Part 2 Electronic Structure Theory

Electron Correlation - Methods beyond Hartree-Fock

Electron Correlation - Methods beyond Hartree-Fock how to approach chemical accuracy Alexander A. Auer Max-Planck-Institute for Chemical Energy Conversion, Mülheim September 4, 2014 MMER Summerschool 2014

Simulation Methods II

Simulation Methods II Maria Fyta Institute for Computational Physics Universität Stuttgart Summer Term 2018 SM II - contents First principles methods Hartree-Fock and beyond Density-funtional-theory Ab

Quantum Mechanical Simulations

Quantum Mechanical Simulations Prof. Yan Wang Woodruff School of Mechanical Engineering Georgia Institute of Technology Atlanta, GA 30332, U.S.A. yan.wang@me.gatech.edu Topics Quantum Monte Carlo Hartree-Fock

Jack Simons, Henry Eyring Scientist and Professor Chemistry Department University of Utah

1. Born-Oppenheimer approx.- energy surfaces 2. Mean-field (Hartree-Fock) theory- orbitals 3. Pros and cons of HF- RHF, UHF 4. Beyond HF- why? 5. First, one usually does HF-how? 6. Basis sets and notations

Advanced Electronic Structure Theory Density functional theory. Dr Fred Manby

Advanced Electronic Structure Theory Density functional theory Dr Fred Manby fred.manby@bris.ac.uk http://www.chm.bris.ac.uk/pt/manby/ Course overview This is a course about density functional theory (DFT)

CHEM3023: Spins, Atoms and Molecules

CHEM3023: Spins, Atoms and Molecules Lecture 4 Molecular orbitals C.-K. Skylaris Learning outcomes Be able to manipulate expressions involving spin orbitals and molecular orbitals Be able to write down

H 2 in the minimal basis

H 2 in the minimal basis Alston J. Misquitta Centre for Condensed Matter and Materials Physics Queen Mary, University of London January 27, 2016 Overview H 2 : The 1-electron basis. The two-electron basis

CHEM3023: Spins, Atoms and Molecules

CHEM3023: Spins, Atoms and Molecules Lecture 5 The Hartree-Fock method C.-K. Skylaris Learning outcomes Be able to use the variational principle in quantum calculations Be able to construct Fock operators

LUMO + 1 LUMO. Tómas Arnar Guðmundsson Report 2 Reikniefnafræði G

Q1: Display all the MOs for N2 in your report and classify each one of them as bonding, antibonding or non-bonding, and say whether the symmetry of the orbital is σ or π. Sketch a molecular orbital diagram

The BCS Model. Sara Changizi. This presenta5on closely follows parts of chapter 6 in Ring & Schuck The nuclear many body problem.

The BCS Model Sara Changizi This presenta5on closely follows parts of chapter 6 in Ring & Schuc The nuclear many body problem. Outline Introduc5on to pairing Essen5al experimental facts The BCS model Pure

Density Func,onal Theory (Chapter 6, Jensen)

Chem 580: DFT Density Func,onal Theory (Chapter 6, Jensen) Hohenberg- Kohn Theorem (Phys. Rev., 136,B864 (1964)): For molecules with a non degenerate ground state, the ground state molecular energy and

v(r i r j ) = h(r i )+ 1 N

Chapter 1 Hartree-Fock Theory 1.1 Formalism For N electrons in an external potential V ext (r), the many-electron Hamiltonian can be written as follows: N H = [ p i i=1 m +V ext(r i )]+ 1 N N v(r i r j

AN INTRODUCTION TO QUANTUM CHEMISTRY. Mark S. Gordon Iowa State University

AN INTRODUCTION TO QUANTUM CHEMISTRY Mark S. Gordon Iowa State University 1 OUTLINE Theoretical Background in Quantum Chemistry Overview of GAMESS Program Applications 2 QUANTUM CHEMISTRY In principle,

The Basics of Theoretical and Computational Chemistry

Bernd M. Rode, Thomas S. Hofer, and Michael D. Kugler The Basics of Theoretical and Computational Chemistry BICENTENNIA BICENTBNN I AL. WILEY-VCH Verlag GmbH & Co. KGaA V Contents Preface IX 1 Introduction

CHEM3023: Spins, Atoms and Molecules

CHEM3023: Spins, Atoms and Molecules CHEM3006P or similar background knowledge is required for this course. This course has two parts: Part 1: Quantum Chemistry techniques for simulations of molecular

The Hartree-Fock approximation

Contents The Born-Oppenheimer approximation Literature Quantum mechanics 2 - Lecture 7 November 21, 2012 Contents The Born-Oppenheimer approximation Literature 1 The Born-Oppenheimer approximation 2 3

Exchange Mechanisms. Erik Koch Institute for Advanced Simulation, Forschungszentrum Jülich. lecture notes:

Exchange Mechanisms Erik Koch Institute for Advanced Simulation, Forschungszentrum Jülich lecture notes: www.cond-mat.de/events/correl Magnetism is Quantum Mechanical QUANTUM MECHANICS THE KEY TO UNDERSTANDING

On the Uniqueness of Molecular Orbitals and limitations of the MO-model.

On the Uniqueness of Molecular Orbitals and limitations of the MO-model. The purpose of these notes is to make clear that molecular orbitals are a particular way to represent many-electron wave functions.

1 Rayleigh-Schrödinger Perturbation Theory

1 Rayleigh-Schrödinger Perturbation Theory All perturbative techniques depend upon a few simple assumptions. The first of these is that we have a mathematical expression for a physical quantity for which

Physics 622: Quantum Mechanics -- Part II --

Physics 622: Quantum Mechanics -- Part II -- Instructors Prof. Seth Aubin Office: room 255, Small Hall, tel: 1-3545 Lab: room 069, Small Hall (new wing), tel: 1-3532 e-mail: saaubi@wm.edu web: http://www.physics.wm.edu/~saubin/index.html

Lecture 5: More about one- Final words about the Hartree-Fock theory. First step above it by the Møller-Plesset perturbation theory.

Lecture 5: More about one- determinant wave functions Final words about the Hartree-Fock theory. First step above it by the Møller-Plesset perturbation theory. Items from Lecture 4 Could the Koopmans theorem

Electronic structure theory: Fundamentals to frontiers. 1. Hartree-Fock theory

Electronic structure theory: Fundamentals to frontiers. 1. Hartree-Fock theory MARTIN HEAD-GORDON, Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley National

One-Electron Hamiltonians

One-Electron Hamiltonians Hartree-Fock and Density Func7onal Theory Christopher J. Cramer @ChemProfCramer 2017 MSSC, July 10, 2017 REVIEW A One-Slide Summary of Quantum Mechanics Fundamental Postulate:

3/23/2010 More basics of DFT Kieron Burke and friends UC Irvine Physics and Chemistry References for ground-state DFT ABC of DFT, by KB and Rudy Magyar, http://dft.uci.edu A Primer in Density Functional

7. Quantum Monte Carlo (QMC)

Molecular Simulations with Chemical and Biological Applications (Part I) 7. Quantum Monte Carlo (QMC) Dr. Mar(n Steinhauser 1 HS 2014 Molecular Simula(ons with Chemical and Biological Applica(ons 1 Introduc5on

Lecture 4: Hartree-Fock Theory

Lecture 4: Hartree-Fock Theory One determinant to rule them all, One determinant to find them, One determinant to bring them all and in the darkness bind them Second quantization rehearsal The formalism

Density Functional Theory for Electrons in Materials

Density Functional Theory for Electrons in Materials Richard M. Martin Department of Physics and Materials Research Laboratory University of Illinois at Urbana-Champaign 1 Density Functional Theory for

Basic quantum Hamiltonian s relativistic corrections. Abstract

Basic quantum Hamiltonian s relativistic corrections Gintautas P. Kamuntavičius Physics Department, Vytautas Magnus University, Vileikos 8, Kaunas 44404, Lithuania (Dated: 2013.03.28) arxiv:1302.0491v2

Lecture 4: methods and terminology, part II

So theory guys have got it made in rooms free of pollution. Instead of problems with the reflux, they have only solutions... In other words, experimentalists will likely die of cancer From working hard,

Electron Correlation

Electron Correlation Levels of QM Theory HΨ=EΨ Born-Oppenheimer approximation Nuclear equation: H n Ψ n =E n Ψ n Electronic equation: H e Ψ e =E e Ψ e Single determinant SCF Semi-empirical methods Correlation

Part 2 Electronic Structure Theory

HS 2014: Vorlesung Part 2 Electronic Structure Theory Dr. Mar'n O. Steinhauser Fraunhofer Ins'tute for High- Speed Dynamics, Ernst- Mach- Ins'tut, EMI, Freiburg, Germany Email: mar(n.steinhauser@unibas.ch

The par/cle-hole picture

Nuclear pairing The par/cle-hole picture The lowest state ground state- of a system A A of N=A fermions with an energy E 0 = ε i i=1 i=1 Fermi level: the highest occupied state with energy ε A The expecta/on

1 Algebra of State Vectors

J. Rothberg October 6, Introduction to Quantum Mechanics: Part Algebra of State Vectors What does the State Vector mean? A state vector is not a property of a physical system, but rather represents an

Introduction to Hartree-Fock Molecular Orbital Theory

Introduction to Hartree-Fock Molecular Orbital Theory C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology Origins of Mathematical Modeling in Chemistry Plato (ca. 428-347

The Overhauser Instability

The Overhauser Instability Zoltán Radnai and Richard Needs TCM Group ESDG Talk 14th February 2007 Typeset by FoilTEX Introduction Hartree-Fock theory and Homogeneous Electron Gas Noncollinear spins and

Beyond the Hartree-Fock Approximation: Configuration Interaction

Beyond the Hartree-Fock Approximation: Configuration Interaction The Hartree-Fock (HF) method uses a single determinant (single electronic configuration) description of the electronic wavefunction. For

CHEM6085: Density Functional Theory Lecture 10

CHEM6085: Density Functional Theory Lecture 10 1) Spin-polarised calculations 2) Geometry optimisation C.-K. Skylaris 1 Unpaired electrons So far we have developed Kohn-Sham DFT for the case of paired

Exchange-Correlation Functional

Exchange-Correlation Functional Aiichiro Nakano Collaboratory for Advanced Computing & Simulations Depts. of Computer Science, Physics & Astronomy, Chemical Engineering & Materials Science, and Biological

Quantum chemical modelling of molecular properties - parameters of EPR spectra

Quantum chemical modelling of molecular properties - parameters of EPR spectra EPR ( electric paramagnetic resonance) spectra can be obtained only for open-shell systems, since they rely on transitions

Instructor background for the discussion points of Section 2

Supplementary Information for: Orbitals Some fiction and some facts Jochen Autschbach Department of Chemistry State University of New York at Buffalo Buffalo, NY 14260 3000, USA Instructor background for

Additional background material on the Nobel Prize in Chemistry 1998

Additional background material on the Nobel Prize in Chemistry 1998 The Royal Swedish Academy of Sciences has decided to award the 1998 Nobel Prize in Chemistry with one half to Professor WALTER KOHN,

Progress toward a Monte Carlo Simulation of the Ice VI-VII Phase Transition

Progress toward a Monte Carlo Simulation of the Ice VI-VII Phase Transition Christina Gower 2010 NSF/REU PROJECT Physics Department University of Notre Dame Advisor: Dr. Kathie E. Newman August 6, 2010

First Principles Calculations to Study the Equilibrium Configuration of Ozone Molecule

First Principles Calculations to Study the Equilibrium Configuration of Ozone Molecule Laxman Mainali 1,2*, Devendra Raj Mishra 2, Mukunda Mani Aryal 2 1 Department of Biophysics, Medical College of Wisconsin,

Introduction to Electronic Structure Theory

Introduction to Electronic Structure Theory C. David Sherrill School of Chemistry and Biochemistry Georgia Institute of Technology June 2002 Last Revised: June 2003 1 Introduction The purpose of these

Physics 622: Quantum Mechanics -- Part II --

Physics 622: Quantum Mechanics -- Part II -- Prof. Seth Aubin Office: room 255, Small Hall, tel: 1-3545 Lab: room 069, Small Hall (new wing), tel: 1-3532 e-mail: saaubi@wm.edu web: http://www.physics.wm.edu/~saubin/index.html

Computational Physics. J. M. Thijssen

Computational Physics J. M. Thijssen Delft University of Technology CAMBRIDGE UNIVERSITY PRESS Contents Preface xi 1 Introduction 1 1.1 Physics and computational physics 1 1.2 Classical mechanics and statistical

Introduction to Computational Chemistry

Introduction to Computational Chemistry Vesa Hänninen Laboratory of Physical Chemistry Chemicum 4th floor vesa.hanninen@helsinki.fi September 10, 2013 Lecture 3. Electron correlation methods September

2 Electronic structure theory

Electronic structure theory. Generalities.. Born-Oppenheimer approximation revisited In Sec..3 (lecture 3) the Born-Oppenheimer approximation was introduced (see also, for instance, [Tannor.]). We are

FYS-6306 QUANTUM THEORY OF MOLECULES AND NANOSTRUCTURES

i FYS-6306 QUANTUM THEORY OF MOLECULES AND NANOSTRUCTURES Credit units: 6 ECTS Lectures: 48 h Tapio Rantala, prof. Tue 10 12 SC203 SG219 8 10 SG312 FirstName.LastName@tut.fi http://www.tut.fi/~trantala/opetus/

Computational Chemistry and Quantum Tunneling

Computational Chemistry and Quantum Tunneling Key Words quantum chemistry, Hartree-Fock theory, density functional theory, variational principle, quantum tunneling, transition state Object It is expected

Tight-Binding Model of Electronic Structures

Tight-Binding Model of Electronic Structures Consider a collection of N atoms. The electronic structure of this system refers to its electronic wave function and the description of how it is related to

Orbital-dependent backflow transformations in quantum Monte Carlo

transformations in quantum Monte Carlo P. Seth, P. López Ríos, and R. J. Needs TCM group, Cavendish Laboratory, University of Cambridge 5 December 2012 VMC and DMC Optimization Wave functions Variational

MO Calculation for a Diatomic Molecule. /4 0 ) i=1 j>i (1/r ij )

MO Calculation for a Diatomic Molecule Introduction The properties of any molecular system can in principle be found by looking at the solutions to the corresponding time independent Schrodinger equation

Molecular Simulation I

Molecular Simulation I Quantum Chemistry Classical Mechanics E = Ψ H Ψ ΨΨ U = E bond +E angle +E torsion +E non-bond Jeffry D. Madura Department of Chemistry & Biochemistry Center for Computational Sciences

Computational Inorganic Chemistry

Computational Inorganic Chemistry Dr. P. Hunt p.hunt@imperial.ac.uk Rm 67 P. Hunt, Handout Introduction Course Description: This course will explore the use of computational methods to gain insight into

SCF calculation on HeH +

SCF calculation on HeH + Markus Meuwly Department of Chemistry, University of Basel, Basel, Switzerland Abstract This document describes the main steps involved in carrying out a SCF calculation on the

Handbook of Computational Quantum Chemistry. DAVID B. COOK The Department of Chemistry, University of Sheffield

Handbook of Computational Quantum Chemistry DAVID B. COOK The Department of Chemistry, University of Sheffield Oxford New York Tokyo OXFORD UNIVERSITY PRESS 1998 CONTENTS 1 Mechanics and molecules 1 1.1

3: Many electrons. Orbital symmetries. l =2 1. m l

3: Many electrons Orbital symmetries Atomic orbitals are labelled according to the principal quantum number, n, and the orbital angular momentum quantum number, l. Electrons in a diatomic molecule experience

Is the homogeneous electron gas homogeneous?

Is the homogeneous electron gas homogeneous? Electron gas (jellium): simplest way to view a metal homogeneous and normal Hartree-Fock: simplest method for many-electron systems a single Slater determinant

Dept of Mechanical Engineering MIT Nanoengineering group

1 Dept of Mechanical Engineering MIT Nanoengineering group » To calculate all the properties of a molecule or crystalline system knowing its atomic information: Atomic species Their coordinates The Symmetry

Group representation theory and quantum physics

Group representation theory and quantum physics Olivier Pfister April 29, 2003 Abstract This is a basic tutorial on the use of group representation theory in quantum physics, in particular for such systems

Lecture 9. Hartree Fock Method and Koopman s Theorem

Lecture 9 Hartree Fock Method and Koopman s Theorem Ψ(N) is approximated as a single slater determinant Φ of N orthogonal One electron spin-orbitals. One electron orbital φ i = φ i (r) χ i (σ) χ i (σ)

Chemistry 3502/4502. Final Exam Part I. May 14, 2005

Chemistry 3502/4502 Final Exam Part I May 14, 2005 1. For which of the below systems is = where H is the Hamiltonian operator and T is the kinetic-energy operator? (a) The free particle (e) The

An Introduction to Quantum Chemistry and Potential Energy Surfaces. Benjamin G. Levine

An Introduction to Quantum Chemistry and Potential Energy Surfaces Benjamin G. Levine This Week s Lecture Potential energy surfaces What are they? What are they good for? How do we use them to solve chemical

3.012 Fund of Mat Sci: Bonding Lecture 10

3.012 Fund of Mat Sci: Bonding Lecture 10 MOLECULES FROM ATOMS Image of a journal article removed for copyright reasons. See Slater, J. C., and G. F. Koster. "Simplified LCAO Method for the Periodic Potential

Quantum Physics II (8.05) Fall 2002 Outline

Quantum Physics II (8.05) Fall 2002 Outline 1. General structure of quantum mechanics. 8.04 was based primarily on wave mechanics. We review that foundation with the intent to build a more formal basis

Reikniefnafræði - Verkefni 2 Haustmisseri 2013 Kennari - Hannes Jónsson

Háskóli Íslands, raunvísindasvið Reikniefnafræði - Verkefni 2 Haustmisseri 2013 Kennari - Hannes Jónsson Guðjón Henning 18. september 2013 1 A. Molecular orbitals of N 2 Q1: Display all the MOs for N 2

Advanced Quantum Chemistry III: Part 3. Haruyuki Nakano. Kyushu University

Advanced Quantum Chemistry III: Part 3 Haruyuki Nakano Kyushu University 2013 Winter Term 1. Hartree-Fock theory Density Functional Theory 2. Hohenberg-Kohn theorem 3. Kohn-Sham method 4. Exchange-correlation

Computational Chemistry I

Computational Chemistry I Text book Cramer: Essentials of Quantum Chemistry, Wiley (2 ed.) Chapter 3. Post Hartree-Fock methods (Cramer: chapter 7) There are many ways to improve the HF method. Most of

Ab- ini&o quantum simula+ons of complex photocataly+c reac+ons

Ab- ini&o quantum simula+ons of complex photocataly+c reac+ons With: Dmitry Vinichenko, Grigory Kolesov, Georgios Tritsaris Department of Physics, Department of Chemistry and Chemical Biology, and School

Angular Momentum in Quantum Mechanics

Angular Momentum in Quantum Mechanics In classical mechanics the angular momentum L = r p of any particle moving in a central field of force is conserved. For the reduced two-body problem this is the content

OVERVIEW OF QUANTUM CHEMISTRY METHODS

OVERVIEW OF QUANTUM CHEMISTRY METHODS Outline I Generalities Correlation, basis sets Spin II Wavefunction methods Hartree-Fock Configuration interaction Coupled cluster Perturbative methods III Density

Chemistry 881 Lecture Topics Fall 2001

Chemistry 881 Lecture Topics Fall 2001 Texts PHYSICAL CHEMISTRY A Molecular Approach McQuarrie and Simon MATHEMATICS for PHYSICAL CHEMISTRY, Mortimer i. Mathematics Review (M, Chapters 1,2,3 & 4; M&S,

Pseudospectral Methods For Op2mal Control. Jus2n Ruths March 27, 2009

Pseudospectral Methods For Op2mal Control Jus2n Ruths March 27, 2009 Introduc2on Pseudospectral methods arose to find solu2ons to Par2al Differen2al Equa2ons Recently adapted for Op2mal Control Key Ideas

Introduction to Density Functional Theory

1 Introduction to Density Functional Theory 21 February 2011; V172 P.Ravindran, FME-course on Ab initio Modelling of solar cell Materials 21 February 2011 Introduction to DFT 2 3 4 Ab initio Computational

Fine Structure Calculations of Atomic Data for Ar XVI

Journal of Modern Physics, 2015, 6, 1609-1630 Published Online September 2015 in SciRes. http://www.scirp.org/journal/jmp http://dx.doi.org/10.4236/jmp.2015.611163 Fine Structure Calculations of Atomic

This is called a singlet or spin singlet, because the so called multiplicity, or number of possible orientations of the total spin, which is

9. Open shell systems The derivation of Hartree-Fock equations (Chapter 7) was done for a special case of a closed shell systems. Closed shell means that each MO is occupied by two electrons with the opposite

Handbook of Computational Quantum Chemistry

Handbook of Computational Quantum Chemistry David B. Cook Dept. of Chemistry University of Sheffield DOVER PUBLICATIONS, INC. Mineola, New York F Contents 1 Mechanics and molecules 1 1.1 1.2 1.3 1.4 1.5

CHEM 6343 Advanced Computational Chemistry. Elfi Kraka, 231 FOSC, ext ,

CHEM 6343 Advanced Computational Chemistry Class location: Lectures, time and location: Lab times and location: Instructor: Elfi Kraka, 231 FOSC, ext 8-2480, ekraka@smu.edu http://smu.edu/catco/ Office

The Hartree-Fock Method

1/41 18. December, 2015 Problem Statement First Quantization Second Quantization References Overview 1. Problem Statement 2. First Quantization 3. Second Quantization 4. 5. References 2/41 Problem Statement

COUPLED-CLUSTER CALCULATIONS OF GROUND AND EXCITED STATES OF NUCLEI

COUPLED-CLUSTER CALCULATIONS OF GROUND AND EXCITED STATES OF NUCLEI Marta Włoch, a Jeffrey R. Gour, a and Piotr Piecuch a,b a Department of Chemistry,Michigan State University, East Lansing, MI 48824 b

Density matrix functional theory vis-á-vis density functional theory

Density matrix functional theory vis-á-vis density functional theory 16.4.007 Ryan Requist Oleg Pankratov 1 Introduction Recently, there has been renewed interest in density matrix functional theory (DMFT)

Numerical Methods in Physics

Numerical Methods in Physics Numerische Methoden in der Physik, 515.421. Instructor: Ass. Prof. Dr. Lilia Boeri Room: PH 03 090 Tel: +43-316- 873 8191 Email Address: l.boeri@tugraz.at Room: TDK Seminarraum

Quantum Chemical and Dynamical Tools for Solving Photochemical Problems

2.165430 3.413060 3.889592 9 H 3.413060 2.165430 1.099610 2.165430 3.413060 10 H 3.889592 3.413060 2.165430 1.099610 2.165430 11 H 3.413060 3.889592 3.413060 2.165430 1.099610 12 H 2.165430 3.413060 3.889592

Detailed derivation of Gaussian orbital based matrix elements in electron structure calculations.

Detailed derivation of Gaussian orbital based matri elements in electron structure calculations. T Petersson and B Hellsing Department of Physics, Väjö University, SE-35 95 Väjö, Sweden Department of Physics,

Wave function methods for the electronic Schrödinger equation

Wave function methods for the electronic Schrödinger equation Zürich 2008 DFG Reseach Center Matheon: Mathematics in Key Technologies A7: Numerical Discretization Methods in Quantum Chemistry DFG Priority

Chemistry 883 Computational Quantum Chemistry

Chemistry 883 Computational Quantum Chemistry Instructor Contact Information Professor Benjamin G. Levine levine@chemistry.msu.edu 215 Chemistry Building 517-353-1113 Office Hours Tuesday 9:00-11:00 am

Lecture B6 Molecular Orbital Theory. Sometimes it's good to be alone.

Lecture B6 Molecular Orbital Theory Sometimes it's good to be alone. Covalent Bond Theories 1. VSEPR (valence shell electron pair repulsion model). A set of empirical rules for predicting a molecular geometry

Molecular Dynamics. Molecules in motion

Molecular Dynamics Molecules in motion 1 Molecules in mo1on Molecules are not sta1c, but move all the 1me Source: h9p://en.wikipedia.org/wiki/kine1c_theory 2 Gasses, liquids and solids Gasses, liquids

Lecture 5. Hartree-Fock Theory. WS2010/11: Introduction to Nuclear and Particle Physics

Lecture 5 Hartree-Fock Theory WS2010/11: Introduction to Nuclear and Particle Physics Particle-number representation: General formalism The simplest starting point for a many-body state is a system of

Hartree, Hartree-Fock and post-hf methods

Hartree, Hartree-Fock and post-hf methods MSE697 fall 2015 Nicolas Onofrio School of Materials Engineering DLR 428 Purdue University nonofrio@purdue.edu 1 The curse of dimensionality Let s consider a multi

Chemistry 4560/5560 Molecular Modeling Fall 2014

Final Exam Name:. User s guide: 1. Read questions carefully and make sure you understand them before answering (if not, ask). 2. Answer only the question that is asked, not a different question. 3. Unless

Solid State Physics (Major, 8 ECTS)

Solid State Physics (Major, 8 ECTS) 1 physicist over 3 in US declares to be a condensed matter physicist (CMP) CMP: solids, amorphous materials, liquids, soft materials 20 CMP physics Nobel prizes + 5

Lecture #1. Review. Postulates of quantum mechanics (1-3) Postulate 1

L1.P1 Lecture #1 Review Postulates of quantum mechanics (1-3) Postulate 1 The state of a system at any instant of time may be represented by a wave function which is continuous and differentiable. Specifically,

Chemistry 2. Your lecturers. Revision H 2 22/04/14. Lecture 1 Quantum Mechanics in Chemistry

Chemistry Lecture 1 Quantum Mechanics in Chemistry Your lecturers 8am Asaph Widmer-Cooper Room 316 asaph.widmer-cooper@sydney.edu.au 1pm Adam Bridgeman Room 543A adam.bridgeman@sydney.edu.au Revision H

Chemistry 3502/4502. Final Exam Part I. May 14, 2005

Advocacy chit Chemistry 350/450 Final Exam Part I May 4, 005. For which of the below systems is = where H is the Hamiltonian operator and T is the kinetic-energy operator? (a) The free particle

Chemistry 483 Lecture Topics Fall 2009

Chemistry 483 Lecture Topics Fall 2009 Text PHYSICAL CHEMISTRY A Molecular Approach McQuarrie and Simon A. Background (M&S,Chapter 1) Blackbody Radiation Photoelectric effect DeBroglie Wavelength Atomic

Variational calculations of the spectra of anharmonic oscillators using displaced gaussian functions

Variational calculations of the spectra of anharmonic oscillators using displaced gaussian functions Jozef Motyčka 1 and Peter Babinec Department of Nuclear Physics and Biophysics, Faculty of Mathematics,

Introduction to numerical projects

Introduction to numerical projects Here follows a brief recipe and recommendation on how to write a report for each project. Give a short description of the nature of the problem and the eventual numerical

Electron Correlation Methods

Electron Correlation Methods HF method: electron-electron interaction is replaced by an average interaction E HF c = E 0 E HF E 0 exact ground state energy E HF HF energy for a given basis set HF E c