This document provides an overview of quantum mechanics (QM) calculation methods. It discusses molecular mechanics, wavefunction methods, electron density methods, including correlation, Hartree-Fock theory, semi-empirical methods, density functional theory, and their relative speed and accuracy. Key aspects that can be calculated using these methods are also listed, such as molecular orbitals, electron density, geometry, energies, spectroscopic properties, and more. Basis sets and handling open-shell systems in calculations are also covered.
These slides are especially made to understand the postulates of quantum mechanics or chemistry better. easily simplified and at one place you will find each of relevant details about the 5 postulates. so go through it & trust me it will help you a lot if you are chemistry or a science student.
well done
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
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.
These slides are especially made to understand the postulates of quantum mechanics or chemistry better. easily simplified and at one place you will find each of relevant details about the 5 postulates. so go through it & trust me it will help you a lot if you are chemistry or a science student.
well done
This presentation is the introduction to Density Functional Theory, an essential computational approach used by Physicist and Quantum Chemist to study Solid State matter.
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.
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
lecture slide on:
Gibbs free energy and Nernst Equation, Faradaic Processes and Factors Affecting Rates of Electrode Reactions, Potentials and Thermodynamics of Cells, Kinetics of Electrode Reactions, Kinetic controlled reactions,Essentials of Electrode Reactions,BUTLER-VOLMER MODEL FOR THE ONE-STEP, ONE-ELECTRON PROCESS,Current-overpotential curves for the system, Mass Transfer by Migration And Diffusion,MASS-TRANSFER-CONTROLLED REACTIONS,
It contains the basic principle of Mossbauer Spectroscopy.
Recoil energy, Dopler shift.
The instrumentation of Mossbauer Spectroscopy.
Hyperfine interactions.
NQR - DEFINITION - ELECTRIC FIELD GRADIENT - NUCLEAR QUADRUPOLE MOMENT - NUCLEAR QUADRUPOLE COUPLING CONSTANT - PRINCIPLE OF NQR - ENERGY OF INTERACTION - SELECTION RULE - FREQUENCY OF TRANSITION - APPLICATIONS
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
CONTENTS
INTRODUCTION
CONCEPTS OF WALSH DIAGRAM
APPLICATION IN TRIATOMIC MOLECULES
[IN AH₂ TYPE OF MOLECULES(BeH₂,BH₂,H₂O)]
INTRODUCTION
Arthur Donald Walsh FRS The introducer of walsh diagram (8 August 1916-23 April 1977) was a British chemist, professor of chemistry at the University of Dundee . He was elected FRS in 1964. He was educated at Loughborough Grammar School.
Walsh diagrams were first introduced in a series of ten papers in one issue of the Journal of the Chemical Society . Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken .
A ppt compiled by Yaseen Aziz Wani pursuing M.Sc Chemistry at University of Kashmir, J&K, India and Naveed Bashir Dar, a student of electrical engg. at NIT Srinagar.
Warm regards to Munnazir Bashir also for providing us with refreshing tea while we were compiling ppt.
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
lecture slide on:
Gibbs free energy and Nernst Equation, Faradaic Processes and Factors Affecting Rates of Electrode Reactions, Potentials and Thermodynamics of Cells, Kinetics of Electrode Reactions, Kinetic controlled reactions,Essentials of Electrode Reactions,BUTLER-VOLMER MODEL FOR THE ONE-STEP, ONE-ELECTRON PROCESS,Current-overpotential curves for the system, Mass Transfer by Migration And Diffusion,MASS-TRANSFER-CONTROLLED REACTIONS,
It contains the basic principle of Mossbauer Spectroscopy.
Recoil energy, Dopler shift.
The instrumentation of Mossbauer Spectroscopy.
Hyperfine interactions.
NQR - DEFINITION - ELECTRIC FIELD GRADIENT - NUCLEAR QUADRUPOLE MOMENT - NUCLEAR QUADRUPOLE COUPLING CONSTANT - PRINCIPLE OF NQR - ENERGY OF INTERACTION - SELECTION RULE - FREQUENCY OF TRANSITION - APPLICATIONS
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
CONTENTS
INTRODUCTION
CONCEPTS OF WALSH DIAGRAM
APPLICATION IN TRIATOMIC MOLECULES
[IN AH₂ TYPE OF MOLECULES(BeH₂,BH₂,H₂O)]
INTRODUCTION
Arthur Donald Walsh FRS The introducer of walsh diagram (8 August 1916-23 April 1977) was a British chemist, professor of chemistry at the University of Dundee . He was elected FRS in 1964. He was educated at Loughborough Grammar School.
Walsh diagrams were first introduced in a series of ten papers in one issue of the Journal of the Chemical Society . Here, he aimed to rationalize the shapes adopted by polyatomic molecules in the ground state as well as in excited states, by applying theoretical contributions made by Mulliken .
A ppt compiled by Yaseen Aziz Wani pursuing M.Sc Chemistry at University of Kashmir, J&K, India and Naveed Bashir Dar, a student of electrical engg. at NIT Srinagar.
Warm regards to Munnazir Bashir also for providing us with refreshing tea while we were compiling ppt.
Lecture slides from a class introducing quantum mechanics to non-majors, giving an overview of black-body radiation, the photoelectric effect, and the Bohr model. Used as part of a course titled "A Brief history of Timekeeping," as a lead-in to talking about atomic clocks
SCF methods, basis sets, and integrals part IIIAkefAfaneh2
Some DFT implementations (such as Octopus) attempt to describe the molecular
Kohn–Sham orbitals on a real-space grid.
• A 3D simulation box is chosen together with a grid spacing, for example 0.5 a0. Then,
a grid in 3D is constructed and the SCF equations are solved on the grid.
• This is different from an MO-LCAO expansion in numerical AOs!
• Pseudopotentials are inevitable for real-space grid methods, but they are not required
when numerical AOs are used.
• A great advantage of the use of numerical AOs as in DMol3 is that the method is free
of the basis-set superposition error (BSSE).
• Because exact atomic orbitals are used, the atoms in a molecule cannot improve
their orbitals artificially using basis functions from other atoms.
Semiclassical mechanics of a non-integrable spin clusterPaul Houle
We study detailed classical-quantum correspondence for a cluster system of three spins with single-axis anisotropic exchange coupling. With autoregressive spectral estimation, we find oscillating terms in the quantum density of states caused by classical periodic orbits: in the slowly varying part of the density of states we see signs of nontrivial topology changes happening to the energy surface as the energy is varied. Also, we can explain the hierarchy of quantum energy levels near the ferromagnetic and antiferromagnetic states with EKB quantization to explain large structures and tunneling to explain small structures.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
3. What can be calculated? Molecular orbitals and their energies Electron density Molecular geometry Relative energies of two molecules NMR shifts IR and Raman frequencies and normal modes Electronic transitions (UV-Vis absorption spectrum), associated changes in electron density, optical rotation Conductivity Ionisation potential, electron affinity, heat of formation Transition states, activation energy Charge distribution Interaction energy between two molecules Solvation energy pKa How accurately can it be calculated?...
4. References Essentials of Computational Chemistry, Christopher Cramer Introduction to Computational Chemistry, Frank Jensen Molecular Modelling: Principles and Applications, Andrew Leach Computational Organic Chemistry, Steven Bachrach(http://comporgchem.com/blog/) (coming soon) Molecular Modelling Basics, Jan Jensen (http://molecularmodelingbasics.blogspot.com/) Quantum Mechanics, Tim Clark, Section 7.4 in Cheminformatics– A Textbook, Ed. Gasteiger and Engel
10. Integrate over a certain volume to find the probability of finding an electron in that volume
11. It follows that ∫|Ψ|2dr = N (number of electrons)Credit: OtherDrK (Flickr)
12. Solving the Schrodinger equation Born-Oppenheimer approximation Since electron motion is so rapid compared to nuclear motion, consider the nuclei as fixed This allows us to simplify the Hamilitonian Variational Principle The true energy of a QM system (as given by the Hamilitonian operator) is always less than the energy found if the Hamilitonian is applied to an incorrect wavefunction To find the true wavefunction, make a reasonable guess and then keep altering it to minimise the energy Hartree-Fock (HF) theory HF theory neglects electron correlation in multi-electron systems Instead, we imagine each electron interacting with a static field of all of the other electrons According to the variational principle, the lowest energy will can get with HF theory will always be greater than the true energy of the system The difference is the correlation energy
14. Linear combination of atomic orbitals (LCAO) The LCAO approximation involves expressing (“expanding”) each molecular orbital (ψ) as a sum of “basis set functions” (φx) centered on each atom ψ φ2 φ3 φ1 H C N Let’s use this parabola for our basis set functions, φx
15. Self-consistent field (SCF) procedure Based on the variational principle and the LCAO approach, a set of equations can be derived that allow the calculation of the molecular orbital coefficients (cx on previous slide) Roothaan-Hall equations The catch is that terms in the equations are weighed by elements of a density matrix P But the elements of P can only be computed if molecular orbitals are known But finding the molecular orbitals requires solving the Roothaan-Hall equations... An iterative procedure is used to get around this Make an initial guess of the values of cx Use these to calculate the elements of P Solve the Roothaan-Hall equations to give new values for cx Use these new values to calculate the elements of P If the new P is not sufficiently similar to the old P, repeat until it converges SCF not guaranteed to converge, espec. if initial guess is poor
16. Basis sets Any set of mathematical functions can be used as a basis How many functions should we use? Which functions should we use? The larger (i.e. the more components in) the basis set... The better the wavefunction can be described And the closer the energy converges towards the limit of that method The slower the calculation – N4 integrals (bottleneck) We would like to use as small a basis set as possible and still describe the wavefunction well A good solution is to use functions that have shape similar to s, p, d and f orbitals and are centered on each of the atoms Slater-Type Orbitals (STOs) Radial decay follows e-r We would like to be able to calculate all of the integrals efficiently Gaussian-Type Orbitals (GTOs) are similar to STOs but have a radial term following e-r^2 More efficient to calculate in integrals but have the wrong shape so... Replace each STO with a sum of 3 Gaussian-Type Orbitals(GTOs)
17. Radial decay of GTO vs STO Image Credit: Essentials of Computational Chemistry, Chris Cramer, Wiley, 2ndEdn.
18. How a sum of three GTOs can approximate a STO Image Credit: Essentials of Computational Chemistry, Chris Cramer, Wiley, 2ndEdn.
19. STO-3G Basis Set A minimal basis set, i.e. it has one basis function per orbital Example: for Li-H, there would be 6 basis functions in total 1s on H & 1s, 2s, 2px, 2py and 2pz on the Li Each basis function is a fixed sum of 3 Gaussian functions whose coefficients are optimised to match a STO Hence the name A minimal basis set is not sufficient to describe the wavefunction However, it may be useful to do a quick initial geometry optimisation
20. Pople’s split-valence basis sets Core orbitals are only weakly affected by binding, whereas valence orbitals can vary widely So we should enable additional flexibility for representing valence orbitals Split-valence basis sets: 3-21G, 6-21G, 4-31G,6-31G, 6-311G “3-21G” implies that each core orbital is represented by single basis function (a sum of 3 GTOs as for STO-3G) but each valence orbital is represented by two basis functions (the first a sum of 2 GTOs, the other a single GTO) In general, molecular orbitals cannot be described just in terms of the atomic orbitals of the atoms E.g. A HF calculation for NH3 with an infinite basis set just consisting of s and p functions predicts that the planar geometry is a minimum Polarisation functions need to be added, corresponding to atomic orbitals of higher angular momentum (e.g. d, f, etc.) 6-31G(d) (“6-31G*”), indicates that d orbitals are added to heavy atoms This basis set is a sort of standard for general purpose calculations 6-31G(3d2fg, 2pd) would indicate that that heavy atoms were polarised by 3 functions, 2 f, one g, while hydrogen atoms were polarised by 2 p and one d. Highest energy MOs of anions and highly excited electronic states tend to be very diffuse (tail off very slowly as the distance to the molecules increases) Add diffuse basis functions: 6-31+G(d), 6-311++G(3df,2pd) A single “+” indicates that heavy atoms have been augmented with an additional diffuse s and a set of diffuse p basis functions; another “+” indicates that hydrogen atoms have also been augmented
21. Handling open-shell systems Restricted Hartree-Fock (RHF or just HF) Closed-shell systems, all electrons paired Two approaches to handle unpaired electrons Restricted Open-shell HF (ROHF) An approximation that reuses the RHF code but handle the unpaired electron using two paired ½ electrons Fails to account for spin polarization Unrestricted HF (UHF) The SCF is carried out separately for all electrons of one spin Corresponding α and β electrons will have different spatial distribution Calculations take twice as long
22. Notation LOT/BS Level of Theory/Basis set Where “Level of Theory” simply means the type of calculation E.g. HF/3-21G or UHF/6-31G(d) Compared to energies, geometry is much less sensitive to the theoretical level So high-level calculations are often carried out at geometries optimised at a lower level (faster) LOT2/BS2//LOT1/BS1 E.g. HF/6-311+G(d)//HF/6-31G