Note
Go to the end to download the full example code.
Molecular dynamics#
Note
These examples can be run without asap3 installed. In that case,
ASE’s Python implementation of the EMT calculator can be used instead, but it
is much slower.
Goal#
In this tutorial, we will learn how to perform basic molecular dynamics (MD) simulations using ASE.
The key objectives are:
Understand how to set up a crystal structure (Cu atoms on an FCC lattice).
Initialize velocities from Maxwell–Boltzmann distribution corresponding to a chosen temperature.
Integrate Newton’s equations of motion using Velocity-Verlet algorithm and monitor the temperature using Langevin thermostat.
Monitor and analyze thermodynamic quantities (potential energy, kinetic energy, total energy, temperature).
Save trajectories and visualize atomic motion with ASE’s GUI.
Explore MD in different scenarios: - Constant energy MD (NVE ensemble) - Constant temperature MD (NVT ensemble) - Isolated nanoparticle simulations
By the end of this tutorial, you should be able to set up your own MD simulations, monitor energy conservation, and visualize system evolution.
Basic Molecular Dynamics Simulation#
We start by creating a copper crystal, assigning random velocities corresponding to Maxwell Boltzmann Distribution at 300 K, and running dynamics in the NVE ensemble (constant energy).
import matplotlib.pyplot as plt
import numpy as np
# choose one of the following implementations of EMT:
# included in ase
# from ase.calculators.emt import EMT
# faster performance
from asap3 import EMT
from ase import units
from ase.cluster.cubic import FaceCenteredCubic as ClusterFCC
from ase.io.trajectory import Trajectory
from ase.lattice.cubic import FaceCenteredCubic as LatticeFCC
from ase.md.langevin import Langevin # for later NPT simulations
from ase.md.velocitydistribution import (
Stationary,
ZeroRotation,
thermalize_momenta,
)
from ase.md.verlet import VelocityVerlet
from ase.optimize import QuasiNewton
from ase.visualize.plot import plot_atoms
# Set up initial positions of Cu atoms on Fcc crystal lattice
size = 10
atoms = LatticeFCC(
directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
symbol='Cu',
size=(size, size, size),
pbc=True,
)
Before setting up the MD simulation, we take a look at the initial structure:
fig, ax = plt.subplots(figsize=(5, 5))
plot_atoms(atoms, ax, rotation=('45x,45y,0z'), show_unit_cell=2, radii=0.75)
plt.tight_layout()
plt.show()
Now let’s run the MD simulation and monitor the kinetic and potential energy of the whole system:
# Describe the interatomic interactions with the Effective Medium Theory (EMT)
atoms.calc = EMT()
# Set the initial velocities corresponding to T=300K from Maxwell Boltzmann
# Distribution
thermalize_momenta(atoms, temperature_K=300)
# We use Velocity Verlet algorithm to integrate the Newton's equations.
timestep_fs = 5
dyn = VelocityVerlet(atoms, timestep_fs * units.fs) # 5 fs time step.
def printenergy(a):
"""
Function to print the thermodynamical properties i.e potential energy,
kinetic energy and total energy
"""
epot = a.get_potential_energy()
ekin = a.get_kinetic_energy()
temp = a.get_temperature()
print(
f'Energy per atom: Epot ={epot:6.3f}eV Ekin = {ekin:.3f}eV '
f'(T={temp:.3f}K) Etot = {epot + ekin:.3f}eV'
)
# Now run the dynamics
print('running a NVE simulation of fcc Cu')
printenergy(atoms)
# init lists to for energy vs time data
time_ps, epot, ekin = [], [], []
mdind = 0
steps_per_block = 10
for i in range(20):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the energies of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
epot.append(atoms.get_potential_energy())
ekin.append(atoms.get_kinetic_energy())
etot = np.array(epot) + np.array(ekin)
# Plot energies vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, epot, label='Potential energy')
ax.plot(time_ps, ekin, label='Kinetic energy')
ax.plot(time_ps, etot, label='Total energy')
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Energy (eV)')
ax.legend(loc='best')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
running a NVE simulation of fcc Cu
Energy per atom: Epot =-2.405eV Ekin = 153.353eV (T=296.598K) Etot = 150.948eV
Energy per atom: Epot =116.204eV Ekin = 35.520eV (T=68.700K) Etot = 151.724eV
Energy per atom: Epot =77.014eV Ekin = 74.573eV (T=144.230K) Etot = 151.587eV
Energy per atom: Epot =69.409eV Ekin = 82.026eV (T=158.646K) Etot = 151.435eV
Energy per atom: Epot =68.689eV Ekin = 82.698eV (T=159.945K) Etot = 151.387eV
Energy per atom: Epot =79.256eV Ekin = 72.293eV (T=139.822K) Etot = 151.549eV
Energy per atom: Epot =77.862eV Ekin = 73.690eV (T=142.523K) Etot = 151.552eV
Energy per atom: Epot =71.942eV Ekin = 79.512eV (T=153.783K) Etot = 151.454eV
Energy per atom: Epot =72.550eV Ekin = 78.919eV (T=152.636K) Etot = 151.469eV
Energy per atom: Epot =77.702eV Ekin = 73.835eV (T=142.803K) Etot = 151.537eV
Energy per atom: Epot =75.119eV Ekin = 76.378eV (T=147.721K) Etot = 151.497eV
Energy per atom: Epot =73.476eV Ekin = 78.003eV (T=150.865K) Etot = 151.480eV
Energy per atom: Epot =74.385eV Ekin = 77.103eV (T=149.124K) Etot = 151.488eV
Energy per atom: Epot =75.897eV Ekin = 75.601eV (T=146.219K) Etot = 151.498eV
Energy per atom: Epot =74.410eV Ekin = 77.081eV (T=149.081K) Etot = 151.491eV
Energy per atom: Epot =73.684eV Ekin = 77.810eV (T=150.491K) Etot = 151.493eV
Energy per atom: Epot =74.620eV Ekin = 76.872eV (T=148.678K) Etot = 151.492eV
Energy per atom: Epot =76.301eV Ekin = 75.187eV (T=145.419K) Etot = 151.488eV
Energy per atom: Epot =72.151eV Ekin = 79.333eV (T=153.436K) Etot = 151.483eV
Energy per atom: Epot =74.826eV Ekin = 76.663eV (T=148.273K) Etot = 151.489eV
Energy per atom: Epot =77.005eV Ekin = 74.498eV (T=144.086K) Etot = 151.503eV
Note how the total energy is conserved, but the kinetic energy quickly drops to half the expected value. Why?
What you learned here:
How to set up a basic MD run.
How to monitor the energy over time.
That total energy is approximately conserved in NVE simulations, what is the error in total energy?
Exercise: Tune the time step from 5fs to 10fs and 50fs, what changes do you observe in total energy?
Constant temperature MD#
In many cases, you want to control temperature (NVT ensemble). This
can be done using a thermostat, like – in this tutorial – Langevin
thermostat.
Compared to the previous example, we replace the line
dyn = VelocityVerlet(...) with
where T is the desired temperature in Kelvin. For that we also imported
the Langevin in the beginning.
The Langevin dynamics will then slowly adjust the total energy of the system so the temperature approaches the desired one.
As a slightly less boring example, let us use this to melt a chunk of
copper by starting the simulation without any momentum of the atoms
(no kinetic energy), and with a desired temperature above the melting
point. We will also save information about the atoms in a trajectory
file called moldyn3.traj.
Note
It is recommended to use the asap3 implementation of the EMT
calculator here, because its performance benefits over the ase
implementation.
size = 10
T = 1500 # Kelvin
# Set up a crystal
atoms = LatticeFCC(
directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
symbol='Cu',
size=(size, size, size),
pbc=False,
)
# Describe the interatomic interactions with the Effective Medium Theory
atoms.calc = EMT()
# We want to run MD with constant energy using the Langevin algorithm
# with a time step of 5 fs, the temperature T and the friction
# coefficient to 0.02 atomic units.
timestep_fs = 5
dyn = Langevin(
atoms, timestep=timestep_fs * units.fs, temperature_K=T, friction=0.02
)
# We also want to save the positions of all atoms after every 100th time step.
traj = Trajectory('fccCu_NPT.traj', 'w', atoms)
# Now run the dynamics
print('running a NVT simulation of fcc Cu')
printenergy(atoms)
time_ps, temperature = [], []
mdind = 0
steps_per_block = 10
for i in range(200):
dyn.run(steps_per_block)
mdind += steps_per_block
printenergy(atoms)
# save the temperature of the current MD step
time_ps.append(mdind * timestep_fs / 1000.0)
temperature.append(atoms.get_temperature())
# Plot temperatures vs time
fig, ax = plt.subplots(figsize=(6, 4))
ax.plot(time_ps, temperature)
ax.set_xlabel('Time (ps)')
ax.set_ylabel('Temperature (K)')
ax.grid(True, linewidth=0.5, alpha=0.5)
plt.tight_layout()
plt.show()
/home/ase/.local/lib/python3.14/site-packages/ase/md/langevin.py:102: FutureWarning: The implementation of `fixcm=True` in `Langevin` does not strictly sample the correct NVT distributions. The deviations are typically small for large systems but can be more pronounced for small systems. Use `fixcm=False` together with `ase.constraints.FixCom`. `fixcm` is deprecated since ASE 3.28.0 and will be removed in a future release.
warnings.warn(msg, FutureWarning)
running a NVT simulation of fcc Cu
Energy per atom: Epot =540.816eV Ekin = 0.000eV (T=0.000K) Etot = 540.816eV
Energy per atom: Epot =599.364eV Ekin = 81.345eV (T=157.329K) Etot = 680.709eV
Energy per atom: Epot =670.486eV Ekin = 136.086eV (T=263.201K) Etot = 806.571eV
Energy per atom: Epot =722.151eV Ekin = 202.733eV (T=392.104K) Etot = 924.884eV
Energy per atom: Epot =780.595eV Ekin = 251.406eV (T=486.241K) Etot = 1032.001eV
Energy per atom: Epot =834.572eV Ekin = 298.090eV (T=576.532K) Etot = 1132.662eV
Energy per atom: Epot =883.235eV Ekin = 339.656eV (T=656.924K) Etot = 1222.891eV
Energy per atom: Epot =922.169eV Ekin = 380.316eV (T=735.564K) Etot = 1302.485eV
Energy per atom: Epot =974.329eV Ekin = 405.964eV (T=785.170K) Etot = 1380.294eV
Energy per atom: Epot =1011.011eV Ekin = 437.288eV (T=845.753K) Etot = 1448.299eV
Energy per atom: Epot =1035.889eV Ekin = 479.703eV (T=927.788K) Etot = 1515.592eV
Energy per atom: Epot =1079.404eV Ekin = 492.057eV (T=951.680K) Etot = 1571.460eV
Energy per atom: Epot =1111.947eV Ekin = 509.762eV (T=985.923K) Etot = 1621.709eV
Energy per atom: Epot =1139.948eV Ekin = 528.364eV (T=1021.902K) Etot = 1668.313eV
Energy per atom: Epot =1169.434eV Ekin = 547.530eV (T=1058.971K) Etot = 1716.964eV
Energy per atom: Epot =1199.799eV Ekin = 560.729eV (T=1084.499K) Etot = 1760.528eV
Energy per atom: Epot =1232.213eV Ekin = 571.424eV (T=1105.183K) Etot = 1803.637eV
Energy per atom: Epot =1255.089eV Ekin = 584.569eV (T=1130.608K) Etot = 1839.658eV
Energy per atom: Epot =1286.756eV Ekin = 592.847eV (T=1146.618K) Etot = 1879.603eV
Energy per atom: Epot =1299.571eV Ekin = 606.757eV (T=1173.520K) Etot = 1906.327eV
Energy per atom: Epot =1334.159eV Ekin = 610.301eV (T=1180.374K) Etot = 1944.460eV
Energy per atom: Epot =1349.744eV Ekin = 626.486eV (T=1211.678K) Etot = 1976.230eV
Energy per atom: Epot =1372.724eV Ekin = 634.244eV (T=1226.683K) Etot = 2006.968eV
Energy per atom: Epot =1398.243eV Ekin = 632.838eV (T=1223.963K) Etot = 2031.081eV
Energy per atom: Epot =1399.467eV Ekin = 652.133eV (T=1261.282K) Etot = 2051.600eV
Energy per atom: Epot =1436.347eV Ekin = 638.199eV (T=1234.333K) Etot = 2074.546eV
Energy per atom: Epot =1441.877eV Ekin = 653.494eV (T=1263.914K) Etot = 2095.371eV
Energy per atom: Epot =1446.898eV Ekin = 680.841eV (T=1316.806K) Etot = 2127.739eV
Energy per atom: Epot =1464.726eV Ekin = 689.127eV (T=1332.831K) Etot = 2153.853eV
Energy per atom: Epot =1475.277eV Ekin = 690.784eV (T=1336.037K) Etot = 2166.062eV
Energy per atom: Epot =1508.973eV Ekin = 677.228eV (T=1309.817K) Etot = 2186.200eV
Energy per atom: Epot =1516.779eV Ekin = 687.002eV (T=1328.722K) Etot = 2203.781eV
Energy per atom: Epot =1515.882eV Ekin = 691.679eV (T=1337.768K) Etot = 2207.562eV
Energy per atom: Epot =1536.477eV Ekin = 690.065eV (T=1334.646K) Etot = 2226.542eV
Energy per atom: Epot =1528.294eV Ekin = 712.147eV (T=1377.354K) Etot = 2240.441eV
Energy per atom: Epot =1554.408eV Ekin = 705.892eV (T=1365.256K) Etot = 2260.300eV
Energy per atom: Epot =1566.485eV Ekin = 703.570eV (T=1360.765K) Etot = 2270.054eV
Energy per atom: Epot =1590.480eV Ekin = 697.498eV (T=1349.022K) Etot = 2287.978eV
Energy per atom: Epot =1590.253eV Ekin = 713.021eV (T=1379.045K) Etot = 2303.274eV
Energy per atom: Epot =1609.758eV Ekin = 715.196eV (T=1383.252K) Etot = 2324.955eV
Energy per atom: Epot =1623.141eV Ekin = 710.276eV (T=1373.735K) Etot = 2333.416eV
Energy per atom: Epot =1627.234eV Ekin = 718.845eV (T=1390.309K) Etot = 2346.079eV
Energy per atom: Epot =1630.553eV Ekin = 728.722eV (T=1409.413K) Etot = 2359.276eV
Energy per atom: Epot =1654.342eV Ekin = 719.429eV (T=1391.438K) Etot = 2373.771eV
Energy per atom: Epot =1650.286eV Ekin = 727.365eV (T=1406.788K) Etot = 2377.651eV
Energy per atom: Epot =1669.611eV Ekin = 719.841eV (T=1392.234K) Etot = 2389.452eV
Energy per atom: Epot =1674.378eV Ekin = 728.033eV (T=1408.079K) Etot = 2402.411eV
Energy per atom: Epot =1683.729eV Ekin = 726.877eV (T=1405.843K) Etot = 2410.606eV
Energy per atom: Epot =1687.417eV Ekin = 731.520eV (T=1414.823K) Etot = 2418.937eV
Energy per atom: Epot =1704.335eV Ekin = 724.455eV (T=1401.159K) Etot = 2428.790eV
Energy per atom: Epot =1707.440eV Ekin = 735.633eV (T=1422.778K) Etot = 2443.073eV
Energy per atom: Epot =1711.274eV Ekin = 741.642eV (T=1434.401K) Etot = 2452.916eV
Energy per atom: Epot =1727.882eV Ekin = 725.568eV (T=1403.311K) Etot = 2453.450eV
Energy per atom: Epot =1721.817eV Ekin = 737.912eV (T=1427.186K) Etot = 2459.729eV
Energy per atom: Epot =1731.103eV Ekin = 739.161eV (T=1429.602K) Etot = 2470.264eV
Energy per atom: Epot =1745.035eV Ekin = 738.672eV (T=1428.656K) Etot = 2483.706eV
Energy per atom: Epot =1740.951eV Ekin = 755.662eV (T=1461.517K) Etot = 2496.613eV
Energy per atom: Epot =1755.248eV Ekin = 746.267eV (T=1443.346K) Etot = 2501.516eV
Energy per atom: Epot =1747.387eV Ekin = 773.844eV (T=1496.682K) Etot = 2521.232eV
Energy per atom: Epot =1780.568eV Ekin = 738.552eV (T=1428.424K) Etot = 2519.120eV
Energy per atom: Epot =1775.749eV Ekin = 742.304eV (T=1435.681K) Etot = 2518.054eV
Energy per atom: Epot =1786.534eV Ekin = 733.604eV (T=1418.854K) Etot = 2520.138eV
Energy per atom: Epot =1795.688eV Ekin = 733.624eV (T=1418.892K) Etot = 2529.311eV
Energy per atom: Epot =1812.488eV Ekin = 721.480eV (T=1395.405K) Etot = 2533.968eV
Energy per atom: Epot =1818.402eV Ekin = 730.146eV (T=1412.166K) Etot = 2548.548eV
Energy per atom: Epot =1811.099eV Ekin = 743.124eV (T=1437.267K) Etot = 2554.223eV
Energy per atom: Epot =1824.117eV Ekin = 733.342eV (T=1418.347K) Etot = 2557.459eV
Energy per atom: Epot =1817.796eV Ekin = 739.238eV (T=1429.751K) Etot = 2557.035eV
Energy per atom: Epot =1822.693eV Ekin = 736.599eV (T=1424.647K) Etot = 2559.293eV
Energy per atom: Epot =1823.860eV Ekin = 736.869eV (T=1425.168K) Etot = 2560.728eV
Energy per atom: Epot =1836.389eV Ekin = 735.855eV (T=1423.208K) Etot = 2572.244eV
Energy per atom: Epot =1841.657eV Ekin = 736.053eV (T=1423.590K) Etot = 2577.710eV
Energy per atom: Epot =1836.424eV Ekin = 748.966eV (T=1448.566K) Etot = 2585.390eV
Energy per atom: Epot =1850.280eV Ekin = 747.133eV (T=1445.020K) Etot = 2597.413eV
Energy per atom: Epot =1849.025eV Ekin = 753.621eV (T=1457.568K) Etot = 2602.646eV
Energy per atom: Epot =1848.631eV Ekin = 751.791eV (T=1454.029K) Etot = 2600.421eV
Energy per atom: Epot =1859.477eV Ekin = 746.120eV (T=1443.061K) Etot = 2605.597eV
Energy per atom: Epot =1866.453eV Ekin = 742.383eV (T=1435.834K) Etot = 2608.837eV
Energy per atom: Epot =1869.244eV Ekin = 738.378eV (T=1428.087K) Etot = 2607.622eV
Energy per atom: Epot =1874.485eV Ekin = 741.393eV (T=1433.918K) Etot = 2615.877eV
Energy per atom: Epot =1873.496eV Ekin = 743.096eV (T=1437.212K) Etot = 2616.591eV
Energy per atom: Epot =1879.857eV Ekin = 732.047eV (T=1415.843K) Etot = 2611.904eV
Energy per atom: Epot =1895.129eV Ekin = 715.184eV (T=1383.228K) Etot = 2610.313eV
Energy per atom: Epot =1873.885eV Ekin = 752.474eV (T=1455.349K) Etot = 2626.359eV
Energy per atom: Epot =1893.692eV Ekin = 741.305eV (T=1433.749K) Etot = 2634.998eV
Energy per atom: Epot =1901.416eV Ekin = 744.985eV (T=1440.865K) Etot = 2646.401eV
Energy per atom: Epot =1904.942eV Ekin = 753.385eV (T=1457.112K) Etot = 2658.327eV
Energy per atom: Epot =1915.267eV Ekin = 752.552eV (T=1455.502K) Etot = 2667.819eV
Energy per atom: Epot =1926.640eV Ekin = 744.907eV (T=1440.715K) Etot = 2671.547eV
Energy per atom: Epot =1918.497eV Ekin = 751.989eV (T=1454.412K) Etot = 2670.486eV
Energy per atom: Epot =1922.723eV Ekin = 765.695eV (T=1480.921K) Etot = 2688.419eV
Energy per atom: Epot =1942.246eV Ekin = 753.392eV (T=1457.126K) Etot = 2695.638eV
Energy per atom: Epot =1938.608eV Ekin = 759.007eV (T=1467.986K) Etot = 2697.615eV
Energy per atom: Epot =1936.203eV Ekin = 758.978eV (T=1467.930K) Etot = 2695.182eV
Energy per atom: Epot =1926.658eV Ekin = 766.736eV (T=1482.934K) Etot = 2693.394eV
Energy per atom: Epot =1940.981eV Ekin = 743.799eV (T=1438.571K) Etot = 2684.780eV
Energy per atom: Epot =1944.570eV Ekin = 753.294eV (T=1456.936K) Etot = 2697.865eV
Energy per atom: Epot =1958.802eV Ekin = 746.594eV (T=1443.978K) Etot = 2705.396eV
Energy per atom: Epot =1956.888eV Ekin = 754.262eV (T=1458.809K) Etot = 2711.150eV
Energy per atom: Epot =1953.775eV Ekin = 752.397eV (T=1455.201K) Etot = 2706.172eV
Energy per atom: Epot =1960.494eV Ekin = 740.788eV (T=1432.749K) Etot = 2701.283eV
Energy per atom: Epot =1957.503eV Ekin = 754.114eV (T=1458.522K) Etot = 2711.617eV
Energy per atom: Epot =1973.493eV Ekin = 741.862eV (T=1434.826K) Etot = 2715.355eV
Energy per atom: Epot =1980.152eV Ekin = 740.636eV (T=1432.454K) Etot = 2720.788eV
Energy per atom: Epot =1983.489eV Ekin = 743.886eV (T=1438.740K) Etot = 2727.375eV
Energy per atom: Epot =1964.257eV Ekin = 756.126eV (T=1462.413K) Etot = 2720.383eV
Energy per atom: Epot =1971.786eV Ekin = 756.282eV (T=1462.716K) Etot = 2728.068eV
Energy per atom: Epot =1976.829eV Ekin = 757.434eV (T=1464.944K) Etot = 2734.263eV
Energy per atom: Epot =1965.937eV Ekin = 768.347eV (T=1486.050K) Etot = 2734.285eV
Energy per atom: Epot =1972.216eV Ekin = 758.463eV (T=1466.933K) Etot = 2730.679eV
Energy per atom: Epot =1975.072eV Ekin = 757.597eV (T=1465.259K) Etot = 2732.670eV
Energy per atom: Epot =1979.441eV Ekin = 752.775eV (T=1455.933K) Etot = 2732.216eV
Energy per atom: Epot =1967.858eV Ekin = 772.310eV (T=1493.714K) Etot = 2740.168eV
Energy per atom: Epot =1982.237eV Ekin = 768.034eV (T=1485.445K) Etot = 2750.272eV
Energy per atom: Epot =1970.567eV Ekin = 777.264eV (T=1503.296K) Etot = 2747.830eV
Energy per atom: Epot =1989.827eV Ekin = 758.444eV (T=1466.897K) Etot = 2748.271eV
Energy per atom: Epot =1974.142eV Ekin = 771.384eV (T=1491.923K) Etot = 2745.525eV
Energy per atom: Epot =1982.918eV Ekin = 763.220eV (T=1476.135K) Etot = 2746.138eV
Energy per atom: Epot =1975.611eV Ekin = 763.344eV (T=1476.374K) Etot = 2738.955eV
Energy per atom: Epot =1984.764eV Ekin = 749.501eV (T=1449.601K) Etot = 2734.265eV
Energy per atom: Epot =1975.326eV Ekin = 771.300eV (T=1491.762K) Etot = 2746.626eV
Energy per atom: Epot =1981.465eV Ekin = 764.983eV (T=1479.544K) Etot = 2746.448eV
Energy per atom: Epot =1983.519eV Ekin = 769.219eV (T=1487.737K) Etot = 2752.738eV
Energy per atom: Epot =1972.209eV Ekin = 770.127eV (T=1489.492K) Etot = 2742.336eV
Energy per atom: Epot =1977.896eV Ekin = 753.976eV (T=1458.256K) Etot = 2731.872eV
Energy per atom: Epot =1979.527eV Ekin = 753.982eV (T=1458.266K) Etot = 2733.509eV
Energy per atom: Epot =1968.923eV Ekin = 758.402eV (T=1466.816K) Etot = 2727.325eV
Energy per atom: Epot =1984.583eV Ekin = 749.843eV (T=1450.262K) Etot = 2734.426eV
Energy per atom: Epot =1981.864eV Ekin = 753.639eV (T=1457.603K) Etot = 2735.503eV
Energy per atom: Epot =1976.695eV Ekin = 766.623eV (T=1482.715K) Etot = 2743.318eV
Energy per atom: Epot =1988.801eV Ekin = 756.857eV (T=1463.828K) Etot = 2745.658eV
Energy per atom: Epot =1998.721eV Ekin = 755.946eV (T=1462.065K) Etot = 2754.666eV
Energy per atom: Epot =1979.654eV Ekin = 767.705eV (T=1484.808K) Etot = 2747.359eV
Energy per atom: Epot =1990.890eV Ekin = 753.474eV (T=1457.284K) Etot = 2744.364eV
Energy per atom: Epot =1978.355eV Ekin = 766.769eV (T=1482.997K) Etot = 2745.124eV
Energy per atom: Epot =1984.157eV Ekin = 761.821eV (T=1473.427K) Etot = 2745.978eV
Energy per atom: Epot =1982.260eV Ekin = 772.489eV (T=1494.060K) Etot = 2754.749eV
Energy per atom: Epot =1985.692eV Ekin = 772.930eV (T=1494.913K) Etot = 2758.621eV
Energy per atom: Epot =1982.097eV Ekin = 773.402eV (T=1495.827K) Etot = 2755.499eV
Energy per atom: Epot =1980.467eV Ekin = 773.224eV (T=1495.482K) Etot = 2753.690eV
Energy per atom: Epot =1975.359eV Ekin = 779.064eV (T=1506.777K) Etot = 2754.422eV
Energy per atom: Epot =1985.431eV Ekin = 767.661eV (T=1484.723K) Etot = 2753.092eV
Energy per atom: Epot =1975.071eV Ekin = 770.312eV (T=1489.851K) Etot = 2745.383eV
Energy per atom: Epot =1976.444eV Ekin = 777.527eV (T=1503.805K) Etot = 2753.971eV
Energy per atom: Epot =1981.605eV Ekin = 768.952eV (T=1487.220K) Etot = 2750.557eV
Energy per atom: Epot =1980.676eV Ekin = 773.848eV (T=1496.689K) Etot = 2754.524eV
Energy per atom: Epot =1982.566eV Ekin = 766.160eV (T=1481.820K) Etot = 2748.726eV
Energy per atom: Epot =1988.699eV Ekin = 765.963eV (T=1481.440K) Etot = 2754.663eV
Energy per atom: Epot =1983.792eV Ekin = 785.554eV (T=1519.331K) Etot = 2769.346eV
Energy per atom: Epot =2001.638eV Ekin = 778.485eV (T=1505.658K) Etot = 2780.123eV
Energy per atom: Epot =2007.509eV Ekin = 770.064eV (T=1489.370K) Etot = 2777.572eV
Energy per atom: Epot =2009.212eV Ekin = 765.327eV (T=1480.209K) Etot = 2774.539eV
Energy per atom: Epot =2018.089eV Ekin = 757.103eV (T=1464.303K) Etot = 2775.192eV
Energy per atom: Epot =2018.307eV Ekin = 755.020eV (T=1460.274K) Etot = 2773.327eV
Energy per atom: Epot =2004.564eV Ekin = 786.847eV (T=1521.830K) Etot = 2791.410eV
Energy per atom: Epot =2026.471eV Ekin = 764.320eV (T=1478.262K) Etot = 2790.791eV
Energy per atom: Epot =2020.656eV Ekin = 772.301eV (T=1493.697K) Etot = 2792.957eV
Energy per atom: Epot =2029.816eV Ekin = 771.126eV (T=1491.424K) Etot = 2800.941eV
Energy per atom: Epot =2021.628eV Ekin = 777.656eV (T=1504.055K) Etot = 2799.284eV
Energy per atom: Epot =2022.045eV Ekin = 777.091eV (T=1502.961K) Etot = 2799.136eV
Energy per atom: Epot =2016.072eV Ekin = 789.756eV (T=1527.456K) Etot = 2805.828eV
Energy per atom: Epot =2026.485eV Ekin = 768.979eV (T=1487.272K) Etot = 2795.463eV
Energy per atom: Epot =2031.515eV Ekin = 766.911eV (T=1483.273K) Etot = 2798.426eV
Energy per atom: Epot =2022.572eV Ekin = 776.095eV (T=1501.035K) Etot = 2798.667eV
Energy per atom: Epot =2025.844eV Ekin = 764.552eV (T=1478.709K) Etot = 2790.395eV
Energy per atom: Epot =2020.371eV Ekin = 764.991eV (T=1479.560K) Etot = 2785.363eV
Energy per atom: Epot =2023.373eV Ekin = 766.580eV (T=1482.633K) Etot = 2789.954eV
Energy per atom: Epot =2027.031eV Ekin = 764.010eV (T=1477.662K) Etot = 2791.041eV
Energy per atom: Epot =2028.986eV Ekin = 764.142eV (T=1477.917K) Etot = 2793.128eV
Energy per atom: Epot =2034.082eV Ekin = 759.565eV (T=1469.064K) Etot = 2793.647eV
Energy per atom: Epot =2019.328eV Ekin = 775.277eV (T=1499.453K) Etot = 2794.605eV
Energy per atom: Epot =2022.727eV Ekin = 772.498eV (T=1494.077K) Etot = 2795.224eV
Energy per atom: Epot =2014.615eV Ekin = 787.177eV (T=1522.468K) Etot = 2801.791eV
Energy per atom: Epot =2014.898eV Ekin = 794.154eV (T=1535.962K) Etot = 2809.052eV
Energy per atom: Epot =2007.532eV Ekin = 799.612eV (T=1546.518K) Etot = 2807.144eV
Energy per atom: Epot =2017.692eV Ekin = 786.604eV (T=1521.362K) Etot = 2804.297eV
Energy per atom: Epot =2025.384eV Ekin = 766.283eV (T=1482.058K) Etot = 2791.668eV
Energy per atom: Epot =2027.776eV Ekin = 764.416eV (T=1478.447K) Etot = 2792.192eV
Energy per atom: Epot =2015.130eV Ekin = 779.256eV (T=1507.149K) Etot = 2794.386eV
Energy per atom: Epot =2015.967eV Ekin = 779.790eV (T=1508.182K) Etot = 2795.757eV
Energy per atom: Epot =2009.683eV Ekin = 796.779eV (T=1541.040K) Etot = 2806.461eV
Energy per atom: Epot =2018.515eV Ekin = 783.904eV (T=1516.138K) Etot = 2802.419eV
Energy per atom: Epot =2018.502eV Ekin = 785.124eV (T=1518.498K) Etot = 2803.626eV
Energy per atom: Epot =2024.364eV Ekin = 784.258eV (T=1516.824K) Etot = 2808.622eV
Energy per atom: Epot =2012.202eV Ekin = 792.970eV (T=1533.673K) Etot = 2805.173eV
Energy per atom: Epot =2011.248eV Ekin = 786.647eV (T=1521.443K) Etot = 2797.895eV
Energy per atom: Epot =2002.501eV Ekin = 799.858eV (T=1546.994K) Etot = 2802.358eV
Energy per atom: Epot =2011.084eV Ekin = 797.466eV (T=1542.369K) Etot = 2808.550eV
Energy per atom: Epot =2013.263eV Ekin = 800.834eV (T=1548.883K) Etot = 2814.097eV
Energy per atom: Epot =2017.917eV Ekin = 796.091eV (T=1539.709K) Etot = 2814.008eV
Energy per atom: Epot =2021.341eV Ekin = 794.003eV (T=1535.672K) Etot = 2815.344eV
Energy per atom: Epot =2027.449eV Ekin = 784.971eV (T=1518.203K) Etot = 2812.420eV
Energy per atom: Epot =2022.234eV Ekin = 783.256eV (T=1514.886K) Etot = 2805.490eV
Energy per atom: Epot =2027.599eV Ekin = 781.070eV (T=1510.657K) Etot = 2808.669eV
Energy per atom: Epot =2024.760eV Ekin = 786.258eV (T=1520.691K) Etot = 2811.018eV
Energy per atom: Epot =2024.474eV Ekin = 778.986eV (T=1506.627K) Etot = 2803.460eV
Energy per atom: Epot =2022.515eV Ekin = 781.067eV (T=1510.652K) Etot = 2803.583eV
Energy per atom: Epot =2030.601eV Ekin = 761.731eV (T=1473.254K) Etot = 2792.331eV
Energy per atom: Epot =2017.498eV Ekin = 783.169eV (T=1514.716K) Etot = 2800.666eV
Energy per atom: Epot =2023.427eV Ekin = 771.155eV (T=1491.480K) Etot = 2794.582eV
Energy per atom: Epot =2018.618eV Ekin = 770.756eV (T=1490.709K) Etot = 2789.374eV
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] 15:27:13 43.457006 1.0818
BFGSLineSearch: 1[ 1] 15:27:13 42.347659 0.2273
BFGSLineSearch: 2[ 2] 15:27:13 42.108454 0.1349
BFGSLineSearch: 3[ 3] 15:27:13 41.964817 0.1138
BFGSLineSearch: 4[ 4] 15:27:13 41.924933 0.0683
BFGSLineSearch: 5[ 5] 15:27:13 41.915346 0.0225
BFGSLineSearch: 6[ 6] 15:27:13 41.914920 0.0059
BFGSLineSearch: 7[ 7] 15:27:13 41.914872 0.0023
BFGSLineSearch: 8[ 9] 15:27:13 41.914855 0.0023
BFGSLineSearch: 9[ 10] 15:27:13 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 14.793eV (T=1230.543K) Etot = 56.707eV
Energy per atom: Epot =50.221eV Ekin = 6.523eV (T=542.649K) Etot = 56.744eV
Energy per atom: Epot =50.543eV Ekin = 6.215eV (T=517.020K) Etot = 56.759eV
Energy per atom: Epot =50.514eV Ekin = 6.239eV (T=519.004K) Etot = 56.753eV
Energy per atom: Epot =51.247eV Ekin = 5.512eV (T=458.541K) Etot = 56.759eV
Energy per atom: Epot =50.469eV Ekin = 6.289eV (T=523.180K) Etot = 56.758eV
Energy per atom: Epot =49.524eV Ekin = 7.223eV (T=600.836K) Etot = 56.747eV
Energy per atom: Epot =48.780eV Ekin = 7.960eV (T=662.176K) Etot = 56.740eV
Energy per atom: Epot =48.853eV Ekin = 7.895eV (T=656.738K) Etot = 56.748eV
Energy per atom: Epot =49.849eV Ekin = 6.910eV (T=574.840K) Etot = 56.759eV
Energy per atom: Epot =50.113eV Ekin = 6.642eV (T=552.563K) Etot = 56.755eV
Energy per atom: Epot =50.471eV Ekin = 6.282eV (T=522.542K) Etot = 56.753eV
Energy per atom: Epot =49.440eV Ekin = 7.310eV (T=608.085K) Etot = 56.750eV
Energy per atom: Epot =49.647eV Ekin = 7.106eV (T=591.117K) Etot = 56.753eV
Energy per atom: Epot =49.063eV Ekin = 7.683eV (T=639.082K) Etot = 56.746eV
Energy per atom: Epot =50.174eV Ekin = 6.573eV (T=546.807K) Etot = 56.747eV
Energy per atom: Epot =50.407eV Ekin = 6.348eV (T=528.047K) Etot = 56.755eV
Energy per atom: Epot =50.056eV Ekin = 6.699eV (T=557.269K) Etot = 56.755eV
Energy per atom: Epot =50.028eV Ekin = 6.729eV (T=559.770K) Etot = 56.757eV
Energy per atom: Epot =49.702eV Ekin = 7.053eV (T=586.692K) Etot = 56.755eV
Energy per atom: Epot =50.297eV Ekin = 6.457eV (T=537.101K) Etot = 56.754eV
Energy per atom: Epot =49.884eV Ekin = 6.869eV (T=571.423K) Etot = 56.753eV
Energy per atom: Epot =50.429eV Ekin = 6.324eV (T=526.093K) Etot = 56.754eV
Energy per atom: Epot =50.130eV Ekin = 6.624eV (T=551.050K) Etot = 56.754eV
Energy per atom: Epot =49.417eV Ekin = 7.336eV (T=610.282K) Etot = 56.754eV
Energy per atom: Epot =49.558eV Ekin = 7.199eV (T=598.870K) Etot = 56.758eV
Energy per atom: Epot =50.250eV Ekin = 6.510eV (T=541.548K) Etot = 56.761eV
Energy per atom: Epot =49.420eV Ekin = 7.333eV (T=610.042K) Etot = 56.754eV
Energy per atom: Epot =50.284eV Ekin = 6.472eV (T=538.398K) Etot = 56.756eV
Energy per atom: Epot =50.452eV Ekin = 6.304eV (T=524.430K) Etot = 56.756eV
Energy per atom: Epot =50.748eV Ekin = 6.009eV (T=499.855K) Etot = 56.757eV
Energy per atom: Epot =49.583eV Ekin = 7.166eV (T=596.135K) Etot = 56.750eV
Energy per atom: Epot =49.018eV Ekin = 7.729eV (T=642.909K) Etot = 56.746eV
Energy per atom: Epot =49.665eV Ekin = 7.089eV (T=589.683K) Etot = 56.754eV
Energy per atom: Epot =50.043eV Ekin = 6.711eV (T=558.288K) Etot = 56.754eV
Energy per atom: Epot =49.742eV Ekin = 7.010eV (T=583.148K) Etot = 56.752eV
Energy per atom: Epot =49.881eV Ekin = 6.874eV (T=571.852K) Etot = 56.756eV
Energy per atom: Epot =50.346eV Ekin = 6.409eV (T=533.123K) Etot = 56.755eV
Energy per atom: Epot =49.428eV Ekin = 7.321eV (T=608.990K) Etot = 56.749eV
Energy per atom: Epot =49.768eV Ekin = 6.986eV (T=581.170K) Etot = 56.754eV
Energy per atom: Epot =49.716eV Ekin = 7.041eV (T=585.689K) Etot = 56.756eV
Energy per atom: Epot =49.436eV Ekin = 7.317eV (T=608.714K) Etot = 56.754eV
Energy per atom: Epot =50.338eV Ekin = 6.421eV (T=534.142K) Etot = 56.759eV
Energy per atom: Epot =49.621eV Ekin = 7.133eV (T=593.354K) Etot = 56.754eV
Energy per atom: Epot =49.416eV Ekin = 7.333eV (T=610.016K) Etot = 56.749eV
Energy per atom: Epot =49.843eV Ekin = 6.912eV (T=575.004K) Etot = 56.756eV
Energy per atom: Epot =49.310eV Ekin = 7.441eV (T=618.956K) Etot = 56.751eV
Energy per atom: Epot =50.244eV Ekin = 6.515eV (T=541.989K) Etot = 56.759eV
Energy per atom: Epot =49.682eV Ekin = 7.070eV (T=588.120K) Etot = 56.752eV
Energy per atom: Epot =49.980eV Ekin = 6.768eV (T=562.979K) Etot = 56.748eV
Energy per atom: Epot =50.441eV Ekin = 6.313eV (T=525.128K) Etot = 56.754eV
Energy per atom: Epot =50.077eV Ekin = 6.672eV (T=554.994K) Etot = 56.749eV
Energy per atom: Epot =49.384eV Ekin = 7.362eV (T=612.457K) Etot = 56.747eV
Energy per atom: Epot =49.869eV Ekin = 6.889eV (T=573.106K) Etot = 56.758eV
Energy per atom: Epot =49.760eV Ekin = 6.996eV (T=581.989K) Etot = 56.756eV
Energy per atom: Epot =49.774eV Ekin = 6.982eV (T=580.785K) Etot = 56.756eV
Energy per atom: Epot =49.963eV Ekin = 6.797eV (T=565.416K) Etot = 56.760eV
Energy per atom: Epot =49.252eV Ekin = 7.501eV (T=623.943K) Etot = 56.752eV
Energy per atom: Epot =49.567eV Ekin = 7.182eV (T=597.483K) Etot = 56.750eV
Energy per atom: Epot =48.826eV Ekin = 7.922eV (T=658.980K) Etot = 56.748eV
Energy per atom: Epot =50.028eV Ekin = 6.725eV (T=559.405K) Etot = 56.753eV
Energy per atom: Epot =49.011eV Ekin = 7.736eV (T=643.543K) Etot = 56.747eV
Energy per atom: Epot =49.516eV Ekin = 7.234eV (T=601.800K) Etot = 56.751eV
Energy per atom: Epot =49.444eV Ekin = 7.311eV (T=608.159K) Etot = 56.755eV
Energy per atom: Epot =50.204eV Ekin = 6.551eV (T=544.938K) Etot = 56.754eV
Energy per atom: Epot =50.039eV Ekin = 6.717eV (T=558.788K) Etot = 56.756eV
Energy per atom: Epot =50.535eV Ekin = 6.225eV (T=517.857K) Etot = 56.760eV
Energy per atom: Epot =49.820eV Ekin = 6.929eV (T=576.431K) Etot = 56.750eV
Energy per atom: Epot =49.418eV Ekin = 7.334eV (T=610.116K) Etot = 56.752eV
Energy per atom: Epot =49.790eV Ekin = 6.965eV (T=579.423K) Etot = 56.755eV
Energy per atom: Epot =49.400eV Ekin = 7.352eV (T=611.570K) Etot = 56.751eV
Energy per atom: Epot =49.173eV Ekin = 7.576eV (T=630.259K) Etot = 56.749eV
Energy per atom: Epot =49.785eV Ekin = 6.963eV (T=579.248K) Etot = 56.749eV
Energy per atom: Epot =50.062eV Ekin = 6.689eV (T=556.418K) Etot = 56.751eV
Energy per atom: Epot =49.885eV Ekin = 6.865eV (T=571.059K) Etot = 56.749eV
Energy per atom: Epot =48.702eV Ekin = 8.040eV (T=668.858K) Etot = 56.743eV
Energy per atom: Epot =49.518eV Ekin = 7.230eV (T=601.450K) Etot = 56.748eV
Energy per atom: Epot =48.953eV Ekin = 7.798eV (T=648.692K) Etot = 56.751eV
Energy per atom: Epot =49.991eV Ekin = 6.766eV (T=562.836K) Etot = 56.757eV
Energy per atom: Epot =49.548eV Ekin = 7.202eV (T=599.115K) Etot = 56.750eV
Energy per atom: Epot =49.782eV Ekin = 6.970eV (T=579.838K) Etot = 56.753eV
Energy per atom: Epot =48.981eV Ekin = 7.766eV (T=645.988K) Etot = 56.747eV
Energy per atom: Epot =49.615eV Ekin = 7.132eV (T=593.286K) Etot = 56.747eV
Energy per atom: Epot =49.781eV Ekin = 6.967eV (T=579.568K) Etot = 56.748eV
Energy per atom: Epot =49.632eV Ekin = 7.121eV (T=592.369K) Etot = 56.753eV
Energy per atom: Epot =48.758eV Ekin = 7.992eV (T=664.839K) Etot = 56.750eV
Energy per atom: Epot =49.425eV Ekin = 7.323eV (T=609.140K) Etot = 56.748eV
Energy per atom: Epot =50.249eV Ekin = 6.504eV (T=541.070K) Etot = 56.754eV
Energy per atom: Epot =49.455eV Ekin = 7.296eV (T=606.922K) Etot = 56.751eV
Energy per atom: Epot =50.323eV Ekin = 6.430eV (T=534.922K) Etot = 56.753eV
Energy per atom: Epot =50.494eV Ekin = 6.263eV (T=520.994K) Etot = 56.757eV
Energy per atom: Epot =49.737eV Ekin = 7.016eV (T=583.597K) Etot = 56.753eV
Energy per atom: Epot =49.112eV Ekin = 7.641eV (T=635.662K) Etot = 56.753eV
Energy per atom: Epot =49.056eV Ekin = 7.697eV (T=640.271K) Etot = 56.753eV
Energy per atom: Epot =50.062eV Ekin = 6.694eV (T=556.877K) Etot = 56.756eV
Energy per atom: Epot =50.210eV Ekin = 6.544eV (T=544.411K) Etot = 56.754eV
Energy per atom: Epot =49.255eV Ekin = 7.498eV (T=623.761K) Etot = 56.753eV
Energy per atom: Epot =49.954eV Ekin = 6.801eV (T=565.756K) Etot = 56.755eV
Energy per atom: Epot =49.852eV Ekin = 6.898eV (T=573.808K) Etot = 56.750eV
Energy per atom: Epot =50.255eV Ekin = 6.502eV (T=540.881K) Etot = 56.757eV
Energy per atom: Epot =49.436eV Ekin = 7.317eV (T=608.708K) Etot = 56.753eV
Energy per atom: Epot =49.448eV Ekin = 7.307eV (T=607.808K) Etot = 56.755eV
Energy per atom: Epot =49.952eV Ekin = 6.802eV (T=565.805K) Etot = 56.754eV
Energy per atom: Epot =49.157eV Ekin = 7.592eV (T=631.531K) Etot = 56.749eV
Energy per atom: Epot =49.464eV Ekin = 7.283eV (T=605.870K) Etot = 56.747eV
Energy per atom: Epot =50.081eV Ekin = 6.670eV (T=554.861K) Etot = 56.751eV
Energy per atom: Epot =49.751eV Ekin = 7.002eV (T=582.490K) Etot = 56.753eV
Energy per atom: Epot =49.973eV Ekin = 6.780eV (T=564.039K) Etot = 56.753eV
Energy per atom: Epot =49.474eV Ekin = 7.280eV (T=605.632K) Etot = 56.754eV
Energy per atom: Epot =49.076eV Ekin = 7.677eV (T=638.634K) Etot = 56.753eV
Energy per atom: Epot =49.562eV Ekin = 7.195eV (T=598.544K) Etot = 56.757eV
Energy per atom: Epot =49.697eV Ekin = 7.058eV (T=587.103K) Etot = 56.755eV
Energy per atom: Epot =49.811eV Ekin = 6.942eV (T=577.521K) Etot = 56.754eV
Energy per atom: Epot =49.909eV Ekin = 6.849eV (T=569.756K) Etot = 56.758eV
Energy per atom: Epot =49.773eV Ekin = 6.983eV (T=580.872K) Etot = 56.756eV
Energy per atom: Epot =49.915eV Ekin = 6.839eV (T=568.937K) Etot = 56.755eV
Energy per atom: Epot =49.680eV Ekin = 7.074eV (T=588.459K) Etot = 56.753eV
Energy per atom: Epot =49.019eV Ekin = 7.727eV (T=642.814K) Etot = 56.747eV
Energy per atom: Epot =49.118eV Ekin = 7.634eV (T=635.007K) Etot = 56.752eV
Energy per atom: Epot =49.463eV Ekin = 7.291eV (T=606.504K) Etot = 56.753eV
Energy per atom: Epot =49.247eV Ekin = 7.500eV (T=623.908K) Etot = 56.748eV
Energy per atom: Epot =49.064eV Ekin = 7.687eV (T=639.453K) Etot = 56.751eV
Energy per atom: Epot =50.225eV Ekin = 6.531eV (T=543.292K) Etot = 56.756eV
Energy per atom: Epot =50.412eV Ekin = 6.341eV (T=527.485K) Etot = 56.753eV
Energy per atom: Epot =50.096eV Ekin = 6.659eV (T=553.954K) Etot = 56.755eV
Energy per atom: Epot =48.991eV Ekin = 7.758eV (T=645.356K) Etot = 56.749eV
Energy per atom: Epot =49.082eV Ekin = 7.663eV (T=637.444K) Etot = 56.745eV
Energy per atom: Epot =49.669eV Ekin = 7.080eV (T=588.937K) Etot = 56.748eV
Energy per atom: Epot =49.436eV Ekin = 7.316eV (T=608.604K) Etot = 56.752eV
Energy per atom: Epot =49.900eV Ekin = 6.851eV (T=569.870K) Etot = 56.751eV
Energy per atom: Epot =49.158eV Ekin = 7.588eV (T=631.185K) Etot = 56.746eV
Energy per atom: Epot =49.740eV Ekin = 7.012eV (T=583.264K) Etot = 56.752eV
Energy per atom: Epot =49.114eV Ekin = 7.637eV (T=635.264K) Etot = 56.750eV
Energy per atom: Epot =48.866eV Ekin = 7.883eV (T=655.750K) Etot = 56.749eV
Energy per atom: Epot =49.430eV Ekin = 7.323eV (T=609.138K) Etot = 56.753eV
Energy per atom: Epot =49.724eV Ekin = 7.029eV (T=584.723K) Etot = 56.753eV
Energy per atom: Epot =49.530eV Ekin = 7.221eV (T=600.661K) Etot = 56.750eV
Energy per atom: Epot =49.577eV Ekin = 7.177eV (T=597.039K) Etot = 56.754eV
Energy per atom: Epot =49.819eV Ekin = 6.935eV (T=576.863K) Etot = 56.754eV
Energy per atom: Epot =48.887eV Ekin = 7.862eV (T=654.038K) Etot = 56.749eV
Energy per atom: Epot =48.319eV Ekin = 8.427eV (T=701.025K) Etot = 56.746eV
Energy per atom: Epot =48.898eV Ekin = 7.853eV (T=653.243K) Etot = 56.751eV
Energy per atom: Epot =49.696eV Ekin = 7.056eV (T=586.974K) Etot = 56.753eV
Energy per atom: Epot =49.702eV Ekin = 7.049eV (T=586.341K) Etot = 56.751eV
Energy per atom: Epot =49.409eV Ekin = 7.342eV (T=610.773K) Etot = 56.751eV
Energy per atom: Epot =49.956eV Ekin = 6.800eV (T=565.697K) Etot = 56.756eV
Energy per atom: Epot =49.277eV Ekin = 7.468eV (T=621.259K) Etot = 56.745eV
Energy per atom: Epot =49.139eV Ekin = 7.601eV (T=632.305K) Etot = 56.740eV
Energy per atom: Epot =49.325eV Ekin = 7.422eV (T=617.398K) Etot = 56.746eV
Energy per atom: Epot =49.839eV Ekin = 6.908eV (T=574.685K) Etot = 56.747eV
Energy per atom: Epot =49.453eV Ekin = 7.297eV (T=607.014K) Etot = 56.750eV
Energy per atom: Epot =49.597eV Ekin = 7.156eV (T=595.255K) Etot = 56.752eV
Energy per atom: Epot =48.696eV Ekin = 8.054eV (T=669.955K) Etot = 56.750eV
Energy per atom: Epot =49.232eV Ekin = 7.523eV (T=625.802K) Etot = 56.754eV
Energy per atom: Epot =49.414eV Ekin = 7.337eV (T=610.359K) Etot = 56.752eV
Energy per atom: Epot =49.896eV Ekin = 6.857eV (T=570.436K) Etot = 56.753eV
Energy per atom: Epot =49.540eV Ekin = 7.213eV (T=600.066K) Etot = 56.753eV
Energy per atom: Epot =49.469eV Ekin = 7.281eV (T=605.680K) Etot = 56.750eV
Energy per atom: Epot =48.985eV Ekin = 7.762eV (T=645.677K) Etot = 56.747eV
Energy per atom: Epot =50.376eV Ekin = 6.378eV (T=530.535K) Etot = 56.754eV
Energy per atom: Epot =49.012eV Ekin = 7.733eV (T=643.273K) Etot = 56.745eV
Energy per atom: Epot =49.660eV Ekin = 7.091eV (T=589.847K) Etot = 56.750eV
Energy per atom: Epot =49.303eV Ekin = 7.446eV (T=619.381K) Etot = 56.748eV
Energy per atom: Epot =49.326eV Ekin = 7.430eV (T=618.083K) Etot = 56.756eV
Energy per atom: Epot =48.853eV Ekin = 7.904eV (T=657.469K) Etot = 56.757eV
Energy per atom: Epot =50.053eV Ekin = 6.699eV (T=557.277K) Etot = 56.752eV
Energy per atom: Epot =49.671eV Ekin = 7.077eV (T=588.703K) Etot = 56.747eV
Energy per atom: Epot =50.185eV Ekin = 6.568eV (T=546.384K) Etot = 56.753eV
Energy per atom: Epot =49.689eV Ekin = 7.066eV (T=587.814K) Etot = 56.755eV
Energy per atom: Epot =50.027eV Ekin = 6.732eV (T=559.980K) Etot = 56.759eV
Energy per atom: Epot =49.388eV Ekin = 7.365eV (T=612.635K) Etot = 56.752eV
Energy per atom: Epot =50.111eV Ekin = 6.645eV (T=552.754K) Etot = 56.756eV
Energy per atom: Epot =49.875eV Ekin = 6.877eV (T=572.046K) Etot = 56.751eV
Energy per atom: Epot =48.771eV Ekin = 7.977eV (T=663.549K) Etot = 56.748eV
Energy per atom: Epot =50.097eV Ekin = 6.658eV (T=553.873K) Etot = 56.755eV
Energy per atom: Epot =49.874eV Ekin = 6.880eV (T=572.321K) Etot = 56.753eV
Energy per atom: Epot =49.693eV Ekin = 7.057eV (T=587.069K) Etot = 56.750eV
Energy per atom: Epot =49.921eV Ekin = 6.830eV (T=568.139K) Etot = 56.751eV
Energy per atom: Epot =49.920eV Ekin = 6.839eV (T=568.893K) Etot = 56.759eV
Energy per atom: Epot =50.032eV Ekin = 6.721eV (T=559.066K) Etot = 56.753eV
Energy per atom: Epot =50.376eV Ekin = 6.379eV (T=530.673K) Etot = 56.755eV
Energy per atom: Epot =48.900eV Ekin = 7.850eV (T=653.047K) Etot = 56.750eV
Energy per atom: Epot =49.177eV Ekin = 7.576eV (T=630.188K) Etot = 56.753eV
Energy per atom: Epot =49.036eV Ekin = 7.714eV (T=641.690K) Etot = 56.750eV
Energy per atom: Epot =49.176eV Ekin = 7.574eV (T=630.022K) Etot = 56.749eV
Energy per atom: Epot =50.415eV Ekin = 6.346eV (T=527.938K) Etot = 56.761eV
Energy per atom: Epot =49.185eV Ekin = 7.566eV (T=629.386K) Etot = 56.751eV
Energy per atom: Epot =49.466eV Ekin = 7.282eV (T=605.783K) Etot = 56.748eV
Energy per atom: Epot =49.583eV Ekin = 7.172eV (T=596.578K) Etot = 56.755eV
Energy per atom: Epot =49.625eV Ekin = 7.131eV (T=593.218K) Etot = 56.756eV
Energy per atom: Epot =49.423eV Ekin = 7.324eV (T=609.297K) Etot = 56.748eV
Energy per atom: Epot =49.721eV Ekin = 7.027eV (T=584.573K) Etot = 56.749eV
Energy per atom: Epot =49.673eV Ekin = 7.084eV (T=589.262K) Etot = 56.757eV
Energy per atom: Epot =48.958eV Ekin = 7.792eV (T=648.172K) Etot = 56.750eV
Energy per atom: Epot =48.931eV Ekin = 7.819eV (T=650.411K) Etot = 56.750eV
Energy per atom: Epot =49.979eV Ekin = 6.769eV (T=563.109K) Etot = 56.748eV
Energy per atom: Epot =49.692eV Ekin = 7.058eV (T=587.143K) Etot = 56.750eV
Energy per atom: Epot =49.347eV Ekin = 7.403eV (T=615.855K) Etot = 56.751eV
Energy per atom: Epot =49.588eV Ekin = 7.167eV (T=596.227K) Etot = 56.755eV
Energy per atom: Epot =48.810eV Ekin = 7.937eV (T=660.292K) Etot = 56.748eV
Energy per atom: Epot =49.876eV Ekin = 6.881eV (T=572.401K) Etot = 56.757eV
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 8.635830509572757e-05 eV
Cumul. energy transfered to the thermostat 0.0027294747833648434 eV
Cumul. energy transfered to the thermostat 0.006095630128623896 eV
Cumul. energy transfered to the thermostat 0.0007046729193007162 eV
Cumul. energy transfered to the thermostat -0.004344508120561809 eV
Cumul. energy transfered to the thermostat -0.009740922145729945 eV
Cumul. energy transfered to the thermostat -0.004494582106036558 eV
Cumul. energy transfered to the thermostat -0.0030092782085454958 eV
Cumul. energy transfered to the thermostat -0.019519543260882455 eV
Cumul. energy transfered to the thermostat -0.022733868220525272 eV
Cumul. energy transfered to the thermostat -0.024097190698645004 eV
Cumul. energy transfered to the thermostat -0.024485820158265635 eV
Cumul. energy transfered to the thermostat -0.022375567472586233 eV
Cumul. energy transfered to the thermostat -0.02744536741334704 eV
Cumul. energy transfered to the thermostat -0.021352291397733827 eV
Cumul. energy transfered to the thermostat -0.0309498203133037 eV
Cumul. energy transfered to the thermostat -0.02689701835568772 eV
Cumul. energy transfered to the thermostat -0.03193535010363514 eV
Cumul. energy transfered to the thermostat -0.023361454962302228 eV
Cumul. energy transfered to the thermostat -0.015567385461226508 eV
Cumul. energy transfered to the thermostat -0.021772933175565615 eV
Cumul. energy transfered to the thermostat -0.02223803152497635 eV
Cumul. energy transfered to the thermostat -0.01998926056056633 eV
Cumul. energy transfered to the thermostat -0.02335403599608875 eV
Cumul. energy transfered to the thermostat -0.01845911384337607 eV
Cumul. energy transfered to the thermostat -0.02006603883876655 eV
Cumul. energy transfered to the thermostat -0.021878539335193486 eV
Cumul. energy transfered to the thermostat -0.02185516907043519 eV
Cumul. energy transfered to the thermostat -0.019316600473435204 eV
Cumul. energy transfered to the thermostat -0.01990411117666437 eV
Cumul. energy transfered to the thermostat -0.018092262193117367 eV
Cumul. energy transfered to the thermostat -0.013962325315462676 eV
Cumul. energy transfered to the thermostat -0.013172019253278771 eV
Cumul. energy transfered to the thermostat -0.011292267167688295 eV
Cumul. energy transfered to the thermostat -0.012629016651066468 eV
Cumul. energy transfered to the thermostat -0.017301711209041143 eV
Cumul. energy transfered to the thermostat -0.009355180299263096 eV
Cumul. energy transfered to the thermostat -0.011394485532852596 eV
Cumul. energy transfered to the thermostat -0.004733466411641418 eV
Cumul. energy transfered to the thermostat -0.0015624771780935512 eV
Cumul. energy transfered to the thermostat 3.300952869491778e-05 eV
Cumul. energy transfered to the thermostat 0.0012809721943264562 eV
Cumul. energy transfered to the thermostat -0.0019495663659510906 eV
Cumul. energy transfered to the thermostat -0.005265595711276262 eV
Cumul. energy transfered to the thermostat -0.011587388595003778 eV
Cumul. energy transfered to the thermostat -0.012324175507694666 eV
Cumul. energy transfered to the thermostat -0.013453914115891684 eV
Cumul. energy transfered to the thermostat -0.011469694378418806 eV
Cumul. energy transfered to the thermostat -0.01341933508454319 eV
Cumul. energy transfered to the thermostat -0.010207253043049062 eV
Cumul. energy transfered to the thermostat -0.010252361942998701 eV
Cumul. energy transfered to the thermostat -0.00893955974947871 eV
Cumul. energy transfered to the thermostat -0.008116339985059532 eV
Cumul. energy transfered to the thermostat -0.011670305588805989 eV
Cumul. energy transfered to the thermostat -0.008251716629822763 eV
Cumul. energy transfered to the thermostat -0.011179044745066273 eV
Cumul. energy transfered to the thermostat -0.011337756058512163 eV
Cumul. energy transfered to the thermostat -0.012526617197330177 eV
Cumul. energy transfered to the thermostat -0.01894675474849198 eV
Cumul. energy transfered to the thermostat -0.017369919857570307 eV
Cumul. energy transfered to the thermostat -0.013101445887499423 eV
Cumul. energy transfered to the thermostat -0.014358861744269237 eV
Cumul. energy transfered to the thermostat -0.01205172920498726 eV
Cumul. energy transfered to the thermostat -0.015241871895975773 eV
Cumul. energy transfered to the thermostat -0.009129081938891111 eV
Cumul. energy transfered to the thermostat -0.01264084218843324 eV
Cumul. energy transfered to the thermostat -0.0068967688350426845 eV
Cumul. energy transfered to the thermostat -0.006805226290101097 eV
Cumul. energy transfered to the thermostat -0.01282070576907961 eV
Cumul. energy transfered to the thermostat -0.01312408785455784 eV
Cumul. energy transfered to the thermostat -0.009878276642376988 eV
Cumul. energy transfered to the thermostat -0.011289406529322716 eV
Cumul. energy transfered to the thermostat -0.013479283931996665 eV
Cumul. energy transfered to the thermostat -0.01672873108144667 eV
Cumul. energy transfered to the thermostat -0.020560096150457514 eV
Cumul. energy transfered to the thermostat -0.009445994738584079 eV
Cumul. energy transfered to the thermostat -0.007072698152523756 eV
Cumul. energy transfered to the thermostat -0.005486390865734474 eV
Cumul. energy transfered to the thermostat 0.00022638830170161432 eV
Cumul. energy transfered to the thermostat -0.00015976139780120616 eV
Cumul. energy transfered to the thermostat 0.0007331529531993146 eV
Cumul. energy transfered to the thermostat 0.0025104056109075098 eV
Cumul. energy transfered to the thermostat 0.002853941557639691 eV
Cumul. energy transfered to the thermostat -0.004723086802325777 eV
Cumul. energy transfered to the thermostat -0.0062267115054559655 eV
Cumul. energy transfered to the thermostat -0.005659138020839039 eV
Cumul. energy transfered to the thermostat -0.005896400585954714 eV
Cumul. energy transfered to the thermostat -0.008876316334211766 eV
Cumul. energy transfered to the thermostat -0.010660535028915686 eV
Cumul. energy transfered to the thermostat -0.01217907363064859 eV
Cumul. energy transfered to the thermostat -0.007508594593222534 eV
Cumul. energy transfered to the thermostat -0.0103376055307573 eV
Cumul. energy transfered to the thermostat -0.008900140819248361 eV
Cumul. energy transfered to the thermostat -0.003195198717252141 eV
Cumul. energy transfered to the thermostat -0.01019750859965028 eV
Cumul. energy transfered to the thermostat -0.0076044314573916905 eV
Cumul. energy transfered to the thermostat -0.008344498274379305 eV
Cumul. energy transfered to the thermostat -0.014668637028749269 eV
Cumul. energy transfered to the thermostat -0.013841470372702691 eV
Cumul. energy transfered to the thermostat -0.009865785022967172 eV