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 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.
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 (
Stationary,
ZeroRotation,
thermalize_momenta,
)
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)
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
thermalize_momenta(atoms, temperature_K=300)
# We use Velocity Verlet algorithm to integrate the Newton's equations.
timestep_fs = 5
dyn = VelocityVerlet(atoms, timestep_fs * units.fs) # 5 fs time step.
def printenergy(a):
"""
Function to print the thermodynamical properties i.e potential energy,
kinetic energy and total energy
"""
epot = a.get_potential_energy()
ekin = a.get_kinetic_energy()
temp = a.get_temperature()
print(
f'Energy per atom: Epot ={epot:6.3f}eV Ekin = {ekin:.3f}eV '
f'(T={temp:.3f}K) Etot = {epot + ekin:.3f}eV'
)
# Now run the dynamics
print('running a NVE simulation of fcc Cu')
printenergy(atoms)
# init lists to for energy vs time data
time_ps, epot, ekin = [], [], []
mdind = 0
steps_per_block = 10
for i in range(20):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the energies of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
epot.append(atoms.get_potential_energy())
ekin.append(atoms.get_kinetic_energy())
etot = np.array(epot) + np.array(ekin)
# Plot energies vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, epot, label='Potential energy')
ax.plot(time_ps, ekin, label='Kinetic energy')
ax.plot(time_ps, etot, label='Total energy')
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Energy (eV)')
ax.legend(loc='best')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
running a NVE simulation of fcc Cu
Energy per atom: Epot =-2.405eV Ekin = 153.362eV (T=296.616K) Etot = 150.958eV
Energy per atom: Epot =115.849eV Ekin = 35.881eV (T=69.398K) Etot = 151.730eV
Energy per atom: Epot =78.087eV Ekin = 73.519eV (T=142.192K) Etot = 151.606eV
Energy per atom: Epot =70.223eV Ekin = 81.230eV (T=157.106K) Etot = 151.453eV
Energy per atom: Epot =67.840eV Ekin = 83.555eV (T=161.602K) Etot = 151.395eV
Energy per atom: Epot =79.280eV Ekin = 72.280eV (T=139.795K) Etot = 151.560eV
Energy per atom: Epot =77.646eV Ekin = 73.908eV (T=142.944K) Etot = 151.554eV
Energy per atom: Epot =73.210eV Ekin = 78.255eV (T=151.352K) Etot = 151.465eV
Energy per atom: Epot =71.149eV Ekin = 80.310eV (T=155.327K) Etot = 151.459eV
Energy per atom: Epot =77.670eV Ekin = 73.868eV (T=142.868K) Etot = 151.538eV
Energy per atom: Epot =75.150eV Ekin = 76.357eV (T=147.681K) Etot = 151.507eV
Energy per atom: Epot =73.576eV Ekin = 77.912eV (T=150.688K) Etot = 151.488eV
Energy per atom: Epot =73.817eV Ekin = 77.672eV (T=150.225K) Etot = 151.489eV
Energy per atom: Epot =77.079eV Ekin = 74.429eV (T=143.953K) Etot = 151.508eV
Energy per atom: Epot =73.315eV Ekin = 78.179eV (T=151.204K) Etot = 151.494eV
Energy per atom: Epot =74.768eV Ekin = 76.744eV (T=148.429K) Etot = 151.512eV
Energy per atom: Epot =73.249eV Ekin = 78.239eV (T=151.320K) Etot = 151.488eV
Energy per atom: Epot =76.416eV Ekin = 75.077eV (T=145.205K) Etot = 151.493eV
Energy per atom: Epot =74.150eV Ekin = 77.354eV (T=149.610K) Etot = 151.504eV
Energy per atom: Epot =74.037eV Ekin = 77.457eV (T=149.808K) Etot = 151.494eV
Energy per atom: Epot =76.002eV Ekin = 75.500eV (T=146.024K) Etot = 151.502eV
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?
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 =601.313eV Ekin = 80.903eV (T=156.474K) Etot = 682.216eV
Energy per atom: Epot =673.180eV Ekin = 138.002eV (T=266.908K) Etot = 811.182eV
Energy per atom: Epot =723.820eV Ekin = 204.248eV (T=395.033K) Etot = 928.068eV
Energy per atom: Epot =780.297eV Ekin = 253.071eV (T=489.461K) Etot = 1033.368eV
Energy per atom: Epot =833.286eV Ekin = 300.584eV (T=581.356K) Etot = 1133.870eV
Energy per atom: Epot =882.674eV Ekin = 341.957eV (T=661.375K) Etot = 1224.631eV
Energy per atom: Epot =922.471eV Ekin = 378.823eV (T=732.676K) Etot = 1301.294eV
Energy per atom: Epot =962.589eV Ekin = 410.065eV (T=793.102K) Etot = 1372.654eV
Energy per atom: Epot =999.742eV Ekin = 444.621eV (T=859.936K) Etot = 1444.363eV
Energy per atom: Epot =1042.642eV Ekin = 462.139eV (T=893.818K) Etot = 1504.782eV
Energy per atom: Epot =1068.652eV Ekin = 488.842eV (T=945.464K) Etot = 1557.494eV
Energy per atom: Epot =1103.419eV Ekin = 504.424eV (T=975.599K) Etot = 1607.843eV
Energy per atom: Epot =1139.127eV Ekin = 520.086eV (T=1005.892K) Etot = 1659.214eV
Energy per atom: Epot =1169.665eV Ekin = 530.886eV (T=1026.779K) Etot = 1700.551eV
Energy per atom: Epot =1192.296eV Ekin = 560.368eV (T=1083.801K) Etot = 1752.665eV
Energy per atom: Epot =1234.325eV Ekin = 562.511eV (T=1087.945K) Etot = 1796.836eV
Energy per atom: Epot =1249.257eV Ekin = 582.940eV (T=1127.457K) Etot = 1832.197eV
Energy per atom: Epot =1271.093eV Ekin = 595.178eV (T=1151.125K) Etot = 1866.270eV
Energy per atom: Epot =1304.707eV Ekin = 591.434eV (T=1143.884K) Etot = 1896.140eV
Energy per atom: Epot =1320.261eV Ekin = 618.800eV (T=1196.813K) Etot = 1939.061eV
Energy per atom: Epot =1346.257eV Ekin = 624.442eV (T=1207.726K) Etot = 1970.699eV
Energy per atom: Epot =1371.708eV Ekin = 626.891eV (T=1212.461K) Etot = 1998.599eV
Energy per atom: Epot =1381.777eV Ekin = 629.854eV (T=1218.192K) Etot = 2011.630eV
Energy per atom: Epot =1396.013eV Ekin = 646.161eV (T=1249.732K) Etot = 2042.174eV
Energy per atom: Epot =1420.197eV Ekin = 645.208eV (T=1247.888K) Etot = 2065.405eV
Energy per atom: Epot =1431.222eV Ekin = 651.982eV (T=1260.990K) Etot = 2083.204eV
Energy per atom: Epot =1443.730eV Ekin = 666.263eV (T=1288.610K) Etot = 2109.993eV
Energy per atom: Epot =1449.670eV Ekin = 678.501eV (T=1312.281K) Etot = 2128.171eV
Energy per atom: Epot =1473.054eV Ekin = 675.540eV (T=1306.553K) Etot = 2148.594eV
Energy per atom: Epot =1492.218eV Ekin = 673.347eV (T=1302.312K) Etot = 2165.566eV
Energy per atom: Epot =1504.295eV Ekin = 682.624eV (T=1320.254K) Etot = 2186.918eV
Energy per atom: Epot =1519.295eV Ekin = 680.629eV (T=1316.395K) Etot = 2199.923eV
Energy per atom: Epot =1535.698eV Ekin = 683.007eV (T=1320.996K) Etot = 2218.705eV
Energy per atom: Epot =1554.676eV Ekin = 687.562eV (T=1329.804K) Etot = 2242.238eV
Energy per atom: Epot =1562.601eV Ekin = 697.034eV (T=1348.124K) Etot = 2259.634eV
Energy per atom: Epot =1574.090eV Ekin = 688.650eV (T=1331.910K) Etot = 2262.741eV
Energy per atom: Epot =1584.882eV Ekin = 692.328eV (T=1339.023K) Etot = 2277.210eV
Energy per atom: Epot =1594.114eV Ekin = 696.612eV (T=1347.308K) Etot = 2290.726eV
Energy per atom: Epot =1604.672eV Ekin = 708.155eV (T=1369.632K) Etot = 2312.826eV
Energy per atom: Epot =1617.123eV Ekin = 705.444eV (T=1364.390K) Etot = 2322.567eV
Energy per atom: Epot =1616.587eV Ekin = 723.073eV (T=1398.486K) Etot = 2339.659eV
Energy per atom: Epot =1630.638eV Ekin = 714.524eV (T=1381.951K) Etot = 2345.162eV
Energy per atom: Epot =1650.527eV Ekin = 705.520eV (T=1364.538K) Etot = 2356.047eV
Energy per atom: Epot =1646.387eV Ekin = 722.901eV (T=1398.153K) Etot = 2369.288eV
Energy per atom: Epot =1665.683eV Ekin = 716.111eV (T=1385.021K) Etot = 2381.794eV
Energy per atom: Epot =1680.949eV Ekin = 717.445eV (T=1387.600K) Etot = 2398.394eV
Energy per atom: Epot =1690.298eV Ekin = 717.928eV (T=1388.535K) Etot = 2408.225eV
Energy per atom: Epot =1703.781eV Ekin = 714.752eV (T=1382.393K) Etot = 2418.533eV
Energy per atom: Epot =1713.428eV Ekin = 713.663eV (T=1380.287K) Etot = 2427.092eV
Energy per atom: Epot =1702.965eV Ekin = 733.966eV (T=1419.554K) Etot = 2436.931eV
Energy per atom: Epot =1716.988eV Ekin = 724.119eV (T=1400.509K) Etot = 2441.107eV
Energy per atom: Epot =1724.916eV Ekin = 730.216eV (T=1412.302K) Etot = 2455.132eV
Energy per atom: Epot =1731.595eV Ekin = 739.742eV (T=1430.725K) Etot = 2471.337eV
Energy per atom: Epot =1743.109eV Ekin = 740.941eV (T=1433.045K) Etot = 2484.050eV
Energy per atom: Epot =1749.062eV Ekin = 734.784eV (T=1421.136K) Etot = 2483.846eV
Energy per atom: Epot =1767.938eV Ekin = 727.625eV (T=1407.291K) Etot = 2495.564eV
Energy per atom: Epot =1776.507eV Ekin = 727.406eV (T=1406.867K) Etot = 2503.913eV
Energy per atom: Epot =1781.040eV Ekin = 734.302eV (T=1420.204K) Etot = 2515.342eV
Energy per atom: Epot =1792.455eV Ekin = 725.926eV (T=1404.004K) Etot = 2518.381eV
Energy per atom: Epot =1793.148eV Ekin = 732.139eV (T=1416.021K) Etot = 2525.287eV
Energy per atom: Epot =1803.650eV Ekin = 720.113eV (T=1392.762K) Etot = 2523.764eV
Energy per atom: Epot =1795.429eV Ekin = 730.220eV (T=1412.310K) Etot = 2525.649eV
Energy per atom: Epot =1806.373eV Ekin = 740.701eV (T=1432.581K) Etot = 2547.075eV
Energy per atom: Epot =1805.898eV Ekin = 740.359eV (T=1431.919K) Etot = 2546.257eV
Energy per atom: Epot =1802.325eV Ekin = 751.615eV (T=1453.690K) Etot = 2553.940eV
Energy per atom: Epot =1832.686eV Ekin = 728.434eV (T=1408.855K) Etot = 2561.120eV
Energy per atom: Epot =1833.941eV Ekin = 731.846eV (T=1415.454K) Etot = 2565.787eV
Energy per atom: Epot =1839.436eV Ekin = 744.542eV (T=1440.008K) Etot = 2583.978eV
Energy per atom: Epot =1850.910eV Ekin = 744.143eV (T=1439.238K) Etot = 2595.053eV
Energy per atom: Epot =1858.073eV Ekin = 752.611eV (T=1455.616K) Etot = 2610.685eV
Energy per atom: Epot =1856.725eV Ekin = 758.776eV (T=1467.538K) Etot = 2615.501eV
Energy per atom: Epot =1861.407eV Ekin = 750.125eV (T=1450.807K) Etot = 2611.532eV
Energy per atom: Epot =1863.361eV Ekin = 754.159eV (T=1458.610K) Etot = 2617.521eV
Energy per atom: Epot =1867.077eV Ekin = 752.806eV (T=1455.993K) Etot = 2619.883eV
Energy per atom: Epot =1874.754eV Ekin = 753.022eV (T=1456.409K) Etot = 2627.776eV
Energy per atom: Epot =1867.761eV Ekin = 766.316eV (T=1482.122K) Etot = 2634.077eV
Energy per atom: Epot =1886.274eV Ekin = 748.984eV (T=1448.599K) Etot = 2635.257eV
Energy per atom: Epot =1886.248eV Ekin = 753.493eV (T=1457.320K) Etot = 2639.741eV
Energy per atom: Epot =1887.232eV Ekin = 756.443eV (T=1463.027K) Etot = 2643.676eV
Energy per atom: Epot =1892.091eV Ekin = 750.869eV (T=1452.246K) Etot = 2642.960eV
Energy per atom: Epot =1898.906eV Ekin = 754.381eV (T=1459.038K) Etot = 2653.287eV
Energy per atom: Epot =1903.143eV Ekin = 747.943eV (T=1446.587K) Etot = 2651.086eV
Energy per atom: Epot =1887.738eV Ekin = 763.120eV (T=1475.940K) Etot = 2650.858eV
Energy per atom: Epot =1917.822eV Ekin = 743.877eV (T=1438.723K) Etot = 2661.699eV
Energy per atom: Epot =1915.856eV Ekin = 750.430eV (T=1451.397K) Etot = 2666.285eV
Energy per atom: Epot =1919.376eV Ekin = 759.873eV (T=1469.660K) Etot = 2679.248eV
Energy per atom: Epot =1930.095eV Ekin = 751.133eV (T=1452.756K) Etot = 2681.228eV
Energy per atom: Epot =1920.143eV Ekin = 768.546eV (T=1486.434K) Etot = 2688.688eV
Energy per atom: Epot =1938.168eV Ekin = 753.219eV (T=1456.791K) Etot = 2691.387eV
Energy per atom: Epot =1924.277eV Ekin = 768.902eV (T=1487.123K) Etot = 2693.179eV
Energy per atom: Epot =1937.144eV Ekin = 757.971eV (T=1465.983K) Etot = 2695.115eV
Energy per atom: Epot =1950.283eV Ekin = 744.926eV (T=1440.752K) Etot = 2695.209eV
Energy per atom: Epot =1945.102eV Ekin = 754.821eV (T=1459.890K) Etot = 2699.923eV
Energy per atom: Epot =1941.390eV Ekin = 755.608eV (T=1461.411K) Etot = 2696.998eV
Energy per atom: Epot =1940.157eV Ekin = 759.664eV (T=1469.257K) Etot = 2699.821eV
Energy per atom: Epot =1938.347eV Ekin = 769.920eV (T=1489.093K) Etot = 2708.267eV
Energy per atom: Epot =1945.837eV Ekin = 767.794eV (T=1484.981K) Etot = 2713.632eV
Energy per atom: Epot =1958.717eV Ekin = 755.602eV (T=1461.400K) Etot = 2714.320eV
Energy per atom: Epot =1969.949eV Ekin = 741.815eV (T=1434.734K) Etot = 2711.764eV
Energy per atom: Epot =1955.140eV Ekin = 768.792eV (T=1486.910K) Etot = 2723.932eV
Energy per atom: Epot =1962.692eV Ekin = 760.239eV (T=1470.369K) Etot = 2722.932eV
Energy per atom: Epot =1969.360eV Ekin = 763.593eV (T=1476.856K) Etot = 2732.953eV
Energy per atom: Epot =1963.243eV Ekin = 774.124eV (T=1497.223K) Etot = 2737.367eV
Energy per atom: Epot =1968.318eV Ekin = 769.555eV (T=1488.386K) Etot = 2737.872eV
Energy per atom: Epot =1964.816eV Ekin = 762.013eV (T=1473.799K) Etot = 2726.828eV
Energy per atom: Epot =1960.433eV Ekin = 773.120eV (T=1495.281K) Etot = 2733.553eV
Energy per atom: Epot =1975.827eV Ekin = 767.804eV (T=1485.000K) Etot = 2743.632eV
Energy per atom: Epot =1971.077eV Ekin = 759.597eV (T=1469.127K) Etot = 2730.675eV
Energy per atom: Epot =1969.817eV Ekin = 769.433eV (T=1488.151K) Etot = 2739.250eV
Energy per atom: Epot =1971.699eV Ekin = 779.674eV (T=1507.958K) Etot = 2751.373eV
Energy per atom: Epot =1962.733eV Ekin = 789.905eV (T=1527.746K) Etot = 2752.639eV
Energy per atom: Epot =1980.016eV Ekin = 774.596eV (T=1498.135K) Etot = 2754.612eV
Energy per atom: Epot =1974.571eV Ekin = 768.382eV (T=1486.119K) Etot = 2742.954eV
Energy per atom: Epot =1980.215eV Ekin = 774.749eV (T=1498.432K) Etot = 2754.964eV
Energy per atom: Epot =1976.459eV Ekin = 772.716eV (T=1494.499K) Etot = 2749.175eV
Energy per atom: Epot =1981.994eV Ekin = 774.869eV (T=1498.663K) Etot = 2756.863eV
Energy per atom: Epot =1989.003eV Ekin = 768.632eV (T=1486.602K) Etot = 2757.636eV
Energy per atom: Epot =1986.754eV Ekin = 774.167eV (T=1497.307K) Etot = 2760.921eV
Energy per atom: Epot =1998.450eV Ekin = 764.414eV (T=1478.443K) Etot = 2762.864eV
Energy per atom: Epot =2007.669eV Ekin = 750.586eV (T=1451.699K) Etot = 2758.255eV
Energy per atom: Epot =2000.579eV Ekin = 761.626eV (T=1473.051K) Etot = 2762.205eV
Energy per atom: Epot =2012.579eV Ekin = 752.092eV (T=1454.612K) Etot = 2764.671eV
Energy per atom: Epot =2000.468eV Ekin = 765.100eV (T=1479.769K) Etot = 2765.568eV
Energy per atom: Epot =1993.156eV Ekin = 783.395eV (T=1515.154K) Etot = 2776.551eV
Energy per atom: Epot =2002.187eV Ekin = 777.622eV (T=1503.988K) Etot = 2779.809eV
Energy per atom: Epot =2005.801eV Ekin = 771.426eV (T=1492.006K) Etot = 2777.228eV
Energy per atom: Epot =2002.921eV Ekin = 768.824eV (T=1486.973K) Etot = 2771.745eV
Energy per atom: Epot =1997.655eV Ekin = 772.651eV (T=1494.374K) Etot = 2770.306eV
Energy per atom: Epot =1999.362eV Ekin = 768.380eV (T=1486.113K) Etot = 2767.742eV
Energy per atom: Epot =1999.649eV Ekin = 772.131eV (T=1493.368K) Etot = 2771.780eV
Energy per atom: Epot =1995.262eV Ekin = 772.738eV (T=1494.542K) Etot = 2767.999eV
Energy per atom: Epot =2016.890eV Ekin = 745.244eV (T=1441.367K) Etot = 2762.134eV
Energy per atom: Epot =2001.868eV Ekin = 772.770eV (T=1494.605K) Etot = 2774.639eV
Energy per atom: Epot =1992.534eV Ekin = 787.333eV (T=1522.771K) Etot = 2779.867eV
Energy per atom: Epot =1993.298eV Ekin = 788.530eV (T=1525.087K) Etot = 2781.828eV
Energy per atom: Epot =2004.189eV Ekin = 778.225eV (T=1505.156K) Etot = 2782.414eV
Energy per atom: Epot =2002.868eV Ekin = 783.564eV (T=1515.480K) Etot = 2786.431eV
Energy per atom: Epot =1997.375eV Ekin = 790.221eV (T=1528.357K) Etot = 2787.597eV
Energy per atom: Epot =2004.698eV Ekin = 780.324eV (T=1509.215K) Etot = 2785.022eV
Energy per atom: Epot =1998.101eV Ekin = 786.681eV (T=1521.510K) Etot = 2784.782eV
Energy per atom: Epot =2000.168eV Ekin = 781.747eV (T=1511.968K) Etot = 2781.915eV
Energy per atom: Epot =2001.060eV Ekin = 782.440eV (T=1513.306K) Etot = 2783.499eV
Energy per atom: Epot =2015.028eV Ekin = 774.662eV (T=1498.263K) Etot = 2789.689eV
Energy per atom: Epot =2010.182eV Ekin = 776.768eV (T=1502.336K) Etot = 2786.949eV
Energy per atom: Epot =2001.501eV Ekin = 780.469eV (T=1509.495K) Etot = 2781.970eV
Energy per atom: Epot =1988.512eV Ekin = 796.303eV (T=1540.119K) Etot = 2784.815eV
Energy per atom: Epot =1989.933eV Ekin = 800.752eV (T=1548.725K) Etot = 2790.685eV
Energy per atom: Epot =1984.431eV Ekin = 793.616eV (T=1534.923K) Etot = 2778.047eV
Energy per atom: Epot =2000.232eV Ekin = 771.941eV (T=1493.000K) Etot = 2772.173eV
Energy per atom: Epot =1995.693eV Ekin = 773.031eV (T=1495.110K) Etot = 2768.724eV
Energy per atom: Epot =2000.283eV Ekin = 769.364eV (T=1488.017K) Etot = 2769.647eV
Energy per atom: Epot =1994.120eV Ekin = 781.773eV (T=1512.016K) Etot = 2775.893eV
Energy per atom: Epot =2002.691eV Ekin = 764.033eV (T=1477.706K) Etot = 2766.724eV
Energy per atom: Epot =1990.239eV Ekin = 773.015eV (T=1495.078K) Etot = 2763.255eV
Energy per atom: Epot =1989.872eV Ekin = 774.422eV (T=1497.800K) Etot = 2764.294eV
Energy per atom: Epot =2002.349eV Ekin = 765.092eV (T=1479.755K) Etot = 2767.441eV
Energy per atom: Epot =1999.071eV Ekin = 770.270eV (T=1489.768K) Etot = 2769.341eV
Energy per atom: Epot =1997.487eV Ekin = 772.115eV (T=1493.337K) Etot = 2769.602eV
Energy per atom: Epot =2019.624eV Ekin = 758.484eV (T=1466.974K) Etot = 2778.108eV
Energy per atom: Epot =2007.252eV Ekin = 768.143eV (T=1485.655K) Etot = 2775.395eV
Energy per atom: Epot =2004.427eV Ekin = 765.080eV (T=1479.731K) Etot = 2769.507eV
Energy per atom: Epot =2008.073eV Ekin = 759.862eV (T=1469.640K) Etot = 2767.936eV
Energy per atom: Epot =2005.350eV Ekin = 759.977eV (T=1469.861K) Etot = 2765.327eV
Energy per atom: Epot =2005.957eV Ekin = 760.470eV (T=1470.815K) Etot = 2766.428eV
Energy per atom: Epot =2006.723eV Ekin = 763.522eV (T=1476.719K) Etot = 2770.246eV
Energy per atom: Epot =2019.543eV Ekin = 760.498eV (T=1470.870K) Etot = 2780.041eV
Energy per atom: Epot =2019.533eV Ekin = 760.235eV (T=1470.361K) Etot = 2779.768eV
Energy per atom: Epot =2011.575eV Ekin = 765.951eV (T=1481.415K) Etot = 2777.525eV
Energy per atom: Epot =2010.777eV Ekin = 757.418eV (T=1464.912K) Etot = 2768.195eV
Energy per atom: Epot =2001.952eV Ekin = 767.041eV (T=1483.525K) Etot = 2768.994eV
Energy per atom: Epot =1990.911eV Ekin = 781.437eV (T=1511.367K) Etot = 2772.348eV
Energy per atom: Epot =2004.602eV Ekin = 768.893eV (T=1487.105K) Etot = 2773.494eV
Energy per atom: Epot =2012.453eV Ekin = 773.123eV (T=1495.288K) Etot = 2785.576eV
Energy per atom: Epot =2016.322eV Ekin = 782.145eV (T=1512.736K) Etot = 2798.467eV
Energy per atom: Epot =2014.175eV Ekin = 789.418eV (T=1526.804K) Etot = 2803.593eV
Energy per atom: Epot =2019.252eV Ekin = 785.952eV (T=1520.100K) Etot = 2805.204eV
Energy per atom: Epot =2020.269eV Ekin = 793.950eV (T=1535.568K) Etot = 2814.218eV
Energy per atom: Epot =2016.996eV Ekin = 789.208eV (T=1526.396K) Etot = 2806.203eV
Energy per atom: Epot =2014.267eV Ekin = 786.966eV (T=1522.060K) Etot = 2801.233eV
Energy per atom: Epot =2023.022eV Ekin = 776.933eV (T=1502.656K) Etot = 2799.955eV
Energy per atom: Epot =2019.761eV Ekin = 777.862eV (T=1504.452K) Etot = 2797.622eV
Energy per atom: Epot =2021.234eV Ekin = 766.670eV (T=1482.807K) Etot = 2787.904eV
Energy per atom: Epot =2022.410eV Ekin = 775.971eV (T=1500.795K) Etot = 2798.381eV
Energy per atom: Epot =2012.776eV Ekin = 786.928eV (T=1521.988K) Etot = 2799.704eV
Energy per atom: Epot =2024.805eV Ekin = 769.311eV (T=1487.915K) Etot = 2794.116eV
Energy per atom: Epot =2011.492eV Ekin = 775.182eV (T=1499.269K) Etot = 2786.674eV
Energy per atom: Epot =2035.621eV Ekin = 754.565eV (T=1459.395K) Etot = 2790.186eV
Energy per atom: Epot =2024.389eV Ekin = 777.488eV (T=1503.729K) Etot = 2801.876eV
Energy per atom: Epot =2026.692eV Ekin = 774.324eV (T=1497.610K) Etot = 2801.016eV
Energy per atom: Epot =2014.741eV Ekin = 785.140eV (T=1518.529K) Etot = 2799.881eV
Energy per atom: Epot =2031.875eV Ekin = 774.728eV (T=1498.391K) Etot = 2806.602eV
Energy per atom: Epot =2022.010eV Ekin = 777.510eV (T=1503.772K) Etot = 2799.521eV
Energy per atom: Epot =2028.387eV Ekin = 760.585eV (T=1471.038K) Etot = 2788.973eV
Energy per atom: Epot =2021.096eV Ekin = 769.428eV (T=1488.141K) Etot = 2790.524eV
Energy per atom: Epot =2026.905eV Ekin = 764.418eV (T=1478.451K) Etot = 2791.323eV
Energy per atom: Epot =2015.046eV Ekin = 775.825eV (T=1500.514K) Etot = 2790.871eV
Energy per atom: Epot =2033.977eV Ekin = 751.482eV (T=1453.432K) Etot = 2785.459eV
Energy per atom: Epot =2022.417eV Ekin = 766.423eV (T=1482.328K) Etot = 2788.840eV
Energy per atom: Epot =2021.215eV Ekin = 771.106eV (T=1491.386K) Etot = 2792.321eV
Energy per atom: Epot =2014.750eV Ekin = 771.376eV (T=1491.908K) Etot = 2786.126eV
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.
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, there 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
thermalize_momenta(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] 14:25:19 43.457006 1.0818
BFGSLineSearch: 1[ 1] 14:25:19 42.347659 0.2273
BFGSLineSearch: 2[ 2] 14:25:19 42.108454 0.1349
BFGSLineSearch: 3[ 3] 14:25:19 41.964817 0.1138
BFGSLineSearch: 4[ 4] 14:25:19 41.924933 0.0683
BFGSLineSearch: 5[ 5] 14:25:19 41.915346 0.0225
BFGSLineSearch: 6[ 6] 14:25:19 41.914920 0.0059
BFGSLineSearch: 7[ 7] 14:25:19 41.914872 0.0023
BFGSLineSearch: 8[ 9] 14:25:19 41.914855 0.0023
BFGSLineSearch: 9[ 10] 14:25:19 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 13.966eV (T=1161.806K) Etot = 55.881eV
Energy per atom: Epot =49.592eV Ekin = 6.328eV (T=526.392K) Etot = 55.920eV
Energy per atom: Epot =50.919eV Ekin = 5.022eV (T=417.767K) Etot = 55.941eV
Energy per atom: Epot =50.803eV Ekin = 5.134eV (T=427.098K) Etot = 55.937eV
Energy per atom: Epot =49.477eV Ekin = 6.451eV (T=536.664K) Etot = 55.929eV
Energy per atom: Epot =49.544eV Ekin = 6.390eV (T=531.603K) Etot = 55.934eV
Energy per atom: Epot =48.659eV Ekin = 7.268eV (T=604.607K) Etot = 55.927eV
Energy per atom: Epot =48.675eV Ekin = 7.251eV (T=603.206K) Etot = 55.926eV
Energy per atom: Epot =49.107eV Ekin = 6.824eV (T=567.667K) Etot = 55.931eV
Energy per atom: Epot =49.874eV Ekin = 6.060eV (T=504.146K) Etot = 55.934eV
Energy per atom: Epot =49.612eV Ekin = 6.318eV (T=525.548K) Etot = 55.930eV
Energy per atom: Epot =49.795eV Ekin = 6.137eV (T=510.511K) Etot = 55.932eV
Energy per atom: Epot =49.511eV Ekin = 6.424eV (T=534.416K) Etot = 55.935eV
Energy per atom: Epot =48.588eV Ekin = 7.338eV (T=610.418K) Etot = 55.926eV
Energy per atom: Epot =48.374eV Ekin = 7.551eV (T=628.167K) Etot = 55.925eV
Energy per atom: Epot =49.074eV Ekin = 6.858eV (T=570.457K) Etot = 55.932eV
Energy per atom: Epot =49.790eV Ekin = 6.142eV (T=510.948K) Etot = 55.932eV
Energy per atom: Epot =49.645eV Ekin = 6.286eV (T=522.896K) Etot = 55.931eV
Energy per atom: Epot =49.867eV Ekin = 6.067eV (T=504.700K) Etot = 55.934eV
Energy per atom: Epot =49.372eV Ekin = 6.560eV (T=545.730K) Etot = 55.932eV
Energy per atom: Epot =48.822eV Ekin = 7.110eV (T=591.457K) Etot = 55.932eV
Energy per atom: Epot =48.951eV Ekin = 6.980eV (T=580.610K) Etot = 55.931eV
Energy per atom: Epot =49.533eV Ekin = 6.397eV (T=532.142K) Etot = 55.929eV
Energy per atom: Epot =49.282eV Ekin = 6.644eV (T=552.691K) Etot = 55.926eV
Energy per atom: Epot =49.130eV Ekin = 6.799eV (T=565.570K) Etot = 55.928eV
Energy per atom: Epot =49.632eV Ekin = 6.300eV (T=524.085K) Etot = 55.932eV
Energy per atom: Epot =48.998eV Ekin = 6.932eV (T=576.615K) Etot = 55.930eV
Energy per atom: Epot =49.352eV Ekin = 6.577eV (T=547.119K) Etot = 55.929eV
Energy per atom: Epot =49.457eV Ekin = 6.471eV (T=538.303K) Etot = 55.928eV
Energy per atom: Epot =49.266eV Ekin = 6.666eV (T=554.528K) Etot = 55.932eV
Energy per atom: Epot =48.728eV Ekin = 7.205eV (T=599.363K) Etot = 55.933eV
Energy per atom: Epot =49.325eV Ekin = 6.606eV (T=549.539K) Etot = 55.931eV
Energy per atom: Epot =49.979eV Ekin = 5.952eV (T=495.101K) Etot = 55.931eV
Energy per atom: Epot =48.956eV Ekin = 6.970eV (T=579.825K) Etot = 55.926eV
Energy per atom: Epot =49.174eV Ekin = 6.750eV (T=561.526K) Etot = 55.924eV
Energy per atom: Epot =49.002eV Ekin = 6.924eV (T=576.007K) Etot = 55.927eV
Energy per atom: Epot =49.188eV Ekin = 6.739eV (T=560.571K) Etot = 55.926eV
Energy per atom: Epot =49.256eV Ekin = 6.672eV (T=554.995K) Etot = 55.927eV
Energy per atom: Epot =48.800eV Ekin = 7.132eV (T=593.292K) Etot = 55.932eV
Energy per atom: Epot =49.121eV Ekin = 6.811eV (T=566.590K) Etot = 55.932eV
Energy per atom: Epot =49.629eV Ekin = 6.302eV (T=524.250K) Etot = 55.931eV
Energy per atom: Epot =49.480eV Ekin = 6.452eV (T=536.702K) Etot = 55.932eV
Energy per atom: Epot =49.491eV Ekin = 6.443eV (T=535.938K) Etot = 55.934eV
Energy per atom: Epot =49.135eV Ekin = 6.793eV (T=565.078K) Etot = 55.928eV
Energy per atom: Epot =49.168eV Ekin = 6.760eV (T=562.330K) Etot = 55.928eV
Energy per atom: Epot =49.910eV Ekin = 6.021eV (T=500.851K) Etot = 55.931eV
Energy per atom: Epot =49.374eV Ekin = 6.555eV (T=545.280K) Etot = 55.929eV
Energy per atom: Epot =48.838eV Ekin = 7.090eV (T=589.761K) Etot = 55.928eV
Energy per atom: Epot =49.827eV Ekin = 6.108eV (T=508.139K) Etot = 55.935eV
Energy per atom: Epot =48.582eV Ekin = 7.344eV (T=610.952K) Etot = 55.926eV
Energy per atom: Epot =50.067eV Ekin = 5.868eV (T=488.177K) Etot = 55.936eV
Energy per atom: Epot =49.177eV Ekin = 6.754eV (T=561.849K) Etot = 55.931eV
Energy per atom: Epot =49.514eV Ekin = 6.416eV (T=533.720K) Etot = 55.930eV
Energy per atom: Epot =49.112eV Ekin = 6.819eV (T=567.277K) Etot = 55.932eV
Energy per atom: Epot =49.207eV Ekin = 6.721eV (T=559.132K) Etot = 55.928eV
Energy per atom: Epot =48.940eV Ekin = 6.986eV (T=581.146K) Etot = 55.926eV
Energy per atom: Epot =50.095eV Ekin = 5.842eV (T=485.975K) Etot = 55.937eV
Energy per atom: Epot =48.855eV Ekin = 7.073eV (T=588.377K) Etot = 55.928eV
Energy per atom: Epot =49.275eV Ekin = 6.656eV (T=553.651K) Etot = 55.930eV
Energy per atom: Epot =50.335eV Ekin = 5.603eV (T=466.071K) Etot = 55.937eV
Energy per atom: Epot =48.960eV Ekin = 6.968eV (T=579.644K) Etot = 55.928eV
Energy per atom: Epot =48.928eV Ekin = 7.000eV (T=582.281K) Etot = 55.927eV
Energy per atom: Epot =49.803eV Ekin = 6.130eV (T=509.944K) Etot = 55.933eV
Energy per atom: Epot =49.041eV Ekin = 6.892eV (T=573.291K) Etot = 55.933eV
Energy per atom: Epot =48.645eV Ekin = 7.281eV (T=605.699K) Etot = 55.926eV
Energy per atom: Epot =49.651eV Ekin = 6.283eV (T=522.680K) Etot = 55.934eV
Energy per atom: Epot =48.856eV Ekin = 7.073eV (T=588.400K) Etot = 55.929eV
Energy per atom: Epot =48.920eV Ekin = 7.007eV (T=582.877K) Etot = 55.927eV
Energy per atom: Epot =49.340eV Ekin = 6.591eV (T=548.249K) Etot = 55.930eV
Energy per atom: Epot =48.957eV Ekin = 6.976eV (T=580.275K) Etot = 55.932eV
Energy per atom: Epot =49.265eV Ekin = 6.670eV (T=554.861K) Etot = 55.935eV
Energy per atom: Epot =49.926eV Ekin = 6.013eV (T=500.181K) Etot = 55.939eV
Energy per atom: Epot =49.324eV Ekin = 6.607eV (T=549.640K) Etot = 55.931eV
Energy per atom: Epot =49.109eV Ekin = 6.817eV (T=567.051K) Etot = 55.925eV
Energy per atom: Epot =48.889eV Ekin = 7.035eV (T=585.188K) Etot = 55.924eV
Energy per atom: Epot =49.584eV Ekin = 6.349eV (T=528.152K) Etot = 55.933eV
Energy per atom: Epot =49.541eV Ekin = 6.390eV (T=531.594K) Etot = 55.931eV
Energy per atom: Epot =48.753eV Ekin = 7.175eV (T=596.865K) Etot = 55.928eV
Energy per atom: Epot =49.194eV Ekin = 6.735eV (T=560.289K) Etot = 55.929eV
Energy per atom: Epot =49.324eV Ekin = 6.608eV (T=549.717K) Etot = 55.932eV
Energy per atom: Epot =48.350eV Ekin = 7.578eV (T=630.346K) Etot = 55.927eV
Energy per atom: Epot =49.486eV Ekin = 6.445eV (T=536.098K) Etot = 55.931eV
Energy per atom: Epot =49.637eV Ekin = 6.292eV (T=523.448K) Etot = 55.929eV
Energy per atom: Epot =49.004eV Ekin = 6.926eV (T=576.133K) Etot = 55.930eV
Energy per atom: Epot =49.938eV Ekin = 5.995eV (T=498.663K) Etot = 55.932eV
Energy per atom: Epot =48.972eV Ekin = 6.957eV (T=578.705K) Etot = 55.929eV
Energy per atom: Epot =49.677eV Ekin = 6.259eV (T=520.660K) Etot = 55.935eV
Energy per atom: Epot =50.171eV Ekin = 5.765eV (T=479.571K) Etot = 55.936eV
Energy per atom: Epot =48.897eV Ekin = 7.029eV (T=584.734K) Etot = 55.926eV
Energy per atom: Epot =48.838eV Ekin = 7.089eV (T=589.697K) Etot = 55.926eV
Energy per atom: Epot =48.196eV Ekin = 7.730eV (T=643.058K) Etot = 55.927eV
Energy per atom: Epot =49.043eV Ekin = 6.884eV (T=572.675K) Etot = 55.928eV
Energy per atom: Epot =48.874eV Ekin = 7.058eV (T=587.133K) Etot = 55.932eV
Energy per atom: Epot =49.401eV Ekin = 6.532eV (T=543.343K) Etot = 55.933eV
Energy per atom: Epot =50.259eV Ekin = 5.675eV (T=472.062K) Etot = 55.934eV
Energy per atom: Epot =48.942eV Ekin = 6.986eV (T=581.143K) Etot = 55.928eV
Energy per atom: Epot =48.975eV Ekin = 6.954eV (T=578.450K) Etot = 55.928eV
Energy per atom: Epot =48.992eV Ekin = 6.937eV (T=577.092K) Etot = 55.929eV
Energy per atom: Epot =49.181eV Ekin = 6.751eV (T=561.576K) Etot = 55.932eV
Energy per atom: Epot =48.504eV Ekin = 7.425eV (T=617.659K) Etot = 55.929eV
Energy per atom: Epot =49.496eV Ekin = 6.436eV (T=535.421K) Etot = 55.932eV
Energy per atom: Epot =48.495eV Ekin = 7.429eV (T=618.031K) Etot = 55.924eV
Energy per atom: Epot =49.466eV Ekin = 6.467eV (T=538.004K) Etot = 55.933eV
Energy per atom: Epot =49.756eV Ekin = 6.179eV (T=514.049K) Etot = 55.936eV
Energy per atom: Epot =48.911eV Ekin = 7.018eV (T=583.800K) Etot = 55.929eV
Energy per atom: Epot =48.717eV Ekin = 7.210eV (T=599.742K) Etot = 55.926eV
Energy per atom: Epot =49.018eV Ekin = 6.912eV (T=574.992K) Etot = 55.930eV
Energy per atom: Epot =48.993eV Ekin = 6.934eV (T=576.824K) Etot = 55.927eV
Energy per atom: Epot =48.912eV Ekin = 7.019eV (T=583.853K) Etot = 55.930eV
Energy per atom: Epot =48.603eV Ekin = 7.322eV (T=609.051K) Etot = 55.924eV
Energy per atom: Epot =49.204eV Ekin = 6.724eV (T=559.328K) Etot = 55.928eV
Energy per atom: Epot =49.541eV Ekin = 6.390eV (T=531.586K) Etot = 55.931eV
Energy per atom: Epot =49.635eV Ekin = 6.295eV (T=523.647K) Etot = 55.930eV
Energy per atom: Epot =49.750eV Ekin = 6.180eV (T=514.124K) Etot = 55.931eV
Energy per atom: Epot =49.176eV Ekin = 6.751eV (T=561.598K) Etot = 55.927eV
Energy per atom: Epot =48.243eV Ekin = 7.680eV (T=638.864K) Etot = 55.923eV
Energy per atom: Epot =49.417eV Ekin = 6.512eV (T=541.691K) Etot = 55.929eV
Energy per atom: Epot =48.841eV Ekin = 7.088eV (T=589.606K) Etot = 55.929eV
Energy per atom: Epot =49.342eV Ekin = 6.589eV (T=548.103K) Etot = 55.931eV
Energy per atom: Epot =49.034eV Ekin = 6.890eV (T=573.162K) Etot = 55.924eV
Energy per atom: Epot =48.405eV Ekin = 7.517eV (T=625.337K) Etot = 55.922eV
Energy per atom: Epot =48.383eV Ekin = 7.544eV (T=627.588K) Etot = 55.928eV
Energy per atom: Epot =49.918eV Ekin = 6.017eV (T=500.545K) Etot = 55.935eV
Energy per atom: Epot =49.382eV Ekin = 6.547eV (T=544.625K) Etot = 55.929eV
Energy per atom: Epot =49.419eV Ekin = 6.512eV (T=541.748K) Etot = 55.932eV
Energy per atom: Epot =48.887eV Ekin = 7.043eV (T=585.873K) Etot = 55.930eV
Energy per atom: Epot =48.530eV Ekin = 7.396eV (T=615.268K) Etot = 55.927eV
Energy per atom: Epot =48.797eV Ekin = 7.129eV (T=593.007K) Etot = 55.926eV
Energy per atom: Epot =48.937eV Ekin = 6.988eV (T=581.347K) Etot = 55.926eV
Energy per atom: Epot =48.937eV Ekin = 6.997eV (T=582.026K) Etot = 55.934eV
Energy per atom: Epot =49.324eV Ekin = 6.609eV (T=549.814K) Etot = 55.934eV
Energy per atom: Epot =49.778eV Ekin = 6.153eV (T=511.860K) Etot = 55.931eV
Energy per atom: Epot =48.901eV Ekin = 7.021eV (T=584.064K) Etot = 55.922eV
Energy per atom: Epot =48.923eV Ekin = 7.002eV (T=582.454K) Etot = 55.924eV
Energy per atom: Epot =48.556eV Ekin = 7.374eV (T=613.451K) Etot = 55.930eV
Energy per atom: Epot =48.410eV Ekin = 7.520eV (T=625.598K) Etot = 55.930eV
Energy per atom: Epot =49.324eV Ekin = 6.613eV (T=550.088K) Etot = 55.937eV
Energy per atom: Epot =49.386eV Ekin = 6.546eV (T=544.504K) Etot = 55.931eV
Energy per atom: Epot =48.916eV Ekin = 7.010eV (T=583.171K) Etot = 55.926eV
Energy per atom: Epot =48.384eV Ekin = 7.543eV (T=627.495K) Etot = 55.927eV
Energy per atom: Epot =49.318eV Ekin = 6.615eV (T=550.250K) Etot = 55.932eV
Energy per atom: Epot =49.672eV Ekin = 6.262eV (T=520.905K) Etot = 55.934eV
Energy per atom: Epot =48.959eV Ekin = 6.978eV (T=580.436K) Etot = 55.937eV
Energy per atom: Epot =48.936eV Ekin = 6.998eV (T=582.177K) Etot = 55.934eV
Energy per atom: Epot =48.915eV Ekin = 7.010eV (T=583.172K) Etot = 55.925eV
Energy per atom: Epot =48.957eV Ekin = 6.969eV (T=579.718K) Etot = 55.926eV
Energy per atom: Epot =48.975eV Ekin = 6.958eV (T=578.808K) Etot = 55.933eV
Energy per atom: Epot =49.584eV Ekin = 6.352eV (T=528.433K) Etot = 55.936eV
Energy per atom: Epot =48.591eV Ekin = 7.338eV (T=610.404K) Etot = 55.929eV
Energy per atom: Epot =48.719eV Ekin = 7.206eV (T=599.479K) Etot = 55.926eV
Energy per atom: Epot =48.920eV Ekin = 7.006eV (T=582.790K) Etot = 55.926eV
Energy per atom: Epot =49.696eV Ekin = 6.235eV (T=518.678K) Etot = 55.932eV
Energy per atom: Epot =48.811eV Ekin = 7.117eV (T=592.058K) Etot = 55.928eV
Energy per atom: Epot =48.495eV Ekin = 7.433eV (T=618.300K) Etot = 55.928eV
Energy per atom: Epot =49.447eV Ekin = 6.486eV (T=539.535K) Etot = 55.933eV
Energy per atom: Epot =48.562eV Ekin = 7.368eV (T=612.932K) Etot = 55.930eV
Energy per atom: Epot =48.991eV Ekin = 6.942eV (T=577.477K) Etot = 55.933eV
Energy per atom: Epot =49.006eV Ekin = 6.924eV (T=575.982K) Etot = 55.930eV
Energy per atom: Epot =49.094eV Ekin = 6.839eV (T=568.919K) Etot = 55.933eV
Energy per atom: Epot =49.332eV Ekin = 6.600eV (T=549.000K) Etot = 55.931eV
Energy per atom: Epot =49.392eV Ekin = 6.537eV (T=543.808K) Etot = 55.930eV
Energy per atom: Epot =48.422eV Ekin = 7.503eV (T=624.127K) Etot = 55.924eV
Energy per atom: Epot =48.633eV Ekin = 7.293eV (T=606.688K) Etot = 55.926eV
Energy per atom: Epot =49.589eV Ekin = 6.345eV (T=527.854K) Etot = 55.934eV
Energy per atom: Epot =48.693eV Ekin = 7.240eV (T=602.235K) Etot = 55.932eV
Energy per atom: Epot =49.195eV Ekin = 6.739eV (T=560.612K) Etot = 55.934eV
Energy per atom: Epot =49.658eV Ekin = 6.275eV (T=521.963K) Etot = 55.932eV
Energy per atom: Epot =49.103eV Ekin = 6.828eV (T=568.038K) Etot = 55.931eV
Energy per atom: Epot =47.844eV Ekin = 8.078eV (T=671.984K) Etot = 55.922eV
Energy per atom: Epot =49.129eV Ekin = 6.802eV (T=565.839K) Etot = 55.931eV
Energy per atom: Epot =49.578eV Ekin = 6.353eV (T=528.514K) Etot = 55.931eV
Energy per atom: Epot =49.073eV Ekin = 6.859eV (T=570.543K) Etot = 55.931eV
Energy per atom: Epot =49.569eV Ekin = 6.366eV (T=529.553K) Etot = 55.934eV
Energy per atom: Epot =48.297eV Ekin = 7.630eV (T=634.713K) Etot = 55.927eV
Energy per atom: Epot =48.717eV Ekin = 7.210eV (T=599.804K) Etot = 55.928eV
Energy per atom: Epot =49.292eV Ekin = 6.641eV (T=552.440K) Etot = 55.933eV
Energy per atom: Epot =49.275eV Ekin = 6.658eV (T=553.847K) Etot = 55.933eV
Energy per atom: Epot =49.613eV Ekin = 6.320eV (T=525.726K) Etot = 55.932eV
Energy per atom: Epot =48.819eV Ekin = 7.107eV (T=591.240K) Etot = 55.926eV
Energy per atom: Epot =49.622eV Ekin = 6.312eV (T=525.090K) Etot = 55.934eV
Energy per atom: Epot =48.917eV Ekin = 7.016eV (T=583.664K) Etot = 55.933eV
Energy per atom: Epot =49.050eV Ekin = 6.884eV (T=572.615K) Etot = 55.934eV
Energy per atom: Epot =48.567eV Ekin = 7.358eV (T=612.077K) Etot = 55.925eV
Energy per atom: Epot =48.643eV Ekin = 7.282eV (T=605.761K) Etot = 55.925eV
Energy per atom: Epot =49.863eV Ekin = 6.072eV (T=505.081K) Etot = 55.935eV
Energy per atom: Epot =49.506eV Ekin = 6.425eV (T=534.510K) Etot = 55.931eV
Energy per atom: Epot =49.243eV Ekin = 6.688eV (T=556.381K) Etot = 55.932eV
Energy per atom: Epot =49.311eV Ekin = 6.621eV (T=550.745K) Etot = 55.932eV
Energy per atom: Epot =49.505eV Ekin = 6.429eV (T=534.771K) Etot = 55.933eV
Energy per atom: Epot =48.768eV Ekin = 7.160eV (T=595.616K) Etot = 55.928eV
Energy per atom: Epot =49.334eV Ekin = 6.594eV (T=548.556K) Etot = 55.928eV
Energy per atom: Epot =49.875eV Ekin = 6.056eV (T=503.752K) Etot = 55.931eV
Energy per atom: Epot =49.415eV Ekin = 6.519eV (T=542.254K) Etot = 55.933eV
Energy per atom: Epot =49.105eV Ekin = 6.825eV (T=567.718K) Etot = 55.930eV
Energy per atom: Epot =48.796eV Ekin = 7.131eV (T=593.243K) Etot = 55.928eV
Energy per atom: Epot =48.869eV Ekin = 7.058eV (T=587.104K) Etot = 55.927eV
Energy per atom: Epot =49.721eV Ekin = 6.211eV (T=516.647K) Etot = 55.931eV
Energy per atom: Epot =48.726eV Ekin = 7.204eV (T=599.238K) Etot = 55.929eV
Energy per atom: Epot =49.130eV Ekin = 6.802eV (T=565.852K) Etot = 55.932eV
Energy per atom: Epot =48.883eV Ekin = 7.043eV (T=585.924K) Etot = 55.927eV
Energy per atom: Epot =49.285eV Ekin = 6.646eV (T=552.872K) Etot = 55.931eV
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?
# Other thermostats are available in ASE,
# the Canonical Sampling Velocity Rescaling (CVSR)
# is one of them. Below you can find example of how to use it.
# An important thing to know is that the atoms object should have
# non-zero velocities before instanciating the dynamics object
from ase.build.bulk import bulk
from ase.md.bussi import Bussi
from ase.md.velocitydistribution import Stationary, thermalize_momenta
from ase.units import fs
cu_fcc = bulk('Cu', 'fcc') * (2, 2, 2)
cu_fcc.calc = EMT()
# CSVR thermostat requires initial velocity.
thermalize_momenta(cu_fcc, temperature_K=300)
Stationary(cu_fcc)
bussi_dyn = Bussi(cu_fcc, 1.0 * fs, temperature_K=300, taut=50)
# It is possible to run the dynamics interactively,
# performing custom actions between steps.
for step in bussi_dyn.irun(100):
print(
f'Cumul. energy transfered to the thermostat'
f' {bussi_dyn.transferred_energy} eV'
)
Cumul. energy transfered to the thermostat 0.0 eV
Cumul. energy transfered to the thermostat -0.008953559301233394 eV
Cumul. energy transfered to the thermostat -0.006126863083529362 eV
Cumul. energy transfered to the thermostat -0.005371139964495733 eV
Cumul. energy transfered to the thermostat -0.005026192362313463 eV
Cumul. energy transfered to the thermostat -0.008285884945346603 eV
Cumul. energy transfered to the thermostat -0.013457261452826134 eV
Cumul. energy transfered to the thermostat -0.006687179824090993 eV
Cumul. energy transfered to the thermostat -0.009039799948684032 eV
Cumul. energy transfered to the thermostat -0.007929361081444881 eV
Cumul. energy transfered to the thermostat -0.00997343265357102 eV
Cumul. energy transfered to the thermostat -0.01225360815529107 eV
Cumul. energy transfered to the thermostat -0.014929977099677352 eV
Cumul. energy transfered to the thermostat -0.010142135825957797 eV
Cumul. energy transfered to the thermostat -0.011157221880542757 eV
Cumul. energy transfered to the thermostat -0.007152988903413149 eV
Cumul. energy transfered to the thermostat -0.01575796996513775 eV
Cumul. energy transfered to the thermostat -0.01710754006701755 eV
Cumul. energy transfered to the thermostat -0.014535562441814682 eV
Cumul. energy transfered to the thermostat -0.016375471858268625 eV
Cumul. energy transfered to the thermostat -0.019532806679723614 eV
Cumul. energy transfered to the thermostat -0.024636663137897065 eV
Cumul. energy transfered to the thermostat -0.02527061044827494 eV
Cumul. energy transfered to the thermostat -0.023774938742593732 eV
Cumul. energy transfered to the thermostat -0.029569049004662562 eV
Cumul. energy transfered to the thermostat -0.024609695948290482 eV
Cumul. energy transfered to the thermostat -0.028739646289019545 eV
Cumul. energy transfered to the thermostat -0.028819524303909966 eV
Cumul. energy transfered to the thermostat -0.031990197139474805 eV
Cumul. energy transfered to the thermostat -0.02775041524420618 eV
Cumul. energy transfered to the thermostat -0.02784257520812817 eV
Cumul. energy transfered to the thermostat -0.0287919068252251 eV
Cumul. energy transfered to the thermostat -0.025621324936892707 eV
Cumul. energy transfered to the thermostat -0.027288007405609934 eV
Cumul. energy transfered to the thermostat -0.027967412465727183 eV
Cumul. energy transfered to the thermostat -0.02482352741438626 eV
Cumul. energy transfered to the thermostat -0.020772211678436004 eV
Cumul. energy transfered to the thermostat -0.016806912514979427 eV
Cumul. energy transfered to the thermostat -0.01730202316153955 eV
Cumul. energy transfered to the thermostat -0.021022223490065845 eV
Cumul. energy transfered to the thermostat -0.0183375630874454 eV
Cumul. energy transfered to the thermostat -0.019136448361417015 eV
Cumul. energy transfered to the thermostat -0.023145175754216152 eV
Cumul. energy transfered to the thermostat -0.020318610384486294 eV
Cumul. energy transfered to the thermostat -0.018485264918292995 eV
Cumul. energy transfered to the thermostat -0.018006498990983524 eV
Cumul. energy transfered to the thermostat -0.016105376750867328 eV
Cumul. energy transfered to the thermostat -0.02189538716137897 eV
Cumul. energy transfered to the thermostat -0.019116933121060012 eV
Cumul. energy transfered to the thermostat -0.016598553161794757 eV
Cumul. energy transfered to the thermostat -0.01831810766922743 eV
Cumul. energy transfered to the thermostat -0.015637910806867012 eV
Cumul. energy transfered to the thermostat -0.008788137295793579 eV
Cumul. energy transfered to the thermostat -0.010464133216901783 eV
Cumul. energy transfered to the thermostat -0.014280009263178024 eV
Cumul. energy transfered to the thermostat -0.009289237415282012 eV
Cumul. energy transfered to the thermostat -0.010575787705929873 eV
Cumul. energy transfered to the thermostat -0.006831381848830446 eV
Cumul. energy transfered to the thermostat -0.001785051140412032 eV
Cumul. energy transfered to the thermostat 0.0057134383740246155 eV
Cumul. energy transfered to the thermostat 0.006066734577995886 eV
Cumul. energy transfered to the thermostat 0.013683416505171308 eV
Cumul. energy transfered to the thermostat 0.014045742979631707 eV
Cumul. energy transfered to the thermostat 0.013293278471524865 eV
Cumul. energy transfered to the thermostat 0.01201563719927655 eV
Cumul. energy transfered to the thermostat 0.01642008678100832 eV
Cumul. energy transfered to the thermostat 0.020888114131456467 eV
Cumul. energy transfered to the thermostat 0.02362168827713683 eV
Cumul. energy transfered to the thermostat 0.024847194970814727 eV
Cumul. energy transfered to the thermostat 0.028491442942415124 eV
Cumul. energy transfered to the thermostat 0.02831296314108407 eV
Cumul. energy transfered to the thermostat 0.026488438032122644 eV
Cumul. energy transfered to the thermostat 0.03365526689548408 eV
Cumul. energy transfered to the thermostat 0.029542317805994745 eV
Cumul. energy transfered to the thermostat 0.027468524357425018 eV
Cumul. energy transfered to the thermostat 0.026866999041017352 eV
Cumul. energy transfered to the thermostat 0.027382755063528042 eV
Cumul. energy transfered to the thermostat 0.02665252423749901 eV
Cumul. energy transfered to the thermostat 0.0257703472672358 eV
Cumul. energy transfered to the thermostat 0.020677463999263873 eV
Cumul. energy transfered to the thermostat 0.02626767830259721 eV
Cumul. energy transfered to the thermostat 0.024321916935695624 eV
Cumul. energy transfered to the thermostat 0.02508389850358596 eV
Cumul. energy transfered to the thermostat 0.0219332897635195 eV
Cumul. energy transfered to the thermostat 0.020327568910277375 eV
Cumul. energy transfered to the thermostat 0.02267004066009025 eV
Cumul. energy transfered to the thermostat 0.018318475774168678 eV
Cumul. energy transfered to the thermostat 0.021612169795185134 eV
Cumul. energy transfered to the thermostat 0.027435024302533986 eV
Cumul. energy transfered to the thermostat 0.027661848921755758 eV
Cumul. energy transfered to the thermostat 0.02528419877446264 eV
Cumul. energy transfered to the thermostat 0.02479676010386527 eV
Cumul. energy transfered to the thermostat 0.027487376069964438 eV
Cumul. energy transfered to the thermostat 0.028272468061637974 eV
Cumul. energy transfered to the thermostat 0.02777150452081578 eV
Cumul. energy transfered to the thermostat 0.028998299378319232 eV
Cumul. energy transfered to the thermostat 0.03286720941260693 eV
Cumul. energy transfered to the thermostat 0.03187692971528721 eV
Cumul. energy transfered to the thermostat 0.030980407037523014 eV
Cumul. energy transfered to the thermostat 0.035709186073896164 eV
Cumul. energy transfered to the thermostat 0.04429914543895594 eV