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 = 158.501eV (T=306.554K) Etot = 156.096eV
Energy per atom: Epot =120.096eV Ekin = 36.801eV (T=71.175K) Etot = 156.896eV
Energy per atom: Epot =80.270eV Ekin = 76.488eV (T=147.935K) Etot = 156.759eV
Energy per atom: Epot =72.625eV Ekin = 83.985eV (T=162.434K) Etot = 156.609eV
Energy per atom: Epot =70.935eV Ekin = 85.620eV (T=165.597K) Etot = 156.555eV
Energy per atom: Epot =82.510eV Ekin = 74.207eV (T=143.524K) Etot = 156.717eV
Energy per atom: Epot =80.069eV Ekin = 76.633eV (T=148.215K) Etot = 156.702eV
Energy per atom: Epot =73.804eV Ekin = 82.800eV (T=160.143K) Etot = 156.604eV
Energy per atom: Epot =74.920eV Ekin = 81.703eV (T=158.021K) Etot = 156.623eV
Energy per atom: Epot =80.840eV Ekin = 75.857eV (T=146.715K) Etot = 156.698eV
Energy per atom: Epot =76.665eV Ekin = 79.990eV (T=154.707K) Etot = 156.655eV
Energy per atom: Epot =76.213eV Ekin = 80.432eV (T=155.562K) Etot = 156.645eV
Energy per atom: Epot =77.242eV Ekin = 79.411eV (T=153.588K) Etot = 156.654eV
Energy per atom: Epot =79.488eV Ekin = 77.177eV (T=149.267K) Etot = 156.665eV
Energy per atom: Epot =75.779eV Ekin = 80.872eV (T=156.414K) Etot = 156.651eV
Energy per atom: Epot =77.040eV Ekin = 79.620eV (T=153.991K) Etot = 156.659eV
Energy per atom: Epot =76.193eV Ekin = 80.451eV (T=155.599K) Etot = 156.644eV
Energy per atom: Epot =80.045eV Ekin = 76.621eV (T=148.192K) Etot = 156.666eV
Energy per atom: Epot =75.583eV Ekin = 81.073eV (T=156.802K) Etot = 156.656eV
Energy per atom: Epot =77.149eV Ekin = 79.499eV (T=153.758K) Etot = 156.648eV
Energy per atom: Epot =79.513eV Ekin = 77.153eV (T=149.221K) Etot = 156.666eV
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 =600.145eV Ekin = 82.957eV (T=160.445K) Etot = 683.102eV
Energy per atom: Epot =670.463eV Ekin = 142.329eV (T=275.276K) Etot = 812.791eV
Energy per atom: Epot =727.429eV Ekin = 200.327eV (T=387.449K) Etot = 927.756eV
Energy per atom: Epot =784.629eV Ekin = 252.908eV (T=489.146K) Etot = 1037.537eV
Energy per atom: Epot =837.079eV Ekin = 301.579eV (T=583.281K) Etot = 1138.658eV
Energy per atom: Epot =887.924eV Ekin = 343.313eV (T=663.998K) Etot = 1231.237eV
Energy per atom: Epot =923.621eV Ekin = 375.550eV (T=726.346K) Etot = 1299.171eV
Energy per atom: Epot =962.110eV Ekin = 406.636eV (T=786.469K) Etot = 1368.745eV
Energy per atom: Epot =999.060eV Ekin = 442.318eV (T=855.482K) Etot = 1441.378eV
Energy per atom: Epot =1035.409eV Ekin = 462.380eV (T=894.283K) Etot = 1497.788eV
Energy per atom: Epot =1064.716eV Ekin = 488.615eV (T=945.025K) Etot = 1553.331eV
Energy per atom: Epot =1105.154eV Ekin = 499.105eV (T=965.312K) Etot = 1604.258eV
Energy per atom: Epot =1128.854eV Ekin = 524.651eV (T=1014.721K) Etot = 1653.505eV
Energy per atom: Epot =1168.560eV Ekin = 538.798eV (T=1042.082K) Etot = 1707.358eV
Energy per atom: Epot =1201.384eV Ekin = 543.925eV (T=1051.999K) Etot = 1745.309eV
Energy per atom: Epot =1215.620eV Ekin = 573.184eV (T=1108.587K) Etot = 1788.803eV
Energy per atom: Epot =1248.152eV Ekin = 576.514eV (T=1115.028K) Etot = 1824.666eV
Energy per atom: Epot =1268.321eV Ekin = 597.154eV (T=1154.947K) Etot = 1865.475eV
Energy per atom: Epot =1299.889eV Ekin = 598.431eV (T=1157.418K) Etot = 1898.320eV
Energy per atom: Epot =1311.262eV Ekin = 614.370eV (T=1188.246K) Etot = 1925.633eV
Energy per atom: Epot =1328.571eV Ekin = 624.009eV (T=1206.887K) Etot = 1952.580eV
Energy per atom: Epot =1343.055eV Ekin = 627.967eV (T=1214.542K) Etot = 1971.021eV
Energy per atom: Epot =1363.761eV Ekin = 640.459eV (T=1238.704K) Etot = 2004.221eV
Energy per atom: Epot =1390.576eV Ekin = 646.231eV (T=1249.867K) Etot = 2036.807eV
Energy per atom: Epot =1411.895eV Ekin = 647.730eV (T=1252.767K) Etot = 2059.625eV
Energy per atom: Epot =1425.734eV Ekin = 669.583eV (T=1295.031K) Etot = 2095.317eV
Energy per atom: Epot =1442.669eV Ekin = 677.834eV (T=1310.989K) Etot = 2120.503eV
Energy per atom: Epot =1447.021eV Ekin = 677.483eV (T=1310.311K) Etot = 2124.503eV
Energy per atom: Epot =1466.946eV Ekin = 685.218eV (T=1325.272K) Etot = 2152.164eV
Energy per atom: Epot =1479.156eV Ekin = 692.724eV (T=1339.789K) Etot = 2171.880eV
Energy per atom: Epot =1497.884eV Ekin = 682.426eV (T=1319.870K) Etot = 2180.310eV
Energy per atom: Epot =1518.579eV Ekin = 666.902eV (T=1289.846K) Etot = 2185.481eV
Energy per atom: Epot =1518.131eV Ekin = 686.502eV (T=1327.754K) Etot = 2204.633eV
Energy per atom: Epot =1526.587eV Ekin = 698.457eV (T=1350.877K) Etot = 2225.045eV
Energy per atom: Epot =1542.987eV Ekin = 697.491eV (T=1349.008K) Etot = 2240.478eV
Energy per atom: Epot =1556.438eV Ekin = 694.867eV (T=1343.934K) Etot = 2251.306eV
Energy per atom: Epot =1559.308eV Ekin = 703.261eV (T=1360.168K) Etot = 2262.569eV
Energy per atom: Epot =1577.465eV Ekin = 699.191eV (T=1352.296K) Etot = 2276.656eV
Energy per atom: Epot =1589.292eV Ekin = 703.755eV (T=1361.124K) Etot = 2293.047eV
Energy per atom: Epot =1602.674eV Ekin = 705.067eV (T=1363.661K) Etot = 2307.742eV
Energy per atom: Epot =1601.611eV Ekin = 720.878eV (T=1394.241K) Etot = 2322.489eV
Energy per atom: Epot =1618.102eV Ekin = 712.995eV (T=1378.995K) Etot = 2331.098eV
Energy per atom: Epot =1623.901eV Ekin = 719.157eV (T=1390.912K) Etot = 2343.058eV
Energy per atom: Epot =1630.828eV Ekin = 718.170eV (T=1389.004K) Etot = 2348.998eV
Energy per atom: Epot =1638.963eV Ekin = 723.390eV (T=1399.099K) Etot = 2362.353eV
Energy per atom: Epot =1644.740eV Ekin = 718.861eV (T=1390.340K) Etot = 2363.601eV
Energy per atom: Epot =1656.188eV Ekin = 722.881eV (T=1398.115K) Etot = 2379.070eV
Energy per atom: Epot =1664.034eV Ekin = 718.344eV (T=1389.339K) Etot = 2382.377eV
Energy per atom: Epot =1674.239eV Ekin = 716.711eV (T=1386.182K) Etot = 2390.950eV
Energy per atom: Epot =1666.810eV Ekin = 738.452eV (T=1428.231K) Etot = 2405.262eV
Energy per atom: Epot =1677.509eV Ekin = 729.696eV (T=1411.295K) Etot = 2407.205eV
Energy per atom: Epot =1693.481eV Ekin = 729.948eV (T=1411.784K) Etot = 2423.430eV
Energy per atom: Epot =1698.572eV Ekin = 737.303eV (T=1426.008K) Etot = 2435.875eV
Energy per atom: Epot =1701.068eV Ekin = 740.826eV (T=1432.822K) Etot = 2441.894eV
Energy per atom: Epot =1718.322eV Ekin = 726.540eV (T=1405.191K) Etot = 2444.862eV
Energy per atom: Epot =1723.383eV Ekin = 729.917eV (T=1411.723K) Etot = 2453.299eV
Energy per atom: Epot =1727.371eV Ekin = 730.364eV (T=1412.588K) Etot = 2457.736eV
Energy per atom: Epot =1736.590eV Ekin = 725.233eV (T=1402.663K) Etot = 2461.823eV
Energy per atom: Epot =1738.255eV Ekin = 741.742eV (T=1434.594K) Etot = 2479.997eV
Energy per atom: Epot =1750.851eV Ekin = 729.839eV (T=1411.572K) Etot = 2480.690eV
Energy per atom: Epot =1762.397eV Ekin = 729.824eV (T=1411.544K) Etot = 2492.221eV
Energy per atom: Epot =1770.993eV Ekin = 731.385eV (T=1414.563K) Etot = 2502.379eV
Energy per atom: Epot =1779.016eV Ekin = 725.568eV (T=1403.312K) Etot = 2504.584eV
Energy per atom: Epot =1802.737eV Ekin = 723.979eV (T=1400.239K) Etot = 2526.716eV
Energy per atom: Epot =1786.386eV Ekin = 745.571eV (T=1442.000K) Etot = 2531.957eV
Energy per atom: Epot =1801.501eV Ekin = 731.682eV (T=1415.136K) Etot = 2533.183eV
Energy per atom: Epot =1813.674eV Ekin = 734.303eV (T=1420.206K) Etot = 2547.977eV
Energy per atom: Epot =1818.654eV Ekin = 736.394eV (T=1424.249K) Etot = 2555.048eV
Energy per atom: Epot =1818.565eV Ekin = 746.452eV (T=1443.703K) Etot = 2565.017eV
Energy per atom: Epot =1815.462eV Ekin = 747.229eV (T=1445.205K) Etot = 2562.690eV
Energy per atom: Epot =1839.571eV Ekin = 728.543eV (T=1409.065K) Etot = 2568.113eV
Energy per atom: Epot =1842.476eV Ekin = 730.022eV (T=1411.926K) Etot = 2572.498eV
Energy per atom: Epot =1822.074eV Ekin = 757.968eV (T=1465.976K) Etot = 2580.041eV
Energy per atom: Epot =1843.205eV Ekin = 739.242eV (T=1429.759K) Etot = 2582.447eV
Energy per atom: Epot =1855.112eV Ekin = 728.180eV (T=1408.364K) Etot = 2583.292eV
Energy per atom: Epot =1844.232eV Ekin = 749.657eV (T=1449.902K) Etot = 2593.889eV
Energy per atom: Epot =1849.275eV Ekin = 748.354eV (T=1447.382K) Etot = 2597.629eV
Energy per atom: Epot =1852.406eV Ekin = 745.140eV (T=1441.166K) Etot = 2597.546eV
Energy per atom: Epot =1860.664eV Ekin = 740.043eV (T=1431.307K) Etot = 2600.706eV
Energy per atom: Epot =1855.905eV Ekin = 747.720eV (T=1446.155K) Etot = 2603.625eV
Energy per atom: Epot =1871.643eV Ekin = 740.041eV (T=1431.303K) Etot = 2611.684eV
Energy per atom: Epot =1879.020eV Ekin = 741.905eV (T=1434.909K) Etot = 2620.924eV
Energy per atom: Epot =1876.912eV Ekin = 754.489eV (T=1459.247K) Etot = 2631.401eV
Energy per atom: Epot =1881.656eV Ekin = 755.827eV (T=1461.836K) Etot = 2637.483eV
Energy per atom: Epot =1882.896eV Ekin = 755.412eV (T=1461.033K) Etot = 2638.308eV
Energy per atom: Epot =1894.612eV Ekin = 748.819eV (T=1448.281K) Etot = 2643.431eV
Energy per atom: Epot =1905.356eV Ekin = 756.980eV (T=1464.065K) Etot = 2662.336eV
Energy per atom: Epot =1898.321eV Ekin = 769.746eV (T=1488.755K) Etot = 2668.066eV
Energy per atom: Epot =1906.782eV Ekin = 767.828eV (T=1485.047K) Etot = 2674.611eV
Energy per atom: Epot =1908.398eV Ekin = 762.810eV (T=1475.342K) Etot = 2671.208eV
Energy per atom: Epot =1916.478eV Ekin = 748.382eV (T=1447.436K) Etot = 2664.860eV
Energy per atom: Epot =1925.831eV Ekin = 742.422eV (T=1435.910K) Etot = 2668.253eV
Energy per atom: Epot =1911.002eV Ekin = 765.033eV (T=1479.641K) Etot = 2676.035eV
Energy per atom: Epot =1925.013eV Ekin = 747.031eV (T=1444.823K) Etot = 2672.044eV
Energy per atom: Epot =1930.589eV Ekin = 750.464eV (T=1451.462K) Etot = 2681.053eV
Energy per atom: Epot =1925.970eV Ekin = 755.348eV (T=1460.909K) Etot = 2681.319eV
Energy per atom: Epot =1933.033eV Ekin = 757.239eV (T=1464.567K) Etot = 2690.272eV
Energy per atom: Epot =1940.891eV Ekin = 757.239eV (T=1464.565K) Etot = 2698.130eV
Energy per atom: Epot =1934.189eV Ekin = 776.698eV (T=1502.202K) Etot = 2710.887eV
Energy per atom: Epot =1946.547eV Ekin = 769.066eV (T=1487.440K) Etot = 2715.613eV
Energy per atom: Epot =1944.313eV Ekin = 772.802eV (T=1494.667K) Etot = 2717.115eV
Energy per atom: Epot =1952.175eV Ekin = 762.716eV (T=1475.158K) Etot = 2714.890eV
Energy per atom: Epot =1947.696eV Ekin = 781.777eV (T=1512.026K) Etot = 2729.473eV
Energy per atom: Epot =1957.038eV Ekin = 787.065eV (T=1522.252K) Etot = 2744.103eV
Energy per atom: Epot =1976.046eV Ekin = 768.105eV (T=1485.581K) Etot = 2744.151eV
Energy per atom: Epot =1963.420eV Ekin = 778.234eV (T=1505.172K) Etot = 2741.654eV
Energy per atom: Epot =1968.824eV Ekin = 774.327eV (T=1497.616K) Etot = 2743.150eV
Energy per atom: Epot =1985.865eV Ekin = 751.101eV (T=1452.695K) Etot = 2736.966eV
Energy per atom: Epot =1984.892eV Ekin = 754.970eV (T=1460.177K) Etot = 2739.862eV
Energy per atom: Epot =1970.556eV Ekin = 768.032eV (T=1485.441K) Etot = 2738.589eV
Energy per atom: Epot =1978.171eV Ekin = 758.194eV (T=1466.413K) Etot = 2736.365eV
Energy per atom: Epot =1964.447eV Ekin = 774.152eV (T=1497.278K) Etot = 2738.600eV
Energy per atom: Epot =1976.476eV Ekin = 764.800eV (T=1479.190K) Etot = 2741.276eV
Energy per atom: Epot =1971.652eV Ekin = 776.996eV (T=1502.779K) Etot = 2748.649eV
Energy per atom: Epot =1988.636eV Ekin = 757.075eV (T=1464.249K) Etot = 2745.711eV
Energy per atom: Epot =1985.995eV Ekin = 751.371eV (T=1453.218K) Etot = 2737.367eV
Energy per atom: Epot =1983.254eV Ekin = 752.087eV (T=1454.601K) Etot = 2735.341eV
Energy per atom: Epot =1977.365eV Ekin = 757.414eV (T=1464.905K) Etot = 2734.779eV
Energy per atom: Epot =1973.707eV Ekin = 767.406eV (T=1484.231K) Etot = 2741.113eV
Energy per atom: Epot =1981.834eV Ekin = 760.463eV (T=1470.802K) Etot = 2742.297eV
Energy per atom: Epot =1987.819eV Ekin = 759.995eV (T=1469.897K) Etot = 2747.814eV
Energy per atom: Epot =1979.604eV Ekin = 773.255eV (T=1495.542K) Etot = 2752.859eV
Energy per atom: Epot =1982.633eV Ekin = 768.706eV (T=1486.744K) Etot = 2751.339eV
Energy per atom: Epot =1986.773eV Ekin = 762.223eV (T=1474.205K) Etot = 2748.995eV
Energy per atom: Epot =2003.420eV Ekin = 764.508eV (T=1478.624K) Etot = 2767.928eV
Energy per atom: Epot =2013.534eV Ekin = 763.828eV (T=1477.311K) Etot = 2777.363eV
Energy per atom: Epot =1984.315eV Ekin = 792.715eV (T=1533.180K) Etot = 2777.030eV
Energy per atom: Epot =2006.681eV Ekin = 777.175eV (T=1503.124K) Etot = 2783.856eV
Energy per atom: Epot =2006.597eV Ekin = 778.406eV (T=1505.505K) Etot = 2785.003eV
Energy per atom: Epot =2001.504eV Ekin = 785.249eV (T=1518.740K) Etot = 2786.753eV
Energy per atom: Epot =2014.418eV Ekin = 770.032eV (T=1489.308K) Etot = 2784.449eV
Energy per atom: Epot =2012.445eV Ekin = 776.576eV (T=1501.965K) Etot = 2789.021eV
Energy per atom: Epot =2003.999eV Ekin = 775.908eV (T=1500.673K) Etot = 2779.907eV
Energy per atom: Epot =2007.164eV Ekin = 760.247eV (T=1470.384K) Etot = 2767.411eV
Energy per atom: Epot =2016.889eV Ekin = 754.028eV (T=1458.355K) Etot = 2770.917eV
Energy per atom: Epot =2004.584eV Ekin = 773.252eV (T=1495.537K) Etot = 2777.836eV
Energy per atom: Epot =1999.810eV Ekin = 772.661eV (T=1494.394K) Etot = 2772.471eV
Energy per atom: Epot =1995.433eV Ekin = 779.926eV (T=1508.444K) Etot = 2775.359eV
Energy per atom: Epot =2009.762eV Ekin = 763.516eV (T=1476.705K) Etot = 2773.278eV
Energy per atom: Epot =1995.746eV Ekin = 772.477eV (T=1494.037K) Etot = 2768.223eV
Energy per atom: Epot =1993.023eV Ekin = 777.072eV (T=1502.926K) Etot = 2770.096eV
Energy per atom: Epot =1989.465eV Ekin = 779.366eV (T=1507.362K) Etot = 2768.831eV
Energy per atom: Epot =1992.873eV Ekin = 777.310eV (T=1503.385K) Etot = 2770.183eV
Energy per atom: Epot =2001.508eV Ekin = 783.217eV (T=1514.811K) Etot = 2784.726eV
Energy per atom: Epot =1998.625eV Ekin = 780.448eV (T=1509.455K) Etot = 2779.073eV
Energy per atom: Epot =1996.942eV Ekin = 784.025eV (T=1516.372K) Etot = 2780.967eV
Energy per atom: Epot =2002.006eV Ekin = 766.932eV (T=1483.312K) Etot = 2768.938eV
Energy per atom: Epot =1998.048eV Ekin = 773.609eV (T=1496.227K) Etot = 2771.657eV
Energy per atom: Epot =1990.628eV Ekin = 782.287eV (T=1513.011K) Etot = 2772.915eV
Energy per atom: Epot =1987.183eV Ekin = 780.027eV (T=1508.640K) Etot = 2767.210eV
Energy per atom: Epot =1986.856eV Ekin = 783.482eV (T=1515.322K) Etot = 2770.338eV
Energy per atom: Epot =2000.673eV Ekin = 768.265eV (T=1485.892K) Etot = 2768.939eV
Energy per atom: Epot =1999.840eV Ekin = 780.934eV (T=1510.394K) Etot = 2780.774eV
Energy per atom: Epot =2001.366eV Ekin = 789.080eV (T=1526.149K) Etot = 2790.446eV
Energy per atom: Epot =2013.584eV Ekin = 773.500eV (T=1496.017K) Etot = 2787.084eV
Energy per atom: Epot =2005.716eV Ekin = 769.865eV (T=1488.986K) Etot = 2775.581eV
Energy per atom: Epot =2000.607eV Ekin = 785.903eV (T=1520.005K) Etot = 2786.510eV
Energy per atom: Epot =2007.580eV Ekin = 776.980eV (T=1502.746K) Etot = 2784.560eV
Energy per atom: Epot =2014.165eV Ekin = 774.534eV (T=1498.016K) Etot = 2788.698eV
Energy per atom: Epot =2015.715eV Ekin = 776.931eV (T=1502.651K) Etot = 2792.646eV
Energy per atom: Epot =2002.883eV Ekin = 790.896eV (T=1529.661K) Etot = 2793.779eV
Energy per atom: Epot =2013.367eV Ekin = 773.874eV (T=1496.739K) Etot = 2787.241eV
Energy per atom: Epot =2015.140eV Ekin = 770.361eV (T=1489.946K) Etot = 2785.501eV
Energy per atom: Epot =2000.516eV Ekin = 770.125eV (T=1489.488K) Etot = 2770.641eV
Energy per atom: Epot =2002.906eV Ekin = 757.736eV (T=1465.528K) Etot = 2760.642eV
Energy per atom: Epot =2003.057eV Ekin = 757.343eV (T=1464.767K) Etot = 2760.400eV
Energy per atom: Epot =1994.162eV Ekin = 773.425eV (T=1495.872K) Etot = 2767.587eV
Energy per atom: Epot =1992.347eV Ekin = 773.332eV (T=1495.691K) Etot = 2765.679eV
Energy per atom: Epot =2001.879eV Ekin = 763.944eV (T=1477.534K) Etot = 2765.823eV
Energy per atom: Epot =1995.000eV Ekin = 765.998eV (T=1481.507K) Etot = 2760.998eV
Energy per atom: Epot =1993.092eV Ekin = 769.113eV (T=1487.531K) Etot = 2762.205eV
Energy per atom: Epot =1976.077eV Ekin = 779.527eV (T=1507.673K) Etot = 2755.604eV
Energy per atom: Epot =1979.785eV Ekin = 789.943eV (T=1527.819K) Etot = 2769.728eV
Energy per atom: Epot =1985.563eV Ekin = 785.852eV (T=1519.907K) Etot = 2771.415eV
Energy per atom: Epot =1993.071eV Ekin = 782.515eV (T=1513.453K) Etot = 2775.586eV
Energy per atom: Epot =2002.380eV Ekin = 773.955eV (T=1496.896K) Etot = 2776.335eV
Energy per atom: Epot =2006.307eV Ekin = 774.126eV (T=1497.228K) Etot = 2780.433eV
Energy per atom: Epot =2010.985eV Ekin = 772.532eV (T=1494.144K) Etot = 2783.517eV
Energy per atom: Epot =2003.964eV Ekin = 776.196eV (T=1501.230K) Etot = 2780.160eV
Energy per atom: Epot =1992.725eV Ekin = 789.670eV (T=1527.291K) Etot = 2782.395eV
Energy per atom: Epot =2002.530eV Ekin = 778.870eV (T=1506.403K) Etot = 2781.400eV
Energy per atom: Epot =1999.062eV Ekin = 779.592eV (T=1507.799K) Etot = 2778.654eV
Energy per atom: Epot =1999.030eV Ekin = 783.255eV (T=1514.884K) Etot = 2782.286eV
Energy per atom: Epot =2001.417eV Ekin = 780.167eV (T=1508.911K) Etot = 2781.584eV
Energy per atom: Epot =2009.655eV Ekin = 774.212eV (T=1497.393K) Etot = 2783.867eV
Energy per atom: Epot =1994.448eV Ekin = 780.370eV (T=1509.303K) Etot = 2774.817eV
Energy per atom: Epot =1997.002eV Ekin = 767.214eV (T=1483.859K) Etot = 2764.216eV
Energy per atom: Epot =1998.686eV Ekin = 769.130eV (T=1487.565K) Etot = 2767.816eV
Energy per atom: Epot =1990.537eV Ekin = 771.737eV (T=1492.606K) Etot = 2762.274eV
Energy per atom: Epot =1985.970eV Ekin = 779.176eV (T=1506.995K) Etot = 2765.147eV
Energy per atom: Epot =1994.027eV Ekin = 773.028eV (T=1495.104K) Etot = 2767.056eV
Energy per atom: Epot =2003.112eV Ekin = 761.869eV (T=1473.521K) Etot = 2764.980eV
Energy per atom: Epot =1982.422eV Ekin = 774.774eV (T=1498.480K) Etot = 2757.196eV
Energy per atom: Epot =2005.018eV Ekin = 763.269eV (T=1476.229K) Etot = 2768.287eV
Energy per atom: Epot =2008.221eV Ekin = 763.306eV (T=1476.300K) Etot = 2771.527eV
Energy per atom: Epot =2002.044eV Ekin = 771.306eV (T=1491.774K) Etot = 2773.351eV
Energy per atom: Epot =2017.916eV Ekin = 760.785eV (T=1471.424K) Etot = 2778.700eV
Energy per atom: Epot =2001.776eV Ekin = 781.805eV (T=1512.079K) Etot = 2783.581eV
Energy per atom: Epot =2002.857eV Ekin = 771.735eV (T=1492.602K) Etot = 2774.592eV
Energy per atom: Epot =2004.031eV Ekin = 767.288eV (T=1484.002K) Etot = 2771.319eV
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] 16:15:19 43.457006 1.0818
BFGSLineSearch: 1[ 1] 16:15:19 42.347659 0.2273
BFGSLineSearch: 2[ 2] 16:15:19 42.108454 0.1349
BFGSLineSearch: 3[ 3] 16:15:19 41.964817 0.1138
BFGSLineSearch: 4[ 4] 16:15:19 41.924933 0.0683
BFGSLineSearch: 5[ 5] 16:15:19 41.915346 0.0225
BFGSLineSearch: 6[ 6] 16:15:19 41.914920 0.0059
BFGSLineSearch: 7[ 7] 16:15:19 41.914872 0.0023
BFGSLineSearch: 8[ 9] 16:15:19 41.914855 0.0023
BFGSLineSearch: 9[ 10] 16:15:19 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 15.717eV (T=1307.463K) Etot = 57.632eV
Energy per atom: Epot =52.067eV Ekin = 5.618eV (T=467.309K) Etot = 57.685eV
Energy per atom: Epot =50.410eV Ekin = 7.275eV (T=605.211K) Etot = 57.685eV
Energy per atom: Epot =49.878eV Ekin = 7.807eV (T=649.429K) Etot = 57.685eV
Energy per atom: Epot =52.113eV Ekin = 5.580eV (T=464.182K) Etot = 57.693eV
Energy per atom: Epot =50.918eV Ekin = 6.767eV (T=562.891K) Etot = 57.685eV
Energy per atom: Epot =50.008eV Ekin = 7.676eV (T=638.552K) Etot = 57.684eV
Energy per atom: Epot =49.676eV Ekin = 8.003eV (T=665.727K) Etot = 57.678eV
Energy per atom: Epot =49.389eV Ekin = 8.286eV (T=689.271K) Etot = 57.675eV
Energy per atom: Epot =49.250eV Ekin = 8.429eV (T=701.205K) Etot = 57.679eV
Energy per atom: Epot =50.092eV Ekin = 7.595eV (T=631.761K) Etot = 57.686eV
Energy per atom: Epot =50.533eV Ekin = 7.151eV (T=594.873K) Etot = 57.684eV
Energy per atom: Epot =51.587eV Ekin = 6.102eV (T=507.589K) Etot = 57.688eV
Energy per atom: Epot =50.804eV Ekin = 6.882eV (T=572.449K) Etot = 57.686eV
Energy per atom: Epot =50.041eV Ekin = 7.640eV (T=635.563K) Etot = 57.682eV
Energy per atom: Epot =50.185eV Ekin = 7.497eV (T=623.691K) Etot = 57.682eV
Energy per atom: Epot =50.581eV Ekin = 7.105eV (T=591.003K) Etot = 57.685eV
Energy per atom: Epot =50.246eV Ekin = 7.440eV (T=618.888K) Etot = 57.685eV
Energy per atom: Epot =50.555eV Ekin = 7.131eV (T=593.224K) Etot = 57.686eV
Energy per atom: Epot =50.662eV Ekin = 7.019eV (T=583.912K) Etot = 57.682eV
Energy per atom: Epot =50.566eV Ekin = 7.121eV (T=592.404K) Etot = 57.687eV
Energy per atom: Epot =49.658eV Ekin = 8.024eV (T=667.524K) Etot = 57.682eV
Energy per atom: Epot =49.525eV Ekin = 8.155eV (T=678.412K) Etot = 57.681eV
Energy per atom: Epot =50.071eV Ekin = 7.616eV (T=633.559K) Etot = 57.687eV
Energy per atom: Epot =50.142eV Ekin = 7.543eV (T=627.465K) Etot = 57.685eV
Energy per atom: Epot =49.659eV Ekin = 8.020eV (T=667.125K) Etot = 57.678eV
Energy per atom: Epot =50.946eV Ekin = 6.741eV (T=560.721K) Etot = 57.686eV
Energy per atom: Epot =51.226eV Ekin = 6.462eV (T=537.560K) Etot = 57.688eV
Energy per atom: Epot =49.933eV Ekin = 7.756eV (T=645.218K) Etot = 57.689eV
Energy per atom: Epot =50.028eV Ekin = 7.657eV (T=636.931K) Etot = 57.684eV
Energy per atom: Epot =50.573eV Ekin = 7.113eV (T=591.693K) Etot = 57.686eV
Energy per atom: Epot =50.100eV Ekin = 7.585eV (T=630.969K) Etot = 57.685eV
Energy per atom: Epot =50.378eV Ekin = 7.308eV (T=607.928K) Etot = 57.686eV
Energy per atom: Epot =51.003eV Ekin = 6.684eV (T=556.047K) Etot = 57.688eV
Energy per atom: Epot =49.914eV Ekin = 7.771eV (T=646.453K) Etot = 57.685eV
Energy per atom: Epot =50.506eV Ekin = 7.183eV (T=597.532K) Etot = 57.690eV
Energy per atom: Epot =50.403eV Ekin = 7.282eV (T=605.775K) Etot = 57.685eV
Energy per atom: Epot =50.213eV Ekin = 7.467eV (T=621.134K) Etot = 57.680eV
Energy per atom: Epot =50.300eV Ekin = 7.380eV (T=613.940K) Etot = 57.680eV
Energy per atom: Epot =50.287eV Ekin = 7.399eV (T=615.523K) Etot = 57.687eV
Energy per atom: Epot =50.100eV Ekin = 7.582eV (T=630.730K) Etot = 57.682eV
Energy per atom: Epot =49.923eV Ekin = 7.753eV (T=644.964K) Etot = 57.677eV
Energy per atom: Epot =49.808eV Ekin = 7.875eV (T=655.072K) Etot = 57.682eV
Energy per atom: Epot =49.703eV Ekin = 7.977eV (T=663.606K) Etot = 57.681eV
Energy per atom: Epot =50.053eV Ekin = 7.632eV (T=634.889K) Etot = 57.685eV
Energy per atom: Epot =48.545eV Ekin = 9.131eV (T=759.562K) Etot = 57.676eV
Energy per atom: Epot =50.877eV Ekin = 6.810eV (T=566.471K) Etot = 57.687eV
Energy per atom: Epot =50.023eV Ekin = 7.658eV (T=637.047K) Etot = 57.681eV
Energy per atom: Epot =50.891eV Ekin = 6.796eV (T=565.326K) Etot = 57.687eV
Energy per atom: Epot =50.597eV Ekin = 7.090eV (T=589.803K) Etot = 57.687eV
Energy per atom: Epot =49.505eV Ekin = 8.175eV (T=680.044K) Etot = 57.680eV
Energy per atom: Epot =50.246eV Ekin = 7.432eV (T=618.251K) Etot = 57.678eV
Energy per atom: Epot =50.389eV Ekin = 7.292eV (T=606.584K) Etot = 57.681eV
Energy per atom: Epot =50.690eV Ekin = 6.993eV (T=581.713K) Etot = 57.683eV
Energy per atom: Epot =49.819eV Ekin = 7.862eV (T=653.985K) Etot = 57.681eV
Energy per atom: Epot =50.229eV Ekin = 7.454eV (T=620.041K) Etot = 57.683eV
Energy per atom: Epot =50.112eV Ekin = 7.571eV (T=629.786K) Etot = 57.683eV
Energy per atom: Epot =50.223eV Ekin = 7.457eV (T=620.316K) Etot = 57.680eV
Energy per atom: Epot =49.745eV Ekin = 7.934eV (T=660.037K) Etot = 57.680eV
Energy per atom: Epot =49.951eV Ekin = 7.732eV (T=643.158K) Etot = 57.683eV
Energy per atom: Epot =50.402eV Ekin = 7.283eV (T=605.843K) Etot = 57.685eV
Energy per atom: Epot =50.455eV Ekin = 7.233eV (T=601.675K) Etot = 57.688eV
Energy per atom: Epot =50.496eV Ekin = 7.194eV (T=598.473K) Etot = 57.690eV
Energy per atom: Epot =49.978eV Ekin = 7.708eV (T=641.196K) Etot = 57.686eV
Energy per atom: Epot =49.983eV Ekin = 7.700eV (T=640.515K) Etot = 57.683eV
Energy per atom: Epot =49.750eV Ekin = 7.931eV (T=659.741K) Etot = 57.681eV
Energy per atom: Epot =50.737eV Ekin = 6.950eV (T=578.184K) Etot = 57.688eV
Energy per atom: Epot =50.079eV Ekin = 7.606eV (T=632.696K) Etot = 57.685eV
Energy per atom: Epot =50.050eV Ekin = 7.634eV (T=635.065K) Etot = 57.684eV
Energy per atom: Epot =50.561eV Ekin = 7.125eV (T=592.729K) Etot = 57.686eV
Energy per atom: Epot =49.668eV Ekin = 8.013eV (T=666.558K) Etot = 57.681eV
Energy per atom: Epot =50.035eV Ekin = 7.647eV (T=636.138K) Etot = 57.682eV
Energy per atom: Epot =50.348eV Ekin = 7.336eV (T=610.273K) Etot = 57.684eV
Energy per atom: Epot =50.357eV Ekin = 7.327eV (T=609.474K) Etot = 57.683eV
Energy per atom: Epot =49.815eV Ekin = 7.870eV (T=654.637K) Etot = 57.684eV
Energy per atom: Epot =49.768eV Ekin = 7.914eV (T=658.359K) Etot = 57.682eV
Energy per atom: Epot =48.930eV Ekin = 8.744eV (T=727.412K) Etot = 57.675eV
Energy per atom: Epot =48.914eV Ekin = 8.764eV (T=729.007K) Etot = 57.677eV
Energy per atom: Epot =49.822eV Ekin = 7.867eV (T=654.424K) Etot = 57.689eV
Energy per atom: Epot =49.726eV Ekin = 7.957eV (T=661.895K) Etot = 57.683eV
Energy per atom: Epot =50.921eV Ekin = 6.767eV (T=562.916K) Etot = 57.687eV
Energy per atom: Epot =50.357eV Ekin = 7.330eV (T=609.740K) Etot = 57.687eV
Energy per atom: Epot =49.063eV Ekin = 8.617eV (T=716.805K) Etot = 57.679eV
Energy per atom: Epot =50.334eV Ekin = 7.353eV (T=611.703K) Etot = 57.687eV
Energy per atom: Epot =49.900eV Ekin = 7.782eV (T=647.381K) Etot = 57.683eV
Energy per atom: Epot =48.501eV Ekin = 9.170eV (T=762.839K) Etot = 57.671eV
Energy per atom: Epot =49.998eV Ekin = 7.686eV (T=639.348K) Etot = 57.684eV
Energy per atom: Epot =50.979eV Ekin = 6.714eV (T=558.501K) Etot = 57.692eV
Energy per atom: Epot =48.935eV Ekin = 8.741eV (T=727.146K) Etot = 57.676eV
Energy per atom: Epot =49.104eV Ekin = 8.574eV (T=713.248K) Etot = 57.678eV
Energy per atom: Epot =50.163eV Ekin = 7.523eV (T=625.807K) Etot = 57.685eV
Energy per atom: Epot =49.933eV Ekin = 7.753eV (T=644.966K) Etot = 57.687eV
Energy per atom: Epot =49.662eV Ekin = 8.023eV (T=667.413K) Etot = 57.686eV
Energy per atom: Epot =50.097eV Ekin = 7.588eV (T=631.211K) Etot = 57.685eV
Energy per atom: Epot =50.324eV Ekin = 7.355eV (T=611.802K) Etot = 57.679eV
Energy per atom: Epot =50.877eV Ekin = 6.808eV (T=566.293K) Etot = 57.684eV
Energy per atom: Epot =50.605eV Ekin = 7.079eV (T=588.865K) Etot = 57.684eV
Energy per atom: Epot =49.992eV Ekin = 7.691eV (T=639.823K) Etot = 57.683eV
Energy per atom: Epot =49.547eV Ekin = 8.139eV (T=677.091K) Etot = 57.686eV
Energy per atom: Epot =49.688eV Ekin = 7.993eV (T=664.918K) Etot = 57.681eV
Energy per atom: Epot =50.192eV Ekin = 7.494eV (T=623.381K) Etot = 57.685eV
Energy per atom: Epot =49.395eV Ekin = 8.281eV (T=688.853K) Etot = 57.676eV
Energy per atom: Epot =50.499eV Ekin = 7.184eV (T=597.589K) Etot = 57.683eV
Energy per atom: Epot =50.777eV Ekin = 6.909eV (T=574.750K) Etot = 57.686eV
Energy per atom: Epot =50.481eV Ekin = 7.204eV (T=599.249K) Etot = 57.685eV
Energy per atom: Epot =49.540eV Ekin = 8.139eV (T=677.014K) Etot = 57.678eV
Energy per atom: Epot =49.845eV Ekin = 7.834eV (T=651.645K) Etot = 57.678eV
Energy per atom: Epot =49.928eV Ekin = 7.753eV (T=644.975K) Etot = 57.681eV
Energy per atom: Epot =50.921eV Ekin = 6.771eV (T=563.219K) Etot = 57.692eV
Energy per atom: Epot =50.745eV Ekin = 6.940eV (T=577.322K) Etot = 57.685eV
Energy per atom: Epot =50.003eV Ekin = 7.680eV (T=638.909K) Etot = 57.683eV
Energy per atom: Epot =50.356eV Ekin = 7.328eV (T=609.627K) Etot = 57.685eV
Energy per atom: Epot =50.225eV Ekin = 7.459eV (T=620.508K) Etot = 57.684eV
Energy per atom: Epot =50.415eV Ekin = 7.275eV (T=605.207K) Etot = 57.690eV
Energy per atom: Epot =50.214eV Ekin = 7.468eV (T=621.207K) Etot = 57.681eV
Energy per atom: Epot =50.059eV Ekin = 7.619eV (T=633.830K) Etot = 57.679eV
Energy per atom: Epot =50.723eV Ekin = 6.963eV (T=579.206K) Etot = 57.685eV
Energy per atom: Epot =51.486eV Ekin = 6.201eV (T=515.862K) Etot = 57.687eV
Energy per atom: Epot =49.997eV Ekin = 7.685eV (T=639.252K) Etot = 57.681eV
Energy per atom: Epot =50.004eV Ekin = 7.678eV (T=638.680K) Etot = 57.682eV
Energy per atom: Epot =50.940eV Ekin = 6.750eV (T=561.489K) Etot = 57.690eV
Energy per atom: Epot =50.667eV Ekin = 7.022eV (T=584.133K) Etot = 57.689eV
Energy per atom: Epot =49.324eV Ekin = 8.356eV (T=695.112K) Etot = 57.680eV
Energy per atom: Epot =51.145eV Ekin = 6.545eV (T=544.454K) Etot = 57.690eV
Energy per atom: Epot =50.076eV Ekin = 7.603eV (T=632.435K) Etot = 57.679eV
Energy per atom: Epot =51.075eV Ekin = 6.614eV (T=550.187K) Etot = 57.689eV
Energy per atom: Epot =50.366eV Ekin = 7.321eV (T=608.998K) Etot = 57.687eV
Energy per atom: Epot =50.509eV Ekin = 7.172eV (T=596.621K) Etot = 57.681eV
Energy per atom: Epot =49.597eV Ekin = 8.085eV (T=672.565K) Etot = 57.682eV
Energy per atom: Epot =49.551eV Ekin = 8.134eV (T=676.614K) Etot = 57.685eV
Energy per atom: Epot =49.465eV Ekin = 8.216eV (T=683.438K) Etot = 57.681eV
Energy per atom: Epot =50.585eV Ekin = 7.103eV (T=590.845K) Etot = 57.688eV
Energy per atom: Epot =50.358eV Ekin = 7.324eV (T=609.254K) Etot = 57.682eV
Energy per atom: Epot =50.201eV Ekin = 7.481eV (T=622.341K) Etot = 57.682eV
Energy per atom: Epot =50.968eV Ekin = 6.718eV (T=558.876K) Etot = 57.687eV
Energy per atom: Epot =49.496eV Ekin = 8.190eV (T=681.257K) Etot = 57.685eV
Energy per atom: Epot =49.381eV Ekin = 8.306eV (T=690.909K) Etot = 57.687eV
Energy per atom: Epot =49.621eV Ekin = 8.061eV (T=670.553K) Etot = 57.682eV
Energy per atom: Epot =49.904eV Ekin = 7.783eV (T=647.431K) Etot = 57.687eV
Energy per atom: Epot =49.633eV Ekin = 8.051eV (T=669.711K) Etot = 57.683eV
Energy per atom: Epot =49.411eV Ekin = 8.273eV (T=688.179K) Etot = 57.684eV
Energy per atom: Epot =50.009eV Ekin = 7.678eV (T=638.678K) Etot = 57.687eV
Energy per atom: Epot =50.925eV Ekin = 6.762eV (T=562.537K) Etot = 57.687eV
Energy per atom: Epot =49.739eV Ekin = 7.942eV (T=660.629K) Etot = 57.680eV
Energy per atom: Epot =49.360eV Ekin = 8.317eV (T=691.866K) Etot = 57.677eV
Energy per atom: Epot =50.527eV Ekin = 7.164eV (T=595.950K) Etot = 57.692eV
Energy per atom: Epot =49.363eV Ekin = 8.329eV (T=692.845K) Etot = 57.691eV
Energy per atom: Epot =49.061eV Ekin = 8.626eV (T=717.540K) Etot = 57.687eV
Energy per atom: Epot =50.384eV Ekin = 7.305eV (T=607.701K) Etot = 57.689eV
Energy per atom: Epot =49.077eV Ekin = 8.600eV (T=715.363K) Etot = 57.676eV
Energy per atom: Epot =50.202eV Ekin = 7.476eV (T=621.930K) Etot = 57.678eV
Energy per atom: Epot =50.030eV Ekin = 7.656eV (T=636.852K) Etot = 57.686eV
Energy per atom: Epot =49.598eV Ekin = 8.087eV (T=672.693K) Etot = 57.685eV
Energy per atom: Epot =49.566eV Ekin = 8.114eV (T=674.937K) Etot = 57.679eV
Energy per atom: Epot =48.872eV Ekin = 8.802eV (T=732.191K) Etot = 57.674eV
Energy per atom: Epot =48.794eV Ekin = 8.888eV (T=739.340K) Etot = 57.682eV
Energy per atom: Epot =49.993eV Ekin = 7.687eV (T=639.435K) Etot = 57.680eV
Energy per atom: Epot =49.285eV Ekin = 8.400eV (T=698.749K) Etot = 57.684eV
Energy per atom: Epot =49.435eV Ekin = 8.251eV (T=686.400K) Etot = 57.686eV
Energy per atom: Epot =49.654eV Ekin = 8.031eV (T=668.054K) Etot = 57.685eV
Energy per atom: Epot =49.859eV Ekin = 7.823eV (T=650.793K) Etot = 57.683eV
Energy per atom: Epot =49.958eV Ekin = 7.724eV (T=642.520K) Etot = 57.682eV
Energy per atom: Epot =49.108eV Ekin = 8.569eV (T=712.802K) Etot = 57.677eV
Energy per atom: Epot =50.137eV Ekin = 7.545eV (T=627.669K) Etot = 57.683eV
Energy per atom: Epot =49.785eV Ekin = 7.899eV (T=657.101K) Etot = 57.684eV
Energy per atom: Epot =49.173eV Ekin = 8.510eV (T=707.881K) Etot = 57.682eV
Energy per atom: Epot =49.697eV Ekin = 7.988eV (T=664.474K) Etot = 57.685eV
Energy per atom: Epot =49.575eV Ekin = 8.105eV (T=674.267K) Etot = 57.680eV
Energy per atom: Epot =49.553eV Ekin = 8.126eV (T=675.948K) Etot = 57.679eV
Energy per atom: Epot =49.493eV Ekin = 8.191eV (T=681.371K) Etot = 57.684eV
Energy per atom: Epot =50.356eV Ekin = 7.342eV (T=610.739K) Etot = 57.698eV
Energy per atom: Epot =50.529eV Ekin = 7.160eV (T=595.645K) Etot = 57.690eV
Energy per atom: Epot =48.920eV Ekin = 8.748eV (T=727.721K) Etot = 57.668eV
Energy per atom: Epot =48.852eV Ekin = 8.821eV (T=733.766K) Etot = 57.673eV
Energy per atom: Epot =50.014eV Ekin = 7.668eV (T=637.900K) Etot = 57.683eV
Energy per atom: Epot =50.215eV Ekin = 7.477eV (T=621.983K) Etot = 57.692eV
Energy per atom: Epot =49.277eV Ekin = 8.405eV (T=699.205K) Etot = 57.682eV
Energy per atom: Epot =49.363eV Ekin = 8.317eV (T=691.845K) Etot = 57.679eV
Energy per atom: Epot =49.658eV Ekin = 8.020eV (T=667.180K) Etot = 57.679eV
Energy per atom: Epot =49.854eV Ekin = 7.826eV (T=651.004K) Etot = 57.679eV
Energy per atom: Epot =49.798eV Ekin = 7.884eV (T=655.873K) Etot = 57.682eV
Energy per atom: Epot =49.996eV Ekin = 7.688eV (T=639.570K) Etot = 57.684eV
Energy per atom: Epot =48.927eV Ekin = 8.752eV (T=728.077K) Etot = 57.679eV
Energy per atom: Epot =49.733eV Ekin = 7.947eV (T=661.086K) Etot = 57.680eV
Energy per atom: Epot =49.941eV Ekin = 7.734eV (T=643.364K) Etot = 57.675eV
Energy per atom: Epot =48.832eV Ekin = 8.845eV (T=735.759K) Etot = 57.676eV
Energy per atom: Epot =50.354eV Ekin = 7.331eV (T=609.832K) Etot = 57.684eV
Energy per atom: Epot =50.429eV Ekin = 7.247eV (T=602.820K) Etot = 57.676eV
Energy per atom: Epot =49.926eV Ekin = 7.752eV (T=644.829K) Etot = 57.677eV
Energy per atom: Epot =49.648eV Ekin = 8.030eV (T=667.990K) Etot = 57.678eV
Energy per atom: Epot =49.157eV Ekin = 8.521eV (T=708.825K) Etot = 57.678eV
Energy per atom: Epot =49.855eV Ekin = 7.828eV (T=651.217K) Etot = 57.683eV
Energy per atom: Epot =49.661eV Ekin = 8.017eV (T=666.942K) Etot = 57.678eV
Energy per atom: Epot =49.888eV Ekin = 7.796eV (T=648.524K) Etot = 57.684eV
Energy per atom: Epot =49.484eV Ekin = 8.200eV (T=682.156K) Etot = 57.685eV
Energy per atom: Epot =50.579eV Ekin = 7.108eV (T=591.269K) Etot = 57.687eV
Energy per atom: Epot =50.184eV Ekin = 7.502eV (T=624.065K) Etot = 57.686eV
Energy per atom: Epot =49.216eV Ekin = 8.466eV (T=704.247K) Etot = 57.681eV
Energy per atom: Epot =51.100eV Ekin = 6.590eV (T=548.208K) Etot = 57.690eV
Energy per atom: Epot =49.479eV Ekin = 8.198eV (T=681.928K) Etot = 57.677eV
Energy per atom: Epot =49.526eV Ekin = 8.151eV (T=678.058K) Etot = 57.677eV
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?