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/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 = 156.097eV (T=301.906K) Etot = 153.693eV
Energy per atom: Epot =117.400eV Ekin = 37.079eV (T=71.714K) Etot = 154.480eV
Energy per atom: Epot =79.252eV Ekin = 75.098eV (T=145.246K) Etot = 154.350eV
Energy per atom: Epot =71.656eV Ekin = 82.541eV (T=159.641K) Etot = 154.196eV
Energy per atom: Epot =69.629eV Ekin = 84.510eV (T=163.449K) Etot = 154.139eV
Energy per atom: Epot =81.194eV Ekin = 73.111eV (T=141.404K) Etot = 154.305eV
Energy per atom: Epot =78.936eV Ekin = 75.365eV (T=145.762K) Etot = 154.301eV
Energy per atom: Epot =73.459eV Ekin = 80.744eV (T=156.165K) Etot = 154.202eV
Energy per atom: Epot =73.324eV Ekin = 80.883eV (T=156.434K) Etot = 154.207eV
Energy per atom: Epot =78.050eV Ekin = 76.223eV (T=147.422K) Etot = 154.273eV
Energy per atom: Epot =76.511eV Ekin = 77.741eV (T=150.358K) Etot = 154.253eV
Energy per atom: Epot =74.751eV Ekin = 79.481eV (T=153.723K) Etot = 154.232eV
Energy per atom: Epot =76.355eV Ekin = 77.889eV (T=150.643K) Etot = 154.243eV
Energy per atom: Epot =77.889eV Ekin = 76.366eV (T=147.699K) Etot = 154.255eV
Energy per atom: Epot =74.289eV Ekin = 79.953eV (T=154.637K) Etot = 154.242eV
Energy per atom: Epot =75.854eV Ekin = 78.401eV (T=151.635K) Etot = 154.255eV
Energy per atom: Epot =75.042eV Ekin = 79.189eV (T=153.158K) Etot = 154.231eV
Energy per atom: Epot =77.881eV Ekin = 76.360eV (T=147.686K) Etot = 154.241eV
Energy per atom: Epot =74.995eV Ekin = 79.249eV (T=153.274K) Etot = 154.244eV
Energy per atom: Epot =74.988eV Ekin = 79.250eV (T=153.276K) Etot = 154.238eV
Energy per atom: Epot =79.748eV Ekin = 74.519eV (T=144.126K) Etot = 154.267eV
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:110: FutureWarning: The implementation of `fixcm=True` in `Langevin` does not strictly sample the correct NVT distributions. The deviations are typically small for large systems but can be more pronounced for small systems. Use `fixcm=False` together with `ase.constraints.FixCom`. `fixcm` is deprecated since ASE 3.28.0 and will be removed in a future release.
warnings.warn(msg, FutureWarning)
running a NVT simulation of fcc Cu
Energy per atom: Epot =540.816eV Ekin = 0.000eV (T=0.000K) Etot = 540.816eV
Energy per atom: Epot =599.863eV Ekin = 81.019eV (T=156.698K) Etot = 680.882eV
Energy per atom: Epot =671.254eV Ekin = 141.663eV (T=273.989K) Etot = 812.917eV
Energy per atom: Epot =733.099eV Ekin = 202.899eV (T=392.425K) Etot = 935.998eV
Energy per atom: Epot =785.005eV Ekin = 258.433eV (T=499.832K) Etot = 1043.438eV
Energy per atom: Epot =839.902eV Ekin = 302.028eV (T=584.149K) Etot = 1141.930eV
Energy per atom: Epot =888.813eV Ekin = 343.352eV (T=664.073K) Etot = 1232.166eV
Energy per atom: Epot =928.437eV Ekin = 379.970eV (T=734.894K) Etot = 1308.407eV
Energy per atom: Epot =968.931eV Ekin = 415.570eV (T=803.748K) Etot = 1384.501eV
Energy per atom: Epot =1006.733eV Ekin = 447.267eV (T=865.054K) Etot = 1454.000eV
Energy per atom: Epot =1040.708eV Ekin = 474.113eV (T=916.975K) Etot = 1514.821eV
Energy per atom: Epot =1074.898eV Ekin = 496.204eV (T=959.701K) Etot = 1571.102eV
Energy per atom: Epot =1109.815eV Ekin = 514.819eV (T=995.705K) Etot = 1624.634eV
Energy per atom: Epot =1142.202eV Ekin = 529.125eV (T=1023.374K) Etot = 1671.327eV
Energy per atom: Epot =1166.478eV Ekin = 547.750eV (T=1059.397K) Etot = 1714.228eV
Energy per atom: Epot =1197.230eV Ekin = 560.633eV (T=1084.313K) Etot = 1757.863eV
Energy per atom: Epot =1226.905eV Ekin = 571.538eV (T=1105.404K) Etot = 1798.443eV
Energy per atom: Epot =1248.783eV Ekin = 584.251eV (T=1129.992K) Etot = 1833.033eV
Energy per atom: Epot =1276.000eV Ekin = 592.524eV (T=1145.994K) Etot = 1868.525eV
Energy per atom: Epot =1307.411eV Ekin = 599.526eV (T=1159.535K) Etot = 1906.937eV
Energy per atom: Epot =1321.798eV Ekin = 610.074eV (T=1179.936K) Etot = 1931.872eV
Energy per atom: Epot =1358.589eV Ekin = 614.793eV (T=1189.064K) Etot = 1973.382eV
Energy per atom: Epot =1381.445eV Ekin = 628.464eV (T=1215.505K) Etot = 2009.910eV
Energy per atom: Epot =1397.328eV Ekin = 639.566eV (T=1236.976K) Etot = 2036.893eV
Energy per atom: Epot =1410.312eV Ekin = 654.920eV (T=1266.672K) Etot = 2065.232eV
Energy per atom: Epot =1421.236eV Ekin = 665.911eV (T=1287.929K) Etot = 2087.147eV
Energy per atom: Epot =1449.322eV Ekin = 657.810eV (T=1272.262K) Etot = 2107.132eV
Energy per atom: Epot =1447.966eV Ekin = 682.499eV (T=1320.013K) Etot = 2130.465eV
Energy per atom: Epot =1485.258eV Ekin = 668.840eV (T=1293.594K) Etot = 2154.098eV
Energy per atom: Epot =1491.057eV Ekin = 682.649eV (T=1320.303K) Etot = 2173.706eV
Energy per atom: Epot =1505.693eV Ekin = 684.610eV (T=1324.095K) Etot = 2190.303eV
Energy per atom: Epot =1520.130eV Ekin = 686.416eV (T=1327.588K) Etot = 2206.546eV
Energy per atom: Epot =1539.816eV Ekin = 675.767eV (T=1306.991K) Etot = 2215.583eV
Energy per atom: Epot =1549.819eV Ekin = 692.775eV (T=1339.887K) Etot = 2242.594eV
Energy per atom: Epot =1549.927eV Ekin = 706.557eV (T=1366.543K) Etot = 2256.484eV
Energy per atom: Epot =1563.177eV Ekin = 692.828eV (T=1339.990K) Etot = 2256.005eV
Energy per atom: Epot =1576.196eV Ekin = 695.758eV (T=1345.656K) Etot = 2271.954eV
Energy per atom: Epot =1582.316eV Ekin = 703.532eV (T=1360.692K) Etot = 2285.848eV
Energy per atom: Epot =1607.786eV Ekin = 697.454eV (T=1348.937K) Etot = 2305.241eV
Energy per atom: Epot =1603.247eV Ekin = 708.860eV (T=1370.996K) Etot = 2312.106eV
Energy per atom: Epot =1595.131eV Ekin = 728.042eV (T=1408.096K) Etot = 2323.172eV
Energy per atom: Epot =1610.368eV Ekin = 723.996eV (T=1400.271K) Etot = 2334.364eV
Energy per atom: Epot =1630.612eV Ekin = 712.342eV (T=1377.731K) Etot = 2342.954eV
Energy per atom: Epot =1632.898eV Ekin = 720.792eV (T=1394.074K) Etot = 2353.689eV
Energy per atom: Epot =1656.805eV Ekin = 705.482eV (T=1364.464K) Etot = 2362.287eV
Energy per atom: Epot =1645.471eV Ekin = 731.199eV (T=1414.202K) Etot = 2376.670eV
Energy per atom: Epot =1654.562eV Ekin = 724.872eV (T=1401.966K) Etot = 2379.434eV
Energy per atom: Epot =1663.987eV Ekin = 726.698eV (T=1405.497K) Etot = 2390.685eV
Energy per atom: Epot =1673.875eV Ekin = 725.103eV (T=1402.412K) Etot = 2398.977eV
Energy per atom: Epot =1675.060eV Ekin = 731.491eV (T=1414.768K) Etot = 2406.551eV
Energy per atom: Epot =1682.710eV Ekin = 726.951eV (T=1405.987K) Etot = 2409.661eV
Energy per atom: Epot =1694.000eV Ekin = 723.892eV (T=1400.069K) Etot = 2417.892eV
Energy per atom: Epot =1698.133eV Ekin = 727.521eV (T=1407.088K) Etot = 2425.654eV
Energy per atom: Epot =1705.616eV Ekin = 732.616eV (T=1416.944K) Etot = 2438.233eV
Energy per atom: Epot =1715.130eV Ekin = 736.819eV (T=1425.073K) Etot = 2451.949eV
Energy per atom: Epot =1720.102eV Ekin = 743.147eV (T=1437.311K) Etot = 2463.249eV
Energy per atom: Epot =1733.007eV Ekin = 736.769eV (T=1424.975K) Etot = 2469.776eV
Energy per atom: Epot =1748.954eV Ekin = 734.493eV (T=1420.573K) Etot = 2483.447eV
Energy per atom: Epot =1749.507eV Ekin = 743.958eV (T=1438.880K) Etot = 2493.465eV
Energy per atom: Epot =1762.574eV Ekin = 730.407eV (T=1412.671K) Etot = 2492.981eV
Energy per atom: Epot =1751.603eV Ekin = 744.958eV (T=1440.814K) Etot = 2496.561eV
Energy per atom: Epot =1776.343eV Ekin = 734.030eV (T=1419.678K) Etot = 2510.374eV
Energy per atom: Epot =1788.869eV Ekin = 733.475eV (T=1418.605K) Etot = 2522.344eV
Energy per atom: Epot =1793.141eV Ekin = 733.390eV (T=1418.440K) Etot = 2526.531eV
Energy per atom: Epot =1799.370eV Ekin = 728.068eV (T=1408.147K) Etot = 2527.438eV
Energy per atom: Epot =1809.089eV Ekin = 730.805eV (T=1413.441K) Etot = 2539.895eV
Energy per atom: Epot =1811.960eV Ekin = 738.619eV (T=1428.554K) Etot = 2550.580eV
Energy per atom: Epot =1814.697eV Ekin = 741.073eV (T=1433.300K) Etot = 2555.770eV
Energy per atom: Epot =1820.151eV Ekin = 741.839eV (T=1434.781K) Etot = 2561.990eV
Energy per atom: Epot =1832.582eV Ekin = 734.934eV (T=1421.426K) Etot = 2567.516eV
Energy per atom: Epot =1832.152eV Ekin = 736.039eV (T=1423.564K) Etot = 2568.191eV
Energy per atom: Epot =1830.719eV Ekin = 732.502eV (T=1416.722K) Etot = 2563.221eV
Energy per atom: Epot =1834.386eV Ekin = 735.434eV (T=1422.394K) Etot = 2569.820eV
Energy per atom: Epot =1839.604eV Ekin = 736.209eV (T=1423.892K) Etot = 2575.812eV
Energy per atom: Epot =1852.810eV Ekin = 725.849eV (T=1403.854K) Etot = 2578.659eV
Energy per atom: Epot =1856.144eV Ekin = 736.268eV (T=1424.006K) Etot = 2592.412eV
Energy per atom: Epot =1861.925eV Ekin = 732.560eV (T=1416.835K) Etot = 2594.485eV
Energy per atom: Epot =1852.745eV Ekin = 747.786eV (T=1446.284K) Etot = 2600.531eV
Energy per atom: Epot =1851.066eV Ekin = 754.721eV (T=1459.695K) Etot = 2605.786eV
Energy per atom: Epot =1852.498eV Ekin = 755.809eV (T=1461.801K) Etot = 2608.307eV
Energy per atom: Epot =1878.824eV Ekin = 742.971eV (T=1436.971K) Etot = 2621.795eV
Energy per atom: Epot =1865.645eV Ekin = 762.647eV (T=1475.026K) Etot = 2628.292eV
Energy per atom: Epot =1877.223eV Ekin = 757.737eV (T=1465.529K) Etot = 2634.959eV
Energy per atom: Epot =1880.075eV Ekin = 765.152eV (T=1479.870K) Etot = 2645.226eV
Energy per atom: Epot =1878.509eV Ekin = 761.380eV (T=1472.575K) Etot = 2639.889eV
Energy per atom: Epot =1892.481eV Ekin = 750.481eV (T=1451.496K) Etot = 2642.962eV
Energy per atom: Epot =1899.228eV Ekin = 752.413eV (T=1455.232K) Etot = 2651.641eV
Energy per atom: Epot =1909.637eV Ekin = 745.835eV (T=1442.509K) Etot = 2655.471eV
Energy per atom: Epot =1899.756eV Ekin = 761.019eV (T=1471.877K) Etot = 2660.775eV
Energy per atom: Epot =1916.771eV Ekin = 745.748eV (T=1442.342K) Etot = 2662.519eV
Energy per atom: Epot =1919.009eV Ekin = 751.393eV (T=1453.259K) Etot = 2670.401eV
Energy per atom: Epot =1927.797eV Ekin = 753.875eV (T=1458.059K) Etot = 2681.671eV
Energy per atom: Epot =1923.323eV Ekin = 756.562eV (T=1463.257K) Etot = 2679.885eV
Energy per atom: Epot =1925.546eV Ekin = 757.916eV (T=1465.876K) Etot = 2683.462eV
Energy per atom: Epot =1930.412eV Ekin = 758.051eV (T=1466.137K) Etot = 2688.463eV
Energy per atom: Epot =1936.708eV Ekin = 759.634eV (T=1469.199K) Etot = 2696.343eV
Energy per atom: Epot =1954.285eV Ekin = 746.142eV (T=1443.103K) Etot = 2700.427eV
Energy per atom: Epot =1947.392eV Ekin = 753.017eV (T=1456.400K) Etot = 2700.409eV
Energy per atom: Epot =1952.778eV Ekin = 741.002eV (T=1433.161K) Etot = 2693.779eV
Energy per atom: Epot =1950.195eV Ekin = 747.070eV (T=1444.898K) Etot = 2697.265eV
Energy per atom: Epot =1963.720eV Ekin = 732.119eV (T=1415.981K) Etot = 2695.838eV
Energy per atom: Epot =1952.807eV Ekin = 747.417eV (T=1445.570K) Etot = 2700.224eV
Energy per atom: Epot =1950.688eV Ekin = 752.470eV (T=1455.343K) Etot = 2703.159eV
Energy per atom: Epot =1947.069eV Ekin = 752.944eV (T=1456.260K) Etot = 2700.014eV
Energy per atom: Epot =1959.222eV Ekin = 752.706eV (T=1455.799K) Etot = 2711.928eV
Energy per atom: Epot =1964.412eV Ekin = 748.282eV (T=1447.243K) Etot = 2712.695eV
Energy per atom: Epot =1966.683eV Ekin = 752.730eV (T=1455.845K) Etot = 2719.413eV
Energy per atom: Epot =1948.627eV Ekin = 771.027eV (T=1491.234K) Etot = 2719.654eV
Energy per atom: Epot =1963.624eV Ekin = 755.552eV (T=1461.304K) Etot = 2719.177eV
Energy per atom: Epot =1957.711eV Ekin = 762.710eV (T=1475.148K) Etot = 2720.421eV
Energy per atom: Epot =1970.614eV Ekin = 749.799eV (T=1450.176K) Etot = 2720.413eV
Energy per atom: Epot =1972.844eV Ekin = 756.985eV (T=1464.075K) Etot = 2729.829eV
Energy per atom: Epot =1971.468eV Ekin = 764.149eV (T=1477.931K) Etot = 2735.618eV
Energy per atom: Epot =1984.457eV Ekin = 741.214eV (T=1433.572K) Etot = 2725.671eV
Energy per atom: Epot =1970.798eV Ekin = 758.428eV (T=1466.867K) Etot = 2729.227eV
Energy per atom: Epot =1986.613eV Ekin = 757.805eV (T=1465.661K) Etot = 2744.418eV
Energy per atom: Epot =1989.122eV Ekin = 753.993eV (T=1458.287K) Etot = 2743.115eV
Energy per atom: Epot =1993.011eV Ekin = 751.512eV (T=1453.490K) Etot = 2744.523eV
Energy per atom: Epot =1989.774eV Ekin = 754.970eV (T=1460.178K) Etot = 2744.744eV
Energy per atom: Epot =1990.459eV Ekin = 755.282eV (T=1460.781K) Etot = 2745.741eV
Energy per atom: Epot =1982.625eV Ekin = 765.699eV (T=1480.928K) Etot = 2748.324eV
Energy per atom: Epot =1984.115eV Ekin = 771.933eV (T=1492.985K) Etot = 2756.047eV
Energy per atom: Epot =1998.277eV Ekin = 773.550eV (T=1496.113K) Etot = 2771.827eV
Energy per atom: Epot =2014.108eV Ekin = 751.815eV (T=1454.076K) Etot = 2765.923eV
Energy per atom: Epot =1996.072eV Ekin = 768.870eV (T=1487.061K) Etot = 2764.942eV
Energy per atom: Epot =2002.744eV Ekin = 765.171eV (T=1479.907K) Etot = 2767.916eV
Energy per atom: Epot =2005.127eV Ekin = 762.721eV (T=1475.169K) Etot = 2767.848eV
Energy per atom: Epot =2017.985eV Ekin = 762.950eV (T=1475.612K) Etot = 2780.935eV
Energy per atom: Epot =2016.624eV Ekin = 767.842eV (T=1485.073K) Etot = 2784.466eV
Energy per atom: Epot =2008.409eV Ekin = 772.039eV (T=1493.191K) Etot = 2780.448eV
Energy per atom: Epot =2018.444eV Ekin = 770.325eV (T=1489.876K) Etot = 2788.769eV
Energy per atom: Epot =2007.845eV Ekin = 775.912eV (T=1500.681K) Etot = 2783.757eV
Energy per atom: Epot =2003.835eV Ekin = 775.760eV (T=1500.388K) Etot = 2779.596eV
Energy per atom: Epot =2010.632eV Ekin = 760.450eV (T=1470.776K) Etot = 2771.082eV
Energy per atom: Epot =1997.586eV Ekin = 771.556eV (T=1492.255K) Etot = 2769.141eV
Energy per atom: Epot =2014.179eV Ekin = 759.874eV (T=1469.662K) Etot = 2774.053eV
Energy per atom: Epot =2000.451eV Ekin = 772.534eV (T=1494.149K) Etot = 2772.985eV
Energy per atom: Epot =2006.330eV Ekin = 772.165eV (T=1493.435K) Etot = 2778.495eV
Energy per atom: Epot =2010.679eV Ekin = 764.168eV (T=1477.967K) Etot = 2774.846eV
Energy per atom: Epot =2005.036eV Ekin = 764.503eV (T=1478.615K) Etot = 2769.539eV
Energy per atom: Epot =2005.477eV Ekin = 762.476eV (T=1474.695K) Etot = 2767.953eV
Energy per atom: Epot =2000.717eV Ekin = 762.395eV (T=1474.539K) Etot = 2763.112eV
Energy per atom: Epot =1997.079eV Ekin = 768.382eV (T=1486.117K) Etot = 2765.461eV
Energy per atom: Epot =1999.442eV Ekin = 767.858eV (T=1485.103K) Etot = 2767.300eV
Energy per atom: Epot =1996.881eV Ekin = 773.899eV (T=1496.787K) Etot = 2770.780eV
Energy per atom: Epot =1984.466eV Ekin = 788.011eV (T=1524.082K) Etot = 2772.477eV
Energy per atom: Epot =2008.070eV Ekin = 772.876eV (T=1494.809K) Etot = 2780.945eV
Energy per atom: Epot =2002.766eV Ekin = 773.705eV (T=1496.412K) Etot = 2776.471eV
Energy per atom: Epot =1986.229eV Ekin = 785.542eV (T=1519.306K) Etot = 2771.770eV
Energy per atom: Epot =1999.966eV Ekin = 777.157eV (T=1503.088K) Etot = 2777.122eV
Energy per atom: Epot =1998.633eV Ekin = 771.775eV (T=1492.679K) Etot = 2770.408eV
Energy per atom: Epot =1991.206eV Ekin = 779.610eV (T=1507.834K) Etot = 2770.816eV
Energy per atom: Epot =1988.539eV Ekin = 776.102eV (T=1501.049K) Etot = 2764.641eV
Energy per atom: Epot =1990.359eV Ekin = 776.070eV (T=1500.987K) Etot = 2766.429eV
Energy per atom: Epot =1997.493eV Ekin = 780.592eV (T=1509.733K) Etot = 2778.086eV
Energy per atom: Epot =1990.917eV Ekin = 784.082eV (T=1516.483K) Etot = 2775.000eV
Energy per atom: Epot =2009.800eV Ekin = 768.810eV (T=1486.945K) Etot = 2778.610eV
Energy per atom: Epot =1997.999eV Ekin = 769.463eV (T=1488.209K) Etot = 2767.462eV
Energy per atom: Epot =2007.869eV Ekin = 759.528eV (T=1468.994K) Etot = 2767.398eV
Energy per atom: Epot =1996.089eV Ekin = 768.982eV (T=1487.277K) Etot = 2765.071eV
Energy per atom: Epot =2009.845eV Ekin = 766.820eV (T=1483.097K) Etot = 2776.665eV
Energy per atom: Epot =2013.879eV Ekin = 760.733eV (T=1471.324K) Etot = 2774.612eV
Energy per atom: Epot =2027.628eV Ekin = 753.464eV (T=1457.266K) Etot = 2781.093eV
Energy per atom: Epot =2003.059eV Ekin = 781.090eV (T=1510.696K) Etot = 2784.148eV
Energy per atom: Epot =2008.224eV Ekin = 767.699eV (T=1484.796K) Etot = 2775.923eV
Energy per atom: Epot =2013.312eV Ekin = 754.781eV (T=1459.812K) Etot = 2768.093eV
Energy per atom: Epot =1999.006eV Ekin = 762.355eV (T=1474.461K) Etot = 2761.360eV
Energy per atom: Epot =2001.102eV Ekin = 754.815eV (T=1459.878K) Etot = 2755.917eV
Energy per atom: Epot =2011.725eV Ekin = 749.939eV (T=1450.447K) Etot = 2761.664eV
Energy per atom: Epot =2004.756eV Ekin = 765.033eV (T=1479.640K) Etot = 2769.788eV
Energy per atom: Epot =1993.548eV Ekin = 781.689eV (T=1511.855K) Etot = 2775.237eV
Energy per atom: Epot =2001.654eV Ekin = 776.840eV (T=1502.476K) Etot = 2778.494eV
Energy per atom: Epot =2005.493eV Ekin = 774.364eV (T=1497.688K) Etot = 2779.857eV
Energy per atom: Epot =1994.871eV Ekin = 773.315eV (T=1495.659K) Etot = 2768.186eV
Energy per atom: Epot =1995.403eV Ekin = 775.694eV (T=1500.260K) Etot = 2771.097eV
Energy per atom: Epot =1999.197eV Ekin = 765.336eV (T=1480.227K) Etot = 2764.533eV
Energy per atom: Epot =1987.214eV Ekin = 776.475eV (T=1501.770K) Etot = 2763.689eV
Energy per atom: Epot =1988.666eV Ekin = 772.831eV (T=1494.722K) Etot = 2761.497eV
Energy per atom: Epot =1986.248eV Ekin = 767.389eV (T=1484.197K) Etot = 2753.637eV
Energy per atom: Epot =1987.586eV Ekin = 758.140eV (T=1466.309K) Etot = 2745.726eV
Energy per atom: Epot =2000.736eV Ekin = 750.490eV (T=1451.513K) Etot = 2751.226eV
Energy per atom: Epot =1992.777eV Ekin = 761.778eV (T=1473.344K) Etot = 2754.554eV
Energy per atom: Epot =1995.388eV Ekin = 751.389eV (T=1453.251K) Etot = 2746.777eV
Energy per atom: Epot =1986.578eV Ekin = 756.646eV (T=1463.419K) Etot = 2743.224eV
Energy per atom: Epot =1990.791eV Ekin = 758.862eV (T=1467.706K) Etot = 2749.654eV
Energy per atom: Epot =1970.020eV Ekin = 781.003eV (T=1510.527K) Etot = 2751.023eV
Energy per atom: Epot =1982.683eV Ekin = 766.688eV (T=1482.841K) Etot = 2749.371eV
Energy per atom: Epot =1986.490eV Ekin = 757.973eV (T=1465.986K) Etot = 2744.464eV
Energy per atom: Epot =1988.903eV Ekin = 764.465eV (T=1478.541K) Etot = 2753.367eV
Energy per atom: Epot =1985.093eV Ekin = 769.774eV (T=1488.810K) Etot = 2754.868eV
Energy per atom: Epot =1983.047eV Ekin = 767.411eV (T=1484.239K) Etot = 2750.457eV
Energy per atom: Epot =1980.830eV Ekin = 767.594eV (T=1484.593K) Etot = 2748.423eV
Energy per atom: Epot =1980.121eV Ekin = 776.546eV (T=1501.907K) Etot = 2756.667eV
Energy per atom: Epot =1975.787eV Ekin = 766.500eV (T=1482.477K) Etot = 2742.287eV
Energy per atom: Epot =1972.230eV Ekin = 771.429eV (T=1492.010K) Etot = 2743.659eV
Energy per atom: Epot =1982.310eV Ekin = 764.365eV (T=1478.348K) Etot = 2746.675eV
Energy per atom: Epot =1970.566eV Ekin = 773.700eV (T=1496.402K) Etot = 2744.266eV
Energy per atom: Epot =1963.281eV Ekin = 775.404eV (T=1499.700K) Etot = 2738.686eV
Energy per atom: Epot =1962.074eV Ekin = 769.827eV (T=1488.913K) Etot = 2731.901eV
Energy per atom: Epot =1974.929eV Ekin = 762.123eV (T=1474.012K) Etot = 2737.052eV
Energy per atom: Epot =1978.128eV Ekin = 763.502eV (T=1476.679K) Etot = 2741.630eV
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] 00:08:53 43.457006 1.0818
BFGSLineSearch: 1[ 1] 00:08:53 42.347659 0.2273
BFGSLineSearch: 2[ 2] 00:08:53 42.108454 0.1349
BFGSLineSearch: 3[ 3] 00:08:53 41.964817 0.1138
BFGSLineSearch: 4[ 4] 00:08:53 41.924933 0.0683
BFGSLineSearch: 5[ 5] 00:08:53 41.915346 0.0225
BFGSLineSearch: 6[ 6] 00:08:53 41.914920 0.0059
BFGSLineSearch: 7[ 7] 00:08:53 41.914872 0.0023
BFGSLineSearch: 8[ 9] 00:08:53 41.914855 0.0023
BFGSLineSearch: 9[ 10] 00:08:53 41.914851 0.0010
/builds/ase/ase/examples/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 = 13.199eV (T=1097.965K) Etot = 55.114eV
Energy per atom: Epot =49.203eV Ekin = 5.944eV (T=494.421K) Etot = 55.147eV
Energy per atom: Epot =49.276eV Ekin = 5.883eV (T=489.350K) Etot = 55.159eV
Energy per atom: Epot =49.411eV Ekin = 5.750eV (T=478.319K) Etot = 55.161eV
Energy per atom: Epot =49.739eV Ekin = 5.424eV (T=451.217K) Etot = 55.163eV
Energy per atom: Epot =49.526eV Ekin = 5.638eV (T=469.040K) Etot = 55.165eV
Energy per atom: Epot =48.504eV Ekin = 6.654eV (T=553.540K) Etot = 55.158eV
Energy per atom: Epot =48.512eV Ekin = 6.644eV (T=552.669K) Etot = 55.156eV
Energy per atom: Epot =48.712eV Ekin = 6.452eV (T=536.722K) Etot = 55.164eV
Energy per atom: Epot =49.234eV Ekin = 5.930eV (T=493.335K) Etot = 55.164eV
Energy per atom: Epot =49.282eV Ekin = 5.878eV (T=488.994K) Etot = 55.160eV
Energy per atom: Epot =49.457eV Ekin = 5.705eV (T=474.613K) Etot = 55.163eV
Energy per atom: Epot =48.956eV Ekin = 6.200eV (T=515.792K) Etot = 55.157eV
Energy per atom: Epot =48.525eV Ekin = 6.628eV (T=551.337K) Etot = 55.153eV
Energy per atom: Epot =49.139eV Ekin = 6.022eV (T=500.928K) Etot = 55.161eV
Energy per atom: Epot =49.381eV Ekin = 5.784eV (T=481.136K) Etot = 55.164eV
Energy per atom: Epot =49.076eV Ekin = 6.085eV (T=506.204K) Etot = 55.161eV
Energy per atom: Epot =48.563eV Ekin = 6.594eV (T=548.491K) Etot = 55.156eV
Energy per atom: Epot =48.995eV Ekin = 6.163eV (T=512.672K) Etot = 55.158eV
Energy per atom: Epot =48.395eV Ekin = 6.759eV (T=562.263K) Etot = 55.154eV
Energy per atom: Epot =49.089eV Ekin = 6.070eV (T=504.953K) Etot = 55.159eV
Energy per atom: Epot =48.121eV Ekin = 7.035eV (T=585.233K) Etot = 55.156eV
Energy per atom: Epot =48.905eV Ekin = 6.256eV (T=520.455K) Etot = 55.161eV
Energy per atom: Epot =49.463eV Ekin = 5.698eV (T=474.029K) Etot = 55.161eV
Energy per atom: Epot =48.540eV Ekin = 6.615eV (T=550.287K) Etot = 55.155eV
Energy per atom: Epot =48.660eV Ekin = 6.493eV (T=540.093K) Etot = 55.153eV
Energy per atom: Epot =47.942eV Ekin = 7.208eV (T=599.605K) Etot = 55.150eV
Energy per atom: Epot =49.255eV Ekin = 5.908eV (T=491.434K) Etot = 55.162eV
Energy per atom: Epot =48.764eV Ekin = 6.396eV (T=532.045K) Etot = 55.159eV
Energy per atom: Epot =49.500eV Ekin = 5.660eV (T=470.814K) Etot = 55.160eV
Energy per atom: Epot =49.747eV Ekin = 5.413eV (T=450.289K) Etot = 55.160eV
Energy per atom: Epot =49.193eV Ekin = 5.966eV (T=496.281K) Etot = 55.159eV
Energy per atom: Epot =48.474eV Ekin = 6.682eV (T=555.887K) Etot = 55.156eV
Energy per atom: Epot =48.896eV Ekin = 6.261eV (T=520.830K) Etot = 55.157eV
Energy per atom: Epot =49.140eV Ekin = 6.019eV (T=500.714K) Etot = 55.159eV
Energy per atom: Epot =49.192eV Ekin = 5.968eV (T=496.467K) Etot = 55.160eV
Energy per atom: Epot =49.373eV Ekin = 5.790eV (T=481.627K) Etot = 55.162eV
Energy per atom: Epot =49.483eV Ekin = 5.675eV (T=472.112K) Etot = 55.158eV
Energy per atom: Epot =48.902eV Ekin = 6.255eV (T=520.308K) Etot = 55.157eV
Energy per atom: Epot =48.114eV Ekin = 7.040eV (T=585.636K) Etot = 55.154eV
Energy per atom: Epot =49.087eV Ekin = 6.071eV (T=505.047K) Etot = 55.158eV
Energy per atom: Epot =48.341eV Ekin = 6.815eV (T=566.892K) Etot = 55.156eV
Energy per atom: Epot =49.075eV Ekin = 6.086eV (T=506.257K) Etot = 55.161eV
Energy per atom: Epot =48.809eV Ekin = 6.350eV (T=528.237K) Etot = 55.159eV
Energy per atom: Epot =48.672eV Ekin = 6.484eV (T=539.417K) Etot = 55.157eV
Energy per atom: Epot =49.059eV Ekin = 6.100eV (T=507.430K) Etot = 55.159eV
Energy per atom: Epot =48.725eV Ekin = 6.435eV (T=535.302K) Etot = 55.160eV
Energy per atom: Epot =48.583eV Ekin = 6.577eV (T=547.098K) Etot = 55.159eV
Energy per atom: Epot =48.511eV Ekin = 6.644eV (T=552.705K) Etot = 55.155eV
Energy per atom: Epot =48.798eV Ekin = 6.361eV (T=529.118K) Etot = 55.159eV
Energy per atom: Epot =48.672eV Ekin = 6.486eV (T=539.534K) Etot = 55.157eV
Energy per atom: Epot =48.722eV Ekin = 6.437eV (T=535.487K) Etot = 55.159eV
Energy per atom: Epot =48.477eV Ekin = 6.683eV (T=555.942K) Etot = 55.160eV
Energy per atom: Epot =48.532eV Ekin = 6.623eV (T=550.910K) Etot = 55.155eV
Energy per atom: Epot =48.321eV Ekin = 6.832eV (T=568.336K) Etot = 55.153eV
Energy per atom: Epot =49.472eV Ekin = 5.692eV (T=473.491K) Etot = 55.164eV
Energy per atom: Epot =48.257eV Ekin = 6.901eV (T=574.037K) Etot = 55.158eV
Energy per atom: Epot =49.040eV Ekin = 6.119eV (T=509.042K) Etot = 55.160eV
Energy per atom: Epot =49.185eV Ekin = 5.976eV (T=497.141K) Etot = 55.161eV
Energy per atom: Epot =48.540eV Ekin = 6.617eV (T=550.449K) Etot = 55.157eV
Energy per atom: Epot =48.493eV Ekin = 6.666eV (T=554.491K) Etot = 55.159eV
Energy per atom: Epot =48.763eV Ekin = 6.401eV (T=532.441K) Etot = 55.163eV
Energy per atom: Epot =48.503eV Ekin = 6.658eV (T=553.834K) Etot = 55.160eV
Energy per atom: Epot =48.363eV Ekin = 6.794eV (T=565.170K) Etot = 55.157eV
Energy per atom: Epot =49.083eV Ekin = 6.080eV (T=505.753K) Etot = 55.162eV
Energy per atom: Epot =48.913eV Ekin = 6.248eV (T=519.781K) Etot = 55.162eV
Energy per atom: Epot =48.426eV Ekin = 6.731eV (T=559.935K) Etot = 55.157eV
Energy per atom: Epot =49.215eV Ekin = 5.947eV (T=494.732K) Etot = 55.162eV
Energy per atom: Epot =48.614eV Ekin = 6.546eV (T=544.555K) Etot = 55.160eV
Energy per atom: Epot =48.068eV Ekin = 7.088eV (T=589.633K) Etot = 55.156eV
Energy per atom: Epot =48.848eV Ekin = 6.315eV (T=525.282K) Etot = 55.162eV
Energy per atom: Epot =48.326eV Ekin = 6.832eV (T=568.369K) Etot = 55.158eV
Energy per atom: Epot =48.563eV Ekin = 6.595eV (T=548.600K) Etot = 55.158eV
Energy per atom: Epot =47.780eV Ekin = 7.373eV (T=613.342K) Etot = 55.153eV
Energy per atom: Epot =49.161eV Ekin = 5.997eV (T=498.862K) Etot = 55.158eV
Energy per atom: Epot =48.720eV Ekin = 6.438eV (T=535.574K) Etot = 55.158eV
Energy per atom: Epot =48.888eV Ekin = 6.273eV (T=521.803K) Etot = 55.161eV
Energy per atom: Epot =48.961eV Ekin = 6.204eV (T=516.052K) Etot = 55.164eV
Energy per atom: Epot =49.002eV Ekin = 6.160eV (T=512.423K) Etot = 55.162eV
Energy per atom: Epot =48.971eV Ekin = 6.187eV (T=514.656K) Etot = 55.158eV
Energy per atom: Epot =47.872eV Ekin = 7.280eV (T=605.565K) Etot = 55.151eV
Energy per atom: Epot =49.064eV Ekin = 6.096eV (T=507.081K) Etot = 55.160eV
Energy per atom: Epot =48.082eV Ekin = 7.069eV (T=588.006K) Etot = 55.150eV
Energy per atom: Epot =48.155eV Ekin = 7.001eV (T=582.354K) Etot = 55.155eV
Energy per atom: Epot =48.958eV Ekin = 6.202eV (T=515.932K) Etot = 55.160eV
Energy per atom: Epot =49.210eV Ekin = 5.948eV (T=494.773K) Etot = 55.158eV
Energy per atom: Epot =49.009eV Ekin = 6.150eV (T=511.566K) Etot = 55.158eV
Energy per atom: Epot =48.500eV Ekin = 6.658eV (T=553.865K) Etot = 55.159eV
Energy per atom: Epot =48.469eV Ekin = 6.691eV (T=556.591K) Etot = 55.159eV
Energy per atom: Epot =47.876eV Ekin = 7.280eV (T=605.601K) Etot = 55.156eV
Energy per atom: Epot =48.772eV Ekin = 6.390eV (T=531.595K) Etot = 55.162eV
Energy per atom: Epot =48.476eV Ekin = 6.682eV (T=555.849K) Etot = 55.158eV
Energy per atom: Epot =48.789eV Ekin = 6.372eV (T=530.064K) Etot = 55.161eV
Energy per atom: Epot =49.125eV Ekin = 6.033eV (T=501.887K) Etot = 55.158eV
Energy per atom: Epot =49.329eV Ekin = 5.835eV (T=485.359K) Etot = 55.164eV
Energy per atom: Epot =49.013eV Ekin = 6.145eV (T=511.213K) Etot = 55.158eV
Energy per atom: Epot =48.257eV Ekin = 6.896eV (T=573.679K) Etot = 55.153eV
Energy per atom: Epot =49.063eV Ekin = 6.099eV (T=507.383K) Etot = 55.162eV
Energy per atom: Epot =48.505eV Ekin = 6.650eV (T=553.195K) Etot = 55.155eV
Energy per atom: Epot =48.762eV Ekin = 6.395eV (T=531.976K) Etot = 55.157eV
Energy per atom: Epot =48.568eV Ekin = 6.592eV (T=548.351K) Etot = 55.160eV
Energy per atom: Epot =49.079eV Ekin = 6.082eV (T=505.981K) Etot = 55.162eV
Energy per atom: Epot =48.659eV Ekin = 6.500eV (T=540.695K) Etot = 55.159eV
Energy per atom: Epot =48.766eV Ekin = 6.393eV (T=531.830K) Etot = 55.159eV
Energy per atom: Epot =48.952eV Ekin = 6.203eV (T=516.027K) Etot = 55.155eV
Energy per atom: Epot =48.758eV Ekin = 6.400eV (T=532.383K) Etot = 55.158eV
Energy per atom: Epot =48.714eV Ekin = 6.444eV (T=536.090K) Etot = 55.158eV
Energy per atom: Epot =49.204eV Ekin = 5.957eV (T=495.536K) Etot = 55.161eV
Energy per atom: Epot =49.088eV Ekin = 6.072eV (T=505.126K) Etot = 55.160eV
Energy per atom: Epot =48.970eV Ekin = 6.191eV (T=515.002K) Etot = 55.161eV
Energy per atom: Epot =48.838eV Ekin = 6.323eV (T=525.971K) Etot = 55.161eV
Energy per atom: Epot =48.165eV Ekin = 6.991eV (T=581.529K) Etot = 55.155eV
Energy per atom: Epot =49.244eV Ekin = 5.914eV (T=491.928K) Etot = 55.157eV
Energy per atom: Epot =48.471eV Ekin = 6.686eV (T=556.204K) Etot = 55.158eV
Energy per atom: Epot =48.652eV Ekin = 6.510eV (T=541.557K) Etot = 55.162eV
Energy per atom: Epot =48.818eV Ekin = 6.342eV (T=527.587K) Etot = 55.160eV
Energy per atom: Epot =48.912eV Ekin = 6.248eV (T=519.775K) Etot = 55.160eV
Energy per atom: Epot =48.427eV Ekin = 6.732eV (T=560.047K) Etot = 55.159eV
Energy per atom: Epot =48.056eV Ekin = 7.097eV (T=590.394K) Etot = 55.154eV
Energy per atom: Epot =48.091eV Ekin = 7.062eV (T=587.439K) Etot = 55.153eV
Energy per atom: Epot =48.068eV Ekin = 7.086eV (T=589.438K) Etot = 55.154eV
Energy per atom: Epot =48.951eV Ekin = 6.212eV (T=516.718K) Etot = 55.163eV
Energy per atom: Epot =49.097eV Ekin = 6.064eV (T=504.420K) Etot = 55.161eV
Energy per atom: Epot =49.134eV Ekin = 6.023eV (T=501.060K) Etot = 55.157eV
Energy per atom: Epot =48.132eV Ekin = 7.021eV (T=584.067K) Etot = 55.153eV
Energy per atom: Epot =49.020eV Ekin = 6.139eV (T=510.721K) Etot = 55.159eV
Energy per atom: Epot =48.131eV Ekin = 7.026eV (T=584.496K) Etot = 55.157eV
Energy per atom: Epot =48.606eV Ekin = 6.552eV (T=545.066K) Etot = 55.159eV
Energy per atom: Epot =48.456eV Ekin = 6.703eV (T=557.572K) Etot = 55.158eV
Energy per atom: Epot =48.973eV Ekin = 6.190eV (T=514.948K) Etot = 55.163eV
Energy per atom: Epot =47.689eV Ekin = 7.466eV (T=621.092K) Etot = 55.155eV
Energy per atom: Epot =47.890eV Ekin = 7.265eV (T=604.343K) Etot = 55.155eV
Energy per atom: Epot =48.985eV Ekin = 6.178eV (T=513.896K) Etot = 55.163eV
Energy per atom: Epot =47.831eV Ekin = 7.325eV (T=609.326K) Etot = 55.156eV
Energy per atom: Epot =47.997eV Ekin = 7.155eV (T=595.198K) Etot = 55.152eV
Energy per atom: Epot =48.075eV Ekin = 7.080eV (T=588.991K) Etot = 55.155eV
Energy per atom: Epot =47.897eV Ekin = 7.261eV (T=603.998K) Etot = 55.158eV
Energy per atom: Epot =47.408eV Ekin = 7.745eV (T=644.283K) Etot = 55.153eV
Energy per atom: Epot =48.064eV Ekin = 7.093eV (T=590.007K) Etot = 55.156eV
Energy per atom: Epot =48.261eV Ekin = 6.900eV (T=574.026K) Etot = 55.161eV
Energy per atom: Epot =47.932eV Ekin = 7.222eV (T=600.736K) Etot = 55.154eV
Energy per atom: Epot =46.787eV Ekin = 8.362eV (T=695.612K) Etot = 55.149eV
Energy per atom: Epot =48.501eV Ekin = 6.655eV (T=553.641K) Etot = 55.156eV
Energy per atom: Epot =48.517eV Ekin = 6.636eV (T=552.004K) Etot = 55.153eV
Energy per atom: Epot =48.237eV Ekin = 6.925eV (T=576.025K) Etot = 55.161eV
Energy per atom: Epot =47.827eV Ekin = 7.329eV (T=609.633K) Etot = 55.155eV
Energy per atom: Epot =48.940eV Ekin = 6.215eV (T=517.031K) Etot = 55.156eV
Energy per atom: Epot =47.686eV Ekin = 7.467eV (T=621.130K) Etot = 55.153eV
Energy per atom: Epot =48.772eV Ekin = 6.389eV (T=531.520K) Etot = 55.161eV
Energy per atom: Epot =48.252eV Ekin = 6.910eV (T=574.829K) Etot = 55.162eV
Energy per atom: Epot =47.625eV Ekin = 7.532eV (T=626.524K) Etot = 55.157eV
Energy per atom: Epot =48.717eV Ekin = 6.440eV (T=535.738K) Etot = 55.157eV
Energy per atom: Epot =47.544eV Ekin = 7.609eV (T=632.992K) Etot = 55.153eV
Energy per atom: Epot =47.925eV Ekin = 7.234eV (T=601.762K) Etot = 55.159eV
Energy per atom: Epot =48.795eV Ekin = 6.367eV (T=529.629K) Etot = 55.162eV
Energy per atom: Epot =48.209eV Ekin = 6.948eV (T=578.014K) Etot = 55.158eV
Energy per atom: Epot =48.451eV Ekin = 6.709eV (T=558.114K) Etot = 55.160eV
Energy per atom: Epot =48.518eV Ekin = 6.644eV (T=552.699K) Etot = 55.162eV
Energy per atom: Epot =48.048eV Ekin = 7.115eV (T=591.896K) Etot = 55.164eV
Energy per atom: Epot =47.565eV Ekin = 7.590eV (T=631.364K) Etot = 55.155eV
Energy per atom: Epot =48.740eV Ekin = 6.416eV (T=533.712K) Etot = 55.156eV
Energy per atom: Epot =48.206eV Ekin = 6.947eV (T=577.930K) Etot = 55.154eV
Energy per atom: Epot =48.582eV Ekin = 6.575eV (T=546.980K) Etot = 55.157eV
Energy per atom: Epot =48.568eV Ekin = 6.590eV (T=548.182K) Etot = 55.158eV
Energy per atom: Epot =48.038eV Ekin = 7.120eV (T=592.304K) Etot = 55.158eV
Energy per atom: Epot =48.111eV Ekin = 7.049eV (T=586.358K) Etot = 55.159eV
Energy per atom: Epot =48.313eV Ekin = 6.847eV (T=569.567K) Etot = 55.160eV
Energy per atom: Epot =48.697eV Ekin = 6.462eV (T=537.553K) Etot = 55.159eV
Energy per atom: Epot =48.128eV Ekin = 7.027eV (T=584.578K) Etot = 55.156eV
Energy per atom: Epot =48.634eV Ekin = 6.525eV (T=542.806K) Etot = 55.159eV
Energy per atom: Epot =47.894eV Ekin = 7.267eV (T=604.506K) Etot = 55.161eV
Energy per atom: Epot =48.659eV Ekin = 6.502eV (T=540.906K) Etot = 55.161eV
Energy per atom: Epot =48.596eV Ekin = 6.560eV (T=545.742K) Etot = 55.157eV
Energy per atom: Epot =47.389eV Ekin = 7.766eV (T=646.061K) Etot = 55.155eV
Energy per atom: Epot =47.910eV Ekin = 7.248eV (T=602.950K) Etot = 55.158eV
Energy per atom: Epot =48.529eV Ekin = 6.629eV (T=551.442K) Etot = 55.158eV
Energy per atom: Epot =48.567eV Ekin = 6.590eV (T=548.233K) Etot = 55.157eV
Energy per atom: Epot =48.142eV Ekin = 7.011eV (T=583.227K) Etot = 55.153eV
Energy per atom: Epot =48.153eV Ekin = 7.002eV (T=582.501K) Etot = 55.156eV
Energy per atom: Epot =48.088eV Ekin = 7.070eV (T=588.152K) Etot = 55.158eV
Energy per atom: Epot =48.013eV Ekin = 7.142eV (T=594.130K) Etot = 55.155eV
Energy per atom: Epot =48.110eV Ekin = 7.051eV (T=586.584K) Etot = 55.162eV
Energy per atom: Epot =47.931eV Ekin = 7.226eV (T=601.087K) Etot = 55.157eV
Energy per atom: Epot =48.763eV Ekin = 6.396eV (T=532.039K) Etot = 55.158eV
Energy per atom: Epot =48.645eV Ekin = 6.518eV (T=542.241K) Etot = 55.163eV
Energy per atom: Epot =47.027eV Ekin = 8.125eV (T=675.893K) Etot = 55.152eV
Energy per atom: Epot =47.891eV Ekin = 7.263eV (T=604.171K) Etot = 55.154eV
Energy per atom: Epot =48.331eV Ekin = 6.828eV (T=567.989K) Etot = 55.159eV
Energy per atom: Epot =47.808eV Ekin = 7.354eV (T=611.737K) Etot = 55.162eV
Energy per atom: Epot =48.052eV Ekin = 7.104eV (T=590.961K) Etot = 55.156eV
Energy per atom: Epot =47.605eV Ekin = 7.549eV (T=627.967K) Etot = 55.154eV
Energy per atom: Epot =48.202eV Ekin = 6.962eV (T=579.110K) Etot = 55.163eV
Energy per atom: Epot =47.930eV Ekin = 7.228eV (T=601.305K) Etot = 55.158eV
Energy per atom: Epot =48.492eV Ekin = 6.667eV (T=554.638K) Etot = 55.160eV
Energy per atom: Epot =48.307eV Ekin = 6.854eV (T=570.196K) Etot = 55.161eV
Energy per atom: Epot =48.296eV Ekin = 6.865eV (T=571.100K) Etot = 55.161eV
Energy per atom: Epot =48.192eV Ekin = 6.968eV (T=579.648K) Etot = 55.160eV
Energy per atom: Epot =48.040eV Ekin = 7.116eV (T=591.994K) Etot = 55.156eV
Energy per atom: Epot =48.251eV Ekin = 6.909eV (T=574.729K) Etot = 55.160eV
Energy per atom: Epot =48.112eV Ekin = 7.049eV (T=586.373K) Etot = 55.161eV
Energy per atom: Epot =47.839eV Ekin = 7.322eV (T=609.118K) Etot = 55.162eV
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?