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 = 151.071eV (T=292.185K) Etot = 148.667eV
Energy per atom: Epot =114.117eV  Ekin = 35.320eV (T=68.311K) Etot = 149.436eV
Energy per atom: Epot =76.330eV  Ekin = 72.974eV (T=141.138K) Etot = 149.303eV
Energy per atom: Epot =68.960eV  Ekin = 80.194eV (T=155.103K) Etot = 149.155eV
Energy per atom: Epot =66.968eV  Ekin = 82.135eV (T=158.856K) Etot = 149.103eV
Energy per atom: Epot =78.841eV  Ekin = 70.425eV (T=136.208K) Etot = 149.266eV
Energy per atom: Epot =75.194eV  Ekin = 74.054eV (T=143.227K) Etot = 149.249eV
Energy per atom: Epot =72.195eV  Ekin = 76.976eV (T=148.877K) Etot = 149.170eV
Energy per atom: Epot =69.579eV  Ekin = 79.587eV (T=153.928K) Etot = 149.166eV
Energy per atom: Epot =77.377eV  Ekin = 71.871eV (T=139.004K) Etot = 149.248eV
Energy per atom: Epot =73.158eV  Ekin = 76.043eV (T=147.074K) Etot = 149.201eV
Energy per atom: Epot =71.991eV  Ekin = 77.198eV (T=149.307K) Etot = 149.189eV
Energy per atom: Epot =73.998eV  Ekin = 75.215eV (T=145.471K) Etot = 149.212eV
Energy per atom: Epot =74.930eV  Ekin = 74.277eV (T=143.659K) Etot = 149.207eV
Energy per atom: Epot =71.314eV  Ekin = 77.875eV (T=150.617K) Etot = 149.189eV
Energy per atom: Epot =74.402eV  Ekin = 74.825eV (T=144.718K) Etot = 149.227eV
Energy per atom: Epot =72.765eV  Ekin = 76.434eV (T=147.831K) Etot = 149.199eV
Energy per atom: Epot =75.121eV  Ekin = 74.081eV (T=143.278K) Etot = 149.201eV
Energy per atom: Epot =71.170eV  Ekin = 78.027eV (T=150.911K) Etot = 149.197eV
Energy per atom: Epot =74.493eV  Ekin = 74.713eV (T=144.501K) Etot = 149.206eV
Energy per atom: Epot =75.817eV  Ekin = 73.397eV (T=141.956K) Etot = 149.214eV

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 =600.074eV  Ekin = 82.644eV (T=159.840K) Etot = 682.718eV
Energy per atom: Epot =673.134eV  Ekin = 141.347eV (T=273.378K) Etot = 814.481eV
Energy per atom: Epot =728.396eV  Ekin = 201.057eV (T=388.861K) Etot = 929.453eV
Energy per atom: Epot =787.047eV  Ekin = 254.356eV (T=491.948K) Etot = 1041.404eV
Energy per atom: Epot =836.533eV  Ekin = 300.302eV (T=580.810K) Etot = 1136.835eV
Energy per atom: Epot =879.926eV  Ekin = 344.682eV (T=666.645K) Etot = 1224.607eV
Energy per atom: Epot =920.931eV  Ekin = 387.207eV (T=748.892K) Etot = 1308.138eV
Energy per atom: Epot =964.997eV  Ekin = 417.764eV (T=807.991K) Etot = 1382.761eV
Energy per atom: Epot =1002.694eV  Ekin = 443.727eV (T=858.206K) Etot = 1446.421eV
Energy per atom: Epot =1041.790eV  Ekin = 465.064eV (T=899.474K) Etot = 1506.854eV
Energy per atom: Epot =1075.058eV  Ekin = 490.570eV (T=948.806K) Etot = 1565.629eV
Energy per atom: Epot =1103.164eV  Ekin = 509.693eV (T=985.790K) Etot = 1612.857eV
Energy per atom: Epot =1137.221eV  Ekin = 522.503eV (T=1010.566K) Etot = 1659.724eV
Energy per atom: Epot =1173.570eV  Ekin = 529.448eV (T=1023.998K) Etot = 1703.018eV
Energy per atom: Epot =1195.176eV  Ekin = 554.115eV (T=1071.707K) Etot = 1749.291eV
Energy per atom: Epot =1222.456eV  Ekin = 560.668eV (T=1084.380K) Etot = 1783.124eV
Energy per atom: Epot =1250.048eV  Ekin = 575.409eV (T=1112.890K) Etot = 1825.456eV
Energy per atom: Epot =1279.918eV  Ekin = 590.243eV (T=1141.581K) Etot = 1870.161eV
Energy per atom: Epot =1307.590eV  Ekin = 596.985eV (T=1154.621K) Etot = 1904.575eV
Energy per atom: Epot =1322.414eV  Ekin = 616.789eV (T=1192.924K) Etot = 1939.203eV
Energy per atom: Epot =1354.598eV  Ekin = 613.064eV (T=1185.719K) Etot = 1967.662eV
Energy per atom: Epot =1361.185eV  Ekin = 640.965eV (T=1239.681K) Etot = 2002.150eV
Energy per atom: Epot =1387.825eV  Ekin = 643.665eV (T=1244.905K) Etot = 2031.490eV
Energy per atom: Epot =1401.606eV  Ekin = 654.726eV (T=1266.297K) Etot = 2056.332eV
Energy per atom: Epot =1408.031eV  Ekin = 663.287eV (T=1282.854K) Etot = 2071.318eV
Energy per atom: Epot =1422.299eV  Ekin = 665.836eV (T=1287.784K) Etot = 2088.135eV
Energy per atom: Epot =1437.362eV  Ekin = 677.106eV (T=1309.582K) Etot = 2114.468eV
Energy per atom: Epot =1456.278eV  Ekin = 670.798eV (T=1297.382K) Etot = 2127.076eV
Energy per atom: Epot =1472.299eV  Ekin = 679.869eV (T=1314.925K) Etot = 2152.168eV
Energy per atom: Epot =1475.564eV  Ekin = 689.009eV (T=1332.603K) Etot = 2164.573eV
Energy per atom: Epot =1508.564eV  Ekin = 679.957eV (T=1315.097K) Etot = 2188.521eV
Energy per atom: Epot =1525.795eV  Ekin = 679.153eV (T=1313.541K) Etot = 2204.949eV
Energy per atom: Epot =1519.694eV  Ekin = 705.567eV (T=1364.628K) Etot = 2225.261eV
Energy per atom: Epot =1540.428eV  Ekin = 698.182eV (T=1350.345K) Etot = 2238.610eV
Energy per atom: Epot =1569.192eV  Ekin = 684.637eV (T=1324.147K) Etot = 2253.829eV
Energy per atom: Epot =1557.437eV  Ekin = 715.361eV (T=1383.570K) Etot = 2272.797eV
Energy per atom: Epot =1577.751eV  Ekin = 713.137eV (T=1379.270K) Etot = 2290.888eV
Energy per atom: Epot =1591.610eV  Ekin = 703.184eV (T=1360.019K) Etot = 2294.794eV
Energy per atom: Epot =1615.591eV  Ekin = 695.289eV (T=1344.749K) Etot = 2310.880eV
Energy per atom: Epot =1607.190eV  Ekin = 714.247eV (T=1381.416K) Etot = 2321.437eV
Energy per atom: Epot =1626.090eV  Ekin = 715.537eV (T=1383.911K) Etot = 2341.627eV
Energy per atom: Epot =1638.621eV  Ekin = 707.588eV (T=1368.537K) Etot = 2346.209eV
Energy per atom: Epot =1650.203eV  Ekin = 709.008eV (T=1371.283K) Etot = 2359.211eV
Energy per atom: Epot =1672.073eV  Ekin = 705.967eV (T=1365.402K) Etot = 2378.040eV
Energy per atom: Epot =1662.714eV  Ekin = 730.239eV (T=1412.346K) Etot = 2392.953eV
Energy per atom: Epot =1684.303eV  Ekin = 714.929eV (T=1382.734K) Etot = 2399.232eV
Energy per atom: Epot =1689.989eV  Ekin = 724.603eV (T=1401.446K) Etot = 2414.592eV
Energy per atom: Epot =1701.944eV  Ekin = 718.447eV (T=1389.538K) Etot = 2420.390eV
Energy per atom: Epot =1706.958eV  Ekin = 729.585eV (T=1411.082K) Etot = 2436.543eV
Energy per atom: Epot =1717.680eV  Ekin = 728.611eV (T=1409.197K) Etot = 2446.291eV
Energy per atom: Epot =1711.537eV  Ekin = 742.015eV (T=1435.122K) Etot = 2453.552eV
Energy per atom: Epot =1723.277eV  Ekin = 743.054eV (T=1437.131K) Etot = 2466.331eV
Energy per atom: Epot =1723.290eV  Ekin = 747.090eV (T=1444.937K) Etot = 2470.380eV
Energy per atom: Epot =1731.542eV  Ekin = 740.717eV (T=1432.611K) Etot = 2472.259eV
Energy per atom: Epot =1724.299eV  Ekin = 750.080eV (T=1450.720K) Etot = 2474.379eV
Energy per atom: Epot =1745.551eV  Ekin = 740.874eV (T=1432.915K) Etot = 2486.425eV
Energy per atom: Epot =1751.335eV  Ekin = 740.024eV (T=1431.272K) Etot = 2491.359eV
Energy per atom: Epot =1753.673eV  Ekin = 742.359eV (T=1435.787K) Etot = 2496.032eV
Energy per atom: Epot =1756.341eV  Ekin = 743.574eV (T=1438.137K) Etot = 2499.915eV
Energy per atom: Epot =1761.462eV  Ekin = 738.356eV (T=1428.046K) Etot = 2499.818eV
Energy per atom: Epot =1772.328eV  Ekin = 741.133eV (T=1433.416K) Etot = 2513.461eV
Energy per atom: Epot =1783.717eV  Ekin = 733.343eV (T=1418.348K) Etot = 2517.060eV
Energy per atom: Epot =1785.782eV  Ekin = 743.130eV (T=1437.278K) Etot = 2528.912eV
Energy per atom: Epot =1788.074eV  Ekin = 739.698eV (T=1430.640K) Etot = 2527.772eV
Energy per atom: Epot =1784.424eV  Ekin = 747.003eV (T=1444.768K) Etot = 2531.427eV
Energy per atom: Epot =1803.714eV  Ekin = 733.874eV (T=1419.375K) Etot = 2537.587eV
Energy per atom: Epot =1794.819eV  Ekin = 741.155eV (T=1433.457K) Etot = 2535.974eV
Energy per atom: Epot =1819.498eV  Ekin = 729.059eV (T=1410.064K) Etot = 2548.558eV
Energy per atom: Epot =1824.303eV  Ekin = 736.475eV (T=1424.407K) Etot = 2560.778eV
Energy per atom: Epot =1807.602eV  Ekin = 750.135eV (T=1450.826K) Etot = 2557.737eV
Energy per atom: Epot =1824.726eV  Ekin = 732.117eV (T=1415.977K) Etot = 2556.843eV
Energy per atom: Epot =1826.764eV  Ekin = 733.609eV (T=1418.864K) Etot = 2560.373eV
Energy per atom: Epot =1834.806eV  Ekin = 731.635eV (T=1415.045K) Etot = 2566.440eV
Energy per atom: Epot =1836.772eV  Ekin = 733.049eV (T=1417.781K) Etot = 2569.821eV
Energy per atom: Epot =1853.708eV  Ekin = 729.067eV (T=1410.079K) Etot = 2582.775eV
Energy per atom: Epot =1850.127eV  Ekin = 741.090eV (T=1433.332K) Etot = 2591.217eV
Energy per atom: Epot =1837.341eV  Ekin = 752.310eV (T=1455.034K) Etot = 2589.652eV
Energy per atom: Epot =1853.806eV  Ekin = 739.404eV (T=1430.071K) Etot = 2593.210eV
Energy per atom: Epot =1854.685eV  Ekin = 747.978eV (T=1446.655K) Etot = 2602.664eV
Energy per atom: Epot =1868.747eV  Ekin = 737.128eV (T=1425.669K) Etot = 2605.874eV
Energy per atom: Epot =1867.889eV  Ekin = 744.992eV (T=1440.880K) Etot = 2612.881eV
Energy per atom: Epot =1891.375eV  Ekin = 737.165eV (T=1425.742K) Etot = 2628.540eV
Energy per atom: Epot =1866.497eV  Ekin = 756.837eV (T=1463.789K) Etot = 2623.334eV
Energy per atom: Epot =1876.175eV  Ekin = 746.347eV (T=1443.500K) Etot = 2622.522eV
Energy per atom: Epot =1869.058eV  Ekin = 759.962eV (T=1469.833K) Etot = 2629.021eV
Energy per atom: Epot =1898.763eV  Ekin = 741.007eV (T=1433.172K) Etot = 2639.770eV
Energy per atom: Epot =1892.841eV  Ekin = 748.720eV (T=1448.089K) Etot = 2641.561eV
Energy per atom: Epot =1885.871eV  Ekin = 753.239eV (T=1456.831K) Etot = 2639.110eV
Energy per atom: Epot =1890.387eV  Ekin = 753.714eV (T=1457.748K) Etot = 2644.101eV
Energy per atom: Epot =1891.860eV  Ekin = 749.860eV (T=1450.295K) Etot = 2641.720eV
Energy per atom: Epot =1890.807eV  Ekin = 752.056eV (T=1454.542K) Etot = 2642.863eV
Energy per atom: Epot =1889.443eV  Ekin = 750.871eV (T=1452.250K) Etot = 2640.314eV
Energy per atom: Epot =1900.777eV  Ekin = 745.028eV (T=1440.950K) Etot = 2645.806eV
Energy per atom: Epot =1901.143eV  Ekin = 752.984eV (T=1456.336K) Etot = 2654.126eV
Energy per atom: Epot =1905.822eV  Ekin = 758.745eV (T=1467.480K) Etot = 2664.568eV
Energy per atom: Epot =1905.238eV  Ekin = 765.192eV (T=1479.948K) Etot = 2670.431eV
Energy per atom: Epot =1929.709eV  Ekin = 739.435eV (T=1430.132K) Etot = 2669.144eV
Energy per atom: Epot =1929.249eV  Ekin = 746.950eV (T=1444.667K) Etot = 2676.199eV
Energy per atom: Epot =1920.411eV  Ekin = 757.924eV (T=1465.892K) Etot = 2678.335eV
Energy per atom: Epot =1924.644eV  Ekin = 761.233eV (T=1472.291K) Etot = 2685.877eV
Energy per atom: Epot =1944.023eV  Ekin = 740.601eV (T=1432.386K) Etot = 2684.624eV
Energy per atom: Epot =1926.609eV  Ekin = 759.805eV (T=1469.530K) Etot = 2686.415eV
Energy per atom: Epot =1937.707eV  Ekin = 751.194eV (T=1452.875K) Etot = 2688.901eV
Energy per atom: Epot =1940.155eV  Ekin = 750.559eV (T=1451.647K) Etot = 2690.715eV
Energy per atom: Epot =1949.439eV  Ekin = 748.113eV (T=1446.916K) Etot = 2697.552eV
Energy per atom: Epot =1941.939eV  Ekin = 767.837eV (T=1485.064K) Etot = 2709.777eV
Energy per atom: Epot =1941.558eV  Ekin = 764.488eV (T=1478.585K) Etot = 2706.045eV
Energy per atom: Epot =1938.859eV  Ekin = 774.898eV (T=1498.720K) Etot = 2713.757eV
Energy per atom: Epot =1935.820eV  Ekin = 778.210eV (T=1505.126K) Etot = 2714.031eV
Energy per atom: Epot =1948.713eV  Ekin = 768.428eV (T=1486.207K) Etot = 2717.141eV
Energy per atom: Epot =1947.037eV  Ekin = 762.062eV (T=1473.895K) Etot = 2709.099eV
Energy per atom: Epot =1948.276eV  Ekin = 758.882eV (T=1467.744K) Etot = 2707.158eV
Energy per atom: Epot =1958.613eV  Ekin = 744.537eV (T=1439.999K) Etot = 2703.150eV
Energy per atom: Epot =1945.208eV  Ekin = 760.988eV (T=1471.817K) Etot = 2706.196eV
Energy per atom: Epot =1934.906eV  Ekin = 772.363eV (T=1493.817K) Etot = 2707.268eV
Energy per atom: Epot =1938.558eV  Ekin = 762.054eV (T=1473.879K) Etot = 2700.612eV
Energy per atom: Epot =1943.131eV  Ekin = 755.765eV (T=1461.716K) Etot = 2698.896eV
Energy per atom: Epot =1956.409eV  Ekin = 757.269eV (T=1464.624K) Etot = 2713.678eV
Energy per atom: Epot =1958.139eV  Ekin = 760.784eV (T=1471.423K) Etot = 2718.923eV
Energy per atom: Epot =1969.779eV  Ekin = 751.439eV (T=1453.349K) Etot = 2721.218eV
Energy per atom: Epot =1970.215eV  Ekin = 764.195eV (T=1478.020K) Etot = 2734.410eV
Energy per atom: Epot =1975.155eV  Ekin = 763.043eV (T=1475.791K) Etot = 2738.198eV
Energy per atom: Epot =1977.427eV  Ekin = 766.455eV (T=1482.391K) Etot = 2743.882eV
Energy per atom: Epot =1980.862eV  Ekin = 768.848eV (T=1487.019K) Etot = 2749.710eV
Energy per atom: Epot =1996.398eV  Ekin = 756.641eV (T=1463.409K) Etot = 2753.039eV
Energy per atom: Epot =1993.925eV  Ekin = 762.829eV (T=1475.377K) Etot = 2756.754eV
Energy per atom: Epot =2005.620eV  Ekin = 738.315eV (T=1427.966K) Etot = 2743.935eV
Energy per atom: Epot =1994.619eV  Ekin = 764.064eV (T=1477.766K) Etot = 2758.683eV
Energy per atom: Epot =1999.681eV  Ekin = 762.188eV (T=1474.137K) Etot = 2761.869eV
Energy per atom: Epot =1990.685eV  Ekin = 772.741eV (T=1494.548K) Etot = 2763.426eV
Energy per atom: Epot =1999.153eV  Ekin = 777.553eV (T=1503.855K) Etot = 2776.706eV
Energy per atom: Epot =1999.595eV  Ekin = 787.994eV (T=1524.049K) Etot = 2787.589eV
Energy per atom: Epot =2012.171eV  Ekin = 772.706eV (T=1494.480K) Etot = 2784.877eV
Energy per atom: Epot =2004.573eV  Ekin = 780.243eV (T=1509.058K) Etot = 2784.816eV
Energy per atom: Epot =2004.910eV  Ekin = 782.943eV (T=1514.279K) Etot = 2787.853eV
Energy per atom: Epot =2003.901eV  Ekin = 779.161eV (T=1506.966K) Etot = 2783.063eV
Energy per atom: Epot =2010.830eV  Ekin = 778.132eV (T=1504.974K) Etot = 2788.961eV
Energy per atom: Epot =2015.202eV  Ekin = 777.114eV (T=1503.006K) Etot = 2792.316eV
Energy per atom: Epot =2012.123eV  Ekin = 778.258eV (T=1505.218K) Etot = 2790.381eV
Energy per atom: Epot =2003.500eV  Ekin = 787.334eV (T=1522.773K) Etot = 2790.835eV
Energy per atom: Epot =2011.271eV  Ekin = 783.630eV (T=1515.609K) Etot = 2794.901eV
Energy per atom: Epot =2019.159eV  Ekin = 780.611eV (T=1509.770K) Etot = 2799.770eV
Energy per atom: Epot =2025.065eV  Ekin = 771.099eV (T=1491.372K) Etot = 2796.164eV
Energy per atom: Epot =2018.414eV  Ekin = 783.007eV (T=1514.404K) Etot = 2801.421eV
Energy per atom: Epot =2021.094eV  Ekin = 780.602eV (T=1509.751K) Etot = 2801.696eV
Energy per atom: Epot =2028.059eV  Ekin = 788.761eV (T=1525.532K) Etot = 2816.820eV
Energy per atom: Epot =2038.131eV  Ekin = 771.266eV (T=1491.695K) Etot = 2809.396eV
Energy per atom: Epot =2022.975eV  Ekin = 780.359eV (T=1509.283K) Etot = 2803.335eV
Energy per atom: Epot =2019.009eV  Ekin = 776.257eV (T=1501.348K) Etot = 2795.266eV
Energy per atom: Epot =2012.919eV  Ekin = 782.077eV (T=1512.605K) Etot = 2794.996eV
Energy per atom: Epot =2001.163eV  Ekin = 774.657eV (T=1498.254K) Etot = 2775.820eV
Energy per atom: Epot =1998.917eV  Ekin = 770.158eV (T=1489.552K) Etot = 2769.075eV
Energy per atom: Epot =2009.483eV  Ekin = 767.284eV (T=1483.995K) Etot = 2776.767eV
Energy per atom: Epot =1990.640eV  Ekin = 787.881eV (T=1523.831K) Etot = 2778.521eV
Energy per atom: Epot =2006.529eV  Ekin = 768.663eV (T=1486.660K) Etot = 2775.191eV
Energy per atom: Epot =2011.659eV  Ekin = 764.267eV (T=1478.160K) Etot = 2775.927eV
Energy per atom: Epot =1994.825eV  Ekin = 770.493eV (T=1490.200K) Etot = 2765.318eV
Energy per atom: Epot =1998.643eV  Ekin = 772.531eV (T=1494.141K) Etot = 2771.174eV
Energy per atom: Epot =2014.372eV  Ekin = 749.250eV (T=1449.115K) Etot = 2763.622eV
Energy per atom: Epot =1996.423eV  Ekin = 767.883eV (T=1485.152K) Etot = 2764.306eV
Energy per atom: Epot =2002.858eV  Ekin = 771.548eV (T=1492.240K) Etot = 2774.405eV
Energy per atom: Epot =1996.398eV  Ekin = 773.551eV (T=1496.115K) Etot = 2769.949eV
Energy per atom: Epot =2001.742eV  Ekin = 774.239eV (T=1497.446K) Etot = 2775.981eV
Energy per atom: Epot =2012.717eV  Ekin = 769.309eV (T=1487.911K) Etot = 2782.026eV
Energy per atom: Epot =2002.239eV  Ekin = 769.456eV (T=1488.195K) Etot = 2771.696eV
Energy per atom: Epot =1990.883eV  Ekin = 783.538eV (T=1515.430K) Etot = 2774.420eV
Energy per atom: Epot =2000.229eV  Ekin = 771.505eV (T=1492.158K) Etot = 2771.734eV
Energy per atom: Epot =1993.956eV  Ekin = 776.421eV (T=1501.665K) Etot = 2770.377eV
Energy per atom: Epot =1996.535eV  Ekin = 776.921eV (T=1502.633K) Etot = 2773.456eV
Energy per atom: Epot =2002.727eV  Ekin = 773.762eV (T=1496.522K) Etot = 2776.488eV
Energy per atom: Epot =2003.596eV  Ekin = 777.052eV (T=1502.887K) Etot = 2780.648eV
Energy per atom: Epot =2011.324eV  Ekin = 774.147eV (T=1497.267K) Etot = 2785.471eV
Energy per atom: Epot =2009.437eV  Ekin = 778.034eV (T=1504.785K) Etot = 2787.471eV
Energy per atom: Epot =2015.397eV  Ekin = 766.079eV (T=1481.664K) Etot = 2781.476eV
Energy per atom: Epot =2000.692eV  Ekin = 769.447eV (T=1488.178K) Etot = 2770.139eV
Energy per atom: Epot =2001.267eV  Ekin = 778.629eV (T=1505.936K) Etot = 2779.896eV
Energy per atom: Epot =2013.761eV  Ekin = 774.403eV (T=1497.763K) Etot = 2788.164eV
Energy per atom: Epot =2021.923eV  Ekin = 766.545eV (T=1482.565K) Etot = 2788.469eV
Energy per atom: Epot =2022.830eV  Ekin = 764.531eV (T=1478.670K) Etot = 2787.361eV
Energy per atom: Epot =2021.293eV  Ekin = 763.347eV (T=1476.379K) Etot = 2784.640eV
Energy per atom: Epot =2007.625eV  Ekin = 776.539eV (T=1501.894K) Etot = 2784.164eV
Energy per atom: Epot =2014.614eV  Ekin = 769.429eV (T=1488.143K) Etot = 2784.043eV
Energy per atom: Epot =2017.573eV  Ekin = 769.171eV (T=1487.644K) Etot = 2786.745eV
Energy per atom: Epot =2017.257eV  Ekin = 771.868eV (T=1492.859K) Etot = 2789.125eV
Energy per atom: Epot =2026.850eV  Ekin = 763.762eV (T=1477.181K) Etot = 2790.611eV
Energy per atom: Epot =2030.237eV  Ekin = 770.222eV (T=1489.676K) Etot = 2800.458eV
Energy per atom: Epot =2020.782eV  Ekin = 786.990eV (T=1522.107K) Etot = 2807.772eV
Energy per atom: Epot =2013.073eV  Ekin = 792.184eV (T=1532.154K) Etot = 2805.257eV
Energy per atom: Epot =2027.233eV  Ekin = 779.507eV (T=1507.634K) Etot = 2806.740eV
Energy per atom: Epot =2008.465eV  Ekin = 787.996eV (T=1524.052K) Etot = 2796.461eV
Energy per atom: Epot =2017.982eV  Ekin = 774.275eV (T=1497.516K) Etot = 2792.258eV
Energy per atom: Epot =2008.150eV  Ekin = 779.716eV (T=1508.039K) Etot = 2787.866eV
Energy per atom: Epot =2007.988eV  Ekin = 772.816eV (T=1494.694K) Etot = 2780.804eV
Energy per atom: Epot =2007.747eV  Ekin = 773.871eV (T=1496.734K) Etot = 2781.618eV
Energy per atom: Epot =2009.656eV  Ekin = 768.972eV (T=1487.258K) Etot = 2778.628eV
Energy per atom: Epot =1991.305eV  Ekin = 776.540eV (T=1501.895K) Etot = 2767.844eV
Energy per atom: Epot =1999.363eV  Ekin = 765.839eV (T=1481.200K) Etot = 2765.202eV
Energy per atom: Epot =1996.937eV  Ekin = 781.922eV (T=1512.305K) Etot = 2778.859eV
Energy per atom: Epot =2007.240eV  Ekin = 773.613eV (T=1496.235K) Etot = 2780.853eV
Energy per atom: Epot =2012.783eV  Ekin = 759.555eV (T=1469.045K) Etot = 2772.338eV

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] 11:54:40       43.457006       1.0818
BFGSLineSearch:    1[  1] 11:54:40       42.347659       0.2273
BFGSLineSearch:    2[  2] 11:54:40       42.108454       0.1349
BFGSLineSearch:    3[  3] 11:54:40       41.964817       0.1138
BFGSLineSearch:    4[  4] 11:54:40       41.924933       0.0683
BFGSLineSearch:    5[  5] 11:54:40       41.915346       0.0225
BFGSLineSearch:    6[  6] 11:54:40       41.914920       0.0059
BFGSLineSearch:    7[  7] 11:54:40       41.914872       0.0023
BFGSLineSearch:    8[  9] 11:54:40       41.914855       0.0023
BFGSLineSearch:    9[ 10] 11:54:40       41.914851       0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV  Ekin = 14.351eV (T=1193.774K) Etot = 56.265eV
Energy per atom: Epot =50.171eV  Ekin = 6.132eV (T=510.101K) Etot = 56.303eV
Energy per atom: Epot =49.466eV  Ekin = 6.847eV (T=569.595K) Etot = 56.314eV
Energy per atom: Epot =50.484eV  Ekin = 5.831eV (T=485.053K) Etot = 56.315eV
Energy per atom: Epot =50.730eV  Ekin = 5.587eV (T=464.788K) Etot = 56.317eV
Energy per atom: Epot =49.918eV  Ekin = 6.398eV (T=532.256K) Etot = 56.316eV
Energy per atom: Epot =48.950eV  Ekin = 7.359eV (T=612.168K) Etot = 56.309eV
Energy per atom: Epot =49.094eV  Ekin = 7.216eV (T=600.236K) Etot = 56.309eV
Energy per atom: Epot =50.022eV  Ekin = 6.290eV (T=523.261K) Etot = 56.312eV
Energy per atom: Epot =49.112eV  Ekin = 7.195eV (T=598.558K) Etot = 56.308eV
Energy per atom: Epot =49.951eV  Ekin = 6.360eV (T=529.069K) Etot = 56.311eV
Energy per atom: Epot =50.534eV  Ekin = 5.778eV (T=480.675K) Etot = 56.312eV
Energy per atom: Epot =49.397eV  Ekin = 6.912eV (T=574.976K) Etot = 56.309eV
Energy per atom: Epot =49.362eV  Ekin = 6.948eV (T=578.016K) Etot = 56.310eV
Energy per atom: Epot =49.413eV  Ekin = 6.894eV (T=573.451K) Etot = 56.307eV
Energy per atom: Epot =49.336eV  Ekin = 6.971eV (T=579.859K) Etot = 56.306eV
Energy per atom: Epot =49.875eV  Ekin = 6.434eV (T=535.191K) Etot = 56.309eV
Energy per atom: Epot =49.433eV  Ekin = 6.875eV (T=571.928K) Etot = 56.308eV
Energy per atom: Epot =50.257eV  Ekin = 6.055eV (T=503.653K) Etot = 56.311eV
Energy per atom: Epot =49.674eV  Ekin = 6.639eV (T=552.315K) Etot = 56.313eV
Energy per atom: Epot =49.536eV  Ekin = 6.781eV (T=564.095K) Etot = 56.317eV
Energy per atom: Epot =49.684eV  Ekin = 6.636eV (T=552.027K) Etot = 56.320eV
Energy per atom: Epot =49.300eV  Ekin = 7.017eV (T=583.728K) Etot = 56.317eV
Energy per atom: Epot =49.608eV  Ekin = 6.706eV (T=557.841K) Etot = 56.314eV
Energy per atom: Epot =48.885eV  Ekin = 7.425eV (T=617.688K) Etot = 56.311eV
Energy per atom: Epot =50.463eV  Ekin = 5.858eV (T=487.300K) Etot = 56.321eV
Energy per atom: Epot =49.691eV  Ekin = 6.626eV (T=551.171K) Etot = 56.317eV
Energy per atom: Epot =49.262eV  Ekin = 7.047eV (T=586.202K) Etot = 56.309eV
Energy per atom: Epot =48.944eV  Ekin = 7.360eV (T=612.249K) Etot = 56.304eV
Energy per atom: Epot =49.094eV  Ekin = 7.215eV (T=600.175K) Etot = 56.309eV
Energy per atom: Epot =49.501eV  Ekin = 6.814eV (T=566.821K) Etot = 56.315eV
Energy per atom: Epot =49.108eV  Ekin = 7.203eV (T=599.233K) Etot = 56.311eV
Energy per atom: Epot =50.292eV  Ekin = 6.024eV (T=501.085K) Etot = 56.316eV
Energy per atom: Epot =49.077eV  Ekin = 7.235eV (T=601.849K) Etot = 56.312eV
Energy per atom: Epot =48.960eV  Ekin = 7.354eV (T=611.776K) Etot = 56.314eV
Energy per atom: Epot =48.981eV  Ekin = 7.331eV (T=609.876K) Etot = 56.312eV
Energy per atom: Epot =49.235eV  Ekin = 7.075eV (T=588.551K) Etot = 56.310eV
Energy per atom: Epot =49.089eV  Ekin = 7.226eV (T=601.085K) Etot = 56.315eV
Energy per atom: Epot =49.111eV  Ekin = 7.205eV (T=599.397K) Etot = 56.316eV
Energy per atom: Epot =49.221eV  Ekin = 7.088eV (T=589.649K) Etot = 56.309eV
Energy per atom: Epot =48.989eV  Ekin = 7.319eV (T=608.823K) Etot = 56.308eV
Energy per atom: Epot =50.128eV  Ekin = 6.185eV (T=514.522K) Etot = 56.313eV
Energy per atom: Epot =49.094eV  Ekin = 7.218eV (T=600.412K) Etot = 56.312eV
Energy per atom: Epot =48.835eV  Ekin = 7.477eV (T=621.989K) Etot = 56.312eV
Energy per atom: Epot =49.883eV  Ekin = 6.433eV (T=535.120K) Etot = 56.316eV
Energy per atom: Epot =49.491eV  Ekin = 6.826eV (T=567.843K) Etot = 56.317eV
Energy per atom: Epot =49.915eV  Ekin = 6.399eV (T=532.294K) Etot = 56.314eV
Energy per atom: Epot =49.850eV  Ekin = 6.466eV (T=537.856K) Etot = 56.316eV
Energy per atom: Epot =48.888eV  Ekin = 7.422eV (T=617.424K) Etot = 56.310eV
Energy per atom: Epot =49.686eV  Ekin = 6.619eV (T=550.592K) Etot = 56.305eV
Energy per atom: Epot =49.005eV  Ekin = 7.298eV (T=607.125K) Etot = 56.303eV
Energy per atom: Epot =49.522eV  Ekin = 6.789eV (T=564.781K) Etot = 56.311eV
Energy per atom: Epot =49.513eV  Ekin = 6.801eV (T=565.750K) Etot = 56.314eV
Energy per atom: Epot =49.721eV  Ekin = 6.591eV (T=548.312K) Etot = 56.313eV
Energy per atom: Epot =49.856eV  Ekin = 6.458eV (T=537.228K) Etot = 56.314eV
Energy per atom: Epot =48.987eV  Ekin = 7.321eV (T=609.047K) Etot = 56.308eV
Energy per atom: Epot =48.936eV  Ekin = 7.374eV (T=613.429K) Etot = 56.310eV
Energy per atom: Epot =49.422eV  Ekin = 6.886eV (T=572.812K) Etot = 56.308eV
Energy per atom: Epot =49.075eV  Ekin = 7.233eV (T=601.652K) Etot = 56.308eV
Energy per atom: Epot =48.632eV  Ekin = 7.679eV (T=638.778K) Etot = 56.310eV
Energy per atom: Epot =49.890eV  Ekin = 6.424eV (T=534.361K) Etot = 56.314eV
Energy per atom: Epot =49.070eV  Ekin = 7.236eV (T=601.934K) Etot = 56.306eV
Energy per atom: Epot =50.069eV  Ekin = 6.247eV (T=519.647K) Etot = 56.316eV
Energy per atom: Epot =49.351eV  Ekin = 6.960eV (T=578.969K) Etot = 56.311eV
Energy per atom: Epot =50.365eV  Ekin = 5.956eV (T=495.424K) Etot = 56.320eV
Energy per atom: Epot =49.082eV  Ekin = 7.231eV (T=601.486K) Etot = 56.313eV
Energy per atom: Epot =49.196eV  Ekin = 7.116eV (T=591.921K) Etot = 56.312eV
Energy per atom: Epot =48.957eV  Ekin = 7.354eV (T=611.773K) Etot = 56.311eV
Energy per atom: Epot =48.631eV  Ekin = 7.676eV (T=638.527K) Etot = 56.307eV
Energy per atom: Epot =49.046eV  Ekin = 7.266eV (T=604.443K) Etot = 56.312eV
Energy per atom: Epot =49.698eV  Ekin = 6.622eV (T=550.836K) Etot = 56.319eV
Energy per atom: Epot =49.911eV  Ekin = 6.408eV (T=533.090K) Etot = 56.319eV
Energy per atom: Epot =49.434eV  Ekin = 6.881eV (T=572.431K) Etot = 56.316eV
Energy per atom: Epot =49.188eV  Ekin = 7.127eV (T=592.891K) Etot = 56.316eV
Energy per atom: Epot =49.368eV  Ekin = 6.942eV (T=577.522K) Etot = 56.311eV
Energy per atom: Epot =48.921eV  Ekin = 7.387eV (T=614.488K) Etot = 56.308eV
Energy per atom: Epot =49.382eV  Ekin = 6.929eV (T=576.412K) Etot = 56.311eV
Energy per atom: Epot =48.896eV  Ekin = 7.416eV (T=616.878K) Etot = 56.311eV
Energy per atom: Epot =48.952eV  Ekin = 7.360eV (T=612.240K) Etot = 56.312eV
Energy per atom: Epot =48.223eV  Ekin = 8.085eV (T=672.530K) Etot = 56.307eV
Energy per atom: Epot =49.766eV  Ekin = 6.548eV (T=544.703K) Etot = 56.314eV
Energy per atom: Epot =49.975eV  Ekin = 6.339eV (T=527.339K) Etot = 56.315eV
Energy per atom: Epot =48.113eV  Ekin = 8.189eV (T=681.202K) Etot = 56.302eV
Energy per atom: Epot =48.644eV  Ekin = 7.664eV (T=637.574K) Etot = 56.308eV
Energy per atom: Epot =48.631eV  Ekin = 7.680eV (T=638.880K) Etot = 56.311eV
Energy per atom: Epot =48.746eV  Ekin = 7.559eV (T=628.776K) Etot = 56.304eV
Energy per atom: Epot =49.265eV  Ekin = 7.044eV (T=585.993K) Etot = 56.309eV
Energy per atom: Epot =49.304eV  Ekin = 7.011eV (T=583.185K) Etot = 56.314eV
Energy per atom: Epot =49.476eV  Ekin = 6.836eV (T=568.622K) Etot = 56.312eV
Energy per atom: Epot =48.654eV  Ekin = 7.653eV (T=636.603K) Etot = 56.306eV
Energy per atom: Epot =48.716eV  Ekin = 7.596eV (T=631.887K) Etot = 56.312eV
Energy per atom: Epot =49.103eV  Ekin = 7.209eV (T=599.724K) Etot = 56.312eV
Energy per atom: Epot =48.697eV  Ekin = 7.607eV (T=632.766K) Etot = 56.304eV
Energy per atom: Epot =48.706eV  Ekin = 7.604eV (T=632.560K) Etot = 56.310eV
Energy per atom: Epot =49.133eV  Ekin = 7.179eV (T=597.167K) Etot = 56.312eV
Energy per atom: Epot =49.506eV  Ekin = 6.801eV (T=565.775K) Etot = 56.307eV
Energy per atom: Epot =48.930eV  Ekin = 7.382eV (T=614.103K) Etot = 56.312eV
Energy per atom: Epot =48.279eV  Ekin = 8.026eV (T=667.670K) Etot = 56.305eV
Energy per atom: Epot =48.961eV  Ekin = 7.342eV (T=610.766K) Etot = 56.303eV
Energy per atom: Epot =49.210eV  Ekin = 7.102eV (T=590.803K) Etot = 56.312eV
Energy per atom: Epot =49.572eV  Ekin = 6.740eV (T=560.672K) Etot = 56.312eV
Energy per atom: Epot =49.809eV  Ekin = 6.504eV (T=541.046K) Etot = 56.313eV
Energy per atom: Epot =49.072eV  Ekin = 7.243eV (T=602.545K) Etot = 56.315eV
Energy per atom: Epot =48.835eV  Ekin = 7.477eV (T=622.018K) Etot = 56.313eV
Energy per atom: Epot =49.041eV  Ekin = 7.276eV (T=605.281K) Etot = 56.317eV
Energy per atom: Epot =48.975eV  Ekin = 7.336eV (T=610.284K) Etot = 56.312eV
Energy per atom: Epot =48.471eV  Ekin = 7.834eV (T=651.683K) Etot = 56.305eV
Energy per atom: Epot =49.568eV  Ekin = 6.747eV (T=561.289K) Etot = 56.315eV
Energy per atom: Epot =49.171eV  Ekin = 7.142eV (T=594.134K) Etot = 56.313eV
Energy per atom: Epot =49.490eV  Ekin = 6.820eV (T=567.341K) Etot = 56.311eV
Energy per atom: Epot =49.448eV  Ekin = 6.865eV (T=571.035K) Etot = 56.312eV
Energy per atom: Epot =49.045eV  Ekin = 7.263eV (T=604.151K) Etot = 56.308eV
Energy per atom: Epot =48.463eV  Ekin = 7.841eV (T=652.243K) Etot = 56.304eV
Energy per atom: Epot =49.227eV  Ekin = 7.081eV (T=589.050K) Etot = 56.308eV
Energy per atom: Epot =48.790eV  Ekin = 7.519eV (T=625.449K) Etot = 56.308eV
Energy per atom: Epot =49.243eV  Ekin = 7.068eV (T=587.921K) Etot = 56.310eV
Energy per atom: Epot =49.407eV  Ekin = 6.899eV (T=573.943K) Etot = 56.307eV
Energy per atom: Epot =48.712eV  Ekin = 7.598eV (T=632.052K) Etot = 56.310eV
Energy per atom: Epot =48.695eV  Ekin = 7.614eV (T=633.385K) Etot = 56.309eV
Energy per atom: Epot =48.943eV  Ekin = 7.363eV (T=612.523K) Etot = 56.307eV
Energy per atom: Epot =48.879eV  Ekin = 7.428eV (T=617.877K) Etot = 56.307eV
Energy per atom: Epot =49.991eV  Ekin = 6.322eV (T=525.926K) Etot = 56.313eV
Energy per atom: Epot =49.071eV  Ekin = 7.240eV (T=602.254K) Etot = 56.311eV
Energy per atom: Epot =48.423eV  Ekin = 7.879eV (T=655.439K) Etot = 56.302eV
Energy per atom: Epot =48.129eV  Ekin = 8.175eV (T=680.049K) Etot = 56.304eV
Energy per atom: Epot =48.621eV  Ekin = 7.688eV (T=639.526K) Etot = 56.309eV
Energy per atom: Epot =49.404eV  Ekin = 6.909eV (T=574.741K) Etot = 56.313eV
Energy per atom: Epot =49.095eV  Ekin = 7.219eV (T=600.498K) Etot = 56.314eV
Energy per atom: Epot =48.837eV  Ekin = 7.477eV (T=621.951K) Etot = 56.314eV
Energy per atom: Epot =49.776eV  Ekin = 6.539eV (T=543.936K) Etot = 56.314eV
Energy per atom: Epot =49.435eV  Ekin = 6.877eV (T=572.083K) Etot = 56.312eV
Energy per atom: Epot =48.736eV  Ekin = 7.576eV (T=630.198K) Etot = 56.312eV
Energy per atom: Epot =48.444eV  Ekin = 7.867eV (T=654.469K) Etot = 56.311eV
Energy per atom: Epot =49.486eV  Ekin = 6.832eV (T=568.309K) Etot = 56.318eV
Energy per atom: Epot =49.098eV  Ekin = 7.214eV (T=600.133K) Etot = 56.313eV
Energy per atom: Epot =49.266eV  Ekin = 7.041eV (T=585.701K) Etot = 56.307eV
Energy per atom: Epot =48.559eV  Ekin = 7.745eV (T=644.315K) Etot = 56.304eV
Energy per atom: Epot =48.441eV  Ekin = 7.868eV (T=654.471K) Etot = 56.308eV
Energy per atom: Epot =48.695eV  Ekin = 7.612eV (T=633.213K) Etot = 56.307eV
Energy per atom: Epot =49.510eV  Ekin = 6.798eV (T=565.481K) Etot = 56.307eV
Energy per atom: Epot =49.265eV  Ekin = 7.041eV (T=585.703K) Etot = 56.306eV
Energy per atom: Epot =49.619eV  Ekin = 6.693eV (T=556.768K) Etot = 56.312eV
Energy per atom: Epot =49.202eV  Ekin = 7.110eV (T=591.416K) Etot = 56.312eV
Energy per atom: Epot =49.075eV  Ekin = 7.236eV (T=601.910K) Etot = 56.310eV
Energy per atom: Epot =48.867eV  Ekin = 7.442eV (T=619.036K) Etot = 56.308eV
Energy per atom: Epot =48.747eV  Ekin = 7.566eV (T=629.368K) Etot = 56.313eV
Energy per atom: Epot =49.072eV  Ekin = 7.241eV (T=602.359K) Etot = 56.313eV
Energy per atom: Epot =48.334eV  Ekin = 7.968eV (T=662.835K) Etot = 56.302eV
Energy per atom: Epot =48.910eV  Ekin = 7.396eV (T=615.227K) Etot = 56.306eV
Energy per atom: Epot =49.132eV  Ekin = 7.175eV (T=596.850K) Etot = 56.307eV
Energy per atom: Epot =48.591eV  Ekin = 7.714eV (T=641.728K) Etot = 56.305eV
Energy per atom: Epot =50.091eV  Ekin = 6.222eV (T=517.628K) Etot = 56.314eV
Energy per atom: Epot =49.162eV  Ekin = 7.151eV (T=594.833K) Etot = 56.313eV
Energy per atom: Epot =48.514eV  Ekin = 7.791eV (T=648.095K) Etot = 56.305eV
Energy per atom: Epot =49.320eV  Ekin = 6.995eV (T=581.854K) Etot = 56.315eV
Energy per atom: Epot =49.324eV  Ekin = 6.989eV (T=581.422K) Etot = 56.313eV
Energy per atom: Epot =48.239eV  Ekin = 8.071eV (T=671.401K) Etot = 56.310eV
Energy per atom: Epot =48.766eV  Ekin = 7.544eV (T=627.549K) Etot = 56.310eV
Energy per atom: Epot =48.504eV  Ekin = 7.798eV (T=648.723K) Etot = 56.302eV
Energy per atom: Epot =48.973eV  Ekin = 7.337eV (T=610.322K) Etot = 56.310eV
Energy per atom: Epot =49.580eV  Ekin = 6.737eV (T=560.438K) Etot = 56.317eV
Energy per atom: Epot =48.647eV  Ekin = 7.660eV (T=637.190K) Etot = 56.307eV
Energy per atom: Epot =48.411eV  Ekin = 7.897eV (T=656.937K) Etot = 56.308eV
Energy per atom: Epot =49.024eV  Ekin = 7.290eV (T=606.410K) Etot = 56.314eV
Energy per atom: Epot =49.770eV  Ekin = 6.545eV (T=544.487K) Etot = 56.315eV
Energy per atom: Epot =49.452eV  Ekin = 6.860eV (T=570.697K) Etot = 56.312eV
Energy per atom: Epot =48.769eV  Ekin = 7.542eV (T=627.393K) Etot = 56.311eV
Energy per atom: Epot =50.078eV  Ekin = 6.238eV (T=518.935K) Etot = 56.316eV
Energy per atom: Epot =49.889eV  Ekin = 6.423eV (T=534.346K) Etot = 56.313eV
Energy per atom: Epot =49.866eV  Ekin = 6.452eV (T=536.760K) Etot = 56.318eV
Energy per atom: Epot =48.884eV  Ekin = 7.427eV (T=617.838K) Etot = 56.311eV
Energy per atom: Epot =49.193eV  Ekin = 7.120eV (T=592.268K) Etot = 56.313eV
Energy per atom: Epot =49.612eV  Ekin = 6.704eV (T=557.690K) Etot = 56.316eV
Energy per atom: Epot =49.018eV  Ekin = 7.294eV (T=606.746K) Etot = 56.311eV
Energy per atom: Epot =49.266eV  Ekin = 7.041eV (T=585.738K) Etot = 56.308eV
Energy per atom: Epot =50.388eV  Ekin = 5.926eV (T=492.968K) Etot = 56.314eV
Energy per atom: Epot =49.266eV  Ekin = 7.044eV (T=585.981K) Etot = 56.310eV
Energy per atom: Epot =49.622eV  Ekin = 6.692eV (T=556.704K) Etot = 56.314eV
Energy per atom: Epot =49.420eV  Ekin = 6.896eV (T=573.620K) Etot = 56.316eV
Energy per atom: Epot =49.168eV  Ekin = 7.143eV (T=594.202K) Etot = 56.311eV
Energy per atom: Epot =50.108eV  Ekin = 6.205eV (T=516.183K) Etot = 56.313eV
Energy per atom: Epot =48.848eV  Ekin = 7.459eV (T=620.469K) Etot = 56.307eV
Energy per atom: Epot =49.235eV  Ekin = 7.079eV (T=588.838K) Etot = 56.313eV
Energy per atom: Epot =49.132eV  Ekin = 7.183eV (T=597.553K) Etot = 56.315eV
Energy per atom: Epot =49.777eV  Ekin = 6.540eV (T=544.031K) Etot = 56.317eV
Energy per atom: Epot =49.103eV  Ekin = 7.204eV (T=599.269K) Etot = 56.307eV
Energy per atom: Epot =48.914eV  Ekin = 7.399eV (T=615.482K) Etot = 56.313eV
Energy per atom: Epot =48.917eV  Ekin = 7.399eV (T=615.506K) Etot = 56.316eV
Energy per atom: Epot =49.569eV  Ekin = 6.746eV (T=561.156K) Etot = 56.315eV
Energy per atom: Epot =49.514eV  Ekin = 6.798eV (T=565.470K) Etot = 56.311eV
Energy per atom: Epot =49.015eV  Ekin = 7.292eV (T=606.596K) Etot = 56.307eV
Energy per atom: Epot =49.146eV  Ekin = 7.166eV (T=596.099K) Etot = 56.312eV
Energy per atom: Epot =49.106eV  Ekin = 7.203eV (T=599.227K) Etot = 56.310eV
Energy per atom: Epot =48.945eV  Ekin = 7.363eV (T=612.541K) Etot = 56.309eV
Energy per atom: Epot =48.947eV  Ekin = 7.364eV (T=612.626K) Etot = 56.311eV
Energy per atom: Epot =49.147eV  Ekin = 7.167eV (T=596.163K) Etot = 56.314eV
Energy per atom: Epot =48.992eV  Ekin = 7.318eV (T=608.737K) Etot = 56.309eV
Energy per atom: Epot =48.868eV  Ekin = 7.441eV (T=619.017K) Etot = 56.309eV
Energy per atom: Epot =48.944eV  Ekin = 7.369eV (T=612.973K) Etot = 56.313eV
Energy per atom: Epot =48.166eV  Ekin = 8.141eV (T=677.257K) Etot = 56.308eV
Energy per atom: Epot =47.891eV  Ekin = 8.416eV (T=700.130K) Etot = 56.308eV

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