SlideShare a Scribd company logo
1 of 45
Download to read offline
• Density FunctionalTheory
• Exchange And CorrelationFunctional
• Its Application
Presentedby: Saibalendu Sarkar
Poulomi Nandi
SuryaPratapSingh
Presentedto: DR. BHABANIS. MALLIK
1
DENSITY FUNCTIONAL THEORY
2
INTRODUCTION
In the period 1995-2000, density functional theory (DFT) showed
a meteoric rise to popularity in quantum-chemistry
calculations:
“a substantial majority of the [quantum chemistry] papers
published today are based on applications of the density
functional theory” [K. Raghavachari, Theor. Chem. Acc., 103,
361 (2000)].
In DFT, one does not attempt to calculate the molecular wave
function. Instead, one works with the electron probability
density, ρ(x,y,z).
Its advantages include less demanding computational effort, less
computer time, and in some cases better agreement with the
experimental values than is obtained from Hartree-Fock
procedures.
3
The schrodinger wave equation for many particle system is given as:
Ĥᴪ({ri},{RI}) = E ᴪ({ri},{RI})
Ĥ = T̂ + V̂coulomb
4
MANY PARTICLE SYSTEM PROBLEM
Born-Oppenheimer Approx.
According to this approximation :
1. Mass of Nuclei is very greater than mass of
electrons.
2. Thus Nuclei are slow and electrons are fast.
3. So, we can decouple the dynamics of Nuclei
and electrons.
4. In other words we can write the Schrodinger
wave equation by separating the electronic
and Nuclei terms.
5. THIS MAKES LIFE MUCH MORE EASIER. 5
Born-Oppenheimer Approx.
6
PROBLEMS WITH THE DIMENSIONS
Let us take a simple molecule H2O :-
Total number of electrons in the molecule = 8+2 =
10 electrons
Three spatial coordinates per electron.
So, Schrodinger equation becomes a 30
Dimensional Problem.
For ‘N’ numbers of electrons there will be ‘3N’
numbers of Dimensions.
WE HAVE TO THINK OF A BETTER WAY!!!!
7
8
DENSITY FUNCTIONAL THEORY
-FROM WAVE FUNCTION TO ELECTRON DENSITY
ELECTRON DENSITY :
n(r) =ᴪ*(r1,r2,....,rN)ᴪ(r1,r2,....,rN)
Z
ELECTRON DENSITY
X
Y
9
DENSITY FUNCTIONAL THEORY
-FROM WAVE FUNCTION TO ELECTRON DENSITY
Now, let the “i”-th electron is treated as
point charge in the field of all other
electrons. This simplifies the “many
electron problem” to “many one-electron
problem” and is written as Hartree
product of N electrons:
10
DENSITY FUNCTIONAL THEORY
-FROM WAVE FUNCTION TO ELECTRON DENSITY
11
DENSITY FUNCTIONAL THEORY
-FROM WAVE FUNCTION TO ELECTRON DENSITY
• Hohenberg and Kohn- at the heart of DFT(1964)
THEOREM 1: The ground state energy E is a
unique functional of electron density:
E = Eo[ρo(r)]
where ρ (r) represents the density function
which itself is a function of position (r).
12
DENSITY FUNCTIONAL THEORY
-FROM WAVE FUNCTION TO ELECTRON DENSITY
THEOREM 2: The electron density that
minimizes the energy of the overall functional
is the true ground state electron density:
E[ρ(r)]>Eo[ρo(r)]
13
THE ENERGY FUNCTIONAL
14
EXCHANGE-CORRELATION
FUNCTIONAL, Exc[n(r)]
• Includes all quantum mechanical terms.
• Not known-needs to be approximated.
• It is a smaller fraction of the total energy.
• Improved results are obtained by relating
exchange correlation with the first derivative
of density.
• Both exchange-correlation are long and short
distance.
• Long distance exchange-correlation is static
and short distance is dynamic. 15
THE KOHN-SHAM SCHEME
Solve a set of single-electron wave functions
that only depends on three spatial variables:
16
HOW TO SOLVE???????
17
SELF-CONSISTENCY SCHEME
1.Assume a trial density function, ρ(r)
COMPARE
3.Calculate the electron density 2.Solve Kohn-sham eq. With ρ (r).
based on the single electron Obtain single electron wave functions.
wave functions
ρ (r) = ∑ᴪ*(r)ᴪ(r)
A. If different, then begin the process from step 2.
4.
B. If identical, true ground state density is obtained.
trial
18
Calculated
APPROX. METHOD AND SOFTWARE
The approximation methods used are
 LDA (Local Density Approximation)
 LSDA (Local Spin Density Approximation)
 GGA (Generalized Gradient Approximation)
 The Xa Method(Hartree–Fock–Slater method)
 Meta-GGA Functionals
 Hybrid GGA
The software which is most popular in calculating DFT is the
VASP (Vienna Ab initio Simulation Package)
19
Density Functional Theorem :
Approximations of Exchange
and Correlation
Functional
20
H{H-F} =T(K.E) + V(e-e) + V(N-e) + E(Exchange)
H{K-S} =[T(K.E,Ks) +V(e-e,ks) +V(N-e)]+{T(K.E) -T(K.E,Ks)}+
{V(e-e) - V(e-e,Ks)} + Ex
=[T(K.E,Ks) + V(e-e,ks) + V(N-e)]+ [∆T + ∆V + Ex]
=T(K.E,Ks) + V(e-e,ks) + V(N-e) + Vxc
21
The Local-Density Approximation
(LDA)
• Exc depends upon electron density (ρ) at each point in space i.e
local value of ρ.
• Homogeneous (or uniform) electron gas (HEG/UEG) model :
Jellium
•If ρ varies extremely slowly with position then Exc is accurately
given by,
εx = exchange-correlation energy per electron of a homogeneous electron
gas of electron density ρ.
For spin unpolarised system
22
Separation of Exchange and
Correlation part
Ex = exchange-energy functional
Ec = correlation-energy functional
23
The Functionals Ex and Ec
•
•Only limiting expressions for Ec(ρ) are known exactly, leading
to numerous different approx. for Ec(ρ) .
•Ec(ρ) can be determined numerically by Monte Carlo simulations
• Ex(ρ) takes a simple analytical form for HEG model
24
Calculation of Vxc
• Therefore, functional derivative of Exc
25
The Local-Spin-Density
Approximation(LSDA)
• For open-shell molecules and molecular geometries near
dissociation it gives better result.
• LSDA allows electrons with opposite spins to have different spatial KS
orbitals
26
Generalization Of Density-
functional Theory
• E.g CH3 and O2 having N(↑) ≠ N(↓) , ρ (↑) ≠ ρ(↓) spin-
DFT will give different orbitals for electrons with different
spins.
• Species with all electrons paired and molecular geometries
in the region of the equilibrium geometry, we can expect
that ρ (↑) = ρ(↓) and LSDA → LDA
27
Generalized Gradient
Approximation(GGA)
• Why do we need gradient corrected functional?
Ex(BECK)
• Becke’s exchange functional is (commonly used Ex [GGA])
= Ex (LSDA)+ ∆ Ex (BECK)
• Commonly used GGA Ec[GGA] include the Lee–Yang–Parr
(LYP) functional
28
Meta-GGA Functionals
• Exchange correlation density functional depend on KS orbital
through the kinetic-energy density i.e on the laplacian of the
orbitals.
• Kohn–Sham kinetic-energy density for the spin-a electrons
29
Hybrid GGA
• It incorporates a portion of exact exchange from H-F
theory with exchange and correlation from other
sources (ab initio or empirical)
• Exc(hybrid) = Ex(exact) + Ex(GGA) + Ec(GGA)
30
Density Functional Theory (DFT)
: Applications
Employing DFT for Computation of Various
Properties
http://www.cecam.ie/wp-content/uploads/2013/06/logo_wid566.jpg
31
Computer Simulation and Modeling: A
Principal Tool in Computational Chemistry
Process of building a computer model, and the
interplay between experiment, simulation, and
theory.
https://en.wikipedia.org/wiki/Computer_simulation#/media/File:Molecula
r_simulation_process.svg
A computer model involves
the expression of the system
that is to be studied in terms
of some Quantum-
Mechanical equations and
algorithms. By contrast,
computer simulation
involves the running of a
computer based program
that contains these
equations.
Simulation, therefore, is the
process of running a model.
32
Systematic Development of
Density Functional Theory (DFT)
Calculations
Hohenburg, Kohn, and Sham’s work was published in 1964 and
1965.
 Soon thereafter, KS DFT using LSDA approximation was applied by
physicists to study crystalline solids.
 Around 1980, LSDA DFT molecular calculations achieved good
results for molecular geometries but failed to give accurate
dissociation energies.
 In mid-1980s, Becke’s work gave accurate dissociation energies.
 In 1988, analytic gradients were implemented in DFT which gave
good result for equilibrium geometries.
 In 1993, Gaussian was employed for DFT calculations.
 In the mid-1990s, a huge growth was experienced in molecular
calculations based on DFT.
https://pictures.royalsociety.org/assets/object_images/0/67/7760/v0_web.jpg
33
What Molecular Properties can be
Calculated using Density Functional Theory
(DFT)Calculations ?
The result of a DFT calculation is an energy value, and It involves
using the probability density functions of the electrons in a
molecule to determine other properties of the molecule.
 Molecular Geometries : Bond Angles, Bond Lengths, Dihedral Angles,
Transition-State Structures( KIE); etc.
 Energy Changes : Atomization Energies, Heats of Formation, and
Heats of reaction; Energy changes related with Isodemic Reactions and
Bond-Separation Energies, Isomerization Energies, Energy Difference
between Conformers, Rotational Barriers, Activation Energies; etc.
 Other Properties : Dipole Moments, Vibrational Frequencies,
Entropies, Gibbs Energy of Solvation, NMR Shielding Constants; etc.
 Hydrogen Bonding
34
How to Do Our Density Functional
(DFT) Calculations ?
 Involves the use of a computer software.
The choice of software depends on its own quirks,
learning curves, availability of documentation,
open/closed-source, and whether the originator of the
software has been banned for life from using it (amongst
other people).
 Most Generally used Quantum Mechanical codes are
Abinit, Quantum Espresso (QE), VASP and Gaussian.
 A list of Quantum Chemistry and Solid State Physics
software with language, basis sets, and methods is as
follows.
35
36
https://en.wikipedia.org/wiki/List_of_quantum_chemistry_and_solid-state_physics_software
37
A Comparison Of Different
Computational Methods
1. Molecular Geometry : Mean Absolute Errors (MAE) in bond lengths (A⁰)
where; A : G2 subset (32 molecules containing only first-row atoms), B : : (108
molecules including first- and second-row atoms), and C : : (40 molecules containing third-row
atoms Ga-Kr.
Level of Theory A B C
MO Models
HF 0.022 0.021
LSDA Functional
SVWN 0.017 0.016
GGA and MGGA
BLYP 0.014 0.021 0.048
Hybrid Functionals
B3LYP 0.004 0.008 0.030
B3PW91 0.008 0.011 0.020
38
2. Energetics :
 Atomization Energies : MAE and maximum errors (kcal/mol)
where; A = G2 subset (32 molecules containing only first-row atoms) , B = G2 set
(55 molecules including first- and second-row atoms), and C = 108 molecules
including first- and second-row atoms.
Level of Theory A B C
MO Models
HF/6-31G 85.9 80.5(184.5) 150.6
LSDA Functional
SVWN/6-31G 35.7 36.4 (84.0)
GGA and MGGA Functional
BLYP/6-31G 5.6 5.3 (18.8)
Hybrid Functionals
B3LYP/6-31G 5.2 (31.5)
B3PW91/6-311++G 4.8
39
 Metal- Ligand Binding Energies : MAE (kcal/mol)
where ; Complex MX+ ; M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and X = ligand.
 Enthalpy of Acivation and Forward Reactions : MAE (kcal/mol)
Level of Theory H CH3 CH2
MO Model
PCI 80 2 2 4
Density Functionals
SWVN 12
B3LYP 5 6 4
Level of Theory Activation Reaction
MO Model
HF/ 6-31G 18.7 3.8
Density Functionals
B3LYP 1.7 4.1 40
 IPs and EAs : MAE (eV)
3. Dipole Moment : D
Level of Theory IPs/G2 EA/G2
MO Model
MP2 0.1 0.1
LSDA Functionals
SVWN/ 6-311 + G 0.7 0.7
GGA and MGGA Functionals
BLYP/ 6-311 + G 0.19 0.11
Hybrid Functionals
B3LYP / aug-cc-pVDZ 0.2 0.1
B3PW91 / 6-311 + G 0.14 0.10
Molecule HF BLYP B3LYP Experiment
NH3 1.62 1.48 1.52 1.47
H2O 1.98 1.80 1.86 1.85
HF 1.92 1.75 1.80 1.83
SO2 1.99 1.57 1.67 1.63 41
Limitations Of Density Functional
Theory (DFT)
http://wordinfo.info/words/images/blindmen-elephant.gif
42
 The Hohenberg-Kohn-Sham theory is basically a ground state theory. LR-TDDFT
can only be applied to certain kind of excited states.
 Since approximate functionals are used, KS-DFT can give an energy below the
true ground state energy; e.g.- a B3LYP/cc-pVTZ geometry optimization of H2O
give an energy of -76.460 hartrees, compared with the true nonrelativistic
energy of -76.438 hartrees.
 Many of the currently used Exc functionals fail for van-der-Waals molecules;
e.g.- the BLYP, B3LYP, and BPW91 functional predict no binding in He2 and Ne2.
However, the PBE functional work fairly well .
Towards Systematic Improvability
 Iterative methods have been devised that take a very accurate ground-sate
molecular energy density found from a high-level calculation (e.g- CI) and use it
to calculate vs for the corresponding reference system and vs can be used to
find vxc and in turn, Exc can be calculated.
 DFT has been applied to give the quantitative definitions of such chemical
concepts as electronegativity, hardness and softness; etc.
43
REFERENCES
• IRA N. LEVINE
• DONALD A. MCQUARRIE
• JULIO DE PAULA AND PETER ATKINS
• CHRISTOPHER J CRAMER
• WIKIPEDIA
• YOUTUBE VIDEOES
44
Dft presentation

More Related Content

What's hot

Gaussian presentation
Gaussian presentationGaussian presentation
Gaussian presentationmojdeh y
 
Intro. to quantum chemistry
Intro. to quantum chemistryIntro. to quantum chemistry
Intro. to quantum chemistryRawat DA Greatt
 
Quantum Chemistry
Quantum ChemistryQuantum Chemistry
Quantum Chemistrybaoilleach
 
Quantum Chemistry II
Quantum Chemistry IIQuantum Chemistry II
Quantum Chemistry IIbaoilleach
 
Hartree method ppt physical chemistry
Hartree method ppt physical chemistryHartree method ppt physical chemistry
Hartree method ppt physical chemistryalikhan1414
 
Born-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptxBorn-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptxNGokila1
 
quantum view of Harmonic oscillator
quantum view of Harmonic oscillator quantum view of Harmonic oscillator
quantum view of Harmonic oscillator Ahmed Haider
 
BIOS 203 Lecture 5: Electronic excited states
BIOS 203 Lecture 5: Electronic excited statesBIOS 203 Lecture 5: Electronic excited states
BIOS 203 Lecture 5: Electronic excited statesbios203
 
Methods available in WIEN2k for the treatment of exchange and correlation ef...
Methods available in WIEN2k for the treatment  of exchange and correlation ef...Methods available in WIEN2k for the treatment  of exchange and correlation ef...
Methods available in WIEN2k for the treatment of exchange and correlation ef...ABDERRAHMANE REGGAD
 
Born–Oppenheimer Approximation.pdf
Born–Oppenheimer Approximation.pdfBorn–Oppenheimer Approximation.pdf
Born–Oppenheimer Approximation.pdfAnjali Devi J S
 

What's hot (20)

NANO266 - Lecture 4 - Introduction to DFT
NANO266 - Lecture 4 - Introduction to DFTNANO266 - Lecture 4 - Introduction to DFT
NANO266 - Lecture 4 - Introduction to DFT
 
Introduction to DFT Part 1
Introduction to DFT Part 1 Introduction to DFT Part 1
Introduction to DFT Part 1
 
Approximations in DFT
Approximations in DFTApproximations in DFT
Approximations in DFT
 
Gaussian presentation
Gaussian presentationGaussian presentation
Gaussian presentation
 
Hartree fock theory
Hartree fock theoryHartree fock theory
Hartree fock theory
 
Intro. to quantum chemistry
Intro. to quantum chemistryIntro. to quantum chemistry
Intro. to quantum chemistry
 
Quantum Chemistry
Quantum ChemistryQuantum Chemistry
Quantum Chemistry
 
Dft calculation by vasp
Dft calculation by vaspDft calculation by vasp
Dft calculation by vasp
 
Quantum Chemistry II
Quantum Chemistry IIQuantum Chemistry II
Quantum Chemistry II
 
Lecture7
Lecture7Lecture7
Lecture7
 
Ab initio md
Ab initio mdAb initio md
Ab initio md
 
Hartree method ppt physical chemistry
Hartree method ppt physical chemistryHartree method ppt physical chemistry
Hartree method ppt physical chemistry
 
NANO266 - Lecture 2 - The Hartree-Fock Approach
NANO266 - Lecture 2 - The Hartree-Fock ApproachNANO266 - Lecture 2 - The Hartree-Fock Approach
NANO266 - Lecture 2 - The Hartree-Fock Approach
 
Born-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptxBorn-Oppenheimer approximation.pptx
Born-Oppenheimer approximation.pptx
 
quantum view of Harmonic oscillator
quantum view of Harmonic oscillator quantum view of Harmonic oscillator
quantum view of Harmonic oscillator
 
BIOS 203 Lecture 5: Electronic excited states
BIOS 203 Lecture 5: Electronic excited statesBIOS 203 Lecture 5: Electronic excited states
BIOS 203 Lecture 5: Electronic excited states
 
Computational chemistry
Computational chemistryComputational chemistry
Computational chemistry
 
Methods available in WIEN2k for the treatment of exchange and correlation ef...
Methods available in WIEN2k for the treatment  of exchange and correlation ef...Methods available in WIEN2k for the treatment  of exchange and correlation ef...
Methods available in WIEN2k for the treatment of exchange and correlation ef...
 
Advanced Molecular Dynamics 2016
Advanced Molecular Dynamics 2016Advanced Molecular Dynamics 2016
Advanced Molecular Dynamics 2016
 
Born–Oppenheimer Approximation.pdf
Born–Oppenheimer Approximation.pdfBorn–Oppenheimer Approximation.pdf
Born–Oppenheimer Approximation.pdf
 

Viewers also liked

Education For Sustainable Development
Education For Sustainable DevelopmentEducation For Sustainable Development
Education For Sustainable DevelopmentJC Corpuz
 
Identitites buidling tool in discourse
Identitites buidling tool in discourseIdentitites buidling tool in discourse
Identitites buidling tool in discourseBeberly Fabayos
 
3Com 3C16793ME
3Com 3C16793ME3Com 3C16793ME
3Com 3C16793MEsavomir
 
ComicReply - Social Media Remix Contest Platform
ComicReply - Social Media Remix Contest PlatformComicReply - Social Media Remix Contest Platform
ComicReply - Social Media Remix Contest PlatformGil Katz
 
Hierarchyof needs (1)SHASHWAT MISHRA
Hierarchyof needs (1)SHASHWAT MISHRAHierarchyof needs (1)SHASHWAT MISHRA
Hierarchyof needs (1)SHASHWAT MISHRAShashwat Mishra
 
1,4- Addition of copper acetylides to unsaturated ketones
1,4- Addition of copper acetylides to unsaturated ketones1,4- Addition of copper acetylides to unsaturated ketones
1,4- Addition of copper acetylides to unsaturated ketonesSaibalendu Sarkar
 
Sim 1, alfi nurfazri, hapzi_ali, artificial_intelligence, universitas_mercu_b...
Sim 1, alfi nurfazri, hapzi_ali, artificial_intelligence, universitas_mercu_b...Sim 1, alfi nurfazri, hapzi_ali, artificial_intelligence, universitas_mercu_b...
Sim 1, alfi nurfazri, hapzi_ali, artificial_intelligence, universitas_mercu_b...Alfi Nurfazri
 
El contratista y la licitación - URACCAN NvG
El contratista y la licitación - URACCAN NvGEl contratista y la licitación - URACCAN NvG
El contratista y la licitación - URACCAN NvGEnrique Santana
 
First aid part 3
First aid part 3First aid part 3
First aid part 3drkalsame
 
Pembangunan mapan dalam islam
Pembangunan mapan dalam islamPembangunan mapan dalam islam
Pembangunan mapan dalam islamNoorNabilah
 
пр Куда идет ИБ в России? (региональные аспекты)
пр Куда идет ИБ в России? (региональные аспекты)пр Куда идет ИБ в России? (региональные аспекты)
пр Куда идет ИБ в России? (региональные аспекты)Andrey Prozorov, CISM, CIPP/E, CDPSE. LA 27001
 
Запятая в сложном предложении
Запятая в сложном предложенииЗапятая в сложном предложении
Запятая в сложном предложенииbarsko
 
Writing a research report
Writing a research reportWriting a research report
Writing a research reportMartin McMorrow
 
Types of companies
Types of companiesTypes of companies
Types of companiesRehaman M
 
First aid part 2
First aid part 2First aid part 2
First aid part 2drkalsame
 
Tutorial LearningApps
Tutorial LearningAppsTutorial LearningApps
Tutorial LearningAppsLorena Preite
 
Science investigation
Science investigationScience investigation
Science investigationTasha
 

Viewers also liked (20)

Education For Sustainable Development
Education For Sustainable DevelopmentEducation For Sustainable Development
Education For Sustainable Development
 
Identitites buidling tool in discourse
Identitites buidling tool in discourseIdentitites buidling tool in discourse
Identitites buidling tool in discourse
 
3Com 3C16793ME
3Com 3C16793ME3Com 3C16793ME
3Com 3C16793ME
 
ComicReply - Social Media Remix Contest Platform
ComicReply - Social Media Remix Contest PlatformComicReply - Social Media Remix Contest Platform
ComicReply - Social Media Remix Contest Platform
 
Hierarchyof needs (1)SHASHWAT MISHRA
Hierarchyof needs (1)SHASHWAT MISHRAHierarchyof needs (1)SHASHWAT MISHRA
Hierarchyof needs (1)SHASHWAT MISHRA
 
1,4- Addition of copper acetylides to unsaturated ketones
1,4- Addition of copper acetylides to unsaturated ketones1,4- Addition of copper acetylides to unsaturated ketones
1,4- Addition of copper acetylides to unsaturated ketones
 
Sim 1, alfi nurfazri, hapzi_ali, artificial_intelligence, universitas_mercu_b...
Sim 1, alfi nurfazri, hapzi_ali, artificial_intelligence, universitas_mercu_b...Sim 1, alfi nurfazri, hapzi_ali, artificial_intelligence, universitas_mercu_b...
Sim 1, alfi nurfazri, hapzi_ali, artificial_intelligence, universitas_mercu_b...
 
SauSsure y pierce
SauSsure y pierceSauSsure y pierce
SauSsure y pierce
 
El contratista y la licitación - URACCAN NvG
El contratista y la licitación - URACCAN NvGEl contratista y la licitación - URACCAN NvG
El contratista y la licitación - URACCAN NvG
 
First aid part 3
First aid part 3First aid part 3
First aid part 3
 
Pembangunan mapan dalam islam
Pembangunan mapan dalam islamPembangunan mapan dalam islam
Pembangunan mapan dalam islam
 
3D Internet
3D Internet3D Internet
3D Internet
 
пр Куда идет ИБ в России? (региональные аспекты)
пр Куда идет ИБ в России? (региональные аспекты)пр Куда идет ИБ в России? (региональные аспекты)
пр Куда идет ИБ в России? (региональные аспекты)
 
Запятая в сложном предложении
Запятая в сложном предложенииЗапятая в сложном предложении
Запятая в сложном предложении
 
Writing a research report
Writing a research reportWriting a research report
Writing a research report
 
Lovely thapa
Lovely thapaLovely thapa
Lovely thapa
 
Types of companies
Types of companiesTypes of companies
Types of companies
 
First aid part 2
First aid part 2First aid part 2
First aid part 2
 
Tutorial LearningApps
Tutorial LearningAppsTutorial LearningApps
Tutorial LearningApps
 
Science investigation
Science investigationScience investigation
Science investigation
 

Similar to Dft presentation

Electronic structure of strongly correlated materials
Electronic structure of strongly correlated materialsElectronic structure of strongly correlated materials
Electronic structure of strongly correlated materialsABDERRAHMANE REGGAD
 
lecture1-230501075743-146580ac computational chemistry .ppt
lecture1-230501075743-146580ac computational chemistry .pptlecture1-230501075743-146580ac computational chemistry .ppt
lecture1-230501075743-146580ac computational chemistry .pptDrSyedZulqarnainHaid
 
第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 1. KKR法
第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 1. KKR法第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 1. KKR法
第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 1. KKR法Computational Materials Science Initiative
 
slides_cedric_weber_1.pdf
slides_cedric_weber_1.pdfslides_cedric_weber_1.pdf
slides_cedric_weber_1.pdfsasdude1
 
Quantum chemical molecular dynamics simulations of graphene hydrogenation
Quantum chemical molecular dynamics simulations of graphene hydrogenationQuantum chemical molecular dynamics simulations of graphene hydrogenation
Quantum chemical molecular dynamics simulations of graphene hydrogenationStephan Irle
 
1 Aminullah Assagaf_Estimation-of-domain-of-attraction-for-the-fract_2021_Non...
1 Aminullah Assagaf_Estimation-of-domain-of-attraction-for-the-fract_2021_Non...1 Aminullah Assagaf_Estimation-of-domain-of-attraction-for-the-fract_2021_Non...
1 Aminullah Assagaf_Estimation-of-domain-of-attraction-for-the-fract_2021_Non...Aminullah Assagaf
 
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical ModelingNANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical ModelingUniversity of California, San Diego
 
Theoretical study of electronic properties of some aromatic rings
Theoretical study of electronic properties of some aromatic ringsTheoretical study of electronic properties of some aromatic rings
Theoretical study of electronic properties of some aromatic ringsAlexander Decker
 
Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...
Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...
Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...Stephan Irle
 
computationalchemistry_12-6.ppt
computationalchemistry_12-6.pptcomputationalchemistry_12-6.ppt
computationalchemistry_12-6.pptsami97008
 
Lecture: Interatomic Potentials Enabled by Machine Learning
Lecture: Interatomic Potentials Enabled by Machine LearningLecture: Interatomic Potentials Enabled by Machine Learning
Lecture: Interatomic Potentials Enabled by Machine LearningDanielSchwalbeKoda
 
DFT Presentation.pptx
DFT Presentation.pptxDFT Presentation.pptx
DFT Presentation.pptxDrRajeshDas
 
Overview combining ab initio with continuum theory
Overview combining ab initio with continuum theoryOverview combining ab initio with continuum theory
Overview combining ab initio with continuum theoryDierk Raabe
 
Computational methods and vibrational properties applied to materials modeling
Computational methods and vibrational properties applied to materials modelingComputational methods and vibrational properties applied to materials modeling
Computational methods and vibrational properties applied to materials modelingcippo1987Ita
 
Molecular modelling for M.Pharm according to PCI syllabus
Molecular modelling for M.Pharm according to PCI syllabusMolecular modelling for M.Pharm according to PCI syllabus
Molecular modelling for M.Pharm according to PCI syllabusShikha Popali
 

Similar to Dft presentation (20)

Electronic structure of strongly correlated materials
Electronic structure of strongly correlated materialsElectronic structure of strongly correlated materials
Electronic structure of strongly correlated materials
 
lecture1-230501075743-146580ac computational chemistry .ppt
lecture1-230501075743-146580ac computational chemistry .pptlecture1-230501075743-146580ac computational chemistry .ppt
lecture1-230501075743-146580ac computational chemistry .ppt
 
lecture1.ppt
lecture1.pptlecture1.ppt
lecture1.ppt
 
第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 1. KKR法
第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 1. KKR法第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 1. KKR法
第5回CCMSハンズオン(ソフトウェア講習会): AkaiKKRチュートリアル 1. KKR法
 
slides_cedric_weber_1.pdf
slides_cedric_weber_1.pdfslides_cedric_weber_1.pdf
slides_cedric_weber_1.pdf
 
first research paper
first research paperfirst research paper
first research paper
 
Quantum chemical molecular dynamics simulations of graphene hydrogenation
Quantum chemical molecular dynamics simulations of graphene hydrogenationQuantum chemical molecular dynamics simulations of graphene hydrogenation
Quantum chemical molecular dynamics simulations of graphene hydrogenation
 
paper
paperpaper
paper
 
1 Aminullah Assagaf_Estimation-of-domain-of-attraction-for-the-fract_2021_Non...
1 Aminullah Assagaf_Estimation-of-domain-of-attraction-for-the-fract_2021_Non...1 Aminullah Assagaf_Estimation-of-domain-of-attraction-for-the-fract_2021_Non...
1 Aminullah Assagaf_Estimation-of-domain-of-attraction-for-the-fract_2021_Non...
 
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical ModelingNANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
NANO266 - Lecture 6 - Molecule Properties from Quantum Mechanical Modeling
 
finland.ppt
finland.pptfinland.ppt
finland.ppt
 
Theoretical study of electronic properties of some aromatic rings
Theoretical study of electronic properties of some aromatic ringsTheoretical study of electronic properties of some aromatic rings
Theoretical study of electronic properties of some aromatic rings
 
AI_HF_6.pdf
AI_HF_6.pdfAI_HF_6.pdf
AI_HF_6.pdf
 
Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...
Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...
Density-Functional Tight-Binding (DFTB) as fast approximate DFT method - An i...
 
computationalchemistry_12-6.ppt
computationalchemistry_12-6.pptcomputationalchemistry_12-6.ppt
computationalchemistry_12-6.ppt
 
Lecture: Interatomic Potentials Enabled by Machine Learning
Lecture: Interatomic Potentials Enabled by Machine LearningLecture: Interatomic Potentials Enabled by Machine Learning
Lecture: Interatomic Potentials Enabled by Machine Learning
 
DFT Presentation.pptx
DFT Presentation.pptxDFT Presentation.pptx
DFT Presentation.pptx
 
Overview combining ab initio with continuum theory
Overview combining ab initio with continuum theoryOverview combining ab initio with continuum theory
Overview combining ab initio with continuum theory
 
Computational methods and vibrational properties applied to materials modeling
Computational methods and vibrational properties applied to materials modelingComputational methods and vibrational properties applied to materials modeling
Computational methods and vibrational properties applied to materials modeling
 
Molecular modelling for M.Pharm according to PCI syllabus
Molecular modelling for M.Pharm according to PCI syllabusMolecular modelling for M.Pharm according to PCI syllabus
Molecular modelling for M.Pharm according to PCI syllabus
 

Recently uploaded

THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptxTHE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptxAkinrotimiOluwadunsi
 
Principles & Formulation of Hair Care Products
Principles & Formulation of Hair Care  ProductsPrinciples & Formulation of Hair Care  Products
Principles & Formulation of Hair Care Productspurwaborkar@gmail.com
 
Controlling Parameters of Carbonate platform Environment
Controlling Parameters of Carbonate platform EnvironmentControlling Parameters of Carbonate platform Environment
Controlling Parameters of Carbonate platform EnvironmentRahulVishwakarma71547
 
Krishi Vigyan Kendras - कृषि विज्ञान केंद्र
Krishi Vigyan Kendras - कृषि विज्ञान केंद्रKrishi Vigyan Kendras - कृषि विज्ञान केंद्र
Krishi Vigyan Kendras - कृषि विज्ञान केंद्रKrashi Coaching
 
World Water Day 22 March 2024 - kiyorndlab
World Water Day 22 March 2024 - kiyorndlabWorld Water Day 22 March 2024 - kiyorndlab
World Water Day 22 March 2024 - kiyorndlabkiyorndlab
 
Contracts with Interdependent Preferences (2)
Contracts with Interdependent Preferences (2)Contracts with Interdependent Preferences (2)
Contracts with Interdependent Preferences (2)GRAPE
 
soft skills question paper set for bba ca
soft skills question paper set for bba casoft skills question paper set for bba ca
soft skills question paper set for bba caohsadfeeling
 
geometric quantization on coadjoint orbits
geometric quantization on coadjoint orbitsgeometric quantization on coadjoint orbits
geometric quantization on coadjoint orbitsHassan Jolany
 
Pests of wheat_Identification, Bionomics, Damage symptoms, IPM_Dr.UPR.pdf
Pests of wheat_Identification, Bionomics, Damage symptoms, IPM_Dr.UPR.pdfPests of wheat_Identification, Bionomics, Damage symptoms, IPM_Dr.UPR.pdf
Pests of wheat_Identification, Bionomics, Damage symptoms, IPM_Dr.UPR.pdfPirithiRaju
 
M.Pharm - Question Bank - Drug Delivery Systems
M.Pharm - Question Bank - Drug Delivery SystemsM.Pharm - Question Bank - Drug Delivery Systems
M.Pharm - Question Bank - Drug Delivery SystemsSumathi Arumugam
 
Digitized Continuous Magnetic Recordings for the August/September 1859 Storms...
Digitized Continuous Magnetic Recordings for the August/September 1859 Storms...Digitized Continuous Magnetic Recordings for the August/September 1859 Storms...
Digitized Continuous Magnetic Recordings for the August/September 1859 Storms...Sérgio Sacani
 
001 Case Study - Submission Point_c1051231_attempt_2023-11-23-14-08-42_ABS CW...
001 Case Study - Submission Point_c1051231_attempt_2023-11-23-14-08-42_ABS CW...001 Case Study - Submission Point_c1051231_attempt_2023-11-23-14-08-42_ABS CW...
001 Case Study - Submission Point_c1051231_attempt_2023-11-23-14-08-42_ABS CW...marwaahmad357
 
biosynthesis of the cell wall and antibiotics
biosynthesis of the cell wall and antibioticsbiosynthesis of the cell wall and antibiotics
biosynthesis of the cell wall and antibioticsSafaFallah
 
SUKDANAN DIAGNOSTIC TEST IN PHYSICAL SCIENCE ANSWER KEYY.pdf
SUKDANAN DIAGNOSTIC TEST IN PHYSICAL SCIENCE ANSWER KEYY.pdfSUKDANAN DIAGNOSTIC TEST IN PHYSICAL SCIENCE ANSWER KEYY.pdf
SUKDANAN DIAGNOSTIC TEST IN PHYSICAL SCIENCE ANSWER KEYY.pdfsantiagojoderickdoma
 
MARKER ASSISTED SELECTION IN CROP IMPROVEMENT
MARKER ASSISTED SELECTION IN CROP IMPROVEMENTMARKER ASSISTED SELECTION IN CROP IMPROVEMENT
MARKER ASSISTED SELECTION IN CROP IMPROVEMENTjipexe1248
 
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdfPests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdfPirithiRaju
 
Bureau of Indian Standards Specification of Shampoo.pptx
Bureau of Indian Standards Specification of Shampoo.pptxBureau of Indian Standards Specification of Shampoo.pptx
Bureau of Indian Standards Specification of Shampoo.pptxkastureyashashree
 

Recently uploaded (20)

Cheminformatics tools and chemistry data underpinning mass spectrometry analy...
Cheminformatics tools and chemistry data underpinning mass spectrometry analy...Cheminformatics tools and chemistry data underpinning mass spectrometry analy...
Cheminformatics tools and chemistry data underpinning mass spectrometry analy...
 
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptxTHE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
THE HISTOLOGY OF THE CARDIOVASCULAR SYSTEM 2024.pptx
 
Data delivery from the US-EPA Center for Computational Toxicology and Exposur...
Data delivery from the US-EPA Center for Computational Toxicology and Exposur...Data delivery from the US-EPA Center for Computational Toxicology and Exposur...
Data delivery from the US-EPA Center for Computational Toxicology and Exposur...
 
Principles & Formulation of Hair Care Products
Principles & Formulation of Hair Care  ProductsPrinciples & Formulation of Hair Care  Products
Principles & Formulation of Hair Care Products
 
Controlling Parameters of Carbonate platform Environment
Controlling Parameters of Carbonate platform EnvironmentControlling Parameters of Carbonate platform Environment
Controlling Parameters of Carbonate platform Environment
 
Krishi Vigyan Kendras - कृषि विज्ञान केंद्र
Krishi Vigyan Kendras - कृषि विज्ञान केंद्रKrishi Vigyan Kendras - कृषि विज्ञान केंद्र
Krishi Vigyan Kendras - कृषि विज्ञान केंद्र
 
World Water Day 22 March 2024 - kiyorndlab
World Water Day 22 March 2024 - kiyorndlabWorld Water Day 22 March 2024 - kiyorndlab
World Water Day 22 March 2024 - kiyorndlab
 
Contracts with Interdependent Preferences (2)
Contracts with Interdependent Preferences (2)Contracts with Interdependent Preferences (2)
Contracts with Interdependent Preferences (2)
 
soft skills question paper set for bba ca
soft skills question paper set for bba casoft skills question paper set for bba ca
soft skills question paper set for bba ca
 
geometric quantization on coadjoint orbits
geometric quantization on coadjoint orbitsgeometric quantization on coadjoint orbits
geometric quantization on coadjoint orbits
 
Pests of wheat_Identification, Bionomics, Damage symptoms, IPM_Dr.UPR.pdf
Pests of wheat_Identification, Bionomics, Damage symptoms, IPM_Dr.UPR.pdfPests of wheat_Identification, Bionomics, Damage symptoms, IPM_Dr.UPR.pdf
Pests of wheat_Identification, Bionomics, Damage symptoms, IPM_Dr.UPR.pdf
 
M.Pharm - Question Bank - Drug Delivery Systems
M.Pharm - Question Bank - Drug Delivery SystemsM.Pharm - Question Bank - Drug Delivery Systems
M.Pharm - Question Bank - Drug Delivery Systems
 
Digitized Continuous Magnetic Recordings for the August/September 1859 Storms...
Digitized Continuous Magnetic Recordings for the August/September 1859 Storms...Digitized Continuous Magnetic Recordings for the August/September 1859 Storms...
Digitized Continuous Magnetic Recordings for the August/September 1859 Storms...
 
Applying Cheminformatics to Develop a Structure Searchable Database of Analyt...
Applying Cheminformatics to Develop a Structure Searchable Database of Analyt...Applying Cheminformatics to Develop a Structure Searchable Database of Analyt...
Applying Cheminformatics to Develop a Structure Searchable Database of Analyt...
 
001 Case Study - Submission Point_c1051231_attempt_2023-11-23-14-08-42_ABS CW...
001 Case Study - Submission Point_c1051231_attempt_2023-11-23-14-08-42_ABS CW...001 Case Study - Submission Point_c1051231_attempt_2023-11-23-14-08-42_ABS CW...
001 Case Study - Submission Point_c1051231_attempt_2023-11-23-14-08-42_ABS CW...
 
biosynthesis of the cell wall and antibiotics
biosynthesis of the cell wall and antibioticsbiosynthesis of the cell wall and antibiotics
biosynthesis of the cell wall and antibiotics
 
SUKDANAN DIAGNOSTIC TEST IN PHYSICAL SCIENCE ANSWER KEYY.pdf
SUKDANAN DIAGNOSTIC TEST IN PHYSICAL SCIENCE ANSWER KEYY.pdfSUKDANAN DIAGNOSTIC TEST IN PHYSICAL SCIENCE ANSWER KEYY.pdf
SUKDANAN DIAGNOSTIC TEST IN PHYSICAL SCIENCE ANSWER KEYY.pdf
 
MARKER ASSISTED SELECTION IN CROP IMPROVEMENT
MARKER ASSISTED SELECTION IN CROP IMPROVEMENTMARKER ASSISTED SELECTION IN CROP IMPROVEMENT
MARKER ASSISTED SELECTION IN CROP IMPROVEMENT
 
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdfPests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
Pests of cumbu_Identification, Binomics, Integrated ManagementDr.UPR.pdf
 
Bureau of Indian Standards Specification of Shampoo.pptx
Bureau of Indian Standards Specification of Shampoo.pptxBureau of Indian Standards Specification of Shampoo.pptx
Bureau of Indian Standards Specification of Shampoo.pptx
 

Dft presentation

  • 1. • Density FunctionalTheory • Exchange And CorrelationFunctional • Its Application Presentedby: Saibalendu Sarkar Poulomi Nandi SuryaPratapSingh Presentedto: DR. BHABANIS. MALLIK 1
  • 3. INTRODUCTION In the period 1995-2000, density functional theory (DFT) showed a meteoric rise to popularity in quantum-chemistry calculations: “a substantial majority of the [quantum chemistry] papers published today are based on applications of the density functional theory” [K. Raghavachari, Theor. Chem. Acc., 103, 361 (2000)]. In DFT, one does not attempt to calculate the molecular wave function. Instead, one works with the electron probability density, ρ(x,y,z). Its advantages include less demanding computational effort, less computer time, and in some cases better agreement with the experimental values than is obtained from Hartree-Fock procedures. 3
  • 4. The schrodinger wave equation for many particle system is given as: Ĥᴪ({ri},{RI}) = E ᴪ({ri},{RI}) Ĥ = T̂ + V̂coulomb 4 MANY PARTICLE SYSTEM PROBLEM
  • 5. Born-Oppenheimer Approx. According to this approximation : 1. Mass of Nuclei is very greater than mass of electrons. 2. Thus Nuclei are slow and electrons are fast. 3. So, we can decouple the dynamics of Nuclei and electrons. 4. In other words we can write the Schrodinger wave equation by separating the electronic and Nuclei terms. 5. THIS MAKES LIFE MUCH MORE EASIER. 5
  • 7. PROBLEMS WITH THE DIMENSIONS Let us take a simple molecule H2O :- Total number of electrons in the molecule = 8+2 = 10 electrons Three spatial coordinates per electron. So, Schrodinger equation becomes a 30 Dimensional Problem. For ‘N’ numbers of electrons there will be ‘3N’ numbers of Dimensions. WE HAVE TO THINK OF A BETTER WAY!!!! 7
  • 8. 8
  • 9. DENSITY FUNCTIONAL THEORY -FROM WAVE FUNCTION TO ELECTRON DENSITY ELECTRON DENSITY : n(r) =ᴪ*(r1,r2,....,rN)ᴪ(r1,r2,....,rN) Z ELECTRON DENSITY X Y 9
  • 10. DENSITY FUNCTIONAL THEORY -FROM WAVE FUNCTION TO ELECTRON DENSITY Now, let the “i”-th electron is treated as point charge in the field of all other electrons. This simplifies the “many electron problem” to “many one-electron problem” and is written as Hartree product of N electrons: 10
  • 11. DENSITY FUNCTIONAL THEORY -FROM WAVE FUNCTION TO ELECTRON DENSITY 11
  • 12. DENSITY FUNCTIONAL THEORY -FROM WAVE FUNCTION TO ELECTRON DENSITY • Hohenberg and Kohn- at the heart of DFT(1964) THEOREM 1: The ground state energy E is a unique functional of electron density: E = Eo[ρo(r)] where ρ (r) represents the density function which itself is a function of position (r). 12
  • 13. DENSITY FUNCTIONAL THEORY -FROM WAVE FUNCTION TO ELECTRON DENSITY THEOREM 2: The electron density that minimizes the energy of the overall functional is the true ground state electron density: E[ρ(r)]>Eo[ρo(r)] 13
  • 15. EXCHANGE-CORRELATION FUNCTIONAL, Exc[n(r)] • Includes all quantum mechanical terms. • Not known-needs to be approximated. • It is a smaller fraction of the total energy. • Improved results are obtained by relating exchange correlation with the first derivative of density. • Both exchange-correlation are long and short distance. • Long distance exchange-correlation is static and short distance is dynamic. 15
  • 16. THE KOHN-SHAM SCHEME Solve a set of single-electron wave functions that only depends on three spatial variables: 16
  • 18. SELF-CONSISTENCY SCHEME 1.Assume a trial density function, ρ(r) COMPARE 3.Calculate the electron density 2.Solve Kohn-sham eq. With ρ (r). based on the single electron Obtain single electron wave functions. wave functions ρ (r) = ∑ᴪ*(r)ᴪ(r) A. If different, then begin the process from step 2. 4. B. If identical, true ground state density is obtained. trial 18 Calculated
  • 19. APPROX. METHOD AND SOFTWARE The approximation methods used are  LDA (Local Density Approximation)  LSDA (Local Spin Density Approximation)  GGA (Generalized Gradient Approximation)  The Xa Method(Hartree–Fock–Slater method)  Meta-GGA Functionals  Hybrid GGA The software which is most popular in calculating DFT is the VASP (Vienna Ab initio Simulation Package) 19
  • 20. Density Functional Theorem : Approximations of Exchange and Correlation Functional 20
  • 21. H{H-F} =T(K.E) + V(e-e) + V(N-e) + E(Exchange) H{K-S} =[T(K.E,Ks) +V(e-e,ks) +V(N-e)]+{T(K.E) -T(K.E,Ks)}+ {V(e-e) - V(e-e,Ks)} + Ex =[T(K.E,Ks) + V(e-e,ks) + V(N-e)]+ [∆T + ∆V + Ex] =T(K.E,Ks) + V(e-e,ks) + V(N-e) + Vxc 21
  • 22. The Local-Density Approximation (LDA) • Exc depends upon electron density (ρ) at each point in space i.e local value of ρ. • Homogeneous (or uniform) electron gas (HEG/UEG) model : Jellium •If ρ varies extremely slowly with position then Exc is accurately given by, εx = exchange-correlation energy per electron of a homogeneous electron gas of electron density ρ. For spin unpolarised system 22
  • 23. Separation of Exchange and Correlation part Ex = exchange-energy functional Ec = correlation-energy functional 23
  • 24. The Functionals Ex and Ec • •Only limiting expressions for Ec(ρ) are known exactly, leading to numerous different approx. for Ec(ρ) . •Ec(ρ) can be determined numerically by Monte Carlo simulations • Ex(ρ) takes a simple analytical form for HEG model 24
  • 25. Calculation of Vxc • Therefore, functional derivative of Exc 25
  • 26. The Local-Spin-Density Approximation(LSDA) • For open-shell molecules and molecular geometries near dissociation it gives better result. • LSDA allows electrons with opposite spins to have different spatial KS orbitals 26
  • 27. Generalization Of Density- functional Theory • E.g CH3 and O2 having N(↑) ≠ N(↓) , ρ (↑) ≠ ρ(↓) spin- DFT will give different orbitals for electrons with different spins. • Species with all electrons paired and molecular geometries in the region of the equilibrium geometry, we can expect that ρ (↑) = ρ(↓) and LSDA → LDA 27
  • 28. Generalized Gradient Approximation(GGA) • Why do we need gradient corrected functional? Ex(BECK) • Becke’s exchange functional is (commonly used Ex [GGA]) = Ex (LSDA)+ ∆ Ex (BECK) • Commonly used GGA Ec[GGA] include the Lee–Yang–Parr (LYP) functional 28
  • 29. Meta-GGA Functionals • Exchange correlation density functional depend on KS orbital through the kinetic-energy density i.e on the laplacian of the orbitals. • Kohn–Sham kinetic-energy density for the spin-a electrons 29
  • 30. Hybrid GGA • It incorporates a portion of exact exchange from H-F theory with exchange and correlation from other sources (ab initio or empirical) • Exc(hybrid) = Ex(exact) + Ex(GGA) + Ec(GGA) 30
  • 31. Density Functional Theory (DFT) : Applications Employing DFT for Computation of Various Properties http://www.cecam.ie/wp-content/uploads/2013/06/logo_wid566.jpg 31
  • 32. Computer Simulation and Modeling: A Principal Tool in Computational Chemistry Process of building a computer model, and the interplay between experiment, simulation, and theory. https://en.wikipedia.org/wiki/Computer_simulation#/media/File:Molecula r_simulation_process.svg A computer model involves the expression of the system that is to be studied in terms of some Quantum- Mechanical equations and algorithms. By contrast, computer simulation involves the running of a computer based program that contains these equations. Simulation, therefore, is the process of running a model. 32
  • 33. Systematic Development of Density Functional Theory (DFT) Calculations Hohenburg, Kohn, and Sham’s work was published in 1964 and 1965.  Soon thereafter, KS DFT using LSDA approximation was applied by physicists to study crystalline solids.  Around 1980, LSDA DFT molecular calculations achieved good results for molecular geometries but failed to give accurate dissociation energies.  In mid-1980s, Becke’s work gave accurate dissociation energies.  In 1988, analytic gradients were implemented in DFT which gave good result for equilibrium geometries.  In 1993, Gaussian was employed for DFT calculations.  In the mid-1990s, a huge growth was experienced in molecular calculations based on DFT. https://pictures.royalsociety.org/assets/object_images/0/67/7760/v0_web.jpg 33
  • 34. What Molecular Properties can be Calculated using Density Functional Theory (DFT)Calculations ? The result of a DFT calculation is an energy value, and It involves using the probability density functions of the electrons in a molecule to determine other properties of the molecule.  Molecular Geometries : Bond Angles, Bond Lengths, Dihedral Angles, Transition-State Structures( KIE); etc.  Energy Changes : Atomization Energies, Heats of Formation, and Heats of reaction; Energy changes related with Isodemic Reactions and Bond-Separation Energies, Isomerization Energies, Energy Difference between Conformers, Rotational Barriers, Activation Energies; etc.  Other Properties : Dipole Moments, Vibrational Frequencies, Entropies, Gibbs Energy of Solvation, NMR Shielding Constants; etc.  Hydrogen Bonding 34
  • 35. How to Do Our Density Functional (DFT) Calculations ?  Involves the use of a computer software. The choice of software depends on its own quirks, learning curves, availability of documentation, open/closed-source, and whether the originator of the software has been banned for life from using it (amongst other people).  Most Generally used Quantum Mechanical codes are Abinit, Quantum Espresso (QE), VASP and Gaussian.  A list of Quantum Chemistry and Solid State Physics software with language, basis sets, and methods is as follows. 35
  • 36. 36
  • 38. A Comparison Of Different Computational Methods 1. Molecular Geometry : Mean Absolute Errors (MAE) in bond lengths (A⁰) where; A : G2 subset (32 molecules containing only first-row atoms), B : : (108 molecules including first- and second-row atoms), and C : : (40 molecules containing third-row atoms Ga-Kr. Level of Theory A B C MO Models HF 0.022 0.021 LSDA Functional SVWN 0.017 0.016 GGA and MGGA BLYP 0.014 0.021 0.048 Hybrid Functionals B3LYP 0.004 0.008 0.030 B3PW91 0.008 0.011 0.020 38
  • 39. 2. Energetics :  Atomization Energies : MAE and maximum errors (kcal/mol) where; A = G2 subset (32 molecules containing only first-row atoms) , B = G2 set (55 molecules including first- and second-row atoms), and C = 108 molecules including first- and second-row atoms. Level of Theory A B C MO Models HF/6-31G 85.9 80.5(184.5) 150.6 LSDA Functional SVWN/6-31G 35.7 36.4 (84.0) GGA and MGGA Functional BLYP/6-31G 5.6 5.3 (18.8) Hybrid Functionals B3LYP/6-31G 5.2 (31.5) B3PW91/6-311++G 4.8 39
  • 40.  Metal- Ligand Binding Energies : MAE (kcal/mol) where ; Complex MX+ ; M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu and X = ligand.  Enthalpy of Acivation and Forward Reactions : MAE (kcal/mol) Level of Theory H CH3 CH2 MO Model PCI 80 2 2 4 Density Functionals SWVN 12 B3LYP 5 6 4 Level of Theory Activation Reaction MO Model HF/ 6-31G 18.7 3.8 Density Functionals B3LYP 1.7 4.1 40
  • 41.  IPs and EAs : MAE (eV) 3. Dipole Moment : D Level of Theory IPs/G2 EA/G2 MO Model MP2 0.1 0.1 LSDA Functionals SVWN/ 6-311 + G 0.7 0.7 GGA and MGGA Functionals BLYP/ 6-311 + G 0.19 0.11 Hybrid Functionals B3LYP / aug-cc-pVDZ 0.2 0.1 B3PW91 / 6-311 + G 0.14 0.10 Molecule HF BLYP B3LYP Experiment NH3 1.62 1.48 1.52 1.47 H2O 1.98 1.80 1.86 1.85 HF 1.92 1.75 1.80 1.83 SO2 1.99 1.57 1.67 1.63 41
  • 42. Limitations Of Density Functional Theory (DFT) http://wordinfo.info/words/images/blindmen-elephant.gif 42
  • 43.  The Hohenberg-Kohn-Sham theory is basically a ground state theory. LR-TDDFT can only be applied to certain kind of excited states.  Since approximate functionals are used, KS-DFT can give an energy below the true ground state energy; e.g.- a B3LYP/cc-pVTZ geometry optimization of H2O give an energy of -76.460 hartrees, compared with the true nonrelativistic energy of -76.438 hartrees.  Many of the currently used Exc functionals fail for van-der-Waals molecules; e.g.- the BLYP, B3LYP, and BPW91 functional predict no binding in He2 and Ne2. However, the PBE functional work fairly well . Towards Systematic Improvability  Iterative methods have been devised that take a very accurate ground-sate molecular energy density found from a high-level calculation (e.g- CI) and use it to calculate vs for the corresponding reference system and vs can be used to find vxc and in turn, Exc can be calculated.  DFT has been applied to give the quantitative definitions of such chemical concepts as electronegativity, hardness and softness; etc. 43
  • 44. REFERENCES • IRA N. LEVINE • DONALD A. MCQUARRIE • JULIO DE PAULA AND PETER ATKINS • CHRISTOPHER J CRAMER • WIKIPEDIA • YOUTUBE VIDEOES 44