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 = 156.906eV (T=303.470K) Etot = 154.501eV
Energy per atom: Epot =118.211eV Ekin = 37.088eV (T=71.731K) Etot = 155.299eV
Energy per atom: Epot =80.074eV Ekin = 75.102eV (T=145.254K) Etot = 155.176eV
Energy per atom: Epot =71.615eV Ekin = 83.394eV (T=161.292K) Etot = 155.009eV
Energy per atom: Epot =68.105eV Ekin = 86.842eV (T=167.960K) Etot = 154.947eV
Energy per atom: Epot =84.245eV Ekin = 70.901eV (T=137.129K) Etot = 155.146eV
Energy per atom: Epot =78.441eV Ekin = 76.671eV (T=148.288K) Etot = 155.112eV
Energy per atom: Epot =73.214eV Ekin = 81.802eV (T=158.213K) Etot = 155.017eV
Energy per atom: Epot =74.016eV Ekin = 81.017eV (T=156.693K) Etot = 155.033eV
Energy per atom: Epot =81.465eV Ekin = 73.653eV (T=142.452K) Etot = 155.118eV
Energy per atom: Epot =74.703eV Ekin = 80.357eV (T=155.417K) Etot = 155.060eV
Energy per atom: Epot =75.627eV Ekin = 79.422eV (T=153.609K) Etot = 155.049eV
Energy per atom: Epot =75.322eV Ekin = 79.737eV (T=154.218K) Etot = 155.059eV
Energy per atom: Epot =79.734eV Ekin = 75.355eV (T=145.743K) Etot = 155.089eV
Energy per atom: Epot =74.753eV Ekin = 80.299eV (T=155.305K) Etot = 155.052eV
Energy per atom: Epot =75.873eV Ekin = 79.194eV (T=153.168K) Etot = 155.067eV
Energy per atom: Epot =75.943eV Ekin = 79.120eV (T=153.025K) Etot = 155.063eV
Energy per atom: Epot =78.884eV Ekin = 76.189eV (T=147.357K) Etot = 155.074eV
Energy per atom: Epot =74.657eV Ekin = 80.405eV (T=155.510K) Etot = 155.062eV
Energy per atom: Epot =75.357eV Ekin = 79.692eV (T=154.131K) Etot = 155.049eV
Energy per atom: Epot =78.986eV Ekin = 76.084eV (T=147.154K) Etot = 155.070eV
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)
dyn.attach(traj.write, interval=100)
# 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 =602.716eV Ekin = 81.008eV (T=156.677K) Etot = 683.725eV
Energy per atom: Epot =670.184eV Ekin = 140.454eV (T=271.651K) Etot = 810.638eV
Energy per atom: Epot =730.603eV Ekin = 200.260eV (T=387.320K) Etot = 930.863eV
Energy per atom: Epot =785.129eV Ekin = 252.509eV (T=488.375K) Etot = 1037.639eV
Energy per atom: Epot =832.255eV Ekin = 299.315eV (T=578.902K) Etot = 1131.570eV
Energy per atom: Epot =881.426eV Ekin = 341.463eV (T=660.420K) Etot = 1222.889eV
Energy per atom: Epot =924.074eV Ekin = 381.146eV (T=737.169K) Etot = 1305.219eV
Energy per atom: Epot =968.238eV Ekin = 410.521eV (T=793.983K) Etot = 1378.759eV
Energy per atom: Epot =997.695eV Ekin = 453.970eV (T=878.017K) Etot = 1451.665eV
Energy per atom: Epot =1045.059eV Ekin = 466.176eV (T=901.625K) Etot = 1511.235eV
Energy per atom: Epot =1071.955eV Ekin = 497.559eV (T=962.321K) Etot = 1569.514eV
Energy per atom: Epot =1113.600eV Ekin = 515.191eV (T=996.425K) Etot = 1628.791eV
Energy per atom: Epot =1145.991eV Ekin = 529.730eV (T=1024.543K) Etot = 1675.720eV
Energy per atom: Epot =1186.676eV Ekin = 538.352eV (T=1041.220K) Etot = 1725.029eV
Energy per atom: Epot =1203.017eV Ekin = 565.158eV (T=1093.064K) Etot = 1768.175eV
Energy per atom: Epot =1226.613eV Ekin = 578.888eV (T=1119.619K) Etot = 1805.500eV
Energy per atom: Epot =1264.045eV Ekin = 583.957eV (T=1129.424K) Etot = 1848.002eV
Energy per atom: Epot =1296.204eV Ekin = 595.269eV (T=1151.302K) Etot = 1891.472eV
Energy per atom: Epot =1316.657eV Ekin = 615.261eV (T=1189.968K) Etot = 1931.917eV
Energy per atom: Epot =1331.650eV Ekin = 614.597eV (T=1188.683K) Etot = 1946.247eV
Energy per atom: Epot =1344.198eV Ekin = 633.097eV (T=1224.464K) Etot = 1977.294eV
Energy per atom: Epot =1373.290eV Ekin = 631.560eV (T=1221.493K) Etot = 2004.851eV
Energy per atom: Epot =1381.859eV Ekin = 645.229eV (T=1247.929K) Etot = 2027.088eV
Energy per atom: Epot =1405.838eV Ekin = 644.188eV (T=1245.915K) Etot = 2050.025eV
Energy per atom: Epot =1422.594eV Ekin = 655.357eV (T=1267.518K) Etot = 2077.951eV
Energy per atom: Epot =1433.946eV Ekin = 665.565eV (T=1287.260K) Etot = 2099.511eV
Energy per atom: Epot =1448.775eV Ekin = 675.983eV (T=1307.411K) Etot = 2124.758eV
Energy per atom: Epot =1466.905eV Ekin = 672.390eV (T=1300.461K) Etot = 2139.295eV
Energy per atom: Epot =1476.788eV Ekin = 675.995eV (T=1307.432K) Etot = 2152.782eV
Energy per atom: Epot =1491.988eV Ekin = 668.545eV (T=1293.024K) Etot = 2160.533eV
Energy per atom: Epot =1497.480eV Ekin = 686.020eV (T=1326.822K) Etot = 2183.499eV
Energy per atom: Epot =1525.450eV Ekin = 674.008eV (T=1303.591K) Etot = 2199.458eV
Energy per atom: Epot =1533.839eV Ekin = 686.420eV (T=1327.596K) Etot = 2220.260eV
Energy per atom: Epot =1558.381eV Ekin = 683.180eV (T=1321.329K) Etot = 2241.560eV
Energy per atom: Epot =1549.923eV Ekin = 702.842eV (T=1359.358K) Etot = 2252.765eV
Energy per atom: Epot =1573.408eV Ekin = 703.920eV (T=1361.443K) Etot = 2277.328eV
Energy per atom: Epot =1581.797eV Ekin = 704.757eV (T=1363.062K) Etot = 2286.554eV
Energy per atom: Epot =1580.887eV Ekin = 718.763eV (T=1390.149K) Etot = 2299.649eV
Energy per atom: Epot =1597.328eV Ekin = 720.474eV (T=1393.459K) Etot = 2317.801eV
Energy per atom: Epot =1618.420eV Ekin = 709.513eV (T=1372.260K) Etot = 2327.933eV
Energy per atom: Epot =1626.118eV Ekin = 720.483eV (T=1393.477K) Etot = 2346.601eV
Energy per atom: Epot =1636.234eV Ekin = 718.745eV (T=1390.115K) Etot = 2354.979eV
Energy per atom: Epot =1653.353eV Ekin = 710.757eV (T=1374.667K) Etot = 2364.110eV
Energy per atom: Epot =1649.310eV Ekin = 725.430eV (T=1403.046K) Etot = 2374.740eV
Energy per atom: Epot =1657.158eV Ekin = 718.201eV (T=1389.062K) Etot = 2375.359eV
Energy per atom: Epot =1663.212eV Ekin = 721.298eV (T=1395.053K) Etot = 2384.510eV
Energy per atom: Epot =1673.976eV Ekin = 713.872eV (T=1380.691K) Etot = 2387.849eV
Energy per atom: Epot =1690.444eV Ekin = 708.102eV (T=1369.530K) Etot = 2398.545eV
Energy per atom: Epot =1686.173eV Ekin = 724.232eV (T=1400.728K) Etot = 2410.405eV
Energy per atom: Epot =1694.244eV Ekin = 727.672eV (T=1407.381K) Etot = 2421.916eV
Energy per atom: Epot =1696.677eV Ekin = 730.291eV (T=1412.447K) Etot = 2426.968eV
Energy per atom: Epot =1719.364eV Ekin = 728.829eV (T=1409.619K) Etot = 2448.194eV
Energy per atom: Epot =1735.452eV Ekin = 729.000eV (T=1409.949K) Etot = 2464.452eV
Energy per atom: Epot =1741.173eV Ekin = 728.328eV (T=1408.650K) Etot = 2469.501eV
Energy per atom: Epot =1743.084eV Ekin = 732.725eV (T=1417.153K) Etot = 2475.809eV
Energy per atom: Epot =1762.634eV Ekin = 730.223eV (T=1412.314K) Etot = 2492.857eV
Energy per atom: Epot =1762.070eV Ekin = 732.907eV (T=1417.507K) Etot = 2494.978eV
Energy per atom: Epot =1783.536eV Ekin = 724.202eV (T=1400.669K) Etot = 2507.738eV
Energy per atom: Epot =1778.964eV Ekin = 726.841eV (T=1405.773K) Etot = 2505.805eV
Energy per atom: Epot =1785.309eV Ekin = 739.080eV (T=1429.444K) Etot = 2524.389eV
Energy per atom: Epot =1799.629eV Ekin = 722.555eV (T=1397.484K) Etot = 2522.184eV
Energy per atom: Epot =1795.231eV Ekin = 729.090eV (T=1410.123K) Etot = 2524.321eV
Energy per atom: Epot =1802.780eV Ekin = 730.180eV (T=1412.232K) Etot = 2532.960eV
Energy per atom: Epot =1807.878eV Ekin = 727.533eV (T=1407.112K) Etot = 2535.411eV
Energy per atom: Epot =1805.579eV Ekin = 734.092eV (T=1419.798K) Etot = 2539.671eV
Energy per atom: Epot =1808.532eV Ekin = 746.566eV (T=1443.923K) Etot = 2555.097eV
Energy per atom: Epot =1818.623eV Ekin = 737.590eV (T=1426.563K) Etot = 2556.213eV
Energy per atom: Epot =1827.872eV Ekin = 729.313eV (T=1410.555K) Etot = 2557.185eV
Energy per atom: Epot =1834.389eV Ekin = 731.887eV (T=1415.534K) Etot = 2566.277eV
Energy per atom: Epot =1851.934eV Ekin = 727.202eV (T=1406.472K) Etot = 2579.136eV
Energy per atom: Epot =1839.598eV Ekin = 748.580eV (T=1447.819K) Etot = 2588.178eV
Energy per atom: Epot =1851.097eV Ekin = 746.928eV (T=1444.623K) Etot = 2598.025eV
Energy per atom: Epot =1869.073eV Ekin = 739.470eV (T=1430.199K) Etot = 2608.543eV
Energy per atom: Epot =1864.197eV Ekin = 746.638eV (T=1444.064K) Etot = 2610.836eV
Energy per atom: Epot =1863.478eV Ekin = 749.596eV (T=1449.784K) Etot = 2613.074eV
Energy per atom: Epot =1869.001eV Ekin = 752.688eV (T=1455.764K) Etot = 2621.689eV
Energy per atom: Epot =1873.724eV Ekin = 759.929eV (T=1469.769K) Etot = 2633.653eV
Energy per atom: Epot =1882.941eV Ekin = 754.927eV (T=1460.095K) Etot = 2637.868eV
Energy per atom: Epot =1888.060eV Ekin = 764.747eV (T=1479.086K) Etot = 2652.807eV
Energy per atom: Epot =1897.671eV Ekin = 757.256eV (T=1464.598K) Etot = 2654.926eV
Energy per atom: Epot =1894.992eV Ekin = 762.269eV (T=1474.294K) Etot = 2657.261eV
Energy per atom: Epot =1900.039eV Ekin = 750.844eV (T=1452.197K) Etot = 2650.883eV
Energy per atom: Epot =1883.298eV Ekin = 774.403eV (T=1497.763K) Etot = 2657.701eV
Energy per atom: Epot =1908.039eV Ekin = 756.397eV (T=1462.938K) Etot = 2664.436eV
Energy per atom: Epot =1919.700eV Ekin = 748.635eV (T=1447.924K) Etot = 2668.335eV
Energy per atom: Epot =1920.750eV Ekin = 755.770eV (T=1461.724K) Etot = 2676.519eV
Energy per atom: Epot =1930.027eV Ekin = 750.019eV (T=1450.601K) Etot = 2680.046eV
Energy per atom: Epot =1922.854eV Ekin = 760.945eV (T=1471.734K) Etot = 2683.799eV
Energy per atom: Epot =1929.463eV Ekin = 747.227eV (T=1445.203K) Etot = 2676.690eV
Energy per atom: Epot =1939.538eV Ekin = 733.704eV (T=1419.048K) Etot = 2673.242eV
Energy per atom: Epot =1930.461eV Ekin = 753.345eV (T=1457.036K) Etot = 2683.806eV
Energy per atom: Epot =1937.758eV Ekin = 745.830eV (T=1442.499K) Etot = 2683.588eV
Energy per atom: Epot =1946.046eV Ekin = 744.659eV (T=1440.235K) Etot = 2690.704eV
Energy per atom: Epot =1945.352eV Ekin = 753.203eV (T=1456.761K) Etot = 2698.556eV
Energy per atom: Epot =1957.291eV Ekin = 738.205eV (T=1427.752K) Etot = 2695.495eV
Energy per atom: Epot =1952.422eV Ekin = 740.022eV (T=1431.266K) Etot = 2692.444eV
Energy per atom: Epot =1949.736eV Ekin = 746.610eV (T=1444.008K) Etot = 2696.345eV
Energy per atom: Epot =1948.614eV Ekin = 754.625eV (T=1459.510K) Etot = 2703.238eV
Energy per atom: Epot =1951.632eV Ekin = 750.397eV (T=1451.333K) Etot = 2702.029eV
Energy per atom: Epot =1951.249eV Ekin = 740.630eV (T=1432.443K) Etot = 2691.879eV
Energy per atom: Epot =1940.146eV Ekin = 752.081eV (T=1454.590K) Etot = 2692.227eV
Energy per atom: Epot =1944.602eV Ekin = 763.188eV (T=1476.073K) Etot = 2707.791eV
Energy per atom: Epot =1941.500eV Ekin = 764.905eV (T=1479.392K) Etot = 2706.405eV
Energy per atom: Epot =1953.621eV Ekin = 750.914eV (T=1452.334K) Etot = 2704.535eV
Energy per atom: Epot =1942.385eV Ekin = 766.633eV (T=1482.735K) Etot = 2709.018eV
Energy per atom: Epot =1942.537eV Ekin = 773.135eV (T=1495.310K) Etot = 2715.672eV
Energy per atom: Epot =1945.187eV Ekin = 771.814eV (T=1492.755K) Etot = 2717.001eV
Energy per atom: Epot =1954.629eV Ekin = 759.660eV (T=1469.248K) Etot = 2714.289eV
Energy per atom: Epot =1947.028eV Ekin = 767.291eV (T=1484.008K) Etot = 2714.320eV
Energy per atom: Epot =1951.694eV Ekin = 759.374eV (T=1468.695K) Etot = 2711.068eV
Energy per atom: Epot =1953.710eV Ekin = 758.727eV (T=1467.444K) Etot = 2712.437eV
Energy per atom: Epot =1953.575eV Ekin = 758.734eV (T=1467.458K) Etot = 2712.310eV
Energy per atom: Epot =1952.496eV Ekin = 760.384eV (T=1470.649K) Etot = 2712.880eV
Energy per atom: Epot =1977.453eV Ekin = 737.042eV (T=1425.504K) Etot = 2714.496eV
Energy per atom: Epot =1970.322eV Ekin = 746.855eV (T=1444.482K) Etot = 2717.177eV
Energy per atom: Epot =1963.597eV Ekin = 753.922eV (T=1458.151K) Etot = 2717.519eV
Energy per atom: Epot =1975.439eV Ekin = 733.923eV (T=1419.471K) Etot = 2709.362eV
Energy per atom: Epot =1958.125eV Ekin = 756.141eV (T=1462.442K) Etot = 2714.265eV
Energy per atom: Epot =1974.136eV Ekin = 745.708eV (T=1442.264K) Etot = 2719.844eV
Energy per atom: Epot =1965.261eV Ekin = 756.463eV (T=1463.065K) Etot = 2721.723eV
Energy per atom: Epot =1971.891eV Ekin = 749.598eV (T=1449.788K) Etot = 2721.489eV
Energy per atom: Epot =1964.342eV Ekin = 762.626eV (T=1474.986K) Etot = 2726.968eV
Energy per atom: Epot =1972.005eV Ekin = 764.610eV (T=1478.823K) Etot = 2736.616eV
Energy per atom: Epot =1980.027eV Ekin = 762.409eV (T=1474.565K) Etot = 2742.436eV
Energy per atom: Epot =1969.547eV Ekin = 773.573eV (T=1496.158K) Etot = 2743.121eV
Energy per atom: Epot =1977.452eV Ekin = 761.582eV (T=1472.966K) Etot = 2739.034eV
Energy per atom: Epot =1976.015eV Ekin = 765.417eV (T=1480.383K) Etot = 2741.432eV
Energy per atom: Epot =1982.975eV Ekin = 764.343eV (T=1478.306K) Etot = 2747.317eV
Energy per atom: Epot =1977.627eV Ekin = 765.718eV (T=1480.966K) Etot = 2743.345eV
Energy per atom: Epot =1991.682eV Ekin = 752.996eV (T=1456.360K) Etot = 2744.678eV
Energy per atom: Epot =1986.152eV Ekin = 759.508eV (T=1468.955K) Etot = 2745.660eV
Energy per atom: Epot =1977.110eV Ekin = 768.037eV (T=1485.450K) Etot = 2745.147eV
Energy per atom: Epot =1991.708eV Ekin = 757.226eV (T=1464.542K) Etot = 2748.935eV
Energy per atom: Epot =1984.623eV Ekin = 769.649eV (T=1488.568K) Etot = 2754.272eV
Energy per atom: Epot =1983.416eV Ekin = 770.582eV (T=1490.372K) Etot = 2753.998eV
Energy per atom: Epot =1981.739eV Ekin = 774.722eV (T=1498.380K) Etot = 2756.461eV
Energy per atom: Epot =1974.292eV Ekin = 769.399eV (T=1488.085K) Etot = 2743.691eV
Energy per atom: Epot =1978.340eV Ekin = 761.249eV (T=1472.321K) Etot = 2739.589eV
Energy per atom: Epot =1978.923eV Ekin = 768.366eV (T=1486.086K) Etot = 2747.289eV
Energy per atom: Epot =1977.315eV Ekin = 777.282eV (T=1503.331K) Etot = 2754.597eV
Energy per atom: Epot =1975.810eV Ekin = 775.062eV (T=1499.038K) Etot = 2750.872eV
Energy per atom: Epot =1989.540eV Ekin = 761.485eV (T=1472.779K) Etot = 2751.025eV
Energy per atom: Epot =1978.925eV Ekin = 769.900eV (T=1489.054K) Etot = 2748.825eV
Energy per atom: Epot =1998.676eV Ekin = 756.222eV (T=1462.600K) Etot = 2754.898eV
Energy per atom: Epot =2001.527eV Ekin = 756.463eV (T=1463.064K) Etot = 2757.989eV
Energy per atom: Epot =1987.356eV Ekin = 772.003eV (T=1493.120K) Etot = 2759.359eV
Energy per atom: Epot =1995.883eV Ekin = 766.586eV (T=1482.643K) Etot = 2762.468eV
Energy per atom: Epot =2002.310eV Ekin = 750.946eV (T=1452.395K) Etot = 2753.257eV
Energy per atom: Epot =1974.251eV Ekin = 777.753eV (T=1504.243K) Etot = 2752.005eV
Energy per atom: Epot =1988.264eV Ekin = 769.982eV (T=1489.212K) Etot = 2758.246eV
Energy per atom: Epot =1979.398eV Ekin = 776.525eV (T=1501.868K) Etot = 2755.923eV
Energy per atom: Epot =1999.029eV Ekin = 748.323eV (T=1447.321K) Etot = 2747.352eV
Energy per atom: Epot =1993.774eV Ekin = 760.635eV (T=1471.135K) Etot = 2754.409eV
Energy per atom: Epot =1982.548eV Ekin = 774.900eV (T=1498.724K) Etot = 2757.448eV
Energy per atom: Epot =1993.756eV Ekin = 763.849eV (T=1477.350K) Etot = 2757.605eV
Energy per atom: Epot =1996.194eV Ekin = 753.460eV (T=1457.257K) Etot = 2749.653eV
Energy per atom: Epot =1993.041eV Ekin = 756.351eV (T=1462.849K) Etot = 2749.393eV
Energy per atom: Epot =1980.016eV Ekin = 758.472eV (T=1466.952K) Etot = 2738.489eV
Energy per atom: Epot =1977.762eV Ekin = 761.056eV (T=1471.948K) Etot = 2738.818eV
Energy per atom: Epot =1979.364eV Ekin = 767.909eV (T=1485.202K) Etot = 2747.273eV
Energy per atom: Epot =1970.415eV Ekin = 779.445eV (T=1507.514K) Etot = 2749.859eV
Energy per atom: Epot =1973.163eV Ekin = 766.475eV (T=1482.429K) Etot = 2739.638eV
Energy per atom: Epot =1984.666eV Ekin = 763.090eV (T=1475.883K) Etot = 2747.756eV
Energy per atom: Epot =1976.256eV Ekin = 769.960eV (T=1489.169K) Etot = 2746.216eV
Energy per atom: Epot =1984.037eV Ekin = 773.283eV (T=1495.598K) Etot = 2757.321eV
Energy per atom: Epot =1995.686eV Ekin = 760.159eV (T=1470.214K) Etot = 2755.845eV
Energy per atom: Epot =1979.152eV Ekin = 770.591eV (T=1490.390K) Etot = 2749.743eV
Energy per atom: Epot =1987.577eV Ekin = 771.782eV (T=1492.694K) Etot = 2759.360eV
Energy per atom: Epot =1990.139eV Ekin = 773.978eV (T=1496.942K) Etot = 2764.118eV
Energy per atom: Epot =1993.199eV Ekin = 778.086eV (T=1504.886K) Etot = 2771.285eV
Energy per atom: Epot =1989.363eV Ekin = 785.527eV (T=1519.277K) Etot = 2774.890eV
Energy per atom: Epot =1991.709eV Ekin = 789.103eV (T=1526.193K) Etot = 2780.812eV
Energy per atom: Epot =1996.759eV Ekin = 782.123eV (T=1512.693K) Etot = 2778.881eV
Energy per atom: Epot =1999.664eV Ekin = 775.206eV (T=1499.316K) Etot = 2774.870eV
Energy per atom: Epot =1999.503eV Ekin = 776.878eV (T=1502.549K) Etot = 2776.380eV
Energy per atom: Epot =2000.419eV Ekin = 768.327eV (T=1486.012K) Etot = 2768.746eV
Energy per atom: Epot =1999.100eV Ekin = 779.585eV (T=1507.785K) Etot = 2778.685eV
Energy per atom: Epot =1981.285eV Ekin = 783.780eV (T=1515.898K) Etot = 2765.065eV
Energy per atom: Epot =1997.233eV Ekin = 767.566eV (T=1484.539K) Etot = 2764.799eV
Energy per atom: Epot =1994.790eV Ekin = 762.188eV (T=1474.137K) Etot = 2756.978eV
Energy per atom: Epot =1994.073eV Ekin = 762.487eV (T=1474.715K) Etot = 2756.560eV
Energy per atom: Epot =1973.765eV Ekin = 778.046eV (T=1504.808K) Etot = 2751.811eV
Energy per atom: Epot =1982.286eV Ekin = 770.781eV (T=1490.758K) Etot = 2753.067eV
Energy per atom: Epot =1978.957eV Ekin = 780.258eV (T=1509.087K) Etot = 2759.215eV
Energy per atom: Epot =1991.029eV Ekin = 766.561eV (T=1482.596K) Etot = 2757.590eV
Energy per atom: Epot =1986.603eV Ekin = 772.683eV (T=1494.436K) Etot = 2759.286eV
Energy per atom: Epot =1998.991eV Ekin = 770.907eV (T=1491.001K) Etot = 2769.898eV
Energy per atom: Epot =1981.138eV Ekin = 778.690eV (T=1506.053K) Etot = 2759.828eV
Energy per atom: Epot =1996.974eV Ekin = 768.928eV (T=1487.173K) Etot = 2765.902eV
Energy per atom: Epot =1987.819eV Ekin = 787.725eV (T=1523.528K) Etot = 2775.543eV
Energy per atom: Epot =1992.049eV Ekin = 781.645eV (T=1511.769K) Etot = 2773.693eV
Energy per atom: Epot =2005.923eV Ekin = 774.006eV (T=1496.996K) Etot = 2779.929eV
Energy per atom: Epot =2007.820eV Ekin = 768.145eV (T=1485.659K) Etot = 2775.965eV
Energy per atom: Epot =1994.379eV Ekin = 784.601eV (T=1517.487K) Etot = 2778.980eV
Energy per atom: Epot =1999.809eV Ekin = 773.852eV (T=1496.696K) Etot = 2773.660eV
Energy per atom: Epot =1998.617eV Ekin = 769.564eV (T=1488.403K) Etot = 2768.181eV
Energy per atom: Epot =1996.091eV Ekin = 781.200eV (T=1510.909K) Etot = 2777.291eV
Energy per atom: Epot =1988.742eV Ekin = 778.535eV (T=1505.755K) Etot = 2767.277eV
Energy per atom: Epot =1997.725eV Ekin = 774.733eV (T=1498.402K) Etot = 2772.458eV
Energy per atom: Epot =2000.966eV Ekin = 777.702eV (T=1504.143K) Etot = 2778.668eV
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] 12:22:00 43.457006 1.0818
BFGSLineSearch: 1[ 1] 12:22:00 42.347659 0.2273
BFGSLineSearch: 2[ 2] 12:22:00 42.108454 0.1349
BFGSLineSearch: 3[ 3] 12:22:00 41.964817 0.1138
BFGSLineSearch: 4[ 4] 12:22:00 41.924933 0.0683
BFGSLineSearch: 5[ 5] 12:22:00 41.915346 0.0225
BFGSLineSearch: 6[ 6] 12:22:00 41.914920 0.0059
BFGSLineSearch: 7[ 7] 12:22:00 41.914872 0.0023
BFGSLineSearch: 8[ 9] 12:22:00 41.914855 0.0023
BFGSLineSearch: 9[ 10] 12:22:00 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 15.087eV (T=1255.001K) Etot = 57.001eV
Energy per atom: Epot =50.547eV Ekin = 6.502eV (T=540.919K) Etot = 57.049eV
Energy per atom: Epot =51.616eV Ekin = 5.457eV (T=453.961K) Etot = 57.073eV
Energy per atom: Epot =51.019eV Ekin = 6.048eV (T=503.098K) Etot = 57.067eV
Energy per atom: Epot =50.606eV Ekin = 6.455eV (T=537.004K) Etot = 57.062eV
Energy per atom: Epot =50.418eV Ekin = 6.647eV (T=552.923K) Etot = 57.065eV
Energy per atom: Epot =49.351eV Ekin = 7.705eV (T=640.915K) Etot = 57.056eV
Energy per atom: Epot =50.120eV Ekin = 6.943eV (T=577.561K) Etot = 57.063eV
Energy per atom: Epot =49.817eV Ekin = 7.244eV (T=602.574K) Etot = 57.060eV
Energy per atom: Epot =50.188eV Ekin = 6.875eV (T=571.912K) Etot = 57.063eV
Energy per atom: Epot =50.294eV Ekin = 6.767eV (T=562.891K) Etot = 57.061eV
Energy per atom: Epot =50.578eV Ekin = 6.481eV (T=539.146K) Etot = 57.059eV
Energy per atom: Epot =50.603eV Ekin = 6.462eV (T=537.516K) Etot = 57.064eV
Energy per atom: Epot =50.250eV Ekin = 6.813eV (T=566.732K) Etot = 57.063eV
Energy per atom: Epot =49.023eV Ekin = 8.036eV (T=668.458K) Etot = 57.059eV
Energy per atom: Epot =49.119eV Ekin = 7.943eV (T=660.746K) Etot = 57.062eV
Energy per atom: Epot =50.510eV Ekin = 6.555eV (T=545.263K) Etot = 57.065eV
Energy per atom: Epot =50.930eV Ekin = 6.138eV (T=510.602K) Etot = 57.068eV
Energy per atom: Epot =50.510eV Ekin = 6.556eV (T=545.412K) Etot = 57.067eV
Energy per atom: Epot =49.646eV Ekin = 7.415eV (T=616.815K) Etot = 57.061eV
Energy per atom: Epot =49.212eV Ekin = 7.842eV (T=652.376K) Etot = 57.054eV
Energy per atom: Epot =49.286eV Ekin = 7.766eV (T=645.998K) Etot = 57.052eV
Energy per atom: Epot =49.823eV Ekin = 7.235eV (T=601.889K) Etot = 57.058eV
Energy per atom: Epot =50.038eV Ekin = 7.025eV (T=584.356K) Etot = 57.063eV
Energy per atom: Epot =49.635eV Ekin = 7.424eV (T=617.592K) Etot = 57.059eV
Energy per atom: Epot =49.893eV Ekin = 7.170eV (T=596.418K) Etot = 57.063eV
Energy per atom: Epot =49.969eV Ekin = 7.093eV (T=590.012K) Etot = 57.061eV
Energy per atom: Epot =49.564eV Ekin = 7.494eV (T=623.407K) Etot = 57.058eV
Energy per atom: Epot =48.706eV Ekin = 8.352eV (T=694.756K) Etot = 57.058eV
Energy per atom: Epot =50.649eV Ekin = 6.418eV (T=533.869K) Etot = 57.067eV
Energy per atom: Epot =49.793eV Ekin = 7.263eV (T=604.163K) Etot = 57.055eV
Energy per atom: Epot =50.670eV Ekin = 6.390eV (T=531.600K) Etot = 57.060eV
Energy per atom: Epot =49.603eV Ekin = 7.455eV (T=620.184K) Etot = 57.059eV
Energy per atom: Epot =49.763eV Ekin = 7.303eV (T=607.471K) Etot = 57.066eV
Energy per atom: Epot =49.943eV Ekin = 7.120eV (T=592.277K) Etot = 57.063eV
Energy per atom: Epot =48.885eV Ekin = 8.171eV (T=679.712K) Etot = 57.056eV
Energy per atom: Epot =49.464eV Ekin = 7.596eV (T=631.845K) Etot = 57.060eV
Energy per atom: Epot =50.727eV Ekin = 6.341eV (T=527.484K) Etot = 57.068eV
Energy per atom: Epot =49.863eV Ekin = 7.203eV (T=599.152K) Etot = 57.065eV
Energy per atom: Epot =50.034eV Ekin = 7.033eV (T=585.015K) Etot = 57.066eV
Energy per atom: Epot =49.426eV Ekin = 7.632eV (T=634.900K) Etot = 57.058eV
Energy per atom: Epot =48.757eV Ekin = 8.299eV (T=690.368K) Etot = 57.056eV
Energy per atom: Epot =49.725eV Ekin = 7.337eV (T=610.344K) Etot = 57.062eV
Energy per atom: Epot =49.629eV Ekin = 7.429eV (T=617.951K) Etot = 57.058eV
Energy per atom: Epot =49.524eV Ekin = 7.533eV (T=626.662K) Etot = 57.057eV
Energy per atom: Epot =50.959eV Ekin = 6.108eV (T=508.116K) Etot = 57.067eV
Energy per atom: Epot =50.178eV Ekin = 6.888eV (T=573.007K) Etot = 57.066eV
Energy per atom: Epot =48.859eV Ekin = 8.198eV (T=681.924K) Etot = 57.057eV
Energy per atom: Epot =50.663eV Ekin = 6.404eV (T=532.732K) Etot = 57.067eV
Energy per atom: Epot =50.317eV Ekin = 6.747eV (T=561.260K) Etot = 57.064eV
Energy per atom: Epot =49.884eV Ekin = 7.176eV (T=596.912K) Etot = 57.060eV
Energy per atom: Epot =49.922eV Ekin = 7.140eV (T=593.917K) Etot = 57.062eV
Energy per atom: Epot =49.277eV Ekin = 7.781eV (T=647.311K) Etot = 57.058eV
Energy per atom: Epot =49.827eV Ekin = 7.238eV (T=602.106K) Etot = 57.065eV
Energy per atom: Epot =49.389eV Ekin = 7.676eV (T=638.510K) Etot = 57.065eV
Energy per atom: Epot =50.386eV Ekin = 6.678eV (T=555.542K) Etot = 57.064eV
Energy per atom: Epot =50.734eV Ekin = 6.329eV (T=526.528K) Etot = 57.064eV
Energy per atom: Epot =50.930eV Ekin = 6.138eV (T=510.565K) Etot = 57.067eV
Energy per atom: Epot =50.195eV Ekin = 6.868eV (T=571.302K) Etot = 57.063eV
Energy per atom: Epot =49.688eV Ekin = 7.375eV (T=613.463K) Etot = 57.063eV
Energy per atom: Epot =49.911eV Ekin = 7.152eV (T=594.940K) Etot = 57.062eV
Energy per atom: Epot =50.403eV Ekin = 6.665eV (T=554.474K) Etot = 57.068eV
Energy per atom: Epot =49.715eV Ekin = 7.348eV (T=611.280K) Etot = 57.063eV
Energy per atom: Epot =50.749eV Ekin = 6.316eV (T=525.427K) Etot = 57.065eV
Energy per atom: Epot =50.233eV Ekin = 6.825eV (T=567.777K) Etot = 57.058eV
Energy per atom: Epot =50.040eV Ekin = 7.016eV (T=583.634K) Etot = 57.056eV
Energy per atom: Epot =49.772eV Ekin = 7.288eV (T=606.297K) Etot = 57.061eV
Energy per atom: Epot =49.977eV Ekin = 7.086eV (T=589.449K) Etot = 57.063eV
Energy per atom: Epot =49.424eV Ekin = 7.637eV (T=635.290K) Etot = 57.061eV
Energy per atom: Epot =50.676eV Ekin = 6.386eV (T=531.241K) Etot = 57.062eV
Energy per atom: Epot =49.481eV Ekin = 7.572eV (T=629.922K) Etot = 57.054eV
Energy per atom: Epot =49.784eV Ekin = 7.276eV (T=605.262K) Etot = 57.060eV
Energy per atom: Epot =49.451eV Ekin = 7.608eV (T=632.912K) Etot = 57.059eV
Energy per atom: Epot =50.301eV Ekin = 6.760eV (T=562.382K) Etot = 57.062eV
Energy per atom: Epot =49.461eV Ekin = 7.595eV (T=631.816K) Etot = 57.057eV
Energy per atom: Epot =50.004eV Ekin = 7.057eV (T=587.077K) Etot = 57.062eV
Energy per atom: Epot =49.845eV Ekin = 7.214eV (T=600.140K) Etot = 57.059eV
Energy per atom: Epot =50.708eV Ekin = 6.360eV (T=529.038K) Etot = 57.067eV
Energy per atom: Epot =49.813eV Ekin = 7.250eV (T=603.118K) Etot = 57.063eV
Energy per atom: Epot =49.400eV Ekin = 7.660eV (T=637.198K) Etot = 57.060eV
Energy per atom: Epot =50.045eV Ekin = 7.015eV (T=583.550K) Etot = 57.060eV
Energy per atom: Epot =50.601eV Ekin = 6.458eV (T=537.212K) Etot = 57.059eV
Energy per atom: Epot =50.498eV Ekin = 6.562eV (T=545.865K) Etot = 57.060eV
Energy per atom: Epot =49.525eV Ekin = 7.535eV (T=626.790K) Etot = 57.059eV
Energy per atom: Epot =50.180eV Ekin = 6.882eV (T=572.493K) Etot = 57.062eV
Energy per atom: Epot =50.183eV Ekin = 6.874eV (T=571.822K) Etot = 57.057eV
Energy per atom: Epot =48.859eV Ekin = 8.192eV (T=681.505K) Etot = 57.051eV
Energy per atom: Epot =50.625eV Ekin = 6.433eV (T=535.118K) Etot = 57.058eV
Energy per atom: Epot =50.149eV Ekin = 6.912eV (T=574.988K) Etot = 57.061eV
Energy per atom: Epot =50.120eV Ekin = 6.945eV (T=577.772K) Etot = 57.065eV
Energy per atom: Epot =50.171eV Ekin = 6.891eV (T=573.261K) Etot = 57.062eV
Energy per atom: Epot =50.215eV Ekin = 6.844eV (T=569.334K) Etot = 57.059eV
Energy per atom: Epot =50.149eV Ekin = 6.911eV (T=574.919K) Etot = 57.060eV
Energy per atom: Epot =49.216eV Ekin = 7.839eV (T=652.130K) Etot = 57.055eV
Energy per atom: Epot =49.771eV Ekin = 7.290eV (T=606.407K) Etot = 57.061eV
Energy per atom: Epot =50.014eV Ekin = 7.053eV (T=586.755K) Etot = 57.068eV
Energy per atom: Epot =49.629eV Ekin = 7.431eV (T=618.164K) Etot = 57.060eV
Energy per atom: Epot =49.516eV Ekin = 7.537eV (T=627.004K) Etot = 57.053eV
Energy per atom: Epot =50.009eV Ekin = 7.050eV (T=586.425K) Etot = 57.058eV
Energy per atom: Epot =49.855eV Ekin = 7.205eV (T=599.338K) Etot = 57.060eV
Energy per atom: Epot =50.653eV Ekin = 6.412eV (T=533.391K) Etot = 57.065eV
Energy per atom: Epot =49.911eV Ekin = 7.150eV (T=594.799K) Etot = 57.061eV
Energy per atom: Epot =50.937eV Ekin = 6.127eV (T=509.662K) Etot = 57.064eV
Energy per atom: Epot =49.808eV Ekin = 7.253eV (T=603.313K) Etot = 57.061eV
Energy per atom: Epot =49.781eV Ekin = 7.276eV (T=605.279K) Etot = 57.057eV
Energy per atom: Epot =49.692eV Ekin = 7.365eV (T=612.642K) Etot = 57.056eV
Energy per atom: Epot =49.377eV Ekin = 7.683eV (T=639.127K) Etot = 57.060eV
Energy per atom: Epot =49.178eV Ekin = 7.880eV (T=655.516K) Etot = 57.058eV
Energy per atom: Epot =49.520eV Ekin = 7.537eV (T=626.974K) Etot = 57.057eV
Energy per atom: Epot =50.878eV Ekin = 6.192eV (T=515.060K) Etot = 57.070eV
Energy per atom: Epot =49.944eV Ekin = 7.118eV (T=592.116K) Etot = 57.062eV
Energy per atom: Epot =49.287eV Ekin = 7.768eV (T=646.229K) Etot = 57.055eV
Energy per atom: Epot =49.573eV Ekin = 7.483eV (T=622.516K) Etot = 57.056eV
Energy per atom: Epot =49.868eV Ekin = 7.194eV (T=598.429K) Etot = 57.062eV
Energy per atom: Epot =49.885eV Ekin = 7.182eV (T=597.477K) Etot = 57.067eV
Energy per atom: Epot =49.209eV Ekin = 7.850eV (T=653.012K) Etot = 57.059eV
Energy per atom: Epot =49.621eV Ekin = 7.437eV (T=618.632K) Etot = 57.058eV
Energy per atom: Epot =50.205eV Ekin = 6.855eV (T=570.213K) Etot = 57.059eV
Energy per atom: Epot =50.982eV Ekin = 6.081eV (T=505.897K) Etot = 57.064eV
Energy per atom: Epot =49.870eV Ekin = 7.189eV (T=598.050K) Etot = 57.059eV
Energy per atom: Epot =49.440eV Ekin = 7.618eV (T=633.736K) Etot = 57.059eV
Energy per atom: Epot =49.236eV Ekin = 7.817eV (T=650.284K) Etot = 57.053eV
Energy per atom: Epot =50.634eV Ekin = 6.425eV (T=534.463K) Etot = 57.059eV
Energy per atom: Epot =49.709eV Ekin = 7.349eV (T=611.364K) Etot = 57.058eV
Energy per atom: Epot =50.173eV Ekin = 6.894eV (T=573.494K) Etot = 57.067eV
Energy per atom: Epot =49.720eV Ekin = 7.342eV (T=610.734K) Etot = 57.062eV
Energy per atom: Epot =50.547eV Ekin = 6.516eV (T=542.021K) Etot = 57.063eV
Energy per atom: Epot =49.351eV Ekin = 7.708eV (T=641.169K) Etot = 57.058eV
Energy per atom: Epot =49.201eV Ekin = 7.851eV (T=653.114K) Etot = 57.052eV
Energy per atom: Epot =49.851eV Ekin = 7.209eV (T=599.723K) Etot = 57.060eV
Energy per atom: Epot =50.504eV Ekin = 6.565eV (T=546.116K) Etot = 57.069eV
Energy per atom: Epot =49.844eV Ekin = 7.220eV (T=600.576K) Etot = 57.064eV
Energy per atom: Epot =49.055eV Ekin = 7.999eV (T=665.439K) Etot = 57.055eV
Energy per atom: Epot =49.510eV Ekin = 7.551eV (T=628.144K) Etot = 57.061eV
Energy per atom: Epot =49.652eV Ekin = 7.404eV (T=615.883K) Etot = 57.055eV
Energy per atom: Epot =49.206eV Ekin = 7.854eV (T=653.341K) Etot = 57.060eV
Energy per atom: Epot =49.814eV Ekin = 7.242eV (T=602.450K) Etot = 57.057eV
Energy per atom: Epot =49.756eV Ekin = 7.295eV (T=606.849K) Etot = 57.051eV
Energy per atom: Epot =49.994eV Ekin = 7.061eV (T=587.372K) Etot = 57.055eV
Energy per atom: Epot =49.478eV Ekin = 7.583eV (T=630.836K) Etot = 57.062eV
Energy per atom: Epot =49.786eV Ekin = 7.278eV (T=605.463K) Etot = 57.064eV
Energy per atom: Epot =48.951eV Ekin = 8.109eV (T=674.575K) Etot = 57.060eV
Energy per atom: Epot =50.037eV Ekin = 7.022eV (T=584.158K) Etot = 57.060eV
Energy per atom: Epot =49.895eV Ekin = 7.165eV (T=596.062K) Etot = 57.061eV
Energy per atom: Epot =50.583eV Ekin = 6.486eV (T=539.579K) Etot = 57.069eV
Energy per atom: Epot =50.674eV Ekin = 6.394eV (T=531.916K) Etot = 57.068eV
Energy per atom: Epot =49.454eV Ekin = 7.603eV (T=632.483K) Etot = 57.057eV
Energy per atom: Epot =48.140eV Ekin = 8.911eV (T=741.242K) Etot = 57.050eV
Energy per atom: Epot =50.096eV Ekin = 6.964eV (T=579.285K) Etot = 57.060eV
Energy per atom: Epot =48.910eV Ekin = 8.146eV (T=677.610K) Etot = 57.056eV
Energy per atom: Epot =49.421eV Ekin = 7.634eV (T=635.082K) Etot = 57.055eV
Energy per atom: Epot =49.564eV Ekin = 7.496eV (T=623.572K) Etot = 57.060eV
Energy per atom: Epot =50.824eV Ekin = 6.247eV (T=519.661K) Etot = 57.071eV
Energy per atom: Epot =49.428eV Ekin = 7.630eV (T=634.717K) Etot = 57.058eV
Energy per atom: Epot =50.328eV Ekin = 6.730eV (T=559.810K) Etot = 57.058eV
Energy per atom: Epot =49.957eV Ekin = 7.099eV (T=590.540K) Etot = 57.056eV
Energy per atom: Epot =49.658eV Ekin = 7.398eV (T=615.454K) Etot = 57.056eV
Energy per atom: Epot =50.465eV Ekin = 6.596eV (T=548.731K) Etot = 57.061eV
Energy per atom: Epot =49.329eV Ekin = 7.724eV (T=642.532K) Etot = 57.053eV
Energy per atom: Epot =49.843eV Ekin = 7.218eV (T=600.462K) Etot = 57.061eV
Energy per atom: Epot =50.658eV Ekin = 6.407eV (T=532.944K) Etot = 57.064eV
Energy per atom: Epot =50.076eV Ekin = 6.994eV (T=581.774K) Etot = 57.070eV
Energy per atom: Epot =49.259eV Ekin = 7.803eV (T=649.088K) Etot = 57.062eV
Energy per atom: Epot =49.399eV Ekin = 7.661eV (T=637.282K) Etot = 57.060eV
Energy per atom: Epot =50.323eV Ekin = 6.739eV (T=560.599K) Etot = 57.062eV
Energy per atom: Epot =50.473eV Ekin = 6.588eV (T=548.069K) Etot = 57.062eV
Energy per atom: Epot =49.885eV Ekin = 7.173eV (T=596.704K) Etot = 57.058eV
Energy per atom: Epot =49.312eV Ekin = 7.745eV (T=644.239K) Etot = 57.057eV
Energy per atom: Epot =49.784eV Ekin = 7.274eV (T=605.128K) Etot = 57.058eV
Energy per atom: Epot =50.173eV Ekin = 6.886eV (T=572.852K) Etot = 57.059eV
Energy per atom: Epot =50.677eV Ekin = 6.389eV (T=531.514K) Etot = 57.066eV
Energy per atom: Epot =49.249eV Ekin = 7.811eV (T=649.768K) Etot = 57.060eV
Energy per atom: Epot =50.190eV Ekin = 6.876eV (T=571.962K) Etot = 57.065eV
Energy per atom: Epot =49.740eV Ekin = 7.318eV (T=608.785K) Etot = 57.058eV
Energy per atom: Epot =50.627eV Ekin = 6.438eV (T=535.544K) Etot = 57.065eV
Energy per atom: Epot =50.136eV Ekin = 6.927eV (T=576.251K) Etot = 57.063eV
Energy per atom: Epot =49.561eV Ekin = 7.499eV (T=623.854K) Etot = 57.061eV
Energy per atom: Epot =48.998eV Ekin = 8.059eV (T=670.405K) Etot = 57.057eV
Energy per atom: Epot =49.177eV Ekin = 7.885eV (T=655.919K) Etot = 57.062eV
Energy per atom: Epot =49.509eV Ekin = 7.553eV (T=628.329K) Etot = 57.062eV
Energy per atom: Epot =49.914eV Ekin = 7.149eV (T=594.727K) Etot = 57.063eV
Energy per atom: Epot =49.520eV Ekin = 7.540eV (T=627.218K) Etot = 57.060eV
Energy per atom: Epot =50.293eV Ekin = 6.770eV (T=563.195K) Etot = 57.063eV
Energy per atom: Epot =50.053eV Ekin = 7.008eV (T=583.007K) Etot = 57.062eV
Energy per atom: Epot =50.713eV Ekin = 6.356eV (T=528.712K) Etot = 57.069eV
Energy per atom: Epot =50.527eV Ekin = 6.542eV (T=544.169K) Etot = 57.069eV
Energy per atom: Epot =49.787eV Ekin = 7.280eV (T=605.574K) Etot = 57.066eV
Energy per atom: Epot =49.599eV Ekin = 7.462eV (T=620.739K) Etot = 57.061eV
Energy per atom: Epot =49.093eV Ekin = 7.965eV (T=662.611K) Etot = 57.058eV
Energy per atom: Epot =49.054eV Ekin = 8.001eV (T=665.570K) Etot = 57.055eV
Energy per atom: Epot =48.706eV Ekin = 8.350eV (T=694.585K) Etot = 57.055eV
Energy per atom: Epot =50.222eV Ekin = 6.844eV (T=569.348K) Etot = 57.066eV
Energy per atom: Epot =49.857eV Ekin = 7.202eV (T=599.100K) Etot = 57.059eV
Energy per atom: Epot =49.535eV Ekin = 7.524eV (T=625.860K) Etot = 57.058eV
Energy per atom: Epot =50.666eV Ekin = 6.397eV (T=532.152K) Etot = 57.064eV
Energy per atom: Epot =49.693eV Ekin = 7.365eV (T=612.652K) Etot = 57.058eV
Energy per atom: Epot =49.808eV Ekin = 7.253eV (T=603.333K) Etot = 57.061eV
Energy per atom: Epot =49.887eV Ekin = 7.177eV (T=596.994K) Etot = 57.063eV
Energy per atom: Epot =49.601eV Ekin = 7.459eV (T=620.467K) Etot = 57.059eV
Energy per atom: Epot =49.465eV Ekin = 7.592eV (T=631.550K) Etot = 57.057eV
Energy per atom: Epot =49.785eV Ekin = 7.271eV (T=604.821K) Etot = 57.055eV
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 -0.006953369732271226 eV
Cumul. energy transfered to the thermostat -0.0004586520887301876 eV
Cumul. energy transfered to the thermostat 0.01326481341585017 eV
Cumul. energy transfered to the thermostat 0.012269378226289082 eV
Cumul. energy transfered to the thermostat 0.007480715692891855 eV
Cumul. energy transfered to the thermostat 0.0013292831886180766 eV
Cumul. energy transfered to the thermostat -0.006858290560865262 eV
Cumul. energy transfered to the thermostat -0.0026729602846931166 eV
Cumul. energy transfered to the thermostat 0.0030371879666493936 eV
Cumul. energy transfered to the thermostat 0.006606405842600842 eV
Cumul. energy transfered to the thermostat 0.006720900690999294 eV
Cumul. energy transfered to the thermostat 0.011694484726897273 eV
Cumul. energy transfered to the thermostat 0.00969877347115539 eV
Cumul. energy transfered to the thermostat 0.008857804740873502 eV
Cumul. energy transfered to the thermostat 0.011160011323254218 eV
Cumul. energy transfered to the thermostat 0.004861471140767429 eV
Cumul. energy transfered to the thermostat 0.006340948281974657 eV
Cumul. energy transfered to the thermostat 0.014756948029244911 eV
Cumul. energy transfered to the thermostat 0.020540300883347996 eV
Cumul. energy transfered to the thermostat 0.01391156068183134 eV
Cumul. energy transfered to the thermostat 0.018234518828312812 eV
Cumul. energy transfered to the thermostat 0.013601326213777427 eV
Cumul. energy transfered to the thermostat 0.015568878237510839 eV
Cumul. energy transfered to the thermostat 0.020643376524168904 eV
Cumul. energy transfered to the thermostat 0.019205751433107515 eV
Cumul. energy transfered to the thermostat 0.017046918344791356 eV
Cumul. energy transfered to the thermostat 0.01818373908268977 eV
Cumul. energy transfered to the thermostat 0.027280072740380905 eV
Cumul. energy transfered to the thermostat 0.03416353669685467 eV
Cumul. energy transfered to the thermostat 0.030329807839992902 eV
Cumul. energy transfered to the thermostat 0.025706975050008424 eV
Cumul. energy transfered to the thermostat 0.03019441053655704 eV
Cumul. energy transfered to the thermostat 0.02451192351209769 eV
Cumul. energy transfered to the thermostat 0.030679440757927424 eV
Cumul. energy transfered to the thermostat 0.032997247169756626 eV
Cumul. energy transfered to the thermostat 0.0419198917017585 eV
Cumul. energy transfered to the thermostat 0.04191480403041937 eV
Cumul. energy transfered to the thermostat 0.04225939266600556 eV
Cumul. energy transfered to the thermostat 0.04854583056533267 eV
Cumul. energy transfered to the thermostat 0.05705247925455707 eV
Cumul. energy transfered to the thermostat 0.05849895965039219 eV
Cumul. energy transfered to the thermostat 0.05884992452646964 eV
Cumul. energy transfered to the thermostat 0.06186649427837134 eV
Cumul. energy transfered to the thermostat 0.06690738652824413 eV
Cumul. energy transfered to the thermostat 0.06501661285546369 eV
Cumul. energy transfered to the thermostat 0.06467282264491425 eV
Cumul. energy transfered to the thermostat 0.0679791447337052 eV
Cumul. energy transfered to the thermostat 0.06554450232412358 eV
Cumul. energy transfered to the thermostat 0.06691301042194019 eV
Cumul. energy transfered to the thermostat 0.06720573704715714 eV
Cumul. energy transfered to the thermostat 0.07017741199943932 eV
Cumul. energy transfered to the thermostat 0.07534886560941532 eV
Cumul. energy transfered to the thermostat 0.07402757736135791 eV
Cumul. energy transfered to the thermostat 0.07134200841611495 eV
Cumul. energy transfered to the thermostat 0.06842811349454189 eV
Cumul. energy transfered to the thermostat 0.0653269539791188 eV
Cumul. energy transfered to the thermostat 0.06450943984738054 eV
Cumul. energy transfered to the thermostat 0.06299770573272147 eV
Cumul. energy transfered to the thermostat 0.06550692177913817 eV
Cumul. energy transfered to the thermostat 0.06898384934139452 eV
Cumul. energy transfered to the thermostat 0.06480106856641056 eV
Cumul. energy transfered to the thermostat 0.06368845028832071 eV
Cumul. energy transfered to the thermostat 0.06421787113467294 eV
Cumul. energy transfered to the thermostat 0.06221239188763798 eV
Cumul. energy transfered to the thermostat 0.06376607000637036 eV
Cumul. energy transfered to the thermostat 0.06304865378283551 eV
Cumul. energy transfered to the thermostat 0.06010593060191449 eV
Cumul. energy transfered to the thermostat 0.06475194412937008 eV
Cumul. energy transfered to the thermostat 0.06766704337077409 eV
Cumul. energy transfered to the thermostat 0.06831912185957106 eV
Cumul. energy transfered to the thermostat 0.06746756558968146 eV
Cumul. energy transfered to the thermostat 0.07093125659354195 eV
Cumul. energy transfered to the thermostat 0.07598264042652118 eV
Cumul. energy transfered to the thermostat 0.07719891627946153 eV
Cumul. energy transfered to the thermostat 0.07677266334190014 eV
Cumul. energy transfered to the thermostat 0.08589840470044084 eV
Cumul. energy transfered to the thermostat 0.08819211058729948 eV
Cumul. energy transfered to the thermostat 0.08481924581560657 eV
Cumul. energy transfered to the thermostat 0.07961208393522812 eV
Cumul. energy transfered to the thermostat 0.0795350751055905 eV
Cumul. energy transfered to the thermostat 0.08595645407452311 eV
Cumul. energy transfered to the thermostat 0.08749729839761575 eV
Cumul. energy transfered to the thermostat 0.08698959428916869 eV
Cumul. energy transfered to the thermostat 0.08740165064525104 eV
Cumul. energy transfered to the thermostat 0.09213022821893209 eV
Cumul. energy transfered to the thermostat 0.08975552642542717 eV
Cumul. energy transfered to the thermostat 0.08678872934311439 eV
Cumul. energy transfered to the thermostat 0.08759724845562956 eV
Cumul. energy transfered to the thermostat 0.09141288263677998 eV
Cumul. energy transfered to the thermostat 0.08977559931747489 eV
Cumul. energy transfered to the thermostat 0.08656788380441618 eV
Cumul. energy transfered to the thermostat 0.08353195393294235 eV
Cumul. energy transfered to the thermostat 0.085078730494324 eV
Cumul. energy transfered to the thermostat 0.0871261219967425 eV
Cumul. energy transfered to the thermostat 0.08861463541871291 eV
Cumul. energy transfered to the thermostat 0.08636829956956632 eV
Cumul. energy transfered to the thermostat 0.0813048388513815 eV
Cumul. energy transfered to the thermostat 0.0831891643892075 eV
Cumul. energy transfered to the thermostat 0.08231477062667002 eV
Cumul. energy transfered to the thermostat 0.08317332764828425 eV