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()
/builds/ase/ase/examples/03-tutorials/md.py:98: DeprecationWarning: Use thermalize_momenta
MaxwellBoltzmannDistribution(atoms, temperature_K=300)
running a NVE simulation of fcc Cu
Energy per atom: Epot =-2.405eV Ekin = 155.997eV (T=301.711K) Etot = 153.592eV
Energy per atom: Epot =117.849eV Ekin = 36.522eV (T=70.637K) Etot = 154.371eV
Energy per atom: Epot =78.586eV Ekin = 75.649eV (T=146.311K) Etot = 154.235eV
Energy per atom: Epot =71.419eV Ekin = 82.675eV (T=159.901K) Etot = 154.095eV
Energy per atom: Epot =70.138eV Ekin = 83.898eV (T=162.266K) Etot = 154.037eV
Energy per atom: Epot =80.028eV Ekin = 74.158eV (T=143.428K) Etot = 154.185eV
Energy per atom: Epot =78.287eV Ekin = 75.898eV (T=146.794K) Etot = 154.185eV
Energy per atom: Epot =75.359eV Ekin = 78.753eV (T=152.315K) Etot = 154.112eV
Energy per atom: Epot =72.607eV Ekin = 81.494eV (T=157.616K) Etot = 154.100eV
Energy per atom: Epot =78.260eV Ekin = 75.908eV (T=146.813K) Etot = 154.168eV
Energy per atom: Epot =76.560eV Ekin = 77.584eV (T=150.054K) Etot = 154.144eV
Energy per atom: Epot =74.600eV Ekin = 79.524eV (T=153.806K) Etot = 154.124eV
Energy per atom: Epot =77.508eV Ekin = 76.640eV (T=148.227K) Etot = 154.147eV
Energy per atom: Epot =75.473eV Ekin = 78.660eV (T=152.134K) Etot = 154.133eV
Energy per atom: Epot =75.849eV Ekin = 78.287eV (T=151.413K) Etot = 154.135eV
Energy per atom: Epot =75.273eV Ekin = 78.874eV (T=152.549K) Etot = 154.147eV
Energy per atom: Epot =76.139eV Ekin = 78.000eV (T=150.858K) Etot = 154.138eV
Energy per atom: Epot =77.511eV Ekin = 76.620eV (T=148.191K) Etot = 154.132eV
Energy per atom: Epot =73.170eV Ekin = 80.957eV (T=156.579K) Etot = 154.128eV
Energy per atom: Epot =76.166eV Ekin = 77.970eV (T=150.802K) Etot = 154.136eV
Energy per atom: Epot =79.282eV Ekin = 74.871eV (T=144.807K) Etot = 154.153eV
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()
/home/ase/.local/lib/python3.13/site-packages/ase/md/langevin.py:102: 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 =540.816eV Ekin = 0.000eV (T=0.000K) Etot = 540.816eV
Energy per atom: Epot =600.029eV Ekin = 80.740eV (T=156.158K) Etot = 680.769eV
Energy per atom: Epot =670.954eV Ekin = 139.408eV (T=269.627K) Etot = 810.361eV
Energy per atom: Epot =728.898eV Ekin = 196.851eV (T=380.726K) Etot = 925.748eV
Energy per atom: Epot =777.400eV Ekin = 254.754eV (T=492.717K) Etot = 1032.154eV
Energy per atom: Epot =833.992eV Ekin = 295.082eV (T=570.714K) Etot = 1129.074eV
Energy per atom: Epot =881.924eV Ekin = 339.427eV (T=656.482K) Etot = 1221.351eV
Energy per atom: Epot =926.617eV Ekin = 377.545eV (T=730.204K) Etot = 1304.162eV
Energy per atom: Epot =964.253eV Ekin = 415.048eV (T=802.740K) Etot = 1379.302eV
Energy per atom: Epot =997.783eV Ekin = 446.135eV (T=862.864K) Etot = 1443.918eV
Energy per atom: Epot =1036.714eV Ekin = 463.249eV (T=895.964K) Etot = 1499.962eV
Energy per atom: Epot =1064.941eV Ekin = 482.117eV (T=932.455K) Etot = 1547.058eV
Energy per atom: Epot =1095.130eV Ekin = 505.841eV (T=978.340K) Etot = 1600.971eV
Energy per atom: Epot =1140.331eV Ekin = 511.181eV (T=988.669K) Etot = 1651.512eV
Energy per atom: Epot =1160.585eV Ekin = 540.505eV (T=1045.385K) Etot = 1701.090eV
Energy per atom: Epot =1187.078eV Ekin = 555.272eV (T=1073.945K) Etot = 1742.351eV
Energy per atom: Epot =1216.913eV Ekin = 569.596eV (T=1101.648K) Etot = 1786.509eV
Energy per atom: Epot =1238.768eV Ekin = 591.691eV (T=1144.383K) Etot = 1830.459eV
Energy per atom: Epot =1276.822eV Ekin = 590.860eV (T=1142.775K) Etot = 1867.682eV
Energy per atom: Epot =1296.175eV Ekin = 600.154eV (T=1160.751K) Etot = 1896.329eV
Energy per atom: Epot =1324.978eV Ekin = 613.763eV (T=1187.070K) Etot = 1938.740eV
Energy per atom: Epot =1344.561eV Ekin = 627.462eV (T=1213.566K) Etot = 1972.023eV
Energy per atom: Epot =1359.425eV Ekin = 640.140eV (T=1238.086K) Etot = 1999.564eV
Energy per atom: Epot =1399.906eV Ekin = 635.830eV (T=1229.751K) Etot = 2035.736eV
Energy per atom: Epot =1399.596eV Ekin = 671.936eV (T=1299.582K) Etot = 2071.531eV
Energy per atom: Epot =1423.234eV Ekin = 668.482eV (T=1292.902K) Etot = 2091.716eV
Energy per atom: Epot =1435.677eV Ekin = 673.163eV (T=1301.956K) Etot = 2108.840eV
Energy per atom: Epot =1453.142eV Ekin = 662.513eV (T=1281.358K) Etot = 2115.655eV
Energy per atom: Epot =1461.109eV Ekin = 672.313eV (T=1300.312K) Etot = 2133.422eV
Energy per atom: Epot =1472.296eV Ekin = 672.708eV (T=1301.076K) Etot = 2145.004eV
Energy per atom: Epot =1486.602eV Ekin = 676.455eV (T=1308.322K) Etot = 2163.057eV
Energy per atom: Epot =1493.073eV Ekin = 683.986eV (T=1322.888K) Etot = 2177.059eV
Energy per atom: Epot =1509.245eV Ekin = 680.954eV (T=1317.023K) Etot = 2190.199eV
Energy per atom: Epot =1525.203eV Ekin = 684.370eV (T=1323.632K) Etot = 2209.574eV
Energy per atom: Epot =1519.078eV Ekin = 691.607eV (T=1337.627K) Etot = 2210.684eV
Energy per atom: Epot =1516.504eV Ekin = 697.736eV (T=1349.483K) Etot = 2214.241eV
Energy per atom: Epot =1535.801eV Ekin = 699.131eV (T=1352.180K) Etot = 2234.931eV
Energy per atom: Epot =1552.228eV Ekin = 697.065eV (T=1348.185K) Etot = 2249.294eV
Energy per atom: Epot =1566.885eV Ekin = 704.694eV (T=1362.939K) Etot = 2271.579eV
Energy per atom: Epot =1570.116eV Ekin = 714.645eV (T=1382.186K) Etot = 2284.761eV
Energy per atom: Epot =1575.746eV Ekin = 713.337eV (T=1379.657K) Etot = 2289.084eV
Energy per atom: Epot =1597.996eV Ekin = 707.814eV (T=1368.973K) Etot = 2305.810eV
Energy per atom: Epot =1599.926eV Ekin = 714.188eV (T=1381.302K) Etot = 2314.114eV
Energy per atom: Epot =1617.680eV Ekin = 708.909eV (T=1371.091K) Etot = 2326.588eV
Energy per atom: Epot =1624.281eV Ekin = 705.284eV (T=1364.082K) Etot = 2329.565eV
Energy per atom: Epot =1625.069eV Ekin = 707.955eV (T=1369.247K) Etot = 2333.024eV
Energy per atom: Epot =1635.045eV Ekin = 713.437eV (T=1379.849K) Etot = 2348.482eV
Energy per atom: Epot =1645.885eV Ekin = 715.434eV (T=1383.712K) Etot = 2361.319eV
Energy per atom: Epot =1662.038eV Ekin = 719.220eV (T=1391.034K) Etot = 2381.258eV
Energy per atom: Epot =1671.331eV Ekin = 711.695eV (T=1376.479K) Etot = 2383.026eV
Energy per atom: Epot =1670.241eV Ekin = 718.591eV (T=1389.817K) Etot = 2388.831eV
Energy per atom: Epot =1665.326eV Ekin = 727.665eV (T=1407.368K) Etot = 2392.992eV
Energy per atom: Epot =1690.912eV Ekin = 715.237eV (T=1383.330K) Etot = 2406.149eV
Energy per atom: Epot =1675.807eV Ekin = 735.642eV (T=1422.796K) Etot = 2411.449eV
Energy per atom: Epot =1709.021eV Ekin = 711.385eV (T=1375.881K) Etot = 2420.406eV
Energy per atom: Epot =1702.848eV Ekin = 725.713eV (T=1403.593K) Etot = 2428.562eV
Energy per atom: Epot =1721.916eV Ekin = 717.005eV (T=1386.749K) Etot = 2438.920eV
Energy per atom: Epot =1726.413eV Ekin = 719.669eV (T=1391.903K) Etot = 2446.082eV
Energy per atom: Epot =1735.688eV Ekin = 708.447eV (T=1370.199K) Etot = 2444.135eV
Energy per atom: Epot =1730.322eV Ekin = 724.620eV (T=1401.479K) Etot = 2454.942eV
Energy per atom: Epot =1723.939eV Ekin = 736.310eV (T=1424.087K) Etot = 2460.248eV
Energy per atom: Epot =1739.118eV Ekin = 728.218eV (T=1408.436K) Etot = 2467.336eV
Energy per atom: Epot =1765.249eV Ekin = 704.381eV (T=1362.335K) Etot = 2469.630eV
Energy per atom: Epot =1742.577eV Ekin = 725.619eV (T=1403.410K) Etot = 2468.196eV
Energy per atom: Epot =1763.176eV Ekin = 720.677eV (T=1393.853K) Etot = 2483.854eV
Energy per atom: Epot =1776.941eV Ekin = 719.695eV (T=1391.952K) Etot = 2496.636eV
Energy per atom: Epot =1785.343eV Ekin = 721.405eV (T=1395.260K) Etot = 2506.748eV
Energy per atom: Epot =1782.540eV Ekin = 733.416eV (T=1418.491K) Etot = 2515.956eV
Energy per atom: Epot =1801.899eV Ekin = 716.571eV (T=1385.910K) Etot = 2518.470eV
Energy per atom: Epot =1790.905eV Ekin = 733.426eV (T=1418.511K) Etot = 2524.332eV
Energy per atom: Epot =1799.781eV Ekin = 740.276eV (T=1431.758K) Etot = 2540.057eV
Energy per atom: Epot =1814.540eV Ekin = 722.310eV (T=1397.010K) Etot = 2536.850eV
Energy per atom: Epot =1819.278eV Ekin = 739.234eV (T=1429.743K) Etot = 2558.512eV
Energy per atom: Epot =1825.117eV Ekin = 748.901eV (T=1448.440K) Etot = 2574.019eV
Energy per atom: Epot =1845.098eV Ekin = 731.037eV (T=1413.890K) Etot = 2576.135eV
Energy per atom: Epot =1840.395eV Ekin = 746.879eV (T=1444.529K) Etot = 2587.275eV
Energy per atom: Epot =1842.648eV Ekin = 752.921eV (T=1456.214K) Etot = 2595.568eV
Energy per atom: Epot =1850.766eV Ekin = 745.082eV (T=1441.054K) Etot = 2595.849eV
Energy per atom: Epot =1858.547eV Ekin = 740.476eV (T=1432.145K) Etot = 2599.023eV
Energy per atom: Epot =1856.232eV Ekin = 745.698eV (T=1442.246K) Etot = 2601.931eV
Energy per atom: Epot =1873.124eV Ekin = 734.302eV (T=1420.204K) Etot = 2607.426eV
Energy per atom: Epot =1878.958eV Ekin = 738.414eV (T=1428.157K) Etot = 2617.372eV
Energy per atom: Epot =1880.593eV Ekin = 746.670eV (T=1444.125K) Etot = 2627.263eV
Energy per atom: Epot =1898.996eV Ekin = 739.824eV (T=1430.885K) Etot = 2638.821eV
Energy per atom: Epot =1899.043eV Ekin = 745.310eV (T=1441.494K) Etot = 2644.353eV
Energy per atom: Epot =1898.401eV Ekin = 745.511eV (T=1441.884K) Etot = 2643.913eV
Energy per atom: Epot =1902.538eV Ekin = 750.413eV (T=1451.364K) Etot = 2652.951eV
Energy per atom: Epot =1911.350eV Ekin = 747.427eV (T=1445.590K) Etot = 2658.778eV
Energy per atom: Epot =1916.125eV Ekin = 739.768eV (T=1430.775K) Etot = 2655.893eV
Energy per atom: Epot =1924.475eV Ekin = 747.033eV (T=1444.827K) Etot = 2671.508eV
Energy per atom: Epot =1923.681eV Ekin = 747.638eV (T=1445.996K) Etot = 2671.319eV
Energy per atom: Epot =1935.318eV Ekin = 726.415eV (T=1404.950K) Etot = 2661.733eV
Energy per atom: Epot =1916.994eV Ekin = 751.797eV (T=1454.040K) Etot = 2668.791eV
Energy per atom: Epot =1925.445eV Ekin = 747.611eV (T=1445.944K) Etot = 2673.056eV
Energy per atom: Epot =1924.771eV Ekin = 751.217eV (T=1452.919K) Etot = 2675.988eV
Energy per atom: Epot =1922.896eV Ekin = 755.154eV (T=1460.533K) Etot = 2678.050eV
Energy per atom: Epot =1936.812eV Ekin = 747.654eV (T=1446.027K) Etot = 2684.466eV
Energy per atom: Epot =1939.333eV Ekin = 752.595eV (T=1455.584K) Etot = 2691.928eV
Energy per atom: Epot =1927.043eV Ekin = 767.438eV (T=1484.292K) Etot = 2694.481eV
Energy per atom: Epot =1948.149eV Ekin = 746.392eV (T=1443.587K) Etot = 2694.541eV
Energy per atom: Epot =1957.387eV Ekin = 742.627eV (T=1436.304K) Etot = 2700.014eV
Energy per atom: Epot =1952.626eV Ekin = 752.207eV (T=1454.834K) Etot = 2704.834eV
Energy per atom: Epot =1951.983eV Ekin = 762.433eV (T=1474.612K) Etot = 2714.416eV
Energy per atom: Epot =1958.223eV Ekin = 760.351eV (T=1470.586K) Etot = 2718.574eV
Energy per atom: Epot =1961.883eV Ekin = 763.700eV (T=1477.061K) Etot = 2725.582eV
Energy per atom: Epot =1966.449eV Ekin = 760.877eV (T=1471.603K) Etot = 2727.326eV
Energy per atom: Epot =1962.634eV Ekin = 768.545eV (T=1486.432K) Etot = 2731.178eV
Energy per atom: Epot =1964.147eV Ekin = 768.039eV (T=1485.454K) Etot = 2732.185eV
Energy per atom: Epot =1967.084eV Ekin = 762.285eV (T=1474.326K) Etot = 2729.369eV
Energy per atom: Epot =1964.266eV Ekin = 768.682eV (T=1486.697K) Etot = 2732.948eV
Energy per atom: Epot =1982.414eV Ekin = 755.952eV (T=1462.077K) Etot = 2738.366eV
Energy per atom: Epot =1976.206eV Ekin = 768.027eV (T=1485.430K) Etot = 2744.233eV
Energy per atom: Epot =1967.903eV Ekin = 781.265eV (T=1511.035K) Etot = 2749.169eV
Energy per atom: Epot =1986.921eV Ekin = 765.513eV (T=1480.569K) Etot = 2752.434eV
Energy per atom: Epot =1979.491eV Ekin = 777.247eV (T=1503.263K) Etot = 2756.738eV
Energy per atom: Epot =1984.830eV Ekin = 770.125eV (T=1489.488K) Etot = 2754.954eV
Energy per atom: Epot =1985.612eV Ekin = 763.120eV (T=1475.940K) Etot = 2748.731eV
Energy per atom: Epot =1994.981eV Ekin = 751.633eV (T=1453.724K) Etot = 2746.614eV
Energy per atom: Epot =1994.050eV Ekin = 764.952eV (T=1479.485K) Etot = 2759.002eV
Energy per atom: Epot =1992.604eV Ekin = 778.285eV (T=1505.272K) Etot = 2770.890eV
Energy per atom: Epot =1995.550eV Ekin = 771.791eV (T=1492.711K) Etot = 2767.341eV
Energy per atom: Epot =1997.004eV Ekin = 775.420eV (T=1499.730K) Etot = 2772.425eV
Energy per atom: Epot =1999.211eV Ekin = 773.900eV (T=1496.791K) Etot = 2773.112eV
Energy per atom: Epot =1998.820eV Ekin = 769.542eV (T=1488.361K) Etot = 2768.361eV
Energy per atom: Epot =1994.532eV Ekin = 767.886eV (T=1485.159K) Etot = 2762.418eV
Energy per atom: Epot =2003.450eV Ekin = 768.761eV (T=1486.850K) Etot = 2772.211eV
Energy per atom: Epot =1998.259eV Ekin = 777.137eV (T=1503.051K) Etot = 2775.396eV
Energy per atom: Epot =2000.697eV Ekin = 779.368eV (T=1507.365K) Etot = 2780.064eV
Energy per atom: Epot =2003.305eV Ekin = 768.379eV (T=1486.113K) Etot = 2771.685eV
Energy per atom: Epot =2010.718eV Ekin = 766.304eV (T=1482.099K) Etot = 2777.022eV
Energy per atom: Epot =2012.941eV Ekin = 758.220eV (T=1466.463K) Etot = 2771.161eV
Energy per atom: Epot =1989.441eV Ekin = 776.872eV (T=1502.537K) Etot = 2766.313eV
Energy per atom: Epot =1993.049eV Ekin = 778.032eV (T=1504.782K) Etot = 2771.081eV
Energy per atom: Epot =2003.629eV Ekin = 770.818eV (T=1490.830K) Etot = 2774.447eV
Energy per atom: Epot =2001.620eV Ekin = 778.832eV (T=1506.329K) Etot = 2780.452eV
Energy per atom: Epot =1985.573eV Ekin = 788.199eV (T=1524.445K) Etot = 2773.771eV
Energy per atom: Epot =2004.655eV Ekin = 768.687eV (T=1486.708K) Etot = 2773.342eV
Energy per atom: Epot =1989.355eV Ekin = 779.992eV (T=1508.573K) Etot = 2769.347eV
Energy per atom: Epot =1989.142eV Ekin = 764.648eV (T=1478.895K) Etot = 2753.789eV
Energy per atom: Epot =1979.368eV Ekin = 774.271eV (T=1497.508K) Etot = 2753.639eV
Energy per atom: Epot =1993.844eV Ekin = 761.820eV (T=1473.426K) Etot = 2755.664eV
Energy per atom: Epot =1983.275eV Ekin = 777.541eV (T=1503.832K) Etot = 2760.815eV
Energy per atom: Epot =1980.049eV Ekin = 786.832eV (T=1521.802K) Etot = 2766.881eV
Energy per atom: Epot =1995.787eV Ekin = 773.705eV (T=1496.414K) Etot = 2769.493eV
Energy per atom: Epot =1985.712eV Ekin = 774.882eV (T=1498.690K) Etot = 2760.595eV
Energy per atom: Epot =1991.996eV Ekin = 762.372eV (T=1474.494K) Etot = 2754.368eV
Energy per atom: Epot =1979.564eV Ekin = 765.354eV (T=1480.261K) Etot = 2744.918eV
Energy per atom: Epot =1973.996eV Ekin = 775.940eV (T=1500.735K) Etot = 2749.936eV
Energy per atom: Epot =1983.695eV Ekin = 759.691eV (T=1469.309K) Etot = 2743.387eV
Energy per atom: Epot =1982.807eV Ekin = 765.930eV (T=1481.375K) Etot = 2748.737eV
Energy per atom: Epot =1982.453eV Ekin = 766.594eV (T=1482.659K) Etot = 2749.047eV
Energy per atom: Epot =1997.814eV Ekin = 759.293eV (T=1468.538K) Etot = 2757.106eV
Energy per atom: Epot =2003.355eV Ekin = 761.571eV (T=1472.945K) Etot = 2764.926eV
Energy per atom: Epot =1993.635eV Ekin = 762.333eV (T=1474.418K) Etot = 2755.968eV
Energy per atom: Epot =2002.267eV Ekin = 756.646eV (T=1463.419K) Etot = 2758.913eV
Energy per atom: Epot =1994.652eV Ekin = 760.656eV (T=1471.176K) Etot = 2755.309eV
Energy per atom: Epot =1993.534eV Ekin = 758.502eV (T=1467.009K) Etot = 2752.036eV
Energy per atom: Epot =1975.307eV Ekin = 776.334eV (T=1501.497K) Etot = 2751.641eV
Energy per atom: Epot =1985.830eV Ekin = 762.320eV (T=1474.393K) Etot = 2748.150eV
Energy per atom: Epot =1995.197eV Ekin = 750.767eV (T=1452.049K) Etot = 2745.964eV
Energy per atom: Epot =1992.877eV Ekin = 752.004eV (T=1454.441K) Etot = 2744.880eV
Energy per atom: Epot =2000.236eV Ekin = 750.485eV (T=1451.504K) Etot = 2750.721eV
Energy per atom: Epot =1988.447eV Ekin = 762.185eV (T=1474.133K) Etot = 2750.632eV
Energy per atom: Epot =1991.037eV Ekin = 763.614eV (T=1476.896K) Etot = 2754.651eV
Energy per atom: Epot =1992.113eV Ekin = 760.137eV (T=1470.171K) Etot = 2752.250eV
Energy per atom: Epot =1996.385eV Ekin = 757.903eV (T=1465.850K) Etot = 2754.288eV
Energy per atom: Epot =1995.848eV Ekin = 759.575eV (T=1469.084K) Etot = 2755.423eV
Energy per atom: Epot =1992.391eV Ekin = 758.922eV (T=1467.820K) Etot = 2751.313eV
Energy per atom: Epot =1992.555eV Ekin = 761.658eV (T=1473.112K) Etot = 2754.213eV
Energy per atom: Epot =1980.931eV Ekin = 773.800eV (T=1496.597K) Etot = 2754.731eV
Energy per atom: Epot =1999.868eV Ekin = 762.953eV (T=1475.618K) Etot = 2762.821eV
Energy per atom: Epot =1984.806eV Ekin = 773.778eV (T=1496.554K) Etot = 2758.584eV
Energy per atom: Epot =1991.738eV Ekin = 771.909eV (T=1492.940K) Etot = 2763.648eV
Energy per atom: Epot =1982.704eV Ekin = 785.012eV (T=1518.281K) Etot = 2767.716eV
Energy per atom: Epot =1993.375eV Ekin = 769.586eV (T=1488.447K) Etot = 2762.962eV
Energy per atom: Epot =1977.586eV Ekin = 795.167eV (T=1537.922K) Etot = 2772.753eV
Energy per atom: Epot =1996.464eV Ekin = 776.632eV (T=1502.073K) Etot = 2773.095eV
Energy per atom: Epot =2003.684eV Ekin = 772.034eV (T=1493.181K) Etot = 2775.718eV
Energy per atom: Epot =1994.668eV Ekin = 782.091eV (T=1512.632K) Etot = 2776.758eV
Energy per atom: Epot =2004.643eV Ekin = 766.196eV (T=1481.891K) Etot = 2770.839eV
Energy per atom: Epot =2002.912eV Ekin = 768.580eV (T=1486.501K) Etot = 2771.492eV
Energy per atom: Epot =2005.017eV Ekin = 764.824eV (T=1479.236K) Etot = 2769.841eV
Energy per atom: Epot =1995.219eV Ekin = 771.699eV (T=1492.532K) Etot = 2766.917eV
Energy per atom: Epot =2002.275eV Ekin = 761.949eV (T=1473.675K) Etot = 2764.224eV
Energy per atom: Epot =2002.193eV Ekin = 762.399eV (T=1474.545K) Etot = 2764.592eV
Energy per atom: Epot =1997.989eV Ekin = 777.582eV (T=1503.912K) Etot = 2775.571eV
Energy per atom: Epot =2005.711eV Ekin = 775.655eV (T=1500.185K) Etot = 2781.366eV
Energy per atom: Epot =1991.230eV Ekin = 776.734eV (T=1502.270K) Etot = 2767.964eV
Energy per atom: Epot =1987.475eV Ekin = 766.601eV (T=1482.673K) Etot = 2754.076eV
Energy per atom: Epot =1998.505eV Ekin = 762.947eV (T=1475.605K) Etot = 2761.451eV
Energy per atom: Epot =1995.817eV Ekin = 760.810eV (T=1471.473K) Etot = 2756.627eV
Energy per atom: Epot =1986.226eV Ekin = 769.300eV (T=1487.894K) Etot = 2755.527eV
Energy per atom: Epot =1988.812eV Ekin = 769.050eV (T=1487.409K) Etot = 2757.862eV
Energy per atom: Epot =1989.629eV Ekin = 776.319eV (T=1501.469K) Etot = 2765.948eV
Energy per atom: Epot =1976.906eV Ekin = 787.333eV (T=1522.770K) Etot = 2764.239eV
Energy per atom: Epot =1993.255eV Ekin = 770.426eV (T=1490.071K) Etot = 2763.681eV
Energy per atom: Epot =1994.003eV Ekin = 760.818eV (T=1471.489K) Etot = 2754.821eV
Energy per atom: Epot =1990.529eV Ekin = 764.859eV (T=1479.305K) Etot = 2755.388eV
Energy per atom: Epot =1979.148eV Ekin = 786.965eV (T=1522.059K) Etot = 2766.113eV
Energy per atom: Epot =2004.117eV Ekin = 763.465eV (T=1476.607K) Etot = 2767.581eV
Energy per atom: Epot =1993.780eV Ekin = 762.892eV (T=1475.499K) Etot = 2756.671eV
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] 00:07:59 43.457006 1.0818
BFGSLineSearch: 1[ 1] 00:07:59 42.347659 0.2273
BFGSLineSearch: 2[ 2] 00:07:59 42.108454 0.1349
BFGSLineSearch: 3[ 3] 00:07:59 41.964817 0.1138
BFGSLineSearch: 4[ 4] 00:07:59 41.924933 0.0683
BFGSLineSearch: 5[ 5] 00:07:59 41.915346 0.0225
BFGSLineSearch: 6[ 6] 00:07:59 41.914920 0.0059
BFGSLineSearch: 7[ 7] 00:07:59 41.914872 0.0023
BFGSLineSearch: 8[ 9] 00:07:59 41.914855 0.0023
BFGSLineSearch: 9[ 10] 00:07:59 41.914851 0.0010
/builds/ase/ase/examples/03-tutorials/md.py:299: DeprecationWarning: Use thermalize_momenta
MaxwellBoltzmannDistribution(atoms, temperature_K=1200)
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 15.735eV (T=1308.955K) Etot = 57.650eV
Energy per atom: Epot =50.389eV Ekin = 7.305eV (T=607.688K) Etot = 57.694eV
Energy per atom: Epot =50.930eV Ekin = 6.775eV (T=563.556K) Etot = 57.704eV
Energy per atom: Epot =52.287eV Ekin = 5.418eV (T=450.722K) Etot = 57.706eV
Energy per atom: Epot =51.176eV Ekin = 6.525eV (T=542.827K) Etot = 57.701eV
Energy per atom: Epot =50.388eV Ekin = 7.317eV (T=608.702K) Etot = 57.705eV
Energy per atom: Epot =50.643eV Ekin = 7.062eV (T=587.467K) Etot = 57.705eV
Energy per atom: Epot =49.324eV Ekin = 8.366eV (T=695.916K) Etot = 57.690eV
Energy per atom: Epot =49.814eV Ekin = 7.880eV (T=655.530K) Etot = 57.694eV
Energy per atom: Epot =49.821eV Ekin = 7.879eV (T=655.408K) Etot = 57.700eV
Energy per atom: Epot =51.584eV Ekin = 6.122eV (T=509.296K) Etot = 57.707eV
Energy per atom: Epot =51.540eV Ekin = 6.166eV (T=512.934K) Etot = 57.706eV
Energy per atom: Epot =50.777eV Ekin = 6.925eV (T=576.080K) Etot = 57.702eV
Energy per atom: Epot =50.535eV Ekin = 7.161eV (T=595.688K) Etot = 57.696eV
Energy per atom: Epot =49.817eV Ekin = 7.879eV (T=655.389K) Etot = 57.695eV
Energy per atom: Epot =50.914eV Ekin = 6.793eV (T=565.121K) Etot = 57.707eV
Energy per atom: Epot =50.947eV Ekin = 6.763eV (T=562.581K) Etot = 57.710eV
Energy per atom: Epot =51.553eV Ekin = 6.151eV (T=511.686K) Etot = 57.704eV
Energy per atom: Epot =51.222eV Ekin = 6.478eV (T=538.889K) Etot = 57.700eV
Energy per atom: Epot =50.586eV Ekin = 7.109eV (T=591.372K) Etot = 57.695eV
Energy per atom: Epot =50.819eV Ekin = 6.879eV (T=572.212K) Etot = 57.698eV
Energy per atom: Epot =50.308eV Ekin = 7.388eV (T=614.617K) Etot = 57.696eV
Energy per atom: Epot =50.943eV Ekin = 6.756eV (T=562.038K) Etot = 57.699eV
Energy per atom: Epot =51.150eV Ekin = 6.552eV (T=545.063K) Etot = 57.702eV
Energy per atom: Epot =50.865eV Ekin = 6.837eV (T=568.737K) Etot = 57.701eV
Energy per atom: Epot =50.656eV Ekin = 7.047eV (T=586.205K) Etot = 57.703eV
Energy per atom: Epot =50.642eV Ekin = 7.055eV (T=586.879K) Etot = 57.697eV
Energy per atom: Epot =50.152eV Ekin = 7.548eV (T=627.914K) Etot = 57.700eV
Energy per atom: Epot =50.606eV Ekin = 7.098eV (T=590.455K) Etot = 57.704eV
Energy per atom: Epot =50.849eV Ekin = 6.852eV (T=570.021K) Etot = 57.702eV
Energy per atom: Epot =50.678eV Ekin = 7.024eV (T=584.343K) Etot = 57.702eV
Energy per atom: Epot =51.087eV Ekin = 6.618eV (T=550.527K) Etot = 57.705eV
Energy per atom: Epot =50.319eV Ekin = 7.382eV (T=614.115K) Etot = 57.702eV
Energy per atom: Epot =51.465eV Ekin = 6.234eV (T=518.609K) Etot = 57.699eV
Energy per atom: Epot =50.308eV Ekin = 7.386eV (T=614.407K) Etot = 57.694eV
Energy per atom: Epot =51.320eV Ekin = 6.383eV (T=530.998K) Etot = 57.703eV
Energy per atom: Epot =50.791eV Ekin = 6.910eV (T=574.800K) Etot = 57.701eV
Energy per atom: Epot =50.900eV Ekin = 6.804eV (T=565.970K) Etot = 57.704eV
Energy per atom: Epot =51.466eV Ekin = 6.240eV (T=519.056K) Etot = 57.706eV
Energy per atom: Epot =50.699eV Ekin = 6.999eV (T=582.232K) Etot = 57.698eV
Energy per atom: Epot =50.487eV Ekin = 7.210eV (T=599.737K) Etot = 57.697eV
Energy per atom: Epot =51.667eV Ekin = 6.035eV (T=502.025K) Etot = 57.702eV
Energy per atom: Epot =51.211eV Ekin = 6.491eV (T=539.987K) Etot = 57.702eV
Energy per atom: Epot =51.599eV Ekin = 6.106eV (T=507.933K) Etot = 57.705eV
Energy per atom: Epot =50.382eV Ekin = 7.316eV (T=608.633K) Etot = 57.698eV
Energy per atom: Epot =50.620eV Ekin = 7.079eV (T=588.852K) Etot = 57.699eV
Energy per atom: Epot =50.659eV Ekin = 7.047eV (T=586.249K) Etot = 57.707eV
Energy per atom: Epot =49.904eV Ekin = 7.798eV (T=648.648K) Etot = 57.702eV
Energy per atom: Epot =50.728eV Ekin = 6.971eV (T=579.859K) Etot = 57.699eV
Energy per atom: Epot =50.490eV Ekin = 7.211eV (T=599.878K) Etot = 57.701eV
Energy per atom: Epot =51.246eV Ekin = 6.462eV (T=537.510K) Etot = 57.707eV
Energy per atom: Epot =50.317eV Ekin = 7.382eV (T=614.088K) Etot = 57.699eV
Energy per atom: Epot =50.397eV Ekin = 7.295eV (T=606.859K) Etot = 57.692eV
Energy per atom: Epot =50.954eV Ekin = 6.748eV (T=561.326K) Etot = 57.701eV
Energy per atom: Epot =50.343eV Ekin = 7.358eV (T=612.114K) Etot = 57.701eV
Energy per atom: Epot =50.359eV Ekin = 7.339eV (T=610.515K) Etot = 57.698eV
Energy per atom: Epot =50.157eV Ekin = 7.539eV (T=627.139K) Etot = 57.696eV
Energy per atom: Epot =50.122eV Ekin = 7.576eV (T=630.211K) Etot = 57.698eV
Energy per atom: Epot =49.882eV Ekin = 7.816eV (T=650.147K) Etot = 57.698eV
Energy per atom: Epot =50.539eV Ekin = 7.163eV (T=595.855K) Etot = 57.702eV
Energy per atom: Epot =49.548eV Ekin = 8.150eV (T=677.933K) Etot = 57.698eV
Energy per atom: Epot =49.585eV Ekin = 8.118eV (T=675.317K) Etot = 57.703eV
Energy per atom: Epot =50.147eV Ekin = 7.553eV (T=628.298K) Etot = 57.700eV
Energy per atom: Epot =50.217eV Ekin = 7.485eV (T=622.647K) Etot = 57.702eV
Energy per atom: Epot =50.430eV Ekin = 7.270eV (T=604.745K) Etot = 57.699eV
Energy per atom: Epot =50.144eV Ekin = 7.557eV (T=628.606K) Etot = 57.700eV
Energy per atom: Epot =50.772eV Ekin = 6.928eV (T=576.323K) Etot = 57.700eV
Energy per atom: Epot =50.324eV Ekin = 7.373eV (T=613.374K) Etot = 57.697eV
Energy per atom: Epot =50.760eV Ekin = 6.941eV (T=577.412K) Etot = 57.701eV
Energy per atom: Epot =49.760eV Ekin = 7.939eV (T=660.378K) Etot = 57.698eV
Energy per atom: Epot =50.525eV Ekin = 7.179eV (T=597.179K) Etot = 57.704eV
Energy per atom: Epot =50.379eV Ekin = 7.323eV (T=609.181K) Etot = 57.702eV
Energy per atom: Epot =50.558eV Ekin = 7.150eV (T=594.745K) Etot = 57.707eV
Energy per atom: Epot =49.404eV Ekin = 8.298eV (T=690.287K) Etot = 57.702eV
Energy per atom: Epot =50.161eV Ekin = 7.538eV (T=627.022K) Etot = 57.698eV
Energy per atom: Epot =50.036eV Ekin = 7.663eV (T=637.427K) Etot = 57.699eV
Energy per atom: Epot =50.420eV Ekin = 7.282eV (T=605.750K) Etot = 57.702eV
Energy per atom: Epot =51.005eV Ekin = 6.699eV (T=557.283K) Etot = 57.704eV
Energy per atom: Epot =49.856eV Ekin = 7.838eV (T=652.038K) Etot = 57.694eV
Energy per atom: Epot =50.002eV Ekin = 7.694eV (T=640.076K) Etot = 57.696eV
Energy per atom: Epot =50.212eV Ekin = 7.485eV (T=622.676K) Etot = 57.697eV
Energy per atom: Epot =50.100eV Ekin = 7.599eV (T=632.146K) Etot = 57.699eV
Energy per atom: Epot =50.364eV Ekin = 7.341eV (T=610.681K) Etot = 57.706eV
Energy per atom: Epot =49.485eV Ekin = 8.213eV (T=683.186K) Etot = 57.697eV
Energy per atom: Epot =50.214eV Ekin = 7.489eV (T=622.966K) Etot = 57.703eV
Energy per atom: Epot =50.026eV Ekin = 7.672eV (T=638.174K) Etot = 57.698eV
Energy per atom: Epot =49.597eV Ekin = 8.098eV (T=673.613K) Etot = 57.695eV
Energy per atom: Epot =49.538eV Ekin = 8.159eV (T=678.707K) Etot = 57.697eV
Energy per atom: Epot =49.991eV Ekin = 7.713eV (T=641.584K) Etot = 57.704eV
Energy per atom: Epot =50.119eV Ekin = 7.583eV (T=630.823K) Etot = 57.702eV
Energy per atom: Epot =49.842eV Ekin = 7.860eV (T=653.884K) Etot = 57.703eV
Energy per atom: Epot =49.708eV Ekin = 7.991eV (T=664.713K) Etot = 57.698eV
Energy per atom: Epot =49.659eV Ekin = 8.037eV (T=668.580K) Etot = 57.696eV
Energy per atom: Epot =50.540eV Ekin = 7.156eV (T=595.244K) Etot = 57.696eV
Energy per atom: Epot =50.380eV Ekin = 7.320eV (T=608.938K) Etot = 57.700eV
Energy per atom: Epot =50.291eV Ekin = 7.408eV (T=616.265K) Etot = 57.699eV
Energy per atom: Epot =49.061eV Ekin = 8.635eV (T=718.343K) Etot = 57.697eV
Energy per atom: Epot =49.994eV Ekin = 7.707eV (T=641.123K) Etot = 57.701eV
Energy per atom: Epot =49.633eV Ekin = 8.064eV (T=670.804K) Etot = 57.697eV
Energy per atom: Epot =49.611eV Ekin = 8.084eV (T=672.472K) Etot = 57.694eV
Energy per atom: Epot =49.974eV Ekin = 7.724eV (T=642.547K) Etot = 57.699eV
Energy per atom: Epot =50.200eV Ekin = 7.506eV (T=624.430K) Etot = 57.707eV
Energy per atom: Epot =50.003eV Ekin = 7.699eV (T=640.418K) Etot = 57.701eV
Energy per atom: Epot =49.917eV Ekin = 7.785eV (T=647.647K) Etot = 57.702eV
Energy per atom: Epot =49.926eV Ekin = 7.772eV (T=646.507K) Etot = 57.698eV
Energy per atom: Epot =50.208eV Ekin = 7.492eV (T=623.193K) Etot = 57.699eV
Energy per atom: Epot =50.112eV Ekin = 7.590eV (T=631.369K) Etot = 57.702eV
Energy per atom: Epot =49.398eV Ekin = 8.298eV (T=690.282K) Etot = 57.696eV
Energy per atom: Epot =48.889eV Ekin = 8.800eV (T=732.012K) Etot = 57.689eV
Energy per atom: Epot =48.470eV Ekin = 9.220eV (T=766.958K) Etot = 57.690eV
Energy per atom: Epot =49.982eV Ekin = 7.722eV (T=642.360K) Etot = 57.704eV
Energy per atom: Epot =49.851eV Ekin = 7.847eV (T=652.756K) Etot = 57.698eV
Energy per atom: Epot =49.620eV Ekin = 8.075eV (T=671.738K) Etot = 57.695eV
Energy per atom: Epot =50.245eV Ekin = 7.453eV (T=619.997K) Etot = 57.698eV
Energy per atom: Epot =50.611eV Ekin = 7.093eV (T=590.030K) Etot = 57.704eV
Energy per atom: Epot =49.923eV Ekin = 7.778eV (T=647.056K) Etot = 57.702eV
Energy per atom: Epot =49.683eV Ekin = 8.017eV (T=666.913K) Etot = 57.701eV
Energy per atom: Epot =49.633eV Ekin = 8.067eV (T=671.090K) Etot = 57.701eV
Energy per atom: Epot =49.127eV Ekin = 8.574eV (T=713.242K) Etot = 57.701eV
Energy per atom: Epot =49.184eV Ekin = 8.516eV (T=708.422K) Etot = 57.700eV
Energy per atom: Epot =49.672eV Ekin = 8.022eV (T=667.287K) Etot = 57.693eV
Energy per atom: Epot =49.449eV Ekin = 8.251eV (T=686.343K) Etot = 57.700eV
Energy per atom: Epot =50.162eV Ekin = 7.539eV (T=627.170K) Etot = 57.702eV
Energy per atom: Epot =50.456eV Ekin = 7.250eV (T=603.068K) Etot = 57.705eV
Energy per atom: Epot =49.619eV Ekin = 8.079eV (T=672.088K) Etot = 57.698eV
Energy per atom: Epot =49.719eV Ekin = 7.981eV (T=663.877K) Etot = 57.699eV
Energy per atom: Epot =49.913eV Ekin = 7.789eV (T=647.946K) Etot = 57.702eV
Energy per atom: Epot =49.435eV Ekin = 8.262eV (T=687.319K) Etot = 57.698eV
Energy per atom: Epot =49.932eV Ekin = 7.771eV (T=646.437K) Etot = 57.703eV
Energy per atom: Epot =50.385eV Ekin = 7.318eV (T=608.758K) Etot = 57.703eV
Energy per atom: Epot =50.385eV Ekin = 7.314eV (T=608.454K) Etot = 57.699eV
Energy per atom: Epot =49.605eV Ekin = 8.088eV (T=672.843K) Etot = 57.693eV
Energy per atom: Epot =50.708eV Ekin = 6.992eV (T=581.622K) Etot = 57.700eV
Energy per atom: Epot =51.448eV Ekin = 6.260eV (T=520.742K) Etot = 57.708eV
Energy per atom: Epot =50.103eV Ekin = 7.603eV (T=632.450K) Etot = 57.706eV
Energy per atom: Epot =49.197eV Ekin = 8.493eV (T=706.518K) Etot = 57.690eV
Energy per atom: Epot =49.805eV Ekin = 7.884eV (T=655.854K) Etot = 57.689eV
Energy per atom: Epot =49.951eV Ekin = 7.747eV (T=644.452K) Etot = 57.698eV
Energy per atom: Epot =49.493eV Ekin = 8.204eV (T=682.487K) Etot = 57.697eV
Energy per atom: Epot =49.313eV Ekin = 8.382eV (T=697.280K) Etot = 57.696eV
Energy per atom: Epot =49.595eV Ekin = 8.104eV (T=674.179K) Etot = 57.699eV
Energy per atom: Epot =49.858eV Ekin = 7.847eV (T=652.795K) Etot = 57.705eV
Energy per atom: Epot =49.528eV Ekin = 8.169eV (T=679.533K) Etot = 57.697eV
Energy per atom: Epot =49.529eV Ekin = 8.168eV (T=679.432K) Etot = 57.697eV
Energy per atom: Epot =49.259eV Ekin = 8.437eV (T=701.886K) Etot = 57.696eV
Energy per atom: Epot =49.709eV Ekin = 7.992eV (T=664.827K) Etot = 57.701eV
Energy per atom: Epot =49.092eV Ekin = 8.603eV (T=715.679K) Etot = 57.695eV
Energy per atom: Epot =49.473eV Ekin = 8.219eV (T=683.717K) Etot = 57.693eV
Energy per atom: Epot =49.160eV Ekin = 8.525eV (T=709.149K) Etot = 57.685eV
Energy per atom: Epot =49.451eV Ekin = 8.239eV (T=685.400K) Etot = 57.690eV
Energy per atom: Epot =50.059eV Ekin = 7.640eV (T=635.519K) Etot = 57.699eV
Energy per atom: Epot =49.984eV Ekin = 7.716eV (T=641.839K) Etot = 57.699eV
Energy per atom: Epot =49.849eV Ekin = 7.848eV (T=652.860K) Etot = 57.697eV
Energy per atom: Epot =49.708eV Ekin = 7.985eV (T=664.282K) Etot = 57.693eV
Energy per atom: Epot =49.778eV Ekin = 7.914eV (T=658.344K) Etot = 57.692eV
Energy per atom: Epot =50.078eV Ekin = 7.618eV (T=633.737K) Etot = 57.697eV
Energy per atom: Epot =49.336eV Ekin = 8.361eV (T=695.484K) Etot = 57.696eV
Energy per atom: Epot =50.085eV Ekin = 7.617eV (T=633.637K) Etot = 57.703eV
Energy per atom: Epot =50.730eV Ekin = 6.971eV (T=579.858K) Etot = 57.701eV
Energy per atom: Epot =49.803eV Ekin = 7.895eV (T=656.774K) Etot = 57.698eV
Energy per atom: Epot =50.319eV Ekin = 7.383eV (T=614.184K) Etot = 57.703eV
Energy per atom: Epot =49.900eV Ekin = 7.794eV (T=648.376K) Etot = 57.694eV
Energy per atom: Epot =48.558eV Ekin = 9.134eV (T=759.808K) Etot = 57.692eV
Energy per atom: Epot =50.595eV Ekin = 7.103eV (T=590.887K) Etot = 57.698eV
Energy per atom: Epot =50.159eV Ekin = 7.535eV (T=626.835K) Etot = 57.694eV
Energy per atom: Epot =50.286eV Ekin = 7.412eV (T=616.593K) Etot = 57.698eV
Energy per atom: Epot =50.230eV Ekin = 7.467eV (T=621.124K) Etot = 57.697eV
Energy per atom: Epot =49.802eV Ekin = 7.896eV (T=656.802K) Etot = 57.698eV
Energy per atom: Epot =51.201eV Ekin = 6.507eV (T=541.268K) Etot = 57.707eV
Energy per atom: Epot =50.580eV Ekin = 7.123eV (T=592.519K) Etot = 57.703eV
Energy per atom: Epot =50.507eV Ekin = 7.192eV (T=598.282K) Etot = 57.699eV
Energy per atom: Epot =49.711eV Ekin = 7.985eV (T=664.256K) Etot = 57.696eV
Energy per atom: Epot =49.828eV Ekin = 7.872eV (T=654.851K) Etot = 57.700eV
Energy per atom: Epot =49.241eV Ekin = 8.455eV (T=703.337K) Etot = 57.696eV
Energy per atom: Epot =49.849eV Ekin = 7.852eV (T=653.167K) Etot = 57.700eV
Energy per atom: Epot =49.596eV Ekin = 8.101eV (T=673.933K) Etot = 57.698eV
Energy per atom: Epot =49.860eV Ekin = 7.840eV (T=652.208K) Etot = 57.701eV
Energy per atom: Epot =49.849eV Ekin = 7.849eV (T=652.906K) Etot = 57.698eV
Energy per atom: Epot =50.706eV Ekin = 6.997eV (T=582.070K) Etot = 57.703eV
Energy per atom: Epot =50.181eV Ekin = 7.524eV (T=625.937K) Etot = 57.706eV
Energy per atom: Epot =49.213eV Ekin = 8.489eV (T=706.168K) Etot = 57.702eV
Energy per atom: Epot =49.460eV Ekin = 8.240eV (T=685.492K) Etot = 57.701eV
Energy per atom: Epot =49.970eV Ekin = 7.734eV (T=643.374K) Etot = 57.704eV
Energy per atom: Epot =50.187eV Ekin = 7.515eV (T=625.157K) Etot = 57.703eV
Energy per atom: Epot =50.893eV Ekin = 6.811eV (T=566.571K) Etot = 57.704eV
Energy per atom: Epot =49.844eV Ekin = 7.850eV (T=652.997K) Etot = 57.694eV
Energy per atom: Epot =50.031eV Ekin = 7.665eV (T=637.610K) Etot = 57.696eV
Energy per atom: Epot =49.171eV Ekin = 8.524eV (T=709.088K) Etot = 57.695eV
Energy per atom: Epot =49.739eV Ekin = 7.962eV (T=662.343K) Etot = 57.701eV
Energy per atom: Epot =50.214eV Ekin = 7.491eV (T=623.138K) Etot = 57.705eV
Energy per atom: Epot =50.561eV Ekin = 7.142eV (T=594.117K) Etot = 57.703eV
Energy per atom: Epot =49.879eV Ekin = 7.823eV (T=650.740K) Etot = 57.702eV
Energy per atom: Epot =49.931eV Ekin = 7.768eV (T=646.198K) Etot = 57.699eV
Energy per atom: Epot =49.560eV Ekin = 8.142eV (T=677.292K) Etot = 57.702eV
Energy per atom: Epot =49.031eV Ekin = 8.667eV (T=721.003K) Etot = 57.698eV
Energy per atom: Epot =48.994eV Ekin = 8.698eV (T=723.541K) Etot = 57.692eV
Energy per atom: Epot =50.186eV Ekin = 7.513eV (T=624.984K) Etot = 57.699eV
Energy per atom: Epot =49.925eV Ekin = 7.777eV (T=646.940K) Etot = 57.702eV
Energy per atom: Epot =49.097eV Ekin = 8.599eV (T=715.350K) Etot = 57.696eV
Energy per atom: Epot =49.646eV Ekin = 8.047eV (T=669.369K) Etot = 57.693eV
Energy per atom: Epot =50.042eV Ekin = 7.657eV (T=636.918K) Etot = 57.699eV
After running the simulation, use Graphical user interface (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?