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 = 155.932eV (T=301.587K) Etot = 153.528eV
Energy per atom: Epot =118.453eV Ekin = 35.865eV (T=69.367K) Etot = 154.319eV
Energy per atom: Epot =78.106eV Ekin = 76.072eV (T=147.130K) Etot = 154.178eV
Energy per atom: Epot =72.044eV Ekin = 81.993eV (T=158.582K) Etot = 154.037eV
Energy per atom: Epot =68.938eV Ekin = 85.033eV (T=164.461K) Etot = 153.971eV
Energy per atom: Epot =81.195eV Ekin = 72.941eV (T=141.074K) Etot = 154.136eV
Energy per atom: Epot =78.206eV Ekin = 75.917eV (T=146.829K) Etot = 154.123eV
Energy per atom: Epot =73.856eV Ekin = 80.186eV (T=155.087K) Etot = 154.042eV
Energy per atom: Epot =72.565eV Ekin = 81.476eV (T=157.582K) Etot = 154.042eV
Energy per atom: Epot =79.639eV Ekin = 74.482eV (T=144.054K) Etot = 154.120eV
Energy per atom: Epot =75.168eV Ekin = 78.919eV (T=152.635K) Etot = 154.086eV
Energy per atom: Epot =74.967eV Ekin = 79.103eV (T=152.992K) Etot = 154.070eV
Energy per atom: Epot =76.613eV Ekin = 77.464eV (T=149.821K) Etot = 154.077eV
Energy per atom: Epot =77.125eV Ekin = 76.962eV (T=148.851K) Etot = 154.087eV
Energy per atom: Epot =75.481eV Ekin = 78.599eV (T=152.017K) Etot = 154.079eV
Energy per atom: Epot =76.070eV Ekin = 78.021eV (T=150.899K) Etot = 154.091eV
Energy per atom: Epot =74.451eV Ekin = 79.617eV (T=153.986K) Etot = 154.068eV
Energy per atom: Epot =78.622eV Ekin = 75.464eV (T=145.955K) Etot = 154.086eV
Energy per atom: Epot =74.279eV Ekin = 79.807eV (T=154.354K) Etot = 154.086eV
Energy per atom: Epot =75.090eV Ekin = 78.979eV (T=152.753K) Etot = 154.070eV
Energy per atom: Epot =79.323eV Ekin = 74.775eV (T=144.622K) Etot = 154.098eV
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 =602.661eV Ekin = 83.846eV (T=162.165K) Etot = 686.507eV
Energy per atom: Epot =675.644eV Ekin = 142.987eV (T=276.549K) Etot = 818.631eV
Energy per atom: Epot =731.342eV Ekin = 205.898eV (T=398.225K) Etot = 937.241eV
Energy per atom: Epot =786.397eV Ekin = 262.864eV (T=508.403K) Etot = 1049.262eV
Energy per atom: Epot =840.457eV Ekin = 307.273eV (T=594.292K) Etot = 1147.730eV
Energy per atom: Epot =893.242eV Ekin = 343.086eV (T=663.558K) Etot = 1236.328eV
Energy per atom: Epot =923.404eV Ekin = 388.940eV (T=752.245K) Etot = 1312.345eV
Energy per atom: Epot =972.349eV Ekin = 418.781eV (T=809.959K) Etot = 1391.130eV
Energy per atom: Epot =1005.978eV Ekin = 443.534eV (T=857.833K) Etot = 1449.512eV
Energy per atom: Epot =1037.746eV Ekin = 477.054eV (T=922.664K) Etot = 1514.800eV
Energy per atom: Epot =1073.312eV Ekin = 503.028eV (T=972.900K) Etot = 1576.340eV
Energy per atom: Epot =1115.343eV Ekin = 512.511eV (T=991.240K) Etot = 1627.854eV
Energy per atom: Epot =1143.532eV Ekin = 531.238eV (T=1027.460K) Etot = 1674.770eV
Energy per atom: Epot =1178.117eV Ekin = 547.167eV (T=1058.268K) Etot = 1725.284eV
Energy per atom: Epot =1208.977eV Ekin = 561.134eV (T=1085.281K) Etot = 1770.111eV
Energy per atom: Epot =1230.404eV Ekin = 581.085eV (T=1123.869K) Etot = 1811.489eV
Energy per atom: Epot =1258.671eV Ekin = 582.552eV (T=1126.706K) Etot = 1841.222eV
Energy per atom: Epot =1286.190eV Ekin = 591.247eV (T=1143.523K) Etot = 1877.437eV
Energy per atom: Epot =1315.497eV Ekin = 593.274eV (T=1147.444K) Etot = 1908.771eV
Energy per atom: Epot =1339.607eV Ekin = 602.989eV (T=1166.233K) Etot = 1942.597eV
Energy per atom: Epot =1346.867eV Ekin = 627.219eV (T=1213.095K) Etot = 1974.086eV
Energy per atom: Epot =1384.369eV Ekin = 625.056eV (T=1208.912K) Etot = 2009.425eV
Energy per atom: Epot =1393.246eV Ekin = 646.357eV (T=1250.111K) Etot = 2039.603eV
Energy per atom: Epot =1418.437eV Ekin = 642.780eV (T=1243.192K) Etot = 2061.217eV
Energy per atom: Epot =1430.404eV Ekin = 654.591eV (T=1266.037K) Etot = 2084.995eV
Energy per atom: Epot =1453.300eV Ekin = 653.965eV (T=1264.826K) Etot = 2107.266eV
Energy per atom: Epot =1461.007eV Ekin = 665.228eV (T=1286.608K) Etot = 2126.234eV
Energy per atom: Epot =1469.396eV Ekin = 677.549eV (T=1310.440K) Etot = 2146.945eV
Energy per atom: Epot =1484.789eV Ekin = 676.783eV (T=1308.958K) Etot = 2161.572eV
Energy per atom: Epot =1487.475eV Ekin = 702.854eV (T=1359.382K) Etot = 2190.329eV
Energy per atom: Epot =1503.358eV Ekin = 691.325eV (T=1337.083K) Etot = 2194.683eV
Energy per atom: Epot =1510.063eV Ekin = 704.387eV (T=1362.347K) Etot = 2214.450eV
Energy per atom: Epot =1531.318eV Ekin = 697.690eV (T=1349.393K) Etot = 2229.008eV
Energy per atom: Epot =1530.178eV Ekin = 710.534eV (T=1374.235K) Etot = 2240.713eV
Energy per atom: Epot =1563.268eV Ekin = 699.979eV (T=1353.821K) Etot = 2263.247eV
Energy per atom: Epot =1569.747eV Ekin = 707.632eV (T=1368.622K) Etot = 2277.379eV
Energy per atom: Epot =1571.676eV Ekin = 711.805eV (T=1376.693K) Etot = 2283.481eV
Energy per atom: Epot =1576.384eV Ekin = 717.115eV (T=1386.963K) Etot = 2293.499eV
Energy per atom: Epot =1599.450eV Ekin = 701.204eV (T=1356.189K) Etot = 2300.654eV
Energy per atom: Epot =1610.984eV Ekin = 698.263eV (T=1350.501K) Etot = 2309.247eV
Energy per atom: Epot =1613.762eV Ekin = 709.783eV (T=1372.781K) Etot = 2323.544eV
Energy per atom: Epot =1612.257eV Ekin = 726.730eV (T=1405.559K) Etot = 2338.987eV
Energy per atom: Epot =1617.112eV Ekin = 726.293eV (T=1404.713K) Etot = 2343.405eV
Energy per atom: Epot =1637.353eV Ekin = 707.185eV (T=1367.756K) Etot = 2344.537eV
Energy per atom: Epot =1660.985eV Ekin = 696.095eV (T=1346.309K) Etot = 2357.080eV
Energy per atom: Epot =1659.778eV Ekin = 711.289eV (T=1375.694K) Etot = 2371.067eV
Energy per atom: Epot =1658.715eV Ekin = 723.415eV (T=1399.148K) Etot = 2382.131eV
Energy per atom: Epot =1667.558eV Ekin = 725.660eV (T=1403.489K) Etot = 2393.218eV
Energy per atom: Epot =1687.593eV Ekin = 718.694eV (T=1390.016K) Etot = 2406.287eV
Energy per atom: Epot =1678.231eV Ekin = 723.032eV (T=1398.406K) Etot = 2401.262eV
Energy per atom: Epot =1697.806eV Ekin = 712.629eV (T=1378.287K) Etot = 2410.435eV
Energy per atom: Epot =1704.464eV Ekin = 708.937eV (T=1371.146K) Etot = 2413.401eV
Energy per atom: Epot =1717.959eV Ekin = 705.703eV (T=1364.891K) Etot = 2423.662eV
Energy per atom: Epot =1710.094eV Ekin = 718.383eV (T=1389.415K) Etot = 2428.477eV
Energy per atom: Epot =1717.695eV Ekin = 728.492eV (T=1408.967K) Etot = 2446.187eV
Energy per atom: Epot =1723.843eV Ekin = 740.246eV (T=1431.700K) Etot = 2464.089eV
Energy per atom: Epot =1732.734eV Ekin = 722.498eV (T=1397.373K) Etot = 2455.232eV
Energy per atom: Epot =1740.944eV Ekin = 727.131eV (T=1406.335K) Etot = 2468.075eV
Energy per atom: Epot =1749.147eV Ekin = 728.547eV (T=1409.073K) Etot = 2477.694eV
Energy per atom: Epot =1747.457eV Ekin = 745.786eV (T=1442.416K) Etot = 2493.243eV
Energy per atom: Epot =1772.038eV Ekin = 741.529eV (T=1434.182K) Etot = 2513.567eV
Energy per atom: Epot =1784.945eV Ekin = 734.173eV (T=1419.955K) Etot = 2519.118eV
Energy per atom: Epot =1791.476eV Ekin = 741.892eV (T=1434.884K) Etot = 2533.368eV
Energy per atom: Epot =1778.674eV Ekin = 756.772eV (T=1463.664K) Etot = 2535.446eV
Energy per atom: Epot =1768.326eV Ekin = 772.204eV (T=1493.509K) Etot = 2540.530eV
Energy per atom: Epot =1787.652eV Ekin = 752.750eV (T=1455.884K) Etot = 2540.402eV
Energy per atom: Epot =1797.224eV Ekin = 750.261eV (T=1451.069K) Etot = 2547.484eV
Energy per atom: Epot =1815.867eV Ekin = 745.369eV (T=1441.609K) Etot = 2561.236eV
Energy per atom: Epot =1813.040eV Ekin = 757.128eV (T=1464.352K) Etot = 2570.169eV
Energy per atom: Epot =1827.820eV Ekin = 744.378eV (T=1439.692K) Etot = 2572.198eV
Energy per atom: Epot =1838.934eV Ekin = 740.793eV (T=1432.759K) Etot = 2579.727eV
Energy per atom: Epot =1848.993eV Ekin = 744.612eV (T=1440.144K) Etot = 2593.604eV
Energy per atom: Epot =1851.344eV Ekin = 742.552eV (T=1436.160K) Etot = 2593.896eV
Energy per atom: Epot =1866.105eV Ekin = 737.733eV (T=1426.839K) Etot = 2603.837eV
Energy per atom: Epot =1864.005eV Ekin = 738.565eV (T=1428.450K) Etot = 2602.570eV
Energy per atom: Epot =1859.019eV Ekin = 767.011eV (T=1483.465K) Etot = 2626.029eV
Energy per atom: Epot =1886.671eV Ekin = 746.807eV (T=1444.390K) Etot = 2633.479eV
Energy per atom: Epot =1887.837eV Ekin = 757.183eV (T=1464.457K) Etot = 2645.020eV
Energy per atom: Epot =1898.975eV Ekin = 744.660eV (T=1440.237K) Etot = 2643.635eV
Energy per atom: Epot =1900.493eV Ekin = 738.886eV (T=1429.071K) Etot = 2639.379eV
Energy per atom: Epot =1905.375eV Ekin = 749.870eV (T=1450.313K) Etot = 2655.245eV
Energy per atom: Epot =1896.370eV Ekin = 750.918eV (T=1452.340K) Etot = 2647.288eV
Energy per atom: Epot =1909.766eV Ekin = 750.508eV (T=1451.548K) Etot = 2660.274eV
Energy per atom: Epot =1913.657eV Ekin = 744.477eV (T=1439.883K) Etot = 2658.133eV
Energy per atom: Epot =1911.957eV Ekin = 745.853eV (T=1442.544K) Etot = 2657.809eV
Energy per atom: Epot =1913.585eV Ekin = 751.664eV (T=1453.783K) Etot = 2665.249eV
Energy per atom: Epot =1908.181eV Ekin = 756.531eV (T=1463.197K) Etot = 2664.712eV
Energy per atom: Epot =1906.380eV Ekin = 758.595eV (T=1467.189K) Etot = 2664.975eV
Energy per atom: Epot =1906.317eV Ekin = 767.559eV (T=1484.526K) Etot = 2673.876eV
Energy per atom: Epot =1916.279eV Ekin = 768.788eV (T=1486.902K) Etot = 2685.067eV
Energy per atom: Epot =1937.938eV Ekin = 750.608eV (T=1451.742K) Etot = 2688.546eV
Energy per atom: Epot =1924.766eV Ekin = 772.311eV (T=1493.717K) Etot = 2697.077eV
Energy per atom: Epot =1924.463eV Ekin = 775.289eV (T=1499.476K) Etot = 2699.752eV
Energy per atom: Epot =1940.096eV Ekin = 751.730eV (T=1453.912K) Etot = 2691.826eV
Energy per atom: Epot =1932.723eV Ekin = 762.807eV (T=1475.334K) Etot = 2695.530eV
Energy per atom: Epot =1945.111eV Ekin = 753.777eV (T=1457.870K) Etot = 2698.888eV
Energy per atom: Epot =1935.443eV Ekin = 760.949eV (T=1471.742K) Etot = 2696.392eV
Energy per atom: Epot =1937.629eV Ekin = 755.426eV (T=1461.059K) Etot = 2693.054eV
Energy per atom: Epot =1940.530eV Ekin = 758.344eV (T=1466.703K) Etot = 2698.874eV
Energy per atom: Epot =1936.634eV Ekin = 754.637eV (T=1459.533K) Etot = 2691.271eV
Energy per atom: Epot =1940.761eV Ekin = 757.745eV (T=1465.544K) Etot = 2698.506eV
Energy per atom: Epot =1958.234eV Ekin = 750.949eV (T=1452.402K) Etot = 2709.184eV
Energy per atom: Epot =1950.384eV Ekin = 762.519eV (T=1474.777K) Etot = 2712.903eV
Energy per atom: Epot =1964.873eV Ekin = 762.641eV (T=1475.014K) Etot = 2727.514eV
Energy per atom: Epot =1967.033eV Ekin = 772.651eV (T=1494.374K) Etot = 2739.684eV
Energy per atom: Epot =1969.012eV Ekin = 772.029eV (T=1493.171K) Etot = 2741.041eV
Energy per atom: Epot =1974.602eV Ekin = 766.260eV (T=1482.013K) Etot = 2740.862eV
Energy per atom: Epot =1980.808eV Ekin = 771.615eV (T=1492.370K) Etot = 2752.423eV
Energy per atom: Epot =1975.882eV Ekin = 774.525eV (T=1497.998K) Etot = 2750.407eV
Energy per atom: Epot =1978.152eV Ekin = 769.186eV (T=1487.673K) Etot = 2747.338eV
Energy per atom: Epot =1990.664eV Ekin = 759.147eV (T=1468.256K) Etot = 2749.810eV
Energy per atom: Epot =1989.274eV Ekin = 762.857eV (T=1475.432K) Etot = 2752.131eV
Energy per atom: Epot =1984.071eV Ekin = 771.858eV (T=1492.840K) Etot = 2755.929eV
Energy per atom: Epot =1986.307eV Ekin = 779.012eV (T=1506.677K) Etot = 2765.319eV
Energy per atom: Epot =1998.419eV Ekin = 767.805eV (T=1485.001K) Etot = 2766.223eV
Energy per atom: Epot =1990.611eV Ekin = 769.851eV (T=1488.959K) Etot = 2760.462eV
Energy per atom: Epot =1989.123eV Ekin = 771.153eV (T=1491.478K) Etot = 2760.277eV
Energy per atom: Epot =1994.409eV Ekin = 762.557eV (T=1474.852K) Etot = 2756.966eV
Energy per atom: Epot =2007.758eV Ekin = 742.560eV (T=1436.176K) Etot = 2750.318eV
Energy per atom: Epot =1996.913eV Ekin = 749.619eV (T=1449.828K) Etot = 2746.531eV
Energy per atom: Epot =1986.507eV Ekin = 765.348eV (T=1480.250K) Etot = 2751.855eV
Energy per atom: Epot =1989.806eV Ekin = 764.027eV (T=1477.694K) Etot = 2753.833eV
Energy per atom: Epot =2000.298eV Ekin = 759.082eV (T=1468.130K) Etot = 2759.379eV
Energy per atom: Epot =1999.006eV Ekin = 762.989eV (T=1475.688K) Etot = 2761.995eV
Energy per atom: Epot =1992.513eV Ekin = 772.926eV (T=1494.906K) Etot = 2765.439eV
Energy per atom: Epot =2005.009eV Ekin = 757.152eV (T=1464.398K) Etot = 2762.161eV
Energy per atom: Epot =2009.989eV Ekin = 757.676eV (T=1465.410K) Etot = 2767.664eV
Energy per atom: Epot =2002.840eV Ekin = 768.291eV (T=1485.941K) Etot = 2771.131eV
Energy per atom: Epot =2010.001eV Ekin = 758.925eV (T=1467.828K) Etot = 2768.926eV
Energy per atom: Epot =2013.646eV Ekin = 764.716eV (T=1479.026K) Etot = 2778.362eV
Energy per atom: Epot =2005.661eV Ekin = 767.988eV (T=1485.355K) Etot = 2773.649eV
Energy per atom: Epot =2004.613eV Ekin = 773.689eV (T=1496.381K) Etot = 2778.302eV
Energy per atom: Epot =2005.876eV Ekin = 773.679eV (T=1496.362K) Etot = 2779.555eV
Energy per atom: Epot =1999.812eV Ekin = 772.759eV (T=1494.584K) Etot = 2772.571eV
Energy per atom: Epot =2004.694eV Ekin = 766.266eV (T=1482.025K) Etot = 2770.959eV
Energy per atom: Epot =1985.011eV Ekin = 787.175eV (T=1522.465K) Etot = 2772.186eV
Energy per atom: Epot =1996.358eV Ekin = 772.863eV (T=1494.785K) Etot = 2769.221eV
Energy per atom: Epot =1988.012eV Ekin = 779.357eV (T=1507.344K) Etot = 2767.369eV
Energy per atom: Epot =1989.195eV Ekin = 774.155eV (T=1497.283K) Etot = 2763.350eV
Energy per atom: Epot =1984.082eV Ekin = 786.783eV (T=1521.707K) Etot = 2770.865eV
Energy per atom: Epot =1996.001eV Ekin = 772.160eV (T=1493.424K) Etot = 2768.161eV
Energy per atom: Epot =1994.791eV Ekin = 773.474eV (T=1495.965K) Etot = 2768.264eV
Energy per atom: Epot =2011.958eV Ekin = 765.264eV (T=1480.088K) Etot = 2777.222eV
Energy per atom: Epot =1996.945eV Ekin = 779.904eV (T=1508.402K) Etot = 2776.849eV
Energy per atom: Epot =1994.306eV Ekin = 785.553eV (T=1519.329K) Etot = 2779.860eV
Energy per atom: Epot =1995.726eV Ekin = 778.505eV (T=1505.696K) Etot = 2774.231eV
Energy per atom: Epot =1989.088eV Ekin = 784.687eV (T=1517.652K) Etot = 2773.775eV
Energy per atom: Epot =2007.052eV Ekin = 774.711eV (T=1498.358K) Etot = 2781.763eV
Energy per atom: Epot =1998.119eV Ekin = 787.516eV (T=1523.124K) Etot = 2785.635eV
Energy per atom: Epot =2001.805eV Ekin = 786.676eV (T=1521.501K) Etot = 2788.481eV
Energy per atom: Epot =1996.202eV Ekin = 789.448eV (T=1526.861K) Etot = 2785.650eV
Energy per atom: Epot =2011.326eV Ekin = 778.553eV (T=1505.788K) Etot = 2789.878eV
Energy per atom: Epot =2013.354eV Ekin = 767.531eV (T=1484.471K) Etot = 2780.885eV
Energy per atom: Epot =2013.816eV Ekin = 763.810eV (T=1477.275K) Etot = 2777.626eV
Energy per atom: Epot =2011.774eV Ekin = 775.202eV (T=1499.307K) Etot = 2786.976eV
Energy per atom: Epot =2017.503eV Ekin = 773.764eV (T=1496.528K) Etot = 2791.268eV
Energy per atom: Epot =2013.942eV Ekin = 780.136eV (T=1508.852K) Etot = 2794.078eV
Energy per atom: Epot =2015.560eV Ekin = 782.564eV (T=1513.548K) Etot = 2798.124eV
Energy per atom: Epot =2006.644eV Ekin = 777.886eV (T=1504.500K) Etot = 2784.530eV
Energy per atom: Epot =1993.464eV Ekin = 789.178eV (T=1526.340K) Etot = 2782.642eV
Energy per atom: Epot =2013.656eV Ekin = 776.799eV (T=1502.397K) Etot = 2790.454eV
Energy per atom: Epot =2012.536eV Ekin = 779.577eV (T=1507.770K) Etot = 2792.113eV
Energy per atom: Epot =1999.977eV Ekin = 790.424eV (T=1528.749K) Etot = 2790.401eV
Energy per atom: Epot =2009.465eV Ekin = 782.893eV (T=1514.184K) Etot = 2792.358eV
Energy per atom: Epot =2004.242eV Ekin = 788.100eV (T=1524.254K) Etot = 2792.342eV
Energy per atom: Epot =2003.896eV Ekin = 785.348eV (T=1518.931K) Etot = 2789.244eV
Energy per atom: Epot =2012.437eV Ekin = 779.339eV (T=1507.309K) Etot = 2791.776eV
Energy per atom: Epot =2009.904eV Ekin = 785.716eV (T=1519.642K) Etot = 2795.620eV
Energy per atom: Epot =2016.775eV Ekin = 785.739eV (T=1519.687K) Etot = 2802.514eV
Energy per atom: Epot =2022.263eV Ekin = 780.234eV (T=1509.040K) Etot = 2802.496eV
Energy per atom: Epot =2024.615eV Ekin = 774.801eV (T=1498.532K) Etot = 2799.416eV
Energy per atom: Epot =2018.572eV Ekin = 773.379eV (T=1495.782K) Etot = 2791.951eV
Energy per atom: Epot =2013.132eV Ekin = 774.626eV (T=1498.194K) Etot = 2787.758eV
Energy per atom: Epot =2015.714eV Ekin = 756.752eV (T=1463.624K) Etot = 2772.466eV
Energy per atom: Epot =2012.994eV Ekin = 765.624eV (T=1480.784K) Etot = 2778.618eV
Energy per atom: Epot =2011.839eV Ekin = 762.770eV (T=1475.264K) Etot = 2774.609eV
Energy per atom: Epot =2015.449eV Ekin = 768.513eV (T=1486.370K) Etot = 2783.962eV
Energy per atom: Epot =2002.218eV Ekin = 768.841eV (T=1487.006K) Etot = 2771.059eV
Energy per atom: Epot =2003.417eV Ekin = 764.573eV (T=1478.752K) Etot = 2767.991eV
Energy per atom: Epot =2002.772eV Ekin = 763.758eV (T=1477.174K) Etot = 2766.530eV
Energy per atom: Epot =2007.618eV Ekin = 764.660eV (T=1478.919K) Etot = 2772.278eV
Energy per atom: Epot =1998.900eV Ekin = 766.530eV (T=1482.536K) Etot = 2765.431eV
Energy per atom: Epot =1988.919eV Ekin = 784.828eV (T=1517.926K) Etot = 2773.747eV
Energy per atom: Epot =1993.745eV Ekin = 789.037eV (T=1526.066K) Etot = 2782.781eV
Energy per atom: Epot =1992.138eV Ekin = 793.550eV (T=1534.794K) Etot = 2785.688eV
Energy per atom: Epot =1998.055eV Ekin = 782.769eV (T=1513.943K) Etot = 2780.824eV
Energy per atom: Epot =1989.998eV Ekin = 793.056eV (T=1533.839K) Etot = 2783.053eV
Energy per atom: Epot =1996.447eV Ekin = 781.946eV (T=1512.352K) Etot = 2778.393eV
Energy per atom: Epot =2002.561eV Ekin = 768.908eV (T=1487.136K) Etot = 2771.469eV
Energy per atom: Epot =1994.857eV Ekin = 782.011eV (T=1512.477K) Etot = 2776.867eV
Energy per atom: Epot =1999.020eV Ekin = 768.117eV (T=1485.606K) Etot = 2767.138eV
Energy per atom: Epot =1998.769eV Ekin = 770.241eV (T=1489.714K) Etot = 2769.010eV
Energy per atom: Epot =2005.631eV Ekin = 760.651eV (T=1471.166K) Etot = 2766.282eV
Energy per atom: Epot =1999.100eV Ekin = 766.037eV (T=1481.581K) Etot = 2765.137eV
Energy per atom: Epot =1993.131eV Ekin = 774.065eV (T=1497.109K) Etot = 2767.196eV
Energy per atom: Epot =2002.489eV Ekin = 771.016eV (T=1491.213K) Etot = 2773.505eV
Energy per atom: Epot =2006.490eV Ekin = 772.988eV (T=1495.027K) Etot = 2779.478eV
Energy per atom: Epot =2006.350eV Ekin = 773.482eV (T=1495.981K) Etot = 2779.832eV
Energy per atom: Epot =2007.922eV Ekin = 762.524eV (T=1474.787K) Etot = 2770.446eV
Energy per atom: Epot =2002.389eV Ekin = 769.070eV (T=1487.448K) Etot = 2771.459eV
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] 11:30:50 43.457006 1.0818
BFGSLineSearch: 1[ 1] 11:30:50 42.347659 0.2273
BFGSLineSearch: 2[ 2] 11:30:50 42.108454 0.1349
BFGSLineSearch: 3[ 3] 11:30:50 41.964817 0.1138
BFGSLineSearch: 4[ 4] 11:30:50 41.924933 0.0683
BFGSLineSearch: 5[ 5] 11:30:50 41.915346 0.0225
BFGSLineSearch: 6[ 6] 11:30:50 41.914920 0.0059
BFGSLineSearch: 7[ 7] 11:30:50 41.914872 0.0023
BFGSLineSearch: 8[ 9] 11:30:50 41.914855 0.0023
BFGSLineSearch: 9[ 10] 11:30:50 41.914851 0.0010
running a NVE simulation of a Cu nanoparticle
Energy per atom: Epot =41.915eV Ekin = 13.427eV (T=1116.948K) Etot = 55.342eV
Energy per atom: Epot =50.365eV Ekin = 5.020eV (T=417.637K) Etot = 55.386eV
Energy per atom: Epot =49.464eV Ekin = 5.923eV (T=492.677K) Etot = 55.387eV
Energy per atom: Epot =49.588eV Ekin = 5.800eV (T=482.487K) Etot = 55.388eV
Energy per atom: Epot =49.680eV Ekin = 5.705eV (T=474.564K) Etot = 55.385eV
Energy per atom: Epot =49.363eV Ekin = 6.020eV (T=500.756K) Etot = 55.382eV
Energy per atom: Epot =48.968eV Ekin = 6.413eV (T=533.514K) Etot = 55.381eV
Energy per atom: Epot =49.296eV Ekin = 6.094eV (T=506.902K) Etot = 55.390eV
Energy per atom: Epot =48.878eV Ekin = 6.509eV (T=541.485K) Etot = 55.387eV
Energy per atom: Epot =48.875eV Ekin = 6.510eV (T=541.517K) Etot = 55.385eV
Energy per atom: Epot =49.608eV Ekin = 5.780eV (T=480.834K) Etot = 55.388eV
Energy per atom: Epot =48.903eV Ekin = 6.481eV (T=539.114K) Etot = 55.384eV
Energy per atom: Epot =48.451eV Ekin = 6.932eV (T=576.654K) Etot = 55.383eV
Energy per atom: Epot =48.522eV Ekin = 6.865eV (T=571.108K) Etot = 55.387eV
Energy per atom: Epot =48.974eV Ekin = 6.412eV (T=533.388K) Etot = 55.386eV
Energy per atom: Epot =49.167eV Ekin = 6.219eV (T=517.378K) Etot = 55.387eV
Energy per atom: Epot =49.182eV Ekin = 6.206eV (T=516.262K) Etot = 55.388eV
Energy per atom: Epot =49.213eV Ekin = 6.175eV (T=513.677K) Etot = 55.388eV
Energy per atom: Epot =48.747eV Ekin = 6.636eV (T=552.055K) Etot = 55.383eV
Energy per atom: Epot =49.223eV Ekin = 6.164eV (T=512.760K) Etot = 55.387eV
Energy per atom: Epot =48.297eV Ekin = 7.086eV (T=589.427K) Etot = 55.382eV
Energy per atom: Epot =48.719eV Ekin = 6.666eV (T=554.556K) Etot = 55.385eV
Energy per atom: Epot =49.239eV Ekin = 6.147eV (T=511.375K) Etot = 55.386eV
Energy per atom: Epot =49.583eV Ekin = 5.803eV (T=482.695K) Etot = 55.385eV
Energy per atom: Epot =49.251eV Ekin = 6.132eV (T=510.131K) Etot = 55.383eV
Energy per atom: Epot =48.283eV Ekin = 7.096eV (T=590.327K) Etot = 55.379eV
Energy per atom: Epot =49.089eV Ekin = 6.294eV (T=523.546K) Etot = 55.383eV
Energy per atom: Epot =49.090eV Ekin = 6.293eV (T=523.492K) Etot = 55.383eV
Energy per atom: Epot =48.175eV Ekin = 7.207eV (T=599.555K) Etot = 55.382eV
Energy per atom: Epot =49.417eV Ekin = 5.968eV (T=496.438K) Etot = 55.385eV
Energy per atom: Epot =49.497eV Ekin = 5.887eV (T=489.745K) Etot = 55.384eV
Energy per atom: Epot =48.968eV Ekin = 6.417eV (T=533.833K) Etot = 55.386eV
Energy per atom: Epot =48.675eV Ekin = 6.710eV (T=558.215K) Etot = 55.385eV
Energy per atom: Epot =49.420eV Ekin = 5.966eV (T=496.287K) Etot = 55.386eV
Energy per atom: Epot =48.702eV Ekin = 6.680eV (T=555.659K) Etot = 55.382eV
Energy per atom: Epot =49.191eV Ekin = 6.195eV (T=515.358K) Etot = 55.386eV
Energy per atom: Epot =49.680eV Ekin = 5.707eV (T=474.708K) Etot = 55.387eV
Energy per atom: Epot =48.244eV Ekin = 7.130eV (T=593.140K) Etot = 55.374eV
Energy per atom: Epot =48.394eV Ekin = 6.983eV (T=580.872K) Etot = 55.377eV
Energy per atom: Epot =49.351eV Ekin = 6.034eV (T=501.965K) Etot = 55.385eV
Energy per atom: Epot =48.974eV Ekin = 6.407eV (T=532.996K) Etot = 55.381eV
Energy per atom: Epot =49.113eV Ekin = 6.272eV (T=521.705K) Etot = 55.384eV
Energy per atom: Epot =48.583eV Ekin = 6.800eV (T=565.672K) Etot = 55.383eV
Energy per atom: Epot =49.273eV Ekin = 6.114eV (T=508.594K) Etot = 55.387eV
Energy per atom: Epot =49.576eV Ekin = 5.813eV (T=483.548K) Etot = 55.389eV
Energy per atom: Epot =49.662eV Ekin = 5.724eV (T=476.192K) Etot = 55.386eV
Energy per atom: Epot =49.127eV Ekin = 6.261eV (T=520.858K) Etot = 55.388eV
Energy per atom: Epot =49.993eV Ekin = 5.400eV (T=449.227K) Etot = 55.393eV
Energy per atom: Epot =48.913eV Ekin = 6.474eV (T=538.541K) Etot = 55.387eV
Energy per atom: Epot =49.193eV Ekin = 6.192eV (T=515.071K) Etot = 55.384eV
Energy per atom: Epot =49.864eV Ekin = 5.522eV (T=459.380K) Etot = 55.387eV
Energy per atom: Epot =48.503eV Ekin = 6.883eV (T=572.552K) Etot = 55.386eV
Energy per atom: Epot =49.432eV Ekin = 5.956eV (T=495.489K) Etot = 55.388eV
Energy per atom: Epot =49.136eV Ekin = 6.249eV (T=519.820K) Etot = 55.385eV
Energy per atom: Epot =48.967eV Ekin = 6.419eV (T=533.954K) Etot = 55.385eV
Energy per atom: Epot =49.074eV Ekin = 6.313eV (T=525.134K) Etot = 55.386eV
Energy per atom: Epot =49.243eV Ekin = 6.143eV (T=510.996K) Etot = 55.385eV
Energy per atom: Epot =49.333eV Ekin = 6.053eV (T=503.511K) Etot = 55.385eV
Energy per atom: Epot =49.346eV Ekin = 6.040eV (T=502.442K) Etot = 55.386eV
Energy per atom: Epot =48.402eV Ekin = 6.981eV (T=580.754K) Etot = 55.384eV
Energy per atom: Epot =49.167eV Ekin = 6.222eV (T=517.584K) Etot = 55.388eV
Energy per atom: Epot =48.454eV Ekin = 6.930eV (T=576.499K) Etot = 55.385eV
Energy per atom: Epot =48.738eV Ekin = 6.646eV (T=552.821K) Etot = 55.384eV
Energy per atom: Epot =48.726eV Ekin = 6.654eV (T=553.502K) Etot = 55.379eV
Energy per atom: Epot =48.822eV Ekin = 6.562eV (T=545.844K) Etot = 55.383eV
Energy per atom: Epot =48.733eV Ekin = 6.653eV (T=553.443K) Etot = 55.386eV
Energy per atom: Epot =48.612eV Ekin = 6.775eV (T=563.600K) Etot = 55.387eV
Energy per atom: Epot =49.103eV Ekin = 6.289eV (T=523.128K) Etot = 55.392eV
Energy per atom: Epot =49.115eV Ekin = 6.270eV (T=521.587K) Etot = 55.385eV
Energy per atom: Epot =48.447eV Ekin = 6.932eV (T=576.624K) Etot = 55.379eV
Energy per atom: Epot =49.021eV Ekin = 6.365eV (T=529.481K) Etot = 55.386eV
Energy per atom: Epot =48.819eV Ekin = 6.566eV (T=546.204K) Etot = 55.385eV
Energy per atom: Epot =48.788eV Ekin = 6.594eV (T=548.565K) Etot = 55.382eV
Energy per atom: Epot =48.340eV Ekin = 7.045eV (T=586.039K) Etot = 55.385eV
Energy per atom: Epot =48.877eV Ekin = 6.511eV (T=541.620K) Etot = 55.388eV
Energy per atom: Epot =49.212eV Ekin = 6.173eV (T=513.497K) Etot = 55.385eV
Energy per atom: Epot =48.959eV Ekin = 6.428eV (T=534.695K) Etot = 55.386eV
Energy per atom: Epot =48.568eV Ekin = 6.816eV (T=567.024K) Etot = 55.384eV
Energy per atom: Epot =49.705eV Ekin = 5.682eV (T=472.684K) Etot = 55.388eV
Energy per atom: Epot =48.218eV Ekin = 7.161eV (T=595.720K) Etot = 55.379eV
Energy per atom: Epot =48.722eV Ekin = 6.661eV (T=554.088K) Etot = 55.382eV
Energy per atom: Epot =49.591eV Ekin = 5.798eV (T=482.280K) Etot = 55.389eV
Energy per atom: Epot =48.522eV Ekin = 6.858eV (T=570.516K) Etot = 55.381eV
Energy per atom: Epot =48.558eV Ekin = 6.827eV (T=567.952K) Etot = 55.385eV
Energy per atom: Epot =48.586eV Ekin = 6.795eV (T=565.274K) Etot = 55.382eV
Energy per atom: Epot =48.633eV Ekin = 6.751eV (T=561.560K) Etot = 55.383eV
Energy per atom: Epot =48.170eV Ekin = 7.211eV (T=599.898K) Etot = 55.381eV
Energy per atom: Epot =49.654eV Ekin = 5.733eV (T=476.906K) Etot = 55.387eV
Energy per atom: Epot =49.163eV Ekin = 6.221eV (T=517.533K) Etot = 55.384eV
Energy per atom: Epot =48.978eV Ekin = 6.407eV (T=532.954K) Etot = 55.385eV
Energy per atom: Epot =49.187eV Ekin = 6.199eV (T=515.711K) Etot = 55.387eV
Energy per atom: Epot =48.176eV Ekin = 7.204eV (T=599.300K) Etot = 55.380eV
Energy per atom: Epot =48.480eV Ekin = 6.902eV (T=574.138K) Etot = 55.382eV
Energy per atom: Epot =48.243eV Ekin = 7.139eV (T=593.892K) Etot = 55.382eV
Energy per atom: Epot =48.681eV Ekin = 6.704eV (T=557.665K) Etot = 55.385eV
Energy per atom: Epot =49.127eV Ekin = 6.259eV (T=520.705K) Etot = 55.386eV
Energy per atom: Epot =49.136eV Ekin = 6.250eV (T=519.945K) Etot = 55.387eV
Energy per atom: Epot =48.116eV Ekin = 7.264eV (T=604.237K) Etot = 55.379eV
Energy per atom: Epot =48.464eV Ekin = 6.920eV (T=575.643K) Etot = 55.384eV
Energy per atom: Epot =48.142eV Ekin = 7.242eV (T=602.409K) Etot = 55.383eV
Energy per atom: Epot =48.224eV Ekin = 7.156eV (T=595.251K) Etot = 55.380eV
Energy per atom: Epot =49.064eV Ekin = 6.322eV (T=525.942K) Etot = 55.386eV
Energy per atom: Epot =49.355eV Ekin = 6.034eV (T=501.961K) Etot = 55.389eV
Energy per atom: Epot =48.841eV Ekin = 6.544eV (T=544.369K) Etot = 55.385eV
Energy per atom: Epot =48.387eV Ekin = 6.996eV (T=581.941K) Etot = 55.383eV
Energy per atom: Epot =48.930eV Ekin = 6.455eV (T=536.938K) Etot = 55.384eV
Energy per atom: Epot =48.617eV Ekin = 6.767eV (T=562.941K) Etot = 55.384eV
Energy per atom: Epot =48.741eV Ekin = 6.644eV (T=552.702K) Etot = 55.385eV
Energy per atom: Epot =49.242eV Ekin = 6.145eV (T=511.198K) Etot = 55.387eV
Energy per atom: Epot =49.103eV Ekin = 6.284eV (T=522.769K) Etot = 55.387eV
Energy per atom: Epot =48.866eV Ekin = 6.518eV (T=542.242K) Etot = 55.384eV
Energy per atom: Epot =49.456eV Ekin = 5.929eV (T=493.229K) Etot = 55.385eV
Energy per atom: Epot =49.074eV Ekin = 6.311eV (T=524.997K) Etot = 55.385eV
Energy per atom: Epot =48.567eV Ekin = 6.815eV (T=566.954K) Etot = 55.382eV
Energy per atom: Epot =48.539eV Ekin = 6.844eV (T=569.362K) Etot = 55.384eV
Energy per atom: Epot =49.173eV Ekin = 6.213eV (T=516.841K) Etot = 55.386eV
Energy per atom: Epot =48.908eV Ekin = 6.473eV (T=538.428K) Etot = 55.380eV
Energy per atom: Epot =49.381eV Ekin = 6.008eV (T=499.794K) Etot = 55.389eV
Energy per atom: Epot =48.343eV Ekin = 7.045eV (T=586.088K) Etot = 55.389eV
Energy per atom: Epot =49.146eV Ekin = 6.240eV (T=519.070K) Etot = 55.386eV
Energy per atom: Epot =48.717eV Ekin = 6.664eV (T=554.336K) Etot = 55.381eV
Energy per atom: Epot =48.417eV Ekin = 6.960eV (T=578.997K) Etot = 55.378eV
Energy per atom: Epot =48.799eV Ekin = 6.580eV (T=547.347K) Etot = 55.379eV
Energy per atom: Epot =48.542eV Ekin = 6.841eV (T=569.100K) Etot = 55.383eV
Energy per atom: Epot =48.460eV Ekin = 6.923eV (T=575.940K) Etot = 55.384eV
Energy per atom: Epot =48.554eV Ekin = 6.827eV (T=567.921K) Etot = 55.381eV
Energy per atom: Epot =48.247eV Ekin = 7.130eV (T=593.144K) Etot = 55.377eV
Energy per atom: Epot =48.173eV Ekin = 7.203eV (T=599.212K) Etot = 55.376eV
Energy per atom: Epot =48.180eV Ekin = 7.199eV (T=598.857K) Etot = 55.379eV
Energy per atom: Epot =48.395eV Ekin = 6.988eV (T=581.341K) Etot = 55.383eV
Energy per atom: Epot =48.684eV Ekin = 6.703eV (T=557.598K) Etot = 55.387eV
Energy per atom: Epot =48.780eV Ekin = 6.601eV (T=549.140K) Etot = 55.381eV
Energy per atom: Epot =48.871eV Ekin = 6.509eV (T=541.440K) Etot = 55.379eV
Energy per atom: Epot =48.785eV Ekin = 6.596eV (T=548.661K) Etot = 55.381eV
Energy per atom: Epot =49.146eV Ekin = 6.240eV (T=519.077K) Etot = 55.386eV
Energy per atom: Epot =48.807eV Ekin = 6.573eV (T=546.819K) Etot = 55.381eV
Energy per atom: Epot =47.687eV Ekin = 7.689eV (T=639.650K) Etot = 55.376eV
Energy per atom: Epot =48.228eV Ekin = 7.156eV (T=595.297K) Etot = 55.384eV
Energy per atom: Epot =48.461eV Ekin = 6.923eV (T=575.915K) Etot = 55.385eV
Energy per atom: Epot =48.285eV Ekin = 7.098eV (T=590.429K) Etot = 55.383eV
Energy per atom: Epot =48.857eV Ekin = 6.527eV (T=542.992K) Etot = 55.384eV
Energy per atom: Epot =49.182eV Ekin = 6.203eV (T=515.994K) Etot = 55.384eV
Energy per atom: Epot =48.974eV Ekin = 6.410eV (T=533.190K) Etot = 55.383eV
Energy per atom: Epot =48.837eV Ekin = 6.549eV (T=544.765K) Etot = 55.386eV
Energy per atom: Epot =48.266eV Ekin = 7.118eV (T=592.102K) Etot = 55.383eV
Energy per atom: Epot =48.024eV Ekin = 7.352eV (T=611.614K) Etot = 55.377eV
Energy per atom: Epot =49.002eV Ekin = 6.384eV (T=531.075K) Etot = 55.386eV
Energy per atom: Epot =48.778eV Ekin = 6.609eV (T=549.818K) Etot = 55.387eV
Energy per atom: Epot =48.304eV Ekin = 7.082eV (T=589.160K) Etot = 55.386eV
Energy per atom: Epot =49.036eV Ekin = 6.352eV (T=528.440K) Etot = 55.388eV
Energy per atom: Epot =48.225eV Ekin = 7.156eV (T=595.312K) Etot = 55.381eV
Energy per atom: Epot =48.923eV Ekin = 6.464eV (T=537.725K) Etot = 55.387eV
Energy per atom: Epot =49.290eV Ekin = 6.099eV (T=507.384K) Etot = 55.390eV
Energy per atom: Epot =48.810eV Ekin = 6.576eV (T=547.015K) Etot = 55.385eV
Energy per atom: Epot =48.412eV Ekin = 6.968eV (T=579.609K) Etot = 55.380eV
Energy per atom: Epot =47.949eV Ekin = 7.426eV (T=617.720K) Etot = 55.375eV
Energy per atom: Epot =48.731eV Ekin = 6.653eV (T=553.412K) Etot = 55.384eV
Energy per atom: Epot =47.920eV Ekin = 7.463eV (T=620.816K) Etot = 55.382eV
Energy per atom: Epot =49.438eV Ekin = 5.951eV (T=495.077K) Etot = 55.389eV
Energy per atom: Epot =48.869eV Ekin = 6.517eV (T=542.105K) Etot = 55.386eV
Energy per atom: Epot =48.837eV Ekin = 6.549eV (T=544.780K) Etot = 55.386eV
Energy per atom: Epot =48.864eV Ekin = 6.523eV (T=542.644K) Etot = 55.387eV
Energy per atom: Epot =48.420eV Ekin = 6.963eV (T=579.240K) Etot = 55.384eV
Energy per atom: Epot =48.267eV Ekin = 7.113eV (T=591.691K) Etot = 55.380eV
Energy per atom: Epot =48.692eV Ekin = 6.691eV (T=556.636K) Etot = 55.384eV
Energy per atom: Epot =48.894eV Ekin = 6.496eV (T=540.369K) Etot = 55.390eV
Energy per atom: Epot =48.194eV Ekin = 7.182eV (T=597.483K) Etot = 55.377eV
Energy per atom: Epot =48.348eV Ekin = 7.031eV (T=584.898K) Etot = 55.379eV
Energy per atom: Epot =49.301eV Ekin = 6.085eV (T=506.160K) Etot = 55.386eV
Energy per atom: Epot =48.530eV Ekin = 6.851eV (T=569.929K) Etot = 55.382eV
Energy per atom: Epot =49.304eV Ekin = 6.081eV (T=505.881K) Etot = 55.386eV
Energy per atom: Epot =48.376eV Ekin = 7.005eV (T=582.694K) Etot = 55.380eV
Energy per atom: Epot =49.290eV Ekin = 6.099eV (T=507.345K) Etot = 55.389eV
Energy per atom: Epot =48.440eV Ekin = 6.944eV (T=577.627K) Etot = 55.384eV
Energy per atom: Epot =48.181eV Ekin = 7.198eV (T=598.775K) Etot = 55.379eV
Energy per atom: Epot =49.442eV Ekin = 5.944eV (T=494.454K) Etot = 55.386eV
Energy per atom: Epot =48.627eV Ekin = 6.752eV (T=561.657K) Etot = 55.379eV
Energy per atom: Epot =48.587eV Ekin = 6.793eV (T=565.117K) Etot = 55.381eV
Energy per atom: Epot =48.768eV Ekin = 6.615eV (T=550.283K) Etot = 55.383eV
Energy per atom: Epot =49.037eV Ekin = 6.351eV (T=528.326K) Etot = 55.388eV
Energy per atom: Epot =49.026eV Ekin = 6.363eV (T=529.298K) Etot = 55.389eV
Energy per atom: Epot =48.238eV Ekin = 7.146eV (T=594.461K) Etot = 55.384eV
Energy per atom: Epot =48.889eV Ekin = 6.494eV (T=540.247K) Etot = 55.384eV
Energy per atom: Epot =48.761eV Ekin = 6.623eV (T=550.983K) Etot = 55.384eV
Energy per atom: Epot =48.808eV Ekin = 6.578eV (T=547.201K) Etot = 55.386eV
Energy per atom: Epot =47.378eV Ekin = 7.999eV (T=665.439K) Etot = 55.378eV
Energy per atom: Epot =48.915eV Ekin = 6.470eV (T=538.200K) Etot = 55.385eV
Energy per atom: Epot =48.895eV Ekin = 6.490eV (T=539.872K) Etot = 55.385eV
Energy per atom: Epot =48.355eV Ekin = 7.029eV (T=584.735K) Etot = 55.384eV
Energy per atom: Epot =48.764eV Ekin = 6.617eV (T=550.412K) Etot = 55.380eV
Energy per atom: Epot =48.527eV Ekin = 6.853eV (T=570.084K) Etot = 55.381eV
Energy per atom: Epot =48.246eV Ekin = 7.139eV (T=593.828K) Etot = 55.384eV
Energy per atom: Epot =48.776eV Ekin = 6.613eV (T=550.149K) Etot = 55.390eV
Energy per atom: Epot =48.896eV Ekin = 6.490eV (T=539.878K) Etot = 55.386eV
Energy per atom: Epot =48.542eV Ekin = 6.840eV (T=569.037K) Etot = 55.382eV
Energy per atom: Epot =48.563eV Ekin = 6.818eV (T=567.171K) Etot = 55.382eV
Energy per atom: Epot =48.860eV Ekin = 6.525eV (T=542.756K) Etot = 55.384eV
Energy per atom: Epot =48.412eV Ekin = 6.969eV (T=579.702K) Etot = 55.381eV
Energy per atom: Epot =48.862eV Ekin = 6.521eV (T=542.441K) Etot = 55.382eV
Energy per atom: Epot =48.159eV Ekin = 7.222eV (T=600.814K) Etot = 55.381eV
Energy per atom: Epot =49.353eV Ekin = 6.034eV (T=501.962K) Etot = 55.387eV
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?