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 = 155.967eV (T=301.653K) Etot = 153.562eV
Energy per atom: Epot =117.421eV Ekin = 36.941eV (T=71.447K) Etot = 154.362eV
Energy per atom: Epot =80.561eV Ekin = 73.685eV (T=142.513K) Etot = 154.246eV
Energy per atom: Epot =70.382eV Ekin = 83.683eV (T=161.851K) Etot = 154.065eV
Energy per atom: Epot =67.921eV Ekin = 86.084eV (T=166.493K) Etot = 154.005eV
Energy per atom: Epot =82.353eV Ekin = 71.848eV (T=138.960K) Etot = 154.201eV
Energy per atom: Epot =79.201eV Ekin = 74.984eV (T=145.025K) Etot = 154.184eV
Energy per atom: Epot =73.112eV Ekin = 80.968eV (T=156.599K) Etot = 154.080eV
Energy per atom: Epot =72.215eV Ekin = 81.873eV (T=158.350K) Etot = 154.088eV
Energy per atom: Epot =80.451eV Ekin = 73.719eV (T=142.578K) Etot = 154.170eV
Energy per atom: Epot =74.346eV Ekin = 79.772eV (T=154.285K) Etot = 154.118eV
Energy per atom: Epot =75.522eV Ekin = 78.592eV (T=152.005K) Etot = 154.115eV
Energy per atom: Epot =76.013eV Ekin = 78.111eV (T=151.074K) Etot = 154.124eV
Energy per atom: Epot =77.685eV Ekin = 76.449eV (T=147.859K) Etot = 154.134eV
Energy per atom: Epot =74.041eV Ekin = 80.072eV (T=154.867K) Etot = 154.113eV
Energy per atom: Epot =75.899eV Ekin = 78.235eV (T=151.313K) Etot = 154.134eV
Energy per atom: Epot =75.084eV Ekin = 79.035eV (T=152.860K) Etot = 154.119eV
Energy per atom: Epot =78.301eV Ekin = 75.826eV (T=146.654K) Etot = 154.128eV
Energy per atom: Epot =75.070eV Ekin = 79.067eV (T=152.923K) Etot = 154.138eV
Energy per atom: Epot =75.111eV Ekin = 79.013eV (T=152.819K) Etot = 154.124eV
Energy per atom: Epot =78.635eV Ekin = 75.500eV (T=146.023K) Etot = 154.135eV
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:111: 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 =601.387eV Ekin = 83.072eV (T=160.669K) Etot = 684.459eV
Energy per atom: Epot =674.023eV Ekin = 142.480eV (T=275.569K) Etot = 816.503eV
Energy per atom: Epot =729.140eV Ekin = 207.220eV (T=400.781K) Etot = 936.360eV
Energy per atom: Epot =791.955eV Ekin = 249.851eV (T=483.233K) Etot = 1041.806eV
Energy per atom: Epot =836.361eV Ekin = 297.504eV (T=575.399K) Etot = 1133.866eV
Energy per atom: Epot =877.036eV Ekin = 346.390eV (T=669.949K) Etot = 1223.426eV
Energy per atom: Epot =931.523eV Ekin = 379.161eV (T=733.331K) Etot = 1310.685eV
Energy per atom: Epot =971.637eV Ekin = 406.064eV (T=785.363K) Etot = 1377.701eV
Energy per atom: Epot =1000.419eV Ekin = 437.574eV (T=846.306K) Etot = 1437.993eV
Energy per atom: Epot =1030.091eV Ekin = 472.082eV (T=913.048K) Etot = 1502.173eV
Energy per atom: Epot =1064.641eV Ekin = 491.185eV (T=949.995K) Etot = 1555.826eV
Energy per atom: Epot =1104.231eV Ekin = 510.198eV (T=986.767K) Etot = 1614.428eV
Energy per atom: Epot =1146.662eV Ekin = 520.326eV (T=1006.356K) Etot = 1666.988eV
Energy per atom: Epot =1161.918eV Ekin = 549.046eV (T=1061.903K) Etot = 1710.964eV
Energy per atom: Epot =1193.067eV Ekin = 558.806eV (T=1080.779K) Etot = 1751.873eV
Energy per atom: Epot =1223.516eV Ekin = 573.442eV (T=1109.086K) Etot = 1796.957eV
Energy per atom: Epot =1259.059eV Ekin = 581.060eV (T=1123.820K) Etot = 1840.118eV
Energy per atom: Epot =1284.841eV Ekin = 598.103eV (T=1156.782K) Etot = 1882.944eV
Energy per atom: Epot =1317.161eV Ekin = 604.722eV (T=1169.585K) Etot = 1921.883eV
Energy per atom: Epot =1334.790eV Ekin = 617.829eV (T=1194.935K) Etot = 1952.619eV
Energy per atom: Epot =1357.431eV Ekin = 622.745eV (T=1204.443K) Etot = 1980.176eV
Energy per atom: Epot =1371.450eV Ekin = 639.204eV (T=1236.276K) Etot = 2010.654eV
Energy per atom: Epot =1389.835eV Ekin = 647.943eV (T=1253.179K) Etot = 2037.779eV
Energy per atom: Epot =1420.474eV Ekin = 644.714eV (T=1246.933K) Etot = 2065.188eV
Energy per atom: Epot =1425.015eV Ekin = 666.348eV (T=1288.775K) Etot = 2091.363eV
Energy per atom: Epot =1439.625eV Ekin = 670.691eV (T=1297.174K) Etot = 2110.316eV
Energy per atom: Epot =1459.680eV Ekin = 672.334eV (T=1300.353K) Etot = 2132.014eV
Energy per atom: Epot =1469.121eV Ekin = 679.260eV (T=1313.748K) Etot = 2148.381eV
Energy per atom: Epot =1479.664eV Ekin = 690.936eV (T=1336.330K) Etot = 2170.599eV
Energy per atom: Epot =1505.041eV Ekin = 689.843eV (T=1334.216K) Etot = 2194.884eV
Energy per atom: Epot =1514.968eV Ekin = 700.556eV (T=1354.936K) Etot = 2215.525eV
Energy per atom: Epot =1532.376eV Ekin = 703.368eV (T=1360.375K) Etot = 2235.744eV
Energy per atom: Epot =1542.152eV Ekin = 712.592eV (T=1378.215K) Etot = 2254.744eV
Energy per atom: Epot =1555.173eV Ekin = 712.117eV (T=1377.295K) Etot = 2267.289eV
Energy per atom: Epot =1572.137eV Ekin = 704.461eV (T=1362.490K) Etot = 2276.598eV
Energy per atom: Epot =1586.629eV Ekin = 701.034eV (T=1355.862K) Etot = 2287.664eV
Energy per atom: Epot =1601.982eV Ekin = 706.213eV (T=1365.878K) Etot = 2308.195eV
Energy per atom: Epot =1594.289eV Ekin = 730.663eV (T=1413.166K) Etot = 2324.952eV
Energy per atom: Epot =1617.839eV Ekin = 719.142eV (T=1390.884K) Etot = 2336.981eV
Energy per atom: Epot =1629.696eV Ekin = 719.387eV (T=1391.357K) Etot = 2349.083eV
Energy per atom: Epot =1635.377eV Ekin = 719.611eV (T=1391.790K) Etot = 2354.988eV
Energy per atom: Epot =1646.381eV Ekin = 723.006eV (T=1398.357K) Etot = 2369.387eV
Energy per atom: Epot =1660.134eV Ekin = 719.399eV (T=1391.381K) Etot = 2379.533eV
Energy per atom: Epot =1665.087eV Ekin = 719.019eV (T=1390.646K) Etot = 2384.107eV
Energy per atom: Epot =1670.224eV Ekin = 713.841eV (T=1380.631K) Etot = 2384.065eV
Energy per atom: Epot =1668.604eV Ekin = 720.167eV (T=1392.866K) Etot = 2388.771eV
Energy per atom: Epot =1679.473eV Ekin = 724.399eV (T=1401.050K) Etot = 2403.872eV
Energy per atom: Epot =1690.406eV Ekin = 723.554eV (T=1399.416K) Etot = 2413.959eV
Energy per atom: Epot =1701.458eV Ekin = 721.820eV (T=1396.063K) Etot = 2423.279eV
Energy per atom: Epot =1725.028eV Ekin = 712.663eV (T=1378.352K) Etot = 2437.691eV
Energy per atom: Epot =1713.324eV Ekin = 738.692eV (T=1428.694K) Etot = 2452.016eV
Energy per atom: Epot =1720.454eV Ekin = 740.689eV (T=1432.557K) Etot = 2461.143eV
Energy per atom: Epot =1733.769eV Ekin = 741.230eV (T=1433.603K) Etot = 2474.998eV
Energy per atom: Epot =1756.897eV Ekin = 723.845eV (T=1399.979K) Etot = 2480.742eV
Energy per atom: Epot =1743.485eV Ekin = 744.692eV (T=1440.300K) Etot = 2488.177eV
Energy per atom: Epot =1763.033eV Ekin = 742.839eV (T=1436.716K) Etot = 2505.872eV
Energy per atom: Epot =1769.345eV Ekin = 738.010eV (T=1427.376K) Etot = 2507.356eV
Energy per atom: Epot =1777.084eV Ekin = 738.338eV (T=1428.010K) Etot = 2515.421eV
Energy per atom: Epot =1796.787eV Ekin = 722.853eV (T=1398.061K) Etot = 2519.641eV
Energy per atom: Epot =1784.251eV Ekin = 742.364eV (T=1435.796K) Etot = 2526.615eV
Energy per atom: Epot =1785.929eV Ekin = 748.640eV (T=1447.934K) Etot = 2534.568eV
Energy per atom: Epot =1805.122eV Ekin = 731.501eV (T=1414.786K) Etot = 2536.623eV
Energy per atom: Epot =1806.948eV Ekin = 743.722eV (T=1438.423K) Etot = 2550.670eV
Energy per atom: Epot =1816.873eV Ekin = 728.192eV (T=1408.387K) Etot = 2545.065eV
Energy per atom: Epot =1817.386eV Ekin = 738.523eV (T=1428.367K) Etot = 2555.909eV
Energy per atom: Epot =1829.477eV Ekin = 732.265eV (T=1416.265K) Etot = 2561.742eV
Energy per atom: Epot =1841.081eV Ekin = 728.367eV (T=1408.726K) Etot = 2569.448eV
Energy per atom: Epot =1835.100eV Ekin = 745.509eV (T=1441.878K) Etot = 2580.608eV
Energy per atom: Epot =1842.209eV Ekin = 729.238eV (T=1410.410K) Etot = 2571.448eV
Energy per atom: Epot =1834.351eV Ekin = 745.206eV (T=1441.293K) Etot = 2579.557eV
Energy per atom: Epot =1840.767eV Ekin = 742.589eV (T=1436.232K) Etot = 2583.356eV
Energy per atom: Epot =1846.386eV Ekin = 735.300eV (T=1422.135K) Etot = 2581.687eV
Energy per atom: Epot =1846.146eV Ekin = 733.978eV (T=1419.577K) Etot = 2580.124eV
Energy per atom: Epot =1844.527eV Ekin = 737.084eV (T=1425.585K) Etot = 2581.611eV
Energy per atom: Epot =1851.584eV Ekin = 731.395eV (T=1414.582K) Etot = 2582.979eV
Energy per atom: Epot =1848.625eV Ekin = 744.727eV (T=1440.368K) Etot = 2593.353eV
Energy per atom: Epot =1863.130eV Ekin = 736.892eV (T=1425.214K) Etot = 2600.022eV
Energy per atom: Epot =1864.639eV Ekin = 742.202eV (T=1435.483K) Etot = 2606.841eV
Energy per atom: Epot =1875.547eV Ekin = 729.450eV (T=1410.820K) Etot = 2604.997eV
Energy per atom: Epot =1866.110eV Ekin = 746.927eV (T=1444.622K) Etot = 2613.038eV
Energy per atom: Epot =1874.070eV Ekin = 745.413eV (T=1441.694K) Etot = 2619.484eV
Energy per atom: Epot =1879.338eV Ekin = 747.658eV (T=1446.036K) Etot = 2626.996eV
Energy per atom: Epot =1881.684eV Ekin = 745.738eV (T=1442.322K) Etot = 2627.422eV
Energy per atom: Epot =1876.066eV Ekin = 751.213eV (T=1452.912K) Etot = 2627.280eV
Energy per atom: Epot =1881.964eV Ekin = 746.684eV (T=1444.151K) Etot = 2628.648eV
Energy per atom: Epot =1889.786eV Ekin = 745.206eV (T=1441.294K) Etot = 2634.992eV
Energy per atom: Epot =1892.027eV Ekin = 752.620eV (T=1455.633K) Etot = 2644.647eV
Energy per atom: Epot =1913.677eV Ekin = 739.693eV (T=1430.630K) Etot = 2653.369eV
Energy per atom: Epot =1910.856eV Ekin = 743.977eV (T=1438.916K) Etot = 2654.833eV
Energy per atom: Epot =1911.896eV Ekin = 746.875eV (T=1444.521K) Etot = 2658.771eV
Energy per atom: Epot =1926.305eV Ekin = 730.519eV (T=1412.887K) Etot = 2656.823eV
Energy per atom: Epot =1927.760eV Ekin = 742.448eV (T=1435.959K) Etot = 2670.208eV
Energy per atom: Epot =1932.806eV Ekin = 739.555eV (T=1430.365K) Etot = 2672.361eV
Energy per atom: Epot =1941.123eV Ekin = 736.513eV (T=1424.481K) Etot = 2677.636eV
Energy per atom: Epot =1950.587eV Ekin = 746.791eV (T=1444.358K) Etot = 2697.378eV
Energy per atom: Epot =1953.078eV Ekin = 745.756eV (T=1442.357K) Etot = 2698.834eV
Energy per atom: Epot =1938.748eV Ekin = 762.037eV (T=1473.846K) Etot = 2700.785eV
Energy per atom: Epot =1949.641eV Ekin = 749.135eV (T=1448.893K) Etot = 2698.777eV
Energy per atom: Epot =1956.196eV Ekin = 748.168eV (T=1447.023K) Etot = 2704.365eV
Energy per atom: Epot =1954.519eV Ekin = 758.737eV (T=1467.463K) Etot = 2713.256eV
Energy per atom: Epot =1958.021eV Ekin = 755.066eV (T=1460.363K) Etot = 2713.087eV
Energy per atom: Epot =1976.304eV Ekin = 750.923eV (T=1452.351K) Etot = 2727.228eV
Energy per atom: Epot =1972.330eV Ekin = 768.701eV (T=1486.734K) Etot = 2741.031eV
Energy per atom: Epot =1980.267eV Ekin = 757.157eV (T=1464.408K) Etot = 2737.424eV
Energy per atom: Epot =1993.165eV Ekin = 744.235eV (T=1439.415K) Etot = 2737.400eV
Energy per atom: Epot =1985.473eV Ekin = 759.481eV (T=1468.903K) Etot = 2744.955eV
Energy per atom: Epot =1992.895eV Ekin = 754.565eV (T=1459.394K) Etot = 2747.460eV
Energy per atom: Epot =1979.652eV Ekin = 771.651eV (T=1492.439K) Etot = 2751.303eV
Energy per atom: Epot =1990.445eV Ekin = 767.865eV (T=1485.118K) Etot = 2758.310eV
Energy per atom: Epot =1981.125eV Ekin = 783.797eV (T=1515.932K) Etot = 2764.922eV
Energy per atom: Epot =2000.184eV Ekin = 765.079eV (T=1479.729K) Etot = 2765.263eV
Energy per atom: Epot =1994.673eV Ekin = 765.829eV (T=1481.180K) Etot = 2760.502eV
Energy per atom: Epot =1987.999eV Ekin = 778.127eV (T=1504.966K) Etot = 2766.126eV
Energy per atom: Epot =1988.766eV Ekin = 777.189eV (T=1503.152K) Etot = 2765.955eV
Energy per atom: Epot =1982.199eV Ekin = 771.461eV (T=1492.072K) Etot = 2753.660eV
Energy per atom: Epot =1996.477eV Ekin = 759.634eV (T=1469.199K) Etot = 2756.111eV
Energy per atom: Epot =1983.087eV Ekin = 777.064eV (T=1502.910K) Etot = 2760.151eV
Energy per atom: Epot =1978.794eV Ekin = 782.226eV (T=1512.894K) Etot = 2761.020eV
Energy per atom: Epot =1992.910eV Ekin = 758.461eV (T=1466.929K) Etot = 2751.371eV
Energy per atom: Epot =1990.536eV Ekin = 760.688eV (T=1471.237K) Etot = 2751.224eV
Energy per atom: Epot =1983.441eV Ekin = 776.554eV (T=1501.923K) Etot = 2759.995eV
Energy per atom: Epot =1997.746eV Ekin = 769.074eV (T=1487.456K) Etot = 2766.820eV
Energy per atom: Epot =2005.254eV Ekin = 766.616eV (T=1482.702K) Etot = 2771.870eV
Energy per atom: Epot =2009.321eV Ekin = 759.577eV (T=1469.089K) Etot = 2768.899eV
Energy per atom: Epot =2012.192eV Ekin = 756.353eV (T=1462.853K) Etot = 2768.545eV
Energy per atom: Epot =1999.771eV Ekin = 763.508eV (T=1476.690K) Etot = 2763.279eV
Energy per atom: Epot =1999.696eV Ekin = 764.643eV (T=1478.886K) Etot = 2764.339eV
Energy per atom: Epot =2012.701eV Ekin = 754.463eV (T=1459.197K) Etot = 2767.164eV
Energy per atom: Epot =1992.608eV Ekin = 768.171eV (T=1485.710K) Etot = 2760.779eV
Energy per atom: Epot =2006.442eV Ekin = 765.119eV (T=1479.806K) Etot = 2771.560eV
Energy per atom: Epot =2000.661eV Ekin = 765.190eV (T=1479.944K) Etot = 2765.851eV
Energy per atom: Epot =2002.189eV Ekin = 770.050eV (T=1489.344K) Etot = 2772.239eV
Energy per atom: Epot =2007.432eV Ekin = 759.667eV (T=1469.261K) Etot = 2767.099eV
Energy per atom: Epot =2005.425eV Ekin = 758.128eV (T=1466.285K) Etot = 2763.553eV
Energy per atom: Epot =2003.168eV Ekin = 762.847eV (T=1475.413K) Etot = 2766.015eV
Energy per atom: Epot =2012.437eV Ekin = 760.113eV (T=1470.125K) Etot = 2772.550eV
Energy per atom: Epot =2016.344eV Ekin = 760.276eV (T=1470.440K) Etot = 2776.619eV
Energy per atom: Epot =2022.890eV Ekin = 748.275eV (T=1447.228K) Etot = 2771.164eV
Energy per atom: Epot =2009.763eV Ekin = 766.640eV (T=1482.748K) Etot = 2776.403eV
Energy per atom: Epot =2013.252eV Ekin = 766.377eV (T=1482.239K) Etot = 2779.629eV
Energy per atom: Epot =2018.169eV Ekin = 764.197eV (T=1478.023K) Etot = 2782.365eV
Energy per atom: Epot =2012.766eV Ekin = 767.512eV (T=1484.436K) Etot = 2780.278eV
Energy per atom: Epot =2015.701eV Ekin = 766.494eV (T=1482.466K) Etot = 2782.194eV
Energy per atom: Epot =2029.390eV Ekin = 763.821eV (T=1477.296K) Etot = 2793.211eV
Energy per atom: Epot =2016.932eV Ekin = 778.211eV (T=1505.127K) Etot = 2795.143eV
Energy per atom: Epot =2033.967eV Ekin = 756.907eV (T=1463.924K) Etot = 2790.874eV
Energy per atom: Epot =2011.304eV Ekin = 781.232eV (T=1510.970K) Etot = 2792.536eV
Energy per atom: Epot =2020.305eV Ekin = 772.344eV (T=1493.781K) Etot = 2792.649eV
Energy per atom: Epot =2035.198eV Ekin = 753.538eV (T=1457.408K) Etot = 2788.736eV
Energy per atom: Epot =2024.605eV Ekin = 765.233eV (T=1480.028K) Etot = 2789.838eV
Energy per atom: Epot =2015.299eV Ekin = 777.805eV (T=1504.342K) Etot = 2793.104eV
Energy per atom: Epot =2025.140eV Ekin = 774.884eV (T=1498.692K) Etot = 2800.024eV
Energy per atom: Epot =2030.320eV Ekin = 770.625eV (T=1490.455K) Etot = 2800.945eV
Energy per atom: Epot =2023.229eV Ekin = 781.489eV (T=1511.468K) Etot = 2804.718eV
Energy per atom: Epot =2023.044eV Ekin = 785.425eV (T=1519.080K) Etot = 2808.468eV
Energy per atom: Epot =2034.464eV Ekin = 774.996eV (T=1498.910K) Etot = 2809.460eV
Energy per atom: Epot =2020.510eV Ekin = 782.744eV (T=1513.895K) Etot = 2803.254eV
Energy per atom: Epot =2015.554eV Ekin = 783.476eV (T=1515.311K) Etot = 2799.030eV
Energy per atom: Epot =2006.002eV Ekin = 794.451eV (T=1536.537K) Etot = 2800.453eV
Energy per atom: Epot =2016.119eV Ekin = 774.227eV (T=1497.422K) Etot = 2790.346eV
Energy per atom: Epot =2020.703eV Ekin = 771.169eV (T=1491.508K) Etot = 2791.872eV
Energy per atom: Epot =2028.914eV Ekin = 754.445eV (T=1459.163K) Etot = 2783.359eV
Energy per atom: Epot =2017.575eV Ekin = 766.162eV (T=1481.824K) Etot = 2783.737eV
Energy per atom: Epot =2008.264eV Ekin = 776.919eV (T=1502.629K) Etot = 2785.183eV
Energy per atom: Epot =2011.101eV Ekin = 772.017eV (T=1493.148K) Etot = 2783.118eV
Energy per atom: Epot =2006.569eV Ekin = 784.455eV (T=1517.204K) Etot = 2791.024eV
Energy per atom: Epot =2008.404eV Ekin = 786.598eV (T=1521.348K) Etot = 2795.002eV
Energy per atom: Epot =2013.597eV Ekin = 775.305eV (T=1499.508K) Etot = 2788.902eV
Energy per atom: Epot =2012.869eV Ekin = 788.172eV (T=1524.394K) Etot = 2801.041eV
Energy per atom: Epot =2012.435eV Ekin = 782.686eV (T=1513.784K) Etot = 2795.122eV
Energy per atom: Epot =2014.473eV Ekin = 785.531eV (T=1519.285K) Etot = 2800.004eV
Energy per atom: Epot =2020.184eV Ekin = 771.180eV (T=1491.529K) Etot = 2791.363eV
Energy per atom: Epot =2002.704eV Ekin = 785.672eV (T=1519.558K) Etot = 2788.377eV
Energy per atom: Epot =2006.382eV Ekin = 778.308eV (T=1505.316K) Etot = 2784.691eV
Energy per atom: Epot =2002.657eV Ekin = 785.846eV (T=1519.895K) Etot = 2788.503eV
Energy per atom: Epot =1987.339eV Ekin = 801.257eV (T=1549.700K) Etot = 2788.596eV
Energy per atom: Epot =1999.040eV Ekin = 790.398eV (T=1528.698K) Etot = 2789.438eV
Energy per atom: Epot =1996.318eV Ekin = 785.076eV (T=1518.405K) Etot = 2781.394eV
Energy per atom: Epot =1997.484eV Ekin = 778.573eV (T=1505.829K) Etot = 2776.057eV
Energy per atom: Epot =1996.103eV Ekin = 788.022eV (T=1524.103K) Etot = 2784.124eV
Energy per atom: Epot =2007.659eV Ekin = 764.730eV (T=1479.055K) Etot = 2772.389eV
Energy per atom: Epot =1997.148eV Ekin = 776.081eV (T=1501.009K) Etot = 2773.229eV
Energy per atom: Epot =2001.201eV Ekin = 775.270eV (T=1499.439K) Etot = 2776.470eV
Energy per atom: Epot =1996.695eV Ekin = 772.552eV (T=1494.183K) Etot = 2769.247eV
Energy per atom: Epot =2003.899eV Ekin = 755.103eV (T=1460.436K) Etot = 2759.002eV
Energy per atom: Epot =1994.517eV Ekin = 768.911eV (T=1487.140K) Etot = 2763.427eV
Energy per atom: Epot =1994.167eV Ekin = 763.898eV (T=1477.446K) Etot = 2758.065eV
Energy per atom: Epot =1994.532eV Ekin = 760.398eV (T=1470.676K) Etot = 2754.930eV
Energy per atom: Epot =1993.341eV Ekin = 757.791eV (T=1465.633K) Etot = 2751.131eV
Energy per atom: Epot =1997.021eV Ekin = 752.442eV (T=1455.288K) Etot = 2749.463eV
Energy per atom: Epot =1997.880eV Ekin = 749.029eV (T=1448.688K) Etot = 2746.910eV
Energy per atom: Epot =1988.052eV Ekin = 768.873eV (T=1487.068K) Etot = 2756.926eV
Energy per atom: Epot =1989.374eV Ekin = 766.625eV (T=1482.720K) Etot = 2755.999eV
Energy per atom: Epot =1996.998eV Ekin = 755.865eV (T=1461.908K) Etot = 2752.863eV
Energy per atom: Epot =1997.472eV Ekin = 760.590eV (T=1471.047K) Etot = 2758.062eV
Energy per atom: Epot =2005.753eV Ekin = 754.665eV (T=1459.589K) Etot = 2760.418eV
Energy per atom: Epot =2001.778eV Ekin = 758.850eV (T=1467.681K) Etot = 2760.628eV
Energy per atom: Epot =1998.437eV Ekin = 756.007eV (T=1462.183K) Etot = 2754.444eV
Energy per atom: Epot =1999.851eV Ekin = 758.255eV (T=1466.531K) Etot = 2758.106eV
Energy per atom: Epot =2000.330eV Ekin = 749.366eV (T=1449.338K) Etot = 2749.695eV
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] 07:17:26 43.457006 1.0818
BFGSLineSearch: 1[ 1] 07:17:26 42.347659 0.2273
BFGSLineSearch: 2[ 2] 07:17:26 42.108454 0.1349
BFGSLineSearch: 3[ 3] 07:17:26 41.964817 0.1138
BFGSLineSearch: 4[ 4] 07:17:26 41.924933 0.0683
BFGSLineSearch: 5[ 5] 07:17:26 41.915346 0.0225
BFGSLineSearch: 6[ 6] 07:17:26 41.914920 0.0059
BFGSLineSearch: 7[ 7] 07:17:26 41.914872 0.0023
BFGSLineSearch: 8[ 9] 07:17:26 41.914855 0.0023
BFGSLineSearch: 9[ 10] 07:17:26 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 11.727eV (T=975.535K) Etot = 53.642eV
Energy per atom: Epot =49.033eV Ekin = 4.649eV (T=386.722K) Etot = 53.682eV
Energy per atom: Epot =48.719eV Ekin = 4.965eV (T=413.051K) Etot = 53.684eV
Energy per atom: Epot =49.107eV Ekin = 4.576eV (T=380.634K) Etot = 53.683eV
Energy per atom: Epot =48.605eV Ekin = 5.077eV (T=422.303K) Etot = 53.681eV
Energy per atom: Epot =47.776eV Ekin = 5.903eV (T=491.022K) Etot = 53.678eV
Energy per atom: Epot =47.740eV Ekin = 5.940eV (T=494.139K) Etot = 53.680eV
Energy per atom: Epot =47.290eV Ekin = 6.388eV (T=531.431K) Etot = 53.678eV
Energy per atom: Epot =48.120eV Ekin = 5.566eV (T=462.977K) Etot = 53.686eV
Energy per atom: Epot =48.107eV Ekin = 5.579eV (T=464.064K) Etot = 53.686eV
Energy per atom: Epot =48.858eV Ekin = 4.828eV (T=401.589K) Etot = 53.686eV
Energy per atom: Epot =47.875eV Ekin = 5.803eV (T=482.725K) Etot = 53.678eV
Energy per atom: Epot =47.699eV Ekin = 5.980eV (T=497.453K) Etot = 53.679eV
Energy per atom: Epot =47.868eV Ekin = 5.815eV (T=483.761K) Etot = 53.683eV
Energy per atom: Epot =47.928eV Ekin = 5.754eV (T=478.689K) Etot = 53.682eV
Energy per atom: Epot =48.370eV Ekin = 5.313eV (T=441.992K) Etot = 53.683eV
Energy per atom: Epot =48.481eV Ekin = 5.205eV (T=432.976K) Etot = 53.686eV
Energy per atom: Epot =47.682eV Ekin = 5.999eV (T=499.074K) Etot = 53.682eV
Energy per atom: Epot =48.442eV Ekin = 5.243eV (T=436.113K) Etot = 53.684eV
Energy per atom: Epot =48.191eV Ekin = 5.491eV (T=456.810K) Etot = 53.683eV
Energy per atom: Epot =48.110eV Ekin = 5.573eV (T=463.558K) Etot = 53.683eV
Energy per atom: Epot =47.973eV Ekin = 5.710eV (T=474.982K) Etot = 53.683eV
Energy per atom: Epot =48.590eV Ekin = 5.095eV (T=423.795K) Etot = 53.685eV
Energy per atom: Epot =47.397eV Ekin = 6.280eV (T=522.405K) Etot = 53.677eV
Energy per atom: Epot =48.189eV Ekin = 5.493eV (T=456.941K) Etot = 53.682eV
Energy per atom: Epot =48.498eV Ekin = 5.187eV (T=431.461K) Etot = 53.685eV
Energy per atom: Epot =48.136eV Ekin = 5.546eV (T=461.362K) Etot = 53.683eV
Energy per atom: Epot =47.842eV Ekin = 5.839eV (T=485.702K) Etot = 53.680eV
Energy per atom: Epot =47.943eV Ekin = 5.741eV (T=477.593K) Etot = 53.684eV
Energy per atom: Epot =48.032eV Ekin = 5.651eV (T=470.102K) Etot = 53.684eV
Energy per atom: Epot =47.926eV Ekin = 5.757eV (T=478.923K) Etot = 53.683eV
Energy per atom: Epot =48.141eV Ekin = 5.545eV (T=461.249K) Etot = 53.686eV
Energy per atom: Epot =48.147eV Ekin = 5.541eV (T=460.906K) Etot = 53.688eV
Energy per atom: Epot =48.189eV Ekin = 5.494eV (T=457.057K) Etot = 53.684eV
Energy per atom: Epot =48.041eV Ekin = 5.640eV (T=469.135K) Etot = 53.681eV
Energy per atom: Epot =48.571eV Ekin = 5.114eV (T=425.441K) Etot = 53.685eV
Energy per atom: Epot =47.635eV Ekin = 6.050eV (T=503.271K) Etot = 53.685eV
Energy per atom: Epot =48.370eV Ekin = 5.317eV (T=442.340K) Etot = 53.687eV
Energy per atom: Epot =47.696eV Ekin = 5.982eV (T=497.634K) Etot = 53.678eV
Energy per atom: Epot =48.277eV Ekin = 5.406eV (T=449.687K) Etot = 53.683eV
Energy per atom: Epot =47.573eV Ekin = 6.107eV (T=507.993K) Etot = 53.679eV
Energy per atom: Epot =48.566eV Ekin = 5.119eV (T=425.826K) Etot = 53.685eV
Energy per atom: Epot =48.576eV Ekin = 5.109eV (T=424.974K) Etot = 53.684eV
Energy per atom: Epot =47.466eV Ekin = 6.215eV (T=516.968K) Etot = 53.680eV
Energy per atom: Epot =48.262eV Ekin = 5.422eV (T=451.030K) Etot = 53.683eV
Energy per atom: Epot =47.947eV Ekin = 5.730eV (T=476.666K) Etot = 53.677eV
Energy per atom: Epot =48.089eV Ekin = 5.590eV (T=465.038K) Etot = 53.679eV
Energy per atom: Epot =47.648eV Ekin = 6.028eV (T=501.411K) Etot = 53.676eV
Energy per atom: Epot =48.370eV Ekin = 5.313eV (T=442.000K) Etot = 53.684eV
Energy per atom: Epot =48.195eV Ekin = 5.488eV (T=456.553K) Etot = 53.683eV
Energy per atom: Epot =47.697eV Ekin = 5.985eV (T=497.873K) Etot = 53.682eV
Energy per atom: Epot =48.330eV Ekin = 5.357eV (T=445.635K) Etot = 53.687eV
Energy per atom: Epot =47.947eV Ekin = 5.735eV (T=477.089K) Etot = 53.682eV
Energy per atom: Epot =48.173eV Ekin = 5.508eV (T=458.203K) Etot = 53.681eV
Energy per atom: Epot =48.105eV Ekin = 5.579eV (T=464.101K) Etot = 53.684eV
Energy per atom: Epot =47.662eV Ekin = 6.018eV (T=500.609K) Etot = 53.680eV
Energy per atom: Epot =48.460eV Ekin = 5.222eV (T=434.402K) Etot = 53.682eV
Energy per atom: Epot =48.351eV Ekin = 5.336eV (T=443.919K) Etot = 53.687eV
Energy per atom: Epot =47.688eV Ekin = 5.997eV (T=498.872K) Etot = 53.685eV
Energy per atom: Epot =48.283eV Ekin = 5.400eV (T=449.244K) Etot = 53.683eV
Energy per atom: Epot =48.065eV Ekin = 5.616eV (T=467.141K) Etot = 53.681eV
Energy per atom: Epot =48.582eV Ekin = 5.105eV (T=424.634K) Etot = 53.687eV
Energy per atom: Epot =48.507eV Ekin = 5.181eV (T=430.951K) Etot = 53.687eV
Energy per atom: Epot =48.362eV Ekin = 5.323eV (T=442.783K) Etot = 53.684eV
Energy per atom: Epot =47.921eV Ekin = 5.761eV (T=479.224K) Etot = 53.682eV
Energy per atom: Epot =47.807eV Ekin = 5.870eV (T=488.313K) Etot = 53.677eV
Energy per atom: Epot =48.697eV Ekin = 4.986eV (T=414.731K) Etot = 53.683eV
Energy per atom: Epot =47.834eV Ekin = 5.848eV (T=486.514K) Etot = 53.683eV
Energy per atom: Epot =47.704eV Ekin = 5.979eV (T=497.332K) Etot = 53.682eV
Energy per atom: Epot =48.169eV Ekin = 5.517eV (T=458.973K) Etot = 53.687eV
Energy per atom: Epot =48.005eV Ekin = 5.681eV (T=472.597K) Etot = 53.686eV
Energy per atom: Epot =47.858eV Ekin = 5.829eV (T=484.853K) Etot = 53.686eV
Energy per atom: Epot =48.427eV Ekin = 5.257eV (T=437.345K) Etot = 53.684eV
Energy per atom: Epot =48.336eV Ekin = 5.344eV (T=444.559K) Etot = 53.680eV
Energy per atom: Epot =48.616eV Ekin = 5.070eV (T=421.779K) Etot = 53.686eV
Energy per atom: Epot =47.910eV Ekin = 5.774eV (T=480.323K) Etot = 53.684eV
Energy per atom: Epot =48.399eV Ekin = 5.287eV (T=439.839K) Etot = 53.687eV
Energy per atom: Epot =47.941eV Ekin = 5.742eV (T=477.632K) Etot = 53.682eV
Energy per atom: Epot =47.998eV Ekin = 5.684eV (T=472.854K) Etot = 53.682eV
Energy per atom: Epot =48.131eV Ekin = 5.551eV (T=461.786K) Etot = 53.683eV
Energy per atom: Epot =48.209eV Ekin = 5.473eV (T=455.311K) Etot = 53.682eV
Energy per atom: Epot =47.916eV Ekin = 5.765eV (T=479.535K) Etot = 53.681eV
Energy per atom: Epot =47.627eV Ekin = 6.054eV (T=503.616K) Etot = 53.681eV
Energy per atom: Epot =48.526eV Ekin = 5.160eV (T=429.259K) Etot = 53.686eV
Energy per atom: Epot =47.807eV Ekin = 5.869eV (T=488.243K) Etot = 53.677eV
Energy per atom: Epot =48.188eV Ekin = 5.493eV (T=456.969K) Etot = 53.681eV
Energy per atom: Epot =48.029eV Ekin = 5.655eV (T=470.425K) Etot = 53.684eV
Energy per atom: Epot =48.190eV Ekin = 5.492eV (T=456.885K) Etot = 53.683eV
Energy per atom: Epot =48.104eV Ekin = 5.581eV (T=464.258K) Etot = 53.685eV
Energy per atom: Epot =48.325eV Ekin = 5.363eV (T=446.150K) Etot = 53.688eV
Energy per atom: Epot =47.914eV Ekin = 5.773eV (T=480.201K) Etot = 53.686eV
Energy per atom: Epot =48.191eV Ekin = 5.494eV (T=457.064K) Etot = 53.685eV
Energy per atom: Epot =48.110eV Ekin = 5.571eV (T=463.412K) Etot = 53.681eV
Energy per atom: Epot =48.347eV Ekin = 5.336eV (T=443.873K) Etot = 53.682eV
Energy per atom: Epot =47.828eV Ekin = 5.850eV (T=486.682K) Etot = 53.678eV
Energy per atom: Epot =48.216eV Ekin = 5.464eV (T=454.501K) Etot = 53.680eV
Energy per atom: Epot =47.983eV Ekin = 5.699eV (T=474.094K) Etot = 53.683eV
Energy per atom: Epot =47.477eV Ekin = 6.204eV (T=516.087K) Etot = 53.681eV
Energy per atom: Epot =47.927eV Ekin = 5.756eV (T=478.799K) Etot = 53.683eV
Energy per atom: Epot =48.757eV Ekin = 4.928eV (T=409.978K) Etot = 53.686eV
Energy per atom: Epot =48.237eV Ekin = 5.447eV (T=453.144K) Etot = 53.684eV
Energy per atom: Epot =48.814eV Ekin = 4.873eV (T=405.385K) Etot = 53.687eV
Energy per atom: Epot =48.147eV Ekin = 5.534eV (T=460.339K) Etot = 53.681eV
Energy per atom: Epot =48.138eV Ekin = 5.542eV (T=461.037K) Etot = 53.681eV
Energy per atom: Epot =47.400eV Ekin = 6.282eV (T=522.583K) Etot = 53.682eV
Energy per atom: Epot =47.737eV Ekin = 5.946eV (T=494.590K) Etot = 53.683eV
Energy per atom: Epot =47.731eV Ekin = 5.953eV (T=495.225K) Etot = 53.684eV
Energy per atom: Epot =47.869eV Ekin = 5.811eV (T=483.405K) Etot = 53.681eV
Energy per atom: Epot =48.574eV Ekin = 5.108eV (T=424.897K) Etot = 53.682eV
Energy per atom: Epot =47.487eV Ekin = 6.194eV (T=515.229K) Etot = 53.680eV
Energy per atom: Epot =47.393eV Ekin = 6.285eV (T=522.791K) Etot = 53.678eV
Energy per atom: Epot =48.150eV Ekin = 5.534eV (T=460.322K) Etot = 53.684eV
Energy per atom: Epot =48.039eV Ekin = 5.643eV (T=469.437K) Etot = 53.682eV
Energy per atom: Epot =48.136eV Ekin = 5.545eV (T=461.301K) Etot = 53.682eV
Energy per atom: Epot =48.233eV Ekin = 5.450eV (T=453.391K) Etot = 53.684eV
Energy per atom: Epot =47.906eV Ekin = 5.775eV (T=480.406K) Etot = 53.681eV
Energy per atom: Epot =48.429eV Ekin = 5.256eV (T=437.227K) Etot = 53.685eV
Energy per atom: Epot =48.113eV Ekin = 5.571eV (T=463.393K) Etot = 53.684eV
Energy per atom: Epot =47.754eV Ekin = 5.925eV (T=492.897K) Etot = 53.679eV
Energy per atom: Epot =47.887eV Ekin = 5.796eV (T=482.161K) Etot = 53.683eV
Energy per atom: Epot =48.058eV Ekin = 5.625eV (T=467.933K) Etot = 53.683eV
Energy per atom: Epot =47.710eV Ekin = 5.968eV (T=496.427K) Etot = 53.678eV
Energy per atom: Epot =48.261eV Ekin = 5.420eV (T=450.874K) Etot = 53.681eV
Energy per atom: Epot =47.897eV Ekin = 5.786eV (T=481.345K) Etot = 53.684eV
Energy per atom: Epot =48.321eV Ekin = 5.364eV (T=446.208K) Etot = 53.685eV
Energy per atom: Epot =48.199eV Ekin = 5.485eV (T=456.290K) Etot = 53.685eV
Energy per atom: Epot =48.253eV Ekin = 5.432eV (T=451.847K) Etot = 53.685eV
Energy per atom: Epot =48.136eV Ekin = 5.549eV (T=461.578K) Etot = 53.685eV
Energy per atom: Epot =48.085eV Ekin = 5.597eV (T=465.566K) Etot = 53.682eV
Energy per atom: Epot =48.148eV Ekin = 5.535eV (T=460.428K) Etot = 53.683eV
Energy per atom: Epot =48.217eV Ekin = 5.469eV (T=454.974K) Etot = 53.686eV
Energy per atom: Epot =47.608eV Ekin = 6.073eV (T=505.222K) Etot = 53.681eV
Energy per atom: Epot =47.836eV Ekin = 5.846eV (T=486.325K) Etot = 53.682eV
Energy per atom: Epot =47.701eV Ekin = 5.982eV (T=497.640K) Etot = 53.684eV
Energy per atom: Epot =47.983eV Ekin = 5.700eV (T=474.188K) Etot = 53.683eV
Energy per atom: Epot =48.676eV Ekin = 5.011eV (T=416.815K) Etot = 53.686eV
Energy per atom: Epot =47.953eV Ekin = 5.729eV (T=476.568K) Etot = 53.682eV
Energy per atom: Epot =47.843eV Ekin = 5.838eV (T=485.665K) Etot = 53.682eV
Energy per atom: Epot =48.141eV Ekin = 5.541eV (T=460.949K) Etot = 53.682eV
Energy per atom: Epot =48.642eV Ekin = 5.043eV (T=419.499K) Etot = 53.685eV
Energy per atom: Epot =48.217eV Ekin = 5.467eV (T=454.782K) Etot = 53.684eV
Energy per atom: Epot =48.360eV Ekin = 5.327eV (T=443.101K) Etot = 53.687eV
Energy per atom: Epot =47.945eV Ekin = 5.739eV (T=477.426K) Etot = 53.684eV
Energy per atom: Epot =47.939eV Ekin = 5.745eV (T=477.869K) Etot = 53.683eV
Energy per atom: Epot =47.276eV Ekin = 6.405eV (T=532.778K) Etot = 53.681eV
Energy per atom: Epot =47.777eV Ekin = 5.909eV (T=491.548K) Etot = 53.686eV
Energy per atom: Epot =48.238eV Ekin = 5.448eV (T=453.195K) Etot = 53.686eV
Energy per atom: Epot =48.293eV Ekin = 5.392eV (T=448.545K) Etot = 53.685eV
Energy per atom: Epot =48.202eV Ekin = 5.481eV (T=455.904K) Etot = 53.683eV
Energy per atom: Epot =47.888eV Ekin = 5.795eV (T=482.085K) Etot = 53.683eV
Energy per atom: Epot =48.325eV Ekin = 5.360eV (T=445.891K) Etot = 53.685eV
Energy per atom: Epot =47.700eV Ekin = 5.980eV (T=497.489K) Etot = 53.680eV
Energy per atom: Epot =47.804eV Ekin = 5.881eV (T=489.194K) Etot = 53.685eV
Energy per atom: Epot =48.357eV Ekin = 5.329eV (T=443.272K) Etot = 53.686eV
Energy per atom: Epot =48.188eV Ekin = 5.495eV (T=457.106K) Etot = 53.683eV
Energy per atom: Epot =48.295eV Ekin = 5.392eV (T=448.532K) Etot = 53.687eV
Energy per atom: Epot =47.791eV Ekin = 5.894eV (T=490.283K) Etot = 53.685eV
Energy per atom: Epot =47.851eV Ekin = 5.831eV (T=485.058K) Etot = 53.682eV
Energy per atom: Epot =48.299eV Ekin = 5.385eV (T=447.980K) Etot = 53.684eV
Energy per atom: Epot =48.633eV Ekin = 5.058eV (T=420.730K) Etot = 53.690eV
Energy per atom: Epot =47.842eV Ekin = 5.844eV (T=486.125K) Etot = 53.686eV
Energy per atom: Epot =48.135eV Ekin = 5.549eV (T=461.588K) Etot = 53.684eV
Energy per atom: Epot =47.841eV Ekin = 5.839eV (T=485.729K) Etot = 53.680eV
Energy per atom: Epot =48.242eV Ekin = 5.437eV (T=452.260K) Etot = 53.678eV
Energy per atom: Epot =47.944eV Ekin = 5.734eV (T=477.031K) Etot = 53.679eV
Energy per atom: Epot =47.758eV Ekin = 5.920eV (T=492.490K) Etot = 53.678eV
Energy per atom: Epot =47.898eV Ekin = 5.781eV (T=480.895K) Etot = 53.679eV
Energy per atom: Epot =48.057eV Ekin = 5.626eV (T=468.038K) Etot = 53.683eV
Energy per atom: Epot =47.950eV Ekin = 5.733eV (T=476.902K) Etot = 53.683eV
Energy per atom: Epot =48.100eV Ekin = 5.585eV (T=464.560K) Etot = 53.685eV
Energy per atom: Epot =48.575eV Ekin = 5.113eV (T=425.369K) Etot = 53.688eV
Energy per atom: Epot =47.925eV Ekin = 5.758eV (T=479.009K) Etot = 53.684eV
Energy per atom: Epot =47.583eV Ekin = 6.094eV (T=506.973K) Etot = 53.678eV
Energy per atom: Epot =47.782eV Ekin = 5.899eV (T=490.725K) Etot = 53.681eV
Energy per atom: Epot =47.942eV Ekin = 5.741eV (T=477.574K) Etot = 53.683eV
Energy per atom: Epot =48.378eV Ekin = 5.308eV (T=441.536K) Etot = 53.685eV
Energy per atom: Epot =48.307eV Ekin = 5.379eV (T=447.439K) Etot = 53.686eV
Energy per atom: Epot =47.746eV Ekin = 5.932eV (T=493.492K) Etot = 53.678eV
Energy per atom: Epot =47.856eV Ekin = 5.821eV (T=484.217K) Etot = 53.677eV
Energy per atom: Epot =48.028eV Ekin = 5.654eV (T=470.320K) Etot = 53.682eV
Energy per atom: Epot =48.445eV Ekin = 5.242eV (T=436.052K) Etot = 53.687eV
Energy per atom: Epot =47.767eV Ekin = 5.915eV (T=492.011K) Etot = 53.681eV
Energy per atom: Epot =47.431eV Ekin = 6.247eV (T=519.678K) Etot = 53.678eV
Energy per atom: Epot =47.752eV Ekin = 5.928eV (T=493.147K) Etot = 53.680eV
Energy per atom: Epot =47.688eV Ekin = 5.992eV (T=498.444K) Etot = 53.680eV
Energy per atom: Epot =47.891eV Ekin = 5.787eV (T=481.439K) Etot = 53.679eV
Energy per atom: Epot =48.425eV Ekin = 5.259eV (T=437.459K) Etot = 53.684eV
Energy per atom: Epot =48.200eV Ekin = 5.482eV (T=456.021K) Etot = 53.682eV
Energy per atom: Epot =48.257eV Ekin = 5.424eV (T=451.221K) Etot = 53.681eV
Energy per atom: Epot =48.067eV Ekin = 5.614eV (T=467.032K) Etot = 53.681eV
Energy per atom: Epot =48.011eV Ekin = 5.672eV (T=471.816K) Etot = 53.683eV
Energy per atom: Epot =47.893eV Ekin = 5.788eV (T=481.452K) Etot = 53.681eV
Energy per atom: Epot =48.097eV Ekin = 5.585eV (T=464.620K) Etot = 53.683eV
Energy per atom: Epot =47.913eV Ekin = 5.772eV (T=480.184K) Etot = 53.685eV
Energy per atom: Epot =48.025eV Ekin = 5.660eV (T=470.854K) Etot = 53.686eV
Energy per atom: Epot =48.108eV Ekin = 5.574eV (T=463.669K) Etot = 53.682eV
Energy per atom: Epot =47.539eV Ekin = 6.141eV (T=510.849K) Etot = 53.680eV
Energy per atom: Epot =48.296eV Ekin = 5.389eV (T=448.283K) Etot = 53.685eV
Energy per atom: Epot =48.202eV Ekin = 5.484eV (T=456.194K) Etot = 53.686eV
Energy per atom: Epot =48.280eV Ekin = 5.404eV (T=449.533K) Etot = 53.684eV
Energy per atom: Epot =48.272eV Ekin = 5.411eV (T=450.097K) Etot = 53.683eV
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?