DOCSLIB.ORG

Multiplets, XMCD

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Multiplets, XMCD the united nations educational, scientific abdus salam and cultural organization international centre for theoretical physics international atomic energy agency SCHOOL ON SYNCHROTRON RADIATION AND APPLICATIONS In memory of J.C. Fuggle & L. Fonda 19 April - 21 May 2004 Miramare - Trieste, Italy 1561/21 ____________________________________________________________ Multiplets, XMCD F. De Groot strada costiera, 11 - 34014 trieste italy - tel. +39 040 2240111 fax +39 040 224163 - [email protected] - www.ictp.trieste.it Multiplets in X-ray Spectroscopy lectures ICTP 2004, by Frank de Groot 1. X-RAYS ................................................................................................................................................ 2 1.1. INTERACTION OF X-RAYS WITH MATTER ....................................................................................... 3 1.1.1 X-ray absorption spectroscopy ................................................................................................ 6 1.1.2 Basics of XAFS Spectroscopy ................................................................................................11 1.2. THE ELECTRONIC STRUCTURE OF SOLIDS ................................................................................... 13 1.2.1. Orbitals in One dimension..................................................................................................... 13 1.2.2. Bloch Functions, Band Structures and k................................................................................ 14 1.2.3. Electronic states in two dimensions.......................................................................................17 1.2.4. Density of States .................................................................................................................... 23 1.2.5. Density Functional Theory and the local spin density approximation ................................. 24 1.3. XANES....................................................................................................................................... 26 1.3.1. Many Body Effects in the ground state .................................................................................. 28 1.3.2 Core hole effects .................................................................................................................... 28 1.3.3. Multiplet effects ..................................................................................................................... 29 1.3.4. The influence of the Matrix element ...................................................................................... 29 1.3.5. Calculations over a large energy range ................................................................................ 29 1.3.6. Approximations in the potential............................................................................................. 30 1.3.7. Real Space versus Reciprocal space calculations ................................................................. 30 1.4. XANES SPECTRAL SHAPE ANALYSIS .......................................................................................... 31 1.4.1. The energy position of X-ray absorption edges ..................................................................... 32 1.4.2. The intensity of the white line ................................................................................................ 35 1.4.3. Peaks at higher energies in the XANES region ..................................................................... 36 1.4.4. The pre-edge region............................................................................................................... 36 2. MULTIPLET EFFECTS................................................................................................................... 38 2.1. WHY IS MULTIPLET THEORY NEEDED? ........................................................................................ 38 2.2. ATOMIC MULTIPLETS.................................................................................................................. 41 2.2.1. Term symbols......................................................................................................................... 41 2.2.2. Matrix elements ..................................................................................................................... 45 2.3. ATOMIC MULTIPLET GROUND STATES OF 3DN SYSTEMS ............................................................... 47 2.3.1. jj coupling.............................................................................................................................. 48 2.4. X-RAY ABSORPTION SPECTRA DESCRIBED WITH ATOMIC MULTIPLETS. ..................................... 49 2.4.1. 2p XAS of 3d transition metals ..............................................................................................49 2.4.2. 3d XAS of rare earths ............................................................................................................ 55 2.4.3. 1s XAS of 3d trnition metls: the pre-edge ............................................................................. 61 3. CRYSTAL FIELD THEORY........................................................................................................... 62 3.1. A SHORT OUTLINE OF GROUP THEORY........................................................................................ 62 3.1.1. Total Symmetry and Multiplication Tables............................................................................ 62 3.2. THE CRYSTAL FIELD MULTIPLET HAMILTONIAN ........................................................................ 63 3.3. CUBIC CRYSTAL FIELDS............................................................................................................... 64 3.3.1. The definitions of the Crystal Field parameters .................................................................... 67 N 3.4. THE ENERGIES OF THE 3D CONFIGURATIONS.............................................................................. 68 3.4.1. The effect of the 3d spin-orbit coupling ................................................................................. 72 3.4.2. The effects on the x-ray absorption calculations ................................................................... 75 3.4.3. 3d0 systems in octahedral symmetry....................................................................................... 76 3.4.4. X-ray absorption spectra of 3dN systems ............................................................................... 82 4. CHARGE TRANSFER EFFECTS................................................................................................... 84 4.1. INITIAL STATE EFFECTS .............................................................................................................. 84 4.2. FINAL STATE EFFECTS ................................................................................................................. 89 4.3. THE X-RAY ABSORPTION SPECTRUM WITH CHARGE TRANSFER EFFECTS...................................... 90 1 Multiplets in X-ray Spectroscopy lectures ICTP 2004, by Frank de Groot 1. X-rays X-rays are defined as the electromagnetic radiation with a wavelength between Ultraviolet radiation and gamma radiation. The border between Ultraviolet radiation and X-rays is not clearly defined but usually set around 10-8meter, i.e. 10 nm. The upper limit of x-rays is usually set at 10-12 meter, i.e. 1 pm, although radiation with an energy above 10-11 meter is also called gamma radiation, in particular if it is created with a radioactive element. X- rays are sub-divided into soft x-rays, between 10 nm and 100 pm and hard x-rays between 100 pm and 1 pm. Soft x-rays are called 'soft' because they do not penetrate air and as such are relatively safe to work with. We will discuss the penetration length of x-rays below. Because of historical reasons, x-rays are often given in Angstroms, where 1 Å equals 10-10 meter or 100 pm. The bottom two axes in the figure give the frequency and the energy of the electromagnetic radiation, using the inverse proportionality between frequency and wavelength , i.e. =c/ , where c is the speed of light 3·108 m/s. This yields x-ray frequencies between 1016 and 1021 Hertz. It is more common to indicate x-rays with their energies E, using E=h , with the energy given in electron volts (eV) or kilo electron volts (keV), where they range between 100 eV and 106 eV. Calculate the energy in electron volt for a x-ray with 1 Å wavelength. Use: E= h = hc/ , with c=3·108 m/s, h=6.6·10-34 and 1 eV = 1.6·10-19 J E (1 Å)= 6.6·10-34 3·108 / 10-10 = 2·10-15 J /1.6·10-19 = 1.2·104 eV=12.4 keV It can be checked in the figure that a wavelength of 10-10meter corresponds to energy slightly above 104 eV. The wavelength of x-rays are of the same size as molecules, which range from 100 pm for small molecule such as water to 10 nm for macromolecules such as enzymes. In particular the distance of 1 Å is important in matter, because it corresponds to a typical interatomic distance. This makes diffraction with x-rays of approximately 1 Å an important technique to determine the interatomic distances and, in general, the structure of matter. X-rays are traditionally produced using x-ray tubes. In a x-ray tube, electrons are accelerated between the anode and the cathode. When they hit the cathode with high energy, they are decelerated through inelastic collisions with atoms in the target material. If the energy of the electrons is high enough this produces a continuous spectrum of
Load more

Recommended publications
  • MODERN DEVELOPMENT of MAGNETIC RESONANCE Abstracts 2020 KAZAN * RUSSIA
    MODERN DEVELOPMENT OF MAGNETIC RESONANCE abstracts 2020 KAZAN * RUSSIA OF MA NT GN E E M T P IC O L R E E V S E O N D A N N R C E E D O M K 20 AZAN 20 MODERN DEVELOPMENT OF MAGNETIC RESONANCE ABSTRACTS OF THE INTERNATIONAL CONFERENCE AND WORKSHOP “DIAMOND-BASED QUANTUM SYSTEMS FOR SENSING AND QUANTUM INFORMATION” Editors: ALEXEY A. KALACHEV KEV M. SALIKHOV KAZAN, SEPTEMBER 28–OCTOBER 2, 2020 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machines or similar means, and storage in data banks. © 2020 Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, Kazan © 2020 Igor A. Aksenov, graphic design Printed in Russian Federation Published by Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, Kazan www.kfti.knc.ru v CHAIRMEN Alexey A. Kalachev Kev M. Salikhov PROGRAM COMMITTEE Kev Salikhov, chairman (Russia) Vadim Atsarkin (Russia) Elena Bagryanskaya (Russia) Pavel Baranov (Russia) Marina Bennati (Germany) Robert Bittl (Germany) Bernhard Blümich (Germany) Michael Bowman (USA) Gerd Buntkowsky (Germany) Sergei Demishev (Russia) Sabine Van Doorslaer (Belgium) Rushana Eremina (Russia) Jack Freed (USA) Philip Hemmer (USA) Konstantin Ivanov (Russia) Alexey Kalachev (Russia) Vladislav Kataev (Germany) Walter Kockenberger (Great Britain) Wolfgang Lubitz (Germany) Anders Lund (Sweden) Sergei Nikitin (Russia) Klaus Möbius (Germany) Hitoshi Ohta (Japan) Igor Ovchinnikov (Russia) Vladimir Skirda (Russia) Alexander Smirnov( Russia) Graham Smith (Great Britain) Mark Smith (Great Britain) Murat Tagirov (Russia) Takeji Takui (Japan) Valery Tarasov (Russia) Violeta Voronkova (Russia) vi LOCAL ORGANIZING COMMITTEE Kalachev A.A., chairman Kupriyanova O.O.
    [Show full text]
  • 4 Muon Capture on the Deuteron 7 4.1 Theoretical Framework
    February 8, 2008 Muon Capture on the Deuteron The MuSun Experiment MuSun Collaboration model-independent connection via EFT http://www.npl.uiuc.edu/exp/musun V.A. Andreeva, R.M. Careye, V.A. Ganzhaa, A. Gardestigh, T. Gorringed, F.E. Grayg, D.W. Hertzogb, M. Hildebrandtc, P. Kammelb, B. Kiburgb, S. Knaackb, P.A. Kravtsova, A.G. Krivshicha, K. Kuboderah, B. Laussc, M. Levchenkoa, K.R. Lynche, E.M. Maeva, O.E. Maeva, F. Mulhauserb, F. Myhrerh, C. Petitjeanc, G.E. Petrova, R. Prieelsf , G.N. Schapkina, G.G. Semenchuka, M.A. Sorokaa, V. Tishchenkod, A.A. Vasilyeva, A.A. Vorobyova, M.E. Vznuzdaeva, P. Winterb aPetersburg Nuclear Physics Institute, Gatchina 188350, Russia bUniversity of Illinois at Urbana-Champaign, Urbana, IL 61801, USA cPaul Scherrer Institute, CH-5232 Villigen PSI, Switzerland dUniversity of Kentucky, Lexington, KY 40506, USA eBoston University, Boston, MA 02215, USA f Universit´eCatholique de Louvain, B-1348 Louvain-la-Neuve, Belgium gRegis University, Denver, CO 80221, USA hUniversity of South Carolina, Columbia, SC 29208, USA Co-spokespersons underlined. 1 Abstract: We propose to measure the rate Λd for muon capture on the deuteron to better than 1.5% precision. This process is the simplest weak interaction process on a nucleus that can both be calculated and measured to a high degree of precision. The measurement will provide a benchmark result, far more precise than any current experimental information on weak interaction processes in the two-nucleon system. Moreover, it can impact our understanding of fundamental reactions of astrophysical interest, like solar pp fusion and the ν + d reactions observed by the Sudbury Neutrino Observatory.
    [Show full text]
  • 7. Examples of Magnetic Energy Diagrams. P.1. April 16, 2002 7
    7. Examples of Magnetic Energy Diagrams. There are several very important cases of electron spin magnetic energy diagrams to examine in detail, because they appear repeatedly in many photochemical systems. The fundamental magnetic energy diagrams are those for a single electron spin at zero and high field and two correlated electron spins at zero and high field. The word correlated will be defined more precisely later, but for now we use it in the sense that the electron spins are correlated by electron exchange interactions and are thereby required to maintain a strict phase relationship. Under these circumstances, the terms singlet and triplet are meaningful in discussing magnetic resonance and chemical reactivity. From these fundamental cases the magnetic energy diagram for coupling of a single electron spin with a nuclear spin (we shall consider only couplings with nuclei with spin 1/2) at zero and high field and the coupling of two correlated electron spins with a nuclear spin are readily derived and extended to the more complicated (and more realistic) cases of couplings of electron spins to more than one nucleus or to magnetic moments generated from other sources (spin orbit coupling, spin lattice coupling, spin photon coupling, etc.). Magentic Energy Diagram for A Single Electron Spin and Two Coupled Electron Spins. Zero Field. Figure 14 displays the magnetic energy level diagram for the two fundamental cases of : (1) a single electron spin, a doublet or D state and (2) two correlated electron spins, which may be a triplet, T, or singlet, S state. In zero field (ignoring the electron exchange interaction and only considering the magnetic interactions) all of the magnetic energy levels are degenerate because there is no preferred orientation of the angular momentum and therefore no preferred orientation of the magnetic moment due to spin.
    [Show full text]
  • Andreev Bound States in the Kondo Quantum Dots Coupled to Superconducting Leads
    IOP PUBLISHING JOURNAL OF PHYSICS: CONDENSED MATTER J. Phys.: Condens. Matter 20 (2008) 415225 (6pp) doi:10.1088/0953-8984/20/41/415225 Andreev bound states in the Kondo quantum dots coupled to superconducting leads Jong Soo Lim and Mahn-Soo Choi Department of Physics, Korea University, Seoul 136-713, Korea E-mail: [email protected] Received 26 May 2008, in final form 4 August 2008 Published 22 September 2008 Online at stacks.iop.org/JPhysCM/20/415225 Abstract We have studied the Kondo quantum dot coupled to two superconducting leads and investigated the subgap Andreev states using the NRG method. Contrary to the recent NCA results (Clerk and Ambegaokar 2000 Phys. Rev. B 61 9109; Sellier et al 2005 Phys. Rev. B 72 174502), we observe Andreev states both below and above the Fermi level. (Some figures in this article are in colour only in the electronic version) 1. Introduction Using the non-crossing approximation (NCA), Clerk and Ambegaokar [8] investigated the close relation between the 0– When a localized spin (in an impurity or a quantum dot) is π transition in IS(φ) and the Andreev states. They found that coupled to BCS-type s-wave superconductors [1], two strong there is only one subgap Andreev state and that the Andreev correlation effects compete with each other. On the one hand, state is located below (above) the Fermi energy EF in the the superconductivity tends to keep the conduction electrons doublet (singlet) state. They provided an intuitively appealing in singlet pairs [1], leaving the local spin unscreened.
    [Show full text]
  • Isotopic Fractionation of Carbon, Deuterium, and Nitrogen: a Full Chemical Study?
    A&A 576, A99 (2015) Astronomy DOI: 10.1051/0004-6361/201425113 & c ESO 2015 Astrophysics Isotopic fractionation of carbon, deuterium, and nitrogen: a full chemical study? E. Roueff1;2, J. C. Loison3, and K. M. Hickson3 1 LERMA, Observatoire de Paris, PSL Research University, CNRS, UMR8112, Place Janssen, 92190 Meudon Cedex, France e-mail: [email protected] 2 Sorbonne Universités, UPMC Univ. Paris 6, 4 Place Jussieu, 75005 Paris, France 3 ISM, Université de Bordeaux – CNRS, UMR 5255, 351 cours de la Libération, 33405 Talence Cedex, France e-mail: [email protected] Received 6 October 2014 / Accepted 5 January 2015 ABSTRACT Context. The increased sensitivity and high spectral resolution of millimeter telescopes allow the detection of an increasing number of isotopically substituted molecules in the interstellar medium. The 14N/15N ratio is difficult to measure directly for molecules con- taining carbon. Aims. Using a time-dependent gas-phase chemical model, we check the underlying hypothesis that the 13C/12C ratio of nitriles and isonitriles is equal to the elemental value. Methods. We built a chemical network that contains D, 13C, and 15N molecular species after a careful check of the possible fraction- ation reactions at work in the gas phase. Results. Model results obtained for two different physical conditions that correspond to a moderately dense cloud in an early evolu- tionary stage and a dense, depleted prestellar core tend to show that ammonia and its singly deuterated form are somewhat enriched 15 14 15 + in N, which agrees with observations. The N/ N ratio in N2H is found to be close to the elemental value, in contrast to previous 15 + models that obtain a significant enrichment, because we found that the fractionation reaction between N and N2H has a barrier in + 15 + + 15 + the entrance channel.
    [Show full text]
  • 7 2 Singleionanisotropy
    7.2 Dipolar Interactions and Single Ion Anisotropy in Metal Ions Up to this point, we have been making two assumptions about the spin carriers in our molecules: 1. There is no coupling between the 2S+1Γ ground state and some excited state(s) arising from the same free-ion state through the spin-orbit coupling. 2. The 2S+1Γ ground state has no first-order angular momentum. Now, let’s look at how to treat molecules for which the first assumption is not true. In other words, molecules in which we can no longer neglect the coupling between the ground state and some excited state(s) arising from the same free-ion state through spin orbit coupling. For simplicity, we will assume that there is no exchange coupling between magnetic centers, so we are dealing with an isolated molecule with, for example, one paramagnetic metal ion. Recall: Lˆ lˆ is the total electronic orbital momentum operator = ∑ i i Sˆ sˆ is the total electronic spin momentum operator = ∑ i i where the sums run over the electrons of the open shells. *NOTE*: The excited states are assumed to be high enough in energy to be totally depopulated in the temperature range of interest. • This spin-orbit coupling between ground and unpopulated excited states may lead to two phenomena: 1. anisotropy of the g-factor 2. and, if the ground state has a larger spin multiplicity than a doublet (i.e., S > ½), zero-field splitting of the ground state energy levels. • Note that this spin-orbit coupling between the ground state and an unpopulated excited state can be described by λLˆ ⋅ Sˆ .
    [Show full text]
  • Robust Coherent Control of Solid-State Spin Qubits Using Anti-Stokes Excitation
    ARTICLE https://doi.org/10.1038/s41467-021-23471-8 OPEN Robust coherent control of solid-state spin qubits using anti-Stokes excitation Jun-Feng Wang 1,2, Fei-Fei Yan1,2, Qiang Li1,2, Zheng-Hao Liu 1,2, Jin-Ming Cui1,2, Zhao-Di Liu1,2, ✉ ✉ ✉ Adam Gali 3,4 , Jin-Shi Xu 1,2 , Chuan-Feng Li 1,2 & Guang-Can Guo1,2 Optically addressable solid-state color center spin qubits have become important platforms for quantum information processing, quantum networks and quantum sensing. The readout 1234567890():,; of color center spin states with optically detected magnetic resonance (ODMR) technology is traditionally based on Stokes excitation, where the energy of the exciting laser is higher than that of the emission photons. Here, we investigate an unconventional approach using anti- Stokes excitation to detect the ODMR signal of silicon vacancy defect spin in silicon carbide, where the exciting laser has lower energy than the emitted photons. Laser power, microwave power and temperature dependence of the anti-Stokes excited ODMR are systematically studied, in which the behavior of ODMR contrast and linewidth is shown to be similar to that of Stokes excitation. However, the ODMR contrast is several times that of the Stokes exci- tation. Coherent control of silicon vacancy spin under anti-Stokes excitation is then realized at room temperature. The spin coherence properties are the same as those of Stokes excitation, but with a signal contrast that is around three times greater. To illustrate the enhanced spin readout contrast under anti-Stokes excitation, we also provide a theoretical model.
    [Show full text]
  • The Nuclear Physics of Muon Capture
    Physics Reports 354 (2001) 243–409 The nuclear physics of muon capture D.F. Measday ∗ University of British Columbia, 6224 Agricultural Rd., Vancouver, BC, Canada V6T 1Z1 Received December 2000; editor: G:E: Brown Contents 4.8. Charged particles 330 4.9. Fission 335 1. Introduction 245 5. -ray studies 343 1.1. Prologue 245 5.1. Introduction 343 1.2. General introduction 245 5.2. Silicon-28 350 1.3. Previous reviews 247 5.3. Lithium, beryllium and boron 360 2. Fundamental concepts 248 5.4. Carbon, nitrogen and oxygen 363 2.1. Properties of the muon and neutrino 248 5.5. Fluorine and neon 372 2.2. Weak interactions 253 5.6. Sodium, magnesium, aluminium, 372 3. Muonic atom 264 phosphorus 3.1. Atomic capture 264 5.7. Sulphur, chlorine, and potassium 377 3.2. Muonic cascade 269 5.8. Calcium 379 3.3. Hyperÿne transition 275 5.9. Heavy elements 383 4. Muon capture in nuclei 281 6. Other topics 387 4.1. Hydrogen 282 6.1. Radiative muon capture 387 4.2. Deuterium and tritium 284 6.2. Summary of g determinations 391 4.3. Helium-3 290 P 6.3. The (; e±) reaction 393 4.4. Helium-4 294 7. Summary 395 4.5. Total capture rate 294 Acknowledgements 396 4.6. General features in nuclei 300 References 397 4.7. Neutron production 311 ∗ Tel.: +1-604-822-5098; fax: +1-604-822-5098. E-mail address: [email protected] (D.F. Measday). 0370-1573/01/$ - see front matter c 2001 Published by Elsevier Science B.V.
    [Show full text]
  • Nuclear Magnetic Resonance Studies on Ethylene and Trimethylene Sulfites and Related Compounds
    r \/ NUCLEAR MAGNETIC RESONANCE STUDIES ON ETHYLENE AND TRIMETHYLENE SULFITES AND RELATED COMPOUNDS Per Albriktsen Department of Chemistry University of Bergen, 1977 UNI VERS I T E TE T I BERGEN Vf.' NUCLEAR MAGNETIC RESONANCE STUDIES ON ETHYLENE AND TRIMETHYLENE SULFITES AND RELATED COMPOUNDS Per Albriktsen With due permission of the Senate of the University of Bergen to be publicly discussed on 26. May 1978 for the degree of Doctor philosophiae BERGEN 1978 NUCLEAR MAGNETIC RESONANCE STUDIES ON ETHYLENE AND TRIMETHYLENE SULFITES AND RELATED COMPOUNDS. Per Albriktsen Department of Chemistry University of Bergen, 1977 ACKNOWLEDGEMENT The author is indebted to Professor J. Dale, University of Oslo, Dr. R. K. Harris, University of East Anglia, England and to JEOL (UK) for the oportunity to use NMR instruments in their laboratories. Financial supports from the J. Meltzers H0yskolefond and Rafinor A/S & Co. are also gratefully acknowledged. Lindas, October 1977 Per Albriktsen CONTENTS 1. INTRODUCTION 1 2. THEORY OF NMR SPECTRA 6 2.1. Spin notations 6 2.2. Analysis of the NMR spectrum 7 2.3. Analysis of the observed spectra 9 2.4. Computer analysis 15 3. THE INTERPRETATION OF SPECTRAL PARAMETERS 18 3.1. Proton chemical shifts in trimethylene sulfites 18 3.2. 13C chemical shift 23 3.3. Proton chemical shifts in five membered sulf ites 25 3.4. Lanthanide induced chemical shifts (LIS) 26 3.5. ASIS in trimethylene sulf ites 29 4. COUPLING CONSTANTS 33 4.1. Geminal proton-proton coupling constants 33 4.1.1. Trimethylene sulfites 34 4.1.2. Five membered ring compounds 35 4.2.
    [Show full text]
  • Modern Development of Magnetic Resonance 2018
    MODERN DEVELOPMENT OF MAGNETIC RESONANCE program 2018 KAZAN * RUSSIA OF MA NT GN E E M T P IC O L R E E V S E O N D A N N R C E E D O M K 18 AZAN 20 MODERN DEVELOPMENT OF MAGNETIC RESONANCE PROGRAM OF THE INTERNATIONAL CONFERENCE KAZAN, SEPTEMBER 24–28, 2018 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, re- production by photocopying machines or similar means, and storage in data banks. © 2018 Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, Kazan © 2018 Igor A. Aksenov, graphic design Printed in Russian Federation Published by Zavoisky Physical-Technical Institute, FRC Kazan Scientific Center of RAS, Kazan www.kfti.knc.ru 5 CHAIRMEn Alexey A. Kalachev Kev M. Salikhov PRogram Committee Kev Salikhov, chairman (Russia) Albert Aganov (Russia) Vadim Atsarkin (Russia) Pavel Baranov (Russia) Marina Bennati (Germany) Bernhard Blümich (Germany) Michael Bowman (USA) Sabine Van Doorslaer (Belgium) Rushana Eremina (Russia) Jack Freed (USA) Ilgiz Garifullin (Russia) Alexey Kalachev (Russia) Walter Kockenberger (Great Britain) Wolfgang Lubitz (Germany) Klaus Möbius (Germany) Hitoshi Ohta (Japan) Igor Ovchinnikov (Russia) Vladimir Skirda (Russia) Murat Tagirov (Russia) Takeji Takui (Japan) Valery Tarasov (Russia) Yurii Tsvetkov (Russia) Violeta Voronkova (Russia) 6 Modern Development of Magnetic Resonance Local OrgAnIzIng Committee Kalachev A.A., chairman Kupriyanova O.O. Mamin R.F., vice-chairman Kurkina N.G. Voronkova V.K., scientific secretary Latypov V.A. Akhmin S.M. Mosina L.V.
    [Show full text]
  • Dissertation Spin Multiplets: Theory and Application
    DISSERTATION SPIN MULTIPLETS: THEORY AND APPLICATION Submitted by Jacob M. Nite Department of Chemistry In partial fulfillment of the requirements For the Degree of Doctor of Philosophy Colorado State University Fort Collins, Colorado Spring 2018 Doctoral Committee: Advisor: Anthony K. Rappé Matthew Shores Yian Shi Siu Au Lee Copyright by Jacob Matthew Nite 2018 All Rights Reserved ABSTRACT SPIN MULTIPLETS: THEORY AND APPLICATION Transition metal complexes have seen an increased use as photocatalysts for organic reactions in recent literature, mostly involving the Ru(II)(bpy)3 family of catalysts. Due to the rarity of ruthenium in the Earth’s crust, alternative catalysts using Earth abundant materials are desirable. Recent literature has shown that chromium based catalysts show great promise as a replacement for ruthenium for some reactions. The mechanisms of these first-row transition metal complexes are significantly more complex than those of the second and third row. The excited state complexities of first- row transition metal complexes are challenges for both experimental and theoretical research. The complexities of the excited states require theoretical methods beyond the standard single reference methods commonly used in the literature. Through the use of recent multi-reference post Hartree Fock (HF) methods as well as a new multi-reference density functional theory (DFT), insights into the character of chromium-based photocatalysts were examined. A new multi-determinant DFT method named few-determinant density functional theory (FD-DFT) was described. FD-DFT incorporates multiple DFT determinants using a finite difference approach to calculate the exchanges between multiple determinants for open shell multiplets. The method is implemented in a generalized bond valence (GVB) wave function, and can be converged through an SCF procedure.
    [Show full text]
  • Arxiv:1808.09798V2 [Physics.Gen-Ph] 29 Apr 2020 Notehgsfrinculns H Parameter the Couplings
    Feynman-Stueckelberg electroweak interactions and isospin entanglement A. F. Bennett∗ College of Earth, Ocean and Atmospheric Sciences Oregon State University 104 CEOAS Administration Building Corvallis, OR 97331-5503, USA (Dated: April 30, 2020) Entanglement in Quantum Field Theory is restricted to spacelike separations to the order of the Compton wavelength ~/mc (e.g., S. J. Summers and R. Werner, J. Math. Phys., 28, 10,2440- 2447, (1987)). Yet spin entanglement of electrons across macroscopic distances has been observed by Hensen et al. (Nature, 526, doi:10.1038/nature/15759, (2015)). The parametrized relativistic quantum mechanics of Feynman and Stueckelberg admits spin singlets, across arbitrary separations, by providing a single covariant wave equation for tensor products of two Dirac spinors (A. F. Bennett, Ann. Phys. 345, 1-16 (2014)). The formalism is extended here from quantum electrodynamics to the electroweak interaction. A relativistic Bell’s inequality for Dirac spinors is extended here to weak isospin. INTRODUCTION The gauge bosons Wµ(x),Bµ(x) and the Higgs field Φ(x) are classical fields, all of which are independent of τ . Their Lagrange densities (x) and (x) are identical The parametrized relativistic quantum mechanics LG LHG (hereafter PM) of R. Feynman [1] and C. Stueckelberg to those of the SM. See [10, p60]. The notation therein [2] can with one exception represent every phenomenon is conventional and is closely followed here. For example, the Higgs self-interaction in is of Quantum Electrodynamics [3–6]. The sole exception LHG is anti-bunching in quantum optics at very low inten- V (Φ) = µ2Φ†Φ+ λ(Φ†Φ)2 .
    [Show full text]