Note
Go to the end to download the full example code.
Molecular dynamics#
Note
These examples can be run without asap3 installed. In that case,
ASE’s Python implementation of the EMT calculator can be used instead, but it
is much slower.
Goal#
In this tutorial, we will learn how to perform basic molecular dynamics (MD) simulations using ASE.
The key objectives are:
Understand how to set up a crystal structure (Cu atoms on an FCC lattice).
Initialize velocities from Maxwell–Boltzmann distribution corresponding to a chosen temperature.
Integrate Newton’s equations of motion using Velocity-Verlet algorithm and we monitor the temperature using Langevin thermostat.
Monitor and analyze thermodynamic quantities (potential energy, kinetic energy, total energy, temperature).
Save trajectories and visualize atomic motion with ASE’s GUI.
Explore MD in different scenarios: - Constant energy MD (NVE ensemble) - Constant temperature MD (NVT ensemble) - Isolated nanoparticle simulations
By the end of this tutorial, you should be able to set up your own MD simulations, monitor energy conservation, and visualize system evolution.
Part 1: Basic Molecular Dynamics Simulation#
We start by creating a copper crystal, assigning random velocities corresponding to Maxwell Boltzmann Distribution at 300 K, and running dynamics in the NVE ensemble (constant energy).
import matplotlib.pyplot as plt
import numpy as np
# choose one of the following implementations of EMT:
# included in ase
# from ase.calculators.emt import EMT
# faster performance
from asap3 import EMT
from ase import units
from ase.cluster.cubic import FaceCenteredCubic as ClusterFCC
from ase.io.trajectory import Trajectory
from ase.lattice.cubic import FaceCenteredCubic as LatticeFCC
from ase.md.langevin import Langevin # for later NPT simulations
from ase.md.velocitydistribution import (
MaxwellBoltzmannDistribution,
Stationary,
ZeroRotation,
)
from ase.md.verlet import VelocityVerlet
from ase.optimize import QuasiNewton
from ase.visualize.plot import plot_atoms
# Set up initial positions of Cu atoms on Fcc crystal lattice
size = 10
atoms = LatticeFCC(
directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
symbol='Cu',
size=(size, size, size),
pbc=True,
)
Before setting up the MD simulation, we take a look at the initial structure:
fig, ax = plt.subplots(figsize=(5, 5))
plot_atoms(atoms, ax, rotation=('45x,45y,0z'), show_unit_cell=2, radii=0.75)
ax.set_axis_off()
plt.tight_layout()
plt.show()
Now let’s run the MD simulation and monitor the kinetic and potential energy of the whole system:
# Describe the interatomic interactions with the Effective Medium Theory (EMT)
atoms.calc = EMT()
# Set the initial velocities corresponding to T=300K from Maxwell Boltzmann
# Distribution
MaxwellBoltzmannDistribution(atoms, temperature_K=300)
# We use Velocity Verlet algorithm to integrate the Newton's equations.
timestep_fs = 5
dyn = VelocityVerlet(atoms, timestep_fs * units.fs) # 5 fs time step.
def printenergy(a):
"""
Function to print the thermodynamical properties i.e potential energy,
kinetic energy and total energy
"""
epot = a.get_potential_energy()
ekin = a.get_kinetic_energy()
temp = a.get_temperature()
print(
f'Energy per atom: Epot ={epot:6.3f}eV Ekin = {ekin:.3f}eV '
f'(T={temp:.3f}K) Etot = {epot + ekin:.3f}eV'
)
# Now run the dynamics
print('running a NVE simulation of fcc Cu')
printenergy(atoms)
# init lists to for energy vs time data
time_ps, epot, ekin = [], [], []
mdind = 0
steps_per_block = 10
for i in range(20):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the energies of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
epot.append(atoms.get_potential_energy())
ekin.append(atoms.get_kinetic_energy())
etot = np.array(epot) + np.array(ekin)
# Plot energies vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, epot, label='Potential energy')
ax.plot(time_ps, ekin, label='Kinetic energy')
ax.plot(time_ps, etot, label='Total energy')
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Energy (eV)')
ax.legend(loc='best')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
running a NVE simulation of fcc Cu
Energy per atom: Epot =-2.405eV Ekin = 153.939eV (T=297.731K) Etot = 151.534eV
Energy per atom: Epot =115.676eV Ekin = 36.639eV (T=70.863K) Etot = 152.315eV
Energy per atom: Epot =78.836eV Ekin = 73.356eV (T=141.876K) Etot = 152.192eV
Energy per atom: Epot =71.036eV Ekin = 81.000eV (T=156.662K) Etot = 152.036eV
Energy per atom: Epot =66.713eV Ekin = 85.249eV (T=164.878K) Etot = 151.962eV
Energy per atom: Epot =81.022eV Ekin = 71.125eV (T=137.562K) Etot = 152.147eV
Energy per atom: Epot =77.447eV Ekin = 74.694eV (T=144.465K) Etot = 152.141eV
Energy per atom: Epot =73.533eV Ekin = 78.518eV (T=151.861K) Etot = 152.051eV
Energy per atom: Epot =70.724eV Ekin = 81.311eV (T=157.263K) Etot = 152.035eV
Energy per atom: Epot =78.454eV Ekin = 73.670eV (T=142.484K) Etot = 152.124eV
Energy per atom: Epot =75.464eV Ekin = 76.634eV (T=148.217K) Etot = 152.098eV
Energy per atom: Epot =74.233eV Ekin = 77.843eV (T=150.556K) Etot = 152.076eV
Energy per atom: Epot =74.723eV Ekin = 77.358eV (T=149.617K) Etot = 152.081eV
Energy per atom: Epot =76.953eV Ekin = 75.135eV (T=145.317K) Etot = 152.088eV
Energy per atom: Epot =73.149eV Ekin = 78.926eV (T=152.650K) Etot = 152.075eV
Energy per atom: Epot =75.533eV Ekin = 76.569eV (T=148.091K) Etot = 152.102eV
Energy per atom: Epot =74.316eV Ekin = 77.763eV (T=150.401K) Etot = 152.079eV
Energy per atom: Epot =76.819eV Ekin = 75.259eV (T=145.557K) Etot = 152.078eV
Energy per atom: Epot =73.442eV Ekin = 78.638eV (T=152.092K) Etot = 152.080eV
Energy per atom: Epot =73.897eV Ekin = 78.179eV (T=151.206K) Etot = 152.076eV
Energy per atom: Epot =77.819eV Ekin = 74.276eV (T=143.656K) Etot = 152.094eV
Note how the total energy is conserved, but the kinetic energy quickly drops to half the expected value. Why?
What you learned here:
How to set up a basic MD run.
How to monitor the energy over time.
That total energy is approximately conserved in NVE simulations, what is the error in total energy?
Exercise: Tune the time step from 5fs to 10fs and 50fs, what changes do you observe in total energy?
Part 2: Constant temperature MD#
In many cases, you want to control temperature (NVT ensemble). This
can be done using a thermostat, like – in this tutorial – Langevin
thermostat.
Compared to the previous example, we replace the line
dyn = VelocityVerlet(...) with
where T is the desired temperature in Kelvin. For that we also imported
the Langevin in the beginning.
The Langevin dynamics will then slowly adjust the total energy of the system so the temperature approaches the desired one.
As a slightly less boring example, let us use this to melt a chunk of
copper by starting the simulation without any momentum of the atoms
(no kinetic energy), and with a desired temperature above the melting
point. We will also save information about the atoms in a trajectory
file called moldyn3.traj.
Note
It is recommended to use the asap3 implementation of the EMT
calculator here, because its performance benefits over the ase
implementation.
size = 10
T = 1500 # Kelvin
# Set up a crystal
atoms = LatticeFCC(
directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
symbol='Cu',
size=(size, size, size),
pbc=False,
)
# Describe the interatomic interactions with the Effective Medium Theory
atoms.calc = EMT()
# We want to run MD with constant energy using the Langevin algorithm
# with a time step of 5 fs, the temperature T and the friction
# coefficient to 0.02 atomic units.
timestep_fs = 5
dyn = Langevin(
atoms, timestep=timestep_fs * units.fs, temperature_K=T, friction=0.02
)
# We also want to save the positions of all atoms after every 100th time step.
traj = Trajectory('fccCu_NPT.traj', 'w', atoms)
# Now run the dynamics
print('running a NVT simulation of fcc Cu')
printenergy(atoms)
time_ps, temperature = [], []
mdind = 0
steps_per_block = 10
for i in range(200):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the temperature of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
temperature.append(atoms.get_temperature())
# Plot temperatures vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, temperature)
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Temperature (K)')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
running a NVT simulation of fcc Cu
Energy per atom: Epot =540.816eV Ekin = 0.000eV (T=0.000K) Etot = 540.816eV
Energy per atom: Epot =598.863eV Ekin = 80.523eV (T=155.738K) Etot = 679.385eV
Energy per atom: Epot =667.798eV Ekin = 140.784eV (T=272.289K) Etot = 808.582eV
Energy per atom: Epot =728.613eV Ekin = 198.353eV (T=383.633K) Etot = 926.967eV
Energy per atom: Epot =782.043eV Ekin = 250.387eV (T=484.270K) Etot = 1032.429eV
Energy per atom: Epot =833.045eV Ekin = 296.620eV (T=573.690K) Etot = 1129.666eV
Energy per atom: Epot =880.122eV Ekin = 344.667eV (T=666.615K) Etot = 1224.788eV
Energy per atom: Epot =924.651eV Ekin = 377.507eV (T=730.132K) Etot = 1302.158eV
Energy per atom: Epot =960.443eV Ekin = 413.592eV (T=799.923K) Etot = 1374.035eV
Energy per atom: Epot =1002.717eV Ekin = 442.939eV (T=856.683K) Etot = 1445.656eV
Energy per atom: Epot =1045.394eV Ekin = 459.935eV (T=889.555K) Etot = 1505.329eV
Energy per atom: Epot =1070.214eV Ekin = 491.334eV (T=950.284K) Etot = 1561.548eV
Energy per atom: Epot =1104.725eV Ekin = 515.744eV (T=997.493K) Etot = 1620.469eV
Energy per atom: Epot =1152.939eV Ekin = 522.116eV (T=1009.817K) Etot = 1675.055eV
Energy per atom: Epot =1171.453eV Ekin = 551.349eV (T=1066.358K) Etot = 1722.802eV
Energy per atom: Epot =1199.826eV Ekin = 565.539eV (T=1093.802K) Etot = 1765.365eV
Energy per atom: Epot =1233.761eV Ekin = 577.075eV (T=1116.113K) Etot = 1810.836eV
Energy per atom: Epot =1274.312eV Ekin = 577.822eV (T=1117.558K) Etot = 1852.134eV
Energy per atom: Epot =1292.661eV Ekin = 599.603eV (T=1159.684K) Etot = 1892.264eV
Energy per atom: Epot =1313.862eV Ekin = 611.384eV (T=1182.469K) Etot = 1925.245eV
Energy per atom: Epot =1351.747eV Ekin = 601.623eV (T=1163.591K) Etot = 1953.370eV
Energy per atom: Epot =1351.465eV Ekin = 632.799eV (T=1223.889K) Etot = 1984.264eV
Energy per atom: Epot =1395.084eV Ekin = 625.946eV (T=1210.634K) Etot = 2021.030eV
Energy per atom: Epot =1404.616eV Ekin = 635.473eV (T=1229.061K) Etot = 2040.089eV
Energy per atom: Epot =1423.387eV Ekin = 645.859eV (T=1249.147K) Etot = 2069.246eV
Energy per atom: Epot =1427.195eV Ekin = 664.208eV (T=1284.636K) Etot = 2091.403eV
Energy per atom: Epot =1445.551eV Ekin = 662.364eV (T=1281.070K) Etot = 2107.915eV
Energy per atom: Epot =1461.591eV Ekin = 662.490eV (T=1281.313K) Etot = 2124.081eV
Energy per atom: Epot =1469.992eV Ekin = 679.986eV (T=1315.152K) Etot = 2149.978eV
Energy per atom: Epot =1491.732eV Ekin = 681.701eV (T=1318.469K) Etot = 2173.433eV
Energy per atom: Epot =1504.393eV Ekin = 675.827eV (T=1307.109K) Etot = 2180.220eV
Energy per atom: Epot =1510.506eV Ekin = 684.366eV (T=1323.623K) Etot = 2194.872eV
Energy per atom: Epot =1513.689eV Ekin = 697.822eV (T=1349.649K) Etot = 2211.511eV
Energy per atom: Epot =1529.800eV Ekin = 692.627eV (T=1339.601K) Etot = 2222.427eV
Energy per atom: Epot =1529.231eV Ekin = 706.263eV (T=1365.974K) Etot = 2235.494eV
Energy per atom: Epot =1552.392eV Ekin = 699.558eV (T=1353.006K) Etot = 2251.950eV
Energy per atom: Epot =1567.349eV Ekin = 700.312eV (T=1354.465K) Etot = 2267.661eV
Energy per atom: Epot =1570.300eV Ekin = 704.403eV (T=1362.377K) Etot = 2274.703eV
Energy per atom: Epot =1594.852eV Ekin = 703.469eV (T=1360.571K) Etot = 2298.321eV
Energy per atom: Epot =1595.073eV Ekin = 718.786eV (T=1390.196K) Etot = 2313.860eV
Energy per atom: Epot =1608.940eV Ekin = 719.191eV (T=1390.977K) Etot = 2328.131eV
Energy per atom: Epot =1621.534eV Ekin = 714.623eV (T=1382.142K) Etot = 2336.156eV
Energy per atom: Epot =1639.036eV Ekin = 710.910eV (T=1374.962K) Etot = 2349.946eV
Energy per atom: Epot =1647.091eV Ekin = 719.407eV (T=1391.397K) Etot = 2366.499eV
Energy per atom: Epot =1661.615eV Ekin = 717.112eV (T=1386.957K) Etot = 2378.728eV
Energy per atom: Epot =1667.732eV Ekin = 715.557eV (T=1383.950K) Etot = 2383.289eV
Energy per atom: Epot =1662.204eV Ekin = 719.817eV (T=1392.189K) Etot = 2382.021eV
Energy per atom: Epot =1675.913eV Ekin = 719.499eV (T=1391.574K) Etot = 2395.412eV
Energy per atom: Epot =1689.797eV Ekin = 714.940eV (T=1382.756K) Etot = 2404.737eV
Energy per atom: Epot =1689.069eV Ekin = 735.534eV (T=1422.586K) Etot = 2424.603eV
Energy per atom: Epot =1706.193eV Ekin = 728.097eV (T=1408.202K) Etot = 2434.289eV
Energy per atom: Epot =1717.573eV Ekin = 724.339eV (T=1400.935K) Etot = 2441.913eV
Energy per atom: Epot =1714.970eV Ekin = 732.216eV (T=1416.169K) Etot = 2447.186eV
Energy per atom: Epot =1718.199eV Ekin = 745.512eV (T=1441.885K) Etot = 2463.710eV
Energy per atom: Epot =1743.893eV Ekin = 724.497eV (T=1401.240K) Etot = 2468.390eV
Energy per atom: Epot =1749.087eV Ekin = 725.709eV (T=1403.585K) Etot = 2474.796eV
Energy per atom: Epot =1764.715eV Ekin = 717.015eV (T=1386.770K) Etot = 2481.731eV
Energy per atom: Epot =1763.228eV Ekin = 722.175eV (T=1396.750K) Etot = 2485.403eV
Energy per atom: Epot =1765.190eV Ekin = 733.640eV (T=1418.924K) Etot = 2498.830eV
Energy per atom: Epot =1777.281eV Ekin = 728.834eV (T=1409.629K) Etot = 2506.115eV
Energy per atom: Epot =1779.726eV Ekin = 739.679eV (T=1430.603K) Etot = 2519.404eV
Energy per atom: Epot =1792.138eV Ekin = 735.794eV (T=1423.090K) Etot = 2527.932eV
Energy per atom: Epot =1799.784eV Ekin = 735.273eV (T=1422.083K) Etot = 2535.057eV
Energy per atom: Epot =1809.850eV Ekin = 742.090eV (T=1435.268K) Etot = 2551.941eV
Energy per atom: Epot =1810.325eV Ekin = 755.741eV (T=1461.670K) Etot = 2566.067eV
Energy per atom: Epot =1831.376eV Ekin = 737.178eV (T=1425.766K) Etot = 2568.554eV
Energy per atom: Epot =1826.084eV Ekin = 758.323eV (T=1466.662K) Etot = 2584.407eV
Energy per atom: Epot =1843.894eV Ekin = 743.645eV (T=1438.274K) Etot = 2587.539eV
Energy per atom: Epot =1836.282eV Ekin = 762.314eV (T=1474.381K) Etot = 2598.595eV
Energy per atom: Epot =1851.235eV Ekin = 754.145eV (T=1458.583K) Etot = 2605.380eV
Energy per atom: Epot =1858.898eV Ekin = 755.257eV (T=1460.733K) Etot = 2614.156eV
Energy per atom: Epot =1874.042eV Ekin = 755.674eV (T=1461.539K) Etot = 2629.716eV
Energy per atom: Epot =1890.356eV Ekin = 743.356eV (T=1437.716K) Etot = 2633.713eV
Energy per atom: Epot =1878.798eV Ekin = 766.100eV (T=1481.705K) Etot = 2644.898eV
Energy per atom: Epot =1892.010eV Ekin = 756.851eV (T=1463.816K) Etot = 2648.861eV
Energy per atom: Epot =1901.023eV Ekin = 756.459eV (T=1463.058K) Etot = 2657.482eV
Energy per atom: Epot =1892.411eV Ekin = 767.766eV (T=1484.926K) Etot = 2660.177eV
Energy per atom: Epot =1902.687eV Ekin = 760.610eV (T=1471.085K) Etot = 2663.297eV
Energy per atom: Epot =1915.968eV Ekin = 748.471eV (T=1447.607K) Etot = 2664.439eV
Energy per atom: Epot =1924.637eV Ekin = 739.710eV (T=1430.663K) Etot = 2664.347eV
Energy per atom: Epot =1924.023eV Ekin = 753.472eV (T=1457.280K) Etot = 2677.495eV
Energy per atom: Epot =1943.500eV Ekin = 736.989eV (T=1425.401K) Etot = 2680.489eV
Energy per atom: Epot =1937.356eV Ekin = 741.345eV (T=1433.826K) Etot = 2678.701eV
Energy per atom: Epot =1941.921eV Ekin = 745.904eV (T=1442.642K) Etot = 2687.825eV
Energy per atom: Epot =1935.396eV Ekin = 744.948eV (T=1440.794K) Etot = 2680.344eV
Energy per atom: Epot =1925.296eV Ekin = 761.976eV (T=1473.727K) Etot = 2687.272eV
Energy per atom: Epot =1928.481eV Ekin = 753.705eV (T=1457.732K) Etot = 2682.187eV
Energy per atom: Epot =1927.826eV Ekin = 752.514eV (T=1455.428K) Etot = 2680.341eV
Energy per atom: Epot =1936.264eV Ekin = 755.808eV (T=1461.798K) Etot = 2692.072eV
Energy per atom: Epot =1927.727eV Ekin = 768.661eV (T=1486.658K) Etot = 2696.389eV
Energy per atom: Epot =1942.699eV Ekin = 762.781eV (T=1475.285K) Etot = 2705.480eV
Energy per atom: Epot =1956.358eV Ekin = 751.406eV (T=1453.284K) Etot = 2707.764eV
Energy per atom: Epot =1953.380eV Ekin = 767.987eV (T=1485.354K) Etot = 2721.367eV
Energy per atom: Epot =1963.696eV Ekin = 763.017eV (T=1475.741K) Etot = 2726.713eV
Energy per atom: Epot =1960.810eV Ekin = 758.910eV (T=1467.799K) Etot = 2719.721eV
Energy per atom: Epot =1968.503eV Ekin = 755.136eV (T=1460.498K) Etot = 2723.638eV
Energy per atom: Epot =1948.448eV Ekin = 767.418eV (T=1484.252K) Etot = 2715.865eV
Energy per atom: Epot =1959.452eV Ekin = 758.458eV (T=1466.924K) Etot = 2717.910eV
Energy per atom: Epot =1976.650eV Ekin = 739.733eV (T=1430.708K) Etot = 2716.384eV
Energy per atom: Epot =1968.456eV Ekin = 747.425eV (T=1445.585K) Etot = 2715.882eV
Energy per atom: Epot =1964.560eV Ekin = 755.360eV (T=1460.932K) Etot = 2719.920eV
Energy per atom: Epot =1951.765eV Ekin = 771.403eV (T=1491.961K) Etot = 2723.169eV
Energy per atom: Epot =1962.672eV Ekin = 761.239eV (T=1472.303K) Etot = 2723.911eV
Energy per atom: Epot =1961.261eV Ekin = 759.207eV (T=1468.372K) Etot = 2720.468eV
Energy per atom: Epot =1961.285eV Ekin = 763.407eV (T=1476.496K) Etot = 2724.692eV
Energy per atom: Epot =1960.211eV Ekin = 762.111eV (T=1473.989K) Etot = 2722.322eV
Energy per atom: Epot =1970.215eV Ekin = 751.684eV (T=1453.822K) Etot = 2721.899eV
Energy per atom: Epot =1971.600eV Ekin = 756.904eV (T=1463.918K) Etot = 2728.503eV
Energy per atom: Epot =1974.634eV Ekin = 752.708eV (T=1455.803K) Etot = 2727.341eV
Energy per atom: Epot =1967.485eV Ekin = 759.278eV (T=1468.511K) Etot = 2726.764eV
Energy per atom: Epot =1980.564eV Ekin = 757.865eV (T=1465.778K) Etot = 2738.430eV
Energy per atom: Epot =1976.660eV Ekin = 761.269eV (T=1472.360K) Etot = 2737.929eV
Energy per atom: Epot =1985.271eV Ekin = 755.666eV (T=1461.523K) Etot = 2740.937eV
Energy per atom: Epot =1981.593eV Ekin = 767.563eV (T=1484.534K) Etot = 2749.156eV
Energy per atom: Epot =1986.714eV Ekin = 762.041eV (T=1473.854K) Etot = 2748.755eV
Energy per atom: Epot =1993.004eV Ekin = 757.472eV (T=1465.018K) Etot = 2750.477eV
Energy per atom: Epot =1989.945eV Ekin = 762.070eV (T=1473.909K) Etot = 2752.014eV
Energy per atom: Epot =1995.695eV Ekin = 767.348eV (T=1484.117K) Etot = 2763.042eV
Energy per atom: Epot =1990.450eV Ekin = 774.460eV (T=1497.873K) Etot = 2764.910eV
Energy per atom: Epot =1991.760eV Ekin = 770.482eV (T=1490.180K) Etot = 2762.243eV
Energy per atom: Epot =2006.163eV Ekin = 751.105eV (T=1452.702K) Etot = 2757.268eV
Energy per atom: Epot =1991.401eV Ekin = 771.040eV (T=1491.258K) Etot = 2762.440eV
Energy per atom: Epot =2012.147eV Ekin = 764.406eV (T=1478.428K) Etot = 2776.553eV
Energy per atom: Epot =2012.581eV Ekin = 766.783eV (T=1483.026K) Etot = 2779.364eV
Energy per atom: Epot =1997.261eV Ekin = 773.887eV (T=1496.764K) Etot = 2771.148eV
Energy per atom: Epot =2000.679eV Ekin = 768.893eV (T=1487.106K) Etot = 2769.571eV
Energy per atom: Epot =2006.063eV Ekin = 777.089eV (T=1502.957K) Etot = 2783.151eV
Energy per atom: Epot =1999.960eV Ekin = 780.365eV (T=1509.293K) Etot = 2780.324eV
Energy per atom: Epot =2006.969eV Ekin = 771.330eV (T=1491.820K) Etot = 2778.299eV
Energy per atom: Epot =2003.868eV Ekin = 775.970eV (T=1500.794K) Etot = 2779.839eV
Energy per atom: Epot =1994.244eV Ekin = 782.412eV (T=1513.252K) Etot = 2776.655eV
Energy per atom: Epot =1991.889eV Ekin = 780.205eV (T=1508.985K) Etot = 2772.094eV
Energy per atom: Epot =2011.491eV Ekin = 759.348eV (T=1468.645K) Etot = 2770.839eV
Energy per atom: Epot =1989.518eV Ekin = 774.482eV (T=1497.915K) Etot = 2763.999eV
Energy per atom: Epot =1991.210eV Ekin = 763.484eV (T=1476.645K) Etot = 2754.694eV
Energy per atom: Epot =1994.301eV Ekin = 764.105eV (T=1477.845K) Etot = 2758.406eV
Energy per atom: Epot =2005.346eV Ekin = 759.128eV (T=1468.220K) Etot = 2764.474eV
Energy per atom: Epot =1990.208eV Ekin = 778.883eV (T=1506.427K) Etot = 2769.091eV
Energy per atom: Epot =2001.588eV Ekin = 776.308eV (T=1501.448K) Etot = 2777.896eV
Energy per atom: Epot =1999.264eV Ekin = 781.131eV (T=1510.776K) Etot = 2780.396eV
Energy per atom: Epot =2015.473eV Ekin = 755.590eV (T=1461.376K) Etot = 2771.063eV
Energy per atom: Epot =2018.765eV Ekin = 760.467eV (T=1470.809K) Etot = 2779.232eV
Energy per atom: Epot =2003.526eV Ekin = 770.844eV (T=1490.879K) Etot = 2774.370eV
Energy per atom: Epot =2014.516eV Ekin = 764.577eV (T=1478.759K) Etot = 2779.093eV
Energy per atom: Epot =2013.329eV Ekin = 755.427eV (T=1461.062K) Etot = 2768.756eV
Energy per atom: Epot =2015.986eV Ekin = 759.580eV (T=1469.094K) Etot = 2775.566eV
Energy per atom: Epot =1992.886eV Ekin = 779.629eV (T=1507.870K) Etot = 2772.515eV
Energy per atom: Epot =1997.883eV Ekin = 763.206eV (T=1476.107K) Etot = 2761.089eV
Energy per atom: Epot =2011.327eV Ekin = 762.865eV (T=1475.448K) Etot = 2774.192eV
Energy per atom: Epot =2010.006eV Ekin = 765.110eV (T=1479.789K) Etot = 2775.116eV
Energy per atom: Epot =2011.068eV Ekin = 769.238eV (T=1487.773K) Etot = 2780.306eV
Energy per atom: Epot =2009.654eV Ekin = 764.114eV (T=1477.862K) Etot = 2773.767eV
Energy per atom: Epot =1998.249eV Ekin = 762.374eV (T=1474.498K) Etot = 2760.623eV
Energy per atom: Epot =1992.976eV Ekin = 769.253eV (T=1487.802K) Etot = 2762.229eV
Energy per atom: Epot =1987.906eV Ekin = 767.217eV (T=1483.865K) Etot = 2755.123eV
Energy per atom: Epot =1999.707eV Ekin = 751.430eV (T=1453.332K) Etot = 2751.137eV
Energy per atom: Epot =1987.568eV Ekin = 769.760eV (T=1488.782K) Etot = 2757.327eV
Energy per atom: Epot =1980.934eV Ekin = 768.433eV (T=1486.217K) Etot = 2749.367eV
Energy per atom: Epot =1980.423eV Ekin = 771.060eV (T=1491.298K) Etot = 2751.484eV
Energy per atom: Epot =1983.338eV Ekin = 772.829eV (T=1494.719K) Etot = 2756.168eV
Energy per atom: Epot =1990.833eV Ekin = 758.915eV (T=1467.807K) Etot = 2749.748eV
Energy per atom: Epot =1982.031eV Ekin = 771.364eV (T=1491.885K) Etot = 2753.395eV
Energy per atom: Epot =1992.867eV Ekin = 763.092eV (T=1475.886K) Etot = 2755.959eV
Energy per atom: Epot =1976.789eV Ekin = 785.118eV (T=1518.487K) Etot = 2761.907eV
Energy per atom: Epot =1976.990eV Ekin = 773.782eV (T=1496.562K) Etot = 2750.772eV
Energy per atom: Epot =1982.989eV Ekin = 754.518eV (T=1459.304K) Etot = 2737.507eV
Energy per atom: Epot =1977.616eV Ekin = 764.689eV (T=1478.975K) Etot = 2742.305eV
Energy per atom: Epot =1992.400eV Ekin = 757.623eV (T=1465.308K) Etot = 2750.023eV
Energy per atom: Epot =1979.409eV Ekin = 766.332eV (T=1482.153K) Etot = 2745.742eV
Energy per atom: Epot =2004.032eV Ekin = 739.351eV (T=1429.969K) Etot = 2743.383eV
Energy per atom: Epot =1983.394eV Ekin = 763.410eV (T=1476.502K) Etot = 2746.804eV
Energy per atom: Epot =1987.997eV Ekin = 764.919eV (T=1479.421K) Etot = 2752.917eV
Energy per atom: Epot =1993.826eV Ekin = 761.079eV (T=1471.992K) Etot = 2754.904eV
Energy per atom: Epot =1988.132eV Ekin = 763.296eV (T=1476.281K) Etot = 2751.428eV
Energy per atom: Epot =1992.625eV Ekin = 758.081eV (T=1466.196K) Etot = 2750.706eV
Energy per atom: Epot =1978.758eV Ekin = 772.609eV (T=1494.292K) Etot = 2751.367eV
Energy per atom: Epot =1995.581eV Ekin = 765.280eV (T=1480.118K) Etot = 2760.861eV
Energy per atom: Epot =2001.447eV Ekin = 766.664eV (T=1482.795K) Etot = 2768.111eV
Energy per atom: Epot =1998.489eV Ekin = 766.386eV (T=1482.258K) Etot = 2764.875eV
Energy per atom: Epot =1990.007eV Ekin = 781.452eV (T=1511.396K) Etot = 2771.459eV
Energy per atom: Epot =1990.105eV Ekin = 777.733eV (T=1504.203K) Etot = 2767.838eV
Energy per atom: Epot =1981.454eV Ekin = 776.545eV (T=1501.907K) Etot = 2757.999eV
Energy per atom: Epot =1995.433eV Ekin = 768.522eV (T=1486.389K) Etot = 2763.956eV
Energy per atom: Epot =1986.854eV Ekin = 782.529eV (T=1513.480K) Etot = 2769.384eV
Energy per atom: Epot =2000.741eV Ekin = 761.337eV (T=1472.492K) Etot = 2762.078eV
Energy per atom: Epot =1986.232eV Ekin = 781.839eV (T=1512.144K) Etot = 2768.070eV
Energy per atom: Epot =1994.108eV Ekin = 776.538eV (T=1501.893K) Etot = 2770.646eV
Energy per atom: Epot =2004.084eV Ekin = 769.711eV (T=1488.689K) Etot = 2773.795eV
Energy per atom: Epot =2013.979eV Ekin = 773.433eV (T=1495.886K) Etot = 2787.411eV
Energy per atom: Epot =2008.135eV Ekin = 773.461eV (T=1495.941K) Etot = 2781.596eV
Energy per atom: Epot =2026.388eV Ekin = 761.054eV (T=1471.944K) Etot = 2787.442eV
Energy per atom: Epot =2013.322eV Ekin = 778.415eV (T=1505.523K) Etot = 2791.738eV
Energy per atom: Epot =2003.696eV Ekin = 789.601eV (T=1527.157K) Etot = 2793.297eV
Energy per atom: Epot =2019.292eV Ekin = 770.977eV (T=1491.137K) Etot = 2790.269eV
Energy per atom: Epot =2020.320eV Ekin = 775.131eV (T=1499.170K) Etot = 2795.451eV
Energy per atom: Epot =2024.051eV Ekin = 759.823eV (T=1469.564K) Etot = 2783.874eV
Energy per atom: Epot =2026.366eV Ekin = 757.288eV (T=1464.661K) Etot = 2783.653eV
Energy per atom: Epot =2022.034eV Ekin = 768.749eV (T=1486.828K) Etot = 2790.783eV
Energy per atom: Epot =2022.453eV Ekin = 774.798eV (T=1498.526K) Etot = 2797.251eV
Energy per atom: Epot =2007.836eV Ekin = 791.669eV (T=1531.156K) Etot = 2799.504eV
Energy per atom: Epot =2015.746eV Ekin = 786.559eV (T=1521.274K) Etot = 2802.305eV
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] 23:37:30 43.457006 1.0818
BFGSLineSearch: 1[ 1] 23:37:30 42.347659 0.2273
BFGSLineSearch: 2[ 2] 23:37:30 42.108454 0.1349
BFGSLineSearch: 3[ 3] 23:37:30 41.964817 0.1138
BFGSLineSearch: 4[ 4] 23:37:30 41.924933 0.0683
BFGSLineSearch: 5[ 5] 23:37:30 41.915346 0.0225
BFGSLineSearch: 6[ 6] 23:37:30 41.914920 0.0059
BFGSLineSearch: 7[ 7] 23:37:30 41.914872 0.0023
BFGSLineSearch: 8[ 9] 23:37:30 41.914855 0.0023
BFGSLineSearch: 9[ 10] 23:37:30 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 17.231eV (T=1433.413K) Etot = 59.146eV
Energy per atom: Epot =51.268eV Ekin = 7.922eV (T=659.023K) Etot = 59.191eV
Energy per atom: Epot =52.909eV Ekin = 6.299eV (T=523.979K) Etot = 59.208eV
Energy per atom: Epot =52.584eV Ekin = 6.620eV (T=550.696K) Etot = 59.204eV
Energy per atom: Epot =52.320eV Ekin = 6.884eV (T=572.626K) Etot = 59.203eV
Energy per atom: Epot =51.428eV Ekin = 7.776eV (T=646.830K) Etot = 59.204eV
Energy per atom: Epot =51.811eV Ekin = 7.392eV (T=614.924K) Etot = 59.203eV
Energy per atom: Epot =50.879eV Ekin = 8.322eV (T=692.252K) Etot = 59.200eV
Energy per atom: Epot =51.254eV Ekin = 7.949eV (T=661.220K) Etot = 59.202eV
Energy per atom: Epot =51.982eV Ekin = 7.223eV (T=600.815K) Etot = 59.205eV
Energy per atom: Epot =52.382eV Ekin = 6.824eV (T=567.642K) Etot = 59.206eV
Energy per atom: Epot =50.635eV Ekin = 8.562eV (T=712.252K) Etot = 59.197eV
Energy per atom: Epot =51.205eV Ekin = 7.993eV (T=664.902K) Etot = 59.198eV
Energy per atom: Epot =50.316eV Ekin = 8.876eV (T=738.356K) Etot = 59.192eV
Energy per atom: Epot =50.451eV Ekin = 8.741eV (T=727.113K) Etot = 59.192eV
Energy per atom: Epot =51.463eV Ekin = 7.735eV (T=643.421K) Etot = 59.197eV
Energy per atom: Epot =51.494eV Ekin = 7.705eV (T=640.982K) Etot = 59.200eV
Energy per atom: Epot =51.661eV Ekin = 7.543eV (T=627.490K) Etot = 59.204eV
Energy per atom: Epot =51.303eV Ekin = 7.897eV (T=656.910K) Etot = 59.200eV
Energy per atom: Epot =50.599eV Ekin = 8.593eV (T=714.826K) Etot = 59.192eV
Energy per atom: Epot =51.120eV Ekin = 8.074eV (T=671.647K) Etot = 59.194eV
Energy per atom: Epot =50.730eV Ekin = 8.464eV (T=704.123K) Etot = 59.194eV
Energy per atom: Epot =51.888eV Ekin = 7.312eV (T=608.278K) Etot = 59.200eV
Energy per atom: Epot =51.891eV Ekin = 7.309eV (T=608.012K) Etot = 59.200eV
Energy per atom: Epot =51.622eV Ekin = 7.581eV (T=630.620K) Etot = 59.202eV
Energy per atom: Epot =51.265eV Ekin = 7.933eV (T=659.958K) Etot = 59.199eV
Energy per atom: Epot =51.197eV Ekin = 7.999eV (T=665.422K) Etot = 59.196eV
Energy per atom: Epot =50.957eV Ekin = 8.238eV (T=685.249K) Etot = 59.195eV
Energy per atom: Epot =51.299eV Ekin = 7.901eV (T=657.285K) Etot = 59.200eV
Energy per atom: Epot =51.886eV Ekin = 7.313eV (T=608.302K) Etot = 59.199eV
Energy per atom: Epot =51.660eV Ekin = 7.538eV (T=627.090K) Etot = 59.199eV
Energy per atom: Epot =51.146eV Ekin = 8.047eV (T=669.443K) Etot = 59.193eV
Energy per atom: Epot =51.095eV Ekin = 8.100eV (T=673.830K) Etot = 59.195eV
Energy per atom: Epot =51.268eV Ekin = 7.937eV (T=660.232K) Etot = 59.205eV
Energy per atom: Epot =51.816eV Ekin = 7.385eV (T=614.330K) Etot = 59.201eV
Energy per atom: Epot =50.832eV Ekin = 8.362eV (T=695.637K) Etot = 59.195eV
Energy per atom: Epot =51.202eV Ekin = 7.996eV (T=665.139K) Etot = 59.198eV
Energy per atom: Epot =50.449eV Ekin = 8.745eV (T=727.464K) Etot = 59.194eV
Energy per atom: Epot =51.580eV Ekin = 7.619eV (T=633.761K) Etot = 59.199eV
Energy per atom: Epot =51.519eV Ekin = 7.684eV (T=639.220K) Etot = 59.203eV
Energy per atom: Epot =51.027eV Ekin = 8.172eV (T=679.819K) Etot = 59.199eV
Energy per atom: Epot =50.760eV Ekin = 8.433eV (T=701.496K) Etot = 59.193eV
Energy per atom: Epot =51.108eV Ekin = 8.091eV (T=673.076K) Etot = 59.199eV
Energy per atom: Epot =50.635eV Ekin = 8.558eV (T=711.928K) Etot = 59.194eV
Energy per atom: Epot =51.183eV Ekin = 8.011eV (T=666.412K) Etot = 59.194eV
Energy per atom: Epot =52.180eV Ekin = 7.018eV (T=583.823K) Etot = 59.198eV
Energy per atom: Epot =51.092eV Ekin = 8.104eV (T=674.116K) Etot = 59.195eV
Energy per atom: Epot =50.444eV Ekin = 8.750eV (T=727.892K) Etot = 59.194eV
Energy per atom: Epot =51.811eV Ekin = 7.391eV (T=614.841K) Etot = 59.202eV
Energy per atom: Epot =51.217eV Ekin = 7.980eV (T=663.859K) Etot = 59.198eV
Energy per atom: Epot =52.187eV Ekin = 7.019eV (T=583.877K) Etot = 59.206eV
Energy per atom: Epot =50.002eV Ekin = 9.189eV (T=764.411K) Etot = 59.191eV
Energy per atom: Epot =51.432eV Ekin = 7.769eV (T=646.296K) Etot = 59.201eV
Energy per atom: Epot =51.180eV Ekin = 8.021eV (T=667.225K) Etot = 59.201eV
Energy per atom: Epot =51.653eV Ekin = 7.554eV (T=628.365K) Etot = 59.206eV
Energy per atom: Epot =51.141eV Ekin = 8.058eV (T=670.335K) Etot = 59.199eV
Energy per atom: Epot =50.698eV Ekin = 8.494eV (T=706.624K) Etot = 59.192eV
Energy per atom: Epot =50.531eV Ekin = 8.664eV (T=720.761K) Etot = 59.196eV
Energy per atom: Epot =51.390eV Ekin = 7.811eV (T=649.735K) Etot = 59.201eV
Energy per atom: Epot =50.715eV Ekin = 8.480eV (T=705.390K) Etot = 59.194eV
Energy per atom: Epot =51.525eV Ekin = 7.671eV (T=638.136K) Etot = 59.196eV
Energy per atom: Epot =50.381eV Ekin = 8.812eV (T=733.030K) Etot = 59.192eV
Energy per atom: Epot =51.056eV Ekin = 8.140eV (T=677.150K) Etot = 59.196eV
Energy per atom: Epot =51.224eV Ekin = 7.969eV (T=662.940K) Etot = 59.194eV
Energy per atom: Epot =51.216eV Ekin = 7.984eV (T=664.152K) Etot = 59.200eV
Energy per atom: Epot =52.224eV Ekin = 6.986eV (T=581.127K) Etot = 59.210eV
Energy per atom: Epot =50.729eV Ekin = 8.473eV (T=704.822K) Etot = 59.202eV
Energy per atom: Epot =51.007eV Ekin = 8.195eV (T=681.688K) Etot = 59.202eV
Energy per atom: Epot =50.892eV Ekin = 8.307eV (T=690.989K) Etot = 59.198eV
Energy per atom: Epot =51.603eV Ekin = 7.593eV (T=631.656K) Etot = 59.197eV
Energy per atom: Epot =51.265eV Ekin = 7.932eV (T=659.832K) Etot = 59.197eV
Energy per atom: Epot =51.409eV Ekin = 7.789eV (T=647.952K) Etot = 59.198eV
Energy per atom: Epot =52.002eV Ekin = 7.202eV (T=599.139K) Etot = 59.204eV
Energy per atom: Epot =52.259eV Ekin = 6.948eV (T=577.993K) Etot = 59.207eV
Energy per atom: Epot =50.978eV Ekin = 8.221eV (T=683.905K) Etot = 59.200eV
Energy per atom: Epot =51.637eV Ekin = 7.565eV (T=629.312K) Etot = 59.202eV
Energy per atom: Epot =51.607eV Ekin = 7.594eV (T=631.715K) Etot = 59.201eV
Energy per atom: Epot =50.989eV Ekin = 8.209eV (T=682.871K) Etot = 59.197eV
Energy per atom: Epot =51.713eV Ekin = 7.488eV (T=622.909K) Etot = 59.201eV
Energy per atom: Epot =51.204eV Ekin = 7.995eV (T=665.097K) Etot = 59.199eV
Energy per atom: Epot =52.353eV Ekin = 6.853eV (T=570.054K) Etot = 59.206eV
Energy per atom: Epot =51.219eV Ekin = 7.979eV (T=663.753K) Etot = 59.198eV
Energy per atom: Epot =51.141eV Ekin = 8.050eV (T=669.690K) Etot = 59.192eV
Energy per atom: Epot =51.188eV Ekin = 8.009eV (T=666.219K) Etot = 59.197eV
Energy per atom: Epot =50.817eV Ekin = 8.379eV (T=697.018K) Etot = 59.196eV
Energy per atom: Epot =51.942eV Ekin = 7.260eV (T=603.931K) Etot = 59.202eV
Energy per atom: Epot =52.778eV Ekin = 6.425eV (T=534.507K) Etot = 59.204eV
Energy per atom: Epot =52.159eV Ekin = 7.044eV (T=585.944K) Etot = 59.203eV
Energy per atom: Epot =50.585eV Ekin = 8.611eV (T=716.305K) Etot = 59.196eV
Energy per atom: Epot =50.210eV Ekin = 8.989eV (T=747.800K) Etot = 59.199eV
Energy per atom: Epot =51.701eV Ekin = 7.510eV (T=624.753K) Etot = 59.212eV
Energy per atom: Epot =50.811eV Ekin = 8.395eV (T=698.340K) Etot = 59.206eV
Energy per atom: Epot =49.920eV Ekin = 9.274eV (T=771.433K) Etot = 59.193eV
Energy per atom: Epot =50.868eV Ekin = 8.328eV (T=692.794K) Etot = 59.196eV
Energy per atom: Epot =51.974eV Ekin = 7.230eV (T=601.422K) Etot = 59.204eV
Energy per atom: Epot =51.023eV Ekin = 8.171eV (T=679.686K) Etot = 59.194eV
Energy per atom: Epot =51.026eV Ekin = 8.162eV (T=678.986K) Etot = 59.188eV
Energy per atom: Epot =49.882eV Ekin = 9.308eV (T=774.289K) Etot = 59.190eV
Energy per atom: Epot =50.939eV Ekin = 8.261eV (T=687.211K) Etot = 59.200eV
Energy per atom: Epot =51.867eV Ekin = 7.334eV (T=610.108K) Etot = 59.201eV
Energy per atom: Epot =51.651eV Ekin = 7.548eV (T=627.925K) Etot = 59.199eV
Energy per atom: Epot =51.584eV Ekin = 7.614eV (T=633.406K) Etot = 59.198eV
Energy per atom: Epot =52.067eV Ekin = 7.135eV (T=593.556K) Etot = 59.202eV
Energy per atom: Epot =51.287eV Ekin = 7.909eV (T=657.914K) Etot = 59.196eV
Energy per atom: Epot =51.166eV Ekin = 8.031eV (T=668.108K) Etot = 59.198eV
Energy per atom: Epot =51.211eV Ekin = 7.994eV (T=664.962K) Etot = 59.204eV
Energy per atom: Epot =50.053eV Ekin = 9.142eV (T=760.482K) Etot = 59.195eV
Energy per atom: Epot =50.902eV Ekin = 8.296eV (T=690.093K) Etot = 59.198eV
Energy per atom: Epot =51.463eV Ekin = 7.740eV (T=643.890K) Etot = 59.204eV
Energy per atom: Epot =52.337eV Ekin = 6.865eV (T=571.040K) Etot = 59.202eV
Energy per atom: Epot =51.382eV Ekin = 7.813eV (T=649.965K) Etot = 59.196eV
Energy per atom: Epot =51.032eV Ekin = 8.167eV (T=679.402K) Etot = 59.199eV
Energy per atom: Epot =51.359eV Ekin = 7.841eV (T=652.292K) Etot = 59.200eV
Energy per atom: Epot =51.522eV Ekin = 7.679eV (T=638.799K) Etot = 59.201eV
Energy per atom: Epot =50.939eV Ekin = 8.261eV (T=687.164K) Etot = 59.199eV
Energy per atom: Epot =51.525eV Ekin = 7.677eV (T=638.623K) Etot = 59.202eV
Energy per atom: Epot =51.054eV Ekin = 8.147eV (T=677.685K) Etot = 59.200eV
Energy per atom: Epot =51.076eV Ekin = 8.127eV (T=676.065K) Etot = 59.203eV
Energy per atom: Epot =51.698eV Ekin = 7.501eV (T=624.018K) Etot = 59.199eV
Energy per atom: Epot =49.777eV Ekin = 9.408eV (T=782.636K) Etot = 59.185eV
Energy per atom: Epot =51.763eV Ekin = 7.435eV (T=618.502K) Etot = 59.198eV
Energy per atom: Epot =51.341eV Ekin = 7.859eV (T=653.750K) Etot = 59.200eV
Energy per atom: Epot =50.802eV Ekin = 8.392eV (T=698.064K) Etot = 59.193eV
Energy per atom: Epot =51.892eV Ekin = 7.313eV (T=608.339K) Etot = 59.205eV
Energy per atom: Epot =51.801eV Ekin = 7.399eV (T=615.460K) Etot = 59.200eV
Energy per atom: Epot =51.561eV Ekin = 7.640eV (T=635.540K) Etot = 59.201eV
Energy per atom: Epot =52.213eV Ekin = 6.989eV (T=581.405K) Etot = 59.202eV
Energy per atom: Epot =51.434eV Ekin = 7.757eV (T=645.277K) Etot = 59.191eV
Energy per atom: Epot =51.261eV Ekin = 7.934eV (T=659.964K) Etot = 59.195eV
Energy per atom: Epot =50.863eV Ekin = 8.330eV (T=692.960K) Etot = 59.193eV
Energy per atom: Epot =51.384eV Ekin = 7.814eV (T=650.013K) Etot = 59.198eV
Energy per atom: Epot =51.231eV Ekin = 7.971eV (T=663.111K) Etot = 59.202eV
Energy per atom: Epot =50.962eV Ekin = 8.239eV (T=685.364K) Etot = 59.201eV
Energy per atom: Epot =50.923eV Ekin = 8.281eV (T=688.872K) Etot = 59.204eV
Energy per atom: Epot =50.596eV Ekin = 8.595eV (T=714.970K) Etot = 59.191eV
Energy per atom: Epot =50.676eV Ekin = 8.516eV (T=708.416K) Etot = 59.192eV
Energy per atom: Epot =51.955eV Ekin = 7.244eV (T=602.623K) Etot = 59.199eV
Energy per atom: Epot =52.435eV Ekin = 6.768eV (T=563.031K) Etot = 59.203eV
Energy per atom: Epot =51.319eV Ekin = 7.878eV (T=655.361K) Etot = 59.197eV
Energy per atom: Epot =50.364eV Ekin = 8.830eV (T=734.525K) Etot = 59.194eV
Energy per atom: Epot =51.148eV Ekin = 8.048eV (T=669.462K) Etot = 59.196eV
Energy per atom: Epot =50.844eV Ekin = 8.350eV (T=694.572K) Etot = 59.193eV
Energy per atom: Epot =51.123eV Ekin = 8.074eV (T=671.666K) Etot = 59.197eV
Energy per atom: Epot =51.416eV Ekin = 7.785eV (T=647.596K) Etot = 59.200eV
Energy per atom: Epot =51.644eV Ekin = 7.555eV (T=628.501K) Etot = 59.200eV
Energy per atom: Epot =50.499eV Ekin = 8.692eV (T=723.029K) Etot = 59.191eV
Energy per atom: Epot =50.132eV Ekin = 9.063eV (T=753.932K) Etot = 59.195eV
Energy per atom: Epot =51.825eV Ekin = 7.378eV (T=613.785K) Etot = 59.203eV
Energy per atom: Epot =50.804eV Ekin = 8.390eV (T=697.913K) Etot = 59.194eV
Energy per atom: Epot =51.027eV Ekin = 8.174eV (T=679.931K) Etot = 59.200eV
Energy per atom: Epot =50.629eV Ekin = 8.570eV (T=712.903K) Etot = 59.198eV
Energy per atom: Epot =51.517eV Ekin = 7.683eV (T=639.159K) Etot = 59.201eV
Energy per atom: Epot =50.349eV Ekin = 8.850eV (T=736.233K) Etot = 59.199eV
Energy per atom: Epot =50.847eV Ekin = 8.350eV (T=694.619K) Etot = 59.197eV
Energy per atom: Epot =49.809eV Ekin = 9.383eV (T=780.550K) Etot = 59.192eV
Energy per atom: Epot =49.667eV Ekin = 9.528eV (T=792.612K) Etot = 59.195eV
Energy per atom: Epot =51.174eV Ekin = 8.025eV (T=667.536K) Etot = 59.199eV
Energy per atom: Epot =52.440eV Ekin = 6.768eV (T=562.967K) Etot = 59.208eV
Energy per atom: Epot =51.792eV Ekin = 7.410eV (T=616.403K) Etot = 59.202eV
Energy per atom: Epot =51.423eV Ekin = 7.777eV (T=646.972K) Etot = 59.200eV
Energy per atom: Epot =50.438eV Ekin = 8.756eV (T=728.356K) Etot = 59.194eV
Energy per atom: Epot =50.478eV Ekin = 8.716eV (T=725.092K) Etot = 59.195eV
Energy per atom: Epot =50.881eV Ekin = 8.316eV (T=691.784K) Etot = 59.197eV
Energy per atom: Epot =50.896eV Ekin = 8.303eV (T=690.716K) Etot = 59.200eV
Energy per atom: Epot =51.124eV Ekin = 8.077eV (T=671.887K) Etot = 59.201eV
Energy per atom: Epot =51.062eV Ekin = 8.139eV (T=677.084K) Etot = 59.201eV
Energy per atom: Epot =51.260eV Ekin = 7.937eV (T=660.256K) Etot = 59.197eV
Energy per atom: Epot =51.180eV Ekin = 8.017eV (T=666.917K) Etot = 59.198eV
Energy per atom: Epot =50.962eV Ekin = 8.239eV (T=685.344K) Etot = 59.200eV
Energy per atom: Epot =51.377eV Ekin = 7.831eV (T=651.394K) Etot = 59.208eV
Energy per atom: Epot =51.104eV Ekin = 8.100eV (T=673.788K) Etot = 59.203eV
Energy per atom: Epot =51.758eV Ekin = 7.446eV (T=619.435K) Etot = 59.204eV
Energy per atom: Epot =50.790eV Ekin = 8.410eV (T=699.631K) Etot = 59.201eV
Energy per atom: Epot =50.886eV Ekin = 8.314eV (T=691.598K) Etot = 59.200eV
Energy per atom: Epot =50.805eV Ekin = 8.386eV (T=697.606K) Etot = 59.191eV
Energy per atom: Epot =50.591eV Ekin = 8.599eV (T=715.346K) Etot = 59.190eV
Energy per atom: Epot =51.220eV Ekin = 7.983eV (T=664.075K) Etot = 59.202eV
Energy per atom: Epot =51.613eV Ekin = 7.592eV (T=631.558K) Etot = 59.205eV
Energy per atom: Epot =51.342eV Ekin = 7.856eV (T=653.535K) Etot = 59.198eV
Energy per atom: Epot =50.612eV Ekin = 8.581eV (T=713.824K) Etot = 59.193eV
Energy per atom: Epot =50.696eV Ekin = 8.504eV (T=707.426K) Etot = 59.200eV
Energy per atom: Epot =51.604eV Ekin = 7.601eV (T=632.278K) Etot = 59.205eV
Energy per atom: Epot =51.739eV Ekin = 7.466eV (T=621.075K) Etot = 59.205eV
Energy per atom: Epot =51.406eV Ekin = 7.797eV (T=648.634K) Etot = 59.204eV
Energy per atom: Epot =50.699eV Ekin = 8.495eV (T=706.667K) Etot = 59.194eV
Energy per atom: Epot =51.268eV Ekin = 7.934eV (T=659.973K) Etot = 59.202eV
Energy per atom: Epot =50.972eV Ekin = 8.230eV (T=684.627K) Etot = 59.203eV
Energy per atom: Epot =51.891eV Ekin = 7.320eV (T=608.911K) Etot = 59.211eV
Energy per atom: Epot =50.612eV Ekin = 8.592eV (T=714.746K) Etot = 59.204eV
Energy per atom: Epot =50.795eV Ekin = 8.406eV (T=699.294K) Etot = 59.201eV
Energy per atom: Epot =50.131eV Ekin = 9.069eV (T=754.408K) Etot = 59.200eV
Energy per atom: Epot =51.347eV Ekin = 7.862eV (T=654.048K) Etot = 59.209eV
Energy per atom: Epot =51.642eV Ekin = 7.560eV (T=628.919K) Etot = 59.203eV
Energy per atom: Epot =50.662eV Ekin = 8.533eV (T=709.813K) Etot = 59.195eV
Energy per atom: Epot =51.003eV Ekin = 8.196eV (T=681.810K) Etot = 59.199eV
Energy per atom: Epot =50.846eV Ekin = 8.350eV (T=694.594K) Etot = 59.196eV
Energy per atom: Epot =51.306eV Ekin = 7.891eV (T=656.449K) Etot = 59.197eV
Energy per atom: Epot =50.795eV Ekin = 8.401eV (T=698.849K) Etot = 59.196eV
Energy per atom: Epot =51.474eV Ekin = 7.727eV (T=642.776K) Etot = 59.201eV
Energy per atom: Epot =52.238eV Ekin = 6.969eV (T=579.758K) Etot = 59.208eV
Energy per atom: Epot =51.006eV Ekin = 8.197eV (T=681.892K) Etot = 59.203eV
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?