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)
ax.set_axis_off()
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 = 154.793eV (T=299.383K) Etot = 152.388eV
Energy per atom: Epot =118.213eV Ekin = 34.967eV (T=67.630K) Etot = 153.181eV
Energy per atom: Epot =77.056eV Ekin = 75.977eV (T=146.947K) Etot = 153.033eV
Energy per atom: Epot =70.612eV Ekin = 82.274eV (T=159.126K) Etot = 152.886eV
Energy per atom: Epot =69.188eV Ekin = 83.648eV (T=161.783K) Etot = 152.837eV
Energy per atom: Epot =80.743eV Ekin = 72.260eV (T=139.757K) Etot = 153.003eV
Energy per atom: Epot =77.974eV Ekin = 75.013eV (T=145.083K) Etot = 152.987eV
Energy per atom: Epot =73.422eV Ekin = 79.479eV (T=153.719K) Etot = 152.901eV
Energy per atom: Epot =71.559eV Ekin = 81.342eV (T=157.323K) Etot = 152.901eV
Energy per atom: Epot =80.149eV Ekin = 72.837eV (T=140.873K) Etot = 152.986eV
Energy per atom: Epot =74.750eV Ekin = 78.189eV (T=151.223K) Etot = 152.938eV
Energy per atom: Epot =73.896eV Ekin = 79.029eV (T=152.849K) Etot = 152.925eV
Energy per atom: Epot =75.374eV Ekin = 77.561eV (T=150.009K) Etot = 152.935eV
Energy per atom: Epot =76.843eV Ekin = 76.097eV (T=147.179K) Etot = 152.941eV
Energy per atom: Epot =74.130eV Ekin = 78.800eV (T=152.406K) Etot = 152.930eV
Energy per atom: Epot =74.974eV Ekin = 77.973eV (T=150.806K) Etot = 152.946eV
Energy per atom: Epot =75.127eV Ekin = 77.809eV (T=150.489K) Etot = 152.936eV
Energy per atom: Epot =78.045eV Ekin = 74.902eV (T=144.866K) Etot = 152.947eV
Energy per atom: Epot =72.959eV Ekin = 79.980eV (T=154.689K) Etot = 152.939eV
Energy per atom: Epot =75.977eV Ekin = 76.965eV (T=148.857K) Etot = 152.942eV
Energy per atom: Epot =78.439eV Ekin = 74.516eV (T=144.120K) Etot = 152.954eV
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 =602.476eV Ekin = 82.763eV (T=160.070K) Etot = 685.239eV
Energy per atom: Epot =672.867eV Ekin = 144.786eV (T=280.029K) Etot = 817.653eV
Energy per atom: Epot =731.915eV Ekin = 205.342eV (T=397.149K) Etot = 937.257eV
Energy per atom: Epot =791.765eV Ekin = 254.641eV (T=492.498K) Etot = 1046.406eV
Energy per atom: Epot =836.764eV Ekin = 311.004eV (T=601.510K) Etot = 1147.768eV
Energy per atom: Epot =891.737eV Ekin = 345.789eV (T=668.786K) Etot = 1237.526eV
Energy per atom: Epot =923.556eV Ekin = 394.170eV (T=762.359K) Etot = 1317.726eV
Energy per atom: Epot =982.779eV Ekin = 409.531eV (T=792.068K) Etot = 1392.310eV
Energy per atom: Epot =1013.624eV Ekin = 446.423eV (T=863.420K) Etot = 1460.047eV
Energy per atom: Epot =1055.416eV Ekin = 465.751eV (T=900.804K) Etot = 1521.168eV
Energy per atom: Epot =1093.055eV Ekin = 487.724eV (T=943.300K) Etot = 1580.779eV
Energy per atom: Epot =1117.199eV Ekin = 509.564eV (T=985.541K) Etot = 1626.763eV
Energy per atom: Epot =1138.719eV Ekin = 536.164eV (T=1036.988K) Etot = 1674.883eV
Energy per atom: Epot =1177.852eV Ekin = 545.439eV (T=1054.927K) Etot = 1723.291eV
Energy per atom: Epot =1201.279eV Ekin = 562.787eV (T=1088.478K) Etot = 1764.066eV
Energy per atom: Epot =1242.550eV Ekin = 568.625eV (T=1099.771K) Etot = 1811.176eV
Energy per atom: Epot =1262.218eV Ekin = 588.725eV (T=1138.646K) Etot = 1850.944eV
Energy per atom: Epot =1277.223eV Ekin = 601.324eV (T=1163.012K) Etot = 1878.547eV
Energy per atom: Epot =1293.610eV Ekin = 617.031eV (T=1193.391K) Etot = 1910.640eV
Energy per atom: Epot =1336.127eV Ekin = 614.299eV (T=1188.108K) Etot = 1950.426eV
Energy per atom: Epot =1363.907eV Ekin = 619.929eV (T=1198.998K) Etot = 1983.836eV
Energy per atom: Epot =1364.723eV Ekin = 649.759eV (T=1256.690K) Etot = 2014.482eV
Energy per atom: Epot =1392.233eV Ekin = 648.714eV (T=1254.670K) Etot = 2040.948eV
Energy per atom: Epot =1411.456eV Ekin = 652.529eV (T=1262.048K) Etot = 2063.985eV
Energy per atom: Epot =1418.515eV Ekin = 665.599eV (T=1287.326K) Etot = 2084.114eV
Energy per atom: Epot =1444.374eV Ekin = 665.267eV (T=1286.684K) Etot = 2109.641eV
Energy per atom: Epot =1463.847eV Ekin = 668.334eV (T=1292.615K) Etot = 2132.181eV
Energy per atom: Epot =1482.471eV Ekin = 672.841eV (T=1301.332K) Etot = 2155.312eV
Energy per atom: Epot =1488.978eV Ekin = 684.418eV (T=1323.723K) Etot = 2173.396eV
Energy per atom: Epot =1500.025eV Ekin = 679.921eV (T=1315.026K) Etot = 2179.946eV
Energy per atom: Epot =1515.876eV Ekin = 688.571eV (T=1331.756K) Etot = 2204.447eV
Energy per atom: Epot =1519.427eV Ekin = 699.352eV (T=1352.607K) Etot = 2218.779eV
Energy per atom: Epot =1547.965eV Ekin = 680.406eV (T=1315.964K) Etot = 2228.370eV
Energy per atom: Epot =1555.966eV Ekin = 689.572eV (T=1333.692K) Etot = 2245.537eV
Energy per atom: Epot =1565.353eV Ekin = 678.933eV (T=1313.116K) Etot = 2244.286eV
Energy per atom: Epot =1564.068eV Ekin = 696.167eV (T=1346.447K) Etot = 2260.235eV
Energy per atom: Epot =1571.130eV Ekin = 697.787eV (T=1349.582K) Etot = 2268.918eV
Energy per atom: Epot =1590.007eV Ekin = 685.285eV (T=1325.400K) Etot = 2275.292eV
Energy per atom: Epot =1598.183eV Ekin = 694.300eV (T=1342.837K) Etot = 2292.483eV
Energy per atom: Epot =1593.118eV Ekin = 708.998eV (T=1371.264K) Etot = 2302.116eV
Energy per atom: Epot =1619.628eV Ekin = 701.499eV (T=1356.759K) Etot = 2321.126eV
Energy per atom: Epot =1623.369eV Ekin = 717.218eV (T=1387.162K) Etot = 2340.587eV
Energy per atom: Epot =1634.876eV Ekin = 719.396eV (T=1391.374K) Etot = 2354.272eV
Energy per atom: Epot =1648.705eV Ekin = 722.704eV (T=1397.772K) Etot = 2371.409eV
Energy per atom: Epot =1659.029eV Ekin = 721.844eV (T=1396.109K) Etot = 2380.873eV
Energy per atom: Epot =1670.716eV Ekin = 724.441eV (T=1401.133K) Etot = 2395.157eV
Energy per atom: Epot =1681.194eV Ekin = 709.482eV (T=1372.199K) Etot = 2390.676eV
Energy per atom: Epot =1687.448eV Ekin = 705.024eV (T=1363.577K) Etot = 2392.471eV
Energy per atom: Epot =1691.117eV Ekin = 712.250eV (T=1377.553K) Etot = 2403.367eV
Energy per atom: Epot =1703.932eV Ekin = 711.537eV (T=1376.174K) Etot = 2415.469eV
Energy per atom: Epot =1716.406eV Ekin = 710.999eV (T=1375.135K) Etot = 2427.406eV
Energy per atom: Epot =1719.388eV Ekin = 713.718eV (T=1380.392K) Etot = 2433.106eV
Energy per atom: Epot =1714.606eV Ekin = 723.372eV (T=1399.064K) Etot = 2437.978eV
Energy per atom: Epot =1730.585eV Ekin = 724.313eV (T=1400.883K) Etot = 2454.897eV
Energy per atom: Epot =1727.395eV Ekin = 737.074eV (T=1425.565K) Etot = 2464.469eV
Energy per atom: Epot =1751.058eV Ekin = 723.130eV (T=1398.596K) Etot = 2474.187eV
Energy per atom: Epot =1749.667eV Ekin = 723.477eV (T=1399.267K) Etot = 2473.143eV
Energy per atom: Epot =1753.345eV Ekin = 722.849eV (T=1398.053K) Etot = 2476.194eV
Energy per atom: Epot =1745.941eV Ekin = 727.838eV (T=1407.702K) Etot = 2473.779eV
Energy per atom: Epot =1768.713eV Ekin = 719.097eV (T=1390.796K) Etot = 2487.810eV
Energy per atom: Epot =1780.822eV Ekin = 726.417eV (T=1404.953K) Etot = 2507.238eV
Energy per atom: Epot =1780.769eV Ekin = 734.256eV (T=1420.116K) Etot = 2515.026eV
Energy per atom: Epot =1786.587eV Ekin = 732.941eV (T=1417.572K) Etot = 2519.528eV
Energy per atom: Epot =1783.279eV Ekin = 743.465eV (T=1437.927K) Etot = 2526.745eV
Energy per atom: Epot =1809.308eV Ekin = 728.995eV (T=1409.940K) Etot = 2538.303eV
Energy per atom: Epot =1812.517eV Ekin = 738.638eV (T=1428.589K) Etot = 2551.155eV
Energy per atom: Epot =1818.503eV Ekin = 734.634eV (T=1420.846K) Etot = 2553.137eV
Energy per atom: Epot =1824.011eV Ekin = 734.472eV (T=1420.533K) Etot = 2558.483eV
Energy per atom: Epot =1832.605eV Ekin = 739.650eV (T=1430.548K) Etot = 2572.255eV
Energy per atom: Epot =1839.714eV Ekin = 731.673eV (T=1415.119K) Etot = 2571.387eV
Energy per atom: Epot =1847.070eV Ekin = 728.542eV (T=1409.064K) Etot = 2575.612eV
Energy per atom: Epot =1838.798eV Ekin = 736.488eV (T=1424.432K) Etot = 2575.286eV
Energy per atom: Epot =1854.530eV Ekin = 730.133eV (T=1412.141K) Etot = 2584.664eV
Energy per atom: Epot =1861.374eV Ekin = 733.528eV (T=1418.706K) Etot = 2594.901eV
Energy per atom: Epot =1871.041eV Ekin = 718.627eV (T=1389.887K) Etot = 2589.668eV
Energy per atom: Epot =1870.376eV Ekin = 726.866eV (T=1405.821K) Etot = 2597.241eV
Energy per atom: Epot =1872.636eV Ekin = 730.792eV (T=1413.416K) Etot = 2603.428eV
Energy per atom: Epot =1870.190eV Ekin = 735.807eV (T=1423.116K) Etot = 2605.998eV
Energy per atom: Epot =1895.986eV Ekin = 721.220eV (T=1394.902K) Etot = 2617.206eV
Energy per atom: Epot =1884.052eV Ekin = 736.331eV (T=1424.127K) Etot = 2620.382eV
Energy per atom: Epot =1890.003eV Ekin = 743.398eV (T=1437.796K) Etot = 2633.401eV
Energy per atom: Epot =1920.622eV Ekin = 722.136eV (T=1396.674K) Etot = 2642.758eV
Energy per atom: Epot =1887.136eV Ekin = 749.058eV (T=1448.743K) Etot = 2636.194eV
Energy per atom: Epot =1910.301eV Ekin = 735.796eV (T=1423.094K) Etot = 2646.098eV
Energy per atom: Epot =1916.698eV Ekin = 742.203eV (T=1435.485K) Etot = 2658.901eV
Energy per atom: Epot =1920.793eV Ekin = 747.527eV (T=1445.782K) Etot = 2668.320eV
Energy per atom: Epot =1938.732eV Ekin = 746.413eV (T=1443.627K) Etot = 2685.144eV
Energy per atom: Epot =1933.696eV Ekin = 748.130eV (T=1446.948K) Etot = 2681.825eV
Energy per atom: Epot =1936.045eV Ekin = 748.297eV (T=1447.272K) Etot = 2684.343eV
Energy per atom: Epot =1946.722eV Ekin = 739.037eV (T=1429.363K) Etot = 2685.760eV
Energy per atom: Epot =1935.074eV Ekin = 756.799eV (T=1463.714K) Etot = 2691.872eV
Energy per atom: Epot =1936.216eV Ekin = 761.640eV (T=1473.079K) Etot = 2697.856eV
Energy per atom: Epot =1936.074eV Ekin = 768.191eV (T=1485.747K) Etot = 2704.265eV
Energy per atom: Epot =1949.076eV Ekin = 762.327eV (T=1474.407K) Etot = 2711.403eV
Energy per atom: Epot =1953.735eV Ekin = 761.208eV (T=1472.243K) Etot = 2714.943eV
Energy per atom: Epot =1966.471eV Ekin = 756.073eV (T=1462.312K) Etot = 2722.545eV
Energy per atom: Epot =1970.449eV Ekin = 755.459eV (T=1461.123K) Etot = 2725.908eV
Energy per atom: Epot =1954.711eV Ekin = 766.136eV (T=1481.774K) Etot = 2720.847eV
Energy per atom: Epot =1959.163eV Ekin = 759.144eV (T=1468.251K) Etot = 2718.307eV
Energy per atom: Epot =1955.389eV Ekin = 771.355eV (T=1491.869K) Etot = 2726.744eV
Energy per atom: Epot =1961.232eV Ekin = 771.364eV (T=1491.885K) Etot = 2732.596eV
Energy per atom: Epot =1956.723eV Ekin = 782.994eV (T=1514.379K) Etot = 2739.717eV
Energy per atom: Epot =1961.378eV Ekin = 777.447eV (T=1503.650K) Etot = 2738.825eV
Energy per atom: Epot =1964.040eV Ekin = 770.461eV (T=1490.138K) Etot = 2734.500eV
Energy per atom: Epot =1965.095eV Ekin = 762.690eV (T=1475.109K) Etot = 2727.785eV
Energy per atom: Epot =1959.764eV Ekin = 756.355eV (T=1462.856K) Etot = 2716.119eV
Energy per atom: Epot =1962.422eV Ekin = 759.904eV (T=1469.721K) Etot = 2722.326eV
Energy per atom: Epot =1963.994eV Ekin = 764.128eV (T=1477.890K) Etot = 2728.123eV
Energy per atom: Epot =1981.796eV Ekin = 750.066eV (T=1450.693K) Etot = 2731.862eV
Energy per atom: Epot =1977.283eV Ekin = 754.614eV (T=1459.490K) Etot = 2731.897eV
Energy per atom: Epot =1978.374eV Ekin = 760.541eV (T=1470.953K) Etot = 2738.916eV
Energy per atom: Epot =1974.777eV Ekin = 766.126eV (T=1481.754K) Etot = 2740.903eV
Energy per atom: Epot =1976.291eV Ekin = 768.563eV (T=1486.468K) Etot = 2744.854eV
Energy per atom: Epot =1983.891eV Ekin = 773.324eV (T=1495.676K) Etot = 2757.215eV
Energy per atom: Epot =1979.005eV Ekin = 781.530eV (T=1511.548K) Etot = 2760.536eV
Energy per atom: Epot =1988.810eV Ekin = 768.886eV (T=1487.093K) Etot = 2757.696eV
Energy per atom: Epot =1987.856eV Ekin = 780.691eV (T=1509.925K) Etot = 2768.547eV
Energy per atom: Epot =1995.500eV Ekin = 771.609eV (T=1492.358K) Etot = 2767.108eV
Energy per atom: Epot =2006.621eV Ekin = 765.517eV (T=1480.577K) Etot = 2772.138eV
Energy per atom: Epot =2006.442eV Ekin = 771.675eV (T=1492.486K) Etot = 2778.116eV
Energy per atom: Epot =2005.967eV Ekin = 780.725eV (T=1509.990K) Etot = 2786.692eV
Energy per atom: Epot =2019.977eV Ekin = 767.630eV (T=1484.662K) Etot = 2787.606eV
Energy per atom: Epot =2009.943eV Ekin = 777.274eV (T=1503.315K) Etot = 2787.217eV
Energy per atom: Epot =2001.373eV Ekin = 785.059eV (T=1518.373K) Etot = 2786.432eV
Energy per atom: Epot =2011.911eV Ekin = 779.828eV (T=1508.255K) Etot = 2791.739eV
Energy per atom: Epot =2021.754eV Ekin = 771.253eV (T=1491.670K) Etot = 2793.007eV
Energy per atom: Epot =2006.073eV Ekin = 788.555eV (T=1525.134K) Etot = 2794.628eV
Energy per atom: Epot =2024.101eV Ekin = 762.543eV (T=1474.824K) Etot = 2786.644eV
Energy per atom: Epot =2021.016eV Ekin = 758.936eV (T=1467.848K) Etot = 2779.952eV
Energy per atom: Epot =2015.549eV Ekin = 770.736eV (T=1490.670K) Etot = 2786.285eV
Energy per atom: Epot =2011.927eV Ekin = 779.805eV (T=1508.210K) Etot = 2791.732eV
Energy per atom: Epot =2021.178eV Ekin = 774.564eV (T=1498.073K) Etot = 2795.741eV
Energy per atom: Epot =2020.169eV Ekin = 782.754eV (T=1513.915K) Etot = 2802.923eV
Energy per atom: Epot =2018.409eV Ekin = 787.058eV (T=1522.239K) Etot = 2805.468eV
Energy per atom: Epot =2022.119eV Ekin = 781.191eV (T=1510.891K) Etot = 2803.310eV
Energy per atom: Epot =2024.891eV Ekin = 772.001eV (T=1493.117K) Etot = 2796.892eV
Energy per atom: Epot =2026.175eV Ekin = 769.613eV (T=1488.498K) Etot = 2795.788eV
Energy per atom: Epot =2019.903eV Ekin = 769.141eV (T=1487.585K) Etot = 2789.043eV
Energy per atom: Epot =2015.265eV Ekin = 767.957eV (T=1485.296K) Etot = 2783.222eV
Energy per atom: Epot =2007.234eV Ekin = 778.392eV (T=1505.477K) Etot = 2785.626eV
Energy per atom: Epot =2020.440eV Ekin = 769.789eV (T=1488.840K) Etot = 2790.229eV
Energy per atom: Epot =2017.182eV Ekin = 775.826eV (T=1500.515K) Etot = 2793.008eV
Energy per atom: Epot =2015.751eV Ekin = 778.542eV (T=1505.768K) Etot = 2794.293eV
Energy per atom: Epot =2032.339eV Ekin = 779.483eV (T=1507.587K) Etot = 2811.822eV
Energy per atom: Epot =2032.293eV Ekin = 778.083eV (T=1504.880K) Etot = 2810.376eV
Energy per atom: Epot =2023.413eV Ekin = 785.117eV (T=1518.485K) Etot = 2808.530eV
Energy per atom: Epot =2023.581eV Ekin = 793.831eV (T=1535.339K) Etot = 2817.412eV
Energy per atom: Epot =2037.961eV Ekin = 771.653eV (T=1492.444K) Etot = 2809.614eV
Energy per atom: Epot =2031.453eV Ekin = 783.003eV (T=1514.397K) Etot = 2814.456eV
Energy per atom: Epot =2046.379eV Ekin = 768.669eV (T=1486.672K) Etot = 2815.048eV
Energy per atom: Epot =2030.727eV Ekin = 771.991eV (T=1493.097K) Etot = 2802.718eV
Energy per atom: Epot =2024.882eV Ekin = 766.025eV (T=1481.558K) Etot = 2790.907eV
Energy per atom: Epot =2018.281eV Ekin = 778.502eV (T=1505.690K) Etot = 2796.782eV
Energy per atom: Epot =2018.452eV Ekin = 783.752eV (T=1515.844K) Etot = 2802.204eV
Energy per atom: Epot =2010.079eV Ekin = 791.769eV (T=1531.351K) Etot = 2801.848eV
Energy per atom: Epot =2012.738eV Ekin = 782.287eV (T=1513.012K) Etot = 2795.025eV
Energy per atom: Epot =2002.867eV Ekin = 785.557eV (T=1519.335K) Etot = 2788.424eV
Energy per atom: Epot =1995.212eV Ekin = 779.502eV (T=1507.625K) Etot = 2774.714eV
Energy per atom: Epot =1990.975eV Ekin = 783.759eV (T=1515.858K) Etot = 2774.734eV
Energy per atom: Epot =1996.152eV Ekin = 776.500eV (T=1501.819K) Etot = 2772.652eV
Energy per atom: Epot =1987.884eV Ekin = 771.115eV (T=1491.404K) Etot = 2758.999eV
Energy per atom: Epot =1983.534eV Ekin = 761.480eV (T=1472.768K) Etot = 2745.014eV
Energy per atom: Epot =1974.221eV Ekin = 766.967eV (T=1483.381K) Etot = 2741.188eV
Energy per atom: Epot =1980.688eV Ekin = 770.665eV (T=1490.533K) Etot = 2751.353eV
Energy per atom: Epot =1979.881eV Ekin = 766.492eV (T=1482.462K) Etot = 2746.372eV
Energy per atom: Epot =1983.200eV Ekin = 765.841eV (T=1481.204K) Etot = 2749.041eV
Energy per atom: Epot =1991.685eV Ekin = 771.789eV (T=1492.708K) Etot = 2763.474eV
Energy per atom: Epot =1994.724eV Ekin = 760.587eV (T=1471.041K) Etot = 2755.310eV
Energy per atom: Epot =1993.814eV Ekin = 763.444eV (T=1476.566K) Etot = 2757.258eV
Energy per atom: Epot =1987.959eV Ekin = 766.276eV (T=1482.044K) Etot = 2754.235eV
Energy per atom: Epot =1989.167eV Ekin = 769.763eV (T=1488.788K) Etot = 2758.930eV
Energy per atom: Epot =1995.280eV Ekin = 775.303eV (T=1499.504K) Etot = 2770.583eV
Energy per atom: Epot =1997.085eV Ekin = 767.663eV (T=1484.727K) Etot = 2764.748eV
Energy per atom: Epot =2002.570eV Ekin = 766.199eV (T=1481.896K) Etot = 2768.770eV
Energy per atom: Epot =1996.793eV Ekin = 770.169eV (T=1489.574K) Etot = 2766.962eV
Energy per atom: Epot =1992.050eV Ekin = 777.592eV (T=1503.931K) Etot = 2769.642eV
Energy per atom: Epot =1986.759eV Ekin = 786.164eV (T=1520.509K) Etot = 2772.922eV
Energy per atom: Epot =1992.484eV Ekin = 773.679eV (T=1496.362K) Etot = 2766.162eV
Energy per atom: Epot =2002.856eV Ekin = 765.203eV (T=1479.969K) Etot = 2768.059eV
Energy per atom: Epot =1993.122eV Ekin = 774.160eV (T=1497.292K) Etot = 2767.282eV
Energy per atom: Epot =1984.914eV Ekin = 778.140eV (T=1504.990K) Etot = 2763.053eV
Energy per atom: Epot =1995.639eV Ekin = 770.810eV (T=1490.813K) Etot = 2766.449eV
Energy per atom: Epot =1981.737eV Ekin = 783.438eV (T=1515.238K) Etot = 2765.175eV
Energy per atom: Epot =1987.431eV Ekin = 766.311eV (T=1482.113K) Etot = 2753.743eV
Energy per atom: Epot =2002.620eV Ekin = 756.287eV (T=1462.726K) Etot = 2758.908eV
Energy per atom: Epot =1992.465eV Ekin = 764.772eV (T=1479.135K) Etot = 2757.237eV
Energy per atom: Epot =1990.026eV Ekin = 764.582eV (T=1478.768K) Etot = 2754.608eV
Energy per atom: Epot =1993.973eV Ekin = 755.116eV (T=1460.461K) Etot = 2749.090eV
Energy per atom: Epot =1995.606eV Ekin = 762.983eV (T=1475.675K) Etot = 2758.589eV
Energy per atom: Epot =1985.452eV Ekin = 768.807eV (T=1486.940K) Etot = 2754.260eV
Energy per atom: Epot =1993.664eV Ekin = 757.043eV (T=1464.187K) Etot = 2750.707eV
Energy per atom: Epot =1995.487eV Ekin = 763.324eV (T=1476.335K) Etot = 2758.811eV
Energy per atom: Epot =1991.916eV Ekin = 778.760eV (T=1506.190K) Etot = 2770.677eV
Energy per atom: Epot =1992.350eV Ekin = 770.288eV (T=1489.804K) Etot = 2762.638eV
Energy per atom: Epot =1992.959eV Ekin = 773.416eV (T=1495.855K) Etot = 2766.375eV
Energy per atom: Epot =1984.882eV Ekin = 779.346eV (T=1507.323K) Etot = 2764.228eV
Energy per atom: Epot =1997.407eV Ekin = 772.622eV (T=1494.319K) Etot = 2770.029eV
Energy per atom: Epot =1985.111eV Ekin = 779.682eV (T=1507.973K) Etot = 2764.793eV
Energy per atom: Epot =1997.482eV Ekin = 769.242eV (T=1487.781K) Etot = 2766.724eV
Energy per atom: Epot =1999.513eV Ekin = 766.436eV (T=1482.354K) Etot = 2765.949eV
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] 10:25:06 43.457006 1.0818
BFGSLineSearch: 1[ 1] 10:25:06 42.347659 0.2273
BFGSLineSearch: 2[ 2] 10:25:06 42.108454 0.1349
BFGSLineSearch: 3[ 3] 10:25:06 41.964817 0.1138
BFGSLineSearch: 4[ 4] 10:25:06 41.924933 0.0683
BFGSLineSearch: 5[ 5] 10:25:06 41.915346 0.0225
BFGSLineSearch: 6[ 6] 10:25:06 41.914920 0.0059
BFGSLineSearch: 7[ 7] 10:25:06 41.914872 0.0023
BFGSLineSearch: 8[ 9] 10:25:06 41.914855 0.0023
BFGSLineSearch: 9[ 10] 10:25:06 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 13.476eV (T=1120.989K) Etot = 55.390eV
Energy per atom: Epot =49.779eV Ekin = 5.650eV (T=469.977K) Etot = 55.429eV
Energy per atom: Epot =49.647eV Ekin = 5.788eV (T=481.518K) Etot = 55.436eV
Energy per atom: Epot =49.559eV Ekin = 5.874eV (T=488.675K) Etot = 55.434eV
Energy per atom: Epot =49.788eV Ekin = 5.649eV (T=469.936K) Etot = 55.437eV
Energy per atom: Epot =48.670eV Ekin = 6.763eV (T=562.622K) Etot = 55.434eV
Energy per atom: Epot =48.294eV Ekin = 7.134eV (T=593.475K) Etot = 55.428eV
Energy per atom: Epot =48.853eV Ekin = 6.578eV (T=547.194K) Etot = 55.431eV
Energy per atom: Epot =48.331eV Ekin = 7.101eV (T=590.703K) Etot = 55.432eV
Energy per atom: Epot =49.175eV Ekin = 6.262eV (T=520.884K) Etot = 55.437eV
Energy per atom: Epot =49.883eV Ekin = 5.555eV (T=462.114K) Etot = 55.438eV
Energy per atom: Epot =49.458eV Ekin = 5.977eV (T=497.174K) Etot = 55.435eV
Energy per atom: Epot =49.496eV Ekin = 5.943eV (T=494.344K) Etot = 55.439eV
Energy per atom: Epot =48.686eV Ekin = 6.747eV (T=561.256K) Etot = 55.433eV
Energy per atom: Epot =49.190eV Ekin = 6.246eV (T=519.550K) Etot = 55.435eV
Energy per atom: Epot =47.862eV Ekin = 7.571eV (T=629.769K) Etot = 55.432eV
Energy per atom: Epot =49.057eV Ekin = 6.380eV (T=530.701K) Etot = 55.437eV
Energy per atom: Epot =49.644eV Ekin = 5.794eV (T=481.962K) Etot = 55.438eV
Energy per atom: Epot =49.784eV Ekin = 5.658eV (T=470.699K) Etot = 55.442eV
Energy per atom: Epot =49.474eV Ekin = 5.964eV (T=496.089K) Etot = 55.438eV
Energy per atom: Epot =48.202eV Ekin = 7.230eV (T=601.449K) Etot = 55.432eV
Energy per atom: Epot =48.633eV Ekin = 6.801eV (T=565.758K) Etot = 55.434eV
Energy per atom: Epot =49.928eV Ekin = 5.511eV (T=458.463K) Etot = 55.439eV
Energy per atom: Epot =49.143eV Ekin = 6.294eV (T=523.538K) Etot = 55.436eV
Energy per atom: Epot =49.380eV Ekin = 6.059eV (T=504.013K) Etot = 55.439eV
Energy per atom: Epot =49.249eV Ekin = 6.188eV (T=514.743K) Etot = 55.437eV
Energy per atom: Epot =48.566eV Ekin = 6.864eV (T=571.010K) Etot = 55.430eV
Energy per atom: Epot =48.879eV Ekin = 6.551eV (T=544.979K) Etot = 55.431eV
Energy per atom: Epot =49.450eV Ekin = 5.986eV (T=497.941K) Etot = 55.436eV
Energy per atom: Epot =49.463eV Ekin = 5.977eV (T=497.168K) Etot = 55.439eV
Energy per atom: Epot =49.116eV Ekin = 6.320eV (T=525.700K) Etot = 55.436eV
Energy per atom: Epot =48.955eV Ekin = 6.479eV (T=538.944K) Etot = 55.434eV
Energy per atom: Epot =49.278eV Ekin = 6.158eV (T=512.256K) Etot = 55.436eV
Energy per atom: Epot =49.173eV Ekin = 6.259eV (T=520.677K) Etot = 55.432eV
Energy per atom: Epot =48.598eV Ekin = 6.832eV (T=568.344K) Etot = 55.430eV
Energy per atom: Epot =49.088eV Ekin = 6.344eV (T=527.730K) Etot = 55.432eV
Energy per atom: Epot =49.904eV Ekin = 5.532eV (T=460.175K) Etot = 55.436eV
Energy per atom: Epot =49.670eV Ekin = 5.768eV (T=479.799K) Etot = 55.438eV
Energy per atom: Epot =49.504eV Ekin = 5.933eV (T=493.532K) Etot = 55.436eV
Energy per atom: Epot =48.744eV Ekin = 6.688eV (T=556.342K) Etot = 55.432eV
Energy per atom: Epot =48.610eV Ekin = 6.820eV (T=567.364K) Etot = 55.431eV
Energy per atom: Epot =48.725eV Ekin = 6.708eV (T=558.002K) Etot = 55.433eV
Energy per atom: Epot =48.538eV Ekin = 6.894eV (T=573.450K) Etot = 55.431eV
Energy per atom: Epot =48.936eV Ekin = 6.499eV (T=540.609K) Etot = 55.435eV
Energy per atom: Epot =49.547eV Ekin = 5.891eV (T=490.022K) Etot = 55.438eV
Energy per atom: Epot =49.769eV Ekin = 5.671eV (T=471.741K) Etot = 55.440eV
Energy per atom: Epot =48.501eV Ekin = 6.931eV (T=576.563K) Etot = 55.432eV
Energy per atom: Epot =48.150eV Ekin = 7.277eV (T=605.347K) Etot = 55.427eV
Energy per atom: Epot =48.846eV Ekin = 6.588eV (T=548.019K) Etot = 55.433eV
Energy per atom: Epot =48.842eV Ekin = 6.595eV (T=548.590K) Etot = 55.437eV
Energy per atom: Epot =49.914eV Ekin = 5.527eV (T=459.745K) Etot = 55.441eV
Energy per atom: Epot =49.441eV Ekin = 5.997eV (T=498.839K) Etot = 55.438eV
Energy per atom: Epot =49.065eV Ekin = 6.375eV (T=530.276K) Etot = 55.439eV
Energy per atom: Epot =48.878eV Ekin = 6.555eV (T=545.315K) Etot = 55.434eV
Energy per atom: Epot =48.930eV Ekin = 6.502eV (T=540.873K) Etot = 55.432eV
Energy per atom: Epot =48.995eV Ekin = 6.440eV (T=535.723K) Etot = 55.435eV
Energy per atom: Epot =49.332eV Ekin = 6.102eV (T=507.594K) Etot = 55.433eV
Energy per atom: Epot =48.164eV Ekin = 7.265eV (T=604.391K) Etot = 55.430eV
Energy per atom: Epot =49.174eV Ekin = 6.262eV (T=520.955K) Etot = 55.437eV
Energy per atom: Epot =49.904eV Ekin = 5.538eV (T=460.697K) Etot = 55.442eV
Energy per atom: Epot =49.535eV Ekin = 5.900eV (T=490.770K) Etot = 55.435eV
Energy per atom: Epot =50.015eV Ekin = 5.422eV (T=451.034K) Etot = 55.437eV
Energy per atom: Epot =49.340eV Ekin = 6.095eV (T=506.988K) Etot = 55.434eV
Energy per atom: Epot =49.275eV Ekin = 6.160eV (T=512.465K) Etot = 55.436eV
Energy per atom: Epot =49.117eV Ekin = 6.319eV (T=525.638K) Etot = 55.436eV
Energy per atom: Epot =48.973eV Ekin = 6.457eV (T=537.161K) Etot = 55.430eV
Energy per atom: Epot =49.843eV Ekin = 5.592eV (T=465.192K) Etot = 55.435eV
Energy per atom: Epot =50.501eV Ekin = 4.940eV (T=410.906K) Etot = 55.441eV
Energy per atom: Epot =49.823eV Ekin = 5.617eV (T=467.237K) Etot = 55.440eV
Energy per atom: Epot =49.083eV Ekin = 6.352eV (T=528.383K) Etot = 55.435eV
Energy per atom: Epot =49.565eV Ekin = 5.875eV (T=488.681K) Etot = 55.439eV
Energy per atom: Epot =49.292eV Ekin = 6.144eV (T=511.065K) Etot = 55.436eV
Energy per atom: Epot =48.975eV Ekin = 6.462eV (T=537.582K) Etot = 55.437eV
Energy per atom: Epot =49.355eV Ekin = 6.083eV (T=506.046K) Etot = 55.439eV
Energy per atom: Epot =49.637eV Ekin = 5.801eV (T=482.534K) Etot = 55.438eV
Energy per atom: Epot =49.658eV Ekin = 5.780eV (T=480.846K) Etot = 55.438eV
Energy per atom: Epot =49.672eV Ekin = 5.768eV (T=479.779K) Etot = 55.440eV
Energy per atom: Epot =49.225eV Ekin = 6.211eV (T=516.641K) Etot = 55.436eV
Energy per atom: Epot =48.880eV Ekin = 6.552eV (T=545.032K) Etot = 55.432eV
Energy per atom: Epot =49.321eV Ekin = 6.116eV (T=508.810K) Etot = 55.437eV
Energy per atom: Epot =49.725eV Ekin = 5.712eV (T=475.201K) Etot = 55.438eV
Energy per atom: Epot =49.256eV Ekin = 6.180eV (T=514.104K) Etot = 55.436eV
Energy per atom: Epot =49.812eV Ekin = 5.631eV (T=468.425K) Etot = 55.443eV
Energy per atom: Epot =49.267eV Ekin = 6.169eV (T=513.169K) Etot = 55.436eV
Energy per atom: Epot =48.794eV Ekin = 6.641eV (T=552.426K) Etot = 55.435eV
Energy per atom: Epot =50.054eV Ekin = 5.388eV (T=448.185K) Etot = 55.441eV
Energy per atom: Epot =49.776eV Ekin = 5.664eV (T=471.159K) Etot = 55.440eV
Energy per atom: Epot =49.066eV Ekin = 6.373eV (T=530.156K) Etot = 55.439eV
Energy per atom: Epot =49.165eV Ekin = 6.273eV (T=521.805K) Etot = 55.438eV
Energy per atom: Epot =48.347eV Ekin = 7.088eV (T=589.587K) Etot = 55.434eV
Energy per atom: Epot =48.768eV Ekin = 6.668eV (T=554.698K) Etot = 55.436eV
Energy per atom: Epot =48.289eV Ekin = 7.141eV (T=594.040K) Etot = 55.430eV
Energy per atom: Epot =49.339eV Ekin = 6.097eV (T=507.226K) Etot = 55.437eV
Energy per atom: Epot =49.714eV Ekin = 5.726eV (T=476.325K) Etot = 55.440eV
Energy per atom: Epot =48.736eV Ekin = 6.698eV (T=557.178K) Etot = 55.433eV
Energy per atom: Epot =48.570eV Ekin = 6.859eV (T=570.614K) Etot = 55.429eV
Energy per atom: Epot =48.283eV Ekin = 7.145eV (T=594.353K) Etot = 55.428eV
Energy per atom: Epot =48.498eV Ekin = 6.930eV (T=576.507K) Etot = 55.429eV
Energy per atom: Epot =49.503eV Ekin = 5.931eV (T=493.408K) Etot = 55.434eV
Energy per atom: Epot =48.330eV Ekin = 7.103eV (T=590.873K) Etot = 55.433eV
Energy per atom: Epot =48.924eV Ekin = 6.508eV (T=541.363K) Etot = 55.432eV
Energy per atom: Epot =48.820eV Ekin = 6.615eV (T=550.293K) Etot = 55.435eV
Energy per atom: Epot =48.654eV Ekin = 6.782eV (T=564.145K) Etot = 55.436eV
Energy per atom: Epot =48.804eV Ekin = 6.631eV (T=551.649K) Etot = 55.435eV
Energy per atom: Epot =48.695eV Ekin = 6.743eV (T=560.929K) Etot = 55.438eV
Energy per atom: Epot =48.606eV Ekin = 6.829eV (T=568.118K) Etot = 55.435eV
Energy per atom: Epot =48.991eV Ekin = 6.443eV (T=536.005K) Etot = 55.434eV
Energy per atom: Epot =49.194eV Ekin = 6.241eV (T=519.203K) Etot = 55.435eV
Energy per atom: Epot =48.392eV Ekin = 7.038eV (T=585.451K) Etot = 55.430eV
Energy per atom: Epot =49.171eV Ekin = 6.265eV (T=521.167K) Etot = 55.436eV
Energy per atom: Epot =48.200eV Ekin = 7.228eV (T=601.309K) Etot = 55.429eV
Energy per atom: Epot =48.377eV Ekin = 7.054eV (T=586.816K) Etot = 55.431eV
Energy per atom: Epot =48.593eV Ekin = 6.843eV (T=569.218K) Etot = 55.436eV
Energy per atom: Epot =49.142eV Ekin = 6.294eV (T=523.543K) Etot = 55.435eV
Energy per atom: Epot =48.537eV Ekin = 6.893eV (T=573.426K) Etot = 55.430eV
Energy per atom: Epot =49.429eV Ekin = 6.007eV (T=499.740K) Etot = 55.437eV
Energy per atom: Epot =49.203eV Ekin = 6.234eV (T=518.622K) Etot = 55.437eV
Energy per atom: Epot =48.389eV Ekin = 7.048eV (T=586.283K) Etot = 55.437eV
Energy per atom: Epot =48.301eV Ekin = 7.127eV (T=592.873K) Etot = 55.428eV
Energy per atom: Epot =47.975eV Ekin = 7.451eV (T=619.798K) Etot = 55.426eV
Energy per atom: Epot =48.780eV Ekin = 6.652eV (T=553.363K) Etot = 55.432eV
Energy per atom: Epot =48.531eV Ekin = 6.903eV (T=574.195K) Etot = 55.433eV
Energy per atom: Epot =48.732eV Ekin = 6.704eV (T=557.668K) Etot = 55.435eV
Energy per atom: Epot =49.467eV Ekin = 5.970eV (T=496.623K) Etot = 55.437eV
Energy per atom: Epot =48.820eV Ekin = 6.612eV (T=550.031K) Etot = 55.432eV
Energy per atom: Epot =48.885eV Ekin = 6.549eV (T=544.770K) Etot = 55.434eV
Energy per atom: Epot =48.200eV Ekin = 7.233eV (T=601.680K) Etot = 55.433eV
Energy per atom: Epot =48.497eV Ekin = 6.936eV (T=576.990K) Etot = 55.433eV
Energy per atom: Epot =48.311eV Ekin = 7.117eV (T=592.025K) Etot = 55.428eV
Energy per atom: Epot =48.732eV Ekin = 6.700eV (T=557.322K) Etot = 55.431eV
Energy per atom: Epot =48.710eV Ekin = 6.726eV (T=559.517K) Etot = 55.436eV
Energy per atom: Epot =48.756eV Ekin = 6.680eV (T=555.722K) Etot = 55.436eV
Energy per atom: Epot =48.431eV Ekin = 7.001eV (T=582.386K) Etot = 55.432eV
Energy per atom: Epot =47.817eV Ekin = 7.609eV (T=632.988K) Etot = 55.426eV
Energy per atom: Epot =48.917eV Ekin = 6.519eV (T=542.253K) Etot = 55.435eV
Energy per atom: Epot =48.381eV Ekin = 7.051eV (T=586.549K) Etot = 55.432eV
Energy per atom: Epot =48.248eV Ekin = 7.181eV (T=597.404K) Etot = 55.429eV
Energy per atom: Epot =48.626eV Ekin = 6.808eV (T=566.341K) Etot = 55.434eV
Energy per atom: Epot =50.024eV Ekin = 5.417eV (T=450.605K) Etot = 55.441eV
Energy per atom: Epot =48.925eV Ekin = 6.510eV (T=541.585K) Etot = 55.436eV
Energy per atom: Epot =48.181eV Ekin = 7.250eV (T=603.105K) Etot = 55.431eV
Energy per atom: Epot =47.743eV Ekin = 7.682eV (T=639.047K) Etot = 55.425eV
Energy per atom: Epot =48.421eV Ekin = 7.010eV (T=583.097K) Etot = 55.430eV
Energy per atom: Epot =48.926eV Ekin = 6.507eV (T=541.288K) Etot = 55.433eV
Energy per atom: Epot =49.288eV Ekin = 6.149eV (T=511.503K) Etot = 55.437eV
Energy per atom: Epot =49.170eV Ekin = 6.266eV (T=521.240K) Etot = 55.436eV
Energy per atom: Epot =48.813eV Ekin = 6.618eV (T=550.550K) Etot = 55.432eV
Energy per atom: Epot =48.637eV Ekin = 6.793eV (T=565.121K) Etot = 55.431eV
Energy per atom: Epot =48.431eV Ekin = 7.002eV (T=582.439K) Etot = 55.433eV
Energy per atom: Epot =49.083eV Ekin = 6.356eV (T=528.732K) Etot = 55.439eV
Energy per atom: Epot =48.729eV Ekin = 6.706eV (T=557.827K) Etot = 55.434eV
Energy per atom: Epot =48.395eV Ekin = 7.037eV (T=585.392K) Etot = 55.432eV
Energy per atom: Epot =49.109eV Ekin = 6.322eV (T=525.938K) Etot = 55.431eV
Energy per atom: Epot =48.451eV Ekin = 6.980eV (T=580.676K) Etot = 55.432eV
Energy per atom: Epot =48.548eV Ekin = 6.888eV (T=573.007K) Etot = 55.436eV
Energy per atom: Epot =48.049eV Ekin = 7.383eV (T=614.147K) Etot = 55.431eV
Energy per atom: Epot =48.822eV Ekin = 6.613eV (T=550.134K) Etot = 55.436eV
Energy per atom: Epot =49.342eV Ekin = 6.094eV (T=506.918K) Etot = 55.435eV
Energy per atom: Epot =49.142eV Ekin = 6.291eV (T=523.345K) Etot = 55.433eV
Energy per atom: Epot =48.037eV Ekin = 7.394eV (T=615.085K) Etot = 55.431eV
Energy per atom: Epot =48.201eV Ekin = 7.233eV (T=601.667K) Etot = 55.434eV
Energy per atom: Epot =49.030eV Ekin = 6.405eV (T=532.850K) Etot = 55.435eV
Energy per atom: Epot =48.544eV Ekin = 6.888eV (T=573.010K) Etot = 55.432eV
Energy per atom: Epot =48.651eV Ekin = 6.782eV (T=564.157K) Etot = 55.433eV
Energy per atom: Epot =48.784eV Ekin = 6.653eV (T=553.470K) Etot = 55.437eV
Energy per atom: Epot =49.004eV Ekin = 6.434eV (T=535.218K) Etot = 55.438eV
Energy per atom: Epot =48.901eV Ekin = 6.530eV (T=543.180K) Etot = 55.431eV
Energy per atom: Epot =48.372eV Ekin = 7.057eV (T=587.076K) Etot = 55.429eV
Energy per atom: Epot =49.156eV Ekin = 6.278eV (T=522.246K) Etot = 55.434eV
Energy per atom: Epot =48.458eV Ekin = 6.971eV (T=579.873K) Etot = 55.429eV
Energy per atom: Epot =47.857eV Ekin = 7.567eV (T=629.447K) Etot = 55.424eV
Energy per atom: Epot =49.248eV Ekin = 6.184eV (T=514.396K) Etot = 55.432eV
Energy per atom: Epot =48.730eV Ekin = 6.703eV (T=557.578K) Etot = 55.432eV
Energy per atom: Epot =48.899eV Ekin = 6.535eV (T=543.613K) Etot = 55.434eV
Energy per atom: Epot =48.763eV Ekin = 6.669eV (T=554.732K) Etot = 55.432eV
Energy per atom: Epot =49.196eV Ekin = 6.238eV (T=518.922K) Etot = 55.434eV
Energy per atom: Epot =48.412eV Ekin = 7.017eV (T=583.680K) Etot = 55.429eV
Energy per atom: Epot =49.176eV Ekin = 6.259eV (T=520.671K) Etot = 55.435eV
Energy per atom: Epot =48.402eV Ekin = 7.033eV (T=585.014K) Etot = 55.435eV
Energy per atom: Epot =49.066eV Ekin = 6.374eV (T=530.236K) Etot = 55.440eV
Energy per atom: Epot =48.408eV Ekin = 7.028eV (T=584.665K) Etot = 55.436eV
Energy per atom: Epot =48.062eV Ekin = 7.369eV (T=612.988K) Etot = 55.431eV
Energy per atom: Epot =48.280eV Ekin = 7.151eV (T=594.857K) Etot = 55.431eV
Energy per atom: Epot =48.994eV Ekin = 6.440eV (T=535.703K) Etot = 55.434eV
Energy per atom: Epot =48.971eV Ekin = 6.465eV (T=537.815K) Etot = 55.436eV
Energy per atom: Epot =48.247eV Ekin = 7.185eV (T=597.711K) Etot = 55.432eV
Energy per atom: Epot =48.537eV Ekin = 6.897eV (T=573.742K) Etot = 55.434eV
Energy per atom: Epot =48.580eV Ekin = 6.850eV (T=569.863K) Etot = 55.431eV
Energy per atom: Epot =49.404eV Ekin = 6.032eV (T=501.813K) Etot = 55.436eV
Energy per atom: Epot =49.195eV Ekin = 6.243eV (T=519.338K) Etot = 55.438eV
Energy per atom: Epot =47.770eV Ekin = 7.659eV (T=637.165K) Etot = 55.429eV
Energy per atom: Epot =48.560eV Ekin = 6.873eV (T=571.762K) Etot = 55.433eV
Energy per atom: Epot =48.889eV Ekin = 6.543eV (T=544.312K) Etot = 55.433eV
Energy per atom: Epot =48.966eV Ekin = 6.470eV (T=538.254K) Etot = 55.437eV
Energy per atom: Epot =48.816eV Ekin = 6.621eV (T=550.806K) Etot = 55.437eV
Energy per atom: Epot =48.440eV Ekin = 6.994eV (T=581.792K) Etot = 55.434eV
Energy per atom: Epot =48.176eV Ekin = 7.253eV (T=603.334K) Etot = 55.429eV
Energy per atom: Epot =49.029eV Ekin = 6.403eV (T=532.667K) Etot = 55.432eV
Energy per atom: Epot =49.387eV Ekin = 6.049eV (T=503.214K) Etot = 55.436eV
Energy per atom: Epot =48.977eV Ekin = 6.459eV (T=537.275K) Etot = 55.436eV
Energy per atom: Epot =49.402eV Ekin = 6.038eV (T=502.312K) Etot = 55.440eV
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 -0.006161720180069038 eV
Cumul. energy transfered to the thermostat -0.009033747322207969 eV
Cumul. energy transfered to the thermostat -0.0039040285890026023 eV
Cumul. energy transfered to the thermostat 0.0020915916440468144 eV
Cumul. energy transfered to the thermostat 0.009632892490257488 eV
Cumul. energy transfered to the thermostat 0.019316073609330013 eV
Cumul. energy transfered to the thermostat 0.015864322195672076 eV
Cumul. energy transfered to the thermostat 0.02096138258600281 eV
Cumul. energy transfered to the thermostat 0.023516594333582455 eV
Cumul. energy transfered to the thermostat 0.0211298166316746 eV
Cumul. energy transfered to the thermostat 0.018912091340046327 eV
Cumul. energy transfered to the thermostat 0.019365108990201645 eV
Cumul. energy transfered to the thermostat 0.02429624530087901 eV
Cumul. energy transfered to the thermostat 0.029936129495270098 eV
Cumul. energy transfered to the thermostat 0.03255542974963223 eV
Cumul. energy transfered to the thermostat 0.03290056327511882 eV
Cumul. energy transfered to the thermostat 0.027019068862568815 eV
Cumul. energy transfered to the thermostat 0.02083584220466768 eV
Cumul. energy transfered to the thermostat 0.023003809006520277 eV
Cumul. energy transfered to the thermostat 0.02203422898306147 eV
Cumul. energy transfered to the thermostat 0.02504594120397767 eV
Cumul. energy transfered to the thermostat 0.025295772416534714 eV
Cumul. energy transfered to the thermostat 0.022288476963763192 eV
Cumul. energy transfered to the thermostat 0.021498920832683427 eV
Cumul. energy transfered to the thermostat 0.019367128268252192 eV
Cumul. energy transfered to the thermostat 0.024698156240843795 eV
Cumul. energy transfered to the thermostat 0.0223410628180743 eV
Cumul. energy transfered to the thermostat 0.024937465144607623 eV
Cumul. energy transfered to the thermostat 0.033118508761547275 eV
Cumul. energy transfered to the thermostat 0.032286448063386215 eV
Cumul. energy transfered to the thermostat 0.035262366324176043 eV
Cumul. energy transfered to the thermostat 0.033729596926050896 eV
Cumul. energy transfered to the thermostat 0.036315840181250635 eV
Cumul. energy transfered to the thermostat 0.035304724417573735 eV
Cumul. energy transfered to the thermostat 0.036234949430903704 eV
Cumul. energy transfered to the thermostat 0.04004038888695321 eV
Cumul. energy transfered to the thermostat 0.04074695327318271 eV
Cumul. energy transfered to the thermostat 0.04207470259473717 eV
Cumul. energy transfered to the thermostat 0.04519953358734703 eV
Cumul. energy transfered to the thermostat 0.04263770001260282 eV
Cumul. energy transfered to the thermostat 0.04087181613407524 eV
Cumul. energy transfered to the thermostat 0.041445099901392814 eV
Cumul. energy transfered to the thermostat 0.04097798403977631 eV
Cumul. energy transfered to the thermostat 0.04141671506703035 eV
Cumul. energy transfered to the thermostat 0.0449087453536203 eV
Cumul. energy transfered to the thermostat 0.04967502572967402 eV
Cumul. energy transfered to the thermostat 0.049714084000171244 eV
Cumul. energy transfered to the thermostat 0.05233316367226728 eV
Cumul. energy transfered to the thermostat 0.049783826363434994 eV
Cumul. energy transfered to the thermostat 0.05081982074442725 eV
Cumul. energy transfered to the thermostat 0.05543829933352367 eV
Cumul. energy transfered to the thermostat 0.05431883368624056 eV
Cumul. energy transfered to the thermostat 0.05605160649754803 eV
Cumul. energy transfered to the thermostat 0.05628838589207329 eV
Cumul. energy transfered to the thermostat 0.05496102828516069 eV
Cumul. energy transfered to the thermostat 0.06125971064796512 eV
Cumul. energy transfered to the thermostat 0.06222405638768277 eV
Cumul. energy transfered to the thermostat 0.06386083673052433 eV
Cumul. energy transfered to the thermostat 0.0650064399215113 eV
Cumul. energy transfered to the thermostat 0.05808325053290049 eV
Cumul. energy transfered to the thermostat 0.05656561904313841 eV
Cumul. energy transfered to the thermostat 0.059700639160060257 eV
Cumul. energy transfered to the thermostat 0.06029868676530261 eV
Cumul. energy transfered to the thermostat 0.06504624334363374 eV
Cumul. energy transfered to the thermostat 0.06436526396661117 eV
Cumul. energy transfered to the thermostat 0.06930229081874122 eV
Cumul. energy transfered to the thermostat 0.0681730797862036 eV
Cumul. energy transfered to the thermostat 0.06869649495354416 eV
Cumul. energy transfered to the thermostat 0.05878211177120056 eV
Cumul. energy transfered to the thermostat 0.062075927603359636 eV
Cumul. energy transfered to the thermostat 0.06658820313355801 eV
Cumul. energy transfered to the thermostat 0.07570799987040853 eV
Cumul. energy transfered to the thermostat 0.08050212062362483 eV
Cumul. energy transfered to the thermostat 0.0860183618690842 eV
Cumul. energy transfered to the thermostat 0.08110760711069329 eV
Cumul. energy transfered to the thermostat 0.07619206198692227 eV
Cumul. energy transfered to the thermostat 0.07575128374535114 eV
Cumul. energy transfered to the thermostat 0.07589451431507145 eV
Cumul. energy transfered to the thermostat 0.07381215192605989 eV
Cumul. energy transfered to the thermostat 0.0765645869373962 eV
Cumul. energy transfered to the thermostat 0.073256782343731 eV
Cumul. energy transfered to the thermostat 0.07808328842583352 eV
Cumul. energy transfered to the thermostat 0.0739180579219525 eV
Cumul. energy transfered to the thermostat 0.07568980141570945 eV
Cumul. energy transfered to the thermostat 0.07082653569945489 eV
Cumul. energy transfered to the thermostat 0.06841482608944162 eV
Cumul. energy transfered to the thermostat 0.0640976706830995 eV
Cumul. energy transfered to the thermostat 0.06719881133214776 eV
Cumul. energy transfered to the thermostat 0.053418912817500996 eV
Cumul. energy transfered to the thermostat 0.04633327483433099 eV
Cumul. energy transfered to the thermostat 0.0486190068056002 eV
Cumul. energy transfered to the thermostat 0.04969317837669828 eV
Cumul. energy transfered to the thermostat 0.04707596181246258 eV
Cumul. energy transfered to the thermostat 0.043307527188088064 eV
Cumul. energy transfered to the thermostat 0.05098341589992047 eV
Cumul. energy transfered to the thermostat 0.049173751765061204 eV
Cumul. energy transfered to the thermostat 0.05010154177087271 eV
Cumul. energy transfered to the thermostat 0.05036945420411002 eV
Cumul. energy transfered to the thermostat 0.04872853870207386 eV
Cumul. energy transfered to the thermostat 0.04962978365157138 eV