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 = 154.948eV (T=299.682K) Etot = 152.543eV
Energy per atom: Epot =117.373eV Ekin = 35.955eV (T=69.540K) Etot = 153.328eV
Energy per atom: Epot =77.380eV Ekin = 75.796eV (T=146.595K) Etot = 153.176eV
Energy per atom: Epot =71.548eV Ekin = 81.495eV (T=157.618K) Etot = 153.042eV
Energy per atom: Epot =69.438eV Ekin = 83.552eV (T=161.597K) Etot = 152.990eV
Energy per atom: Epot =80.249eV Ekin = 72.890eV (T=140.976K) Etot = 153.140eV
Energy per atom: Epot =77.415eV Ekin = 75.718eV (T=146.446K) Etot = 153.133eV
Energy per atom: Epot =73.806eV Ekin = 79.243eV (T=153.264K) Etot = 153.049eV
Energy per atom: Epot =72.289eV Ekin = 80.763eV (T=156.203K) Etot = 153.052eV
Energy per atom: Epot =79.168eV Ekin = 73.956eV (T=143.037K) Etot = 153.124eV
Energy per atom: Epot =74.794eV Ekin = 78.290eV (T=151.419K) Etot = 153.083eV
Energy per atom: Epot =74.348eV Ekin = 78.728eV (T=152.267K) Etot = 153.076eV
Energy per atom: Epot =74.983eV Ekin = 78.097eV (T=151.046K) Etot = 153.080eV
Energy per atom: Epot =77.079eV Ekin = 76.012eV (T=147.014K) Etot = 153.092eV
Energy per atom: Epot =73.904eV Ekin = 79.174eV (T=153.129K) Etot = 153.078eV
Energy per atom: Epot =76.139eV Ekin = 76.962eV (T=148.851K) Etot = 153.101eV
Energy per atom: Epot =74.122eV Ekin = 78.955eV (T=152.705K) Etot = 153.077eV
Energy per atom: Epot =77.108eV Ekin = 75.973eV (T=146.938K) Etot = 153.081eV
Energy per atom: Epot =74.463eV Ekin = 78.619eV (T=152.055K) Etot = 153.082eV
Energy per atom: Epot =74.883eV Ekin = 78.197eV (T=151.240K) Etot = 153.080eV
Energy per atom: Epot =78.122eV Ekin = 74.977eV (T=145.012K) Etot = 153.099eV
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 =601.725eV Ekin = 80.694eV (T=156.069K) Etot = 682.418eV
Energy per atom: Epot =669.463eV Ekin = 143.355eV (T=277.262K) Etot = 812.818eV
Energy per atom: Epot =727.957eV Ekin = 202.534eV (T=391.718K) Etot = 930.490eV
Energy per atom: Epot =783.096eV Ekin = 255.639eV (T=494.427K) Etot = 1038.735eV
Energy per atom: Epot =831.946eV Ekin = 293.418eV (T=567.496K) Etot = 1125.364eV
Energy per atom: Epot =890.000eV Ekin = 330.306eV (T=638.841K) Etot = 1220.306eV
Energy per atom: Epot =920.016eV Ekin = 374.094eV (T=723.531K) Etot = 1294.111eV
Energy per atom: Epot =960.199eV Ekin = 410.658eV (T=794.248K) Etot = 1370.857eV
Energy per atom: Epot =1003.071eV Ekin = 436.900eV (T=845.003K) Etot = 1439.971eV
Energy per atom: Epot =1041.591eV Ekin = 461.609eV (T=892.792K) Etot = 1503.200eV
Energy per atom: Epot =1071.996eV Ekin = 488.972eV (T=945.714K) Etot = 1560.967eV
Energy per atom: Epot =1101.252eV Ekin = 509.227eV (T=984.890K) Etot = 1610.479eV
Energy per atom: Epot =1130.718eV Ekin = 534.254eV (T=1033.293K) Etot = 1664.972eV
Energy per atom: Epot =1173.726eV Ekin = 535.697eV (T=1036.084K) Etot = 1709.423eV
Energy per atom: Epot =1197.617eV Ekin = 548.383eV (T=1060.619K) Etot = 1746.000eV
Energy per atom: Epot =1210.733eV Ekin = 573.038eV (T=1108.305K) Etot = 1783.771eV
Energy per atom: Epot =1246.918eV Ekin = 576.407eV (T=1114.822K) Etot = 1823.325eV
Energy per atom: Epot =1274.611eV Ekin = 591.580eV (T=1144.166K) Etot = 1866.191eV
Energy per atom: Epot =1295.707eV Ekin = 605.086eV (T=1170.290K) Etot = 1900.793eV
Energy per atom: Epot =1320.437eV Ekin = 610.015eV (T=1179.822K) Etot = 1930.452eV
Energy per atom: Epot =1344.538eV Ekin = 615.678eV (T=1190.774K) Etot = 1960.215eV
Energy per atom: Epot =1364.939eV Ekin = 626.751eV (T=1212.191K) Etot = 1991.690eV
Energy per atom: Epot =1376.324eV Ekin = 644.630eV (T=1246.770K) Etot = 2020.954eV
Energy per atom: Epot =1403.710eV Ekin = 646.117eV (T=1249.646K) Etot = 2049.827eV
Energy per atom: Epot =1410.546eV Ekin = 666.396eV (T=1288.867K) Etot = 2076.942eV
Energy per atom: Epot =1430.322eV Ekin = 664.966eV (T=1286.103K) Etot = 2095.289eV
Energy per atom: Epot =1442.749eV Ekin = 674.001eV (T=1303.577K) Etot = 2116.750eV
Energy per atom: Epot =1465.916eV Ekin = 678.670eV (T=1312.606K) Etot = 2144.585eV
Energy per atom: Epot =1477.399eV Ekin = 679.004eV (T=1313.253K) Etot = 2156.403eV
Energy per atom: Epot =1491.925eV Ekin = 675.996eV (T=1307.435K) Etot = 2167.921eV
Energy per atom: Epot =1495.613eV Ekin = 694.062eV (T=1342.376K) Etot = 2189.675eV
Energy per atom: Epot =1513.809eV Ekin = 692.745eV (T=1339.830K) Etot = 2206.554eV
Energy per atom: Epot =1531.970eV Ekin = 686.798eV (T=1328.327K) Etot = 2218.768eV
Energy per atom: Epot =1544.264eV Ekin = 689.085eV (T=1332.750K) Etot = 2233.349eV
Energy per atom: Epot =1557.569eV Ekin = 687.861eV (T=1330.384K) Etot = 2245.430eV
Energy per atom: Epot =1564.734eV Ekin = 687.369eV (T=1329.432K) Etot = 2252.103eV
Energy per atom: Epot =1566.922eV Ekin = 709.072eV (T=1371.407K) Etot = 2275.994eV
Energy per atom: Epot =1578.269eV Ekin = 705.353eV (T=1364.215K) Etot = 2283.622eV
Energy per atom: Epot =1600.029eV Ekin = 701.360eV (T=1356.492K) Etot = 2301.389eV
Energy per atom: Epot =1602.564eV Ekin = 708.322eV (T=1369.956K) Etot = 2310.886eV
Energy per atom: Epot =1601.896eV Ekin = 718.430eV (T=1389.507K) Etot = 2320.326eV
Energy per atom: Epot =1619.465eV Ekin = 722.159eV (T=1396.719K) Etot = 2341.625eV
Energy per atom: Epot =1636.084eV Ekin = 713.298eV (T=1379.580K) Etot = 2349.381eV
Energy per atom: Epot =1649.205eV Ekin = 710.289eV (T=1373.760K) Etot = 2359.493eV
Energy per atom: Epot =1663.154eV Ekin = 710.474eV (T=1374.119K) Etot = 2373.628eV
Energy per atom: Epot =1662.579eV Ekin = 729.390eV (T=1410.704K) Etot = 2391.969eV
Energy per atom: Epot =1672.067eV Ekin = 717.868eV (T=1388.419K) Etot = 2389.934eV
Energy per atom: Epot =1669.671eV Ekin = 731.154eV (T=1414.115K) Etot = 2400.825eV
Energy per atom: Epot =1681.732eV Ekin = 728.516eV (T=1409.014K) Etot = 2410.249eV
Energy per atom: Epot =1689.519eV Ekin = 738.216eV (T=1427.775K) Etot = 2427.736eV
Energy per atom: Epot =1692.172eV Ekin = 740.812eV (T=1432.794K) Etot = 2432.984eV
Energy per atom: Epot =1691.845eV Ekin = 740.247eV (T=1431.701K) Etot = 2432.092eV
Energy per atom: Epot =1704.530eV Ekin = 732.034eV (T=1415.817K) Etot = 2436.564eV
Energy per atom: Epot =1727.371eV Ekin = 726.674eV (T=1405.451K) Etot = 2454.045eV
Energy per atom: Epot =1727.350eV Ekin = 732.285eV (T=1416.304K) Etot = 2459.636eV
Energy per atom: Epot =1738.200eV Ekin = 727.816eV (T=1407.659K) Etot = 2466.016eV
Energy per atom: Epot =1739.794eV Ekin = 726.612eV (T=1405.331K) Etot = 2466.406eV
Energy per atom: Epot =1746.728eV Ekin = 727.269eV (T=1406.601K) Etot = 2473.997eV
Energy per atom: Epot =1767.648eV Ekin = 718.433eV (T=1389.512K) Etot = 2486.081eV
Energy per atom: Epot =1755.131eV Ekin = 732.947eV (T=1417.582K) Etot = 2488.077eV
Energy per atom: Epot =1790.069eV Ekin = 707.977eV (T=1369.290K) Etot = 2498.046eV
Energy per atom: Epot =1781.675eV Ekin = 717.220eV (T=1387.167K) Etot = 2498.896eV
Energy per atom: Epot =1790.789eV Ekin = 718.243eV (T=1389.144K) Etot = 2509.032eV
Energy per atom: Epot =1787.431eV Ekin = 720.300eV (T=1393.123K) Etot = 2507.731eV
Energy per atom: Epot =1789.525eV Ekin = 729.726eV (T=1411.354K) Etot = 2519.252eV
Energy per atom: Epot =1800.888eV Ekin = 712.477eV (T=1377.993K) Etot = 2513.366eV
Energy per atom: Epot =1807.820eV Ekin = 713.163eV (T=1379.319K) Etot = 2520.983eV
Energy per atom: Epot =1797.710eV Ekin = 735.726eV (T=1422.958K) Etot = 2533.436eV
Energy per atom: Epot =1814.247eV Ekin = 730.461eV (T=1412.776K) Etot = 2544.709eV
Energy per atom: Epot =1818.121eV Ekin = 735.947eV (T=1423.385K) Etot = 2554.068eV
Energy per atom: Epot =1816.730eV Ekin = 747.570eV (T=1445.866K) Etot = 2564.301eV
Energy per atom: Epot =1824.273eV Ekin = 745.953eV (T=1442.737K) Etot = 2570.225eV
Energy per atom: Epot =1822.268eV Ekin = 755.619eV (T=1461.433K) Etot = 2577.888eV
Energy per atom: Epot =1834.546eV Ekin = 746.029eV (T=1442.884K) Etot = 2580.575eV
Energy per atom: Epot =1844.301eV Ekin = 738.668eV (T=1428.649K) Etot = 2582.970eV
Energy per atom: Epot =1836.705eV Ekin = 750.406eV (T=1451.351K) Etot = 2587.111eV
Energy per atom: Epot =1841.868eV Ekin = 747.493eV (T=1445.717K) Etot = 2589.362eV
Energy per atom: Epot =1848.663eV Ekin = 747.791eV (T=1446.293K) Etot = 2596.454eV
Energy per atom: Epot =1843.547eV Ekin = 751.811eV (T=1454.067K) Etot = 2595.358eV
Energy per atom: Epot =1856.589eV Ekin = 747.686eV (T=1446.090K) Etot = 2604.275eV
Energy per atom: Epot =1868.226eV Ekin = 731.977eV (T=1415.707K) Etot = 2600.202eV
Energy per atom: Epot =1865.448eV Ekin = 736.264eV (T=1423.999K) Etot = 2601.712eV
Energy per atom: Epot =1877.425eV Ekin = 733.419eV (T=1418.497K) Etot = 2610.844eV
Energy per atom: Epot =1875.556eV Ekin = 730.561eV (T=1412.968K) Etot = 2606.117eV
Energy per atom: Epot =1877.085eV Ekin = 737.512eV (T=1426.413K) Etot = 2614.598eV
Energy per atom: Epot =1884.608eV Ekin = 725.966eV (T=1404.081K) Etot = 2610.573eV
Energy per atom: Epot =1872.576eV Ekin = 744.536eV (T=1439.997K) Etot = 2617.112eV
Energy per atom: Epot =1886.497eV Ekin = 734.174eV (T=1419.957K) Etot = 2620.671eV
Energy per atom: Epot =1891.968eV Ekin = 743.176eV (T=1437.368K) Etot = 2635.145eV
Energy per atom: Epot =1899.550eV Ekin = 735.303eV (T=1422.140K) Etot = 2634.853eV
Energy per atom: Epot =1888.664eV Ekin = 748.406eV (T=1447.483K) Etot = 2637.070eV
Energy per atom: Epot =1898.589eV Ekin = 743.448eV (T=1437.894K) Etot = 2642.037eV
Energy per atom: Epot =1905.101eV Ekin = 736.151eV (T=1423.780K) Etot = 2641.251eV
Energy per atom: Epot =1897.729eV Ekin = 749.566eV (T=1449.726K) Etot = 2647.295eV
Energy per atom: Epot =1912.900eV Ekin = 740.437eV (T=1432.070K) Etot = 2653.337eV
Energy per atom: Epot =1922.873eV Ekin = 734.106eV (T=1419.824K) Etot = 2656.979eV
Energy per atom: Epot =1924.181eV Ekin = 736.443eV (T=1424.346K) Etot = 2660.625eV
Energy per atom: Epot =1917.984eV Ekin = 747.873eV (T=1446.451K) Etot = 2665.857eV
Energy per atom: Epot =1921.152eV Ekin = 755.712eV (T=1461.613K) Etot = 2676.864eV
Energy per atom: Epot =1917.868eV Ekin = 757.780eV (T=1465.613K) Etot = 2675.648eV
Energy per atom: Epot =1927.606eV Ekin = 755.613eV (T=1461.421K) Etot = 2683.218eV
Energy per atom: Epot =1932.034eV Ekin = 758.874eV (T=1467.729K) Etot = 2690.909eV
Energy per atom: Epot =1933.650eV Ekin = 763.192eV (T=1476.079K) Etot = 2696.841eV
Energy per atom: Epot =1944.037eV Ekin = 753.795eV (T=1457.906K) Etot = 2697.833eV
Energy per atom: Epot =1937.597eV Ekin = 766.963eV (T=1483.372K) Etot = 2704.560eV
Energy per atom: Epot =1937.261eV Ekin = 765.615eV (T=1480.767K) Etot = 2702.876eV
Energy per atom: Epot =1937.212eV Ekin = 769.363eV (T=1488.016K) Etot = 2706.576eV
Energy per atom: Epot =1962.150eV Ekin = 755.847eV (T=1461.874K) Etot = 2717.997eV
Energy per atom: Epot =1959.176eV Ekin = 759.638eV (T=1469.205K) Etot = 2718.814eV
Energy per atom: Epot =1971.729eV Ekin = 750.221eV (T=1450.994K) Etot = 2721.950eV
Energy per atom: Epot =1978.494eV Ekin = 754.455eV (T=1459.182K) Etot = 2732.949eV
Energy per atom: Epot =1964.131eV Ekin = 770.055eV (T=1489.353K) Etot = 2734.186eV
Energy per atom: Epot =1967.850eV Ekin = 767.894eV (T=1485.174K) Etot = 2735.744eV
Energy per atom: Epot =1984.437eV Ekin = 760.934eV (T=1471.713K) Etot = 2745.372eV
Energy per atom: Epot =1998.026eV Ekin = 753.121eV (T=1456.601K) Etot = 2751.147eV
Energy per atom: Epot =1987.299eV Ekin = 762.359eV (T=1474.469K) Etot = 2749.658eV
Energy per atom: Epot =1993.802eV Ekin = 772.752eV (T=1494.569K) Etot = 2766.553eV
Energy per atom: Epot =2012.373eV Ekin = 760.610eV (T=1471.085K) Etot = 2772.982eV
Energy per atom: Epot =2005.164eV Ekin = 765.318eV (T=1480.191K) Etot = 2770.482eV
Energy per atom: Epot =1994.051eV Ekin = 768.331eV (T=1486.020K) Etot = 2762.382eV
Energy per atom: Epot =2004.475eV Ekin = 756.761eV (T=1463.642K) Etot = 2761.237eV
Energy per atom: Epot =1986.739eV Ekin = 770.614eV (T=1490.434K) Etot = 2757.353eV
Energy per atom: Epot =1987.064eV Ekin = 767.358eV (T=1484.137K) Etot = 2754.422eV
Energy per atom: Epot =1979.511eV Ekin = 773.155eV (T=1495.350K) Etot = 2752.666eV
Energy per atom: Epot =1980.698eV Ekin = 778.310eV (T=1505.318K) Etot = 2759.007eV
Energy per atom: Epot =1977.633eV Ekin = 777.389eV (T=1503.539K) Etot = 2755.022eV
Energy per atom: Epot =1976.971eV Ekin = 770.445eV (T=1490.108K) Etot = 2747.416eV
Energy per atom: Epot =1989.532eV Ekin = 766.280eV (T=1482.053K) Etot = 2755.812eV
Energy per atom: Epot =1969.363eV Ekin = 782.583eV (T=1513.584K) Etot = 2751.946eV
Energy per atom: Epot =1983.265eV Ekin = 766.901eV (T=1483.254K) Etot = 2750.166eV
Energy per atom: Epot =1998.345eV Ekin = 755.636eV (T=1461.466K) Etot = 2753.981eV
Energy per atom: Epot =1990.847eV Ekin = 766.862eV (T=1483.178K) Etot = 2757.709eV
Energy per atom: Epot =1992.031eV Ekin = 775.664eV (T=1500.201K) Etot = 2767.695eV
Energy per atom: Epot =1989.817eV Ekin = 773.800eV (T=1496.597K) Etot = 2763.618eV
Energy per atom: Epot =2008.932eV Ekin = 755.740eV (T=1461.666K) Etot = 2764.672eV
Energy per atom: Epot =2022.830eV Ekin = 737.352eV (T=1426.104K) Etot = 2760.183eV
Energy per atom: Epot =2008.282eV Ekin = 763.933eV (T=1477.513K) Etot = 2772.215eV
Energy per atom: Epot =2014.928eV Ekin = 753.906eV (T=1458.119K) Etot = 2768.833eV
Energy per atom: Epot =2007.366eV Ekin = 769.034eV (T=1487.379K) Etot = 2776.400eV
Energy per atom: Epot =2000.610eV Ekin = 777.075eV (T=1502.930K) Etot = 2777.685eV
Energy per atom: Epot =1996.002eV Ekin = 781.488eV (T=1511.467K) Etot = 2777.490eV
Energy per atom: Epot =1994.812eV Ekin = 776.918eV (T=1502.627K) Etot = 2771.731eV
Energy per atom: Epot =2004.624eV Ekin = 763.493eV (T=1476.661K) Etot = 2768.117eV
Energy per atom: Epot =2008.430eV Ekin = 761.423eV (T=1472.659K) Etot = 2769.854eV
Energy per atom: Epot =2000.048eV Ekin = 778.256eV (T=1505.216K) Etot = 2778.305eV
Energy per atom: Epot =2001.928eV Ekin = 770.014eV (T=1489.274K) Etot = 2771.942eV
Energy per atom: Epot =2003.301eV Ekin = 764.908eV (T=1479.399K) Etot = 2768.209eV
Energy per atom: Epot =1993.946eV Ekin = 769.343eV (T=1487.977K) Etot = 2763.289eV
Energy per atom: Epot =1996.352eV Ekin = 771.600eV (T=1492.342K) Etot = 2767.952eV
Energy per atom: Epot =1986.728eV Ekin = 782.471eV (T=1513.366K) Etot = 2769.198eV
Energy per atom: Epot =1986.188eV Ekin = 782.920eV (T=1514.235K) Etot = 2769.107eV
Energy per atom: Epot =1991.066eV Ekin = 780.193eV (T=1508.961K) Etot = 2771.259eV
Energy per atom: Epot =1999.196eV Ekin = 774.999eV (T=1498.915K) Etot = 2774.195eV
Energy per atom: Epot =1991.880eV Ekin = 784.216eV (T=1516.742K) Etot = 2776.096eV
Energy per atom: Epot =1995.820eV Ekin = 774.506eV (T=1497.962K) Etot = 2770.325eV
Energy per atom: Epot =1992.932eV Ekin = 763.835eV (T=1477.323K) Etot = 2756.767eV
Energy per atom: Epot =1989.726eV Ekin = 761.565eV (T=1472.932K) Etot = 2751.291eV
Energy per atom: Epot =1990.505eV Ekin = 761.960eV (T=1473.696K) Etot = 2752.465eV
Energy per atom: Epot =2000.201eV Ekin = 761.131eV (T=1472.094K) Etot = 2761.332eV
Energy per atom: Epot =1997.915eV Ekin = 767.674eV (T=1484.748K) Etot = 2765.589eV
Energy per atom: Epot =1989.931eV Ekin = 766.353eV (T=1482.193K) Etot = 2756.283eV
Energy per atom: Epot =1989.930eV Ekin = 760.522eV (T=1470.916K) Etot = 2750.452eV
Energy per atom: Epot =1978.694eV Ekin = 770.760eV (T=1490.717K) Etot = 2749.454eV
Energy per atom: Epot =1976.283eV Ekin = 768.572eV (T=1486.485K) Etot = 2744.854eV
Energy per atom: Epot =1973.535eV Ekin = 763.981eV (T=1477.606K) Etot = 2737.516eV
Energy per atom: Epot =1974.517eV Ekin = 762.755eV (T=1475.234K) Etot = 2737.272eV
Energy per atom: Epot =1966.245eV Ekin = 773.236eV (T=1495.506K) Etot = 2739.482eV
Energy per atom: Epot =1968.523eV Ekin = 766.659eV (T=1482.784K) Etot = 2735.181eV
Energy per atom: Epot =1971.274eV Ekin = 764.066eV (T=1477.771K) Etot = 2735.340eV
Energy per atom: Epot =1977.214eV Ekin = 753.689eV (T=1457.700K) Etot = 2730.903eV
Energy per atom: Epot =1973.680eV Ekin = 760.457eV (T=1470.789K) Etot = 2734.137eV
Energy per atom: Epot =1975.782eV Ekin = 760.269eV (T=1470.426K) Etot = 2736.050eV
Energy per atom: Epot =1971.286eV Ekin = 769.448eV (T=1488.179K) Etot = 2740.734eV
Energy per atom: Epot =1979.965eV Ekin = 763.872eV (T=1477.395K) Etot = 2743.837eV
Energy per atom: Epot =1978.278eV Ekin = 765.464eV (T=1480.474K) Etot = 2743.742eV
Energy per atom: Epot =2001.038eV Ekin = 745.703eV (T=1442.254K) Etot = 2746.740eV
Energy per atom: Epot =1978.346eV Ekin = 761.544eV (T=1472.893K) Etot = 2739.890eV
Energy per atom: Epot =1975.693eV Ekin = 772.755eV (T=1494.576K) Etot = 2748.448eV
Energy per atom: Epot =1979.589eV Ekin = 768.773eV (T=1486.873K) Etot = 2748.361eV
Energy per atom: Epot =1991.103eV Ekin = 752.266eV (T=1454.949K) Etot = 2743.369eV
Energy per atom: Epot =1995.970eV Ekin = 751.774eV (T=1453.996K) Etot = 2747.744eV
Energy per atom: Epot =1989.678eV Ekin = 756.761eV (T=1463.642K) Etot = 2746.439eV
Energy per atom: Epot =1994.004eV Ekin = 743.286eV (T=1437.581K) Etot = 2737.290eV
Energy per atom: Epot =1989.764eV Ekin = 749.747eV (T=1450.075K) Etot = 2739.510eV
Energy per atom: Epot =1981.304eV Ekin = 756.497eV (T=1463.132K) Etot = 2737.802eV
Energy per atom: Epot =1978.634eV Ekin = 766.949eV (T=1483.346K) Etot = 2745.583eV
Energy per atom: Epot =1994.008eV Ekin = 756.688eV (T=1463.501K) Etot = 2750.696eV
Energy per atom: Epot =1988.387eV Ekin = 765.819eV (T=1481.160K) Etot = 2754.206eV
Energy per atom: Epot =1986.540eV Ekin = 764.855eV (T=1479.297K) Etot = 2751.395eV
Energy per atom: Epot =1978.068eV Ekin = 775.271eV (T=1499.441K) Etot = 2753.339eV
Energy per atom: Epot =1994.321eV Ekin = 758.100eV (T=1466.231K) Etot = 2752.420eV
Energy per atom: Epot =1980.630eV Ekin = 765.594eV (T=1480.725K) Etot = 2746.224eV
Energy per atom: Epot =1981.201eV Ekin = 769.753eV (T=1488.769K) Etot = 2750.953eV
Energy per atom: Epot =1991.726eV Ekin = 763.113eV (T=1475.928K) Etot = 2754.839eV
Energy per atom: Epot =1981.482eV Ekin = 774.230eV (T=1497.429K) Etot = 2755.712eV
Energy per atom: Epot =1982.761eV Ekin = 770.891eV (T=1490.971K) Etot = 2753.652eV
Energy per atom: Epot =1981.508eV Ekin = 766.960eV (T=1483.368K) Etot = 2748.468eV
Energy per atom: Epot =1986.226eV Ekin = 766.345eV (T=1482.178K) Etot = 2752.571eV
Energy per atom: Epot =1989.858eV Ekin = 763.011eV (T=1475.730K) Etot = 2752.869eV
Energy per atom: Epot =1987.789eV Ekin = 766.789eV (T=1483.037K) Etot = 2754.578eV
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] 10:12:26 43.457006 1.0818
BFGSLineSearch: 1[ 1] 10:12:26 42.347659 0.2273
BFGSLineSearch: 2[ 2] 10:12:26 42.108454 0.1349
BFGSLineSearch: 3[ 3] 10:12:26 41.964817 0.1138
BFGSLineSearch: 4[ 4] 10:12:26 41.924933 0.0683
BFGSLineSearch: 5[ 5] 10:12:26 41.915346 0.0225
BFGSLineSearch: 6[ 6] 10:12:26 41.914920 0.0059
BFGSLineSearch: 7[ 7] 10:12:26 41.914872 0.0023
BFGSLineSearch: 8[ 9] 10:12:26 41.914855 0.0023
BFGSLineSearch: 9[ 10] 10:12:26 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 16.285eV (T=1354.728K) Etot = 58.200eV
Energy per atom: Epot =50.557eV Ekin = 7.679eV (T=638.828K) Etot = 58.237eV
Energy per atom: Epot =51.711eV Ekin = 6.545eV (T=544.426K) Etot = 58.255eV
Energy per atom: Epot =52.026eV Ekin = 6.229eV (T=518.171K) Etot = 58.255eV
Energy per atom: Epot =51.907eV Ekin = 6.346eV (T=527.927K) Etot = 58.254eV
Energy per atom: Epot =51.543eV Ekin = 6.708eV (T=557.986K) Etot = 58.251eV
Energy per atom: Epot =50.607eV Ekin = 7.640eV (T=635.543K) Etot = 58.247eV
Energy per atom: Epot =50.120eV Ekin = 8.127eV (T=676.034K) Etot = 58.246eV
Energy per atom: Epot =50.410eV Ekin = 7.837eV (T=651.946K) Etot = 58.247eV
Energy per atom: Epot =50.592eV Ekin = 7.655eV (T=636.793K) Etot = 58.247eV
Energy per atom: Epot =50.975eV Ekin = 7.278eV (T=605.417K) Etot = 58.253eV
Energy per atom: Epot =50.978eV Ekin = 7.271eV (T=604.818K) Etot = 58.249eV
Energy per atom: Epot =51.830eV Ekin = 6.423eV (T=534.274K) Etot = 58.253eV
Energy per atom: Epot =50.476eV Ekin = 7.771eV (T=646.463K) Etot = 58.248eV
Energy per atom: Epot =50.793eV Ekin = 7.455eV (T=620.167K) Etot = 58.248eV
Energy per atom: Epot =49.964eV Ekin = 8.278eV (T=688.645K) Etot = 58.243eV
Energy per atom: Epot =50.871eV Ekin = 7.376eV (T=613.596K) Etot = 58.247eV
Energy per atom: Epot =51.383eV Ekin = 6.870eV (T=571.507K) Etot = 58.253eV
Energy per atom: Epot =50.273eV Ekin = 7.972eV (T=663.124K) Etot = 58.245eV
Energy per atom: Epot =50.542eV Ekin = 7.706eV (T=641.072K) Etot = 58.248eV
Energy per atom: Epot =49.887eV Ekin = 8.363eV (T=695.674K) Etot = 58.249eV
Energy per atom: Epot =49.643eV Ekin = 8.600eV (T=715.420K) Etot = 58.243eV
Energy per atom: Epot =51.369eV Ekin = 6.878eV (T=572.164K) Etot = 58.247eV
Energy per atom: Epot =50.537eV Ekin = 7.709eV (T=641.246K) Etot = 58.246eV
Energy per atom: Epot =51.597eV Ekin = 6.656eV (T=553.712K) Etot = 58.253eV
Energy per atom: Epot =49.501eV Ekin = 8.746eV (T=727.515K) Etot = 58.247eV
Energy per atom: Epot =50.871eV Ekin = 7.382eV (T=614.052K) Etot = 58.253eV
Energy per atom: Epot =51.517eV Ekin = 6.733eV (T=560.093K) Etot = 58.250eV
Energy per atom: Epot =51.266eV Ekin = 6.983eV (T=580.871K) Etot = 58.249eV
Energy per atom: Epot =50.558eV Ekin = 7.693eV (T=639.988K) Etot = 58.251eV
Energy per atom: Epot =50.566eV Ekin = 7.684eV (T=639.181K) Etot = 58.250eV
Energy per atom: Epot =50.652eV Ekin = 7.594eV (T=631.706K) Etot = 58.246eV
Energy per atom: Epot =50.382eV Ekin = 7.871eV (T=654.761K) Etot = 58.253eV
Energy per atom: Epot =50.251eV Ekin = 8.003eV (T=665.737K) Etot = 58.254eV
Energy per atom: Epot =51.146eV Ekin = 7.108eV (T=591.292K) Etot = 58.254eV
Energy per atom: Epot =50.669eV Ekin = 7.585eV (T=630.935K) Etot = 58.253eV
Energy per atom: Epot =51.182eV Ekin = 7.077eV (T=588.684K) Etot = 58.259eV
Energy per atom: Epot =50.419eV Ekin = 7.832eV (T=651.524K) Etot = 58.251eV
Energy per atom: Epot =51.316eV Ekin = 6.937eV (T=577.078K) Etot = 58.253eV
Energy per atom: Epot =51.047eV Ekin = 7.207eV (T=599.523K) Etot = 58.254eV
Energy per atom: Epot =51.115eV Ekin = 7.134eV (T=593.455K) Etot = 58.250eV
Energy per atom: Epot =50.858eV Ekin = 7.387eV (T=614.525K) Etot = 58.245eV
Energy per atom: Epot =52.104eV Ekin = 6.150eV (T=511.595K) Etot = 58.254eV
Energy per atom: Epot =51.204eV Ekin = 7.047eV (T=586.256K) Etot = 58.251eV
Energy per atom: Epot =50.304eV Ekin = 7.941eV (T=660.592K) Etot = 58.246eV
Energy per atom: Epot =50.497eV Ekin = 7.749eV (T=644.574K) Etot = 58.246eV
Energy per atom: Epot =50.421eV Ekin = 7.825eV (T=650.909K) Etot = 58.245eV
Energy per atom: Epot =51.788eV Ekin = 6.469eV (T=538.169K) Etot = 58.257eV
Energy per atom: Epot =50.819eV Ekin = 7.429eV (T=618.031K) Etot = 58.248eV
Energy per atom: Epot =50.652eV Ekin = 7.595eV (T=631.774K) Etot = 58.247eV
Energy per atom: Epot =49.966eV Ekin = 8.277eV (T=688.504K) Etot = 58.242eV
Energy per atom: Epot =50.230eV Ekin = 8.008eV (T=666.192K) Etot = 58.239eV
Energy per atom: Epot =50.928eV Ekin = 7.320eV (T=608.900K) Etot = 58.247eV
Energy per atom: Epot =51.586eV Ekin = 6.668eV (T=554.667K) Etot = 58.254eV
Energy per atom: Epot =51.062eV Ekin = 7.191eV (T=598.153K) Etot = 58.252eV
Energy per atom: Epot =50.272eV Ekin = 7.980eV (T=663.793K) Etot = 58.251eV
Energy per atom: Epot =51.204eV Ekin = 7.050eV (T=586.429K) Etot = 58.253eV
Energy per atom: Epot =50.966eV Ekin = 7.287eV (T=606.209K) Etot = 58.253eV
Energy per atom: Epot =51.203eV Ekin = 7.055eV (T=586.907K) Etot = 58.258eV
Energy per atom: Epot =51.540eV Ekin = 6.712eV (T=558.387K) Etot = 58.253eV
Energy per atom: Epot =51.271eV Ekin = 6.984eV (T=580.953K) Etot = 58.254eV
Energy per atom: Epot =50.411eV Ekin = 7.838eV (T=652.011K) Etot = 58.249eV
Energy per atom: Epot =51.006eV Ekin = 7.239eV (T=602.190K) Etot = 58.245eV
Energy per atom: Epot =51.420eV Ekin = 6.823eV (T=567.601K) Etot = 58.243eV
Energy per atom: Epot =50.816eV Ekin = 7.432eV (T=618.215K) Etot = 58.248eV
Energy per atom: Epot =51.479eV Ekin = 6.776eV (T=563.712K) Etot = 58.256eV
Energy per atom: Epot =51.303eV Ekin = 6.949eV (T=578.083K) Etot = 58.252eV
Energy per atom: Epot =51.619eV Ekin = 6.634eV (T=551.836K) Etot = 58.253eV
Energy per atom: Epot =52.153eV Ekin = 6.102eV (T=507.571K) Etot = 58.254eV
Energy per atom: Epot =51.124eV Ekin = 7.125eV (T=592.734K) Etot = 58.250eV
Energy per atom: Epot =50.775eV Ekin = 7.473eV (T=621.680K) Etot = 58.248eV
Energy per atom: Epot =50.862eV Ekin = 7.382eV (T=614.082K) Etot = 58.244eV
Energy per atom: Epot =51.729eV Ekin = 6.521eV (T=542.426K) Etot = 58.250eV
Energy per atom: Epot =51.474eV Ekin = 6.779eV (T=563.957K) Etot = 58.254eV
Energy per atom: Epot =50.946eV Ekin = 7.305eV (T=607.687K) Etot = 58.251eV
Energy per atom: Epot =50.704eV Ekin = 7.541eV (T=627.340K) Etot = 58.246eV
Energy per atom: Epot =51.308eV Ekin = 6.943eV (T=577.582K) Etot = 58.251eV
Energy per atom: Epot =50.678eV Ekin = 7.571eV (T=629.835K) Etot = 58.250eV
Energy per atom: Epot =50.169eV Ekin = 8.076eV (T=671.832K) Etot = 58.245eV
Energy per atom: Epot =50.585eV Ekin = 7.661eV (T=637.254K) Etot = 58.245eV
Energy per atom: Epot =52.323eV Ekin = 5.932eV (T=493.460K) Etot = 58.255eV
Energy per atom: Epot =50.118eV Ekin = 8.129eV (T=676.233K) Etot = 58.247eV
Energy per atom: Epot =50.185eV Ekin = 8.062eV (T=670.616K) Etot = 58.247eV
Energy per atom: Epot =51.730eV Ekin = 6.522eV (T=542.510K) Etot = 58.251eV
Energy per atom: Epot =51.537eV Ekin = 6.718eV (T=558.827K) Etot = 58.255eV
Energy per atom: Epot =50.996eV Ekin = 7.256eV (T=603.639K) Etot = 58.252eV
Energy per atom: Epot =50.553eV Ekin = 7.698eV (T=640.394K) Etot = 58.251eV
Energy per atom: Epot =50.708eV Ekin = 7.543eV (T=627.442K) Etot = 58.251eV
Energy per atom: Epot =50.085eV Ekin = 8.162eV (T=678.976K) Etot = 58.247eV
Energy per atom: Epot =50.983eV Ekin = 7.269eV (T=604.716K) Etot = 58.252eV
Energy per atom: Epot =49.846eV Ekin = 8.396eV (T=698.465K) Etot = 58.243eV
Energy per atom: Epot =50.120eV Ekin = 8.121eV (T=675.538K) Etot = 58.241eV
Energy per atom: Epot =50.170eV Ekin = 8.073eV (T=671.554K) Etot = 58.243eV
Energy per atom: Epot =50.812eV Ekin = 7.436eV (T=618.569K) Etot = 58.248eV
Energy per atom: Epot =50.623eV Ekin = 7.618eV (T=633.696K) Etot = 58.241eV
Energy per atom: Epot =50.702eV Ekin = 7.545eV (T=627.611K) Etot = 58.246eV
Energy per atom: Epot =50.704eV Ekin = 7.547eV (T=627.818K) Etot = 58.251eV
Energy per atom: Epot =50.934eV Ekin = 7.317eV (T=608.648K) Etot = 58.250eV
Energy per atom: Epot =50.618eV Ekin = 7.629eV (T=634.615K) Etot = 58.247eV
Energy per atom: Epot =51.197eV Ekin = 7.052eV (T=586.643K) Etot = 58.250eV
Energy per atom: Epot =51.424eV Ekin = 6.824eV (T=567.635K) Etot = 58.247eV
Energy per atom: Epot =51.126eV Ekin = 7.126eV (T=592.816K) Etot = 58.253eV
Energy per atom: Epot =50.996eV Ekin = 7.258eV (T=603.789K) Etot = 58.254eV
Energy per atom: Epot =50.923eV Ekin = 7.331eV (T=609.802K) Etot = 58.254eV
Energy per atom: Epot =51.195eV Ekin = 7.058eV (T=587.105K) Etot = 58.253eV
Energy per atom: Epot =51.523eV Ekin = 6.727eV (T=559.608K) Etot = 58.250eV
Energy per atom: Epot =51.268eV Ekin = 6.986eV (T=581.105K) Etot = 58.254eV
Energy per atom: Epot =51.402eV Ekin = 6.850eV (T=569.823K) Etot = 58.252eV
Energy per atom: Epot =51.808eV Ekin = 6.446eV (T=536.212K) Etot = 58.254eV
Energy per atom: Epot =51.029eV Ekin = 7.222eV (T=600.754K) Etot = 58.251eV
Energy per atom: Epot =50.463eV Ekin = 7.781eV (T=647.294K) Etot = 58.245eV
Energy per atom: Epot =51.346eV Ekin = 6.904eV (T=574.303K) Etot = 58.250eV
Energy per atom: Epot =51.129eV Ekin = 7.121eV (T=592.331K) Etot = 58.249eV
Energy per atom: Epot =51.293eV Ekin = 6.957eV (T=578.753K) Etot = 58.250eV
Energy per atom: Epot =50.863eV Ekin = 7.386eV (T=614.441K) Etot = 58.249eV
Energy per atom: Epot =50.864eV Ekin = 7.390eV (T=614.708K) Etot = 58.253eV
Energy per atom: Epot =50.098eV Ekin = 8.149eV (T=677.882K) Etot = 58.247eV
Energy per atom: Epot =50.378eV Ekin = 7.868eV (T=654.473K) Etot = 58.246eV
Energy per atom: Epot =51.194eV Ekin = 7.056eV (T=586.977K) Etot = 58.250eV
Energy per atom: Epot =51.070eV Ekin = 7.184eV (T=597.592K) Etot = 58.254eV
Energy per atom: Epot =49.947eV Ekin = 8.297eV (T=690.166K) Etot = 58.243eV
Energy per atom: Epot =50.267eV Ekin = 7.977eV (T=663.544K) Etot = 58.244eV
Energy per atom: Epot =50.214eV Ekin = 8.032eV (T=668.130K) Etot = 58.246eV
Energy per atom: Epot =50.808eV Ekin = 7.437eV (T=618.624K) Etot = 58.245eV
Energy per atom: Epot =50.069eV Ekin = 8.174eV (T=680.008K) Etot = 58.243eV
Energy per atom: Epot =51.542eV Ekin = 6.711eV (T=558.298K) Etot = 58.254eV
Energy per atom: Epot =50.910eV Ekin = 7.339eV (T=610.536K) Etot = 58.249eV
Energy per atom: Epot =51.315eV Ekin = 6.939eV (T=577.198K) Etot = 58.254eV
Energy per atom: Epot =49.492eV Ekin = 8.751eV (T=728.000K) Etot = 58.243eV
Energy per atom: Epot =50.413eV Ekin = 7.833eV (T=651.584K) Etot = 58.246eV
Energy per atom: Epot =50.627eV Ekin = 7.621eV (T=633.963K) Etot = 58.248eV
Energy per atom: Epot =51.158eV Ekin = 7.093eV (T=590.032K) Etot = 58.251eV
Energy per atom: Epot =51.065eV Ekin = 7.185eV (T=597.718K) Etot = 58.250eV
Energy per atom: Epot =50.739eV Ekin = 7.505eV (T=624.325K) Etot = 58.244eV
Energy per atom: Epot =50.000eV Ekin = 8.246eV (T=685.990K) Etot = 58.247eV
Energy per atom: Epot =50.865eV Ekin = 7.387eV (T=614.502K) Etot = 58.252eV
Energy per atom: Epot =50.910eV Ekin = 7.343eV (T=610.808K) Etot = 58.253eV
Energy per atom: Epot =51.376eV Ekin = 6.879eV (T=572.228K) Etot = 58.255eV
Energy per atom: Epot =50.652eV Ekin = 7.592eV (T=631.529K) Etot = 58.244eV
Energy per atom: Epot =50.237eV Ekin = 8.005eV (T=665.937K) Etot = 58.242eV
Energy per atom: Epot =51.310eV Ekin = 6.946eV (T=577.843K) Etot = 58.257eV
Energy per atom: Epot =50.642eV Ekin = 7.610eV (T=633.084K) Etot = 58.252eV
Energy per atom: Epot =49.859eV Ekin = 8.388eV (T=697.733K) Etot = 58.247eV
Energy per atom: Epot =50.745eV Ekin = 7.506eV (T=624.395K) Etot = 58.251eV
Energy per atom: Epot =51.078eV Ekin = 7.168eV (T=596.282K) Etot = 58.246eV
Energy per atom: Epot =51.008eV Ekin = 7.237eV (T=602.014K) Etot = 58.244eV
Energy per atom: Epot =50.585eV Ekin = 7.666eV (T=637.744K) Etot = 58.252eV
Energy per atom: Epot =49.670eV Ekin = 8.574eV (T=713.241K) Etot = 58.244eV
Energy per atom: Epot =51.136eV Ekin = 7.111eV (T=591.499K) Etot = 58.246eV
Energy per atom: Epot =50.088eV Ekin = 8.152eV (T=678.139K) Etot = 58.240eV
Energy per atom: Epot =50.602eV Ekin = 7.649eV (T=636.257K) Etot = 58.251eV
Energy per atom: Epot =51.493eV Ekin = 6.763eV (T=562.615K) Etot = 58.256eV
Energy per atom: Epot =50.663eV Ekin = 7.588eV (T=631.220K) Etot = 58.251eV
Energy per atom: Epot =50.484eV Ekin = 7.767eV (T=646.071K) Etot = 58.250eV
Energy per atom: Epot =50.897eV Ekin = 7.354eV (T=611.772K) Etot = 58.251eV
Energy per atom: Epot =50.721eV Ekin = 7.533eV (T=626.606K) Etot = 58.253eV
Energy per atom: Epot =50.749eV Ekin = 7.502eV (T=624.040K) Etot = 58.250eV
Energy per atom: Epot =50.837eV Ekin = 7.411eV (T=616.531K) Etot = 58.248eV
Energy per atom: Epot =50.622eV Ekin = 7.628eV (T=634.557K) Etot = 58.250eV
Energy per atom: Epot =50.560eV Ekin = 7.693eV (T=639.953K) Etot = 58.253eV
Energy per atom: Epot =49.799eV Ekin = 8.446eV (T=702.604K) Etot = 58.246eV
Energy per atom: Epot =49.640eV Ekin = 8.603eV (T=715.688K) Etot = 58.243eV
Energy per atom: Epot =51.590eV Ekin = 6.662eV (T=554.159K) Etot = 58.252eV
Energy per atom: Epot =50.597eV Ekin = 7.651eV (T=636.427K) Etot = 58.247eV
Energy per atom: Epot =50.088eV Ekin = 8.162eV (T=678.945K) Etot = 58.249eV
Energy per atom: Epot =49.753eV Ekin = 8.493eV (T=706.485K) Etot = 58.246eV
Energy per atom: Epot =51.125eV Ekin = 7.128eV (T=592.978K) Etot = 58.253eV
Energy per atom: Epot =50.210eV Ekin = 8.040eV (T=668.796K) Etot = 58.249eV
Energy per atom: Epot =51.080eV Ekin = 7.169eV (T=596.383K) Etot = 58.250eV
Energy per atom: Epot =51.046eV Ekin = 7.202eV (T=599.111K) Etot = 58.248eV
Energy per atom: Epot =50.449eV Ekin = 7.800eV (T=648.892K) Etot = 58.249eV
Energy per atom: Epot =51.051eV Ekin = 7.201eV (T=599.057K) Etot = 58.252eV
Energy per atom: Epot =50.784eV Ekin = 7.466eV (T=621.106K) Etot = 58.251eV
Energy per atom: Epot =49.506eV Ekin = 8.727eV (T=726.006K) Etot = 58.233eV
Energy per atom: Epot =49.453eV Ekin = 8.787eV (T=730.954K) Etot = 58.240eV
Energy per atom: Epot =50.536eV Ekin = 7.712eV (T=641.563K) Etot = 58.249eV
Energy per atom: Epot =50.507eV Ekin = 7.744eV (T=644.163K) Etot = 58.251eV
Energy per atom: Epot =50.663eV Ekin = 7.587eV (T=631.132K) Etot = 58.250eV
Energy per atom: Epot =50.939eV Ekin = 7.310eV (T=608.110K) Etot = 58.249eV
Energy per atom: Epot =50.454eV Ekin = 7.796eV (T=648.535K) Etot = 58.250eV
Energy per atom: Epot =49.567eV Ekin = 8.678eV (T=721.901K) Etot = 58.245eV
Energy per atom: Epot =50.129eV Ekin = 8.120eV (T=675.440K) Etot = 58.249eV
Energy per atom: Epot =50.344eV Ekin = 7.907eV (T=657.796K) Etot = 58.251eV
Energy per atom: Epot =51.163eV Ekin = 7.088eV (T=589.604K) Etot = 58.251eV
Energy per atom: Epot =50.972eV Ekin = 7.277eV (T=605.346K) Etot = 58.249eV
Energy per atom: Epot =51.041eV Ekin = 7.207eV (T=599.522K) Etot = 58.248eV
Energy per atom: Epot =50.525eV Ekin = 7.719eV (T=642.109K) Etot = 58.244eV
Energy per atom: Epot =50.989eV Ekin = 7.257eV (T=603.724K) Etot = 58.246eV
Energy per atom: Epot =51.477eV Ekin = 6.774eV (T=563.510K) Etot = 58.251eV
Energy per atom: Epot =51.328eV Ekin = 6.921eV (T=575.772K) Etot = 58.250eV
Energy per atom: Epot =50.851eV Ekin = 7.401eV (T=615.679K) Etot = 58.252eV
Energy per atom: Epot =50.772eV Ekin = 7.483eV (T=622.525K) Etot = 58.256eV
Energy per atom: Epot =50.322eV Ekin = 7.926eV (T=659.314K) Etot = 58.248eV
Energy per atom: Epot =50.132eV Ekin = 8.114eV (T=675.011K) Etot = 58.246eV
Energy per atom: Epot =49.836eV Ekin = 8.411eV (T=699.651K) Etot = 58.247eV
Energy per atom: Epot =49.940eV Ekin = 8.306eV (T=690.960K) Etot = 58.246eV
Energy per atom: Epot =50.535eV Ekin = 7.712eV (T=641.520K) Etot = 58.247eV
Energy per atom: Epot =50.874eV Ekin = 7.372eV (T=613.283K) Etot = 58.247eV
Energy per atom: Epot =50.523eV Ekin = 7.725eV (T=642.598K) Etot = 58.248eV
Energy per atom: Epot =50.388eV Ekin = 7.858eV (T=653.650K) Etot = 58.245eV
Energy per atom: Epot =51.024eV Ekin = 7.227eV (T=601.157K) Etot = 58.250eV
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?