ekin = 6.566eV (T=546.199K) Etot = 56.321eV
Energy per atom: Epot =48.886eV Ekin = 7.433eV (T=618.312K) Etot = 56.319eV
Energy per atom: Epot =48.548eV Ekin = 7.767eV (T=646.138K) Etot = 56.315eV
Energy per atom: Epot =49.022eV Ekin = 7.294eV (T=606.724K) Etot = 56.316eV
Energy per atom: Epot =49.132eV Ekin = 7.188eV (T=597.909K) Etot = 56.320eV
Energy per atom: Epot =48.949eV Ekin = 7.370eV (T=613.103K) Etot = 56.319eV
Energy per atom: Epot =49.155eV Ekin = 7.165eV (T=596.001K) Etot = 56.319eV
Energy per atom: Epot =49.772eV Ekin = 6.553eV (T=545.133K) Etot = 56.325eV
Energy per atom: Epot =48.860eV Ekin = 7.460eV (T=620.531K) Etot = 56.319eV
Energy per atom: Epot =49.417eV Ekin = 6.902eV (T=574.161K) Etot = 56.319eV
Energy per atom: Epot =48.880eV Ekin = 7.437eV (T=618.647K) Etot = 56.317eV
Energy per atom: Epot =48.346eV Ekin = 7.969eV (T=662.949K) Etot = 56.315eV
Energy per atom: Epot =49.591eV Ekin = 6.732eV (T=559.989K) Etot = 56.323eV
Energy per atom: Epot =48.814eV Ekin = 7.507eV (T=624.507K) Etot = 56.321eV
Energy per atom: Epot =49.047eV Ekin = 7.271eV (T=604.845K) Etot = 56.318eV
Energy per atom: Epot =49.256eV Ekin = 7.061eV (T=587.394K) Etot = 56.317eV
Energy per atom: Epot =49.677eV Ekin = 6.645eV (T=552.764K) Etot = 56.321eV
Energy per atom: Epot =49.425eV Ekin = 6.897eV (T=573.729K) Etot = 56.322eV
Energy per atom: Epot =48.872eV Ekin = 7.447eV (T=619.465K) Etot = 56.319eV
Energy per atom: Epot =48.457eV Ekin = 7.859eV (T=653.777K) Etot = 56.317eV
Energy per atom: Epot =49.031eV Ekin = 7.288eV (T=606.249K) Etot = 56.319eV
Energy per atom: Epot =48.553eV Ekin = 7.767eV (T=646.106K) Etot = 56.320eV
Energy per atom: Epot =49.365eV Ekin = 6.959eV (T=578.889K) Etot = 56.324eV
Energy per atom: Epot =49.549eV Ekin = 6.771eV (T=563.268K) Etot = 56.320eV
Energy per atom: Epot =49.893eV Ekin = 6.432eV (T=535.022K) Etot = 56.325eV
Energy per atom: Epot =49.102eV Ekin = 7.215eV (T=600.154K) Etot = 56.316eV
Energy per atom: Epot =49.255eV Ekin = 7.065eV (T=587.727K) Etot = 56.321eV
Energy per atom: Epot =49.134eV Ekin = 7.185eV (T=597.708K) Etot = 56.319eV
Energy per atom: Epot =49.096eV Ekin = 7.220eV (T=600.631K) Etot = 56.317eV
Energy per atom: Epot =49.584eV Ekin = 6.739eV (T=560.576K) Etot = 56.322eV
Energy per atom: Epot =49.821eV Ekin = 6.503eV (T=540.936K) Etot = 56.324eV
Energy per atom: Epot =49.687eV Ekin = 6.637eV (T=552.087K) Etot = 56.323eV
Energy per atom: Epot =49.135eV Ekin = 7.187eV (T=597.864K) Etot = 56.322eV
Energy per atom: Epot =49.033eV Ekin = 7.291eV (T=606.478K) Etot = 56.323eV
Energy per atom: Epot =49.357eV Ekin = 6.967eV (T=579.521K) Etot = 56.323eV
Energy per atom: Epot =49.868eV Ekin = 6.454eV (T=536.862K) Etot = 56.321eV
Energy per atom: Epot =49.867eV Ekin = 6.455eV (T=537.000K) Etot = 56.322eV
Energy per atom: Epot =49.227eV Ekin = 7.094eV (T=590.165K) Etot = 56.322eV
Energy per atom: Epot =48.753eV Ekin = 7.563eV (T=629.116K) Etot = 56.316eV
Energy per atom: Epot =49.607eV Ekin = 6.715eV (T=558.596K) Etot = 56.322eV
Energy per atom: Epot =48.778eV Ekin = 7.542eV (T=627.408K) Etot = 56.320eV
Energy per atom: Epot =48.879eV Ekin = 7.443eV (T=619.142K) Etot = 56.322eV
Energy per atom: Epot =49.360eV Ekin = 6.963eV (T=579.257K) Etot = 56.323eV
Energy per atom: Epot =50.380eV Ekin = 5.945eV (T=494.561K) Etot = 56.326eV
Energy per atom: Epot =50.148eV Ekin = 6.174eV (T=513.605K) Etot = 56.322eV
Energy per atom: Epot =49.805eV Ekin = 6.515eV (T=541.999K) Etot = 56.321eV
Energy per atom: Epot =49.193eV Ekin = 7.125eV (T=592.690K) Etot = 56.318eV
Energy per atom: Epot =48.544eV Ekin = 7.775eV (T=646.742K) Etot = 56.319eV
Energy per atom: Epot =49.465eV Ekin = 6.856eV (T=570.349K) Etot = 56.321eV
Energy per atom: Epot =50.529eV Ekin = 5.792eV (T=481.822K) Etot = 56.321eV
Energy per atom: Epot =48.477eV Ekin = 7.838eV (T=651.984K) Etot = 56.315eV
Energy per atom: Epot =49.787eV Ekin = 6.539eV (T=543.968K) Etot = 56.326eV
Energy per atom: Epot =48.760eV Ekin = 7.557eV (T=628.668K) Etot = 56.317eV
Energy per atom: Epot =48.915eV Ekin = 7.402eV (T=615.763K) Etot = 56.317eV
Energy per atom: Epot =48.142eV Ekin = 8.174eV (T=679.938K) Etot = 56.315eV
Energy per atom: Epot =49.360eV Ekin = 6.961eV (T=579.035K) Etot = 56.321eV
Energy per atom: Epot =50.313eV Ekin = 6.014eV (T=500.294K) Etot = 56.327eV
Energy per atom: Epot =48.493eV Ekin = 7.828eV (T=651.153K) Etot = 56.321eV
Energy per atom: Epot =48.926eV Ekin = 7.393eV (T=615.039K) Etot = 56.319eV
Energy per atom: Epot =48.626eV Ekin = 7.686eV (T=639.389K) Etot = 56.312eV
Energy per atom: Epot =48.766eV Ekin = 7.547eV (T=627.811K) Etot = 56.313eV
Energy per atom: Epot =48.150eV Ekin = 8.164eV (T=679.104K) Etot = 56.314eV
Energy per atom: Epot =49.777eV Ekin = 6.545eV (T=544.444K) Etot = 56.322eV
Energy per atom: Epot =49.675eV Ekin = 6.643eV (T=552.634K) Etot = 56.319eV
Energy per atom: Epot =48.030eV Ekin = 8.282eV (T=688.949K) Etot = 56.312eV
Energy per atom: Epot =49.730eV Ekin = 6.591eV (T=548.299K) Etot = 56.321eV
Energy per atom: Epot =49.670eV Ekin = 6.650eV (T=553.200K) Etot = 56.321eV
Energy per atom: Epot =49.934eV Ekin = 6.387eV (T=531.298K) Etot = 56.321eV
Energy per atom: Epot =49.507eV Ekin = 6.816eV (T=566.980K) Etot = 56.322eV
Energy per atom: Epot =49.361eV Ekin = 6.960eV (T=578.982K) Etot = 56.321eV
Energy per atom: Epot =48.960eV Ekin = 7.356eV (T=611.944K) Etot = 56.316eV
Energy per atom: Epot =49.794eV Ekin = 6.528eV (T=543.014K) Etot = 56.322eV
Energy per atom: Epot =49.891eV Ekin = 6.430eV (T=534.891K) Etot = 56.321eV
Energy per atom: Epot =49.302eV Ekin = 7.022eV (T=584.151K) Etot = 56.325eV
Energy per atom: Epot =49.478eV Ekin = 6.849eV (T=569.749K) Etot = 56.327eV
Energy per atom: Epot =49.689eV Ekin = 6.635eV (T=551.907K) Etot = 56.323eV
Energy per atom: Epot =49.231eV Ekin = 7.086eV (T=589.463K) Etot = 56.317eV
Energy per atom: Epot =49.650eV Ekin = 6.669eV (T=554.780K) Etot = 56.319eV
Energy per atom: Epot =49.189eV Ekin = 7.131eV (T=593.233K) Etot = 56.320eV
Energy per atom: Epot =50.705eV Ekin = 5.627eV (T=468.128K) Etot = 56.332eV
Energy per atom: Epot =49.502eV Ekin = 6.825eV (T=567.726K) Etot = 56.326eV
Energy per atom: Epot =50.006eV Ekin = 6.319eV (T=525.695K) Etot = 56.326eV
Energy per atom: Epot =49.497eV Ekin = 6.822eV (T=567.534K) Etot = 56.320eV
Energy per atom: Epot =49.292eV Ekin = 7.027eV (T=584.514K) Etot = 56.318eV
Energy per atom: Epot =49.023eV Ekin = 7.298eV (T=607.071K) Etot = 56.321eV
Energy per atom: Epot =49.161eV Ekin = 7.156eV (T=595.294K) Etot = 56.317eV
Energy per atom: Epot =48.816eV Ekin = 7.500eV (T=623.894K) Etot = 56.316eV
Energy per atom: Epot =49.828eV Ekin = 6.493eV (T=540.117K) Etot = 56.321eV
Energy per atom: Epot =49.259eV Ekin = 7.060eV (T=587.277K) Etot = 56.319eV
Energy per atom: Epot =49.720eV Ekin = 6.605eV (T=549.451K) Etot = 56.325eV
Energy per atom: Epot =49.217eV Ekin = 7.103eV (T=590.833K) Etot = 56.319eV
Energy per atom: Epot =49.270eV Ekin = 7.050eV (T=586.435K) Etot = 56.320eV
Energy per atom: Epot =48.559eV Ekin = 7.759eV (T=645.427K) Etot = 56.318eV
Energy per atom: Epot =49.260eV Ekin = 7.059eV (T=587.173K) Etot = 56.318eV
Energy per atom: Epot =49.218eV Ekin = 7.102eV (T=590.824K) Etot = 56.320eV
Energy per atom: Epot =50.062eV Ekin = 6.261eV (T=520.792K) Etot = 56.323eV
Energy per atom: Epot =49.324eV Ekin = 6.995eV (T=581.904K) Etot = 56.320eV
Energy per atom: Epot =49.530eV Ekin = 6.793eV (T=565.084K) Etot = 56.323eV
Energy per atom: Epot =50.099eV Ekin = 6.224eV (T=517.769K) Etot = 56.323eV
After running the simulation, use ASE’s GUI to compare the resulting
trajectory with how it looks if you comment out either the line that says
Stationary(atoms), ZeroRotation(atoms) or both:
ase gui nanoparticleCu_NVE.traj
Try playing the movie with a high frame rate and set frame skipping to a low number. Can you spot the subtle difference?