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Quantum Crystallography†
Chemical Science View Article Online MINIREVIEW View Journal | View Issue Quantum crystallography† Simon Grabowsky,*a Alessandro Genoni*bc and Hans-Beat Burgi*de Cite this: Chem. Sci.,2017,8,4159 ¨ Approximate wavefunctions can be improved by constraining them to reproduce observations derived from diffraction and scattering experiments. Conversely, charge density models, incorporating electron-density distributions, atomic positions and atomic motion, can be improved by supplementing diffraction Received 16th December 2016 experiments with quantum chemically calculated, tailor-made electron densities (form factors). In both Accepted 3rd March 2017 cases quantum chemistry and diffraction/scattering experiments are combined into a single, integrated DOI: 10.1039/c6sc05504d tool. The development of quantum crystallographic research is reviewed. Some results obtained by rsc.li/chemical-science quantum crystallography illustrate the potential and limitations of this field. 1. Introduction today's organic, inorganic and physical chemistry. These tools are usually employed separately. Diffraction and scattering Quantum chemistry methods and crystal structure determina- experiments provide structures at the atomic scale, while the Creative Commons Attribution 3.0 Unported Licence. tion are highly developed research tools, indispensable in techniques of quantum chemistry provide wavefunctions and aUniversitat¨ Bremen, Fachbereich 2 – Biologie/Chemie, Institut fur¨ Anorganische eUniversitat¨ Zurich,¨ Institut fur¨ Chemie, Winterthurerstrasse 190, CH-8057 Zurich,¨ Chemie und Kristallographie, Leobener Str. NW2, 28359 Bremen, Germany. Switzerland E-mail: [email protected] † Dedicated to Prof. Louis J. Massa on the occasion of his 75th birthday and to bCNRS, Laboratoire SRSMC, UMR 7565, Vandoeuvre-l`es-Nancy, F-54506, France Prof. Dylan Jayatilaka on the occasion of his 50th birthday in recognition of their cUniversit´e de Lorraine, Laboratoire SRSMC, UMR 7565, Vandoeuvre-l`es-Nancy, F- pioneering contributions to the eld of X-ray quantum crystallography. -
Quantum Reform
feature Quantum reform Leonie Mueck Quantum computers potentially offer a faster way to calculate chemical properties, but the exact implications of this speed-up have only become clear over the last year. The first quantum computers are likely to enable calculations that cannot be performed classically, which might reform quantum chemistry — but we should not expect a revolution. t had been an exhausting day at the 2012 International Congress of Quantum IChemistry with countless presentations reporting faster and more accurate methods for calculating chemical information using computers. In the dry July heat of Boulder, Colorado, a bunch of young researchers decided to end the day with a cool beer, but the scientific discussion didn’t fade away. Thoughts on the pros and cons of all the methods — the approximations they involved and the chemical problems that they could solve — bounced across the table, until somebody said “Anyway, in a few years we will have a quantum computer and our approximate methods will be obsolete”. An eerie silence followed. What a frustrating thought! They were devoting their careers to quantum chemistry — working LIBRARY PHOTO RICHARD KAIL/SCIENCE tirelessly on applying the laws of quantum mechanics to treat complex chemical of them offering a different trade-off between cannot do on a ‘classical’ computer, it does problems with a computer. And in one fell accuracy and computational feasibility. not look like all the conventional quantum- swoop, would all of those efforts be wasted Enter the universal quantum computer. chemical methods will become obsolete or as chemists turn to quantum computers and This dream machine would basically work that quantum chemists will be out of their their enormous computing power? like a normal digital computer; it would jobs in the foreseeable future. -
Quantum Chemistry and Spectroscopy – Spring 2018
CHE 336 – Quantum Chemistry and Spectroscopy – Spring 2018 Instructor: Dr. Jessica Sarver Email: [email protected] Office: HSC 364 (email hours: 8 am – 10 pm) Office Hours: 10am-12pm Tuesday, 2-3pm Wednesday, 10:30-11:30am Friday, or by appointment Course Description (from Westminster undergraduate catalog) Quantum chemistry and spectroscopy is the study of the microscopic behavior of matter and its interaction with electromagnetic radiation. Topics include the formulation and application of quantum mechanical models, atomic and molecular structure, and various spectroscopic techniques. Laboratory activities demonstrate the fundamental principles of physical chemistry. Methods that will be used during the laboratory portion include: polarimetry, UV-Vis and fluorescence spectroscopies, electrochemistry, and computational/molecular modeling. Prerequisites: C- grade in CHE 117 and MTH 152 and PHY 152. Course Outcomes The chemistry major outcomes are: • Describe and explain quantum theory and the three quantum mechanical models of motion. • Describe and explain how these theories/models are applied and incorporated to applications of atomic/molecular structure and spectroscopy. • Describe and explain the principles of four major types of spectroscopy and their applications. • Describe and explain the measurable thermodynamic parameters for physical and chemical processes and equilibria. • Describe and explain how chemical kinetics can be used to investigate time-dependent processes. • Solve mathematical problems based on physical chemical principles and connect the numerical results with these principles. Textbook The text for this course is Physical Chemistry, 10th Ed. by Atkins and de Paula. Readings and problem set questions will be assigned from this text. You are strongly urged to get a copy of this textbook and complete all the assigned readings and homework. -
Complex Chemical Reaction Networks from Heuristics-Aided Quantum Chemistry
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Harvard University - DASH Complex Chemical Reaction Networks from Heuristics-Aided Quantum Chemistry The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters. Citation Rappoport, Dmitrij, Cooper J. Galvin, Dmitry Zubarev, and Alán Aspuru-Guzik. 2014. “Complex Chemical Reaction Networks from Heuristics-Aided Quantum Chemistry.” Journal of Chemical Theory and Computation 10 (3) (March 11): 897–907. Published Version doi:10.1021/ct401004r Accessed February 19, 2015 5:14:37 PM EST Citable Link http://nrs.harvard.edu/urn-3:HUL.InstRepos:12697373 Terms of Use This article was downloaded from Harvard University's DASH repository, and is made available under the terms and conditions applicable to Open Access Policy Articles, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#OAP (Article begins on next page) Complex Chemical Reaction Networks from Heuristics-Aided Quantum Chemistry Dmitrij Rappoport,∗,† Cooper J Galvin,‡ Dmitry Yu. Zubarev,† and Alán Aspuru-Guzik∗,† Department of Chemistry and Chemical Biology, Harvard University, 12 Oxford Street, Cambridge, MA 02138, USA, and Pomona College, 333 North College Way, Claremont, CA 91711, USA E-mail: [email protected]; [email protected] Abstract While structures and reactivities of many small molecules can be computed efficiently and accurately using quantum chemical methods, heuristic approaches remain essential for mod- eling complex structures and large-scale chemical systems. Here we present heuristics-aided quantum chemical methodology applicable to complex chemical reaction networks such as those arising in metabolism and prebiotic chemistry. -
Introduction to Quantum Chemistry
Chem. 140B Dr. J.A. Mack Introduction to Quantum Chemistry Why as a chemist, do you need to learn this material? 140B Dr. Mack 1 Without Quantum Mechanics, how would you explain: • Periodic trends in properties of the elements • Structure of compounds e.g. Tetrahedral carbon in ethane, planar ethylene, etc. • Bond lengths/strengths • Discrete spectral lines (IR, NMR, Atomic Absorption, etc.) • Electron Microscopy & surface science Without Quantum Mechanics, chemistry would be a purely empirical science. (We would be no better than biologists…) 140B Dr. Mack 2 1 Classical Physics On the basis of experiments, in particular those performed by Galileo, Newton came up with his laws of motion: 1. A body moves with a constant velocity (possibly zero) unless it is acted upon by a force. 2. The “rate of change of motion”, i.e. the rate of change of momentum, is proportional to the impressed force and occurs in the direction of the applied force. 3. To every action there is an equal and opposite reaction. 4. The gravitational force of attraction between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. m m F = G × 1 2 r 2 140B Dr. Mack 3 The Failures of Classical Mechanics 1. Black Body Radiation: The Ultraviolet Catastrophe 2. The Photoelectric Effect: Einstein's belt buckle 3. The de Broglie relationship: Dude you have a wavelength! 4. The double-slit experiment: More wave/particle duality 5. Atomic Line Spectra: The 1st observation of quantum levels 140B Dr. Mack 4 2 Black Body Radiation Light Waves: Electromagnetic Radiation Light is composed of two perpendicular oscillating vectors waves: A magnetic field & an electric field As the light wave passes through a substance, the oscillating fields can stimulate the movement of electrons in a substance. -
Computational Analysis of the Mechanism of Chemical Reactions
Computational Analysis of the Mechanism of Chemical Reactions in Terms of Reaction Phases: Hidden Intermediates and Hidden Transition States ELFI KRAKA* AND DIETER CREMER Department of Chemistry, Southern Methodist University, 3215 Daniel Avenue, Dallas, Texas 75275-0314 RECEIVED ON JANUARY 9, 2009 CON SPECTUS omputational approaches to understanding chemical reac- Ction mechanisms generally begin by establishing the rel- ative energies of the starting materials, transition state, and products, that is, the stationary points on the potential energy surface of the reaction complex. Examining the intervening spe- cies via the intrinsic reaction coordinate (IRC) offers further insight into the fate of the reactants by delineating, step-by- step, the energetics involved along the reaction path between the stationary states. For a detailed analysis of the mechanism and dynamics of a chemical reaction, the reaction path Hamiltonian (RPH) and the united reaction valley approach (URVA) are an effi- cient combination. The chemical conversion of the reaction complex is reflected by the changes in the reaction path direction t(s) and reaction path curvature k(s), both expressed as a function of the path length s. This information can be used to partition the reaction path, and by this the reaction mech- anism, of a chemical reaction into reaction phases describing chemically relevant changes of the reaction complex: (i) a contact phase characterized by van der Waals interactions, (ii) a preparation phase, in which the reactants prepare for the chemical processes, (iii) one or more transition state phases, in which the chemical processes of bond cleavage and bond formation take place, (iv) a product adjustment phase, and (v) a separation phase. -
Six Phases of Cosmic Chemistry
Six Phases of Cosmic Chemistry Lukasz Lamza The Pontifical University of John Paul II Department of Philosophy, Chair of Philosophy of Nature Kanonicza 9, Rm. 203 31-002 Kraków, Poland e-mail: [email protected] 1. Introduction The steady development of astrophysical and cosmological sciences has led to a growing appreciation of the continuity of cosmic history throughout which all known phenomena come to being. This also includes chemical phenomena and there are numerous theoretical attempts to rewrite chemistry as a “historical” science (Haken 1978; Earley 2004). It seems therefore vital to organize the immense volume of chemical data – from astrophysical nuclear chemistry to biochemistry of living cells – in a consistent and quantitative fashion, one that would help to appreciate the unfolding of chemical phenomena throughout cosmic time. Although numerous specialist reviews exist (e.g. Shaw 2006; Herbst 2001; Hazen et al. 2008) that illustrate the growing appreciation for cosmic chemical history, several issues still need to be solved. First of all, such works discuss only a given subset of cosmic chemistry (astrochemistry, chemistry of life etc.) using the usual tools and languages of these particular disciplines which does not facilitate drawing large-scale conclusions. Second, they discuss the history of chemical structures and not chemical processes – which implicitly leaves out half of the totality chemical phenomena as non-historical. While it may now seem obvious that certain chemical structures such as aromatic hydrocarbons or pyrazines have a certain cosmic “history”, it might cause more controversy to argue that chemical processes such as catalysis or polymerization also have their “histories”. -
Quantum Mechanics of Atoms and Molecules Lectures, the University of Manchester 2005
Quantum Mechanics of Atoms and Molecules Lectures, The University of Manchester 2005 Dr. T. Brandes April 29, 2005 CONTENTS I. Short Historical Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 I.1 Atoms and Molecules as a Concept . 1 I.2 Discovery of Atoms . 1 I.3 Theory of Atoms: Quantum Mechanics . 2 II. Some Revision, Fine-Structure of Atomic Spectra : : : : : : : : : : : : : : : : : : : : : 3 II.1 Hydrogen Atom (non-relativistic) . 3 II.2 A `Mini-Molecule': Perturbation Theory vs Non-Perturbative Bonding . 6 II.3 Hydrogen Atom: Fine Structure . 9 III. Introduction into Many-Particle Systems : : : : : : : : : : : : : : : : : : : : : : : : : 14 III.1 Indistinguishable Particles . 14 III.2 2-Fermion Systems . 18 III.3 Two-electron Atoms and Ions . 23 IV. The Hartree-Fock Method : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 24 IV.1 The Hartree Equations, Atoms, and the Periodic Table . 24 IV.2 Hamiltonian for N Fermions . 26 IV.3 Hartree-Fock Equations . 28 V. Molecules : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 35 V.1 Introduction . 35 V.2 The Born-Oppenheimer Approximation . 36 + V.3 The Hydrogen Molecule Ion H2 . 39 V.4 Hartree-Fock for Molecules . 45 VI. Time-Dependent Fields : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 48 VI.1 Time-Dependence in Quantum Mechanics . 48 VI.2 Time-dependent Hamiltonians . 50 VI.3 Time-Dependent Perturbation Theory . 53 VII.Interaction with Light : : : : : : : : : : : : : : : : : : : : : : : -
CHEM 743 “Quantum Chemistry” S'15
CHEM 743 \Quantum Chemistry" S'15 Instructor: Sophya Garashchuk∗ Dept of Chemistry and Biochemistry, University of South Carolina, Columbia y (Dated: January 7, 2015) Syllabus • Learning outcomes: (i) the students will gain theoretical knowledge in quantum mechanics and computer skills enabling them to use modern electronic structure codes and simulations with confidence and intelligence to better understand chemical processes; (ii) the students will be able to set up their own input files and interpret/visualize output files for standard quantum chemistry programs/packages that might be relevant to their research; (iii) the students will improve general critical thinking and problem-solving skills as well as improve their skills of independent computer-aided research through extensive use of electronically available resources. • Prerequisites: CHEM 542 or equivalent, i. e. Physical Chemistry - Quantum Mechanics and Spectroscopy • Classes will take place MW 9:40-10:55 AM at PSC 101. We will work with Maple, Q-Chem, Spartan, ADF Class materials and assignments or links to them will be posted on Blackboard Computer and software support: Jun Zhou [email protected] Ph: (803) 777-5492 College of Arts & Sciences Sumwalt College 228 • Office hours: Tue 10-11 am, GSRC 407. I am generally available Mon-Fri 9:00 AM { 5PM. You can just drop by, call or e-mail to check if I am available, or if you have difficulty reaching me, make an appointment. • The suggested general quantum chemistry textbook is \Introduction to Quantum Mechanics in Chemistry", by M. A. Ratner and G. C. Schatz, Prentice-Hall, New Jersey, 2001. Used copies are available through BN.com. -
Chemistry (CHEM) 1
Chemistry (CHEM) 1 Chemistry (CHEM) CHEM 117. Chemical Concepts and Applications. 3 Credits. Introduction to general and organic chemistry, with applications drawn from the health, environmental, and materials sciences. Prereq or Coreq: MATH 103, MATH 104 or MATH 107 or Math placement. CHEM 117L. Chem Concepts and Applications Lab. 1 Credit. Introduction to general and organic chemistry, with applications drawn from the health, environmental, and materials sciences. Prereq or Coreq: MATH 103, MATH 104, MATH 107 or Math placement. CHEM 121L. General Chemistry I Laboratory. 1 Credit. Matter, measurement, atoms, ions, molecules, reactions, chemical calculations, thermochemistry, bonding, molecular geometry, periodicity, and gases. Prereq or Coreq: MATH 103 or MATH 107 or Math placement. CHEM 121. General Chemistry I. 3 Credits. Matter, measurement, atoms, ions, molecules, reactions, chemical calculations, thermochemistry, bonding, molecular geometry, periodicity, and gases. Prereq or Coreq: MATH 103 or MATH 107 or Math placement. CHEM 122L. General Chemistry II Laboratory. 1 Credit. Intermolecular forces, liquids, solids, kinetics, equilibria, acids and bases, solution chemistry, precipitation, thermodynamics, and electrochemistry. Prereq: CHEM 121L. CHEM 122. General Chemistry II. 3 Credits. Intermolecular forces, liquids, solids, kinetics, equilibria, acids and bases, solution chemistry, precipitation, thermodynamics, and electrochemistry. Prereq: CHEM 121. CHEM 140. Organic Chemical Concepts and Applications. 1 Credit. Introduction to organic chemistry for pre-nursing and other students who need to meet the prerequisite for CHEM 260. CHEM 150. Principles of Chemistry I. 3 Credits. Chemistry for students with good high school preparation in mathematics and science. Electronic structure, stoichiometry, molecular geometry, ionic and covalent bonding, energetics of chemical reactions, gases, transition metal chemistry. -
Electronic Structure Calculations in Quantum Chemistry
Electronic Structure Calculations in Quantum Chemistry Alexander B. Pacheco User Services Consultant LSU HPC & LONI [email protected] HPC Training Louisiana State University Baton Rouge Nov 16, 2011 Electronic Structure Calculations in Quantum Chemistry Nov 11, 2011 HPC@LSU - http://www.hpc.lsu.edu 1 / 55 Outline 1 Introduction 2 Ab Initio Methods 3 Density Functional Theory 4 Semi-empirical Methods 5 Basis Sets 6 Molecular Mechanics 7 Quantum Mechanics/Molecular Mechanics (QM/MM) 8 Computational Chemistry Programs 9 Exercises 10 Tips for Quantum Chemical Calculations Electronic Structure Calculations in Quantum Chemistry Nov 11, 2011 HPC@LSU - http://www.hpc.lsu.edu 2 / 55 Introduction What is Computational Chemistry? Computational Chemistry is a branch of chemistry that uses computer science to assist in solving chemical problems. Incorporates the results of theoretical chemistry into efficient computer programs. Application to single molecule, groups of molecules, liquids or solids. Calculates the structure and properties of interest. Computational Chemistry Methods range from 1 Highly accurate (Ab-initio,DFT) feasible for small systems 2 Less accurate (semi-empirical) 3 Very Approximate (Molecular Mechanics) large systems Electronic Structure Calculations in Quantum Chemistry Nov 11, 2011 HPC@LSU - http://www.hpc.lsu.edu 3 / 55 Introduction Theoretical Chemistry can be broadly divided into two main categories 1 Static Methods ) Time-Independent Schrödinger Equation H^ Ψ = EΨ ♦ Quantum Chemical/Ab Initio /Electronic Structure Methods ♦ Molecular Mechanics 2 Dynamical Methods ) Time-Dependent Schrödinger Equation @ { Ψ = H^ Ψ ~@t ♦ Classical Molecular Dynamics ♦ Semi-classical and Ab-Initio Molecular Dynamics Electronic Structure Calculations in Quantum Chemistry Nov 11, 2011 HPC@LSU - http://www.hpc.lsu.edu 4 / 55 Tutorial Goals Provide a brief introduction to Electronic Structure Calculations in Quantum Chemistry. -
Quantum Crystallography: Current Developments and Future
DOI:10.1002/chem.201705952 Concept & Physical Chemistry Quantum Crystallography:CurrentDevelopments and Future Perspectives Alessandro Genoni,*[a] Lukas Bucˇinsky´,[b] NicolasClaiser,[c] JuliaContreras-García,[d] Birger Dittrich,[e] PaulinaM.Dominiak,[f] Enrique Espinosa,[c] Carlo Gatti,[g] Paolo Giannozzi,[h] Jean-Michel Gillet,[i] Dylan Jayatilaka,[j] Piero Macchi,[k] AndersØ.Madsen,[l] Lou Massa,[m] ChØrifF.Matta,[n] Kenneth M. Merz,Jr. ,[o] Philip N. H. Nakashima,[p] Holger Ott,[q] Ulf Ryde,[r] Karlheinz Schwarz,[s] Marek Sierka,[t] and SimonGrabowsky*[u] Chem. Eur.J.2018, 24,10881 –10905 10881 2018 Wiley-VCH Verlag GmbH &Co. KGaA, Weinheim Concept Abstract: Crystallographyand quantum mechanics have Nevertheless, many other active andemerging research always been tightly connected because reliable quantum areas involving quantum mechanics andscattering experi- mechanical models are neededtodetermine crystal struc- ments are not covered by the originaldefinition although tures. Due to this natural synergy,nowadays accurate distri- they enable to observeand explain quantum phenomenaas butions of electrons in space can be obtained from diffrac- accurately and successfully as theoriginalstrategies. There- tion and scattering experiments.Inthe original definition of fore, we give an overview over current research that is relat- quantum crystallography (QCr) given by Massa,Karle and ed to abroader notion of QCr,and discuss optionshow QCr Huang, direct extraction of wavefunctions or density matri- can evolve to become acomplete and independent domain ces from measured intensities of reflectionsor, conversely, of natural sciences. The goal of this paper is to initiate dis- ad hoc quantum mechanical calculations to enhancethe ac- cussionsaround QCr,but not to find afinal definition of the curacy of the crystallographic refinement are implicated.