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 = 157.254eV (T=304.143K) Etot = 154.849eV
Energy per atom: Epot =119.699eV Ekin = 35.951eV (T=69.533K) Etot = 155.650eV
Energy per atom: Epot =78.201eV Ekin = 77.300eV (T=149.504K) Etot = 155.501eV
Energy per atom: Epot =73.250eV Ekin = 82.121eV (T=158.828K) Etot = 155.370eV
Energy per atom: Epot =69.411eV Ekin = 85.891eV (T=166.121K) Etot = 155.302eV
Energy per atom: Epot =81.582eV Ekin = 73.884eV (T=142.897K) Etot = 155.466eV
Energy per atom: Epot =79.453eV Ekin = 76.006eV (T=147.002K) Etot = 155.459eV
Energy per atom: Epot =74.923eV Ekin = 80.449eV (T=155.595K) Etot = 155.372eV
Energy per atom: Epot =72.466eV Ekin = 82.899eV (T=160.333K) Etot = 155.365eV
Energy per atom: Epot =80.673eV Ekin = 74.779eV (T=144.630K) Etot = 155.452eV
Energy per atom: Epot =76.568eV Ekin = 78.844eV (T=152.492K) Etot = 155.412eV
Energy per atom: Epot =74.874eV Ekin = 80.513eV (T=155.720K) Etot = 155.387eV
Energy per atom: Epot =76.935eV Ekin = 78.472eV (T=151.771K) Etot = 155.407eV
Energy per atom: Epot =78.869eV Ekin = 76.551eV (T=148.056K) Etot = 155.420eV
Energy per atom: Epot =74.393eV Ekin = 80.999eV (T=156.660K) Etot = 155.393eV
Energy per atom: Epot =78.097eV Ekin = 77.334eV (T=149.572K) Etot = 155.431eV
Energy per atom: Epot =74.835eV Ekin = 80.564eV (T=155.817K) Etot = 155.399eV
Energy per atom: Epot =78.505eV Ekin = 76.901eV (T=148.732K) Etot = 155.405eV
Energy per atom: Epot =75.250eV Ekin = 80.154eV (T=155.025K) Etot = 155.404eV
Energy per atom: Epot =76.701eV Ekin = 78.706eV (T=152.225K) Etot = 155.407eV
Energy per atom: Epot =78.676eV Ekin = 76.738eV (T=148.417K) Etot = 155.414eV
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 =600.997eV Ekin = 80.128eV (T=154.975K) Etot = 681.125eV
Energy per atom: Epot =670.965eV Ekin = 141.191eV (T=273.075K) Etot = 812.156eV
Energy per atom: Epot =730.262eV Ekin = 205.063eV (T=396.610K) Etot = 935.325eV
Energy per atom: Epot =790.570eV Ekin = 255.819eV (T=494.776K) Etot = 1046.388eV
Energy per atom: Epot =839.153eV Ekin = 303.540eV (T=587.072K) Etot = 1142.693eV
Energy per atom: Epot =889.223eV Ekin = 346.876eV (T=670.889K) Etot = 1236.099eV
Energy per atom: Epot =929.257eV Ekin = 389.487eV (T=753.302K) Etot = 1318.744eV
Energy per atom: Epot =969.426eV Ekin = 423.029eV (T=818.175K) Etot = 1392.455eV
Energy per atom: Epot =1012.772eV Ekin = 440.343eV (T=851.663K) Etot = 1453.116eV
Energy per atom: Epot =1050.771eV Ekin = 466.047eV (T=901.375K) Etot = 1516.818eV
Energy per atom: Epot =1080.869eV Ekin = 493.651eV (T=954.765K) Etot = 1574.521eV
Energy per atom: Epot =1119.152eV Ekin = 509.062eV (T=984.571K) Etot = 1628.214eV
Energy per atom: Epot =1144.167eV Ekin = 530.114eV (T=1025.286K) Etot = 1674.281eV
Energy per atom: Epot =1182.029eV Ekin = 538.956eV (T=1042.389K) Etot = 1720.986eV
Energy per atom: Epot =1214.123eV Ekin = 550.235eV (T=1064.203K) Etot = 1764.358eV
Energy per atom: Epot =1227.121eV Ekin = 581.078eV (T=1123.856K) Etot = 1808.199eV
Energy per atom: Epot =1252.623eV Ekin = 595.850eV (T=1152.426K) Etot = 1848.473eV
Energy per atom: Epot =1289.421eV Ekin = 600.251eV (T=1160.939K) Etot = 1889.673eV
Energy per atom: Epot =1325.919eV Ekin = 593.921eV (T=1148.695K) Etot = 1919.840eV
Energy per atom: Epot =1335.795eV Ekin = 616.825eV (T=1192.994K) Etot = 1952.621eV
Energy per atom: Epot =1352.524eV Ekin = 628.244eV (T=1215.078K) Etot = 1980.767eV
Energy per atom: Epot =1362.640eV Ekin = 638.739eV (T=1235.377K) Etot = 2001.379eV
Energy per atom: Epot =1402.396eV Ekin = 624.411eV (T=1207.665K) Etot = 2026.807eV
Energy per atom: Epot =1407.717eV Ekin = 652.733eV (T=1262.442K) Etot = 2060.449eV
Energy per atom: Epot =1421.156eV Ekin = 657.892eV (T=1272.420K) Etot = 2079.048eV
Energy per atom: Epot =1449.752eV Ekin = 657.741eV (T=1272.129K) Etot = 2107.494eV
Energy per atom: Epot =1451.333eV Ekin = 685.084eV (T=1325.012K) Etot = 2136.417eV
Energy per atom: Epot =1476.245eV Ekin = 675.719eV (T=1306.900K) Etot = 2151.965eV
Energy per atom: Epot =1485.425eV Ekin = 684.995eV (T=1324.840K) Etot = 2170.420eV
Energy per atom: Epot =1492.400eV Ekin = 687.635eV (T=1329.946K) Etot = 2180.035eV
Energy per atom: Epot =1499.891eV Ekin = 697.277eV (T=1348.594K) Etot = 2197.168eV
Energy per atom: Epot =1525.384eV Ekin = 692.137eV (T=1338.654K) Etot = 2217.522eV
Energy per atom: Epot =1538.628eV Ekin = 698.756eV (T=1351.456K) Etot = 2237.384eV
Energy per atom: Epot =1550.639eV Ekin = 697.365eV (T=1348.764K) Etot = 2248.003eV
Energy per atom: Epot =1554.195eV Ekin = 698.089eV (T=1350.164K) Etot = 2252.284eV
Energy per atom: Epot =1579.254eV Ekin = 695.401eV (T=1344.966K) Etot = 2274.655eV
Energy per atom: Epot =1594.471eV Ekin = 699.913eV (T=1353.692K) Etot = 2294.384eV
Energy per atom: Epot =1586.783eV Ekin = 721.889eV (T=1396.195K) Etot = 2308.671eV
Energy per atom: Epot =1597.256eV Ekin = 722.595eV (T=1397.562K) Etot = 2319.851eV
Energy per atom: Epot =1621.386eV Ekin = 711.510eV (T=1376.122K) Etot = 2332.896eV
Energy per atom: Epot =1633.200eV Ekin = 718.131eV (T=1388.928K) Etot = 2351.331eV
Energy per atom: Epot =1635.927eV Ekin = 718.078eV (T=1388.826K) Etot = 2354.006eV
Energy per atom: Epot =1645.470eV Ekin = 713.881eV (T=1380.708K) Etot = 2359.352eV
Energy per atom: Epot =1655.597eV Ekin = 712.307eV (T=1377.664K) Etot = 2367.904eV
Energy per atom: Epot =1676.011eV Ekin = 692.574eV (T=1339.499K) Etot = 2368.585eV
Energy per atom: Epot =1673.517eV Ekin = 709.255eV (T=1371.762K) Etot = 2382.773eV
Energy per atom: Epot =1678.951eV Ekin = 715.767eV (T=1384.355K) Etot = 2394.717eV
Energy per atom: Epot =1685.314eV Ekin = 727.642eV (T=1407.324K) Etot = 2412.957eV
Energy per atom: Epot =1698.032eV Ekin = 718.204eV (T=1389.069K) Etot = 2416.236eV
Energy per atom: Epot =1700.537eV Ekin = 725.267eV (T=1402.729K) Etot = 2425.804eV
Energy per atom: Epot =1715.613eV Ekin = 718.442eV (T=1389.529K) Etot = 2434.054eV
Energy per atom: Epot =1715.449eV Ekin = 726.616eV (T=1405.338K) Etot = 2442.064eV
Energy per atom: Epot =1726.814eV Ekin = 724.089eV (T=1400.452K) Etot = 2450.903eV
Energy per atom: Epot =1728.379eV Ekin = 728.876eV (T=1409.709K) Etot = 2457.255eV
Energy per atom: Epot =1729.833eV Ekin = 727.204eV (T=1406.476K) Etot = 2457.037eV
Energy per atom: Epot =1744.383eV Ekin = 722.298eV (T=1396.987K) Etot = 2466.680eV
Energy per atom: Epot =1755.207eV Ekin = 716.022eV (T=1384.849K) Etot = 2471.229eV
Energy per atom: Epot =1755.560eV Ekin = 716.708eV (T=1386.176K) Etot = 2472.269eV
Energy per atom: Epot =1764.385eV Ekin = 706.558eV (T=1366.544K) Etot = 2470.943eV
Energy per atom: Epot =1765.957eV Ekin = 714.813eV (T=1382.511K) Etot = 2480.770eV
Energy per atom: Epot =1768.021eV Ekin = 728.362eV (T=1408.715K) Etot = 2496.382eV
Energy per atom: Epot =1770.795eV Ekin = 725.794eV (T=1403.749K) Etot = 2496.589eV
Energy per atom: Epot =1781.645eV Ekin = 728.213eV (T=1408.428K) Etot = 2509.858eV
Energy per atom: Epot =1785.807eV Ekin = 732.825eV (T=1417.348K) Etot = 2518.633eV
Energy per atom: Epot =1783.648eV Ekin = 737.706eV (T=1426.787K) Etot = 2521.354eV
Energy per atom: Epot =1800.773eV Ekin = 725.021eV (T=1402.255K) Etot = 2525.795eV
Energy per atom: Epot =1802.915eV Ekin = 733.250eV (T=1418.168K) Etot = 2536.164eV
Energy per atom: Epot =1818.784eV Ekin = 720.357eV (T=1393.233K) Etot = 2539.141eV
Energy per atom: Epot =1832.907eV Ekin = 718.333eV (T=1389.318K) Etot = 2551.240eV
Energy per atom: Epot =1835.614eV Ekin = 721.934eV (T=1396.283K) Etot = 2557.548eV
Energy per atom: Epot =1833.767eV Ekin = 726.343eV (T=1404.810K) Etot = 2560.110eV
Energy per atom: Epot =1838.555eV Ekin = 730.576eV (T=1412.998K) Etot = 2569.131eV
Energy per atom: Epot =1850.558eV Ekin = 727.370eV (T=1406.797K) Etot = 2577.928eV
Energy per atom: Epot =1845.082eV Ekin = 737.473eV (T=1426.337K) Etot = 2582.555eV
Energy per atom: Epot =1857.369eV Ekin = 730.800eV (T=1413.432K) Etot = 2588.170eV
Energy per atom: Epot =1848.870eV Ekin = 741.877eV (T=1434.854K) Etot = 2590.747eV
Energy per atom: Epot =1849.632eV Ekin = 748.795eV (T=1448.234K) Etot = 2598.426eV
Energy per atom: Epot =1870.863eV Ekin = 734.363eV (T=1420.321K) Etot = 2605.225eV
Energy per atom: Epot =1876.578eV Ekin = 740.206eV (T=1431.623K) Etot = 2616.785eV
Energy per atom: Epot =1882.896eV Ekin = 748.287eV (T=1447.253K) Etot = 2631.184eV
Energy per atom: Epot =1890.856eV Ekin = 751.336eV (T=1453.150K) Etot = 2642.192eV
Energy per atom: Epot =1902.677eV Ekin = 749.075eV (T=1448.777K) Etot = 2651.753eV
Energy per atom: Epot =1910.769eV Ekin = 744.700eV (T=1440.315K) Etot = 2655.469eV
Energy per atom: Epot =1911.718eV Ekin = 754.514eV (T=1459.297K) Etot = 2666.233eV
Energy per atom: Epot =1910.942eV Ekin = 753.503eV (T=1457.340K) Etot = 2664.444eV
Energy per atom: Epot =1909.893eV Ekin = 751.165eV (T=1452.818K) Etot = 2661.057eV
Energy per atom: Epot =1918.314eV Ekin = 742.604eV (T=1436.261K) Etot = 2660.918eV
Energy per atom: Epot =1928.628eV Ekin = 736.939eV (T=1425.304K) Etot = 2665.567eV
Energy per atom: Epot =1920.745eV Ekin = 741.314eV (T=1433.765K) Etot = 2662.059eV
Energy per atom: Epot =1904.586eV Ekin = 760.394eV (T=1470.669K) Etot = 2664.980eV
Energy per atom: Epot =1904.416eV Ekin = 757.394eV (T=1464.865K) Etot = 2661.810eV
Energy per atom: Epot =1928.973eV Ekin = 738.979eV (T=1429.250K) Etot = 2667.952eV
Energy per atom: Epot =1912.602eV Ekin = 741.655eV (T=1434.425K) Etot = 2654.257eV
Energy per atom: Epot =1910.039eV Ekin = 753.537eV (T=1457.407K) Etot = 2663.576eV
Energy per atom: Epot =1918.896eV Ekin = 747.094eV (T=1444.945K) Etot = 2665.990eV
Energy per atom: Epot =1922.828eV Ekin = 742.394eV (T=1435.855K) Etot = 2665.222eV
Energy per atom: Epot =1923.768eV Ekin = 746.155eV (T=1443.128K) Etot = 2669.922eV
Energy per atom: Epot =1918.491eV Ekin = 758.627eV (T=1467.251K) Etot = 2677.118eV
Energy per atom: Epot =1924.661eV Ekin = 751.282eV (T=1453.044K) Etot = 2675.943eV
Energy per atom: Epot =1943.379eV Ekin = 740.979eV (T=1433.118K) Etot = 2684.358eV
Energy per atom: Epot =1939.159eV Ekin = 766.892eV (T=1483.235K) Etot = 2706.050eV
Energy per atom: Epot =1958.621eV Ekin = 746.556eV (T=1443.904K) Etot = 2705.176eV
Energy per atom: Epot =1955.711eV Ekin = 751.576eV (T=1453.613K) Etot = 2707.287eV
Energy per atom: Epot =1950.949eV Ekin = 760.121eV (T=1470.140K) Etot = 2711.069eV
Energy per atom: Epot =1949.900eV Ekin = 759.387eV (T=1468.721K) Etot = 2709.287eV
Energy per atom: Epot =1956.113eV Ekin = 759.877eV (T=1469.668K) Etot = 2715.989eV
Energy per atom: Epot =1971.090eV Ekin = 755.361eV (T=1460.935K) Etot = 2726.451eV
Energy per atom: Epot =1966.890eV Ekin = 760.520eV (T=1470.912K) Etot = 2727.410eV
Energy per atom: Epot =1982.623eV Ekin = 744.423eV (T=1439.778K) Etot = 2727.046eV
Energy per atom: Epot =1985.853eV Ekin = 753.619eV (T=1457.565K) Etot = 2739.473eV
Energy per atom: Epot =1981.026eV Ekin = 761.882eV (T=1473.545K) Etot = 2742.908eV
Energy per atom: Epot =1983.988eV Ekin = 773.409eV (T=1495.840K) Etot = 2757.396eV
Energy per atom: Epot =1996.690eV Ekin = 769.626eV (T=1488.523K) Etot = 2766.316eV
Energy per atom: Epot =2002.056eV Ekin = 773.200eV (T=1495.436K) Etot = 2775.256eV
Energy per atom: Epot =2007.675eV Ekin = 776.250eV (T=1501.334K) Etot = 2783.924eV
Energy per atom: Epot =2011.785eV Ekin = 768.111eV (T=1485.594K) Etot = 2779.896eV
Energy per atom: Epot =2013.741eV Ekin = 773.014eV (T=1495.077K) Etot = 2786.755eV
Energy per atom: Epot =2000.703eV Ekin = 774.534eV (T=1498.017K) Etot = 2775.237eV
Energy per atom: Epot =2010.068eV Ekin = 755.080eV (T=1460.390K) Etot = 2765.148eV
Energy per atom: Epot =1993.051eV Ekin = 770.402eV (T=1490.024K) Etot = 2763.453eV
Energy per atom: Epot =1985.601eV Ekin = 771.394eV (T=1491.942K) Etot = 2756.994eV
Energy per atom: Epot =1994.580eV Ekin = 765.030eV (T=1479.634K) Etot = 2759.610eV
Energy per atom: Epot =1988.241eV Ekin = 771.926eV (T=1492.972K) Etot = 2760.166eV
Energy per atom: Epot =1976.787eV Ekin = 778.341eV (T=1505.380K) Etot = 2755.129eV
Energy per atom: Epot =1978.160eV Ekin = 786.050eV (T=1520.289K) Etot = 2764.210eV
Energy per atom: Epot =1990.033eV Ekin = 772.967eV (T=1494.986K) Etot = 2763.001eV
Energy per atom: Epot =1977.680eV Ekin = 783.315eV (T=1514.999K) Etot = 2760.994eV
Energy per atom: Epot =1980.300eV Ekin = 774.597eV (T=1498.138K) Etot = 2754.897eV
Energy per atom: Epot =1979.216eV Ekin = 774.626eV (T=1498.194K) Etot = 2753.842eV
Energy per atom: Epot =1977.435eV Ekin = 767.191eV (T=1483.814K) Etot = 2744.626eV
Energy per atom: Epot =1979.178eV Ekin = 770.232eV (T=1489.695K) Etot = 2749.410eV
Energy per atom: Epot =1971.231eV Ekin = 770.509eV (T=1490.231K) Etot = 2741.740eV
Energy per atom: Epot =1978.428eV Ekin = 757.319eV (T=1464.721K) Etot = 2735.747eV
Energy per atom: Epot =1974.169eV Ekin = 769.783eV (T=1488.827K) Etot = 2743.951eV
Energy per atom: Epot =1968.407eV Ekin = 774.732eV (T=1498.399K) Etot = 2743.139eV
Energy per atom: Epot =1975.178eV Ekin = 769.992eV (T=1489.231K) Etot = 2745.170eV
Energy per atom: Epot =1991.152eV Ekin = 753.412eV (T=1457.163K) Etot = 2744.564eV
Energy per atom: Epot =1988.138eV Ekin = 766.215eV (T=1481.927K) Etot = 2754.353eV
Energy per atom: Epot =1997.950eV Ekin = 749.537eV (T=1449.669K) Etot = 2747.487eV
Energy per atom: Epot =1989.639eV Ekin = 756.697eV (T=1463.519K) Etot = 2746.336eV
Energy per atom: Epot =1993.415eV Ekin = 756.834eV (T=1463.783K) Etot = 2750.249eV
Energy per atom: Epot =1985.090eV Ekin = 760.460eV (T=1470.796K) Etot = 2745.550eV
Energy per atom: Epot =1994.210eV Ekin = 758.078eV (T=1466.189K) Etot = 2752.288eV
Energy per atom: Epot =1987.590eV Ekin = 766.119eV (T=1481.741K) Etot = 2753.709eV
Energy per atom: Epot =1984.191eV Ekin = 768.977eV (T=1487.268K) Etot = 2753.168eV
Energy per atom: Epot =1989.571eV Ekin = 757.070eV (T=1464.239K) Etot = 2746.641eV
Energy per atom: Epot =1993.094eV Ekin = 757.000eV (T=1464.103K) Etot = 2750.093eV
Energy per atom: Epot =1990.444eV Ekin = 758.241eV (T=1466.504K) Etot = 2748.685eV
Energy per atom: Epot =1995.921eV Ekin = 755.284eV (T=1460.785K) Etot = 2751.205eV
Energy per atom: Epot =2001.183eV Ekin = 764.817eV (T=1479.222K) Etot = 2766.000eV
Energy per atom: Epot =2015.687eV Ekin = 758.625eV (T=1467.247K) Etot = 2774.312eV
Energy per atom: Epot =2005.923eV Ekin = 772.348eV (T=1493.788K) Etot = 2778.271eV
Energy per atom: Epot =2022.221eV Ekin = 754.155eV (T=1458.602K) Etot = 2776.377eV
Energy per atom: Epot =2013.070eV Ekin = 760.261eV (T=1470.410K) Etot = 2773.330eV
Energy per atom: Epot =2015.305eV Ekin = 765.808eV (T=1481.140K) Etot = 2781.113eV
Energy per atom: Epot =2008.718eV Ekin = 765.409eV (T=1480.368K) Etot = 2774.127eV
Energy per atom: Epot =2018.139eV Ekin = 768.408eV (T=1486.168K) Etot = 2786.547eV
Energy per atom: Epot =2013.972eV Ekin = 775.009eV (T=1498.934K) Etot = 2788.981eV
Energy per atom: Epot =2006.689eV Ekin = 786.335eV (T=1520.841K) Etot = 2793.024eV
Energy per atom: Epot =2007.631eV Ekin = 789.177eV (T=1526.336K) Etot = 2796.807eV
Energy per atom: Epot =2009.726eV Ekin = 784.022eV (T=1516.367K) Etot = 2793.748eV
Energy per atom: Epot =2014.300eV Ekin = 775.573eV (T=1500.026K) Etot = 2789.873eV
Energy per atom: Epot =2012.126eV Ekin = 770.395eV (T=1490.010K) Etot = 2782.520eV
Energy per atom: Epot =2005.157eV Ekin = 765.463eV (T=1480.471K) Etot = 2770.619eV
Energy per atom: Epot =2001.416eV Ekin = 761.414eV (T=1472.641K) Etot = 2762.830eV
Energy per atom: Epot =1990.595eV Ekin = 780.638eV (T=1509.821K) Etot = 2771.233eV
Energy per atom: Epot =1993.041eV Ekin = 775.198eV (T=1499.301K) Etot = 2768.239eV
Energy per atom: Epot =1992.436eV Ekin = 780.331eV (T=1509.227K) Etot = 2772.766eV
Energy per atom: Epot =2007.148eV Ekin = 770.656eV (T=1490.517K) Etot = 2777.805eV
Energy per atom: Epot =2004.162eV Ekin = 783.166eV (T=1514.710K) Etot = 2787.328eV
Energy per atom: Epot =2004.941eV Ekin = 780.189eV (T=1508.953K) Etot = 2785.130eV
Energy per atom: Epot =2015.340eV Ekin = 757.221eV (T=1464.531K) Etot = 2772.561eV
Energy per atom: Epot =2005.133eV Ekin = 770.115eV (T=1489.469K) Etot = 2775.248eV
Energy per atom: Epot =2011.870eV Ekin = 765.701eV (T=1480.933K) Etot = 2777.571eV
Energy per atom: Epot =2010.083eV Ekin = 768.136eV (T=1485.642K) Etot = 2778.219eV
Energy per atom: Epot =2007.002eV Ekin = 768.678eV (T=1486.690K) Etot = 2775.679eV
Energy per atom: Epot =2007.481eV Ekin = 779.986eV (T=1508.560K) Etot = 2787.467eV
Energy per atom: Epot =2003.822eV Ekin = 783.554eV (T=1515.461K) Etot = 2787.376eV
Energy per atom: Epot =2007.843eV Ekin = 779.775eV (T=1508.153K) Etot = 2787.618eV
Energy per atom: Epot =2011.684eV Ekin = 765.153eV (T=1479.873K) Etot = 2776.837eV
Energy per atom: Epot =2024.914eV Ekin = 753.155eV (T=1456.668K) Etot = 2778.070eV
Energy per atom: Epot =2006.794eV Ekin = 769.922eV (T=1489.097K) Etot = 2776.716eV
Energy per atom: Epot =2010.949eV Ekin = 773.639eV (T=1496.285K) Etot = 2784.588eV
Energy per atom: Epot =2011.830eV Ekin = 773.510eV (T=1496.036K) Etot = 2785.341eV
Energy per atom: Epot =1999.248eV Ekin = 778.397eV (T=1505.488K) Etot = 2777.645eV
Energy per atom: Epot =2005.438eV Ekin = 776.914eV (T=1502.620K) Etot = 2782.352eV
Energy per atom: Epot =2008.907eV Ekin = 777.375eV (T=1503.511K) Etot = 2786.282eV
Energy per atom: Epot =2011.544eV Ekin = 770.165eV (T=1489.567K) Etot = 2781.709eV
Energy per atom: Epot =2009.175eV Ekin = 773.884eV (T=1496.759K) Etot = 2783.058eV
Energy per atom: Epot =2010.716eV Ekin = 778.333eV (T=1505.364K) Etot = 2789.049eV
Energy per atom: Epot =2018.496eV Ekin = 759.304eV (T=1468.560K) Etot = 2777.800eV
Energy per atom: Epot =2006.883eV Ekin = 762.420eV (T=1474.587K) Etot = 2769.303eV
Energy per atom: Epot =2007.251eV Ekin = 766.727eV (T=1482.916K) Etot = 2773.978eV
Energy per atom: Epot =2001.986eV Ekin = 768.118eV (T=1485.606K) Etot = 2770.103eV
Energy per atom: Epot =2003.330eV Ekin = 759.982eV (T=1469.872K) Etot = 2763.312eV
Energy per atom: Epot =1995.294eV Ekin = 763.148eV (T=1475.995K) Etot = 2758.443eV
Energy per atom: Epot =1989.913eV Ekin = 762.359eV (T=1474.469K) Etot = 2752.272eV
Energy per atom: Epot =1991.351eV Ekin = 757.609eV (T=1465.281K) Etot = 2748.959eV
Energy per atom: Epot =1988.252eV Ekin = 762.985eV (T=1475.679K) Etot = 2751.237eV
Energy per atom: Epot =1977.898eV Ekin = 772.448eV (T=1493.982K) Etot = 2750.346eV
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] 12:03:37 43.457006 1.0818
BFGSLineSearch: 1[ 1] 12:03:37 42.347659 0.2273
BFGSLineSearch: 2[ 2] 12:03:37 42.108454 0.1349
BFGSLineSearch: 3[ 3] 12:03:37 41.964817 0.1138
BFGSLineSearch: 4[ 4] 12:03:37 41.924933 0.0683
BFGSLineSearch: 5[ 5] 12:03:37 41.915346 0.0225
BFGSLineSearch: 6[ 6] 12:03:37 41.914920 0.0059
BFGSLineSearch: 7[ 7] 12:03:37 41.914872 0.0023
BFGSLineSearch: 8[ 9] 12:03:37 41.914855 0.0023
BFGSLineSearch: 9[ 10] 12:03:37 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 14.823eV (T=1233.095K) Etot = 56.738eV
Energy per atom: Epot =49.306eV Ekin = 7.464eV (T=620.934K) Etot = 56.770eV
Energy per atom: Epot =51.168eV Ekin = 5.622eV (T=467.688K) Etot = 56.790eV
Energy per atom: Epot =51.482eV Ekin = 5.307eV (T=441.433K) Etot = 56.789eV
Energy per atom: Epot =51.197eV Ekin = 5.589eV (T=464.953K) Etot = 56.786eV
Energy per atom: Epot =50.170eV Ekin = 6.611eV (T=549.962K) Etot = 56.781eV
Energy per atom: Epot =50.023eV Ekin = 6.759eV (T=562.234K) Etot = 56.782eV
Energy per atom: Epot =49.412eV Ekin = 7.369eV (T=613.012K) Etot = 56.781eV
Energy per atom: Epot =49.759eV Ekin = 7.022eV (T=584.176K) Etot = 56.782eV
Energy per atom: Epot =50.139eV Ekin = 6.643eV (T=552.623K) Etot = 56.782eV
Energy per atom: Epot =50.672eV Ekin = 6.116eV (T=508.805K) Etot = 56.788eV
Energy per atom: Epot =50.699eV Ekin = 6.086eV (T=506.307K) Etot = 56.786eV
Energy per atom: Epot =49.749eV Ekin = 7.029eV (T=584.712K) Etot = 56.778eV
Energy per atom: Epot =50.395eV Ekin = 6.389eV (T=531.495K) Etot = 56.784eV
Energy per atom: Epot =49.996eV Ekin = 6.787eV (T=564.563K) Etot = 56.783eV
Energy per atom: Epot =49.499eV Ekin = 7.283eV (T=605.859K) Etot = 56.782eV
Energy per atom: Epot =49.784eV Ekin = 7.000eV (T=582.286K) Etot = 56.784eV
Energy per atom: Epot =49.577eV Ekin = 7.203eV (T=599.202K) Etot = 56.780eV
Energy per atom: Epot =49.098eV Ekin = 7.678eV (T=638.739K) Etot = 56.777eV
Energy per atom: Epot =49.434eV Ekin = 7.345eV (T=611.036K) Etot = 56.779eV
Energy per atom: Epot =49.565eV Ekin = 7.216eV (T=600.265K) Etot = 56.780eV
Energy per atom: Epot =48.558eV Ekin = 8.217eV (T=683.577K) Etot = 56.776eV
Energy per atom: Epot =49.322eV Ekin = 7.463eV (T=620.783K) Etot = 56.784eV
Energy per atom: Epot =49.832eV Ekin = 6.953eV (T=578.419K) Etot = 56.785eV
Energy per atom: Epot =49.426eV Ekin = 7.353eV (T=611.654K) Etot = 56.779eV
Energy per atom: Epot =49.605eV Ekin = 7.176eV (T=596.913K) Etot = 56.781eV
Energy per atom: Epot =49.880eV Ekin = 6.902eV (T=574.180K) Etot = 56.782eV
Energy per atom: Epot =49.344eV Ekin = 7.437eV (T=618.625K) Etot = 56.781eV
Energy per atom: Epot =49.325eV Ekin = 7.454eV (T=620.076K) Etot = 56.779eV
Energy per atom: Epot =49.841eV Ekin = 6.944eV (T=577.671K) Etot = 56.785eV
Energy per atom: Epot =49.102eV Ekin = 7.683eV (T=639.143K) Etot = 56.785eV
Energy per atom: Epot =49.425eV Ekin = 7.359eV (T=612.195K) Etot = 56.784eV
Energy per atom: Epot =49.663eV Ekin = 7.118eV (T=592.139K) Etot = 56.781eV
Energy per atom: Epot =49.573eV Ekin = 7.208eV (T=599.578K) Etot = 56.781eV
Energy per atom: Epot =49.089eV Ekin = 7.689eV (T=639.607K) Etot = 56.778eV
Energy per atom: Epot =49.106eV Ekin = 7.667eV (T=637.808K) Etot = 56.774eV
Energy per atom: Epot =49.706eV Ekin = 7.075eV (T=588.567K) Etot = 56.781eV
Energy per atom: Epot =49.442eV Ekin = 7.343eV (T=610.814K) Etot = 56.785eV
Energy per atom: Epot =49.733eV Ekin = 7.046eV (T=586.156K) Etot = 56.780eV
Energy per atom: Epot =49.242eV Ekin = 7.533eV (T=626.672K) Etot = 56.775eV
Energy per atom: Epot =49.266eV Ekin = 7.515eV (T=625.134K) Etot = 56.781eV
Energy per atom: Epot =49.459eV Ekin = 7.320eV (T=608.949K) Etot = 56.779eV
Energy per atom: Epot =49.700eV Ekin = 7.078eV (T=588.777K) Etot = 56.778eV
Energy per atom: Epot =49.377eV Ekin = 7.401eV (T=615.666K) Etot = 56.778eV
Energy per atom: Epot =49.095eV Ekin = 7.675eV (T=638.478K) Etot = 56.771eV
Energy per atom: Epot =49.492eV Ekin = 7.279eV (T=605.554K) Etot = 56.771eV
Energy per atom: Epot =50.211eV Ekin = 6.573eV (T=546.822K) Etot = 56.784eV
Energy per atom: Epot =48.317eV Ekin = 8.456eV (T=703.392K) Etot = 56.773eV
Energy per atom: Epot =49.366eV Ekin = 7.407eV (T=616.168K) Etot = 56.773eV
Energy per atom: Epot =49.410eV Ekin = 7.373eV (T=613.312K) Etot = 56.783eV
Energy per atom: Epot =49.620eV Ekin = 7.162eV (T=595.743K) Etot = 56.782eV
Energy per atom: Epot =49.581eV Ekin = 7.200eV (T=598.947K) Etot = 56.781eV
Energy per atom: Epot =48.730eV Ekin = 8.045eV (T=669.209K) Etot = 56.775eV
Energy per atom: Epot =50.200eV Ekin = 6.580eV (T=547.358K) Etot = 56.780eV
Energy per atom: Epot =49.314eV Ekin = 7.469eV (T=621.325K) Etot = 56.783eV
Energy per atom: Epot =49.837eV Ekin = 6.945eV (T=577.760K) Etot = 56.783eV
Energy per atom: Epot =49.296eV Ekin = 7.483eV (T=622.481K) Etot = 56.779eV
Energy per atom: Epot =48.901eV Ekin = 7.880eV (T=655.516K) Etot = 56.781eV
Energy per atom: Epot =48.858eV Ekin = 7.922eV (T=659.000K) Etot = 56.780eV
Energy per atom: Epot =49.706eV Ekin = 7.078eV (T=588.773K) Etot = 56.784eV
Energy per atom: Epot =48.967eV Ekin = 7.811eV (T=649.761K) Etot = 56.778eV
Energy per atom: Epot =48.777eV Ekin = 7.999eV (T=665.443K) Etot = 56.776eV
Energy per atom: Epot =49.701eV Ekin = 7.082eV (T=589.088K) Etot = 56.783eV
Energy per atom: Epot =50.580eV Ekin = 6.209eV (T=516.544K) Etot = 56.789eV
Energy per atom: Epot =49.233eV Ekin = 7.547eV (T=627.849K) Etot = 56.780eV
Energy per atom: Epot =48.664eV Ekin = 8.115eV (T=675.076K) Etot = 56.779eV
Energy per atom: Epot =50.147eV Ekin = 6.638eV (T=552.199K) Etot = 56.785eV
Energy per atom: Epot =49.452eV Ekin = 7.325eV (T=609.349K) Etot = 56.777eV
Energy per atom: Epot =49.809eV Ekin = 6.972eV (T=579.984K) Etot = 56.781eV
Energy per atom: Epot =49.938eV Ekin = 6.841eV (T=569.078K) Etot = 56.779eV
Energy per atom: Epot =49.558eV Ekin = 7.222eV (T=600.773K) Etot = 56.780eV
Energy per atom: Epot =49.019eV Ekin = 7.759eV (T=645.433K) Etot = 56.778eV
Energy per atom: Epot =48.024eV Ekin = 8.748eV (T=727.716K) Etot = 56.772eV
Energy per atom: Epot =49.120eV Ekin = 7.657eV (T=636.965K) Etot = 56.777eV
Energy per atom: Epot =48.764eV Ekin = 8.010eV (T=666.284K) Etot = 56.774eV
Energy per atom: Epot =49.352eV Ekin = 7.427eV (T=617.852K) Etot = 56.779eV
Energy per atom: Epot =49.893eV Ekin = 6.885eV (T=572.765K) Etot = 56.779eV
Energy per atom: Epot =49.207eV Ekin = 7.568eV (T=629.549K) Etot = 56.775eV
Energy per atom: Epot =49.178eV Ekin = 7.600eV (T=632.233K) Etot = 56.778eV
Energy per atom: Epot =49.702eV Ekin = 7.080eV (T=588.922K) Etot = 56.782eV
Energy per atom: Epot =49.820eV Ekin = 6.963eV (T=579.188K) Etot = 56.782eV
Energy per atom: Epot =49.030eV Ekin = 7.752eV (T=644.897K) Etot = 56.782eV
Energy per atom: Epot =50.076eV Ekin = 6.709eV (T=558.123K) Etot = 56.785eV
Energy per atom: Epot =49.335eV Ekin = 7.443eV (T=619.162K) Etot = 56.779eV
Energy per atom: Epot =49.294eV Ekin = 7.489eV (T=623.025K) Etot = 56.784eV
Energy per atom: Epot =49.052eV Ekin = 7.729eV (T=642.928K) Etot = 56.781eV
Energy per atom: Epot =49.221eV Ekin = 7.559eV (T=628.774K) Etot = 56.779eV
Energy per atom: Epot =49.545eV Ekin = 7.234eV (T=601.778K) Etot = 56.780eV
Energy per atom: Epot =48.480eV Ekin = 8.292eV (T=689.764K) Etot = 56.772eV
Energy per atom: Epot =49.756eV Ekin = 7.020eV (T=583.993K) Etot = 56.776eV
Energy per atom: Epot =49.761eV Ekin = 7.018eV (T=583.790K) Etot = 56.779eV
Energy per atom: Epot =49.127eV Ekin = 7.648eV (T=636.203K) Etot = 56.775eV
Energy per atom: Epot =48.336eV Ekin = 8.441eV (T=702.162K) Etot = 56.777eV
Energy per atom: Epot =49.318eV Ekin = 7.470eV (T=621.412K) Etot = 56.788eV
Energy per atom: Epot =49.409eV Ekin = 7.373eV (T=613.329K) Etot = 56.782eV
Energy per atom: Epot =49.208eV Ekin = 7.566eV (T=629.384K) Etot = 56.774eV
Energy per atom: Epot =48.476eV Ekin = 8.295eV (T=690.046K) Etot = 56.771eV
Energy per atom: Epot =48.947eV Ekin = 7.835eV (T=651.729K) Etot = 56.781eV
Energy per atom: Epot =48.832eV Ekin = 7.947eV (T=661.076K) Etot = 56.779eV
Energy per atom: Epot =49.627eV Ekin = 7.150eV (T=594.806K) Etot = 56.777eV
Energy per atom: Epot =48.843eV Ekin = 7.935eV (T=660.068K) Etot = 56.777eV
Energy per atom: Epot =49.221eV Ekin = 7.558eV (T=628.763K) Etot = 56.779eV
Energy per atom: Epot =49.265eV Ekin = 7.514eV (T=625.062K) Etot = 56.779eV
Energy per atom: Epot =49.619eV Ekin = 7.163eV (T=595.864K) Etot = 56.782eV
Energy per atom: Epot =49.781eV Ekin = 7.005eV (T=582.734K) Etot = 56.786eV
Energy per atom: Epot =48.865eV Ekin = 7.921eV (T=658.887K) Etot = 56.786eV
Energy per atom: Epot =49.562eV Ekin = 7.223eV (T=600.830K) Etot = 56.785eV
Energy per atom: Epot =50.277eV Ekin = 6.508eV (T=541.346K) Etot = 56.785eV
Energy per atom: Epot =49.666eV Ekin = 7.110eV (T=591.480K) Etot = 56.777eV
Energy per atom: Epot =49.665eV Ekin = 7.114eV (T=591.750K) Etot = 56.779eV
Energy per atom: Epot =49.622eV Ekin = 7.159eV (T=595.533K) Etot = 56.781eV
Energy per atom: Epot =48.603eV Ekin = 8.172eV (T=679.816K) Etot = 56.775eV
Energy per atom: Epot =49.041eV Ekin = 7.738eV (T=643.679K) Etot = 56.779eV
Energy per atom: Epot =48.043eV Ekin = 8.731eV (T=726.337K) Etot = 56.774eV
Energy per atom: Epot =49.343eV Ekin = 7.440eV (T=618.915K) Etot = 56.783eV
Energy per atom: Epot =48.918eV Ekin = 7.862eV (T=654.018K) Etot = 56.780eV
Energy per atom: Epot =49.101eV Ekin = 7.675eV (T=638.461K) Etot = 56.776eV
Energy per atom: Epot =48.834eV Ekin = 7.946eV (T=661.012K) Etot = 56.780eV
Energy per atom: Epot =48.744eV Ekin = 8.035eV (T=668.401K) Etot = 56.779eV
Energy per atom: Epot =49.174eV Ekin = 7.607eV (T=632.811K) Etot = 56.781eV
Energy per atom: Epot =49.308eV Ekin = 7.470eV (T=621.437K) Etot = 56.778eV
Energy per atom: Epot =49.157eV Ekin = 7.623eV (T=634.157K) Etot = 56.781eV
Energy per atom: Epot =49.630eV Ekin = 7.156eV (T=595.262K) Etot = 56.785eV
Energy per atom: Epot =49.469eV Ekin = 7.310eV (T=608.067K) Etot = 56.779eV
Energy per atom: Epot =49.529eV Ekin = 7.251eV (T=603.186K) Etot = 56.780eV
Energy per atom: Epot =49.321eV Ekin = 7.456eV (T=620.277K) Etot = 56.777eV
Energy per atom: Epot =49.352eV Ekin = 7.423eV (T=617.461K) Etot = 56.774eV
Energy per atom: Epot =49.101eV Ekin = 7.677eV (T=638.643K) Etot = 56.778eV
Energy per atom: Epot =48.511eV Ekin = 8.271eV (T=688.039K) Etot = 56.782eV
Energy per atom: Epot =49.187eV Ekin = 7.595eV (T=631.839K) Etot = 56.782eV
Energy per atom: Epot =49.765eV Ekin = 7.021eV (T=584.024K) Etot = 56.786eV
Energy per atom: Epot =48.706eV Ekin = 8.070eV (T=671.325K) Etot = 56.776eV
Energy per atom: Epot =47.863eV Ekin = 8.912eV (T=741.341K) Etot = 56.775eV
Energy per atom: Epot =49.882eV Ekin = 6.904eV (T=574.343K) Etot = 56.786eV
Energy per atom: Epot =49.305eV Ekin = 7.477eV (T=621.976K) Etot = 56.782eV
Energy per atom: Epot =49.160eV Ekin = 7.620eV (T=633.855K) Etot = 56.780eV
Energy per atom: Epot =50.159eV Ekin = 6.624eV (T=551.009K) Etot = 56.783eV
Energy per atom: Epot =48.714eV Ekin = 8.064eV (T=670.796K) Etot = 56.778eV
Energy per atom: Epot =47.779eV Ekin = 8.996eV (T=748.354K) Etot = 56.776eV
Energy per atom: Epot =49.414eV Ekin = 7.366eV (T=612.772K) Etot = 56.780eV
Energy per atom: Epot =49.184eV Ekin = 7.592eV (T=631.551K) Etot = 56.776eV
Energy per atom: Epot =48.610eV Ekin = 8.166eV (T=679.283K) Etot = 56.776eV
Energy per atom: Epot =49.675eV Ekin = 7.107eV (T=591.236K) Etot = 56.782eV
Energy per atom: Epot =49.096eV Ekin = 7.682eV (T=639.075K) Etot = 56.778eV
Energy per atom: Epot =49.424eV Ekin = 7.359eV (T=612.130K) Etot = 56.783eV
Energy per atom: Epot =48.474eV Ekin = 8.300eV (T=690.414K) Etot = 56.773eV
Energy per atom: Epot =48.700eV Ekin = 8.074eV (T=671.654K) Etot = 56.774eV
Energy per atom: Epot =48.870eV Ekin = 7.905eV (T=657.622K) Etot = 56.776eV
Energy per atom: Epot =49.833eV Ekin = 6.949eV (T=578.096K) Etot = 56.782eV
Energy per atom: Epot =48.625eV Ekin = 8.155eV (T=678.395K) Etot = 56.780eV
Energy per atom: Epot =49.835eV Ekin = 6.945eV (T=577.713K) Etot = 56.780eV
Energy per atom: Epot =49.927eV Ekin = 6.851eV (T=569.919K) Etot = 56.778eV
Energy per atom: Epot =49.546eV Ekin = 7.238eV (T=602.087K) Etot = 56.783eV
Energy per atom: Epot =49.018eV Ekin = 7.762eV (T=645.653K) Etot = 56.780eV
Energy per atom: Epot =49.296eV Ekin = 7.482eV (T=622.407K) Etot = 56.778eV
Energy per atom: Epot =49.815eV Ekin = 6.969eV (T=579.693K) Etot = 56.784eV
Energy per atom: Epot =49.738eV Ekin = 7.046eV (T=586.112K) Etot = 56.784eV
Energy per atom: Epot =49.344eV Ekin = 7.441eV (T=619.031K) Etot = 56.786eV
Energy per atom: Epot =48.512eV Ekin = 8.265eV (T=687.512K) Etot = 56.777eV
Energy per atom: Epot =49.739eV Ekin = 7.036eV (T=585.289K) Etot = 56.775eV
Energy per atom: Epot =50.020eV Ekin = 6.763eV (T=562.576K) Etot = 56.782eV
Energy per atom: Epot =50.338eV Ekin = 6.450eV (T=536.542K) Etot = 56.788eV
Energy per atom: Epot =49.811eV Ekin = 6.971eV (T=579.928K) Etot = 56.782eV
Energy per atom: Epot =49.569eV Ekin = 7.210eV (T=599.738K) Etot = 56.779eV
Energy per atom: Epot =48.896eV Ekin = 7.878eV (T=655.365K) Etot = 56.774eV
Energy per atom: Epot =48.989eV Ekin = 7.789eV (T=647.915K) Etot = 56.777eV
Energy per atom: Epot =49.167eV Ekin = 7.616eV (T=633.566K) Etot = 56.784eV
Energy per atom: Epot =49.993eV Ekin = 6.791eV (T=564.958K) Etot = 56.784eV
Energy per atom: Epot =50.530eV Ekin = 6.258eV (T=520.589K) Etot = 56.788eV
Energy per atom: Epot =50.088eV Ekin = 6.696eV (T=557.058K) Etot = 56.784eV
Energy per atom: Epot =49.580eV Ekin = 7.204eV (T=599.257K) Etot = 56.784eV
Energy per atom: Epot =49.809eV Ekin = 6.975eV (T=580.203K) Etot = 56.783eV
Energy per atom: Epot =49.067eV Ekin = 7.710eV (T=641.336K) Etot = 56.777eV
Energy per atom: Epot =49.572eV Ekin = 7.205eV (T=599.390K) Etot = 56.777eV
Energy per atom: Epot =49.568eV Ekin = 7.210eV (T=599.801K) Etot = 56.778eV
Energy per atom: Epot =50.045eV Ekin = 6.738eV (T=560.485K) Etot = 56.783eV
Energy per atom: Epot =49.734eV Ekin = 7.045eV (T=586.081K) Etot = 56.779eV
Energy per atom: Epot =49.108eV Ekin = 7.660eV (T=637.239K) Etot = 56.769eV
Energy per atom: Epot =49.489eV Ekin = 7.285eV (T=606.022K) Etot = 56.774eV
Energy per atom: Epot =50.183eV Ekin = 6.597eV (T=548.742K) Etot = 56.780eV
Energy per atom: Epot =50.094eV Ekin = 6.690eV (T=556.546K) Etot = 56.785eV
Energy per atom: Epot =49.751eV Ekin = 7.033eV (T=585.025K) Etot = 56.784eV
Energy per atom: Epot =49.708eV Ekin = 7.075eV (T=588.560K) Etot = 56.783eV
Energy per atom: Epot =50.048eV Ekin = 6.732eV (T=559.973K) Etot = 56.779eV
Energy per atom: Epot =50.617eV Ekin = 6.161eV (T=512.513K) Etot = 56.778eV
Energy per atom: Epot =50.358eV Ekin = 6.423eV (T=534.304K) Etot = 56.781eV
Energy per atom: Epot =49.102eV Ekin = 7.674eV (T=638.365K) Etot = 56.776eV
Energy per atom: Epot =49.589eV Ekin = 7.185eV (T=597.669K) Etot = 56.774eV
Energy per atom: Epot =49.080eV Ekin = 7.694eV (T=640.000K) Etot = 56.774eV
Energy per atom: Epot =49.696eV Ekin = 7.080eV (T=588.978K) Etot = 56.777eV
Energy per atom: Epot =49.952eV Ekin = 6.828eV (T=567.957K) Etot = 56.779eV
Energy per atom: Epot =50.027eV Ekin = 6.754eV (T=561.859K) Etot = 56.782eV
Energy per atom: Epot =50.594eV Ekin = 6.191eV (T=514.983K) Etot = 56.784eV
Energy per atom: Epot =50.147eV Ekin = 6.630eV (T=551.530K) Etot = 56.777eV
Energy per atom: Epot =50.170eV Ekin = 6.609eV (T=549.800K) Etot = 56.779eV
Energy per atom: Epot =49.696eV Ekin = 7.086eV (T=589.495K) Etot = 56.782eV
Energy per atom: Epot =50.251eV Ekin = 6.538eV (T=543.834K) Etot = 56.789eV
Energy per atom: Epot =49.338eV Ekin = 7.445eV (T=619.309K) Etot = 56.783eV
Energy per atom: Epot =49.437eV Ekin = 7.348eV (T=611.216K) Etot = 56.784eV
Energy per atom: Epot =48.636eV Ekin = 8.137eV (T=676.906K) Etot = 56.773eV
Energy per atom: Epot =50.267eV Ekin = 6.513eV (T=541.820K) Etot = 56.780eV
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 -0.0019402260619084425 eV
Cumul. energy transfered to the thermostat -0.00956753525704368 eV
Cumul. energy transfered to the thermostat -0.011572633839153395 eV
Cumul. energy transfered to the thermostat -0.014482979724435035 eV
Cumul. energy transfered to the thermostat -0.009441241865170522 eV
Cumul. energy transfered to the thermostat -0.009433366786281878 eV
Cumul. energy transfered to the thermostat -0.020305055438069583 eV
Cumul. energy transfered to the thermostat -0.019938840262696243 eV
Cumul. energy transfered to the thermostat -0.018193834422432987 eV
Cumul. energy transfered to the thermostat -0.016651826121134066 eV
Cumul. energy transfered to the thermostat -0.009958056321630706 eV
Cumul. energy transfered to the thermostat -0.012139900446254376 eV
Cumul. energy transfered to the thermostat -0.009768729537847786 eV
Cumul. energy transfered to the thermostat -0.016214283147126328 eV
Cumul. energy transfered to the thermostat -0.010226971975343307 eV
Cumul. energy transfered to the thermostat -0.006656405701792397 eV
Cumul. energy transfered to the thermostat -0.00459630149481592 eV
Cumul. energy transfered to the thermostat -0.0024181511411694593 eV
Cumul. energy transfered to the thermostat 0.007178405517625213 eV
Cumul. energy transfered to the thermostat 0.008923457207775582 eV
Cumul. energy transfered to the thermostat 0.0034220739003173817 eV
Cumul. energy transfered to the thermostat -0.001596252926272618 eV
Cumul. energy transfered to the thermostat 0.007244028907900313 eV
Cumul. energy transfered to the thermostat 0.01337242954391993 eV
Cumul. energy transfered to the thermostat 0.012690980066226605 eV
Cumul. energy transfered to the thermostat 0.014442062929249674 eV
Cumul. energy transfered to the thermostat 0.013567876172302484 eV
Cumul. energy transfered to the thermostat 0.00983035956924973 eV
Cumul. energy transfered to the thermostat 0.0184954917054471 eV
Cumul. energy transfered to the thermostat 0.016476986227269404 eV
Cumul. energy transfered to the thermostat 0.0075186220138821255 eV
Cumul. energy transfered to the thermostat 0.010608671339483492 eV
Cumul. energy transfered to the thermostat 0.014208736073443085 eV
Cumul. energy transfered to the thermostat 0.011358436399747967 eV
Cumul. energy transfered to the thermostat 0.010411364339088958 eV
Cumul. energy transfered to the thermostat 0.008779427835080495 eV
Cumul. energy transfered to the thermostat 0.008058639044094415 eV
Cumul. energy transfered to the thermostat 0.00915099635210778 eV
Cumul. energy transfered to the thermostat 0.011392561736232753 eV
Cumul. energy transfered to the thermostat 0.016764852533721144 eV
Cumul. energy transfered to the thermostat 0.01760394988440447 eV
Cumul. energy transfered to the thermostat 0.017509717691997 eV
Cumul. energy transfered to the thermostat 0.014958074431596897 eV
Cumul. energy transfered to the thermostat 0.013877618543065066 eV
Cumul. energy transfered to the thermostat 0.01453819902248393 eV
Cumul. energy transfered to the thermostat 0.017917192070598914 eV
Cumul. energy transfered to the thermostat 0.015547815073302324 eV
Cumul. energy transfered to the thermostat 0.015166588091540905 eV
Cumul. energy transfered to the thermostat 0.01652702159809106 eV
Cumul. energy transfered to the thermostat 0.015477907480049206 eV
Cumul. energy transfered to the thermostat 0.0159853724713548 eV
Cumul. energy transfered to the thermostat 0.02026890229170609 eV
Cumul. energy transfered to the thermostat 0.01545627028661561 eV
Cumul. energy transfered to the thermostat 0.015322512318542713 eV
Cumul. energy transfered to the thermostat 0.013188847347990825 eV
Cumul. energy transfered to the thermostat 0.013214028715759232 eV
Cumul. energy transfered to the thermostat 0.017829540286013995 eV
Cumul. energy transfered to the thermostat 0.017502977271655958 eV
Cumul. energy transfered to the thermostat 0.01775048191022325 eV
Cumul. energy transfered to the thermostat 0.021245364974859075 eV
Cumul. energy transfered to the thermostat 0.020446663834390425 eV
Cumul. energy transfered to the thermostat 0.020483445076536936 eV
Cumul. energy transfered to the thermostat 0.016809433792231446 eV
Cumul. energy transfered to the thermostat 0.012912441094498267 eV
Cumul. energy transfered to the thermostat 0.01160395868131941 eV
Cumul. energy transfered to the thermostat 0.007911625978654264 eV
Cumul. energy transfered to the thermostat 0.008582350695068245 eV
Cumul. energy transfered to the thermostat 0.008820792577455381 eV
Cumul. energy transfered to the thermostat 0.007609315034974977 eV
Cumul. energy transfered to the thermostat 0.010367055748790198 eV
Cumul. energy transfered to the thermostat 0.004762113248643178 eV
Cumul. energy transfered to the thermostat 0.002766772418301227 eV
Cumul. energy transfered to the thermostat -0.0012637477545205684 eV
Cumul. energy transfered to the thermostat -0.0028530226945796345 eV
Cumul. energy transfered to the thermostat -0.0036117432830995357 eV
Cumul. energy transfered to the thermostat -0.0010760813196213411 eV
Cumul. energy transfered to the thermostat -0.0031748498766756574 eV
Cumul. energy transfered to the thermostat -0.008256003002082325 eV
Cumul. energy transfered to the thermostat -0.002705050713431123 eV
Cumul. energy transfered to the thermostat -0.007069913330079032 eV
Cumul. energy transfered to the thermostat -0.012310920399702741 eV
Cumul. energy transfered to the thermostat -0.009499128849400771 eV
Cumul. energy transfered to the thermostat -0.009876441380029452 eV
Cumul. energy transfered to the thermostat -0.007949169535895906 eV
Cumul. energy transfered to the thermostat -0.011983964878827833 eV
Cumul. energy transfered to the thermostat -0.011767388682890184 eV
Cumul. energy transfered to the thermostat -0.009986160120459523 eV
Cumul. energy transfered to the thermostat -0.010432497981937875 eV
Cumul. energy transfered to the thermostat -0.008863342869585207 eV
Cumul. energy transfered to the thermostat -0.016309095340484865 eV
Cumul. energy transfered to the thermostat -0.017789005714065016 eV
Cumul. energy transfered to the thermostat -0.025107614507566912 eV
Cumul. energy transfered to the thermostat -0.0228342944810749 eV
Cumul. energy transfered to the thermostat -0.02149403810510267 eV
Cumul. energy transfered to the thermostat -0.02584544713945527 eV
Cumul. energy transfered to the thermostat -0.025060346861118323 eV
Cumul. energy transfered to the thermostat -0.030284438846191558 eV
Cumul. energy transfered to the thermostat -0.03127620995087662 eV
Cumul. energy transfered to the thermostat -0.03197673295710037 eV
Cumul. energy transfered to the thermostat -0.0312099642061048 eV