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 =-22.726eV Ekin = 154.735eV (T=299.270K) Etot = 132.009eV
Energy per atom: Epot =97.116eV Ekin = 35.682eV (T=69.013K) Etot = 132.799eV
Energy per atom: Epot =58.092eV Ekin = 74.565eV (T=144.215K) Etot = 132.657eV
Energy per atom: Epot =49.717eV Ekin = 82.796eV (T=160.134K) Etot = 132.512eV
Energy per atom: Epot =49.224eV Ekin = 83.234eV (T=160.982K) Etot = 132.458eV
Energy per atom: Epot =59.520eV Ekin = 73.092eV (T=141.366K) Etot = 132.612eV
Energy per atom: Epot =58.423eV Ekin = 74.190eV (T=143.490K) Etot = 132.613eV
Energy per atom: Epot =52.388eV Ekin = 80.125eV (T=154.969K) Etot = 132.513eV
Energy per atom: Epot =51.639eV Ekin = 80.882eV (T=156.433K) Etot = 132.521eV
Energy per atom: Epot =59.018eV Ekin = 73.584eV (T=142.318K) Etot = 132.602eV
Energy per atom: Epot =54.708eV Ekin = 77.851eV (T=150.570K) Etot = 132.559eV
Energy per atom: Epot =53.818eV Ekin = 78.720eV (T=152.251K) Etot = 132.538eV
Energy per atom: Epot =55.395eV Ekin = 77.167eV (T=149.248K) Etot = 132.563eV
Energy per atom: Epot =56.226eV Ekin = 76.340eV (T=147.648K) Etot = 132.565eV
Energy per atom: Epot =53.901eV Ekin = 78.647eV (T=152.109K) Etot = 132.548eV
Energy per atom: Epot =54.480eV Ekin = 78.084eV (T=151.021K) Etot = 132.564eV
Energy per atom: Epot =54.155eV Ekin = 78.398eV (T=151.629K) Etot = 132.553eV
Energy per atom: Epot =58.343eV Ekin = 74.225eV (T=143.558K) Etot = 132.568eV
Energy per atom: Epot =53.124eV Ekin = 79.425eV (T=153.615K) Etot = 132.549eV
Energy per atom: Epot =53.178eV Ekin = 79.362eV (T=153.494K) Etot = 132.541eV
Energy per atom: Epot =59.192eV Ekin = 73.385eV (T=141.933K) Etot = 132.577eV
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()
/build/python-ase-iXAd1o/python-ase-3.28.0/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 =524.308eV Ekin = 0.000eV (T=0.000K) Etot = 524.308eV
Energy per atom: Epot =583.831eV Ekin = 83.126eV (T=160.773K) Etot = 666.957eV
Energy per atom: Epot =655.913eV Ekin = 139.146eV (T=269.121K) Etot = 795.060eV
Energy per atom: Epot =709.843eV Ekin = 203.074eV (T=392.762K) Etot = 912.917eV
Energy per atom: Epot =765.844eV Ekin = 251.635eV (T=486.683K) Etot = 1017.479eV
Energy per atom: Epot =815.815eV Ekin = 304.454eV (T=588.840K) Etot = 1120.269eV
Energy per atom: Epot =868.858eV Ekin = 344.221eV (T=665.754K) Etot = 1213.079eV
Energy per atom: Epot =911.849eV Ekin = 383.358eV (T=741.448K) Etot = 1295.207eV
Energy per atom: Epot =948.326eV Ekin = 419.637eV (T=811.615K) Etot = 1367.964eV
Energy per atom: Epot =994.381eV Ekin = 447.941eV (T=866.357K) Etot = 1442.322eV
Energy per atom: Epot =1038.986eV Ekin = 462.646eV (T=894.797K) Etot = 1501.632eV
Energy per atom: Epot =1059.946eV Ekin = 496.696eV (T=960.653K) Etot = 1556.642eV
Energy per atom: Epot =1085.524eV Ekin = 522.719eV (T=1010.984K) Etot = 1608.243eV
Energy per atom: Epot =1131.302eV Ekin = 526.530eV (T=1018.354K) Etot = 1657.832eV
Energy per atom: Epot =1160.231eV Ekin = 543.356eV (T=1050.898K) Etot = 1703.588eV
Energy per atom: Epot =1195.355eV Ekin = 549.810eV (T=1063.380K) Etot = 1745.165eV
Energy per atom: Epot =1209.893eV Ekin = 585.485eV (T=1132.378K) Etot = 1795.377eV
Energy per atom: Epot =1244.645eV Ekin = 590.263eV (T=1141.620K) Etot = 1834.908eV
Energy per atom: Epot =1266.446eV Ekin = 599.480eV (T=1159.446K) Etot = 1865.926eV
Energy per atom: Epot =1305.678eV Ekin = 586.006eV (T=1133.386K) Etot = 1891.684eV
Energy per atom: Epot =1300.437eV Ekin = 619.944eV (T=1199.026K) Etot = 1920.381eV
Energy per atom: Epot =1323.756eV Ekin = 627.396eV (T=1213.439K) Etot = 1951.152eV
Energy per atom: Epot =1368.640eV Ekin = 618.995eV (T=1197.189K) Etot = 1987.634eV
Energy per atom: Epot =1372.696eV Ekin = 639.238eV (T=1236.341K) Etot = 2011.933eV
Energy per atom: Epot =1389.899eV Ekin = 653.819eV (T=1264.544K) Etot = 2043.718eV
Energy per atom: Epot =1411.765eV Ekin = 654.450eV (T=1265.763K) Etot = 2066.215eV
Energy per atom: Epot =1419.535eV Ekin = 664.751eV (T=1285.686K) Etot = 2084.286eV
Energy per atom: Epot =1431.228eV Ekin = 669.973eV (T=1295.786K) Etot = 2101.201eV
Energy per atom: Epot =1446.585eV Ekin = 676.204eV (T=1307.837K) Etot = 2122.789eV
Energy per atom: Epot =1468.491eV Ekin = 664.280eV (T=1284.775K) Etot = 2132.771eV
Energy per atom: Epot =1475.573eV Ekin = 676.883eV (T=1309.151K) Etot = 2152.456eV
Energy per atom: Epot =1493.922eV Ekin = 679.556eV (T=1314.321K) Etot = 2173.478eV
Energy per atom: Epot =1502.443eV Ekin = 676.967eV (T=1309.314K) Etot = 2179.411eV
Energy per atom: Epot =1522.361eV Ekin = 680.687eV (T=1316.508K) Etot = 2203.048eV
Energy per atom: Epot =1517.798eV Ekin = 701.809eV (T=1357.359K) Etot = 2219.607eV
Energy per atom: Epot =1537.932eV Ekin = 697.804eV (T=1349.613K) Etot = 2235.736eV
Energy per atom: Epot =1550.851eV Ekin = 700.000eV (T=1353.861K) Etot = 2250.851eV
Energy per atom: Epot =1558.387eV Ekin = 703.932eV (T=1361.465K) Etot = 2262.318eV
Energy per atom: Epot =1565.601eV Ekin = 702.904eV (T=1359.477K) Etot = 2268.504eV
Energy per atom: Epot =1576.251eV Ekin = 696.574eV (T=1347.235K) Etot = 2272.825eV
Energy per atom: Epot =1583.663eV Ekin = 703.167eV (T=1359.986K) Etot = 2286.830eV
Energy per atom: Epot =1597.352eV Ekin = 705.419eV (T=1364.341K) Etot = 2302.771eV
Energy per atom: Epot =1618.554eV Ekin = 704.160eV (T=1361.907K) Etot = 2322.714eV
Energy per atom: Epot =1621.288eV Ekin = 715.254eV (T=1383.364K) Etot = 2336.543eV
Energy per atom: Epot =1633.529eV Ekin = 717.968eV (T=1388.613K) Etot = 2351.497eV
Energy per atom: Epot =1642.149eV Ekin = 720.743eV (T=1393.979K) Etot = 2362.892eV
Energy per atom: Epot =1634.937eV Ekin = 740.914eV (T=1432.992K) Etot = 2375.851eV
Energy per atom: Epot =1640.830eV Ekin = 728.875eV (T=1409.707K) Etot = 2369.705eV
Energy per atom: Epot =1646.536eV Ekin = 736.102eV (T=1423.686K) Etot = 2382.638eV
Energy per atom: Epot =1656.319eV Ekin = 738.978eV (T=1429.247K) Etot = 2395.296eV
Energy per atom: Epot =1671.672eV Ekin = 731.872eV (T=1415.504K) Etot = 2403.544eV
Energy per atom: Epot =1676.989eV Ekin = 746.044eV (T=1442.914K) Etot = 2423.033eV
Energy per atom: Epot =1680.764eV Ekin = 746.430eV (T=1443.661K) Etot = 2427.194eV
Energy per atom: Epot =1690.062eV Ekin = 738.169eV (T=1427.684K) Etot = 2428.232eV
Energy per atom: Epot =1691.026eV Ekin = 753.179eV (T=1456.713K) Etot = 2444.204eV
Energy per atom: Epot =1710.270eV Ekin = 735.005eV (T=1421.563K) Etot = 2445.275eV
Energy per atom: Epot =1708.370eV Ekin = 747.184eV (T=1445.120K) Etot = 2455.554eV
Energy per atom: Epot =1721.619eV Ekin = 731.115eV (T=1414.040K) Etot = 2452.734eV
Energy per atom: Epot =1731.635eV Ekin = 726.739eV (T=1405.577K) Etot = 2458.374eV
Energy per atom: Epot =1742.322eV Ekin = 725.316eV (T=1402.824K) Etot = 2467.638eV
Energy per atom: Epot =1743.457eV Ekin = 745.614eV (T=1442.081K) Etot = 2489.071eV
Energy per atom: Epot =1752.894eV Ekin = 746.069eV (T=1442.963K) Etot = 2498.963eV
Energy per atom: Epot =1776.179eV Ekin = 728.269eV (T=1408.535K) Etot = 2504.448eV
Energy per atom: Epot =1777.562eV Ekin = 740.310eV (T=1431.823K) Etot = 2517.871eV
Energy per atom: Epot =1795.843eV Ekin = 732.955eV (T=1417.599K) Etot = 2528.798eV
Energy per atom: Epot =1797.125eV Ekin = 745.230eV (T=1441.339K) Etot = 2542.355eV
Energy per atom: Epot =1806.583eV Ekin = 744.067eV (T=1439.090K) Etot = 2550.650eV
Energy per atom: Epot =1813.774eV Ekin = 740.621eV (T=1432.426K) Etot = 2554.395eV
Energy per atom: Epot =1822.430eV Ekin = 738.993eV (T=1429.277K) Etot = 2561.423eV
Energy per atom: Epot =1830.856eV Ekin = 734.329eV (T=1420.256K) Etot = 2565.185eV
Energy per atom: Epot =1815.263eV Ekin = 755.709eV (T=1461.606K) Etot = 2570.972eV
Energy per atom: Epot =1826.088eV Ekin = 748.511eV (T=1447.686K) Etot = 2574.599eV
Energy per atom: Epot =1834.275eV Ekin = 751.724eV (T=1453.900K) Etot = 2585.999eV
Energy per atom: Epot =1832.771eV Ekin = 768.375eV (T=1486.104K) Etot = 2601.147eV
Energy per atom: Epot =1852.780eV Ekin = 756.516eV (T=1463.167K) Etot = 2609.295eV
Energy per atom: Epot =1851.403eV Ekin = 745.881eV (T=1442.599K) Etot = 2597.284eV
Energy per atom: Epot =1843.426eV Ekin = 753.699eV (T=1457.719K) Etot = 2597.125eV
Energy per atom: Epot =1848.740eV Ekin = 749.779eV (T=1450.138K) Etot = 2598.519eV
Energy per atom: Epot =1847.237eV Ekin = 761.405eV (T=1472.623K) Etot = 2608.642eV
Energy per atom: Epot =1855.542eV Ekin = 754.391eV (T=1459.058K) Etot = 2609.934eV
Energy per atom: Epot =1866.641eV Ekin = 744.718eV (T=1440.350K) Etot = 2611.359eV
Energy per atom: Epot =1863.151eV Ekin = 746.420eV (T=1443.641K) Etot = 2609.570eV
Energy per atom: Epot =1859.110eV Ekin = 757.494eV (T=1465.060K) Etot = 2616.604eV
Energy per atom: Epot =1866.110eV Ekin = 740.873eV (T=1432.914K) Etot = 2606.983eV
Energy per atom: Epot =1855.404eV Ekin = 749.264eV (T=1449.142K) Etot = 2604.668eV
Energy per atom: Epot =1879.670eV Ekin = 737.672eV (T=1426.722K) Etot = 2617.342eV
Energy per atom: Epot =1864.292eV Ekin = 749.510eV (T=1449.617K) Etot = 2613.802eV
Energy per atom: Epot =1868.562eV Ekin = 745.260eV (T=1441.398K) Etot = 2613.822eV
Energy per atom: Epot =1872.910eV Ekin = 737.522eV (T=1426.432K) Etot = 2610.433eV
Energy per atom: Epot =1876.806eV Ekin = 744.791eV (T=1440.491K) Etot = 2621.597eV
Energy per atom: Epot =1880.542eV Ekin = 748.020eV (T=1446.736K) Etot = 2628.562eV
Energy per atom: Epot =1882.903eV Ekin = 743.511eV (T=1438.014K) Etot = 2626.413eV
Energy per atom: Epot =1886.989eV Ekin = 752.870eV (T=1456.116K) Etot = 2639.859eV
Energy per atom: Epot =1899.033eV Ekin = 733.070eV (T=1417.821K) Etot = 2632.102eV
Energy per atom: Epot =1895.819eV Ekin = 747.467eV (T=1445.666K) Etot = 2643.285eV
Energy per atom: Epot =1901.266eV Ekin = 739.184eV (T=1429.646K) Etot = 2640.450eV
Energy per atom: Epot =1891.517eV Ekin = 740.516eV (T=1432.222K) Etot = 2632.033eV
Energy per atom: Epot =1891.438eV Ekin = 754.113eV (T=1458.519K) Etot = 2645.550eV
Energy per atom: Epot =1909.637eV Ekin = 738.467eV (T=1428.260K) Etot = 2648.104eV
Energy per atom: Epot =1902.465eV Ekin = 754.758eV (T=1459.767K) Etot = 2657.222eV
Energy per atom: Epot =1903.818eV Ekin = 762.659eV (T=1475.049K) Etot = 2666.477eV
Energy per atom: Epot =1924.411eV Ekin = 743.738eV (T=1438.453K) Etot = 2668.149eV
Energy per atom: Epot =1908.331eV Ekin = 751.115eV (T=1452.721K) Etot = 2659.445eV
Energy per atom: Epot =1911.931eV Ekin = 751.685eV (T=1453.824K) Etot = 2663.616eV
Energy per atom: Epot =1917.107eV Ekin = 752.634eV (T=1455.659K) Etot = 2669.740eV
Energy per atom: Epot =1923.693eV Ekin = 754.316eV (T=1458.912K) Etot = 2678.009eV
Energy per atom: Epot =1928.459eV Ekin = 760.770eV (T=1471.396K) Etot = 2689.229eV
Energy per atom: Epot =1935.562eV Ekin = 758.765eV (T=1467.518K) Etot = 2694.327eV
Energy per atom: Epot =1927.115eV Ekin = 767.791eV (T=1484.975K) Etot = 2694.906eV
Energy per atom: Epot =1924.319eV Ekin = 770.806eV (T=1490.806K) Etot = 2695.125eV
Energy per atom: Epot =1942.100eV Ekin = 749.193eV (T=1449.004K) Etot = 2691.292eV
Energy per atom: Epot =1950.168eV Ekin = 748.199eV (T=1447.082K) Etot = 2698.367eV
Energy per atom: Epot =1936.817eV Ekin = 779.411eV (T=1507.448K) Etot = 2716.228eV
Energy per atom: Epot =1946.643eV Ekin = 769.352eV (T=1487.993K) Etot = 2715.995eV
Energy per atom: Epot =1944.567eV Ekin = 778.263eV (T=1505.229K) Etot = 2722.831eV
Energy per atom: Epot =1952.321eV Ekin = 772.742eV (T=1494.550K) Etot = 2725.063eV
Energy per atom: Epot =1946.029eV Ekin = 773.217eV (T=1495.469K) Etot = 2719.246eV
Energy per atom: Epot =1952.292eV Ekin = 771.946eV (T=1493.011K) Etot = 2724.238eV
Energy per atom: Epot =1948.736eV Ekin = 775.795eV (T=1500.456K) Etot = 2724.531eV
Energy per atom: Epot =1948.492eV Ekin = 767.421eV (T=1484.260K) Etot = 2715.913eV
Energy per atom: Epot =1952.355eV Ekin = 767.711eV (T=1484.820K) Etot = 2720.066eV
Energy per atom: Epot =1949.245eV Ekin = 774.964eV (T=1498.847K) Etot = 2724.209eV
Energy per atom: Epot =1956.562eV Ekin = 767.216eV (T=1483.863K) Etot = 2723.778eV
Energy per atom: Epot =1947.675eV Ekin = 774.126eV (T=1497.226K) Etot = 2721.800eV
Energy per atom: Epot =1951.398eV Ekin = 761.147eV (T=1472.124K) Etot = 2712.545eV
Energy per atom: Epot =1953.175eV Ekin = 758.745eV (T=1467.479K) Etot = 2711.920eV
Energy per atom: Epot =1941.606eV Ekin = 778.034eV (T=1504.786K) Etot = 2719.640eV
Energy per atom: Epot =1953.607eV Ekin = 760.927eV (T=1471.700K) Etot = 2714.535eV
Energy per atom: Epot =1959.499eV Ekin = 754.473eV (T=1459.216K) Etot = 2713.972eV
Energy per atom: Epot =1960.586eV Ekin = 750.187eV (T=1450.927K) Etot = 2710.773eV
Energy per atom: Epot =1942.229eV Ekin = 786.026eV (T=1520.242K) Etot = 2728.255eV
Energy per atom: Epot =1970.746eV Ekin = 756.311eV (T=1462.772K) Etot = 2727.057eV
Energy per atom: Epot =1950.458eV Ekin = 778.469eV (T=1505.627K) Etot = 2728.927eV
Energy per atom: Epot =1968.119eV Ekin = 757.873eV (T=1465.793K) Etot = 2725.993eV
Energy per atom: Epot =1957.832eV Ekin = 768.485eV (T=1486.317K) Etot = 2726.317eV
Energy per atom: Epot =1968.391eV Ekin = 765.097eV (T=1479.763K) Etot = 2733.488eV
Energy per atom: Epot =1968.308eV Ekin = 776.148eV (T=1501.137K) Etot = 2744.456eV
Energy per atom: Epot =1957.569eV Ekin = 773.739eV (T=1496.478K) Etot = 2731.308eV
Energy per atom: Epot =1949.430eV Ekin = 773.284eV (T=1495.599K) Etot = 2722.714eV
Energy per atom: Epot =1942.908eV Ekin = 774.907eV (T=1498.738K) Etot = 2717.815eV
Energy per atom: Epot =1960.045eV Ekin = 763.887eV (T=1477.424K) Etot = 2723.932eV
Energy per atom: Epot =1963.270eV Ekin = 762.636eV (T=1475.005K) Etot = 2725.907eV
Energy per atom: Epot =1957.068eV Ekin = 768.673eV (T=1486.681K) Etot = 2725.741eV
Energy per atom: Epot =1962.697eV Ekin = 760.692eV (T=1471.245K) Etot = 2723.390eV
Energy per atom: Epot =1965.579eV Ekin = 770.905eV (T=1490.997K) Etot = 2736.484eV
Energy per atom: Epot =1957.724eV Ekin = 778.707eV (T=1506.088K) Etot = 2736.431eV
Energy per atom: Epot =1963.811eV Ekin = 778.493eV (T=1505.674K) Etot = 2742.304eV
Energy per atom: Epot =1966.816eV Ekin = 774.432eV (T=1497.819K) Etot = 2741.248eV
Energy per atom: Epot =1967.656eV Ekin = 773.335eV (T=1495.698K) Etot = 2740.991eV
Energy per atom: Epot =1971.635eV Ekin = 771.368eV (T=1491.893K) Etot = 2743.004eV
Energy per atom: Epot =1963.662eV Ekin = 767.538eV (T=1484.485K) Etot = 2731.200eV
Energy per atom: Epot =1956.001eV Ekin = 781.821eV (T=1512.109K) Etot = 2737.822eV
Energy per atom: Epot =1969.901eV Ekin = 773.544eV (T=1496.101K) Etot = 2743.445eV
Energy per atom: Epot =1986.557eV Ekin = 766.756eV (T=1482.973K) Etot = 2753.313eV
Energy per atom: Epot =1985.282eV Ekin = 779.628eV (T=1507.868K) Etot = 2764.910eV
Energy per atom: Epot =1990.194eV Ekin = 763.462eV (T=1476.601K) Etot = 2753.656eV
Energy per atom: Epot =1985.309eV Ekin = 768.807eV (T=1486.940K) Etot = 2754.117eV
Energy per atom: Epot =1974.901eV Ekin = 768.599eV (T=1486.537K) Etot = 2743.500eV
Energy per atom: Epot =1973.865eV Ekin = 767.412eV (T=1484.241K) Etot = 2741.276eV
Energy per atom: Epot =1977.862eV Ekin = 755.229eV (T=1460.678K) Etot = 2733.091eV
Energy per atom: Epot =1964.412eV Ekin = 775.678eV (T=1500.229K) Etot = 2740.090eV
Energy per atom: Epot =1971.545eV Ekin = 767.063eV (T=1483.566K) Etot = 2738.608eV
Energy per atom: Epot =1968.264eV Ekin = 773.580eV (T=1496.170K) Etot = 2741.844eV
Energy per atom: Epot =1978.637eV Ekin = 766.040eV (T=1481.588K) Etot = 2744.677eV
Energy per atom: Epot =1955.480eV Ekin = 781.258eV (T=1511.020K) Etot = 2736.737eV
Energy per atom: Epot =1977.343eV Ekin = 761.934eV (T=1473.646K) Etot = 2739.277eV
Energy per atom: Epot =1965.834eV Ekin = 764.212eV (T=1478.053K) Etot = 2730.046eV
Energy per atom: Epot =1967.297eV Ekin = 763.984eV (T=1477.611K) Etot = 2731.281eV
Energy per atom: Epot =1968.592eV Ekin = 766.970eV (T=1483.387K) Etot = 2735.562eV
Energy per atom: Epot =1955.033eV Ekin = 783.829eV (T=1515.994K) Etot = 2738.862eV
Energy per atom: Epot =1960.288eV Ekin = 773.493eV (T=1496.002K) Etot = 2733.781eV
Energy per atom: Epot =1958.800eV Ekin = 763.996eV (T=1477.634K) Etot = 2722.795eV
Energy per atom: Epot =1932.372eV Ekin = 789.159eV (T=1526.302K) Etot = 2721.531eV
Energy per atom: Epot =1948.731eV Ekin = 775.585eV (T=1500.049K) Etot = 2724.316eV
Energy per atom: Epot =1949.784eV Ekin = 773.829eV (T=1496.653K) Etot = 2723.613eV
Energy per atom: Epot =1949.861eV Ekin = 758.258eV (T=1466.537K) Etot = 2708.119eV
Energy per atom: Epot =1944.261eV Ekin = 762.751eV (T=1475.226K) Etot = 2707.011eV
Energy per atom: Epot =1950.473eV Ekin = 759.564eV (T=1469.064K) Etot = 2710.038eV
Energy per atom: Epot =1951.962eV Ekin = 761.121eV (T=1472.073K) Etot = 2713.083eV
Energy per atom: Epot =1932.696eV Ekin = 776.351eV (T=1501.531K) Etot = 2709.048eV
Energy per atom: Epot =1944.883eV Ekin = 765.847eV (T=1481.215K) Etot = 2710.730eV
Energy per atom: Epot =1930.606eV Ekin = 780.190eV (T=1508.956K) Etot = 2710.796eV
Energy per atom: Epot =1944.083eV Ekin = 763.224eV (T=1476.142K) Etot = 2707.307eV
Energy per atom: Epot =1942.095eV Ekin = 769.954eV (T=1489.158K) Etot = 2712.049eV
Energy per atom: Epot =1937.518eV Ekin = 768.525eV (T=1486.394K) Etot = 2706.043eV
Energy per atom: Epot =1936.308eV Ekin = 760.487eV (T=1470.847K) Etot = 2696.794eV
Energy per atom: Epot =1929.387eV Ekin = 779.354eV (T=1507.339K) Etot = 2708.741eV
Energy per atom: Epot =1940.367eV Ekin = 773.771eV (T=1496.540K) Etot = 2714.138eV
Energy per atom: Epot =1946.645eV Ekin = 770.109eV (T=1489.458K) Etot = 2716.754eV
Energy per atom: Epot =1946.158eV Ekin = 762.698eV (T=1475.124K) Etot = 2708.856eV
Energy per atom: Epot =1954.406eV Ekin = 767.305eV (T=1484.034K) Etot = 2721.710eV
Energy per atom: Epot =1955.124eV Ekin = 768.420eV (T=1486.192K) Etot = 2723.545eV
Energy per atom: Epot =1953.078eV Ekin = 772.364eV (T=1493.820K) Etot = 2725.442eV
Energy per atom: Epot =1956.012eV Ekin = 767.607eV (T=1484.619K) Etot = 2723.619eV
Energy per atom: Epot =1953.705eV Ekin = 769.642eV (T=1488.554K) Etot = 2723.346eV
Energy per atom: Epot =1948.892eV Ekin = 764.216eV (T=1478.060K) Etot = 2713.108eV
Energy per atom: Epot =1943.752eV Ekin = 762.823eV (T=1475.367K) Etot = 2706.575eV
Energy per atom: Epot =1944.054eV Ekin = 770.364eV (T=1489.951K) Etot = 2714.417eV
Energy per atom: Epot =1949.179eV Ekin = 769.134eV (T=1487.571K) Etot = 2718.312eV
Energy per atom: Epot =1950.936eV Ekin = 761.103eV (T=1472.039K) Etot = 2712.039eV
Energy per atom: Epot =1949.228eV Ekin = 760.952eV (T=1471.747K) Etot = 2710.180eV
After running the simulation, you can study the result with the command
ase gui fccCu_NPT.traj
Try plotting the kinetic energy. Like in the temperature vs time plot you will not see a well-defined melting point due to finite size effects (including surface melting), but you will probably see an almost flat region where the inside of the system melts. The outermost layers melt at a lower temperature.
Note
The Langevin dynamics will by default keep the position and momentum of the center of mass unperturbed. This is another improvement over just setting momenta corresponding to a temperature, as we did before.
Part 3: Isolated particle MD#
When simulating isolated particles with MD, it is sometimes preferable to set random momenta corresponding to a specific temperature and let the system evolve freely. With a relatively high temperature, the is however a risk that the collection of atoms will drift out of the simulation box because the randomized momenta gave the center of mass a small but non-zero velocity too.
Let us see what happens when we propagate a nanoparticle:
size = 4
atoms = ClusterFCC(
'Cu',
surfaces=[[1, 0, 0], [1, 1, 0], [1, 1, 1]],
layers=(size, size, size),
vacuum=4,
)
# asap3 requires a non-zero cell even if pbc are not applied
atoms.cell = [40] * 3
atoms.set_pbc(False) # isolated cluster (explicit, for clarity)
# Describe the interatomic interactions with the Effective Medium Theory
atoms.calc = EMT()
# Quick relaxation of the cluster
qn = QuasiNewton(atoms)
qn.run(fmax=0.001, steps=10)
# Set the momenta corresponding to T=1200 K
MaxwellBoltzmannDistribution(atoms, temperature_K=1200)
Stationary(atoms) # zero linear momentum
ZeroRotation(atoms) # zero angular momentum
# Run MD using the Velocity Verlet algorithm and save trajectory
dyn = VelocityVerlet(atoms, 5 * units.fs, trajectory='nanoparticleCu_NVE.traj')
print('running a NVE simulation of a Cu nanoparticle')
printenergy(atoms)
steps_per_block = 10
for i in range(200):
dyn.run(steps_per_block)
printenergy(atoms)
Step[ FC] Time Energy fmax
BFGSLineSearch: 0[ 0] 09:41:06 43.245239 1.0870
BFGSLineSearch: 1[ 1] 09:41:06 42.120661 0.2296
BFGSLineSearch: 2[ 2] 09:41:06 41.867789 0.1409
BFGSLineSearch: 3[ 3] 09:41:06 41.713030 0.1175
BFGSLineSearch: 4[ 4] 09:41:06 41.671285 0.0689
BFGSLineSearch: 5[ 5] 09:41:07 41.661506 0.0228
BFGSLineSearch: 6[ 6] 09:41:07 41.661063 0.0064
BFGSLineSearch: 7[ 7] 09:41:07 41.661007 0.0025
BFGSLineSearch: 8[ 8] 09:41:07 41.660988 0.0021
BFGSLineSearch: 9[ 9] 09:41:07 41.660979 0.0011
BFGSLineSearch: 10[ 10] 09:41:07 41.660978 0.0004
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.661eV Ekin = 16.174eV (T=1345.477K) Etot = 57.835eV
Energy per atom: Epot =50.449eV Ekin = 7.433eV (T=618.367K) Etot = 57.882eV
Energy per atom: Epot =51.315eV Ekin = 6.585eV (T=547.817K) Etot = 57.900eV
Energy per atom: Epot =51.347eV Ekin = 6.544eV (T=544.378K) Etot = 57.891eV
Energy per atom: Epot =50.607eV Ekin = 7.280eV (T=605.633K) Etot = 57.887eV
Energy per atom: Epot =50.135eV Ekin = 7.752eV (T=644.830K) Etot = 57.886eV
Energy per atom: Epot =49.863eV Ekin = 8.023eV (T=667.427K) Etot = 57.887eV
Energy per atom: Epot =49.957eV Ekin = 7.930eV (T=659.640K) Etot = 57.886eV
Energy per atom: Epot =49.866eV Ekin = 8.024eV (T=667.475K) Etot = 57.890eV
Energy per atom: Epot =50.903eV Ekin = 6.988eV (T=581.310K) Etot = 57.891eV
Energy per atom: Epot =51.080eV Ekin = 6.810eV (T=566.497K) Etot = 57.890eV
Energy per atom: Epot =49.835eV Ekin = 8.051eV (T=669.744K) Etot = 57.886eV
Energy per atom: Epot =50.396eV Ekin = 7.494eV (T=623.380K) Etot = 57.890eV
Energy per atom: Epot =49.414eV Ekin = 8.472eV (T=704.717K) Etot = 57.885eV
Energy per atom: Epot =49.587eV Ekin = 8.297eV (T=690.235K) Etot = 57.884eV
Energy per atom: Epot =50.575eV Ekin = 7.319eV (T=608.804K) Etot = 57.893eV
Energy per atom: Epot =51.134eV Ekin = 6.759eV (T=562.234K) Etot = 57.893eV
Energy per atom: Epot =50.820eV Ekin = 7.068eV (T=587.997K) Etot = 57.888eV
Energy per atom: Epot =50.421eV Ekin = 7.470eV (T=621.419K) Etot = 57.892eV
Energy per atom: Epot =50.693eV Ekin = 7.194eV (T=598.485K) Etot = 57.887eV
Energy per atom: Epot =49.716eV Ekin = 8.169eV (T=679.543K) Etot = 57.885eV
Energy per atom: Epot =50.313eV Ekin = 7.579eV (T=630.461K) Etot = 57.892eV
Energy per atom: Epot =50.996eV Ekin = 6.902eV (T=574.148K) Etot = 57.898eV
Energy per atom: Epot =50.623eV Ekin = 7.266eV (T=604.410K) Etot = 57.889eV
Energy per atom: Epot =50.775eV Ekin = 7.111eV (T=591.526K) Etot = 57.886eV
Energy per atom: Epot =50.413eV Ekin = 7.474eV (T=621.732K) Etot = 57.887eV
Energy per atom: Epot =50.755eV Ekin = 7.131eV (T=593.232K) Etot = 57.886eV
Energy per atom: Epot =50.131eV Ekin = 7.754eV (T=644.987K) Etot = 57.885eV
Energy per atom: Epot =50.055eV Ekin = 7.831eV (T=651.422K) Etot = 57.886eV
Energy per atom: Epot =50.449eV Ekin = 7.443eV (T=619.187K) Etot = 57.892eV
Energy per atom: Epot =51.090eV Ekin = 6.804eV (T=565.980K) Etot = 57.894eV
Energy per atom: Epot =50.434eV Ekin = 7.456eV (T=620.210K) Etot = 57.890eV
Energy per atom: Epot =50.804eV Ekin = 7.090eV (T=589.768K) Etot = 57.894eV
Energy per atom: Epot =49.890eV Ekin = 7.997eV (T=665.246K) Etot = 57.887eV
Energy per atom: Epot =51.431eV Ekin = 6.462eV (T=537.578K) Etot = 57.894eV
Energy per atom: Epot =50.133eV Ekin = 7.755eV (T=645.115K) Etot = 57.888eV
Energy per atom: Epot =50.842eV Ekin = 7.050eV (T=586.436K) Etot = 57.892eV
Energy per atom: Epot =49.913eV Ekin = 7.972eV (T=663.188K) Etot = 57.885eV
Energy per atom: Epot =51.160eV Ekin = 6.733eV (T=560.090K) Etot = 57.893eV
Energy per atom: Epot =51.481eV Ekin = 6.413eV (T=533.505K) Etot = 57.894eV
Energy per atom: Epot =50.638eV Ekin = 7.250eV (T=603.124K) Etot = 57.888eV
Energy per atom: Epot =50.466eV Ekin = 7.421eV (T=617.335K) Etot = 57.887eV
Energy per atom: Epot =51.082eV Ekin = 6.816eV (T=566.971K) Etot = 57.898eV
Energy per atom: Epot =50.328eV Ekin = 7.562eV (T=629.047K) Etot = 57.890eV
Energy per atom: Epot =50.209eV Ekin = 7.684eV (T=639.173K) Etot = 57.893eV
Energy per atom: Epot =50.198eV Ekin = 7.692eV (T=639.834K) Etot = 57.889eV
Energy per atom: Epot =50.324eV Ekin = 7.557eV (T=628.618K) Etot = 57.880eV
Energy per atom: Epot =50.835eV Ekin = 7.050eV (T=586.489K) Etot = 57.885eV
Energy per atom: Epot =50.702eV Ekin = 7.187eV (T=597.829K) Etot = 57.889eV
Energy per atom: Epot =50.708eV Ekin = 7.184eV (T=597.583K) Etot = 57.891eV
Energy per atom: Epot =51.151eV Ekin = 6.739eV (T=560.582K) Etot = 57.890eV
Energy per atom: Epot =51.138eV Ekin = 6.757eV (T=562.128K) Etot = 57.895eV
Energy per atom: Epot =50.639eV Ekin = 7.252eV (T=603.265K) Etot = 57.891eV
Energy per atom: Epot =50.581eV Ekin = 7.304eV (T=607.566K) Etot = 57.885eV
Energy per atom: Epot =50.443eV Ekin = 7.444eV (T=619.211K) Etot = 57.887eV
Energy per atom: Epot =50.742eV Ekin = 7.149eV (T=594.678K) Etot = 57.891eV
Energy per atom: Epot =51.128eV Ekin = 6.764eV (T=562.669K) Etot = 57.892eV
Energy per atom: Epot =51.102eV Ekin = 6.796eV (T=565.373K) Etot = 57.899eV
Energy per atom: Epot =49.681eV Ekin = 8.208eV (T=682.818K) Etot = 57.889eV
Energy per atom: Epot =50.540eV Ekin = 7.349eV (T=611.364K) Etot = 57.889eV
Energy per atom: Epot =49.703eV Ekin = 8.182eV (T=680.670K) Etot = 57.885eV
Energy per atom: Epot =50.565eV Ekin = 7.325eV (T=609.311K) Etot = 57.890eV
Energy per atom: Epot =50.897eV Ekin = 6.990eV (T=581.456K) Etot = 57.887eV
Energy per atom: Epot =49.846eV Ekin = 8.034eV (T=668.328K) Etot = 57.880eV
Energy per atom: Epot =50.471eV Ekin = 7.415eV (T=616.809K) Etot = 57.886eV
Energy per atom: Epot =51.164eV Ekin = 6.732eV (T=559.986K) Etot = 57.896eV
Energy per atom: Epot =50.413eV Ekin = 7.480eV (T=622.208K) Etot = 57.893eV
Energy per atom: Epot =50.470eV Ekin = 7.422eV (T=617.436K) Etot = 57.893eV
Energy per atom: Epot =50.220eV Ekin = 7.673eV (T=638.311K) Etot = 57.894eV
Energy per atom: Epot =50.555eV Ekin = 7.337eV (T=610.368K) Etot = 57.893eV
Energy per atom: Epot =50.905eV Ekin = 6.989eV (T=581.392K) Etot = 57.894eV
Energy per atom: Epot =50.529eV Ekin = 7.361eV (T=612.309K) Etot = 57.890eV
Energy per atom: Epot =50.202eV Ekin = 7.686eV (T=639.334K) Etot = 57.888eV
Energy per atom: Epot =50.425eV Ekin = 7.462eV (T=620.712K) Etot = 57.886eV
Energy per atom: Epot =50.524eV Ekin = 7.365eV (T=612.706K) Etot = 57.890eV
Energy per atom: Epot =51.345eV Ekin = 6.552eV (T=545.008K) Etot = 57.897eV
Energy per atom: Epot =51.949eV Ekin = 5.951eV (T=495.039K) Etot = 57.900eV
Energy per atom: Epot =50.555eV Ekin = 7.334eV (T=610.125K) Etot = 57.889eV
Energy per atom: Epot =50.034eV Ekin = 7.847eV (T=652.761K) Etot = 57.881eV
Energy per atom: Epot =51.056eV Ekin = 6.829eV (T=568.062K) Etot = 57.885eV
Energy per atom: Epot =51.031eV Ekin = 6.859eV (T=570.567K) Etot = 57.890eV
Energy per atom: Epot =51.726eV Ekin = 6.174eV (T=513.552K) Etot = 57.900eV
Energy per atom: Epot =50.866eV Ekin = 7.027eV (T=584.526K) Etot = 57.893eV
Energy per atom: Epot =50.417eV Ekin = 7.475eV (T=621.833K) Etot = 57.892eV
Energy per atom: Epot =50.654eV Ekin = 7.236eV (T=601.916K) Etot = 57.890eV
Energy per atom: Epot =49.923eV Ekin = 7.959eV (T=662.082K) Etot = 57.882eV
Energy per atom: Epot =50.553eV Ekin = 7.336eV (T=610.237K) Etot = 57.889eV
Energy per atom: Epot =50.105eV Ekin = 7.785eV (T=647.584K) Etot = 57.890eV
Energy per atom: Epot =50.453eV Ekin = 7.441eV (T=618.981K) Etot = 57.894eV
Energy per atom: Epot =51.217eV Ekin = 6.681eV (T=555.801K) Etot = 57.899eV
Energy per atom: Epot =50.276eV Ekin = 7.614eV (T=633.424K) Etot = 57.890eV
Energy per atom: Epot =49.876eV Ekin = 8.014eV (T=666.627K) Etot = 57.890eV
Energy per atom: Epot =50.286eV Ekin = 7.607eV (T=632.778K) Etot = 57.892eV
Energy per atom: Epot =50.150eV Ekin = 7.743eV (T=644.132K) Etot = 57.893eV
Energy per atom: Epot =50.724eV Ekin = 7.165eV (T=596.013K) Etot = 57.888eV
Energy per atom: Epot =50.439eV Ekin = 7.452eV (T=619.920K) Etot = 57.891eV
Energy per atom: Epot =50.651eV Ekin = 7.240eV (T=602.245K) Etot = 57.891eV
Energy per atom: Epot =49.498eV Ekin = 8.386eV (T=697.641K) Etot = 57.884eV
Energy per atom: Epot =51.074eV Ekin = 6.823eV (T=567.554K) Etot = 57.897eV
Energy per atom: Epot =50.406eV Ekin = 7.482eV (T=622.440K) Etot = 57.889eV
Energy per atom: Epot =49.947eV Ekin = 7.934eV (T=660.037K) Etot = 57.881eV
Energy per atom: Epot =51.031eV Ekin = 6.860eV (T=570.629K) Etot = 57.891eV
Energy per atom: Epot =50.990eV Ekin = 6.910eV (T=574.799K) Etot = 57.900eV
Energy per atom: Epot =49.833eV Ekin = 8.056eV (T=670.158K) Etot = 57.889eV
Energy per atom: Epot =51.025eV Ekin = 6.868eV (T=571.339K) Etot = 57.893eV
Energy per atom: Epot =50.245eV Ekin = 7.646eV (T=636.038K) Etot = 57.891eV
Energy per atom: Epot =50.690eV Ekin = 7.205eV (T=599.355K) Etot = 57.894eV
Energy per atom: Epot =50.390eV Ekin = 7.504eV (T=624.272K) Etot = 57.894eV
Energy per atom: Epot =49.452eV Ekin = 8.433eV (T=701.493K) Etot = 57.885eV
Energy per atom: Epot =50.613eV Ekin = 7.279eV (T=605.534K) Etot = 57.892eV
Energy per atom: Epot =49.803eV Ekin = 8.080eV (T=672.183K) Etot = 57.884eV
Energy per atom: Epot =50.167eV Ekin = 7.717eV (T=641.980K) Etot = 57.884eV
Energy per atom: Epot =50.094eV Ekin = 7.790eV (T=648.029K) Etot = 57.884eV
Energy per atom: Epot =49.281eV Ekin = 8.607eV (T=715.946K) Etot = 57.888eV
Energy per atom: Epot =49.867eV Ekin = 8.024eV (T=667.502K) Etot = 57.891eV
Energy per atom: Epot =49.456eV Ekin = 8.427eV (T=701.038K) Etot = 57.883eV
Energy per atom: Epot =50.837eV Ekin = 7.052eV (T=586.666K) Etot = 57.889eV
Energy per atom: Epot =50.788eV Ekin = 7.101eV (T=590.699K) Etot = 57.889eV
Energy per atom: Epot =51.305eV Ekin = 6.592eV (T=548.378K) Etot = 57.897eV
Energy per atom: Epot =50.076eV Ekin = 7.813eV (T=649.950K) Etot = 57.889eV
Energy per atom: Epot =50.877eV Ekin = 7.013eV (T=583.392K) Etot = 57.890eV
Energy per atom: Epot =49.975eV Ekin = 7.913eV (T=658.229K) Etot = 57.888eV
Energy per atom: Epot =49.238eV Ekin = 8.649eV (T=719.451K) Etot = 57.887eV
Energy per atom: Epot =49.904eV Ekin = 7.988eV (T=664.461K) Etot = 57.892eV
Energy per atom: Epot =50.381eV Ekin = 7.517eV (T=625.292K) Etot = 57.898eV
Energy per atom: Epot =49.840eV Ekin = 8.050eV (T=669.624K) Etot = 57.890eV
Energy per atom: Epot =50.632eV Ekin = 7.259eV (T=603.887K) Etot = 57.892eV
Energy per atom: Epot =49.389eV Ekin = 8.498eV (T=706.929K) Etot = 57.887eV
Energy per atom: Epot =50.937eV Ekin = 6.959eV (T=578.929K) Etot = 57.897eV
Energy per atom: Epot =50.221eV Ekin = 7.665eV (T=637.610K) Etot = 57.886eV
Energy per atom: Epot =50.166eV Ekin = 7.719eV (T=642.154K) Etot = 57.886eV
Energy per atom: Epot =50.283eV Ekin = 7.605eV (T=632.675K) Etot = 57.889eV
Energy per atom: Epot =51.045eV Ekin = 6.842eV (T=569.162K) Etot = 57.887eV
Energy per atom: Epot =50.449eV Ekin = 7.436eV (T=618.590K) Etot = 57.885eV
Energy per atom: Epot =50.118eV Ekin = 7.772eV (T=646.538K) Etot = 57.890eV
Energy per atom: Epot =49.514eV Ekin = 8.377eV (T=696.894K) Etot = 57.891eV
Energy per atom: Epot =49.965eV Ekin = 7.929eV (T=659.600K) Etot = 57.894eV
Energy per atom: Epot =49.859eV Ekin = 8.034eV (T=668.352K) Etot = 57.893eV
Energy per atom: Epot =49.554eV Ekin = 8.335eV (T=693.329K) Etot = 57.889eV
Energy per atom: Epot =50.102eV Ekin = 7.792eV (T=648.154K) Etot = 57.894eV
Energy per atom: Epot =49.733eV Ekin = 8.162eV (T=678.984K) Etot = 57.896eV
Energy per atom: Epot =50.356eV Ekin = 7.541eV (T=627.295K) Etot = 57.896eV
Energy per atom: Epot =50.028eV Ekin = 7.867eV (T=654.391K) Etot = 57.895eV
Energy per atom: Epot =50.380eV Ekin = 7.511eV (T=624.830K) Etot = 57.891eV
Energy per atom: Epot =50.246eV Ekin = 7.641eV (T=635.615K) Etot = 57.887eV
Energy per atom: Epot =49.367eV Ekin = 8.515eV (T=708.302K) Etot = 57.881eV
Energy per atom: Epot =49.688eV Ekin = 8.199eV (T=682.041K) Etot = 57.887eV
Energy per atom: Epot =49.462eV Ekin = 8.421eV (T=700.480K) Etot = 57.882eV
Energy per atom: Epot =49.983eV Ekin = 7.903eV (T=657.383K) Etot = 57.886eV
Energy per atom: Epot =50.049eV Ekin = 7.838eV (T=651.981K) Etot = 57.887eV
Energy per atom: Epot =49.943eV Ekin = 7.945eV (T=660.887K) Etot = 57.888eV
Energy per atom: Epot =51.500eV Ekin = 6.403eV (T=532.616K) Etot = 57.902eV
Energy per atom: Epot =50.346eV Ekin = 7.545eV (T=627.607K) Etot = 57.890eV
Energy per atom: Epot =49.041eV Ekin = 8.838eV (T=735.239K) Etot = 57.879eV
Energy per atom: Epot =50.259eV Ekin = 7.628eV (T=634.519K) Etot = 57.887eV
Energy per atom: Epot =51.096eV Ekin = 6.799eV (T=565.559K) Etot = 57.895eV
Energy per atom: Epot =49.058eV Ekin = 8.823eV (T=733.958K) Etot = 57.882eV
Energy per atom: Epot =49.444eV Ekin = 8.443eV (T=702.378K) Etot = 57.887eV
Energy per atom: Epot =50.591eV Ekin = 7.300eV (T=607.262K) Etot = 57.891eV
Energy per atom: Epot =49.968eV Ekin = 7.919eV (T=658.773K) Etot = 57.888eV
Energy per atom: Epot =50.786eV Ekin = 7.110eV (T=591.476K) Etot = 57.897eV
Energy per atom: Epot =50.008eV Ekin = 7.879eV (T=655.407K) Etot = 57.886eV
Energy per atom: Epot =50.375eV Ekin = 7.507eV (T=624.515K) Etot = 57.882eV
Energy per atom: Epot =50.662eV Ekin = 7.230eV (T=601.452K) Etot = 57.892eV
Energy per atom: Epot =49.887eV Ekin = 8.009eV (T=666.251K) Etot = 57.896eV
Energy per atom: Epot =49.617eV Ekin = 8.273eV (T=688.177K) Etot = 57.889eV
Energy per atom: Epot =50.558eV Ekin = 7.326eV (T=609.438K) Etot = 57.884eV
Energy per atom: Epot =50.258eV Ekin = 7.626eV (T=634.394K) Etot = 57.884eV
Energy per atom: Epot =50.322eV Ekin = 7.570eV (T=629.741K) Etot = 57.892eV
Energy per atom: Epot =50.402eV Ekin = 7.492eV (T=623.194K) Etot = 57.893eV
Energy per atom: Epot =49.629eV Ekin = 8.258eV (T=686.928K) Etot = 57.887eV
Energy per atom: Epot =49.570eV Ekin = 8.320eV (T=692.090K) Etot = 57.890eV
Energy per atom: Epot =49.755eV Ekin = 8.134eV (T=676.665K) Etot = 57.889eV
Energy per atom: Epot =50.369eV Ekin = 7.525eV (T=625.963K) Etot = 57.894eV
Energy per atom: Epot =49.654eV Ekin = 8.235eV (T=685.077K) Etot = 57.889eV
Energy per atom: Epot =49.249eV Ekin = 8.638eV (T=718.537K) Etot = 57.887eV
Energy per atom: Epot =49.348eV Ekin = 8.544eV (T=710.719K) Etot = 57.891eV
Energy per atom: Epot =49.642eV Ekin = 8.247eV (T=686.057K) Etot = 57.889eV
Energy per atom: Epot =49.130eV Ekin = 8.754eV (T=728.218K) Etot = 57.884eV
Energy per atom: Epot =50.508eV Ekin = 7.388eV (T=614.578K) Etot = 57.896eV
Energy per atom: Epot =49.475eV Ekin = 8.413eV (T=699.838K) Etot = 57.888eV
Energy per atom: Epot =50.260eV Ekin = 7.633eV (T=634.973K) Etot = 57.893eV
Energy per atom: Epot =49.703eV Ekin = 8.189eV (T=681.230K) Etot = 57.892eV
Energy per atom: Epot =49.813eV Ekin = 8.074eV (T=671.610K) Etot = 57.887eV
Energy per atom: Epot =50.362eV Ekin = 7.527eV (T=626.174K) Etot = 57.889eV
Energy per atom: Epot =49.923eV Ekin = 7.966eV (T=662.631K) Etot = 57.889eV
Energy per atom: Epot =50.742eV Ekin = 7.149eV (T=594.735K) Etot = 57.892eV
Energy per atom: Epot =49.908eV Ekin = 7.979eV (T=663.765K) Etot = 57.887eV
Energy per atom: Epot =49.971eV Ekin = 7.915eV (T=658.434K) Etot = 57.886eV
Energy per atom: Epot =50.130eV Ekin = 7.757eV (T=645.260K) Etot = 57.887eV
Energy per atom: Epot =49.316eV Ekin = 8.568eV (T=712.701K) Etot = 57.883eV
Energy per atom: Epot =49.095eV Ekin = 8.791eV (T=731.283K) Etot = 57.886eV
Energy per atom: Epot =50.797eV Ekin = 7.097eV (T=590.414K) Etot = 57.894eV
Energy per atom: Epot =50.050eV Ekin = 7.844eV (T=652.536K) Etot = 57.894eV
Energy per atom: Epot =50.145eV Ekin = 7.747eV (T=644.438K) Etot = 57.892eV
Energy per atom: Epot =49.408eV Ekin = 8.483eV (T=705.703K) Etot = 57.892eV
Energy per atom: Epot =50.097eV Ekin = 7.793eV (T=648.250K) Etot = 57.890eV
Energy per atom: Epot =48.575eV Ekin = 9.300eV (T=773.599K) Etot = 57.875eV
Energy per atom: Epot =49.932eV Ekin = 7.952eV (T=661.539K) Etot = 57.885eV
Energy per atom: Epot =50.508eV Ekin = 7.379eV (T=613.843K) Etot = 57.888eV
Energy per atom: Epot =49.713eV Ekin = 8.169eV (T=679.517K) Etot = 57.881eV
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?
Total running time of the script: (22 minutes 45.278 seconds)