Other methods to consider electron correlation: Coupled-Cluster and Perturbation Theory
|
|
- Catherine Powers
- 6 years ago
- Views:
Transcription
1 Other methods to consider electron correlation: Coupled-Cluster and Perturbation Theory Péter G. Szalay Eötvös Loránd University Institute of Chemistry H-1518 Budapest, P.O.Box 32, Hungary
2 Inclusion of the electron correlation Eötvös Loránd University, Institute of Chemistry 1
3 Inclusion of the electron correlation Perturbation Theory (PT) - use HF as start Configuration Interaction (CI) - expand the wave function on several determinants Coupled Cluster (CC) - exponential expansion of the wave function (Density Functional Theory - DFT) Eötvös Loránd University, Institute of Chemistry 1
4 Inclusion of the electron correlation Perturbation Theory (PT) - use HF as start Configuration Interaction (CI) - expand the wave function on several determinants Coupled Cluster (CC) - exponential expansion of the wave function (Density Functional Theory - DFT) Eötvös Loránd University, Institute of Chemistry 1
5 Inclusion of the electron correlation Perturbation Theory (PT) - use HF as start Configuration Interaction (CI) - expand the wave function on several determinants Coupled Cluster (CC) - exponential expansion of the wave function (Density Functional Theory - DFT) Eötvös Loránd University, Institute of Chemistry 1
6 Inclusion of the electron correlation Perturbation Theory (PT) - use HF as start Configuration Interaction (CI) - expand the wave function on several determinants Coupled Cluster (CC) - exponential expansion of the wave function (Density Functional Theory - DFT) Eötvös Loránd University, Institute of Chemistry 1
7 Perturbation theory (PT) Usual Rayleigh-Schrödinger Perturbation Theory with Ĥ 0 = i ˆf(i) i.e. sum of the one-electron Fock-operators (Møller-Plesset partitioning) 1st order: Hartre-Fock method 2nd order: MP2 or MBPT(2) method 3rd order: MP3 of MBPT(3) method etc. Eötvös Loránd University, Institute of Chemistry 2
8 Perturbation theory (PT) MP2: cheap way to include electron correlation MP3: usually not any better than MP2 MP4: often very good but expensive Main problems: series may not converge HF must be a good starting point gets very expensive Eötvös Loránd University, Institute of Chemistry 3
9 Perturbation theory (PT) If the HF is not a good starting point, use a CAS wave function instead CASPT2 and CASPT3 methods Disadvantages: definition of the reference space is not straightforward not variational gradient is expensive (no public program yet!) with the increasing size of the CAS gets expensive states are not orthogonal transition moments can be calculated by some tricks Eötvös Loránd University, Institute of Chemistry 4
10 The Coupled-Cluster method Wave function: Ψ CC = e T Φ 0 Eötvös Loránd University, Institute of Chemistry 5
11 The Coupled-Cluster method Wave function: Ψ CC = e T Φ 0 T n is an excitation operator: T = T 1 + T T n Φ 0 = 1 n! abc...ijk... t abc.. ijk..φ abc.. ijk.. Eötvös Loránd University, Institute of Chemistry 5
12 The Coupled-Cluster method Wave function: Ψ CC = e T Φ 0 T n is an excitation operator: T = T 1 + T Truncated versions: T n Φ 0 = 1 n! abc...ijk... t abc.. ijk..φ abc.. ijk.. CCSD (T = T 1 + T 2 ) CCSD(T) (T = T 1 + T 2 + approximate T 3 ) Eötvös Loránd University, Institute of Chemistry 5
13 The Coupled-Cluster method Wave function: Ψ CC = e T Φ 0 T n is an excitation operator: T = T 1 + T Truncated versions: T n Φ 0 = 1 n! abc...ijk... t abc.. ijk..φ abc.. ijk.. CCSD (T = T 1 + T 2 ) CCSD(T) (T = T 1 + T 2 + approximate T 3 ) Very popular and very accurate for ground states! Eötvös Loránd University, Institute of Chemistry 5
14 The Coupled-Cluster method Advantages of CCSD: size-extensive since multiplicatively separable : e T A e T B = e T A+T B where T A and T B are the cluster operators for system A and B respectively. higher excitations are present with respect to CISD: e T = 1 + T 1 + T T T 1 T T i.e. also quadruple excitations are present which where used before to correct CISD!! Eötvös Loránd University, Institute of Chemistry 6
15 The Coupled-Cluster method Advantages of CCSD: size-extensive since multiplicatively separable : e T A e T B = e T A+T B where T A and T B are the cluster operators for system A and B respectively. higher excitations are present with respect to CISD: e T = 1 + T 1 + T T T 1 T T i.e. also quadruple excitations are present which where used before to correct CISD!! Eötvös Loránd University, Institute of Chemistry 6
16 The Coupled-Cluster method Why do we not use CC instead of CI? Eötvös Loránd University, Institute of Chemistry 7
17 The Coupled-Cluster method Why do we not use CC instead of CI? Disadvantages of the CC methods: not variational gradient calculations cost twice as much not an eigenvalue problem only for ground state (But: excited states with symmetry different from ground state) multireference extension is not straightforward spin-contamination for open shell systems because of the products Eötvös Loránd University, Institute of Chemistry 7
18 The Coupled-Cluster method Why do we not use CC instead of CI? Disadvantages of the CC methods: not variational gradient calculations cost twice as much not an eigenvalue problem only for ground state (But: excited states with symmetry different from ground state) multireference extension is not straightforward spin-contamination for open shell systems because of the products Eötvös Loránd University, Institute of Chemistry 7
19 The Coupled-Cluster method Why do we not use CC instead of CI? Disadvantages of the CC methods: not variational gradient calculations cost twice as much not an eigenvalue problem only for ground state (But: excited states with symmetry different from ground state) multireference extension is not straightforward spin-contamination for open shell systems because of the products Eötvös Loránd University, Institute of Chemistry 7
20 The Coupled-Cluster method Why do we not use CC instead of CI? Disadvantages of the CC methods: not variational gradient calculations cost twice as much not an eigenvalue problem only for ground state (But: excited states with symmetry different from ground state) multireference extension is not straightforward spin-contamination for open shell systems because of the products The second problem can be solved (see later) while the other ones not use MR-AQCC if multireference method is needed!! Eötvös Loránd University, Institute of Chemistry 7
21 Excited states in CC theory CC equations are not eigenvalue equations only the ground state can be calculated. But again Linear Response Theory (LRT) or equivalently Equation of Motion (EOM) formalism can be used. A simple representation of the EOM-CC method: Consider CI: Ĥ(φ 0 + i c i φ i ) = E(φ 0 + i c i φ i ) Ĥ(1 + Ĉ)φ 0 = E(1 + Ĉ)φ 0 We know that CC is a very good wave function for the ground state replace φ 0 by the CC wave function: Ĥ(1 + Ĉ)e ˆT φ 0 = E(1 + Ĉ)e ˆT φ 0 Eötvös Loránd University, Institute of Chemistry 8
22 Excited states in CC theory Since ˆT and Ĉ commute, we can write: Ĥe ˆT (1 + Ĉ)φ 0 = Ee ˆT (1 + Ĉ)φ 0 Now we multiply from the left by e ˆT : e ˆT Ĥe ˆT (1 + Ĉ)φ 0 = E(1 + Ĉ)φ 0 Introduce the notation: H = e ˆT Ĥ N e ˆT and our equation now becomes: H(1 + Ĉ)φ 0 = E(1 + Ĉ)φ 0 Excitation energies can be obtained by diagonalizing H!!!!! Eötvös Loránd University, Institute of Chemistry 9
23 Excited states in CC theory Disadvantages of EOM-CCSD: only states dominated by single excitations if the CCSD is not adequate to describe the ground state, the reults are unreliable problem potential energy surfaces!! not fully variational (because of ˆT ) extra costs to obtain gradients Advantages of EOM-CCSD very accurate if the above requiremts are fulfilled ( ev) straightforward to use, no definition of multireference space are neede Eötvös Loránd University, Institute of Chemistry 10
24 Vertical excitation energies (in ev) of trans-1,3-butadiene Method/State 1 1 B u 2 1 A g EOM-CCSD a EOM-CCSD( T ) a CASPT2 b CASPT2 c MR-SDCI d MR-AQCC e experiment 5.92 f a J.D. Watts, R. Gwaltney and R.J. Bartlett, J. Chem. Phys., 105, 6979 (1996). b L. Serrano-Andres, M. Merchan, I. Nebot-Gil, R. Lindh and B.O. Roos, J. Chem. Phys., 98, 3151 (1993). c B. Ostojic and W. Domcke, Chem. Phys., 269, 1 (2001). d P.G. Szalay, A. Karpfen and H. Lischka, Chem. Phys., 130, 219 (1989). e M. Dallos and H. Lischka, Theor. Chem. Acc., 112, 56 (2004). f O.A. Mosher, W.M. Flicker and A. Kuppermann, J. Chem. Phys., 59, 6502 (1973). Eötvös Loránd University, Institute of Chemistry 11
Methods for Treating Electron Correlation CHEM 430
Methods for Treating Electron Correlation CHEM 430 Electron Correlation Energy in the Hartree-Fock approximation, each electron sees the average density of all of the other electrons two electrons cannot
More informationElectron 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
More informationMichal Dallos, Hans Lischka
Theor Chem Acc (2004) 112: 16 26 DOI 10.1007/s00214-003-0557-9 Regular article A systematic theoretical investigation of the lowest valence- and Rydberg-excited singlet states of trans-butadiene. The character
More informationAccurate description of potential energy surfaces by ab initio methods : a review and application to ozone
Accurate description of potential energy surfaces by ab initio methods : a review and application to ozone Péter G. Szalay Laboratory of Theoretical Chemistry Institute of Chemistry Eötvös Loránd University,
More informationMolecular properties in quantum chemistry
Molecular properties in quantum chemistry Monika Musiał Department of Theoretical Chemistry Outline 1 Main computational schemes for correlated calculations 2 Developmentoftheabinitiomethodsforthe calculation
More informationIntroduction 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
More informationNWChem: Coupled Cluster Method (Tensor Contraction Engine)
NWChem: Coupled Cluster Method (ensor Contraction Engine) What we want to solve H Ψ = E Ψ Many Particle Systems Molecular/Atomic Physics, Quantum Chemistry (electronic Schrödinger equations) Solid State
More informationOVERVIEW 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
More information1 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
More informationElectron 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
More information4 Post-Hartree Fock Methods: MPn and Configuration Interaction
4 Post-Hartree Fock Methods: MPn and Configuration Interaction In the limit of a complete basis, the Hartree-Fock (HF) energy in the complete basis set limit (ECBS HF ) yields an upper boundary to the
More informationCoupled-Cluster Perturbative Triples for Bond Breaking
Coupled-Cluster Perturbative Triples for Bond Breaking Andrew G. Taube and Rodney J. Bartlett Quantum Theory Project University of Florida INT CC Meeting Seattle July 8, 2008 Why does chemistry need triples?
More informationPéter G. Szalay Eötvös Loránd University, Budapest, Hungary
cn0066 Configuration Interaction: Consistency Corrections for Size- Péter G. Szalay Eötvös Loránd University, Budapest, Hungary Abstract In this article, the size-consistency corrected MR-CI methods are
More informationBeyond 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
More informationElectric properties of molecules
Electric properties of molecules For a molecule in a uniform electric fielde the Hamiltonian has the form: Ĥ(E) = Ĥ + E ˆµ x where we assume that the field is directed along the x axis and ˆµ x is the
More informationNWChem: Coupled Cluster Method (Tensor Contraction Engine)
NWChem: Coupled Cluster Method (Tensor Contraction Engine) Why CC is important?! Correlation effects are important!! CC is size-extensive theory: can be used to describe dissociation processes.! Higher-order
More informationMulti-reference Density Functional Theory. COLUMBUS Workshop Argonne National Laboratory 15 August 2005
Multi-reference Density Functional Theory COLUMBUS Workshop Argonne National Laboratory 15 August 2005 Capt Eric V. Beck Air Force Institute of Technology Department of Engineering Physics 2950 Hobson
More informationComputational Methods. Chem 561
Computational Methods Chem 561 Lecture Outline 1. Ab initio methods a) HF SCF b) Post-HF methods 2. Density Functional Theory 3. Semiempirical methods 4. Molecular Mechanics Computational Chemistry " Computational
More informationCoupled-Cluster Theory. Nuclear Structure
Coupled-Cluster Theory! for Nuclear Structure!!!! Sven Binder INSTITUT FÜR KERNPHYSIK! 1 Nuclear Interactions from Chiral EFT NN 3N 4N NLO LO N 2 LO +... N 3 LO +... +... +... 2 Nuclear Interactions from
More informationIntroduction to Electronic Structure Theory
CSC/PRACE Spring School in Computational Chemistry 2017 Introduction to Electronic Structure Theory Mikael Johansson http://www.iki.fi/~mpjohans Objective: To get familiarised with the, subjectively chosen,
More informationQUANTUM CHEMISTRY FOR TRANSITION METALS
QUANTUM CHEMISTRY FOR TRANSITION METALS Outline I Introduction II Correlation Static correlation effects MC methods DFT III Relativity Generalities From 4 to 1 components Effective core potential Outline
More informationBuilding a wavefunction within the Complete-Active. Cluster with Singles and Doubles formalism: straightforward description of quasidegeneracy
Building a wavefunction within the Complete-Active Active-Space Coupled-Cluster Cluster with Singles and Doubles formalism: straightforward description of quasidegeneracy Dmitry I. Lyakh (Karazin Kharkiv
More informationAdvanced 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/ 6 Strengths of DFT DFT is one of many theories used by (computational)
More informationCOUPLED-CLUSTER BASED METHODS FOR EXCITED STATE ENERGIES AND GRADIENTS STEVEN RAY GWALTNEY
COUPLED-CLUSTER BASED METHODS FOR EXCITED STATE ENERGIES AND GRADIENTS By STEVEN RAY GWALTNEY A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE
More informationElectron 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
More informationOrbital dependent correlation potentials in ab initio density functional theory
Orbital dependent correlation potentials in ab initio density functional theory noniterative - one step - calculations Ireneusz Grabowski Institute of Physics Nicolaus Copernicus University Toruń, Poland
More informationIntroduction to Computational Chemistry: Theory
Introduction to Computational Chemistry: Theory Dr Andrew Gilbert Rm 118, Craig Building, RSC andrew.gilbert@anu.edu.au 3023 Course Lectures Introduction Hartree Fock Theory Basis Sets Lecture 1 1 Introduction
More informationJack 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
More informationAb initio calculations for potential energy surfaces. D. Talbi GRAAL- Montpellier
Ab initio calculations for potential energy surfaces D. Talbi GRAAL- Montpellier A theoretical study of a reaction is a two step process I-Electronic calculations : techniques of quantum chemistry potential
More informationIntroduction to multiconfigurational quantum chemistry. Emmanuel Fromager
Institut de Chimie, Strasbourg, France Page 1 Emmanuel Fromager Institut de Chimie de Strasbourg - Laboratoire de Chimie Quantique - Université de Strasbourg /CNRS M2 lecture, Strasbourg, France. Notations
More informationAb Initio Electromagnetic Transitions with the IMSRG
Ab Initio Electromagnetic Transitions with the IMSRG Nathan Parzuchowski Michigan State University March, 017 1 / 1 Outline IMSRG IMSRG rotates the Hamiltonian into a coordinate system where simple methods
More informationIntroduction to Computational Quantum Chemistry: Theory
Introduction to Computational Quantum Chemistry: Theory Dr Andrew Gilbert Rm 118, Craig Building, RSC 3108 Course Lectures 2007 Introduction Hartree Fock Theory Configuration Interaction Lectures 1 Introduction
More informationQuantum Chemistry Methods
1 Quantum Chemistry Methods T. Helgaker, Department of Chemistry, University of Oslo, Norway The electronic Schrödinger equation Hartree Fock theory self-consistent field theory basis functions and basis
More information( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r)
Born Oppenheimer Approximation: Ĥ el ( R)Ψ el ( r;r) = E el ( R)Ψ el ( r;r) For a molecule with N electrons and M nuclei: Ĥ el What is E el (R)? s* potential surface Reaction Barrier Unstable intermediate
More informationRecent Advances in the MRexpT approach
Recent Advances in the MRexpT approach Michael Hanrath University of Cologne Institute for Theoretical Chemistry July 8, 008 Michael Hanrath, Univ. of Cologne, Theor. Chemistry Advances MRexpT July 8,
More informationChemistry 334 Part 2: Computational Quantum Chemistry
Chemistry 334 Part 2: Computational Quantum Chemistry 1. Definition Louis Scudiero, Ben Shepler and Kirk Peterson Washington State University January 2006 Computational chemistry is an area of theoretical
More informationWave 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
More informationAN 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,
More informationWähringerstraße 17, A-1090 Vienna, Austria 2 Mathematical Institute, Leipzig University, Augustus-Platz, D Leipzig, Germany
Determination of Energy Minima and Saddle Points Using Multireference Configuration Interaction Methods in Combination with Reduced Gradient Following: The S 0 Surface of H 2 COand the T 1 and T 2 Surfaces
More informationSession 1. Introduction to Computational Chemistry. Computational (chemistry education) and/or (Computational chemistry) education
Session 1 Introduction to Computational Chemistry 1 Introduction to Computational Chemistry Computational (chemistry education) and/or (Computational chemistry) education First one: Use computational tools
More informationPerformance of Hartree-Fock and Correlated Methods
Chemistry 460 Fall 2017 Dr. Jean M. Standard December 4, 2017 Performance of Hartree-Fock and Correlated Methods Hartree-Fock Methods Hartree-Fock methods generally yield optimized geomtries and molecular
More informationCoupled-cluster and perturbation methods for macromolecules
Coupled-cluster and perturbation methods for macromolecules So Hirata Quantum Theory Project and MacroCenter Departments of Chemistry & Physics, University of Florida Contents Accurate electronic structure
More informationPredictive Computing for Solids and Liquids
Predictive Computing for Solids and Liquids So Hirata Department of Chemistry May 214 Blue Waters Symposium 1 Schrödinger equation for a water molecule 1-particle, 3-dimensional partial differential equation
More informationChemistry 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
More informationUsing BLIS for tensor computations in Q-Chem
Using BLIS for tensor computations in Q-Chem Evgeny Epifanovsky Q-Chem BLIS Retreat, September 19 20, 2016 Q-Chem is an integrated software suite for modeling the properties of molecular systems from first
More informationConvergence of many-body wavefunction expansions using a plane wave basis: From the homogeneous electron gas to the solid state
Convergence of many-body wavefunction expansions using a plane wave basis: From the homogeneous electron gas to the solid state TCM Electronic Structure Discussion Group James Shepherd (CUC3, Alavi Group)
More informationAn 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
More informationThe Nuclear Many Body Problem Lecture 4. Coupled Cluster theory and its application to medium sized nuclei.
The Nuclear Many Body Problem Lecture 4 Coupled Cluster theory and its application to medium sized nuclei. Extending the Ab Initio program beyond the lightest nuclei. Need a theory which scales softly
More informationJack 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
More informationHartree, 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
More informationAlgorithmic Challenges in Photodynamics Simulations on HPC systems
Algorithmic Challenges in Photodynamics Simulations on HPC systems Felix Plasser González Research Group Institute for Theoretical Chemistry, University of Vienna, Austria Bratislava, 21 st March 2016
More informationA Whirlwind Introduction to Coupled Cluster Response Theory. 1 Time-Independent Coupled Cluster Theory
A Whirlwind Introduction to Coupled Cluster Response Theory T. Daniel Crawford, Virginia Tech, Blacksburg, Virginia, U.S.A. 1 Time-Independent Coupled Cluster Theory If the Hamiltonian is independent of
More informationDensity Functional Theory. Martin Lüders Daresbury Laboratory
Density Functional Theory Martin Lüders Daresbury Laboratory Ab initio Calculations Hamiltonian: (without external fields, non-relativistic) impossible to solve exactly!! Electrons Nuclei Electron-Nuclei
More informationInternally Contracted Multireference Coupled Cluster Theory. Computer Aided Implementation of Advanced Electronic Structure Methods.
Internally Contracted Multireference Coupled Cluster Theory. Computer Aided Implementation of Advanced Electronic Structure Methods. Marcel Nooijen Chemistry Department University of Waterloo nooijen@uwaterloo.ca
More informationQUANTUM CHEMISTRY PROJECT 3: ATOMIC AND MOLECULAR STRUCTURE
Chemistry 460 Fall 2017 Dr. Jean M. Standard November 1, 2017 QUANTUM CHEMISTRY PROJECT 3: ATOMIC AND MOLECULAR STRUCTURE OUTLINE In this project, you will carry out quantum mechanical calculations of
More informationComputational 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
More informationIntroduction to Density Functional Theory
Introduction to Density Functional Theory S. Sharma Institut für Physik Karl-Franzens-Universität Graz, Austria 19th October 2005 Synopsis Motivation 1 Motivation : where can one use DFT 2 : 1 Elementary
More informationJack 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
More informationComparison of Nuclear Configuration Interaction Calculations and Coupled Cluster Calculations
Comparison of Nuclear Configuration Interaction Calculations and Coupled Cluster Calculations Mihai Horoi Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA Support
More informationTheoretical and Computational Studies of Interstellar C2nH and SiC2m+1H. Ryan Fortenberry
Theoretical and Computational Studies of Interstellar C2nH and SiC2m+1H Ryan Fortenberry 1 Introduction Astrobiology Pillars of Creation Titan Interstellar Spectra DIBs 1.0 SiC3H Comparison Spectrum 0.8
More informationExplicitly Correlated Methods for Large Molecular Systems
Explicitly Correlated Methods for Large Molecular Systems Fabijan Pavošević Dissertation submitted to the Faculty of the Virginia Polytechnic Institute and State University in partial fulfillment of the
More informationHigh-level Quantum Chemistry Methods and Benchmark Datasets for Molecules
High-level Quantum Chemistry Methods and Benchmark Datasets for Molecules Markus Schneider Fritz Haber Institute of the MPS, Berlin, Germany École Polytechnique Fédérale de Lausanne, Switzerland دانشگاه
More informationBenchmark studies of variational, unitary and extended coupled cluster methods
Benchmark studies of variational, unitary and extended coupled cluster methods Bridgette Cooper and Peter J. Knowles Citation: The Journal of Chemical Physics 133, 23412 (21); doi: 1.163/1.352564 View
More informationDirect Minimization in Density Functional Theory
Direct Minimization in Density Functional Theory FOCM Hongkong 2008 Partners joint paper with: J. Blauert, T. Rohwedder (TU Berlin), A. Neelov (U Basel) joint EU NEST project BigDFT together with Dr. Thierry
More informationFull configuration interaction potential energy curves for breaking bonds to hydrogen: An assessment of single-reference correlation methods
JOURNAL OF CHEMICAL PHYSICS VOLUME 118, NUMBER 4 22 JANUARY 2003 Full configuration interaction potential energy curves for breaking bonds to hydrogen: An assessment of single-reference correlation methods
More informationWalter Kohn was awarded with the Nobel Prize in Chemistry in 1998 for his development of the density functional theory.
Walter Kohn was awarded with the Nobel Prize in Chemistry in 1998 for his development of the density functional theory. Walter Kohn receiving his Nobel Prize from His Majesty the King at the Stockholm
More informationThe MCSCF Method *, Molecular Orbitals, Reference Spaces and COLUMBUS Input
The MCSCF Method *, Molecular Orbitals, Reference Spaces and COLUMBUS Input Hans Lischka University of Vienna *Excerpt of a course presented by R. Shepard, Argonne National Laboratory, at the Workshop
More informationMODERN ELECTRONIC STRUCTURE THEORY: Electron Correlation
5.61 Physical Chemistry Lecture #30 1 MODERN ELECTRONIC STRUCTURE THEORY: Electron Correlation In the previous lecture, we covered all the ingredients necessary to choose a good atomic orbital basis set.
More informationG1-3 These methods are based on ab initio molecular orbital calculations. Electron correlation is calculated using MP2 or MP4 and QCI.
23. High Accuracy Energy Methods 23.1 Gaussian-n Methods The method keywords G1, G2, G2MP2, G3, G3MP2, G3B3, G3MP2B3, G4, and G4MP2 perform high accuracy complex energy computations in Gaussian. Essentially,
More informationExercise 1: Structure and dipole moment of a small molecule
Introduction to computational chemistry Exercise 1: Structure and dipole moment of a small molecule Vesa Hänninen 1 Introduction In this exercise the equilibrium structure and the dipole moment of a small
More informationPotential Energy Surfaces for Quantum Dynamics Simulations: From ab initio Computations to Vibrational State Determinations
Potential Energy Surfaces for Quantum Dynamics Simulations: From ab initio Computations to Vibrational State Determinations by Ekadashi Pradhan A thesis submitted in partial fulfillment of the requirements
More informationTime-dependent linear-response variational Monte Carlo.
Time-dependent linear-response variational Monte Carlo. Bastien Mussard bastien.mussard@colorado.edu https://mussard.github.io/ Julien Toulouse julien.toulouse@upmc.fr Sorbonne University, Paris (web)
More informationDEVELOPMENT OF PREDICTIVE ELECTRONIC STRUCTURE METHODS AND THEIR APPLICATION TO ATMOSPHERIC CHEMISTRY, COMBUSTION, AND BIOLOGICALLY RELEVANT SYSTEMS
DEVELOPMENT OF PREDICTIVE ELECTRONIC STRUCTURE METHODS AND THEIR APPLICATION TO ATMOSPHERIC CHEMISTRY, COMBUSTION, AND BIOLOGICALLY RELEVANT SYSTEMS by Evgeny Epifanovskiy A Dissertation Presented to the
More informationJack 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
More informationConvergence properties of the coupled-cluster method: the accurate calculation of molecular properties for light systems
1 Convergence properties of the coupled-cluster method: the accurate calculation of molecular properties for light systems T. Helgaker Centre for Theoretical and Computational Chemistry, Department of
More informationSelected Publications of Prof. Dr. Wenjian Liu
Selected Publications of Prof. Dr. Wenjian Liu College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China 1 Fundamentals of relativistic molecular quantum mechanics 1. Handbook
More informationSelf-consistent intermediate Hamiltonians: A coupled cluster type formulation of the singles and doubles configuration interaction matrix dressing
Self-consistent intermediate Hamiltonians: A coupled cluster type formulation of the singles and doubles configuration interaction matrix dressing I. Nebot-Gil and J. Sánchez-Marín Departament de Química
More informationFaddeev Random Phase Approximation (FRPA) Application to Molecules
Faddeev Random Phase Approximation (FRPA) Application to Molecules Matthias Degroote Center for Molecular Modeling (CMM) Ghent University INT 2011 Spring Program Fermions from Cold Atoms to Neutron Stars:
More informationThe electronic spectrum of pyrrole
JOURNAL OF CHEMICAL PHYSICS VOLUME 111, NUMBER 2 8 JULY 1999 The electronic spectrum of pyrrole Ove Christiansen a) and Jürgen Gauss Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz,
More informationAb initio asymptotic-expansion coefficients for pair energies in Møller-Plesset perturbation theory for atoms
Ab initio asymptotic-expansion coefficients for pair energies in Møller-Plesset perturbation theory for atoms K. JANKOWSKI a, R. SŁUPSKI a, and J. R. FLORES b a Nicholas Copernicus University 87-100 Toruń,
More informationCOUPLED-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
More informationCalculations of band structures
Chemistry and Physics at Albany Planning for the Future Calculations of band structures using wave-function based correlation methods Elke Pahl Centre of Theoretical Chemistry and Physics Institute of
More informationSupporting Information
Supporting Information Computational Evidence of Inversion of 1 L a and 1 L b -Derived Excited States in Naphthalene Excimer Formation from ab Initio Multireference Theory with Large Active Space: DMRG-CASPT2
More informationTo Multireference or not to Multireference: That is the Question?
Int. J. Mol. Sci. 2002, 3, 579-603 International Journal of Molecular Sciences ISSN 1422-0067 www.mdpi.org/ijms/ To Multireference or not to Multireference: That is the Question? Rodney J. Bartlett Quantum
More informationThe calculation of the universal density functional by Lieb maximization
The calculation of the universal density functional by Lieb maximization Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry,
More informationImporting ab-initio theory into DFT: Some applications of the Lieb variation principle
Importing ab-initio theory into DFT: Some applications of the Lieb variation principle Trygve Helgaker, Andy Teale, and Sonia Coriani Centre for Theoretical and Computational Chemistry (CTCC), Department
More informationCoupled Cluster Theory and Tensor Decomposition Techniques
Coupled Cluster Theory and Tensor Decomposition Techniques Alexander A. Auer Atomistic Modelling Group Interface Chemistry and Surface Engineering Hierarchy of quantum chemical methods Analysis of orbitals
More informationTDDFT as a tool in biophysics
TDDFT as a tool in biophysics The primary event in vision Robert Send Universität Karlsruhe 09.09.08 Robert Send TDDFT as a tool in biophysics 09.09.08 1 / 28 Outline 1 Human vision 2 The methods 3 The
More informationJoint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data January 2012
2327-3 Joint ICTP-IAEA Workshop on Fusion Plasma Modelling using Atomic and Molecular Data 23-27 January 2012 Qunatum Methods for Plasma-Facing Materials Alain ALLOUCHE Univ.de Provence, Lab.de la Phys.
More informationTHE DEVELOPMENT OF THE CBS-Wes METHOD
Wesleyan University THE DEVELOPMENT OF THE CBS-Wes METHOD By Duminda Sampath Ranasinghe Faculty Advisor: Prof. George A. Petersson A Dissertation submitted to the Faculty of Wesleyan University in partial
More informationCopyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and
Copyright is owned by the Author of the thesis. Permission is given for a copy to be downloaded by an individual for the purpose of research and private study only. The thesis may not be reproduced elsewhere
More informationAb initio treatment of electron correlations in polymers: Lithium hydride
JOURNAL OF CHEMICAL PHYSICS VOLUME 112, NUMBER 10 8 MARCH 2000 Ab initio treatment of electron correlations in polymers: Lithium hydride chain and beryllium hydride polymer Ayjamal Abdurahman a) Max-Planck-Institut
More informationBeyond Hartree-Fock: MP2 and Coupled-Cluster Methods for Large Systems
John von Neumann Institute for Computing Beyond Hartree-Fock: MP2 and Coupled-Cluster Methods for Large Systems Christof Hättig published in Computational Nanoscience: Do It Yourself, J. Grotendorst, S.
More informationAB INITIO METHODS IN COMPUTATIONAL QUANTUM CHEMISTRY
AB INITIO METHODS IN COMPUTATIONAL QUANTUM CHEMISTRY Aneesh. M.H A theoretical study on the regioselectivity of electrophilic reactions of heterosubstituted allyl systems Thesis. Department of Chemistry,
More informationCoupled cluster methods including triple excitations for excited states of radicals
THE JOURNAL OF CHEMICAL PHYSICS 122, 054110 2005 Coupled cluster methods including triple excitations for excited states of radicals Christopher E. Smith Department of Chemistry, Virginia Tech, Blacksburg,
More informationApproximating the basis set dependence of coupled cluster calculations: Evaluation of perturbation theory approximations for stable molecules
JOURNAL OF CHEMICAL PHYSICS VOLUME 113, NUMBER 18 8 NOVEMBER 2000 Approximating the basis set dependence of coupled cluster calculations: Evaluation of perturbation theory approximations for stable molecules
More informationMulticonfigurational methods in MOLCAS
Multiconfigurational methods in MOLCAS Valera Veryazov Valera.Veryazov@teokem.lu.se Division of Theoretical Chemistry Lund University Sweden CASSCF//CASPT2 p. 1/?? Overview What is correlation? CASPT2
More informationIntroduction to computational chemistry Exercise I: Structure and electronic energy of a small molecule. Vesa Hänninen
Introduction to computational chemistry Exercise I: Structure and electronic energy of a small molecule Vesa Hänninen 1 Introduction In this exercise the equilibrium structure and the electronic energy
More informationCOPYRIGHTED MATERIAL. Quantum Mechanics for Organic Chemistry &CHAPTER 1
&CHAPTER 1 Quantum Mechanics for Organic Chemistry Computational chemistry, as explored in this book, will be restricted to quantum mechanical descriptions of the molecules of interest. This should not
More informationdiradicals, and triradicals
The spin-flip electronic structure method: A shortcut in the Fock space towards accurate description of bond-breaking, diradicals, and triradicals Anna I. Krylov February 18, 2005 Abstract The spin-flip
More information