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Ab-initio Density Functional Theory:from quantum dots to solar cell
Saifful Kamaluddin MuzakirStaf ID: 01009 019 276 3844
[email protected]/Saifful Kamaluddin
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Simulation vs animationResult
Fundamental
Input
Calculation
Realistic
Usage
Investigative Technologies Inc.
Unknown Known
Scientific based
Fiction/imaginary
Fundamental parameter
Script/storyboard
Complicated Simple or none
Eq.’s accuracy dependency
Script’s dependency
Predict results
Tellresults
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The advantages of simulation
wet lab
Excited state
Absorption spectroscopy
Ground state
IR spectroscopy
Electron density
Cluster size
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Ab initio
Dr. Izan
Experimental data
Crystallographic profile, number
of electrons, neutrons,
protons
OUTPUT Material
properties
1
2
…..
1,000,000
Mathsfunctions & functionals
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Function
Vito Volterra “Theory of functionals and of Integral and Integro-Differential Equations” (1930)
OUTPUT y
y = f(x) = 2x+3
“y is a function of x”
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Functional
“z is a functional of x”
z =g(x)+h(x)-i(x)
OUTPUT z
i(x)=x+2h(x)=4xg(x)=2x
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Density Functional Theory
“Total ground state energy of a system is a functional of electron density”
ΣE= Σ(K.E)+ Σ(P.E)
OUTPUTTotal Ground State Energy
P.En-nP.Ee-eP.Ee-nK.Ee Exc
electron density, ρ ρ ρ ρ
K.En
ρ ρ
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From Schrödinger’s equation to DFT
Hψ= Eψ
H Ψ: Probability amplitude of particle in a state
E: Calculated Eigenvalue /
energy
Mathematical function that describe a system in the form of summation of K.E & P.E
Predicts the evolution behaviour of a dynamic system
Determine by Functional
Determine by Basis set
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DFT evolution
• Early DFT (1970s):• Hψ= Eψ• (ΣE)ψ=(ΣK.E + ΣP.E)ψ
=(K.Enuc + K.Eelec. + P.En-n + P.Ee-n + P.Ee-e)ψ
• Modern DFT (1990s):
(ΣE)ψ=[K.Eelec. + P.Ee-n + P.Ee-e + Exc]ψ
• (ΣE)ψ=[K.Ee(ρ)+ P.Ee-n(ρ) + P.Ee-e(ρ) + Exc(ρ)]ψ
Nucleus is heavy and ~static: K.E= ~0
Nucleus is neutralized:
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Basis set & Functional (model)
Basis set:Set of wavefunction,
ψ
Functional:System modeling, H
Shape of each atom’s orbitals (AOs)
Calculations with approximations &
corrections
1. Molecular Orbitals (MOs)
2. Energy (Errol G. Lewars, 2011)
(Warren J. Hehre. Wavefunction Inc. 1996)
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Choice of functionalSystem Size
Very big>250,000 atoms
Molecular mechanics
(<250,000 atoms) Big-Small
Qualitative result/ Short on time?
Yes No
Small <12 atoms
RHF
UHFSame orbital
spatial functions for all electrons
Different functions
ions, excited state…
paired e- species
Ab initio: HF
DFT: B3LYP
Semi empirical (G09 W)
PM3 ZINDO Etc..
There other models not listed. Here are the most common
DISCLAIMER: The accuracy of results also heavily depends on the basis set used!
Accu
racy
Incr
ease
sAccu
racy
Incr
ease
s
MORE FUNCTIONAL DETAILS:http://www.gaussian.com/g_tech/g_ur/k_dft.htm
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Limitation of basis set
http://www.gaussian.com/g_tech/g_ur/m_basis_sets.htm
CdSe
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Basis set choices
Narrow down choices: by limitation
Literature review: Any previous theoretical
work?
Use the same basis set Use all short-listed basis sets
Simulate resultsComparison with previous
experimental work. Any published work?
Realistic molecular/cluster model
Produce own experimental results
YES NO
YES
NO
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Basis set accuracy:comparison with experimental data
Dye 1
Ligand-QD
Dye 2
CdSe QD
Literature
List of basis set: http://www.gaussian.com/g_tech/g_ur/m_basis_sets.htm
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Application: Quantum dot solar cell
A. Electron injections:Is it POSSIBLE & EFFICIENT?
QDLigand
e-
Wor
king
ele
ctro
deLigand
Ligand
Ligand
Ligand
Ligand
Ligand
Ligand
Quantum dot
TiO2
TiO2
Electrolyte
Coun
ter e
lect
rode
e-
e-
e-
e-
e-
B. Ligand-QD adsorptionIs it POSSIBLE & HOW STRONG?
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Series of simulation
Structure optimization
Frequency simulation
Energy calculation
Full population simulation
Size calculation
INPUT Optimization of: Bond length, Angle and Dihedral angle
Positive vibrational frequency: A realistic molecular/cluster model
Energy: Ground state & excited state
Visualization of excited and ground state’s electron density
Size of modeled molecule/cluster
With estimated parameters (to be optimized)
PROCESSES RESULTS
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Input preparations
• Input:– Molecules (i.e., ligand molecules)– Quasi-Crystals (Quantum dots semiconductor)
• Drawing Tools:– ChemDraw– Chem3D– Gaussview
• Ab initio DFT Tool: Gaussian 09W
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Input: Ligand molecule
What is a molecule?A group of atoms bonded together, representing the smallest
fundamental unit of a chemical compound that can take part in a chemical reaction
A single molecule can represents a system consists of ten/hundreds/thousands/millions/billions of
them
Merriam-Webster Dictionary
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Input Step 1: Draw molecule
OHHO
OO
HS
OHHO
OO
HS
Select All, Grab & Drag to
Draw using Chemdraw
Chemdraw 3D & release
Save As *.mol2
Molecule
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Input Step 2: Labeling molecule
Open *.mol2 file using Gaussview 5.0
1. Right click2. Select “View”
Molecule
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Input Step 3: Rearrange numbers
• Click “edit” – “Atom list”• A new interface appears: showing labels.
Rearrange the numbers in a nice flow.
Before & After
Computer generated Z-Matrix:Pro: Can be straight away use as simulation input.Con: Tested & may cause longer simulation time.Solution: Spend time building our own Z-Matrix
Molecule
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Input Step 4: Building z-matrix• Define all atoms using:
– Bond length– Angle– Dihedral angle
• 1H need no definition: starts from here• 2O is connected to 1H by A BOND• 3C is connected to 2O by A BOND is bent from 1H by AN ANGLE• 4O is connected to 3C by A BOND is bent from 2O by AN ANGLE is twisted from 1H by a DIHEDRAL ANGLE• 5C is…next slide
Molecule
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Input Step 5: Defining bond, angle & dihedral angle
• 5C is connected to by a bond is bent from by an angle is twisted from by a dihedral angle
?
?
?
3C
2O
1H
3C
1H
5C
2O
3C
1H
2O5C
3C5C
1H
2O
Molecule
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Input Step 6: Z-matrix, the format1H 2O is connected to 1H by A BOND3C is connected to 2O by A BOND is bent from 1H by AN ANGLE4O is connected to 3C by A BOND is bent from 2O by AN ANGLE is twisted from 1H by a DIHEDRAL ANGLE
HO 1 B1C 2 B2 1 A1O 3 B3 2 A2 1 D1
A description of an atom must be:1. In 1 LINE2. Each line is meant for 1 atom’s description ONLY3. May use any symbol for bond, angle and dihedral4. B1, B2, A1…D1….must be stated as simulation parameters and the value will be
optimized OR as CONSTANTi. stated in DECIMAL POINT as INDICATION of CONSTANT, i.e., 1.546
ii. stated in the form of 1. ONLY as INDICATION of TO BE OPTIMIZED (Will show the full format later)
Molecule
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Input Step 7: Estimating bond length
HO 1 B1C 2 B2 1 A1C 3 B3 2 A2 1 D1
If we want to:(a) Make it as constant, change B1 with “0.96” in the Z-Matrix(b) Optimize the value, write “B1=1.”
Molecule
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Input Step 8: Estimating angle
HO 1 B1C 2 B2 1 A1C 3 B3 2 A2 1 D1
B2=1.43A1=109.47122
Molecule
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Input Step 9: Estimating dihedral angle
HO 1 B1C 2 B2 1 A1C 3 B3 2 A2 1 D1
B3=1.2584A2=120.0
D1=30.0
Molecule
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Input Step 10: Full Z-Matrix
• TEST the z-matrix:– Open Gaussian 09W– Click “File” & “New”– Key in %section,route section and title as indicated– Copy & Paste the Z-matrix in the “Molecule Specification” field– Save Job As….(any name)– Open the file using Gaussview 5.0– If the Z-Matrix is CORRECT, it will show the same molecule
model as the reference
FULL Z-MATRIX
Molecule
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Input: DoneBuild
reference molecule
Build Z-matrix
YES
Is the model similar to the reference molecule?
ERROR/NO
ChemdrawGaussview
GaussviewWord
processing
GaussianZ-matrix testing
RUN the simulation on
Gaussian
Rearrange labelsWrite down z-matrix
From 2D to 3DBuilding z-matrix
REFINE THE MODEL:Check Z-matrix andGaussian setting
WHICH PROCESS?
Key in setting, z-matrix & save the MODEL
Molecule
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Series of simulation
Structure optimization
Frequency simulation
Energy calculation
Full population simulation
Size calculation
INPUT Optimization of: Bond length, Angle and Dihedral angle
Positive vibrational frequency: A realistic molecular/cluster model
Energy: Ground state & excited state
Visualization of excited and ground state’s electron density
Size of modeled molecule/cluster
With estimated parameters (to be optimized)
PROCESSES RESULTS
Molecule
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%Section fieldMolecule
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%Section field
• The directory to save “.chk” file (a file that records all calculations, achievable at any simulation process by using “check” command in “Route Section”):%chk= C:\g09w\PbTe.chk
• Stating the amount of memory usage in MW (megawords). 1 MW=3.81 MBytes%mem=200MW
Molecule
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Route Section fieldMolecule
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Route Section 1: Geometry opt.
• Stating the command line of simulation:
• # opt b3lyp/lanl2dz direct optcyc=100
Functional Basis set
Geometry optimization command
Max number of optimization
No calculation storage required (faster process)
Job initiation
Molecule
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Route Section 2: Frequency
• Stating the command line of simulation:
• #n b3lyp/lanl2dz direct freq geom=check guess=check
Frequency command Retrieve molecular orbitals data from
“.chk” file (previous geometry opt.)
Default:Normal print level of output
Retrieve internal coordinate from “.chk” file (previous geometry opt.)
Molecule
Without “geom=check” and “guess=check” command:Have to state “Optimized Z-matrix” in the “Molecule Spec” field
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Route Section 3: Energy
• Stating the command line of simulation:
#n b3lyp/lanl2dz direct TD (direct, singlet, root=1, Nstates=50)geom=check guess=check
Singlet excited state Number of each type of state to be solved. Default=3
Time dependent
State of interest. Default is 1 (first excited state)
Molecule
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Route Section 4: Full population
• Stating the command line of simulation:
#n b3lyp/lanl2dz pop=full geom=check guess=check
Molecular orbitals visualization, total atomic charge and orbital energies
Molecule
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Route Section 5: Cluster size estimation
• Stating the command line of simulation:
#p b3lyp/lanl2dz scrf=pcm geom=check
• Choices of solvent (to be specified in command line): http://www.gaussian.com/g_tech/g_ur/k_scrf.htm
Additional output (execution timing, messages etc)
Use with energy, geometry opt, freq calc to model systems in solution
Calculate volume & surface area of cluster in solution. Default: Water
Molecule
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Charge & MultiplicityMolecule
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Charge & multiplicity
• Charge: total charge of the molecule OR cluster = 0
NUMBER CHARGE TOTALC 4 4 16O 4 -2 -8H 6 -1 -6S 1 -2 -2
TOTAL CHARGE 0
Molecule
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Charge & multiplicity
• Multiplicity/spin multiplicity: describes how the electrons of the system exist
• 2S+1=spin multiplicity, where S is total spin quantum number
• S=n(1/2) where n=unpaired electron
OO
OO
S
H H
H
H
HH
Inorganic ChemistryJ.E. House, Academic Press 2008
mercaptosuccinic acid molecule
Molecule
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The rough model: mercaptosuccinic acid
H
H
H
H
H
H
O O
OO C C
CCS
Element Config. Valence e-
H 1 1
C 2.4 4
O 2.6 6
S 2.8.6 6
O O
OO
SHH
HH
HH
C
CC
C
UNPAIRED ELECTRON, n=0Spin multiplicity, 2S+1=2(n(1/2))+1=2(0)+1=1
Molecule
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Running the simulation
1. Click RUN2. Pop up
message: specifying output directory
Molecule
Specify *.chk directory & memory
Command line
Your desired title
Molecule/cluster charge & spin multiplicity
Molecule/cluster’s Z-Matrix
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Extracting result:Structure optimization
Optimization complete
Input for NEXT SIMULATION
Double click the output
Open in Gaussview
Save as Gaussian Input Files (.gjf)
Frequency simulation
Energy calculation
Full population simulation
Size calculation
Work doesn’t kill,But worry does
-unknown post graduate student
Molecule
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Input for Frequency, Energy, Full Population & Size
1. Open Gaussian2. Click File3. Click Open4. Select the saved
“Structure optimization output” which saved as .gjf
5. A new interface appears (as shown)
6. Change “Route Section” to frequency/energy/full population/size command
7. Leave “Molecule Specification” blank
8. Click RUN9. Specify output directory
Molecule
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Analyzing result:Frequency simulation
Completed Freq. simulation
Double click the output
Open in Gaussview
REALISTIC MOLECULAR MODEL:Positive frequencies
Molecule
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Analyzing result:Energy simulation
Completed Energy calculation
Double click the output
Open in Gaussview
Absorption curve Oscillator strength
Molecule
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Analyzing result:Full Population
Completed Full Population
Double click the output
Open in Gaussview
Excited state energy, LUMO=-0.14320 H x 26.211=-3.753 eVGround state energy, HOMO: -0.26601 H x 26.211=-6.972 eV
LUMO
HOMO
Molecule
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Analyzing result:Molecule size
Completed Size calculation
Double click the output
Open in GaussviewSurface area (sphere)= 4πr2
197.708 Å2 = 12.568 r2
r = 3.966 Åd = 7.932 Å
Molecule
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Input: QD semiconductor
• BULK semiconductor:– Crystal– Bond length, angle and dihedral angle are constant
• QUANTUM DOT semiconductor:– Quasi-crystal– Bond length, angle & dihedral angle
change due to surface relaxations– FULL OPTIMIZATION (bond length, angle & dihedral)
Crystal
Puzder et al Phys. Rev. Lett. 92, 217401 (2004) Self-Healing of CdSe Nanocrystals: First-Principles Calculations
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Input Step 1: Download CIF
• Download (example: CdSe) CIF file from: www.crystallography.net
• Based on the CIF, build our own cluster
Crystal
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Input Step 2: Open PBC Crystal
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Input Step 3: Make bigger clusterCrystal
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Input Step 4: Making smallest meaningful cluster
Crystal
Jose et. al J. Am. Chem. Soc. 2006, 128, 629-636
SaveClick “Results”
Click “View Files”Delete “TV”
SaveClose & open again
(CdSe)3
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Spin multiplicity
• Singlet State: 2S+1=1– 2(nx1/2)+1=1– n=0 (no unpaired electrons/all electrons are paired)– No resultant magnetic moment– Magnetic moment produced by electron spin +1/2 and
-1/2 cancel out each other– The materials becomes diamagnetic– Produce slight magnetic field opposing external
magnetic field– Bulk CdSe is a diamagnetic material
Crystal
Neeleshwar et. al. Physical Review B, 2005
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Spin multiplicityState 2S+1 S=nx1/2 n
Doublet 2 ½ 1
Triplet 3 1 2
Quadruplet 4 3 ½ 3
Pentuplet… 5… 2… 4…
Material properties: Paramagnetic, Ferromagnetic, Antiferromagnetic, FerrimagneticBACK TO LITERATURE REVIEW
Crystal
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Input Step 5: Z-Matrix Preparation & Start
Crystal
SIZE 1 cluster
Rearrange labels
Z-matrix constructions
Z-matrix testing
GEOMETRY optimization
SIZE 2 cluster SIZE n cluster
FREQUENCYsimulation FULL POP SIZE
calculation
HOW can we say our cluster is a REALISTIC cluster model?
NOT OK
OK
ENERGYcalculations
FREQUENCYsimulation
SIZEcalculation
ENERGYcalculations
POSITIVE
COMPARE with experimental work
Calculated sizeAbsorption
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Analysis: A realistic cluster model
R. Jose et.al. J. Am. Chem. Soc. 2006
Crystal
Experiment Simulation
Size Matching
Absorption is structure correlated
Realistic Cluster Model?
NOYES
Meaningful simulated results
1st excitonic peak-oscillator strength
comparison
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QD+Ligand model:Reference model preparation
CrystalMolecule
OPTIMIZATION PARAMETER:1. The bond between QD and Ligand2. The angle & dihedral angle in ligand
1. Open Ligand & QD model in Gaussview2. Copy Ligand model3. Left click on the QD model to add ligand model4. Adjustment of position needed5. Link “H” in –SH functional group to Cd atom of
QD using: (from literature)6. Save reference model
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QD+Ligand model:z-matrix preparations
1. Change ligand’s Z-matrix numbering by adding 26 to the current reference number
2. Ligand’s atom number 1 will be = 1+26=27
3. 2 will be 2+26=28…so on & so forth
This Se is the 26th defined atom
QD’s Z-matrix: With pre-optimized bond length, angle & dihedral angle
Ligand’s Z-matrix: With fixed bond length. Angle & dihedral angle are to be optimized
CrystalMolecule
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QD+Ligand model:The new Z-matrix
QD
Ligand
REDEFINE THE FIRST THREE ATOM OF LIGAND’S MOLECULE
H, 8, X1, 14, Y1, 20, Z1S, 27, 1.31, 8, Y2, 6, Z2C, 28, 1.78, 27, Y3, 8, Z3
X1=3.Y1=86.Y2=147.Y3=109.Z1=-113.Z2=-173.Z3=92.
FINALIZED Z-MATRIX
CrystalMolecule
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Result analyses: Magic size cluster
• Determination of electronically stable QD structure for synthesis. (1.5nm in CdSe):– Largest quantities with identical properties– Efficient electron injections
SC
WHICH ONE OF THESE CLUSTERS, ELECTRONICALLY STABLE?R. Jose et al & Saifful et al
(CdSe)6 (CdSe)13 (CdSe)16
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Result analyses: LUMOQD-LUMOligand comparison
SC
QDLigand
e-
LUMO=-3.897 eVLUMO=-4.188 eV
HOMO=-6.529 eVHOMO = -7.238 eV
ELECTRON INJECTIONS:
INEFFICIENT
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Result analyses:Electron injection efficiency
SC
Electron population at ligand
Electron populations at QDELECTRON INJECTIONS:
INEFFICIENT
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Result analyses:QD-Ligand adsorption & strength
SC
QDLigand
Energy: X Energy: Y
QDLigand
Energy: ZAdsorption Energy Ead=Z-(X+Y)
B3LYP/LANLDZ B3LYP/LANLDZ
B3LYP/LANLDZ
EXOTHERMIC
ENDOTHERMIC
Ead=+ΔH=Ereleased – Eused=NEGATIVEEnergy released (bond making) > Energy used (bond breaking)
ΔH=Ereleased – Eused=POSITIVEEnergy released (bond making) <Energy used (bond breaking)
Physisorption Chemisorption
<0.4 eV >0.4 eV
Ead=-
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Result analyses:Adsorption: Basis Set Superposition Errors
SC
QDLigand
Energy: X
QDLigand
Energy: ZAdsorption Energy Ead=(Z+ΔBSSE)-(X+Y)
B3LYP/LANLDZ B3LYP/LANLDZ
B3LYP/LANLDZ
Zhanpeisov et. al. J. Am. Chem. Soc. 2004
Will not be covered, for the time being
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DFT Kick Start(David S. Sholl et. al.2009)