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 = 154.760eV (T=299.320K) Etot = 152.356eV
Energy per atom: Epot =117.053eV Ekin = 36.089eV (T=69.799K) Etot = 153.142eV
Energy per atom: Epot =78.000eV Ekin = 75.002eV (T=145.059K) Etot = 153.001eV
Energy per atom: Epot =70.886eV Ekin = 81.968eV (T=158.533K) Etot = 152.854eV
Energy per atom: Epot =68.662eV Ekin = 84.142eV (T=162.738K) Etot = 152.804eV
Energy per atom: Epot =81.251eV Ekin = 71.722eV (T=138.716K) Etot = 152.973eV
Energy per atom: Epot =77.407eV Ekin = 75.541eV (T=146.103K) Etot = 152.948eV
Energy per atom: Epot =72.894eV Ekin = 79.966eV (T=154.661K) Etot = 152.860eV
Energy per atom: Epot =71.917eV Ekin = 80.948eV (T=156.560K) Etot = 152.865eV
Energy per atom: Epot =79.738eV Ekin = 73.206eV (T=141.588K) Etot = 152.945eV
Energy per atom: Epot =73.631eV Ekin = 79.261eV (T=153.298K) Etot = 152.892eV
Energy per atom: Epot =74.653eV Ekin = 78.239eV (T=151.321K) Etot = 152.892eV
Energy per atom: Epot =75.357eV Ekin = 77.546eV (T=149.981K) Etot = 152.903eV
Energy per atom: Epot =76.886eV Ekin = 76.023eV (T=147.036K) Etot = 152.910eV
Energy per atom: Epot =73.651eV Ekin = 79.241eV (T=153.258K) Etot = 152.891eV
Energy per atom: Epot =75.169eV Ekin = 77.745eV (T=150.365K) Etot = 152.914eV
Energy per atom: Epot =75.383eV Ekin = 77.520eV (T=149.930K) Etot = 152.903eV
Energy per atom: Epot =77.850eV Ekin = 75.059eV (T=145.170K) Etot = 152.909eV
Energy per atom: Epot =72.829eV Ekin = 80.068eV (T=154.858K) Etot = 152.897eV
Energy per atom: Epot =74.607eV Ekin = 78.287eV (T=151.414K) Etot = 152.893eV
Energy per atom: Epot =79.181eV Ekin = 73.739eV (T=142.618K) Etot = 152.920eV
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 =601.206eV Ekin = 84.349eV (T=163.139K) Etot = 685.556eV
Energy per atom: Epot =673.372eV Ekin = 144.433eV (T=279.345K) Etot = 817.804eV
Energy per atom: Epot =730.715eV Ekin = 206.664eV (T=399.705K) Etot = 937.379eV
Energy per atom: Epot =785.611eV Ekin = 260.475eV (T=503.782K) Etot = 1046.087eV
Energy per atom: Epot =841.131eV Ekin = 297.895eV (T=576.156K) Etot = 1139.026eV
Energy per atom: Epot =878.551eV Ekin = 346.493eV (T=670.147K) Etot = 1225.044eV
Energy per atom: Epot =923.541eV Ekin = 379.701eV (T=734.374K) Etot = 1303.241eV
Energy per atom: Epot =962.667eV Ekin = 409.695eV (T=792.386K) Etot = 1372.362eV
Energy per atom: Epot =1000.709eV Ekin = 442.289eV (T=855.425K) Etot = 1442.998eV
Energy per atom: Epot =1040.335eV Ekin = 468.823eV (T=906.744K) Etot = 1509.157eV
Energy per atom: Epot =1075.498eV Ekin = 501.605eV (T=970.147K) Etot = 1577.103eV
Energy per atom: Epot =1121.187eV Ekin = 508.109eV (T=982.728K) Etot = 1629.296eV
Energy per atom: Epot =1155.786eV Ekin = 533.039eV (T=1030.943K) Etot = 1688.825eV
Energy per atom: Epot =1179.609eV Ekin = 551.207eV (T=1066.082K) Etot = 1730.816eV
Energy per atom: Epot =1218.929eV Ekin = 558.853eV (T=1080.871K) Etot = 1777.782eV
Energy per atom: Epot =1239.175eV Ekin = 574.899eV (T=1111.904K) Etot = 1814.074eV
Energy per atom: Epot =1269.662eV Ekin = 592.499eV (T=1145.944K) Etot = 1862.161eV
Energy per atom: Epot =1305.422eV Ekin = 592.885eV (T=1146.691K) Etot = 1898.306eV
Energy per atom: Epot =1324.241eV Ekin = 616.651eV (T=1192.657K) Etot = 1940.892eV
Energy per atom: Epot =1356.419eV Ekin = 616.798eV (T=1192.941K) Etot = 1973.217eV
Energy per atom: Epot =1374.693eV Ekin = 623.573eV (T=1206.044K) Etot = 1998.266eV
Energy per atom: Epot =1378.786eV Ekin = 644.647eV (T=1246.803K) Etot = 2023.433eV
Energy per atom: Epot =1405.115eV Ekin = 646.375eV (T=1250.145K) Etot = 2051.489eV
Energy per atom: Epot =1423.288eV Ekin = 652.445eV (T=1261.886K) Etot = 2075.734eV
Energy per atom: Epot =1443.355eV Ekin = 655.225eV (T=1267.262K) Etot = 2098.580eV
Energy per atom: Epot =1463.227eV Ekin = 662.231eV (T=1280.812K) Etot = 2125.457eV
Energy per atom: Epot =1474.030eV Ekin = 664.739eV (T=1285.662K) Etot = 2138.769eV
Energy per atom: Epot =1489.767eV Ekin = 668.922eV (T=1293.754K) Etot = 2158.689eV
Energy per atom: Epot =1494.480eV Ekin = 684.293eV (T=1323.483K) Etot = 2178.774eV
Energy per atom: Epot =1513.750eV Ekin = 686.016eV (T=1326.815K) Etot = 2199.766eV
Energy per atom: Epot =1512.884eV Ekin = 692.148eV (T=1338.674K) Etot = 2205.032eV
Energy per atom: Epot =1528.784eV Ekin = 692.617eV (T=1339.582K) Etot = 2221.401eV
Energy per atom: Epot =1526.718eV Ekin = 709.020eV (T=1371.306K) Etot = 2235.738eV
Energy per atom: Epot =1547.046eV Ekin = 703.576eV (T=1360.778K) Etot = 2250.622eV
Energy per atom: Epot =1557.505eV Ekin = 697.693eV (T=1349.399K) Etot = 2255.197eV
Energy per atom: Epot =1561.224eV Ekin = 709.863eV (T=1372.937K) Etot = 2271.087eV
Energy per atom: Epot =1568.940eV Ekin = 715.749eV (T=1384.321K) Etot = 2284.688eV
Energy per atom: Epot =1589.407eV Ekin = 716.433eV (T=1385.643K) Etot = 2305.839eV
Energy per atom: Epot =1597.678eV Ekin = 722.959eV (T=1398.266K) Etot = 2320.637eV
Energy per atom: Epot =1604.399eV Ekin = 726.484eV (T=1405.084K) Etot = 2330.884eV
Energy per atom: Epot =1623.947eV Ekin = 718.846eV (T=1390.310K) Etot = 2342.793eV
Energy per atom: Epot =1637.106eV Ekin = 712.745eV (T=1378.511K) Etot = 2349.851eV
Energy per atom: Epot =1633.346eV Ekin = 732.888eV (T=1417.468K) Etot = 2366.233eV
Energy per atom: Epot =1647.597eV Ekin = 726.073eV (T=1404.289K) Etot = 2373.670eV
Energy per atom: Epot =1656.672eV Ekin = 726.202eV (T=1404.538K) Etot = 2382.874eV
Energy per atom: Epot =1657.752eV Ekin = 733.867eV (T=1419.362K) Etot = 2391.618eV
Energy per atom: Epot =1675.617eV Ekin = 726.261eV (T=1404.651K) Etot = 2401.878eV
Energy per atom: Epot =1688.535eV Ekin = 729.559eV (T=1411.030K) Etot = 2418.094eV
Energy per atom: Epot =1696.875eV Ekin = 730.265eV (T=1412.396K) Etot = 2427.140eV
Energy per atom: Epot =1696.326eV Ekin = 740.560eV (T=1432.307K) Etot = 2436.886eV
Energy per atom: Epot =1711.332eV Ekin = 735.336eV (T=1422.203K) Etot = 2446.668eV
Energy per atom: Epot =1715.096eV Ekin = 736.921eV (T=1425.269K) Etot = 2452.017eV
Energy per atom: Epot =1730.120eV Ekin = 728.291eV (T=1408.577K) Etot = 2458.410eV
Energy per atom: Epot =1738.390eV Ekin = 727.787eV (T=1407.603K) Etot = 2466.177eV
Energy per atom: Epot =1753.366eV Ekin = 727.928eV (T=1407.877K) Etot = 2481.295eV
Energy per atom: Epot =1756.396eV Ekin = 735.779eV (T=1423.060K) Etot = 2492.175eV
Energy per atom: Epot =1759.422eV Ekin = 734.824eV (T=1421.213K) Etot = 2494.246eV
Energy per atom: Epot =1770.782eV Ekin = 727.799eV (T=1407.626K) Etot = 2498.581eV
Energy per atom: Epot =1777.853eV Ekin = 718.923eV (T=1390.459K) Etot = 2496.776eV
Energy per atom: Epot =1791.175eV Ekin = 715.565eV (T=1383.964K) Etot = 2506.739eV
Energy per atom: Epot =1782.000eV Ekin = 734.958eV (T=1421.473K) Etot = 2516.958eV
Energy per atom: Epot =1795.740eV Ekin = 725.120eV (T=1402.446K) Etot = 2520.860eV
Energy per atom: Epot =1795.931eV Ekin = 728.896eV (T=1409.748K) Etot = 2524.827eV
Energy per atom: Epot =1807.489eV Ekin = 720.984eV (T=1394.446K) Etot = 2528.473eV
Energy per atom: Epot =1805.589eV Ekin = 727.703eV (T=1407.442K) Etot = 2533.292eV
Energy per atom: Epot =1798.718eV Ekin = 737.679eV (T=1426.735K) Etot = 2536.397eV
Energy per atom: Epot =1809.057eV Ekin = 743.582eV (T=1438.151K) Etot = 2552.638eV
Energy per atom: Epot =1821.813eV Ekin = 733.079eV (T=1417.839K) Etot = 2554.892eV
Energy per atom: Epot =1817.328eV Ekin = 745.319eV (T=1441.512K) Etot = 2562.647eV
Energy per atom: Epot =1825.756eV Ekin = 746.672eV (T=1444.128K) Etot = 2572.427eV
Energy per atom: Epot =1830.874eV Ekin = 744.802eV (T=1440.512K) Etot = 2575.676eV
Energy per atom: Epot =1835.183eV Ekin = 746.376eV (T=1443.556K) Etot = 2581.559eV
Energy per atom: Epot =1836.080eV Ekin = 743.719eV (T=1438.418K) Etot = 2579.799eV
Energy per atom: Epot =1858.225eV Ekin = 728.606eV (T=1409.187K) Etot = 2586.831eV
Energy per atom: Epot =1841.529eV Ekin = 755.548eV (T=1461.295K) Etot = 2597.077eV
Energy per atom: Epot =1853.444eV Ekin = 742.769eV (T=1436.580K) Etot = 2596.213eV
Energy per atom: Epot =1850.308eV Ekin = 752.328eV (T=1455.067K) Etot = 2602.635eV
Energy per atom: Epot =1866.995eV Ekin = 740.447eV (T=1432.088K) Etot = 2607.441eV
Energy per atom: Epot =1862.539eV Ekin = 741.193eV (T=1433.531K) Etot = 2603.731eV
Energy per atom: Epot =1860.000eV Ekin = 752.205eV (T=1454.829K) Etot = 2612.205eV
Energy per atom: Epot =1877.898eV Ekin = 731.384eV (T=1414.560K) Etot = 2609.282eV
Energy per atom: Epot =1861.053eV Ekin = 745.965eV (T=1442.761K) Etot = 2607.018eV
Energy per atom: Epot =1883.612eV Ekin = 729.552eV (T=1411.016K) Etot = 2613.164eV
Energy per atom: Epot =1864.551eV Ekin = 751.233eV (T=1452.949K) Etot = 2615.784eV
Energy per atom: Epot =1876.476eV Ekin = 750.500eV (T=1451.533K) Etot = 2626.976eV
Energy per atom: Epot =1883.349eV Ekin = 748.043eV (T=1446.780K) Etot = 2631.392eV
Energy per atom: Epot =1885.600eV Ekin = 746.386eV (T=1443.575K) Etot = 2631.986eV
Energy per atom: Epot =1897.796eV Ekin = 744.451eV (T=1439.833K) Etot = 2642.247eV
Energy per atom: Epot =1905.130eV Ekin = 749.882eV (T=1450.336K) Etot = 2655.012eV
Energy per atom: Epot =1913.993eV Ekin = 757.168eV (T=1464.430K) Etot = 2671.161eV
Energy per atom: Epot =1925.247eV Ekin = 745.926eV (T=1442.686K) Etot = 2671.173eV
Energy per atom: Epot =1914.081eV Ekin = 754.034eV (T=1458.368K) Etot = 2668.115eV
Energy per atom: Epot =1918.579eV Ekin = 744.357eV (T=1439.651K) Etot = 2662.936eV
Energy per atom: Epot =1925.818eV Ekin = 747.993eV (T=1446.683K) Etot = 2673.811eV
Energy per atom: Epot =1937.436eV Ekin = 742.208eV (T=1435.496K) Etot = 2679.645eV
Energy per atom: Epot =1929.481eV Ekin = 765.459eV (T=1480.465K) Etot = 2694.940eV
Energy per atom: Epot =1938.804eV Ekin = 747.522eV (T=1445.772K) Etot = 2686.325eV
Energy per atom: Epot =1915.685eV Ekin = 772.795eV (T=1494.653K) Etot = 2688.480eV
Energy per atom: Epot =1927.166eV Ekin = 762.074eV (T=1473.917K) Etot = 2689.240eV
Energy per atom: Epot =1938.361eV Ekin = 747.296eV (T=1445.336K) Etot = 2685.657eV
Energy per atom: Epot =1922.929eV Ekin = 765.296eV (T=1480.148K) Etot = 2688.225eV
Energy per atom: Epot =1935.493eV Ekin = 759.841eV (T=1469.598K) Etot = 2695.334eV
Energy per atom: Epot =1943.295eV Ekin = 746.784eV (T=1444.346K) Etot = 2690.079eV
Energy per atom: Epot =1941.588eV Ekin = 759.124eV (T=1468.211K) Etot = 2700.712eV
Energy per atom: Epot =1941.202eV Ekin = 770.910eV (T=1491.007K) Etot = 2712.112eV
Energy per atom: Epot =1952.989eV Ekin = 757.186eV (T=1464.463K) Etot = 2710.175eV
Energy per atom: Epot =1944.698eV Ekin = 766.105eV (T=1481.714K) Etot = 2710.802eV
Energy per atom: Epot =1943.046eV Ekin = 762.859eV (T=1475.436K) Etot = 2705.905eV
Energy per atom: Epot =1940.792eV Ekin = 764.229eV (T=1478.086K) Etot = 2705.021eV
Energy per atom: Epot =1958.795eV Ekin = 747.090eV (T=1444.937K) Etot = 2705.885eV
Energy per atom: Epot =1955.043eV Ekin = 755.519eV (T=1461.239K) Etot = 2710.562eV
Energy per atom: Epot =1939.025eV Ekin = 770.073eV (T=1489.388K) Etot = 2709.098eV
Energy per atom: Epot =1949.683eV Ekin = 765.150eV (T=1479.866K) Etot = 2714.833eV
Energy per atom: Epot =1962.128eV Ekin = 765.212eV (T=1479.987K) Etot = 2727.341eV
Energy per atom: Epot =1957.345eV Ekin = 769.773eV (T=1488.807K) Etot = 2727.117eV
Energy per atom: Epot =1968.926eV Ekin = 769.465eV (T=1488.212K) Etot = 2738.391eV
Energy per atom: Epot =1977.822eV Ekin = 754.240eV (T=1458.765K) Etot = 2732.062eV
Energy per atom: Epot =1975.130eV Ekin = 758.051eV (T=1466.136K) Etot = 2733.181eV
Energy per atom: Epot =1969.742eV Ekin = 772.536eV (T=1494.152K) Etot = 2742.278eV
Energy per atom: Epot =1987.558eV Ekin = 752.517eV (T=1455.433K) Etot = 2740.075eV
Energy per atom: Epot =1989.626eV Ekin = 762.404eV (T=1474.556K) Etot = 2752.030eV
Energy per atom: Epot =1986.840eV Ekin = 758.358eV (T=1466.730K) Etot = 2745.198eV
Energy per atom: Epot =1979.360eV Ekin = 763.904eV (T=1477.456K) Etot = 2743.264eV
Energy per atom: Epot =1982.378eV Ekin = 769.246eV (T=1487.790K) Etot = 2751.624eV
Energy per atom: Epot =1989.733eV Ekin = 765.833eV (T=1481.188K) Etot = 2755.566eV
Energy per atom: Epot =1984.831eV Ekin = 764.275eV (T=1478.174K) Etot = 2749.106eV
Energy per atom: Epot =1985.502eV Ekin = 767.336eV (T=1484.095K) Etot = 2752.839eV
Energy per atom: Epot =1995.698eV Ekin = 759.851eV (T=1469.619K) Etot = 2755.550eV
Energy per atom: Epot =1995.360eV Ekin = 763.735eV (T=1477.129K) Etot = 2759.095eV
Energy per atom: Epot =1976.811eV Ekin = 776.539eV (T=1501.894K) Etot = 2753.350eV
Energy per atom: Epot =1990.183eV Ekin = 764.112eV (T=1477.859K) Etot = 2754.295eV
Energy per atom: Epot =2002.589eV Ekin = 758.454eV (T=1466.916K) Etot = 2761.043eV
Energy per atom: Epot =2001.582eV Ekin = 770.686eV (T=1490.575K) Etot = 2772.268eV
Energy per atom: Epot =2007.936eV Ekin = 759.274eV (T=1468.502K) Etot = 2767.210eV
Energy per atom: Epot =2006.066eV Ekin = 761.535eV (T=1472.875K) Etot = 2767.601eV
Energy per atom: Epot =2019.373eV Ekin = 760.238eV (T=1470.366K) Etot = 2779.611eV
Energy per atom: Epot =2008.846eV Ekin = 774.525eV (T=1497.998K) Etot = 2783.370eV
Energy per atom: Epot =2001.470eV Ekin = 768.684eV (T=1486.702K) Etot = 2770.154eV
Energy per atom: Epot =2003.338eV Ekin = 766.454eV (T=1482.388K) Etot = 2769.792eV
Energy per atom: Epot =2002.610eV Ekin = 758.713eV (T=1467.416K) Etot = 2761.323eV
Energy per atom: Epot =2005.038eV Ekin = 756.916eV (T=1463.942K) Etot = 2761.954eV
Energy per atom: Epot =2001.086eV Ekin = 757.938eV (T=1465.918K) Etot = 2759.024eV
Energy per atom: Epot =1995.346eV Ekin = 765.566eV (T=1480.671K) Etot = 2760.912eV
Energy per atom: Epot =2007.694eV Ekin = 751.183eV (T=1452.853K) Etot = 2758.877eV
Energy per atom: Epot =1998.058eV Ekin = 758.928eV (T=1467.834K) Etot = 2756.986eV
Energy per atom: Epot =2003.457eV Ekin = 753.091eV (T=1456.543K) Etot = 2756.548eV
Energy per atom: Epot =1991.969eV Ekin = 769.283eV (T=1487.861K) Etot = 2761.253eV
Energy per atom: Epot =1979.643eV Ekin = 777.515eV (T=1503.782K) Etot = 2757.158eV
Energy per atom: Epot =1998.933eV Ekin = 752.131eV (T=1454.686K) Etot = 2751.064eV
Energy per atom: Epot =2001.759eV Ekin = 751.944eV (T=1454.325K) Etot = 2753.703eV
Energy per atom: Epot =1992.381eV Ekin = 766.615eV (T=1482.700K) Etot = 2758.995eV
Energy per atom: Epot =1998.784eV Ekin = 757.409eV (T=1464.895K) Etot = 2756.193eV
Energy per atom: Epot =1995.240eV Ekin = 763.375eV (T=1476.433K) Etot = 2758.614eV
Energy per atom: Epot =2008.060eV Ekin = 764.102eV (T=1477.841K) Etot = 2772.163eV
Energy per atom: Epot =1997.138eV Ekin = 765.061eV (T=1479.695K) Etot = 2762.200eV
Energy per atom: Epot =2000.920eV Ekin = 763.090eV (T=1475.882K) Etot = 2764.010eV
Energy per atom: Epot =2002.655eV Ekin = 758.184eV (T=1466.393K) Etot = 2760.839eV
Energy per atom: Epot =2000.808eV Ekin = 761.993eV (T=1473.760K) Etot = 2762.801eV
Energy per atom: Epot =1999.016eV Ekin = 767.808eV (T=1485.007K) Etot = 2766.824eV
Energy per atom: Epot =2013.825eV Ekin = 750.019eV (T=1450.602K) Etot = 2763.845eV
Energy per atom: Epot =1999.384eV Ekin = 770.081eV (T=1489.403K) Etot = 2769.465eV
Energy per atom: Epot =2002.281eV Ekin = 766.571eV (T=1482.615K) Etot = 2768.852eV
Energy per atom: Epot =2002.654eV Ekin = 767.126eV (T=1483.688K) Etot = 2769.780eV
Energy per atom: Epot =2008.991eV Ekin = 769.110eV (T=1487.525K) Etot = 2778.101eV
Energy per atom: Epot =2001.851eV Ekin = 765.637eV (T=1480.808K) Etot = 2767.487eV
Energy per atom: Epot =1995.775eV Ekin = 762.422eV (T=1474.591K) Etot = 2758.197eV
Energy per atom: Epot =1993.600eV Ekin = 766.166eV (T=1481.832K) Etot = 2759.767eV
Energy per atom: Epot =1998.728eV Ekin = 762.192eV (T=1474.146K) Etot = 2760.921eV
Energy per atom: Epot =2009.485eV Ekin = 762.660eV (T=1475.051K) Etot = 2772.146eV
Energy per atom: Epot =2003.822eV Ekin = 767.367eV (T=1484.154K) Etot = 2771.189eV
Energy per atom: Epot =2001.246eV Ekin = 773.956eV (T=1496.898K) Etot = 2775.202eV
Energy per atom: Epot =1999.857eV Ekin = 774.111eV (T=1497.198K) Etot = 2773.968eV
Energy per atom: Epot =1987.366eV Ekin = 790.011eV (T=1527.951K) Etot = 2777.377eV
Energy per atom: Epot =1993.155eV Ekin = 771.430eV (T=1492.013K) Etot = 2764.585eV
Energy per atom: Epot =1982.683eV Ekin = 774.607eV (T=1498.157K) Etot = 2757.290eV
Energy per atom: Epot =1988.825eV Ekin = 768.178eV (T=1485.722K) Etot = 2757.002eV
Energy per atom: Epot =1986.744eV Ekin = 773.817eV (T=1496.630K) Etot = 2760.561eV
Energy per atom: Epot =1978.806eV Ekin = 784.329eV (T=1516.960K) Etot = 2763.135eV
Energy per atom: Epot =1993.825eV Ekin = 776.035eV (T=1500.918K) Etot = 2769.860eV
Energy per atom: Epot =1985.870eV Ekin = 782.716eV (T=1513.841K) Etot = 2768.586eV
Energy per atom: Epot =1995.575eV Ekin = 785.973eV (T=1520.139K) Etot = 2781.547eV
Energy per atom: Epot =1998.334eV Ekin = 781.811eV (T=1512.091K) Etot = 2780.145eV
Energy per atom: Epot =2006.545eV Ekin = 775.485eV (T=1499.856K) Etot = 2782.030eV
Energy per atom: Epot =2007.717eV Ekin = 769.872eV (T=1488.999K) Etot = 2777.589eV
Energy per atom: Epot =1997.780eV Ekin = 783.253eV (T=1514.879K) Etot = 2781.033eV
Energy per atom: Epot =2003.644eV Ekin = 773.246eV (T=1495.525K) Etot = 2776.890eV
Energy per atom: Epot =2004.339eV Ekin = 776.931eV (T=1502.653K) Etot = 2781.270eV
Energy per atom: Epot =2007.752eV Ekin = 771.376eV (T=1491.909K) Etot = 2779.129eV
Energy per atom: Epot =2020.970eV Ekin = 758.894eV (T=1467.767K) Etot = 2779.864eV
Energy per atom: Epot =2006.254eV Ekin = 768.726eV (T=1486.784K) Etot = 2774.980eV
Energy per atom: Epot =1997.928eV Ekin = 777.045eV (T=1502.874K) Etot = 2774.974eV
Energy per atom: Epot =2003.911eV Ekin = 771.920eV (T=1492.960K) Etot = 2775.831eV
Energy per atom: Epot =2004.651eV Ekin = 764.176eV (T=1477.983K) Etot = 2768.827eV
Energy per atom: Epot =2001.818eV Ekin = 771.146eV (T=1491.463K) Etot = 2772.964eV
Energy per atom: Epot =1994.193eV Ekin = 774.271eV (T=1497.507K) Etot = 2768.463eV
Energy per atom: Epot =1987.008eV Ekin = 774.693eV (T=1498.324K) Etot = 2761.701eV
Energy per atom: Epot =1992.985eV Ekin = 777.363eV (T=1503.488K) Etot = 2770.348eV
Energy per atom: Epot =1993.733eV Ekin = 771.556eV (T=1492.257K) Etot = 2765.289eV
Energy per atom: Epot =2006.400eV Ekin = 760.527eV (T=1470.925K) Etot = 2766.927eV
Energy per atom: Epot =2005.703eV Ekin = 763.664eV (T=1476.993K) Etot = 2769.367eV
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] 20:14:16 43.457006 1.0818
BFGSLineSearch: 1[ 1] 20:14:16 42.347659 0.2273
BFGSLineSearch: 2[ 2] 20:14:16 42.108454 0.1349
BFGSLineSearch: 3[ 3] 20:14:16 41.964817 0.1138
BFGSLineSearch: 4[ 4] 20:14:16 41.924933 0.0683
BFGSLineSearch: 5[ 5] 20:14:16 41.915346 0.0225
BFGSLineSearch: 6[ 6] 20:14:16 41.914920 0.0059
BFGSLineSearch: 7[ 7] 20:14:16 41.914872 0.0023
BFGSLineSearch: 8[ 9] 20:14:16 41.914855 0.0023
BFGSLineSearch: 9[ 10] 20:14:16 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 14.057eV (T=1169.346K) Etot = 55.972eV
Energy per atom: Epot =50.499eV Ekin = 5.518eV (T=458.989K) Etot = 56.016eV
Energy per atom: Epot =49.842eV Ekin = 6.172eV (T=513.432K) Etot = 56.014eV
Energy per atom: Epot =50.805eV Ekin = 5.215eV (T=433.843K) Etot = 56.020eV
Energy per atom: Epot =49.412eV Ekin = 6.604eV (T=549.365K) Etot = 56.016eV
Energy per atom: Epot =49.530eV Ekin = 6.486eV (T=539.548K) Etot = 56.016eV
Energy per atom: Epot =49.543eV Ekin = 6.473eV (T=538.453K) Etot = 56.016eV
Energy per atom: Epot =48.629eV Ekin = 7.381eV (T=613.969K) Etot = 56.010eV
Energy per atom: Epot =48.228eV Ekin = 7.781eV (T=647.269K) Etot = 56.009eV
Energy per atom: Epot =49.482eV Ekin = 6.532eV (T=543.383K) Etot = 56.014eV
Energy per atom: Epot =50.079eV Ekin = 5.940eV (T=494.165K) Etot = 56.019eV
Energy per atom: Epot =49.773eV Ekin = 6.247eV (T=519.636K) Etot = 56.020eV
Energy per atom: Epot =49.231eV Ekin = 6.788eV (T=564.631K) Etot = 56.019eV
Energy per atom: Epot =48.687eV Ekin = 7.327eV (T=609.523K) Etot = 56.014eV
Energy per atom: Epot =48.316eV Ekin = 7.690eV (T=639.727K) Etot = 56.007eV
Energy per atom: Epot =49.817eV Ekin = 6.202eV (T=515.949K) Etot = 56.019eV
Energy per atom: Epot =49.902eV Ekin = 6.116eV (T=508.754K) Etot = 56.018eV
Energy per atom: Epot =48.629eV Ekin = 7.378eV (T=613.768K) Etot = 56.007eV
Energy per atom: Epot =50.616eV Ekin = 5.406eV (T=449.719K) Etot = 56.022eV
Energy per atom: Epot =49.279eV Ekin = 6.734eV (T=560.190K) Etot = 56.013eV
Energy per atom: Epot =48.211eV Ekin = 7.800eV (T=648.857K) Etot = 56.011eV
Energy per atom: Epot =49.115eV Ekin = 6.902eV (T=574.148K) Etot = 56.017eV
Energy per atom: Epot =49.883eV Ekin = 6.134eV (T=510.251K) Etot = 56.017eV
Energy per atom: Epot =49.920eV Ekin = 6.097eV (T=507.196K) Etot = 56.017eV
Energy per atom: Epot =49.935eV Ekin = 6.083eV (T=506.009K) Etot = 56.018eV
Energy per atom: Epot =49.093eV Ekin = 6.922eV (T=575.784K) Etot = 56.015eV
Energy per atom: Epot =48.903eV Ekin = 7.111eV (T=591.538K) Etot = 56.014eV
Energy per atom: Epot =49.294eV Ekin = 6.721eV (T=559.116K) Etot = 56.016eV
Energy per atom: Epot =48.925eV Ekin = 7.090eV (T=589.753K) Etot = 56.015eV
Energy per atom: Epot =49.377eV Ekin = 6.639eV (T=552.296K) Etot = 56.016eV
Energy per atom: Epot =48.887eV Ekin = 7.131eV (T=593.230K) Etot = 56.018eV
Energy per atom: Epot =49.055eV Ekin = 6.961eV (T=579.046K) Etot = 56.016eV
Energy per atom: Epot =49.292eV Ekin = 6.723eV (T=559.222K) Etot = 56.015eV
Energy per atom: Epot =49.376eV Ekin = 6.643eV (T=552.611K) Etot = 56.019eV
Energy per atom: Epot =49.693eV Ekin = 6.327eV (T=526.282K) Etot = 56.020eV
Energy per atom: Epot =49.622eV Ekin = 6.395eV (T=531.965K) Etot = 56.017eV
Energy per atom: Epot =49.647eV Ekin = 6.373eV (T=530.144K) Etot = 56.019eV
Energy per atom: Epot =49.417eV Ekin = 6.601eV (T=549.099K) Etot = 56.018eV
Energy per atom: Epot =49.193eV Ekin = 6.821eV (T=567.384K) Etot = 56.013eV
Energy per atom: Epot =49.496eV Ekin = 6.523eV (T=542.615K) Etot = 56.019eV
Energy per atom: Epot =49.726eV Ekin = 6.295eV (T=523.695K) Etot = 56.021eV
Energy per atom: Epot =49.484eV Ekin = 6.532eV (T=543.388K) Etot = 56.016eV
Energy per atom: Epot =49.592eV Ekin = 6.429eV (T=534.818K) Etot = 56.021eV
Energy per atom: Epot =49.449eV Ekin = 6.570eV (T=546.503K) Etot = 56.019eV
Energy per atom: Epot =48.854eV Ekin = 7.158eV (T=595.471K) Etot = 56.012eV
Energy per atom: Epot =49.513eV Ekin = 6.503eV (T=540.966K) Etot = 56.016eV
Energy per atom: Epot =48.318eV Ekin = 7.697eV (T=640.280K) Etot = 56.015eV
Energy per atom: Epot =49.026eV Ekin = 6.992eV (T=581.663K) Etot = 56.018eV
Energy per atom: Epot =49.996eV Ekin = 6.025eV (T=501.159K) Etot = 56.020eV
Energy per atom: Epot =49.388eV Ekin = 6.628eV (T=551.347K) Etot = 56.016eV
Energy per atom: Epot =49.019eV Ekin = 6.991eV (T=581.589K) Etot = 56.011eV
Energy per atom: Epot =49.993eV Ekin = 6.024eV (T=501.086K) Etot = 56.017eV
Energy per atom: Epot =48.833eV Ekin = 7.178eV (T=597.143K) Etot = 56.011eV
Energy per atom: Epot =48.426eV Ekin = 7.590eV (T=631.346K) Etot = 56.015eV
Energy per atom: Epot =49.429eV Ekin = 6.593eV (T=548.414K) Etot = 56.021eV
Energy per atom: Epot =49.479eV Ekin = 6.539eV (T=543.968K) Etot = 56.018eV
Energy per atom: Epot =49.922eV Ekin = 6.097eV (T=507.186K) Etot = 56.019eV
Energy per atom: Epot =48.934eV Ekin = 7.082eV (T=589.092K) Etot = 56.015eV
Energy per atom: Epot =48.787eV Ekin = 7.230eV (T=601.437K) Etot = 56.017eV
Energy per atom: Epot =49.386eV Ekin = 6.633eV (T=551.774K) Etot = 56.019eV
Energy per atom: Epot =49.068eV Ekin = 6.947eV (T=577.934K) Etot = 56.016eV
Energy per atom: Epot =49.453eV Ekin = 6.566eV (T=546.187K) Etot = 56.019eV
Energy per atom: Epot =49.706eV Ekin = 6.314eV (T=525.214K) Etot = 56.020eV
Energy per atom: Epot =49.725eV Ekin = 6.291eV (T=523.307K) Etot = 56.015eV
Energy per atom: Epot =48.723eV Ekin = 7.287eV (T=606.173K) Etot = 56.010eV
Energy per atom: Epot =49.297eV Ekin = 6.722eV (T=559.203K) Etot = 56.019eV
Energy per atom: Epot =48.887eV Ekin = 7.128eV (T=592.966K) Etot = 56.015eV
Energy per atom: Epot =49.366eV Ekin = 6.647eV (T=552.930K) Etot = 56.013eV
Energy per atom: Epot =49.308eV Ekin = 6.706eV (T=557.808K) Etot = 56.013eV
Energy per atom: Epot =48.944eV Ekin = 7.070eV (T=588.145K) Etot = 56.014eV
Energy per atom: Epot =49.036eV Ekin = 6.978eV (T=580.513K) Etot = 56.014eV
Energy per atom: Epot =50.136eV Ekin = 5.886eV (T=489.632K) Etot = 56.022eV
Energy per atom: Epot =49.494eV Ekin = 6.522eV (T=542.567K) Etot = 56.016eV
Energy per atom: Epot =48.124eV Ekin = 7.881eV (T=655.628K) Etot = 56.006eV
Energy per atom: Epot =49.119eV Ekin = 6.896eV (T=573.645K) Etot = 56.015eV
Energy per atom: Epot =49.151eV Ekin = 6.857eV (T=570.388K) Etot = 56.008eV
Energy per atom: Epot =48.981eV Ekin = 7.029eV (T=584.743K) Etot = 56.011eV
Energy per atom: Epot =49.290eV Ekin = 6.723eV (T=559.267K) Etot = 56.013eV
Energy per atom: Epot =48.695eV Ekin = 7.313eV (T=608.335K) Etot = 56.008eV
Energy per atom: Epot =48.905eV Ekin = 7.108eV (T=591.318K) Etot = 56.014eV
Energy per atom: Epot =49.771eV Ekin = 6.250eV (T=519.933K) Etot = 56.021eV
Energy per atom: Epot =49.708eV Ekin = 6.308eV (T=524.777K) Etot = 56.016eV
Energy per atom: Epot =49.493eV Ekin = 6.523eV (T=542.640K) Etot = 56.016eV
Energy per atom: Epot =49.185eV Ekin = 6.828eV (T=568.028K) Etot = 56.013eV
Energy per atom: Epot =49.770eV Ekin = 6.245eV (T=519.509K) Etot = 56.015eV
Energy per atom: Epot =49.176eV Ekin = 6.836eV (T=568.622K) Etot = 56.012eV
Energy per atom: Epot =49.256eV Ekin = 6.755eV (T=561.930K) Etot = 56.011eV
Energy per atom: Epot =49.020eV Ekin = 6.993eV (T=581.736K) Etot = 56.014eV
Energy per atom: Epot =49.234eV Ekin = 6.781eV (T=564.087K) Etot = 56.015eV
Energy per atom: Epot =48.980eV Ekin = 7.026eV (T=584.451K) Etot = 56.006eV
Energy per atom: Epot =49.421eV Ekin = 6.597eV (T=548.801K) Etot = 56.018eV
Energy per atom: Epot =49.982eV Ekin = 6.040eV (T=502.455K) Etot = 56.023eV
Energy per atom: Epot =49.168eV Ekin = 6.848eV (T=569.696K) Etot = 56.017eV
Energy per atom: Epot =49.321eV Ekin = 6.698eV (T=557.200K) Etot = 56.019eV
Energy per atom: Epot =48.701eV Ekin = 7.313eV (T=608.322K) Etot = 56.013eV
Energy per atom: Epot =48.492eV Ekin = 7.521eV (T=625.657K) Etot = 56.013eV
Energy per atom: Epot =49.544eV Ekin = 6.474eV (T=538.509K) Etot = 56.017eV
Energy per atom: Epot =48.933eV Ekin = 7.084eV (T=589.280K) Etot = 56.017eV
Energy per atom: Epot =48.815eV Ekin = 7.202eV (T=599.110K) Etot = 56.017eV
Energy per atom: Epot =49.326eV Ekin = 6.694eV (T=556.811K) Etot = 56.019eV
Energy per atom: Epot =49.449eV Ekin = 6.568eV (T=546.335K) Etot = 56.017eV
Energy per atom: Epot =49.603eV Ekin = 6.414eV (T=533.527K) Etot = 56.017eV
Energy per atom: Epot =49.223eV Ekin = 6.792eV (T=564.967K) Etot = 56.014eV
Energy per atom: Epot =49.494eV Ekin = 6.524eV (T=542.706K) Etot = 56.018eV
Energy per atom: Epot =49.005eV Ekin = 7.012eV (T=583.306K) Etot = 56.017eV
Energy per atom: Epot =49.160eV Ekin = 6.853eV (T=570.109K) Etot = 56.014eV
Energy per atom: Epot =49.229eV Ekin = 6.790eV (T=564.805K) Etot = 56.018eV
Energy per atom: Epot =49.542eV Ekin = 6.478eV (T=538.855K) Etot = 56.020eV
Energy per atom: Epot =49.286eV Ekin = 6.728eV (T=559.711K) Etot = 56.015eV
Energy per atom: Epot =49.535eV Ekin = 6.485eV (T=539.450K) Etot = 56.019eV
Energy per atom: Epot =48.912eV Ekin = 7.106eV (T=591.093K) Etot = 56.017eV
Energy per atom: Epot =49.776eV Ekin = 6.246eV (T=519.582K) Etot = 56.022eV
Energy per atom: Epot =48.799eV Ekin = 7.213eV (T=600.044K) Etot = 56.013eV
Energy per atom: Epot =48.668eV Ekin = 7.338eV (T=610.437K) Etot = 56.006eV
Energy per atom: Epot =49.013eV Ekin = 6.994eV (T=581.783K) Etot = 56.007eV
Energy per atom: Epot =49.146eV Ekin = 6.865eV (T=571.067K) Etot = 56.010eV
Energy per atom: Epot =48.572eV Ekin = 7.438eV (T=618.727K) Etot = 56.010eV
Energy per atom: Epot =49.888eV Ekin = 6.132eV (T=510.080K) Etot = 56.020eV
Energy per atom: Epot =49.474eV Ekin = 6.541eV (T=544.129K) Etot = 56.015eV
Energy per atom: Epot =49.457eV Ekin = 6.558eV (T=545.562K) Etot = 56.016eV
Energy per atom: Epot =48.816eV Ekin = 7.197eV (T=598.696K) Etot = 56.013eV
Energy per atom: Epot =48.784eV Ekin = 7.231eV (T=601.527K) Etot = 56.015eV
Energy per atom: Epot =48.686eV Ekin = 7.328eV (T=609.619K) Etot = 56.015eV
Energy per atom: Epot =49.285eV Ekin = 6.730eV (T=559.884K) Etot = 56.016eV
Energy per atom: Epot =49.302eV Ekin = 6.711eV (T=558.281K) Etot = 56.014eV
Energy per atom: Epot =49.029eV Ekin = 6.985eV (T=581.085K) Etot = 56.014eV
Energy per atom: Epot =48.409eV Ekin = 7.599eV (T=632.109K) Etot = 56.008eV
Energy per atom: Epot =49.215eV Ekin = 6.802eV (T=565.806K) Etot = 56.016eV
Energy per atom: Epot =49.343eV Ekin = 6.675eV (T=555.285K) Etot = 56.018eV
Energy per atom: Epot =49.107eV Ekin = 6.909eV (T=574.746K) Etot = 56.016eV
Energy per atom: Epot =49.391eV Ekin = 6.623eV (T=550.932K) Etot = 56.014eV
Energy per atom: Epot =48.885eV Ekin = 7.126eV (T=592.820K) Etot = 56.011eV
Energy per atom: Epot =48.883eV Ekin = 7.127eV (T=592.853K) Etot = 56.009eV
Energy per atom: Epot =49.258eV Ekin = 6.754eV (T=561.879K) Etot = 56.013eV
Energy per atom: Epot =48.887eV Ekin = 7.126eV (T=592.765K) Etot = 56.013eV
Energy per atom: Epot =49.133eV Ekin = 6.886eV (T=572.835K) Etot = 56.019eV
Energy per atom: Epot =49.454eV Ekin = 6.567eV (T=546.248K) Etot = 56.021eV
Energy per atom: Epot =49.270eV Ekin = 6.747eV (T=561.277K) Etot = 56.017eV
Energy per atom: Epot =49.140eV Ekin = 6.873eV (T=571.771K) Etot = 56.014eV
Energy per atom: Epot =48.973eV Ekin = 7.041eV (T=585.742K) Etot = 56.014eV
Energy per atom: Epot =48.626eV Ekin = 7.391eV (T=614.821K) Etot = 56.017eV
Energy per atom: Epot =48.996eV Ekin = 7.021eV (T=584.051K) Etot = 56.017eV
Energy per atom: Epot =49.613eV Ekin = 6.408eV (T=533.082K) Etot = 56.021eV
Energy per atom: Epot =50.052eV Ekin = 5.971eV (T=496.693K) Etot = 56.023eV
Energy per atom: Epot =49.086eV Ekin = 6.930eV (T=576.456K) Etot = 56.016eV
Energy per atom: Epot =48.840eV Ekin = 7.169eV (T=596.344K) Etot = 56.009eV
Energy per atom: Epot =49.041eV Ekin = 6.970eV (T=579.850K) Etot = 56.012eV
Energy per atom: Epot =48.669eV Ekin = 7.346eV (T=611.060K) Etot = 56.015eV
Energy per atom: Epot =49.000eV Ekin = 7.017eV (T=583.695K) Etot = 56.017eV
Energy per atom: Epot =49.042eV Ekin = 6.975eV (T=580.211K) Etot = 56.016eV
Energy per atom: Epot =49.644eV Ekin = 6.374eV (T=530.272K) Etot = 56.018eV
Energy per atom: Epot =49.471eV Ekin = 6.543eV (T=544.300K) Etot = 56.014eV
Energy per atom: Epot =48.747eV Ekin = 7.265eV (T=604.343K) Etot = 56.012eV
Energy per atom: Epot =48.108eV Ekin = 7.903eV (T=657.387K) Etot = 56.011eV
Energy per atom: Epot =49.333eV Ekin = 6.686eV (T=556.202K) Etot = 56.019eV
Energy per atom: Epot =49.570eV Ekin = 6.450eV (T=536.588K) Etot = 56.020eV
Energy per atom: Epot =48.603eV Ekin = 7.408eV (T=616.236K) Etot = 56.010eV
Energy per atom: Epot =48.873eV Ekin = 7.140eV (T=593.937K) Etot = 56.013eV
Energy per atom: Epot =49.701eV Ekin = 6.315eV (T=525.288K) Etot = 56.016eV
Energy per atom: Epot =49.245eV Ekin = 6.772eV (T=563.321K) Etot = 56.017eV
Energy per atom: Epot =49.627eV Ekin = 6.395eV (T=532.005K) Etot = 56.022eV
Energy per atom: Epot =49.508eV Ekin = 6.515eV (T=541.952K) Etot = 56.023eV
Energy per atom: Epot =49.592eV Ekin = 6.426eV (T=534.557K) Etot = 56.018eV
Energy per atom: Epot =49.078eV Ekin = 6.934eV (T=576.838K) Etot = 56.013eV
Energy per atom: Epot =48.911eV Ekin = 7.103eV (T=590.863K) Etot = 56.014eV
Energy per atom: Epot =49.636eV Ekin = 6.385eV (T=531.130K) Etot = 56.021eV
Energy per atom: Epot =49.229eV Ekin = 6.785eV (T=564.448K) Etot = 56.015eV
Energy per atom: Epot =49.342eV Ekin = 6.674eV (T=555.164K) Etot = 56.015eV
Energy per atom: Epot =49.469eV Ekin = 6.548eV (T=544.676K) Etot = 56.017eV
Energy per atom: Epot =49.681eV Ekin = 6.341eV (T=527.495K) Etot = 56.022eV
Energy per atom: Epot =48.711eV Ekin = 7.304eV (T=607.587K) Etot = 56.015eV
Energy per atom: Epot =48.756eV Ekin = 7.259eV (T=603.873K) Etot = 56.016eV
Energy per atom: Epot =49.969eV Ekin = 6.052eV (T=503.454K) Etot = 56.021eV
Energy per atom: Epot =49.985eV Ekin = 6.030eV (T=501.644K) Etot = 56.015eV
Energy per atom: Epot =48.633eV Ekin = 7.376eV (T=613.583K) Etot = 56.009eV
Energy per atom: Epot =48.936eV Ekin = 7.080eV (T=588.953K) Etot = 56.016eV
Energy per atom: Epot =49.716eV Ekin = 6.303eV (T=524.298K) Etot = 56.018eV
Energy per atom: Epot =49.662eV Ekin = 6.357eV (T=528.854K) Etot = 56.020eV
Energy per atom: Epot =49.295eV Ekin = 6.718eV (T=558.819K) Etot = 56.012eV
Energy per atom: Epot =49.704eV Ekin = 6.311eV (T=525.030K) Etot = 56.016eV
Energy per atom: Epot =49.752eV Ekin = 6.270eV (T=521.539K) Etot = 56.021eV
Energy per atom: Epot =48.591eV Ekin = 7.423eV (T=617.489K) Etot = 56.013eV
Energy per atom: Epot =49.765eV Ekin = 6.252eV (T=520.072K) Etot = 56.017eV
Energy per atom: Epot =50.166eV Ekin = 5.854eV (T=486.946K) Etot = 56.019eV
Energy per atom: Epot =49.676eV Ekin = 6.341eV (T=527.524K) Etot = 56.017eV
Energy per atom: Epot =48.974eV Ekin = 7.044eV (T=586.003K) Etot = 56.018eV
Energy per atom: Epot =48.692eV Ekin = 7.321eV (T=609.037K) Etot = 56.013eV
Energy per atom: Epot =49.706eV Ekin = 6.309eV (T=524.802K) Etot = 56.014eV
Energy per atom: Epot =49.925eV Ekin = 6.093eV (T=506.872K) Etot = 56.018eV
Energy per atom: Epot =49.088eV Ekin = 6.928eV (T=576.346K) Etot = 56.016eV
Energy per atom: Epot =48.998eV Ekin = 7.020eV (T=583.991K) Etot = 56.018eV
Energy per atom: Epot =49.063eV Ekin = 6.949eV (T=578.078K) Etot = 56.013eV
Energy per atom: Epot =50.293eV Ekin = 5.729eV (T=476.561K) Etot = 56.022eV
Energy per atom: Epot =50.289eV Ekin = 5.732eV (T=476.825K) Etot = 56.021eV
Energy per atom: Epot =49.377eV Ekin = 6.637eV (T=552.145K) Etot = 56.014eV
Energy per atom: Epot =49.030eV Ekin = 6.984eV (T=580.966K) Etot = 56.014eV
Energy per atom: Epot =49.080eV Ekin = 6.934eV (T=576.830K) Etot = 56.014eV
Energy per atom: Epot =49.290eV Ekin = 6.726eV (T=559.547K) Etot = 56.016eV
Energy per atom: Epot =49.923eV Ekin = 6.099eV (T=507.314K) Etot = 56.021eV
Energy per atom: Epot =48.822eV Ekin = 7.193eV (T=598.326K) Etot = 56.015eV
Energy per atom: Epot =49.556eV Ekin = 6.463eV (T=537.635K) Etot = 56.019eV
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 0.0015937772634454928 eV
Cumul. energy transfered to the thermostat -7.597877740726094e-05 eV
Cumul. energy transfered to the thermostat 0.0021258411287881553 eV
Cumul. energy transfered to the thermostat -0.0014701740839679301 eV
Cumul. energy transfered to the thermostat 0.005120089359893119 eV
Cumul. energy transfered to the thermostat 0.012719627718066584 eV
Cumul. energy transfered to the thermostat 0.005423337906506892 eV
Cumul. energy transfered to the thermostat 0.009218731634806021 eV
Cumul. energy transfered to the thermostat 0.015678350941135972 eV
Cumul. energy transfered to the thermostat 0.012181543564158487 eV
Cumul. energy transfered to the thermostat 0.008067132265888986 eV
Cumul. energy transfered to the thermostat 0.005280489545423246 eV
Cumul. energy transfered to the thermostat 0.005569717362932869 eV
Cumul. energy transfered to the thermostat 0.009554498219930874 eV
Cumul. energy transfered to the thermostat 0.009289119923141242 eV
Cumul. energy transfered to the thermostat 0.010347440463287996 eV
Cumul. energy transfered to the thermostat 0.01616285136401291 eV
Cumul. energy transfered to the thermostat 0.012695396181877051 eV
Cumul. energy transfered to the thermostat 0.015066857777795175 eV
Cumul. energy transfered to the thermostat 0.016426285962171116 eV
Cumul. energy transfered to the thermostat 0.0181447645328131 eV
Cumul. energy transfered to the thermostat 0.019332680785669007 eV
Cumul. energy transfered to the thermostat 0.013195338512142338 eV
Cumul. energy transfered to the thermostat 0.013947550928807294 eV
Cumul. energy transfered to the thermostat 0.012743988688635502 eV
Cumul. energy transfered to the thermostat 0.011701848016849072 eV
Cumul. energy transfered to the thermostat 0.020065783221541 eV
Cumul. energy transfered to the thermostat 0.021015077742125736 eV
Cumul. energy transfered to the thermostat 0.017315827618969677 eV
Cumul. energy transfered to the thermostat 0.02036496512620236 eV
Cumul. energy transfered to the thermostat 0.023211451440440147 eV
Cumul. energy transfered to the thermostat 0.02364989838023376 eV
Cumul. energy transfered to the thermostat 0.027715807358087853 eV
Cumul. energy transfered to the thermostat 0.03093254961268378 eV
Cumul. energy transfered to the thermostat 0.03790210194440568 eV
Cumul. energy transfered to the thermostat 0.03892024213127174 eV
Cumul. energy transfered to the thermostat 0.04403065771158728 eV
Cumul. energy transfered to the thermostat 0.04654774752256014 eV
Cumul. energy transfered to the thermostat 0.04936559451657471 eV
Cumul. energy transfered to the thermostat 0.04722923736015036 eV
Cumul. energy transfered to the thermostat 0.04509095225464535 eV
Cumul. energy transfered to the thermostat 0.04172809200295209 eV
Cumul. energy transfered to the thermostat 0.041726039978806424 eV
Cumul. energy transfered to the thermostat 0.03770572374125492 eV
Cumul. energy transfered to the thermostat 0.03227000217092424 eV
Cumul. energy transfered to the thermostat 0.029457500236236646 eV
Cumul. energy transfered to the thermostat 0.030757946820347076 eV
Cumul. energy transfered to the thermostat 0.031861789114358406 eV
Cumul. energy transfered to the thermostat 0.03597634340195207 eV
Cumul. energy transfered to the thermostat 0.03559569605054893 eV
Cumul. energy transfered to the thermostat 0.035313869179147764 eV
Cumul. energy transfered to the thermostat 0.03682707161710223 eV
Cumul. energy transfered to the thermostat 0.041154887004636743 eV
Cumul. energy transfered to the thermostat 0.037803906274513 eV
Cumul. energy transfered to the thermostat 0.03130947488422885 eV
Cumul. energy transfered to the thermostat 0.02991548600936825 eV
Cumul. energy transfered to the thermostat 0.0263816324327377 eV
Cumul. energy transfered to the thermostat 0.025781553444395814 eV
Cumul. energy transfered to the thermostat 0.02754677091972399 eV
Cumul. energy transfered to the thermostat 0.02693897701373543 eV
Cumul. energy transfered to the thermostat 0.023999819958723346 eV
Cumul. energy transfered to the thermostat 0.023038450314787046 eV
Cumul. energy transfered to the thermostat 0.02559479565664441 eV
Cumul. energy transfered to the thermostat 0.025726513105503484 eV
Cumul. energy transfered to the thermostat 0.02479270851770621 eV
Cumul. energy transfered to the thermostat 0.0223585326582153 eV
Cumul. energy transfered to the thermostat 0.01889240627717806 eV
Cumul. energy transfered to the thermostat 0.022072869398373503 eV
Cumul. energy transfered to the thermostat 0.020433922774742316 eV
Cumul. energy transfered to the thermostat 0.021540057456716034 eV
Cumul. energy transfered to the thermostat 0.022263445616899497 eV
Cumul. energy transfered to the thermostat 0.02136105498332869 eV
Cumul. energy transfered to the thermostat 0.02104605470794713 eV
Cumul. energy transfered to the thermostat 0.022289562236445824 eV
Cumul. energy transfered to the thermostat 0.024088695803712666 eV
Cumul. energy transfered to the thermostat 0.027479536187681033 eV
Cumul. energy transfered to the thermostat 0.029223414922802754 eV
Cumul. energy transfered to the thermostat 0.029430598397403633 eV
Cumul. energy transfered to the thermostat 0.029536537719196773 eV
Cumul. energy transfered to the thermostat 0.028987679237580975 eV
Cumul. energy transfered to the thermostat 0.028613794287901756 eV
Cumul. energy transfered to the thermostat 0.02894661221384413 eV
Cumul. energy transfered to the thermostat 0.032025399093211726 eV
Cumul. energy transfered to the thermostat 0.02946787157981579 eV
Cumul. energy transfered to the thermostat 0.024273727913894955 eV
Cumul. energy transfered to the thermostat 0.024121830548013506 eV
Cumul. energy transfered to the thermostat 0.024038424444177794 eV
Cumul. energy transfered to the thermostat 0.021818517302084027 eV
Cumul. energy transfered to the thermostat 0.019756313211049883 eV
Cumul. energy transfered to the thermostat 0.019337952755872825 eV
Cumul. energy transfered to the thermostat 0.018196520370692082 eV
Cumul. energy transfered to the thermostat 0.01626104371325427 eV
Cumul. energy transfered to the thermostat 0.013156050749457677 eV
Cumul. energy transfered to the thermostat 0.015473117371723142 eV
Cumul. energy transfered to the thermostat 0.01838367012151109 eV
Cumul. energy transfered to the thermostat 0.015040716506974139 eV
Cumul. energy transfered to the thermostat 0.015054525072269823 eV
Cumul. energy transfered to the thermostat 0.011850769920910484 eV
Cumul. energy transfered to the thermostat 0.01110934408901778 eV
Cumul. energy transfered to the thermostat 0.009051111554152846 eV