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 = 158.622eV (T=306.789K) Etot = 156.218eV
Energy per atom: Epot =119.719eV Ekin = 37.301eV (T=72.143K) Etot = 157.020eV
Energy per atom: Epot =81.302eV Ekin = 75.588eV (T=146.195K) Etot = 156.891eV
Energy per atom: Epot =71.793eV Ekin = 84.933eV (T=164.268K) Etot = 156.726eV
Energy per atom: Epot =70.830eV Ekin = 85.844eV (T=166.030K) Etot = 156.674eV
Energy per atom: Epot =82.532eV Ekin = 74.315eV (T=143.731K) Etot = 156.847eV
Energy per atom: Epot =78.955eV Ekin = 77.874eV (T=150.614K) Etot = 156.829eV
Energy per atom: Epot =76.247eV Ekin = 80.500eV (T=155.693K) Etot = 156.746eV
Energy per atom: Epot =73.322eV Ekin = 83.417eV (T=161.336K) Etot = 156.739eV
Energy per atom: Epot =81.273eV Ekin = 75.550eV (T=146.121K) Etot = 156.824eV
Energy per atom: Epot =77.872eV Ekin = 78.918eV (T=152.633K) Etot = 156.789eV
Energy per atom: Epot =75.291eV Ekin = 81.472eV (T=157.575K) Etot = 156.763eV
Energy per atom: Epot =77.427eV Ekin = 79.352eV (T=153.474K) Etot = 156.779eV
Energy per atom: Epot =78.864eV Ekin = 77.923eV (T=150.709K) Etot = 156.787eV
Energy per atom: Epot =76.726eV Ekin = 80.051eV (T=154.825K) Etot = 156.777eV
Energy per atom: Epot =77.236eV Ekin = 79.554eV (T=153.865K) Etot = 156.790eV
Energy per atom: Epot =75.780eV Ekin = 80.987eV (T=156.636K) Etot = 156.767eV
Energy per atom: Epot =79.190eV Ekin = 77.590eV (T=150.066K) Etot = 156.780eV
Energy per atom: Epot =76.641eV Ekin = 80.142eV (T=155.002K) Etot = 156.783eV
Energy per atom: Epot =76.284eV Ekin = 80.485eV (T=155.666K) Etot = 156.769eV
Energy per atom: Epot =80.586eV Ekin = 76.211eV (T=147.399K) Etot = 156.797eV
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 =599.025eV Ekin = 80.269eV (T=155.248K) Etot = 679.294eV
Energy per atom: Epot =667.632eV Ekin = 140.747eV (T=272.218K) Etot = 808.380eV
Energy per atom: Epot =728.836eV Ekin = 195.984eV (T=379.050K) Etot = 924.820eV
Energy per atom: Epot =780.872eV Ekin = 250.061eV (T=483.639K) Etot = 1030.932eV
Energy per atom: Epot =829.368eV Ekin = 302.291eV (T=584.657K) Etot = 1131.659eV
Energy per atom: Epot =878.144eV Ekin = 345.376eV (T=667.988K) Etot = 1223.520eV
Energy per atom: Epot =916.561eV Ekin = 388.031eV (T=750.486K) Etot = 1304.592eV
Energy per atom: Epot =972.857eV Ekin = 409.833eV (T=792.654K) Etot = 1382.690eV
Energy per atom: Epot =1004.028eV Ekin = 440.334eV (T=851.645K) Etot = 1444.362eV
Energy per atom: Epot =1037.810eV Ekin = 471.891eV (T=912.678K) Etot = 1509.700eV
Energy per atom: Epot =1078.641eV Ekin = 485.479eV (T=938.958K) Etot = 1564.119eV
Energy per atom: Epot =1107.238eV Ekin = 506.856eV (T=980.304K) Etot = 1614.094eV
Energy per atom: Epot =1144.989eV Ekin = 523.962eV (T=1013.389K) Etot = 1668.952eV
Energy per atom: Epot =1181.508eV Ekin = 547.390eV (T=1058.700K) Etot = 1728.898eV
Energy per atom: Epot =1205.523eV Ekin = 567.171eV (T=1096.958K) Etot = 1772.694eV
Energy per atom: Epot =1242.692eV Ekin = 563.439eV (T=1089.739K) Etot = 1806.130eV
Energy per atom: Epot =1251.933eV Ekin = 590.634eV (T=1142.338K) Etot = 1842.567eV
Energy per atom: Epot =1285.276eV Ekin = 602.851eV (T=1165.966K) Etot = 1888.127eV
Energy per atom: Epot =1317.386eV Ekin = 601.356eV (T=1163.074K) Etot = 1918.741eV
Energy per atom: Epot =1346.851eV Ekin = 611.551eV (T=1182.792K) Etot = 1958.402eV
Energy per atom: Epot =1363.919eV Ekin = 627.271eV (T=1213.196K) Etot = 1991.190eV
Energy per atom: Epot =1395.367eV Ekin = 627.013eV (T=1212.698K) Etot = 2022.380eV
Energy per atom: Epot =1400.869eV Ekin = 642.389eV (T=1242.436K) Etot = 2043.258eV
Energy per atom: Epot =1423.505eV Ekin = 644.506eV (T=1246.530K) Etot = 2068.011eV
Energy per atom: Epot =1440.179eV Ekin = 650.648eV (T=1258.409K) Etot = 2090.826eV
Energy per atom: Epot =1451.088eV Ekin = 668.110eV (T=1292.184K) Etot = 2119.199eV
Energy per atom: Epot =1460.916eV Ekin = 670.276eV (T=1296.371K) Etot = 2131.191eV
Energy per atom: Epot =1474.420eV Ekin = 674.329eV (T=1304.211K) Etot = 2148.748eV
Energy per atom: Epot =1495.885eV Ekin = 675.958eV (T=1307.362K) Etot = 2171.843eV
Energy per atom: Epot =1501.684eV Ekin = 687.957eV (T=1330.570K) Etot = 2189.642eV
Energy per atom: Epot =1511.738eV Ekin = 693.865eV (T=1341.995K) Etot = 2205.603eV
Energy per atom: Epot =1527.909eV Ekin = 696.826eV (T=1347.721K) Etot = 2224.734eV
Energy per atom: Epot =1537.392eV Ekin = 701.525eV (T=1356.810K) Etot = 2238.917eV
Energy per atom: Epot =1549.085eV Ekin = 701.302eV (T=1356.379K) Etot = 2250.387eV
Energy per atom: Epot =1545.937eV Ekin = 708.283eV (T=1369.881K) Etot = 2254.220eV
Energy per atom: Epot =1555.188eV Ekin = 712.464eV (T=1377.967K) Etot = 2267.652eV
Energy per atom: Epot =1578.954eV Ekin = 702.915eV (T=1359.499K) Etot = 2281.869eV
Energy per atom: Epot =1578.914eV Ekin = 710.948eV (T=1375.034K) Etot = 2289.861eV
Energy per atom: Epot =1584.889eV Ekin = 714.611eV (T=1382.120K) Etot = 2299.500eV
Energy per atom: Epot =1608.355eV Ekin = 700.889eV (T=1355.580K) Etot = 2309.244eV
Energy per atom: Epot =1621.089eV Ekin = 705.608eV (T=1364.708K) Etot = 2326.697eV
Energy per atom: Epot =1609.286eV Ekin = 730.353eV (T=1412.567K) Etot = 2339.639eV
Energy per atom: Epot =1632.905eV Ekin = 711.377eV (T=1375.866K) Etot = 2344.283eV
Energy per atom: Epot =1635.853eV Ekin = 722.824eV (T=1398.004K) Etot = 2358.676eV
Energy per atom: Epot =1649.833eV Ekin = 729.122eV (T=1410.185K) Etot = 2378.955eV
Energy per atom: Epot =1657.476eV Ekin = 737.249eV (T=1425.903K) Etot = 2394.725eV
Energy per atom: Epot =1663.287eV Ekin = 734.565eV (T=1420.713K) Etot = 2397.852eV
Energy per atom: Epot =1667.633eV Ekin = 738.012eV (T=1427.379K) Etot = 2405.645eV
Energy per atom: Epot =1696.666eV Ekin = 720.288eV (T=1393.099K) Etot = 2416.954eV
Energy per atom: Epot =1697.814eV Ekin = 738.912eV (T=1429.121K) Etot = 2436.726eV
Energy per atom: Epot =1720.485eV Ekin = 726.515eV (T=1405.142K) Etot = 2447.000eV
Energy per atom: Epot =1721.255eV Ekin = 741.883eV (T=1434.866K) Etot = 2463.138eV
Energy per atom: Epot =1722.362eV Ekin = 741.308eV (T=1433.755K) Etot = 2463.670eV
Energy per atom: Epot =1732.177eV Ekin = 737.459eV (T=1426.311K) Etot = 2469.636eV
Energy per atom: Epot =1741.508eV Ekin = 741.845eV (T=1434.793K) Etot = 2483.354eV
Energy per atom: Epot =1757.659eV Ekin = 732.081eV (T=1415.909K) Etot = 2489.740eV
Energy per atom: Epot =1762.146eV Ekin = 728.835eV (T=1409.630K) Etot = 2490.981eV
Energy per atom: Epot =1770.383eV Ekin = 719.426eV (T=1391.432K) Etot = 2489.809eV
Energy per atom: Epot =1762.240eV Ekin = 737.809eV (T=1426.986K) Etot = 2500.049eV
Energy per atom: Epot =1768.521eV Ekin = 730.459eV (T=1412.771K) Etot = 2498.980eV
Energy per atom: Epot =1783.473eV Ekin = 721.606eV (T=1395.648K) Etot = 2505.078eV
Energy per atom: Epot =1777.124eV Ekin = 741.081eV (T=1433.316K) Etot = 2518.205eV
Energy per atom: Epot =1773.458eV Ekin = 746.303eV (T=1443.414K) Etot = 2519.761eV
Energy per atom: Epot =1788.035eV Ekin = 735.671eV (T=1422.852K) Etot = 2523.706eV
Energy per atom: Epot =1780.777eV Ekin = 744.202eV (T=1439.352K) Etot = 2524.979eV
Energy per atom: Epot =1799.620eV Ekin = 739.943eV (T=1431.114K) Etot = 2539.563eV
Energy per atom: Epot =1802.133eV Ekin = 739.164eV (T=1429.607K) Etot = 2541.296eV
Energy per atom: Epot =1810.391eV Ekin = 749.035eV (T=1448.699K) Etot = 2559.426eV
Energy per atom: Epot =1818.011eV Ekin = 746.306eV (T=1443.422K) Etot = 2564.318eV
Energy per atom: Epot =1818.214eV Ekin = 748.738eV (T=1448.125K) Etot = 2566.953eV
Energy per atom: Epot =1827.534eV Ekin = 739.210eV (T=1429.697K) Etot = 2566.744eV
Energy per atom: Epot =1828.266eV Ekin = 744.207eV (T=1439.360K) Etot = 2572.473eV
Energy per atom: Epot =1825.493eV Ekin = 747.191eV (T=1445.132K) Etot = 2572.683eV
Energy per atom: Epot =1848.248eV Ekin = 728.190eV (T=1408.382K) Etot = 2576.438eV
Energy per atom: Epot =1845.164eV Ekin = 736.864eV (T=1425.159K) Etot = 2582.028eV
Energy per atom: Epot =1849.447eV Ekin = 740.280eV (T=1431.766K) Etot = 2589.727eV
Energy per atom: Epot =1854.828eV Ekin = 739.171eV (T=1429.621K) Etot = 2593.999eV
Energy per atom: Epot =1862.613eV Ekin = 744.530eV (T=1439.985K) Etot = 2607.142eV
Energy per atom: Epot =1868.979eV Ekin = 738.269eV (T=1427.876K) Etot = 2607.248eV
Energy per atom: Epot =1869.432eV Ekin = 740.004eV (T=1431.231K) Etot = 2609.436eV
Energy per atom: Epot =1887.617eV Ekin = 742.399eV (T=1435.864K) Etot = 2630.016eV
Energy per atom: Epot =1891.877eV Ekin = 741.153eV (T=1433.455K) Etot = 2633.030eV
Energy per atom: Epot =1903.772eV Ekin = 738.551eV (T=1428.422K) Etot = 2642.323eV
Energy per atom: Epot =1903.576eV Ekin = 755.759eV (T=1461.704K) Etot = 2659.335eV
Energy per atom: Epot =1897.218eV Ekin = 764.669eV (T=1478.936K) Etot = 2661.887eV
Energy per atom: Epot =1909.454eV Ekin = 761.305eV (T=1472.431K) Etot = 2670.759eV
Energy per atom: Epot =1917.628eV Ekin = 764.375eV (T=1478.367K) Etot = 2682.003eV
Energy per atom: Epot =1915.560eV Ekin = 759.840eV (T=1469.596K) Etot = 2675.399eV
Energy per atom: Epot =1923.540eV Ekin = 755.621eV (T=1461.436K) Etot = 2679.161eV
Energy per atom: Epot =1925.077eV Ekin = 755.730eV (T=1461.649K) Etot = 2680.807eV
Energy per atom: Epot =1930.400eV Ekin = 752.675eV (T=1455.739K) Etot = 2683.076eV
Energy per atom: Epot =1939.073eV Ekin = 744.448eV (T=1439.826K) Etot = 2683.520eV
Energy per atom: Epot =1938.729eV Ekin = 756.875eV (T=1463.862K) Etot = 2695.604eV
Energy per atom: Epot =1954.426eV Ekin = 749.423eV (T=1449.450K) Etot = 2703.849eV
Energy per atom: Epot =1962.095eV Ekin = 743.707eV (T=1438.395K) Etot = 2705.802eV
Energy per atom: Epot =1949.861eV Ekin = 755.869eV (T=1461.917K) Etot = 2705.730eV
Energy per atom: Epot =1949.056eV Ekin = 761.144eV (T=1472.119K) Etot = 2710.200eV
Energy per atom: Epot =1966.695eV Ekin = 751.995eV (T=1454.423K) Etot = 2718.690eV
Energy per atom: Epot =1966.930eV Ekin = 749.993eV (T=1450.553K) Etot = 2716.923eV
Energy per atom: Epot =1961.618eV Ekin = 763.295eV (T=1476.279K) Etot = 2724.913eV
Energy per atom: Epot =1957.361eV Ekin = 767.144eV (T=1483.723K) Etot = 2724.505eV
Energy per atom: Epot =1965.999eV Ekin = 753.679eV (T=1457.680K) Etot = 2719.678eV
Energy per atom: Epot =1957.632eV Ekin = 773.014eV (T=1495.076K) Etot = 2730.646eV
Energy per atom: Epot =1944.443eV Ekin = 776.289eV (T=1501.410K) Etot = 2720.732eV
Energy per atom: Epot =1951.232eV Ekin = 769.641eV (T=1488.553K) Etot = 2720.873eV
Energy per atom: Epot =1949.269eV Ekin = 777.160eV (T=1503.095K) Etot = 2726.429eV
Energy per atom: Epot =1970.346eV Ekin = 757.404eV (T=1464.885K) Etot = 2727.750eV
Energy per atom: Epot =1958.625eV Ekin = 768.141eV (T=1485.651K) Etot = 2726.766eV
Energy per atom: Epot =1963.337eV Ekin = 765.545eV (T=1480.631K) Etot = 2728.882eV
Energy per atom: Epot =1970.114eV Ekin = 774.025eV (T=1497.031K) Etot = 2744.138eV
Energy per atom: Epot =1971.914eV Ekin = 781.029eV (T=1510.577K) Etot = 2752.943eV
Energy per atom: Epot =1987.428eV Ekin = 755.333eV (T=1460.880K) Etot = 2742.761eV
Energy per atom: Epot =1979.310eV Ekin = 769.154eV (T=1487.611K) Etot = 2748.465eV
Energy per atom: Epot =1976.503eV Ekin = 783.690eV (T=1515.724K) Etot = 2760.192eV
Energy per atom: Epot =1992.619eV Ekin = 769.696eV (T=1488.659K) Etot = 2762.315eV
Energy per atom: Epot =1982.195eV Ekin = 778.332eV (T=1505.361K) Etot = 2760.527eV
Energy per atom: Epot =1983.402eV Ekin = 770.277eV (T=1489.782K) Etot = 2753.678eV
Energy per atom: Epot =2001.297eV Ekin = 761.862eV (T=1473.507K) Etot = 2763.159eV
Energy per atom: Epot =1995.110eV Ekin = 762.604eV (T=1474.942K) Etot = 2757.713eV
Energy per atom: Epot =1989.588eV Ekin = 769.476eV (T=1488.233K) Etot = 2759.063eV
Energy per atom: Epot =1986.605eV Ekin = 775.895eV (T=1500.649K) Etot = 2762.501eV
Energy per atom: Epot =2009.833eV Ekin = 764.081eV (T=1477.798K) Etot = 2773.914eV
Energy per atom: Epot =2005.691eV Ekin = 770.046eV (T=1489.337K) Etot = 2775.737eV
Energy per atom: Epot =2012.001eV Ekin = 760.389eV (T=1470.659K) Etot = 2772.390eV
Energy per atom: Epot =2006.824eV Ekin = 779.203eV (T=1507.046K) Etot = 2786.027eV
Energy per atom: Epot =2008.012eV Ekin = 767.657eV (T=1484.716K) Etot = 2775.669eV
Energy per atom: Epot =2022.746eV Ekin = 756.772eV (T=1463.662K) Etot = 2779.517eV
Energy per atom: Epot =2013.500eV Ekin = 765.608eV (T=1480.752K) Etot = 2779.108eV
Energy per atom: Epot =2007.944eV Ekin = 776.182eV (T=1501.203K) Etot = 2784.126eV
Energy per atom: Epot =2004.803eV Ekin = 774.400eV (T=1497.756K) Etot = 2779.202eV
Energy per atom: Epot =2004.450eV Ekin = 777.854eV (T=1504.437K) Etot = 2782.303eV
Energy per atom: Epot =2026.183eV Ekin = 760.150eV (T=1470.196K) Etot = 2786.333eV
Energy per atom: Epot =2004.164eV Ekin = 781.398eV (T=1511.291K) Etot = 2785.562eV
Energy per atom: Epot =2018.560eV Ekin = 773.400eV (T=1495.823K) Etot = 2791.960eV
Energy per atom: Epot =2008.698eV Ekin = 792.032eV (T=1531.859K) Etot = 2800.730eV
Energy per atom: Epot =2022.136eV Ekin = 775.795eV (T=1500.456K) Etot = 2797.931eV
Energy per atom: Epot =2011.284eV Ekin = 785.480eV (T=1519.188K) Etot = 2796.764eV
Energy per atom: Epot =2009.994eV Ekin = 784.401eV (T=1517.099K) Etot = 2794.394eV
Energy per atom: Epot =2021.977eV Ekin = 777.682eV (T=1504.105K) Etot = 2799.660eV
Energy per atom: Epot =2005.574eV Ekin = 789.702eV (T=1527.353K) Etot = 2795.276eV
Energy per atom: Epot =2003.155eV Ekin = 796.299eV (T=1540.111K) Etot = 2799.454eV
Energy per atom: Epot =2017.340eV Ekin = 790.090eV (T=1528.102K) Etot = 2807.429eV
Energy per atom: Epot =2008.345eV Ekin = 795.126eV (T=1537.844K) Etot = 2803.472eV
Energy per atom: Epot =2004.986eV Ekin = 793.529eV (T=1534.755K) Etot = 2798.515eV
Energy per atom: Epot =2018.189eV Ekin = 781.057eV (T=1510.632K) Etot = 2799.246eV
Energy per atom: Epot =2012.489eV Ekin = 786.287eV (T=1520.748K) Etot = 2798.776eV
Energy per atom: Epot =2013.945eV Ekin = 781.815eV (T=1512.099K) Etot = 2795.761eV
Energy per atom: Epot =2016.186eV Ekin = 795.814eV (T=1539.173K) Etot = 2811.999eV
Energy per atom: Epot =2030.736eV Ekin = 779.794eV (T=1508.189K) Etot = 2810.530eV
Energy per atom: Epot =2026.443eV Ekin = 790.085eV (T=1528.093K) Etot = 2816.528eV
Energy per atom: Epot =2020.859eV Ekin = 783.287eV (T=1514.945K) Etot = 2804.146eV
Energy per atom: Epot =2025.570eV Ekin = 773.212eV (T=1495.460K) Etot = 2798.782eV
Energy per atom: Epot =2008.255eV Ekin = 786.929eV (T=1521.989K) Etot = 2795.184eV
Energy per atom: Epot =2011.520eV Ekin = 778.654eV (T=1505.984K) Etot = 2790.174eV
Energy per atom: Epot =2017.475eV Ekin = 769.213eV (T=1487.726K) Etot = 2786.688eV
Energy per atom: Epot =2014.604eV Ekin = 772.691eV (T=1494.452K) Etot = 2787.296eV
Energy per atom: Epot =2019.461eV Ekin = 766.847eV (T=1483.149K) Etot = 2786.307eV
Energy per atom: Epot =2006.866eV Ekin = 774.978eV (T=1498.875K) Etot = 2781.844eV
Energy per atom: Epot =2009.667eV Ekin = 773.779eV (T=1496.556K) Etot = 2783.446eV
Energy per atom: Epot =2004.868eV Ekin = 778.380eV (T=1505.454K) Etot = 2783.248eV
Energy per atom: Epot =2004.123eV Ekin = 774.775eV (T=1498.482K) Etot = 2778.897eV
Energy per atom: Epot =2008.081eV Ekin = 776.020eV (T=1500.891K) Etot = 2784.102eV
Energy per atom: Epot =2006.112eV Ekin = 784.277eV (T=1516.860K) Etot = 2790.390eV
Energy per atom: Epot =1999.058eV Ekin = 793.149eV (T=1534.020K) Etot = 2792.208eV
Energy per atom: Epot =2001.882eV Ekin = 789.627eV (T=1527.207K) Etot = 2791.509eV
Energy per atom: Epot =2011.816eV Ekin = 782.466eV (T=1513.357K) Etot = 2794.282eV
Energy per atom: Epot =2012.585eV Ekin = 777.223eV (T=1503.217K) Etot = 2789.808eV
Energy per atom: Epot =2005.495eV Ekin = 776.898eV (T=1502.589K) Etot = 2782.393eV
Energy per atom: Epot =2000.301eV Ekin = 788.398eV (T=1524.831K) Etot = 2788.700eV
Energy per atom: Epot =2006.485eV Ekin = 780.395eV (T=1509.352K) Etot = 2786.880eV
Energy per atom: Epot =2004.324eV Ekin = 787.685eV (T=1523.451K) Etot = 2792.008eV
Energy per atom: Epot =1997.281eV Ekin = 794.963eV (T=1537.528K) Etot = 2792.244eV
Energy per atom: Epot =2000.368eV Ekin = 792.918eV (T=1533.573K) Etot = 2793.286eV
Energy per atom: Epot =1998.084eV Ekin = 795.040eV (T=1537.677K) Etot = 2793.124eV
Energy per atom: Epot =2012.496eV Ekin = 783.626eV (T=1515.602K) Etot = 2796.123eV
Energy per atom: Epot =2006.668eV Ekin = 782.097eV (T=1512.643K) Etot = 2788.765eV
Energy per atom: Epot =2011.246eV Ekin = 772.106eV (T=1493.319K) Etot = 2783.352eV
Energy per atom: Epot =1999.394eV Ekin = 779.412eV (T=1507.451K) Etot = 2778.806eV
Energy per atom: Epot =2008.991eV Ekin = 771.023eV (T=1491.225K) Etot = 2780.013eV
Energy per atom: Epot =1988.879eV Ekin = 785.380eV (T=1518.993K) Etot = 2774.260eV
Energy per atom: Epot =1985.673eV Ekin = 789.931eV (T=1527.795K) Etot = 2775.604eV
Energy per atom: Epot =2003.843eV Ekin = 778.225eV (T=1505.155K) Etot = 2782.068eV
Energy per atom: Epot =2007.956eV Ekin = 774.978eV (T=1498.874K) Etot = 2782.934eV
Energy per atom: Epot =2001.761eV Ekin = 786.649eV (T=1521.448K) Etot = 2788.410eV
Energy per atom: Epot =2009.021eV Ekin = 773.766eV (T=1496.531K) Etot = 2782.787eV
Energy per atom: Epot =2008.004eV Ekin = 775.101eV (T=1499.113K) Etot = 2783.105eV
Energy per atom: Epot =1996.755eV Ekin = 778.372eV (T=1505.439K) Etot = 2775.127eV
Energy per atom: Epot =1999.826eV Ekin = 777.895eV (T=1504.516K) Etot = 2777.721eV
Energy per atom: Epot =2008.644eV Ekin = 767.439eV (T=1484.294K) Etot = 2776.083eV
Energy per atom: Epot =2002.375eV Ekin = 779.719eV (T=1508.044K) Etot = 2782.094eV
Energy per atom: Epot =2003.088eV Ekin = 772.662eV (T=1494.396K) Etot = 2775.751eV
Energy per atom: Epot =2000.746eV Ekin = 770.028eV (T=1489.301K) Etot = 2770.773eV
Energy per atom: Epot =2006.245eV Ekin = 761.312eV (T=1472.443K) Etot = 2767.557eV
Energy per atom: Epot =1993.876eV Ekin = 775.093eV (T=1499.097K) Etot = 2768.968eV
Energy per atom: Epot =1995.610eV Ekin = 768.416eV (T=1486.184K) Etot = 2764.027eV
Energy per atom: Epot =1995.697eV Ekin = 769.008eV (T=1487.329K) Etot = 2764.705eV
Energy per atom: Epot =1982.384eV Ekin = 780.437eV (T=1509.432K) Etot = 2762.821eV
Energy per atom: Epot =1981.783eV Ekin = 782.023eV (T=1512.501K) Etot = 2763.806eV
Energy per atom: Epot =1991.493eV Ekin = 773.094eV (T=1495.231K) Etot = 2764.587eV
Energy per atom: Epot =1973.650eV Ekin = 791.075eV (T=1530.009K) Etot = 2764.725eV
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] 20:07:12 43.457006 1.0818
BFGSLineSearch: 1[ 1] 20:07:12 42.347659 0.2273
BFGSLineSearch: 2[ 2] 20:07:12 42.108454 0.1349
BFGSLineSearch: 3[ 3] 20:07:12 41.964817 0.1138
BFGSLineSearch: 4[ 4] 20:07:12 41.924933 0.0683
BFGSLineSearch: 5[ 5] 20:07:12 41.915346 0.0225
BFGSLineSearch: 6[ 6] 20:07:12 41.914920 0.0059
BFGSLineSearch: 7[ 7] 20:07:12 41.914872 0.0023
BFGSLineSearch: 8[ 9] 20:07:12 41.914855 0.0023
BFGSLineSearch: 9[ 10] 20:07:12 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 15.215eV (T=1265.648K) Etot = 57.129eV
Energy per atom: Epot =50.899eV Ekin = 6.277eV (T=522.149K) Etot = 57.176eV
Energy per atom: Epot =51.203eV Ekin = 5.974eV (T=496.949K) Etot = 57.177eV
Energy per atom: Epot =50.895eV Ekin = 6.279eV (T=522.359K) Etot = 57.175eV
Energy per atom: Epot =51.951eV Ekin = 5.231eV (T=435.188K) Etot = 57.182eV
Energy per atom: Epot =50.451eV Ekin = 6.723eV (T=559.266K) Etot = 57.174eV
Energy per atom: Epot =49.546eV Ekin = 7.623eV (T=634.095K) Etot = 57.168eV
Energy per atom: Epot =50.036eV Ekin = 7.139eV (T=593.833K) Etot = 57.174eV
Energy per atom: Epot =50.117eV Ekin = 7.065eV (T=587.707K) Etot = 57.182eV
Energy per atom: Epot =49.245eV Ekin = 7.930eV (T=659.689K) Etot = 57.175eV
Energy per atom: Epot =50.013eV Ekin = 7.161eV (T=595.705K) Etot = 57.174eV
Energy per atom: Epot =50.579eV Ekin = 6.595eV (T=548.638K) Etot = 57.174eV
Energy per atom: Epot =50.477eV Ekin = 6.693eV (T=556.764K) Etot = 57.170eV
Energy per atom: Epot =50.251eV Ekin = 6.923eV (T=575.889K) Etot = 57.174eV
Energy per atom: Epot =49.763eV Ekin = 7.409eV (T=616.346K) Etot = 57.172eV
Energy per atom: Epot =49.952eV Ekin = 7.224eV (T=600.950K) Etot = 57.176eV
Energy per atom: Epot =49.981eV Ekin = 7.198eV (T=598.745K) Etot = 57.179eV
Energy per atom: Epot =49.930eV Ekin = 7.251eV (T=603.194K) Etot = 57.181eV
Energy per atom: Epot =50.421eV Ekin = 6.758eV (T=562.182K) Etot = 57.179eV
Energy per atom: Epot =50.832eV Ekin = 6.345eV (T=527.796K) Etot = 57.177eV
Energy per atom: Epot =50.141eV Ekin = 7.035eV (T=585.226K) Etot = 57.177eV
Energy per atom: Epot =50.313eV Ekin = 6.866eV (T=571.147K) Etot = 57.179eV
Energy per atom: Epot =49.391eV Ekin = 7.787eV (T=647.748K) Etot = 57.177eV
Energy per atom: Epot =49.534eV Ekin = 7.636eV (T=635.220K) Etot = 57.170eV
Energy per atom: Epot =49.786eV Ekin = 7.382eV (T=614.124K) Etot = 57.168eV
Energy per atom: Epot =50.110eV Ekin = 7.066eV (T=587.788K) Etot = 57.176eV
Energy per atom: Epot =49.598eV Ekin = 7.575eV (T=630.101K) Etot = 57.172eV
Energy per atom: Epot =50.208eV Ekin = 6.967eV (T=579.560K) Etot = 57.175eV
Energy per atom: Epot =50.069eV Ekin = 7.105eV (T=591.043K) Etot = 57.174eV
Energy per atom: Epot =49.749eV Ekin = 7.423eV (T=617.513K) Etot = 57.173eV
Energy per atom: Epot =50.022eV Ekin = 7.149eV (T=594.674K) Etot = 57.171eV
Energy per atom: Epot =50.006eV Ekin = 7.168eV (T=596.254K) Etot = 57.174eV
Energy per atom: Epot =50.437eV Ekin = 6.738eV (T=560.528K) Etot = 57.175eV
Energy per atom: Epot =50.138eV Ekin = 7.033eV (T=585.031K) Etot = 57.171eV
Energy per atom: Epot =50.005eV Ekin = 7.172eV (T=596.608K) Etot = 57.177eV
Energy per atom: Epot =49.731eV Ekin = 7.440eV (T=618.916K) Etot = 57.171eV
Energy per atom: Epot =49.364eV Ekin = 7.807eV (T=649.413K) Etot = 57.171eV
Energy per atom: Epot =49.787eV Ekin = 7.386eV (T=614.436K) Etot = 57.173eV
Energy per atom: Epot =50.453eV Ekin = 6.728eV (T=559.664K) Etot = 57.181eV
Energy per atom: Epot =49.061eV Ekin = 8.104eV (T=674.157K) Etot = 57.165eV
Energy per atom: Epot =50.256eV Ekin = 6.917eV (T=575.425K) Etot = 57.174eV
Energy per atom: Epot =49.995eV Ekin = 7.178eV (T=597.132K) Etot = 57.173eV
Energy per atom: Epot =49.693eV Ekin = 7.477eV (T=621.952K) Etot = 57.170eV
Energy per atom: Epot =50.543eV Ekin = 6.633eV (T=551.794K) Etot = 57.177eV
Energy per atom: Epot =49.281eV Ekin = 7.884eV (T=655.884K) Etot = 57.166eV
Energy per atom: Epot =50.011eV Ekin = 7.162eV (T=595.747K) Etot = 57.172eV
Energy per atom: Epot =50.894eV Ekin = 6.286eV (T=522.939K) Etot = 57.181eV
Energy per atom: Epot =49.948eV Ekin = 7.227eV (T=601.172K) Etot = 57.175eV
Energy per atom: Epot =49.594eV Ekin = 7.576eV (T=630.226K) Etot = 57.170eV
Energy per atom: Epot =49.197eV Ekin = 7.974eV (T=663.346K) Etot = 57.171eV
Energy per atom: Epot =50.275eV Ekin = 6.903eV (T=574.261K) Etot = 57.178eV
Energy per atom: Epot =48.805eV Ekin = 8.366eV (T=695.925K) Etot = 57.171eV
Energy per atom: Epot =50.601eV Ekin = 6.581eV (T=547.483K) Etot = 57.182eV
Energy per atom: Epot =50.307eV Ekin = 6.876eV (T=571.962K) Etot = 57.182eV
Energy per atom: Epot =49.590eV Ekin = 7.584eV (T=630.900K) Etot = 57.174eV
Energy per atom: Epot =50.135eV Ekin = 7.037eV (T=585.358K) Etot = 57.172eV
Energy per atom: Epot =49.972eV Ekin = 7.198eV (T=598.791K) Etot = 57.170eV
Energy per atom: Epot =50.251eV Ekin = 6.926eV (T=576.120K) Etot = 57.177eV
Energy per atom: Epot =50.000eV Ekin = 7.168eV (T=596.321K) Etot = 57.168eV
Energy per atom: Epot =50.397eV Ekin = 6.776eV (T=563.661K) Etot = 57.173eV
Energy per atom: Epot =50.725eV Ekin = 6.455eV (T=536.946K) Etot = 57.180eV
Energy per atom: Epot =50.238eV Ekin = 6.938eV (T=577.130K) Etot = 57.175eV
Energy per atom: Epot =50.156eV Ekin = 7.018eV (T=583.781K) Etot = 57.174eV
Energy per atom: Epot =49.763eV Ekin = 7.411eV (T=616.537K) Etot = 57.175eV
Energy per atom: Epot =50.270eV Ekin = 6.904eV (T=574.284K) Etot = 57.173eV
Energy per atom: Epot =49.973eV Ekin = 7.196eV (T=598.651K) Etot = 57.169eV
Energy per atom: Epot =49.607eV Ekin = 7.562eV (T=629.059K) Etot = 57.169eV
Energy per atom: Epot =50.153eV Ekin = 7.023eV (T=584.199K) Etot = 57.176eV
Energy per atom: Epot =50.020eV Ekin = 7.152eV (T=594.958K) Etot = 57.172eV
Energy per atom: Epot =49.987eV Ekin = 7.184eV (T=597.616K) Etot = 57.172eV
Energy per atom: Epot =49.876eV Ekin = 7.295eV (T=606.836K) Etot = 57.171eV
Energy per atom: Epot =50.555eV Ekin = 6.623eV (T=550.909K) Etot = 57.177eV
Energy per atom: Epot =50.260eV Ekin = 6.917eV (T=575.440K) Etot = 57.177eV
Energy per atom: Epot =49.869eV Ekin = 7.303eV (T=607.511K) Etot = 57.172eV
Energy per atom: Epot =50.855eV Ekin = 6.327eV (T=526.332K) Etot = 57.182eV
Energy per atom: Epot =48.832eV Ekin = 8.339eV (T=693.732K) Etot = 57.172eV
Energy per atom: Epot =49.386eV Ekin = 7.783eV (T=647.400K) Etot = 57.169eV
Energy per atom: Epot =50.017eV Ekin = 7.155eV (T=595.232K) Etot = 57.173eV
Energy per atom: Epot =49.586eV Ekin = 7.588eV (T=631.214K) Etot = 57.174eV
Energy per atom: Epot =49.893eV Ekin = 7.280eV (T=605.588K) Etot = 57.173eV
Energy per atom: Epot =49.999eV Ekin = 7.175eV (T=596.860K) Etot = 57.173eV
Energy per atom: Epot =50.269eV Ekin = 6.905eV (T=574.399K) Etot = 57.174eV
Energy per atom: Epot =49.613eV Ekin = 7.559eV (T=628.818K) Etot = 57.172eV
Energy per atom: Epot =49.715eV Ekin = 7.461eV (T=620.676K) Etot = 57.176eV
Energy per atom: Epot =50.418eV Ekin = 6.758eV (T=562.200K) Etot = 57.176eV
Energy per atom: Epot =49.479eV Ekin = 7.693eV (T=639.925K) Etot = 57.171eV
Energy per atom: Epot =49.141eV Ekin = 8.029eV (T=667.913K) Etot = 57.170eV
Energy per atom: Epot =49.386eV Ekin = 7.786eV (T=647.664K) Etot = 57.171eV
Energy per atom: Epot =50.743eV Ekin = 6.434eV (T=535.235K) Etot = 57.177eV
Energy per atom: Epot =49.848eV Ekin = 7.325eV (T=609.369K) Etot = 57.173eV
Energy per atom: Epot =49.401eV Ekin = 7.770eV (T=646.392K) Etot = 57.171eV
Energy per atom: Epot =49.754eV Ekin = 7.416eV (T=616.927K) Etot = 57.170eV
Energy per atom: Epot =50.318eV Ekin = 6.859eV (T=570.546K) Etot = 57.176eV
Energy per atom: Epot =50.000eV Ekin = 7.173eV (T=596.694K) Etot = 57.173eV
Energy per atom: Epot =49.573eV Ekin = 7.599eV (T=632.109K) Etot = 57.172eV
Energy per atom: Epot =50.882eV Ekin = 6.299eV (T=523.993K) Etot = 57.182eV
Energy per atom: Epot =50.515eV Ekin = 6.664eV (T=554.395K) Etot = 57.180eV
Energy per atom: Epot =50.705eV Ekin = 6.474eV (T=538.534K) Etot = 57.179eV
Energy per atom: Epot =49.887eV Ekin = 7.291eV (T=606.491K) Etot = 57.177eV
Energy per atom: Epot =50.485eV Ekin = 6.693eV (T=556.765K) Etot = 57.178eV
Energy per atom: Epot =49.825eV Ekin = 7.352eV (T=611.600K) Etot = 57.177eV
Energy per atom: Epot =50.762eV Ekin = 6.419eV (T=533.959K) Etot = 57.181eV
Energy per atom: Epot =50.910eV Ekin = 6.268eV (T=521.380K) Etot = 57.178eV
Energy per atom: Epot =49.700eV Ekin = 7.477eV (T=621.995K) Etot = 57.177eV
Energy per atom: Epot =49.345eV Ekin = 7.831eV (T=651.433K) Etot = 57.176eV
Energy per atom: Epot =50.731eV Ekin = 6.446eV (T=536.240K) Etot = 57.177eV
Energy per atom: Epot =50.653eV Ekin = 6.520eV (T=542.338K) Etot = 57.172eV
Energy per atom: Epot =50.143eV Ekin = 7.031eV (T=584.908K) Etot = 57.174eV
Energy per atom: Epot =50.221eV Ekin = 6.955eV (T=578.556K) Etot = 57.176eV
Energy per atom: Epot =50.910eV Ekin = 6.269eV (T=521.500K) Etot = 57.179eV
Energy per atom: Epot =50.838eV Ekin = 6.342eV (T=527.546K) Etot = 57.180eV
Energy per atom: Epot =50.085eV Ekin = 7.090eV (T=589.824K) Etot = 57.176eV
Energy per atom: Epot =50.541eV Ekin = 6.635eV (T=551.924K) Etot = 57.175eV
Energy per atom: Epot =50.158eV Ekin = 7.022eV (T=584.172K) Etot = 57.181eV
Energy per atom: Epot =50.253eV Ekin = 6.925eV (T=576.067K) Etot = 57.178eV
Energy per atom: Epot =50.163eV Ekin = 7.013eV (T=583.360K) Etot = 57.176eV
Energy per atom: Epot =49.875eV Ekin = 7.301eV (T=607.362K) Etot = 57.176eV
Energy per atom: Epot =50.614eV Ekin = 6.565eV (T=546.088K) Etot = 57.178eV
Energy per atom: Epot =49.747eV Ekin = 7.425eV (T=617.670K) Etot = 57.173eV
Energy per atom: Epot =50.614eV Ekin = 6.564eV (T=546.073K) Etot = 57.179eV
Energy per atom: Epot =49.712eV Ekin = 7.461eV (T=620.694K) Etot = 57.174eV
Energy per atom: Epot =50.214eV Ekin = 6.958eV (T=578.820K) Etot = 57.172eV
Energy per atom: Epot =50.425eV Ekin = 6.749eV (T=561.452K) Etot = 57.175eV
Energy per atom: Epot =50.108eV Ekin = 7.070eV (T=588.100K) Etot = 57.177eV
Energy per atom: Epot =50.114eV Ekin = 7.062eV (T=587.465K) Etot = 57.176eV
Energy per atom: Epot =49.458eV Ekin = 7.712eV (T=641.546K) Etot = 57.170eV
Energy per atom: Epot =49.513eV Ekin = 7.658eV (T=637.011K) Etot = 57.170eV
Energy per atom: Epot =50.331eV Ekin = 6.845eV (T=569.439K) Etot = 57.176eV
Energy per atom: Epot =50.230eV Ekin = 6.946eV (T=577.773K) Etot = 57.175eV
Energy per atom: Epot =50.091eV Ekin = 7.083eV (T=589.208K) Etot = 57.174eV
Energy per atom: Epot =50.704eV Ekin = 6.477eV (T=538.781K) Etot = 57.181eV
Energy per atom: Epot =50.140eV Ekin = 7.027eV (T=584.556K) Etot = 57.167eV
Energy per atom: Epot =50.075eV Ekin = 7.099eV (T=590.514K) Etot = 57.173eV
Energy per atom: Epot =49.937eV Ekin = 7.238eV (T=602.095K) Etot = 57.175eV
Energy per atom: Epot =49.715eV Ekin = 7.454eV (T=620.071K) Etot = 57.169eV
Energy per atom: Epot =50.134eV Ekin = 7.040eV (T=585.647K) Etot = 57.174eV
Energy per atom: Epot =50.644eV Ekin = 6.533eV (T=543.453K) Etot = 57.177eV
Energy per atom: Epot =50.713eV Ekin = 6.465eV (T=537.780K) Etot = 57.178eV
Energy per atom: Epot =50.528eV Ekin = 6.654eV (T=553.532K) Etot = 57.182eV
Energy per atom: Epot =49.790eV Ekin = 7.384eV (T=614.244K) Etot = 57.174eV
Energy per atom: Epot =49.651eV Ekin = 7.522eV (T=625.699K) Etot = 57.173eV
Energy per atom: Epot =50.440eV Ekin = 6.736eV (T=560.351K) Etot = 57.176eV
Energy per atom: Epot =50.312eV Ekin = 6.864eV (T=570.994K) Etot = 57.176eV
Energy per atom: Epot =49.631eV Ekin = 7.542eV (T=627.402K) Etot = 57.173eV
Energy per atom: Epot =49.707eV Ekin = 7.467eV (T=621.159K) Etot = 57.174eV
Energy per atom: Epot =50.184eV Ekin = 6.993eV (T=581.697K) Etot = 57.177eV
Energy per atom: Epot =49.630eV Ekin = 7.548eV (T=627.884K) Etot = 57.177eV
Energy per atom: Epot =49.268eV Ekin = 7.904eV (T=657.531K) Etot = 57.172eV
Energy per atom: Epot =49.734eV Ekin = 7.439eV (T=618.840K) Etot = 57.173eV
Energy per atom: Epot =50.971eV Ekin = 6.208eV (T=516.420K) Etot = 57.179eV
Energy per atom: Epot =50.210eV Ekin = 6.967eV (T=579.547K) Etot = 57.177eV
Energy per atom: Epot =50.166eV Ekin = 7.009eV (T=583.054K) Etot = 57.175eV
Energy per atom: Epot =50.523eV Ekin = 6.654eV (T=553.515K) Etot = 57.177eV
Energy per atom: Epot =50.980eV Ekin = 6.197eV (T=515.540K) Etot = 57.177eV
Energy per atom: Epot =49.840eV Ekin = 7.334eV (T=610.053K) Etot = 57.173eV
Energy per atom: Epot =49.718eV Ekin = 7.456eV (T=620.271K) Etot = 57.174eV
Energy per atom: Epot =49.441eV Ekin = 7.732eV (T=643.235K) Etot = 57.174eV
Energy per atom: Epot =49.638eV Ekin = 7.535eV (T=626.847K) Etot = 57.173eV
Energy per atom: Epot =49.620eV Ekin = 7.550eV (T=628.051K) Etot = 57.170eV
Energy per atom: Epot =49.012eV Ekin = 8.164eV (T=679.154K) Etot = 57.176eV
Energy per atom: Epot =50.109eV Ekin = 7.073eV (T=588.385K) Etot = 57.182eV
Energy per atom: Epot =49.555eV Ekin = 7.623eV (T=634.138K) Etot = 57.179eV
Energy per atom: Epot =49.929eV Ekin = 7.248eV (T=602.896K) Etot = 57.176eV
Energy per atom: Epot =49.539eV Ekin = 7.633eV (T=634.985K) Etot = 57.172eV
Energy per atom: Epot =50.021eV Ekin = 7.154eV (T=595.141K) Etot = 57.175eV
Energy per atom: Epot =49.434eV Ekin = 7.737eV (T=643.636K) Etot = 57.171eV
Energy per atom: Epot =49.241eV Ekin = 7.936eV (T=660.139K) Etot = 57.176eV
Energy per atom: Epot =48.598eV Ekin = 8.572eV (T=713.038K) Etot = 57.169eV
Energy per atom: Epot =50.294eV Ekin = 6.884eV (T=572.618K) Etot = 57.178eV
Energy per atom: Epot =48.147eV Ekin = 9.023eV (T=750.596K) Etot = 57.170eV
Energy per atom: Epot =49.797eV Ekin = 7.373eV (T=613.365K) Etot = 57.171eV
Energy per atom: Epot =49.923eV Ekin = 7.256eV (T=603.570K) Etot = 57.178eV
Energy per atom: Epot =49.502eV Ekin = 7.677eV (T=638.618K) Etot = 57.179eV
Energy per atom: Epot =49.242eV Ekin = 7.935eV (T=660.121K) Etot = 57.177eV
Energy per atom: Epot =49.062eV Ekin = 8.112eV (T=674.776K) Etot = 57.173eV
Energy per atom: Epot =50.193eV Ekin = 6.981eV (T=580.737K) Etot = 57.174eV
Energy per atom: Epot =49.361eV Ekin = 7.812eV (T=649.853K) Etot = 57.173eV
Energy per atom: Epot =49.888eV Ekin = 7.291eV (T=606.500K) Etot = 57.179eV
Energy per atom: Epot =50.339eV Ekin = 6.839eV (T=568.935K) Etot = 57.179eV
Energy per atom: Epot =49.123eV Ekin = 8.044eV (T=669.132K) Etot = 57.167eV
Energy per atom: Epot =49.897eV Ekin = 7.278eV (T=605.401K) Etot = 57.175eV
Energy per atom: Epot =49.193eV Ekin = 7.981eV (T=663.878K) Etot = 57.173eV
Energy per atom: Epot =49.165eV Ekin = 8.005eV (T=665.948K) Etot = 57.170eV
Energy per atom: Epot =48.442eV Ekin = 8.719eV (T=725.264K) Etot = 57.161eV
Energy per atom: Epot =49.716eV Ekin = 7.460eV (T=620.578K) Etot = 57.176eV
Energy per atom: Epot =50.047eV Ekin = 7.133eV (T=593.386K) Etot = 57.180eV
Energy per atom: Epot =49.387eV Ekin = 7.783eV (T=647.453K) Etot = 57.170eV
Energy per atom: Epot =49.996eV Ekin = 7.179eV (T=597.188K) Etot = 57.175eV
Energy per atom: Epot =49.562eV Ekin = 7.614eV (T=633.348K) Etot = 57.175eV
Energy per atom: Epot =49.316eV Ekin = 7.855eV (T=653.468K) Etot = 57.171eV
Energy per atom: Epot =49.240eV Ekin = 7.932eV (T=659.875K) Etot = 57.172eV
Energy per atom: Epot =49.171eV Ekin = 8.005eV (T=665.922K) Etot = 57.176eV
Energy per atom: Epot =50.083eV Ekin = 7.099eV (T=590.570K) Etot = 57.182eV
Energy per atom: Epot =48.415eV Ekin = 8.750eV (T=727.911K) Etot = 57.166eV
Energy per atom: Epot =49.312eV Ekin = 7.861eV (T=653.917K) Etot = 57.173eV
Energy per atom: Epot =49.566eV Ekin = 7.612eV (T=633.228K) Etot = 57.178eV
Energy per atom: Epot =49.510eV Ekin = 7.666eV (T=637.722K) Etot = 57.176eV
Energy per atom: Epot =49.392eV Ekin = 7.778eV (T=647.043K) Etot = 57.170eV
Energy per atom: Epot =49.337eV Ekin = 7.837eV (T=651.911K) Etot = 57.174eV
Energy per atom: Epot =49.338eV Ekin = 7.833eV (T=651.631K) Etot = 57.172eV
Energy per atom: Epot =48.636eV Ekin = 8.536eV (T=710.100K) Etot = 57.172eV
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?