Molecular dynamics

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()
md

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()
md
running a NVE simulation of fcc Cu
Energy per atom: Epot =-2.405eV  Ekin = 159.735eV (T=308.942K) Etot = 157.331eV
Energy per atom: Epot =121.861eV  Ekin = 36.277eV (T=70.163K) Etot = 158.138eV
Energy per atom: Epot =79.564eV  Ekin = 78.417eV (T=151.666K) Etot = 157.982eV
Energy per atom: Epot =72.612eV  Ekin = 85.229eV (T=164.840K) Etot = 157.841eV
Energy per atom: Epot =72.032eV  Ekin = 85.764eV (T=165.875K) Etot = 157.797eV
Energy per atom: Epot =83.742eV  Ekin = 74.217eV (T=143.542K) Etot = 157.959eV
Energy per atom: Epot =79.224eV  Ekin = 78.706eV (T=152.224K) Etot = 157.930eV
Energy per atom: Epot =77.021eV  Ekin = 80.837eV (T=156.347K) Etot = 157.858eV
Energy per atom: Epot =74.344eV  Ekin = 83.510eV (T=161.516K) Etot = 157.854eV
Energy per atom: Epot =81.745eV  Ekin = 76.188eV (T=147.354K) Etot = 157.933eV
Energy per atom: Epot =77.121eV  Ekin = 80.762eV (T=156.201K) Etot = 157.884eV
Energy per atom: Epot =76.431eV  Ekin = 81.440eV (T=157.512K) Etot = 157.871eV
Energy per atom: Epot =78.189eV  Ekin = 79.708eV (T=154.163K) Etot = 157.897eV
Energy per atom: Epot =79.647eV  Ekin = 78.253eV (T=151.349K) Etot = 157.900eV
Energy per atom: Epot =76.023eV  Ekin = 81.853eV (T=158.310K) Etot = 157.875eV
Energy per atom: Epot =77.988eV  Ekin = 79.919eV (T=154.569K) Etot = 157.907eV
Energy per atom: Epot =76.737eV  Ekin = 81.149eV (T=156.949K) Etot = 157.886eV
Energy per atom: Epot =81.069eV  Ekin = 76.825eV (T=148.586K) Etot = 157.894eV
Energy per atom: Epot =76.233eV  Ekin = 81.658eV (T=157.934K) Etot = 157.891eV
Energy per atom: Epot =76.980eV  Ekin = 80.902eV (T=156.471K) Etot = 157.882eV
Energy per atom: Epot =80.195eV  Ekin = 77.703eV (T=150.284K) Etot = 157.898eV

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

dyn = Langevin(atoms, timestep=5 * units.fs, temperature_K=T,
friction=0.02)

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()
md
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 =599.972eV  Ekin = 82.205eV (T=158.991K) Etot = 682.177eV
Energy per atom: Epot =672.213eV  Ekin = 140.843eV (T=272.403K) Etot = 813.057eV
Energy per atom: Epot =727.158eV  Ekin = 201.790eV (T=390.279K) Etot = 928.948eV
Energy per atom: Epot =781.348eV  Ekin = 256.759eV (T=496.594K) Etot = 1038.107eV
Energy per atom: Epot =832.730eV  Ekin = 301.707eV (T=583.528K) Etot = 1134.437eV
Energy per atom: Epot =884.720eV  Ekin = 341.319eV (T=660.141K) Etot = 1226.039eV
Energy per atom: Epot =927.002eV  Ekin = 381.965eV (T=738.754K) Etot = 1308.967eV
Energy per atom: Epot =976.594eV  Ekin = 417.843eV (T=808.145K) Etot = 1394.437eV
Energy per atom: Epot =1015.387eV  Ekin = 450.212eV (T=870.750K) Etot = 1465.599eV
Energy per atom: Epot =1043.250eV  Ekin = 480.295eV (T=928.933K) Etot = 1523.545eV
Energy per atom: Epot =1082.070eV  Ekin = 500.506eV (T=968.022K) Etot = 1582.576eV
Energy per atom: Epot =1114.915eV  Ekin = 513.489eV (T=993.133K) Etot = 1628.405eV
Energy per atom: Epot =1146.345eV  Ekin = 526.644eV (T=1018.576K) Etot = 1672.990eV
Energy per atom: Epot =1180.541eV  Ekin = 543.243eV (T=1050.679K) Etot = 1723.784eV
Energy per atom: Epot =1201.107eV  Ekin = 560.656eV (T=1084.357K) Etot = 1761.763eV
Energy per atom: Epot =1240.142eV  Ekin = 567.867eV (T=1098.304K) Etot = 1808.009eV
Energy per atom: Epot =1256.063eV  Ekin = 596.756eV (T=1154.178K) Etot = 1852.819eV
Energy per atom: Epot =1292.784eV  Ekin = 588.693eV (T=1138.584K) Etot = 1881.477eV
Energy per atom: Epot =1313.310eV  Ekin = 602.161eV (T=1164.631K) Etot = 1915.471eV
Energy per atom: Epot =1339.652eV  Ekin = 602.447eV (T=1165.185K) Etot = 1942.099eV
Energy per atom: Epot =1342.616eV  Ekin = 635.468eV (T=1229.050K) Etot = 1978.084eV
Energy per atom: Epot =1376.010eV  Ekin = 634.272eV (T=1226.737K) Etot = 2010.281eV
Energy per atom: Epot =1390.225eV  Ekin = 645.828eV (T=1249.088K) Etot = 2036.053eV
Energy per atom: Epot =1415.532eV  Ekin = 644.287eV (T=1246.108K) Etot = 2059.820eV
Energy per atom: Epot =1425.901eV  Ekin = 655.572eV (T=1267.934K) Etot = 2081.474eV
Energy per atom: Epot =1444.253eV  Ekin = 654.012eV (T=1264.917K) Etot = 2098.266eV
Energy per atom: Epot =1448.299eV  Ekin = 677.946eV (T=1311.206K) Etot = 2126.245eV
Energy per atom: Epot =1464.841eV  Ekin = 680.576eV (T=1316.294K) Etot = 2145.417eV
Energy per atom: Epot =1487.571eV  Ekin = 678.839eV (T=1312.934K) Etot = 2166.410eV
Energy per atom: Epot =1505.883eV  Ekin = 678.295eV (T=1311.881K) Etot = 2184.178eV
Energy per atom: Epot =1508.757eV  Ekin = 689.118eV (T=1332.814K) Etot = 2197.875eV
Energy per atom: Epot =1523.368eV  Ekin = 694.560eV (T=1343.340K) Etot = 2217.928eV
Energy per atom: Epot =1537.434eV  Ekin = 702.065eV (T=1357.854K) Etot = 2239.498eV
Energy per atom: Epot =1558.578eV  Ekin = 694.238eV (T=1342.717K) Etot = 2252.816eV
Energy per atom: Epot =1564.139eV  Ekin = 711.040eV (T=1375.214K) Etot = 2275.180eV
Energy per atom: Epot =1578.612eV  Ekin = 694.730eV (T=1343.669K) Etot = 2273.342eV
Energy per atom: Epot =1583.579eV  Ekin = 699.373eV (T=1352.648K) Etot = 2282.952eV
Energy per atom: Epot =1592.511eV  Ekin = 702.761eV (T=1359.201K) Etot = 2295.272eV
Energy per atom: Epot =1599.974eV  Ekin = 706.421eV (T=1366.279K) Etot = 2306.394eV
Energy per atom: Epot =1621.183eV  Ekin = 699.594eV (T=1353.076K) Etot = 2320.777eV
Energy per atom: Epot =1624.637eV  Ekin = 712.381eV (T=1377.807K) Etot = 2337.018eV
Energy per atom: Epot =1634.119eV  Ekin = 718.201eV (T=1389.063K) Etot = 2352.319eV
Energy per atom: Epot =1646.660eV  Ekin = 713.934eV (T=1380.811K) Etot = 2360.594eV
Energy per atom: Epot =1659.033eV  Ekin = 711.775eV (T=1376.634K) Etot = 2370.808eV
Energy per atom: Epot =1668.405eV  Ekin = 721.467eV (T=1395.379K) Etot = 2389.872eV
Energy per atom: Epot =1682.209eV  Ekin = 716.911eV (T=1386.568K) Etot = 2399.120eV
Energy per atom: Epot =1681.150eV  Ekin = 733.245eV (T=1418.159K) Etot = 2414.394eV
Energy per atom: Epot =1683.937eV  Ekin = 742.548eV (T=1436.153K) Etot = 2426.485eV
Energy per atom: Epot =1699.882eV  Ekin = 736.089eV (T=1423.660K) Etot = 2435.971eV
Energy per atom: Epot =1715.110eV  Ekin = 735.915eV (T=1423.324K) Etot = 2451.025eV
Energy per atom: Epot =1711.320eV  Ekin = 747.100eV (T=1444.956K) Etot = 2458.420eV
Energy per atom: Epot =1739.657eV  Ekin = 726.087eV (T=1404.316K) Etot = 2465.744eV
Energy per atom: Epot =1747.252eV  Ekin = 725.313eV (T=1402.818K) Etot = 2472.565eV
Energy per atom: Epot =1749.302eV  Ekin = 734.818eV (T=1421.202K) Etot = 2484.119eV
Energy per atom: Epot =1756.435eV  Ekin = 735.296eV (T=1422.126K) Etot = 2491.731eV
Energy per atom: Epot =1746.243eV  Ekin = 742.155eV (T=1435.392K) Etot = 2488.398eV
Energy per atom: Epot =1766.746eV  Ekin = 732.218eV (T=1416.173K) Etot = 2498.964eV
Energy per atom: Epot =1784.506eV  Ekin = 732.934eV (T=1417.558K) Etot = 2517.440eV
Energy per atom: Epot =1774.907eV  Ekin = 751.788eV (T=1454.024K) Etot = 2526.695eV
Energy per atom: Epot =1791.829eV  Ekin = 742.934eV (T=1436.899K) Etot = 2534.763eV
Energy per atom: Epot =1799.170eV  Ekin = 731.207eV (T=1414.218K) Etot = 2530.377eV
Energy per atom: Epot =1799.415eV  Ekin = 743.207eV (T=1437.428K) Etot = 2542.622eV
Energy per atom: Epot =1808.356eV  Ekin = 746.424eV (T=1443.650K) Etot = 2554.781eV
Energy per atom: Epot =1816.898eV  Ekin = 738.073eV (T=1427.498K) Etot = 2554.971eV
Energy per atom: Epot =1808.646eV  Ekin = 754.147eV (T=1458.585K) Etot = 2562.793eV
Energy per atom: Epot =1826.674eV  Ekin = 748.724eV (T=1448.097K) Etot = 2575.398eV
Energy per atom: Epot =1834.495eV  Ekin = 747.912eV (T=1446.528K) Etot = 2582.407eV
Energy per atom: Epot =1842.792eV  Ekin = 738.202eV (T=1427.746K) Etot = 2580.993eV
Energy per atom: Epot =1846.995eV  Ekin = 735.402eV (T=1422.332K) Etot = 2582.397eV
Energy per atom: Epot =1853.659eV  Ekin = 733.543eV (T=1418.737K) Etot = 2587.202eV
Energy per atom: Epot =1852.353eV  Ekin = 740.563eV (T=1432.312K) Etot = 2592.915eV
Energy per atom: Epot =1852.427eV  Ekin = 750.495eV (T=1451.522K) Etot = 2602.922eV
Energy per atom: Epot =1855.454eV  Ekin = 753.056eV (T=1456.475K) Etot = 2608.509eV
Energy per atom: Epot =1859.903eV  Ekin = 750.153eV (T=1450.861K) Etot = 2610.056eV
Energy per atom: Epot =1866.650eV  Ekin = 749.598eV (T=1449.787K) Etot = 2616.247eV
Energy per atom: Epot =1854.392eV  Ekin = 755.946eV (T=1462.065K) Etot = 2610.338eV
Energy per atom: Epot =1877.496eV  Ekin = 744.598eV (T=1440.117K) Etot = 2622.094eV
Energy per atom: Epot =1883.727eV  Ekin = 736.629eV (T=1424.705K) Etot = 2620.356eV
Energy per atom: Epot =1874.821eV  Ekin = 751.835eV (T=1454.114K) Etot = 2626.656eV
Energy per atom: Epot =1886.528eV  Ekin = 745.656eV (T=1442.163K) Etot = 2632.183eV
Energy per atom: Epot =1893.360eV  Ekin = 743.892eV (T=1438.752K) Etot = 2637.251eV
Energy per atom: Epot =1890.855eV  Ekin = 747.017eV (T=1444.796K) Etot = 2637.872eV
Energy per atom: Epot =1909.779eV  Ekin = 745.131eV (T=1441.149K) Etot = 2654.910eV
Energy per atom: Epot =1914.019eV  Ekin = 757.012eV (T=1464.127K) Etot = 2671.030eV
Energy per atom: Epot =1917.866eV  Ekin = 758.486eV (T=1466.978K) Etot = 2676.352eV
Energy per atom: Epot =1919.347eV  Ekin = 751.706eV (T=1453.865K) Etot = 2671.053eV
Energy per atom: Epot =1938.627eV  Ekin = 741.735eV (T=1434.580K) Etot = 2680.362eV
Energy per atom: Epot =1940.891eV  Ekin = 733.910eV (T=1419.447K) Etot = 2674.801eV
Energy per atom: Epot =1922.955eV  Ekin = 750.931eV (T=1452.365K) Etot = 2673.886eV
Energy per atom: Epot =1925.563eV  Ekin = 748.837eV (T=1448.316K) Etot = 2674.400eV
Energy per atom: Epot =1916.346eV  Ekin = 756.748eV (T=1463.616K) Etot = 2673.094eV
Energy per atom: Epot =1923.645eV  Ekin = 756.321eV (T=1462.790K) Etot = 2679.966eV
Energy per atom: Epot =1937.503eV  Ekin = 752.427eV (T=1455.260K) Etot = 2689.930eV
Energy per atom: Epot =1941.731eV  Ekin = 750.863eV (T=1452.235K) Etot = 2692.594eV
Energy per atom: Epot =1939.573eV  Ekin = 759.057eV (T=1468.083K) Etot = 2698.630eV
Energy per atom: Epot =1935.459eV  Ekin = 775.987eV (T=1500.826K) Etot = 2711.446eV
Energy per atom: Epot =1933.298eV  Ekin = 773.844eV (T=1496.683K) Etot = 2707.143eV
Energy per atom: Epot =1941.050eV  Ekin = 771.418eV (T=1491.990K) Etot = 2712.468eV
Energy per atom: Epot =1958.380eV  Ekin = 764.832eV (T=1479.252K) Etot = 2723.212eV
Energy per atom: Epot =1961.465eV  Ekin = 766.329eV (T=1482.147K) Etot = 2727.794eV
Energy per atom: Epot =1963.892eV  Ekin = 765.240eV (T=1480.040K) Etot = 2729.132eV
Energy per atom: Epot =1951.719eV  Ekin = 777.302eV (T=1503.370K) Etot = 2729.021eV
Energy per atom: Epot =1956.336eV  Ekin = 786.069eV (T=1520.326K) Etot = 2742.405eV
Energy per atom: Epot =1974.693eV  Ekin = 765.940eV (T=1481.395K) Etot = 2740.634eV
Energy per atom: Epot =1973.759eV  Ekin = 772.418eV (T=1493.924K) Etot = 2746.177eV
Energy per atom: Epot =1984.276eV  Ekin = 760.904eV (T=1471.655K) Etot = 2745.180eV
Energy per atom: Epot =1976.830eV  Ekin = 759.420eV (T=1468.784K) Etot = 2736.250eV
Energy per atom: Epot =1977.573eV  Ekin = 763.511eV (T=1476.696K) Etot = 2741.084eV
Energy per atom: Epot =1981.021eV  Ekin = 760.084eV (T=1470.069K) Etot = 2741.105eV
Energy per atom: Epot =1975.804eV  Ekin = 761.456eV (T=1472.721K) Etot = 2737.260eV
Energy per atom: Epot =1979.787eV  Ekin = 755.630eV (T=1461.455K) Etot = 2735.418eV
Energy per atom: Epot =1978.923eV  Ekin = 758.583eV (T=1467.166K) Etot = 2737.507eV
Energy per atom: Epot =1985.253eV  Ekin = 752.148eV (T=1454.719K) Etot = 2737.401eV
Energy per atom: Epot =1983.316eV  Ekin = 763.861eV (T=1477.373K) Etot = 2747.176eV
Energy per atom: Epot =1998.419eV  Ekin = 749.643eV (T=1449.875K) Etot = 2748.062eV
Energy per atom: Epot =1987.594eV  Ekin = 750.346eV (T=1451.235K) Etot = 2737.941eV
Energy per atom: Epot =1991.395eV  Ekin = 753.040eV (T=1456.444K) Etot = 2744.434eV
Energy per atom: Epot =1983.458eV  Ekin = 766.995eV (T=1483.435K) Etot = 2750.453eV
Energy per atom: Epot =1994.837eV  Ekin = 761.061eV (T=1471.958K) Etot = 2755.898eV
Energy per atom: Epot =2000.994eV  Ekin = 757.303eV (T=1464.690K) Etot = 2758.297eV
Energy per atom: Epot =1987.141eV  Ekin = 769.171eV (T=1487.644K) Etot = 2756.313eV
Energy per atom: Epot =1975.149eV  Ekin = 780.372eV (T=1509.307K) Etot = 2755.521eV
Energy per atom: Epot =1981.964eV  Ekin = 769.916eV (T=1489.084K) Etot = 2751.879eV
Energy per atom: Epot =1989.439eV  Ekin = 765.594eV (T=1480.725K) Etot = 2755.032eV
Energy per atom: Epot =2005.363eV  Ekin = 752.074eV (T=1454.577K) Etot = 2757.437eV
Energy per atom: Epot =2002.684eV  Ekin = 756.710eV (T=1463.544K) Etot = 2759.395eV
Energy per atom: Epot =1993.386eV  Ekin = 761.663eV (T=1473.123K) Etot = 2755.049eV
Energy per atom: Epot =1980.917eV  Ekin = 780.383eV (T=1509.330K) Etot = 2761.300eV
Energy per atom: Epot =1977.392eV  Ekin = 787.211eV (T=1522.534K) Etot = 2764.603eV
Energy per atom: Epot =1995.415eV  Ekin = 778.280eV (T=1505.262K) Etot = 2773.696eV
Energy per atom: Epot =1993.449eV  Ekin = 778.039eV (T=1504.795K) Etot = 2771.488eV
Energy per atom: Epot =1985.053eV  Ekin = 797.943eV (T=1543.291K) Etot = 2782.995eV
Energy per atom: Epot =1988.234eV  Ekin = 789.594eV (T=1527.144K) Etot = 2777.828eV
Energy per atom: Epot =1985.411eV  Ekin = 782.933eV (T=1514.260K) Etot = 2768.343eV
Energy per atom: Epot =1995.489eV  Ekin = 776.919eV (T=1502.629K) Etot = 2772.408eV
Energy per atom: Epot =2006.206eV  Ekin = 765.235eV (T=1480.032K) Etot = 2771.442eV
Energy per atom: Epot =1996.294eV  Ekin = 786.024eV (T=1520.238K) Etot = 2782.318eV
Energy per atom: Epot =1997.489eV  Ekin = 793.180eV (T=1534.079K) Etot = 2790.669eV
Energy per atom: Epot =1998.622eV  Ekin = 783.420eV (T=1515.201K) Etot = 2782.042eV
Energy per atom: Epot =2005.214eV  Ekin = 786.863eV (T=1521.861K) Etot = 2792.077eV
Energy per atom: Epot =2001.196eV  Ekin = 791.080eV (T=1530.017K) Etot = 2792.276eV
Energy per atom: Epot =2016.420eV  Ekin = 778.103eV (T=1504.919K) Etot = 2794.523eV
Energy per atom: Epot =1998.120eV  Ekin = 793.205eV (T=1534.128K) Etot = 2791.325eV
Energy per atom: Epot =2010.175eV  Ekin = 778.309eV (T=1505.318K) Etot = 2788.485eV
Energy per atom: Epot =2017.911eV  Ekin = 773.286eV (T=1495.602K) Etot = 2791.197eV
Energy per atom: Epot =2024.311eV  Ekin = 770.302eV (T=1489.831K) Etot = 2794.613eV
Energy per atom: Epot =2021.566eV  Ekin = 780.156eV (T=1508.890K) Etot = 2801.723eV
Energy per atom: Epot =2013.000eV  Ekin = 782.398eV (T=1513.225K) Etot = 2795.398eV
Energy per atom: Epot =2021.571eV  Ekin = 772.061eV (T=1493.233K) Etot = 2793.631eV
Energy per atom: Epot =2008.949eV  Ekin = 779.231eV (T=1507.100K) Etot = 2788.180eV
Energy per atom: Epot =2022.470eV  Ekin = 770.087eV (T=1489.416K) Etot = 2792.557eV
Energy per atom: Epot =2021.620eV  Ekin = 769.653eV (T=1488.577K) Etot = 2791.273eV
Energy per atom: Epot =2024.827eV  Ekin = 767.776eV (T=1484.946K) Etot = 2792.603eV
Energy per atom: Epot =2019.620eV  Ekin = 776.707eV (T=1502.219K) Etot = 2796.327eV
Energy per atom: Epot =2027.560eV  Ekin = 771.229eV (T=1491.624K) Etot = 2798.790eV
Energy per atom: Epot =2032.189eV  Ekin = 764.244eV (T=1478.115K) Etot = 2796.433eV
Energy per atom: Epot =2026.229eV  Ekin = 768.485eV (T=1486.316K) Etot = 2794.713eV
Energy per atom: Epot =2009.333eV  Ekin = 771.036eV (T=1491.251K) Etot = 2780.369eV
Energy per atom: Epot =2009.537eV  Ekin = 766.541eV (T=1482.558K) Etot = 2776.079eV
Energy per atom: Epot =2014.277eV  Ekin = 766.552eV (T=1482.578K) Etot = 2780.829eV
Energy per atom: Epot =2011.145eV  Ekin = 767.570eV (T=1484.548K) Etot = 2778.715eV
Energy per atom: Epot =2005.202eV  Ekin = 767.751eV (T=1484.898K) Etot = 2772.953eV
Energy per atom: Epot =2007.484eV  Ekin = 766.669eV (T=1482.805K) Etot = 2774.153eV
Energy per atom: Epot =1997.386eV  Ekin = 778.021eV (T=1504.761K) Etot = 2775.408eV
Energy per atom: Epot =2012.687eV  Ekin = 762.384eV (T=1474.517K) Etot = 2775.071eV
Energy per atom: Epot =1998.162eV  Ekin = 785.032eV (T=1518.320K) Etot = 2783.193eV
Energy per atom: Epot =2005.222eV  Ekin = 782.687eV (T=1513.785K) Etot = 2787.909eV
Energy per atom: Epot =2003.302eV  Ekin = 787.121eV (T=1522.361K) Etot = 2790.423eV
Energy per atom: Epot =1995.967eV  Ekin = 800.707eV (T=1548.637K) Etot = 2796.674eV
Energy per atom: Epot =2001.846eV  Ekin = 785.164eV (T=1518.576K) Etot = 2787.010eV
Energy per atom: Epot =2004.849eV  Ekin = 791.180eV (T=1530.212K) Etot = 2796.029eV
Energy per atom: Epot =2006.784eV  Ekin = 788.572eV (T=1525.168K) Etot = 2795.356eV
Energy per atom: Epot =2023.654eV  Ekin = 767.103eV (T=1483.645K) Etot = 2790.757eV
Energy per atom: Epot =2016.041eV  Ekin = 783.147eV (T=1514.674K) Etot = 2799.188eV
Energy per atom: Epot =2019.481eV  Ekin = 778.667eV (T=1506.010K) Etot = 2798.148eV
Energy per atom: Epot =2015.195eV  Ekin = 777.456eV (T=1503.668K) Etot = 2792.651eV
Energy per atom: Epot =2014.127eV  Ekin = 786.521eV (T=1521.200K) Etot = 2800.648eV
Energy per atom: Epot =2005.873eV  Ekin = 778.663eV (T=1506.001K) Etot = 2784.536eV
Energy per atom: Epot =2001.362eV  Ekin = 777.581eV (T=1503.910K) Etot = 2778.943eV
Energy per atom: Epot =2020.552eV  Ekin = 762.301eV (T=1474.356K) Etot = 2782.853eV
Energy per atom: Epot =2009.470eV  Ekin = 781.001eV (T=1510.523K) Etot = 2790.471eV
Energy per atom: Epot =2007.047eV  Ekin = 774.344eV (T=1497.648K) Etot = 2781.391eV
Energy per atom: Epot =2000.540eV  Ekin = 770.265eV (T=1489.759K) Etot = 2770.805eV
Energy per atom: Epot =2010.242eV  Ekin = 757.575eV (T=1465.217K) Etot = 2767.818eV
Energy per atom: Epot =2008.394eV  Ekin = 768.143eV (T=1485.655K) Etot = 2776.537eV
Energy per atom: Epot =2016.156eV  Ekin = 771.519eV (T=1492.184K) Etot = 2787.674eV
Energy per atom: Epot =2023.819eV  Ekin = 773.332eV (T=1495.691K) Etot = 2797.151eV
Energy per atom: Epot =2020.721eV  Ekin = 771.654eV (T=1492.446K) Etot = 2792.375eV
Energy per atom: Epot =2021.549eV  Ekin = 767.943eV (T=1485.268K) Etot = 2789.492eV
Energy per atom: Epot =2027.216eV  Ekin = 767.241eV (T=1483.911K) Etot = 2794.457eV
Energy per atom: Epot =2037.376eV  Ekin = 759.184eV (T=1468.329K) Etot = 2796.560eV
Energy per atom: Epot =2027.589eV  Ekin = 773.847eV (T=1496.688K) Etot = 2801.436eV
Energy per atom: Epot =2022.330eV  Ekin = 784.223eV (T=1516.755K) Etot = 2806.553eV
Energy per atom: Epot =2029.580eV  Ekin = 778.269eV (T=1505.240K) Etot = 2807.848eV
Energy per atom: Epot =2033.460eV  Ekin = 773.991eV (T=1496.967K) Etot = 2807.451eV
Energy per atom: Epot =2019.177eV  Ekin = 784.671eV (T=1517.622K) Etot = 2803.847eV
Energy per atom: Epot =2031.866eV  Ekin = 773.281eV (T=1495.593K) Etot = 2805.147eV
Energy per atom: Epot =2010.996eV  Ekin = 790.458eV (T=1528.815K) Etot = 2801.454eV
Energy per atom: Epot =2024.339eV  Ekin = 763.395eV (T=1476.472K) Etot = 2787.734eV
Energy per atom: Epot =2026.564eV  Ekin = 757.083eV (T=1464.264K) Etot = 2783.646eV

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] 09:02:00       43.457006       1.0818
BFGSLineSearch:    1[  1] 09:02:00       42.347659       0.2273
BFGSLineSearch:    2[  2] 09:02:00       42.108454       0.1349
BFGSLineSearch:    3[  3] 09:02:00       41.964817       0.1138
BFGSLineSearch:    4[  4] 09:02:00       41.924933       0.0683
BFGSLineSearch:    5[  5] 09:02:00       41.915346       0.0225
BFGSLineSearch:    6[  6] 09:02:00       41.914920       0.0059
BFGSLineSearch:    7[  7] 09:02:00       41.914872       0.0023
BFGSLineSearch:    8[  9] 09:02:00       41.914855       0.0023
BFGSLineSearch:    9[ 10] 09:02:00       41.914851       0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV  Ekin = 17.668eV (T=1469.770K) Etot = 59.583eV
Energy per atom: Epot =52.365eV  Ekin = 7.276eV (T=605.297K) Etot = 59.642eV
Energy per atom: Epot =52.238eV  Ekin = 7.408eV (T=616.221K) Etot = 59.646eV
Energy per atom: Epot =54.055eV  Ekin = 5.593eV (T=465.247K) Etot = 59.647eV
Energy per atom: Epot =52.595eV  Ekin = 7.048eV (T=586.340K) Etot = 59.644eV
Energy per atom: Epot =51.897eV  Ekin = 7.744eV (T=644.222K) Etot = 59.641eV
Energy per atom: Epot =52.083eV  Ekin = 7.558eV (T=628.763K) Etot = 59.641eV
Energy per atom: Epot =51.610eV  Ekin = 8.029eV (T=667.920K) Etot = 59.639eV
Energy per atom: Epot =51.248eV  Ekin = 8.393eV (T=698.169K) Etot = 59.641eV
Energy per atom: Epot =52.620eV  Ekin = 7.032eV (T=585.007K) Etot = 59.652eV
Energy per atom: Epot =52.913eV  Ekin = 6.738eV (T=560.492K) Etot = 59.650eV
Energy per atom: Epot =51.900eV  Ekin = 7.741eV (T=643.929K) Etot = 59.641eV
Energy per atom: Epot =52.288eV  Ekin = 7.349eV (T=611.351K) Etot = 59.637eV
Energy per atom: Epot =51.596eV  Ekin = 8.037eV (T=668.573K) Etot = 59.633eV
Energy per atom: Epot =51.346eV  Ekin = 8.285eV (T=689.160K) Etot = 59.630eV
Energy per atom: Epot =51.835eV  Ekin = 7.804eV (T=649.163K) Etot = 59.639eV
Energy per atom: Epot =51.900eV  Ekin = 7.740eV (T=643.902K) Etot = 59.640eV
Energy per atom: Epot =52.726eV  Ekin = 6.918eV (T=575.477K) Etot = 59.644eV
Energy per atom: Epot =52.327eV  Ekin = 7.317eV (T=608.710K) Etot = 59.645eV
Energy per atom: Epot =52.044eV  Ekin = 7.598eV (T=632.010K) Etot = 59.642eV
Energy per atom: Epot =51.961eV  Ekin = 7.678eV (T=638.676K) Etot = 59.639eV
Energy per atom: Epot =51.054eV  Ekin = 8.581eV (T=713.848K) Etot = 59.635eV
Energy per atom: Epot =51.876eV  Ekin = 7.768eV (T=646.171K) Etot = 59.644eV
Energy per atom: Epot =52.140eV  Ekin = 7.501eV (T=623.999K) Etot = 59.641eV
Energy per atom: Epot =52.474eV  Ekin = 7.166eV (T=596.123K) Etot = 59.640eV
Energy per atom: Epot =51.839eV  Ekin = 7.800eV (T=648.843K) Etot = 59.638eV
Energy per atom: Epot =52.029eV  Ekin = 7.615eV (T=633.427K) Etot = 59.643eV
Energy per atom: Epot =51.147eV  Ekin = 8.489eV (T=706.145K) Etot = 59.636eV
Energy per atom: Epot =51.472eV  Ekin = 8.163eV (T=679.030K) Etot = 59.634eV
Energy per atom: Epot =52.087eV  Ekin = 7.555eV (T=628.475K) Etot = 59.642eV
Energy per atom: Epot =52.330eV  Ekin = 7.316eV (T=608.602K) Etot = 59.647eV
Energy per atom: Epot =50.718eV  Ekin = 8.923eV (T=742.278K) Etot = 59.641eV
Energy per atom: Epot =51.467eV  Ekin = 8.171eV (T=679.678K) Etot = 59.638eV
Energy per atom: Epot =51.314eV  Ekin = 8.324eV (T=692.467K) Etot = 59.638eV
Energy per atom: Epot =51.421eV  Ekin = 8.221eV (T=683.867K) Etot = 59.642eV
Energy per atom: Epot =51.497eV  Ekin = 8.145eV (T=677.515K) Etot = 59.642eV
Energy per atom: Epot =51.261eV  Ekin = 8.376eV (T=696.789K) Etot = 59.638eV
Energy per atom: Epot =51.324eV  Ekin = 8.314eV (T=691.593K) Etot = 59.638eV
Energy per atom: Epot =51.830eV  Ekin = 7.812eV (T=649.858K) Etot = 59.642eV
Energy per atom: Epot =51.866eV  Ekin = 7.773eV (T=646.643K) Etot = 59.640eV
Energy per atom: Epot =50.900eV  Ekin = 8.730eV (T=726.245K) Etot = 59.630eV
Energy per atom: Epot =52.076eV  Ekin = 7.567eV (T=629.456K) Etot = 59.643eV
Energy per atom: Epot =50.906eV  Ekin = 8.730eV (T=726.208K) Etot = 59.636eV
Energy per atom: Epot =51.594eV  Ekin = 8.047eV (T=669.376K) Etot = 59.641eV
Energy per atom: Epot =51.873eV  Ekin = 7.773eV (T=646.634K) Etot = 59.646eV
Energy per atom: Epot =51.514eV  Ekin = 8.125eV (T=675.919K) Etot = 59.640eV
Energy per atom: Epot =50.802eV  Ekin = 8.834eV (T=734.862K) Etot = 59.636eV
Energy per atom: Epot =52.400eV  Ekin = 7.241eV (T=602.361K) Etot = 59.641eV
Energy per atom: Epot =52.059eV  Ekin = 7.578eV (T=630.420K) Etot = 59.637eV
Energy per atom: Epot =51.582eV  Ekin = 8.053eV (T=669.874K) Etot = 59.634eV
Energy per atom: Epot =51.857eV  Ekin = 7.781eV (T=647.246K) Etot = 59.638eV
Energy per atom: Epot =52.174eV  Ekin = 7.465eV (T=621.019K) Etot = 59.639eV
Energy per atom: Epot =51.146eV  Ekin = 8.487eV (T=705.995K) Etot = 59.633eV
Energy per atom: Epot =51.774eV  Ekin = 7.860eV (T=653.863K) Etot = 59.634eV
Energy per atom: Epot =51.802eV  Ekin = 7.838eV (T=652.019K) Etot = 59.640eV
Energy per atom: Epot =51.127eV  Ekin = 8.517eV (T=708.465K) Etot = 59.644eV
Energy per atom: Epot =51.536eV  Ekin = 8.104eV (T=674.121K) Etot = 59.639eV
Energy per atom: Epot =51.957eV  Ekin = 7.683eV (T=639.136K) Etot = 59.640eV
Energy per atom: Epot =51.579eV  Ekin = 8.056eV (T=670.138K) Etot = 59.635eV
Energy per atom: Epot =51.922eV  Ekin = 7.714eV (T=641.708K) Etot = 59.636eV
Energy per atom: Epot =51.798eV  Ekin = 7.840eV (T=652.143K) Etot = 59.637eV
Energy per atom: Epot =51.715eV  Ekin = 7.928eV (T=659.483K) Etot = 59.643eV
Energy per atom: Epot =51.329eV  Ekin = 8.305eV (T=690.866K) Etot = 59.634eV
Energy per atom: Epot =51.192eV  Ekin = 8.443eV (T=702.338K) Etot = 59.635eV
Energy per atom: Epot =51.726eV  Ekin = 7.918eV (T=658.688K) Etot = 59.644eV
Energy per atom: Epot =51.608eV  Ekin = 8.037eV (T=668.603K) Etot = 59.645eV
Energy per atom: Epot =51.786eV  Ekin = 7.856eV (T=653.503K) Etot = 59.642eV
Energy per atom: Epot =52.938eV  Ekin = 6.706eV (T=557.848K) Etot = 59.644eV
Energy per atom: Epot =51.308eV  Ekin = 8.327eV (T=692.713K) Etot = 59.635eV
Energy per atom: Epot =50.449eV  Ekin = 9.181eV (T=763.721K) Etot = 59.629eV
Energy per atom: Epot =51.098eV  Ekin = 8.541eV (T=710.515K) Etot = 59.639eV
Energy per atom: Epot =51.798eV  Ekin = 7.845eV (T=652.612K) Etot = 59.643eV
Energy per atom: Epot =51.395eV  Ekin = 8.237eV (T=685.244K) Etot = 59.633eV
Energy per atom: Epot =51.865eV  Ekin = 7.770eV (T=646.340K) Etot = 59.635eV
Energy per atom: Epot =52.301eV  Ekin = 7.338eV (T=610.427K) Etot = 59.639eV
Energy per atom: Epot =50.838eV  Ekin = 8.792eV (T=731.398K) Etot = 59.630eV
Energy per atom: Epot =51.309eV  Ekin = 8.326eV (T=692.575K) Etot = 59.634eV
Energy per atom: Epot =51.623eV  Ekin = 8.013eV (T=666.599K) Etot = 59.636eV
Energy per atom: Epot =52.488eV  Ekin = 7.153eV (T=595.055K) Etot = 59.641eV
Energy per atom: Epot =51.124eV  Ekin = 8.514eV (T=708.214K) Etot = 59.638eV
Energy per atom: Epot =51.655eV  Ekin = 7.982eV (T=664.016K) Etot = 59.637eV
Energy per atom: Epot =51.304eV  Ekin = 8.330eV (T=692.908K) Etot = 59.633eV
Energy per atom: Epot =50.809eV  Ekin = 8.828eV (T=734.406K) Etot = 59.637eV
Energy per atom: Epot =51.976eV  Ekin = 7.671eV (T=638.136K) Etot = 59.647eV
Energy per atom: Epot =51.497eV  Ekin = 8.145eV (T=677.556K) Etot = 59.642eV
Energy per atom: Epot =51.608eV  Ekin = 8.031eV (T=668.075K) Etot = 59.639eV
Energy per atom: Epot =50.468eV  Ekin = 9.164eV (T=762.321K) Etot = 59.632eV
Energy per atom: Epot =51.829eV  Ekin = 7.811eV (T=649.791K) Etot = 59.640eV
Energy per atom: Epot =50.409eV  Ekin = 9.221eV (T=767.057K) Etot = 59.630eV
Energy per atom: Epot =52.040eV  Ekin = 7.598eV (T=632.044K) Etot = 59.638eV
Energy per atom: Epot =51.459eV  Ekin = 8.177eV (T=680.185K) Etot = 59.636eV
Energy per atom: Epot =51.301eV  Ekin = 8.331eV (T=693.067K) Etot = 59.633eV
Energy per atom: Epot =51.240eV  Ekin = 8.395eV (T=698.321K) Etot = 59.634eV
Energy per atom: Epot =51.443eV  Ekin = 8.196eV (T=681.822K) Etot = 59.639eV
Energy per atom: Epot =51.329eV  Ekin = 8.313eV (T=691.490K) Etot = 59.641eV
Energy per atom: Epot =51.523eV  Ekin = 8.119eV (T=675.397K) Etot = 59.642eV
Energy per atom: Epot =51.506eV  Ekin = 8.138eV (T=676.950K) Etot = 59.644eV
Energy per atom: Epot =51.041eV  Ekin = 8.596eV (T=715.056K) Etot = 59.636eV
Energy per atom: Epot =51.442eV  Ekin = 8.192eV (T=681.482K) Etot = 59.634eV
Energy per atom: Epot =52.366eV  Ekin = 7.277eV (T=605.320K) Etot = 59.643eV
Energy per atom: Epot =51.546eV  Ekin = 8.096eV (T=673.514K) Etot = 59.643eV
Energy per atom: Epot =51.862eV  Ekin = 7.784eV (T=647.501K) Etot = 59.646eV
Energy per atom: Epot =51.430eV  Ekin = 8.212eV (T=683.149K) Etot = 59.642eV
Energy per atom: Epot =51.890eV  Ekin = 7.756eV (T=645.195K) Etot = 59.646eV
Energy per atom: Epot =51.406eV  Ekin = 8.236eV (T=685.116K) Etot = 59.642eV
Energy per atom: Epot =51.069eV  Ekin = 8.574eV (T=713.211K) Etot = 59.643eV
Energy per atom: Epot =50.833eV  Ekin = 8.805eV (T=732.470K) Etot = 59.638eV
Energy per atom: Epot =50.893eV  Ekin = 8.740eV (T=727.052K) Etot = 59.633eV
Energy per atom: Epot =52.716eV  Ekin = 6.931eV (T=576.602K) Etot = 59.648eV
Energy per atom: Epot =51.711eV  Ekin = 7.929eV (T=659.577K) Etot = 59.640eV
Energy per atom: Epot =51.241eV  Ekin = 8.394eV (T=698.280K) Etot = 59.636eV
Energy per atom: Epot =52.023eV  Ekin = 7.622eV (T=634.026K) Etot = 59.645eV
Energy per atom: Epot =51.035eV  Ekin = 8.605eV (T=715.827K) Etot = 59.640eV
Energy per atom: Epot =51.398eV  Ekin = 8.246eV (T=685.919K) Etot = 59.644eV
Energy per atom: Epot =51.747eV  Ekin = 7.897eV (T=656.935K) Etot = 59.644eV
Energy per atom: Epot =50.635eV  Ekin = 9.000eV (T=748.702K) Etot = 59.635eV
Energy per atom: Epot =51.282eV  Ekin = 8.357eV (T=695.176K) Etot = 59.639eV
Energy per atom: Epot =50.778eV  Ekin = 8.858eV (T=736.907K) Etot = 59.636eV
Energy per atom: Epot =51.155eV  Ekin = 8.482eV (T=705.603K) Etot = 59.637eV
Energy per atom: Epot =50.374eV  Ekin = 9.263eV (T=770.563K) Etot = 59.637eV
Energy per atom: Epot =51.710eV  Ekin = 7.931eV (T=659.715K) Etot = 59.641eV
Energy per atom: Epot =51.318eV  Ekin = 8.320eV (T=692.123K) Etot = 59.638eV
Energy per atom: Epot =51.193eV  Ekin = 8.443eV (T=702.340K) Etot = 59.636eV
Energy per atom: Epot =51.116eV  Ekin = 8.520eV (T=708.727K) Etot = 59.636eV
Energy per atom: Epot =52.587eV  Ekin = 7.053eV (T=586.691K) Etot = 59.640eV
Energy per atom: Epot =52.101eV  Ekin = 7.539eV (T=627.147K) Etot = 59.640eV
Energy per atom: Epot =51.811eV  Ekin = 7.832eV (T=651.506K) Etot = 59.642eV
Energy per atom: Epot =52.131eV  Ekin = 7.517eV (T=625.276K) Etot = 59.648eV
Energy per atom: Epot =50.735eV  Ekin = 8.898eV (T=740.233K) Etot = 59.634eV
Energy per atom: Epot =51.095eV  Ekin = 8.542eV (T=710.561K) Etot = 59.637eV
Energy per atom: Epot =50.888eV  Ekin = 8.754eV (T=728.197K) Etot = 59.641eV
Energy per atom: Epot =51.156eV  Ekin = 8.489eV (T=706.201K) Etot = 59.646eV
Energy per atom: Epot =52.402eV  Ekin = 7.253eV (T=603.361K) Etot = 59.655eV
Energy per atom: Epot =51.441eV  Ekin = 8.206eV (T=682.629K) Etot = 59.647eV
Energy per atom: Epot =51.322eV  Ekin = 8.316eV (T=691.795K) Etot = 59.638eV
Energy per atom: Epot =50.557eV  Ekin = 9.079eV (T=755.229K) Etot = 59.636eV
Energy per atom: Epot =51.923eV  Ekin = 7.720eV (T=642.232K) Etot = 59.643eV
Energy per atom: Epot =51.827eV  Ekin = 7.812eV (T=649.879K) Etot = 59.639eV
Energy per atom: Epot =52.381eV  Ekin = 7.263eV (T=604.215K) Etot = 59.644eV
Energy per atom: Epot =50.760eV  Ekin = 8.883eV (T=738.978K) Etot = 59.643eV
Energy per atom: Epot =50.350eV  Ekin = 9.292eV (T=772.980K) Etot = 59.642eV
Energy per atom: Epot =51.915eV  Ekin = 7.722eV (T=642.332K) Etot = 59.637eV
Energy per atom: Epot =51.171eV  Ekin = 8.468eV (T=704.398K) Etot = 59.639eV
Energy per atom: Epot =51.222eV  Ekin = 8.423eV (T=700.687K) Etot = 59.645eV
Energy per atom: Epot =51.094eV  Ekin = 8.547eV (T=710.957K) Etot = 59.641eV
Energy per atom: Epot =51.600eV  Ekin = 8.040eV (T=668.816K) Etot = 59.640eV
Energy per atom: Epot =50.454eV  Ekin = 9.179eV (T=763.565K) Etot = 59.633eV
Energy per atom: Epot =50.226eV  Ekin = 9.409eV (T=782.723K) Etot = 59.636eV
Energy per atom: Epot =51.046eV  Ekin = 8.598eV (T=715.205K) Etot = 59.643eV
Energy per atom: Epot =51.957eV  Ekin = 7.692eV (T=639.900K) Etot = 59.649eV
Energy per atom: Epot =51.101eV  Ekin = 8.539eV (T=710.370K) Etot = 59.641eV
Energy per atom: Epot =50.065eV  Ekin = 9.563eV (T=795.490K) Etot = 59.628eV
Energy per atom: Epot =50.802eV  Ekin = 8.834eV (T=734.876K) Etot = 59.636eV
Energy per atom: Epot =50.845eV  Ekin = 8.791eV (T=731.263K) Etot = 59.636eV
Energy per atom: Epot =50.415eV  Ekin = 9.220eV (T=766.964K) Etot = 59.634eV
Energy per atom: Epot =51.322eV  Ekin = 8.316eV (T=691.763K) Etot = 59.637eV
Energy per atom: Epot =50.372eV  Ekin = 9.262eV (T=770.461K) Etot = 59.634eV
Energy per atom: Epot =51.018eV  Ekin = 8.617eV (T=716.854K) Etot = 59.636eV
Energy per atom: Epot =49.920eV  Ekin = 9.714eV (T=808.093K) Etot = 59.634eV
Energy per atom: Epot =51.129eV  Ekin = 8.518eV (T=708.611K) Etot = 59.648eV
Energy per atom: Epot =51.005eV  Ekin = 8.631eV (T=718.015K) Etot = 59.637eV
Energy per atom: Epot =50.052eV  Ekin = 9.575eV (T=796.522K) Etot = 59.627eV
Energy per atom: Epot =51.564eV  Ekin = 8.079eV (T=672.026K) Etot = 59.642eV
Energy per atom: Epot =51.182eV  Ekin = 8.458eV (T=703.590K) Etot = 59.640eV
Energy per atom: Epot =51.771eV  Ekin = 7.873eV (T=654.940K) Etot = 59.645eV
Energy per atom: Epot =51.120eV  Ekin = 8.518eV (T=708.542K) Etot = 59.638eV
Energy per atom: Epot =51.578eV  Ekin = 8.062eV (T=670.675K) Etot = 59.640eV
Energy per atom: Epot =50.835eV  Ekin = 8.796eV (T=731.675K) Etot = 59.630eV
Energy per atom: Epot =51.045eV  Ekin = 8.587eV (T=714.327K) Etot = 59.632eV
Energy per atom: Epot =51.773eV  Ekin = 7.867eV (T=654.395K) Etot = 59.640eV
Energy per atom: Epot =51.997eV  Ekin = 7.650eV (T=636.390K) Etot = 59.647eV
Energy per atom: Epot =51.423eV  Ekin = 8.224eV (T=684.160K) Etot = 59.647eV
Energy per atom: Epot =51.674eV  Ekin = 7.967eV (T=662.769K) Etot = 59.641eV
Energy per atom: Epot =50.921eV  Ekin = 8.714eV (T=724.925K) Etot = 59.636eV
Energy per atom: Epot =50.414eV  Ekin = 9.227eV (T=767.524K) Etot = 59.641eV
Energy per atom: Epot =51.323eV  Ekin = 8.319eV (T=692.033K) Etot = 59.642eV
Energy per atom: Epot =51.159eV  Ekin = 8.477eV (T=705.180K) Etot = 59.636eV
Energy per atom: Epot =50.197eV  Ekin = 9.438eV (T=785.122K) Etot = 59.635eV
Energy per atom: Epot =51.059eV  Ekin = 8.584eV (T=714.069K) Etot = 59.643eV
Energy per atom: Epot =50.583eV  Ekin = 9.052eV (T=752.992K) Etot = 59.635eV
Energy per atom: Epot =50.340eV  Ekin = 9.293eV (T=773.088K) Etot = 59.633eV
Energy per atom: Epot =50.865eV  Ekin = 8.776eV (T=730.073K) Etot = 59.642eV
Energy per atom: Epot =51.432eV  Ekin = 8.212eV (T=683.160K) Etot = 59.645eV
Energy per atom: Epot =51.464eV  Ekin = 8.179eV (T=680.372K) Etot = 59.642eV
Energy per atom: Epot =51.752eV  Ekin = 7.888eV (T=656.154K) Etot = 59.639eV
Energy per atom: Epot =50.834eV  Ekin = 8.800eV (T=732.062K) Etot = 59.634eV
Energy per atom: Epot =50.232eV  Ekin = 9.408eV (T=782.608K) Etot = 59.640eV
Energy per atom: Epot =50.639eV  Ekin = 9.007eV (T=749.299K) Etot = 59.646eV
Energy per atom: Epot =50.581eV  Ekin = 9.059eV (T=753.559K) Etot = 59.640eV
Energy per atom: Epot =51.730eV  Ekin = 7.912eV (T=658.170K) Etot = 59.642eV
Energy per atom: Epot =51.514eV  Ekin = 8.125eV (T=675.874K) Etot = 59.639eV
Energy per atom: Epot =51.076eV  Ekin = 8.560eV (T=712.115K) Etot = 59.637eV
Energy per atom: Epot =51.623eV  Ekin = 8.014eV (T=666.693K) Etot = 59.638eV
Energy per atom: Epot =51.172eV  Ekin = 8.468eV (T=704.437K) Etot = 59.640eV
Energy per atom: Epot =52.076eV  Ekin = 7.571eV (T=629.806K) Etot = 59.647eV
Energy per atom: Epot =50.398eV  Ekin = 9.239eV (T=768.563K) Etot = 59.637eV
Energy per atom: Epot =50.725eV  Ekin = 8.912eV (T=741.324K) Etot = 59.636eV
Energy per atom: Epot =50.496eV  Ekin = 9.143eV (T=760.566K) Etot = 59.639eV
Energy per atom: Epot =50.727eV  Ekin = 8.913eV (T=741.455K) Etot = 59.640eV
Energy per atom: Epot =50.601eV  Ekin = 9.039eV (T=751.886K) Etot = 59.640eV
Energy per atom: Epot =51.128eV  Ekin = 8.513eV (T=708.203K) Etot = 59.641eV

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?

Gallery generated by Sphinx-Gallery

Contents