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()
/builds/ase/ase-deploy/examples/03-tutorials/md.py:98: DeprecationWarning: Use thermalize_momenta
MaxwellBoltzmannDistribution(atoms, temperature_K=300)
running a NVE simulation of fcc Cu
Energy per atom: Epot =-2.405eV Ekin = 153.577eV (T=297.031K) Etot = 151.172eV
Energy per atom: Epot =116.960eV Ekin = 34.993eV (T=67.679K) Etot = 151.952eV
Energy per atom: Epot =77.259eV Ekin = 74.549eV (T=144.185K) Etot = 151.808eV
Energy per atom: Epot =69.300eV Ekin = 82.364eV (T=159.300K) Etot = 151.665eV
Energy per atom: Epot =69.345eV Ekin = 82.273eV (T=159.123K) Etot = 151.618eV
Energy per atom: Epot =79.705eV Ekin = 72.066eV (T=139.381K) Etot = 151.771eV
Energy per atom: Epot =77.169eV Ekin = 74.594eV (T=144.272K) Etot = 151.763eV
Energy per atom: Epot =73.148eV Ekin = 78.530eV (T=151.884K) Etot = 151.678eV
Energy per atom: Epot =70.732eV Ekin = 80.940eV (T=156.545K) Etot = 151.672eV
Energy per atom: Epot =78.679eV Ekin = 73.083eV (T=141.349K) Etot = 151.762eV
Energy per atom: Epot =75.083eV Ekin = 76.634eV (T=148.217K) Etot = 151.716eV
Energy per atom: Epot =72.997eV Ekin = 78.691eV (T=152.196K) Etot = 151.688eV
Energy per atom: Epot =74.382eV Ekin = 77.334eV (T=149.570K) Etot = 151.716eV
Energy per atom: Epot =77.320eV Ekin = 74.408eV (T=143.911K) Etot = 151.728eV
Energy per atom: Epot =73.395eV Ekin = 78.304eV (T=151.447K) Etot = 151.699eV
Energy per atom: Epot =73.407eV Ekin = 78.308eV (T=151.454K) Etot = 151.715eV
Energy per atom: Epot =75.643eV Ekin = 76.076eV (T=147.138K) Etot = 151.719eV
Energy per atom: Epot =76.421eV Ekin = 75.290eV (T=145.617K) Etot = 151.711eV
Energy per atom: Epot =72.944eV Ekin = 78.764eV (T=152.336K) Etot = 151.708eV
Energy per atom: Epot =73.881eV Ekin = 77.823eV (T=150.517K) Etot = 151.704eV
Energy per atom: Epot =78.395eV Ekin = 73.337eV (T=141.841K) Etot = 151.733eV
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()
/home/ase/.local/lib/python3.13/site-packages/ase/md/langevin.py:102: FutureWarning: The implementation of `fixcm=True` in `Langevin` does not strictly sample the correct NVT distributions. The deviations are typically small for large systems but can be more pronounced for small systems. Use `fixcm=False` together with `ase.constraints.FixCom`. `fixcm` is deprecated since ASE 3.28.0 and will be removed in a future release.
warnings.warn(msg, FutureWarning)
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 =600.443eV Ekin = 81.184eV (T=157.016K) Etot = 681.627eV
Energy per atom: Epot =674.585eV Ekin = 142.140eV (T=274.911K) Etot = 816.725eV
Energy per atom: Epot =726.187eV Ekin = 203.564eV (T=393.710K) Etot = 929.751eV
Energy per atom: Epot =781.699eV Ekin = 250.632eV (T=484.745K) Etot = 1032.332eV
Energy per atom: Epot =827.593eV Ekin = 298.980eV (T=578.252K) Etot = 1126.573eV
Energy per atom: Epot =881.917eV Ekin = 329.256eV (T=636.810K) Etot = 1211.174eV
Energy per atom: Epot =920.246eV Ekin = 375.654eV (T=726.548K) Etot = 1295.900eV
Energy per atom: Epot =957.537eV Ekin = 408.226eV (T=789.544K) Etot = 1365.763eV
Energy per atom: Epot =991.069eV Ekin = 441.968eV (T=854.804K) Etot = 1433.037eV
Energy per atom: Epot =1031.237eV Ekin = 463.352eV (T=896.163K) Etot = 1494.589eV
Energy per atom: Epot =1069.290eV Ekin = 486.280eV (T=940.508K) Etot = 1555.570eV
Energy per atom: Epot =1109.849eV Ekin = 505.719eV (T=978.105K) Etot = 1615.568eV
Energy per atom: Epot =1135.797eV Ekin = 532.835eV (T=1030.549K) Etot = 1668.632eV
Energy per atom: Epot =1163.097eV Ekin = 552.623eV (T=1068.820K) Etot = 1715.720eV
Energy per atom: Epot =1195.855eV Ekin = 558.102eV (T=1079.419K) Etot = 1753.957eV
Energy per atom: Epot =1230.809eV Ekin = 562.726eV (T=1088.362K) Etot = 1793.535eV
Energy per atom: Epot =1261.246eV Ekin = 566.582eV (T=1095.818K) Etot = 1827.827eV
Energy per atom: Epot =1275.054eV Ekin = 583.921eV (T=1129.353K) Etot = 1858.975eV
Energy per atom: Epot =1302.007eV Ekin = 590.569eV (T=1142.213K) Etot = 1892.577eV
Energy per atom: Epot =1324.895eV Ekin = 603.953eV (T=1168.098K) Etot = 1928.849eV
Energy per atom: Epot =1342.538eV Ekin = 620.972eV (T=1201.013K) Etot = 1963.509eV
Energy per atom: Epot =1365.334eV Ekin = 623.667eV (T=1206.225K) Etot = 1989.001eV
Energy per atom: Epot =1385.589eV Ekin = 637.651eV (T=1233.273K) Etot = 2023.240eV
Energy per atom: Epot =1409.244eV Ekin = 631.626eV (T=1221.620K) Etot = 2040.870eV
Energy per atom: Epot =1413.701eV Ekin = 654.475eV (T=1265.811K) Etot = 2068.176eV
Energy per atom: Epot =1429.130eV Ekin = 656.960eV (T=1270.619K) Etot = 2086.091eV
Energy per atom: Epot =1451.472eV Ekin = 662.080eV (T=1280.521K) Etot = 2113.552eV
Energy per atom: Epot =1471.116eV Ekin = 661.301eV (T=1279.013K) Etot = 2132.416eV
Energy per atom: Epot =1473.333eV Ekin = 671.418eV (T=1298.581K) Etot = 2144.751eV
Energy per atom: Epot =1492.121eV Ekin = 675.173eV (T=1305.843K) Etot = 2167.294eV
Energy per atom: Epot =1501.580eV Ekin = 679.375eV (T=1313.970K) Etot = 2180.955eV
Energy per atom: Epot =1511.798eV Ekin = 683.124eV (T=1321.221K) Etot = 2194.922eV
Energy per atom: Epot =1517.447eV Ekin = 697.910eV (T=1349.819K) Etot = 2215.358eV
Energy per atom: Epot =1537.633eV Ekin = 688.127eV (T=1330.898K) Etot = 2225.761eV
Energy per atom: Epot =1567.664eV Ekin = 673.295eV (T=1302.211K) Etot = 2240.958eV
Energy per atom: Epot =1564.059eV Ekin = 681.311eV (T=1317.716K) Etot = 2245.370eV
Energy per atom: Epot =1563.585eV Ekin = 701.929eV (T=1357.592K) Etot = 2265.514eV
Energy per atom: Epot =1569.560eV Ekin = 701.645eV (T=1357.042K) Etot = 2271.205eV
Energy per atom: Epot =1591.763eV Ekin = 698.776eV (T=1351.493K) Etot = 2290.538eV
Energy per atom: Epot =1606.161eV Ekin = 691.021eV (T=1336.494K) Etot = 2297.181eV
Energy per atom: Epot =1613.210eV Ekin = 700.612eV (T=1355.044K) Etot = 2313.821eV
Energy per atom: Epot =1610.408eV Ekin = 729.229eV (T=1410.393K) Etot = 2339.638eV
Energy per atom: Epot =1640.026eV Ekin = 717.108eV (T=1386.950K) Etot = 2357.134eV
Energy per atom: Epot =1648.009eV Ekin = 731.138eV (T=1414.085K) Etot = 2379.148eV
Energy per atom: Epot =1677.047eV Ekin = 704.599eV (T=1362.755K) Etot = 2381.646eV
Energy per atom: Epot =1694.928eV Ekin = 698.279eV (T=1350.533K) Etot = 2393.208eV
Energy per atom: Epot =1680.979eV Ekin = 707.724eV (T=1368.799K) Etot = 2388.703eV
Energy per atom: Epot =1678.354eV Ekin = 718.017eV (T=1388.708K) Etot = 2396.372eV
Energy per atom: Epot =1688.035eV Ekin = 721.236eV (T=1394.932K) Etot = 2409.270eV
Energy per atom: Epot =1701.115eV Ekin = 718.328eV (T=1389.308K) Etot = 2419.442eV
Energy per atom: Epot =1696.773eV Ekin = 728.450eV (T=1408.885K) Etot = 2425.222eV
Energy per atom: Epot =1723.432eV Ekin = 717.881eV (T=1388.444K) Etot = 2441.313eV
Energy per atom: Epot =1737.056eV Ekin = 725.087eV (T=1402.382K) Etot = 2462.143eV
Energy per atom: Epot =1745.977eV Ekin = 725.070eV (T=1402.348K) Etot = 2471.047eV
Energy per atom: Epot =1753.681eV Ekin = 720.492eV (T=1393.494K) Etot = 2474.173eV
Energy per atom: Epot =1758.009eV Ekin = 724.394eV (T=1401.042K) Etot = 2482.403eV
Energy per atom: Epot =1772.394eV Ekin = 737.709eV (T=1426.793K) Etot = 2510.103eV
Energy per atom: Epot =1776.415eV Ekin = 733.254eV (T=1418.178K) Etot = 2509.670eV
Energy per atom: Epot =1771.392eV Ekin = 740.327eV (T=1431.857K) Etot = 2511.719eV
Energy per atom: Epot =1774.900eV Ekin = 758.057eV (T=1466.147K) Etot = 2532.957eV
Energy per atom: Epot =1797.688eV Ekin = 736.186eV (T=1423.848K) Etot = 2533.874eV
Energy per atom: Epot =1788.773eV Ekin = 751.949eV (T=1454.334K) Etot = 2540.722eV
Energy per atom: Epot =1797.765eV Ekin = 743.937eV (T=1438.840K) Etot = 2541.702eV
Energy per atom: Epot =1813.385eV Ekin = 742.145eV (T=1435.373K) Etot = 2555.530eV
Energy per atom: Epot =1809.726eV Ekin = 744.696eV (T=1440.306K) Etot = 2554.422eV
Energy per atom: Epot =1824.071eV Ekin = 750.872eV (T=1452.252K) Etot = 2574.944eV
Energy per atom: Epot =1832.834eV Ekin = 746.761eV (T=1444.301K) Etot = 2579.595eV
Energy per atom: Epot =1837.361eV Ekin = 758.120eV (T=1466.270K) Etot = 2595.481eV
Energy per atom: Epot =1855.676eV Ekin = 739.108eV (T=1429.499K) Etot = 2594.784eV
Energy per atom: Epot =1841.474eV Ekin = 757.010eV (T=1464.123K) Etot = 2598.483eV
Energy per atom: Epot =1866.596eV Ekin = 735.294eV (T=1422.123K) Etot = 2601.890eV
Energy per atom: Epot =1865.804eV Ekin = 737.586eV (T=1426.555K) Etot = 2603.389eV
Energy per atom: Epot =1872.800eV Ekin = 746.672eV (T=1444.128K) Etot = 2619.471eV
Energy per atom: Epot =1883.687eV Ekin = 742.210eV (T=1435.498K) Etot = 2625.896eV
Energy per atom: Epot =1884.055eV Ekin = 751.641eV (T=1453.740K) Etot = 2635.697eV
Energy per atom: Epot =1890.279eV Ekin = 745.250eV (T=1441.379K) Etot = 2635.529eV
Energy per atom: Epot =1876.219eV Ekin = 766.889eV (T=1483.230K) Etot = 2643.108eV
Energy per atom: Epot =1889.325eV Ekin = 747.443eV (T=1445.621K) Etot = 2636.769eV
Energy per atom: Epot =1886.061eV Ekin = 741.165eV (T=1433.478K) Etot = 2627.226eV
Energy per atom: Epot =1911.300eV Ekin = 725.300eV (T=1402.794K) Etot = 2636.600eV
Energy per atom: Epot =1895.681eV Ekin = 739.275eV (T=1429.821K) Etot = 2634.956eV
Energy per atom: Epot =1889.919eV Ekin = 758.947eV (T=1467.869K) Etot = 2648.866eV
Energy per atom: Epot =1894.491eV Ekin = 768.468eV (T=1486.285K) Etot = 2662.960eV
Energy per atom: Epot =1918.301eV Ekin = 748.986eV (T=1448.605K) Etot = 2667.288eV
Energy per atom: Epot =1919.124eV Ekin = 753.757eV (T=1457.832K) Etot = 2672.881eV
Energy per atom: Epot =1913.583eV Ekin = 763.658eV (T=1476.980K) Etot = 2677.240eV
Energy per atom: Epot =1922.816eV Ekin = 762.860eV (T=1475.437K) Etot = 2685.676eV
Energy per atom: Epot =1938.353eV Ekin = 755.480eV (T=1461.163K) Etot = 2693.832eV
Energy per atom: Epot =1930.365eV Ekin = 764.955eV (T=1479.490K) Etot = 2695.320eV
Energy per atom: Epot =1932.573eV Ekin = 760.958eV (T=1471.760K) Etot = 2693.532eV
Energy per atom: Epot =1943.127eV Ekin = 754.455eV (T=1459.181K) Etot = 2697.582eV
Energy per atom: Epot =1941.639eV Ekin = 756.054eV (T=1462.275K) Etot = 2697.694eV
Energy per atom: Epot =1932.974eV Ekin = 768.861eV (T=1487.045K) Etot = 2701.835eV
Energy per atom: Epot =1932.398eV Ekin = 769.938eV (T=1489.128K) Etot = 2702.336eV
Energy per atom: Epot =1942.072eV Ekin = 764.830eV (T=1479.248K) Etot = 2706.902eV
Energy per atom: Epot =1945.325eV Ekin = 769.087eV (T=1487.482K) Etot = 2714.412eV
Energy per atom: Epot =1945.107eV Ekin = 778.168eV (T=1505.044K) Etot = 2723.275eV
Energy per atom: Epot =1944.823eV Ekin = 780.565eV (T=1509.681K) Etot = 2725.388eV
Energy per atom: Epot =1951.176eV Ekin = 774.621eV (T=1498.184K) Etot = 2725.797eV
Energy per atom: Epot =1949.069eV Ekin = 769.304eV (T=1487.901K) Etot = 2718.373eV
Energy per atom: Epot =1965.698eV Ekin = 759.480eV (T=1468.900K) Etot = 2725.178eV
Energy per atom: Epot =1965.136eV Ekin = 768.062eV (T=1485.498K) Etot = 2733.198eV
Energy per atom: Epot =1965.286eV Ekin = 759.646eV (T=1469.221K) Etot = 2724.931eV
Energy per atom: Epot =1955.364eV Ekin = 774.557eV (T=1498.061K) Etot = 2729.921eV
Energy per atom: Epot =1964.466eV Ekin = 779.562eV (T=1507.741K) Etot = 2744.028eV
Energy per atom: Epot =1967.502eV Ekin = 768.296eV (T=1485.952K) Etot = 2735.798eV
Energy per atom: Epot =1959.951eV Ekin = 776.614eV (T=1502.040K) Etot = 2736.566eV
Energy per atom: Epot =1968.649eV Ekin = 774.229eV (T=1497.426K) Etot = 2742.878eV
Energy per atom: Epot =1980.284eV Ekin = 765.861eV (T=1481.241K) Etot = 2746.145eV
Energy per atom: Epot =1984.635eV Ekin = 768.125eV (T=1485.621K) Etot = 2752.760eV
Energy per atom: Epot =1972.530eV Ekin = 784.795eV (T=1517.863K) Etot = 2757.325eV
Energy per atom: Epot =1987.560eV Ekin = 763.660eV (T=1476.985K) Etot = 2751.220eV
Energy per atom: Epot =1990.477eV Ekin = 763.973eV (T=1477.591K) Etot = 2754.450eV
Energy per atom: Epot =2000.261eV Ekin = 757.904eV (T=1465.853K) Etot = 2758.165eV
Energy per atom: Epot =1993.325eV Ekin = 761.450eV (T=1472.710K) Etot = 2754.774eV
Energy per atom: Epot =1986.916eV Ekin = 766.821eV (T=1483.099K) Etot = 2753.737eV
Energy per atom: Epot =1989.314eV Ekin = 766.233eV (T=1481.961K) Etot = 2755.547eV
Energy per atom: Epot =1974.901eV Ekin = 776.553eV (T=1501.921K) Etot = 2751.454eV
Energy per atom: Epot =1991.803eV Ekin = 760.978eV (T=1471.797K) Etot = 2752.781eV
Energy per atom: Epot =1982.756eV Ekin = 779.998eV (T=1508.585K) Etot = 2762.754eV
Energy per atom: Epot =1982.147eV Ekin = 779.734eV (T=1508.073K) Etot = 2761.881eV
Energy per atom: Epot =1990.398eV Ekin = 783.774eV (T=1515.888K) Etot = 2774.172eV
Energy per atom: Epot =1997.878eV Ekin = 777.591eV (T=1503.930K) Etot = 2775.469eV
Energy per atom: Epot =1993.548eV Ekin = 773.790eV (T=1496.578K) Etot = 2767.338eV
Energy per atom: Epot =2002.940eV Ekin = 768.812eV (T=1486.949K) Etot = 2771.752eV
Energy per atom: Epot =1993.185eV Ekin = 787.369eV (T=1522.840K) Etot = 2780.555eV
Energy per atom: Epot =1981.661eV Ekin = 791.603eV (T=1531.028K) Etot = 2773.264eV
Energy per atom: Epot =1998.758eV Ekin = 773.714eV (T=1496.430K) Etot = 2772.472eV
Energy per atom: Epot =1986.469eV Ekin = 785.824eV (T=1519.852K) Etot = 2772.293eV
Energy per atom: Epot =1992.909eV Ekin = 776.152eV (T=1501.146K) Etot = 2769.061eV
Energy per atom: Epot =1988.364eV Ekin = 777.901eV (T=1504.528K) Etot = 2766.265eV
Energy per atom: Epot =1986.739eV Ekin = 777.556eV (T=1503.862K) Etot = 2764.296eV
Energy per atom: Epot =1985.915eV Ekin = 776.528eV (T=1501.873K) Etot = 2762.443eV
Energy per atom: Epot =1991.522eV Ekin = 780.820eV (T=1510.174K) Etot = 2772.342eV
Energy per atom: Epot =1995.409eV Ekin = 774.235eV (T=1497.438K) Etot = 2769.644eV
Energy per atom: Epot =1995.168eV Ekin = 771.594eV (T=1492.331K) Etot = 2766.762eV
Energy per atom: Epot =1992.984eV Ekin = 768.739eV (T=1486.808K) Etot = 2761.723eV
Energy per atom: Epot =1993.505eV Ekin = 764.890eV (T=1479.364K) Etot = 2758.395eV
Energy per atom: Epot =1988.356eV Ekin = 769.997eV (T=1489.241K) Etot = 2758.353eV
Energy per atom: Epot =1995.448eV Ekin = 768.702eV (T=1486.737K) Etot = 2764.150eV
Energy per atom: Epot =1990.520eV Ekin = 767.820eV (T=1485.031K) Etot = 2758.341eV
Energy per atom: Epot =1993.078eV Ekin = 767.627eV (T=1484.658K) Etot = 2760.705eV
Energy per atom: Epot =1990.550eV Ekin = 774.707eV (T=1498.352K) Etot = 2765.258eV
Energy per atom: Epot =1985.579eV Ekin = 791.009eV (T=1529.881K) Etot = 2776.588eV
Energy per atom: Epot =1997.390eV Ekin = 785.903eV (T=1520.006K) Etot = 2783.294eV
Energy per atom: Epot =2006.430eV Ekin = 772.538eV (T=1494.155K) Etot = 2778.968eV
Energy per atom: Epot =1996.887eV Ekin = 782.964eV (T=1514.320K) Etot = 2779.850eV
Energy per atom: Epot =2003.880eV Ekin = 778.535eV (T=1505.754K) Etot = 2782.415eV
Energy per atom: Epot =1997.374eV Ekin = 778.272eV (T=1505.245K) Etot = 2775.646eV
Energy per atom: Epot =1996.360eV Ekin = 775.456eV (T=1499.799K) Etot = 2771.816eV
Energy per atom: Epot =2001.950eV Ekin = 774.834eV (T=1498.597K) Etot = 2776.785eV
Energy per atom: Epot =1990.449eV Ekin = 785.332eV (T=1518.900K) Etot = 2775.780eV
Energy per atom: Epot =1994.443eV Ekin = 768.992eV (T=1487.297K) Etot = 2763.435eV
Energy per atom: Epot =1996.825eV Ekin = 767.062eV (T=1483.564K) Etot = 2763.887eV
Energy per atom: Epot =1999.947eV Ekin = 770.722eV (T=1490.643K) Etot = 2770.669eV
Energy per atom: Epot =1985.724eV Ekin = 776.811eV (T=1502.419K) Etot = 2762.534eV
Energy per atom: Epot =1989.875eV Ekin = 779.192eV (T=1507.025K) Etot = 2769.067eV
Energy per atom: Epot =2005.129eV Ekin = 761.369eV (T=1472.555K) Etot = 2766.499eV
Energy per atom: Epot =2006.287eV Ekin = 757.080eV (T=1464.259K) Etot = 2763.367eV
Energy per atom: Epot =1995.955eV Ekin = 765.907eV (T=1481.330K) Etot = 2761.861eV
Energy per atom: Epot =2013.214eV Ekin = 742.373eV (T=1435.815K) Etot = 2755.587eV
Energy per atom: Epot =1992.639eV Ekin = 770.071eV (T=1489.384K) Etot = 2762.710eV
Energy per atom: Epot =2002.424eV Ekin = 755.831eV (T=1461.843K) Etot = 2758.255eV
Energy per atom: Epot =1970.761eV Ekin = 775.714eV (T=1500.299K) Etot = 2746.475eV
Energy per atom: Epot =1989.503eV Ekin = 755.192eV (T=1460.608K) Etot = 2744.695eV
Energy per atom: Epot =1976.482eV Ekin = 763.637eV (T=1476.941K) Etot = 2740.120eV
Energy per atom: Epot =1974.097eV Ekin = 771.177eV (T=1491.523K) Etot = 2745.274eV
Energy per atom: Epot =1986.965eV Ekin = 765.665eV (T=1480.862K) Etot = 2752.630eV
Energy per atom: Epot =1973.303eV Ekin = 786.637eV (T=1521.425K) Etot = 2759.940eV
Energy per atom: Epot =1982.306eV Ekin = 777.588eV (T=1503.923K) Etot = 2759.894eV
Energy per atom: Epot =1985.653eV Ekin = 771.388eV (T=1491.931K) Etot = 2757.040eV
Energy per atom: Epot =1990.470eV Ekin = 771.886eV (T=1492.895K) Etot = 2762.357eV
Energy per atom: Epot =1983.169eV Ekin = 780.933eV (T=1510.392K) Etot = 2764.101eV
Energy per atom: Epot =1986.811eV Ekin = 774.160eV (T=1497.292K) Etot = 2760.971eV
Energy per atom: Epot =1997.109eV Ekin = 765.478eV (T=1480.500K) Etot = 2762.586eV
Energy per atom: Epot =1985.290eV Ekin = 773.744eV (T=1496.488K) Etot = 2759.034eV
Energy per atom: Epot =1979.926eV Ekin = 777.983eV (T=1504.687K) Etot = 2757.909eV
Energy per atom: Epot =1977.349eV Ekin = 782.457eV (T=1513.340K) Etot = 2759.806eV
Energy per atom: Epot =1978.567eV Ekin = 777.364eV (T=1503.491K) Etot = 2755.932eV
Energy per atom: Epot =1983.431eV Ekin = 780.938eV (T=1510.401K) Etot = 2764.369eV
Energy per atom: Epot =1967.751eV Ekin = 800.365eV (T=1547.976K) Etot = 2768.116eV
Energy per atom: Epot =1984.529eV Ekin = 778.706eV (T=1506.084K) Etot = 2763.234eV
Energy per atom: Epot =1992.297eV Ekin = 769.084eV (T=1487.475K) Etot = 2761.381eV
Energy per atom: Epot =1991.097eV Ekin = 768.057eV (T=1485.490K) Etot = 2759.154eV
Energy per atom: Epot =1994.478eV Ekin = 770.958eV (T=1491.100K) Etot = 2765.436eV
Energy per atom: Epot =1990.094eV Ekin = 786.548eV (T=1521.253K) Etot = 2776.643eV
Energy per atom: Epot =1984.049eV Ekin = 793.026eV (T=1533.782K) Etot = 2777.075eV
Energy per atom: Epot =1990.614eV Ekin = 791.764eV (T=1531.340K) Etot = 2782.378eV
Energy per atom: Epot =2000.591eV Ekin = 783.923eV (T=1516.175K) Etot = 2784.514eV
Energy per atom: Epot =1996.100eV Ekin = 782.368eV (T=1513.168K) Etot = 2778.469eV
Energy per atom: Epot =1997.272eV Ekin = 782.876eV (T=1514.149K) Etot = 2780.147eV
Energy per atom: Epot =2022.015eV Ekin = 758.552eV (T=1467.106K) Etot = 2780.567eV
Energy per atom: Epot =2005.649eV Ekin = 772.703eV (T=1494.476K) Etot = 2778.353eV
Energy per atom: Epot =2008.729eV Ekin = 772.762eV (T=1494.590K) Etot = 2781.491eV
Energy per atom: Epot =2004.299eV Ekin = 774.836eV (T=1498.601K) Etot = 2779.135eV
Energy per atom: Epot =2014.363eV Ekin = 769.549eV (T=1488.374K) Etot = 2783.912eV
Energy per atom: Epot =2015.016eV Ekin = 773.638eV (T=1496.282K) Etot = 2788.654eV
Energy per atom: Epot =2021.971eV Ekin = 767.489eV (T=1484.390K) Etot = 2789.460eV
Energy per atom: Epot =2010.430eV Ekin = 779.371eV (T=1507.370K) Etot = 2789.800eV
Energy per atom: Epot =2011.493eV Ekin = 771.532eV (T=1492.209K) Etot = 2783.024eV
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] 20:07:50 43.457006 1.0818
BFGSLineSearch: 1[ 1] 20:07:50 42.347659 0.2273
BFGSLineSearch: 2[ 2] 20:07:50 42.108454 0.1349
BFGSLineSearch: 3[ 3] 20:07:50 41.964817 0.1138
BFGSLineSearch: 4[ 4] 20:07:50 41.924933 0.0683
BFGSLineSearch: 5[ 5] 20:07:50 41.915346 0.0225
BFGSLineSearch: 6[ 6] 20:07:50 41.914920 0.0059
BFGSLineSearch: 7[ 7] 20:07:50 41.914872 0.0023
BFGSLineSearch: 8[ 9] 20:07:50 41.914855 0.0023
BFGSLineSearch: 9[ 10] 20:07:50 41.914851 0.0010
/builds/ase/ase-deploy/examples/03-tutorials/md.py:299: DeprecationWarning: Use thermalize_momenta
MaxwellBoltzmannDistribution(atoms, temperature_K=1200)
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 13.800eV (T=1147.940K) Etot = 55.714eV
Energy per atom: Epot =49.621eV Ekin = 6.132eV (T=510.120K) Etot = 55.754eV
Energy per atom: Epot =50.330eV Ekin = 5.436eV (T=452.216K) Etot = 55.766eV
Energy per atom: Epot =50.369eV Ekin = 5.399eV (T=449.120K) Etot = 55.768eV
Energy per atom: Epot =50.063eV Ekin = 5.701eV (T=474.288K) Etot = 55.764eV
Energy per atom: Epot =50.296eV Ekin = 5.469eV (T=454.933K) Etot = 55.765eV
Energy per atom: Epot =49.303eV Ekin = 6.458eV (T=537.233K) Etot = 55.761eV
Energy per atom: Epot =48.994eV Ekin = 6.768eV (T=562.980K) Etot = 55.762eV
Energy per atom: Epot =49.025eV Ekin = 6.739eV (T=560.604K) Etot = 55.764eV
Energy per atom: Epot =48.799eV Ekin = 6.960eV (T=578.996K) Etot = 55.760eV
Energy per atom: Epot =49.574eV Ekin = 6.185eV (T=514.536K) Etot = 55.760eV
Energy per atom: Epot =49.640eV Ekin = 6.121eV (T=509.192K) Etot = 55.761eV
Energy per atom: Epot =49.719eV Ekin = 6.046eV (T=502.962K) Etot = 55.765eV
Energy per atom: Epot =48.702eV Ekin = 7.060eV (T=587.288K) Etot = 55.761eV
Energy per atom: Epot =48.181eV Ekin = 7.575eV (T=630.120K) Etot = 55.756eV
Energy per atom: Epot =49.073eV Ekin = 6.689eV (T=556.429K) Etot = 55.762eV
Energy per atom: Epot =50.092eV Ekin = 5.676eV (T=472.171K) Etot = 55.768eV
Energy per atom: Epot =50.247eV Ekin = 5.520eV (T=459.223K) Etot = 55.767eV
Energy per atom: Epot =49.291eV Ekin = 6.469eV (T=538.163K) Etot = 55.761eV
Energy per atom: Epot =49.500eV Ekin = 6.262eV (T=520.954K) Etot = 55.762eV
Energy per atom: Epot =49.353eV Ekin = 6.407eV (T=532.959K) Etot = 55.760eV
Energy per atom: Epot =48.337eV Ekin = 7.420eV (T=617.203K) Etot = 55.756eV
Energy per atom: Epot =49.927eV Ekin = 5.842eV (T=485.951K) Etot = 55.769eV
Energy per atom: Epot =49.436eV Ekin = 6.327eV (T=526.341K) Etot = 55.764eV
Energy per atom: Epot =49.621eV Ekin = 6.144eV (T=511.080K) Etot = 55.765eV
Energy per atom: Epot =48.322eV Ekin = 7.434eV (T=618.369K) Etot = 55.756eV
Energy per atom: Epot =49.429eV Ekin = 6.330eV (T=526.559K) Etot = 55.759eV
Energy per atom: Epot =49.266eV Ekin = 6.497eV (T=540.435K) Etot = 55.762eV
Energy per atom: Epot =50.143eV Ekin = 5.625eV (T=467.965K) Etot = 55.768eV
Energy per atom: Epot =49.655eV Ekin = 6.111eV (T=508.394K) Etot = 55.766eV
Energy per atom: Epot =50.258eV Ekin = 5.511eV (T=458.425K) Etot = 55.769eV
Energy per atom: Epot =49.986eV Ekin = 5.780eV (T=480.854K) Etot = 55.766eV
Energy per atom: Epot =49.617eV Ekin = 6.148eV (T=511.408K) Etot = 55.764eV
Energy per atom: Epot =49.144eV Ekin = 6.616eV (T=550.370K) Etot = 55.760eV
Energy per atom: Epot =49.784eV Ekin = 5.978eV (T=497.323K) Etot = 55.763eV
Energy per atom: Epot =49.193eV Ekin = 6.567eV (T=546.299K) Etot = 55.761eV
Energy per atom: Epot =49.690eV Ekin = 6.071eV (T=505.066K) Etot = 55.762eV
Energy per atom: Epot =49.580eV Ekin = 6.181eV (T=514.186K) Etot = 55.761eV
Energy per atom: Epot =49.215eV Ekin = 6.544eV (T=544.338K) Etot = 55.759eV
Energy per atom: Epot =49.576eV Ekin = 6.185eV (T=514.472K) Etot = 55.760eV
Energy per atom: Epot =49.530eV Ekin = 6.232eV (T=518.425K) Etot = 55.762eV
Energy per atom: Epot =48.935eV Ekin = 6.825eV (T=567.761K) Etot = 55.760eV
Energy per atom: Epot =48.739eV Ekin = 7.021eV (T=584.039K) Etot = 55.760eV
Energy per atom: Epot =49.327eV Ekin = 6.435eV (T=535.342K) Etot = 55.763eV
Energy per atom: Epot =49.305eV Ekin = 6.456eV (T=537.045K) Etot = 55.761eV
Energy per atom: Epot =49.029eV Ekin = 6.731eV (T=559.915K) Etot = 55.759eV
Energy per atom: Epot =49.970eV Ekin = 5.795eV (T=482.047K) Etot = 55.764eV
Energy per atom: Epot =49.004eV Ekin = 6.755eV (T=561.906K) Etot = 55.758eV
Energy per atom: Epot =49.018eV Ekin = 6.743eV (T=560.944K) Etot = 55.762eV
Energy per atom: Epot =49.371eV Ekin = 6.391eV (T=531.616K) Etot = 55.761eV
Energy per atom: Epot =49.453eV Ekin = 6.306eV (T=524.581K) Etot = 55.759eV
Energy per atom: Epot =48.713eV Ekin = 7.042eV (T=585.787K) Etot = 55.755eV
Energy per atom: Epot =49.400eV Ekin = 6.362eV (T=529.229K) Etot = 55.762eV
Energy per atom: Epot =49.371eV Ekin = 6.392eV (T=531.754K) Etot = 55.763eV
Energy per atom: Epot =48.928eV Ekin = 6.827eV (T=567.955K) Etot = 55.756eV
Energy per atom: Epot =49.108eV Ekin = 6.652eV (T=553.387K) Etot = 55.761eV
Energy per atom: Epot =49.166eV Ekin = 6.594eV (T=548.545K) Etot = 55.760eV
Energy per atom: Epot =49.401eV Ekin = 6.361eV (T=529.158K) Etot = 55.762eV
Energy per atom: Epot =49.332eV Ekin = 6.431eV (T=534.960K) Etot = 55.762eV
Energy per atom: Epot =49.155eV Ekin = 6.609eV (T=549.750K) Etot = 55.764eV
Energy per atom: Epot =48.250eV Ekin = 7.508eV (T=624.573K) Etot = 55.758eV
Energy per atom: Epot =49.486eV Ekin = 6.279eV (T=522.324K) Etot = 55.765eV
Energy per atom: Epot =48.628eV Ekin = 7.131eV (T=593.219K) Etot = 55.759eV
Energy per atom: Epot =49.603eV Ekin = 6.159eV (T=512.352K) Etot = 55.762eV
Energy per atom: Epot =49.165eV Ekin = 6.600eV (T=549.043K) Etot = 55.765eV
Energy per atom: Epot =49.144eV Ekin = 6.618eV (T=550.556K) Etot = 55.762eV
Energy per atom: Epot =49.054eV Ekin = 6.705eV (T=557.801K) Etot = 55.759eV
Energy per atom: Epot =49.531eV Ekin = 6.229eV (T=518.199K) Etot = 55.760eV
Energy per atom: Epot =49.676eV Ekin = 6.087eV (T=506.360K) Etot = 55.763eV
Energy per atom: Epot =48.937eV Ekin = 6.827eV (T=567.882K) Etot = 55.763eV
Energy per atom: Epot =49.156eV Ekin = 6.608eV (T=549.666K) Etot = 55.764eV
Energy per atom: Epot =49.261eV Ekin = 6.495eV (T=540.258K) Etot = 55.756eV
Energy per atom: Epot =49.578eV Ekin = 6.182eV (T=514.240K) Etot = 55.760eV
Energy per atom: Epot =49.790eV Ekin = 5.977eV (T=497.180K) Etot = 55.767eV
Energy per atom: Epot =49.140eV Ekin = 6.622eV (T=550.820K) Etot = 55.762eV
Energy per atom: Epot =48.677eV Ekin = 7.084eV (T=589.287K) Etot = 55.761eV
Energy per atom: Epot =49.639eV Ekin = 6.128eV (T=509.791K) Etot = 55.768eV
Energy per atom: Epot =48.963eV Ekin = 6.791eV (T=564.934K) Etot = 55.754eV
Energy per atom: Epot =48.934eV Ekin = 6.822eV (T=567.503K) Etot = 55.756eV
Energy per atom: Epot =49.036eV Ekin = 6.726eV (T=559.494K) Etot = 55.761eV
Energy per atom: Epot =48.291eV Ekin = 7.465eV (T=621.008K) Etot = 55.756eV
Energy per atom: Epot =49.326eV Ekin = 6.435eV (T=535.286K) Etot = 55.761eV
Energy per atom: Epot =48.575eV Ekin = 7.179eV (T=597.219K) Etot = 55.755eV
Energy per atom: Epot =49.092eV Ekin = 6.671eV (T=554.904K) Etot = 55.763eV
Energy per atom: Epot =49.763eV Ekin = 6.006eV (T=499.608K) Etot = 55.769eV
Energy per atom: Epot =49.397eV Ekin = 6.367eV (T=529.664K) Etot = 55.764eV
Energy per atom: Epot =47.995eV Ekin = 7.761eV (T=645.623K) Etot = 55.756eV
Energy per atom: Epot =49.113eV Ekin = 6.645eV (T=552.756K) Etot = 55.758eV
Energy per atom: Epot =49.678eV Ekin = 6.088eV (T=506.418K) Etot = 55.766eV
Energy per atom: Epot =48.681eV Ekin = 7.080eV (T=588.993K) Etot = 55.761eV
Energy per atom: Epot =49.228eV Ekin = 6.539eV (T=543.934K) Etot = 55.767eV
Energy per atom: Epot =48.832eV Ekin = 6.928eV (T=576.324K) Etot = 55.760eV
Energy per atom: Epot =49.700eV Ekin = 6.067eV (T=504.687K) Etot = 55.767eV
Energy per atom: Epot =49.009eV Ekin = 6.753eV (T=561.762K) Etot = 55.762eV
Energy per atom: Epot =48.833eV Ekin = 6.920eV (T=575.630K) Etot = 55.753eV
Energy per atom: Epot =49.048eV Ekin = 6.705eV (T=557.780K) Etot = 55.753eV
Energy per atom: Epot =49.105eV Ekin = 6.652eV (T=553.349K) Etot = 55.757eV
Energy per atom: Epot =49.221eV Ekin = 6.539eV (T=543.989K) Etot = 55.760eV
Energy per atom: Epot =48.774eV Ekin = 6.984eV (T=581.003K) Etot = 55.758eV
Energy per atom: Epot =49.255eV Ekin = 6.506eV (T=541.193K) Etot = 55.761eV
Energy per atom: Epot =48.659eV Ekin = 7.100eV (T=590.598K) Etot = 55.759eV
Energy per atom: Epot =48.963eV Ekin = 6.797eV (T=565.406K) Etot = 55.760eV
Energy per atom: Epot =49.269eV Ekin = 6.491eV (T=539.981K) Etot = 55.760eV
Energy per atom: Epot =49.791eV Ekin = 5.975eV (T=497.016K) Etot = 55.766eV
Energy per atom: Epot =48.746eV Ekin = 7.014eV (T=583.507K) Etot = 55.760eV
Energy per atom: Epot =49.062eV Ekin = 6.700eV (T=557.338K) Etot = 55.762eV
Energy per atom: Epot =48.994eV Ekin = 6.765eV (T=562.792K) Etot = 55.760eV
Energy per atom: Epot =48.908eV Ekin = 6.853eV (T=570.108K) Etot = 55.762eV
Energy per atom: Epot =49.309eV Ekin = 6.450eV (T=536.572K) Etot = 55.759eV
Energy per atom: Epot =48.623eV Ekin = 7.135eV (T=593.565K) Etot = 55.759eV
Energy per atom: Epot =48.841eV Ekin = 6.923eV (T=575.875K) Etot = 55.764eV
Energy per atom: Epot =48.806eV Ekin = 6.956eV (T=578.659K) Etot = 55.762eV
Energy per atom: Epot =49.692eV Ekin = 6.071eV (T=505.039K) Etot = 55.763eV
Energy per atom: Epot =49.554eV Ekin = 6.205eV (T=516.186K) Etot = 55.759eV
Energy per atom: Epot =49.572eV Ekin = 6.191eV (T=515.000K) Etot = 55.763eV
Energy per atom: Epot =49.099eV Ekin = 6.661eV (T=554.065K) Etot = 55.759eV
Energy per atom: Epot =49.567eV Ekin = 6.192eV (T=515.072K) Etot = 55.759eV
Energy per atom: Epot =49.563eV Ekin = 6.195eV (T=515.364K) Etot = 55.758eV
Energy per atom: Epot =49.083eV Ekin = 6.677eV (T=555.445K) Etot = 55.760eV
Energy per atom: Epot =48.737eV Ekin = 7.021eV (T=584.044K) Etot = 55.758eV
Energy per atom: Epot =48.857eV Ekin = 6.906eV (T=574.446K) Etot = 55.762eV
Energy per atom: Epot =48.566eV Ekin = 7.192eV (T=598.313K) Etot = 55.758eV
Energy per atom: Epot =48.752eV Ekin = 7.002eV (T=582.504K) Etot = 55.754eV
Energy per atom: Epot =49.325eV Ekin = 6.437eV (T=535.445K) Etot = 55.762eV
Energy per atom: Epot =48.982eV Ekin = 6.781eV (T=564.090K) Etot = 55.763eV
Energy per atom: Epot =49.965eV Ekin = 5.803eV (T=482.767K) Etot = 55.768eV
Energy per atom: Epot =49.678eV Ekin = 6.083eV (T=505.985K) Etot = 55.760eV
Energy per atom: Epot =49.217eV Ekin = 6.543eV (T=544.309K) Etot = 55.760eV
Energy per atom: Epot =48.925eV Ekin = 6.834eV (T=568.483K) Etot = 55.758eV
Energy per atom: Epot =49.377eV Ekin = 6.385eV (T=531.124K) Etot = 55.761eV
Energy per atom: Epot =49.590eV Ekin = 6.172eV (T=513.468K) Etot = 55.762eV
Energy per atom: Epot =49.454eV Ekin = 6.308eV (T=524.703K) Etot = 55.762eV
Energy per atom: Epot =49.231eV Ekin = 6.533eV (T=543.430K) Etot = 55.763eV
Energy per atom: Epot =49.376eV Ekin = 6.389eV (T=531.505K) Etot = 55.766eV
Energy per atom: Epot =49.601eV Ekin = 6.162eV (T=512.565K) Etot = 55.763eV
Energy per atom: Epot =49.305eV Ekin = 6.456eV (T=537.067K) Etot = 55.762eV
Energy per atom: Epot =49.012eV Ekin = 6.750eV (T=561.478K) Etot = 55.761eV
Energy per atom: Epot =48.623eV Ekin = 7.139eV (T=593.904K) Etot = 55.763eV
Energy per atom: Epot =48.951eV Ekin = 6.814eV (T=566.815K) Etot = 55.765eV
Energy per atom: Epot =49.616eV Ekin = 6.149eV (T=511.506K) Etot = 55.765eV
Energy per atom: Epot =49.277eV Ekin = 6.480eV (T=539.007K) Etot = 55.756eV
Energy per atom: Epot =49.118eV Ekin = 6.644eV (T=552.677K) Etot = 55.762eV
Energy per atom: Epot =48.874eV Ekin = 6.886eV (T=572.859K) Etot = 55.760eV
Energy per atom: Epot =49.195eV Ekin = 6.567eV (T=546.266K) Etot = 55.762eV
Energy per atom: Epot =48.723eV Ekin = 7.042eV (T=585.838K) Etot = 55.766eV
Energy per atom: Epot =49.041eV Ekin = 6.719eV (T=558.948K) Etot = 55.760eV
Energy per atom: Epot =48.987eV Ekin = 6.771eV (T=563.264K) Etot = 55.758eV
Energy per atom: Epot =48.817eV Ekin = 6.941eV (T=577.378K) Etot = 55.758eV
Energy per atom: Epot =49.215eV Ekin = 6.547eV (T=544.632K) Etot = 55.762eV
Energy per atom: Epot =48.861eV Ekin = 6.899eV (T=573.916K) Etot = 55.760eV
Energy per atom: Epot =49.525eV Ekin = 6.239eV (T=518.988K) Etot = 55.763eV
Energy per atom: Epot =47.858eV Ekin = 7.897eV (T=656.896K) Etot = 55.755eV
Energy per atom: Epot =48.111eV Ekin = 7.643eV (T=635.771K) Etot = 55.754eV
Energy per atom: Epot =49.234eV Ekin = 6.525eV (T=542.822K) Etot = 55.759eV
Energy per atom: Epot =49.099eV Ekin = 6.666eV (T=554.562K) Etot = 55.765eV
Energy per atom: Epot =48.851eV Ekin = 6.912eV (T=574.950K) Etot = 55.763eV
Energy per atom: Epot =49.887eV Ekin = 5.878eV (T=488.959K) Etot = 55.765eV
Energy per atom: Epot =48.826eV Ekin = 6.937eV (T=577.096K) Etot = 55.763eV
Energy per atom: Epot =48.178eV Ekin = 7.585eV (T=630.929K) Etot = 55.763eV
Energy per atom: Epot =48.985eV Ekin = 6.779eV (T=563.882K) Etot = 55.764eV
Energy per atom: Epot =48.710eV Ekin = 7.045eV (T=586.033K) Etot = 55.755eV
Energy per atom: Epot =49.226eV Ekin = 6.530eV (T=543.226K) Etot = 55.757eV
Energy per atom: Epot =49.347eV Ekin = 6.416eV (T=533.703K) Etot = 55.763eV
Energy per atom: Epot =48.290eV Ekin = 7.466eV (T=621.090K) Etot = 55.756eV
Energy per atom: Epot =49.189eV Ekin = 6.572eV (T=546.685K) Etot = 55.761eV
Energy per atom: Epot =48.830eV Ekin = 6.932eV (T=576.651K) Etot = 55.762eV
Energy per atom: Epot =48.444eV Ekin = 7.318eV (T=608.766K) Etot = 55.762eV
Energy per atom: Epot =48.617eV Ekin = 7.142eV (T=594.136K) Etot = 55.759eV
Energy per atom: Epot =49.318eV Ekin = 6.443eV (T=536.011K) Etot = 55.762eV
Energy per atom: Epot =48.796eV Ekin = 6.964eV (T=579.285K) Etot = 55.760eV
Energy per atom: Epot =49.080eV Ekin = 6.678eV (T=555.489K) Etot = 55.758eV
Energy per atom: Epot =48.441eV Ekin = 7.315eV (T=608.545K) Etot = 55.756eV
Energy per atom: Epot =48.558eV Ekin = 7.208eV (T=599.572K) Etot = 55.766eV
Energy per atom: Epot =48.924eV Ekin = 6.842eV (T=569.166K) Etot = 55.766eV
Energy per atom: Epot =49.345eV Ekin = 6.413eV (T=533.516K) Etot = 55.758eV
Energy per atom: Epot =49.597eV Ekin = 6.164eV (T=512.803K) Etot = 55.761eV
Energy per atom: Epot =47.615eV Ekin = 8.136eV (T=676.804K) Etot = 55.751eV
Energy per atom: Epot =48.494eV Ekin = 7.265eV (T=604.359K) Etot = 55.759eV
Energy per atom: Epot =49.288eV Ekin = 6.478eV (T=538.864K) Etot = 55.766eV
Energy per atom: Epot =48.839eV Ekin = 6.922eV (T=575.780K) Etot = 55.761eV
Energy per atom: Epot =48.389eV Ekin = 7.372eV (T=613.287K) Etot = 55.762eV
Energy per atom: Epot =48.945eV Ekin = 6.819eV (T=567.220K) Etot = 55.764eV
Energy per atom: Epot =48.720eV Ekin = 7.041eV (T=585.755K) Etot = 55.762eV
Energy per atom: Epot =49.220eV Ekin = 6.545eV (T=544.431K) Etot = 55.764eV
Energy per atom: Epot =48.474eV Ekin = 7.282eV (T=605.728K) Etot = 55.756eV
Energy per atom: Epot =48.563eV Ekin = 7.192eV (T=598.268K) Etot = 55.755eV
Energy per atom: Epot =49.137eV Ekin = 6.624eV (T=551.017K) Etot = 55.761eV
Energy per atom: Epot =49.381eV Ekin = 6.378eV (T=530.598K) Etot = 55.760eV
Energy per atom: Epot =49.264eV Ekin = 6.493eV (T=540.094K) Etot = 55.756eV
Energy per atom: Epot =49.012eV Ekin = 6.744eV (T=561.048K) Etot = 55.756eV
Energy per atom: Epot =48.776eV Ekin = 6.980eV (T=580.680K) Etot = 55.756eV
Energy per atom: Epot =49.182eV Ekin = 6.575eV (T=546.965K) Etot = 55.757eV
Energy per atom: Epot =48.967eV Ekin = 6.788eV (T=564.699K) Etot = 55.756eV
Energy per atom: Epot =49.179eV Ekin = 6.584eV (T=547.736K) Etot = 55.764eV
Energy per atom: Epot =49.567eV Ekin = 6.197eV (T=515.498K) Etot = 55.764eV
Energy per atom: Epot =48.963eV Ekin = 6.794eV (T=565.197K) Etot = 55.757eV
Energy per atom: Epot =49.374eV Ekin = 6.389eV (T=531.469K) Etot = 55.763eV
Energy per atom: Epot =49.314eV Ekin = 6.449eV (T=536.481K) Etot = 55.764eV
Energy per atom: Epot =48.945eV Ekin = 6.818eV (T=567.184K) Etot = 55.763eV
Energy per atom: Epot =49.301eV Ekin = 6.463eV (T=537.653K) Etot = 55.764eV
Energy per atom: Epot =49.028eV Ekin = 6.739eV (T=560.591K) Etot = 55.767eV
After running the simulation, use Graphical user interface (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?