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IMA Newsletter #384

September 2008

2008-2009 Program

Mathematics and Chemistry

See http://www.ima.umn.edu/2008-2009 for a full description of the 2008-2009 program on Mathematics and Chemistry.

News and Notes
A new director for the MCIM

Carme Calderer has accepted the position of Director of the Minnesota Center for Industrial Mathematics. She is Professor in the School of Mathematics at the University of Minnesota and her research interests are in applied mathematics, analysis, continuum mechanics, soft condensed matter physics and materials science, with an emphasis on liquid crystals, ferroic materials, partial differential equations and calculus of variations. IMA and MCIM collaborate on Mathematical Modeling in Industry summer program and the IMA/MCIM Industrial Problems Seminars.

Associate Director for Diversity

Cheri Shakiban will continue her services at the IMA (on a part time basis) as the Associate Director for Diversity. She is Professor in the Mathematics Department at the University of St. Thomas and her research interests are in applied mathematics.

IMA Public Lecture Series

Math Matters lectures feature distinguished mathematicians and scientists who are also superb expositors able to illuminate the role mathematics is playing in understanding our world and shaping our lives. The lectures are aimed at a broad audience.

IMA Events

IMA Tutorial

Mathematical and Computational Approaches to Quantum Chemistry

September 26-27, 2008

Organizers: Eric Cances (CERMICS), Juan C. Meza (Lawrence Berkeley Laboratory)

IMA Annual Program Year Workshop

Mathematical and Algorithmic Challenges in Electronic Structure Theory

September 29 - October 3, 2008

Organizers: Eric Cances (CERMICS), Anna Krylov (University of Southern California), Juan C. Meza (Lawrence Berkeley Laboratory), John P. Perdew (Tulane University)
Schedule

Monday, September 1

All DayLabor Day. The IMA is closed.

Thursday, September 4

11:15a-12:15p Arthur Szlam, UCLA k-planes for classificationVincent Hall 570 AMS

Tuesday, September 9

10:45a-11:15aCoffee breakLind Hall 400

Wednesday, September 10

10:30a-11:00aCoffee and snackLind Hall 400
11:00a-12:00pOrientation for IMA Visitors and PostdocsLind Hall 305

Thursday, September 11

10:15a-10:45aCoffee and snackEE/CS 3-176
10:45a-12:00pIMA Postdoc Show and TellEE/CS 3-180
10:45-11:00Xianjin Chen (University of Minnesota)
11:00-11:15Mark S. Herman (University of Minnesota)
11:15-11:30Yunkyong Hyon (University of Minnesota)
11:30-11:45Mark Iwen (University of Minnesota)
11:45-12:00Srividhya Jeyaraman (University of Minnesota)
12:00p-1:30pLunch and Poster SessionLind Hall 400
1:30p-2:30pIMA Postdoc Show and TellEE/CS 3-180
1:30-1:45 Yongfeng Li (University of Minnesota)
1:45-2:00 Tsvetanka Sendova (University of Minnesota)
2:00-2:15 Wei Xiong (University of Minnesota)
2:15-2:30Vasileios Maroulas (University of Minnesota)

Friday, September 12

10:45a-11:15aCoffee break Lind Hall 400

Monday, September 15

10:45a-11:15aCoffee breakLind Hall 400
2:30p-3:30pMath 8994: Topics in classical and quantum mechanics
Electronic structure calculations and molecular simulation: A mathematical initiation
Eric Cances (CERMICS)
Claude Le Bris (CERMICS)
Lind Hall 305

Tuesday, September 16

10:45a-11:15aCoffee breakLind Hall 400

Wednesday, September 17

10:45a-11:15aCoffee breakLind Hall 400
2:30p-3:30pMath 8994: Topics in classical and quantum mechanics
Electronic structure calculations and molecular simulation: A mathematical initiation
Eric Cances (CERMICS)
Claude Le Bris (CERMICS)
Lind Hall 305

Thursday, September 18

10:45a-11:15aCoffee breakLind Hall 400
11:15a-12:15pDigital Biology: the role of solvation and hydrophobicityRidgway Scott (University of Chicago)Vincent Hall 570 AMS
3:20p-4:20pColloquium: Some mathematical questions arising in polymeric fluid simulationsClaude Le Bris (CERMICS)Vincent Hall 16

Friday, September 19

10:45a-11:15aCoffee breakLind Hall 400

Monday, September 22

10:45a-11:15aCoffee breakLind Hall 400
2:30p-3:30pMath 8994: Topics in classical and quantum mechanics
Electronic structure calculations and molecular simulation: A mathematical initiation
Eric Cances (CERMICS)
Claude Le Bris (CERMICS)
Lind Hall 305

Tuesday, September 23

11:15a-12:15pTwo stable methods for multiple unstable solutions to semilinear variational elliptic systems Xianjin Chen (University of Minnesota)Lind Hall 305 PS

Wednesday, September 24

10:45a-11:15aCoffee breakLind Hall 400
2:30p-3:30pMath 8994: Topics in classical and quantum mechanics
Electronic structure calculations and molecular
Eric Cances (CERMICS)
Claude Le Bris (CERMICS)
Lind Hall 305

Thursday, September 25

10:45a-11:15aCoffee breakLind Hall 400
11:15a-12:15p Yoichiro Mori, University of Minnesota
A three-dimensional model of cellular electrical activity
Vincent Hall 570 AMS

Friday, September 26

All DayThe Physics-Chemistry Viewpoint T9.26-27.08
8:15a-8:45aCoffee and registrationEE/CS 3-176 T9.26-27.08
8:50a-9:00aWelcome Fadil Santosa (University of Minnesota) T9.26-27.08
9:00a-10:30aIntroduction to quantum mechanicsAlexander V. Nemukhin (Moscow State University)EE/CS 3-180 T9.26-27.08
10:30a-11:00aBreakEE/CS 3-176 T9.26-27.08
11:00a-12:00pMathematical modeling of electronic structuresEric Cances (CERMICS)EE/CS 3-180 T9.26-27.08
12:00p-2:00pLunch T9.26-27.08
2:00p-3:00pWave function methods in chemistryLyudmila V. Slipchenko (Iowa State University)EE/CS 3-180 T9.26-27.08
3:00p-3:30pCoupled-cluster and equation-of-motion approaches to electron correlationAnna Krylov (University of Southern California)EE/CS 3-180 T9.26-27.08
3:30p-4:00pBreak EE/CS 3-176 T9.26-27.08
4:00p-5:00pAlgorithms and computational aspects of DFT calculations Part IJuan C. Meza (Lawrence Berkeley National Laboratory)EE/CS 3-180 T9.26-27.08
5:00p-5:15pGroup photo T9.26-27.08

Saturday, September 27

All DayMathematical and Computational Issues T9.26-27.08
9:00a-9:30aCoffeeEE/CS 3-176 T9.26-27.08
9:30a-10:30aPhysics of density functional theory (parts I and II)John P. Perdew (Tulane University)EE/CS 3-180 T9.26-27.08
10:30a-11:00aBreakEE/CS 3-176 T9.26-27.08
11:00a-12:00pMathematical aspects of density functional theoryEric Cances (CERMICS)EE/CS 3-180 T9.26-27.08
12:00p-2:00pLunch T9.26-27.08
2:00p-3:00pPhysics of density functional theory (part II)John P. Perdew (Tulane University)EE/CS 3-180 T9.26-27.08
3:00p-3:30pBreakEE/CS 3-180 T9.26-27.08
3:30p-4:30pAlgorithms and computational aspects of DFT calculations part IIJuan C. Meza (Lawrence Berkeley National Laboratory)EE/CS 3-180 T9.26-27.08

Monday, September 29

All DayWavefunction Theory Session
Chair: Rodney J. Bartlett (University of Florida)
W9.29-10.3.08
8:15a-9:00aRegistration and coffeeEE/CS 3-176 W9.29-10.3.08
9:00a-9:15aWelcome to the IMAFadil Santosa (University of Minnesota)EE/CS 3-180 W9.29-10.3.08
9:15a-10:05aCoulomb resolution and low-rank approximationsPeter M.W. Gill (Australian National University)EE/CS 3-180 W9.29-10.3.08
10:05a-10:35aCoffeeEE/CS 3-176 W9.29-10.3.08
10:35a-11:25aCholesky decomposition techniques in quantum chemical implementationsRoland Lindh (Lund University)EE/CS 3-180 W9.29-10.3.08
11:25a-1:30pLunch W9.29-10.3.08
1:30p-2:20pCoupled cluster approaches for modeling large molecular systems in various environmentsKarol Kowalski (Pacific Northwest National Laboratory)EE/CS 3-180 W9.29-10.3.08
2:25p-3:15pConical intersections in quantum chemistrySpiridoula Matsika (Temple University)EE/CS 3-180 W9.29-10.3.08
3:15p-3:30pGroup Photo W9.29-10.3.08
3:30p-4:00pCoffeeEE/CS 3-176 W9.29-10.3.08
4:00p-4:40pSecond chances: Some problems for mathematicians in quantum chemistry Rodney J. Bartlett (University of Florida)EE/CS 3-180 W9.29-10.3.08
4:40p-7:00pPoster Session and Reception: 4:40-7:00
Poster submissions welcome from all participants
Lind Hall 400 W9.29-10.3.08
Full-dimensional potential energy surfaces for small moleculesBastiaan J. Braams (Emory University)
Contact geometry and conductance of crossed nanotube junctions under pressureFelipe Alfonso Bulat (Duke University)
Development of explicitly correlated Hartree-Fock and multicomponent density functional theory for capturing electron-proton correlationArindam Chakraborty (Pennsylvania State University)
Insights into current limitations of density functional theoryAron J. Cohen (Duke University)
Time-dependent relativistic density functional theory for complex linear response based on the zeroth order regular approximationAjitha Devarajan (Iowa State University)
Relativistic GVVPT2 via Molcas-UNDMol tandemAjitha Devarajan (Iowa State University)
Alexander Gaenko (Iowa State University)
Mark R. Hoffmann (University of North Dakota)
Roland Lindh (Lund University)
Effects of hyperconjugation on the ionization energy of 1-hydroxyethyl radicalKadir Diri (University of Southern California)
The reduced density matrix method: Applications of the T2' N-representability condition and development of accurate semidefinite solverMituhiro Fukuda (Tokyo Institute of Technology)
Modeling properties of the chromophore from the green fluorescent proteinBella Grigorenko (M.V. Lomonosov Moscow State University)
Orbital dependent functionals in DFT, Optimized effective potential methodsAndreas Görling (Friedrich-Alexander-Universität Erlangen-Nürnberg)
Does Moller-Plesset perturbation theory converge? A Look at two-electron systemsGeorge A. Hagedorn (Virginia Polytechnic Institute and State University)
Mark S. Herman (University of Minnesota)
Born-Oppenheimer corrections near a Renner-Teller crossingMark S. Herman (University of Minnesota)
A fast algorithm for generalized Van Vleck perturbation theory Mark R. Hoffmann (University of North Dakota)
Toward real-life petascale applications: Experience at ERDCOlexandr Isayev (Jackson State University)
Delocalization errors in density functionals and implications for main-group thermochemistry Erin R. Johnson (Duke University)
A benchmark evaluation of spin-component scaled MP2 on the ethylene dimer potential energy surface Rollin A. King (Bethel University)
Parallel implementation of coupled cluster methods in NWChemKarol Kowalski (Pacific Northwest National Laboratory)
Hybrid functionals with local range separation Aliaksandr Krukau (Rice University)
A non-iterative perturbative triples correction for the spin-flipping and spin-conserving equation-of-motion coupled-cluster methods with single and double substitutionsAnna Krylov (University of Southern California)
Quantal and classical geometric phases in moleculesFlorence J. Lin (University of Southern California)
QCDFT: Quantum simulations of materials at micron scales and beyondGang Lu (California State University)
Robust mixing for ab-initio quantum mechanical calculations Russell Luke (University of Delaware)
Laurence D. Marks (Northwestern University)
The discontinuous nature of the exchange-correlation functional--critical for strongly correlated systems Paula Mori-Sánchez (Duke University)
Calculations of free energy profiles with the quantum mechanical- molecular mechanical (QM/MM) potential energy functions using DFT approximations in the QM subsystemAlexander V. Nemukhin (Moscow State University)
Reduced basis method for nanodevices simulationGeorge Pau (Lawrence Berkeley National Laboratory)
Climbing Jacob's ladder of density functional approximationsJohn P. Perdew (Tulane University)
Surrogate modeling for geometry optimization in material design Marielba Rojas (Technical University of Denmark)
Describing Forster energy transfer in TD-DFTEspen Sagvolden (University of California, Irvine)
Novel exact solution methodologies in wavefunction analysisValentino Anthony Simpao (Mathematical Consultant Services)
Water-benzene interactions: An effective fragment potential study Lyudmila V. Slipchenko (Iowa State University)
van der Waals-corrected density functional theory Jianmin Tao (Los Alamos National Laboratory)
Adiabatic connection forms in DFT: H2 and the He isoelectronic series David J. Tozer (University of Durham)
Estimating valence-state mixing from constrained density functional theory calculations with fractional numbers of electronsSteven M. Valone (Los Alamos National Laboratory)
Improving the accuracy of the nonlocal van der Waals density functional with minimal empiricism Oleg A. Vydrov (Massachusetts Institute of Technology)
An FFT-based algorithm for the generalized Born theory of biomolecule solvationZhenli Xu (University of North Carolina - Charlotte)

Tuesday, September 30

All Day9:00a-9:50am Wavefunction Theory Session (continued)

10:20am Density Functional Theory for Physics and Chemistry Session
Chair: David J. Tozer (University of Durham)

W9.29-10.3.08
8:30a-9:00aCoffeeEE/CS 3-176 W9.29-10.3.08
9:00a-9:50aTractable valence space models for strong electron correlationsMartin Head-Gordon (University of California, Berkeley)EE/CS 3-180 W9.29-10.3.08
9:50a-10:20aCoffeeEE/CS 3-176 W9.29-10.3.08
10:20a-11:10aReconnecting wavefunction and density-functional theory Kieron J. Burke (University of California, Irvine)EE/CS 3-180 W9.29-10.3.08
11:15a-12:05pThe role of nonlocal exchange in density functionalsGustavo E. Scuseria (Rice University)EE/CS 3-180 W9.29-10.3.08
12:05p-2:00pLunch W9.29-10.3.08
2:00p-2:50pOn exact relations in DFTMelvyn P. Levy (Duke University)EE/CS 3-180 W9.29-10.3.08
2:50p-3:20pCoffeeEE/CS 3-176 W9.29-10.3.08
3:20p-3:50pNSF CHE-DMR-DMS SOLAR energy initiativeHenry A. Warchall (National Science Foundation)EE/CS 3-180 W9.29-10.3.08
3:50p-4:40pVan der Waals interactions and density-functional theoryAxel D. Becke (Dalhousie University)EE/CS 3-180 W9.29-10.3.08
4:40p-5:20pSecond chances: The chair of the day will deliver a 30 minutes overview of the field followed by a discussion. David J. Tozer (University of Durham)EE/CS 3-180 W9.29-10.3.08

Wednesday, October 1

All Day9:00am-12:05pm Density Functional Theory for Physics and Chemistry Session (continued)

2:00pm DFT Math Session
Chair: Heinz Siedentop (Ludwig-Maximilians-Universität München)

W9.29-10.3.08
8:30a-9:00aCoffeeEE/CS 3-176 W9.29-10.3.08
9:00a-9:50aTBAEberhard K. U. Gross (Freie Universität Berlin)EE/CS 3-180 W9.29-10.3.08
9:50a-10:20aCoffeeEE/CS 3-176 W9.29-10.3.08
10:20a-11:10aVan der Waals density functional: theory, implementations, and applicationsDavid Langreth (Rutgers University)EE/CS 3-180 W9.29-10.3.08
11:15a-12:05pNew density functionals with broad applicability for thermochemistry, thermochemical kinetics, noncovalent interactions, transition metals, and spectroscopyDonald G. Truhlar (University of Minnesota)EE/CS 3-180 W9.29-10.3.08
12:05p-2:00pLunch W9.29-10.3.08
2:00p-2:50pOpen mathematical issues in quantum chemistry: a personal perspectiveClaude Le Bris (CERMICS)EE/CS 3-180 W9.29-10.3.08
2:50p-3:20pCoffeeEE/CS 3-176 W9.29-10.3.08
3:20p-4:10pExact embedding of local defects in crystalsMathieu Lewin (Université de Cergy-Pontoise)EE/CS 3-180 W9.29-10.3.08

Thursday, October 2

All Day 9:00am-11:55am DFT Math Session (continued)
Chair: Heinz Siedentop (Ludwig-Maximilians-Universität München)

2:00pm Algorithms Session
Chair: François Gygi (University of California, Davis)

W9.29-10.3.08
8:30a-9:00aCoffeeEE/CS 3-176 W9.29-10.3.08
9:00a-9:50aA linear scaling subspace iteration algorithm with optimally localized non-orthogonal wave functions for Kohn-Sham density functional theoryCarlos J. Garcia-Cervera (University of California, Santa Barbara)EE/CS 3-180 W9.29-10.3.08
9:50a-10:20aCoffeeEE/CS 3-176 W9.29-10.3.08
10:20a-11:10aConstruction of exponentially localized Wannier functionsGianluca Panati (Università di Roma "La Sapienza")EE/CS 3-180 W9.29-10.3.08
11:15a-11:55aSecond chances: The chair of the day will deliver a 30 minutes overview of the field followed by a discussion. Heinz Siedentop (Ludwig-Maximilians-Universität München)EE/CS 3-180 W9.29-10.3.08
11:55a-2:00pLunch W9.29-10.3.08
2:00p-2:50pMathematical and algorithmic challenges in the simulation of electronic structure and dynamics on quantum computersAlán Aspuru-Guzik (Harvard University)EE/CS 3-180 W9.29-10.3.08
2:50p-3:20pCoffeeEE/CS 3-176 W9.29-10.3.08
3:20p-4:10pAugmented basis sets in finite cluster DFTJames W. Davenport (Brookhaven National Laboratory)EE/CS 3-180 W9.29-10.3.08
6:30p-8:30pWorkshop dinner at Caspian Bistro Caspian Bistro
2418 University Ave SE
Minneapolis, MN 55414
612-623-1133
W9.29-10.3.08

Friday, October 3

All Day Algorithms Session (continued)
Chair: François Gygi (University of California, Davis)
W9.29-10.3.08
8:30a-9:00aCoffeeEE/CS 3-176 W9.29-10.3.08
9:00a-9:50aFirst-principles molecular dynamics for petascale computersFrançois Gygi (University of California, Davis)EE/CS 3-180 W9.29-10.3.08
9:50a-10:20aCoffeeEE/CS 3-176 W9.29-10.3.08
10:20a-11:10aModern optimization tools and electronic structure calculationsJosé Mario Martínez (State University of Campinas (UNICAMP))EE/CS 3-180 W9.29-10.3.08
11:15a-12:05pPartition-of-unity finite-element approach for large, accurate ab initio electronic structure calculations John E. Pask (Lawrence Livermore National Laboratory)EE/CS 3-180 W9.29-10.3.08
12:05p-1:45pLunch W9.29-10.3.08
1:25p-2:25p Dealing with stiffness in low-Mach number flowsCaroline Gatti-Bono (Lawrence Livermore National Laboratory)Vincent Hall 570 IPS
1:45p-2:35pA direct constrained minimization algorithm for solving the Kohn-Sham equationsChao Yang (Lawrence Berkeley National Laboratory)EE/CS 3-180 W9.29-10.3.08
2:35p-3:05pCoffeeEE/CS 3-176 W9.29-10.3.08
3:05p-3:45pSecond chances: The chair of the day will deliver a 30 minutes overview of the field followed by a discussion.François Gygi (University of California, Davis)EE/CS 3-180 W9.29-10.3.08
3:45p-3:55pClosing remarkEE/CS 3-180 W9.29-10.3.08

Event Legend:

AMS Applied Mathematics Seminar
IPSIndustrial Problems Seminar
PSIMA Postdoc Seminar
T9.26-27.08Mathematical and Computational Approaches to Quantum Chemistry
W9.29-10.3.08Mathematical and Algorithmic Challenges in Electronic Structure Theory
Abstracts
Alán Aspuru-Guzik (Harvard University) Mathematical and algorithmic challenges in the simulation of electronic structure and dynamics on quantum computers
Abstract: The exact simulation of quantum mechanical systems on classical computers generally scales exponentially with the size of the system N. Using quantum computers, the computational resources required to carry out the simulation are polynomial. Our group has been working in the development and characterization of quantum computational algorithms for the simulation of chemical systems. We will give a tutorial on our algorithms for the simulation of molecular electronic structure, molecular properties and quantum dynamics, and will discuss the opportunities, open questions and challenges in the field of simulation of physical systems using quantum computers or dedicated quantum devices.
Rodney J. Bartlett (University of Florida) Second chances: Some problems for mathematicians in quantum chemistry
Abstract: No Abstract
Axel D. Becke (Dalhousie University) Van der Waals interactions and density-functional theory
Abstract: The application of conventional GGA, and meta-GGA, density functionals to van der Waals complexes is fraught with difficulties. Conventional functionals do not contain the physics of the dispersion interaction. To make matters worse, the exchange part alone can yield anything from severe over “binding” to severe over repulsion depending on the choice of functional. We rectify these problems by a) adding a dispersion term with nonempirical C6, C8, and C10 dispersion coefficients (the Becke-Johnson dispersion model), b) selecting a GGA exchange functional (PW86, also nonempirical) that gives excellent agreement with exact Hartree-Fock exchange repulsion curves. The result is a simple GGA+dispersion theory giving excellent noble-gas pair interaction energies for He through Kr with only two adjustable parameters in the dispersion cutoff.
Bastiaan J. Braams (Emory University) Full-dimensional potential energy surfaces for small molecules
Abstract: Studies of molecular dynamics and molecular spectroscopy generally start from the Born-Oppenheimer approximation and require some form of analytical potential energy surface fitted to ab initio electronic structure calculations. We have used computational invariant theory and the MAGMA computer algebra system as an aid to develop representations for the potential energy and dipole moment surfaces that are fully invariant under permutations of like nuclei. We express the potential energy surface in terms of internuclear distances using basis functions that are manifestly invariant. A dipole moment is represented with use of effective charges at positions of the nuclei, which must transform as a covariant, rather than as an invariant, under permutations of like nuclei. Malonaldehyde (CHOHCHCHO) provides an illustrative application. The associated molecular permutational symmmetry group is of order 288 (4!3!2!) and the use of full permutational symmetry makes it possible to obtain a compact representation for the surface.
Felipe Alfonso Bulat (Duke University) Contact geometry and conductance of crossed nanotube junctions under pressure
Abstract: We explored the relative stability, structure, and conductance of crossed nanotube junctions with dispersion corrected density functional theory. We found that the most stable junction geometry, not studied before, displays the smallest conductance. While the conductance increases as force is applied, it levels off very rapidly. This behavior contrasts with a less stable junction geometry that show steady increase of the conductance as force is applied. Electromechanical sensing devices based on this effect should exploit the conductance changes close to equilibrium.
Kieron J. Burke (University of California, Irvine) Reconnecting wavefunction and density-functional theory
Abstract: Recent work in my group has focussed on the semiclassical origins of density functional theory, and how much of modern DFT can be understood in these terms, including the limitations of present approximations. I will discuss this in detail for model systems, describing a method that avoids DFT altogether. This leads to a grand algorithmic challenge, whose solution could revolutionize electronic structure calculations, by allowing much larger numbers of electrons to be tackled.
Eric Cances (CERMICS) Mathematical aspects of density functional theory
Abstract: No Abstract
Eric Cances (CERMICS) Mathematical modeling of electronic structures
Abstract: Quantum Chemistry aims at understanding the properties of matter through the modelling of its behaviour at a subatomic scale, where matter is described as an assembly of nuclei and electrons. At this scale, the equation that rules the interactions between these constitutive elements is the Schrdinger equation. It can be considered (except in few special cases notably those involving relativistic phenomena or nuclear reactions) as a universal model for at least three reasons. First it contains all the physical information of the system under consideration so that any of the properties of this system can be deduced in theory from the Schrdinger equation associated to it. Second, the Schrdinger equation does not involve any empirical parameter, except some fundamental constants of Physics (the Planck constant, the mass and charge of the electron, ...); it can thus be written for any kind of molecular system provided its chemical composition, in terms of natures of nuclei and number of electrons, is known. Third, this model enjoys remarkable predictive capabilities, as confirmed by comparisons with a large amount of experimental data of various types. Unfortunately, the Schrödinger equation cannot be directly simulated, except for very small chemical systems. It indeed reads as a time-dependent 3(M+N)-dimensional partial differential equation, where M is the number of nuclei and N the number of the electrons in the system under consideration. On the basis of asymptotic and semiclassical limit arguments, it is however often possible to approximate the Schrdinger dynamics by the so-called Born-Oppenheimer dynamics, in which nuclei behave as classical point-like particles. The internuclei (or interatomic) potential can be computed ab initio, by solving the time-independent electronic Schrödinger equation. The latter equation is a 3N-dimensional partial differential equation (it is in fact a spectral problem), for which several approximation methods are available. The main of them are the wavefunction methods and the Density Functional Theory (DFT). In my first lecture (Mathematical modelling of electronic structures), I will present the mathematical properties of the time-independent electronic Schrödinger equation, and show how to construct variational approximations of this equation, in the framework of wavefunction methods. I will mainly deal with the Hartree-Fock approximation; more advanced wavefunction methods will then be presented in the lectures by L. Slipchenko and A. Krylov. In my second lecture (Mathematical aspects of density functional theory), I will examine the mathematical foundations of DFT. I will compare the constrained-search approach proposed by Levy and involving pure states, with the one proposed by Lieb and involving mixed states. These two approaches lead to Kohn-Sham and extended Kohn-Sham models respectively. I will then review the mathematical properties of the Kohn-Sham LDA and GGA models (corresponding to the first two rungs of the ladder of approximations previously presented by J. Perdew). Lastly, I will introduce the concept of bulk (or thermodynamic) limit, which allows one to rigorously derive DFT models for the condensed phase from molecular DFT models by letting the number of nuclei and electrons go to infinity in an appropriate way.
Eric Cances (CERMICS), Claude Le Bris (CERMICS) Math 8994: Topics in classical and quantum mechanics
Electronic structure calculations and molecular simulation: A mathematical initiation
Abstract: Meeting time: Mondays and Wednesdays 2:30 ‐ 3:30 pm Room 305 Lind Hall. The course will present the basics of the quantum theory commonly used in computational chemistry for electronic structure calculations, and the basics of molecular dynamics simulations. The perspective is definitely mathematical. After the presentation of the models, the mathematical properties will be examined. The state of the art of the mathematical knowledge will be mentioned. Numerical analysis and scientific computing questions will also be thoroughly investigated. The course is intended for students and researchers with a solid mathematical background in mathematical analysis and numerical analysis. Familiarity with the models in molecular simulation in the broad sense is not needed. The purpose of the course to introduce the audience to the field. This is a 1‐3 credit course offered through the School of Mathematics. Non‐student participants are welcome to audit without registering. Note that no particular knowledge of quantum mechanics or classical mechanics will be necessary: the basic elements will be presented. For additional information and course registration, please contact: Markus Keel (keel@math.umn.edu).
Arindam Chakraborty (Pennsylvania State University) Development of explicitly correlated Hartree-Fock and multicomponent density functional theory for capturing electron-proton correlation
Abstract: Recent advances in treating electrons and nuclei (typically protons) quantum mechanically without the Born-Oppenheimer approximation using nuclear-electronic orbital (NEO) method and multicomponent density functional theory (MCDFT) is presented. Electron-proton dynamical correlation is highly significant because of the attractive electrostatic interaction between the electron and the proton. Inadequate treatment of electron-proton correlation produces nuclear densities that are too localized, resulting in abnormally high stretching frequencies, as well as inaccuracies in thermally averaged geometries and isotope effects. To address this problem, an explicitly correlated Hartree-Fock (NEO-XCHF) scheme has been formulated to include explicit electron-proton correlation directly into the nuclear-electronic orbital self-consistent-field framework. This approach is based on a general ansatz for the nuclear-electronic wavefunction in which explicit dependence on the electron-proton distance is incorporated into the total wavefunction using Gaussian-type geminal functions. A multicomponent density functional theory (MCDFT) has also been formulated by developing electron-proton functionals based on the explicitly correlated ansatz for the nuclear-electronic wavefunction. Benchmark calculations illustrate that these new methods significantly improve the description of the nuclear densities, thereby leading to more accurate hydrogen vibrational frequencies and vibrationally averaged geometries.
Xianjin Chen (University of Minnesota) Two stable methods for multiple unstable solutions to semilinear variational elliptic systems
Abstract: Exhibiting many novel new phenomena that are not present in the single equation case, systems are much more interesting in many applications. Motivated by the growing experimental observations and studies of various nonlinear vector phenomena (e.g., spatial vector solitons) arising in diverse physical contexts (e.g., condensed matter physics, nonlinear optics, etc), the speaker will give an overview of some computational theory and methods for finding multiple unstable solutions (e.g., saddle points) to three types of nonlinear variational elliptic systems: cooperative, noncooperative, and Hamiltonian. In particular, two local characterizations of multiple unstable solutions to variational elliptic systems as well as two stable methods (called the local min-orthogonal method and the local min-max-orthogonal method) for finding saddle points of finite or infinite Morse index will be presented. Finally, both methods were applied to solve elliptic systems of those three types mentioned for multiple unstable solutions.
Aron J. Cohen (Duke University) Insights into current limitations of density functional theory
Abstract: Density functional theory of electronic structure is widely and successfully applied in simulations throughout engineering and sciences. However, for many predicted properties there are spectacular failures that can be traced to the delocalization error and static correlation error of commonly used approximations. These errors can be characterized and understood through the perspective of fractional charges and fractional spins introduced recently. Reducing these errors will open new frontiers for applications of density functional theory.
James W. Davenport (Brookhaven National Laboratory) Augmented basis sets in finite cluster DFT
Abstract: Density functional theory provides a systematic approach to the electronic structure of atoms, molecules and solids. It requires the repeated solution of single particle Schrodinger equations in a self consistent loop. Most techniques involve some sort of basis set, the most common ones being plane waves or Gaussians. In crystalline materials the most accurate solutions involve augmented basis sets. These combine numerical solutions of the Schrodinger equation in regions near the atomic nucleii with so called ‘tail functions’ in more distant regions. In the linear augmented plane wave (LAPW) method the tail functions are plane waves. This formulation has been incorporated into the WIEN2k code. With the current interest in nanoscale clusters, biomolecules, and other finite systems it is desirable to have a comparably accurate method for these. While it is always possible to build supercells, it is often convenient to have completely localized functions which eliminate interaction between periodic images. We recently proposed a finite cluster version of the linear augmented Slater-type orbital (LASTO) method [1]. STO’s have the correct behavior at large distances and possess an addition theorem – they can be re-expanded about other sites with analytic coefficients. We solve the Poisson equation by replacing the spherical part of the density near the nucleii with a smooth pseudo-density. The full potential, including the non-sphrical piece is then solved on a grid. Examples of small clusters and comparison with the Gaussian based program NWChem will be given. [1] K. S. Kang, J. W. Davenport, J. Glimm, D. E. Keyes, and M. McGuigan, submitted to J. Computational Chemistry.
Ajitha Devarajan (Iowa State University) Time-dependent relativistic density functional theory for complex linear response based on the zeroth order regular approximation
Abstract: Joint work with Alexander Gaenko and Jochen Autschbach. We develop a time-dependence quasirelativistic density functional ther based on the ZORA approximation for computing frequency dependent linear response of molecules. Density fitting was used for the calculation of complex components of the frequency dependent dipole-dipole polarizability. CPKS equations based on 2-componenent ZORA response were derived. Using damping techniques excitation energy corresponding to the poles of the polarizability curves were calculated. We present the results of the calculations of complex dipole-dipole polarizability, of two and three dimensional gold clusters, and absorption spectra of heavy metal oxides.
Ajitha Devarajan (Iowa State University), Alexander Gaenko (Iowa State University), Mark R. Hoffmann (University of North Dakota), Roland Lindh (Lund University) Relativistic GVVPT2 via Molcas-UNDMol tandem
Abstract: We have implemented relativisitic GVVPT2 using DKH integrals and ANO-RCC basis sets from Molcas package. It is done by developing an interface code accessing and transforming one- and two-electron integral array, making it available for any method implemented within the UNDMol package. The relativistic GVVPT2 is applied to calculations of ground and excited states potential energy curves of TiC and CrH.
Kadir Diri (University of Southern California) Effects of hyperconjugation on the ionization energy of 1-hydroxyethyl radical
Abstract: Spectroscopic studies of the hydroxymethyl and 1-hydroxyethyl radicals have found an unusually large difference in their ionization energies (IE). The anticipated decrease in the IE of the latter radical due to its larger size does not fully account for the experimentally observed difference of 0.92 eV. Here we investigated the problem with the aid of electronic structure calculations. We found that the large drop in the IE of 1-hydroxyethyl radical is a result of the combined effects of the destabilization of its highest occupied molecular orbital and the stabilization of the corresponding cation due to hyperconjugation. This qualitative explanation agrees with a simple Huckel-like approach and is also consistent with Natural Bond Orbital calculation results.
Mituhiro Fukuda (Tokyo Institute of Technology) The reduced density matrix method: Applications of the T2' N-representability condition and development of accurate semidefinite solver
Abstract: We are interested in realizing the variational calculation with the 2-order Reduced Density Matrix (2-RDM) for fermionic systems. The known necessary N-representability conditions P, Q, G, T1, and T2' are imposed, resulting in an optimization problem called semidefinite programming (SDP) problem. The ground state energies for various small atoms and molecules were calculated. Additionally, we show some results of the one-dimensional Hubbard model for high correlation limit using multiple precision arithmetic version of the solver.
Carlos J. Garcia-Cervera (University of California, Santa Barbara) A linear scaling subspace iteration algorithm with optimally localized non-orthogonal wave functions for Kohn-Sham density functional theory
Abstract: We present a new linear scaling method for electronic structure computations in the context of Kohn-Sham density functional theory (DFT). The method is based on a subspace iteration, and takes advantage of the non-orthogonal formulation of the Kohn-Sham functional, and the improved localization properties of non-orthogonal wave functions. We demonstrate the efficiency of the algorithm for practical applications by performing fully three-dimensional computations of the electronic density of alkane chains. This is joint work with Jianfeng Lu, Yulin Xuan, and Weinan E, at Princeton University.
Caroline Gatti-Bono (Lawrence Livermore National Laboratory) Dealing with stiffness in low-Mach number flows
Abstract: Numerical simulation of low-Mach number flows presents challenges because of the stiffness introduced by the disparity of time scales between acoustic and convective motions. In particular, the acoustic, high-speed modes often contain little energy but determine the time step for explicit schemes through the CFL condition. A natural idea is therefore to separate the acoustic modes from the rest of the solution and to treat them implicitly, while the advective motions are treated explicitly or semi-implicitly. In this talk, we present a numerical allspeed algorithm that respects low-Mach number asymptotics but is suitable for any Mach number. We use a splitting method based on a Hodge/Helmholtz decomposition of the velocities to separate the fast acoustic dynamics from the slower anelastic dynamics. The acoustic waves are treated implicitly, while the advection is treated semi-implicitly. The splitting mechanism is demonstrated on two applications. The first application is a combustive flow, where Euler equations are completed by an enthalpy evolution equation. Then, we present a stratified atmospheric flow where the presence of gravity waves adds one more degree of complexity. Benchmark results are presented that compare well with the literature.
Peter M.W. Gill (Australian National University) Coulomb resolution and low-rank approximations
Abstract: The Resolution of the Identity (RI) is widely used in many-body algorithms. It expresses the completeness of a set of functions that possess the familiar orthonormality property. In the first part of my lecture, I will discuss functions that possess an analogous property called Coulomb-orthonormality and which permit us to resolve the two-particle Coulomb operator into a sum of products of one-particle functions. Connections to Cholesky decomposition and Kronecker-product approximation will be made. In the second part of the lecture, I will present and discuss numerical applications of Coulomb resolution in the context of electronic structure theory.
Bella Grigorenko (M.V. Lomonosov Moscow State University) Modeling properties of the chromophore from the green fluorescent protein
Abstract: The green fluorescent protein (GFP) is widely used in biochemical and medical studies as a biomarker in living cells. Modeling properties of GFP is an essential step in the efforts to enhance efficiency of this in vivo marker and to expand the area of its applications. We apply the methods of electronic structure calculations, including the quantum chemistry methods and the combined quantum mechanical – molecular mechanical (QM/MM) approaches, to describe the structure, spectra and transformations of the GFP chromophore, 4-hydroxybenzylidene-imidazolinone, in the gas phase, solutions and in the protein matrix. We compare the results of calculations for the cis-trans chromophore isomerization in the ground electronic state in the gas phase by using the DFT approach PBE0/6-31+G** and the CASSCF(12,11)/cc-pVDZ approximation. The energy profiles computed with both methods are markedly different in the vicinity of the saddle point. The isomerization paths computed in the QM/MM approach for the chromophore buried inside the water cluster show that the CASSCF results are better consistent with the experimental observations than the DFT findings. We also report the results of QM/MM calculations with the DFT approximations in the QM subsystem for the geometry configurations of the chromophore binding pocket inside the protein by assuming various protonation states of the chromophore unit, anionic, neutral, zwitterionic, cationic. These structures are employed for calculations of the photoexcitation pathways in GFP.
François Gygi (University of California, Davis) First-principles molecular dynamics for petascale computers
Abstract: First-principles molecular dynamics (FPMD) is a simulation method that combines molecular dynamics with the accuracy of a quantum mechanical description of electronic structure. It is increasingly used to address problems of structure determination, statistical mechanics, and electronic structure of solids, liquids and nanoparticles. The high computational cost of this approach makes it a good candidate for use on large-scale computers. In order to achieve high performance on terascale and petascale computers, current FPMD algorithms have to be reexamined and redesigned. We present new, large-scale parallel algorithms developed for FPMD simulations on computers including O(103) to O(104) CPUs. Examples include the problem of simultaneous diagonalization of symmetric matrices used in the calculation of Maximally Localized Wannier Functions (MLWFs), and the Orthogonal Procrustes problem that arises in the context of Born-Oppenheimer molecular dynamics simulations. Supported by NSF-OCI PetaApps through grant 0749217.
Andreas Görling (Friedrich-Alexander-Universität Erlangen-Nürnberg) Orbital dependent functionals in DFT, Optimized effective potential methods
Abstract: A new generation of density-functional methods is based on orbital-dependent funtionals. With orbital-dependent functionals long-standing problems like the occurence of unphysical Coulomb self-interactions or the qualitatively wrong description of charge-transfer excitation in time-dependent density-functional theory can be solved. Orbital-dependent functionals indeed may represent the future of density-functional theory. In oder to determine exchange-correlation potentials corresponding to orbital-dependent energy functionals, however, it is necessary to solve a numerically very demanding integral equation with the optimized effective potential (OEP) method. Methods to handle this integral equation thus are required for the further development of density-functional methods. The numerical stability of the OEP integral equation is investigated and method to solve it are presented.
George A. Hagedorn (Virginia Polytechnic Institute and State University), Mark S. Herman (University of Minnesota) Does Moller-Plesset perturbation theory converge? A Look at two-electron systems
Abstract: We study convergence or divergence of the Moller–Plesset perturbation series for systems with two electrons and a single nucleus of charge Z > 0. This question is essentially to determine if the radius of convergence of a power series in the complex perturbation parameter lambda is greater than 1. We examine a simple one-dimensional model with delta functions in place of Coulomb potentials and the realistic three-dimensional model. For each model, we show rigorously that if the nuclear charge Z is sufficiently large, there are no singularities for real values of lambda between -1 and 1. Using a finite difference scheme, we present numerical results for the delta function model.
Martin Head-Gordon (University of California, Berkeley) Tractable valence space models for strong electron correlations
Abstract: Wave function-based quantum chemistry has two traditional lines of development – one based on molecular orbitals (MO's), and the other on valence bond (VB) theory. Both offer advantages and disadvantages for the challenging problem of describing strong correlations, such as the breaking of chemical bonds, or the low-spin (antiferromagnetic) coupling of electrons on different centers. Within MO methods, strong correlations can be viewed as those arising within a valence orbital active space. One reasonable definition of such a space is to supply one correlating orbital for each valence occupied orbital. Exact solution of the Schrodinger equation in this space is exponentially difficult with its size, and therefore approximations are imperative. The most common workaround is to truncate the number of orbitals defining the active space, and then solve the truncated problem, as is done in CASSCF. An important alternative is to systematically approximate the Schrödinger equation in the full valence space, for example by using coupled cluster theory ideas. I shall discuss progress in this direction. Within spin-coupled VB theory, the target wave function consists of a set of non-orthogonal orbitals, one for each valence electron, that are spin-coupled together into a state of the desired overall spin-multiplicity. The number of active orbitals is identical with the valence space MO problem discussed above, though the problem is not identical. Exact solution of the VB problem is exponentially difficult with molecular size, and therefore approximations are imperative. Again, the most common approach is to seek the exact solution in a truncated valence orbital space, where other orbitals are simply treated in mean-field. It is possible, however, to also consider approximations that do not truncate the space, but rather reduce the complexity. A new way of doing this will be introduced and contrasted with the MO-based approaches.
Mark S. Herman (University of Minnesota) Born-Oppenheimer corrections near a Renner-Teller crossing
Abstract: We perform a rigorous mathematical analysis of the bending modes of a linear triatomic molecule that exhibits the Renner-Teller effect. Assuming the potentials are smooth, we prove that the wave functions and energy levels have asymptotic expansions in powers of epsilon, where the fourth power of epsilon is the ratio of an electron mass to the mass of a nucleus. To prove the validity of the expansion, we must prove various properties of the leading order equations and their solutions. The leading order eigenvalue problem is analyzed in terms of a parameter b, which is equivalent to the parameter originally used by Renner. Perturbation theory and finite difference calculations suggest that there is a crossing involving the ground bending vibrational state near b=0.925. The crossing involves two states with different degeneracy.
Mark R. Hoffmann (University of North Dakota) A fast algorithm for generalized Van Vleck perturbation theory
Abstract: A recent algorithmic revision of second order Generalized van Vleck perturbation theory (GVVPT2) has proven to make the method efficacious for many challenging molecular systems. 1 An extension to third order (GVVPT3) has been demonstrated to be a close approximation to multireference configuration interaction including single and double excitations (MRCISD). 2 To improve the computing efficiency, new GVVPT codes have been developed to take advantage of recently implemented configuration-driven configuration interaction (CI) with unitary group approach (UGA).
Olexandr Isayev (Jackson State University) Toward real-life petascale applications: Experience at ERDC
Abstract: Joint work with Jerzy Leszczynski, Computational Center for Molecular Structure and Interactions, Jackson State University, Jackson MS and Leonid Gorb, US Army ERDC, Vicksburg, MS. With the June announcement that RoadRunner supercomputer is the first system to reach the petaflop level, the HPC community is entering a realm of unprecedented computing power. More petascale computing systems will soon be available to the scientific community. Recent studies in the productivity of HPC platforms point to better software as a key enabler to science on these systems. The combination of computationally demanding electronic structure methods with molecular dynamics is highly dependent on high-performance computing resources. The availability of such applications constitutes a big opportunity to evaluate both capabilities and limits of any HPC system and software application within the framework of a real-life feasibility study. The performance of benchmarks from the AIMD and hybrid QM/MM simulations on two high performance computing platforms will be discussed. Looking toward maximizing the computational time/performance ratio, we analyzed performance data for the Cray XT3/XT4 architectures available at ERDC.
Erin R. Johnson (Duke University) Delocalization errors in density functionals and implications for main-group thermochemistry
Abstract: The difficultly of approximate density functionals in describing the energetics of Diels-Alder reactions and dimerization of aluminum complexes is analyzed. Both of these reaction classes involve formation of cyclic or bicyclic products, which are found to be under-bound by the majority of functionals considered. We present a consistent view of these results from the perspective of delocalization error. This error causes approximate functionals give too low energy for delocalized densities or too high energy for localized densities, as in the cyclic and bicyclic reaction products. This interpretation allows us to understand better a wide range of errors in main-group thermochemistry obtained with popular density functionals. In general, functionals with minimal delocalization error should be used for theoretical studies of reactions where there is a loss of extended conjugation or formation of highly branched, cyclic, and cage-like molecules.
Rollin A. King (Bethel University) A benchmark evaluation of spin-component scaled MP2 on the ethylene dimer potential energy surface
Abstract: The bimolecular interaction potentials for various configurations of the ethylene dimer computed with coupled-cluster and spin-component scaled MP2 are reported. Of particular interest is any bias for particular orientations of the sigma- and pi-bonds introduced by the scaling of correlation components.
Karol Kowalski (Pacific Northwest National Laboratory) Coupled cluster approaches for modeling large molecular systems in various environments
Abstract: Joint work with Marat Valiev, Niri Govind, Peng-Dong Fan, W.A. de Jong (William R Wiley Environmental Molecular Sciences Laboratory and Chemical Sciences Division, Pacific Northwest National Laboratory P.O. Box 999, MS K1-96, Richland, WA 99352) and Jeff R. Hammond (The University of Chicago). The coupled-cluster (CC) methodology has become a leading formalism not only in gas-phase calculations but also in modeling systems for which the inclusion of the surrounding environment is critical for a comprehensive understanding of complex photochemical reactions. At the same time it has been proven that high-level CC formalisms are capable of providing highly adequate characterization of excitation energies and excited-state potential energy surfaces. With the ever increasing power of computer platforms and highly scalable codes, very accurate QM/MM calculations for large molecules (defining the quantum region) can be routinely performed in the foreseeable future even with iterative methods accounting for the effect of triples ( CCSDT-n/EOMCCSDT-n). We will discuss several components of recently developed and implemented CC methodologies in NWChem. This includes: (1) Novel iterative/non-iterative methods accounting for the effect of triply excited configurations, (2) Massively parallel implementations of the CC theories based on the manifold of singly and doubly excited configurations. Several examples will illustrate how these approaches can be used in multiscale QM/MM framework.
Karol Kowalski (Pacific Northwest National Laboratory) Parallel implementation of coupled cluster methods in NWChem
Abstract: Over the last decade the coupled-cluster (CC) methodology played a dominant role in highly accurate predictions of electronic structure. For this reason, the need for more efficient parallel implementations is obvious. Currently, the existing NWChem implementation can scale across thousand of CPUs and can be used in correlating 250 electrons. Additionally, the CC codes can be used as a quantum mechanical component of various multiscale approaches.
Aliaksandr Krukau (Rice University) Hybrid functionals with local range separation
Abstract: Range-separated (screened) hybrid functionals provide a powerful strategy for incorporating nonlocal exact (Hartree-Fock-type) exchange into density functional theory. Existing implementations of range separation use a fixed, system-independent screening parameter. Here, we propose a novel method that uses a position-dependent screening. These locally range-separated (LRS) hybrids add substantial flexibility for describing diverse electronic structures and satisfy a high-density scaling constraint better than the fixed screening approximation does.
Anna Krylov (University of Southern California) Coupled-cluster and equation-of-motion approaches to electron correlation
Abstract: Coupled-cluster (CC) and equation-of-motion coupled-cluster (EOM-CC) methods are the most reliable and versatile tools of electronic structure theory. The exponential CC ansatz ensures size-extensivity. By increasing the excitation level, systematic approximations approaching the exact many-body solution are possible. EOM extends the CC methodology (applicable to the wave functions dominated by a single Slater determinant) to the open-shell and electronically excited species with multi-configurational wave-functions. The lecture will present an overview of CC and EOM-CC methods and highlight their important formal properties. Suggested reading: 1. T. Helgaker, P. Jorgensen, and J. Olsen, Molecular electronic structure theory; Wiley & Sons, 2000. 2. A. I. Krylov, Equation-of-motion coupled-cluster methods for open-shell and electronically excited species: The hitchhiker's guide to Fock space Ann. Rev. Phys. Chem. v. 59, 433 (2008). 3. D. Mukherjee and S. Pal, Use of cluster expansion methods in the open-shell correlation problem, Adv. Quantum Chem. v. 20, 291 (1989). 4. R.J. Bartlett and J.F. Stanton, Applications of post-Hartree-Fock methods: A tutorial, Rev. Comp. Chem. v. 5, 65 (1994).
Anna Krylov (University of Southern California) A non-iterative perturbative triples correction for the spin-flipping and spin-conserving equation-of-motion coupled-cluster methods with single and double substitutions
Abstract: Joint work with P.U. Manohar. A non-iterative N7 triples correction for the equation-of-motion coupled-cluster wave functions with single and double substitutions (EOM-CCSD) is presented. The correction is derived by second order perturbation treatment of the similarity-transformed CCSD Hamiltonian. The spin-conserving variant of the correction is identical to the triples correction of Piecuch and coworkers [Mol. Phys. 104, 2149 (2006)] derived within method-of-moments framework and is not size-intensive. The spin-flip variant of the correction is size-intensive. The performance of the correction is demonstrated by calculations of electronic excitation energies in methylene, nitrenium ion, cyclobutadiene, ortho-, meta-, and para- benzynes, 1,2,3-tridehydrobenzene, as well as C-C bond-breaking in ethane. In all cases except cyclobutadiene, the absolute values of the correction for energy differences were 0.1 eV or less. In cyclobutadiene, the absolute values of the correction were as large as 0.4 eV. In most cases, the corrections reduced the errors against the benchmark values by about a factor of 2 to 3, the absolute errors being less 0.04 eV.
David Langreth (Rutgers University) Van der Waals density functional: theory, implementations, and applications
Abstract: The van der Waals density functional of Dion, Rydberg, Schroder, Langreth, and Lundqvist [Phys. Rev. Lett. 92, 246401 (2004)] will be reviewed, discussing implementations and applications by our group and others. New results relevalent for hydrogen storage in metal-organic framework (MOF) materials, as well for the intercalation of drug molecules in DNA will be presented.
Claude Le Bris (CERMICS) Open mathematical issues in quantum chemistry: a personal perspective
Abstract: I will overview some open mathematical questions related to the models and techniques of computational quantum chemistry. The talk is based upon a recent article coauthored with E. Cances and PL. Lions, and published in Nonlinearity, volume 21, T165-T176, 2008.
Claude Le Bris (CERMICS) Colloquium: Some mathematical questions arising in polymeric fluid simulations
Abstract: We review some recent mathematical contributions related to the modelling of polymeric flows. Modern simulations involve multiscale models that couple a kinetic description of the microstructure of the fluid with a macroscopic description of the flow. The former takes the form of a Fokker- Planck equation while the latter is a non-Newtonian form of the incompressible Navier-Stokes equations. The well-posedness of such multiscale models will be first examined. Then some theoretical questions related to the existence of solutions to Fokker- Planck type equations (or stochastic differential equations) with Sobolev regular coefficients will be addressed. Finally, some numerical issues and challenges will be mentioned. This talk is based upon a series of works incollaboration with B. Jourdain and T. Lelievre, and with PL. Lions.
Melvyn P. Levy (Duke University) On exact relations in DFT
Abstract: A number of exact relations are briefly discussed in terms of present developments and goals in DFT. In addition, conjectured relations are presented.
Mathieu Lewin (Université de Cergy-Pontoise) Exact embedding of local defects in crystals
Abstract: By means of rigorous thermodynamic limit arguments, we derive a new variational model providing exact embedding of local defects in insulating or semiconducting crystals. A natural way to obtain variational discretizations of this model is to expand the perturbation of the periodic density matrix generated by the defect in a basis of precomputed maximally localized Wannier functions of the host crystal. This approach can be used within any semi-empirical or Density Functional Theory framework. This is a joint work with Eric Cancès and Amélie Deleurence (Ecole Nationale des Ponts et Chaussées, France).
Florence J. Lin (University of Southern California) Quantal and classical geometric phases in molecules
Abstract: The quantal geometric phase [1-3] in a Born-Oppenheimer (adiabatic) electronic wavefunction is a net phase change for nuclear motion over a closed path. Effects of the quantal geometric phase have been observed in theoretical studies of the vibrational spectra of cyclic trinitrogen (N3) molecule [4, 5]. Making a classical-quantum correspondence [6] relates the quantal geometric phase to a classical one for cyclic nuclear motion in N-body molecular dynamics. Each is described differential geometrically as the holonomy of a connection [7], physically in terms of the internal angular momentum, and with examples. The classical geometric phase [8] is a net angle of overall rotation in the center-of-mass frame. A net rotation of 20 degrees has been observed experimentally in a triatomic photodissociation and a net overall rotation of 42 degrees has been observed computationally in protein dynamics. The Hamiltonian operator in a generalized Born-Oppenheimer Schrodinger equation for the electronic wavefunction is related to a classical Hamiltonian for N-body molecular dynamics. Both the quantal and classical geometric phases arise due to non-zero internal angular momentum in N-body molecular dynamics. References:
[1] C. A. Mead and D. G. Truhlar, J. Chem. Phys. 70, 2284 (1979).
[2] M. V. Berry, Proc. Royal Soc. London A 392, 45 (1984).
[3] B. Simon, Phys. Rev. Lett. 51, 2167 (1983).
[4] D. Babikov, B. K. Kendrick, P. Zhang, and K. Morokuma, J. Chem. Phys. 122, 044315 (2005).
[5] D. Babikov, V. A. Mozhayskiy, and A. I. Krylov, J. Chem. Phys. 125, 084306 (2006).
[6] F. J. Lin, Quantal and classical geometric phases, 2008.
[7] J. E. Marsden, R. Montgomery, and T. Ratiu, Memoirs of the American Mathematical Society, Vol. 88, No. 436, American Mathematical Society, Providence, RI, 1990.
[8] F. J. Lin, Discrete and Continuous Dynamical Systems, Supplement 2007, 655 (2007).
Roland Lindh (Lund University) Cholesky decomposition techniques in quantum chemical implementations
Abstract: In this presentation I will give a review of the Cholesky Decomposition (CD) as it has been implemented in the MOLCAS program package. These examples will include conventional CD, as implemented for the HF, CASSCF, MP2, DFT, CASPT2 and CC methods, to the recent 1-center CD approximation. In addition, the aCD abd acCD techniques for the on-the-fly generation of RI auxiliary basis functions will be discussed. Analytic CD gradients will be introduced for CD-HF, CD-DFT(pure and hybrid), and CD-CASSCF. If time allows I will briefly discuss the use of CD technique for the fast evaluation of the exchange energy in CD-HF through the use of CD localized orbitals.
Gang Lu (California State University) QCDFT: Quantum simulations of materials at micron scales and beyond
Abstract: We present a novel multiscale modeling approach that can simulate multi-million atoms effectively via density functional theory. The method is based on the framework of the quasicontinuum (QC) approach with orbital-free density functional theory (OFDFT) as its sole energetics formulation. The local QC part is formulated by the Cauchy-Born hypothesis with OFDFT calculations for strain energy and stress. The nonlocal QC part is treated by an OFDFT-based embedding approach, which couples OFDFT nonlocal atoms to local region atoms. The method - QCDFT- is applied to a nanoindentation study of an Al thin film, and the results are compared to a conventional QC approach. The results suggest that QCDFT represents a new direction for the quantum simulation of materials at length scales that are relevant to experiments.
Russell Luke (University of Delaware), Laurence D. Marks (Northwestern University) Robust mixing for ab-initio quantum mechanical calculations
Abstract: We study the general problem of mixing for ab-initio quantum-mechanical problems. Guided by general mathematical principles and the underlying physics, we propose a multisecant form of Broyden's second method for solving the self-consistent field equations of Kohn-Sham density functional theory. The algorithm is robust, requires relatively little fine-tuning and appears to outperform the current state of the art, converging for cases that defeat many other methods. We compare our technique to the conventional methods for problems ranging from simple to nearly pathological.
José Mario Martínez (State University of Campinas (UNICAMP)) Modern optimization tools and electronic structure calculations
Abstract: Optimization concepts will be reviewed with an eye on their proved or potential application in Electronic Structure Calculations and other Chemical Physics problems. We will discuss the role of trust-region schemes, line searches, linearly and nonlinearly constrained optimization, Inexact Restoration and SQP methods and the type of convergence theories that may be useful in order to explain the practical behavior of the methods. Emphasis will be given on general principles instead of algorithmic details.
Spiridoula Matsika (Temple University) Conical intersections in quantum chemistry
Abstract: In the quantum mechanical treatment of molecules we use the Born-Oppenheimer (adiabatic) approximation, in which the motion of nuclei and electrons is separated. In this approximation the coupling between different electronic states is neglected and nuclei move on a single electronic potential energy surface. Nevertheless, non-adiabatic processes where the coupling between different electronic states becomes large and important. These processes are facilitated by the close proximity of potential energy surfaces, and especially by the extreme case where the potential energy surfaces become degenerate forming conical intersections. Modeling non-adiabatic processes requires accurate calculation of electronic structure states and their coupling. Methods for calculating excited states, the non-adiabatic couplings and conical intersections will be discussed.
Juan C. Meza (Lawrence Berkeley National Laboratory) Algorithms and computational aspects of DFT calculations Part I
Abstract: No Abstract
Juan C. Meza (Lawrence Berkeley National Laboratory) Algorithms and computational aspects of DFT calculations part II
Abstract: No Abstract
Paula Mori-Sánchez (Duke University) The discontinuous nature of the exchange-correlation functional--critical for strongly correlated systems
Abstract: Standard approximations for the exchange-correlation functional have been found to give big errors for the linearity condition of fractional charges, leading to delocalization error, and the constancy condition of fractional spins, leading to static correlation error. These two conditions are now unified for states with both fractional charge and fractional spin: the exact energy functional is a plane, linear along the fractional charge coordinate and constant along the fractional spin coordinate with a line of discontinuity at the integer. This sheds light on the nature of the derivative discontinuity and illustrates the need for a discontinuous functional of the orbitals or density. This is key for the application of DFT to strongly correlated systems.
Alexander V. Nemukhin (Moscow State University) Introduction to quantum mechanics
Abstract: My task is to discuss the basic principles of Quantum Mechanics which are crucial for the electronic structure theory. The following topics will be covered: the correspondence principle which connects Classical Mechanics and Quantum Mechanics; the uncertainty principle and related questions; the superposition principle. We shall discuss the Hilbert space of wavefunctions, and the operators associated with the observables. We shall illustrate the theory by considering the properties of angular momentum (orbital and spin). The theory of hydrogen atom will constitute the important part of the lecture.
Alexander V. Nemukhin (Moscow State University) Calculations of free energy profiles with the quantum mechanical- molecular mechanical (QM/MM) potential energy functions using DFT approximations in the QM subsystem
Abstract: The quantum mechanical - molecular mechanical (QM/MM) potential energy functions are used in calculations of the potential of mean force (PMF) following the conventional molecular dynamics (MD) based procedure. Constant temperature MD simulations, in particular, allowing for rigid-body MD algorithms, are performed for the canonical (NVT) ensemble in conjunction with the Nose-Poincare thermostat. The umbrella sampling technique and the weighted histogram analysis method are applied for PMF calculations. Two versions of the QM/MM method, namely, the mechanically embedded cluster technique and the flexible effective fragment approach are considered for potential energy estimates. The QM subsystem can be described by various electronic structure approximations including the DFT and multiconfigurational CASSCF methods. Conventional force field parameters can be employed in the MM subsystem. The computer program utilizes the PC GAMESS (A. Granovsky) and TINKER (J. Ponder) molecular modeling packages. The first application considered the mechanisms of proton conduction in the gramicidin A ion channel. The chain of nine water molecules inside the channel constituted the QM part described by the B3LYP/6-31G* approximation. The peptide walls of the gramicidin channel and two clusters of 20 water molecules placed at both ends of the channel constituted the MM subsystem described by the AMBER force field parameters. For the energy consuming stage of the water file reorientation inside the channel we calculated the activation free energy barrier of 7.7 kcal/mol at 300K as compared to 6.5 kcal/mol in experimental studies.
Gianluca Panati (Università di Roma "La Sapienza") Construction of exponentially localized Wannier functions
Abstract: The exponential localization of Wannier functions in two or three dimensions is proven for all insulators that display time-reversal symmetry, settling a long-standing conjecture. The proof make use of geometric techniques, which also imply that Chern insulators cannot display exponentially localized Wannier functions. Finally, a new algorithm to explicitly construct the exponentially localized Wannier functions is exhibited.
John E. Pask (Lawrence Livermore National Laboratory) Partition-of-unity finite-element approach for large, accurate ab initio electronic structure calculations
Abstract: Principle Collaborator: Natarajan Sukumar (University of California, Davis) Over the past few decades, the planewave (PW) pseudopotential method has established itself as the dominant method for large, accurate, density-functional calculations in condensed matter. However, due to its global Fourier basis, the PW method suffers from substantial inefficiencies in parallelization and applications involving highly localized states, such as those involving 1st-row or transition-metal atoms, or other atoms at extreme conditions. Modern real-space approaches, such as finite-difference (FD) and finite-element (FE) methods, can address these deficiencies without sacrificing rigorous, systematic improvability but have until now required much larger bases to attain the required accuracy. Here, we present a new real-space FE based method which employs modern partition-of-unity FE techniques to substantially reduce the number of basis functions required, by building known atomic physics into the Hilbert space basis, without sacrificing locality or systematic improvability. We discuss pseudopotential as well as all-electron applications. Initial results show order-of-magnitude improvements relative to current state-of-the-art PW and adaptive-mesh FE methods for systems involving localized states such as d- and f-electron metals and/or other atoms at extreme conditions. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
George Pau (Lawrence Berkeley National Laboratory) Reduced basis method for nanodevices simulation
Abstract: Simulation of ballistic transport in nanodevices are usually computationally intensive. To improve the efficiency of this simulation, the subband decomposition method approximates the solution $psi(x_1,x_2)$ by $sum_{i=1}^{n_e} varphi_i(x_1) xi_i(x_2;x_1)$, where $xi_i(x_2;x_1)$, $1 leq i leq n_e$ are solutions to an eigenvalue problem in the $x_2$-direction and parameterized by $x_1$; $varphi_i(x_1)$ are solutions to a Schr"{o}dinger equation with open boundary conditions; and $(x_1,x_2)$ denotes a point in the simulation domain $Omega$. However, determination of $xi_i(cdot;x_1)$ based on, say, finite element method, at all grid points in the $x_1$ direction can still be expensive. Here we propose approximating $xi_i(cdot;x_1)$ using the reduced basis method. By exploiting {em a posteriori} error estimators and greedy sampling algorithm, we can construct very efficient reduced basis approximation space for $xi_i(cdot;x_1)$. The computational cost only grows marginally when mesh spacing in the $x_2$-direction decreases, compared to exponential increase for a finite element approximation.
John P. Perdew (Tulane University) Physics of density functional theory (parts I and II)
Abstract: Electronic structure theory predicts what atoms, molecules and solids can exist, and with what properties. The density functional theory (DFT) of Hohenberg, Kohn and Sham 1964-65 is now the most widely used method of electronic structure calculation in both condensed matter physics and quantum chemistry. Walter Kohn and John Pople shared the 1998 Nobel Prize in Chemistry for this theory and for its computational implementation. This tutorial will begin by explaining why the computational demands are far smaller in DFT than in many-electron wavefunction theory, especially for large molecules and for solids. Two fundamental theorems of DFT will be presented and proven by the transparent constrained-search approach of Levy: (1) The ground-state electron density n of a system of N electrons in the presence of an external scalar multiplicative potential v determines v and hence all properties of the system. (2) There exists a universal density functional Q[n] such that minimization of Q[n] + for given N and v yields the ground-state density n and energy E. For accurate approximation of Q[n], one needs to introduce single-electron Kohn-Sham orbitals that yield the non-interacting kinetic energy part of Q[n] exactly, reducing the ground-state problem to a problem of noninteracting electrons moving in a selfconsistent density-dependent effective potential. Then the only part of Q[n] that must be approximated is the many-body exchange-correlation energy E_xc[n], which will be defined precisely. From the definition, many exact properties of E_xc[n] can be derived and employed as constraints to construct nonempirical or empirical approximations to E_xc[n]. Some important constraints will be reviewed. A ladder of approximations, from the simplest local density approximation to the most elaborate nonlocal approximations, will be reviewed, the surprising success of even the simplest one will be explained, and error estimates for each level will be presented. It will become apparent that local or semilocal approximations can suffice for most properties of most systems at or near the equilibrium nuclear positions, but that full nonlocality is needed to describe situations in which electrons are shared between separated subsystems, with noninteger average electron number in each subsystem. The exact density functional theory of such systems, as presented by Perdew, Parr, Levy and Balduz 1982, will be presented. The time-dependent density functional theory, which can describe time-dependent and excited states, will be briefly reviewed. Some outstanding physical and mathematical problems of DFT will be summarized.
John P. Perdew (Tulane University) Climbing Jacob's ladder of density functional approximations
Abstract: The exchange-correlation energy of Kohn-Sham density functional theory can be written as the integral over all space of an exchange-correlation energy density, which is a function of various density-dependent ingredients. Adding ingredients can produce approximations that satisfy more exact constraints, or fit data better. In our vision, the ladder has five rungs: (1) the local spin density approximation (LSDA), which uses only the local electron spin densities as ingredients, (2) the generalized gradient approximation (GGA), which adds the density gradients, (3) the meta-GGA, which adds the orbital kinetic energy densities, (4) the hyper-GGA, which adds the fully-nonlocal exact exchange energy densities, and (5) the generalized random phase approximation, which adds the unoccupied Kohn-Sham orbitals. All rungs but the fourth have been constructed without empiricism. Some recent developments will be sketched: (a) The bifurcation of the second rung into standard GGA's and GGA's for solids. (b) Possible refinement of the meta-GGA by recovering the gradient expansion for exchange over a wide range of density gradients, as in the PBEsol GGA for solids. Since meta-GGA is not much more expensive than GGA, and is potentially much more accurate for systems near equilibrium, an improved meta-GGA could replace LSDA or GGA in applications. (c) A hyper-GGA that interpolates between meta-GGA exchange (in normal regions where the errors of meta-GGA exchange and correlation tend to cancel) and exact exchange (in abnormal regions where no such cancellation is possible). Extensive abnormal regions can occur in open subsystems connected by stretched bonds.
Marielba Rojas (Technical University of Denmark) Surrogate modeling for geometry optimization in material design
Abstract: The first step in electronic-structure calculations is geometry optimization: finding an atomic configuration that minimizes the energy. A popular and successful model for the energy is the total-energy functional from density-functional theory. However, the evaluation of this functional at a given geometry is computationally expensive. Therefore, standard minimization techniques may be costly in practice. We propose a new approach for geometry optimization based on surrogate modeling. We describe our approach and present preliminary results.
Espen Sagvolden (University of California, Irvine) Describing Forster energy transfer in TD-DFT
Abstract: Joint work with Filipp Furche. We study the ability of TD-DFT to correctly predict the splitting of closely spaced singlet excited states in a system of two spatially separated chromophores. We find that functionals without at least a certain fraction of Hartree-Fock exchange kernel fare very poorly at this task because of a known problem these functionals have with the underestimation of charge-transfer excitation energies.
Fadil Santosa (University of Minnesota) Welcome to the IMA
Abstract: No Abstract
Gustavo E. Scuseria (Rice University) The role of nonlocal exchange in density functionals
Abstract: This presentation will address our current efforts to develop more accurate exchange-correlation forms for density functional theory. There are two leading themes in our current work: range separation and local weights. On the first theme, I will present a three-range hybrid functional and discuss the rationale for the success of screened functionals like HSE and LC-wPBE. On the second theme, the emphasis will be on new metrics for local hybridization and local range separation. Much of the focus will be on the seemingly dissimilar needs between solids and molecules, and on the computational challenge of including nonlocal (Hartree-Fock type) exchange efficiently in condensed systems.
Valentino Anthony Simpao (Mathematical Consultant Services) Novel exact solution methodologies in wavefunction analysis
Abstract: A viable methodology for the exact analytical solution of the multiparticle Schrodinger and Dirac equations has long been considered a holy grail of theoretical chemistry. Since a benchmark work by Torres-Vega and Frederick in the 1990's[1], the Quantum Phase Space Representation (QPSR) has been explored as an alternate method for solving various physical systems, including the harmonic oscillator[2], Morse oscillator[3], one-dimensional hydrogen atom[4], and classical Liouville dynamics under the Wigner function[5]. QPSR approaches are particularly challenging because of the complexity of phase space wave functions and the fact that the number of coordinates doubles in the phase space representation. These challenges have heretofore prevented the exact solution of the multiparticle equation in phase space. Recently, Simpao* has developed an exact analytical symbolic solution scheme for broad classes of differential equations utilizing the Heaviside Operational Ansatz (HOA). It is proposed to apply this novel methodology to QPSR problems to obtain exact solutions for real chemical systems and their dynamics. In his preliminary work, Simpao* has already applied this method to a number of simple systems, including the harmonic oscillator, with solutions in agreement to those obtained by Li [refs.2,3,4,5]. He has also demonstrated the exact solution to the radial Schrodinger Equation for an N-particle system with pairwise Coulomb interaction**. In addition to the Schrodinger Equation, the HOA method is capable of treating the Dirac equation*** as well as differential systems governing both relativistic and non-relativistic particle dynamics. Applying these methods would allow us to pursue further exploration of this methodology, starting with the exact solution of multielectron atoms and moving toward complex molecules and reaction dynamics. It is believed that the coupling of HOA with QPSR represents not only a fundamental breakthrough in theoretical physical chemistry, but it is promising as a basis for exact solution algorithms that would have tremendous impact on the capabilities of computational chemistry. As the theoretical foundation for spectroscopy is the Schrodinger equation, the significance of this discovery to the enhanced analysis of spectroscopic data is obvious. For example, the analysis of the Compton line in momentum spectroscopy necessitates the consideration of the momentum wavefunction for the molecular system under study. The novel methods *,**,*** allow the exact determination of the momentum[and configuration] space wavefunction from the QPSR wavefunction by way of a Fourier Transform. For example,the primariy focus of the PREPRINT ** is the pairwise 1/rij interaction in context of the radial equation in the nonrelativistic Schrodinger case. This application of the exact solution ansatz developed above corresponds to the problem of n-particles with pairwise Coulomb interaction;scaling the parameters and variables of the problem yields the exact solution of the QPSR Schrodinger equation for the first-principles general polyatomic molecular Hamiltonian. Upon a straightforward slight adaptation of this non-relativistic Schrodinger result, the QPSR Dirac equation addressed in *** immediately yields the relativistic counterpart for the first -principles general polyatomic molecular Hamiltonian solution. 1. Torres-Vega, G. and J.H. Frederick, A quantum-mechanical representation in phase space. Journal of Chemical Physics, 1993. 98(4): p. 3103-20. 2. Li, Q.S. and J. Lu, Rigorous solutions of diatomic molecule oscillator with empirical potential function in phase space. Journal of Chemical Physics, 2000. 113(11): p. 4565-4571. 3. Hu, X.-G. and Q.S. Li, Morse oscillator in a quantum phase-space representation: rigorous solutions. Journal of Physics A: Mathematical and General, 1999. 32(1): p. 139-146. 4. Li, Q.S. and J. Lu, One-dimensional hydrogen atom in quantum phase-space representation: rigorous solutions. Chemical Physics Letters, 2001. 336(1,2): p. 118-122. 5. Li, Q.S., G.M. Wei, and L.Q. Lu, Relationship between the Wigner function and the probability density function in quantum phase space representation. Physical Review A: Atomic, Molecular, and Optical Physics, 2004. 70(2): p. 022105/1-022105/5. * Electronic Journal of Theoretical Physics,1 (2004), 10-16
** PREPRINT Toward Chemical Applications of Heaviside Operational Ansatz: Exact Solution of Radial Schrodinger Equation for Nonrelativistic N-particle System with Pairwise 1/rij Radial Potential in Quantum Phase Space[now published MAY 2008 Journal of Mathematical Chemistry]
*** Electronic Journal of Theoretical Physics, 3, No. 10 (2006) 239-247 http://www.springerlink.com/content/225x523327771420/?p=a04f3c2e1352400b87bde6ac7331e4b2π=9
Lyudmila V. Slipchenko (Iowa State University) Wave function methods in chemistry
Abstract: After separating the electronic end nuclear coordinates through the Born-Oppenheimer approximation, one may attempt to solve the electronic Schrodinger equation by a hierarchy of wave function techniques. The lowest level in this hierarchy and the core method of the wave function quantum chemistry is the Hartree-Fock (HF) model, in which each electron moves in a mean field created by all other electrons. In order to get a chemical accuracy, one needs to correlate the motion of the electrons. This may be achieved by either the perturbation theory or by the configuration interaction procedure, employed on the top of the HF wave function. Basic ideas and approximations used in these wave function methods, as well as numerical approaches, challenges, and limitations will be discussed.
Lyudmila V. Slipchenko (Iowa State University) Water-benzene interactions: An effective fragment potential study
Abstract: Structures and binding in small water-benzene complexes (1-8 water molecules and 1-2 benzene molecules) are studied using the general effective fragment potential (EFP) method. The lowest energy conformers of the clusters were found using a Monte-Carlo technique. The EFP method accurately predicts structures and binding energies in the water-benzene complexes. Benzene is polarizable and consequently participates in hydrogen bond networking of water. Since the water-benzene interactions are only slightly weaker than water-water interactions, structures with different numbers of water-water, benzene-water, and benzene-benzene bonds often have very similar binding energies. This is a challenge for computational methods.
Jianmin Tao (Los Alamos National Laboratory) van der Waals-corrected density functional theory
Abstract: Conventional density functional approximations for the exchange-correlation energy fail to describe an important class of systems formed by the van der Waals (vdW) interaction, because they are unable to account for the long-range part of the vdW interaction, while they may describe the short-range part well. Here we first propose a density functional to simulate the coefficient C_6 of the leading term of the long-range part. Then we construct a nonempirical vdW-corrected meta-GGA functional by properly building the long-range part into a sophiscated meta-generalized gradient approximation (meta-GGA). Numerical tests on diverse atom pairs show that the proposed C_6 model is remarkably accurate. Applications of the vdW-corrected meta-GGA functional to rare-gas dimers show that the binding energy curves and bond lengths obtained with the vdW-corrected meta-GGA are well improved over those with the original meta-GGA, and agree fairly well with experiments.
David J. Tozer (University of Durham) Adiabatic connection forms in DFT: H2 and the He isoelectronic series
Abstract: Full configuration interaction (FCI) data are used to quantify the accuracy of approximate adiabatic connection (AC) forms in describing two challenging problems in density functional theory—the singlet ground state potential energy curve of H2 in a restricted formalism and the energies of the helium isoelectronic series, H− to Ne8+. For H2, an exponential-based form yields a potential energy curve that is virtually indistinguishable from the FCI curve, eliminating the unphysical barrier to dissociation observed previously with a [1,1]-Padé-based form and with the random phase approximation. For the helium isoelectronic series, the Padé-based form gives the best overall description, followed by the exponential form, with errors that are orders of magnitude smaller than those from a standard hybrid functional. Particular attention is paid to the limiting behavior of the AC forms with increasing bond distance in H2 and increasing atomic number in the isoelectronic series; several forms describe both limits correctly. The study illustrates the very high quality results that can be obtained using exchange-correlation functionals based on simple AC forms, when near-exact data are used to determine the parameters in the forms.
Donald G. Truhlar (University of Minnesota) New density functionals with broad applicability for thermochemistry, thermochemical kinetics, noncovalent interactions, transition metals, and spectroscopy
Abstract: This lecture reports on work carried out in collaboration with Yan Zhao. We have developed a suite of density functionals. All four functionals are accurate for noncovalent interactions and medium-range correlation energy. The functional with broadest capability, M06, is uniquely well suited for good performance on both transition-metal and main group-chemistry; it also gives good results for barrier heights. Another functional, M06-L has no Hartree-Fock exchange, which allows for very fast calculations on large systems, and it is especially good for transition-metal chemistry and NMR chemical shieldings. M08-2X and an earlier version, M06-2X, have the very best performance for main-group thermochemistry, barrier heights, and noncovalent interactions. M06-HF has no one-electron self-interaction error and is the best functional for charge transfer spectroscopy. A general characteristic of the whole suite is the optimized inclusion of kinetic energy density and higher separate accuracy of medium-range exchange and correlation contributions with less cancellation of errors than previous functionals [1-4]; for example, the functionals are compatible with a range of Hartree-Fock exchange and, although one or another of them may be more highly recommended for one or another property or application, all four are better on average than the very popular B3LYP functional. A few sample applications, including catalytic systems [5,6] and nanomaterials [7], will also be discussed. Recent work on lattice constants, band gaps, and an improved version of M06-2X will be summarized if time permits. [1] "Design of Density Functionals by Combining the Method of Constraint Satisfaction with Parametrization for Thermochemistry, Thermochemical Kinetics, and Noncovalent Interactions," Zhao, Y. ; Schultz, N. E.; Truhlar, D. G.; J. Chem. Theory Comput. 2006, 2, 364-382.
[2] "A New Local Density Functional for Main Group Thermochemistry, Transition Metal Bonding, Thermochemical Kinetics, and Noncovalent Interactions," Zhao, Y.; Truhlar, D. G. J. Chem. Phys. 2006, 125, 194101/1-18.
[3] “The M06 Suite of Density Functionals for Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, and Transition Elements: Two New Functionals and Systematic Testing of Four M06-Class Functionals and 12 Other Functionals,” Zhao, Y.; Truhlar, D. G. Theor. Chem. Acc. 2008, 120, 215-241.
[4] "Density Functionals with Broad Applicability in Chemistry," Zhao, Y.; Truhlar, D. G. Acc. Chem. Res. 2008 41, 157-167.
[5] “Attractive Noncovalent Interactions in Grubbs Second-Generation Ru Catalysts for Olefin Metathesis," Zhao, Y.; Truhlar, D. G. Org. Lett. 2007, 9, 1967-1970.
[6] "Benchmark Data for Interactions in Zeolite Model Complexes and Their Use for Assessment and Validation of Electronic Structure Methods," Zhao, Y.; Truhlar, D. G. J. Phys. Chem. C 2008, 112, 6860-6868.
[7] "Size-Selective Supramolecular Chemistry in a Hydrocarbon Nanoring," Zhao, Y.; Truhlar, D. G. J. Am. Chem. Soc.2007, 129, 8440-8442.
Steven M. Valone (Los Alamos National Laboratory) Estimating valence-state mixing from constrained density functional theory calculations with fractional numbers of electrons
Abstract: Constrained density functional theory methods (C-DFT) have been developed by several groups [1,2] to construct localized charge or spin states. At the same time, others have suggested ways of constructing variable-charge potential energy surfaces from certain valence-bond (VB) states [3,4]. In general, mainstream electronic structure codes do not generate the desired valence-bond states, and does not mix them in the manner needed to construct variable-charge potentials. C-DFT does provide estimates of the desired, individual valence-bond states and energies, but does not directly give the state mixing. While there are methods to overcome this limitation [5], here we explore an alternative. That alternative, notionally suggested in Ref. 3, is to deduce state-mixing from C-DFT with fractional charges. One assumes that the normal integer-charge VB states remain the same when describing a state composed of atoms with fractional charges. For instance, we use C-DFT to calculate the energies for the three charge distributions for a geometrically symmetric water molecule. Two of the constrained VB states are integer-charge distributions, one with all atoms being neutral and a second with the oxygen integer being anionic and one of the hydrogens cationic. The third VB state places half of a negative and positive charge on the oxygen and one hydrogen, respectively. We present our initial efforts to calculate the variational energy surface for a water molecule at several bond-lengths along the symmetric stretch vibrational mode. To capture the fractional charge behavior of the energies, the B3LYP functional is employed [5-7]. [1] Q Wu and T Van Voorhis, Phys. Rev. A 72, 024502 (2005).
[2] J Behler, B Delley, K Reuter, and M Scheffler, Phys. Rev. B 75, 115409 (2007).
[3] SM Valone and SR Atlas, J. Chem. Phys. 120, 7262 (2004).
[4] SM Valone, J Li, and S Jindal, IJQC 108, 1452 (2008).
[5] Q Wu and T Van Voorhis, J. Chem. Phys. 125, 164105 (2006).
[6] AD Becke, J. Chem. Phys. 98, 5648 (1993).
[7] C Lee, W Yang, and RG Parr, Phys. Rev. B 37, 785 (1988).
Oleg A. Vydrov (Massachusetts Institute of Technology) Improving the accuracy of the nonlocal van der Waals density functional with minimal empiricism
Abstract: Nearly all common density functional approximations fail to adequately describe dispersion interactions responsible for binding in van der Waals complexes. One of the most promising new methods is the nonlocal van der Waals density functional (vdW-DF) of Ref. [1], which was derived from first principles, describes dispersion interactions in a seamless fashion, and yields the correct asymptotics. Recently we reported a self-consistent implementation of vdW-DF with Gaussian basis functions [2]. Our code includes analytic gradients of the energy with respect to nuclear displacements, enabling efficient geometry optimizations. vdW-DF tends to overbind molecular complexes, especially if used in combination with Hartree-Fock exchange. We propose a slightly simplified construction of the nonlocal vdW-DF correlation functional, for which we also derive a semilocal gradient correction. This correction reduces the overbinding tendency and improves the accuracy of vdW-DF. Adjusting an empirical parameter in the semilocal part, vdW-DF can be made compatible with different exchange approximations. [1] M. Dion, H. Rydberg, E. Schroder, D.C. Langreth, and B.I. Lundqvist, Phys.Rev.Lett. 92, 246401 (2004). [2] O.A. Vydrov, Q. Wu, and T. Van Voorhis, J.Chem.Phys. 129, 014106 (2008).
Zhenli Xu (University of North Carolina - Charlotte) An FFT-based algorithm for the generalized Born theory of biomolecule solvation
Abstract: A new method for calculating effective atomic radii within the generalized Born (GB) model of implicit solvation is proposed, for use in computer simulations of bio-molecules. First, a new formulation for the GB radii is developed, in which smooth kernels are used to eliminate the divergence in volume integrals intrinsic in the model. Next, the Fast Fourier Transform (FFT) algorithm is applied to integrate smoothed functions, taking advantage of the rapid spectral decay provided by the smoothing. The total cost of the proposed algorithm scales as O(N^3logN+M) where M is the number of atoms comprised in a molecule, and N is the number of FFT grid points in one dimension, which depends only on the geometry of the molecule and the spectral decay of the smooth kernel but not on M. To validate our algorithm, numerical tests are performed for three solute models: one spherical object for which exact solutions exist and two protein molecules of differing size. The tests show that our algorithm is able to reach the accuracy of other existing GB implementations, while offering much lower computational cost.
Chao Yang (Lawrence Berkeley National Laboratory) A direct constrained minimization algorithm for solving the Kohn-Sham equations
Abstract: I will present a direct constrained minimization (DCM) algorithm for solving the Kohn-Sham equations. The key ingredients of this algorithm involve projecting the Kohn-Sham total energy functional into a sequences of subspaces of small dimensions and seeking the minimizer of total energy functional within each subspace. The minimizer of a subspace energy functional not only provides a search direction along which the KS total energy functional decreases but also gives an optimal ``step-length" to move along this search direction. I will provide some numerical examples to demonstrate the efficiency and accuracy of this approach and compare it with the widely used method of self-consistent field (SCF) iteration. I will also discuss a few other numerical issues in algorithms designed to solve the Kohn-Sham equations.
Visitors in Residence
Wesley D. Allen University of Georgia 9/28/2008 - 10/1/2008
Donald G. Aronson University of Minnesota 9/1/2002 - 8/31/2009
Amartya Sankar Banerjee University of Minnesota 9/26/2008 - 10/3/2008
Rodney J. Bartlett University of Florida 9/28/2008 - 10/1/2008
Axel D. Becke Dalhousie University 9/28/2008 - 10/3/2008
Bastiaan J. Braams Emory University 9/28/2008 - 11/8/2008
Peter Brune University of Chicago 9/8/2008 - 6/30/2009
Felipe Alfonso Bulat Duke University 9/28/2008 - 10/4/2008
Kieron J. Burke University of California, Irvine 9/29/2008 - 10/2/2008
Sun-Sig Byun University of Iowa 9/26/2008 - 10/4/2008
Maria-Carme T. Calderer University of Minnesota 9/1/2008 - 6/30/2009
Hannah Callender University of Minnesota 9/1/2007 - 8/31/2009
Eric Cances CERMICS 9/1/2008 - 12/23/2008
Larry Carson 3M 9/26/2008 - 9/27/2008
Isabelle Catto Université de Paris IX (Paris-Dauphine) 9/26/2008 - 10/3/2008
Alessandro Cembran University of Minnesota 9/26/2008 - 10/3/2008
Arindam Chakraborty Pennsylvania State University 9/28/2008 - 10/3/2008
Xianjin Chen University of Minnesota 9/1/2008 - 8/31/2010
Daniel M. Chipman University of Notre Dame 9/14/2008 - 12/13/2008
Hi Jun Choe University of Iowa 9/28/2008 - 10/4/2008
Matteo Cococcioni University of Minnesota 9/29/2008 - 10/3/2008
Aron J. Cohen Duke University 9/28/2008 - 10/3/2008
Gemma Comellas University of Illinois at Urbana-Champaign 9/25/2008 - 9/28/2008
Ludovica Cecilia Cotta-Ramusino University of Minnesota 10/1/2007 - 8/30/2009
Nathan R. M. Crawford University of California, Irvine 9/27/2008 - 10/4/2008
James W. Davenport Brookhaven National Laboratory 9/28/2008 - 10/3/2008
Ajitha Devarajan Iowa State University 9/28/2008 - 10/3/2008
Kadir Diri University of Southern California 9/28/2008 - 10/3/2008
Olivier Dubois University of Minnesota 9/3/2007 - 8/31/2009
Weinan E Princeton University 9/28/2008 - 10/3/2008
Maria Esteban Université de Paris IX (Paris-Dauphine) 9/27/2008 - 11/15/2008
Kai Fan North Carolina State University 9/25/2008 - 10/4/2008
Daniel Flath Macalester College 8/27/2008 - 12/20/2008
Andrea Floris Freie Universität Berlin 9/28/2008 - 10/3/2008
Christopher Fraser University of Chicago 8/27/2008 - 6/30/2009
Mituhiro Fukuda Tokyo Institute of Technology 9/25/2008 - 10/4/2008
Alexander Gaenko Iowa State University 9/28/2008 - 10/3/2008
Weiguo Gao Fudan University 9/27/2008 - 12/13/2008
Carlos J. Garcia-Cervera University of California, Santa Barbara 9/2/2008 - 12/12/2008
Peter M.W. Gill Australian National University 9/28/2008 - 10/3/2008
Benjamin David Goddard University of Warwick 9/29/2008 - 10/10/2008
Jay Gopalakrishnan University of Florida 9/1/2008 - 2/28/2009
Andreas Görling Friedrich-Alexander-Universität Erlangen-Nürnberg 9/28/2008 - 10/3/2008
Bella Grigorenko M.V. Lomonosov Moscow State University 9/28/2008 - 10/3/2008
Eberhard K. U. Gross Freie Universität Berlin 9/28/2008 - 10/3/2008
Francesca Guerra University of Minnesota 9/27/2008 - 9/27/2008
François Gygi University of California, Davis 9/30/2008 - 10/3/2008
George A. Hagedorn Virginia Polytechnic Institute and State University 9/28/2008 - 10/3/2008
Timothy F. Havel Massachusetts Institute of Technology 9/28/2008 - 10/3/2008
Martin Head-Gordon University of California, Berkeley 9/28/2008 - 10/3/2008
John Heapy University of Minnesota 9/26/2008 - 9/27/2008
Mark S. Herman University of Minnesota 9/1/2008 - 8/31/2010
Masahiro Higashi University of Minnesota 9/26/2008 - 10/3/2008
Peter Hinow University of Minnesota 9/1/2007 - 8/31/2009
Mark R. Hoffmann University of North Dakota 9/28/2008 - 10/3/2008
Ming Huang University of Minnesota 9/26/2008 - 9/27/2008
Dirk Hundertmark University of Illinois at Urbana-Champaign 9/28/2008 - 10/10/2008
Yunkyong Hyon University of Minnesota 9/1/2008 - 8/31/2010
Olexandr Isayev Jackson State University 9/28/2008 - 10/4/2008
Mark Iwen University of Minnesota 9/1/2008 - 8/31/2010
Alexander Izzo Bowling Green State University 9/1/2008 - 6/30/2009
Srividhya Jeyaraman University of Minnesota 9/1/2008 - 8/31/2010
Lijian Jiang University of Minnesota 9/1/2008 - 8/31/2010
Erin R. Johnson Duke University 9/28/2008 - 10/3/2008
Markus Keel University of Minnesota 7/21/2008 - 6/30/2009
Yongho Kim University of Minnesota 9/26/2008 - 10/3/2008
Rollin A. King Bethel University 9/29/2008 - 10/3/2008
Mario Koppen TU München 9/28/2008 - 10/3/2008
Karol Kowalski Pacific Northwest National Laboratory 9/28/2008 - 10/3/2008
Aliaksandr Krukau Rice University 9/28/2008 - 10/3/2008
Anna Krylov University of Southern California 9/25/2008 - 12/25/2008
Harun Kurkcu University of Minnesota 9/25/2008 - 9/28/2008
David Langreth Rutgers University 9/29/2008 - 10/2/2008
Claude Le Bris CERMICS 9/11/2008 - 5/30/2009
Chiun-Chang Lee National Taiwan University 8/26/2008 - 7/31/2009
Hannah Ruth Leverentz University of Minnesota 9/26/2008 - 9/27/2008
Melvyn P. Levy Duke University 9/28/2008 - 10/8/2008
Mathieu Lewin Université de Cergy-Pontoise 9/26/2008 - 10/25/2008
Yongfeng Li University of Minnesota 9/1/2008 - 8/31/2010
Florence J. Lin University of Southern California 9/29/2008 - 10/2/2008
Tai-Chia Lin National Taiwan University 8/23/2008 - 7/31/2009
Roland Lindh Lund University 9/28/2008 - 10/4/2008
Chun Liu University of Minnesota 9/1/2008 - 8/31/2010
Carlos Silva Lopez University of Minnesota 9/26/2008 - 10/3/2008
Gang Lu California State University 9/28/2008 - 10/4/2008
Jianfeng Lu Princeton University 9/25/2008 - 10/4/2008
Russell Luke University of Delaware 9/28/2008 - 10/3/2008
Mitchell Luskin University of Minnesota 9/1/2008 - 6/30/2009
Taylor Joseph Mach Bethel University 9/29/2008 - 10/3/2008
Laurence D. Marks Northwestern University 9/28/2008 - 10/3/2008
Vasileios Maroulas University of Minnesota 9/1/2008 - 8/31/2010
José Mario Martínez State University of Campinas (UNICAMP) 9/28/2008 - 10/3/2008
Spiridoula Matsika Temple University 9/28/2008 - 9/30/2008
Juan C. Meza Lawrence Berkeley National Laboratory 9/25/2008 - 10/4/2008
Steven L. Mielke University of Minnesota 9/26/2008 - 10/3/2008
Paula Mori-Sánchez Duke University 9/28/2008 - 10/3/2008
Junalyn Navarra-Madsen Texas Woman's University 9/25/2008 - 10/3/2008
Alexander V. Nemukhin Moscow State University 9/25/2008 - 10/3/2008
Olalla Nieto Faza University of Minnesota 9/26/2008 - 10/3/2008
Miao-Jung Yvonne Ou Oak Ridge National Laboratory 9/25/2008 - 10/3/2008
Adam Paetznick General Dynamics Advanced Information Systems 9/26/2008 - 9/27/2008
Gianluca Panati Università di Roma "La Sapienza" 9/24/2008 - 10/4/2008
John E. Pask Lawrence Livermore National Laboratory 9/30/2008 - 10/4/2008
George Pau Lawrence Berkeley National Laboratory 9/28/2008 - 10/3/2008
John P. Perdew Tulane University 9/26/2008 - 10/3/2008
Emil Prodan Yeshiva University 9/28/2008 - 10/10/2008
Marielba Rojas Technical University of Denmark 9/28/2008 - 10/4/2008
Adrienn Ruzsinszky Tulane University 9/26/2008 - 10/3/2008
Daniel Sadowsky University of Minnesota 9/26/2008 - 9/27/2008
Espen Sagvolden University of California, Irvine 9/28/2008 - 9/30/2008
Fadil Santosa University of Minnesota 7/1/2008 - 6/30/2010
Arnd Scheel University of Minnesota 9/1/2008 - 6/30/2009
Ridgway Scott University of Chicago 9/1/2008 - 6/30/2009
Gustavo E. Scuseria Rice University 9/29/2008 - 10/1/2008
Tsvetanka Sendova University of Minnesota 9/1/2008 - 8/31/2010
Tsvetanka Sendova University of Minnesota 9/1/2008 - 10/31/2008
Yuk Sham University of Minnesota 9/1/2008 - 6/30/2009
Jie Shen Purdue University 9/25/2008 - 9/28/2008
David C. Sherrill Georgia Institute of Technology 9/29/2008 - 10/1/2008
Tei Shi University of Minnesota 9/26/2008 - 9/27/2008
Heinz Siedentop Ludwig-Maximilians-Universität München 9/22/2008 - 12/18/2008
Ronald Siegel University of Minnesota 9/27/2008 - 9/27/2008
Lyudmila V. Slipchenko Iowa State University 9/25/2008 - 10/2/2008
Slava Sorkin University of Minnesota 9/26/2008 - 9/27/2008
Vijay Kumar Srivastava University of Minnesota 9/26/2008 - 9/27/2008
Andrew M. Stein University of Minnesota 9/1/2007 - 8/31/2009
Gabriel Stoltz École Nationale des Ponts-et-Chaussées (ENPC) 9/23/2008 - 10/2/2008
Jianwei Sun Tulane University 9/28/2008 - 10/4/2008
Jianmin Tao Los Alamos National Laboratory 9/28/2008 - 10/3/2008
David J. Tozer University of Durham 9/27/2008 - 10/4/2008
Donald G. Truhlar University of Minnesota 9/1/2008 - 6/30/2009
Erkan Tüzel University of Minnesota 9/1/2007 - 8/31/2009
George Vacek Hewlett Packard 9/28/2008 - 10/3/2008
Rosendo Valero University of Minnesota 9/26/2008 - 10/3/2008
Steven M. Valone Los Alamos National Laboratory 9/8/2008 - 11/30/2008
Oleg A. Vydrov Massachusetts Institute of Technology 9/28/2008 - 10/4/2008
Homer Walker Worcester Polytechnic Institute 9/28/2008 - 10/3/2008
Bo Wang University of Minnesota 9/26/2008 - 9/27/2008
Zhian Wang University of Minnesota 9/1/2007 - 8/31/2009
Henry A. Warchall National Science Foundation 9/29/2008 - 10/1/2008
Dexuan Xie University of Wisconsin 9/4/2008 - 12/15/2008
Wei Xiong University of Minnesota 9/1/2008 - 8/31/2010
Zhenli Xu University of North Carolina - Charlotte 9/25/2008 - 10/3/2008
Chao Yang Lawrence Berkeley National Laboratory 9/8/2008 - 11/8/2008
Ke Yang University of Minnesota 9/26/2008 - 10/3/2008
Weitao Yang Duke University 9/28/2008 - 10/3/2008
Meiyu Zhao University of Minnesota 9/26/2008 - 9/27/2008
Yan Zhao University of Minnesota 9/26/2008 - 9/27/2008
Weigang Zhong University of Minnesota 9/1/2008 - 8/31/2010
Legend: Postdoc or Industrial Postdoc Long-term Visitor

IMA Affiliates:
Arizona State University, Boeing, Carnegie Mellon University, Corning, ExxonMobil, Ford, General Motors, Georgia Institute of Technology, Honeywell, IBM, Indiana University, Iowa State University, Kent State University, Lawrence Livermore National Laboratory, Lockheed Martin, Los Alamos National Laboratory, Medtronic, Michigan State University, Michigan Technological University, Microsoft Research, Mississippi State University, Motorola, Northern Illinois University, Ohio State University, Pennsylvania State University, Purdue University, Rice University, Rutgers University, Sandia National Laboratories, Schlumberger-Doll, Schlumberger-Doll Research, Seoul National University, Siemens, Telcordia, Texas A & M University, University of Central Florida, University of Chicago, University of Cincinnati, University of Delaware, University of Houston, University of Illinois at Urbana-Champaign, University of Iowa, University of Kentucky, University of Maryland, University of Michigan, University of Minnesota, University of Notre Dame, University of Pittsburgh, University of Tennessee, University of Texas, University of Wisconsin, University of Wyoming, US Air Force Research Laboratory, Wayne State University, Worcester Polytechnic Institute