The document discusses density functional theory (DFT) and its implementation in the VASP software. It explains key concepts like the Kohn-Sham approach for approximating the many-body Schrodinger equation and the use of pseudopotentials and plane wave basis sets. It also summarizes some example calculations done in VASP like determining the binding energy of O2, equilibrium lattice constant of Cu, and band structures of Si and graphene. Key input and output files of VASP are also outlined.
Lecture 3: 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.
1. DFT+U is a method that adds Hubbard corrections to DFT to better account for localized electrons and electronic correlations in transition metal oxides that LDA/GGA cannot describe accurately.
2. It introduces an on-site Coulomb repulsion term U to the energy functional that favors electron localization and integer orbital occupations.
3. The U parameter can be computed using linear response theory by perturbing occupation matrices and evaluating screened response matrices in a supercell calculation.
Lecture 4: 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.
Lecture 2: 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.
Lecture 6: 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.
This document discusses the density of states function for semiconductors. It begins by deriving the density of states function for a free electron gas confined to a 3D infinite potential well. It then extends this concept to semiconductors by approximating the conduction and valence band energy-momentum relationships as parabolic functions, with electron and hole effective masses. Finally, it provides an example calculation of the total number of states in silicon between the conduction band edge and the edge plus thermal energy (kT) at 300K.
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.
The document discusses density functional theory (DFT) and its implementation in the VASP software. It explains key concepts like the Kohn-Sham approach for approximating the many-body Schrodinger equation and the use of pseudopotentials and plane wave basis sets. It also summarizes some example calculations done in VASP like determining the binding energy of O2, equilibrium lattice constant of Cu, and band structures of Si and graphene. Key input and output files of VASP are also outlined.
Lecture 3: 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.
1. DFT+U is a method that adds Hubbard corrections to DFT to better account for localized electrons and electronic correlations in transition metal oxides that LDA/GGA cannot describe accurately.
2. It introduces an on-site Coulomb repulsion term U to the energy functional that favors electron localization and integer orbital occupations.
3. The U parameter can be computed using linear response theory by perturbing occupation matrices and evaluating screened response matrices in a supercell calculation.
Lecture 4: 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.
Lecture 2: 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.
Lecture 6: 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.
This document discusses the density of states function for semiconductors. It begins by deriving the density of states function for a free electron gas confined to a 3D infinite potential well. It then extends this concept to semiconductors by approximating the conduction and valence band energy-momentum relationships as parabolic functions, with electron and hole effective masses. Finally, it provides an example calculation of the total number of states in silicon between the conduction band edge and the edge plus thermal energy (kT) at 300K.
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.
Materials Modelling: From theory to solar cells (Lecture 1)cdtpv
This document provides an overview of a mini-module on materials modelling for solar energy applications. It introduces the lecturers and outlines the course structure, which includes lectures on modelling, interfaces, and multi-scale approaches. It also describes a literature review activity where students will present a research paper using materials modelling in photovoltaics. Recommended textbooks are provided on topics like bonding in solids, computational chemistry, and density functional theory for solids.
This document contains notes from the first lecture of the MIT course 10.637 (quantum chemical simulation). The key points covered include:
- An introduction to atomistic and quantum chemical simulations and how they can provide insights into materials, catalysts, and chemical systems at the nanoscale.
- An overview of the course content, which will cover classical force fields, electronic structure theory, sampling methods, excited state methods and applications in various fields.
- Details on assignments, grading, and expectations upon completing the course.
- Case studies demonstrating different simulation techniques, including reaction discovery in nanoreactors, modeling protein-ligand binding, predicting singlet fission rates, and computational screening of surface catalysts.
The document describes a practical session on DFT+U calculations. It discusses calculations on FeO using GGA and GGA+U to find insulating and metallic states. It also covers calculating the Hubbard U parameter for NiO using linear response and extrapolating to larger supercells. Finally, it proposes an exercise to perform GGA, GGA+U calculations on Cu2O, calculate the U parameter, and investigate changes to the density of states.
Lecture 5: 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.
The document discusses the semiconductor in thermal equilibrium. It defines equilibrium as a state where no external forces are acting on the semiconductor. The main charge carriers in semiconductors are electrons and holes. The density of electrons and holes depends on the density of states function and the Fermi distribution function. The distributions of electrons and holes with respect to energy are given by the density of allowed quantum states times the probability of occupation. Expressions are derived for the thermal equilibrium concentrations of electrons and holes. The intrinsic carrier concentration is defined as the concentration of electrons equal to the concentration of holes in an intrinsic semiconductor. Equations are given relating the intrinsic carrier concentration to material properties.
The document provides contact information for Statistics Homework Helper, including their website, email address, and phone number. It offers help with Statistics Homework through online tutoring services.
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.
The document discusses the pn junction diode. It describes the ideal current-voltage relationship of a pn junction diode. When a forward bias is applied, it lowers the potential barrier and allows electrons from the n-region and holes from the p-region to be injected across the depletion region, becoming minority carriers. This creates an excess minority carrier concentration that diffuses away from the junction and recombines. The current is calculated from the minority carrier diffusion currents at the edges of the depletion region. The total current is expressed as a function of the applied voltage and follows an exponential relationship.
The density of energy states (D(E)) is defined as the number of energy states per unit volume in an energy interval. It is used to calculate the number of charge carriers per unit volume of any solid. D(E) can be derived from quantum mechanics by considering the number of allowed energy states within spheres of increasing radius in momentum space. The final expression for D(E) is proportional to the square root of the energy and depends on material properties such as the effective mass of charge carriers and volume of the material.
1. The document discusses classical scattering theory and introduces concepts like Thomson scattering, polarization factors, and vector addition of waves when describing scattering processes.
2. It examines scattering by both single electrons and groups of electrons, defining atomic scattering factors to account for coherent scattering from whole atoms.
3. Examples and equations are provided to describe incoherent scattering processes like Compton scattering and how they contribute to the total scattering observed from materials.
The document discusses the geometry and factors involved in calculating the integrated intensity collected from single crystals, mosaic crystals, and powder samples during X-ray diffraction experiments. It describes how the integrated intensity is affected by the crystal structure, sample thickness, absorption, and factors like the Lorentz-polarization factor and multiplicity. It also discusses the differences between primary and secondary extinction effects in perfect and mosaic crystals.
Feynman diagrams are pictorial representations of particle reaction amplitudes. They allow calculations of rates and cross sections for physical processes like muon decay or electron-positron scattering to be greatly simplified. Each diagram has a strict mathematical interpretation corresponding to terms in a power series expansion of the reaction amplitude. Diagrams become more complex at higher orders but must be combined correctly while respecting conservation laws and process symmetries to obtain the total amplitude. The anomalous magnetic moment of particles like the electron and muon can be calculated order-by-order using Feynman diagrams, with remarkable agreement between theory and precise measurements.
Prediction of electronic and magnetic properties of Full Heusler Alloy – Ir2CrAlIOSR Journals
This document summarizes a study that used density functional theory calculations to predict the structural, electronic, and magnetic properties of the full Heusler alloy Ir2CrAl. The calculations found that Ir2CrAl has:
1) A lattice constant of 5.9648 Å after structural optimization, with a bulk modulus of 270.9 GPa.
2) Half-metallic behavior with 100% spin polarization at the Fermi level, due to an indirect band gap of 0.3 eV in the minority spin channel.
3) Ferromagnetic ordering with a total magnetic moment of 3 μB per formula unit, in agreement with Slater-Pauling rules for Heusler alloys.
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.
Density functional theory (DFT) provides an alternative approach to calculate properties of molecules by working with electron density rather than wave functions. DFT relies on two theorems linking the ground state energy and electron density. Approximations must be made for the exchange-correlation functional, with popular approximations including LDA, GGA, and hybrid functionals. DFT calculations can determine properties like molecular geometries, energies, vibrational frequencies, and more using software packages. While computationally efficient, DFT has limitations such as its reliance on approximate exchange-correlation functionals.
This presentation discusses a computational chemistry study of the interaction energies of molecules bonded through chalcogen bonds. The study examined 40 molecules total where the substituent X bonded to selenium, which was also bonded to CH3 or H, was varied. The substituents included H, F, CH3, CF3, etc. Computational methods included DFT calculations at the MP2/aug-cc-pVTZ level to determine binding energies and natural bond orbital analysis. Key concepts explained include basis sets, geometry optimization, basis set superposition error and counterpoise correction.
I am Joshua M. I am a Statistical Physics Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from, Michigan State University, UK
I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Statistical Physics Assignments .
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.
Parameters for Classical Force Fields, E. TajkhorshidTCBG
This document discusses force field parameters for molecular dynamics (MD) simulations. It covers topology and parameter files, which contain information like atom types, bonds, angles, and nonbonded parameters that an MD code uses. It describes how to make topology files for ligands, cofactors, and special residues and how to develop missing parameters. It also explains the functional forms of bonded (bond, angle, dihedral) and nonbonded (electrostatic, van der Waals) terms in the CHARMM force field. Finally, it provides guidance on obtaining parameters from literature or other sources, transferring parameters through analogy, and optimizing parameters to fit experimental data or quantum calculations when needed to parameterize new systems for MD simulations.
An alternative way to calculate spin ground state of organometallic complexes. Shown for more than one metallic centers and complex formalism, For more please feel free to mail me.
Morish Kumar is seeking a challenging position that allows growth. He has 10 years of experience in sales, customer service, and team leadership. Currently he is a Store Manager at US Polo Store, where he handles sales, team management, key performance indicators, inventory, and customer loyalty programs. Previously he held several promotions in roles at Nokia Mobile including sales promoter, product trainer, and field force area sales manager. He has a Bachelor's degree in Commerce and skills in Microsoft Office, communication, and organization.
This document provides guidance on drafting an effective mission statement for a school. It recommends forming a committee to guide the process and get input from all staff. The committee should examine exemplar mission statements to identify common patterns and ensure the new statement expresses the school's purpose, expected actions, and staff's role in improvement. When drafting, the statement should be specific, value-driven, inspiring, plausible, and either focus on short-term or long-term goals. It should use clear language and be concise at 2-5 sentences to communicate the school's core purpose and focus.
Materials Modelling: From theory to solar cells (Lecture 1)cdtpv
This document provides an overview of a mini-module on materials modelling for solar energy applications. It introduces the lecturers and outlines the course structure, which includes lectures on modelling, interfaces, and multi-scale approaches. It also describes a literature review activity where students will present a research paper using materials modelling in photovoltaics. Recommended textbooks are provided on topics like bonding in solids, computational chemistry, and density functional theory for solids.
This document contains notes from the first lecture of the MIT course 10.637 (quantum chemical simulation). The key points covered include:
- An introduction to atomistic and quantum chemical simulations and how they can provide insights into materials, catalysts, and chemical systems at the nanoscale.
- An overview of the course content, which will cover classical force fields, electronic structure theory, sampling methods, excited state methods and applications in various fields.
- Details on assignments, grading, and expectations upon completing the course.
- Case studies demonstrating different simulation techniques, including reaction discovery in nanoreactors, modeling protein-ligand binding, predicting singlet fission rates, and computational screening of surface catalysts.
The document describes a practical session on DFT+U calculations. It discusses calculations on FeO using GGA and GGA+U to find insulating and metallic states. It also covers calculating the Hubbard U parameter for NiO using linear response and extrapolating to larger supercells. Finally, it proposes an exercise to perform GGA, GGA+U calculations on Cu2O, calculate the U parameter, and investigate changes to the density of states.
Lecture 5: 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.
The document discusses the semiconductor in thermal equilibrium. It defines equilibrium as a state where no external forces are acting on the semiconductor. The main charge carriers in semiconductors are electrons and holes. The density of electrons and holes depends on the density of states function and the Fermi distribution function. The distributions of electrons and holes with respect to energy are given by the density of allowed quantum states times the probability of occupation. Expressions are derived for the thermal equilibrium concentrations of electrons and holes. The intrinsic carrier concentration is defined as the concentration of electrons equal to the concentration of holes in an intrinsic semiconductor. Equations are given relating the intrinsic carrier concentration to material properties.
The document provides contact information for Statistics Homework Helper, including their website, email address, and phone number. It offers help with Statistics Homework through online tutoring services.
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.
The document discusses the pn junction diode. It describes the ideal current-voltage relationship of a pn junction diode. When a forward bias is applied, it lowers the potential barrier and allows electrons from the n-region and holes from the p-region to be injected across the depletion region, becoming minority carriers. This creates an excess minority carrier concentration that diffuses away from the junction and recombines. The current is calculated from the minority carrier diffusion currents at the edges of the depletion region. The total current is expressed as a function of the applied voltage and follows an exponential relationship.
The density of energy states (D(E)) is defined as the number of energy states per unit volume in an energy interval. It is used to calculate the number of charge carriers per unit volume of any solid. D(E) can be derived from quantum mechanics by considering the number of allowed energy states within spheres of increasing radius in momentum space. The final expression for D(E) is proportional to the square root of the energy and depends on material properties such as the effective mass of charge carriers and volume of the material.
1. The document discusses classical scattering theory and introduces concepts like Thomson scattering, polarization factors, and vector addition of waves when describing scattering processes.
2. It examines scattering by both single electrons and groups of electrons, defining atomic scattering factors to account for coherent scattering from whole atoms.
3. Examples and equations are provided to describe incoherent scattering processes like Compton scattering and how they contribute to the total scattering observed from materials.
The document discusses the geometry and factors involved in calculating the integrated intensity collected from single crystals, mosaic crystals, and powder samples during X-ray diffraction experiments. It describes how the integrated intensity is affected by the crystal structure, sample thickness, absorption, and factors like the Lorentz-polarization factor and multiplicity. It also discusses the differences between primary and secondary extinction effects in perfect and mosaic crystals.
Feynman diagrams are pictorial representations of particle reaction amplitudes. They allow calculations of rates and cross sections for physical processes like muon decay or electron-positron scattering to be greatly simplified. Each diagram has a strict mathematical interpretation corresponding to terms in a power series expansion of the reaction amplitude. Diagrams become more complex at higher orders but must be combined correctly while respecting conservation laws and process symmetries to obtain the total amplitude. The anomalous magnetic moment of particles like the electron and muon can be calculated order-by-order using Feynman diagrams, with remarkable agreement between theory and precise measurements.
Prediction of electronic and magnetic properties of Full Heusler Alloy – Ir2CrAlIOSR Journals
This document summarizes a study that used density functional theory calculations to predict the structural, electronic, and magnetic properties of the full Heusler alloy Ir2CrAl. The calculations found that Ir2CrAl has:
1) A lattice constant of 5.9648 Å after structural optimization, with a bulk modulus of 270.9 GPa.
2) Half-metallic behavior with 100% spin polarization at the Fermi level, due to an indirect band gap of 0.3 eV in the minority spin channel.
3) Ferromagnetic ordering with a total magnetic moment of 3 μB per formula unit, in agreement with Slater-Pauling rules for Heusler alloys.
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.
Density functional theory (DFT) provides an alternative approach to calculate properties of molecules by working with electron density rather than wave functions. DFT relies on two theorems linking the ground state energy and electron density. Approximations must be made for the exchange-correlation functional, with popular approximations including LDA, GGA, and hybrid functionals. DFT calculations can determine properties like molecular geometries, energies, vibrational frequencies, and more using software packages. While computationally efficient, DFT has limitations such as its reliance on approximate exchange-correlation functionals.
This presentation discusses a computational chemistry study of the interaction energies of molecules bonded through chalcogen bonds. The study examined 40 molecules total where the substituent X bonded to selenium, which was also bonded to CH3 or H, was varied. The substituents included H, F, CH3, CF3, etc. Computational methods included DFT calculations at the MP2/aug-cc-pVTZ level to determine binding energies and natural bond orbital analysis. Key concepts explained include basis sets, geometry optimization, basis set superposition error and counterpoise correction.
I am Joshua M. I am a Statistical Physics Assignment Expert at statisticsassignmenthelp.com. I hold a Masters in Statistics from, Michigan State University, UK
I have been helping students with their homework for the past 5 years. I solve assignments related to Statistics.
Visit statisticsassignmenthelp.com or email info@statisticsassignmenthelp.com.
You can also call on +1 678 648 4277 for any assistance with Statistical Physics Assignments .
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.
Parameters for Classical Force Fields, E. TajkhorshidTCBG
This document discusses force field parameters for molecular dynamics (MD) simulations. It covers topology and parameter files, which contain information like atom types, bonds, angles, and nonbonded parameters that an MD code uses. It describes how to make topology files for ligands, cofactors, and special residues and how to develop missing parameters. It also explains the functional forms of bonded (bond, angle, dihedral) and nonbonded (electrostatic, van der Waals) terms in the CHARMM force field. Finally, it provides guidance on obtaining parameters from literature or other sources, transferring parameters through analogy, and optimizing parameters to fit experimental data or quantum calculations when needed to parameterize new systems for MD simulations.
An alternative way to calculate spin ground state of organometallic complexes. Shown for more than one metallic centers and complex formalism, For more please feel free to mail me.
Morish Kumar is seeking a challenging position that allows growth. He has 10 years of experience in sales, customer service, and team leadership. Currently he is a Store Manager at US Polo Store, where he handles sales, team management, key performance indicators, inventory, and customer loyalty programs. Previously he held several promotions in roles at Nokia Mobile including sales promoter, product trainer, and field force area sales manager. He has a Bachelor's degree in Commerce and skills in Microsoft Office, communication, and organization.
This document provides guidance on drafting an effective mission statement for a school. It recommends forming a committee to guide the process and get input from all staff. The committee should examine exemplar mission statements to identify common patterns and ensure the new statement expresses the school's purpose, expected actions, and staff's role in improvement. When drafting, the statement should be specific, value-driven, inspiring, plausible, and either focus on short-term or long-term goals. It should use clear language and be concise at 2-5 sentences to communicate the school's core purpose and focus.
El documento define a un ser humano integral como aquel que piensa con claridad y orden, explica sus pensamientos y acciones, y es consciente de sus motivaciones, valores e impedimentos. Reconoce sus fortalezas y debilidades y es capaz de enfrentar sus dificultades. Sabe cuándo iniciar y terminar procesos de pensamiento y acción de acuerdo a principios y valores.
Dr. Santosh Kumari has over 30 years of experience as a scientist at the Indian Agricultural Research Institute in New Delhi. She has risen through the ranks from Scientist to Principal Scientist. She has extensive experience in teaching plant physiology and supervising students. Her research focuses on physiological and molecular mechanisms of abiotic stress tolerance in crops like wheat, mustard, and chickpea. Some of her significant achievements include identifying genes and epialleles involved in drought tolerance, studying the role of aquaporins and ABA in wheat's response to water stress, and analyzing amino acid profiles under drought. She has guided multiple students and published widely in her field.
ISBR's students took part in HR Showcase 2015 , a mega event organised by NHRD, Bangalore at White Feather on 11th September. Here students got the opportunity to interact with few of the best coporates in the industry. They benefitted by some of the eminent speakers from the industry who mentioned the emerging HR technologies and practices to shape the future business and society. It was a great learning experience for students soon to be employed.
El documento describe los pasos para ensamblar un computador de escritorio, incluyendo la instalación de la fuente de poder, la conexión del microprocesador y el disipador de calor a la tarjeta madre, la conexión de la memoria RAM y las unidades de almacenamiento, y la conexión de los cables de energía y datos. El ensamble fue diseñado y editado por Juan Daniel Espinosa Mora para su profesor Jairo Segundo Inagan Rodríguez como un proyecto escolar en el año 2015.
1) The study evaluated converting 210 stable liver transplant recipients from twice-daily tacrolimus to a once-daily prolonged-release formulation on a 1 mg to 1 mg basis.
2) Seven patients (3.3%) withdrew from the conversion due to side effects. Liver enzymes increased mildly in some patients but renal function and uric acid levels improved.
3) Seven additional patients (3.4%) experienced suspected acute rejection after converting, though three cases were attributed to non-adherence. Most patients reported more social/travel flexibility with once-daily dosing.
This document provides guidance on communicating a school's marketing plan to staff and monitoring its progress. It recommends fully involving staff by explaining how the marketing plan fits the school's mission and priorities, as well as how staff can promote the school through examples. Staff should be offered professional development opportunities to improve their skills. The document also advises analyzing social media engagement, followers, and content to evaluate the marketing plan's effectiveness and make adjustments where needed. Print materials like brochures should align with branding standards.
The document discusses potential font and title options for a new music magazine. It considers fonts like "Modern No. 20", "Baskerville", and "Futura", settling on "Modern No. 20" as it looks stylish and professional. Several title options are proposed, including "MM", "One", "TMM", and "Diverge". The chosen title is "One" as it is simple yet ambiguous, aiming to intrigue readers and stand out from other pop music magazines. A black, dark grey, light grey and white color scheme is selected to make the magazine look sleek, professional and stylish.
IFN691 Case Study Presentation Slides by Tian LuNutty Sky
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive functioning. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms.
This document contains the resume of Hytham Eltoum Hassan, a Sudanese national born in 1971. He has over 20 years of experience in accounting and finance roles in Saudi Arabia, most recently as Finance Manager for Dash Control Systems and Al Inma Medical Services from 2007 to 2013. He holds a Bachelor's Degree in Accounting from Khartoum University and specialized training in management accounting. He is proficient in English and Arabic and has strong computer skills including Excel, PowerPoint, and Word.
The document provides ideas for designing a final project website. It suggests using older fonts to give the site a historic "scribe" appearance. It also recommends adding scrolls, parchment backgrounds, and neutral earth-toned colors. Additionally, it mentions including a prominent price request form that allows users to submit information to the owner's email for maintenance and updates.
The Complex Dependency Programme aims to establish a multi-agency approach to supporting 10,000 vulnerable people across several regions. It received £5 million in funding in 2014. Key aspects of the program include integrated teams providing a single point of access, coordinated case management, evidence-based interventions, and performance management to realize benefits and ensure accountability. The governance structure brings together multiple partners to oversee delivery and achieve the program's vision of a more empowering, coordinated system.
Este documento describe los pasos para particionar un disco duro de 60 GB en 3 particiones usando el software Partition Wizard. Primero se revisa la capacidad del disco duro, luego se descarga e instala el software y se ejecuta. A continuación, se reduce el tamaño de la partición principal a 20 GB y se crean dos particiones adicionales de 20 GB cada una para datos y música. Finalmente, se aplican los cambios reiniciando el equipo.
The document discusses several conventions used in magazine design, including slogans, mastheads, fonts, images, and page elements. On the cover, magazines typically use slogans to stand out, mastheads at the top left for branding, taglines to advertise articles, and a dominant celebrity image linked to the feature article. Inside, contents pages list articles through headings, images, page numbers and the magazine logo. Double page spreads feature a dominant celebrity image and quote, the celebrity's name in bold, columns of text, and consistent colors throughout.
Solution of morse potential for face centre cube using embedded atom methodAlexander Decker
1. The document presents an analytical method for determining parameters for the Morse potential for face-centered cubic crystals by fitting the Morse potential to the embedded atom method.
2. The method derives analytical expressions for the Morse potential parameters α and D by equating the total energy expressions from the Morse potential and embedded atom method.
3. The derived Morse potential parameters are then used to calculate the compressibility and Gruneisen's constant for various face-centered cubic metals, showing good agreement with experimental values.
Using the two forms of Fish-Bone potential (I and II), a self-consistent calculations are carried out to perform the analysis of binding energies, root mean square radii and form factors using different configuration symmetries of 20Ne nucleus. A computer simulation search program has been introduced to solve this problem. The Hilbert space was restricted to three and four dimensional variational function space spanned by single spherical harmonic oscillator orbits. A comparison using Td and D3h configuration symmetries are carried out.
1. The document discusses using the method of double-time Green's functions to study vacancy migration in a one-dimensional lattice. It derives expressions for the diffusion coefficient that account for phonon scattering and lattice rearrangement during vacancy motion.
2. The diffusion coefficient D is expressed using linear response theory as a correlation function involving the velocity operator. Approximations are made to simplify the calculation, yielding expressions for D involving spectral intensities and the mass operator and damping of the double-time Green's function.
3. The spectral intensity is expressed in terms of the mass operator and damping, and the integral of the diffusion coefficient expression is evaluated in the nearest-neighbor approximation, resulting in final expressions for the diagonal and
Eh4 energy harvesting due to random excitations and optimal designUniversity of Glasgow
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1
ECE 6340
Fall 2013
Homework 8
Assignment: Please do Probs. 1-9 and 13 from the set below.
1) In dynamics, we have the equation
E j Aω= − −∇Φ .
(a) Show that in statics, the scalar potential function Φ can be interpreted as a voltage
function. That is, show that in statics
( ) ( )
B
AB
A
V E dr A B≡ ⋅ = Φ −Φ∫ .
(b) Next, explain why this equation is not true (in general) in dynamics.
(c) Explain why the voltage drop (defined as the line integral of the electric field, as
defined above) depends on the path from A to B in dynamics, using Faraday’s law.
(d) Does the right-hand side of the above equation (the difference in the potential
function) depend on the path, in dynamics?
Hint: Note that, according to calculus, for any function ψ we have
dr dx dy dz d
x y z
ψ ψ ψ
ψ ψ
∂ ∂ ∂
∇ ⋅ = + + =
∂ ∂ ∂
.
2) Starting with Maxwell’s equations, show that the electric field radiated by an impressed
current density source J i in an infinite homogeneous region satisfies the equation
( )2 2 iE k E E j Jωµ∇ + = ∇ ∇⋅ + .
Then use Ampere’s law (or, if you prefer, the continuity equation and the electric Gauss
law) to show that this equation may be written as
( )2 2 1 i iE k E J j J
j
ωµ
σ ωε
∇ + = − ∇ ∇⋅ +
+
.
2
Note that the total current density is the sum of the impressed current density and the
conduction current density, the latter obeying Ohm’s law (J c = σE).
Explain why this equation for the electric field would be harder to solve than the equation
that was derived in class for the magnetic vector potential.
3) Show that magnetic field radiated by an impressed current density source satisfies the
equation
2 2 iH k H J∇ + = −∇× .
Explain why this equation for the magnetic field would be harder to solve than the
equation that was derived in class for the magnetic vector potential.
4) Show that in a homogenous region of space the scalar electric potential satisfies the
equation
2 2
i
v
c
k
ρ
ε
∇ Φ + Φ = − ,
where ivρ is the impressed (source) charge density, which is the charge density that goes
along with the impressed current density, being related by
i ivJ jωρ∇⋅ = −
Hint: Start with E j Aω= − −∇Φ and take the divergence of both sides. Also, take the
divergence of both sides of Ampere’s law and use the continuity equation for the
impressed current (given above) to show that
1 ii v
c c
E J
j
ρ
ωε ε
∇⋅ = − ∇⋅ = .
Note: It is also true from the electric Gauss law that
vE
ρ
ε
∇⋅ = ,
but we prefer to have only an impressed (source) charge density on the right-hand side of
the equation for the potential Φ. In the time-harmonic steady state, assuming a
homogeneous and isotropic region, it follows that ρv = ρvi. That is, there is no charge
3
density arising from the conduction current. (If there were no impressed current sources,
the total charge density would therefore be ze ...
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Tersoff Potential:Inter-atomic Potential for Semi-conductors
1. Tersoff Potential:
Interatomic Potential for
Covalent System
B. Tech. Project
Guide: Prof. Abhijit Chatterjee
Submitted By
Pallavi Kumari (Y9397)
4th Year Undergraduate Student
Department of Chemical Engineering
IIT Kanpur
2. Introduction
To predict structural properties and energetic of a complex system, a new approach to formulation of
interatomic potential is formulated by J.Tersoff. The basic of this approach is that, in real system, the strength
of each bond (i.e., the bond order) depends upon the local environment. In general, atoms with many
neighbors form weaker bonds than an atom with few neighbors. Utilizing this general idea, a new empirical
potential “tersoff potential” is formulated for silicon.
For determination of exact nature of properties and phenomenon like surface reconstructions, diffusion paths
and barriers, reaction co-ordinate and barriers, and thermal and mechanical properties, the total energy of a
system of atoms as a function of the atomic co-ordinate is required.
Among existing models which give an empirical interatomic potential E({r}), the Keating Model is the most
famous. It is roughly analogous to Taylor expansions of the energy about its minimum. The energy of N
interacting particles can be written as
(1)
Where rn is the position of nth atom and Vm is “m-body potential”.
Bond Order
While constructing an accurate potential, it is natural to abandon the use of N-body form. Since the bond
strength or bond order depends on local geometry, an environment dependent bond-order is included in
interatomic potential. The interatomic potential can be written in the form
(2)
Vij = fc (rij) [aij fR (rij) + bij fA (rij)] (3)
where E is total energy of the system. The indices I and j run over the atoms of the system and rij is the
distance from atom I to atom j. The function fR represents a repulsive pair potential which includes the
orthogonalization energy when atomic wave functions overlap, and fA represents an attractive pair potential
associated with bonding. The function fc is a smooth cutoff function to limit the range of potential.
The function bij is a measure of bond order and a monotonically decreasing function of the co-ordination of
atom I and j. The function aij consists of range limiting terms.
The function fR , fA , fc , aij and bij are taken as
fR (r) = A exp (λ1r) (4)
fA (r) = -B exp (λ2r) (5)
The cutoff function fc is a continuous function and has derivative for all r. R is chosen to include only the first-
neighbor shell.
3. fc (r) =
bij =(1+βnξijn)-1/2n (7)
ξij = fc(rik) g(θijk) exp[λ33(rij -rik)3] (8)
g(θ) = 1 + c2/d2 - c2/[d2 +(h-cosθ)2] (9)
Θijk is the bond angle between bonds ij and ik.
aij = (1+αnηijn)-1/2n (10)
ηij = fc(rik) exp[λ33(rij -rik)3] (11)
Parameters
Parameter Value
A 3264.7 eV
B 95.373 eV
λ1 3.2394 A°-1
λ2 1.3258 A°-1
λ3 1.3258 A°-1
α 0
β 0.33675
c 4.8381
d 2.0417
n 22.956
h 0
R 3.0 A°
D 0.2 A°
As α=0, from equation (10) aij = 1
Implementation of Potential Energy and Force
Energy
In equation (1), the factor of ½ takes care that, a bond is considered once. So if we eliminate this factor of ½
by
(12)
Then,
Vij = fc(rij)[aij fR (rij) + fA(rij)] (13)
(6)
4. Since R is chosen to include only the first-neighbor shell, for every i-atom it is wiser to choose only the first-
neighbor shell atom of i-atom as j-atom. The function fR and fA can be calculated easily by retrieving
parameters from input file where all the parameters are stored. For simplification in calculation of function fc
fc = ½ - ½ Sin [ (π/2)*(MAX(rij,Rij-Dij)-Rij)/Dij ] when rij < (Rij+Dij)
For calculation of ξij, again it is wiser to consider only the first-neighbor shell atom of i-atom as k-atom.
Similarly for calculation of ξji, again it is better to consider only the first-neighbor shell atom of j-atom as k-
atom. Cosθ can be easily calculated by dot product of rij and rik.
Force
As the interatomic potential is calculated by taking account of i, j and k-atom, it will contribute to forces on
these atom by
Fiζ = -
Fjζ = -
Fkζ = -
Where ζ = x,y,z and Fiζ is force on i-atom in ζ direction and so on.
Proceeding for Fiζ and putting aij = 1
Fiζ = - (14)
Leaving the summation part as it will be taken care by recursive addition within the loop
Fiζ = - * * - * [ *
* ] (15a)
Fjζ = - * * - * [ *
* ] (15b)
5. Results
The above model is applied to a close packed Silicon cube. The energy calculated from the above model is
found to be -9590.9802 eV. The model has 1000 atoms and each bond is shared between 2 atoms. Hence
Enery of one atom = (-9590.9802)/(2*1000) = -4.7954 eV
As this is an uniform packing, distance between any two adjacent atoms will be the same. Retrieving that
distance from the code which is 2.3512 A°, and assuming Si-Si bond to be tetrahedral & taking their bond
angle to be 109.4°, rjk is calculated.
rjk = = 3.835
cos θ = -0.33
From equation 9; g(θ) = 1.41147
From equation 8; ξij = 3.4244
From equation 7; bij = 0.9305
As neighborhood of every atom is same, bji = bij = 0.9305
From equation 4; fR = 3264.7 exp (-3.2394* 2.3512) = 1.6068 eV
From equation 5; fA = -97.373 exp(-1.3258*2.3512) = -4.3113 eV
From equation 3; Energy of one bond = 1*[1.6068 - 0.9305*4.3113] = -2.4047 eV
As each atom has 4 bonds and each bond is shared between 2 atoms;
Energy of one atom = 2*(-2.404) = -4.8094 eV
From literature
Fig: Cohesive energy vs volumeper atom of silicon in the diamond, simple cubic(sc), β-tin(β), simple
hexagonal (sh), bcc and fcc structures.
109.4
i
j
k
6. This graph was re-ploted with the help of pixel, the minimum energy is found to be -4.63 eV. As we are
dealing with a packing in equilibrium, the minimum energy is the energy we were looking for.
Deviation from expected result = (-4.63+4.7954) = 0.1654 eV
Considering a particular pair of atom, Force on one atom if found to be -2.0771x - 2.0771y - 2.0771z
While force on another atom j is found to be 2.0771x + 2.0771y + 2.0771z.
This force can be verified by displacing the atom by Δr and calculating its energy.
Fiζ =-
Acknowledgement
I would like to thank my B.Tech Project Guide Prof. Abhijit Chatterjee for giving me an opportunity to work in
this new field which has helped me envisioned about the deeper aspect of technologies in chemical
engineering. I would also like to acknowledge the contribution of Ms. Shraddha D. Mule to guide me through
this project.
References
1. J. Tersoff; New Empirical approach for the structure and energy of covalent systems; Physical Review
B, Volume 37, Number 12.
2. DonaldW Brenner,Olga A Shenderova, Judith A Harrison, Steven J Stuart, Boris Ni and Susan B
Sinnott; A second-generation reactive empirical bond order (REBO) potential energy expression for
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