Fixed-Node quantum Monte Carlo for Chemistry
|
|
- Harry Strickland
- 5 years ago
- Views:
Transcription
1 Fixed-Node quantum Monte Carlo for Chemistry Michel Caffarel Lab. Physique et Chimie Quantiques, CNRS-IRSAMC, Université de Toulouse caffarel@irsamc.ups-tlse.fr. p.1/29
2 The N-body problem of Chemistry We are essentially interested in the ground-state and low-lying excited states properties (T = 0 quantum problem) Main difficulties : ============ Coulombic potential (nuclear attractions and electronic repulsion) Fermions (electrons) in 3D ordinary space. N large but finite. Very high accuracy on eigensolutions is required. = a very difficult (the most difficult?) N-body quantum problem!. p.2/29
3 The chemical Hamiltonian H = i,σ i h j a + iσ a jσ + i,j,k,lσσ ij 1/r 12 kl a + iσ a+ jσ a kσ a lσ where i denotes a set of N orthonormal i one-particle basis functions (molecular orbitals) with N 10n electrons!!. p.3/29
4 Chemical accuracy Atomization energies : E 0 /E Energy barriers, electronic affinities, etc. E 0 /E Weak intermolcular forces (Hydrogen bonds, van der Waals forces) E 0 /E p.4/29
5 Standard approaches Density Functional Theories (DFT) good but ill-controlled Ab initio wavefunction based approaches (SCF and post-scf) good but badly-converged quantum Monte Carlo (QMC)?. p.5/29
6 Essential points of QMC I Variational Monte Carlo (VMC) = Markov Chain Monte Carlo with density Π = ψt 2 (standard Metropolis scheme) ψ T = known trial wave function (use of the long-term experience of ab initio quantum chemistry) Variational energy : (Ψ T,HΨ T )/(Ψ T, Ψ T ) is computed as a simple average E V MC = E L Π where the local energy is defined as E L = HΨ T /Ψ T. p.6/29
7 Trial wavefunction ψ T ψ T ( r 1,..., r nelec ) = N c K=1c K exp [ i,j,α U K (r iα,r jα,r ij )] φ (K) α φ (K) β Spin-free formalism N c = number of determinants exp U K = Jastrow factors φ α,β ( r) = one-electron spatial orbitals (K) Without Jastrow factors : standard forms (SCF, DFT, VB, MCSCF, CI,...) No particular constraints on the orbitals (gaussians, slaters, splines,...). p.7/29
8 Jastrow factor Typical form : exp α U(r iα,r jα,r ij ) (1) <i,j> U(r iα,r jα,r ij ) = s(x ij )+p (α) (x iα )+c 1 x 2 iαx 2 jα+c 2 (x 2 iα+x 2 jα)x 2 ij+c 3 x 2 ij (2) with x ij = x iα = r ij 1 + b σ r ij r iα 1 + b α r iα s(x) = s 1 x + s 2 x 2 + s 3 x 3 + s 4 x 4 p (α) (x) = p (α) 1 x + p(α) 2 x2 + p (α) 3 x3 + p (α) 4 x4,. p.8/29
9 Essential points of QMC II Optimization of the parameters entering ψ T by minimizing energy or variance of energy : Not so easy but we are able to optimize relatively well quite a large number of parameters (main problem : energy computed stochastically). Note that some interesting progress has been made very recently (see, Umrigar et al. Phys. Rev. Lett (2007)). p.9/29
10 Essential points of QMC III DIFFUSION MONTE CARLO (DMC) : Markov Chain Monte Carlo of VMC + branching process : the configurations are multiplied or killed proportionally to w : w exp[ τ(e L E T )] It can be shown that the probability density is no longer ψ 2 T, like in VMC, but Π DMC ψ T φ 0 φ 0 = unknown ground-state and we have : E 0 = E L Π. p.10/29
11 Particle Statistics However, pb. with statistics : Bosons : Φ 0 has a constant sign no problem Fermions (e.g., chemistry) : Φ 0 antisymmetric under the exchange of spin-like fermions Φ 0 has no longer a constant sign.. p.11/29
12 Essential points of QMC III The positive density generated by the usual Fixed-Node (FN) DMC for fermions is biased : where HΦ 0,FN = E 0,FN Φ 0,FN Π DMC = Ψ T Φ 0,FN with Φ 0,FN = 0 whenener Ψ T = 0 Nodal hypersurfaces of Ψ T = 0 are usually not exact fixed-node error Variational property : E 0,FN E 0. p.12/29
13 Benchmark Grossman Réf : J.C. Grossman J.Chem.Phys. 117, 1434 (2002).. p.13/29
14 Benchmark Grossman, 2002 G1 set Pople and collab. (1990) = 55 molecules. Atomisation energies FN-DMC, pseudo-potential for representing the effect of 1s electrons, mono-configurational wavefunction Mean absolute deviation : ǫ MAD FN-DMC : ǫ MAD = 2.9kcal/mol LDA : ǫ MAD 40kcal/mol GGA : (B3LYP et B3PW91) ǫ MAD 2.5kcal/mol CCSD(T)/aug-cc-pVQZ ǫ MAD 2.8kcal/mol. p.14/29
15 . p.15/29
16 Reducing errors in FN-DMC for chemistry Two types of errors : I. Statistical error like in any Monte Carlo scheme II.Systematic errors (biases) : mainly the fixed-node error, the other biases can be controlled.. p.16/29
17 Statistical error For a stable calculation (bosons or fermions treated with FN approximation) : F Π + δf with where σ(f) = δf = F 2 F 2 σ(f) N/Nc N = number of Monte Carlo steps N c = correlation time in unit of time step. p.17/29
18 Sign problem For an unstable calculation where fermions are treated exactly (nodal release-type approaches) : δe e(e F E B )N N where : E F = fermion ground-state energy, E F O(N) E B = boson ground-state energy, E B O(N γ ) with γ > 1 famous sign problem. p.18/29
19 Reducing statistical errors δf = σ(f) N/Nc where σ(f) = F 2 F 2 An efficient way of decreasing ǫ is to reduce σ : Improved or renormalized estimators : F Π = F Π and σ 2 ( F) << σ 2 (F). (3) Strategy developed during these last years [R.Assaraf and MC, PRL 83 (1999),, JCP 113 (2000) and JCP 119 (2003)]. p.19/29
20 Reducing statistical errors Here, recent application to one-body densities and properties (R.Assaraf et al. Phys.Rev.E (2007)) Improved estimator : N ρ(r) = i=1 δ(r i r) Π (4) ρ(r) = 1 4π N 1 [ r i r g] 2 i (fπ) Π Π, (5) i=1 where f,g two arbit. funct. adjusted to lower statistical errors. p.20/29
21 Reducing statistical errors ρ (r) Usual Estimator Simple Improved Estimator Best Improved Estimator Exact p.21/29
22 Reducing statistical errors (H O) 2 2 Best Usual 0.6 ρ p.22/29
23 Reducing statistical errors Advantages : Errors can be greatly reduced (orders of magnitude) Can be used for any type of Monte Carlo simulation Compute density everywhere in space The density is much smoother over a larget set of grid points ( for the water dimer, below). p.23/29
24 Fixed-Node Error and Chemistry Correlation energy : CE E 0 (exact) - E 0 [mean-field(scf)] CE/E 0 (exact) 1/1000 The fixed-node is small a few percent of the correlation energy (relative error on E 0 of about a few 1/100000!!)... However :. p.24/29
25 Dissociation barrier of O 4 [Collaboration with A. Ramírez-Solís, R. Hernández-Lamoneda (Cuernavaca, Mexique) and A. Scemama (Paris, LCT)]. O 4 (metastable) O 4 (transition state, TS) 2 O 2 (triplet) Expt : some indications that the barrier between O 4 and O 4 (TS) is greater than 10 kcal. FN-DMC calculations : O 4 O 4 (TS) = /- 2.9 kcal with SCF nodes O 4 O 4 (TS) = 12. +/- 1.6 kcal with MCSCF nodes Most sophisticated ab initio calculations (CCSD(T),ACPF) : 8-9 kcal. p.25/29
26 Fixed-Node DMC for Cr 2 Experimental binding energy a.u. SCF Binding energy (basis set= [20s12p9d5f] ) E(Cr 2 )-2 E(Cr) = a.u. unbound (by far!) molecule Fixed-node DMC calculation : SCF nodes : E(Cr 2 )-2 E(Cr) = (3) Cr 2 is not bound (or slightly bound) at the Fixed-SCF Node DMC level!!. p.26/29
27 Fixed-Node DMC for Cr 2 Very interesting comparison with Scuseria s calculation (1991) : Scuseria : (10s8p3d2f1g) E SCF (R opt = 2.76)= a.u. Here : (20s12p9d5f ) E SCF (R = 3.2)= a.u. Correlated calculations for E 0 : E 0 [CCSD(T) ;R opt = 3.03]= a.u. E 0 [FN-DMC ;R = 3.2 ]= (24) a.u. (about 1.1 a.u. lower!!) Binding energies : Scuseria : Here : +0.01(3) monoconfigurational nodes is the problem.... p.27/29
28 Some conclusions We need either : to improve the trial wave functions with the hope that nodal hypersurfaces are improved (e.g., Umrigar and coll.) or : to get some physical insight into fermionic nodes for coulombic systems (e.g., Bressanini et coll., Mitas et coll.) or : to solve the sign problem (e.g., almost everyone in QMC..). p.28/29
29 Bibliography BOSONS : D.M. Ceperley, Path Integrals in the theory of condensed helium, Rev. Mod.Phys (1995). FERMIONS : W.M.C. Foulkes, L. Mitas, R.J. Needs, and G. Rajagopal, Quantum Monte Carlo of Solids Rev.Mod.Phys. 73, 33 (2001) QMC in COMPUTATIONAL CHEMISTRY : B.L. Hammond, W.A. Lester,Jr., and P.J. Reynolds in Monte Carlo Methods in Ab Initio Quantum Chemistry, World Scientific Lecture and course notes in chemistry Vol.1 (1994).. p.29/29
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
More informationOptimization of quantum Monte Carlo wave functions by energy minimization
Optimization of quantum Monte Carlo wave functions by energy minimization Julien Toulouse, Roland Assaraf, Cyrus J. Umrigar Laboratoire de Chimie Théorique, Université Pierre et Marie Curie and CNRS, Paris,
More informationRecent advances in quantum Monte Carlo for quantum chemistry: optimization of wave functions and calculation of observables
Recent advances in quantum Monte Carlo for quantum chemistry: optimization of wave functions and calculation of observables Julien Toulouse 1, Cyrus J. Umrigar 2, Roland Assaraf 1 1 Laboratoire de Chimie
More informationQMC dissociation energy of the water dimer: Time step errors and backflow calculations
QMC dissociation energy of the water dimer: Time step errors and backflow calculations Idoia G. de Gurtubay and Richard J. Needs TCM group. Cavendish Laboratory University of Cambridge Idoia G. de Gurtubay.
More informationQuantum Monte Carlo wave functions and their optimization for quantum chemistry
Quantum Monte Carlo wave functions and their optimization for quantum chemistry Julien Toulouse Université Pierre & Marie Curie and CNRS, Paris, France CEA Saclay, SPhN Orme des Merisiers April 2015 Outline
More informationQuantum Monte Carlo methods
Quantum Monte Carlo methods Lubos Mitas North Carolina State University Urbana, August 2006 Lubos_Mitas@ncsu.edu H= 1 2 i i 2 i, I Z I r ii i j 1 r ij E ion ion H r 1, r 2,... =E r 1, r 2,... - ground
More informationAb-initio molecular dynamics for High pressure Hydrogen
Ab-initio molecular dynamics for High pressure Hydrogen Claudio Attaccalite Institut d'electronique, Microélectronique et Nanotechnologie (IEMN), Lille Outline A brief introduction to Quantum Monte Carlo
More informationOptimization of quantum Monte Carlo (QMC) wave functions by energy minimization
Optimization of quantum Monte Carlo (QMC) wave functions by energy minimization Julien Toulouse, Cyrus Umrigar, Roland Assaraf Cornell Theory Center, Cornell University, Ithaca, New York, USA. Laboratoire
More informationSize-extensive wave functions for QMC A linear-scaling GVB approach
Size-extensive wave functions for QMC A linear-scaling GVB approach Claudia Filippi, University of Twente, The Netherlands Francesco Fracchia, University of Pisa, Italy Claudio Amovilli, University of
More informationIntroduction to Path Integral Monte Carlo. Part I.
Introduction to Path Integral Monte Carlo. Part I. Alexey Filinov, Jens Böning, Michael Bonitz Institut für Theoretische Physik und Astrophysik, Christian-Albrechts-Universität zu Kiel, D-24098 Kiel, Germany
More informationAn Overview of Quantum Monte Carlo Methods. David M. Ceperley
An Overview of Quantum Monte Carlo Methods David M. Ceperley Department of Physics and National Center for Supercomputing Applications University of Illinois Urbana-Champaign Urbana, Illinois 61801 In
More informationWave Function Optimization and VMC
Wave Function Optimization and VMC Jeremy McMinis The University of Illinois July 26, 2012 Outline Motivation History of Wave Function Optimization Optimization in QMCPACK Multideterminant Example Motivation:
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 informationQuantum Monte Carlo backflow calculations of benzene dimers
Quantum Monte Carlo backflow calculations of benzene dimers Kathleen Schwarz*, Cyrus Umrigar**, Richard Hennig*** *Cornell University Department of Chemistry, **Cornell University Department of Physics,
More informationarxiv: v2 [physics.chem-ph] 11 Mar 2011
Quantum Monte Carlo with Jastrow-Valence-Bond wave functions Benoît Braïda 1, Julien Toulouse 1, Michel Caffarel 2, and C. J. Umrigar 3 1 Laboratoire de Chimie Théorique, Université Pierre et Marie Curie
More informationThe Nature of the Interlayer Interaction in Bulk. and Few-Layer Phosphorus
Supporting Information for: The Nature of the Interlayer Interaction in Bulk and Few-Layer Phosphorus L. Shulenburger, A.D. Baczewski, Z. Zhu, J. Guan, and D. Tománek, Sandia National Laboratories, Albuquerque,
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 informationQuantum Monte Carlo for excited state calculations
Quantum Monte Carlo for excited state calculations Claudia Filippi MESA+ Institute for Nanotechnology, Universiteit Twente, The Netherlands Winter School in Theoretical Chemistry, Helsinki, Finland, Dec
More informationQMC dissociation energies of three-electron hemibonded radical cation dimers... and water clusters
QMC dissociation energies of three-electron hemibonded radical cation dimers... and water clusters Idoia G. de Gurtubay TCM group. Cavendish Laboratory University of Cambridge Idoia G. de Gurtubay. Quantum
More informationLec20 Fri 3mar17
564-17 Lec20 Fri 3mar17 [PDF]GAUSSIAN 09W TUTORIAL www.molcalx.com.cn/wp-content/uploads/2015/01/gaussian09w_tutorial.pdf by A Tomberg - Cited by 8 - Related articles GAUSSIAN 09W TUTORIAL. AN INTRODUCTION
More informationIntroduction to density-functional theory. 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. Institut
More informationQUANTUM MONTE CARLO METHOD: PERFORMANCE ANALYSIS ON MODEL SYSTEMS
Vol. 79 (1991) ACTA PHYSICA POLONICA A No 6 ΟΝ THE FIXED-NODE IMPORTANCE-SAMPLING QUANTUM MONTE CARLO METHOD: PERFORMANCE ANALYSIS ON MODEL SYSTEMS A. CHŁOBOWSKI Κ. Gumiński Department of Theoretical Chemistry,
More informationFirst- principles studies of spin-crossover molecules
Vallico di Sotto, 30 th July 2012 First- principles studies of spin-crossover molecules Andrea Droghetti and Stefano Sanvito School of Physics and CRANN, Trinity College Dublin Dario Alfe' London Centre
More informationResonating Valence Bond wave function with molecular orbitals: application to diatomic molecules
Resonating Valence Bond wave function with molecular orbitals: application to diatomic molecules M. Marchi 1,2, S. Azadi 2, M. Casula 3, S. Sorella 1,2 1 DEMOCRITOS, National Simulation Center, 34014,
More informationDiffusion Monte Carlo
Diffusion Monte Carlo Notes for Boulder Summer School 2010 Bryan Clark July 22, 2010 Diffusion Monte Carlo The big idea: VMC is a useful technique, but often we want to sample observables of the true ground
More informationElectronic structure theory: Fundamentals to frontiers. 2. Density functional theory
Electronic structure theory: Fundamentals to frontiers. 2. Density functional theory MARTIN HEAD-GORDON, Department of Chemistry, University of California, and Chemical Sciences Division, Lawrence Berkeley
More informationφ α (R) φ α ψ 0 e nτ(e α E T ). (2)
Atomic Scale Simulations Projector Quantum Monte Carlo Projector Monte Carlo We now turn to a potentially more powerful method where a function of the Hamiltonian projects out the the ground state, hence
More informationAnion-π and π-π cooperative interactions
Chapter 5 Anion-π and π-π cooperative interactions 5.1 Introduction The design of selective receptors of anionic species is a very active area of research within supramolecular chemistry due to the potential
More informationQuantum Monte Carlo Benchmarks Density Functionals: Si Defects
Quantum Monte Carlo Benchmarks Density Functionals: Si Defects K P Driver, W D Parker, R G Hennig, J W Wilkins (OSU) C J Umrigar (Cornell), R Martin, E Batista, B Uberuaga (LANL), J Heyd, G Scuseria (Rice)
More informationAll-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe
All-electron quantum Monte Carlo calculations for the noble gas atoms He to Xe A. Ma, N. D. Drummond, M. D. Towler, and R. J. Needs Theory of Condensed Matter Group, Cavendish Laboratory, University of
More informationarxiv:physics/ v2 [physics.chem-ph] 9 Apr 2005
Electronic Quantum Monte Carlo Calculations of Atomic Forces, Vibrations, and Anharmonicities arxiv:physics/0411209v2 [physics.chem-ph] 9 Apr 2005 Myung Won Lee a), Massimo Mella b), and Andrew M. Rappe
More informationDensity Functional Theory - II part
Density Functional Theory - II part antonino.polimeno@unipd.it Overview From theory to practice Implementation Functionals Local functionals Gradient Others From theory to practice From now on, if not
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 informationMethods for calculating forces within quantum Monte Carlo
Methods for calculating forces within quantum Monte Carlo A Badinski 1,2, P D Haynes 1,3, J R Trail 1,4, and R J Needs 1 1 Theory of Condensed Matter Group, Cavendish Laboratory, Cambridge CB3 0HE, UK
More informationAb-initio simulation of liquid water by quantum Monte Carlo
Ab-initio simulation of liquid water by quantum Monte Carlo Sandro Sorella G. Mazzola & Y. Luo SISSA, IOM DEMOCRITOS, Trieste A. Zen, L. Guidoni U. of L Aquila, L Aquila 28 July 2014, Mike Towler Institute,
More informationTowards accurate all-electron quantum Monte Carlo calculations of transition-metal systems: Spectroscopy of the copper atom
THE JOURNAL OF CHEMICAL PHYSICS 123, 094102 2005 Towards accurate all-electron quantum Monte Carlo calculations of transition-metal systems: Spectroscopy of the copper atom Michel Caffarel, a Jean-Pierre
More informationSoftware optimization for petaflops/s scale Quantum Monte Carlo simulations
Software optimization for petaflops/s scale Quantum Monte Carlo simulations A. Scemama 1, M. Caffarel 1, E. Oseret 2, W. Jalby 2 1 Laboratoire de Chimie et Physique Quantiques / IRSAMC, Toulouse, France
More informationDevelopment and application of statistical and quantum mechanical methods for modelling molecular ensembles
Development and application of statistical and quantum mechanical methods for modelling molecular ensembles By Ellen T. Swann A thesis submitted for the degree of Doctor of Philosophy of the Australian
More informationCorrelation in correlated materials (mostly transition metal oxides) Lucas K. Wagner University of Illinois at Urbana-Champaign
Correlation in correlated materials (mostly transition metal oxides) Lucas K. Wagner University of Illinois at Urbana-Champaign Understanding of correlated materials is mostly phenomenological FN- DMC
More informationTeoría del Funcional de la Densidad (Density Functional Theory)
Teoría del Funcional de la Densidad (Density Functional Theory) Motivation: limitations of the standard approach based on the wave function. The electronic density n(r) as the key variable: Functionals
More informationMulticonfiguration wave functions for quantum Monte Carlo calculations of first-row diatomic molecules
Multiconfiguration wave functions for quantum Monte Carlo calculations of first-row diatomic molecules Claudia Filippi Laboratory of Atomic and Solid State Physics and Theory Center, Cornell University,
More informationAuxiliary-field quantum Monte Carlo calculations of excited states and strongly correlated systems
Auxiliary-field quantum Monte Carlo calculations of excited states and strongly correlated systems Formally simple -- a framework for going beyond DFT? Random walks in non-orthogonal Slater determinant
More informationVan der Waals Interactions Between Thin Metallic Wires and Layers
Van der Waals Interactions Between Thin Metallic Wires and Layers N. D. Drummond and R. J. Needs TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom Quantum Monte
More informationKevin Driver 1 Shuai Zhang 1 Burkhard Militzer 1 R. E. Cohen 2.
Quantum Monte Carlo Simulations of a Single Iron Impurity in MgO Kevin Driver 1 Shuai Zhang 1 Burkhard Militzer 1 R. E. Cohen 2 1 Department of Earth & Planetary Science University of California, Berkeley
More informationRandom Estimates in QMC
Page 1 Random Estimates in QMC J.R. Trail and R.J. Needs Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, UK February 2007 Page 2 Numerical Integration Unkown function,
More informationContinuum variational and diffusion quantum Monte Carlo calculations
Continuum variational and diffusion quantum Monte Carlo calculations R J Needs, M D Towler, N D Drummond and P López Ríos Theory of Condensed Matter Group, Cavendish Laboratory, Cambridge CB3 0HE, UK Abstract.
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 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 informationMethods of Fermion Monte Carlo
Methods of Fermion Monte Carlo Malvin H. Kalos kalos@llnl.gov Institute for Nuclear Theory University of Washington Seattle, USA July, 2013 LLNL-PRES-XXXXXX This work was performed under the auspices of
More informationQuantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid
Quantum Monte Carlo study of the ground state of the two-dimensional Fermi fluid N. D. Drummond and R. J. Needs TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge
More informationElectronic Structure Calculations and Density Functional Theory
Electronic Structure Calculations and Density Functional Theory Rodolphe Vuilleumier Pôle de chimie théorique Département de chimie de l ENS CNRS Ecole normale supérieure UPMC Formation ModPhyChem Lyon,
More informationNew applications of Diffusion Quantum Monte Carlo
New applications of Diffusion Quantum Monte Carlo Paul R. C. Kent (ORNL) Graphite: P. Ganesh, J. Kim, C. Park, M. Yoon, F. A. Reboredo (ORNL) Platinum: W. Parker, A. Benali, N. Romero (ANL), J. Greeley
More informationModule 6 1. Density functional theory
Module 6 1. Density functional theory Updated May 12, 2016 B A DDFT C K A bird s-eye view of density-functional theory Authors: Klaus Capelle G http://arxiv.org/abs/cond-mat/0211443 R https://trac.cc.jyu.fi/projects/toolbox/wiki/dft
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 informationStudy of Ozone in Tribhuvan University, Kathmandu, Nepal. Prof. S. Gurung Central Department of Physics, Tribhuvan University, Kathmandu, Nepal
Study of Ozone in Tribhuvan University, Kathmandu, Nepal Prof. S. Gurung Central Department of Physics, Tribhuvan University, Kathmandu, Nepal 1 Country of the Mt Everest 2 View of the Mt Everest 3 4 5
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 informationthe abdus salam international centre for theoretical physics
united nations educational, scientific and cultural organization the abdus salam international centre for theoretical physics international atomic energy agency SMR 1595-16 Joint DEMOCRITOS - ICTP School
More informationCHEM3023: 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
More informationQuantum Monte Carlo simulations of solids
Quantum Monte Carlo simulations of solids W. M. C. Foulkes CMTH Group, Department of Physics, Imperial College of Science, Technology and Medicine, Prince Consort Road, London SW7 2BZ, England L. Mitas
More informationThe QMC Petascale Project
The QMC Petascale Project Richard G. Hennig What will a petascale computer look like? What are the limitations of current QMC algorithms for petascale computers? How can Quantum Monte Carlo algorithms
More informationLecture 8: Introduction to Density Functional Theory
Lecture 8: Introduction to Density Functional Theory Marie Curie Tutorial Series: Modeling Biomolecules December 6-11, 2004 Mark Tuckerman Dept. of Chemistry and Courant Institute of Mathematical Science
More informationComputational methods: Coupled Electron Ion Monte Carlo Path Integral Monte Carlo Examples: Electron gas Hydrogen
! Computational methods: Coupled Electron Ion Monte Carlo Path Integral Monte Carlo Examples: Electron gas Hydrogen WHO DID THE WORK? Miguel Morales, Livermore Carlo Pierleoni: L Aquila, Italy Jeff McMahon
More information3: 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
More informationICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below
ICCP Project 2 - Advanced Monte Carlo Methods Choose one of the three options below Introduction In statistical physics Monte Carlo methods are considered to have started in the Manhattan project (1940
More informationVariational Monte Carlo Optimization and Excited States
Variational Monte Carlo Optimization and Excited States Eric Neuscamman August 9, 2018 motivation charge transfer core spectroscopy double excitations the menu aperitif: number counting Jastrows main course:
More informationMany-body wavefunctions for normal liquid 3 He
Many-body wavefunctions for normal liquid 3 He Markus Holzmann, 1 Bernard Bernu, 1 and D. M. Ceperley 2 1 LPTMC, UMR 7600 of CNRS, Université Pierre et Marie Curie, Paris, France 2 Department of Physics
More informationTheory and Applications of Quantum Monte Carlo. Michael John Deible. B.Sc.Ed. in Chemistry Education, Indiana University of Pennsylvania, 2008
TITLE PAGE Theory and Applications of Quantum Monte Carlo by Michael John Deible B.Sc.Ed. in Chemistry Education, Indiana University of Pennsylvania, 2008 Submitted to the Graduate Faculty of the Dietrich
More informationThe Schrödinger equation for many-electron systems
The Schrödinger equation for many-electron systems Ĥ!( x,, x ) = E!( x,, x ) 1 N 1 1 Z 1 Ĥ = " $ # " $ + $ 2 r 2 A j j A, j RAj i, j < i a linear differential equation in 4N variables (atomic units) (3
More informationDensity 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)
More informationenergy. Finally, we combine these developments with the recently proposed inhomogeneous backflow transformations.
ABSTRACT BAJDICH, MICHAL. Generalized Pairing Wave Functions and Nodal Properties for Electronic Structure Quantum Monte Carlo. (Under the direction of Prof. Lubos Mitas.) The quantum Monte Carlo (QMC)
More informationMETALLIZATION AND DISSOCIATION IN HIGH PRESSURE LIQUID HYDROGEN BY AN EFFICIENT MOLECULAR DYNAMICS WITH QUANTUM MONTE CARLO
METALLIZATION AND DISSOCIATION IN HIGH PRESSURE LIQUID HYDROGEN BY AN EFFICIENT MOLECULAR DYNAMICS WITH QUANTUM MONTE CARLO Author: Guglielmo Mazzola Supervisor: Prof. Sandro Sorella A thesis submitted
More informationChemistry 120A 2nd Midterm. 1. (36 pts) For this question, recall the energy levels of the Hydrogenic Hamiltonian (1-electron):
April 6th, 24 Chemistry 2A 2nd Midterm. (36 pts) For this question, recall the energy levels of the Hydrogenic Hamiltonian (-electron): E n = m e Z 2 e 4 /2 2 n 2 = E Z 2 /n 2, n =, 2, 3,... where Ze is
More informationQuantum Monte Carlo simulation of spin-polarized tritium
Higher-order actions and their applications in many-body, few-body, classical problems Quantum Monte Carlo simulation of spin-polarized tritium I. Bešlić, L. Vranješ Markić, University of Split, Croatia
More informationGround-state properties, excitations, and response of the 2D Fermi gas
Ground-state properties, excitations, and response of the 2D Fermi gas Introduction: 2D FG and a condensed matter perspective Auxiliary-field quantum Monte Carlo calculations - exact* here Results on spin-balanced
More informationNodal surfaces and interdimensional degeneracies
THE JOURNAL OF CHEMICAL PHYSICS 142, 214112 (2015) Nodal surfaces and interdimensional degeneracies Pierre-François Loos 1,a) and Dario Bressanini 2,b) 1 Research School of Chemistry, Australian National
More informationTheoretical study of electronic and atomic structures of (MnO)n
Theoretical study of electronic and atomic structures of (MnO)n Hiori Kino, a Lucas K. Wagner b and Lubos Mitas c a National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan.
More information( R) MOLECULES: VALENCE BOND DESCRIPTION VALENCE BOND APPROXIMATION METHOD. Example: H 2. at some fixed R, repeat for many different values
5.6 004 Lecture #9 page MOLECULES: VLENCE OND DESCRIPTION VLENCE OND PPROXIMTION METHOD Example: H H = + + r r r r r R Determine E ( R) at some fixed R, repeat for many different values Electronic Schrodinger
More informationExploring deep Earth minerals with accurate theory
Exploring deep Earth minerals with accurate theory K.P. Driver, R.E. Cohen, Z. Wu, B. Militzer, P. Lopez Rios, M. Towler, R. Needs, and J.W. Wilkins Funding: NSF, DOE; Computation: NCAR, TeraGrid, NCSA,
More informationObservations on variational and projector Monte Carlo Methods
Observations on variational and projector Monte Carlo Methods C. J. Umrigar Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA (Dated: September 29, 2015) Variational
More informationQuantum Monte Carlo. QMC methods in the continuum
Quantum Monte Carlo Premise: need to use simulation techniques to solve manybody quantum problems just as you need them classically. Both the wavefunction and expectation values are determined by the simulations.
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 informationElectronic structure quantum Monte Carlo methods and variable spins: beyond fixedphase/node
Electronic structure quantum Monte Carlo methods and variable spins: beyond fixedphase/node approximations Cody Melton, M. Chandler Bennett, L. Mitas, with A. Ambrosetti, F. Pederiva North Carolina State
More informationGEM4 Summer School OpenCourseWare
GEM4 Summer School OpenCourseWare http://gem4.educommons.net/ http://www.gem4.org/ Lecture: Molecular Mechanics by Ju Li. Given August 9, 2006 during the GEM4 session at MIT in Cambridge, MA. Please use
More informationDensity Functional Theory: from theory to Applications
Density Functional Theory: from theory to Applications Uni Mainz November 29, 2010 The self interaction error and its correction Perdew-Zunger SIC Average-density approximation Weighted density approximation
More informationChapter 19 Quantum Monte Carlo Calculations of Electronic Excitation Energies: The Case of the Singlet n π (CO) Transition in Acrolein
Chapter 19 Quantum Monte Carlo Calculations of Electronic Excitation Energies: The Case of the Singlet n π (CO) Transition in Acrolein Julien Toulouse, Michel Caffarel, Peter Reinhardt, Philip E. Hoggan,
More informationIntroduction to Quantum Monte Carlo Methods Applied to the Electron Gas
Introduction to Quantum Monte Carlo Methods Applied to the Electron Gas D. M. Ceperley Physics Department and NCSA, University of Illinois Urbana-Champaign, Urbana, IL, USA 1. Introduction In these lectures,
More informationarxiv: v1 [cond-mat.quant-gas] 9 May 2011
Atomic Fermi gas at the unitary limit by quantum Monte Carlo methods: Effects of the interaction range Xin Li, Jindřich Kolorenč,,2 and Lubos Mitas Department of Physics, North Carolina State University,
More informationPrinciples of Quantum Mechanics
Principles of Quantum Mechanics - indistinguishability of particles: bosons & fermions bosons: total wavefunction is symmetric upon interchange of particle coordinates (space,spin) fermions: total wavefuncftion
More informationExchange-Correlation Functional
Exchange-Correlation Functional Aiichiro Nakano Collaboratory for Advanced Computing & Simulations Depts. of Computer Science, Physics & Astronomy, Chemical Engineering & Materials Science, and Biological
More informationIntroduction 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
More informationI. QUANTUM MONTE CARLO METHODS: INTRODUCTION AND BASICS
I. QUANTUM MONTE CARLO METHODS: INTRODUCTION AND BASICS Markus Holzmann LPMMC, UJF, Grenoble, and LPTMC, UPMC, Paris markus@lptl.jussieu.fr http://www.lptl.jussieu.fr/users/markus (Dated: January 24, 2012)
More informationBayero Journal of Pure and Applied Sciences, 3(1): Received: September, 2009 Accepted: May, 2010
Bajopas Volume 3 Number June Bayero Journal of Pure and Applied Sciences, 3(: - 7 Received: September, 9 Accepted: May, VARIAIONAL QUANUM MON CARLO CALCULAION OF H GROUND SA NRG OF HDROGN MOLCUL Suleiman,
More informationThe Self Interaction Correction revisited
The Self Interaction Correction revisited Explicit dynamics of clusters and molecules under irradiation Spectroscopic accuracy at low energy SIC problem : one electron interacts with its own mean-field!
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 informationSet the initial conditions r i. Update neighborlist. Get new forces F i
v Set the initial conditions r i ( t 0 ), v i ( t 0 ) Update neighborlist Quantum mechanical models Get new forces F i ( r i ) Solve the equations of motion numerically over time step Δt : r i ( t n )
More informationSemistochastic Quantum Monte Carlo A Hybrid of Exact Diagonalization and QMC Methods and Optimization of FN-PMC energies and FN-PMC forces
Semistochastic Quantum Monte Carlo A Hybrid of Exact Diagonalization and QMC Methods and Optimization of FN-PMC energies and FN-PMC forces Cyrus Umrigar Physics Department, Cornell University, Ithaca.
More information7. 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
More informationChapter 2 Quantum chemistry using auxiliary field Monte Carlo
Chapter 2 Quantum chemistry using auxiliary field Monte Carlo 1. The Hubbard-Stratonovich Transformation 2. Neuhauser s shifted contour 3. Calculation of forces and PESs 4. Multireference AFMC 5. Examples
More informationMolecular Mechanics: The Ab Initio Foundation
Molecular Mechanics: The Ab Initio Foundation Ju Li GEM4 Summer School 2006 Cell and Molecular Mechanics in BioMedicine August 7 18, 2006, MIT, Cambridge, MA, USA 2 Outline Why are electrons quantum? Born-Oppenheimer
More informationAccurate barrier heights using diffusion Monte Carlo
Accurate barrier heights using diffusion Monte Carlo Kittithat Krongchon, Brian Busemeyer, and Lucas K. Wagner Department of Physics, University of Illinois at Urbana-Champaign (Dated: March 9, 217) Fixed
More information