DOCSLIB.ORG

Relativistic Coupled Cluster Theory - in Molecular Properties and in Electronic Structure Avijit Shee

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Relativistic Coupled Cluster Theory - in Molecular Properties and in Electronic Structure Avijit Shee Relativistic coupled cluster theory - in molecular properties and in electronic structure Avijit Shee To cite this version: Avijit Shee. Relativistic coupled cluster theory - in molecular properties and in electronic structure. Mechanics of materials [physics.class-ph]. Université Paul Sabatier - Toulouse III, 2016. English. NNT : 2016TOU30053. tel-01515345 HAL Id: tel-01515345 https://tel.archives-ouvertes.fr/tel-01515345 Submitted on 27 Apr 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. 5)µ4& &OWVFEFMPCUFOUJPOEV %0$503"5%&-6/*7&34*5²%&506-064& %ÏMJWSÏQBS Université Toulouse 3 Paul Sabatier (UT3 Paul Sabatier) 1SÏTFOUÏFFUTPVUFOVFQBS Avijit Shee le 26th January, 2016 5JUSF Relativistic Coupled Cluster Theory – in Molecular Properties and in Electronic Structure ²DPMF EPDUPSBMF et discipline ou spécialité ED SDM : Physique de la matière - CO090 6OJUÏEFSFDIFSDIF Laboratoire de Chimie et Physique Quantiques (UMR5626) %JSFDUFVSUSJDF T EFʾÒTF Trond Saue (Directeur) Timo Fleig (Co-Directeur) Jury : Trygve Helgaker Professeur Rapporteur Jürgen Gauss Professeur Rapporteur Valerie Vallet Directeur de Recherche Examinateur Laurent Maron Professeur Rapporteur Timo Fleig Professeur Directeur Trond Saue Directeur de Recherche Directeur A Thesis submitted for the degree of Doctor of Philosophy Relativistic Coupled Cluster Theory { in Molecular Properties and in Electronic Structure Avijit Shee Universit´eToulouse III { Paul Sabatier Contents Acknowledgements iii 1. Introduction 1 2. Publication List 3 I. Electronic Structure 4 3. Brief Overview of Relativistic Electronic Structure Theory 5 3.1. Relativistic Molecular Hamiltonian . .5 3.1.1. Elimination of Spin . .8 3.1.2. 4-component to 2-component . 10 3.2. Relativistic Mean Field Theory . 11 3.3. Relativistic Correlation Methods . 14 3.4. Single Reference Methods: . 17 3.4.1. Relativistic CI: . 17 3.4.2. Relativistic MP2: . 18 3.4.3. Relativistic Coupled Cluster . 19 3.5. Multi-Configurational Methods: . 20 3.5.1. MCSCF . 21 3.5.2. CASPT2 and NEVPT2 . 21 3.5.3. DMRG . 21 3.6. Approximate Correlation methods . 22 4. Application of Relativistic Correlation Methods 24 4.1. Comparison of Computational Cost Between Relativistic and Non-Relativistic Methods: . 24 4.2. Improvements to the Computational Scheme: . 25 4.3. Papers . 27 4.3.1. Paper I : A theoretical benchmark study of the spectro- scopic constants of the very heavy rare gas dimers ..... 27 4.3.2. Paper II : 4-component relativistic calculations of L3 ion- ization and excitations for the isoelectronic species UO2+, + OUN and UN2 Phys.Chem.Chem.Phys. DOI:10.1039/C6CP00262E 37 i Contents II. Molecular properties 52 5. Molecular Properties with ab-initio Relativistic Methods 53 5.1. Molecule Under External field . 54 5.2. Effect of Spin-Orbit coupling on molecular properties . 56 5.2.1. Electronic g-tensor . 56 5.2.2. NMR shielding . 57 5.2.3. Parity Violation . 59 5.3. Coupled Relativistic and Correlation Effect on Molecular properties: . 60 5.4. Numerical vs Analytical approach . 61 6. Implementation of the 4c Analytical Coupled Cluster Gradient 64 6.1. Time Reversal Symmetry . 65 6.2. Double Group Symmetry . 65 6.3. Paper III: Analytic Gradient at the 4-component Relativistic Cou- pled Cluster Level with Inclusion of Spin-Orbit Coupling (manuscript) 67 7. Summary and Future Perspective 98 III. Appendices 100 A. Integrals in Kramer's Pair Basis 101 B. Sorting of Integrals in Double Group Symmetry-DPD Scheme 109 C. C4∗ Character Table 112 IV. Additional Paper 113 ii Acknowledgements First and foremost, I would like to thank my supervisor Trond Saue. I would like to mention his help to settle me down in this very much `french' country, will remember several nights of watching sports together, going for lunch among many other instances, in the non-scientific side. On the scientific side, I learnt from him what sort of theoretical rigour one should follow. Other than that his programming tips, even latex tips were very helpful. Next I like to thank Debashis Mukherjee, with whom I started working in electronic structure theory back in Kolkata, India. Countless hours of discussion with him taught me very basic to very sophisticated aspects of that domain, and that teaching has not finished yet. I like to thank Luuk Visscher to be a collaborator in the gradient project. Several Skype sessions with him was not only helpful in terms of technicalities, but also it gave me hope, confidence and enthusiasm to finish that project. I like to thank Sangita Sen. We started working on a MRCC project together, which was successful on the one hand, but on the other it has not been exploited to its full capacity so far. Hopefully, there will be time to make the full use of that theory. Apart from that, several hours of `inexperienced' scientific discussion with her helped me to gain a lot of experiences, taught me several things which are otherwise difficult to grasp. From the DIRAC family I would like to thank specially Stefan Knecht, for his collab- oration in one article and, Radovan Bast for technical advices and for his ideas about modern coding practice. Very friendly and lively atmosphere of our annual DIRAC meeting always makes me feel that science can also be a joyous experience. Fantastic people associated with it help to create that atmosphere. Thanks to all of them. I will like to thank all the past and present members of the LCPQ group, specially to Adel and Nathaniel for their patience to help me in french language related sufferings. Also, I like to thank the members of my previous group in IACS - Rahul Maitra, Debalina Sinha, Shubhrodeep Pathak, Avijit Sen, Pradipta Samanta, for giving me memories to cherish. I will like to mention the names of few other scientists, short term work or discussions with whom were very enlightening - Daniel Crawford, Ed Valeev, Marcel Nooijen, Toru Shiozaki, Lan Cheng, Matthias Hanauer among few others. Thanks to Ranajoy, Pratyay, Jishnu, Anjan, Vivek, Biplab, my friends back in India (though a few of them are living in abroad). Life always feels better around them. Last but not the least I want to mention my younger brother, elder sister and my parents for their silent support and help. There are no words to thank them. iii To my parents... 1. Introduction \You see, we're in a funny position: It's not that we're looking for the theory, we've got the theory { a good, good candidate { but we're in the step in the science that we need to compare the theory to experiment by seeing what the consequences are and checking it. We're stuck in seeing what the consequences are, and it's my aim, it's my desire to see if I can work out a way to work out what the consequences of this theory are (LAUGHS). It's a kind of a crazy position to be in, to have a theory that you can't work out the consequences of ... I can't stand it, I have to figure it out. Someday, maybe. Let George Do It". ....Richard P. Feynman in `The Pleasure of Finding Things Out' With the crowning success in explaining some enigmatic behaviour of heavy element chemistry [50], relativity made firm its foothold in electronic structure theory in the early 1980s. Nowadays it has widespread application, for instance, in the domain of lan- thanide and actinide chemistry - for the studies of single molecule magnets, luminescent complexes etc. Lanthanide and actinide compounds normally consist of several open- shells, which is considered as a strong correlation problem. The effect of relativity and correlation is certainly not additive [77], and one needs to develop a correlation method within the framework of relativity (meaning based on the Dirac equation). But, the over- whelming computational cost of a relativistic correlation method precludes the routine use of them, which has made its application domain somewhat limited. It is therefore necessary not only to develop new methodology and computational techniques, but also to study the existing methodologies for the challenging problems. This thesis includes studies of such kind along with implementation and use of new methods. In the first part of this thesis I will provide some background of relativistic electronic structure theory. I will mostly be focusing on the intricacies pertaining to the domains which are not really present in the non-relativistic version. Hamiltonians and different methodologies - starting from the mean field theory to the sophisticated most recent correlation theories will be touched upon. Thereby, one will be able to see the breadth and scope of this field. I will emphasize the theoretical details of the Coupled Cluster theory, since a large part of the discussions in this thesis will revolve around that method. In the next chapter, I will first discuss why relativistic theories are so much more expensive and what measures had been undertaken to deal with that problem. Nonethe- less, as already discussed, it is of paramount interest to study relativity and correlation together and we will get into the business of studying problems where both of them have major roles to play. We have studied the problem of heavy and superheavy rare gas dimers. This study has provided benchmark spectroscopic constants for these systems. Moreover, it has shown at least one example where the interplay between the Gaunt interaction and correlation can be very dramatic indeed.
Load more

Recommended publications
  • Correlation.Pdf
    INTRODUCTION TO THE ELECTRONIC CORRELATION PROBLEM PAUL E.S. WORMER Institute of Theoretical Chemistry, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands Contents 1 Introduction 2 2 Rayleigh-SchrÄodinger perturbation theory 4 3 M¿ller-Plesset perturbation theory 7 4 Diagrammatic perturbation theory 9 5 Unlinked clusters 14 6 Convergence of MP perturbation theory 17 7 Second quantization 18 8 Coupled cluster Ansatz 21 9 Coupled cluster equations 26 9.1 Exact CC equations . 26 9.2 The CCD equations . 30 9.3 CC theory versus MP theory . 32 9.4 CCSD(T) . 33 A Hartree-Fock, Slater-Condon, Brillouin 34 B Exponential structure of the wavefunction 37 C Bibliography 40 1 1 Introduction These are notes for a six hour lecture series on the electronic correlation problem, given by the author at a Dutch national winterschool in 1999. The main purpose of this course was to give some theoretical background on the M¿ller-Plesset and coupled cluster methods. Both computational methods are available in many quantum chemical \black box" programs. The audi- ence consisted of graduate students, mostly with an undergraduate chemistry education and doing research in theoretical chemistry. A basic knowledge of quantum mechanics and quantum chemistry is pre- supposed. In particular a knowledge of Slater determinants, Slater-Condon rules and Hartree-Fock theory is a prerequisite of understanding the following notes. In Appendix A this theory is reviewed briefly. Because of time limitations hardly any proofs are given, the theory is sketchily outlined. No attempt is made to integrate out the spin, the theory is formulated in terms of spin-orbitals only.
    [Show full text]
  • Effective Hamiltonians Derived from Equation-Of-Motion Coupled-Cluster
    Effective Hamiltonians derived from equation-of-motion coupled-cluster wave-functions: Theory and application to the Hubbard and Heisenberg Hamiltonians Pavel Pokhilkoa and Anna I. Krylova a Department of Chemistry, University of Southern California, Los Angeles, California 90089-0482 Effective Hamiltonians, which are commonly used for fitting experimental observ- ables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not triv- ial. In this contribution, we apply Bloch's formalism to equation-of-motion coupled- cluster (EOM-CC) wave functions to rigorously derive effective Hamiltonians in the Bloch's and des Cloizeaux's forms. We report the key equations and illustrate the theory by examples of systems with electronic states of covalent and ionic characters. We show that the Hubbard and Heisenberg Hamiltonians are extracted directly from the so-obtained effective Hamiltonians. By making quantitative connections between many-body states and simple models, the approach also facilitates the analysis of the correlated wave functions. Artifacts affecting the quality of electronic structure calculations such as spin contamination are also discussed. I. INTRODUCTION Coarse graining is commonly used in computational chemistry and physics. It is ex- ploited in a number of classic models serving as a foundation of modern solid-state physics: tight binding[1, 2], Drude{Sommerfeld's model[3{5], Hubbard's [6] and Heisenberg's[7{9] Hamiltonians. These models explain macroscopic properties of materials through effective interactions whose strengths are treated as model parameters. The values of these pa- rameters are determined either from more sophisticated theoretical models or by fitting to experimental observables.
    [Show full text]
  • Møller–Plesset Perturbation Theory: from Small Molecule Methods to Methods for Thousands of Atoms Dieter Cremer∗
    Advanced Review Møller–Plesset perturbation theory: from small molecule methods to methods for thousands of atoms Dieter Cremer∗ The development of Møller–Plesset perturbation theory (MPPT) has seen four dif- ferent periods in almost 80 years. In the first 40 years (period 1), MPPT was largely ignored because the focus of quantum chemists was on variational methods. Af- ter the development of many-body perturbation theory by theoretical physicists in the 1950s and 1960s, a second 20-year long period started, during which MPn methods up to order n = 6 were developed and computer-programed. In the late 1980s and in the 1990s (period 3), shortcomings of MPPT became obvious, espe- cially the sometimes erratic or even divergent behavior of the MPn series. The physical usefulness of MPPT was questioned and it was suggested to abandon the theory. Since the 1990s (period 4), the focus of method development work has been almost exclusively on MP2. A wealth of techniques and approaches has been put forward to convert MP2 from a O(M5) computational problem into a low- order or linear-scaling task that can handle molecules with thousands of atoms. In addition, the accuracy of MP2 has been systematically improved by introducing spin scaling, dispersion corrections, orbital optimization, or explicit correlation. The coming years will see a continuously strong development in MPPT that will have an essential impact on other quantum chemical methods. C 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 509–530 DOI: 10.1002/wcms.58 INTRODUCTION Hylleraas2 on the description of two-electron prob- erturbation theory has been used since the early lems with the help of perturbation theory.
    [Show full text]
  • Arxiv:1710.00259V1 [Physics.Chem-Ph] 30 Sep 2017 a Relativistically Correct Electron Interaction
    One-step treatment of spin-orbit coupling and electron correlation in large active spaces Bastien Mussard1, ∗ and Sandeep Sharma1, y 1Department of Chemistry and Biochemistry, University of Colorado Boulder, Boulder, CO 80302, USA In this work we demonstrate that the heat bath configuration interaction (HCI) and its semis- tochastic extension can be used to treat relativistic effects and electron correlation on an equal footing in large active spaces to calculate the low energy spectrum of several systems including halogens group atoms (F, Cl, Br, I), coinage atoms (Cu, Au) and the Neptunyl(VI) dioxide radical. This work demonstrates that despite a significant increase in the size of the Hilbert space due to spin symmetry breaking by the spin-orbit coupling terms, HCI retains the ability to discard large parts of the low importance Hilbert space to deliver converged absolute and relative energies. For instance, by using just over 107 determinants we get converged excitation energies for Au atom in an active space containing (150o,25e) which has over 1030 determinants. We also investigate the accuracy of five different two-component relativistic Hamiltonians in which different levels of ap- proximations are made in deriving the one-electron and two-electrons Hamiltonians, ranging from Breit-Pauli (BP) to various flavors of exact two-component (X2C) theory. The relative accuracy of the different Hamiltonians are compared on systems that range in atomic number from first row atoms to actinides. I. INTRODUCTION can become large and it is more appropriate to treat them on an equal footing with the spin-free terms and electron Relativistic effects play an important role in a correlation.
    [Show full text]
  • Jaguar 5.5 User Manual Copyright © 2003 Schrödinger, L.L.C
    Jaguar 5.5 User Manual Copyright © 2003 Schrödinger, L.L.C. All rights reserved. Schrödinger, FirstDiscovery, Glide, Impact, Jaguar, Liaison, LigPrep, Maestro, Prime, QSite, and QikProp are trademarks of Schrödinger, L.L.C. MacroModel is a registered trademark of Schrödinger, L.L.C. To the maximum extent permitted by applicable law, this publication is provided “as is” without warranty of any kind. This publication may contain trademarks of other companies. October 2003 Contents Chapter 1: Introduction.......................................................................................1 1.1 Conventions Used in This Manual.......................................................................2 1.2 Citing Jaguar in Publications ...............................................................................3 Chapter 2: The Maestro Graphical User Interface...........................................5 2.1 Starting Maestro...................................................................................................5 2.2 The Maestro Main Window .................................................................................7 2.3 Maestro Projects ..................................................................................................7 2.4 Building a Structure.............................................................................................9 2.5 Atom Selection ..................................................................................................10 2.6 Toolbar Controls ................................................................................................11
    [Show full text]
  • Coupled Cluster Methods in Quantum Chemistry
    Title: Coupled Cluster methods in quantum chemistry Name: Thorsten Rohwedder, Reinhold Schneider Al./Addr.: Technische UniversitatBerlin Coupled Cluster methods in quantum chemistry Short description Coupled Cluster methods applied in quantum chemistry reformulate the electronic Schrodinger equation as a nonlinear equation, enabling the computation of size- consistent high-precision approximations of the ground state solution for weakly cor- related systems. Introduction The Coupled Cluster method (CC method) is one of the most successful and frequently used approaches for the computation of atomic and molecular electronic structure, i.e. for the solution of the stationary electronic Schrodinger equation, whenever high ac- curacy is required. In contrast to Hartree-Fock type methods (HF) or methods from density functional theory (see the respective entries in this work), high accuracy meth- ods have to account in particular for the quantum-mechanical phenomenon of electronic correlation. If a preliminarily calculated reference solution { usually provided by a HF calculation { already is a good approximation to the sought ground state wave func- tion, the problem is said to be weakly correlated. CC as a post-Hartree-Fock method (also see the entry by M. Lewin) then enables an ecient, accurate and size-extensive description of solutions of the electronic Schrodingerequation. In this context, the 2 size-extensivity of the CC approach is a key aspect, re ecting the correct scaling of correlation energy with respect to the number of electrons. CC methods were initially developed for the treatment of many body quantum systems in nuclear physics in the 1950s and were used for quantum chemical calculations since the 1966 initial work by Paldus and Czek,see (Czek,1991) for a historical overview.
    [Show full text]
  • CHEM:4480 Introduction to Molecular Modeling
    CHEM:4480:001 Introduction to Molecular Modeling Fall 2018 Instructor Dr. Sara E. Mason Office: W339 CB, Phone: (319) 335-2761, Email: [email protected] Lecture 11:00 AM - 12:15 PM, Tuesday/Thursday. Primary Location: W228 CB. Please note that we will often meet in one of the Chemistry Computer Labs. Notice about class being held outside of the primary location will be posted to the course ICON site by 24 hours prior to the start of class. Office Tuesday 12:30-2 PM (EXCEPT for DoC faculty meeting days 9/4, 10/2, 10/9, 11/6, Hour and 12/4), Thursday 12:30-2, or by appointment Department Dr. James Gloer DEO Administrative Office: E331 CB Administrative Phone: (319) 335-1350 Administrative Email: [email protected] Text Instead of a course text, assigned readings will be given throughout the semester in forms such as journal articles or library reserves. Website http://icon.uiowa.edu Course To develop practical skills associated with chemical modeling based on quantum me- Objectives chanics and computational chemistry such as working with shell commands, math- ematical software, and modeling packages. We will also work to develop a basic understanding of quantum mechanics, approximate methods, and electronic struc- ture. Technical computing, pseudopotential generation, density functional theory software, (along with other optional packages) will be used hands-on to gain experi- ence in data manipulation and modeling. We will use both a traditional classroom setting and hands-on learning in computer labs to achieve course goals. Course Topics • Introduction: It’s a quantum world! • Dirac notation and matrix mechanics (a.k.a.
    [Show full text]
  • The Molpro Quantum Chemistry Package
    The Molpro Quantum Chemistry package Hans-Joachim Werner,1, a) Peter J. Knowles,2, b) Frederick R. Manby,3, c) Joshua A. Black,1, d) Klaus Doll,1, e) Andreas Heßelmann,1, f) Daniel Kats,4, g) Andreas K¨ohn,1, h) Tatiana Korona,5, i) David A. Kreplin,1, j) Qianli Ma,1, k) Thomas F. Miller, III,6, l) Alexander Mitrushchenkov,7, m) Kirk A. Peterson,8, n) Iakov Polyak,2, o) 1, p) 2, q) Guntram Rauhut, and Marat Sibaev 1)Institut f¨ur Theoretische Chemie, Universit¨at Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany 2)School of Chemistry, Cardiff University, Main Building, Park Place, Cardiff CF10 3AT, United Kingdom 3)School of Chemistry, University of Bristol, Cantock’s Close, Bristol BS8 1TS, United Kingdom 4)Max-Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany 5)Faculty of Chemistry, University of Warsaw, L. Pasteura 1 St., 02-093 Warsaw, Poland 6)Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States 7)MSME, Univ Gustave Eiffel, UPEC, CNRS, F-77454, Marne-la- Vall´ee, France 8)Washington State University, Department of Chemistry, Pullman, WA 99164-4630 1 Molpro is a general purpose quantum chemistry software package with a long devel- opment history. It was originally focused on accurate wavefunction calculations for small molecules, but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding and anharmonic vibrational spectra.
    [Show full text]
  • Massive-Parallel Implementation of the Resolution-Of-Identity Coupled
    Article Cite This: J. Chem. Theory Comput. 2019, 15, 4721−4734 pubs.acs.org/JCTC Massive-Parallel Implementation of the Resolution-of-Identity Coupled-Cluster Approaches in the Numeric Atom-Centered Orbital Framework for Molecular Systems † § † † ‡ § § Tonghao Shen, , Zhenyu Zhu, Igor Ying Zhang,*, , , and Matthias Scheffler † Department of Chemistry, Fudan University, Shanghai 200433, China ‡ Shanghai Key Laboratory of Molecular Catalysis and Innovative Materials, MOE Key Laboratory of Computational Physical Science, Fudan University, Shanghai 200433, China § Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany *S Supporting Information ABSTRACT: We present a massive-parallel implementation of the resolution of identity (RI) coupled-cluster approach that includes single, double, and perturbatively triple excitations, namely, RI-CCSD(T), in the FHI-aims package for molecular systems. A domain-based distributed-memory algorithm in the MPI/OpenMP hybrid framework has been designed to effectively utilize the memory bandwidth and significantly minimize the interconnect communication, particularly for the tensor contraction in the evaluation of the particle−particle ladder term. Our implementation features a rigorous avoidance of the on- the-fly disk storage and excellent strong scaling of up to 10 000 and more cores. Taking a set of molecules with different sizes, we demonstrate that the parallel performance of our CCSD(T) code is competitive with the CC implementations in state-of- the-art high-performance-computing computational chemistry packages. We also demonstrate that the numerical error due to the use of RI approximation in our RI-CCSD(T) method is negligibly small. Together with the correlation-consistent numeric atom-centered orbital (NAO) basis sets, NAO-VCC-nZ, the method is applied to produce accurate theoretical reference data for 22 bio-oriented weak interactions (S22), 11 conformational energies of gaseous cysteine conformers (CYCONF), and 32 Downloaded via FRITZ HABER INST DER MPI on January 8, 2021 at 22:13:06 (UTC).
    [Show full text]
  • US DOE SC ASCR FY11 Software Effectiveness SC GG 3.1/2.5.2 Improve Computational Science Capabilities
    US DOE SC ASCR FY11 Software Effectiveness SC GG 3.1/2.5.2 Improve Computational Science Capabilities K. J. Roche High Performance Computing Group, Pacific Northwest National Laboratory Nuclear Theory Group, Department of Physics, University of Washington Presentation to ASCAC, Washington, D.C. , November 2, 2011 Tuesday, November 1, 2011 1 LAMMPS Paul Crozier, Steve Plimpton, Mark Brown, Christian Trott OMEN, NEMO 5 Gerhard Klimeck, Mathieu Luisier, Sebastian Steiger, Michael Povolotskyi, Hong-Hyun Park, Tillman Kubis OSIRIS Warren Mori, Ricardo Fonseca, Asher Davidson, Frank Tsung, Jorge Vieira, Frederico Fiuza, Panagiotis Spentzouris eSTOMP Steve Yabusaki, Yilin Fang, Bruce Palmer, Manojkumar Krishnan Rebecca Hartman-Baker Ricky Kendall Don Maxwell Bronson Messer Vira j Paropkari David Skinner Jack Wells Cary Whitney Rice HPC Toolkit group DOE ASCR, OLCF and NERSC staf Tuesday, November 1, 2011 2 • Metric Statement, Processing • FY11 Applications Intro Problems Enhancements Results • FY12 Nominations Tuesday, November 1, 2011 3 US OMB PART DOE SC ASCR Annual Goal with Quarterly Updates (SC GG 3.1/2.5.2) Improve computational science capabilities, defined as the average annual percentage increase in the computational effectiveness (either by simulating the same problem in less time or simulating a larger problem in the same time) of a subset of application codes. To those ‘on the clock’ with this work, it means more than just satisfying the language of this metric. Tuesday, November 1, 2011 4 accept • COMPLEXITY LP LR PROBLEMS M M M • reject • ALGORITHMS • MACHINES Measured time for machine M to generate the language of the problem plus time to generate the language of the result plus the time to accept or reject the language of the result.
    [Show full text]
  • Efficient Two-Component Relativistic Method to Obtain Electronic
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by DSpace at Waseda University Efficient Two-Component Relativistic Method to Obtain Electronic and Molecular Structures of Heavy-Element Systems ͷిࢠঢ়ଶ͓Αͼ෼ࢠߏ଄ͷͨΊͷܥॏݩૉ ޮ཰తͳ 2 ੒෼૬ର࿦๏ February 2017 Waseda University Graduate School of Advanced Science and Engineering Department of Chemistry and Biochemistry, Research on Electronic State Theory Yuya NAKAJIMA தౢɹ༟໵ Contents Chapter 1 General introduction 1 References . ................................ 6 Chapter 2 Theoretical background 7 2.1 Dirac Hamiltonian . ....................... 7 2.2 The IODKH method ....................... 9 2.3 The LUT scheme . ........................ 12 2.4 Spin-free and spin-dependent formalisms . ......... 14 2.5 The FCP method . ........................ 16 2.6 The GHF method . ........................ 19 2.7 The Analytical energy derivative for the GHF method . 21 References . ................................ 24 Chapter 3 Analytical energy gradient for spin-free infinite-order Douglas–Kroll–Hess method with local unitary transfor- mation 25 3.1 Introduction . .......................... 25 3.2 Theory and implementation . ................. 27 3.2.1 Energy gradient for IODKH . ........... 27 3.2.2 Analytical derivative for the space transformation matrices . ......................... 30 3.2.3 Energy gradient for LUT-IODKH . .......... 32 3.2.4 Implementation . ................... 33 i 3.3 Numerical assessments . .................. 34 3.3.1 Computational details . ................ 34 3.3.2 Numerical gradient values ............... 37 3.3.3 Accuracies of IODKH/C and LUT-IODKH/C methods 38 3.3.4 Computational cost of the LUT scheme ........ 45 3.3.5 Metal complexes . ................... 47 3.3.6 Heavier analogues of ethylene . ........... 48 3.3.7 Harmonic frequencies of diatomic molecules . 49 3.4 Conclusion .
    [Show full text]
  • The Electron Affinity of the Uranium Atom
    The electron affinity of the uranium atom Cite as: J. Chem. Phys. 154, 224307 (2021); https://doi.org/10.1063/5.0046315 Submitted: 02 February 2021 . Accepted: 18 May 2021 . Published Online: 10 June 2021 Sandra M. Ciborowski, Gaoxiang Liu, Moritz Blankenhorn, Rachel M. Harris, Mary A. Marshall, Zhaoguo Zhu, Kit H. Bowen, and Kirk A. Peterson ARTICLES YOU MAY BE INTERESTED IN Ultrahigh sensitive transient absorption spectrometer Review of Scientific Instruments 92, 053002 (2021); https://doi.org/10.1063/5.0048115 A dual-magneto-optical-trap atom gravity gradiometer for determining the Newtonian gravitational constant Review of Scientific Instruments 92, 053202 (2021); https://doi.org/10.1063/5.0040701 How accurate is the determination of equilibrium structures for van der Waals complexes? The dimer N2O⋯CO as an example The Journal of Chemical Physics 154, 194302 (2021); https://doi.org/10.1063/5.0048603 J. Chem. Phys. 154, 224307 (2021); https://doi.org/10.1063/5.0046315 154, 224307 © 2021 Author(s). The Journal ARTICLE of Chemical Physics scitation.org/journal/jcp The electron affinity of the uranium atom Cite as: J. Chem. Phys. 154, 224307 (2021); doi: 10.1063/5.0046315 Submitted: 2 February 2021 • Accepted: 18 May 2021 • Published Online: 10 June 2021 Sandra M. Ciborowski,1 Gaoxiang Liu,1 Moritz Blankenhorn,1 Rachel M. Harris,1 Mary A. Marshall,1 Zhaoguo Zhu,1 Kit H. Bowen,1,a) and Kirk A. Peterson2,a) AFFILIATIONS 1 Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA 2 Department of Chemistry, Washington State University, Pullman, Washington 99162, USA a)Authors to whom correspondence should be addressed: [email protected] and [email protected] ABSTRACT The results of a combined experimental and computational study of the uranium atom are presented with the aim of determining its electron affinity.
    [Show full text]