DOCSLIB.ORG

Between Accuracy and Manageability: Computational Imperatives in Quantum Chemistry

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Between Accuracy and Manageability: Computational Imperatives in Quantum Chemistry HSNS3901_02 1/12/09 3:33 PM Page 32 BUHM SOON PARK∗ Between Accuracy and Manageability: Computational Imperatives in Quantum Chemistry ABSTRACT This article explores the place of computation in the history of quantum theory by ex- amining the development of several approximation methods to solve the Schrödinger equation without using empirical information, as these were worked out in the years from 1927 to 1933. These ab initio methods, as they became known, produced the results that helped validate the use of quantum mechanics in many-body atomic and molecular systems, but carrying out the computations became increasingly laborious and difficult as better agreement between theory and experiment was pursued and more complex systems were tackled. I argue that computational work in the early years of quantum chemistry shows an emerging practice of theory that required human labor, technological improvement (computers), and mathematical ingenuity. KEY WORDS: computation, computer, quantum chemistry, practice of theory, approximation method, ab initio, Douglas Hartree, John Slater, Walter Heitler, Hubert James INTRODUCTION In the traditional narrative of the history of quantum physics, the problem of chemical binding appears only briefly at the end of the long march toward quantum mechanics. It is usually introduced as one of the exemplary problems *School of Humanities and Social Sciences, Korea Advanced Institute of Science and Tech- nology (KAIST), 335 Gwahangno, Yuseong-gu, Daejeon, Korea; [email protected]. The following abbreviations are used: AHC, Annals of the History of Computing; HSPS, His- torical Studies in the Physical and Biological Sciences; JCP, Journal of Chemical Physics; JSP, John C. Slater Papers, American Philosophical Society, Philadelphia; PCPS, Proceedings of the Cam- bridge Philosophical Society; PR, Physical Review; PRS, Proceedings of the Royal Society; RMP, Reviews of Modern Physics; SCF, self-consistent field; SHPMP, Studies in History and Philosophy of Modern Physics; ZP, Zeitschrift für Physik. Historical Studies in the Natural Sciences, Vol. 39, Number 1, pps. 32–62. ISSN 1939-1811, electronic ISSN 1939-182X. © 2009 by the Regents of the University of California. All rights reserved. Please direct all requests for permission to photocopy or reproduce article content through the University of California Press’s Rights and Permissions website, http://www.ucpressjournals.com/reprintinfo.asp. DOI: 10.1525/hsns.2009.39.1.32. 32 | HSNS3901_02 1/12/09 3:33 PM Page 33 BETWEEN ACCURACY AND MANAGEABILITY | 33 that quantum mechanics solved, thereby validating its general applicability. Singularly recognized as groundbreaking is Walter Heitler and Fritz London’s famous paper of 1927, which provided a theoretical explanation of why two hy- drogen atoms combine to form a molecule.1 The possibility of understanding the whole territory of chemistry with quantum mechanics—a reductionist ideal shared by other physicists—seemed within Heitler and London’s reach.2 In- deed, excitement about the new theoretical framework abounded in the late 1920s. As the historian Max Jammer put it: “Satisfied that the theory ‘works,’ since it provided unambiguous answers whenever invoked, physicists engaged themselves rather in solving problems which so far had defied all previous at- tempts or which promised to open up new avenues of research.”3 However, historians of quantum physics, including Jammer, have paid lit- tle attention to whether the reductionist program worked well or faced diffi- culties in chemistry after 1927. It seems that they have largely believed that quantum chemistry, a new field which came into being after Heitler and Lon- don’s paper, successfully carried out the mission of reducing chemistry to physics. Historians of quantum chemistry have been rather critical of this picture. They have shown that early optimism about reductionism quickly devolved into pes- simism in the 1930s in the face of the complexity of chemical systems, and that quantum chemistry developed into a discipline with diverse methodologies, indigenous languages, and separate institutional bases. To them, the acceptance of quantum mechanics in chemistry has not necessarily meant the reduction of one discipline to another.4 1. Walter Heitler and Fritz London, “Wechselwirkung neutraler Atome und homöopolare Bindung nach der Quantenmechanik,” ZP 44 (1927): 455–72. 2. For instance, Paul Dirac made an oft-quoted statement that “the underlying physical laws for the mathematical theory of a large part of physics and the whole of chemistry are thus com- pletely known.” P. A. M. Dirac, “Quantum Mechanics of Many-Electron Systems,” PRS A123 (1929): 714–33, on 714. 3. Max Jammer, The Conceptual Development of Quantum Mechanics, 2nd ed. (College Park, MD: American Institute of Physics, 1989), 359–60, 384–86. 4. Kostas Gavroglu and Ana I. Simões, “The Americans, the Germans, and the Beginnings of Quantum Chemistry: The Confluence of Diverging Traditions,” HSPS 25, no. 1 (1994): 47–110; Eric R. Scerri, “Has Chemistry at Least Been Approximately Reduced to Quantum Mechanics?” Proceedings of the Biennial Meeting of the Philosophy of Science Association 1 (1994): 160–70; Mary Jo Nye, From Chemical Philosophy to Theoretical Chemistry (Berkeley: University of California Press, 1993); Silvan S. Schweber, “The Young John Clarke Slater and the Development of Quantum Chemistry,” HSPS 20, no. 2 (1990): 339–406. See also Ana I. Simões, “Chemical Physics and Quan- tum Chemistry in the Twentieth Century,” in The Cambridge History of Science, Vol. 5: The Modern Physical and Mathematical Sciences, ed. Mary Jo Nye (Cambridge: University of Cambridge HSNS3901_02 1/12/09 3:33 PM Page 34 34 |PARK While agreeing in general with the latter point of view,5 I would point out that most historians of quantum chemistry have not fully examined the efforts made following Heitler and London to solve the Schrödinger equation for multi-electron atomic or molecular systems without using empirical data.6 This paper thus aims to reassess the place of the pioneers of ab initio methods in the history of quantum theory. I suggest that we broaden our attention from the conceptual development of quantum mechanics to the practice of theory in order to appreciate the significance of computation-oriented work in the spread of quantum mechanics into various problems in physics and chemistry. By the “practice of theory” I mean, in this case, a set of activities required to solve the Schrödinger equation, such as devising approximate Hamiltonians and trial functions, calculating complicated integrals, and formulating schemes to nar- row the gap between theory and experiment. There was no dearth of problems to solve. And yet, the more complex the atomic or molecular system, the more difficult the problem, especially because of the increasing amount of labor that computations involved. A compromise had to be reached between defining a manageable problem and solving it accurately. What, then, would be this ac- ceptable compromise? By shifting our focus to the practice of theory, we can see who sought to solve the wave equation using ab initio approaches and how they tested the level of compromise between manageability and accuracy. It is worth noting that graduate students, postdoctoral scholars, and junior faculty members created this domain of study, not the inventors of quantum mechanics. That is, the multi-electron atomic or molecular system presented itself as an Press, 2003), 394–412; Ana I. Simões, “Dirac’s Claim and the Chemists,” Physics in Perspective 4 (2002): 253–66. Most recently, see Martha L. Harris, “Chemical Reductionism Revisited: Lewis, Pauling, and the Physico-Chemical Nature of the Chemical Bond,” Studies in History and Phi- losophy of Science 39 (2008): 78–90. 5. Buhm Soon Park, “In the ‘Context of Pedagogy’: Teaching Strategy and Theory Change in Quantum Chemistry,” in Pedagogy and the Practice of Science: Historical and Contemporary Per- spectives, ed. David Kaiser (Cambridge, MA: MIT Press, 2005), 287–319; Buhm Soon Park, “Chem- ical Translators: Pauling, Wheland, and Their Strategies for Teaching the Theory of Resonance,” British Journal for the History of Science 32 (1999): 21–46. 6. One notable exception is Andrea Woody, “Putting Quantum Mechanics to Work in Chem- istry: The Power of Diagrammatic Representation,” Philosophy of Science, Proceedings 67 (2000), S612–S627. And yet, Woody gives much attention to the emergence of diagrammatic represen- tation of molecular orbitals as a way of getting around computational difficulties. I focus more on the nature of computational constraints and some developments in approximation methods during this period. The term ab initio, which means “from the beginning,” was first used around 1950. Peter W. Atkins, Quanta: A Handbook of Concepts, 2nd ed. (Oxford: Oxford University Press, 1991), 1. HSNS3901_02 1/12/09 3:33 PM Page 35 BETWEEN ACCURACY AND MANAGEABILITY | 35 entry-level problem for those who aspired to learn and master quantum theory, although they were located at various universities around the world.7 MAKING APPROXIMATIONS The point of departure for the problem of many-electron atoms was the nor- mal helium atom—the two-electron system. Various approximation methods were first developed and tested for the helium atom before being applied to larger atoms, and that experience would prove important for quantum chem- istry in its wake. Outstanding agreement between theory and experiment for the helium problem was achieved by the Norwegian
Load more

Recommended publications
  • Autonomy and Automation Computational Modeling, Reduction, and Explanation in Quantum Chemistry Johannes Lenhard, Bielefeld Univ
    Autonomy and Automation Computational modeling, reduction, and explanation in quantum chemistry Johannes Lenhard, Bielefeld University preprint abstract This paper discusses how computational modeling combines the autonomy of models with the automation of computational procedures. In particular, the case of ab initio methods in quantum chemistry will be investigated to draw two lessons from the analysis of computational modeling. The first belongs to general philosophy of science: Computational modeling faces a trade-off and enlarges predictive force at the cost of explanatory force. The other lesson is about the philosophy of chemistry: The methodology of computational modeling puts into doubt claims about the reduction of chemistry to physics. 1. Introduction In philosophy of science, there is a lively debate about the role and characteristics of models. The present paper wants to make a contribution to this debate about computational modeling in particular.1 Although there is agreement about the importance of computers in recent science, often their part is seen as merely accelerating computations. Of course, speed is a critical issue in practices of computation, because it restricts or enlarges the range of tractability for computational strategies.2 However, it will be argued in this paper that the conception of computational modeling, is not merely a matter of speed, i.e., not only amplifying already existing approaches, but has much wider philosophical significance. 1 There may be considerable overlap with the issue of simulation, but the argumentation of this paper does not depend on this part of terminology. 2 This has been aptly expressed in the part of Paul Humphreys’ book (2004) that deals with computational science.
    [Show full text]
  • 1.1 Effective Nuclear Charge 1.2 Effective Nuclear Charge 1.3
    Periodic Trends Periodic Trends 1.1 Effective Nuclear Charge 1.2 Effective Nuclear Charge The interaction between the nuclear charge and the Zeff = nuclear charge actually experienced by an valence electrons (how many? how far away?) is electron critical Simplest approximation The nuclear charge experienced by the valence Zeff = Z - # core electrons electrons (Zeff ) impacts how tightly the valence electrons are held Assumption How tightly the valence electrons are held influences atomic size, ionization energy, electron affinity, and Examples reactivity Periodic Trends Periodic Trends 1.3 Effective Nuclear Charge 1.4 Slater’s Rules Slater’s rules acknowledge the imperfect shielding Slater’s rules assume imperfect shielding caused by orbital penetration Zeff = Z – where is calculated using Slater’s rules 1. GthbitlidGroup the orbitals in order: (1s) (2s,2p) (3s,3p) (3d) (4s,4p) (4d) (4f) (5s,5p)… 2. To determine , sum up the following contributions for the electron of interest: a. 0 (zero) for all electrons in groups outside (to the right of) the one being considered b. 0.35 for each of the other electrons in the same ggp(proup (except for 1s group where 0.30 is used) c. If the electron is in a (ns,np) group, 0.85 for each electron in the next innermost (to the left) group d. If the electron is in a (nd) or (nf) group, 1.00 for each electron in the next innermost (to the left) group e. 1.00 for each electron in the still lower (farther in) groups 1 Periodic Trends Periodic Trends 1.5 Using Slater’s Rules 1.6 Using Slater’s Rules What do the 1.0, 0.85 and 0.35 factors mean? Fluorine’s Zeff calculated using the simple approximation = 7 and using Slater’s rules = 5.20.
    [Show full text]
  • CHEM 1A03 UNIT 3: Periodic Trends Introduction
    CHEM 1A03 UNIT 3: Periodic Trends Introduction Hey! Thanks for opening up this Chemistry Periodic Trends Review! The education team at WebStraw McMaster has put together a comprehensive breakdown for you that covers all the key concepts for Chemistry Periodic Trends Members of our team have taken the course in previous years, and we understand better than anyone else what specific ideas and concepts tend to trip students up throughout the semester. We are essentially offering you the key takeaways from the course, after having completed the course ourselves. Before you read further, also keep in mind that these review packages are not meant to be a tool for you to learn the course from scratch. The content presented below was designed with the assumption that you already have a preliminary understanding of Periodic Trends. Our goal is to help give you a more in-depth understanding of key outcomes, as well as to help you see how concepts relate/connect to one another within the scope of the course as a whole. We do our best to cover every topic within the unit; however, some testable outcomes may not be discussed. With that said, best of luck in your studying! Remember to make good use of your time, but to also take breaks as well. Yousef Abumustafa & Julia Ma The WebStraw McMaster Chemistry team WebStraw McMaster Periodic properties of elements The periodic table is divided into called columns called groups that group elements with similar chemical/physical properties together and rows called periods that group elements with the same
    [Show full text]
  • Important Factoids in Understanding Effective Nuclear Charge
    CHEM 1B Important Factoids in Understanding Effective Nuclear Charge To understand the concept of effective nuclear charge, we focus on one electron (usually a valence or outer electron) and consider the forces the other charged particles exert on this electron. In an atom with more than one electron, each electron will ‘feel’ both attractive forces from the positive nucleus and repulsive forces from the other electrons. Qualitatively, Zeff is the NET (or effective) ATTRACTIVE charge that the electron ‘feels’, taking into account both the attractive and repulsive forces. The attractive part of Zeff is just Z, the positive charge on the nucleus ‘pulling’ on the electron (i.e. the atomic number) The repulsive part, repulsion from the other electrons, is referred to as ‘shielding’. It gets this designation because an electron is ‘shielded’ from the pull of the positive nucleus by the repulsion of the other electrons. To provide shielding an electron must have its probability density closer to the nucleus than the outer electron (and thus partially neutralize the + nuclear charge). Thus Zeffective=+Z ‐(shielding of other electrons) [note the + sign for the attractive part and –sign for the repulsive part] MORE SHIELDING ï LOWER Zeff LESS SHIELDING ï HIGHER Zeff In terms of Zeff and the principal quantum number n of the outer electron, the ionization energy and size of an atom can be approximated as: 22 2 18ZZeff 18 eff 11 n EnZeff, 2.18 10 J22 and IE 2.18 10 J and ravg 5.28 10 m nn Zeff An approximate Zeff can be obtained empirically from experimental ionization energies: 12 nIE2 experimental Zeff 18 2.18 10 J The lecture will discuss: For 1‐electron atoms or ions [H, He+, Li2+, Be3+, etc.] there is no shielding and Zeff∫Z [Z=+1, +2, +3, +4, etc.] For He 1s2 the second electron (in the same 1s shell) provides 0.66 shielding [reduces the pull of the nucleus from Z= +2 to Zeffº1.34] For Li 1s22s each of the two 1s electrons provides 0.84 shielding for the outer 2s electron [the two reduce the pull of the nucleus from Z=+3 to Zeffº3‐2ä0.87=1.26.
    [Show full text]
  • AP Chemistry: 2017-18 Semester Review: Chapters 6 Thru 9, 11.2-11.3
    AP Chemistry: 2017-18 Semester Review: MULTIPLE CHOICE Section Chapters 6 thru 9, 11.2-11.3 Chp. 6 1) Which one of the following is correct? A) ν ÷ λ = c B) ν = cλ C) λ = c ν D) νλ = c E) ν + λ = c Page Ref: Sec. 6.1 2) In the Bohr model of the atom, _____. A) electrons travel in circular paths called orbitals B) electron paths are controlled by probability C) electrons can have any energy D) electron energies are quantized E) both A and C Page Ref: Sec. 6.3 3) Which one of the following is an incorrect orbital notation? A) 4dxy B) 3py C) 4s D) 2s E) 3f Page Ref: Sec. 6.5 4) Which electron configuration represents a violation of the Pauli exclusion principle? A) B) C) D) E) Page Ref: Sec. 6.8 1 5) The ground state electron configuration of Ga is __________. A) B) C) D) E) [Ar] Page Ref: Sec. 6.8 6) Which electron configuration represents a violation of Hund's rule for an atom in its ground state? A) B) C) D) E) Page Ref: Sec. 6.8 7) Which two elements have the same ground-state electron configuration? A) Pd and Pt B) Fe and Cu C) Cu and Ag D) Cl and Ar E) No two elements have the same ground-state electron configuration. Page Ref: Sec. 6.8 Chp. 7 1) In which set of elements would all members be expected to have very similar chemical properties? A) O, S, Se B) S, Se, Si C) N, O, F D) Ne, Na, Mg E) Na, Mg, K Page Ref: Sec.
    [Show full text]
  • Fritz London a Scientific Biography
    Fritz London a scientific biography Kostas Gavroglu University of Athens, Greece CAMBRIDGE UNIVERSITY PRESS Contents Preface page xni Acknowledgements xxi 1 From philosophy to physics 1 The years that left nothing unaffected 2 The appeal of ideas 5 Goethe as a scientist 7 How absolute is our knowledge? 8 Acquiring knowledge 10 London's teachers in philosophy: Alexander Pfander and Erich Becher 11 Husserl's teachings 12 Abhorrence of reductionist schemata 14 The philosophy thesis 15 Tolman's principle of similitude 23 The necessary clarifications 25 Work on quantum theory 26 Transformation theory 28 Unsuccessful attempts at unification 31 2 The years in Berlin and the beginnings of quantum chemistry 38 The mysterious bond 39 London in Zurich 42 Binding forces 44 The Pauli exclusion principle 48 [ix] X FRITZ LONDON The early years in Berlin 49 Reactions to the Heitler—London paper 51 Polyelectronic molecules and the application of group theory to problems of chemical valence 53 Chemists as physicists? 57 London's first contacts in Berlin 59 Marriage 61 Job offers 64 Intermolecular forces 66 The book which could not be written 69 Leningrad and Rome 71 Difficulties with group theory 74 Linus Pauling's resonance structures 75 Robert Mulliken's molecular orbitals 78 Trying to save what could not be saved 82 3 Oxford and superconductivity 96 The rise of the Nazis 97 The changes at the University 102 Going to Oxford 105 Lindemann, Simon and Heinz London 106 Electricity in the very cold 110 The end of old certainties 113 The thermodynamic treatment
    [Show full text]
  • From Physical Chemistry to Chemical Physics, 1913-1941
    International Workshop on the History of Chemistry 2015 Tokyo From Physical Chemistry to Chemical Physics, 1913-1941 Jeremiah James Ludwig-Maximillian University, Munich, Germany There has never been one unique name for the intersection of chemistry and physics. Nor has it ever been defined by a single, stable set of methods. Nevertheless, it is possible and arguably rewarding to distinguish changes in the constellation of terms and techniques that have defined the intersection over the years. I will speak today about one such change, the advent and ascendancy of chemical physics in the interwar period. When the young Friedrich Wilhelm Ostwald first began to formulate his campaign for “physical chemistry” in 1877, he used the term almost interchangeably with two others, “general chemistry” and “theoretical chemistry.” According to his vision of what would soon become a new chemical discipline, physical chemistry would investigate and formulate the general principles that underlie all chemical reactions and phenomena. The primary strategy that he and his allies used to generate these principles was to formulate mathematical “laws” or “rules” generalizing the results of numerous experiments, often performed using measuring apparatus borrowed from physics. Their main fields of inquiry were thermochemistry and solution theory, and they avoided and often openly maligned speculations regarding structures or mechanisms that might underlie the macroscopic regularities embodied in their laws.1 In the first decades of the 20th-century, the modern atomic theory was firmly established, and with only a slight delay, the methods of 19th-century physical chemistry lost a considerable proportion of their audience. Theories relying upon atomistic thinking began to reshape the disciplinary intersections of chemistry and physics, and by the end of the 1930s, cutting-edge research into the general principles of chemistry looked quite different than it had at the turn of the century.
    [Show full text]
  • Lanthanides.Pdf
    Lanthanides [A] LANTHANIDES : 4f block elements Definition: The f- block (inner transition) elements containing partially filled 4f-subshells are known as Lanthanides or Lanthanones because of their close similarities with element lanthanum (atomic no: 57). The fourteen elements from atomic no: 58 to 71 constitute lanthanides. Nos. Name Symbol Electronic configuration 0 1 2 1. Lanthanum La57 [Xe] 4f 5d 6s 2 0 2 2. Cerium Ce58 [Xe] 4f 5d 6s 3 0 2 3. Praseodymium Pr59 [Xe] 4f 5d 6s 4 0 2 4. Neodymium Nd60 [Xe] 4f 5d 6s 5 0 2 5. Promethium Pm61 [Xe]4f 5d 6s 6 0 2 6. Samarium Sm62 [Xe]4f 5d 6s 7 0 2 7. Europium Eu63 [Xe] 4f 5d 6s 7 1 2 8. Gadolinium Gd64 [Xe] 4f 5d 6s 9 0 2 9. Terbium Tb65 [Xe] 4f 5d 6s 10 0 2 10. Dysprosium Dy66 [Xe] 4f 5d 6s 11 0 2 11. Holmium Ho67 [Xe] 4f 5d 6s 12 0 2 12. Erbium Er68 [Xe] 4f 5d 6s 13 0 2 13. Thulium Tm69 [Xe] 4f 5d 6s 14 0 2 14. Ytterbium Yb70 [Xe] 4f 5d 6s 14 1 2 15. Lutetium Lu71 [Xe] 4f 5d 6s From the above electronic configuration it can be seen that at La 5d orbital is singly occupied but after La further filling of 5d orbital is discontinued. As the nuclear charge increases by one unit from La to Ce, 4f orbitals were higher in energy upto Lu, fall slightly below the 5d level 4f- orbitals, therefore begin to fill and are completely filled up to Lu, before filling of 5d orbital is resumed.
    [Show full text]
  • Theory and Experiment in the Quantum-Relativity Revolution
    Theory and Experiment in the Quantum-Relativity Revolution expanded version of lecture presented at American Physical Society meeting, 2/14/10 (Abraham Pais History of Physics Prize for 2009) by Stephen G. Brush* Abstract Does new scientific knowledge come from theory (whose predictions are confirmed by experiment) or from experiment (whose results are explained by theory)? Either can happen, depending on whether theory is ahead of experiment or experiment is ahead of theory at a particular time. In the first case, new theoretical hypotheses are made and their predictions are tested by experiments. But even when the predictions are successful, we can’t be sure that some other hypothesis might not have produced the same prediction. In the second case, as in a detective story, there are already enough facts, but several theories have failed to explain them. When a new hypothesis plausibly explains all of the facts, it may be quickly accepted before any further experiments are done. In the quantum-relativity revolution there are examples of both situations. Because of the two-stage development of both relativity (“special,” then “general”) and quantum theory (“old,” then “quantum mechanics”) in the period 1905-1930, we can make a double comparison of acceptance by prediction and by explanation. A curious anti- symmetry is revealed and discussed. _____________ *Distinguished University Professor (Emeritus) of the History of Science, University of Maryland. Home address: 108 Meadowlark Terrace, Glen Mills, PA 19342. Comments welcome. 1 “Science walks forward on two feet, namely theory and experiment. ... Sometimes it is only one foot which is put forward first, sometimes the other, but continuous progress is only made by the use of both – by theorizing and then testing, or by finding new relations in the process of experimenting and then bringing the theoretical foot up and pushing it on beyond, and so on in unending alterations.” Robert A.
    [Show full text]
  • Chapter 7 Periodic Properties of the Elements Learning Outcomes
    Chapter 7 Periodic Properties of the Elements Learning Outcomes: Explain the meaning of effective nuclear charge, Zeff, and how Zeff depends on nuclear charge and electron configuration. Predict the trends in atomic radii, ionic radii, ionization energy, and electron affinity by using the periodic table. Explain how the radius of an atom changes upon losing electrons to form a cation or gaining electrons to form an anion. Write the electron configurations of ions. Explain how the ionization energy changes as we remove successive electrons, and the jump in ionization energy that occurs when the ionization corresponds to removing a core electron. Explain how irregularities in the periodic trends for electron affinity can be related to electron configuration. Explain the differences in chemical and physical properties of metals and nonmetals, including the basicity of metal oxides and the acidity of nonmetal oxides. Correlate atomic properties, such as ionization energy, with electron configuration, and explain how these relate to the chemical reactivity and physical properties of the alkali and alkaline earth metals (groups 1A and 2A). Write balanced equations for the reactions of the group 1A and 2A metals with water, oxygen, hydrogen, and the halogens. List and explain the unique characteristics of hydrogen. Correlate the atomic properties (such as ionization energy, electron configuration, and electron affinity) of group 6A, 7A, and 8A elements with their chemical reactivity and physical properties. Development of Periodic Table •Dmitri Mendeleev and Lothar Meyer (~1869) independently came to the same conclusion about how elements should be grouped in the periodic table. •Henry Moseley (1913) developed the concept of atomic numbers (the number of protons in the nucleus of an atom) 1 Predictions and the Periodic Table Mendeleev, for instance, predicted the discovery of germanium (which he called eka-silicon) as an element with an atomic weight between that of zinc and arsenic, but with chemical properties similar to those of silicon.
    [Show full text]
  • The London Equations Aria Yom Abstract: the London Equations Were the First Successful Attempt at Characterizing the Electrodynamic Behavior of Superconductors
    The London Equations Aria Yom Abstract: The London Equations were the first successful attempt at characterizing the electrodynamic behavior of superconductors. In this paper we review the motivation, derivation, and modification of the London equations since 1935. We also mention further developments by Pippard and others. The shaping influences of experiments on theory are investigated. Introduction: Following the discovery of superconductivity in supercooled mercury by Heike Onnes in 1911, and its subsequent discovery in various other metals, the early pioneers of condensed matter physics were faced with a mystery which continues to be unraveled today. Early experiments showed that below a critical temperature, a conventional conductor could abruptly transition into a superconducting state, wherein currents seemed to flow without resistance. This motivated a simple model of a superconductor as one in which charges were influenced only by the Lorentz force from an external field, and not by any dissipative interactions. This would lead to the following equation: 푚 푑퐽 = 퐸 (1) 푛푒2 푑푡 Where m, e, and n are the mass, charge, and density of the charge carriers, commonly taken to be electrons at the time this equation was being considered. In the following we combine these variables into a new constant both for convenience and because the mass, charge, and density of the charge carriers are often subtle concepts. 푚 Λ = 푛푒2 This equation, however, seems to imply that the crystal lattice which supports superconductivity is somehow invisible to the superconducting charges themselves. Further, to suggest that the charges flow without friction implies, as the Londons put it, “a premature theory.” Instead, the Londons desired a theory more in line with what Gorter and Casimir had conceived [3], whereby a persistent current is spontaneously generated to minimize the free energy of the system.
    [Show full text]
  • The Original Remark of Fritz London in 1938 ' Linking the Phenomenon of Superfluidity in He II with Boee-Einetein Con
    IC/65A63 INTERNAL REPORT (Limited distribution) The original remark of Fritz London in 1938 ' linking the phenomenon of superfluidity in He II with Boee-Einetein con- •-International Atomic Energy Agency densation ( BEC ) has inspired a great deal of theory and ana experiment. On the other hand, the excitation spectrum was put I '!:-f. .Uni,ted^.Kati>ifis Educational Scientific and Cultural Organization on a solid microscopic basis by the remarkable variational 2 INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS calculation of Peynman and Cohen ( PC ), which connected the excitation Bpectrum with the dynamic structure factor obtained from inelastic neutron acatteringt and at the same BIOPHYSICS AND THE MICROSCOPIC THEORY OF He II * time pointed out the relevance of backflow. In spite of the importance of the FC variational calculation, which was later J. Chela-Florea ** improved upon by the Monte Carlo calculation of the excitation International Centre for Theoretical Physics, Trieste, Italy spectrum of He II, a few questions remain unanswered. Chief among these are: and (a) What ie the microscopic nature of He II? In particular, H.B. Ghassit what is the nature of the roton? Department of Physics, University of Jordan, Amman, Jordan (b) Are there any new excitations contributing to the disper- and International Centre for Theoretical Physics, Trieste, Italy sion relation? (c) How good is the PC wave function? (d) What is the connection between BEC and superfluidity? ABSTRACT The difficulty in obtaining completely satisfactory ans- Bose-Einstein condensation and solitonic propagation have recently wers to the above questions lieB partly in two experimental teen uhovn to be intimately related in "biosysteras.
    [Show full text]