Note
Go to the end to download the full example code.
Molecular dynamics#
Note
These examples can be run without asap3 installed. In that case,
ASE’s Python implementation of the EMT calculator can be used instead, but it
is much slower.
Goal#
In this tutorial, we will learn how to perform basic molecular dynamics (MD) simulations using ASE.
The key objectives are:
Understand how to set up a crystal structure (Cu atoms on an FCC lattice).
Initialize velocities from Maxwell–Boltzmann distribution corresponding to a chosen temperature.
Integrate Newton’s equations of motion using Velocity-Verlet algorithm and we monitor the temperature using Langevin thermostat.
Monitor and analyze thermodynamic quantities (potential energy, kinetic energy, total energy, temperature).
Save trajectories and visualize atomic motion with ASE’s GUI.
Explore MD in different scenarios: - Constant energy MD (NVE ensemble) - Constant temperature MD (NVT ensemble) - Isolated nanoparticle simulations
By the end of this tutorial, you should be able to set up your own MD simulations, monitor energy conservation, and visualize system evolution.
Part 1: Basic Molecular Dynamics Simulation#
We start by creating a copper crystal, assigning random velocities corresponding to Maxwell Boltzmann Distribution at 300 K, and running dynamics in the NVE ensemble (constant energy).
import matplotlib.pyplot as plt
import numpy as np
# choose one of the following implementations of EMT:
# included in ase
from ase.calculators.emt import EMT
# faster performance
#from asap3 import EMT
from ase import units
from ase.cluster.cubic import FaceCenteredCubic as ClusterFCC
from ase.io.trajectory import Trajectory
from ase.lattice.cubic import FaceCenteredCubic as LatticeFCC
from ase.md.langevin import Langevin # for later NPT simulations
from ase.md.velocitydistribution import (
MaxwellBoltzmannDistribution,
Stationary,
ZeroRotation,
)
from ase.md.verlet import VelocityVerlet
from ase.optimize import QuasiNewton
from ase.visualize.plot import plot_atoms
# Set up initial positions of Cu atoms on Fcc crystal lattice
size = 10
atoms = LatticeFCC(
directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
symbol='Cu',
size=(size, size, size),
pbc=True,
)
Before setting up the MD simulation, we take a look at the initial structure:
fig, ax = plt.subplots(figsize=(5, 5))
plot_atoms(atoms, ax, rotation=('45x,45y,0z'), show_unit_cell=2, radii=0.75)
ax.set_axis_off()
plt.tight_layout()
plt.show()
Now let’s run the MD simulation and monitor the kinetic and potential energy of the whole system:
# Describe the interatomic interactions with the Effective Medium Theory (EMT)
atoms.calc = EMT()
# Set the initial velocities corresponding to T=300K from Maxwell Boltzmann
# Distribution
MaxwellBoltzmannDistribution(atoms, temperature_K=300)
# We use Velocity Verlet algorithm to integrate the Newton's equations.
timestep_fs = 5
dyn = VelocityVerlet(atoms, timestep_fs * units.fs) # 5 fs time step.
def printenergy(a):
"""
Function to print the thermodynamical properties i.e potential energy,
kinetic energy and total energy
"""
epot = a.get_potential_energy()
ekin = a.get_kinetic_energy()
temp = a.get_temperature()
print(
f'Energy per atom: Epot ={epot:6.3f}eV Ekin = {ekin:.3f}eV '
f'(T={temp:.3f}K) Etot = {epot + ekin:.3f}eV'
)
# Now run the dynamics
print('running a NVE simulation of fcc Cu')
printenergy(atoms)
# init lists to for energy vs time data
time_ps, epot, ekin = [], [], []
mdind = 0
steps_per_block = 10
for i in range(20):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the energies of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
epot.append(atoms.get_potential_energy())
ekin.append(atoms.get_kinetic_energy())
etot = np.array(epot) + np.array(ekin)
# Plot energies vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, epot, label='Potential energy')
ax.plot(time_ps, ekin, label='Kinetic energy')
ax.plot(time_ps, etot, label='Total energy')
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Energy (eV)')
ax.legend(loc='best')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
running a NVE simulation of fcc Cu
Energy per atom: Epot =-22.726eV Ekin = 154.888eV (T=299.568K) Etot = 132.162eV
Energy per atom: Epot =97.454eV Ekin = 35.500eV (T=68.659K) Etot = 132.954eV
Energy per atom: Epot =57.522eV Ekin = 75.283eV (T=145.604K) Etot = 132.805eV
Energy per atom: Epot =50.947eV Ekin = 81.720eV (T=158.054K) Etot = 132.667eV
Energy per atom: Epot =48.560eV Ekin = 84.044eV (T=162.548K) Etot = 132.604eV
Energy per atom: Epot =60.008eV Ekin = 72.761eV (T=140.725K) Etot = 132.768eV
Energy per atom: Epot =57.868eV Ekin = 74.895eV (T=144.853K) Etot = 132.763eV
Energy per atom: Epot =53.051eV Ekin = 79.620eV (T=153.993K) Etot = 132.671eV
Energy per atom: Epot =50.854eV Ekin = 81.810eV (T=158.227K) Etot = 132.664eV
Energy per atom: Epot =59.821eV Ekin = 72.934eV (T=141.061K) Etot = 132.755eV
Energy per atom: Epot =54.514eV Ekin = 78.202eV (T=151.249K) Etot = 132.716eV
Energy per atom: Epot =53.980eV Ekin = 78.715eV (T=152.242K) Etot = 132.695eV
Energy per atom: Epot =55.115eV Ekin = 77.587eV (T=150.059K) Etot = 132.701eV
Energy per atom: Epot =56.420eV Ekin = 76.294eV (T=147.559K) Etot = 132.714eV
Energy per atom: Epot =53.554eV Ekin = 79.147eV (T=153.077K) Etot = 132.701eV
Energy per atom: Epot =55.932eV Ekin = 76.791eV (T=148.520K) Etot = 132.723eV
Energy per atom: Epot =53.038eV Ekin = 79.657eV (T=154.064K) Etot = 132.695eV
Energy per atom: Epot =58.636eV Ekin = 74.081eV (T=143.280K) Etot = 132.718eV
Energy per atom: Epot =52.711eV Ekin = 79.990eV (T=154.707K) Etot = 132.701eV
Energy per atom: Epot =54.044eV Ekin = 78.659eV (T=152.133K) Etot = 132.702eV
Energy per atom: Epot =59.379eV Ekin = 73.352eV (T=141.869K) Etot = 132.731eV
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()
/build/reproducible-path/python-ase-3.28.0/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 =524.308eV Ekin = 0.000eV (T=0.000K) Etot = 524.308eV
Energy per atom: Epot =583.243eV Ekin = 80.961eV (T=156.586K) Etot = 664.204eV
Energy per atom: Epot =652.321eV Ekin = 143.113eV (T=276.792K) Etot = 795.434eV
Energy per atom: Epot =712.622eV Ekin = 198.753eV (T=384.405K) Etot = 911.375eV
Energy per atom: Epot =767.449eV Ekin = 249.952eV (T=483.429K) Etot = 1017.401eV
Energy per atom: Epot =814.971eV Ekin = 298.645eV (T=577.605K) Etot = 1113.616eV
Energy per atom: Epot =862.999eV Ekin = 346.576eV (T=670.308K) Etot = 1209.575eV
Energy per atom: Epot =901.616eV Ekin = 387.494eV (T=749.447K) Etot = 1289.109eV
Energy per atom: Epot =952.521eV Ekin = 409.738eV (T=792.469K) Etot = 1362.259eV
Energy per atom: Epot =991.698eV Ekin = 441.754eV (T=854.391K) Etot = 1433.452eV
Energy per atom: Epot =1038.785eV Ekin = 456.566eV (T=883.039K) Etot = 1495.351eV
Energy per atom: Epot =1071.720eV Ekin = 481.414eV (T=931.096K) Etot = 1553.134eV
Energy per atom: Epot =1099.196eV Ekin = 514.189eV (T=994.487K) Etot = 1613.386eV
Energy per atom: Epot =1130.545eV Ekin = 539.330eV (T=1043.111K) Etot = 1669.875eV
Energy per atom: Epot =1165.473eV Ekin = 552.357eV (T=1068.307K) Etot = 1717.831eV
Energy per atom: Epot =1186.999eV Ekin = 570.155eV (T=1102.729K) Etot = 1757.154eV
Energy per atom: Epot =1222.650eV Ekin = 580.063eV (T=1121.893K) Etot = 1802.713eV
Energy per atom: Epot =1245.040eV Ekin = 591.318eV (T=1143.660K) Etot = 1836.358eV
Energy per atom: Epot =1271.304eV Ekin = 595.781eV (T=1152.293K) Etot = 1867.085eV
Energy per atom: Epot =1299.896eV Ekin = 604.355eV (T=1168.875K) Etot = 1904.251eV
Energy per atom: Epot =1322.935eV Ekin = 616.122eV (T=1191.633K) Etot = 1939.057eV
Energy per atom: Epot =1353.759eV Ekin = 622.615eV (T=1204.191K) Etot = 1976.374eV
Energy per atom: Epot =1377.882eV Ekin = 625.012eV (T=1208.827K) Etot = 2002.893eV
Energy per atom: Epot =1393.349eV Ekin = 636.967eV (T=1231.949K) Etot = 2030.316eV
Energy per atom: Epot =1411.091eV Ekin = 657.280eV (T=1271.237K) Etot = 2068.371eV
Energy per atom: Epot =1419.999eV Ekin = 673.700eV (T=1302.995K) Etot = 2093.700eV
Energy per atom: Epot =1441.778eV Ekin = 669.139eV (T=1294.173K) Etot = 2110.917eV
Energy per atom: Epot =1454.847eV Ekin = 662.366eV (T=1281.073K) Etot = 2117.212eV
Energy per atom: Epot =1462.797eV Ekin = 680.797eV (T=1316.720K) Etot = 2143.594eV
Energy per atom: Epot =1482.271eV Ekin = 681.642eV (T=1318.355K) Etot = 2163.914eV
Energy per atom: Epot =1497.469eV Ekin = 689.908eV (T=1334.342K) Etot = 2187.377eV
Energy per atom: Epot =1521.655eV Ekin = 690.093eV (T=1334.700K) Etot = 2211.748eV
Energy per atom: Epot =1538.810eV Ekin = 681.319eV (T=1317.730K) Etot = 2220.128eV
Energy per atom: Epot =1541.657eV Ekin = 695.340eV (T=1344.847K) Etot = 2236.996eV
Energy per atom: Epot =1549.761eV Ekin = 702.237eV (T=1358.187K) Etot = 2251.997eV
Energy per atom: Epot =1557.909eV Ekin = 708.328eV (T=1369.968K) Etot = 2266.237eV
Energy per atom: Epot =1570.705eV Ekin = 703.187eV (T=1360.024K) Etot = 2273.891eV
Energy per atom: Epot =1585.589eV Ekin = 699.223eV (T=1352.359K) Etot = 2284.813eV
Energy per atom: Epot =1592.229eV Ekin = 708.220eV (T=1369.760K) Etot = 2300.449eV
Energy per atom: Epot =1613.610eV Ekin = 703.506eV (T=1360.641K) Etot = 2317.115eV
Energy per atom: Epot =1627.113eV Ekin = 699.370eV (T=1352.642K) Etot = 2326.483eV
Energy per atom: Epot =1618.945eV Ekin = 718.742eV (T=1390.109K) Etot = 2337.686eV
Energy per atom: Epot =1626.475eV Ekin = 717.314eV (T=1387.347K) Etot = 2343.788eV
Energy per atom: Epot =1634.190eV Ekin = 716.537eV (T=1385.845K) Etot = 2350.726eV
Energy per atom: Epot =1650.070eV Ekin = 711.906eV (T=1376.887K) Etot = 2361.975eV
Energy per atom: Epot =1643.966eV Ekin = 728.726eV (T=1409.420K) Etot = 2372.692eV
Energy per atom: Epot =1662.514eV Ekin = 730.468eV (T=1412.788K) Etot = 2392.981eV
Energy per atom: Epot =1679.900eV Ekin = 718.992eV (T=1390.594K) Etot = 2398.893eV
Energy per atom: Epot =1677.764eV Ekin = 740.480eV (T=1432.153K) Etot = 2418.244eV
Energy per atom: Epot =1694.891eV Ekin = 725.320eV (T=1402.833K) Etot = 2420.211eV
Energy per atom: Epot =1713.613eV Ekin = 721.468eV (T=1395.381K) Etot = 2435.080eV
Energy per atom: Epot =1713.685eV Ekin = 726.868eV (T=1405.826K) Etot = 2440.553eV
Energy per atom: Epot =1712.008eV Ekin = 724.663eV (T=1401.562K) Etot = 2436.671eV
Energy per atom: Epot =1721.922eV Ekin = 725.572eV (T=1403.319K) Etot = 2447.494eV
Energy per atom: Epot =1712.408eV Ekin = 740.744eV (T=1432.662K) Etot = 2453.152eV
Energy per atom: Epot =1731.511eV Ekin = 736.349eV (T=1424.163K) Etot = 2467.860eV
Energy per atom: Epot =1738.158eV Ekin = 730.742eV (T=1413.318K) Etot = 2468.899eV
Energy per atom: Epot =1739.800eV Ekin = 731.885eV (T=1415.530K) Etot = 2471.685eV
Energy per atom: Epot =1749.128eV Ekin = 720.320eV (T=1393.161K) Etot = 2469.448eV
Energy per atom: Epot =1747.094eV Ekin = 729.766eV (T=1411.432K) Etot = 2476.861eV
Energy per atom: Epot =1756.095eV Ekin = 726.229eV (T=1404.591K) Etot = 2482.325eV
Energy per atom: Epot =1770.666eV Ekin = 730.380eV (T=1412.618K) Etot = 2501.046eV
Energy per atom: Epot =1771.858eV Ekin = 737.805eV (T=1426.979K) Etot = 2509.663eV
Energy per atom: Epot =1766.183eV Ekin = 749.779eV (T=1450.137K) Etot = 2515.961eV
Energy per atom: Epot =1771.045eV Ekin = 755.027eV (T=1460.288K) Etot = 2526.072eV
Energy per atom: Epot =1790.580eV Ekin = 740.944eV (T=1433.051K) Etot = 2531.524eV
Energy per atom: Epot =1792.911eV Ekin = 752.090eV (T=1454.607K) Etot = 2545.000eV
Energy per atom: Epot =1799.150eV Ekin = 749.949eV (T=1450.466K) Etot = 2549.098eV
Energy per atom: Epot =1804.621eV Ekin = 751.155eV (T=1452.800K) Etot = 2555.777eV
Energy per atom: Epot =1807.150eV Ekin = 762.685eV (T=1475.099K) Etot = 2569.835eV
Energy per atom: Epot =1826.650eV Ekin = 759.527eV (T=1468.991K) Etot = 2586.177eV
Energy per atom: Epot =1843.044eV Ekin = 744.487eV (T=1439.903K) Etot = 2587.531eV
Energy per atom: Epot =1845.291eV Ekin = 738.945eV (T=1429.183K) Etot = 2584.236eV
Energy per atom: Epot =1849.500eV Ekin = 748.404eV (T=1447.479K) Etot = 2597.904eV
Energy per atom: Epot =1844.110eV Ekin = 757.399eV (T=1464.875K) Etot = 2601.508eV
Energy per atom: Epot =1847.477eV Ekin = 755.793eV (T=1461.770K) Etot = 2603.270eV
Energy per atom: Epot =1858.274eV Ekin = 743.969eV (T=1438.900K) Etot = 2602.243eV
Energy per atom: Epot =1858.382eV Ekin = 749.023eV (T=1448.676K) Etot = 2607.405eV
Energy per atom: Epot =1859.909eV Ekin = 764.749eV (T=1479.090K) Etot = 2624.658eV
Energy per atom: Epot =1859.926eV Ekin = 760.879eV (T=1471.605K) Etot = 2620.805eV
Energy per atom: Epot =1881.533eV Ekin = 741.761eV (T=1434.631K) Etot = 2623.295eV
Energy per atom: Epot =1860.552eV Ekin = 758.876eV (T=1467.732K) Etot = 2619.428eV
Energy per atom: Epot =1874.287eV Ekin = 748.150eV (T=1446.987K) Etot = 2622.437eV
Energy per atom: Epot =1872.414eV Ekin = 747.833eV (T=1446.375K) Etot = 2620.247eV
Energy per atom: Epot =1890.560eV Ekin = 747.506eV (T=1445.742K) Etot = 2638.067eV
Energy per atom: Epot =1886.944eV Ekin = 754.401eV (T=1459.077K) Etot = 2641.345eV
Energy per atom: Epot =1883.258eV Ekin = 760.959eV (T=1471.762K) Etot = 2644.217eV
Energy per atom: Epot =1869.933eV Ekin = 779.121eV (T=1506.888K) Etot = 2649.054eV
Energy per atom: Epot =1876.571eV Ekin = 760.393eV (T=1470.666K) Etot = 2636.964eV
Energy per atom: Epot =1886.756eV Ekin = 756.693eV (T=1463.510K) Etot = 2643.449eV
Energy per atom: Epot =1896.516eV Ekin = 750.070eV (T=1450.701K) Etot = 2646.587eV
Energy per atom: Epot =1882.751eV Ekin = 769.958eV (T=1489.167K) Etot = 2652.709eV
Energy per atom: Epot =1886.436eV Ekin = 771.208eV (T=1491.583K) Etot = 2657.644eV
Energy per atom: Epot =1904.612eV Ekin = 766.035eV (T=1481.578K) Etot = 2670.647eV
Energy per atom: Epot =1900.771eV Ekin = 765.183eV (T=1479.931K) Etot = 2665.954eV
Energy per atom: Epot =1902.935eV Ekin = 766.125eV (T=1481.752K) Etot = 2669.060eV
Energy per atom: Epot =1914.681eV Ekin = 749.819eV (T=1450.215K) Etot = 2664.500eV
Energy per atom: Epot =1916.353eV Ekin = 759.784eV (T=1469.488K) Etot = 2676.136eV
Energy per atom: Epot =1921.057eV Ekin = 758.385eV (T=1466.783K) Etot = 2679.443eV
Energy per atom: Epot =1924.747eV Ekin = 747.621eV (T=1445.965K) Etot = 2672.369eV
Energy per atom: Epot =1919.773eV Ekin = 754.116eV (T=1458.525K) Etot = 2673.889eV
Energy per atom: Epot =1921.377eV Ekin = 762.354eV (T=1474.459K) Etot = 2683.731eV
Energy per atom: Epot =1906.144eV Ekin = 771.567eV (T=1492.277K) Etot = 2677.711eV
Energy per atom: Epot =1912.201eV Ekin = 767.619eV (T=1484.643K) Etot = 2679.821eV
Energy per atom: Epot =1919.531eV Ekin = 756.477eV (T=1463.093K) Etot = 2676.008eV
Energy per atom: Epot =1920.024eV Ekin = 768.471eV (T=1486.290K) Etot = 2688.496eV
Energy per atom: Epot =1932.574eV Ekin = 762.474eV (T=1474.691K) Etot = 2695.048eV
Energy per atom: Epot =1937.013eV Ekin = 765.287eV (T=1480.131K) Etot = 2702.300eV
Energy per atom: Epot =1930.873eV Ekin = 764.975eV (T=1479.529K) Etot = 2695.848eV
Energy per atom: Epot =1927.449eV Ekin = 768.535eV (T=1486.414K) Etot = 2695.984eV
Energy per atom: Epot =1945.037eV Ekin = 762.035eV (T=1473.842K) Etot = 2707.072eV
Energy per atom: Epot =1955.079eV Ekin = 748.488eV (T=1447.640K) Etot = 2703.567eV
Energy per atom: Epot =1937.084eV Ekin = 767.203eV (T=1483.837K) Etot = 2704.286eV
Energy per atom: Epot =1951.922eV Ekin = 762.289eV (T=1474.333K) Etot = 2714.211eV
Energy per atom: Epot =1962.387eV Ekin = 748.977eV (T=1448.587K) Etot = 2711.364eV
Energy per atom: Epot =1935.118eV Ekin = 777.772eV (T=1504.279K) Etot = 2712.890eV
Energy per atom: Epot =1962.189eV Ekin = 758.324eV (T=1466.664K) Etot = 2720.513eV
Energy per atom: Epot =1948.687eV Ekin = 766.198eV (T=1481.893K) Etot = 2714.885eV
Energy per atom: Epot =1964.244eV Ekin = 760.191eV (T=1470.275K) Etot = 2724.435eV
Energy per atom: Epot =1949.756eV Ekin = 776.707eV (T=1502.220K) Etot = 2726.464eV
Energy per atom: Epot =1949.938eV Ekin = 783.561eV (T=1515.475K) Etot = 2733.499eV
Energy per atom: Epot =1957.459eV Ekin = 779.115eV (T=1506.877K) Etot = 2736.574eV
Energy per atom: Epot =1951.607eV Ekin = 788.891eV (T=1525.783K) Etot = 2740.498eV
Energy per atom: Epot =1966.760eV Ekin = 790.906eV (T=1529.681K) Etot = 2757.666eV
Energy per atom: Epot =1964.167eV Ekin = 793.290eV (T=1534.291K) Etot = 2757.457eV
Energy per atom: Epot =1969.911eV Ekin = 782.761eV (T=1513.928K) Etot = 2752.672eV
Energy per atom: Epot =1980.599eV Ekin = 773.327eV (T=1495.681K) Etot = 2753.925eV
Energy per atom: Epot =1982.245eV Ekin = 770.728eV (T=1490.654K) Etot = 2752.972eV
Energy per atom: Epot =1973.992eV Ekin = 783.698eV (T=1515.740K) Etot = 2757.690eV
Energy per atom: Epot =1974.971eV Ekin = 773.102eV (T=1495.247K) Etot = 2748.074eV
Energy per atom: Epot =1969.167eV Ekin = 792.881eV (T=1533.502K) Etot = 2762.048eV
Energy per atom: Epot =1973.048eV Ekin = 793.652eV (T=1534.993K) Etot = 2766.700eV
Energy per atom: Epot =1991.845eV Ekin = 774.769eV (T=1498.470K) Etot = 2766.614eV
Energy per atom: Epot =1974.059eV Ekin = 780.861eV (T=1510.252K) Etot = 2754.920eV
Energy per atom: Epot =1974.596eV Ekin = 782.412eV (T=1513.252K) Etot = 2757.007eV
Energy per atom: Epot =1979.156eV Ekin = 784.562eV (T=1517.412K) Etot = 2763.719eV
Energy per atom: Epot =1969.016eV Ekin = 791.103eV (T=1530.062K) Etot = 2760.119eV
Energy per atom: Epot =1980.672eV Ekin = 780.405eV (T=1509.371K) Etot = 2761.077eV
Energy per atom: Epot =1980.136eV Ekin = 787.433eV (T=1522.964K) Etot = 2767.570eV
Energy per atom: Epot =1972.005eV Ekin = 781.657eV (T=1511.792K) Etot = 2753.662eV
Energy per atom: Epot =1981.208eV Ekin = 771.743eV (T=1492.618K) Etot = 2752.951eV
Energy per atom: Epot =1976.415eV Ekin = 776.187eV (T=1501.214K) Etot = 2752.602eV
Energy per atom: Epot =1979.956eV Ekin = 777.930eV (T=1504.584K) Etot = 2757.886eV
Energy per atom: Epot =1977.058eV Ekin = 779.542eV (T=1507.702K) Etot = 2756.600eV
Energy per atom: Epot =1974.792eV Ekin = 777.243eV (T=1503.256K) Etot = 2752.035eV
Energy per atom: Epot =1980.523eV Ekin = 770.360eV (T=1489.944K) Etot = 2750.883eV
Energy per atom: Epot =1972.842eV Ekin = 763.655eV (T=1476.976K) Etot = 2736.497eV
Energy per atom: Epot =1967.327eV Ekin = 762.045eV (T=1473.861K) Etot = 2729.372eV
Energy per atom: Epot =1968.780eV Ekin = 767.562eV (T=1484.532K) Etot = 2736.342eV
Energy per atom: Epot =1984.323eV Ekin = 758.762eV (T=1467.512K) Etot = 2743.085eV
Energy per atom: Epot =1965.640eV Ekin = 775.531eV (T=1499.945K) Etot = 2741.171eV
Energy per atom: Epot =1978.116eV Ekin = 768.936eV (T=1487.189K) Etot = 2747.052eV
Energy per atom: Epot =1976.838eV Ekin = 766.055eV (T=1481.617K) Etot = 2742.893eV
Energy per atom: Epot =1974.288eV Ekin = 764.827eV (T=1479.243K) Etot = 2739.115eV
Energy per atom: Epot =1968.514eV Ekin = 772.029eV (T=1493.172K) Etot = 2740.543eV
Energy per atom: Epot =1968.331eV Ekin = 770.110eV (T=1489.460K) Etot = 2738.442eV
Energy per atom: Epot =1964.011eV Ekin = 773.506eV (T=1496.028K) Etot = 2737.517eV
Energy per atom: Epot =1983.771eV Ekin = 756.477eV (T=1463.092K) Etot = 2740.248eV
Energy per atom: Epot =1971.955eV Ekin = 767.539eV (T=1484.488K) Etot = 2739.494eV
Energy per atom: Epot =1976.532eV Ekin = 767.084eV (T=1483.608K) Etot = 2743.617eV
Energy per atom: Epot =1978.863eV Ekin = 764.360eV (T=1478.338K) Etot = 2743.223eV
Energy per atom: Epot =1984.589eV Ekin = 771.022eV (T=1491.224K) Etot = 2755.611eV
Energy per atom: Epot =1979.322eV Ekin = 769.726eV (T=1488.718K) Etot = 2749.048eV
Energy per atom: Epot =1976.087eV Ekin = 761.905eV (T=1473.590K) Etot = 2737.992eV
Energy per atom: Epot =1972.939eV Ekin = 776.521eV (T=1501.860K) Etot = 2749.460eV
Energy per atom: Epot =1983.557eV Ekin = 774.734eV (T=1498.402K) Etot = 2758.291eV
Energy per atom: Epot =1975.545eV Ekin = 787.556eV (T=1523.203K) Etot = 2763.101eV
Energy per atom: Epot =1991.470eV Ekin = 773.230eV (T=1495.494K) Etot = 2764.700eV
Energy per atom: Epot =1981.747eV Ekin = 774.691eV (T=1498.319K) Etot = 2756.438eV
Energy per atom: Epot =1968.653eV Ekin = 771.195eV (T=1491.558K) Etot = 2739.848eV
Energy per atom: Epot =1974.006eV Ekin = 763.870eV (T=1477.390K) Etot = 2737.876eV
Energy per atom: Epot =1958.741eV Ekin = 778.450eV (T=1505.589K) Etot = 2737.191eV
Energy per atom: Epot =1969.087eV Ekin = 764.806eV (T=1479.202K) Etot = 2733.893eV
Energy per atom: Epot =1967.415eV Ekin = 759.432eV (T=1468.807K) Etot = 2726.847eV
Energy per atom: Epot =1965.963eV Ekin = 751.638eV (T=1453.732K) Etot = 2717.601eV
Energy per atom: Epot =1963.582eV Ekin = 753.126eV (T=1456.611K) Etot = 2716.708eV
Energy per atom: Epot =1955.459eV Ekin = 757.957eV (T=1465.954K) Etot = 2713.416eV
Energy per atom: Epot =1951.131eV Ekin = 762.488eV (T=1474.718K) Etot = 2713.619eV
Energy per atom: Epot =1963.551eV Ekin = 753.813eV (T=1457.940K) Etot = 2717.364eV
Energy per atom: Epot =1949.771eV Ekin = 765.218eV (T=1479.997K) Etot = 2714.989eV
Energy per atom: Epot =1952.623eV Ekin = 769.441eV (T=1488.166K) Etot = 2722.064eV
Energy per atom: Epot =1947.933eV Ekin = 777.060eV (T=1502.902K) Etot = 2724.993eV
Energy per atom: Epot =1962.375eV Ekin = 754.466eV (T=1459.203K) Etot = 2716.841eV
Energy per atom: Epot =1959.683eV Ekin = 755.631eV (T=1461.456K) Etot = 2715.314eV
Energy per atom: Epot =1940.308eV Ekin = 778.063eV (T=1504.842K) Etot = 2718.372eV
Energy per atom: Epot =1952.518eV Ekin = 758.040eV (T=1466.116K) Etot = 2710.558eV
Energy per atom: Epot =1945.797eV Ekin = 764.409eV (T=1478.434K) Etot = 2710.206eV
Energy per atom: Epot =1944.415eV Ekin = 773.886eV (T=1496.764K) Etot = 2718.302eV
Energy per atom: Epot =1933.514eV Ekin = 780.113eV (T=1508.806K) Etot = 2713.626eV
Energy per atom: Epot =1934.756eV Ekin = 770.624eV (T=1490.453K) Etot = 2705.380eV
Energy per atom: Epot =1941.313eV Ekin = 759.323eV (T=1468.597K) Etot = 2700.636eV
Energy per atom: Epot =1943.863eV Ekin = 763.949eV (T=1477.544K) Etot = 2707.812eV
Energy per atom: Epot =1946.838eV Ekin = 757.485eV (T=1465.042K) Etot = 2704.323eV
Energy per atom: Epot =1939.156eV Ekin = 776.329eV (T=1501.487K) Etot = 2715.485eV
Energy per atom: Epot =1952.914eV Ekin = 763.974eV (T=1477.593K) Etot = 2716.888eV
Energy per atom: Epot =1949.057eV Ekin = 769.680eV (T=1488.628K) Etot = 2718.738eV
Energy per atom: Epot =1953.863eV Ekin = 762.377eV (T=1474.504K) Etot = 2716.240eV
Energy per atom: Epot =1964.352eV Ekin = 749.051eV (T=1448.730K) Etot = 2713.403eV
Energy per atom: Epot =1953.473eV Ekin = 752.925eV (T=1456.222K) Etot = 2706.397eV
Energy per atom: Epot =1947.980eV Ekin = 754.722eV (T=1459.698K) Etot = 2702.703eV
Energy per atom: Epot =1952.187eV Ekin = 756.541eV (T=1463.217K) Etot = 2708.728eV
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] 13:27:15 43.245239 1.0870
BFGSLineSearch: 1[ 1] 13:27:15 42.120661 0.2296
BFGSLineSearch: 2[ 2] 13:27:15 41.867789 0.1409
BFGSLineSearch: 3[ 3] 13:27:15 41.713030 0.1175
BFGSLineSearch: 4[ 4] 13:27:15 41.671285 0.0689
BFGSLineSearch: 5[ 5] 13:27:15 41.661506 0.0228
BFGSLineSearch: 6[ 6] 13:27:15 41.661063 0.0064
BFGSLineSearch: 7[ 7] 13:27:15 41.661007 0.0025
BFGSLineSearch: 8[ 8] 13:27:15 41.660988 0.0021
BFGSLineSearch: 9[ 9] 13:27:15 41.660979 0.0011
BFGSLineSearch: 10[ 10] 13:27:15 41.660978 0.0004
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.661eV Ekin = 17.797eV (T=1480.491K) Etot = 59.458eV
Energy per atom: Epot =52.323eV Ekin = 7.184eV (T=597.582K) Etot = 59.507eV
Energy per atom: Epot =52.092eV Ekin = 7.420eV (T=617.284K) Etot = 59.512eV
Energy per atom: Epot =52.861eV Ekin = 6.655eV (T=553.629K) Etot = 59.516eV
Energy per atom: Epot =52.918eV Ekin = 6.592eV (T=548.356K) Etot = 59.510eV
Energy per atom: Epot =52.087eV Ekin = 7.426eV (T=617.724K) Etot = 59.512eV
Energy per atom: Epot =51.888eV Ekin = 7.616eV (T=633.573K) Etot = 59.504eV
Energy per atom: Epot =50.964eV Ekin = 8.538eV (T=710.249K) Etot = 59.502eV
Energy per atom: Epot =50.574eV Ekin = 8.931eV (T=742.962K) Etot = 59.505eV
Energy per atom: Epot =50.713eV Ekin = 8.793eV (T=731.467K) Etot = 59.507eV
Energy per atom: Epot =51.555eV Ekin = 7.957eV (T=661.897K) Etot = 59.512eV
Energy per atom: Epot =52.072eV Ekin = 7.439eV (T=618.826K) Etot = 59.511eV
Energy per atom: Epot =52.213eV Ekin = 7.299eV (T=607.191K) Etot = 59.513eV
Energy per atom: Epot =51.351eV Ekin = 8.155eV (T=678.397K) Etot = 59.506eV
Energy per atom: Epot =50.543eV Ekin = 8.958eV (T=745.217K) Etot = 59.501eV
Energy per atom: Epot =51.301eV Ekin = 8.208eV (T=682.821K) Etot = 59.509eV
Energy per atom: Epot =51.918eV Ekin = 7.596eV (T=631.854K) Etot = 59.513eV
Energy per atom: Epot =51.260eV Ekin = 8.251eV (T=686.401K) Etot = 59.511eV
Energy per atom: Epot =52.489eV Ekin = 7.027eV (T=584.562K) Etot = 59.516eV
Energy per atom: Epot =51.450eV Ekin = 8.060eV (T=670.523K) Etot = 59.511eV
Energy per atom: Epot =51.765eV Ekin = 7.750eV (T=644.666K) Etot = 59.515eV
Energy per atom: Epot =51.259eV Ekin = 8.251eV (T=686.358K) Etot = 59.510eV
Energy per atom: Epot =50.402eV Ekin = 9.095eV (T=756.595K) Etot = 59.497eV
Energy per atom: Epot =51.173eV Ekin = 8.334eV (T=693.242K) Etot = 59.506eV
Energy per atom: Epot =50.424eV Ekin = 9.081eV (T=755.394K) Etot = 59.504eV
Energy per atom: Epot =51.931eV Ekin = 7.582eV (T=630.693K) Etot = 59.513eV
Energy per atom: Epot =51.225eV Ekin = 8.282eV (T=688.971K) Etot = 59.508eV
Energy per atom: Epot =51.064eV Ekin = 8.436eV (T=701.768K) Etot = 59.500eV
Energy per atom: Epot =52.044eV Ekin = 7.463eV (T=620.836K) Etot = 59.508eV
Energy per atom: Epot =51.567eV Ekin = 7.939eV (T=660.427K) Etot = 59.506eV
Energy per atom: Epot =51.900eV Ekin = 7.609eV (T=632.983K) Etot = 59.509eV
Energy per atom: Epot =52.195eV Ekin = 7.316eV (T=608.626K) Etot = 59.512eV
Energy per atom: Epot =52.535eV Ekin = 6.976eV (T=580.301K) Etot = 59.511eV
Energy per atom: Epot =52.820eV Ekin = 6.693eV (T=556.761K) Etot = 59.513eV
Energy per atom: Epot =51.917eV Ekin = 7.591eV (T=631.452K) Etot = 59.508eV
Energy per atom: Epot =52.128eV Ekin = 7.376eV (T=613.616K) Etot = 59.505eV
Energy per atom: Epot =52.571eV Ekin = 6.936eV (T=576.990K) Etot = 59.508eV
Energy per atom: Epot =52.359eV Ekin = 7.151eV (T=594.902K) Etot = 59.511eV
Energy per atom: Epot =51.429eV Ekin = 8.080eV (T=672.138K) Etot = 59.508eV
Energy per atom: Epot =52.115eV Ekin = 7.402eV (T=615.722K) Etot = 59.516eV
Energy per atom: Epot =51.617eV Ekin = 7.893eV (T=656.574K) Etot = 59.509eV
Energy per atom: Epot =51.672eV Ekin = 7.840eV (T=652.200K) Etot = 59.512eV
Energy per atom: Epot =51.961eV Ekin = 7.550eV (T=628.081K) Etot = 59.511eV
Energy per atom: Epot =52.520eV Ekin = 6.994eV (T=581.789K) Etot = 59.514eV
Energy per atom: Epot =52.414eV Ekin = 7.102eV (T=590.827K) Etot = 59.516eV
Energy per atom: Epot =51.075eV Ekin = 8.433eV (T=701.548K) Etot = 59.509eV
Energy per atom: Epot =51.363eV Ekin = 8.148eV (T=677.828K) Etot = 59.512eV
Energy per atom: Epot =50.817eV Ekin = 8.687eV (T=722.666K) Etot = 59.504eV
Energy per atom: Epot =51.823eV Ekin = 7.690eV (T=639.698K) Etot = 59.513eV
Energy per atom: Epot =52.197eV Ekin = 7.314eV (T=608.447K) Etot = 59.511eV
Energy per atom: Epot =52.947eV Ekin = 6.564eV (T=546.047K) Etot = 59.512eV
Energy per atom: Epot =52.362eV Ekin = 7.149eV (T=594.715K) Etot = 59.511eV
Energy per atom: Epot =51.837eV Ekin = 7.671eV (T=638.102K) Etot = 59.508eV
Energy per atom: Epot =51.236eV Ekin = 8.273eV (T=688.188K) Etot = 59.509eV
Energy per atom: Epot =50.859eV Ekin = 8.647eV (T=719.306K) Etot = 59.506eV
Energy per atom: Epot =50.744eV Ekin = 8.756eV (T=728.384K) Etot = 59.500eV
Energy per atom: Epot =51.164eV Ekin = 8.337eV (T=693.520K) Etot = 59.501eV
Energy per atom: Epot =51.678eV Ekin = 7.827eV (T=651.082K) Etot = 59.505eV
Energy per atom: Epot =51.097eV Ekin = 8.407eV (T=699.358K) Etot = 59.504eV
Energy per atom: Epot =51.154eV Ekin = 8.355eV (T=695.059K) Etot = 59.510eV
Energy per atom: Epot =51.053eV Ekin = 8.452eV (T=703.131K) Etot = 59.506eV
Energy per atom: Epot =51.029eV Ekin = 8.475eV (T=705.045K) Etot = 59.504eV
Energy per atom: Epot =50.418eV Ekin = 9.090eV (T=756.139K) Etot = 59.508eV
Energy per atom: Epot =51.633eV Ekin = 7.877eV (T=655.247K) Etot = 59.510eV
Energy per atom: Epot =51.248eV Ekin = 8.255eV (T=686.702K) Etot = 59.503eV
Energy per atom: Epot =51.473eV Ekin = 8.030eV (T=668.022K) Etot = 59.504eV
Energy per atom: Epot =51.040eV Ekin = 8.455eV (T=703.355K) Etot = 59.496eV
Energy per atom: Epot =51.256eV Ekin = 8.247eV (T=686.037K) Etot = 59.503eV
Energy per atom: Epot =51.181eV Ekin = 8.319eV (T=692.026K) Etot = 59.500eV
Energy per atom: Epot =50.380eV Ekin = 9.120eV (T=758.688K) Etot = 59.500eV
Energy per atom: Epot =51.707eV Ekin = 7.804eV (T=649.159K) Etot = 59.511eV
Energy per atom: Epot =52.201eV Ekin = 7.314eV (T=608.440K) Etot = 59.516eV
Energy per atom: Epot =50.701eV Ekin = 8.806eV (T=732.516K) Etot = 59.507eV
Energy per atom: Epot =51.396eV Ekin = 8.115eV (T=675.039K) Etot = 59.511eV
Energy per atom: Epot =51.623eV Ekin = 7.890eV (T=656.325K) Etot = 59.513eV
Energy per atom: Epot =51.114eV Ekin = 8.394eV (T=698.307K) Etot = 59.509eV
Energy per atom: Epot =50.951eV Ekin = 8.549eV (T=711.140K) Etot = 59.499eV
Energy per atom: Epot =50.921eV Ekin = 8.582eV (T=713.881K) Etot = 59.503eV
Energy per atom: Epot =51.566eV Ekin = 7.942eV (T=660.654K) Etot = 59.508eV
Energy per atom: Epot =51.759eV Ekin = 7.750eV (T=644.729K) Etot = 59.509eV
Energy per atom: Epot =50.974eV Ekin = 8.532eV (T=709.735K) Etot = 59.506eV
Energy per atom: Epot =51.564eV Ekin = 7.944eV (T=660.824K) Etot = 59.508eV
Energy per atom: Epot =51.410eV Ekin = 8.099eV (T=673.742K) Etot = 59.509eV
Energy per atom: Epot =51.691eV Ekin = 7.813eV (T=649.943K) Etot = 59.504eV
Energy per atom: Epot =50.679eV Ekin = 8.825eV (T=734.099K) Etot = 59.503eV
Energy per atom: Epot =49.898eV Ekin = 9.612eV (T=799.551K) Etot = 59.510eV
Energy per atom: Epot =50.676eV Ekin = 8.828eV (T=734.392K) Etot = 59.504eV
Energy per atom: Epot =50.470eV Ekin = 9.029eV (T=751.082K) Etot = 59.499eV
Energy per atom: Epot =51.458eV Ekin = 8.044eV (T=669.147K) Etot = 59.502eV
Energy per atom: Epot =51.753eV Ekin = 7.753eV (T=644.986K) Etot = 59.507eV
Energy per atom: Epot =51.112eV Ekin = 8.398eV (T=698.638K) Etot = 59.510eV
Energy per atom: Epot =51.216eV Ekin = 8.297eV (T=690.162K) Etot = 59.513eV
Energy per atom: Epot =50.837eV Ekin = 8.677eV (T=721.823K) Etot = 59.514eV
Energy per atom: Epot =50.783eV Ekin = 8.728eV (T=726.077K) Etot = 59.512eV
Energy per atom: Epot =50.425eV Ekin = 9.082eV (T=755.497K) Etot = 59.507eV
Energy per atom: Epot =51.774eV Ekin = 7.732eV (T=643.206K) Etot = 59.507eV
Energy per atom: Epot =50.924eV Ekin = 8.579eV (T=713.630K) Etot = 59.502eV
Energy per atom: Epot =52.719eV Ekin = 6.798eV (T=565.487K) Etot = 59.516eV
Energy per atom: Epot =51.780eV Ekin = 7.736eV (T=643.555K) Etot = 59.516eV
Energy per atom: Epot =51.571eV Ekin = 7.936eV (T=660.187K) Etot = 59.507eV
Energy per atom: Epot =51.080eV Ekin = 8.418eV (T=700.241K) Etot = 59.498eV
Energy per atom: Epot =50.038eV Ekin = 9.459eV (T=786.870K) Etot = 59.497eV
Energy per atom: Epot =50.605eV Ekin = 8.905eV (T=740.786K) Etot = 59.510eV
Energy per atom: Epot =51.016eV Ekin = 8.491eV (T=706.305K) Etot = 59.506eV
Energy per atom: Epot =51.008eV Ekin = 8.497eV (T=706.796K) Etot = 59.505eV
Energy per atom: Epot =50.457eV Ekin = 9.047eV (T=752.598K) Etot = 59.504eV
Energy per atom: Epot =50.662eV Ekin = 8.843eV (T=735.627K) Etot = 59.505eV
Energy per atom: Epot =49.366eV Ekin = 10.133eV (T=842.957K) Etot = 59.499eV
Energy per atom: Epot =50.065eV Ekin = 9.434eV (T=784.782K) Etot = 59.499eV
Energy per atom: Epot =51.374eV Ekin = 8.125eV (T=675.890K) Etot = 59.499eV
Energy per atom: Epot =50.391eV Ekin = 9.107eV (T=757.568K) Etot = 59.498eV
Energy per atom: Epot =50.581eV Ekin = 8.921eV (T=742.081K) Etot = 59.501eV
Energy per atom: Epot =51.622eV Ekin = 7.883eV (T=655.785K) Etot = 59.505eV
Energy per atom: Epot =50.364eV Ekin = 9.139eV (T=760.280K) Etot = 59.503eV
Energy per atom: Epot =51.568eV Ekin = 7.944eV (T=660.805K) Etot = 59.511eV
Energy per atom: Epot =50.762eV Ekin = 8.748eV (T=727.695K) Etot = 59.510eV
Energy per atom: Epot =50.038eV Ekin = 9.462eV (T=787.082K) Etot = 59.500eV
Energy per atom: Epot =50.883eV Ekin = 8.622eV (T=717.261K) Etot = 59.505eV
Energy per atom: Epot =50.666eV Ekin = 8.834eV (T=734.833K) Etot = 59.500eV
Energy per atom: Epot =51.289eV Ekin = 8.211eV (T=683.044K) Etot = 59.500eV
Energy per atom: Epot =51.423eV Ekin = 8.083eV (T=672.432K) Etot = 59.507eV
Energy per atom: Epot =50.699eV Ekin = 8.810eV (T=732.890K) Etot = 59.509eV
Energy per atom: Epot =51.563eV Ekin = 7.947eV (T=661.075K) Etot = 59.510eV
Energy per atom: Epot =50.852eV Ekin = 8.653eV (T=719.792K) Etot = 59.504eV
Energy per atom: Epot =50.485eV Ekin = 9.024eV (T=750.654K) Etot = 59.508eV
Energy per atom: Epot =50.818eV Ekin = 8.694eV (T=723.209K) Etot = 59.512eV
Energy per atom: Epot =49.895eV Ekin = 9.606eV (T=799.071K) Etot = 59.501eV
Energy per atom: Epot =51.733eV Ekin = 7.779eV (T=647.098K) Etot = 59.511eV
Energy per atom: Epot =51.121eV Ekin = 8.386eV (T=697.620K) Etot = 59.508eV
Energy per atom: Epot =49.284eV Ekin = 10.213eV (T=849.606K) Etot = 59.497eV
Energy per atom: Epot =51.003eV Ekin = 8.507eV (T=707.632K) Etot = 59.510eV
Energy per atom: Epot =51.098eV Ekin = 8.415eV (T=700.042K) Etot = 59.513eV
Energy per atom: Epot =51.497eV Ekin = 8.015eV (T=666.721K) Etot = 59.512eV
Energy per atom: Epot =51.545eV Ekin = 7.966eV (T=662.622K) Etot = 59.510eV
Energy per atom: Epot =52.026eV Ekin = 7.488eV (T=622.908K) Etot = 59.514eV
Energy per atom: Epot =50.175eV Ekin = 9.328eV (T=775.949K) Etot = 59.503eV
Energy per atom: Epot =51.281eV Ekin = 8.232eV (T=684.770K) Etot = 59.512eV
Energy per atom: Epot =49.967eV Ekin = 9.538eV (T=793.424K) Etot = 59.505eV
Energy per atom: Epot =50.381eV Ekin = 9.126eV (T=759.178K) Etot = 59.508eV
Energy per atom: Epot =50.194eV Ekin = 9.306eV (T=774.151K) Etot = 59.500eV
Energy per atom: Epot =51.284eV Ekin = 8.223eV (T=684.037K) Etot = 59.507eV
Energy per atom: Epot =51.510eV Ekin = 8.004eV (T=665.865K) Etot = 59.515eV
Energy per atom: Epot =50.740eV Ekin = 8.763eV (T=728.936K) Etot = 59.503eV
Energy per atom: Epot =51.205eV Ekin = 8.300eV (T=690.422K) Etot = 59.505eV
Energy per atom: Epot =50.197eV Ekin = 9.308eV (T=774.262K) Etot = 59.504eV
Energy per atom: Epot =50.411eV Ekin = 9.099eV (T=756.946K) Etot = 59.510eV
Energy per atom: Epot =49.907eV Ekin = 9.596eV (T=798.279K) Etot = 59.504eV
Energy per atom: Epot =51.193eV Ekin = 8.314eV (T=691.597K) Etot = 59.506eV
Energy per atom: Epot =51.451eV Ekin = 8.060eV (T=670.464K) Etot = 59.511eV
Energy per atom: Epot =50.089eV Ekin = 9.416eV (T=783.275K) Etot = 59.505eV
Energy per atom: Epot =49.129eV Ekin = 10.374eV (T=862.939K) Etot = 59.503eV
Energy per atom: Epot =49.962eV Ekin = 9.546eV (T=794.074K) Etot = 59.508eV
Energy per atom: Epot =50.384eV Ekin = 9.124eV (T=759.017K) Etot = 59.509eV
Energy per atom: Epot =50.584eV Ekin = 8.925eV (T=742.450K) Etot = 59.509eV
Energy per atom: Epot =50.672eV Ekin = 8.833eV (T=734.746K) Etot = 59.504eV
Energy per atom: Epot =50.921eV Ekin = 8.586eV (T=714.208K) Etot = 59.507eV
Energy per atom: Epot =50.998eV Ekin = 8.515eV (T=708.298K) Etot = 59.513eV
Energy per atom: Epot =49.629eV Ekin = 9.869eV (T=820.994K) Etot = 59.498eV
Energy per atom: Epot =51.521eV Ekin = 7.982eV (T=663.980K) Etot = 59.502eV
Energy per atom: Epot =49.908eV Ekin = 9.597eV (T=798.381K) Etot = 59.505eV
Energy per atom: Epot =51.518eV Ekin = 7.997eV (T=665.239K) Etot = 59.515eV
Energy per atom: Epot =50.183eV Ekin = 9.318eV (T=775.108K) Etot = 59.501eV
Energy per atom: Epot =50.623eV Ekin = 8.880eV (T=738.729K) Etot = 59.504eV
Energy per atom: Epot =50.824eV Ekin = 8.680eV (T=722.078K) Etot = 59.504eV
Energy per atom: Epot =50.015eV Ekin = 9.482eV (T=788.795K) Etot = 59.497eV
Energy per atom: Epot =51.184eV Ekin = 8.320eV (T=692.112K) Etot = 59.504eV
Energy per atom: Epot =50.483eV Ekin = 9.016eV (T=750.010K) Etot = 59.499eV
Energy per atom: Epot =50.689eV Ekin = 8.818eV (T=733.513K) Etot = 59.506eV
Energy per atom: Epot =50.914eV Ekin = 8.592eV (T=714.769K) Etot = 59.507eV
Energy per atom: Epot =52.364eV Ekin = 7.149eV (T=594.674K) Etot = 59.513eV
Energy per atom: Epot =50.449eV Ekin = 9.053eV (T=753.113K) Etot = 59.502eV
Energy per atom: Epot =49.315eV Ekin = 10.183eV (T=847.057K) Etot = 59.498eV
Energy per atom: Epot =50.610eV Ekin = 8.900eV (T=740.381K) Etot = 59.510eV
Energy per atom: Epot =49.921eV Ekin = 9.587eV (T=797.496K) Etot = 59.508eV
Energy per atom: Epot =51.603eV Ekin = 7.911eV (T=658.060K) Etot = 59.514eV
Energy per atom: Epot =50.166eV Ekin = 9.336eV (T=776.620K) Etot = 59.502eV
Energy per atom: Epot =51.038eV Ekin = 8.468eV (T=704.387K) Etot = 59.506eV
Energy per atom: Epot =50.325eV Ekin = 9.188eV (T=764.337K) Etot = 59.513eV
Energy per atom: Epot =51.350eV Ekin = 8.163eV (T=679.052K) Etot = 59.513eV
Energy per atom: Epot =50.299eV Ekin = 9.204eV (T=765.663K) Etot = 59.503eV
Energy per atom: Epot =50.836eV Ekin = 8.670eV (T=721.244K) Etot = 59.506eV
Energy per atom: Epot =50.356eV Ekin = 9.153eV (T=761.382K) Etot = 59.508eV
Energy per atom: Epot =49.978eV Ekin = 9.523eV (T=792.185K) Etot = 59.501eV
Energy per atom: Epot =49.858eV Ekin = 9.645eV (T=802.375K) Etot = 59.504eV
Energy per atom: Epot =50.300eV Ekin = 9.204eV (T=765.624K) Etot = 59.504eV
Energy per atom: Epot =50.176eV Ekin = 9.329eV (T=776.083K) Etot = 59.506eV
Energy per atom: Epot =51.217eV Ekin = 8.290eV (T=689.589K) Etot = 59.507eV
Energy per atom: Epot =50.246eV Ekin = 9.257eV (T=770.052K) Etot = 59.503eV
Energy per atom: Epot =50.025eV Ekin = 9.481eV (T=788.681K) Etot = 59.506eV
Energy per atom: Epot =50.908eV Ekin = 8.599eV (T=715.344K) Etot = 59.507eV
Energy per atom: Epot =50.453eV Ekin = 9.048eV (T=752.686K) Etot = 59.501eV
Energy per atom: Epot =50.746eV Ekin = 8.760eV (T=728.717K) Etot = 59.506eV
Energy per atom: Epot =50.666eV Ekin = 8.840eV (T=735.399K) Etot = 59.506eV
Energy per atom: Epot =50.917eV Ekin = 8.597eV (T=715.155K) Etot = 59.514eV
Energy per atom: Epot =50.384eV Ekin = 9.122eV (T=758.846K) Etot = 59.506eV
Energy per atom: Epot =50.112eV Ekin = 9.391eV (T=781.198K) Etot = 59.503eV
Energy per atom: Epot =49.863eV Ekin = 9.644eV (T=802.233K) Etot = 59.507eV
Energy per atom: Epot =50.542eV Ekin = 8.964eV (T=745.693K) Etot = 59.506eV
Energy per atom: Epot =50.546eV Ekin = 8.952eV (T=744.702K) Etot = 59.498eV
Energy per atom: Epot =50.078eV Ekin = 9.417eV (T=783.357K) Etot = 59.495eV
Energy per atom: Epot =50.690eV Ekin = 8.815eV (T=733.298K) Etot = 59.505eV
After running the simulation, use ASE’s GUI to compare the resulting
trajectory with how it looks if you comment out either the line that says
Stationary(atoms), ZeroRotation(atoms) or both:
ase gui nanoparticleCu_NVE.traj
Try playing the movie with a high frame rate and set frame skipping to a low number. Can you spot the subtle difference?
Total running time of the script: (24 minutes 41.791 seconds)