-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
Practice #1 Potential energy curve of Diatomic Curve 1.1 RHF
Calculation of the HCl molecule at a fixed geometry 1.1.1 Draw a
schematic showing how the molecule is oriented in relation to the
Cartesian axes 1.1.2 Nuclear energy repulsion - How could you
calculate this last value? Check that this data is coherent
with your input The Nuclear Energy Repulsion could be calculated
by Coulomb Laws for the interactions of two point charges [1], so
in this practice we should take care to transform the units of the
output file that are in hartress to electronvolts. F = k !!!!!!
[1]
Calculations Distance 1,3 K 9,9875x109 Nm2/C2. Energy Force (Cl
H) 144,711eV/ (output) Nuclear Energy 6,913 Hartrees 6,92 Hartrees
(Output ) Comparing the value of the output data, we can observe
that the work for the calculated value is the same as the output
value.
1.1.3 How many iterations have been required in this HF-LCAO
calculation? After 7 RHF-LCAO interactions that had perform to do
the calculation of the RHF energy. 1.1.4 Electric dipole moment:
Taking into account the orientation of the molecule on the
Cartesian axes,
check that this moment is a vector directed from the atom with a
net negative charge to the one with positive charge The coordinates
of the vector form in the HCl molecule are:
DX DY DZ 0,00000 0,0000 1,527104
Input Data Internuclear Distance 1,3 K 9.,875x109 Nm2/C2. Atomic
Charge (Cl) 17 atoms Atomic Charge (H) 1 atoms
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
1.2 Potential energy curve for HCL 1.2.1 Build up a table of
values of the distance R in Angstroms and U (TOTAL ENERGY) and
Vnuc
(NUCLEAR ENERGY REPULSION) energies. Obtain the electronic
energy values (Eel) for each distance, subtracting the Vnuc column
to the U column. Represent graphically, the total energy as a
function of distance, together with its two components: Eel, Vnu.
Identify the three curves. To what limit must tend the internuclear
repulsion for R-> 0 and R-> ?
Intramolecular Distance U (eV) Vnuc (eV) Eel (eV)
0,6 -453,64015860 14,99335540 -468,63351400 0,7 -454,26315750
12,85144748 -467,11460500 0,8 -454,64843290 11,24501655
-465,89344940 0,9 -454,88298610 9,99557026 -464,87855630 1,0
-455,02045240 8,99601324 -464,01646560 1,1 -455,09548250 8,17819385
-463,27367630 1,2 -455,13052760 7,49667770 -462,62720530 1,3
-455,14014990 6,92001018 -462,06016010 1,4 -455,13380300 6,42572374
-461,55952680 1,6 -455,09562540 5,62250827 -460,71813370 1,8
-455,04374990 4,99778513 -460,04153500 2,0 -454,99038070 4,49800662
-459,48838730 3,0 -454,81224670 2,99867108 -457,81091780 4,0
-454,75589720 2,24900331 -457,00490050
-455,500 -455,000 -454,500 -454,000 -453,500 0 0,5 1 1,5 2 2,5 3
3,5 4
Total E
nergy (eV)
Intramolecular Distance
Total Energy (eV)
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
According to the Coulomb Laws the limit of the internuclear
repulsion for R-> 0 should tends to infinity and for R->
should tends to zero. 1.3 Equilibrium Internuclear Distance and
Dissociation Energy 1.3.1 How many HF calculations were necessary
to find the equilibrium geometry in our case? After 3 HF
calculations the equilibrium is reached for the geometry. 1.3.2
Write down the equilibrium distance obtained by the calculation and
compare it with the
experimental value: 1.275 . How would explain the difference? We
can determinate a difference between the calculation (1.3024) and
the experimental values (1.275) about of the less state of energy
reached, because the set point performed some calculations using
previous results. 1.3.3 Using the U(4) value as an approximation to
U() (we can consider the H-Cl bond almost broken
for 4 ), estimate the molecules dissociation energy as De = U()
- U(Re) and compare this value with the experimental one: De = 4,62
eV.
0,0 2,0 4,0 6,0 8,0 10,0
12,0 14,0 16,0
0 0,5 1 1,5 2 2,5 3 3,5 4 Nuclear Ene
rgy repu
lsin (eV)
Intermolecular Distance
Nuclear Energy repulsin (eV)
-470,000 -468,000 -466,000 -464,000 -462,000 -460,000 -458,000
-456,000 0 0,5 1 1,5 2 2,5 3 3,5 4
Electron
ic Ene
rgy (eV)
Intermolecular Distance
Electronic Energy (eV)
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
The U(4) value is 10.45 eV obtained by multiplying it for 27.2
the estimate of the molecules dissociation energy that has been
determined on 0.3842 Hartrees. relatively equal to the experimental
value of 4.62 eV. 1.3.4 Use of Configuration Interaction method:
Plot UCI(R) and compare it with UHF(R). Comment the
differences.
Intramolecular Distance U (eV) Vnuc (eV) Eel (eV) 0,6
-453,64579720 14,99335540 -468,63915260 0,7 -454,26891920
12,85144748 -467,12036670 0,8 -454,65438950 11,24501655
-465,89940600 0,9 -454,88958510 9,99557026 -464,88515540 1,0
-455,02829160 8,99601324 -464,02430480 1,1 -455,10526820 8,17819385
-463,28346200 1,2 -455,14306670 7,49667770 -462,63974440 1,3
-455,15634000 6,92001018 -462,07635020 1,4 -455,15462560 6,42572374
-461,58034930 1,6 -455,12900380 5,62250827 -460,75151210 1,8
-455,09462980 4,99778513 -460,09241490 2,0 -455,06392890 4,49800662
-459,56193560 3,0 -455,01375070 2,99867108 -458,01242180 4,0
-455,01239780 2,24900331 -457,26140110
-455,500 -455,000 -454,500 -454,000 -453,500 0 0,5 1 1,5 2 2,5 3
3,5 4
Total E
nergy (eV)
Intramolecular Distance
Total Energy (eV)
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
The shape of the curves follows relatively the same path,
changing a little bit in the values of the Electronic Energy and
the Total Energy, excepting for the nuclear Energy repulsion values
that are the same. 1.3.5 Optimize the geometry of the HCl molecule
using the CI method. Recalculate the dissociation energy
and compare the final theoretical values (Re and De) with the
previously mentioned experimental values.
Recalculation of the dissociation energy gave 3.93 eV value,
quite similar to the experimental value (4.62eV) 1.4 Effect of
Basis set 1.4.1 The CI and HF methods are both variational: they
converge to the best numerical solution as more
basis functions are included in the description of the molecular
orbitals. Recalculate the potential energy curve for the CI and
obtain new estimations of Re and De using the CI method and the
6-31G(d,p) basis.
0,0 2,0 4,0 6,0 8,0 10,0
12,0 14,0 16,0
0 0,5 1 1,5 2 2,5 3 3,5 4
Nuclear Ene
rgy repu
lsin (eV)
Intermolecular Distance
Nuclear Energy repulsin (eV)
-470,000 -468,000 -466,000 -464,000 -462,000 -460,000 -458,000
-456,000 0 0,5 1 1,5 2 2,5 3 3,5 4
Electron
ic Ene
rgy (eV)
Intermolecular Distance
Electronic Energy (eV)
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
Intramolecular Distance U (eV) Vnuc (eV) Eel (eV)
0,6 -458,826166 14,9933554 -473,8195214 0,7 -459,3262139
12,85144748 -472,1776614 0,8 -459,7865938 11,24501655 -471,0316103
0,9 -459,9856942 9,995570263 -469,9812645 1,0 -460,0947078
8,996013237 -469,0907211 1,1 -460,1494589 8,178193852 -468,3276527
1,2 -460,1716403 7,496677698 -467,668318 1,3 -460,1746039
6,920010182 -467,0946141 1,4 -460,1665495 6,425723741 -466,5922733
1,6 -460,1356411 5,622508273 -465,7581493 1,8 -460,10054
4,997785132 -465,0983251 2,0 -460,0693179 4,498006619 -464,5673245
3,0 -459,9921514 2,998671079 -462,9908225 4,0 -458,826166
14,9933554 -473,8195214
-460,400 -460,200 -460,000 -459,800 -459,600 -459,400 -459,200
-459,000 -458,800 -458,600 0 0,5 1 1,5 2 2,5 3 3,5 4
Total E
nergy (eV)
Intramolecular Distance
Total Energy (eV)
0,0 2,0 4,0 6,0 8,0 10,0
12,0 14,0 16,0
0 0,5 1 1,5 2 2,5 3 3,5 4
Nuclear Ene
rgy repu
lsin (eV)
Intermolecular Distance
Nuclear Energy repulsin (eV)
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
The comparison between the experimental and the new Re obtained
(1.269) and the De (5.37eV) by the optimization geometry
calculation, are similar. 1.4.2 Fitting the data in a Morse
Function The Morse function [2] describes the shape of the total
energy function and with the help of the QtiPlot software, we could
find the values that can permit to fit the data obtained in 1.4.1
exercise. U r = D! 1 e!(!!!!) ! [2] = -1.9277 Re =1.269 De
=5.37eV
Practice #2 Molecular Dynamics Simulations 2 Unit 1: Carbon
nanotubes morphology and gas physisorption
-476,000 -474,000 -472,000 -470,000 -468,000 -466,000 -464,000
-462,000 -460,000 0 0,5 1 1,5 2 2,5 3 3,5 4
Electron
ic Ene
rgy (eV)
Intermolecular Distance
Electronic Energy (eV)
-5 0 5
10 15 20 25 30 35 40
0 1 2 3 4 5
Total Energy Vs Morse Function
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
2.1.1 Use the tubebash.sh tool to generate carbon nanotubes with
different morphologie
Carbon nanotubes with different morphologies with the chiral
indices (n=10,m=10) for 80 atoms (n=10,m=0) for 180 atoms
2.1.2 For each CNT in Ex.1.1, generate a nanotube bundle using
the tool nanotube_bundle.x
The carbon nanotubes separation in the bundle
5 10
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
2.1.3 Use tubebash.sh to generate a CNT with chirality (10,0) or
(10,10) and 6 units. Next, employing the
tool initconf.x, build up the simulation cell. This consists of
a nanotube bundle with hexagonal symmetry with periodic boundary
conditions along X and Y, while Z is left unbound. An ensemble of
gas H2 molecules is set on top of the bundle (use between 30 and 90
molecules). Visualize the initial configuration of the MD
simulation and identify the hexagonal symmetry according to the
boundary conditions.
960 C and 120 H atoms (60 H2) CNT (10,10) 5 of Separation (CNT)
4 of Separation molecules (H2) Hexagonal Periodicity
2.1.4 Open the FIELD file contained in the same directory.
Discuss the different parameters of the
potential and make the necessary modifications according to the
number of C atoms and H2 molecules in your simulation. Notice that
no parameters are defined for C - C between and inside the
nanotubes. How do you interpret this? Open the CONTROL file,
observe and comment the parameters of the simulation
CONFIG FILE: Contains Positions, Dimensions, boundary
conditions, atomic labels, coordinates, velocities and forces. 2nd
line ; 0 (coordinates in the file.) 6parallelogram boundary
conditions with no periodicity in the z direction
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
CONTROL FILE Parameters for the simulation (temperature,
timestep, time). In This file: Temperature =150K Steps for the
calculation (300000)
FIELD FILE: It is the force field File Nature and type of the
force
2.1.5 Run the MD simulation using DLPOLY.X. Open the OUTPUT file
and examine the outcome of the
simulation.
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
i. Analyze the evolution of the total energy and its components
with time. Analyze the evolution of
temperature with time.
Temperature When the steps increases the temperature reach a
stable value.
Energies The Van der Waal forces decreases when the time pass,
thus the energy decreases
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
ii. Visualize the geometry at the end of the simulation. In
order to do this use the draw_final.sh shell
command.
Molecules of Hydrogen have been desorved, because they are
decomposing Geometry at the last step of the simulation. It is
possible to see that most of the H2 molecules have been desorbed.
In fact, there are only 36 H atoms from the original 120. Even some
molecules seems to be decomposed.
iii. Run the traj.sh tool and use xmgrace to represent the
z-trajectories of the gas molecules.
Computed z-Trajectories obtained in xmgrace
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
3 MD simulation of the Ar clusters 3.1 Working Directory
UNIT2/Exercise. Visualize the initial structure (Ar_cluster500.xyz)
using the VMD or
Avogadro visualization software. Convert the XYZ geometry file
into a CONFIG file for DLPOLY using the tool XYZtoCONFIG.x. (select
no boundary conditions). Open the CONFIG file and compare with the
XYZ file. Ar cluster (VMD.) Config File OUTPUT:
System Temperature: 59.121 K Total energy: -200.93 units
Configurational energy: -288.87 units
3.2 Running the MD calculations at a higher T value System
Temperature: 80K Total energy: -158.76 units Configurational
energy: -278.80 units
-
UNIVERSITY OF BARCELONA GABRIEL MARIO BRITO
MASTER IN NANOSCIENCE AND NANOTECHNOLOGY MODELLING AND
SIMULATION
3.3 Running the MD calculations for a range of T values to
calculate the caloric curve. This is a useful tool to monitor the
occurrence of phase transitions, which imply a jump of E(T) if
first-order, or in a derivative of E(T) if second- or higher order.
Run the MD simulation for a Temperature range of your choice (close
to the initial value) and plot the Configuration Energy (Ecfg) as a
function of T. T defined in control file (50 -80 K)
System Temperature Total Energy Configurational energy 50 59,121
-200,93 -288,87 52 50,966 -231,98 -307,79 54 52,221 -230,47 -308,14
56 55,53 -221,48 -304,07 58 57,79 -217,65 -303,6 60 61,27 -209,39
-300,52 62 63,498 -206,64 -301,09 64 65,48 -204,54 -301,94 66
65,555 -206,91 -304,42 68 3,08E+43 4,58E+43 6,91E+16 70 8,69E+30
1,29E+31 8,26E+10 72 72,316 -15,848 -124,41 74 73,694 -14,105
-123,72 76 76,037 -10,612 -123,71 78 77,96 -7,801 -123,76 80 80,704
-158,76 -278,8
-1E+43 0 1E+43 2E+43 3E+43 4E+43 5E+43
50 55 60 65 70 75 80
Total Energy