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 = 153.612eV (T=297.099K) Etot = 151.207eV
Energy per atom: Epot =116.476eV Ekin = 35.513eV (T=68.685K) Etot = 151.989eV
Energy per atom: Epot =77.346eV Ekin = 74.502eV (T=144.094K) Etot = 151.848eV
Energy per atom: Epot =69.528eV Ekin = 82.168eV (T=158.920K) Etot = 151.696eV
Energy per atom: Epot =68.667eV Ekin = 82.982eV (T=160.495K) Etot = 151.649eV
Energy per atom: Epot =81.034eV Ekin = 70.784eV (T=136.902K) Etot = 151.818eV
Energy per atom: Epot =75.841eV Ekin = 75.949eV (T=146.892K) Etot = 151.790eV
Energy per atom: Epot =73.654eV Ekin = 78.067eV (T=150.988K) Etot = 151.720eV
Energy per atom: Epot =71.349eV Ekin = 80.369eV (T=155.441K) Etot = 151.718eV
Energy per atom: Epot =78.967eV Ekin = 72.827eV (T=140.853K) Etot = 151.794eV
Energy per atom: Epot =74.165eV Ekin = 77.588eV (T=150.062K) Etot = 151.752eV
Energy per atom: Epot =74.264eV Ekin = 77.476eV (T=149.845K) Etot = 151.740eV
Energy per atom: Epot =74.255eV Ekin = 77.491eV (T=149.875K) Etot = 151.747eV
Energy per atom: Epot =77.060eV Ekin = 74.704eV (T=144.483K) Etot = 151.764eV
Energy per atom: Epot =73.090eV Ekin = 78.647eV (T=152.111K) Etot = 151.737eV
Energy per atom: Epot =75.104eV Ekin = 76.661eV (T=148.269K) Etot = 151.765eV
Energy per atom: Epot =73.977eV Ekin = 77.768eV (T=150.410K) Etot = 151.745eV
Energy per atom: Epot =76.755eV Ekin = 74.992eV (T=145.041K) Etot = 151.747eV
Energy per atom: Epot =72.558eV Ekin = 79.186eV (T=153.152K) Etot = 151.744eV
Energy per atom: Epot =75.282eV Ekin = 76.472eV (T=147.904K) Etot = 151.755eV
Energy per atom: Epot =77.519eV Ekin = 74.244eV (T=143.595K) Etot = 151.763eV
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 =598.192eV Ekin = 82.490eV (T=159.543K) Etot = 680.682eV
Energy per atom: Epot =669.971eV Ekin = 138.603eV (T=268.071K) Etot = 808.574eV
Energy per atom: Epot =727.815eV Ekin = 198.071eV (T=383.087K) Etot = 925.886eV
Energy per atom: Epot =785.261eV Ekin = 251.708eV (T=486.825K) Etot = 1036.969eV
Energy per atom: Epot =836.134eV Ekin = 301.941eV (T=583.980K) Etot = 1138.075eV
Energy per atom: Epot =886.969eV Ekin = 335.956eV (T=649.768K) Etot = 1222.924eV
Energy per atom: Epot =926.416eV Ekin = 381.307eV (T=737.480K) Etot = 1307.723eV
Energy per atom: Epot =965.250eV Ekin = 412.740eV (T=798.275K) Etot = 1377.990eV
Energy per atom: Epot =1001.044eV Ekin = 438.523eV (T=848.141K) Etot = 1439.567eV
Energy per atom: Epot =1033.627eV Ekin = 461.234eV (T=892.067K) Etot = 1494.861eV
Energy per atom: Epot =1067.713eV Ekin = 480.230eV (T=928.807K) Etot = 1547.944eV
Energy per atom: Epot =1095.927eV Ekin = 501.406eV (T=969.762K) Etot = 1597.332eV
Energy per atom: Epot =1121.472eV Ekin = 520.132eV (T=1005.981K) Etot = 1641.604eV
Energy per atom: Epot =1154.223eV Ekin = 537.233eV (T=1039.056K) Etot = 1691.457eV
Energy per atom: Epot =1187.805eV Ekin = 544.341eV (T=1052.802K) Etot = 1732.146eV
Energy per atom: Epot =1215.118eV Ekin = 554.900eV (T=1073.225K) Etot = 1770.018eV
Energy per atom: Epot =1237.695eV Ekin = 576.608eV (T=1115.210K) Etot = 1814.303eV
Energy per atom: Epot =1266.399eV Ekin = 586.472eV (T=1134.287K) Etot = 1852.871eV
Energy per atom: Epot =1285.926eV Ekin = 593.414eV (T=1147.715K) Etot = 1879.341eV
Energy per atom: Epot =1307.883eV Ekin = 608.047eV (T=1176.016K) Etot = 1915.930eV
Energy per atom: Epot =1336.640eV Ekin = 612.172eV (T=1183.995K) Etot = 1948.812eV
Energy per atom: Epot =1345.319eV Ekin = 634.725eV (T=1227.613K) Etot = 1980.044eV
Energy per atom: Epot =1375.847eV Ekin = 626.841eV (T=1212.364K) Etot = 2002.688eV
Energy per atom: Epot =1385.757eV Ekin = 646.825eV (T=1251.016K) Etot = 2032.582eV
Energy per atom: Epot =1413.112eV Ekin = 641.777eV (T=1241.252K) Etot = 2054.889eV
Energy per atom: Epot =1435.640eV Ekin = 651.943eV (T=1260.914K) Etot = 2087.583eV
Energy per atom: Epot =1440.106eV Ekin = 668.992eV (T=1293.889K) Etot = 2109.098eV
Energy per atom: Epot =1459.462eV Ekin = 675.909eV (T=1307.266K) Etot = 2135.371eV
Energy per atom: Epot =1487.244eV Ekin = 675.319eV (T=1306.126K) Etot = 2162.563eV
Energy per atom: Epot =1495.576eV Ekin = 685.754eV (T=1326.308K) Etot = 2181.331eV
Energy per atom: Epot =1523.754eV Ekin = 679.976eV (T=1315.132K) Etot = 2203.730eV
Energy per atom: Epot =1538.757eV Ekin = 687.105eV (T=1328.921K) Etot = 2225.862eV
Energy per atom: Epot =1552.268eV Ekin = 680.469eV (T=1316.086K) Etot = 2232.737eV
Energy per atom: Epot =1562.250eV Ekin = 696.695eV (T=1347.469K) Etot = 2258.945eV
Energy per atom: Epot =1559.899eV Ekin = 708.882eV (T=1371.040K) Etot = 2268.781eV
Energy per atom: Epot =1578.231eV Ekin = 704.717eV (T=1362.983K) Etot = 2282.948eV
Energy per atom: Epot =1581.238eV Ekin = 711.680eV (T=1376.451K) Etot = 2292.918eV
Energy per atom: Epot =1586.100eV Ekin = 719.103eV (T=1390.807K) Etot = 2305.203eV
Energy per atom: Epot =1594.894eV Ekin = 719.334eV (T=1391.255K) Etot = 2314.228eV
Energy per atom: Epot =1612.232eV Ekin = 710.401eV (T=1373.977K) Etot = 2322.633eV
Energy per atom: Epot =1620.673eV Ekin = 707.396eV (T=1368.166K) Etot = 2328.069eV
Energy per atom: Epot =1631.319eV Ekin = 715.757eV (T=1384.336K) Etot = 2347.075eV
Energy per atom: Epot =1638.170eV Ekin = 715.516eV (T=1383.870K) Etot = 2353.686eV
Energy per atom: Epot =1650.982eV Ekin = 716.740eV (T=1386.238K) Etot = 2367.723eV
Energy per atom: Epot =1655.898eV Ekin = 723.271eV (T=1398.870K) Etot = 2379.170eV
Energy per atom: Epot =1675.207eV Ekin = 709.615eV (T=1372.458K) Etot = 2384.822eV
Energy per atom: Epot =1674.788eV Ekin = 722.116eV (T=1396.634K) Etot = 2396.904eV
Energy per atom: Epot =1681.461eV Ekin = 721.610eV (T=1395.657K) Etot = 2403.071eV
Energy per atom: Epot =1682.967eV Ekin = 728.124eV (T=1408.255K) Etot = 2411.091eV
Energy per atom: Epot =1696.258eV Ekin = 727.012eV (T=1406.105K) Etot = 2423.270eV
Energy per atom: Epot =1717.535eV Ekin = 710.283eV (T=1373.749K) Etot = 2427.818eV
Energy per atom: Epot =1713.885eV Ekin = 731.724eV (T=1415.218K) Etot = 2445.609eV
Energy per atom: Epot =1713.352eV Ekin = 742.459eV (T=1435.980K) Etot = 2455.811eV
Energy per atom: Epot =1720.490eV Ekin = 733.627eV (T=1418.898K) Etot = 2454.117eV
Energy per atom: Epot =1734.545eV Ekin = 731.771eV (T=1415.308K) Etot = 2466.316eV
Energy per atom: Epot =1735.261eV Ekin = 737.609eV (T=1426.599K) Etot = 2472.870eV
Energy per atom: Epot =1731.343eV Ekin = 742.054eV (T=1435.198K) Etot = 2473.397eV
Energy per atom: Epot =1742.338eV Ekin = 737.435eV (T=1426.263K) Etot = 2479.773eV
Energy per atom: Epot =1754.312eV Ekin = 735.980eV (T=1423.450K) Etot = 2490.292eV
Energy per atom: Epot =1760.403eV Ekin = 739.128eV (T=1429.538K) Etot = 2499.531eV
Energy per atom: Epot =1771.010eV Ekin = 734.943eV (T=1421.443K) Etot = 2505.953eV
Energy per atom: Epot =1788.636eV Ekin = 724.934eV (T=1402.085K) Etot = 2513.570eV
Energy per atom: Epot =1798.968eV Ekin = 724.496eV (T=1401.238K) Etot = 2523.464eV
Energy per atom: Epot =1778.564eV Ekin = 746.142eV (T=1443.104K) Etot = 2524.706eV
Energy per atom: Epot =1792.664eV Ekin = 738.382eV (T=1428.094K) Etot = 2531.046eV
Energy per atom: Epot =1809.090eV Ekin = 740.342eV (T=1431.886K) Etot = 2549.432eV
Energy per atom: Epot =1820.894eV Ekin = 732.255eV (T=1416.246K) Etot = 2553.149eV
Energy per atom: Epot =1830.067eV Ekin = 740.023eV (T=1431.270K) Etot = 2570.090eV
Energy per atom: Epot =1836.492eV Ekin = 738.319eV (T=1427.973K) Etot = 2574.811eV
Energy per atom: Epot =1844.002eV Ekin = 730.535eV (T=1412.918K) Etot = 2574.537eV
Energy per atom: Epot =1843.795eV Ekin = 735.995eV (T=1423.478K) Etot = 2579.790eV
Energy per atom: Epot =1854.675eV Ekin = 737.545eV (T=1426.477K) Etot = 2592.220eV
Energy per atom: Epot =1858.383eV Ekin = 742.319eV (T=1435.710K) Etot = 2600.702eV
Energy per atom: Epot =1862.758eV Ekin = 750.895eV (T=1452.297K) Etot = 2613.653eV
Energy per atom: Epot =1872.869eV Ekin = 743.014eV (T=1437.053K) Etot = 2615.883eV
Energy per atom: Epot =1874.027eV Ekin = 754.855eV (T=1459.956K) Etot = 2628.882eV
Energy per atom: Epot =1879.792eV Ekin = 748.561eV (T=1447.782K) Etot = 2628.353eV
Energy per atom: Epot =1867.005eV Ekin = 770.537eV (T=1490.285K) Etot = 2637.542eV
Energy per atom: Epot =1895.665eV Ekin = 744.750eV (T=1440.411K) Etot = 2640.415eV
Energy per atom: Epot =1894.340eV Ekin = 744.617eV (T=1440.154K) Etot = 2638.957eV
Energy per atom: Epot =1882.977eV Ekin = 752.481eV (T=1455.363K) Etot = 2635.457eV
Energy per atom: Epot =1890.856eV Ekin = 753.186eV (T=1456.726K) Etot = 2644.042eV
Energy per atom: Epot =1904.018eV Ekin = 743.124eV (T=1437.266K) Etot = 2647.142eV
Energy per atom: Epot =1896.368eV Ekin = 759.840eV (T=1469.596K) Etot = 2656.208eV
Energy per atom: Epot =1901.470eV Ekin = 763.151eV (T=1476.001K) Etot = 2664.622eV
Energy per atom: Epot =1911.764eV Ekin = 753.347eV (T=1457.040K) Etot = 2665.112eV
Energy per atom: Epot =1915.114eV Ekin = 760.221eV (T=1470.334K) Etot = 2675.335eV
Energy per atom: Epot =1917.599eV Ekin = 757.268eV (T=1464.622K) Etot = 2674.867eV
Energy per atom: Epot =1920.968eV Ekin = 753.710eV (T=1457.740K) Etot = 2674.678eV
Energy per atom: Epot =1913.233eV Ekin = 766.206eV (T=1481.909K) Etot = 2679.439eV
Energy per atom: Epot =1928.606eV Ekin = 754.021eV (T=1458.342K) Etot = 2682.628eV
Energy per atom: Epot =1941.907eV Ekin = 747.870eV (T=1446.445K) Etot = 2689.777eV
Energy per atom: Epot =1926.488eV Ekin = 763.845eV (T=1477.343K) Etot = 2690.334eV
Energy per atom: Epot =1938.809eV Ekin = 753.217eV (T=1456.788K) Etot = 2692.026eV
Energy per atom: Epot =1949.541eV Ekin = 743.969eV (T=1438.901K) Etot = 2693.511eV
Energy per atom: Epot =1940.555eV Ekin = 757.189eV (T=1464.468K) Etot = 2697.743eV
Energy per atom: Epot =1953.849eV Ekin = 746.736eV (T=1444.253K) Etot = 2700.585eV
Energy per atom: Epot =1950.373eV Ekin = 755.655eV (T=1461.503K) Etot = 2706.028eV
Energy per atom: Epot =1945.365eV Ekin = 770.567eV (T=1490.343K) Etot = 2715.932eV
Energy per atom: Epot =1964.339eV Ekin = 759.382eV (T=1468.711K) Etot = 2723.722eV
Energy per atom: Epot =1962.134eV Ekin = 751.331eV (T=1453.139K) Etot = 2713.465eV
Energy per atom: Epot =1956.813eV Ekin = 758.182eV (T=1466.391K) Etot = 2714.996eV
Energy per atom: Epot =1957.894eV Ekin = 758.649eV (T=1467.294K) Etot = 2716.543eV
Energy per atom: Epot =1952.801eV Ekin = 767.370eV (T=1484.160K) Etot = 2720.170eV
Energy per atom: Epot =1958.217eV Ekin = 763.802eV (T=1477.260K) Etot = 2722.019eV
Energy per atom: Epot =1954.346eV Ekin = 772.116eV (T=1493.340K) Etot = 2726.462eV
Energy per atom: Epot =1962.983eV Ekin = 764.145eV (T=1477.923K) Etot = 2727.129eV
Energy per atom: Epot =1959.340eV Ekin = 766.550eV (T=1482.575K) Etot = 2725.890eV
Energy per atom: Epot =1967.610eV Ekin = 760.928eV (T=1471.700K) Etot = 2728.538eV
Energy per atom: Epot =1971.423eV Ekin = 760.908eV (T=1471.663K) Etot = 2732.332eV
Energy per atom: Epot =1975.893eV Ekin = 762.720eV (T=1475.167K) Etot = 2738.613eV
Energy per atom: Epot =1963.000eV Ekin = 770.066eV (T=1489.375K) Etot = 2733.066eV
Energy per atom: Epot =1977.509eV Ekin = 760.293eV (T=1470.473K) Etot = 2737.803eV
Energy per atom: Epot =1985.960eV Ekin = 762.482eV (T=1474.706K) Etot = 2748.442eV
Energy per atom: Epot =1974.153eV Ekin = 775.676eV (T=1500.226K) Etot = 2749.829eV
Energy per atom: Epot =1977.695eV Ekin = 768.635eV (T=1486.606K) Etot = 2746.329eV
Energy per atom: Epot =1986.675eV Ekin = 766.134eV (T=1481.771K) Etot = 2752.810eV
Energy per atom: Epot =1991.952eV Ekin = 770.363eV (T=1489.949K) Etot = 2762.315eV
Energy per atom: Epot =1981.345eV Ekin = 776.570eV (T=1501.954K) Etot = 2757.915eV
Energy per atom: Epot =1998.358eV Ekin = 763.684eV (T=1477.031K) Etot = 2762.042eV
Energy per atom: Epot =1997.214eV Ekin = 761.781eV (T=1473.350K) Etot = 2758.994eV
Energy per atom: Epot =1985.275eV Ekin = 785.985eV (T=1520.163K) Etot = 2771.259eV
Energy per atom: Epot =1996.406eV Ekin = 764.044eV (T=1477.728K) Etot = 2760.451eV
Energy per atom: Epot =1995.822eV Ekin = 763.336eV (T=1476.358K) Etot = 2759.158eV
Energy per atom: Epot =1994.259eV Ekin = 761.368eV (T=1472.552K) Etot = 2755.626eV
Energy per atom: Epot =1997.103eV Ekin = 750.859eV (T=1452.226K) Etot = 2747.962eV
Energy per atom: Epot =1988.535eV Ekin = 761.416eV (T=1472.646K) Etot = 2749.952eV
Energy per atom: Epot =2003.952eV Ekin = 754.388eV (T=1459.052K) Etot = 2758.340eV
Energy per atom: Epot =2013.156eV Ekin = 750.578eV (T=1451.684K) Etot = 2763.735eV
Energy per atom: Epot =2007.761eV Ekin = 769.119eV (T=1487.543K) Etot = 2776.880eV
Energy per atom: Epot =2013.077eV Ekin = 759.327eV (T=1468.605K) Etot = 2772.404eV
Energy per atom: Epot =2001.066eV Ekin = 769.577eV (T=1488.429K) Etot = 2770.643eV
Energy per atom: Epot =2012.092eV Ekin = 750.898eV (T=1452.303K) Etot = 2762.990eV
Energy per atom: Epot =2000.676eV Ekin = 768.366eV (T=1486.087K) Etot = 2769.042eV
Energy per atom: Epot =2012.088eV Ekin = 760.867eV (T=1471.582K) Etot = 2772.954eV
Energy per atom: Epot =2013.318eV Ekin = 760.753eV (T=1471.362K) Etot = 2774.071eV
Energy per atom: Epot =2005.186eV Ekin = 777.059eV (T=1502.899K) Etot = 2782.244eV
Energy per atom: Epot =2008.527eV Ekin = 773.972eV (T=1496.930K) Etot = 2782.500eV
Energy per atom: Epot =2007.341eV Ekin = 768.843eV (T=1487.008K) Etot = 2776.183eV
Energy per atom: Epot =2006.395eV Ekin = 767.146eV (T=1483.728K) Etot = 2773.541eV
Energy per atom: Epot =1992.707eV Ekin = 782.431eV (T=1513.290K) Etot = 2775.138eV
Energy per atom: Epot =2004.260eV Ekin = 769.623eV (T=1488.517K) Etot = 2773.883eV
Energy per atom: Epot =2000.115eV Ekin = 768.727eV (T=1486.784K) Etot = 2768.842eV
Energy per atom: Epot =1982.713eV Ekin = 782.091eV (T=1512.631K) Etot = 2764.803eV
Energy per atom: Epot =1988.560eV Ekin = 775.788eV (T=1500.442K) Etot = 2764.348eV
Energy per atom: Epot =1979.896eV Ekin = 780.599eV (T=1509.746K) Etot = 2760.495eV
Energy per atom: Epot =1978.039eV Ekin = 778.362eV (T=1505.419K) Etot = 2756.401eV
Energy per atom: Epot =1969.449eV Ekin = 783.742eV (T=1515.825K) Etot = 2753.191eV
Energy per atom: Epot =1978.776eV Ekin = 777.521eV (T=1503.794K) Etot = 2756.297eV
Energy per atom: Epot =1986.302eV Ekin = 768.674eV (T=1486.682K) Etot = 2754.976eV
Energy per atom: Epot =1979.172eV Ekin = 777.263eV (T=1503.294K) Etot = 2756.435eV
Energy per atom: Epot =1970.519eV Ekin = 787.025eV (T=1522.174K) Etot = 2757.544eV
Energy per atom: Epot =1992.519eV Ekin = 763.088eV (T=1475.878K) Etot = 2755.607eV
Energy per atom: Epot =1991.515eV Ekin = 764.918eV (T=1479.418K) Etot = 2756.432eV
Energy per atom: Epot =1994.878eV Ekin = 758.213eV (T=1466.450K) Etot = 2753.091eV
Energy per atom: Epot =1990.741eV Ekin = 762.963eV (T=1475.636K) Etot = 2753.703eV
Energy per atom: Epot =1990.894eV Ekin = 767.197eV (T=1483.825K) Etot = 2758.091eV
Energy per atom: Epot =1989.381eV Ekin = 771.393eV (T=1491.940K) Etot = 2760.774eV
Energy per atom: Epot =1986.203eV Ekin = 777.959eV (T=1504.640K) Etot = 2764.162eV
Energy per atom: Epot =1987.731eV Ekin = 776.873eV (T=1502.539K) Etot = 2764.603eV
Energy per atom: Epot =1980.923eV Ekin = 773.534eV (T=1496.082K) Etot = 2754.457eV
Energy per atom: Epot =1989.089eV Ekin = 769.638eV (T=1488.547K) Etot = 2758.727eV
Energy per atom: Epot =1991.022eV Ekin = 767.744eV (T=1484.884K) Etot = 2758.766eV
Energy per atom: Epot =1977.157eV Ekin = 785.804eV (T=1519.813K) Etot = 2762.961eV
Energy per atom: Epot =1995.886eV Ekin = 762.937eV (T=1475.587K) Etot = 2758.824eV
Energy per atom: Epot =1994.720eV Ekin = 765.766eV (T=1481.058K) Etot = 2760.486eV
Energy per atom: Epot =1997.875eV Ekin = 777.999eV (T=1504.717K) Etot = 2775.874eV
Energy per atom: Epot =1995.723eV Ekin = 770.871eV (T=1490.932K) Etot = 2766.595eV
Energy per atom: Epot =1996.568eV Ekin = 770.480eV (T=1490.175K) Etot = 2767.047eV
Energy per atom: Epot =1992.183eV Ekin = 770.036eV (T=1489.317K) Etot = 2762.219eV
Energy per atom: Epot =1994.064eV Ekin = 774.662eV (T=1498.264K) Etot = 2768.726eV
Energy per atom: Epot =1992.889eV Ekin = 767.013eV (T=1483.470K) Etot = 2759.902eV
Energy per atom: Epot =2013.317eV Ekin = 750.395eV (T=1451.330K) Etot = 2763.712eV
Energy per atom: Epot =2003.045eV Ekin = 755.739eV (T=1461.665K) Etot = 2758.784eV
Energy per atom: Epot =1998.428eV Ekin = 764.910eV (T=1479.402K) Etot = 2763.338eV
Energy per atom: Epot =1994.347eV Ekin = 768.200eV (T=1485.766K) Etot = 2762.547eV
Energy per atom: Epot =1972.574eV Ekin = 781.899eV (T=1512.261K) Etot = 2754.473eV
Energy per atom: Epot =1986.784eV Ekin = 770.715eV (T=1490.631K) Etot = 2757.499eV
Energy per atom: Epot =1983.750eV Ekin = 777.294eV (T=1503.355K) Etot = 2761.044eV
Energy per atom: Epot =1991.449eV Ekin = 765.397eV (T=1480.345K) Etot = 2756.846eV
Energy per atom: Epot =2000.725eV Ekin = 759.988eV (T=1469.884K) Etot = 2760.713eV
Energy per atom: Epot =1987.254eV Ekin = 773.265eV (T=1495.562K) Etot = 2760.519eV
Energy per atom: Epot =1999.365eV Ekin = 767.162eV (T=1483.758K) Etot = 2766.527eV
Energy per atom: Epot =1980.842eV Ekin = 785.596eV (T=1519.412K) Etot = 2766.438eV
Energy per atom: Epot =1980.169eV Ekin = 788.020eV (T=1524.098K) Etot = 2768.189eV
Energy per atom: Epot =1990.659eV Ekin = 773.565eV (T=1496.141K) Etot = 2764.224eV
Energy per atom: Epot =1976.209eV Ekin = 788.155eV (T=1524.360K) Etot = 2764.364eV
Energy per atom: Epot =1986.460eV Ekin = 770.376eV (T=1489.975K) Etot = 2756.836eV
Energy per atom: Epot =1979.846eV Ekin = 771.850eV (T=1492.825K) Etot = 2751.696eV
Energy per atom: Epot =1979.132eV Ekin = 765.356eV (T=1480.266K) Etot = 2744.489eV
Energy per atom: Epot =1984.595eV Ekin = 762.234eV (T=1474.226K) Etot = 2746.828eV
Energy per atom: Epot =1988.665eV Ekin = 764.475eV (T=1478.561K) Etot = 2753.140eV
Energy per atom: Epot =1977.082eV Ekin = 784.753eV (T=1517.781K) Etot = 2761.836eV
Energy per atom: Epot =1982.407eV Ekin = 773.107eV (T=1495.256K) Etot = 2755.514eV
Energy per atom: Epot =1979.469eV Ekin = 778.155eV (T=1505.020K) Etot = 2757.625eV
Energy per atom: Epot =1976.060eV Ekin = 775.684eV (T=1500.241K) Etot = 2751.744eV
Energy per atom: Epot =1975.276eV Ekin = 772.601eV (T=1494.277K) Etot = 2747.877eV
Energy per atom: Epot =1978.384eV Ekin = 767.040eV (T=1483.521K) Etot = 2745.424eV
Energy per atom: Epot =1982.069eV Ekin = 757.845eV (T=1465.739K) Etot = 2739.914eV
Energy per atom: Epot =1984.335eV Ekin = 759.610eV (T=1469.152K) Etot = 2743.945eV
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] 10:10:29 43.457006 1.0818
BFGSLineSearch: 1[ 1] 10:10:29 42.347659 0.2273
BFGSLineSearch: 2[ 2] 10:10:29 42.108454 0.1349
BFGSLineSearch: 3[ 3] 10:10:29 41.964817 0.1138
BFGSLineSearch: 4[ 4] 10:10:29 41.924933 0.0683
BFGSLineSearch: 5[ 5] 10:10:29 41.915346 0.0225
BFGSLineSearch: 6[ 6] 10:10:29 41.914920 0.0059
BFGSLineSearch: 7[ 7] 10:10:29 41.914872 0.0023
BFGSLineSearch: 8[ 9] 10:10:29 41.914855 0.0023
BFGSLineSearch: 9[ 10] 10:10:29 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 13.876eV (T=1154.311K) Etot = 55.791eV
Energy per atom: Epot =49.574eV Ekin = 6.251eV (T=520.040K) Etot = 55.825eV
Energy per atom: Epot =50.106eV Ekin = 5.729eV (T=476.548K) Etot = 55.834eV
Energy per atom: Epot =50.503eV Ekin = 5.334eV (T=443.696K) Etot = 55.837eV
Energy per atom: Epot =50.053eV Ekin = 5.779eV (T=480.723K) Etot = 55.832eV
Energy per atom: Epot =49.447eV Ekin = 6.383eV (T=530.943K) Etot = 55.830eV
Energy per atom: Epot =48.742eV Ekin = 7.083eV (T=589.210K) Etot = 55.825eV
Energy per atom: Epot =48.061eV Ekin = 7.764eV (T=645.881K) Etot = 55.825eV
Energy per atom: Epot =48.498eV Ekin = 7.329eV (T=609.679K) Etot = 55.827eV
Energy per atom: Epot =50.324eV Ekin = 5.511eV (T=458.443K) Etot = 55.835eV
Energy per atom: Epot =49.612eV Ekin = 6.223eV (T=517.641K) Etot = 55.835eV
Energy per atom: Epot =49.727eV Ekin = 6.106eV (T=507.963K) Etot = 55.833eV
Energy per atom: Epot =49.946eV Ekin = 5.888eV (T=489.812K) Etot = 55.834eV
Energy per atom: Epot =49.155eV Ekin = 6.676eV (T=555.368K) Etot = 55.831eV
Energy per atom: Epot =48.211eV Ekin = 7.618eV (T=633.695K) Etot = 55.828eV
Energy per atom: Epot =48.745eV Ekin = 7.083eV (T=589.204K) Etot = 55.828eV
Energy per atom: Epot =49.654eV Ekin = 6.177eV (T=513.815K) Etot = 55.831eV
Energy per atom: Epot =49.072eV Ekin = 6.757eV (T=562.118K) Etot = 55.829eV
Energy per atom: Epot =48.778eV Ekin = 7.048eV (T=586.266K) Etot = 55.826eV
Energy per atom: Epot =49.763eV Ekin = 6.071eV (T=505.017K) Etot = 55.834eV
Energy per atom: Epot =49.455eV Ekin = 6.379eV (T=530.612K) Etot = 55.833eV
Energy per atom: Epot =48.826eV Ekin = 7.004eV (T=582.677K) Etot = 55.830eV
Energy per atom: Epot =49.618eV Ekin = 6.215eV (T=517.024K) Etot = 55.834eV
Energy per atom: Epot =49.271eV Ekin = 6.558eV (T=545.566K) Etot = 55.829eV
Energy per atom: Epot =49.411eV Ekin = 6.417eV (T=533.830K) Etot = 55.829eV
Energy per atom: Epot =50.159eV Ekin = 5.676eV (T=472.165K) Etot = 55.835eV
Energy per atom: Epot =49.562eV Ekin = 6.269eV (T=521.488K) Etot = 55.831eV
Energy per atom: Epot =48.767eV Ekin = 7.060eV (T=587.284K) Etot = 55.826eV
Energy per atom: Epot =49.756eV Ekin = 6.081eV (T=505.871K) Etot = 55.837eV
Energy per atom: Epot =50.368eV Ekin = 5.474eV (T=455.397K) Etot = 55.843eV
Energy per atom: Epot =49.180eV Ekin = 6.652eV (T=553.390K) Etot = 55.832eV
Energy per atom: Epot =49.911eV Ekin = 5.926eV (T=492.969K) Etot = 55.837eV
Energy per atom: Epot =49.194eV Ekin = 6.637eV (T=552.150K) Etot = 55.831eV
Energy per atom: Epot =49.060eV Ekin = 6.768eV (T=562.985K) Etot = 55.828eV
Energy per atom: Epot =49.754eV Ekin = 6.080eV (T=505.794K) Etot = 55.834eV
Energy per atom: Epot =49.144eV Ekin = 6.691eV (T=556.564K) Etot = 55.835eV
Energy per atom: Epot =49.278eV Ekin = 6.558eV (T=545.499K) Etot = 55.836eV
Energy per atom: Epot =48.982eV Ekin = 6.847eV (T=569.573K) Etot = 55.829eV
Energy per atom: Epot =49.111eV Ekin = 6.717eV (T=558.767K) Etot = 55.828eV
Energy per atom: Epot =48.845eV Ekin = 6.981eV (T=580.725K) Etot = 55.826eV
Energy per atom: Epot =49.519eV Ekin = 6.311eV (T=524.992K) Etot = 55.830eV
Energy per atom: Epot =48.723eV Ekin = 7.100eV (T=590.661K) Etot = 55.823eV
Energy per atom: Epot =49.758eV Ekin = 6.072eV (T=505.135K) Etot = 55.830eV
Energy per atom: Epot =50.387eV Ekin = 5.449eV (T=453.271K) Etot = 55.836eV
Energy per atom: Epot =49.094eV Ekin = 6.739eV (T=560.602K) Etot = 55.833eV
Energy per atom: Epot =49.485eV Ekin = 6.349eV (T=528.131K) Etot = 55.834eV
Energy per atom: Epot =49.101eV Ekin = 6.730eV (T=559.864K) Etot = 55.831eV
Energy per atom: Epot =49.283eV Ekin = 6.548eV (T=544.667K) Etot = 55.831eV
Energy per atom: Epot =48.999eV Ekin = 6.829eV (T=568.102K) Etot = 55.828eV
Energy per atom: Epot =49.090eV Ekin = 6.744eV (T=561.036K) Etot = 55.834eV
Energy per atom: Epot =48.744eV Ekin = 7.088eV (T=589.633K) Etot = 55.832eV
Energy per atom: Epot =49.055eV Ekin = 6.778eV (T=563.799K) Etot = 55.833eV
Energy per atom: Epot =49.291eV Ekin = 6.543eV (T=544.306K) Etot = 55.834eV
Energy per atom: Epot =49.830eV Ekin = 6.006eV (T=499.605K) Etot = 55.836eV
Energy per atom: Epot =50.240eV Ekin = 5.596eV (T=465.516K) Etot = 55.836eV
Energy per atom: Epot =49.805eV Ekin = 6.028eV (T=501.477K) Etot = 55.833eV
Energy per atom: Epot =49.566eV Ekin = 6.268eV (T=521.425K) Etot = 55.834eV
Energy per atom: Epot =48.664eV Ekin = 7.166eV (T=596.114K) Etot = 55.830eV
Energy per atom: Epot =48.740eV Ekin = 7.090eV (T=589.775K) Etot = 55.830eV
Energy per atom: Epot =49.396eV Ekin = 6.434eV (T=535.237K) Etot = 55.830eV
Energy per atom: Epot =49.094eV Ekin = 6.737eV (T=560.406K) Etot = 55.831eV
Energy per atom: Epot =49.178eV Ekin = 6.658eV (T=553.889K) Etot = 55.836eV
Energy per atom: Epot =49.532eV Ekin = 6.301eV (T=524.197K) Etot = 55.833eV
Energy per atom: Epot =49.697eV Ekin = 6.136eV (T=510.446K) Etot = 55.833eV
Energy per atom: Epot =48.896eV Ekin = 6.934eV (T=576.809K) Etot = 55.830eV
Energy per atom: Epot =48.459eV Ekin = 7.367eV (T=612.862K) Etot = 55.826eV
Energy per atom: Epot =49.438eV Ekin = 6.393eV (T=531.832K) Etot = 55.831eV
Energy per atom: Epot =49.824eV Ekin = 6.008eV (T=499.822K) Etot = 55.833eV
Energy per atom: Epot =49.485eV Ekin = 6.348eV (T=528.093K) Etot = 55.833eV
Energy per atom: Epot =49.612eV Ekin = 6.221eV (T=517.536K) Etot = 55.833eV
Energy per atom: Epot =49.706eV Ekin = 6.124eV (T=509.465K) Etot = 55.830eV
Energy per atom: Epot =49.785eV Ekin = 6.045eV (T=502.864K) Etot = 55.830eV
Energy per atom: Epot =49.181eV Ekin = 6.647eV (T=552.977K) Etot = 55.828eV
Energy per atom: Epot =49.902eV Ekin = 5.934eV (T=493.633K) Etot = 55.836eV
Energy per atom: Epot =49.539eV Ekin = 6.300eV (T=524.089K) Etot = 55.839eV
Energy per atom: Epot =49.280eV Ekin = 6.556eV (T=545.404K) Etot = 55.836eV
Energy per atom: Epot =49.104eV Ekin = 6.730eV (T=559.830K) Etot = 55.834eV
Energy per atom: Epot =49.735eV Ekin = 6.101eV (T=507.558K) Etot = 55.837eV
Energy per atom: Epot =48.748eV Ekin = 7.080eV (T=588.992K) Etot = 55.829eV
Energy per atom: Epot =49.212eV Ekin = 6.621eV (T=550.755K) Etot = 55.833eV
Energy per atom: Epot =49.570eV Ekin = 6.260eV (T=520.744K) Etot = 55.830eV
Energy per atom: Epot =48.966eV Ekin = 6.865eV (T=571.061K) Etot = 55.831eV
Energy per atom: Epot =48.660eV Ekin = 7.172eV (T=596.633K) Etot = 55.832eV
Energy per atom: Epot =48.840eV Ekin = 6.987eV (T=581.209K) Etot = 55.826eV
Energy per atom: Epot =49.014eV Ekin = 6.816eV (T=566.978K) Etot = 55.830eV
Energy per atom: Epot =48.799eV Ekin = 7.028eV (T=584.596K) Etot = 55.827eV
Energy per atom: Epot =49.917eV Ekin = 5.914eV (T=492.006K) Etot = 55.831eV
Energy per atom: Epot =49.713eV Ekin = 6.123eV (T=509.345K) Etot = 55.836eV
Energy per atom: Epot =49.439eV Ekin = 6.397eV (T=532.110K) Etot = 55.835eV
Energy per atom: Epot =49.116eV Ekin = 6.714eV (T=558.518K) Etot = 55.830eV
Energy per atom: Epot =48.939eV Ekin = 6.888eV (T=572.965K) Etot = 55.827eV
Energy per atom: Epot =49.420eV Ekin = 6.408eV (T=533.046K) Etot = 55.828eV
Energy per atom: Epot =49.449eV Ekin = 6.386eV (T=531.199K) Etot = 55.835eV
Energy per atom: Epot =48.604eV Ekin = 7.225eV (T=601.005K) Etot = 55.829eV
Energy per atom: Epot =49.854eV Ekin = 5.979eV (T=497.354K) Etot = 55.832eV
Energy per atom: Epot =49.420eV Ekin = 6.412eV (T=533.393K) Etot = 55.832eV
Energy per atom: Epot =49.517eV Ekin = 6.316eV (T=525.406K) Etot = 55.833eV
Energy per atom: Epot =49.323eV Ekin = 6.509eV (T=541.495K) Etot = 55.832eV
Energy per atom: Epot =49.509eV Ekin = 6.321eV (T=525.819K) Etot = 55.830eV
Energy per atom: Epot =49.813eV Ekin = 6.021eV (T=500.905K) Etot = 55.834eV
Energy per atom: Epot =49.473eV Ekin = 6.356eV (T=528.774K) Etot = 55.829eV
Energy per atom: Epot =49.324eV Ekin = 6.507eV (T=541.296K) Etot = 55.831eV
Energy per atom: Epot =49.003eV Ekin = 6.831eV (T=568.214K) Etot = 55.834eV
Energy per atom: Epot =49.355eV Ekin = 6.480eV (T=539.021K) Etot = 55.835eV
Energy per atom: Epot =49.277eV Ekin = 6.560eV (T=545.710K) Etot = 55.837eV
Energy per atom: Epot =50.154eV Ekin = 5.680eV (T=472.502K) Etot = 55.835eV
Energy per atom: Epot =49.376eV Ekin = 6.451eV (T=536.672K) Etot = 55.827eV
Energy per atom: Epot =50.118eV Ekin = 5.720eV (T=475.865K) Etot = 55.838eV
Energy per atom: Epot =49.556eV Ekin = 6.279eV (T=522.291K) Etot = 55.834eV
Energy per atom: Epot =49.527eV Ekin = 6.306eV (T=524.585K) Etot = 55.833eV
Energy per atom: Epot =49.340eV Ekin = 6.493eV (T=540.126K) Etot = 55.833eV
Energy per atom: Epot =49.496eV Ekin = 6.341eV (T=527.450K) Etot = 55.836eV
Energy per atom: Epot =48.977eV Ekin = 6.862eV (T=570.812K) Etot = 55.839eV
Energy per atom: Epot =48.839eV Ekin = 6.995eV (T=581.870K) Etot = 55.834eV
Energy per atom: Epot =49.457eV Ekin = 6.379eV (T=530.610K) Etot = 55.836eV
Energy per atom: Epot =48.899eV Ekin = 6.930eV (T=576.461K) Etot = 55.828eV
Energy per atom: Epot =48.532eV Ekin = 7.294eV (T=606.737K) Etot = 55.826eV
Energy per atom: Epot =49.990eV Ekin = 5.843eV (T=486.028K) Etot = 55.833eV
Energy per atom: Epot =50.059eV Ekin = 5.777eV (T=480.565K) Etot = 55.836eV
Energy per atom: Epot =49.497eV Ekin = 6.338eV (T=527.202K) Etot = 55.834eV
Energy per atom: Epot =49.412eV Ekin = 6.419eV (T=533.944K) Etot = 55.831eV
Energy per atom: Epot =48.928eV Ekin = 6.904eV (T=574.300K) Etot = 55.831eV
Energy per atom: Epot =48.895eV Ekin = 6.937eV (T=577.034K) Etot = 55.831eV
Energy per atom: Epot =48.533eV Ekin = 7.293eV (T=606.682K) Etot = 55.826eV
Energy per atom: Epot =49.225eV Ekin = 6.607eV (T=549.573K) Etot = 55.832eV
Energy per atom: Epot =49.663eV Ekin = 6.173eV (T=513.533K) Etot = 55.837eV
Energy per atom: Epot =48.877eV Ekin = 6.953eV (T=578.399K) Etot = 55.830eV
Energy per atom: Epot =48.774eV Ekin = 7.057eV (T=587.050K) Etot = 55.831eV
Energy per atom: Epot =49.492eV Ekin = 6.341eV (T=527.499K) Etot = 55.833eV
Energy per atom: Epot =50.358eV Ekin = 5.476eV (T=455.550K) Etot = 55.835eV
Energy per atom: Epot =50.572eV Ekin = 5.265eV (T=437.968K) Etot = 55.836eV
Energy per atom: Epot =49.776eV Ekin = 6.057eV (T=503.897K) Etot = 55.834eV
Energy per atom: Epot =50.138eV Ekin = 5.705eV (T=474.547K) Etot = 55.843eV
Energy per atom: Epot =48.345eV Ekin = 7.487eV (T=622.811K) Etot = 55.832eV
Energy per atom: Epot =49.535eV Ekin = 6.298eV (T=523.887K) Etot = 55.833eV
Energy per atom: Epot =49.157eV Ekin = 6.671eV (T=554.918K) Etot = 55.828eV
Energy per atom: Epot =48.771eV Ekin = 7.057eV (T=587.085K) Etot = 55.829eV
Energy per atom: Epot =49.472eV Ekin = 6.364eV (T=529.404K) Etot = 55.836eV
Energy per atom: Epot =50.219eV Ekin = 5.621eV (T=467.558K) Etot = 55.839eV
Energy per atom: Epot =49.683eV Ekin = 6.150eV (T=511.634K) Etot = 55.833eV
Energy per atom: Epot =49.105eV Ekin = 6.725eV (T=559.400K) Etot = 55.830eV
Energy per atom: Epot =49.387eV Ekin = 6.447eV (T=536.274K) Etot = 55.833eV
Energy per atom: Epot =49.112eV Ekin = 6.719eV (T=558.896K) Etot = 55.831eV
Energy per atom: Epot =49.908eV Ekin = 5.920eV (T=492.463K) Etot = 55.828eV
Energy per atom: Epot =50.675eV Ekin = 5.161eV (T=429.350K) Etot = 55.836eV
Energy per atom: Epot =50.411eV Ekin = 5.423eV (T=451.143K) Etot = 55.835eV
Energy per atom: Epot =49.148eV Ekin = 6.678eV (T=555.519K) Etot = 55.826eV
Energy per atom: Epot =49.348eV Ekin = 6.480eV (T=539.029K) Etot = 55.828eV
Energy per atom: Epot =49.039eV Ekin = 6.787eV (T=564.547K) Etot = 55.826eV
Energy per atom: Epot =49.819eV Ekin = 6.016eV (T=500.463K) Etot = 55.835eV
Energy per atom: Epot =50.093eV Ekin = 5.741eV (T=477.615K) Etot = 55.835eV
Energy per atom: Epot =49.958eV Ekin = 5.875eV (T=488.748K) Etot = 55.834eV
Energy per atom: Epot =49.334eV Ekin = 6.497eV (T=540.451K) Etot = 55.831eV
Energy per atom: Epot =49.566eV Ekin = 6.268eV (T=521.376K) Etot = 55.833eV
Energy per atom: Epot =49.561eV Ekin = 6.271eV (T=521.689K) Etot = 55.832eV
Energy per atom: Epot =49.538eV Ekin = 6.291eV (T=523.356K) Etot = 55.829eV
Energy per atom: Epot =49.371eV Ekin = 6.457eV (T=537.152K) Etot = 55.828eV
Energy per atom: Epot =49.629eV Ekin = 6.205eV (T=516.163K) Etot = 55.834eV
Energy per atom: Epot =50.652eV Ekin = 5.185eV (T=431.307K) Etot = 55.837eV
Energy per atom: Epot =49.857eV Ekin = 5.979eV (T=497.334K) Etot = 55.835eV
Energy per atom: Epot =49.151eV Ekin = 6.683eV (T=555.918K) Etot = 55.834eV
Energy per atom: Epot =49.607eV Ekin = 6.228eV (T=518.119K) Etot = 55.835eV
Energy per atom: Epot =49.687eV Ekin = 6.153eV (T=511.832K) Etot = 55.840eV
Energy per atom: Epot =48.525eV Ekin = 7.310eV (T=608.052K) Etot = 55.835eV
Energy per atom: Epot =48.991eV Ekin = 6.841eV (T=569.120K) Etot = 55.832eV
Energy per atom: Epot =49.090eV Ekin = 6.742eV (T=560.860K) Etot = 55.832eV
Energy per atom: Epot =49.548eV Ekin = 6.284eV (T=522.739K) Etot = 55.832eV
Energy per atom: Epot =49.485eV Ekin = 6.347eV (T=528.007K) Etot = 55.832eV
Energy per atom: Epot =50.251eV Ekin = 5.585eV (T=464.568K) Etot = 55.836eV
Energy per atom: Epot =49.746eV Ekin = 6.082eV (T=505.923K) Etot = 55.828eV
Energy per atom: Epot =49.391eV Ekin = 6.439eV (T=535.649K) Etot = 55.830eV
Energy per atom: Epot =49.446eV Ekin = 6.386eV (T=531.211K) Etot = 55.832eV
Energy per atom: Epot =49.501eV Ekin = 6.334eV (T=526.881K) Etot = 55.835eV
Energy per atom: Epot =49.440eV Ekin = 6.393eV (T=531.814K) Etot = 55.833eV
Energy per atom: Epot =49.197eV Ekin = 6.636eV (T=551.993K) Etot = 55.832eV
Energy per atom: Epot =49.180eV Ekin = 6.652eV (T=553.375K) Etot = 55.832eV
Energy per atom: Epot =49.193eV Ekin = 6.637eV (T=552.131K) Etot = 55.830eV
Energy per atom: Epot =49.280eV Ekin = 6.550eV (T=544.882K) Etot = 55.831eV
Energy per atom: Epot =49.353eV Ekin = 6.480eV (T=539.020K) Etot = 55.833eV
Energy per atom: Epot =49.184eV Ekin = 6.648eV (T=553.015K) Etot = 55.832eV
Energy per atom: Epot =49.828eV Ekin = 6.007eV (T=499.733K) Etot = 55.836eV
Energy per atom: Epot =49.419eV Ekin = 6.416eV (T=533.689K) Etot = 55.834eV
Energy per atom: Epot =49.233eV Ekin = 6.599eV (T=548.975K) Etot = 55.832eV
Energy per atom: Epot =48.929eV Ekin = 6.895eV (T=573.587K) Etot = 55.824eV
Energy per atom: Epot =49.894eV Ekin = 5.939eV (T=494.004K) Etot = 55.833eV
Energy per atom: Epot =49.059eV Ekin = 6.771eV (T=563.216K) Etot = 55.829eV
Energy per atom: Epot =49.371eV Ekin = 6.463eV (T=537.667K) Etot = 55.834eV
Energy per atom: Epot =49.819eV Ekin = 6.018eV (T=500.648K) Etot = 55.838eV
Energy per atom: Epot =48.460eV Ekin = 7.367eV (T=612.834K) Etot = 55.827eV
Energy per atom: Epot =49.857eV Ekin = 5.978eV (T=497.268K) Etot = 55.835eV
Energy per atom: Epot =49.756eV Ekin = 6.079eV (T=505.671K) Etot = 55.834eV
Energy per atom: Epot =48.420eV Ekin = 7.403eV (T=615.844K) Etot = 55.823eV
Energy per atom: Epot =49.600eV Ekin = 6.230eV (T=518.242K) Etot = 55.830eV
Energy per atom: Epot =49.323eV Ekin = 6.503eV (T=540.961K) Etot = 55.826eV
Energy per atom: Epot =49.653eV Ekin = 6.179eV (T=514.014K) Etot = 55.832eV
Energy per atom: Epot =49.584eV Ekin = 6.251eV (T=519.973K) Etot = 55.834eV
Energy per atom: Epot =50.000eV Ekin = 5.834eV (T=485.314K) Etot = 55.834eV
Energy per atom: Epot =50.607eV Ekin = 5.233eV (T=435.275K) Etot = 55.839eV
Energy per atom: Epot =50.012eV Ekin = 5.825eV (T=484.580K) Etot = 55.837eV
Energy per atom: Epot =49.187eV Ekin = 6.641eV (T=552.478K) Etot = 55.828eV
Energy per atom: Epot =48.994eV Ekin = 6.834eV (T=568.493K) Etot = 55.828eV
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?