Note
Go to the end to download the full example code.
Molecular dynamics#
Note
These examples can be run without asap3 installed. In that case,
ASE’s Python implementation of the EMT calculator can be used instead, but it
is much slower.
Goal#
In this tutorial, we will learn how to perform basic molecular dynamics (MD) simulations using ASE.
The key objectives are:
Understand how to set up a crystal structure (Cu atoms on an FCC lattice).
Initialize velocities from Maxwell–Boltzmann distribution corresponding to a chosen temperature.
Integrate Newton’s equations of motion using Velocity-Verlet algorithm and we monitor the temperature using Langevin thermostat.
Monitor and analyze thermodynamic quantities (potential energy, kinetic energy, total energy, temperature).
Save trajectories and visualize atomic motion with ASE’s GUI.
Explore MD in different scenarios: - Constant energy MD (NVE ensemble) - Constant temperature MD (NVT ensemble) - Isolated nanoparticle simulations
By the end of this tutorial, you should be able to set up your own MD simulations, monitor energy conservation, and visualize system evolution.
Part 1: Basic Molecular Dynamics Simulation#
We start by creating a copper crystal, assigning random velocities corresponding to Maxwell Boltzmann Distribution at 300 K, and running dynamics in the NVE ensemble (constant energy).
import matplotlib.pyplot as plt
import numpy as np
# choose one of the following implementations of EMT:
# included in ase
# from ase.calculators.emt import EMT
# faster performance
from asap3 import EMT
from ase import units
from ase.cluster.cubic import FaceCenteredCubic as ClusterFCC
from ase.io.trajectory import Trajectory
from ase.lattice.cubic import FaceCenteredCubic as LatticeFCC
from ase.md.langevin import Langevin # for later NPT simulations
from ase.md.velocitydistribution import (
MaxwellBoltzmannDistribution,
Stationary,
ZeroRotation,
)
from ase.md.verlet import VelocityVerlet
from ase.optimize import QuasiNewton
from ase.visualize.plot import plot_atoms
# Set up initial positions of Cu atoms on Fcc crystal lattice
size = 10
atoms = LatticeFCC(
directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
symbol='Cu',
size=(size, size, size),
pbc=True,
)
Before setting up the MD simulation, we take a look at the initial structure:
fig, ax = plt.subplots(figsize=(5, 5))
plot_atoms(atoms, ax, rotation=('45x,45y,0z'), show_unit_cell=2, radii=0.75)
ax.set_axis_off()
plt.tight_layout()
plt.show()
Now let’s run the MD simulation and monitor the kinetic and potential energy of the whole system:
# Describe the interatomic interactions with the Effective Medium Theory (EMT)
atoms.calc = EMT()
# Set the initial velocities corresponding to T=300K from Maxwell Boltzmann
# Distribution
MaxwellBoltzmannDistribution(atoms, temperature_K=300)
# We use Velocity Verlet algorithm to integrate the Newton's equations.
timestep_fs = 5
dyn = VelocityVerlet(atoms, timestep_fs * units.fs) # 5 fs time step.
def printenergy(a):
"""
Function to print the thermodynamical properties i.e potential energy,
kinetic energy and total energy
"""
epot = a.get_potential_energy()
ekin = a.get_kinetic_energy()
temp = a.get_temperature()
print(
f'Energy per atom: Epot ={epot:6.3f}eV Ekin = {ekin:.3f}eV '
f'(T={temp:.3f}K) Etot = {epot + ekin:.3f}eV'
)
# Now run the dynamics
print('running a NVE simulation of fcc Cu')
printenergy(atoms)
# init lists to for energy vs time data
time_ps, epot, ekin = [], [], []
mdind = 0
steps_per_block = 10
for i in range(20):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the energies of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
epot.append(atoms.get_potential_energy())
ekin.append(atoms.get_kinetic_energy())
etot = np.array(epot) + np.array(ekin)
# Plot energies vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, epot, label='Potential energy')
ax.plot(time_ps, ekin, label='Kinetic energy')
ax.plot(time_ps, etot, label='Total energy')
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Energy (eV)')
ax.legend(loc='best')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
running a NVE simulation of fcc Cu
Energy per atom: Epot =-2.405eV Ekin = 158.471eV (T=306.497K) Etot = 156.066eV
Energy per atom: Epot =120.042eV Ekin = 36.827eV (T=71.227K) Etot = 156.869eV
Energy per atom: Epot =79.402eV Ekin = 77.323eV (T=149.550K) Etot = 156.725eV
Energy per atom: Epot =72.927eV Ekin = 83.651eV (T=161.789K) Etot = 156.578eV
Energy per atom: Epot =70.639eV Ekin = 85.885eV (T=166.108K) Etot = 156.523eV
Energy per atom: Epot =82.301eV Ekin = 74.389eV (T=143.874K) Etot = 156.690eV
Energy per atom: Epot =79.109eV Ekin = 77.565eV (T=150.017K) Etot = 156.674eV
Energy per atom: Epot =75.406eV Ekin = 81.188eV (T=157.024K) Etot = 156.593eV
Energy per atom: Epot =74.157eV Ekin = 82.436eV (T=159.439K) Etot = 156.593eV
Energy per atom: Epot =80.217eV Ekin = 76.445eV (T=147.851K) Etot = 156.662eV
Energy per atom: Epot =77.027eV Ekin = 79.602eV (T=153.956K) Etot = 156.629eV
Energy per atom: Epot =76.464eV Ekin = 80.153eV (T=155.024K) Etot = 156.617eV
Energy per atom: Epot =77.484eV Ekin = 79.148eV (T=153.079K) Etot = 156.632eV
Energy per atom: Epot =78.388eV Ekin = 78.247eV (T=151.336K) Etot = 156.635eV
Energy per atom: Epot =76.928eV Ekin = 79.699eV (T=154.144K) Etot = 156.627eV
Energy per atom: Epot =75.700eV Ekin = 80.928eV (T=156.522K) Etot = 156.629eV
Energy per atom: Epot =75.631eV Ekin = 80.983eV (T=156.629K) Etot = 156.614eV
Energy per atom: Epot =80.391eV Ekin = 76.244eV (T=147.463K) Etot = 156.635eV
Energy per atom: Epot =76.542eV Ekin = 80.089eV (T=154.900K) Etot = 156.632eV
Energy per atom: Epot =74.637eV Ekin = 81.971eV (T=158.539K) Etot = 156.608eV
Energy per atom: Epot =81.400eV Ekin = 75.252eV (T=145.543K) Etot = 156.652eV
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 =601.168eV Ekin = 83.076eV (T=160.676K) Etot = 684.244eV
Energy per atom: Epot =673.466eV Ekin = 145.393eV (T=281.203K) Etot = 818.860eV
Energy per atom: Epot =734.695eV Ekin = 204.564eV (T=395.645K) Etot = 939.259eV
Energy per atom: Epot =789.211eV Ekin = 257.116eV (T=497.284K) Etot = 1046.327eV
Energy per atom: Epot =841.433eV Ekin = 301.799eV (T=583.705K) Etot = 1143.232eV
Energy per atom: Epot =884.401eV Ekin = 339.061eV (T=655.773K) Etot = 1223.462eV
Energy per atom: Epot =923.987eV Ekin = 378.425eV (T=731.907K) Etot = 1302.412eV
Energy per atom: Epot =962.936eV Ekin = 412.866eV (T=798.518K) Etot = 1375.801eV
Energy per atom: Epot =1003.168eV Ekin = 444.560eV (T=859.818K) Etot = 1447.728eV
Energy per atom: Epot =1045.146eV Ekin = 461.895eV (T=893.344K) Etot = 1507.041eV
Energy per atom: Epot =1077.174eV Ekin = 491.692eV (T=950.974K) Etot = 1568.865eV
Energy per atom: Epot =1108.096eV Ekin = 513.938eV (T=994.001K) Etot = 1622.034eV
Energy per atom: Epot =1137.456eV Ekin = 534.613eV (T=1033.988K) Etot = 1672.068eV
Energy per atom: Epot =1173.074eV Ekin = 540.661eV (T=1045.686K) Etot = 1713.736eV
Energy per atom: Epot =1212.512eV Ekin = 549.614eV (T=1063.001K) Etot = 1762.126eV
Energy per atom: Epot =1230.384eV Ekin = 563.693eV (T=1090.231K) Etot = 1794.077eV
Energy per atom: Epot =1244.645eV Ekin = 587.582eV (T=1136.434K) Etot = 1832.227eV
Energy per atom: Epot =1290.148eV Ekin = 591.321eV (T=1143.667K) Etot = 1881.469eV
Energy per atom: Epot =1310.484eV Ekin = 594.692eV (T=1150.186K) Etot = 1905.176eV
Energy per atom: Epot =1320.239eV Ekin = 610.558eV (T=1180.873K) Etot = 1930.797eV
Energy per atom: Epot =1350.439eV Ekin = 621.675eV (T=1202.374K) Etot = 1972.114eV
Energy per atom: Epot =1361.634eV Ekin = 641.006eV (T=1239.761K) Etot = 2002.639eV
Energy per atom: Epot =1383.943eV Ekin = 647.525eV (T=1252.371K) Etot = 2031.468eV
Energy per atom: Epot =1417.345eV Ekin = 647.695eV (T=1252.698K) Etot = 2065.040eV
Energy per atom: Epot =1420.760eV Ekin = 669.894eV (T=1295.633K) Etot = 2090.654eV
Energy per atom: Epot =1428.538eV Ekin = 674.676eV (T=1304.882K) Etot = 2103.214eV
Energy per atom: Epot =1454.667eV Ekin = 665.602eV (T=1287.332K) Etot = 2120.269eV
Energy per atom: Epot =1469.375eV Ekin = 677.180eV (T=1309.725K) Etot = 2146.555eV
Energy per atom: Epot =1486.344eV Ekin = 683.107eV (T=1321.188K) Etot = 2169.451eV
Energy per atom: Epot =1501.871eV Ekin = 694.061eV (T=1342.374K) Etot = 2195.931eV
Energy per atom: Epot =1521.476eV Ekin = 686.478eV (T=1327.708K) Etot = 2207.954eV
Energy per atom: Epot =1515.035eV Ekin = 709.402eV (T=1372.046K) Etot = 2224.437eV
Energy per atom: Epot =1564.235eV Ekin = 674.119eV (T=1303.804K) Etot = 2238.354eV
Energy per atom: Epot =1557.549eV Ekin = 705.695eV (T=1364.876K) Etot = 2263.245eV
Energy per atom: Epot =1571.809eV Ekin = 703.329eV (T=1360.300K) Etot = 2275.139eV
Energy per atom: Epot =1578.932eV Ekin = 706.045eV (T=1365.553K) Etot = 2284.978eV
Energy per atom: Epot =1590.756eV Ekin = 699.852eV (T=1353.575K) Etot = 2290.608eV
Energy per atom: Epot =1603.302eV Ekin = 696.551eV (T=1347.190K) Etot = 2299.853eV
Energy per atom: Epot =1599.470eV Ekin = 723.065eV (T=1398.470K) Etot = 2322.535eV
Energy per atom: Epot =1620.405eV Ekin = 712.537eV (T=1378.109K) Etot = 2332.942eV
Energy per atom: Epot =1637.574eV Ekin = 706.074eV (T=1365.609K) Etot = 2343.649eV
Energy per atom: Epot =1646.305eV Ekin = 718.280eV (T=1389.216K) Etot = 2364.585eV
Energy per atom: Epot =1643.482eV Ekin = 734.385eV (T=1420.365K) Etot = 2377.868eV
Energy per atom: Epot =1662.622eV Ekin = 729.178eV (T=1410.295K) Etot = 2391.800eV
Energy per atom: Epot =1676.738eV Ekin = 718.695eV (T=1390.019K) Etot = 2395.433eV
Energy per atom: Epot =1691.860eV Ekin = 716.938eV (T=1386.621K) Etot = 2408.798eV
Energy per atom: Epot =1680.622eV Ekin = 726.251eV (T=1404.632K) Etot = 2406.872eV
Energy per atom: Epot =1691.166eV Ekin = 727.853eV (T=1407.731K) Etot = 2419.019eV
Energy per atom: Epot =1692.397eV Ekin = 739.718eV (T=1430.680K) Etot = 2432.116eV
Energy per atom: Epot =1714.255eV Ekin = 726.492eV (T=1405.099K) Etot = 2440.747eV
Energy per atom: Epot =1719.039eV Ekin = 740.216eV (T=1431.642K) Etot = 2459.255eV
Energy per atom: Epot =1732.152eV Ekin = 739.786eV (T=1430.811K) Etot = 2471.938eV
Energy per atom: Epot =1746.380eV Ekin = 733.716eV (T=1419.070K) Etot = 2480.096eV
Energy per atom: Epot =1759.936eV Ekin = 731.907eV (T=1415.571K) Etot = 2491.843eV
Energy per atom: Epot =1735.150eV Ekin = 763.952eV (T=1477.549K) Etot = 2499.102eV
Energy per atom: Epot =1760.661eV Ekin = 745.357eV (T=1441.585K) Etot = 2506.018eV
Energy per atom: Epot =1773.215eV Ekin = 743.807eV (T=1438.588K) Etot = 2517.023eV
Energy per atom: Epot =1772.192eV Ekin = 748.942eV (T=1448.520K) Etot = 2521.134eV
Energy per atom: Epot =1771.934eV Ekin = 744.026eV (T=1439.011K) Etot = 2515.960eV
Energy per atom: Epot =1783.011eV Ekin = 745.954eV (T=1442.739K) Etot = 2528.965eV
Energy per atom: Epot =1784.744eV Ekin = 747.140eV (T=1445.035K) Etot = 2531.884eV
Energy per atom: Epot =1806.089eV Ekin = 727.699eV (T=1407.434K) Etot = 2533.788eV
Energy per atom: Epot =1814.534eV Ekin = 725.471eV (T=1403.125K) Etot = 2540.006eV
Energy per atom: Epot =1801.891eV Ekin = 737.679eV (T=1426.735K) Etot = 2539.569eV
Energy per atom: Epot =1819.479eV Ekin = 733.406eV (T=1418.470K) Etot = 2552.885eV
Energy per atom: Epot =1821.761eV Ekin = 734.348eV (T=1420.293K) Etot = 2556.109eV
Energy per atom: Epot =1830.486eV Ekin = 730.646eV (T=1413.132K) Etot = 2561.132eV
Energy per atom: Epot =1828.393eV Ekin = 744.999eV (T=1440.893K) Etot = 2573.392eV
Energy per atom: Epot =1834.020eV Ekin = 745.171eV (T=1441.226K) Etot = 2579.191eV
Energy per atom: Epot =1851.192eV Ekin = 732.839eV (T=1417.375K) Etot = 2584.032eV
Energy per atom: Epot =1850.525eV Ekin = 743.269eV (T=1437.546K) Etot = 2593.793eV
Energy per atom: Epot =1846.174eV Ekin = 752.494eV (T=1455.388K) Etot = 2598.668eV
Energy per atom: Epot =1848.098eV Ekin = 751.803eV (T=1454.052K) Etot = 2599.901eV
Energy per atom: Epot =1853.861eV Ekin = 754.340eV (T=1458.960K) Etot = 2608.202eV
Energy per atom: Epot =1859.737eV Ekin = 749.478eV (T=1449.555K) Etot = 2609.215eV
Energy per atom: Epot =1867.027eV Ekin = 747.472eV (T=1445.675K) Etot = 2614.499eV
Energy per atom: Epot =1865.001eV Ekin = 749.694eV (T=1449.973K) Etot = 2614.695eV
Energy per atom: Epot =1874.149eV Ekin = 739.489eV (T=1430.236K) Etot = 2613.638eV
Energy per atom: Epot =1870.650eV Ekin = 738.893eV (T=1429.083K) Etot = 2609.543eV
Energy per atom: Epot =1870.923eV Ekin = 738.457eV (T=1428.241K) Etot = 2609.380eV
Energy per atom: Epot =1879.304eV Ekin = 737.197eV (T=1425.803K) Etot = 2616.501eV
Energy per atom: Epot =1883.072eV Ekin = 744.056eV (T=1439.069K) Etot = 2627.128eV
Energy per atom: Epot =1885.806eV Ekin = 746.927eV (T=1444.622K) Etot = 2632.733eV
Energy per atom: Epot =1891.782eV Ekin = 744.907eV (T=1440.715K) Etot = 2636.689eV
Energy per atom: Epot =1883.010eV Ekin = 756.922eV (T=1463.954K) Etot = 2639.932eV
Energy per atom: Epot =1893.229eV Ekin = 751.208eV (T=1452.901K) Etot = 2644.436eV
Energy per atom: Epot =1902.552eV Ekin = 744.459eV (T=1439.849K) Etot = 2647.012eV
Energy per atom: Epot =1904.859eV Ekin = 753.143eV (T=1456.644K) Etot = 2658.002eV
Energy per atom: Epot =1914.577eV Ekin = 739.493eV (T=1430.244K) Etot = 2654.070eV
Energy per atom: Epot =1915.628eV Ekin = 741.003eV (T=1433.164K) Etot = 2656.631eV
Energy per atom: Epot =1906.028eV Ekin = 753.675eV (T=1457.674K) Etot = 2659.704eV
Energy per atom: Epot =1922.498eV Ekin = 746.997eV (T=1444.757K) Etot = 2669.495eV
Energy per atom: Epot =1927.565eV Ekin = 747.558eV (T=1445.842K) Etot = 2675.123eV
Energy per atom: Epot =1938.222eV Ekin = 744.293eV (T=1439.527K) Etot = 2682.515eV
Energy per atom: Epot =1946.375eV Ekin = 739.911eV (T=1431.053K) Etot = 2686.286eV
Energy per atom: Epot =1947.212eV Ekin = 747.283eV (T=1445.310K) Etot = 2694.494eV
Energy per atom: Epot =1943.626eV Ekin = 752.937eV (T=1456.245K) Etot = 2696.563eV
Energy per atom: Epot =1941.738eV Ekin = 761.708eV (T=1473.209K) Etot = 2703.445eV
Energy per atom: Epot =1946.277eV Ekin = 763.122eV (T=1475.945K) Etot = 2709.400eV
Energy per atom: Epot =1945.887eV Ekin = 756.640eV (T=1463.408K) Etot = 2702.528eV
Energy per atom: Epot =1948.727eV Ekin = 758.815eV (T=1467.614K) Etot = 2707.542eV
Energy per atom: Epot =1947.396eV Ekin = 770.053eV (T=1489.350K) Etot = 2717.449eV
Energy per atom: Epot =1956.823eV Ekin = 766.269eV (T=1482.030K) Etot = 2723.092eV
Energy per atom: Epot =1963.941eV Ekin = 764.036eV (T=1477.713K) Etot = 2727.978eV
Energy per atom: Epot =1960.462eV Ekin = 769.582eV (T=1488.439K) Etot = 2730.044eV
Energy per atom: Epot =1961.800eV Ekin = 774.826eV (T=1498.581K) Etot = 2736.626eV
Energy per atom: Epot =1966.101eV Ekin = 764.650eV (T=1478.899K) Etot = 2730.751eV
Energy per atom: Epot =1951.813eV Ekin = 783.104eV (T=1514.591K) Etot = 2734.917eV
Energy per atom: Epot =1965.741eV Ekin = 767.887eV (T=1485.159K) Etot = 2733.627eV
Energy per atom: Epot =1969.905eV Ekin = 769.316eV (T=1487.923K) Etot = 2739.220eV
Energy per atom: Epot =1978.831eV Ekin = 762.767eV (T=1475.257K) Etot = 2741.597eV
Energy per atom: Epot =1976.268eV Ekin = 779.868eV (T=1508.332K) Etot = 2756.136eV
Energy per atom: Epot =1981.770eV Ekin = 770.921eV (T=1491.029K) Etot = 2752.691eV
Energy per atom: Epot =1975.368eV Ekin = 782.381eV (T=1513.192K) Etot = 2757.749eV
Energy per atom: Epot =1990.631eV Ekin = 765.662eV (T=1480.857K) Etot = 2756.293eV
Energy per atom: Epot =1989.293eV Ekin = 755.281eV (T=1460.779K) Etot = 2744.574eV
Energy per atom: Epot =1994.351eV Ekin = 747.493eV (T=1445.716K) Etot = 2741.844eV
Energy per atom: Epot =1997.870eV Ekin = 755.250eV (T=1460.719K) Etot = 2753.120eV
Energy per atom: Epot =1994.909eV Ekin = 763.254eV (T=1476.200K) Etot = 2758.163eV
Energy per atom: Epot =1993.398eV Ekin = 772.904eV (T=1494.864K) Etot = 2766.302eV
Energy per atom: Epot =2001.013eV Ekin = 755.580eV (T=1461.358K) Etot = 2756.593eV
Energy per atom: Epot =1984.573eV Ekin = 773.913eV (T=1496.815K) Etot = 2758.486eV
Energy per atom: Epot =1979.754eV Ekin = 763.105eV (T=1475.911K) Etot = 2742.859eV
Energy per atom: Epot =1973.399eV Ekin = 769.940eV (T=1489.131K) Etot = 2743.339eV
Energy per atom: Epot =1984.419eV Ekin = 753.765eV (T=1457.848K) Etot = 2738.185eV
Energy per atom: Epot =1977.107eV Ekin = 757.844eV (T=1465.736K) Etot = 2734.951eV
Energy per atom: Epot =1971.168eV Ekin = 774.514eV (T=1497.977K) Etot = 2745.681eV
Energy per atom: Epot =1983.509eV Ekin = 773.155eV (T=1495.349K) Etot = 2756.664eV
Energy per atom: Epot =1992.860eV Ekin = 763.364eV (T=1476.411K) Etot = 2756.223eV
Energy per atom: Epot =1993.198eV Ekin = 760.354eV (T=1470.590K) Etot = 2753.552eV
Energy per atom: Epot =1992.032eV Ekin = 760.491eV (T=1470.856K) Etot = 2752.523eV
Energy per atom: Epot =1992.801eV Ekin = 764.714eV (T=1479.024K) Etot = 2757.515eV
Energy per atom: Epot =1999.085eV Ekin = 760.591eV (T=1471.048K) Etot = 2759.675eV
Energy per atom: Epot =1993.087eV Ekin = 766.842eV (T=1483.139K) Etot = 2759.929eV
Energy per atom: Epot =2006.533eV Ekin = 754.812eV (T=1459.873K) Etot = 2761.346eV
Energy per atom: Epot =1986.255eV Ekin = 767.950eV (T=1485.282K) Etot = 2754.205eV
Energy per atom: Epot =1988.376eV Ekin = 765.608eV (T=1480.752K) Etot = 2753.984eV
Energy per atom: Epot =1986.265eV Ekin = 766.298eV (T=1482.087K) Etot = 2752.563eV
Energy per atom: Epot =1998.195eV Ekin = 755.692eV (T=1461.575K) Etot = 2753.887eV
Energy per atom: Epot =2000.972eV Ekin = 757.211eV (T=1464.512K) Etot = 2758.183eV
Energy per atom: Epot =1984.741eV Ekin = 774.192eV (T=1497.354K) Etot = 2758.932eV
Energy per atom: Epot =1988.020eV Ekin = 761.738eV (T=1473.268K) Etot = 2749.758eV
Energy per atom: Epot =1982.762eV Ekin = 781.167eV (T=1510.845K) Etot = 2763.929eV
Energy per atom: Epot =2005.108eV Ekin = 759.846eV (T=1469.608K) Etot = 2764.953eV
Energy per atom: Epot =2003.581eV Ekin = 766.955eV (T=1483.357K) Etot = 2770.536eV
Energy per atom: Epot =2002.444eV Ekin = 768.213eV (T=1485.791K) Etot = 2770.657eV
Energy per atom: Epot =2013.861eV Ekin = 756.887eV (T=1463.885K) Etot = 2770.748eV
Energy per atom: Epot =2017.958eV Ekin = 750.997eV (T=1452.494K) Etot = 2768.955eV
Energy per atom: Epot =2004.530eV Ekin = 776.129eV (T=1501.101K) Etot = 2780.659eV
Energy per atom: Epot =2008.173eV Ekin = 776.343eV (T=1501.515K) Etot = 2784.516eV
Energy per atom: Epot =1999.387eV Ekin = 797.343eV (T=1542.131K) Etot = 2796.730eV
Energy per atom: Epot =2012.066eV Ekin = 783.117eV (T=1514.617K) Etot = 2795.184eV
Energy per atom: Epot =1995.063eV Ekin = 785.833eV (T=1519.870K) Etot = 2780.897eV
Energy per atom: Epot =1995.734eV Ekin = 780.298eV (T=1509.163K) Etot = 2776.032eV
Energy per atom: Epot =2003.043eV Ekin = 773.361eV (T=1495.747K) Etot = 2776.404eV
Energy per atom: Epot =2010.959eV Ekin = 776.573eV (T=1501.960K) Etot = 2787.532eV
Energy per atom: Epot =2003.084eV Ekin = 776.561eV (T=1501.937K) Etot = 2779.646eV
Energy per atom: Epot =2011.825eV Ekin = 773.429eV (T=1495.879K) Etot = 2785.254eV
Energy per atom: Epot =2003.946eV Ekin = 769.081eV (T=1487.470K) Etot = 2773.027eV
Energy per atom: Epot =2005.427eV Ekin = 766.860eV (T=1483.173K) Etot = 2772.287eV
Energy per atom: Epot =2000.356eV Ekin = 756.810eV (T=1463.737K) Etot = 2757.167eV
Energy per atom: Epot =2013.814eV Ekin = 747.926eV (T=1446.554K) Etot = 2761.740eV
Energy per atom: Epot =1991.156eV Ekin = 771.036eV (T=1491.251K) Etot = 2762.192eV
Energy per atom: Epot =1999.842eV Ekin = 768.023eV (T=1485.423K) Etot = 2767.865eV
Energy per atom: Epot =1993.272eV Ekin = 774.600eV (T=1498.144K) Etot = 2767.873eV
Energy per atom: Epot =1996.587eV Ekin = 778.173eV (T=1505.055K) Etot = 2774.760eV
Energy per atom: Epot =2014.220eV Ekin = 769.958eV (T=1489.165K) Etot = 2784.177eV
Energy per atom: Epot =2008.853eV Ekin = 782.355eV (T=1513.143K) Etot = 2791.208eV
Energy per atom: Epot =2009.129eV Ekin = 788.657eV (T=1525.331K) Etot = 2797.786eV
Energy per atom: Epot =2005.120eV Ekin = 797.747eV (T=1542.912K) Etot = 2802.868eV
Energy per atom: Epot =2019.766eV Ekin = 780.886eV (T=1510.302K) Etot = 2800.652eV
Energy per atom: Epot =2012.673eV Ekin = 788.085eV (T=1524.224K) Etot = 2800.758eV
Energy per atom: Epot =2011.544eV Ekin = 779.204eV (T=1507.049K) Etot = 2790.748eV
Energy per atom: Epot =2016.700eV Ekin = 773.493eV (T=1496.002K) Etot = 2790.193eV
Energy per atom: Epot =2024.039eV Ekin = 773.547eV (T=1496.107K) Etot = 2797.586eV
Energy per atom: Epot =2026.529eV Ekin = 774.219eV (T=1497.408K) Etot = 2800.749eV
Energy per atom: Epot =2023.647eV Ekin = 774.365eV (T=1497.689K) Etot = 2798.011eV
Energy per atom: Epot =2024.957eV Ekin = 777.087eV (T=1502.953K) Etot = 2802.044eV
Energy per atom: Epot =2023.437eV Ekin = 771.025eV (T=1491.230K) Etot = 2794.462eV
Energy per atom: Epot =2010.280eV Ekin = 786.508eV (T=1521.175K) Etot = 2796.788eV
Energy per atom: Epot =2014.207eV Ekin = 779.127eV (T=1506.900K) Etot = 2793.334eV
Energy per atom: Epot =1999.307eV Ekin = 789.059eV (T=1526.108K) Etot = 2788.366eV
Energy per atom: Epot =2007.751eV Ekin = 782.219eV (T=1512.879K) Etot = 2789.970eV
Energy per atom: Epot =2007.959eV Ekin = 776.508eV (T=1501.835K) Etot = 2784.468eV
Energy per atom: Epot =2005.403eV Ekin = 783.112eV (T=1514.607K) Etot = 2788.515eV
Energy per atom: Epot =1997.442eV Ekin = 788.410eV (T=1524.854K) Etot = 2785.853eV
Energy per atom: Epot =1996.013eV Ekin = 790.583eV (T=1529.056K) Etot = 2786.596eV
Energy per atom: Epot =1998.297eV Ekin = 789.217eV (T=1526.414K) Etot = 2787.514eV
Energy per atom: Epot =2006.884eV Ekin = 780.585eV (T=1509.719K) Etot = 2787.469eV
Energy per atom: Epot =2008.237eV Ekin = 777.406eV (T=1503.570K) Etot = 2785.643eV
Energy per atom: Epot =2000.307eV Ekin = 783.210eV (T=1514.795K) Etot = 2783.517eV
Energy per atom: Epot =2006.840eV Ekin = 776.347eV (T=1501.523K) Etot = 2783.187eV
Energy per atom: Epot =2007.089eV Ekin = 787.185eV (T=1522.485K) Etot = 2794.274eV
Energy per atom: Epot =2015.495eV Ekin = 777.208eV (T=1503.187K) Etot = 2792.703eV
Energy per atom: Epot =2012.952eV Ekin = 779.646eV (T=1507.904K) Etot = 2792.599eV
Energy per atom: Epot =2015.269eV Ekin = 777.673eV (T=1504.088K) Etot = 2792.943eV
Energy per atom: Epot =2023.563eV Ekin = 771.853eV (T=1492.832K) Etot = 2795.417eV
Energy per atom: Epot =2024.592eV Ekin = 773.256eV (T=1495.544K) Etot = 2797.848eV
Energy per atom: Epot =2020.344eV Ekin = 766.556eV (T=1482.585K) Etot = 2786.900eV
Energy per atom: Epot =2015.932eV Ekin = 775.511eV (T=1499.906K) Etot = 2791.443eV
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] 14:41:30 43.457006 1.0818
BFGSLineSearch: 1[ 1] 14:41:30 42.347659 0.2273
BFGSLineSearch: 2[ 2] 14:41:30 42.108454 0.1349
BFGSLineSearch: 3[ 3] 14:41:30 41.964817 0.1138
BFGSLineSearch: 4[ 4] 14:41:30 41.924933 0.0683
BFGSLineSearch: 5[ 5] 14:41:30 41.915346 0.0225
BFGSLineSearch: 6[ 6] 14:41:30 41.914920 0.0059
BFGSLineSearch: 7[ 7] 14:41:30 41.914872 0.0023
BFGSLineSearch: 8[ 9] 14:41:30 41.914855 0.0023
BFGSLineSearch: 9[ 10] 14:41:30 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 13.780eV (T=1146.312K) Etot = 55.695eV
Energy per atom: Epot =49.965eV Ekin = 5.776eV (T=480.454K) Etot = 55.741eV
Energy per atom: Epot =49.693eV Ekin = 6.062eV (T=504.269K) Etot = 55.755eV
Energy per atom: Epot =49.751eV Ekin = 6.002eV (T=499.284K) Etot = 55.753eV
Energy per atom: Epot =50.277eV Ekin = 5.477eV (T=455.629K) Etot = 55.755eV
Energy per atom: Epot =49.199eV Ekin = 6.554eV (T=545.222K) Etot = 55.754eV
Energy per atom: Epot =49.033eV Ekin = 6.720eV (T=559.046K) Etot = 55.753eV
Energy per atom: Epot =48.513eV Ekin = 7.240eV (T=602.252K) Etot = 55.753eV
Energy per atom: Epot =48.643eV Ekin = 7.111eV (T=591.563K) Etot = 55.755eV
Energy per atom: Epot =49.626eV Ekin = 6.129eV (T=509.873K) Etot = 55.756eV
Energy per atom: Epot =49.926eV Ekin = 5.832eV (T=485.131K) Etot = 55.758eV
Energy per atom: Epot =49.417eV Ekin = 6.340eV (T=527.403K) Etot = 55.757eV
Energy per atom: Epot =50.150eV Ekin = 5.608eV (T=466.513K) Etot = 55.758eV
Energy per atom: Epot =48.935eV Ekin = 6.819eV (T=567.280K) Etot = 55.754eV
Energy per atom: Epot =48.885eV Ekin = 6.866eV (T=571.198K) Etot = 55.752eV
Energy per atom: Epot =49.466eV Ekin = 6.288eV (T=523.048K) Etot = 55.754eV
Energy per atom: Epot =49.404eV Ekin = 6.352eV (T=528.379K) Etot = 55.755eV
Energy per atom: Epot =49.731eV Ekin = 6.027eV (T=501.342K) Etot = 55.757eV
Energy per atom: Epot =49.379eV Ekin = 6.377eV (T=530.509K) Etot = 55.756eV
Energy per atom: Epot =49.208eV Ekin = 6.549eV (T=544.800K) Etot = 55.757eV
Energy per atom: Epot =48.774eV Ekin = 6.975eV (T=580.255K) Etot = 55.749eV
Energy per atom: Epot =49.018eV Ekin = 6.730eV (T=559.876K) Etot = 55.749eV
Energy per atom: Epot =48.952eV Ekin = 6.799eV (T=565.602K) Etot = 55.752eV
Energy per atom: Epot =48.906eV Ekin = 6.842eV (T=569.182K) Etot = 55.748eV
Energy per atom: Epot =49.957eV Ekin = 5.799eV (T=482.395K) Etot = 55.756eV
Energy per atom: Epot =49.605eV Ekin = 6.154eV (T=511.942K) Etot = 55.759eV
Energy per atom: Epot =49.396eV Ekin = 6.363eV (T=529.356K) Etot = 55.760eV
Energy per atom: Epot =49.035eV Ekin = 6.720eV (T=559.045K) Etot = 55.755eV
Energy per atom: Epot =49.027eV Ekin = 6.726eV (T=559.521K) Etot = 55.753eV
Energy per atom: Epot =49.813eV Ekin = 5.942eV (T=494.258K) Etot = 55.755eV
Energy per atom: Epot =48.959eV Ekin = 6.789eV (T=564.782K) Etot = 55.749eV
Energy per atom: Epot =49.306eV Ekin = 6.447eV (T=536.344K) Etot = 55.753eV
Energy per atom: Epot =49.220eV Ekin = 6.531eV (T=543.327K) Etot = 55.751eV
Energy per atom: Epot =49.205eV Ekin = 6.543eV (T=544.274K) Etot = 55.748eV
Energy per atom: Epot =49.199eV Ekin = 6.557eV (T=545.425K) Etot = 55.756eV
Energy per atom: Epot =48.815eV Ekin = 6.937eV (T=577.062K) Etot = 55.752eV
Energy per atom: Epot =48.877eV Ekin = 6.878eV (T=572.116K) Etot = 55.754eV
Energy per atom: Epot =49.479eV Ekin = 6.274eV (T=521.883K) Etot = 55.753eV
Energy per atom: Epot =49.523eV Ekin = 6.228eV (T=518.082K) Etot = 55.751eV
Energy per atom: Epot =49.485eV Ekin = 6.270eV (T=521.584K) Etot = 55.755eV
Energy per atom: Epot =49.440eV Ekin = 6.314eV (T=525.248K) Etot = 55.754eV
Energy per atom: Epot =49.067eV Ekin = 6.686eV (T=556.160K) Etot = 55.752eV
Energy per atom: Epot =49.189eV Ekin = 6.565eV (T=546.128K) Etot = 55.754eV
Energy per atom: Epot =48.980eV Ekin = 6.774eV (T=563.520K) Etot = 55.755eV
Energy per atom: Epot =48.465eV Ekin = 7.284eV (T=605.970K) Etot = 55.750eV
Energy per atom: Epot =49.129eV Ekin = 6.624eV (T=551.016K) Etot = 55.753eV
Energy per atom: Epot =49.494eV Ekin = 6.261eV (T=520.843K) Etot = 55.755eV
Energy per atom: Epot =49.392eV Ekin = 6.357eV (T=528.849K) Etot = 55.750eV
Energy per atom: Epot =49.128eV Ekin = 6.623eV (T=550.931K) Etot = 55.751eV
Energy per atom: Epot =49.120eV Ekin = 6.634eV (T=551.863K) Etot = 55.755eV
Energy per atom: Epot =49.260eV Ekin = 6.490eV (T=539.889K) Etot = 55.750eV
Energy per atom: Epot =48.654eV Ekin = 7.096eV (T=590.312K) Etot = 55.750eV
Energy per atom: Epot =49.489eV Ekin = 6.270eV (T=521.542K) Etot = 55.759eV
Energy per atom: Epot =48.877eV Ekin = 6.874eV (T=571.830K) Etot = 55.751eV
Energy per atom: Epot =49.596eV Ekin = 6.159eV (T=512.340K) Etot = 55.755eV
Energy per atom: Epot =48.567eV Ekin = 7.179eV (T=597.208K) Etot = 55.747eV
Energy per atom: Epot =49.123eV Ekin = 6.629eV (T=551.433K) Etot = 55.752eV
Energy per atom: Epot =48.983eV Ekin = 6.770eV (T=563.153K) Etot = 55.752eV
Energy per atom: Epot =49.381eV Ekin = 6.373eV (T=530.139K) Etot = 55.754eV
Energy per atom: Epot =49.766eV Ekin = 5.990eV (T=498.288K) Etot = 55.756eV
Energy per atom: Epot =49.640eV Ekin = 6.114eV (T=508.608K) Etot = 55.754eV
Energy per atom: Epot =49.550eV Ekin = 6.210eV (T=516.579K) Etot = 55.760eV
Energy per atom: Epot =48.879eV Ekin = 6.872eV (T=571.672K) Etot = 55.751eV
Energy per atom: Epot =48.400eV Ekin = 7.346eV (T=611.120K) Etot = 55.746eV
Energy per atom: Epot =49.350eV Ekin = 6.409eV (T=533.133K) Etot = 55.759eV
Energy per atom: Epot =49.595eV Ekin = 6.164eV (T=512.783K) Etot = 55.759eV
Energy per atom: Epot =49.352eV Ekin = 6.400eV (T=532.391K) Etot = 55.752eV
Energy per atom: Epot =49.300eV Ekin = 6.452eV (T=536.696K) Etot = 55.752eV
Energy per atom: Epot =49.066eV Ekin = 6.686eV (T=556.161K) Etot = 55.752eV
Energy per atom: Epot =48.835eV Ekin = 6.915eV (T=575.273K) Etot = 55.750eV
Energy per atom: Epot =48.801eV Ekin = 6.951eV (T=578.205K) Etot = 55.751eV
Energy per atom: Epot =49.878eV Ekin = 5.877eV (T=488.925K) Etot = 55.756eV
Energy per atom: Epot =49.554eV Ekin = 6.199eV (T=515.712K) Etot = 55.754eV
Energy per atom: Epot =49.421eV Ekin = 6.335eV (T=526.946K) Etot = 55.756eV
Energy per atom: Epot =49.502eV Ekin = 6.254eV (T=520.231K) Etot = 55.756eV
Energy per atom: Epot =49.161eV Ekin = 6.590eV (T=548.168K) Etot = 55.750eV
Energy per atom: Epot =48.997eV Ekin = 6.757eV (T=562.122K) Etot = 55.754eV
Energy per atom: Epot =48.719eV Ekin = 7.029eV (T=584.694K) Etot = 55.748eV
Energy per atom: Epot =49.705eV Ekin = 6.049eV (T=503.183K) Etot = 55.754eV
Energy per atom: Epot =49.158eV Ekin = 6.597eV (T=548.784K) Etot = 55.755eV
Energy per atom: Epot =49.445eV Ekin = 6.311eV (T=525.005K) Etot = 55.757eV
Energy per atom: Epot =48.947eV Ekin = 6.805eV (T=566.085K) Etot = 55.752eV
Energy per atom: Epot =49.418eV Ekin = 6.333eV (T=526.801K) Etot = 55.751eV
Energy per atom: Epot =49.041eV Ekin = 6.712eV (T=558.336K) Etot = 55.753eV
Energy per atom: Epot =49.163eV Ekin = 6.592eV (T=548.336K) Etot = 55.754eV
Energy per atom: Epot =49.833eV Ekin = 5.922eV (T=492.608K) Etot = 55.755eV
Energy per atom: Epot =50.029eV Ekin = 5.728eV (T=476.482K) Etot = 55.757eV
Energy per atom: Epot =49.920eV Ekin = 5.834eV (T=485.316K) Etot = 55.754eV
Energy per atom: Epot =48.991eV Ekin = 6.760eV (T=562.372K) Etot = 55.751eV
Energy per atom: Epot =48.761eV Ekin = 6.991eV (T=581.521K) Etot = 55.751eV
Energy per atom: Epot =48.679eV Ekin = 7.075eV (T=588.574K) Etot = 55.755eV
Energy per atom: Epot =48.587eV Ekin = 7.167eV (T=596.191K) Etot = 55.754eV
Energy per atom: Epot =49.334eV Ekin = 6.420eV (T=534.024K) Etot = 55.754eV
Energy per atom: Epot =49.633eV Ekin = 6.119eV (T=509.032K) Etot = 55.752eV
Energy per atom: Epot =49.592eV Ekin = 6.158eV (T=512.258K) Etot = 55.750eV
Energy per atom: Epot =49.532eV Ekin = 6.223eV (T=517.698K) Etot = 55.756eV
Energy per atom: Epot =49.339eV Ekin = 6.417eV (T=533.843K) Etot = 55.757eV
Energy per atom: Epot =48.763eV Ekin = 6.985eV (T=581.039K) Etot = 55.747eV
Energy per atom: Epot =49.412eV Ekin = 6.337eV (T=527.112K) Etot = 55.748eV
Energy per atom: Epot =49.170eV Ekin = 6.583eV (T=547.604K) Etot = 55.753eV
Energy per atom: Epot =49.203eV Ekin = 6.555eV (T=545.283K) Etot = 55.758eV
Energy per atom: Epot =49.774eV Ekin = 5.984eV (T=497.812K) Etot = 55.758eV
Energy per atom: Epot =49.089eV Ekin = 6.660eV (T=554.021K) Etot = 55.749eV
Energy per atom: Epot =49.085eV Ekin = 6.665eV (T=554.459K) Etot = 55.750eV
Energy per atom: Epot =48.550eV Ekin = 7.202eV (T=599.077K) Etot = 55.751eV
Energy per atom: Epot =48.986eV Ekin = 6.773eV (T=563.423K) Etot = 55.759eV
Energy per atom: Epot =49.661eV Ekin = 6.097eV (T=507.206K) Etot = 55.758eV
Energy per atom: Epot =49.258eV Ekin = 6.492eV (T=540.020K) Etot = 55.749eV
Energy per atom: Epot =49.419eV Ekin = 6.335eV (T=527.024K) Etot = 55.755eV
Energy per atom: Epot =49.432eV Ekin = 6.327eV (T=526.338K) Etot = 55.760eV
Energy per atom: Epot =48.888eV Ekin = 6.863eV (T=570.941K) Etot = 55.752eV
Energy per atom: Epot =49.354eV Ekin = 6.396eV (T=532.059K) Etot = 55.750eV
Energy per atom: Epot =49.784eV Ekin = 5.972eV (T=496.799K) Etot = 55.756eV
Energy per atom: Epot =49.694eV Ekin = 6.060eV (T=504.106K) Etot = 55.754eV
Energy per atom: Epot =49.932eV Ekin = 5.823eV (T=484.405K) Etot = 55.755eV
Energy per atom: Epot =49.351eV Ekin = 6.403eV (T=532.654K) Etot = 55.754eV
Energy per atom: Epot =48.431eV Ekin = 7.319eV (T=608.826K) Etot = 55.750eV
Energy per atom: Epot =49.641eV Ekin = 6.117eV (T=508.820K) Etot = 55.758eV
Energy per atom: Epot =48.604eV Ekin = 7.147eV (T=594.522K) Etot = 55.751eV
Energy per atom: Epot =49.174eV Ekin = 6.580eV (T=547.336K) Etot = 55.753eV
Energy per atom: Epot =49.248eV Ekin = 6.504eV (T=541.035K) Etot = 55.752eV
Energy per atom: Epot =49.303eV Ekin = 6.451eV (T=536.612K) Etot = 55.753eV
Energy per atom: Epot =49.128eV Ekin = 6.626eV (T=551.204K) Etot = 55.755eV
Energy per atom: Epot =49.606eV Ekin = 6.150eV (T=511.608K) Etot = 55.757eV
Energy per atom: Epot =49.574eV Ekin = 6.181eV (T=514.145K) Etot = 55.755eV
Energy per atom: Epot =48.761eV Ekin = 6.988eV (T=581.337K) Etot = 55.749eV
Energy per atom: Epot =49.536eV Ekin = 6.216eV (T=517.061K) Etot = 55.752eV
Energy per atom: Epot =50.268eV Ekin = 5.489eV (T=456.648K) Etot = 55.758eV
Energy per atom: Epot =49.604eV Ekin = 6.154eV (T=511.943K) Etot = 55.758eV
Energy per atom: Epot =49.381eV Ekin = 6.376eV (T=530.367K) Etot = 55.757eV
Energy per atom: Epot =49.777eV Ekin = 5.976eV (T=497.143K) Etot = 55.754eV
Energy per atom: Epot =49.290eV Ekin = 6.461eV (T=537.440K) Etot = 55.751eV
Energy per atom: Epot =48.967eV Ekin = 6.782eV (T=564.163K) Etot = 55.749eV
Energy per atom: Epot =49.586eV Ekin = 6.168eV (T=513.058K) Etot = 55.754eV
Energy per atom: Epot =49.515eV Ekin = 6.242eV (T=519.232K) Etot = 55.757eV
Energy per atom: Epot =49.518eV Ekin = 6.239eV (T=518.990K) Etot = 55.756eV
Energy per atom: Epot =49.169eV Ekin = 6.581eV (T=547.435K) Etot = 55.749eV
Energy per atom: Epot =49.239eV Ekin = 6.514eV (T=541.900K) Etot = 55.754eV
Energy per atom: Epot =49.182eV Ekin = 6.573eV (T=546.822K) Etot = 55.756eV
Energy per atom: Epot =48.941eV Ekin = 6.811eV (T=566.621K) Etot = 55.752eV
Energy per atom: Epot =49.983eV Ekin = 5.773eV (T=480.228K) Etot = 55.756eV
Energy per atom: Epot =49.287eV Ekin = 6.469eV (T=538.134K) Etot = 55.756eV
Energy per atom: Epot =49.261eV Ekin = 6.494eV (T=540.235K) Etot = 55.755eV
Energy per atom: Epot =48.852eV Ekin = 6.898eV (T=573.791K) Etot = 55.750eV
Energy per atom: Epot =49.031eV Ekin = 6.719eV (T=558.939K) Etot = 55.750eV
Energy per atom: Epot =48.844eV Ekin = 6.911eV (T=574.891K) Etot = 55.755eV
Energy per atom: Epot =49.789eV Ekin = 5.967eV (T=496.389K) Etot = 55.756eV
Energy per atom: Epot =49.631eV Ekin = 6.123eV (T=509.319K) Etot = 55.754eV
Energy per atom: Epot =49.185eV Ekin = 6.571eV (T=546.643K) Etot = 55.756eV
Energy per atom: Epot =49.091eV Ekin = 6.666eV (T=554.497K) Etot = 55.756eV
Energy per atom: Epot =49.341eV Ekin = 6.415eV (T=533.604K) Etot = 55.756eV
Energy per atom: Epot =48.603eV Ekin = 7.146eV (T=594.440K) Etot = 55.748eV
Energy per atom: Epot =48.612eV Ekin = 7.136eV (T=593.591K) Etot = 55.748eV
Energy per atom: Epot =49.900eV Ekin = 5.853eV (T=486.898K) Etot = 55.753eV
Energy per atom: Epot =49.624eV Ekin = 6.132eV (T=510.117K) Etot = 55.757eV
Energy per atom: Epot =49.699eV Ekin = 6.057eV (T=503.823K) Etot = 55.755eV
Energy per atom: Epot =50.128eV Ekin = 5.626eV (T=467.979K) Etot = 55.754eV
Energy per atom: Epot =49.245eV Ekin = 6.508eV (T=541.338K) Etot = 55.752eV
Energy per atom: Epot =49.655eV Ekin = 6.102eV (T=507.581K) Etot = 55.757eV
Energy per atom: Epot =48.969eV Ekin = 6.779eV (T=563.893K) Etot = 55.748eV
Energy per atom: Epot =48.456eV Ekin = 7.290eV (T=606.400K) Etot = 55.745eV
Energy per atom: Epot =49.113eV Ekin = 6.638eV (T=552.220K) Etot = 55.752eV
Energy per atom: Epot =49.233eV Ekin = 6.521eV (T=542.486K) Etot = 55.754eV
Energy per atom: Epot =49.918eV Ekin = 5.842eV (T=485.964K) Etot = 55.760eV
Energy per atom: Epot =49.234eV Ekin = 6.522eV (T=542.559K) Etot = 55.757eV
Energy per atom: Epot =48.603eV Ekin = 7.146eV (T=594.476K) Etot = 55.749eV
Energy per atom: Epot =49.234eV Ekin = 6.519eV (T=542.308K) Etot = 55.753eV
Energy per atom: Epot =49.142eV Ekin = 6.611eV (T=549.909K) Etot = 55.753eV
Energy per atom: Epot =49.642eV Ekin = 6.112eV (T=508.438K) Etot = 55.754eV
Energy per atom: Epot =49.412eV Ekin = 6.341eV (T=527.449K) Etot = 55.752eV
Energy per atom: Epot =49.474eV Ekin = 6.278eV (T=522.210K) Etot = 55.752eV
Energy per atom: Epot =49.474eV Ekin = 6.280eV (T=522.433K) Etot = 55.754eV
Energy per atom: Epot =49.548eV Ekin = 6.211eV (T=516.632K) Etot = 55.759eV
Energy per atom: Epot =48.972eV Ekin = 6.783eV (T=564.269K) Etot = 55.756eV
Energy per atom: Epot =49.030eV Ekin = 6.724eV (T=559.328K) Etot = 55.753eV
Energy per atom: Epot =49.325eV Ekin = 6.430eV (T=534.856K) Etot = 55.755eV
Energy per atom: Epot =48.527eV Ekin = 7.224eV (T=600.913K) Etot = 55.750eV
Energy per atom: Epot =49.028eV Ekin = 6.724eV (T=559.345K) Etot = 55.752eV
Energy per atom: Epot =49.753eV Ekin = 6.004eV (T=499.489K) Etot = 55.757eV
Energy per atom: Epot =48.772eV Ekin = 6.979eV (T=580.585K) Etot = 55.751eV
Energy per atom: Epot =49.652eV Ekin = 6.106eV (T=507.934K) Etot = 55.758eV
Energy per atom: Epot =48.928eV Ekin = 6.824eV (T=567.686K) Etot = 55.752eV
Energy per atom: Epot =48.953eV Ekin = 6.797eV (T=565.378K) Etot = 55.750eV
Energy per atom: Epot =48.902eV Ekin = 6.847eV (T=569.617K) Etot = 55.750eV
Energy per atom: Epot =49.273eV Ekin = 6.478eV (T=538.873K) Etot = 55.750eV
Energy per atom: Epot =49.222eV Ekin = 6.527eV (T=542.949K) Etot = 55.749eV
Energy per atom: Epot =48.870eV Ekin = 6.882eV (T=572.520K) Etot = 55.752eV
Energy per atom: Epot =49.228eV Ekin = 6.526eV (T=542.855K) Etot = 55.754eV
Energy per atom: Epot =48.681eV Ekin = 7.063eV (T=587.571K) Etot = 55.745eV
Energy per atom: Epot =49.311eV Ekin = 6.440eV (T=535.689K) Etot = 55.751eV
Energy per atom: Epot =49.101eV Ekin = 6.653eV (T=553.433K) Etot = 55.754eV
Energy per atom: Epot =49.451eV Ekin = 6.304eV (T=524.401K) Etot = 55.754eV
Energy per atom: Epot =49.135eV Ekin = 6.617eV (T=550.409K) Etot = 55.752eV
Energy per atom: Epot =48.948eV Ekin = 6.804eV (T=565.994K) Etot = 55.752eV
Energy per atom: Epot =49.219eV Ekin = 6.534eV (T=543.558K) Etot = 55.753eV
Energy per atom: Epot =49.518eV Ekin = 6.237eV (T=518.798K) Etot = 55.754eV
Energy per atom: Epot =48.773eV Ekin = 6.979eV (T=580.558K) Etot = 55.752eV
Energy per atom: Epot =49.317eV Ekin = 6.441eV (T=535.807K) Etot = 55.758eV
Energy per atom: Epot =49.361eV Ekin = 6.395eV (T=532.008K) Etot = 55.757eV
Energy per atom: Epot =49.028eV Ekin = 6.724eV (T=559.375K) Etot = 55.752eV
Energy per atom: Epot =49.639eV Ekin = 6.115eV (T=508.661K) Etot = 55.753eV
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?