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 = 156.300eV (T=302.298K) Etot = 153.895eV
Energy per atom: Epot =119.284eV Ekin = 35.412eV (T=68.490K) Etot = 154.696eV
Energy per atom: Epot =77.916eV Ekin = 76.626eV (T=148.202K) Etot = 154.543eV
Energy per atom: Epot =71.706eV Ekin = 82.698eV (T=159.944K) Etot = 154.404eV
Energy per atom: Epot =69.762eV Ekin = 84.585eV (T=163.595K) Etot = 154.347eV
Energy per atom: Epot =81.355eV Ekin = 73.159eV (T=141.495K) Etot = 154.514eV
Energy per atom: Epot =80.468eV Ekin = 74.043eV (T=143.206K) Etot = 154.511eV
Energy per atom: Epot =71.689eV Ekin = 82.702eV (T=159.953K) Etot = 154.391eV
Energy per atom: Epot =72.773eV Ekin = 81.636eV (T=157.891K) Etot = 154.409eV
Energy per atom: Epot =80.820eV Ekin = 73.675eV (T=142.494K) Etot = 154.495eV
Energy per atom: Epot =76.150eV Ekin = 78.309eV (T=151.456K) Etot = 154.459eV
Energy per atom: Epot =74.786eV Ekin = 79.649eV (T=154.049K) Etot = 154.435eV
Energy per atom: Epot =76.768eV Ekin = 77.678eV (T=150.236K) Etot = 154.446eV
Energy per atom: Epot =76.976eV Ekin = 77.474eV (T=149.841K) Etot = 154.450eV
Energy per atom: Epot =75.569eV Ekin = 78.877eV (T=152.554K) Etot = 154.445eV
Energy per atom: Epot =75.189eV Ekin = 79.260eV (T=153.295K) Etot = 154.449eV
Energy per atom: Epot =74.939eV Ekin = 79.497eV (T=153.753K) Etot = 154.435eV
Energy per atom: Epot =78.459eV Ekin = 75.993eV (T=146.977K) Etot = 154.452eV
Energy per atom: Epot =75.297eV Ekin = 79.158eV (T=153.099K) Etot = 154.456eV
Energy per atom: Epot =74.212eV Ekin = 80.221eV (T=155.155K) Etot = 154.433eV
Energy per atom: Epot =79.696eV Ekin = 74.761eV (T=144.594K) Etot = 154.457eV
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/python3.14/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 =598.720eV Ekin = 82.148eV (T=158.881K) Etot = 680.868eV
Energy per atom: Epot =668.922eV Ekin = 140.412eV (T=271.569K) Etot = 809.334eV
Energy per atom: Epot =729.289eV Ekin = 198.779eV (T=384.456K) Etot = 928.068eV
Energy per atom: Epot =781.930eV Ekin = 255.430eV (T=494.023K) Etot = 1037.360eV
Energy per atom: Epot =837.359eV Ekin = 298.007eV (T=576.371K) Etot = 1135.365eV
Energy per atom: Epot =880.430eV Ekin = 336.803eV (T=651.407K) Etot = 1217.233eV
Energy per atom: Epot =918.762eV Ekin = 381.057eV (T=736.998K) Etot = 1299.820eV
Energy per atom: Epot =961.613eV Ekin = 411.814eV (T=796.483K) Etot = 1373.427eV
Energy per atom: Epot =1001.328eV Ekin = 436.206eV (T=843.661K) Etot = 1437.534eV
Energy per atom: Epot =1030.002eV Ekin = 479.364eV (T=927.131K) Etot = 1509.366eV
Energy per atom: Epot =1080.852eV Ekin = 495.096eV (T=957.559K) Etot = 1575.948eV
Energy per atom: Epot =1117.859eV Ekin = 516.296eV (T=998.562K) Etot = 1634.155eV
Energy per atom: Epot =1150.939eV Ekin = 522.348eV (T=1010.266K) Etot = 1673.287eV
Energy per atom: Epot =1173.392eV Ekin = 555.799eV (T=1074.964K) Etot = 1729.192eV
Energy per atom: Epot =1204.756eV Ekin = 563.986eV (T=1090.799K) Etot = 1768.743eV
Energy per atom: Epot =1232.626eV Ekin = 575.933eV (T=1113.905K) Etot = 1808.560eV
Energy per atom: Epot =1256.234eV Ekin = 587.494eV (T=1136.264K) Etot = 1843.728eV
Energy per atom: Epot =1264.151eV Ekin = 605.173eV (T=1170.458K) Etot = 1869.324eV
Energy per atom: Epot =1299.254eV Ekin = 606.299eV (T=1172.636K) Etot = 1905.553eV
Energy per atom: Epot =1340.382eV Ekin = 590.787eV (T=1142.633K) Etot = 1931.168eV
Energy per atom: Epot =1359.545eV Ekin = 606.672eV (T=1173.356K) Etot = 1966.217eV
Energy per atom: Epot =1359.046eV Ekin = 632.713eV (T=1223.723K) Etot = 1991.759eV
Energy per atom: Epot =1385.240eV Ekin = 631.555eV (T=1221.483K) Etot = 2016.795eV
Energy per atom: Epot =1412.174eV Ekin = 633.899eV (T=1226.016K) Etot = 2046.073eV
Energy per atom: Epot =1411.849eV Ekin = 653.287eV (T=1263.514K) Etot = 2065.136eV
Energy per atom: Epot =1428.906eV Ekin = 661.068eV (T=1278.563K) Etot = 2089.974eV
Energy per atom: Epot =1456.099eV Ekin = 663.678eV (T=1283.612K) Etot = 2119.777eV
Energy per atom: Epot =1459.140eV Ekin = 684.214eV (T=1323.330K) Etot = 2143.354eV
Energy per atom: Epot =1485.667eV Ekin = 676.088eV (T=1307.613K) Etot = 2161.754eV
Energy per atom: Epot =1487.843eV Ekin = 695.048eV (T=1344.284K) Etot = 2182.892eV
Energy per atom: Epot =1523.647eV Ekin = 686.412eV (T=1327.581K) Etot = 2210.060eV
Energy per atom: Epot =1519.686eV Ekin = 702.455eV (T=1358.609K) Etot = 2222.141eV
Energy per atom: Epot =1538.585eV Ekin = 705.414eV (T=1364.332K) Etot = 2243.999eV
Energy per atom: Epot =1553.861eV Ekin = 698.329eV (T=1350.629K) Etot = 2252.190eV
Energy per atom: Epot =1559.306eV Ekin = 719.757eV (T=1392.072K) Etot = 2279.063eV
Energy per atom: Epot =1590.454eV Ekin = 705.243eV (T=1364.001K) Etot = 2295.697eV
Energy per atom: Epot =1589.293eV Ekin = 720.671eV (T=1393.841K) Etot = 2309.964eV
Energy per atom: Epot =1593.407eV Ekin = 723.981eV (T=1400.243K) Etot = 2317.388eV
Energy per atom: Epot =1619.914eV Ekin = 705.992eV (T=1365.449K) Etot = 2325.906eV
Energy per atom: Epot =1628.407eV Ekin = 703.206eV (T=1360.062K) Etot = 2331.613eV
Energy per atom: Epot =1644.970eV Ekin = 702.855eV (T=1359.382K) Etot = 2347.825eV
Energy per atom: Epot =1648.951eV Ekin = 719.395eV (T=1391.373K) Etot = 2368.346eV
Energy per atom: Epot =1652.819eV Ekin = 726.841eV (T=1405.775K) Etot = 2379.660eV
Energy per atom: Epot =1686.241eV Ekin = 705.013eV (T=1363.557K) Etot = 2391.254eV
Energy per atom: Epot =1675.251eV Ekin = 732.101eV (T=1415.947K) Etot = 2407.352eV
Energy per atom: Epot =1683.029eV Ekin = 738.016eV (T=1427.386K) Etot = 2421.045eV
Energy per atom: Epot =1695.076eV Ekin = 738.327eV (T=1427.989K) Etot = 2433.403eV
Energy per atom: Epot =1711.346eV Ekin = 735.590eV (T=1422.694K) Etot = 2446.935eV
Energy per atom: Epot =1726.938eV Ekin = 737.376eV (T=1426.149K) Etot = 2464.314eV
Energy per atom: Epot =1731.488eV Ekin = 745.436eV (T=1441.738K) Etot = 2476.924eV
Energy per atom: Epot =1729.798eV Ekin = 746.645eV (T=1444.077K) Etot = 2476.443eV
Energy per atom: Epot =1751.787eV Ekin = 737.644eV (T=1426.667K) Etot = 2489.431eV
Energy per atom: Epot =1756.531eV Ekin = 731.128eV (T=1414.065K) Etot = 2487.659eV
Energy per atom: Epot =1744.433eV Ekin = 745.441eV (T=1441.748K) Etot = 2489.874eV
Energy per atom: Epot =1752.050eV Ekin = 730.198eV (T=1412.266K) Etot = 2482.248eV
Energy per atom: Epot =1757.561eV Ekin = 742.952eV (T=1436.934K) Etot = 2500.513eV
Energy per atom: Epot =1753.362eV Ekin = 754.204eV (T=1458.697K) Etot = 2507.566eV
Energy per atom: Epot =1759.149eV Ekin = 743.841eV (T=1438.653K) Etot = 2502.989eV
Energy per atom: Epot =1758.834eV Ekin = 740.149eV (T=1431.513K) Etot = 2498.983eV
Energy per atom: Epot =1780.281eV Ekin = 730.300eV (T=1412.464K) Etot = 2510.581eV
Energy per atom: Epot =1776.996eV Ekin = 744.679eV (T=1440.274K) Etot = 2521.675eV
Energy per atom: Epot =1785.240eV Ekin = 742.079eV (T=1435.244K) Etot = 2527.318eV
Energy per atom: Epot =1787.193eV Ekin = 744.753eV (T=1440.418K) Etot = 2531.946eV
Energy per atom: Epot =1791.241eV Ekin = 737.997eV (T=1427.351K) Etot = 2529.239eV
Energy per atom: Epot =1787.258eV Ekin = 746.437eV (T=1443.673K) Etot = 2533.694eV
Energy per atom: Epot =1813.978eV Ekin = 735.441eV (T=1422.407K) Etot = 2549.419eV
Energy per atom: Epot =1811.308eV Ekin = 729.849eV (T=1411.591K) Etot = 2541.157eV
Energy per atom: Epot =1815.331eV Ekin = 732.104eV (T=1415.953K) Etot = 2547.435eV
Energy per atom: Epot =1815.761eV Ekin = 730.948eV (T=1413.718K) Etot = 2546.709eV
Energy per atom: Epot =1815.295eV Ekin = 733.220eV (T=1418.112K) Etot = 2548.515eV
Energy per atom: Epot =1809.491eV Ekin = 742.874eV (T=1436.782K) Etot = 2552.365eV
Energy per atom: Epot =1824.322eV Ekin = 731.820eV (T=1415.403K) Etot = 2556.142eV
Energy per atom: Epot =1829.260eV Ekin = 737.516eV (T=1426.419K) Etot = 2566.776eV
Energy per atom: Epot =1837.833eV Ekin = 724.427eV (T=1401.105K) Etot = 2562.260eV
Energy per atom: Epot =1838.618eV Ekin = 726.430eV (T=1404.979K) Etot = 2565.049eV
Energy per atom: Epot =1846.527eV Ekin = 734.261eV (T=1420.126K) Etot = 2580.789eV
Energy per atom: Epot =1858.656eV Ekin = 733.162eV (T=1417.999K) Etot = 2591.818eV
Energy per atom: Epot =1862.887eV Ekin = 724.441eV (T=1401.131K) Etot = 2587.328eV
Energy per atom: Epot =1863.890eV Ekin = 733.853eV (T=1419.335K) Etot = 2597.743eV
Energy per atom: Epot =1877.667eV Ekin = 719.787eV (T=1392.130K) Etot = 2597.454eV
Energy per atom: Epot =1867.000eV Ekin = 743.254eV (T=1437.518K) Etot = 2610.254eV
Energy per atom: Epot =1883.280eV Ekin = 736.844eV (T=1425.120K) Etot = 2620.124eV
Energy per atom: Epot =1870.384eV Ekin = 754.720eV (T=1459.695K) Etot = 2625.104eV
Energy per atom: Epot =1890.403eV Ekin = 743.714eV (T=1438.408K) Etot = 2634.117eV
Energy per atom: Epot =1884.885eV Ekin = 759.225eV (T=1468.407K) Etot = 2644.110eV
Energy per atom: Epot =1898.242eV Ekin = 739.623eV (T=1430.494K) Etot = 2637.865eV
Energy per atom: Epot =1904.748eV Ekin = 741.880eV (T=1434.860K) Etot = 2646.628eV
Energy per atom: Epot =1888.801eV Ekin = 758.337eV (T=1466.690K) Etot = 2647.138eV
Energy per atom: Epot =1911.792eV Ekin = 745.908eV (T=1442.650K) Etot = 2657.700eV
Energy per atom: Epot =1909.205eV Ekin = 751.016eV (T=1452.531K) Etot = 2660.222eV
Energy per atom: Epot =1909.675eV Ekin = 759.166eV (T=1468.293K) Etot = 2668.841eV
Energy per atom: Epot =1912.008eV Ekin = 763.765eV (T=1477.187K) Etot = 2675.773eV
Energy per atom: Epot =1918.726eV Ekin = 757.142eV (T=1464.379K) Etot = 2675.868eV
Energy per atom: Epot =1908.534eV Ekin = 763.271eV (T=1476.232K) Etot = 2671.805eV
Energy per atom: Epot =1915.457eV Ekin = 761.036eV (T=1471.909K) Etot = 2676.493eV
Energy per atom: Epot =1914.969eV Ekin = 762.645eV (T=1475.021K) Etot = 2677.614eV
Energy per atom: Epot =1922.267eV Ekin = 759.592eV (T=1469.117K) Etot = 2681.859eV
Energy per atom: Epot =1921.147eV Ekin = 751.202eV (T=1452.891K) Etot = 2672.349eV
Energy per atom: Epot =1919.660eV Ekin = 759.755eV (T=1469.431K) Etot = 2679.415eV
Energy per atom: Epot =1930.054eV Ekin = 752.789eV (T=1455.960K) Etot = 2682.843eV
Energy per atom: Epot =1916.885eV Ekin = 776.317eV (T=1501.465K) Etot = 2693.202eV
Energy per atom: Epot =1937.413eV Ekin = 761.304eV (T=1472.428K) Etot = 2698.716eV
Energy per atom: Epot =1932.963eV Ekin = 775.836eV (T=1500.534K) Etot = 2708.799eV
Energy per atom: Epot =1947.705eV Ekin = 766.495eV (T=1482.467K) Etot = 2714.200eV
Energy per atom: Epot =1943.387eV Ekin = 769.882eV (T=1489.018K) Etot = 2713.269eV
Energy per atom: Epot =1937.635eV Ekin = 773.207eV (T=1495.449K) Etot = 2710.842eV
Energy per atom: Epot =1950.097eV Ekin = 764.992eV (T=1479.560K) Etot = 2715.089eV
Energy per atom: Epot =1954.974eV Ekin = 760.096eV (T=1470.093K) Etot = 2715.070eV
Energy per atom: Epot =1950.593eV Ekin = 758.713eV (T=1467.417K) Etot = 2709.306eV
Energy per atom: Epot =1946.697eV Ekin = 772.217eV (T=1493.535K) Etot = 2718.914eV
Energy per atom: Epot =1955.821eV Ekin = 768.284eV (T=1485.928K) Etot = 2724.105eV
Energy per atom: Epot =1957.811eV Ekin = 771.214eV (T=1491.596K) Etot = 2729.025eV
Energy per atom: Epot =1955.412eV Ekin = 773.022eV (T=1495.092K) Etot = 2728.434eV
Energy per atom: Epot =1961.008eV Ekin = 755.084eV (T=1460.398K) Etot = 2716.092eV
Energy per atom: Epot =1962.471eV Ekin = 758.204eV (T=1466.433K) Etot = 2720.676eV
Energy per atom: Epot =1971.835eV Ekin = 753.891eV (T=1458.091K) Etot = 2725.726eV
Energy per atom: Epot =1978.744eV Ekin = 753.920eV (T=1458.147K) Etot = 2732.664eV
Energy per atom: Epot =1982.688eV Ekin = 744.045eV (T=1439.048K) Etot = 2726.733eV
Energy per atom: Epot =1982.841eV Ekin = 745.433eV (T=1441.732K) Etot = 2728.273eV
Energy per atom: Epot =1983.926eV Ekin = 750.583eV (T=1451.694K) Etot = 2734.510eV
Energy per atom: Epot =1996.500eV Ekin = 757.717eV (T=1465.490K) Etot = 2754.216eV
Energy per atom: Epot =1989.352eV Ekin = 765.384eV (T=1480.319K) Etot = 2754.736eV
Energy per atom: Epot =1986.783eV Ekin = 763.912eV (T=1477.472K) Etot = 2750.695eV
Energy per atom: Epot =1991.693eV Ekin = 767.206eV (T=1483.842K) Etot = 2758.899eV
Energy per atom: Epot =1991.736eV Ekin = 770.444eV (T=1490.105K) Etot = 2762.179eV
Energy per atom: Epot =1982.573eV Ekin = 775.460eV (T=1499.807K) Etot = 2758.033eV
Energy per atom: Epot =1987.555eV Ekin = 755.364eV (T=1460.940K) Etot = 2742.919eV
Energy per atom: Epot =1973.776eV Ekin = 771.590eV (T=1492.322K) Etot = 2745.366eV
Energy per atom: Epot =1992.173eV Ekin = 751.241eV (T=1452.965K) Etot = 2743.413eV
Energy per atom: Epot =1978.026eV Ekin = 768.925eV (T=1487.167K) Etot = 2746.951eV
Energy per atom: Epot =1986.003eV Ekin = 771.591eV (T=1492.325K) Etot = 2757.595eV
Energy per atom: Epot =1997.889eV Ekin = 762.366eV (T=1474.481K) Etot = 2760.255eV
Energy per atom: Epot =1992.236eV Ekin = 769.265eV (T=1487.825K) Etot = 2761.500eV
Energy per atom: Epot =1994.653eV Ekin = 767.728eV (T=1484.852K) Etot = 2762.380eV
Energy per atom: Epot =1996.364eV Ekin = 768.051eV (T=1485.478K) Etot = 2764.415eV
Energy per atom: Epot =1984.213eV Ekin = 772.839eV (T=1494.739K) Etot = 2757.052eV
Energy per atom: Epot =1999.435eV Ekin = 766.885eV (T=1483.222K) Etot = 2766.320eV
Energy per atom: Epot =1998.465eV Ekin = 769.882eV (T=1489.018K) Etot = 2768.347eV
Energy per atom: Epot =1997.526eV Ekin = 775.507eV (T=1499.898K) Etot = 2773.033eV
Energy per atom: Epot =2004.990eV Ekin = 769.157eV (T=1487.616K) Etot = 2774.146eV
Energy per atom: Epot =2004.105eV Ekin = 767.640eV (T=1484.682K) Etot = 2771.744eV
Energy per atom: Epot =2007.293eV Ekin = 778.430eV (T=1505.552K) Etot = 2785.723eV
Energy per atom: Epot =2008.152eV Ekin = 782.630eV (T=1513.674K) Etot = 2790.781eV
Energy per atom: Epot =2007.870eV Ekin = 782.472eV (T=1513.369K) Etot = 2790.342eV
Energy per atom: Epot =2008.217eV Ekin = 787.538eV (T=1523.167K) Etot = 2795.754eV
Energy per atom: Epot =2008.968eV Ekin = 784.704eV (T=1517.685K) Etot = 2793.672eV
Energy per atom: Epot =2009.908eV Ekin = 788.784eV (T=1525.578K) Etot = 2798.693eV
Energy per atom: Epot =2009.510eV Ekin = 789.930eV (T=1527.793K) Etot = 2799.440eV
Energy per atom: Epot =2020.866eV Ekin = 786.614eV (T=1521.380K) Etot = 2807.480eV
Energy per atom: Epot =2010.608eV Ekin = 777.069eV (T=1502.918K) Etot = 2787.677eV
Energy per atom: Epot =2023.918eV Ekin = 773.098eV (T=1495.239K) Etot = 2797.016eV
Energy per atom: Epot =2006.440eV Ekin = 791.802eV (T=1531.414K) Etot = 2798.242eV
Energy per atom: Epot =2014.949eV Ekin = 794.179eV (T=1536.011K) Etot = 2809.128eV
Energy per atom: Epot =2033.511eV Ekin = 763.439eV (T=1476.558K) Etot = 2796.950eV
Energy per atom: Epot =2028.223eV Ekin = 766.206eV (T=1481.910K) Etot = 2794.430eV
Energy per atom: Epot =2022.881eV Ekin = 776.017eV (T=1500.884K) Etot = 2798.897eV
Energy per atom: Epot =2016.132eV Ekin = 782.601eV (T=1513.618K) Etot = 2798.732eV
Energy per atom: Epot =2018.608eV Ekin = 774.531eV (T=1498.011K) Etot = 2793.139eV
Energy per atom: Epot =2019.563eV Ekin = 780.773eV (T=1510.084K) Etot = 2800.337eV
Energy per atom: Epot =2028.866eV Ekin = 765.212eV (T=1479.987K) Etot = 2794.078eV
Energy per atom: Epot =2024.775eV Ekin = 762.753eV (T=1475.231K) Etot = 2787.528eV
Energy per atom: Epot =2022.851eV Ekin = 768.926eV (T=1487.171K) Etot = 2791.777eV
Energy per atom: Epot =2027.133eV Ekin = 764.832eV (T=1479.252K) Etot = 2791.965eV
Energy per atom: Epot =2028.004eV Ekin = 764.381eV (T=1478.379K) Etot = 2792.385eV
Energy per atom: Epot =2025.218eV Ekin = 776.780eV (T=1502.360K) Etot = 2801.998eV
Energy per atom: Epot =2006.958eV Ekin = 784.864eV (T=1517.995K) Etot = 2791.822eV
Energy per atom: Epot =2010.634eV Ekin = 784.533eV (T=1517.355K) Etot = 2795.167eV
Energy per atom: Epot =2017.261eV Ekin = 782.672eV (T=1513.755K) Etot = 2799.932eV
Energy per atom: Epot =2027.510eV Ekin = 759.872eV (T=1469.660K) Etot = 2787.383eV
Energy per atom: Epot =2014.679eV Ekin = 775.816eV (T=1500.495K) Etot = 2790.495eV
Energy per atom: Epot =2021.236eV Ekin = 770.452eV (T=1490.122K) Etot = 2791.688eV
Energy per atom: Epot =2010.359eV Ekin = 782.819eV (T=1514.040K) Etot = 2793.179eV
Energy per atom: Epot =2023.153eV Ekin = 767.282eV (T=1483.991K) Etot = 2790.435eV
Energy per atom: Epot =2019.367eV Ekin = 783.405eV (T=1515.173K) Etot = 2802.772eV
Energy per atom: Epot =2028.410eV Ekin = 780.638eV (T=1509.822K) Etot = 2809.048eV
Energy per atom: Epot =2021.046eV Ekin = 796.915eV (T=1541.304K) Etot = 2817.961eV
Energy per atom: Epot =2035.117eV Ekin = 779.131eV (T=1506.908K) Etot = 2814.248eV
Energy per atom: Epot =2026.594eV Ekin = 785.487eV (T=1519.200K) Etot = 2812.081eV
Energy per atom: Epot =2028.565eV Ekin = 780.307eV (T=1509.182K) Etot = 2808.873eV
Energy per atom: Epot =2024.202eV Ekin = 797.605eV (T=1542.638K) Etot = 2821.807eV
Energy per atom: Epot =2028.546eV Ekin = 787.777eV (T=1523.630K) Etot = 2816.323eV
Energy per atom: Epot =2027.708eV Ekin = 783.278eV (T=1514.927K) Etot = 2810.986eV
Energy per atom: Epot =2025.709eV Ekin = 779.963eV (T=1508.517K) Etot = 2805.673eV
Energy per atom: Epot =2020.067eV Ekin = 787.702eV (T=1523.483K) Etot = 2807.769eV
Energy per atom: Epot =2012.048eV Ekin = 787.045eV (T=1522.213K) Etot = 2799.093eV
Energy per atom: Epot =2014.302eV Ekin = 783.597eV (T=1515.545K) Etot = 2797.900eV
Energy per atom: Epot =2021.601eV Ekin = 772.124eV (T=1493.354K) Etot = 2793.725eV
Energy per atom: Epot =2006.703eV Ekin = 785.652eV (T=1519.519K) Etot = 2792.355eV
Energy per atom: Epot =2020.463eV Ekin = 767.746eV (T=1484.887K) Etot = 2788.209eV
Energy per atom: Epot =2015.229eV Ekin = 774.199eV (T=1497.369K) Etot = 2789.429eV
Energy per atom: Epot =2007.424eV Ekin = 778.603eV (T=1505.885K) Etot = 2786.027eV
Energy per atom: Epot =2013.613eV Ekin = 784.143eV (T=1516.601K) Etot = 2797.756eV
Energy per atom: Epot =2015.415eV Ekin = 775.541eV (T=1499.963K) Etot = 2790.955eV
Energy per atom: Epot =2022.417eV Ekin = 768.614eV (T=1486.566K) Etot = 2791.031eV
Energy per atom: Epot =2027.980eV Ekin = 771.853eV (T=1492.831K) Etot = 2799.833eV
Energy per atom: Epot =2032.536eV Ekin = 776.374eV (T=1501.574K) Etot = 2808.910eV
Energy per atom: Epot =2030.605eV Ekin = 771.333eV (T=1491.825K) Etot = 2801.938eV
Energy per atom: Epot =2008.630eV Ekin = 794.771eV (T=1537.155K) Etot = 2803.401eV
Energy per atom: Epot =2023.040eV Ekin = 776.164eV (T=1501.168K) Etot = 2799.203eV
Energy per atom: Epot =2008.830eV Ekin = 790.630eV (T=1529.146K) Etot = 2799.459eV
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] 00:08:19 43.457006 1.0818
BFGSLineSearch: 1[ 1] 00:08:19 42.347659 0.2273
BFGSLineSearch: 2[ 2] 00:08:19 42.108454 0.1349
BFGSLineSearch: 3[ 3] 00:08:19 41.964817 0.1138
BFGSLineSearch: 4[ 4] 00:08:19 41.924933 0.0683
BFGSLineSearch: 5[ 5] 00:08:19 41.915346 0.0225
BFGSLineSearch: 6[ 6] 00:08:19 41.914920 0.0059
BFGSLineSearch: 7[ 7] 00:08:19 41.914872 0.0023
BFGSLineSearch: 8[ 9] 00:08:19 41.914855 0.0023
BFGSLineSearch: 9[ 10] 00:08:19 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 = 13.132eV (T=1092.425K) Etot = 55.047eV
Energy per atom: Epot =49.470eV Ekin = 5.612eV (T=466.816K) Etot = 55.081eV
Energy per atom: Epot =49.472eV Ekin = 5.617eV (T=467.270K) Etot = 55.089eV
Energy per atom: Epot =49.377eV Ekin = 5.711eV (T=475.117K) Etot = 55.089eV
Energy per atom: Epot =49.753eV Ekin = 5.336eV (T=443.859K) Etot = 55.089eV
Energy per atom: Epot =49.627eV Ekin = 5.461eV (T=454.310K) Etot = 55.088eV
Energy per atom: Epot =48.963eV Ekin = 6.123eV (T=509.356K) Etot = 55.086eV
Energy per atom: Epot =48.609eV Ekin = 6.473eV (T=538.440K) Etot = 55.082eV
Energy per atom: Epot =47.589eV Ekin = 7.493eV (T=623.318K) Etot = 55.082eV
Energy per atom: Epot =49.089eV Ekin = 6.002eV (T=499.256K) Etot = 55.090eV
Energy per atom: Epot =49.752eV Ekin = 5.343eV (T=444.504K) Etot = 55.095eV
Energy per atom: Epot =48.871eV Ekin = 6.215eV (T=517.019K) Etot = 55.086eV
Energy per atom: Epot =48.135eV Ekin = 6.949eV (T=578.026K) Etot = 55.084eV
Energy per atom: Epot =49.252eV Ekin = 5.840eV (T=485.792K) Etot = 55.092eV
Energy per atom: Epot =48.959eV Ekin = 6.131eV (T=510.040K) Etot = 55.090eV
Energy per atom: Epot =48.725eV Ekin = 6.363eV (T=529.284K) Etot = 55.088eV
Energy per atom: Epot =49.057eV Ekin = 6.029eV (T=501.563K) Etot = 55.086eV
Energy per atom: Epot =49.044eV Ekin = 6.047eV (T=503.020K) Etot = 55.091eV
Energy per atom: Epot =48.619eV Ekin = 6.467eV (T=537.982K) Etot = 55.087eV
Energy per atom: Epot =48.475eV Ekin = 6.609eV (T=549.819K) Etot = 55.085eV
Energy per atom: Epot =48.434eV Ekin = 6.650eV (T=553.205K) Etot = 55.084eV
Energy per atom: Epot =49.051eV Ekin = 6.034eV (T=501.958K) Etot = 55.085eV
Energy per atom: Epot =49.411eV Ekin = 5.677eV (T=472.234K) Etot = 55.088eV
Energy per atom: Epot =49.437eV Ekin = 5.650eV (T=469.978K) Etot = 55.087eV
Energy per atom: Epot =49.004eV Ekin = 6.083eV (T=506.023K) Etot = 55.087eV
Energy per atom: Epot =48.684eV Ekin = 6.406eV (T=532.862K) Etot = 55.089eV
Energy per atom: Epot =48.753eV Ekin = 6.334eV (T=526.906K) Etot = 55.087eV
Energy per atom: Epot =48.265eV Ekin = 6.814eV (T=566.820K) Etot = 55.079eV
Energy per atom: Epot =48.115eV Ekin = 6.966eV (T=579.494K) Etot = 55.081eV
Energy per atom: Epot =49.678eV Ekin = 5.412eV (T=450.206K) Etot = 55.090eV
Energy per atom: Epot =49.037eV Ekin = 6.050eV (T=503.298K) Etot = 55.088eV
Energy per atom: Epot =48.579eV Ekin = 6.509eV (T=541.459K) Etot = 55.088eV
Energy per atom: Epot =48.311eV Ekin = 6.772eV (T=563.307K) Etot = 55.083eV
Energy per atom: Epot =48.856eV Ekin = 6.227eV (T=517.998K) Etot = 55.083eV
Energy per atom: Epot =48.197eV Ekin = 6.890eV (T=573.167K) Etot = 55.087eV
Energy per atom: Epot =49.066eV Ekin = 6.023eV (T=501.029K) Etot = 55.089eV
Energy per atom: Epot =49.479eV Ekin = 5.610eV (T=466.640K) Etot = 55.088eV
Energy per atom: Epot =49.695eV Ekin = 5.395eV (T=448.831K) Etot = 55.090eV
Energy per atom: Epot =49.045eV Ekin = 6.044eV (T=502.743K) Etot = 55.088eV
Energy per atom: Epot =48.610eV Ekin = 6.477eV (T=538.828K) Etot = 55.087eV
Energy per atom: Epot =48.512eV Ekin = 6.573eV (T=546.822K) Etot = 55.086eV
Energy per atom: Epot =49.293eV Ekin = 5.797eV (T=482.258K) Etot = 55.091eV
Energy per atom: Epot =49.199eV Ekin = 5.894eV (T=490.321K) Etot = 55.093eV
Energy per atom: Epot =48.192eV Ekin = 6.896eV (T=573.623K) Etot = 55.087eV
Energy per atom: Epot =48.866eV Ekin = 6.219eV (T=517.373K) Etot = 55.086eV
Energy per atom: Epot =49.733eV Ekin = 5.356eV (T=445.585K) Etot = 55.089eV
Energy per atom: Epot =49.784eV Ekin = 5.307eV (T=441.481K) Etot = 55.091eV
Energy per atom: Epot =48.301eV Ekin = 6.783eV (T=564.236K) Etot = 55.084eV
Energy per atom: Epot =48.934eV Ekin = 6.153eV (T=511.883K) Etot = 55.087eV
Energy per atom: Epot =49.152eV Ekin = 5.936eV (T=493.809K) Etot = 55.088eV
Energy per atom: Epot =48.776eV Ekin = 6.310eV (T=524.937K) Etot = 55.087eV
Energy per atom: Epot =48.189eV Ekin = 6.897eV (T=573.762K) Etot = 55.086eV
Energy per atom: Epot =49.201eV Ekin = 5.888eV (T=489.843K) Etot = 55.089eV
Energy per atom: Epot =49.001eV Ekin = 6.085eV (T=506.195K) Etot = 55.086eV
Energy per atom: Epot =50.015eV Ekin = 5.079eV (T=422.520K) Etot = 55.094eV
Energy per atom: Epot =49.294eV Ekin = 5.796eV (T=482.126K) Etot = 55.090eV
Energy per atom: Epot =48.764eV Ekin = 6.322eV (T=525.944K) Etot = 55.087eV
Energy per atom: Epot =49.106eV Ekin = 5.983eV (T=497.705K) Etot = 55.089eV
Energy per atom: Epot =48.717eV Ekin = 6.368eV (T=529.697K) Etot = 55.085eV
Energy per atom: Epot =48.726eV Ekin = 6.357eV (T=528.837K) Etot = 55.084eV
Energy per atom: Epot =48.470eV Ekin = 6.614eV (T=550.209K) Etot = 55.084eV
Energy per atom: Epot =48.963eV Ekin = 6.125eV (T=509.482K) Etot = 55.088eV
Energy per atom: Epot =48.559eV Ekin = 6.526eV (T=542.849K) Etot = 55.085eV
Energy per atom: Epot =49.139eV Ekin = 5.951eV (T=495.002K) Etot = 55.089eV
Energy per atom: Epot =48.880eV Ekin = 6.206eV (T=516.231K) Etot = 55.086eV
Energy per atom: Epot =48.607eV Ekin = 6.478eV (T=538.908K) Etot = 55.086eV
Energy per atom: Epot =49.106eV Ekin = 5.987eV (T=498.040K) Etot = 55.093eV
Energy per atom: Epot =48.552eV Ekin = 6.534eV (T=543.518K) Etot = 55.086eV
Energy per atom: Epot =49.315eV Ekin = 5.775eV (T=480.427K) Etot = 55.091eV
Energy per atom: Epot =49.238eV Ekin = 5.855eV (T=487.036K) Etot = 55.093eV
Energy per atom: Epot =49.099eV Ekin = 5.992eV (T=498.429K) Etot = 55.091eV
Energy per atom: Epot =48.338eV Ekin = 6.749eV (T=561.442K) Etot = 55.087eV
Energy per atom: Epot =49.200eV Ekin = 5.894eV (T=490.313K) Etot = 55.094eV
Energy per atom: Epot =48.452eV Ekin = 6.632eV (T=551.717K) Etot = 55.084eV
Energy per atom: Epot =48.435eV Ekin = 6.650eV (T=553.178K) Etot = 55.085eV
Energy per atom: Epot =48.558eV Ekin = 6.527eV (T=542.946K) Etot = 55.085eV
Energy per atom: Epot =48.590eV Ekin = 6.495eV (T=540.319K) Etot = 55.085eV
Energy per atom: Epot =49.054eV Ekin = 6.035eV (T=502.054K) Etot = 55.090eV
Energy per atom: Epot =48.108eV Ekin = 6.971eV (T=579.927K) Etot = 55.080eV
Energy per atom: Epot =48.562eV Ekin = 6.522eV (T=542.572K) Etot = 55.084eV
Energy per atom: Epot =48.080eV Ekin = 7.005eV (T=582.714K) Etot = 55.085eV
Energy per atom: Epot =48.334eV Ekin = 6.753eV (T=561.717K) Etot = 55.086eV
Energy per atom: Epot =48.669eV Ekin = 6.418eV (T=533.900K) Etot = 55.087eV
Energy per atom: Epot =49.216eV Ekin = 5.872eV (T=488.475K) Etot = 55.088eV
Energy per atom: Epot =49.105eV Ekin = 5.981eV (T=497.565K) Etot = 55.086eV
Energy per atom: Epot =48.596eV Ekin = 6.494eV (T=540.203K) Etot = 55.089eV
Energy per atom: Epot =48.860eV Ekin = 6.231eV (T=518.338K) Etot = 55.091eV
Energy per atom: Epot =48.925eV Ekin = 6.160eV (T=512.408K) Etot = 55.085eV
Energy per atom: Epot =49.244eV Ekin = 5.844eV (T=486.163K) Etot = 55.088eV
Energy per atom: Epot =48.723eV Ekin = 6.361eV (T=529.176K) Etot = 55.084eV
Energy per atom: Epot =48.426eV Ekin = 6.659eV (T=553.928K) Etot = 55.085eV
Energy per atom: Epot =48.270eV Ekin = 6.815eV (T=566.898K) Etot = 55.085eV
Energy per atom: Epot =48.269eV Ekin = 6.817eV (T=567.062K) Etot = 55.085eV
Energy per atom: Epot =47.881eV Ekin = 7.200eV (T=598.963K) Etot = 55.081eV
Energy per atom: Epot =48.452eV Ekin = 6.632eV (T=551.678K) Etot = 55.084eV
Energy per atom: Epot =48.983eV Ekin = 6.108eV (T=508.079K) Etot = 55.091eV
Energy per atom: Epot =48.762eV Ekin = 6.326eV (T=526.257K) Etot = 55.088eV
Energy per atom: Epot =48.883eV Ekin = 6.206eV (T=516.284K) Etot = 55.089eV
Energy per atom: Epot =49.746eV Ekin = 5.346eV (T=444.674K) Etot = 55.092eV
Energy per atom: Epot =49.468eV Ekin = 5.617eV (T=467.250K) Etot = 55.085eV
Energy per atom: Epot =49.262eV Ekin = 5.827eV (T=484.731K) Etot = 55.089eV
Energy per atom: Epot =48.598eV Ekin = 6.487eV (T=539.651K) Etot = 55.086eV
Energy per atom: Epot =48.403eV Ekin = 6.682eV (T=555.817K) Etot = 55.085eV
Energy per atom: Epot =49.222eV Ekin = 5.868eV (T=488.162K) Etot = 55.090eV
Energy per atom: Epot =48.442eV Ekin = 6.646eV (T=552.841K) Etot = 55.088eV
Energy per atom: Epot =48.514eV Ekin = 6.572eV (T=546.729K) Etot = 55.086eV
Energy per atom: Epot =48.935eV Ekin = 6.151eV (T=511.715K) Etot = 55.087eV
Energy per atom: Epot =49.485eV Ekin = 5.604eV (T=466.149K) Etot = 55.089eV
Energy per atom: Epot =49.026eV Ekin = 6.061eV (T=504.154K) Etot = 55.087eV
Energy per atom: Epot =48.680eV Ekin = 6.404eV (T=532.725K) Etot = 55.084eV
Energy per atom: Epot =48.377eV Ekin = 6.710eV (T=558.177K) Etot = 55.087eV
Energy per atom: Epot =48.302eV Ekin = 6.784eV (T=564.379K) Etot = 55.087eV
Energy per atom: Epot =47.721eV Ekin = 7.362eV (T=612.410K) Etot = 55.082eV
Energy per atom: Epot =49.129eV Ekin = 5.961eV (T=495.884K) Etot = 55.091eV
Energy per atom: Epot =49.407eV Ekin = 5.682eV (T=472.673K) Etot = 55.089eV
Energy per atom: Epot =49.244eV Ekin = 5.848eV (T=486.438K) Etot = 55.091eV
Energy per atom: Epot =48.520eV Ekin = 6.573eV (T=546.748K) Etot = 55.092eV
Energy per atom: Epot =48.538eV Ekin = 6.550eV (T=544.907K) Etot = 55.089eV
Energy per atom: Epot =48.884eV Ekin = 6.206eV (T=516.292K) Etot = 55.090eV
Energy per atom: Epot =48.850eV Ekin = 6.243eV (T=519.292K) Etot = 55.092eV
Energy per atom: Epot =48.477eV Ekin = 6.611eV (T=549.912K) Etot = 55.088eV
Energy per atom: Epot =48.595eV Ekin = 6.492eV (T=540.078K) Etot = 55.087eV
Energy per atom: Epot =49.191eV Ekin = 5.898eV (T=490.633K) Etot = 55.089eV
Energy per atom: Epot =48.993eV Ekin = 6.094eV (T=506.977K) Etot = 55.088eV
Energy per atom: Epot =48.299eV Ekin = 6.787eV (T=564.616K) Etot = 55.086eV
Energy per atom: Epot =48.764eV Ekin = 6.325eV (T=526.163K) Etot = 55.089eV
Energy per atom: Epot =49.004eV Ekin = 6.083eV (T=506.016K) Etot = 55.087eV
Energy per atom: Epot =48.824eV Ekin = 6.262eV (T=520.898K) Etot = 55.085eV
Energy per atom: Epot =48.604eV Ekin = 6.480eV (T=539.010K) Etot = 55.084eV
Energy per atom: Epot =48.702eV Ekin = 6.383eV (T=530.980K) Etot = 55.085eV
Energy per atom: Epot =48.744eV Ekin = 6.346eV (T=527.910K) Etot = 55.090eV
Energy per atom: Epot =49.030eV Ekin = 6.064eV (T=504.451K) Etot = 55.094eV
Energy per atom: Epot =48.206eV Ekin = 6.881eV (T=572.426K) Etot = 55.087eV
Energy per atom: Epot =48.287eV Ekin = 6.797eV (T=565.403K) Etot = 55.084eV
Energy per atom: Epot =49.253eV Ekin = 5.839eV (T=485.761K) Etot = 55.092eV
Energy per atom: Epot =48.795eV Ekin = 6.290eV (T=523.223K) Etot = 55.085eV
Energy per atom: Epot =49.077eV Ekin = 6.013eV (T=500.168K) Etot = 55.089eV
Energy per atom: Epot =48.302eV Ekin = 6.783eV (T=564.238K) Etot = 55.084eV
Energy per atom: Epot =48.376eV Ekin = 6.708eV (T=557.979K) Etot = 55.083eV
Energy per atom: Epot =48.940eV Ekin = 6.147eV (T=511.348K) Etot = 55.087eV
Energy per atom: Epot =49.036eV Ekin = 6.051eV (T=503.402K) Etot = 55.088eV
Energy per atom: Epot =48.852eV Ekin = 6.239eV (T=518.967K) Etot = 55.090eV
Energy per atom: Epot =48.397eV Ekin = 6.691eV (T=556.588K) Etot = 55.088eV
Energy per atom: Epot =48.287eV Ekin = 6.797eV (T=565.434K) Etot = 55.084eV
Energy per atom: Epot =47.956eV Ekin = 7.127eV (T=592.849K) Etot = 55.083eV
Energy per atom: Epot =48.475eV Ekin = 6.609eV (T=549.816K) Etot = 55.085eV
Energy per atom: Epot =48.281eV Ekin = 6.806eV (T=566.147K) Etot = 55.087eV
Energy per atom: Epot =49.211eV Ekin = 5.880eV (T=489.146K) Etot = 55.092eV
Energy per atom: Epot =48.207eV Ekin = 6.877eV (T=572.096K) Etot = 55.085eV
Energy per atom: Epot =49.076eV Ekin = 6.013eV (T=500.182K) Etot = 55.089eV
Energy per atom: Epot =48.508eV Ekin = 6.580eV (T=547.340K) Etot = 55.088eV
Energy per atom: Epot =48.335eV Ekin = 6.750eV (T=561.534K) Etot = 55.085eV
Energy per atom: Epot =48.902eV Ekin = 6.183eV (T=514.371K) Etot = 55.086eV
Energy per atom: Epot =49.617eV Ekin = 5.473eV (T=455.277K) Etot = 55.090eV
Energy per atom: Epot =48.619eV Ekin = 6.466eV (T=537.854K) Etot = 55.085eV
Energy per atom: Epot =48.398eV Ekin = 6.687eV (T=556.247K) Etot = 55.085eV
Energy per atom: Epot =47.572eV Ekin = 7.512eV (T=624.929K) Etot = 55.084eV
Energy per atom: Epot =47.599eV Ekin = 7.485eV (T=622.664K) Etot = 55.085eV
Energy per atom: Epot =48.324eV Ekin = 6.765eV (T=562.789K) Etot = 55.090eV
Energy per atom: Epot =48.074eV Ekin = 7.015eV (T=583.525K) Etot = 55.089eV
Energy per atom: Epot =49.343eV Ekin = 5.748eV (T=478.115K) Etot = 55.091eV
Energy per atom: Epot =48.639eV Ekin = 6.448eV (T=536.377K) Etot = 55.087eV
Energy per atom: Epot =48.357eV Ekin = 6.734eV (T=560.211K) Etot = 55.091eV
Energy per atom: Epot =48.286eV Ekin = 6.804eV (T=566.000K) Etot = 55.090eV
Energy per atom: Epot =48.534eV Ekin = 6.554eV (T=545.211K) Etot = 55.089eV
Energy per atom: Epot =47.824eV Ekin = 7.261eV (T=604.024K) Etot = 55.085eV
Energy per atom: Epot =48.936eV Ekin = 6.153eV (T=511.824K) Etot = 55.089eV
Energy per atom: Epot =49.533eV Ekin = 5.558eV (T=462.320K) Etot = 55.091eV
Energy per atom: Epot =49.032eV Ekin = 6.057eV (T=503.870K) Etot = 55.089eV
Energy per atom: Epot =48.171eV Ekin = 6.911eV (T=574.918K) Etot = 55.082eV
Energy per atom: Epot =48.247eV Ekin = 6.838eV (T=568.789K) Etot = 55.084eV
Energy per atom: Epot =48.238eV Ekin = 6.845eV (T=569.419K) Etot = 55.083eV
Energy per atom: Epot =48.302eV Ekin = 6.782eV (T=564.206K) Etot = 55.084eV
Energy per atom: Epot =48.462eV Ekin = 6.625eV (T=551.073K) Etot = 55.087eV
Energy per atom: Epot =48.907eV Ekin = 6.182eV (T=514.263K) Etot = 55.089eV
Energy per atom: Epot =49.037eV Ekin = 6.052eV (T=503.446K) Etot = 55.089eV
Energy per atom: Epot =48.305eV Ekin = 6.779eV (T=563.923K) Etot = 55.084eV
Energy per atom: Epot =48.721eV Ekin = 6.361eV (T=529.190K) Etot = 55.083eV
Energy per atom: Epot =48.311eV Ekin = 6.768eV (T=563.040K) Etot = 55.080eV
Energy per atom: Epot =48.228eV Ekin = 6.857eV (T=570.448K) Etot = 55.086eV
Energy per atom: Epot =48.110eV Ekin = 6.975eV (T=580.243K) Etot = 55.085eV
Energy per atom: Epot =49.253eV Ekin = 5.838eV (T=485.637K) Etot = 55.091eV
Energy per atom: Epot =48.673eV Ekin = 6.414eV (T=533.520K) Etot = 55.086eV
Energy per atom: Epot =48.434eV Ekin = 6.651eV (T=553.267K) Etot = 55.085eV
Energy per atom: Epot =48.161eV Ekin = 6.922eV (T=575.824K) Etot = 55.083eV
Energy per atom: Epot =48.167eV Ekin = 6.920eV (T=575.622K) Etot = 55.086eV
Energy per atom: Epot =48.551eV Ekin = 6.539eV (T=543.991K) Etot = 55.091eV
Energy per atom: Epot =49.093eV Ekin = 6.000eV (T=499.156K) Etot = 55.094eV
Energy per atom: Epot =48.654eV Ekin = 6.433eV (T=535.114K) Etot = 55.087eV
Energy per atom: Epot =49.198eV Ekin = 5.890eV (T=489.968K) Etot = 55.088eV
Energy per atom: Epot =48.162eV Ekin = 6.925eV (T=576.101K) Etot = 55.088eV
Energy per atom: Epot =48.123eV Ekin = 6.958eV (T=578.794K) Etot = 55.081eV
Energy per atom: Epot =48.524eV Ekin = 6.561eV (T=545.770K) Etot = 55.085eV
Energy per atom: Epot =48.542eV Ekin = 6.546eV (T=544.567K) Etot = 55.089eV
Energy per atom: Epot =48.737eV Ekin = 6.349eV (T=528.141K) Etot = 55.086eV
Energy per atom: Epot =48.715eV Ekin = 6.370eV (T=529.877K) Etot = 55.085eV
Energy per atom: Epot =48.900eV Ekin = 6.188eV (T=514.754K) Etot = 55.088eV
Energy per atom: Epot =48.799eV Ekin = 6.289eV (T=523.160K) Etot = 55.088eV
Energy per atom: Epot =48.201eV Ekin = 6.881eV (T=572.438K) Etot = 55.082eV
Energy per atom: Epot =48.629eV Ekin = 6.454eV (T=536.862K) Etot = 55.083eV
Energy per atom: Epot =48.475eV Ekin = 6.610eV (T=549.824K) Etot = 55.085eV
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?