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 we 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.
Part 1: 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 (
MaxwellBoltzmannDistribution,
Stationary,
ZeroRotation,
)
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
MaxwellBoltzmannDistribution(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 = 153.929eV (T=297.712K) Etot = 151.525eV
Energy per atom: Epot =116.958eV Ekin = 35.353eV (T=68.375K) Etot = 152.311eV
Energy per atom: Epot =76.762eV Ekin = 75.404eV (T=145.838K) Etot = 152.166eV
Energy per atom: Epot =71.956eV Ekin = 80.075eV (T=154.872K) Etot = 152.030eV
Energy per atom: Epot =67.414eV Ekin = 84.550eV (T=163.527K) Etot = 151.964eV
Energy per atom: Epot =79.354eV Ekin = 72.773eV (T=140.749K) Etot = 152.127eV
Energy per atom: Epot =78.985eV Ekin = 73.148eV (T=141.474K) Etot = 152.133eV
Energy per atom: Epot =72.598eV Ekin = 79.438eV (T=153.641K) Etot = 152.036eV
Energy per atom: Epot =71.698eV Ekin = 80.331eV (T=155.366K) Etot = 152.029eV
Energy per atom: Epot =78.133eV Ekin = 73.973eV (T=143.070K) Etot = 152.106eV
Energy per atom: Epot =74.883eV Ekin = 77.196eV (T=149.304K) Etot = 152.079eV
Energy per atom: Epot =73.948eV Ekin = 78.110eV (T=151.072K) Etot = 152.059eV
Energy per atom: Epot =74.984eV Ekin = 77.084eV (T=149.087K) Etot = 152.067eV
Energy per atom: Epot =76.457eV Ekin = 75.625eV (T=146.266K) Etot = 152.082eV
Energy per atom: Epot =73.016eV Ekin = 79.043eV (T=152.877K) Etot = 152.059eV
Energy per atom: Epot =75.613eV Ekin = 76.468eV (T=147.896K) Etot = 152.081eV
Energy per atom: Epot =73.476eV Ekin = 78.588eV (T=151.996K) Etot = 152.064eV
Energy per atom: Epot =77.656eV Ekin = 74.423eV (T=143.941K) Etot = 152.080eV
Energy per atom: Epot =73.727eV Ekin = 78.347eV (T=151.529K) Etot = 152.074eV
Energy per atom: Epot =74.484eV Ekin = 77.582eV (T=150.050K) Etot = 152.066eV
Energy per atom: Epot =76.761eV Ekin = 75.315eV (T=145.666K) Etot = 152.076eV
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?
Part 2: 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()
running a NVT simulation of fcc Cu
Energy per atom: Epot =540.816eV Ekin = 0.000eV (T=0.000K) Etot = 540.816eV
Energy per atom: Epot =601.497eV Ekin = 82.685eV (T=159.921K) Etot = 684.183eV
Energy per atom: Epot =671.855eV Ekin = 140.177eV (T=271.115K) Etot = 812.032eV
Energy per atom: Epot =725.145eV Ekin = 206.314eV (T=399.030K) Etot = 931.459eV
Energy per atom: Epot =782.777eV Ekin = 258.969eV (T=500.868K) Etot = 1041.746eV
Energy per atom: Epot =842.815eV Ekin = 299.226eV (T=578.729K) Etot = 1142.041eV
Energy per atom: Epot =888.107eV Ekin = 343.704eV (T=664.754K) Etot = 1231.811eV
Energy per atom: Epot =924.642eV Ekin = 384.271eV (T=743.213K) Etot = 1308.913eV
Energy per atom: Epot =974.450eV Ekin = 411.521eV (T=795.916K) Etot = 1385.971eV
Energy per atom: Epot =1005.403eV Ekin = 447.045eV (T=864.624K) Etot = 1452.448eV
Energy per atom: Epot =1041.388eV Ekin = 463.296eV (T=896.055K) Etot = 1504.684eV
Energy per atom: Epot =1071.533eV Ekin = 492.617eV (T=952.765K) Etot = 1564.150eV
Energy per atom: Epot =1105.168eV Ekin = 508.596eV (T=983.668K) Etot = 1613.763eV
Energy per atom: Epot =1146.162eV Ekin = 519.460eV (T=1004.680K) Etot = 1665.622eV
Energy per atom: Epot =1173.453eV Ekin = 540.263eV (T=1044.916K) Etot = 1713.716eV
Energy per atom: Epot =1203.499eV Ekin = 555.420eV (T=1074.230K) Etot = 1758.919eV
Energy per atom: Epot =1232.395eV Ekin = 575.962eV (T=1113.960K) Etot = 1808.357eV
Energy per atom: Epot =1250.501eV Ekin = 595.195eV (T=1151.159K) Etot = 1845.696eV
Energy per atom: Epot =1283.451eV Ekin = 590.582eV (T=1142.236K) Etot = 1874.033eV
Energy per atom: Epot =1301.373eV Ekin = 609.934eV (T=1179.666K) Etot = 1911.307eV
Energy per atom: Epot =1329.132eV Ekin = 614.047eV (T=1187.621K) Etot = 1943.179eV
Energy per atom: Epot =1362.029eV Ekin = 614.352eV (T=1188.210K) Etot = 1976.381eV
Energy per atom: Epot =1374.380eV Ekin = 630.453eV (T=1219.350K) Etot = 2004.832eV
Energy per atom: Epot =1390.031eV Ekin = 640.653eV (T=1239.079K) Etot = 2030.684eV
Energy per atom: Epot =1403.895eV Ekin = 642.758eV (T=1243.151K) Etot = 2046.653eV
Energy per atom: Epot =1416.822eV Ekin = 655.940eV (T=1268.644K) Etot = 2072.762eV
Energy per atom: Epot =1435.852eV Ekin = 659.185eV (T=1274.922K) Etot = 2095.037eV
Energy per atom: Epot =1459.637eV Ekin = 655.387eV (T=1267.575K) Etot = 2115.024eV
Energy per atom: Epot =1465.311eV Ekin = 671.918eV (T=1299.547K) Etot = 2137.229eV
Energy per atom: Epot =1475.697eV Ekin = 683.237eV (T=1321.439K) Etot = 2158.934eV
Energy per atom: Epot =1494.475eV Ekin = 674.633eV (T=1304.798K) Etot = 2169.107eV
Energy per atom: Epot =1510.856eV Ekin = 684.460eV (T=1323.805K) Etot = 2195.316eV
Energy per atom: Epot =1516.791eV Ekin = 688.304eV (T=1331.241K) Etot = 2205.095eV
Energy per atom: Epot =1540.068eV Ekin = 686.108eV (T=1326.993K) Etot = 2226.176eV
Energy per atom: Epot =1542.449eV Ekin = 695.792eV (T=1345.723K) Etot = 2238.242eV
Energy per atom: Epot =1558.425eV Ekin = 700.104eV (T=1354.063K) Etot = 2258.529eV
Energy per atom: Epot =1571.262eV Ekin = 704.138eV (T=1361.863K) Etot = 2275.400eV
Energy per atom: Epot =1581.618eV Ekin = 719.801eV (T=1392.159K) Etot = 2301.419eV
Energy per atom: Epot =1590.760eV Ekin = 725.001eV (T=1402.216K) Etot = 2315.762eV
Energy per atom: Epot =1615.257eV Ekin = 714.704eV (T=1382.299K) Etot = 2329.961eV
Energy per atom: Epot =1619.757eV Ekin = 724.669eV (T=1401.573K) Etot = 2344.426eV
Energy per atom: Epot =1637.906eV Ekin = 714.387eV (T=1381.686K) Etot = 2352.293eV
Energy per atom: Epot =1642.700eV Ekin = 709.637eV (T=1372.500K) Etot = 2352.337eV
Energy per atom: Epot =1656.209eV Ekin = 711.857eV (T=1376.793K) Etot = 2368.065eV
Energy per atom: Epot =1650.143eV Ekin = 723.388eV (T=1399.096K) Etot = 2373.532eV
Energy per atom: Epot =1660.445eV Ekin = 727.236eV (T=1406.538K) Etot = 2387.681eV
Energy per atom: Epot =1664.395eV Ekin = 734.175eV (T=1419.959K) Etot = 2398.570eV
Energy per atom: Epot =1674.152eV Ekin = 723.389eV (T=1399.096K) Etot = 2397.541eV
Energy per atom: Epot =1679.995eV Ekin = 726.683eV (T=1405.469K) Etot = 2406.678eV
Energy per atom: Epot =1682.691eV Ekin = 728.164eV (T=1408.332K) Etot = 2410.855eV
Energy per atom: Epot =1694.263eV Ekin = 729.096eV (T=1410.136K) Etot = 2423.359eV
Energy per atom: Epot =1700.776eV Ekin = 727.430eV (T=1406.913K) Etot = 2428.206eV
Energy per atom: Epot =1705.564eV Ekin = 732.502eV (T=1416.723K) Etot = 2438.066eV
Energy per atom: Epot =1717.977eV Ekin = 725.988eV (T=1404.125K) Etot = 2443.966eV
Energy per atom: Epot =1729.689eV Ekin = 733.797eV (T=1419.226K) Etot = 2463.486eV
Energy per atom: Epot =1729.245eV Ekin = 741.420eV (T=1433.971K) Etot = 2470.665eV
Energy per atom: Epot =1755.423eV Ekin = 723.270eV (T=1398.867K) Etot = 2478.693eV
Energy per atom: Epot =1749.039eV Ekin = 732.312eV (T=1416.355K) Etot = 2481.350eV
Energy per atom: Epot =1764.462eV Ekin = 722.266eV (T=1396.926K) Etot = 2486.728eV
Energy per atom: Epot =1768.881eV Ekin = 730.102eV (T=1412.081K) Etot = 2498.983eV
Energy per atom: Epot =1776.399eV Ekin = 733.164eV (T=1418.003K) Etot = 2509.563eV
Energy per atom: Epot =1778.200eV Ekin = 731.993eV (T=1415.738K) Etot = 2510.193eV
Energy per atom: Epot =1791.028eV Ekin = 735.632eV (T=1422.776K) Etot = 2526.660eV
Energy per atom: Epot =1797.373eV Ekin = 747.918eV (T=1446.539K) Etot = 2545.292eV
Energy per atom: Epot =1794.739eV Ekin = 749.426eV (T=1449.456K) Etot = 2544.166eV
Energy per atom: Epot =1823.305eV Ekin = 728.949eV (T=1409.851K) Etot = 2552.255eV
Energy per atom: Epot =1820.311eV Ekin = 748.799eV (T=1448.242K) Etot = 2569.110eV
Energy per atom: Epot =1826.262eV Ekin = 747.853eV (T=1446.413K) Etot = 2574.115eV
Energy per atom: Epot =1847.816eV Ekin = 732.710eV (T=1417.125K) Etot = 2580.526eV
Energy per atom: Epot =1845.416eV Ekin = 746.826eV (T=1444.426K) Etot = 2592.242eV
Energy per atom: Epot =1860.798eV Ekin = 738.425eV (T=1428.177K) Etot = 2599.223eV
Energy per atom: Epot =1862.508eV Ekin = 740.570eV (T=1432.326K) Etot = 2603.078eV
Energy per atom: Epot =1875.076eV Ekin = 737.761eV (T=1426.895K) Etot = 2612.838eV
Energy per atom: Epot =1883.128eV Ekin = 742.696eV (T=1436.439K) Etot = 2625.824eV
Energy per atom: Epot =1892.848eV Ekin = 731.280eV (T=1414.358K) Etot = 2624.127eV
Energy per atom: Epot =1880.379eV Ekin = 748.067eV (T=1446.827K) Etot = 2628.447eV
Energy per atom: Epot =1890.010eV Ekin = 742.509eV (T=1436.078K) Etot = 2632.520eV
Energy per atom: Epot =1888.400eV Ekin = 751.923eV (T=1454.285K) Etot = 2640.323eV
Energy per atom: Epot =1899.956eV Ekin = 737.408eV (T=1426.211K) Etot = 2637.364eV
Energy per atom: Epot =1894.167eV Ekin = 743.912eV (T=1438.790K) Etot = 2638.079eV
Energy per atom: Epot =1889.536eV Ekin = 755.732eV (T=1461.651K) Etot = 2645.268eV
Energy per atom: Epot =1901.541eV Ekin = 747.830eV (T=1446.369K) Etot = 2649.371eV
Energy per atom: Epot =1910.075eV Ekin = 749.379eV (T=1449.365K) Etot = 2659.454eV
Energy per atom: Epot =1912.343eV Ekin = 751.900eV (T=1454.240K) Etot = 2664.242eV
Energy per atom: Epot =1911.101eV Ekin = 750.271eV (T=1451.089K) Etot = 2661.372eV
Energy per atom: Epot =1917.507eV Ekin = 740.041eV (T=1431.303K) Etot = 2657.548eV
Energy per atom: Epot =1914.963eV Ekin = 748.384eV (T=1447.439K) Etot = 2663.347eV
Energy per atom: Epot =1927.978eV Ekin = 747.875eV (T=1446.455K) Etot = 2675.853eV
Energy per atom: Epot =1924.851eV Ekin = 752.359eV (T=1455.128K) Etot = 2677.210eV
Energy per atom: Epot =1921.501eV Ekin = 753.272eV (T=1456.893K) Etot = 2674.773eV
Energy per atom: Epot =1935.560eV Ekin = 745.376eV (T=1441.623K) Etot = 2680.936eV
Energy per atom: Epot =1927.948eV Ekin = 750.302eV (T=1451.150K) Etot = 2678.251eV
Energy per atom: Epot =1939.615eV Ekin = 748.384eV (T=1447.440K) Etot = 2687.999eV
Energy per atom: Epot =1935.676eV Ekin = 752.327eV (T=1455.065K) Etot = 2688.003eV
Energy per atom: Epot =1943.646eV Ekin = 744.288eV (T=1439.518K) Etot = 2687.935eV
Energy per atom: Epot =1950.501eV Ekin = 744.293eV (T=1439.528K) Etot = 2694.795eV
Energy per atom: Epot =1955.720eV Ekin = 742.074eV (T=1435.236K) Etot = 2697.794eV
Energy per atom: Epot =1950.600eV Ekin = 757.513eV (T=1465.095K) Etot = 2708.112eV
Energy per atom: Epot =1953.990eV Ekin = 751.887eV (T=1454.215K) Etot = 2705.877eV
Energy per atom: Epot =1954.733eV Ekin = 748.824eV (T=1448.290K) Etot = 2703.557eV
Energy per atom: Epot =1946.548eV Ekin = 755.250eV (T=1460.719K) Etot = 2701.798eV
Energy per atom: Epot =1951.783eV Ekin = 752.428eV (T=1455.260K) Etot = 2704.211eV
Energy per atom: Epot =1965.129eV Ekin = 737.546eV (T=1426.478K) Etot = 2702.675eV
Energy per atom: Epot =1959.108eV Ekin = 748.747eV (T=1448.142K) Etot = 2707.855eV
Energy per atom: Epot =1954.871eV Ekin = 768.046eV (T=1485.469K) Etot = 2722.917eV
Energy per atom: Epot =1952.249eV Ekin = 773.777eV (T=1496.552K) Etot = 2726.026eV
Energy per atom: Epot =1956.650eV Ekin = 769.330eV (T=1487.951K) Etot = 2725.980eV
Energy per atom: Epot =1966.817eV Ekin = 768.432eV (T=1486.215K) Etot = 2735.250eV
Energy per atom: Epot =1970.563eV Ekin = 768.129eV (T=1485.628K) Etot = 2738.692eV
Energy per atom: Epot =1960.869eV Ekin = 778.855eV (T=1506.373K) Etot = 2739.724eV
Energy per atom: Epot =1960.914eV Ekin = 778.757eV (T=1506.183K) Etot = 2739.671eV
Energy per atom: Epot =1978.412eV Ekin = 766.751eV (T=1482.963K) Etot = 2745.162eV
Energy per atom: Epot =1961.328eV Ekin = 781.177eV (T=1510.865K) Etot = 2742.505eV
Energy per atom: Epot =1973.478eV Ekin = 768.787eV (T=1486.902K) Etot = 2742.265eV
Energy per atom: Epot =1974.649eV Ekin = 764.908eV (T=1479.399K) Etot = 2739.557eV
Energy per atom: Epot =1979.513eV Ekin = 759.303eV (T=1468.558K) Etot = 2738.816eV
Energy per atom: Epot =1969.218eV Ekin = 764.652eV (T=1478.904K) Etot = 2733.871eV
Energy per atom: Epot =1982.834eV Ekin = 747.261eV (T=1445.268K) Etot = 2730.095eV
Energy per atom: Epot =1973.458eV Ekin = 759.930eV (T=1469.772K) Etot = 2733.389eV
Energy per atom: Epot =1996.845eV Ekin = 730.040eV (T=1411.962K) Etot = 2726.885eV
Energy per atom: Epot =2000.801eV Ekin = 742.649eV (T=1436.349K) Etot = 2743.450eV
Energy per atom: Epot =2003.546eV Ekin = 755.825eV (T=1461.831K) Etot = 2759.371eV
Energy per atom: Epot =1994.062eV Ekin = 759.272eV (T=1468.498K) Etot = 2753.334eV
Energy per atom: Epot =2000.587eV Ekin = 762.874eV (T=1475.465K) Etot = 2763.462eV
Energy per atom: Epot =2001.236eV Ekin = 766.041eV (T=1481.589K) Etot = 2767.277eV
Energy per atom: Epot =2015.306eV Ekin = 750.245eV (T=1451.039K) Etot = 2765.551eV
Energy per atom: Epot =2010.263eV Ekin = 765.351eV (T=1480.255K) Etot = 2775.614eV
Energy per atom: Epot =2008.217eV Ekin = 765.152eV (T=1479.870K) Etot = 2773.369eV
Energy per atom: Epot =1993.198eV Ekin = 781.723eV (T=1511.920K) Etot = 2774.921eV
Energy per atom: Epot =2003.449eV Ekin = 782.435eV (T=1513.297K) Etot = 2785.884eV
Energy per atom: Epot =2000.359eV Ekin = 781.433eV (T=1511.359K) Etot = 2781.792eV
Energy per atom: Epot =1989.222eV Ekin = 800.689eV (T=1548.602K) Etot = 2789.911eV
Energy per atom: Epot =1989.111eV Ekin = 798.463eV (T=1544.297K) Etot = 2787.574eV
Energy per atom: Epot =1996.684eV Ekin = 786.601eV (T=1521.355K) Etot = 2783.286eV
Energy per atom: Epot =2002.972eV Ekin = 771.914eV (T=1492.948K) Etot = 2774.886eV
Energy per atom: Epot =1993.433eV Ekin = 774.569eV (T=1498.084K) Etot = 2768.002eV
Energy per atom: Epot =2004.543eV Ekin = 762.952eV (T=1475.616K) Etot = 2767.495eV
Energy per atom: Epot =1998.178eV Ekin = 765.648eV (T=1480.830K) Etot = 2763.826eV
Energy per atom: Epot =1993.266eV Ekin = 772.804eV (T=1494.670K) Etot = 2766.070eV
Energy per atom: Epot =1990.017eV Ekin = 774.134eV (T=1497.243K) Etot = 2764.151eV
Energy per atom: Epot =1996.346eV Ekin = 770.236eV (T=1489.704K) Etot = 2766.582eV
Energy per atom: Epot =1984.892eV Ekin = 777.847eV (T=1504.425K) Etot = 2762.739eV
Energy per atom: Epot =1983.583eV Ekin = 772.002eV (T=1493.120K) Etot = 2755.586eV
Energy per atom: Epot =2001.516eV Ekin = 762.875eV (T=1475.467K) Etot = 2764.391eV
Energy per atom: Epot =1994.288eV Ekin = 767.194eV (T=1483.821K) Etot = 2761.483eV
Energy per atom: Epot =2015.023eV Ekin = 754.445eV (T=1459.162K) Etot = 2769.468eV
Energy per atom: Epot =1998.824eV Ekin = 769.412eV (T=1488.110K) Etot = 2768.236eV
Energy per atom: Epot =1988.055eV Ekin = 778.259eV (T=1505.220K) Etot = 2766.313eV
Energy per atom: Epot =2010.858eV Ekin = 757.829eV (T=1465.707K) Etot = 2768.686eV
Energy per atom: Epot =2016.944eV Ekin = 744.087eV (T=1439.129K) Etot = 2761.030eV
Energy per atom: Epot =2006.524eV Ekin = 764.059eV (T=1477.757K) Etot = 2770.583eV
Energy per atom: Epot =2007.681eV Ekin = 762.964eV (T=1475.640K) Etot = 2770.645eV
Energy per atom: Epot =2004.016eV Ekin = 767.914eV (T=1485.212K) Etot = 2771.930eV
Energy per atom: Epot =2010.139eV Ekin = 762.146eV (T=1474.058K) Etot = 2772.286eV
Energy per atom: Epot =1999.853eV Ekin = 773.396eV (T=1495.815K) Etot = 2773.249eV
Energy per atom: Epot =1996.471eV Ekin = 768.728eV (T=1486.788K) Etot = 2765.199eV
Energy per atom: Epot =1988.936eV Ekin = 762.930eV (T=1475.574K) Etot = 2751.867eV
Energy per atom: Epot =1999.585eV Ekin = 766.877eV (T=1483.207K) Etot = 2766.463eV
Energy per atom: Epot =1984.626eV Ekin = 777.566eV (T=1503.880K) Etot = 2762.192eV
Energy per atom: Epot =1987.129eV Ekin = 781.532eV (T=1511.551K) Etot = 2768.661eV
Energy per atom: Epot =1990.273eV Ekin = 774.498eV (T=1497.947K) Etot = 2764.771eV
Energy per atom: Epot =2004.569eV Ekin = 770.261eV (T=1489.752K) Etot = 2774.830eV
Energy per atom: Epot =1998.034eV Ekin = 774.212eV (T=1497.393K) Etot = 2772.246eV
Energy per atom: Epot =1992.445eV Ekin = 791.134eV (T=1530.122K) Etot = 2783.579eV
Energy per atom: Epot =2001.438eV Ekin = 790.228eV (T=1528.369K) Etot = 2791.665eV
Energy per atom: Epot =1998.432eV Ekin = 786.054eV (T=1520.296K) Etot = 2784.485eV
Energy per atom: Epot =2004.908eV Ekin = 770.256eV (T=1489.742K) Etot = 2775.164eV
Energy per atom: Epot =1994.632eV Ekin = 777.333eV (T=1503.430K) Etot = 2771.966eV
Energy per atom: Epot =1989.581eV Ekin = 788.600eV (T=1525.220K) Etot = 2778.181eV
Energy per atom: Epot =2008.360eV Ekin = 770.164eV (T=1489.564K) Etot = 2778.524eV
Energy per atom: Epot =2005.894eV Ekin = 787.766eV (T=1523.608K) Etot = 2793.661eV
Energy per atom: Epot =2015.101eV Ekin = 771.496eV (T=1492.141K) Etot = 2786.597eV
Energy per atom: Epot =2005.915eV Ekin = 786.438eV (T=1521.040K) Etot = 2792.354eV
Energy per atom: Epot =2005.149eV Ekin = 794.430eV (T=1536.498K) Etot = 2799.579eV
Energy per atom: Epot =2009.627eV Ekin = 784.097eV (T=1516.512K) Etot = 2793.724eV
Energy per atom: Epot =2011.746eV Ekin = 781.758eV (T=1511.988K) Etot = 2793.504eV
Energy per atom: Epot =2000.539eV Ekin = 788.436eV (T=1524.903K) Etot = 2788.975eV
Energy per atom: Epot =1999.592eV Ekin = 786.943eV (T=1522.017K) Etot = 2786.536eV
Energy per atom: Epot =2017.004eV Ekin = 772.413eV (T=1493.914K) Etot = 2789.417eV
Energy per atom: Epot =2019.295eV Ekin = 772.785eV (T=1494.633K) Etot = 2792.079eV
Energy per atom: Epot =2014.782eV Ekin = 774.748eV (T=1498.431K) Etot = 2789.530eV
Energy per atom: Epot =2005.588eV Ekin = 778.803eV (T=1506.272K) Etot = 2784.390eV
Energy per atom: Epot =2018.681eV Ekin = 767.838eV (T=1485.065K) Etot = 2786.519eV
Energy per atom: Epot =2028.860eV Ekin = 769.487eV (T=1488.255K) Etot = 2798.347eV
Energy per atom: Epot =2013.598eV Ekin = 793.704eV (T=1535.092K) Etot = 2807.301eV
Energy per atom: Epot =2020.893eV Ekin = 776.033eV (T=1500.916K) Etot = 2796.926eV
Energy per atom: Epot =2007.345eV Ekin = 780.635eV (T=1509.816K) Etot = 2787.980eV
Energy per atom: Epot =2030.147eV Ekin = 759.039eV (T=1468.047K) Etot = 2789.186eV
Energy per atom: Epot =2013.346eV Ekin = 783.353eV (T=1515.072K) Etot = 2796.698eV
Energy per atom: Epot =2017.074eV Ekin = 778.383eV (T=1505.461K) Etot = 2795.458eV
Energy per atom: Epot =2025.413eV Ekin = 771.687eV (T=1492.510K) Etot = 2797.100eV
Energy per atom: Epot =2011.507eV Ekin = 788.010eV (T=1524.079K) Etot = 2799.516eV
Energy per atom: Epot =2022.783eV Ekin = 781.501eV (T=1511.491K) Etot = 2804.284eV
Energy per atom: Epot =2010.609eV Ekin = 781.169eV (T=1510.849K) Etot = 2791.778eV
Energy per atom: Epot =2020.673eV Ekin = 770.791eV (T=1490.777K) Etot = 2791.465eV
Energy per atom: Epot =2020.599eV Ekin = 764.971eV (T=1479.520K) Etot = 2785.570eV
Energy per atom: Epot =2007.277eV Ekin = 780.143eV (T=1508.865K) Etot = 2787.420eV
Energy per atom: Epot =2008.895eV Ekin = 782.136eV (T=1512.718K) Etot = 2791.031eV
Energy per atom: Epot =2015.142eV Ekin = 781.856eV (T=1512.177K) Etot = 2796.998eV
Energy per atom: Epot =2019.292eV Ekin = 781.859eV (T=1512.184K) Etot = 2801.151eV
Energy per atom: Epot =2003.617eV Ekin = 791.557eV (T=1530.941K) Etot = 2795.175eV
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.
Part 3: 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, the 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
MaxwellBoltzmannDistribution(atoms, temperature_K=1200)
Stationary(atoms) # zero linear momentum
ZeroRotation(atoms) # zero angular momentum
# Run MD using the Velocity Verlet algorithm and save trajectory
dyn = VelocityVerlet(atoms, 5 * units.fs, trajectory='nanoparticleCu_NVE.traj')
print('running a NVE simulation of a Cu nanoparticle')
printenergy(atoms)
steps_per_block = 10
for i in range(200):
dyn.run(steps_per_block)
printenergy(atoms)
Step[ FC] Time Energy fmax
BFGSLineSearch: 0[ 0] 12:10:02 43.457006 1.0818
BFGSLineSearch: 1[ 1] 12:10:02 42.347659 0.2273
BFGSLineSearch: 2[ 2] 12:10:02 42.108454 0.1349
BFGSLineSearch: 3[ 3] 12:10:02 41.964817 0.1138
BFGSLineSearch: 4[ 4] 12:10:02 41.924933 0.0683
BFGSLineSearch: 5[ 5] 12:10:02 41.915346 0.0225
BFGSLineSearch: 6[ 6] 12:10:02 41.914920 0.0059
BFGSLineSearch: 7[ 7] 12:10:02 41.914872 0.0023
BFGSLineSearch: 8[ 9] 12:10:02 41.914855 0.0023
BFGSLineSearch: 9[ 10] 12:10:02 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 14.232eV (T=1183.945K) Etot = 56.147eV
Energy per atom: Epot =50.277eV Ekin = 5.919eV (T=492.416K) Etot = 56.196eV
Energy per atom: Epot =50.037eV Ekin = 6.165eV (T=512.818K) Etot = 56.202eV
Energy per atom: Epot =50.884eV Ekin = 5.318eV (T=442.361K) Etot = 56.202eV
Energy per atom: Epot =50.708eV Ekin = 5.496eV (T=457.207K) Etot = 56.204eV
Energy per atom: Epot =49.881eV Ekin = 6.323eV (T=525.947K) Etot = 56.203eV
Energy per atom: Epot =49.227eV Ekin = 6.968eV (T=579.653K) Etot = 56.195eV
Energy per atom: Epot =48.634eV Ekin = 7.559eV (T=628.769K) Etot = 56.193eV
Energy per atom: Epot =48.282eV Ekin = 7.913eV (T=658.270K) Etot = 56.195eV
Energy per atom: Epot =49.855eV Ekin = 6.345eV (T=527.812K) Etot = 56.200eV
Energy per atom: Epot =49.889eV Ekin = 6.312eV (T=525.091K) Etot = 56.201eV
Energy per atom: Epot =49.967eV Ekin = 6.236eV (T=518.716K) Etot = 56.203eV
Energy per atom: Epot =49.515eV Ekin = 6.680eV (T=555.693K) Etot = 56.195eV
Energy per atom: Epot =49.040eV Ekin = 7.157eV (T=595.330K) Etot = 56.196eV
Energy per atom: Epot =48.086eV Ekin = 8.107eV (T=674.376K) Etot = 56.193eV
Energy per atom: Epot =49.500eV Ekin = 6.702eV (T=557.522K) Etot = 56.202eV
Energy per atom: Epot =50.610eV Ekin = 5.598eV (T=465.646K) Etot = 56.208eV
Energy per atom: Epot =50.188eV Ekin = 6.016eV (T=500.463K) Etot = 56.204eV
Energy per atom: Epot =49.796eV Ekin = 6.409eV (T=533.143K) Etot = 56.205eV
Energy per atom: Epot =49.063eV Ekin = 7.134eV (T=593.454K) Etot = 56.197eV
Energy per atom: Epot =49.729eV Ekin = 6.468eV (T=538.036K) Etot = 56.197eV
Energy per atom: Epot =49.744eV Ekin = 6.455eV (T=536.974K) Etot = 56.199eV
Energy per atom: Epot =49.617eV Ekin = 6.580eV (T=547.374K) Etot = 56.197eV
Energy per atom: Epot =49.430eV Ekin = 6.766eV (T=562.863K) Etot = 56.196eV
Energy per atom: Epot =50.734eV Ekin = 5.472eV (T=455.181K) Etot = 56.206eV
Energy per atom: Epot =50.066eV Ekin = 6.135eV (T=510.325K) Etot = 56.201eV
Energy per atom: Epot =49.868eV Ekin = 6.328eV (T=526.404K) Etot = 56.196eV
Energy per atom: Epot =50.163eV Ekin = 6.038eV (T=502.291K) Etot = 56.201eV
Energy per atom: Epot =49.650eV Ekin = 6.551eV (T=544.938K) Etot = 56.201eV
Energy per atom: Epot =50.033eV Ekin = 6.164eV (T=512.777K) Etot = 56.197eV
Energy per atom: Epot =49.766eV Ekin = 6.430eV (T=534.902K) Etot = 56.197eV
Energy per atom: Epot =50.322eV Ekin = 5.878eV (T=488.957K) Etot = 56.200eV
Energy per atom: Epot =50.055eV Ekin = 6.145eV (T=511.161K) Etot = 56.200eV
Energy per atom: Epot =49.544eV Ekin = 6.652eV (T=553.382K) Etot = 56.196eV
Energy per atom: Epot =50.661eV Ekin = 5.543eV (T=461.067K) Etot = 56.204eV
Energy per atom: Epot =50.186eV Ekin = 6.013eV (T=500.192K) Etot = 56.199eV
Energy per atom: Epot =50.057eV Ekin = 6.140eV (T=510.757K) Etot = 56.197eV
Energy per atom: Epot =50.623eV Ekin = 5.579eV (T=464.134K) Etot = 56.202eV
Energy per atom: Epot =49.995eV Ekin = 6.205eV (T=516.211K) Etot = 56.201eV
Energy per atom: Epot =49.885eV Ekin = 6.313eV (T=525.154K) Etot = 56.198eV
Energy per atom: Epot =49.436eV Ekin = 6.759eV (T=562.227K) Etot = 56.195eV
Energy per atom: Epot =49.709eV Ekin = 6.492eV (T=540.039K) Etot = 56.201eV
Energy per atom: Epot =50.303eV Ekin = 5.901eV (T=490.863K) Etot = 56.203eV
Energy per atom: Epot =49.929eV Ekin = 6.267eV (T=521.343K) Etot = 56.196eV
Energy per atom: Epot =50.042eV Ekin = 6.161eV (T=512.472K) Etot = 56.203eV
Energy per atom: Epot =49.190eV Ekin = 7.008eV (T=582.978K) Etot = 56.198eV
Energy per atom: Epot =49.602eV Ekin = 6.598eV (T=548.880K) Etot = 56.200eV
Energy per atom: Epot =49.027eV Ekin = 7.170eV (T=596.420K) Etot = 56.197eV
Energy per atom: Epot =49.505eV Ekin = 6.693eV (T=556.789K) Etot = 56.199eV
Energy per atom: Epot =49.120eV Ekin = 7.078eV (T=588.753K) Etot = 56.197eV
Energy per atom: Epot =49.410eV Ekin = 6.790eV (T=564.829K) Etot = 56.199eV
Energy per atom: Epot =49.774eV Ekin = 6.429eV (T=534.807K) Etot = 56.203eV
Energy per atom: Epot =49.602eV Ekin = 6.600eV (T=549.014K) Etot = 56.202eV
Energy per atom: Epot =49.587eV Ekin = 6.612eV (T=550.012K) Etot = 56.199eV
Energy per atom: Epot =49.274eV Ekin = 6.922eV (T=575.780K) Etot = 56.196eV
Energy per atom: Epot =49.790eV Ekin = 6.410eV (T=533.255K) Etot = 56.200eV
Energy per atom: Epot =49.956eV Ekin = 6.246eV (T=519.552K) Etot = 56.202eV
Energy per atom: Epot =50.301eV Ekin = 5.901eV (T=490.856K) Etot = 56.201eV
Energy per atom: Epot =49.751eV Ekin = 6.443eV (T=535.974K) Etot = 56.194eV
Energy per atom: Epot =49.620eV Ekin = 6.573eV (T=546.810K) Etot = 56.193eV
Energy per atom: Epot =49.614eV Ekin = 6.586eV (T=547.877K) Etot = 56.200eV
Energy per atom: Epot =50.158eV Ekin = 6.043eV (T=502.692K) Etot = 56.201eV
Energy per atom: Epot =49.152eV Ekin = 7.036eV (T=585.310K) Etot = 56.189eV
Energy per atom: Epot =49.151eV Ekin = 7.040eV (T=585.608K) Etot = 56.191eV
Energy per atom: Epot =49.679eV Ekin = 6.520eV (T=542.381K) Etot = 56.199eV
Energy per atom: Epot =49.688eV Ekin = 6.508eV (T=541.354K) Etot = 56.196eV
Energy per atom: Epot =49.900eV Ekin = 6.297eV (T=523.787K) Etot = 56.196eV
Energy per atom: Epot =49.620eV Ekin = 6.576eV (T=547.068K) Etot = 56.196eV
Energy per atom: Epot =50.211eV Ekin = 5.992eV (T=498.474K) Etot = 56.203eV
Energy per atom: Epot =49.547eV Ekin = 6.656eV (T=553.674K) Etot = 56.203eV
Energy per atom: Epot =49.461eV Ekin = 6.737eV (T=560.430K) Etot = 56.198eV
Energy per atom: Epot =50.036eV Ekin = 6.163eV (T=512.709K) Etot = 56.200eV
Energy per atom: Epot =48.773eV Ekin = 7.423eV (T=617.469K) Etot = 56.195eV
Energy per atom: Epot =49.641eV Ekin = 6.561eV (T=545.761K) Etot = 56.202eV
Energy per atom: Epot =50.504eV Ekin = 5.701eV (T=474.282K) Etot = 56.206eV
Energy per atom: Epot =49.371eV Ekin = 6.826eV (T=567.854K) Etot = 56.197eV
Energy per atom: Epot =50.075eV Ekin = 6.122eV (T=509.249K) Etot = 56.197eV
Energy per atom: Epot =50.219eV Ekin = 5.982eV (T=497.643K) Etot = 56.201eV
Energy per atom: Epot =49.254eV Ekin = 6.945eV (T=577.698K) Etot = 56.199eV
Energy per atom: Epot =49.666eV Ekin = 6.537eV (T=543.825K) Etot = 56.203eV
Energy per atom: Epot =50.502eV Ekin = 5.701eV (T=474.280K) Etot = 56.204eV
Energy per atom: Epot =49.251eV Ekin = 6.945eV (T=577.763K) Etot = 56.197eV
Energy per atom: Epot =49.465eV Ekin = 6.731eV (T=559.965K) Etot = 56.196eV
Energy per atom: Epot =49.669eV Ekin = 6.527eV (T=542.956K) Etot = 56.196eV
Energy per atom: Epot =49.351eV Ekin = 6.842eV (T=569.202K) Etot = 56.194eV
Energy per atom: Epot =50.172eV Ekin = 6.027eV (T=501.332K) Etot = 56.199eV
Energy per atom: Epot =49.709eV Ekin = 6.494eV (T=540.222K) Etot = 56.203eV
Energy per atom: Epot =49.254eV Ekin = 6.942eV (T=577.512K) Etot = 56.196eV
Energy per atom: Epot =49.748eV Ekin = 6.447eV (T=536.278K) Etot = 56.195eV
Energy per atom: Epot =49.093eV Ekin = 7.104eV (T=590.957K) Etot = 56.197eV
Energy per atom: Epot =49.323eV Ekin = 6.879eV (T=572.237K) Etot = 56.202eV
Energy per atom: Epot =49.402eV Ekin = 6.794eV (T=565.163K) Etot = 56.196eV
Energy per atom: Epot =49.681eV Ekin = 6.516eV (T=542.048K) Etot = 56.197eV
Energy per atom: Epot =50.065eV Ekin = 6.139eV (T=510.705K) Etot = 56.204eV
Energy per atom: Epot =49.676eV Ekin = 6.528eV (T=543.024K) Etot = 56.203eV
Energy per atom: Epot =49.351eV Ekin = 6.846eV (T=569.522K) Etot = 56.197eV
Energy per atom: Epot =49.263eV Ekin = 6.932eV (T=576.682K) Etot = 56.196eV
Energy per atom: Epot =49.330eV Ekin = 6.870eV (T=571.530K) Etot = 56.200eV
Energy per atom: Epot =50.214eV Ekin = 5.989eV (T=498.220K) Etot = 56.203eV
Energy per atom: Epot =49.539eV Ekin = 6.660eV (T=554.054K) Etot = 56.199eV
Energy per atom: Epot =48.987eV Ekin = 7.212eV (T=599.936K) Etot = 56.199eV
Energy per atom: Epot =49.374eV Ekin = 6.831eV (T=568.225K) Etot = 56.205eV
Energy per atom: Epot =49.349eV Ekin = 6.854eV (T=570.154K) Etot = 56.203eV
Energy per atom: Epot =49.281eV Ekin = 6.914eV (T=575.170K) Etot = 56.195eV
Energy per atom: Epot =49.810eV Ekin = 6.387eV (T=531.342K) Etot = 56.197eV
Energy per atom: Epot =49.417eV Ekin = 6.780eV (T=564.041K) Etot = 56.197eV
Energy per atom: Epot =49.564eV Ekin = 6.636eV (T=551.996K) Etot = 56.199eV
Energy per atom: Epot =49.497eV Ekin = 6.701eV (T=557.424K) Etot = 56.198eV
Energy per atom: Epot =50.263eV Ekin = 5.938eV (T=493.973K) Etot = 56.202eV
Energy per atom: Epot =49.435eV Ekin = 6.762eV (T=562.496K) Etot = 56.197eV
Energy per atom: Epot =50.106eV Ekin = 6.096eV (T=507.111K) Etot = 56.202eV
Energy per atom: Epot =49.802eV Ekin = 6.398eV (T=532.230K) Etot = 56.201eV
Energy per atom: Epot =49.570eV Ekin = 6.631eV (T=551.617K) Etot = 56.201eV
Energy per atom: Epot =49.783eV Ekin = 6.422eV (T=534.203K) Etot = 56.205eV
Energy per atom: Epot =49.836eV Ekin = 6.361eV (T=529.190K) Etot = 56.198eV
Energy per atom: Epot =49.866eV Ekin = 6.333eV (T=526.783K) Etot = 56.198eV
Energy per atom: Epot =50.576eV Ekin = 5.633eV (T=468.597K) Etot = 56.209eV
Energy per atom: Epot =48.632eV Ekin = 7.563eV (T=629.121K) Etot = 56.195eV
Energy per atom: Epot =49.703eV Ekin = 6.497eV (T=540.428K) Etot = 56.199eV
Energy per atom: Epot =49.274eV Ekin = 6.923eV (T=575.877K) Etot = 56.196eV
Energy per atom: Epot =49.094eV Ekin = 7.102eV (T=590.769K) Etot = 56.196eV
Energy per atom: Epot =49.569eV Ekin = 6.635eV (T=551.939K) Etot = 56.204eV
Energy per atom: Epot =48.728eV Ekin = 7.469eV (T=621.352K) Etot = 56.197eV
Energy per atom: Epot =49.141eV Ekin = 7.057eV (T=587.019K) Etot = 56.198eV
Energy per atom: Epot =50.241eV Ekin = 5.960eV (T=495.814K) Etot = 56.201eV
Energy per atom: Epot =49.297eV Ekin = 6.899eV (T=573.876K) Etot = 56.196eV
Energy per atom: Epot =48.934eV Ekin = 7.268eV (T=604.627K) Etot = 56.202eV
Energy per atom: Epot =49.212eV Ekin = 6.988eV (T=581.285K) Etot = 56.199eV
Energy per atom: Epot =49.909eV Ekin = 6.294eV (T=523.560K) Etot = 56.203eV
Energy per atom: Epot =48.643eV Ekin = 7.554eV (T=628.426K) Etot = 56.197eV
Energy per atom: Epot =50.220eV Ekin = 5.985eV (T=497.869K) Etot = 56.205eV
Energy per atom: Epot =49.887eV Ekin = 6.315eV (T=525.342K) Etot = 56.203eV
Energy per atom: Epot =48.933eV Ekin = 7.268eV (T=604.579K) Etot = 56.201eV
Energy per atom: Epot =49.870eV Ekin = 6.333eV (T=526.826K) Etot = 56.203eV
Energy per atom: Epot =48.853eV Ekin = 7.345eV (T=610.998K) Etot = 56.198eV
Energy per atom: Epot =48.653eV Ekin = 7.544eV (T=627.597K) Etot = 56.198eV
Energy per atom: Epot =48.467eV Ekin = 7.730eV (T=642.992K) Etot = 56.196eV
Energy per atom: Epot =48.780eV Ekin = 7.415eV (T=616.798K) Etot = 56.194eV
Energy per atom: Epot =50.253eV Ekin = 5.949eV (T=494.887K) Etot = 56.202eV
Energy per atom: Epot =49.643eV Ekin = 6.555eV (T=545.261K) Etot = 56.198eV
Energy per atom: Epot =49.032eV Ekin = 7.164eV (T=595.922K) Etot = 56.196eV
Energy per atom: Epot =49.448eV Ekin = 6.750eV (T=561.535K) Etot = 56.198eV
Energy per atom: Epot =49.577eV Ekin = 6.624eV (T=550.999K) Etot = 56.201eV
Energy per atom: Epot =49.620eV Ekin = 6.578eV (T=547.224K) Etot = 56.199eV
Energy per atom: Epot =49.186eV Ekin = 7.011eV (T=583.226K) Etot = 56.197eV
Energy per atom: Epot =49.376eV Ekin = 6.824eV (T=567.695K) Etot = 56.200eV
Energy per atom: Epot =48.483eV Ekin = 7.713eV (T=641.608K) Etot = 56.196eV
Energy per atom: Epot =49.697eV Ekin = 6.501eV (T=540.810K) Etot = 56.198eV
Energy per atom: Epot =49.806eV Ekin = 6.392eV (T=531.715K) Etot = 56.198eV
Energy per atom: Epot =49.564eV Ekin = 6.639eV (T=552.291K) Etot = 56.203eV
Energy per atom: Epot =48.915eV Ekin = 7.277eV (T=605.388K) Etot = 56.193eV
Energy per atom: Epot =48.889eV Ekin = 7.307eV (T=607.815K) Etot = 56.195eV
Energy per atom: Epot =49.395eV Ekin = 6.805eV (T=566.087K) Etot = 56.200eV
Energy per atom: Epot =49.607eV Ekin = 6.596eV (T=548.734K) Etot = 56.203eV
Energy per atom: Epot =48.438eV Ekin = 7.756eV (T=645.190K) Etot = 56.194eV
Energy per atom: Epot =48.805eV Ekin = 7.391eV (T=614.861K) Etot = 56.197eV
Energy per atom: Epot =49.143eV Ekin = 7.052eV (T=586.652K) Etot = 56.195eV
Energy per atom: Epot =48.881eV Ekin = 7.313eV (T=608.333K) Etot = 56.194eV
Energy per atom: Epot =48.271eV Ekin = 7.919eV (T=658.774K) Etot = 56.190eV
Energy per atom: Epot =49.233eV Ekin = 6.966eV (T=579.502K) Etot = 56.199eV
Energy per atom: Epot =48.948eV Ekin = 7.248eV (T=602.908K) Etot = 56.195eV
Energy per atom: Epot =49.414eV Ekin = 6.785eV (T=564.449K) Etot = 56.199eV
Energy per atom: Epot =48.409eV Ekin = 7.787eV (T=647.784K) Etot = 56.196eV
Energy per atom: Epot =48.588eV Ekin = 7.604eV (T=632.555K) Etot = 56.192eV
Energy per atom: Epot =49.366eV Ekin = 6.829eV (T=568.103K) Etot = 56.196eV
Energy per atom: Epot =48.355eV Ekin = 7.839eV (T=652.067K) Etot = 56.193eV
Energy per atom: Epot =49.362eV Ekin = 6.832eV (T=568.319K) Etot = 56.194eV
Energy per atom: Epot =48.999eV Ekin = 7.192eV (T=598.271K) Etot = 56.191eV
Energy per atom: Epot =48.860eV Ekin = 7.335eV (T=610.138K) Etot = 56.195eV
Energy per atom: Epot =48.612eV Ekin = 7.581eV (T=630.648K) Etot = 56.193eV
Energy per atom: Epot =49.078eV Ekin = 7.117eV (T=592.055K) Etot = 56.195eV
Energy per atom: Epot =48.518eV Ekin = 7.680eV (T=638.832K) Etot = 56.198eV
Energy per atom: Epot =49.177eV Ekin = 7.020eV (T=583.946K) Etot = 56.196eV
Energy per atom: Epot =49.675eV Ekin = 6.519eV (T=542.298K) Etot = 56.194eV
Energy per atom: Epot =49.722eV Ekin = 6.472eV (T=538.421K) Etot = 56.195eV
Energy per atom: Epot =49.419eV Ekin = 6.779eV (T=563.934K) Etot = 56.198eV
Energy per atom: Epot =48.613eV Ekin = 7.580eV (T=630.574K) Etot = 56.193eV
Energy per atom: Epot =48.680eV Ekin = 7.513eV (T=624.993K) Etot = 56.193eV
Energy per atom: Epot =49.365eV Ekin = 6.829eV (T=568.073K) Etot = 56.194eV
Energy per atom: Epot =48.860eV Ekin = 7.335eV (T=610.157K) Etot = 56.195eV
Energy per atom: Epot =48.735eV Ekin = 7.456eV (T=620.265K) Etot = 56.191eV
Energy per atom: Epot =49.212eV Ekin = 6.982eV (T=580.775K) Etot = 56.193eV
Energy per atom: Epot =49.006eV Ekin = 7.190eV (T=598.099K) Etot = 56.196eV
Energy per atom: Epot =48.800eV Ekin = 7.396eV (T=615.244K) Etot = 56.196eV
Energy per atom: Epot =48.248eV Ekin = 7.948eV (T=661.136K) Etot = 56.195eV
Energy per atom: Epot =48.665eV Ekin = 7.533eV (T=626.672K) Etot = 56.198eV
Energy per atom: Epot =49.068eV Ekin = 7.131eV (T=593.209K) Etot = 56.199eV
Energy per atom: Epot =49.324eV Ekin = 6.875eV (T=571.923K) Etot = 56.200eV
Energy per atom: Epot =48.810eV Ekin = 7.392eV (T=614.933K) Etot = 56.202eV
Energy per atom: Epot =49.543eV Ekin = 6.664eV (T=554.348K) Etot = 56.207eV
Energy per atom: Epot =48.469eV Ekin = 7.726eV (T=642.694K) Etot = 56.195eV
Energy per atom: Epot =49.319eV Ekin = 6.880eV (T=572.289K) Etot = 56.198eV
Energy per atom: Epot =49.036eV Ekin = 7.164eV (T=595.928K) Etot = 56.200eV
Energy per atom: Epot =48.778eV Ekin = 7.422eV (T=617.411K) Etot = 56.200eV
Energy per atom: Epot =49.366eV Ekin = 6.837eV (T=568.780K) Etot = 56.203eV
Energy per atom: Epot =48.511eV Ekin = 7.683eV (T=639.160K) Etot = 56.195eV
Energy per atom: Epot =48.721eV Ekin = 7.471eV (T=621.494K) Etot = 56.193eV
Energy per atom: Epot =48.970eV Ekin = 7.229eV (T=601.395K) Etot = 56.199eV
Energy per atom: Epot =50.172eV Ekin = 6.036eV (T=502.112K) Etot = 56.208eV
Energy per atom: Epot =49.004eV Ekin = 7.190eV (T=598.104K) Etot = 56.194eV
Energy per atom: Epot =48.608eV Ekin = 7.585eV (T=630.951K) Etot = 56.193eV
After running the simulation, use ASE’s 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?