In computational physics and Quantum chemistry, the Hartree–Fock (HF) method also known as self consistent method is a method of approximation for the determination of the wave function and the energy of a quantum many-body system or many electron system in a stationary state
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
(If visualization is slow, please try downloading the file.)
Part 2 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
(If visualization is slow, please try downloading the file.)
Part 2 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
(If visualization is slow, please try downloading the file.)
Part 1 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
NQR - DEFINITION - ELECTRIC FIELD GRADIENT - NUCLEAR QUADRUPOLE MOMENT - NUCLEAR QUADRUPOLE COUPLING CONSTANT - PRINCIPLE OF NQR - ENERGY OF INTERACTION - SELECTION RULE - FREQUENCY OF TRANSITION - APPLICATIONS
It contains the basic principle of Mossbauer Spectroscopy.
Recoil energy, Dopler shift.
The instrumentation of Mossbauer Spectroscopy.
Hyperfine interactions.
Lecture 8: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
For UG students of All Engineering Branches (Mechanical Engg., Chemical Engg., Instrumentation Engg., Food Technology) and PG students of Chemistry, Physics, Biochemistry, Pharmacy
The link of the video lecture at YouTube is
https://www.youtube.com/watch?v=t3QDG8ZIX-8
UCSD NANO 266 Quantum Mechanical Modelling of Materials and Nanostructures is a graduate class that provides students with a highly practical introduction to the application of first principles quantum mechanical simulations to model, understand and predict the properties of materials and nano-structures. The syllabus includes: a brief introduction to quantum mechanics and the Hartree-Fock and density functional theory (DFT) formulations; practical simulation considerations such as convergence, selection of the appropriate functional and parameters; interpretation of the results from simulations, including the limits of accuracy of each method. Several lab sessions provide students with hands-on experience in the conduct of simulations. A key aspect of the course is in the use of programming to facilitate calculations and analysis.
(If visualization is slow, please try downloading the file.)
Part 1 of a tutorial given in the Brazilian Physical Society meeting, ENFMC. Abstract: Density-functional theory (DFT) was developed 50 years ago, connecting fundamental quantum methods from early days of quantum mechanics to our days of computer-powered science. Today DFT is the most widely used method in electronic structure calculations. It helps moving forward materials sciences from a single atom to nanoclusters and biomolecules, connecting solid-state, quantum chemistry, atomic and molecular physics, biophysics and beyond. In this tutorial, I will try to clarify this pathway under a historical view, presenting the DFT pillars and its building blocks, namely, the Hohenberg-Kohn theorem, the Kohn-Sham scheme, the local density approximation (LDA) and generalized gradient approximation (GGA). I would like to open the black box misconception of the method, and present a more pedagogical and solid perspective on DFT.
NQR - DEFINITION - ELECTRIC FIELD GRADIENT - NUCLEAR QUADRUPOLE MOMENT - NUCLEAR QUADRUPOLE COUPLING CONSTANT - PRINCIPLE OF NQR - ENERGY OF INTERACTION - SELECTION RULE - FREQUENCY OF TRANSITION - APPLICATIONS
It contains the basic principle of Mossbauer Spectroscopy.
Recoil energy, Dopler shift.
The instrumentation of Mossbauer Spectroscopy.
Hyperfine interactions.
Lecture 8: Introduction to Quantum Chemical Simulation graduate course taught at MIT in Fall 2014 by Heather Kulik. This course covers: wavefunction theory, density functional theory, force fields and molecular dynamics and sampling.
For UG students of All Engineering Branches (Mechanical Engg., Chemical Engg., Instrumentation Engg., Food Technology) and PG students of Chemistry, Physics, Biochemistry, Pharmacy
The link of the video lecture at YouTube is
https://www.youtube.com/watch?v=t3QDG8ZIX-8
STRUCTURE OF ATOM
Sub atomic Particles
Atomic Models
Atomic spectrum of hydrogen atom:
Photoelectric effect
Planck’s quantum theory
Heisenberg’s uncertainty principle
Quantum Numbers
Rules for filling of electrons in various orbitals
Usually, analysis is not considered an easy subject and it can't be understood on its own if you don't have some proper notes and clear concepts so I am here to help you in analysis for clearing few concepts on UV-Visible spectrophotometer, soon will come up with a new set of notes on new topic depending upon the response.
Describe the Schroedinger wavefunctions and energies of electrons in an atom leading to the 3 quantum numbers. These can be also observed in the line spectra of atoms.
This is a schrodinger equation and also Heiseinberg's uncertainty principle.
It is necessary to know this equation for the quantum mechanic. The wave equation, uncertainty principle of Heisenberg, time dependent and independent of schrodinguer...
Nuclear Gravitation Field Theory Demonstrates Strong Nuclear Force is GravityKen Wright
Nuclear Gravitation Field Theory (NGFT) evaluates Strong Nuclear Force with respect to Newton's Law of Gravity, and General Relativity. NGFT demonstrates that when enough nucleons are present in the nucleus to classically form a near perfect spherical shape, the proton and neutron energy levels fill in the same way the electron energy levels fill indicating the potential function is proportional to 1/r^2. NGFT demonstrates the intensity of the Nuclear Gravitation Field is stronger than the Nuclear Electric Field in order to hold the protons and neutrons together in the Nucleus. The Nuclear Gravitation Field at the surface of the Nucleus rivals that of a Neutron Star or Black Hole, therefore, it drops like a rock just outside the Nuclear surface due to Space-Time Compression. The Nuclear Gravitation Field then propagates outward with the feeble intensity we see as gravity.
The update demonstrates the apparent "saturation" of the Strong Nuclear Force occurs because of Space-Time Compression occurring within the Nucleus. This effect can only occur if the Strong Nuclear Force is Gravity.
Physics is one of the fundamental subjects taken up at school level and so forth for students aspiring to major in science or engineering streams. In addition to a strong mathematical background, an intuitive approach is essential to understand the concepts of Physics. Some of the major topics in Physics discussed at high school and college levels are mechanics, particle dynamics, electromagnetism, current electricity, modern physics, nuclear physics, thermodynamics, wave physics, ray optics, wave optics, etc. At college and university levels, as the calculus part in physics increases, the complexity of Physics Homework Help, Physics Assignment Help, Physics Project Help, Physics Term Paper Help, Physics Dissertation Help and Physics Thesis Help also increases, and students are observed to be looking for more than just classroom teaching.
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Nonequilibrium Thermodynamics of Turing-Hopf Interplay in Presence of Cross D...Premashis Kumar
A systematic introduction to nonequilibrium thermodynamics of dynamical instabilities are considered for an open nonlinear system beyond conventional Turing pattern in presence of cross diffusion. An altered condition of Turing instability in presence of cross diffusion is best reflected through a critical control parameter and wave number containing both the self- and cross-diffusion coefficients. Our main focus is on entropic and energetic cost of Turing-Hopf interplay in stationary pattern formation. Depending on the relative dispositions of Turing-Hopf codimensional instabilities from the reaction-diffusion equation it clarifies two aspects: energy cost of pattern formation, especially how Hopf instability can be utilized to dictate a stationary concentration profile, and the possibility of revealing nonequilibrium phase transition. In the Brusselator model, to understand these phenomena, we have analyzed through the relevant complex Ginzberg-Landau equation using multiscale Krylov-Bogolyubov averaging method. Due to Hopf instability it is observed that the cross-diffusion parameters can be a source of huge change in free-energy and concentration profiles.
This is a research paper presentation.Name of the paper is '-Information thermodynamics of turing pattern.It has been published by Espasito group in september 2018 edition of Physics review letter.I presented this slides as a part of evaluation of my PhD coursework..
SQUID METAMATERIALS IN THE LIGHT OF KURAMOTO MODELPremashis Kumar
SQUID metamaterials exhibit extraordinary properties like tunability, multistability,
negative magnetic permeability. We have tried to figure out a model suitable for describing
the collective behavior of globally coupled SQUID metamaterials. Mean field Kuramoto
model is a simple but successful model for explaining synchronization in many composite
systems. Kuramoto model’s success in explaining the synchronization in Josephson
junction arrays indicates that one can also transform model of SQUID metamaterials into
Kuramoto model under proper assumptions. So, we have investigated the main features
of mean-field Kuramoto model and possible variants of Kuramoto model numerically to
find out a more relevant model and corresponding modified order parameter to describe
the coherence of SQUID metamaterials that significantly affects the performance of SQUID
metamaterials.
Chimera is a counter-intuitive spatiotemporal state where two completely different states can coexist in the collective behavior of identical oscillators.SQUID metamaterials are a kind of Superconducting metamaterials.Chimeras can appear in SQUID metamaterials in the case of both local and nonlocal interactions between SQUIDs.This slide also includes an introduction to The Kuramoto model which is the most accepted model of synchronization.
One dimensional flow,Bifurcation and Metamaterial in nonlinear dynamicsPremashis Kumar
When dealing with real life systems, we try to interpret the systems qualitatively rather than
quantitatively as most of them is nonlinear in behaviour and have extremely complex dynamics.
Most fundamental approach is interpreting the differential equation vector field, and then
drawing vector fields analogous to flows of the fluid in line. By this phase portrait analysis we
can easily say how the system evolves with time. Whereas by exploiting bifurcation diagram we
can visualise the transitions due changes in parameters of dynamical system. Metamaterial is
man-made material that can be made of nonlinear materials and hence had a nonlinear response
to the electromagnetic wave. In addition, exotic properties such as a negative refractive index,
metamaterials create opportunities to tailor the phase matching conditions that must be satisfied
in any nonlinear optical structure. Here we don’t want to look at the metamaterials as a material
scientist rather our main concern is the dynamics of the metamaterial and prediction of different
phases that it is passing through.
An optical time-domain reflectometer (OTDR) is an optoelectronic instrument used to characterize an optical fiber. An OTDR is the optical equivalent of an electronic time domain reflectometer. It injects a series of optical pulses into the fiber under test and extracts, from the same end of the fiber, light that is scattered (Rayleigh backscatter) or reflected back from points along the fiber. The scattered or reflected light that is gathered back is used to characterize the optical fiber. This is equivalent to the way that an electronic time-domain meter measures reflections caused by changes in the impedance of the cable under test. The strength of the return pulses is measured and integrated as a function of time, and plotted as a function of fiber length.
Giant magnetoresistance and their applicationsPremashis Kumar
Giant magnetoresistance (GMR) is a quantum mechanical magnetoresistance effect observed in multilayers composed of alternating ferromagnetic and non-magnetic conductive layers. The 2007 Nobel Prize in Physics was awarded to Albert Fert and Peter Grünberg for the discovery of GMR.
The effect is observed as a significant change in the electrical resistance depending on whether the magnetization of adjacent ferromagnetic layers are in a parallel or an antiparallel alignment. The overall resistance is relatively low for parallel alignment and relatively high for antiparallel alignment. The magnetization direction can be controlled, for example, by applying an external magnetic field. The effect is based on the dependence of electron scattering on the spin orientation.
An Optical Time Domain Reflectometer (OTDR) is an important instrument used by organizations to certify the performance of new fiber optics links and detect problems with existing fiber links.
The term phase transition (or phase change) is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma (physics). A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium certain properties of the medium change, often discontinuously, as a result of the change of some external condition, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions are common in nature and used today in many technologies.
Presentation on measuring magnetic property of samplePremashis Kumar
I gave this presentation during my iii semester M.Sc program.This is about experiment technique to measure magnetization.Here we discuss induction method magnetometry.
In this slide you can find a brief history,progress and futuristic model of space research.It was used as presentation in central university of Rajasthan in M.Sc B.Ed course.
Slide 1: Title Slide
Extrachromosomal Inheritance
Slide 2: Introduction to Extrachromosomal Inheritance
Definition: Extrachromosomal inheritance refers to the transmission of genetic material that is not found within the nucleus.
Key Components: Involves genes located in mitochondria, chloroplasts, and plasmids.
Slide 3: Mitochondrial Inheritance
Mitochondria: Organelles responsible for energy production.
Mitochondrial DNA (mtDNA): Circular DNA molecule found in mitochondria.
Inheritance Pattern: Maternally inherited, meaning it is passed from mothers to all their offspring.
Diseases: Examples include Leber’s hereditary optic neuropathy (LHON) and mitochondrial myopathy.
Slide 4: Chloroplast Inheritance
Chloroplasts: Organelles responsible for photosynthesis in plants.
Chloroplast DNA (cpDNA): Circular DNA molecule found in chloroplasts.
Inheritance Pattern: Often maternally inherited in most plants, but can vary in some species.
Examples: Variegation in plants, where leaf color patterns are determined by chloroplast DNA.
Slide 5: Plasmid Inheritance
Plasmids: Small, circular DNA molecules found in bacteria and some eukaryotes.
Features: Can carry antibiotic resistance genes and can be transferred between cells through processes like conjugation.
Significance: Important in biotechnology for gene cloning and genetic engineering.
Slide 6: Mechanisms of Extrachromosomal Inheritance
Non-Mendelian Patterns: Do not follow Mendel’s laws of inheritance.
Cytoplasmic Segregation: During cell division, organelles like mitochondria and chloroplasts are randomly distributed to daughter cells.
Heteroplasmy: Presence of more than one type of organellar genome within a cell, leading to variation in expression.
Slide 7: Examples of Extrachromosomal Inheritance
Four O’clock Plant (Mirabilis jalapa): Shows variegated leaves due to different cpDNA in leaf cells.
Petite Mutants in Yeast: Result from mutations in mitochondrial DNA affecting respiration.
Slide 8: Importance of Extrachromosomal Inheritance
Evolution: Provides insight into the evolution of eukaryotic cells.
Medicine: Understanding mitochondrial inheritance helps in diagnosing and treating mitochondrial diseases.
Agriculture: Chloroplast inheritance can be used in plant breeding and genetic modification.
Slide 9: Recent Research and Advances
Gene Editing: Techniques like CRISPR-Cas9 are being used to edit mitochondrial and chloroplast DNA.
Therapies: Development of mitochondrial replacement therapy (MRT) for preventing mitochondrial diseases.
Slide 10: Conclusion
Summary: Extrachromosomal inheritance involves the transmission of genetic material outside the nucleus and plays a crucial role in genetics, medicine, and biotechnology.
Future Directions: Continued research and technological advancements hold promise for new treatments and applications.
Slide 11: Questions and Discussion
Invite Audience: Open the floor for any questions or further discussion on the topic.
A brief information about the SCOP protein database used in bioinformatics.
The Structural Classification of Proteins (SCOP) database is a comprehensive and authoritative resource for the structural and evolutionary relationships of proteins. It provides a detailed and curated classification of protein structures, grouping them into families, superfamilies, and folds based on their structural and sequence similarities.
The increased availability of biomedical data, particularly in the public domain, offers the opportunity to better understand human health and to develop effective therapeutics for a wide range of unmet medical needs. However, data scientists remain stymied by the fact that data remain hard to find and to productively reuse because data and their metadata i) are wholly inaccessible, ii) are in non-standard or incompatible representations, iii) do not conform to community standards, and iv) have unclear or highly restricted terms and conditions that preclude legitimate reuse. These limitations require a rethink on data can be made machine and AI-ready - the key motivation behind the FAIR Guiding Principles. Concurrently, while recent efforts have explored the use of deep learning to fuse disparate data into predictive models for a wide range of biomedical applications, these models often fail even when the correct answer is already known, and fail to explain individual predictions in terms that data scientists can appreciate. These limitations suggest that new methods to produce practical artificial intelligence are still needed.
In this talk, I will discuss our work in (1) building an integrative knowledge infrastructure to prepare FAIR and "AI-ready" data and services along with (2) neurosymbolic AI methods to improve the quality of predictions and to generate plausible explanations. Attention is given to standards, platforms, and methods to wrangle knowledge into simple, but effective semantic and latent representations, and to make these available into standards-compliant and discoverable interfaces that can be used in model building, validation, and explanation. Our work, and those of others in the field, creates a baseline for building trustworthy and easy to deploy AI models in biomedicine.
Bio
Dr. Michel Dumontier is the Distinguished Professor of Data Science at Maastricht University, founder and executive director of the Institute of Data Science, and co-founder of the FAIR (Findable, Accessible, Interoperable and Reusable) data principles. His research explores socio-technological approaches for responsible discovery science, which includes collaborative multi-modal knowledge graphs, privacy-preserving distributed data mining, and AI methods for drug discovery and personalized medicine. His work is supported through the Dutch National Research Agenda, the Netherlands Organisation for Scientific Research, Horizon Europe, the European Open Science Cloud, the US National Institutes of Health, and a Marie-Curie Innovative Training Network. He is the editor-in-chief for the journal Data Science and is internationally recognized for his contributions in bioinformatics, biomedical informatics, and semantic technologies including ontologies and linked data.
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
3. PERTURBATION THEORY
VARIATIONAL PRINCIPLE
WKB APPROXIMATION
Judge the quality of the wave functions by the energy
Any approximation to the ground state wave function will yield an
expectation value of the Hamiltonian that is greater than or equal to the
ground state energy i.e.
4. The Born-Oppenheimer Approximation
The motion of atomic nuclei and electrons in a molecule
can be separated.
ψ 𝑇=ψ 𝑒×ψ 𝑛
6. Electronic Schrödinger Equation for a System of
Many Electrons
1
2
𝑖=1
𝑁
𝛻2
KINETIC ENERGY
OF ELECTRONS
INTERACTION
BETWEEN ALL
NUCLEI AND
ELECTRONS
𝒊=𝟏
𝑵
𝒋>𝒊
𝑵
𝟏
𝒓𝒊𝒋
COULOMBIC
REPULSION
BETWEEN
ELECTRONS
𝒊=𝟏
𝑵
𝑨=𝟏
𝑴
𝒁 𝑨
𝒓 𝒂𝒊
7. Hartree’s Self-Consistent Field (SCF)
Approach.
For a trial wave function ,It permits the many-particle problem
to be reduced to problem of single particle.
This method invokes orbital approximation i.e. Complex wave
function of many electron system
ψ (r1, r2,…..,𝑟𝑛) = ψ𝑖(𝑟𝑖).
WHATIS SCF
METHOD?
An iterative
method
8.
9. 𝑯 𝒆𝒍𝒆𝒄= 𝟏
𝑵
𝒉 𝒆𝒍𝒆𝒄
𝒊
Ideal method for a computer as easily written as an algorithm.
Gaussian
Wave
function
Calculate
Charge
Density
Calculate
Potential
Solve
Schrodinger
equation
Calculate
Charge
density
Is Charge
Density
Same as
before?
YES
NO
ST
O
P
10. Comparison with other approximation:
Perturbation
theory with
hydrogen-
like wave
functions
Variational
theory with
effective Z
Numerical
Hartree(-
Fock)
result
Experi
mental
result
E=-5.5𝑅 𝑦 E=-5.695Ry E=-5.724Ry E=-5.807Ry
11. Hatree-Fock Method
• In 1930,Fock pointed out that Hatree
wave function violates Pauli exclusion principle.
Two identical fermions cannot
occupy the same quantum state simultaneously
Wave function has to be anti-symmetric.
12. • Antisymmetric Function is defined as ψ (r1,r2)=-ψ (r2,r1).
• Main simplification :
In this model we need to use simple possible antisymmetric space one
can imagine : Antisymmetric Tensor product.
• For N=2, we have
where α is the electron spin Eigen function.
13. Slater Determinant
• A function which is determinant of atomic orbitals Slater determinant.
• For many electrons
Wave function of a multi-electron system that
satisfies
1.Anti-symmetric requirements
2.The Pauli exclusion principle.
14. Schrodinger Energy in ground state for a single slater determinant
Hatree-Fock energy.
The quantity we can measure is Electronic density ρ.
Answer is
Energy
Determine energy directly from
the minimizing orbitals BUT………
16. CRUCIAL OBSERVATION
• In theory HF limit is achieved by an infinite basis set.
• In practice finite basis sets that can approach HF limit as
efficiently as possible.
• Hatree-Fock energy is invariant under Unitary transformation on
ψ 𝟏to ψ 𝑵.
• Non-linear problem , so HF ground state energy will be
smallest Eigen value and Eigen operator of Fock operator.
“Hartree-Fock method, give us approximate wave functions
for the atoms which have errors in total enery of only a
fraction of 1%” - J. C. SLATER