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 = 156.118eV (T=301.946K) Etot = 153.713eV
Energy per atom: Epot =118.143eV Ekin = 36.355eV (T=70.313K) Etot = 154.498eV
Energy per atom: Epot =79.017eV Ekin = 75.340eV (T=145.714K) Etot = 154.357eV
Energy per atom: Epot =70.932eV Ekin = 83.278eV (T=161.068K) Etot = 154.211eV
Energy per atom: Epot =69.433eV Ekin = 84.723eV (T=163.862K) Etot = 154.156eV
Energy per atom: Epot =81.968eV Ekin = 72.365eV (T=139.961K) Etot = 154.333eV
Energy per atom: Epot =78.130eV Ekin = 76.178eV (T=147.335K) Etot = 154.308eV
Energy per atom: Epot =74.168eV Ekin = 80.049eV (T=154.822K) Etot = 154.217eV
Energy per atom: Epot =72.363eV Ekin = 81.857eV (T=158.319K) Etot = 154.221eV
Energy per atom: Epot =80.577eV Ekin = 73.729eV (T=142.599K) Etot = 154.307eV
Energy per atom: Epot =75.765eV Ekin = 78.500eV (T=151.825K) Etot = 154.265eV
Energy per atom: Epot =73.781eV Ekin = 80.454eV (T=155.606K) Etot = 154.235eV
Energy per atom: Epot =76.679eV Ekin = 77.585eV (T=150.056K) Etot = 154.264eV
Energy per atom: Epot =77.777eV Ekin = 76.495eV (T=147.949K) Etot = 154.272eV
Energy per atom: Epot =75.017eV Ekin = 79.236eV (T=153.250K) Etot = 154.253eV
Energy per atom: Epot =75.312eV Ekin = 78.954eV (T=152.704K) Etot = 154.266eV
Energy per atom: Epot =75.747eV Ekin = 78.508eV (T=151.841K) Etot = 154.255eV
Energy per atom: Epot =78.681eV Ekin = 75.583eV (T=146.185K) Etot = 154.264eV
Energy per atom: Epot =73.949eV Ekin = 80.309eV (T=155.324K) Etot = 154.258eV
Energy per atom: Epot =74.427eV Ekin = 79.814eV (T=154.367K) Etot = 154.241eV
Energy per atom: Epot =79.852eV Ekin = 74.423eV (T=143.941K) Etot = 154.275eV
Note how the total energy is conserved, but the kinetic energy quickly drops to half the expected value. Why?
What you learned here:
How to set up a basic MD run.
How to monitor the energy over time.
That total energy is approximately conserved in NVE simulations, what is the error in total energy?
Exercise: Tune the time step from 5fs to 10fs and 50fs, what changes do you observe in total energy?
Part 2: Constant temperature MD#
In many cases, you want to control temperature (NVT ensemble). This
can be done using a thermostat, like – in this tutorial – Langevin
thermostat.
Compared to the previous example, we replace the line
dyn = VelocityVerlet(...) with
where T is the desired temperature in Kelvin. For that we also imported
the Langevin in the beginning.
The Langevin dynamics will then slowly adjust the total energy of the system so the temperature approaches the desired one.
As a slightly less boring example, let us use this to melt a chunk of
copper by starting the simulation without any momentum of the atoms
(no kinetic energy), and with a desired temperature above the melting
point. We will also save information about the atoms in a trajectory
file called moldyn3.traj.
Note
It is recommended to use the asap3 implementation of the EMT
calculator here, because its performance benefits over the ase
implementation.
size = 10
T = 1500 # Kelvin
# Set up a crystal
atoms = LatticeFCC(
directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
symbol='Cu',
size=(size, size, size),
pbc=False,
)
# Describe the interatomic interactions with the Effective Medium Theory
atoms.calc = EMT()
# We want to run MD with constant energy using the Langevin algorithm
# with a time step of 5 fs, the temperature T and the friction
# coefficient to 0.02 atomic units.
timestep_fs = 5
dyn = Langevin(
atoms, timestep=timestep_fs * units.fs, temperature_K=T, friction=0.02
)
# We also want to save the positions of all atoms after every 100th time step.
traj = Trajectory('fccCu_NPT.traj', 'w', atoms)
# Now run the dynamics
print('running a NVT simulation of fcc Cu')
printenergy(atoms)
time_ps, temperature = [], []
mdind = 0
steps_per_block = 10
for i in range(200):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the temperature of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
temperature.append(atoms.get_temperature())
# Plot temperatures vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, temperature)
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Temperature (K)')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
/home/ase/.local/lib/python3.13/site-packages/ase/md/langevin.py:110: FutureWarning: The implementation of `fixcm=True` in `Langevin` does not strictly sample the correct NVT distributions. The deviations are typically small for large systems but can be more pronounced for small systems. Use `fixcm=False` together with `ase.constraints.FixCom`. `fixcm` is deprecated since ASE 3.28.0 and will be removed in a future release.
warnings.warn(msg, FutureWarning)
running a NVT simulation of fcc Cu
Energy per atom: Epot =540.816eV Ekin = 0.000eV (T=0.000K) Etot = 540.816eV
Energy per atom: Epot =600.120eV Ekin = 81.933eV (T=158.465K) Etot = 682.053eV
Energy per atom: Epot =670.700eV Ekin = 139.054eV (T=268.943K) Etot = 809.754eV
Energy per atom: Epot =728.196eV Ekin = 196.161eV (T=379.393K) Etot = 924.358eV
Energy per atom: Epot =785.669eV Ekin = 255.306eV (T=493.785K) Etot = 1040.976eV
Energy per atom: Epot =835.621eV Ekin = 306.582eV (T=592.957K) Etot = 1142.203eV
Energy per atom: Epot =887.213eV Ekin = 344.950eV (T=667.164K) Etot = 1232.163eV
Energy per atom: Epot =926.450eV Ekin = 379.131eV (T=733.272K) Etot = 1305.581eV
Energy per atom: Epot =965.128eV Ekin = 414.277eV (T=801.248K) Etot = 1379.405eV
Energy per atom: Epot =1005.950eV Ekin = 445.106eV (T=860.874K) Etot = 1451.056eV
Energy per atom: Epot =1045.185eV Ekin = 471.044eV (T=911.039K) Etot = 1516.228eV
Energy per atom: Epot =1081.473eV Ekin = 500.614eV (T=968.231K) Etot = 1582.087eV
Energy per atom: Epot =1124.336eV Ekin = 509.169eV (T=984.778K) Etot = 1633.505eV
Energy per atom: Epot =1145.080eV Ekin = 536.019eV (T=1036.707K) Etot = 1681.099eV
Energy per atom: Epot =1171.741eV Ekin = 552.393eV (T=1068.377K) Etot = 1724.135eV
Energy per atom: Epot =1208.232eV Ekin = 556.894eV (T=1077.082K) Etot = 1765.127eV
Energy per atom: Epot =1233.437eV Ekin = 575.180eV (T=1112.448K) Etot = 1808.617eV
Energy per atom: Epot =1255.924eV Ekin = 592.618eV (T=1146.174K) Etot = 1848.542eV
Energy per atom: Epot =1291.825eV Ekin = 594.779eV (T=1150.355K) Etot = 1886.604eV
Energy per atom: Epot =1327.843eV Ekin = 588.397eV (T=1138.010K) Etot = 1916.239eV
Energy per atom: Epot =1341.958eV Ekin = 604.964eV (T=1170.053K) Etot = 1946.922eV
Energy per atom: Epot =1362.001eV Ekin = 619.544eV (T=1198.253K) Etot = 1981.545eV
Energy per atom: Epot =1375.973eV Ekin = 632.640eV (T=1223.581K) Etot = 2008.614eV
Energy per atom: Epot =1418.422eV Ekin = 625.907eV (T=1210.558K) Etot = 2044.328eV
Energy per atom: Epot =1417.693eV Ekin = 657.244eV (T=1271.167K) Etot = 2074.937eV
Energy per atom: Epot =1448.251eV Ekin = 650.370eV (T=1257.872K) Etot = 2098.621eV
Energy per atom: Epot =1453.898eV Ekin = 666.409eV (T=1288.894K) Etot = 2120.307eV
Energy per atom: Epot =1476.650eV Ekin = 673.971eV (T=1303.518K) Etot = 2150.621eV
Energy per atom: Epot =1491.710eV Ekin = 682.126eV (T=1319.290K) Etot = 2173.836eV
Energy per atom: Epot =1502.101eV Ekin = 701.218eV (T=1356.217K) Etot = 2203.320eV
Energy per atom: Epot =1512.900eV Ekin = 696.141eV (T=1346.398K) Etot = 2209.041eV
Energy per atom: Epot =1523.368eV Ekin = 702.921eV (T=1359.510K) Etot = 2226.289eV
Energy per atom: Epot =1532.757eV Ekin = 706.405eV (T=1366.249K) Etot = 2239.163eV
Energy per atom: Epot =1547.665eV Ekin = 703.502eV (T=1360.635K) Etot = 2251.167eV
Energy per atom: Epot =1570.414eV Ekin = 693.862eV (T=1341.989K) Etot = 2264.276eV
Energy per atom: Epot =1572.860eV Ekin = 704.381eV (T=1362.334K) Etot = 2277.241eV
Energy per atom: Epot =1577.047eV Ekin = 718.417eV (T=1389.481K) Etot = 2295.464eV
Energy per atom: Epot =1589.278eV Ekin = 714.752eV (T=1382.392K) Etot = 2304.030eV
Energy per atom: Epot =1604.386eV Ekin = 712.977eV (T=1378.959K) Etot = 2317.363eV
Energy per atom: Epot =1616.975eV Ekin = 715.197eV (T=1383.254K) Etot = 2332.172eV
Energy per atom: Epot =1624.485eV Ekin = 723.679eV (T=1399.658K) Etot = 2348.164eV
Energy per atom: Epot =1630.524eV Ekin = 731.498eV (T=1414.781K) Etot = 2362.022eV
Energy per atom: Epot =1644.631eV Ekin = 736.363eV (T=1424.190K) Etot = 2380.994eV
Energy per atom: Epot =1662.862eV Ekin = 725.905eV (T=1403.962K) Etot = 2388.766eV
Energy per atom: Epot =1671.771eV Ekin = 726.977eV (T=1406.037K) Etot = 2398.748eV
Energy per atom: Epot =1674.335eV Ekin = 742.868eV (T=1436.771K) Etot = 2417.203eV
Energy per atom: Epot =1693.829eV Ekin = 734.066eV (T=1419.748K) Etot = 2427.895eV
Energy per atom: Epot =1702.140eV Ekin = 740.110eV (T=1431.438K) Etot = 2442.251eV
Energy per atom: Epot =1710.536eV Ekin = 743.593eV (T=1438.174K) Etot = 2454.129eV
Energy per atom: Epot =1701.118eV Ekin = 760.059eV (T=1470.021K) Etot = 2461.177eV
Energy per atom: Epot =1734.328eV Ekin = 727.940eV (T=1407.900K) Etot = 2462.268eV
Energy per atom: Epot =1732.577eV Ekin = 733.090eV (T=1417.860K) Etot = 2465.667eV
Energy per atom: Epot =1750.881eV Ekin = 725.328eV (T=1402.847K) Etot = 2476.209eV
Energy per atom: Epot =1757.505eV Ekin = 726.879eV (T=1405.848K) Etot = 2484.384eV
Energy per atom: Epot =1754.797eV Ekin = 738.328eV (T=1427.990K) Etot = 2493.125eV
Energy per atom: Epot =1775.968eV Ekin = 729.723eV (T=1411.348K) Etot = 2505.691eV
Energy per atom: Epot =1779.042eV Ekin = 732.669eV (T=1417.046K) Etot = 2511.711eV
Energy per atom: Epot =1767.963eV Ekin = 749.038eV (T=1448.704K) Etot = 2517.000eV
Energy per atom: Epot =1792.375eV Ekin = 733.325eV (T=1418.314K) Etot = 2525.700eV
Energy per atom: Epot =1781.943eV Ekin = 747.386eV (T=1445.509K) Etot = 2529.329eV
Energy per atom: Epot =1799.434eV Ekin = 751.160eV (T=1452.809K) Etot = 2550.595eV
Energy per atom: Epot =1822.351eV Ekin = 737.734eV (T=1426.842K) Etot = 2560.085eV
Energy per atom: Epot =1805.255eV Ekin = 747.328eV (T=1445.398K) Etot = 2552.584eV
Energy per atom: Epot =1817.696eV Ekin = 737.611eV (T=1426.604K) Etot = 2555.307eV
Energy per atom: Epot =1816.309eV Ekin = 748.705eV (T=1448.060K) Etot = 2565.014eV
Energy per atom: Epot =1818.645eV Ekin = 741.452eV (T=1434.032K) Etot = 2560.096eV
Energy per atom: Epot =1829.081eV Ekin = 738.852eV (T=1429.004K) Etot = 2567.932eV
Energy per atom: Epot =1831.421eV Ekin = 738.742eV (T=1428.792K) Etot = 2570.164eV
Energy per atom: Epot =1820.648eV Ekin = 748.531eV (T=1447.725K) Etot = 2569.179eV
Energy per atom: Epot =1824.163eV Ekin = 744.088eV (T=1439.130K) Etot = 2568.251eV
Energy per atom: Epot =1832.537eV Ekin = 745.769eV (T=1442.383K) Etot = 2578.307eV
Energy per atom: Epot =1832.667eV Ekin = 752.099eV (T=1454.625K) Etot = 2584.766eV
Energy per atom: Epot =1836.270eV Ekin = 761.764eV (T=1473.317K) Etot = 2598.034eV
Energy per atom: Epot =1848.273eV Ekin = 756.192eV (T=1462.541K) Etot = 2604.465eV
Energy per atom: Epot =1839.751eV Ekin = 763.098eV (T=1475.897K) Etot = 2602.849eV
Energy per atom: Epot =1845.702eV Ekin = 750.990eV (T=1452.480K) Etot = 2596.691eV
Energy per atom: Epot =1846.774eV Ekin = 751.378eV (T=1453.230K) Etot = 2598.152eV
Energy per atom: Epot =1856.648eV Ekin = 746.012eV (T=1442.853K) Etot = 2602.660eV
Energy per atom: Epot =1860.365eV Ekin = 738.456eV (T=1428.238K) Etot = 2598.821eV
Energy per atom: Epot =1862.919eV Ekin = 732.892eV (T=1417.477K) Etot = 2595.811eV
Energy per atom: Epot =1859.732eV Ekin = 749.060eV (T=1448.747K) Etot = 2608.792eV
Energy per atom: Epot =1862.743eV Ekin = 739.724eV (T=1430.690K) Etot = 2602.467eV
Energy per atom: Epot =1878.245eV Ekin = 735.536eV (T=1422.592K) Etot = 2613.782eV
Energy per atom: Epot =1871.171eV Ekin = 751.298eV (T=1453.076K) Etot = 2622.469eV
Energy per atom: Epot =1879.363eV Ekin = 757.387eV (T=1464.853K) Etot = 2636.751eV
Energy per atom: Epot =1890.230eV Ekin = 754.956eV (T=1460.151K) Etot = 2645.187eV
Energy per atom: Epot =1888.358eV Ekin = 761.066eV (T=1471.968K) Etot = 2649.424eV
Energy per atom: Epot =1904.667eV Ekin = 755.722eV (T=1461.632K) Etot = 2660.388eV
Energy per atom: Epot =1912.823eV Ekin = 733.014eV (T=1417.712K) Etot = 2645.837eV
Energy per atom: Epot =1915.065eV Ekin = 727.139eV (T=1406.351K) Etot = 2642.204eV
Energy per atom: Epot =1911.504eV Ekin = 739.423eV (T=1430.109K) Etot = 2650.928eV
Energy per atom: Epot =1908.829eV Ekin = 752.462eV (T=1455.327K) Etot = 2661.291eV
Energy per atom: Epot =1928.930eV Ekin = 738.483eV (T=1428.290K) Etot = 2667.413eV
Energy per atom: Epot =1924.461eV Ekin = 753.598eV (T=1457.525K) Etot = 2678.059eV
Energy per atom: Epot =1927.346eV Ekin = 759.790eV (T=1469.500K) Etot = 2687.136eV
Energy per atom: Epot =1928.815eV Ekin = 765.246eV (T=1480.053K) Etot = 2694.062eV
Energy per atom: Epot =1929.292eV Ekin = 764.046eV (T=1477.731K) Etot = 2693.338eV
Energy per atom: Epot =1940.864eV Ekin = 756.986eV (T=1464.077K) Etot = 2697.850eV
Energy per atom: Epot =1934.981eV Ekin = 753.964eV (T=1458.233K) Etot = 2688.945eV
Energy per atom: Epot =1934.647eV Ekin = 760.178eV (T=1470.251K) Etot = 2694.826eV
Energy per atom: Epot =1940.341eV Ekin = 755.557eV (T=1461.313K) Etot = 2695.898eV
Energy per atom: Epot =1951.752eV Ekin = 751.121eV (T=1452.733K) Etot = 2702.873eV
Energy per atom: Epot =1944.676eV Ekin = 758.929eV (T=1467.835K) Etot = 2703.606eV
Energy per atom: Epot =1944.194eV Ekin = 762.875eV (T=1475.467K) Etot = 2707.069eV
Energy per atom: Epot =1949.673eV Ekin = 765.483eV (T=1480.510K) Etot = 2715.156eV
Energy per atom: Epot =1966.869eV Ekin = 756.707eV (T=1463.538K) Etot = 2723.577eV
Energy per atom: Epot =1965.752eV Ekin = 759.560eV (T=1469.055K) Etot = 2725.312eV
Energy per atom: Epot =1960.196eV Ekin = 764.440eV (T=1478.493K) Etot = 2724.635eV
Energy per atom: Epot =1977.102eV Ekin = 750.210eV (T=1450.972K) Etot = 2727.312eV
Energy per atom: Epot =1966.740eV Ekin = 763.356eV (T=1476.397K) Etot = 2730.096eV
Energy per atom: Epot =1969.222eV Ekin = 760.643eV (T=1471.150K) Etot = 2729.865eV
Energy per atom: Epot =1968.320eV Ekin = 763.363eV (T=1476.410K) Etot = 2731.682eV
Energy per atom: Epot =1967.828eV Ekin = 761.461eV (T=1472.731K) Etot = 2729.288eV
Energy per atom: Epot =1977.580eV Ekin = 759.965eV (T=1469.838K) Etot = 2737.545eV
Energy per atom: Epot =1961.391eV Ekin = 772.757eV (T=1494.580K) Etot = 2734.148eV
Energy per atom: Epot =1972.410eV Ekin = 753.121eV (T=1456.602K) Etot = 2725.532eV
Energy per atom: Epot =1953.526eV Ekin = 764.013eV (T=1477.667K) Etot = 2717.539eV
Energy per atom: Epot =1963.326eV Ekin = 763.060eV (T=1475.824K) Etot = 2726.385eV
Energy per atom: Epot =1968.850eV Ekin = 758.602eV (T=1467.202K) Etot = 2727.452eV
Energy per atom: Epot =1976.032eV Ekin = 751.568eV (T=1453.597K) Etot = 2727.599eV
Energy per atom: Epot =1971.424eV Ekin = 751.622eV (T=1453.703K) Etot = 2723.047eV
Energy per atom: Epot =1970.228eV Ekin = 759.958eV (T=1469.824K) Etot = 2730.186eV
Energy per atom: Epot =1959.512eV Ekin = 772.489eV (T=1494.060K) Etot = 2732.001eV
Energy per atom: Epot =1964.559eV Ekin = 763.593eV (T=1476.855K) Etot = 2728.151eV
Energy per atom: Epot =1978.750eV Ekin = 750.831eV (T=1452.173K) Etot = 2729.582eV
Energy per atom: Epot =1984.125eV Ekin = 748.002eV (T=1446.701K) Etot = 2732.127eV
Energy per atom: Epot =1976.230eV Ekin = 760.366eV (T=1470.613K) Etot = 2736.595eV
Energy per atom: Epot =1986.867eV Ekin = 764.511eV (T=1478.632K) Etot = 2751.378eV
Energy per atom: Epot =1996.639eV Ekin = 760.099eV (T=1470.098K) Etot = 2756.738eV
Energy per atom: Epot =1986.210eV Ekin = 774.823eV (T=1498.574K) Etot = 2761.032eV
Energy per atom: Epot =1986.796eV Ekin = 771.114eV (T=1491.402K) Etot = 2757.911eV
Energy per atom: Epot =1996.208eV Ekin = 755.742eV (T=1461.670K) Etot = 2751.950eV
Energy per atom: Epot =1997.762eV Ekin = 765.642eV (T=1480.818K) Etot = 2763.404eV
Energy per atom: Epot =2002.897eV Ekin = 776.200eV (T=1501.239K) Etot = 2779.097eV
Energy per atom: Epot =1994.098eV Ekin = 775.925eV (T=1500.706K) Etot = 2770.023eV
Energy per atom: Epot =2003.501eV Ekin = 764.649eV (T=1478.897K) Etot = 2768.150eV
Energy per atom: Epot =1994.536eV Ekin = 778.231eV (T=1505.167K) Etot = 2772.767eV
Energy per atom: Epot =1993.905eV Ekin = 793.510eV (T=1534.718K) Etot = 2787.415eV
Energy per atom: Epot =1999.502eV Ekin = 786.249eV (T=1520.674K) Etot = 2785.750eV
Energy per atom: Epot =2005.999eV Ekin = 790.072eV (T=1528.068K) Etot = 2796.071eV
Energy per atom: Epot =1999.046eV Ekin = 789.179eV (T=1526.340K) Etot = 2788.225eV
Energy per atom: Epot =2000.933eV Ekin = 783.974eV (T=1516.273K) Etot = 2784.907eV
Energy per atom: Epot =2001.057eV Ekin = 777.210eV (T=1503.191K) Etot = 2778.266eV
Energy per atom: Epot =2009.872eV Ekin = 771.069eV (T=1491.315K) Etot = 2780.941eV
Energy per atom: Epot =1999.146eV Ekin = 776.642eV (T=1502.093K) Etot = 2775.788eV
Energy per atom: Epot =1992.468eV Ekin = 775.860eV (T=1500.581K) Etot = 2768.328eV
Energy per atom: Epot =2002.731eV Ekin = 770.902eV (T=1490.992K) Etot = 2773.633eV
Energy per atom: Epot =2001.316eV Ekin = 769.657eV (T=1488.584K) Etot = 2770.973eV
Energy per atom: Epot =2002.153eV Ekin = 768.575eV (T=1486.491K) Etot = 2770.728eV
Energy per atom: Epot =2009.239eV Ekin = 759.686eV (T=1469.299K) Etot = 2768.925eV
Energy per atom: Epot =1992.492eV Ekin = 776.834eV (T=1502.464K) Etot = 2769.326eV
Energy per atom: Epot =2010.339eV Ekin = 761.843eV (T=1473.470K) Etot = 2772.182eV
Energy per atom: Epot =2005.759eV Ekin = 769.612eV (T=1488.497K) Etot = 2775.371eV
Energy per atom: Epot =2017.030eV Ekin = 758.341eV (T=1466.698K) Etot = 2775.371eV
Energy per atom: Epot =2018.198eV Ekin = 766.578eV (T=1482.628K) Etot = 2784.776eV
Energy per atom: Epot =2014.194eV Ekin = 771.520eV (T=1492.187K) Etot = 2785.714eV
Energy per atom: Epot =2022.585eV Ekin = 759.098eV (T=1468.161K) Etot = 2781.683eV
Energy per atom: Epot =2014.743eV Ekin = 767.460eV (T=1484.335K) Etot = 2782.203eV
Energy per atom: Epot =1999.342eV Ekin = 774.608eV (T=1498.160K) Etot = 2773.951eV
Energy per atom: Epot =2000.003eV Ekin = 771.608eV (T=1492.358K) Etot = 2771.611eV
Energy per atom: Epot =2012.517eV Ekin = 761.188eV (T=1472.203K) Etot = 2773.705eV
Energy per atom: Epot =2017.720eV Ekin = 756.563eV (T=1463.259K) Etot = 2774.283eV
Energy per atom: Epot =2005.691eV Ekin = 763.087eV (T=1475.876K) Etot = 2768.778eV
Energy per atom: Epot =2002.268eV Ekin = 772.161eV (T=1493.426K) Etot = 2774.429eV
Energy per atom: Epot =2012.562eV Ekin = 765.524eV (T=1480.591K) Etot = 2778.086eV
Energy per atom: Epot =2008.348eV Ekin = 778.422eV (T=1505.537K) Etot = 2786.770eV
Energy per atom: Epot =2009.903eV Ekin = 772.920eV (T=1494.895K) Etot = 2782.823eV
Energy per atom: Epot =1997.831eV Ekin = 787.988eV (T=1524.037K) Etot = 2785.819eV
Energy per atom: Epot =2007.559eV Ekin = 772.780eV (T=1494.623K) Etot = 2780.338eV
Energy per atom: Epot =2018.467eV Ekin = 775.322eV (T=1499.539K) Etot = 2793.788eV
Energy per atom: Epot =2012.086eV Ekin = 773.996eV (T=1496.976K) Etot = 2786.082eV
Energy per atom: Epot =2022.704eV Ekin = 760.298eV (T=1470.483K) Etot = 2783.003eV
Energy per atom: Epot =2007.332eV Ekin = 773.199eV (T=1495.434K) Etot = 2780.531eV
Energy per atom: Epot =2012.594eV Ekin = 774.873eV (T=1498.672K) Etot = 2787.467eV
Energy per atom: Epot =2007.784eV Ekin = 770.929eV (T=1491.044K) Etot = 2778.713eV
Energy per atom: Epot =2009.471eV Ekin = 772.280eV (T=1493.656K) Etot = 2781.751eV
Energy per atom: Epot =2001.036eV Ekin = 771.314eV (T=1491.789K) Etot = 2772.350eV
Energy per atom: Epot =2006.283eV Ekin = 766.934eV (T=1483.318K) Etot = 2773.218eV
Energy per atom: Epot =1997.581eV Ekin = 777.135eV (T=1503.047K) Etot = 2774.716eV
Energy per atom: Epot =1998.464eV Ekin = 775.022eV (T=1498.961K) Etot = 2773.486eV
Energy per atom: Epot =2007.748eV Ekin = 770.515eV (T=1490.242K) Etot = 2778.263eV
Energy per atom: Epot =1987.122eV Ekin = 792.908eV (T=1533.554K) Etot = 2780.031eV
Energy per atom: Epot =2014.097eV Ekin = 766.356eV (T=1482.198K) Etot = 2780.452eV
Energy per atom: Epot =2005.376eV Ekin = 774.329eV (T=1497.619K) Etot = 2779.705eV
Energy per atom: Epot =2000.028eV Ekin = 774.093eV (T=1497.163K) Etot = 2774.122eV
Energy per atom: Epot =2007.186eV Ekin = 769.028eV (T=1487.367K) Etot = 2776.214eV
Energy per atom: Epot =2000.828eV Ekin = 778.808eV (T=1506.282K) Etot = 2779.636eV
Energy per atom: Epot =1989.583eV Ekin = 786.508eV (T=1521.175K) Etot = 2776.091eV
Energy per atom: Epot =1994.389eV Ekin = 789.685eV (T=1527.320K) Etot = 2784.075eV
Energy per atom: Epot =2008.943eV Ekin = 773.400eV (T=1495.824K) Etot = 2782.343eV
Energy per atom: Epot =2002.928eV Ekin = 793.058eV (T=1533.844K) Etot = 2795.986eV
Energy per atom: Epot =2007.712eV Ekin = 782.613eV (T=1513.642K) Etot = 2790.326eV
Energy per atom: Epot =2019.744eV Ekin = 783.079eV (T=1514.543K) Etot = 2802.824eV
Energy per atom: Epot =2017.895eV Ekin = 779.469eV (T=1507.562K) Etot = 2797.365eV
Energy per atom: Epot =2006.443eV Ekin = 788.855eV (T=1525.714K) Etot = 2795.298eV
Energy per atom: Epot =2014.750eV Ekin = 780.326eV (T=1509.218K) Etot = 2795.076eV
Energy per atom: Epot =2017.775eV Ekin = 776.916eV (T=1502.623K) Etot = 2794.691eV
Energy per atom: Epot =2010.097eV Ekin = 782.297eV (T=1513.030K) Etot = 2792.394eV
Energy per atom: Epot =2006.837eV Ekin = 787.105eV (T=1522.330K) Etot = 2793.942eV
Energy per atom: Epot =2003.520eV Ekin = 797.587eV (T=1542.604K) Etot = 2801.108eV
Energy per atom: Epot =2015.709eV Ekin = 784.943eV (T=1518.147K) Etot = 2800.652eV
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] 11:21:47 43.457006 1.0818
BFGSLineSearch: 1[ 1] 11:21:47 42.347659 0.2273
BFGSLineSearch: 2[ 2] 11:21:47 42.108454 0.1349
BFGSLineSearch: 3[ 3] 11:21:47 41.964817 0.1138
BFGSLineSearch: 4[ 4] 11:21:47 41.924933 0.0683
BFGSLineSearch: 5[ 5] 11:21:47 41.915346 0.0225
BFGSLineSearch: 6[ 6] 11:21:47 41.914920 0.0059
BFGSLineSearch: 7[ 7] 11:21:47 41.914872 0.0023
BFGSLineSearch: 8[ 9] 11:21:47 41.914855 0.0023
BFGSLineSearch: 9[ 10] 11:21:47 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 15.444eV (T=1284.758K) Etot = 57.359eV
Energy per atom: Epot =51.326eV Ekin = 6.079eV (T=505.710K) Etot = 57.406eV
Energy per atom: Epot =51.576eV Ekin = 5.841eV (T=485.903K) Etot = 57.417eV
Energy per atom: Epot =51.314eV Ekin = 6.099eV (T=507.374K) Etot = 57.413eV
Energy per atom: Epot =50.218eV Ekin = 7.188eV (T=597.960K) Etot = 57.406eV
Energy per atom: Epot =49.439eV Ekin = 7.972eV (T=663.130K) Etot = 57.410eV
Energy per atom: Epot =49.487eV Ekin = 7.919eV (T=658.722K) Etot = 57.406eV
Energy per atom: Epot =49.582eV Ekin = 7.820eV (T=650.521K) Etot = 57.402eV
Energy per atom: Epot =49.614eV Ekin = 7.789eV (T=647.908K) Etot = 57.403eV
Energy per atom: Epot =50.752eV Ekin = 6.657eV (T=553.780K) Etot = 57.409eV
Energy per atom: Epot =51.052eV Ekin = 6.359eV (T=528.954K) Etot = 57.411eV
Energy per atom: Epot =51.143eV Ekin = 6.268eV (T=521.426K) Etot = 57.412eV
Energy per atom: Epot =49.481eV Ekin = 7.926eV (T=659.297K) Etot = 57.406eV
Energy per atom: Epot =50.527eV Ekin = 6.886eV (T=572.831K) Etot = 57.413eV
Energy per atom: Epot =49.454eV Ekin = 7.947eV (T=661.092K) Etot = 57.401eV
Energy per atom: Epot =50.007eV Ekin = 7.400eV (T=615.578K) Etot = 57.407eV
Energy per atom: Epot =51.257eV Ekin = 6.157eV (T=512.154K) Etot = 57.414eV
Energy per atom: Epot =50.803eV Ekin = 6.607eV (T=549.636K) Etot = 57.410eV
Energy per atom: Epot =49.987eV Ekin = 7.421eV (T=617.310K) Etot = 57.407eV
Energy per atom: Epot =48.970eV Ekin = 8.431eV (T=701.376K) Etot = 57.402eV
Energy per atom: Epot =49.525eV Ekin = 7.875eV (T=655.126K) Etot = 57.400eV
Energy per atom: Epot =49.398eV Ekin = 8.004eV (T=665.825K) Etot = 57.402eV
Energy per atom: Epot =50.676eV Ekin = 6.732eV (T=560.049K) Etot = 57.409eV
Energy per atom: Epot =51.291eV Ekin = 6.122eV (T=509.268K) Etot = 57.413eV
Energy per atom: Epot =50.015eV Ekin = 7.389eV (T=614.689K) Etot = 57.404eV
Energy per atom: Epot =50.075eV Ekin = 7.328eV (T=609.610K) Etot = 57.403eV
Energy per atom: Epot =50.473eV Ekin = 6.931eV (T=576.541K) Etot = 57.403eV
Energy per atom: Epot =50.084eV Ekin = 7.325eV (T=609.340K) Etot = 57.409eV
Energy per atom: Epot =49.194eV Ekin = 8.209eV (T=682.885K) Etot = 57.403eV
Energy per atom: Epot =50.876eV Ekin = 6.535eV (T=543.664K) Etot = 57.411eV
Energy per atom: Epot =50.374eV Ekin = 7.037eV (T=585.394K) Etot = 57.411eV
Energy per atom: Epot =49.716eV Ekin = 7.690eV (T=639.694K) Etot = 57.406eV
Energy per atom: Epot =50.750eV Ekin = 6.660eV (T=553.981K) Etot = 57.410eV
Energy per atom: Epot =50.278eV Ekin = 7.130eV (T=593.141K) Etot = 57.409eV
Energy per atom: Epot =49.997eV Ekin = 7.410eV (T=616.393K) Etot = 57.406eV
Energy per atom: Epot =50.164eV Ekin = 7.244eV (T=602.571K) Etot = 57.408eV
Energy per atom: Epot =50.133eV Ekin = 7.278eV (T=605.438K) Etot = 57.411eV
Energy per atom: Epot =49.789eV Ekin = 7.618eV (T=633.728K) Etot = 57.407eV
Energy per atom: Epot =50.467eV Ekin = 6.945eV (T=577.690K) Etot = 57.411eV
Energy per atom: Epot =50.173eV Ekin = 7.236eV (T=601.898K) Etot = 57.409eV
Energy per atom: Epot =49.585eV Ekin = 7.821eV (T=650.596K) Etot = 57.406eV
Energy per atom: Epot =50.367eV Ekin = 7.043eV (T=585.842K) Etot = 57.410eV
Energy per atom: Epot =50.533eV Ekin = 6.878eV (T=572.190K) Etot = 57.411eV
Energy per atom: Epot =51.082eV Ekin = 6.329eV (T=526.516K) Etot = 57.412eV
Energy per atom: Epot =49.929eV Ekin = 7.478eV (T=622.085K) Etot = 57.407eV
Energy per atom: Epot =50.036eV Ekin = 7.372eV (T=613.221K) Etot = 57.408eV
Energy per atom: Epot =50.740eV Ekin = 6.670eV (T=554.841K) Etot = 57.410eV
Energy per atom: Epot =50.467eV Ekin = 6.941eV (T=577.411K) Etot = 57.408eV
Energy per atom: Epot =49.960eV Ekin = 7.445eV (T=619.332K) Etot = 57.405eV
Energy per atom: Epot =49.728eV Ekin = 7.674eV (T=638.351K) Etot = 57.402eV
Energy per atom: Epot =50.301eV Ekin = 7.101eV (T=590.715K) Etot = 57.402eV
Energy per atom: Epot =50.165eV Ekin = 7.236eV (T=601.934K) Etot = 57.401eV
Energy per atom: Epot =50.289eV Ekin = 7.115eV (T=591.874K) Etot = 57.404eV
Energy per atom: Epot =50.582eV Ekin = 6.827eV (T=567.952K) Etot = 57.409eV
Energy per atom: Epot =49.551eV Ekin = 7.854eV (T=653.361K) Etot = 57.405eV
Energy per atom: Epot =50.837eV Ekin = 6.575eV (T=546.945K) Etot = 57.412eV
Energy per atom: Epot =49.734eV Ekin = 7.674eV (T=638.365K) Etot = 57.408eV
Energy per atom: Epot =49.422eV Ekin = 7.986eV (T=664.359K) Etot = 57.408eV
Energy per atom: Epot =49.970eV Ekin = 7.437eV (T=618.644K) Etot = 57.407eV
Energy per atom: Epot =50.194eV Ekin = 7.217eV (T=600.382K) Etot = 57.411eV
Energy per atom: Epot =51.214eV Ekin = 6.199eV (T=515.703K) Etot = 57.414eV
Energy per atom: Epot =50.896eV Ekin = 6.516eV (T=542.005K) Etot = 57.411eV
Energy per atom: Epot =50.459eV Ekin = 6.952eV (T=578.323K) Etot = 57.411eV
Energy per atom: Epot =50.339eV Ekin = 7.071eV (T=588.192K) Etot = 57.409eV
Energy per atom: Epot =51.073eV Ekin = 6.339eV (T=527.321K) Etot = 57.412eV
Energy per atom: Epot =50.003eV Ekin = 7.403eV (T=615.842K) Etot = 57.406eV
Energy per atom: Epot =50.929eV Ekin = 6.479eV (T=538.983K) Etot = 57.408eV
Energy per atom: Epot =50.608eV Ekin = 6.799eV (T=565.580K) Etot = 57.407eV
Energy per atom: Epot =50.404eV Ekin = 7.000eV (T=582.347K) Etot = 57.405eV
Energy per atom: Epot =50.560eV Ekin = 6.846eV (T=569.476K) Etot = 57.406eV
Energy per atom: Epot =50.297eV Ekin = 7.107eV (T=591.240K) Etot = 57.405eV
Energy per atom: Epot =49.963eV Ekin = 7.438eV (T=618.782K) Etot = 57.402eV
Energy per atom: Epot =50.140eV Ekin = 7.265eV (T=604.367K) Etot = 57.405eV
Energy per atom: Epot =50.826eV Ekin = 6.585eV (T=547.750K) Etot = 57.411eV
Energy per atom: Epot =50.351eV Ekin = 7.060eV (T=587.308K) Etot = 57.411eV
Energy per atom: Epot =50.757eV Ekin = 6.652eV (T=553.395K) Etot = 57.410eV
Energy per atom: Epot =51.408eV Ekin = 6.004eV (T=499.422K) Etot = 57.412eV
Energy per atom: Epot =50.537eV Ekin = 6.873eV (T=571.762K) Etot = 57.410eV
Energy per atom: Epot =50.319eV Ekin = 7.090eV (T=589.803K) Etot = 57.409eV
Energy per atom: Epot =50.645eV Ekin = 6.760eV (T=562.382K) Etot = 57.406eV
Energy per atom: Epot =50.219eV Ekin = 7.187eV (T=597.834K) Etot = 57.405eV
Energy per atom: Epot =51.296eV Ekin = 6.117eV (T=508.869K) Etot = 57.413eV
Energy per atom: Epot =50.459eV Ekin = 6.945eV (T=577.732K) Etot = 57.404eV
Energy per atom: Epot =49.476eV Ekin = 7.929eV (T=659.586K) Etot = 57.405eV
Energy per atom: Epot =51.009eV Ekin = 6.403eV (T=532.664K) Etot = 57.412eV
Energy per atom: Epot =51.191eV Ekin = 6.222eV (T=517.553K) Etot = 57.412eV
Energy per atom: Epot =50.314eV Ekin = 7.092eV (T=589.977K) Etot = 57.406eV
Energy per atom: Epot =50.789eV Ekin = 6.624eV (T=551.017K) Etot = 57.413eV
Energy per atom: Epot =50.201eV Ekin = 7.207eV (T=599.550K) Etot = 57.409eV
Energy per atom: Epot =49.988eV Ekin = 7.417eV (T=616.999K) Etot = 57.405eV
Energy per atom: Epot =49.614eV Ekin = 7.792eV (T=648.169K) Etot = 57.406eV
Energy per atom: Epot =50.456eV Ekin = 6.954eV (T=578.477K) Etot = 57.410eV
Energy per atom: Epot =50.032eV Ekin = 7.372eV (T=613.280K) Etot = 57.404eV
Energy per atom: Epot =50.483eV Ekin = 6.925eV (T=576.095K) Etot = 57.409eV
Energy per atom: Epot =49.951eV Ekin = 7.455eV (T=620.164K) Etot = 57.406eV
Energy per atom: Epot =50.094eV Ekin = 7.310eV (T=608.134K) Etot = 57.405eV
Energy per atom: Epot =50.566eV Ekin = 6.845eV (T=569.423K) Etot = 57.411eV
Energy per atom: Epot =49.962eV Ekin = 7.447eV (T=619.459K) Etot = 57.409eV
Energy per atom: Epot =50.620eV Ekin = 6.790eV (T=564.875K) Etot = 57.410eV
Energy per atom: Epot =50.511eV Ekin = 6.897eV (T=573.732K) Etot = 57.408eV
Energy per atom: Epot =50.560eV Ekin = 6.852eV (T=570.031K) Etot = 57.412eV
Energy per atom: Epot =50.641eV Ekin = 6.770eV (T=563.198K) Etot = 57.411eV
Energy per atom: Epot =50.016eV Ekin = 7.391eV (T=614.807K) Etot = 57.406eV
Energy per atom: Epot =50.621eV Ekin = 6.788eV (T=564.655K) Etot = 57.408eV
Energy per atom: Epot =50.201eV Ekin = 7.207eV (T=599.537K) Etot = 57.408eV
Energy per atom: Epot =50.362eV Ekin = 7.049eV (T=586.344K) Etot = 57.410eV
Energy per atom: Epot =50.960eV Ekin = 6.454eV (T=536.903K) Etot = 57.414eV
Energy per atom: Epot =49.341eV Ekin = 8.062eV (T=670.686K) Etot = 57.403eV
Energy per atom: Epot =50.183eV Ekin = 7.225eV (T=601.059K) Etot = 57.409eV
Energy per atom: Epot =49.981eV Ekin = 7.426eV (T=617.735K) Etot = 57.407eV
Energy per atom: Epot =50.243eV Ekin = 7.164eV (T=595.956K) Etot = 57.407eV
Energy per atom: Epot =49.524eV Ekin = 7.874eV (T=655.016K) Etot = 57.398eV
Energy per atom: Epot =49.410eV Ekin = 7.995eV (T=665.047K) Etot = 57.405eV
Energy per atom: Epot =49.347eV Ekin = 8.059eV (T=670.398K) Etot = 57.406eV
Energy per atom: Epot =50.494eV Ekin = 6.914eV (T=575.171K) Etot = 57.409eV
Energy per atom: Epot =50.906eV Ekin = 6.508eV (T=541.359K) Etot = 57.414eV
Energy per atom: Epot =49.913eV Ekin = 7.498eV (T=623.694K) Etot = 57.411eV
Energy per atom: Epot =50.899eV Ekin = 6.511eV (T=541.649K) Etot = 57.410eV
Energy per atom: Epot =50.324eV Ekin = 7.078eV (T=588.774K) Etot = 57.402eV
Energy per atom: Epot =50.242eV Ekin = 7.158eV (T=595.483K) Etot = 57.400eV
Energy per atom: Epot =50.538eV Ekin = 6.872eV (T=571.681K) Etot = 57.411eV
Energy per atom: Epot =49.528eV Ekin = 7.879eV (T=655.444K) Etot = 57.407eV
Energy per atom: Epot =49.279eV Ekin = 8.121eV (T=675.581K) Etot = 57.401eV
Energy per atom: Epot =49.912eV Ekin = 7.497eV (T=623.666K) Etot = 57.409eV
Energy per atom: Epot =49.445eV Ekin = 7.960eV (T=662.168K) Etot = 57.405eV
Energy per atom: Epot =49.106eV Ekin = 8.292eV (T=689.809K) Etot = 57.398eV
Energy per atom: Epot =49.198eV Ekin = 8.204eV (T=682.442K) Etot = 57.402eV
Energy per atom: Epot =50.314eV Ekin = 7.094eV (T=590.094K) Etot = 57.407eV
Energy per atom: Epot =49.839eV Ekin = 7.570eV (T=629.761K) Etot = 57.409eV
Energy per atom: Epot =49.956eV Ekin = 7.454eV (T=620.040K) Etot = 57.410eV
Energy per atom: Epot =50.049eV Ekin = 7.356eV (T=611.946K) Etot = 57.405eV
Energy per atom: Epot =50.115eV Ekin = 7.293eV (T=606.697K) Etot = 57.408eV
Energy per atom: Epot =49.453eV Ekin = 7.953eV (T=661.610K) Etot = 57.406eV
Energy per atom: Epot =49.194eV Ekin = 8.213eV (T=683.208K) Etot = 57.407eV
Energy per atom: Epot =49.581eV Ekin = 7.831eV (T=651.417K) Etot = 57.412eV
Energy per atom: Epot =50.644eV Ekin = 6.770eV (T=563.161K) Etot = 57.414eV
Energy per atom: Epot =50.509eV Ekin = 6.903eV (T=574.247K) Etot = 57.412eV
Energy per atom: Epot =49.259eV Ekin = 8.149eV (T=677.861K) Etot = 57.408eV
Energy per atom: Epot =49.972eV Ekin = 7.435eV (T=618.504K) Etot = 57.407eV
Energy per atom: Epot =49.788eV Ekin = 7.618eV (T=633.749K) Etot = 57.406eV
Energy per atom: Epot =49.289eV Ekin = 8.117eV (T=675.234K) Etot = 57.406eV
Energy per atom: Epot =49.306eV Ekin = 8.098eV (T=673.634K) Etot = 57.403eV
Energy per atom: Epot =50.108eV Ekin = 7.298eV (T=607.133K) Etot = 57.407eV
Energy per atom: Epot =49.594eV Ekin = 7.814eV (T=650.045K) Etot = 57.408eV
Energy per atom: Epot =50.148eV Ekin = 7.267eV (T=604.484K) Etot = 57.414eV
Energy per atom: Epot =49.563eV Ekin = 7.840eV (T=652.179K) Etot = 57.403eV
Energy per atom: Epot =49.825eV Ekin = 7.576eV (T=630.250K) Etot = 57.401eV
Energy per atom: Epot =49.655eV Ekin = 7.748eV (T=644.492K) Etot = 57.402eV
Energy per atom: Epot =49.701eV Ekin = 7.705eV (T=640.985K) Etot = 57.406eV
Energy per atom: Epot =50.089eV Ekin = 7.322eV (T=609.052K) Etot = 57.411eV
Energy per atom: Epot =50.340eV Ekin = 7.066eV (T=587.765K) Etot = 57.406eV
Energy per atom: Epot =49.608eV Ekin = 7.795eV (T=648.421K) Etot = 57.402eV
Energy per atom: Epot =50.409eV Ekin = 7.005eV (T=582.739K) Etot = 57.414eV
Energy per atom: Epot =49.306eV Ekin = 8.103eV (T=674.084K) Etot = 57.409eV
Energy per atom: Epot =49.395eV Ekin = 8.012eV (T=666.469K) Etot = 57.407eV
Energy per atom: Epot =50.198eV Ekin = 7.217eV (T=600.341K) Etot = 57.415eV
Energy per atom: Epot =50.001eV Ekin = 7.411eV (T=616.514K) Etot = 57.412eV
Energy per atom: Epot =48.662eV Ekin = 8.740eV (T=727.012K) Etot = 57.401eV
Energy per atom: Epot =50.068eV Ekin = 7.339eV (T=610.483K) Etot = 57.407eV
Energy per atom: Epot =49.280eV Ekin = 8.119eV (T=675.368K) Etot = 57.398eV
Energy per atom: Epot =49.106eV Ekin = 8.299eV (T=690.372K) Etot = 57.405eV
Energy per atom: Epot =49.983eV Ekin = 7.425eV (T=617.635K) Etot = 57.407eV
Energy per atom: Epot =49.084eV Ekin = 8.318eV (T=691.959K) Etot = 57.402eV
Energy per atom: Epot =48.839eV Ekin = 8.565eV (T=712.498K) Etot = 57.404eV
Energy per atom: Epot =49.221eV Ekin = 8.190eV (T=681.321K) Etot = 57.412eV
Energy per atom: Epot =49.462eV Ekin = 7.945eV (T=660.954K) Etot = 57.408eV
Energy per atom: Epot =49.069eV Ekin = 8.337eV (T=693.493K) Etot = 57.405eV
Energy per atom: Epot =49.578eV Ekin = 7.831eV (T=651.425K) Etot = 57.409eV
Energy per atom: Epot =50.080eV Ekin = 7.332eV (T=609.960K) Etot = 57.413eV
Energy per atom: Epot =50.326eV Ekin = 7.084eV (T=589.300K) Etot = 57.410eV
Energy per atom: Epot =48.743eV Ekin = 8.660eV (T=720.358K) Etot = 57.402eV
Energy per atom: Epot =48.817eV Ekin = 8.591eV (T=714.681K) Etot = 57.408eV
Energy per atom: Epot =49.804eV Ekin = 7.609eV (T=632.988K) Etot = 57.414eV
Energy per atom: Epot =48.893eV Ekin = 8.513eV (T=708.187K) Etot = 57.406eV
Energy per atom: Epot =48.644eV Ekin = 8.758eV (T=728.579K) Etot = 57.402eV
Energy per atom: Epot =49.190eV Ekin = 8.212eV (T=683.163K) Etot = 57.402eV
Energy per atom: Epot =49.436eV Ekin = 7.963eV (T=662.427K) Etot = 57.400eV
Energy per atom: Epot =50.342eV Ekin = 7.069eV (T=588.076K) Etot = 57.412eV
Energy per atom: Epot =48.657eV Ekin = 8.749eV (T=727.764K) Etot = 57.406eV
Energy per atom: Epot =48.655eV Ekin = 8.750eV (T=727.859K) Etot = 57.404eV
Energy per atom: Epot =49.184eV Ekin = 8.226eV (T=684.308K) Etot = 57.410eV
Energy per atom: Epot =48.592eV Ekin = 8.815eV (T=733.302K) Etot = 57.407eV
Energy per atom: Epot =49.095eV Ekin = 8.309eV (T=691.180K) Etot = 57.403eV
Energy per atom: Epot =50.378eV Ekin = 7.031eV (T=584.899K) Etot = 57.409eV
Energy per atom: Epot =50.158eV Ekin = 7.252eV (T=603.229K) Etot = 57.409eV
Energy per atom: Epot =49.574eV Ekin = 7.831eV (T=651.466K) Etot = 57.405eV
Energy per atom: Epot =48.829eV Ekin = 8.567eV (T=712.663K) Etot = 57.396eV
Energy per atom: Epot =48.371eV Ekin = 9.025eV (T=750.749K) Etot = 57.396eV
Energy per atom: Epot =49.568eV Ekin = 7.835eV (T=651.801K) Etot = 57.403eV
Energy per atom: Epot =48.841eV Ekin = 8.564eV (T=712.411K) Etot = 57.405eV
Energy per atom: Epot =49.000eV Ekin = 8.410eV (T=699.629K) Etot = 57.410eV
Energy per atom: Epot =49.314eV Ekin = 8.094eV (T=673.326K) Etot = 57.408eV
Energy per atom: Epot =49.044eV Ekin = 8.358eV (T=695.232K) Etot = 57.401eV
Energy per atom: Epot =50.245eV Ekin = 7.164eV (T=595.961K) Etot = 57.409eV
Energy per atom: Epot =48.178eV Ekin = 9.226eV (T=767.498K) Etot = 57.404eV
Energy per atom: Epot =49.251eV Ekin = 8.154eV (T=678.324K) Etot = 57.405eV
Energy per atom: Epot =49.165eV Ekin = 8.241eV (T=685.512K) Etot = 57.405eV
Energy per atom: Epot =49.181eV Ekin = 8.223eV (T=684.057K) Etot = 57.404eV
Energy per atom: Epot =49.323eV Ekin = 8.084eV (T=672.450K) Etot = 57.407eV
Energy per atom: Epot =48.843eV Ekin = 8.566eV (T=712.556K) Etot = 57.409eV
Energy per atom: Epot =49.127eV Ekin = 8.278eV (T=688.618K) Etot = 57.405eV
After running the simulation, use Graphical user interface (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?