DOCSLIB.ORG

Chemical Shift (Δ)

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Chemical Shift (Δ) Chapter 9 ● Nuclear Magnetic Resonance Ch. 9 - 1 1. Introduction Classic methods for organic structure determination ● Boiling point ● Refractive index ● Solubility tests ● Functional group tests ● Derivative preparation ● Sodium fusion (to identify N, Cl, Br, I & S) ● Mixture melting point ● Combustion analysis ● Degradation Ch. 9 - 2 Classic methods for organic structure determination ● Require large quantities of sample and are time consuming Ch. 9 - 3 Spectroscopic methods for organic structure determination a) Mass Spectroscopy (MS) ● Molecular Mass & characteristic fragmentation pattern b) Infrared Spectroscopy (IR) ● Characteristic functional groups c) Ultraviolet Spectroscopy (UV) ● Characteristic chromophore d) Nuclear Magnetic Resonance (NMR) Ch. 9 - 4 Spectroscopic methods for organic structure determination ● Combination of these spectroscopic techniques provides a rapid, accurate and powerful tool for Identification and Structure Elucidation of organic compounds ● Rapid ● Effective in mg and microgram quantities Ch. 9 - 5 General steps for structure elucidation 1. Elemental analysis ● Empirical formula ● e.g. C2H4O 2. Mass spectroscopy ● Molecular weight ● Molecular formula ● e.g. C4H8O2, C6H12O3 … etc. ● Characteristic fragmentation pattern for certain functional groups Ch. 9 - 6 General steps for structure elucidation 3. From molecular formula ● Double bond equivalent (DBE) 4. Infrared spectroscopy (IR) ● Identify some specific functional groups ● e.g. C=O, C–O, O–H, COOH, NH2 … etc. Ch. 9 - 7 General steps for structure elucidation 5. UV ● Sometimes useful especially for conjugated systems ● e.g. dienes, aromatics, enones 6. 1H, 13C NMR and other advanced NMR techniques ● Full structure determination Ch. 9 - 8 Electromagnetic spectrum cosmic X-rays ultraviolet visible infrared micro- radio- & γ-rays wave wave λ: 0.1nm 200nm 400nm 800nm 50µm IR X-Ray UV NMR Crystallography 1Å = 10-10m 1nm = 10-9m 1µm = 10-6m Ch. 9 - 9 2. Nuclear Magnetic Resonance (NMR) Spectroscopy A graph that shows the characteristic energy absorption frequencies and intensities for a sample in a magnetic field is called a nuclear magnetic resonance (NMR) spectrum Ch. 9 - 10 Ch. 9 - 11 1. The number of signals in the spectrum tells us how many different sets of protons there are in the molecule 2. The position of the signals in the spectrum along the x-axis tells us about the magnetic environment of each set of protons arising largely from the electron density in their environment Ch. 9 - 12 3. The area under the signal tells us about how many protons there are in the set being measured 4. The multiplicity (or splitting pattern) of each signal tells us about the number of protons on atoms adjacent to the one whose signal is being measured Ch. 9 - 13 Typical 1H NMR spectrum ● Chemical Shift (δ) ● Integration (areas of peaks ⇒ no. of H) ● Multiplicity (spin-spin splitting) and coupling constant Ch. 9 - 14 Typical 1H NMR spectrum 1 Record as: H NMR (300 MHz, CDCl3): δ 4.35 (2H, t, J = 7.2 Hz, Hc) 2.05 (2H, sextet, J = 7.2 Hz, Hb) 1.02 (3H, t, J = 7.2 Hz, Ha) chemical coupling shift (δ) no. of H constant in ppm (integration) multiplicity in Hz Ch. 9 - 15 2A. Chemical Shift The position of a signal along the x-axis of an NMR spectrum is called its chemical shift The chemical shift of each signal gives information about the structural environment of the nuclei producing that signal Counting the number of signals in a 1H NMR spectrum indicates, at a first approximation, the number of distinct proton environments in a molecule Ch. 9 - 16 Ch. 9 - 17 Ch. 9 - 18 Normal range of 1H NMR "upfield" (more shielded) "downfield" (deshielded) 15 -10 (low field δ ppm (high field strength) strength) Ch. 9 - 19 Reference compound Me ● TMS = tetramethylsilane Me Si Me Me as a reference standard (0 ppm) ● Reasons for the choice of TMS as reference Resonance position at higher field than other organic compounds Unreactive and stable, not toxic Volatile and easily removed o (B.P. = 28 C) Ch. 9 - 20 NMR solvent ● Normal NMR solvents should not contain hydrogen ● Common solvents CDCl3 C6D6 CD3OD CD3COCD3 (d6-acetone) Ch. 9 - 21 The 300-MHz 1H NMR spectrum of 1,4-dimethylbenzene Ch. 9 - 22 2B. Integration of Signal Areas Integral Step Heights The area under each signal in a 1H NMR spectrum is proportional to the number of hydrogen atoms producing that signal It is signal area (integration), not signal height, that gives information about the number of hydrogen atoms Ch. 9 - 23 Ha Ha Hb R O Hb b H 3 Hb 2 Ha Hb Ha Ch. 9 - 24 2C. Coupling (Signal Splitting) Coupling is caused by the magnetic effect of nonequivalent hydrogen atoms that are within 2 or 3 bonds of the hydrogens producing the signal The n+1 rule ● Rule of Multiplicity: If a proton (or a set of magnetically equivalent nuclei) has n neighbors of magnetically equivalent protons. It’s multiplicity is n + 1 Ch. 9 - 25 Examples (1) b a H H Ha: multiplicity = 3 + 1 = 4 (a quartet) Hb C C Cl Hb: multiplicity = 2 + 1 = 3 (a triplet) Hb Ha (2) a b H H Ha: multiplicity = 2 + 1 = 3 (a triplet) Cl C C Cl Hb: multiplicity = 1 + 1 = 2 (a doublet) Cl Hb Ch. 9 - 26 Ch. 9 - 27 Examples (3) Hb Ha Ha: multiplicity = 6 + 1 = 7 (a septet) Hb C C Br Hb Hb Hb: multiplicity = 1 + 1 = 2 (a doublet) Hb Hb Note: All Hb’s are chemically and magnetically equivalent. Ch. 9 - 28 Pascal’s Triangle ● Use to predict relative intensity of various peaks in multiplet ● Given by the coefficient of binomial expansion (a + b)n singlet (s) 1 doublet (d) 1 1 triplet (t) 1 2 1 quartet (q) 1 3 3 1 quintet 1 4 6 4 1 sextet 1 5 10 10 5 1 Ch. 9 - 29 Pascal’s Triangle Ha Hb Due to symmetry, Ha ● For Br C C Br and Hb are Cl Cl identical ⇒ a singlet Ha Hb Ha ≠ Hb Cl C C Br ● For ⇒ two doublets Cl Br Ch. 9 - 30 3. How to Interpret Proton NMR Spectra 1. Count the number of signals to determine how many distinct proton environments are in the molecule (neglecting, for the time being, the possibility of overlapping signals) 2. Use chemical shift tables or charts to correlate chemical shifts with possible structural environments Ch. 9 - 31 3. Determine the relative area of each signal, as compared with the area of other signals, as an indication of the relative number of protons producing the signal 4. Interpret the splitting pattern for each signal to determine how many hydrogen atoms are present on carbon atoms adjacent to those producing the signal and sketch possible molecular fragments 5. Join the fragments to make a molecule in a fashion that is consistent with the data Ch. 9 - 32 Example: 1H NMR (300 MHz) of an unknown compound with molecular formula C3H7Br Ch. 9 - 33 Three distinct signals at ~ δ3.4, 1.8 and 1.1 ppm ⇒ δ3.4 ppm: likely to be near an electronegative group (Br) Ch. 9 - 34 δ (ppm): 3.4 1.8 1.1 Integral: 2 2 3 Ch. 9 - 35 δ (ppm): 3.4 1.8 1.1 Multiplicity: triplet sextet triplet 2 H's on 5 H's on 2 H's on adjacent C adjacent C adjacent C Ch. 9 - 36 Complete structure: most upfield signal most downfield signal CH2 CH3 Br CH2 • 2 H's from • 2 H's from • 3 H's from integration integration integration • triplet • sextet • triplet Ch. 9 - 37 4. Nuclear Spin: The Origin of the Signal The magnetic The spinning field associated proton with a spinning resembles a tiny proton bar magnet Ch. 9 - 38 Ch. 9 - 39 Ch. 9 - 40 Spin quantum number (I) 1H: I = ½ (two spin states: +½ or -½) ⇒ (similar for 13C, 19F, 31P) 12C, 16O, 32S: I = 0 ⇒ These nuclei do not give an NMR spectrum Ch. 9 - 41 5. Detecting the Signal: Fourier Transform NMR Spectrometers Ch. 9 - 42 Ch. 9 - 43 6. Shielding & Deshielding of Protons All protons do not absorb energy at the same frequency in a given external magnetic field Lower chemical shift values correspond with lower frequency Higher chemical shift values correspond with higher frequency "upfield" (more shielded) "downfield" (deshielded) 15 -10 (low field δ ppm (high field strength) strength) Ch. 9 - 44 Ch. 9 - 45 Deshielding by electronegative groups CH3X X = F OH Cl Br I H Electro- 4.0 3.5 3.1 2.8 2.5 2.1 negativity δ (ppm) 4.26 3.40 3.05 2.68 2.16 0.23 ● Greater electronegativity Deshielding of the proton Larger δ Ch. 9 - 46 Shielding and deshielding by circulation of π electrons ● If we were to consider only the relative electronegativities of carbon in its three hybridization states, we might expect the following order of protons attached to each type of carbon: (higher (lower sp < sp2 < sp3 frequency) frequency) Ch. 9 - 47 ● In fact, protons of terminal alkynes absorb between δ 2.0 and δ 3.0, and the order is (higher (lower sp2 < sp < sp3 frequency) frequency) Ch. 9 - 48 ● This upfield shift (lower frequency) of the absorption of protons of terminal alkynes is a result of shielding produced by the circulating π electrons of the triple bond H Shielded (δ 2 – 3 ppm) Ch. 9 - 49 ● Aromatic system Shielded region Deshielded region Ch. 9 - 50 ● e.g. Hc Hd Hb Ha δ (ppm) Ha & Hb: 7.9 & 7.4 (deshielded) Hc & Hd: 0.91 – 1.2 (shielded) Ch. 9 - 51 ● Alkenes H Deshielded (δ 4.5 – 7 ppm) Ch. 9 - 52 ● Aldehydes R O H Electronegativity effect + Anisotropy effect ⇒ δ = 8.5 – 10 ppm (deshielded) Ch.
Load more

Recommended publications
  • Review Sheet on Determining Term Symbols
    Review Sheet on Determining Term Symbols Term symbols for electronic configurations are useful not only to the spectroscopist but also to the inorganic chemist interested in understanding electronic and magnetic properties of molecules. We will concentrate on the method of Douglas and McDaniel (p. 26ff); however, you may find other treatments equal or superior to the D & M method. Term symbols are a shorthand method used to describe the energy, angular momentum, and spin multiplicity of an atom in any particular state. The general form is a given as Tj where T is a capital letter corresponding to the value of L (the angular momentum quantum number) and may be assigned as S, P, D, F, G, … for |L| = 0, 1, 2, 3, 4, … respectively. The superscript “a” is called the spin multiplicity and can be evaluated as a = 2S +1 where S is the spin quantum number. The subscript “j” is the numerical value of J, a new quantum number defined as: J = l +S, which corresponds to the total orbital and spin angular momentum of the system. The term symbol 3P is read as triplet – Pee state and indicates that there are two unpaired electrons in a state with maximum orbital angular momentum, L=1. The number of microstates (N) of a system corresponds to the total number of distinct arrangements for “e” number of electrons to be placed in “n” number of possible orbital positions. N = # of microstates = n!/(e!(n-e)!) For a set of p orbitals n = 6 since there are 2 positions in each orbital.
    [Show full text]
  • States of Oxygen Liquid and Singlet Oxygen Photodynamic Therapy
    Oxygen States of Oxygen As far as allotropes go, oxygen as an element is fairly uninteresting, with ozone (O3, closed-shell and C2v symmetric like SO2) and O2 being the stable molecular forms. Most of our attention today will be devoted to the O2 molecule that is so critically connected with life on Earth. 2 2 2 4 2 O2 has the following valence electron configuration: (1σg) (1σu) (2σg) (1πu) (1πg) . It is be- cause of the presence of only two electrons in the two π* orbitals labelled 1πg that oxygen is paramagnetic with a triplet (the spin multiplicity \triplet" is given by 2S+1; here S, the total spin quantum number, is 0.5 + 0.5 = 1). There are six possible ways to arrange the two electrons in the two degenerate π* orbitals. These different ways of arranging the electrons in the open shell are called \microstates". Further, because there are six microstates, we can say that the total degeneracy of the electronic states 2 3 − arising from (1πg) configuration must be equal to six. The ground state of O2 is labeled Σg , the left superscript 3 indicating that this is a triplet state. It is singly degenerate orbitally and triply degenerate in terms of spin multiplicity; the total degeneracy (three for the ground state) is given by the spin times the orbital degeneracy. 1 The first excited state of O2 is labeled ∆g, and this has a spin degeneracy of one and an orbital degeneracy of two for a total degeneracy of two. This state corresponds to spin pairing of the electrons in the same π* orbital.
    [Show full text]
  • Photochemical and Magnetic Properties of Complex and Nuclear Chemistry
    • Programme: MSc in Chemistry • Course Code: MSCHE2001C04 • Course Title: Photochemical and magnetic properties of complex and nuclear chemistry • Unit: Electronic spectra of coordination compounds • Course Coordinator: Dr. Jagannath Roy, Associate Professor, Department of Chemistry, Central University of South Bihar Note: These materials are only for classroom teaching purpose at Central University of South Bihar. All the data/figures/materials are taken from text books, e-books, research articles, wikipedia and other online resources. 1 Course Objectives: 1. To make students understand structure and propeties of inorganic compounds 2. To accuaint the students with the electronic spectroscopy of coordination compounds 3. To introduce the concepts of magnetochemistry among the students for analysing the properties of complexes. 4. To equip the students with necessary skills in photochemical reaction transition metal complexes 5. To develop knowledge among the students on nuclear and radio chemistry Learning Outcomes: After completion of the course, learners will be able to: 1. Analyze the optical/electronic spectra of coordination compounds 2. Make use of the photochemical behaviour of complexes in designing solar cells and other applications. 3. Design and perform photochemical reactions of transition metal complexes 4. Analyze the magnetic properties of complexes 5. Explain the various phenomena taking place in the nucleus 6. Understand the working of nuclear reactors 2 Lecture-1 Lecture Topic- Introduction to the Electronic Spectra of Transition Metal complexes 3 Crystal field theory (CFT) is ideal for d1 (d9) systems but tends to fail for the more common multi- electron systems. This is because of electron-electron repulsions in addition to the crystal field effects on the repulsion of the metal electrons by the ligand electrons.
    [Show full text]
  • The Chemistry of Carbene-Stabilized
    THE CHEMISTRY OF CARBENE-STABILIZED MAIN GROUP DIATOMIC ALLOTROPES by MARIHAM ABRAHAM (Under the Direction of Gregory H. Robinson) ABSTRACT The syntheses and molecular structures of carbene-stabilized arsenic derivatives of 1 1 i 1 1 AsCl3 (L :AsCl3 (1); L : = :C{N(2,6- Pr2C6H3)CH}2), and As2 (L :As–As:L (2)), are presented herein. The potassium graphite reduction of 1 afforded the carbene-stabilized diarsenic complex, 2. Notably, compound 2 is the first Lewis base stabilized diatomic molecule of the Group 13–15 elements, in the formal oxidation state of zero, in the fourth period or lower of the Periodic Table. Compound 2 contains one As–As σ-bond and two lone pairs of electrons on each arsenic atom. In an effort to study the chemistry of the electron-rich compound 2, it was combined with an electron-deficient Lewis acid, GaCl3. The addition of two equivalents of GaCl3 to 2 resulted in one-electron oxidation of 2 to 1 1 •+ – •+ – give [L :As As:L ] [GaCl4] (6 [GaCl4] ). Conversely, the addition of four equivalents of GaCl3 to 2 resulted in two- electron oxidation of 2 to give 1 1 2+ – 2+ – •+ [L :As=As:L ] [GaCl4 ]2 (6 [GaCl4 ]2). Strikingly, 6 represents the first arsenic radical to be structurally characterized in the solid state. The research project also explored the reactivity of carbene-stabilized disilicon, (L1:Si=Si:L1 (7)), with borane. The reaction of 7 with BH3·THF afforded two unique compounds: one containing a parent silylene (:SiH2) unit (8), and another containing a three-membered silylene ring (9).
    [Show full text]
  • Photochemical Generation of Carbenes and Ketenes from Phenanthrene-Based Precursors Part I: Dimethylalkylidene Part II: Diphenylketene
    Colby College Digital Commons @ Colby Honors Theses Student Research 2017 Photochemical Generation of Carbenes and Ketenes from Phenanthrene-based Precursors Part I: Dimethylalkylidene Part II: Diphenylketene Tarini S. Hardikar Student Tarini Hardikar Colby College Follow this and additional works at: https://digitalcommons.colby.edu/honorstheses Part of the Organic Chemistry Commons Colby College theses are protected by copyright. They may be viewed or downloaded from this site for the purposes of research and scholarship. Reproduction or distribution for commercial purposes is prohibited without written permission of the author. Recommended Citation Hardikar, Tarini S. and Hardikar, Tarini, "Photochemical Generation of Carbenes and Ketenes from Phenanthrene-based Precursors Part I: Dimethylalkylidene Part II: Diphenylketene" (2017). Honors Theses. Paper 948. https://digitalcommons.colby.edu/honorstheses/948 This Honors Thesis (Open Access) is brought to you for free and open access by the Student Research at Digital Commons @ Colby. It has been accepted for inclusion in Honors Theses by an authorized administrator of Digital Commons @ Colby. Photochemical Generation of Carbenes and Ketenes from Phenanthrene-based Precursors Part I: Dimethylalkylidene Part II: Diphenylketene TARINI HARDIKAR A Thesis Presented to the Department of Chemistry, Colby College, Waterville, ME In Partial Fulfillment of the Requirements for Graduation With Honors in Chemistry SUBMITTED MAY 2017 Photochemical Generation of Carbenes and Ketenes from Phenanthrene-based Precursors Part I: Dimethylalkylidene Part II: Diphenylketene TARINI HARDIKAR Approved: (Mentor: Dasan M. Thamattoor, Professor of Chemistry) (Reader: Rebecca R. Conry, Associate Professor of Chemistry) “NOW WE KNOW” - Dasan M. Thamattoor Vitae Tarini Shekhar Hardikar was born in Vadodara, Gujarat, India in 1996. She graduated from the S.N.
    [Show full text]
  • Arxiv:1906.08544V1 [Cond-Mat.Mes-Hall]
    Exchange rules for diradical π-conjugated hydrocarbons R. Ortiz1,2,4, R. A. Boto3, N. Garc´ıa-Mart´ınez1,2, J. C. Sancho-Garc´ıa4, M. Melle-Franco3, J. Fern´andez-Rossier1∗ (1) QuantaLab, International Iberian Nanotechnology Laboratory (INL), Av. Mestre Jos´eVeiga, 4715-330 Braga, Portugal (2)Departamento de F´ısica Aplicada, Universidad de Alicante, 03690, Sant Vicent del Raspeig, Spain (3) CICECO, Departamento de Qu´ımica, Universidade de Aveiro, 3810-193 Aveiro, Portugal and (4)Departamento de Qu´ımica F´ısica, Universidad de Alicante, 03690, Sant Vicent del Raspeig, Spain (Dated: June 21, 2019) A variety of planar π-conjugated hydrocarbons such as heptauthrene, Clar’s goblet and, recently synthesized, triangulene have two electrons occupying two degenerate molecular orbitals. The re- sulting spin of the interacting ground state is often correctly anticipated as S = 1, extending the application of Hund’s rules to these systems, but this is not correct in some instances. Here we provide a set of rules to correctly predict the existence of zero mode states, as well as the spin multiplicity of both the ground state and the low-lying excited states, together with their open- or closed-shell nature. This is accomplished using a combination of analytical arguments and configu- ration interaction calculations with a Hubbard model, both backed by quantum chemistry methods with a larger Gaussian basis set. Our results go beyond the well established Lieb’s theorem and Ovchinnikov’s rule, as we address the multiplicity and the open-/closed-shell nature of both ground and excited states. PACS numbers: I.
    [Show full text]
  • Nitrogen Versus Phosphorus
    The Free Atom Atomic energy levels, valence orbital ionization energies (VOIE) Electronegativity for carbon: 2.5 Electronegativity for hydrogen: 2.2 Inorganic Chemistry 5.03 The Free Atom Atomic energy levels, valence orbital ionization energies (VOIE) Electronegativity for carbon: 2.5 Electronegativity for hydrogen: 2.2 Inorganic Chemistry 5.03 The Free Atom Atomic energy levels, valence orbital ionization energies (VOIE) Electronegativity for carbon: 2.5 Electronegativity for hydrogen: 2.2 Inorganic Chemistry 5.03 The Free Atom Atomic energy levels, valence orbital ionization energies (VOIE) Quartet ground state, spin multiplicity given by 3 2S + 1 = 2( 2 ) + 1 = 4 3 1 1 3 Four possible values for the spin: + 2 , + 2 , − 2 , − 2 Inorganic Chemistry 5.03 The Free Atom Atomic energy levels, valence orbital ionization energies (VOIE) Quartet ground state, spin multiplicity given by 3 2S + 1 = 2( 2 ) + 1 = 4 3 1 1 3 Four possible values for the spin: + 2 , + 2 , − 2 , − 2 Inorganic Chemistry 5.03 The Free Atom Atomic energy levels, valence orbital ionization energies (VOIE) Quartet ground state, spin multiplicity given by 3 2S + 1 = 2( 2 ) + 1 = 4 3 1 1 3 Four possible values for the spin: + 2 , + 2 , − 2 , − 2 Inorganic Chemistry 5.03 Single versus Triple Bonds Atomic energy levels, valence orbital ionization energies (VOIE) ◦ ∆Hf for P2 is +144 kJ/mol ◦ ∆Hf for P≡N is +104 kJ/mol Inorganic Chemistry 5.03 Single versus Triple Bonds Atomic energy levels, valence orbital ionization energies (VOIE) ◦ ∆Hf for P2 is +144 kJ/mol ◦ ∆Hf for P≡N
    [Show full text]
  • Recent Progress in Quinoidal Singlet Biradical Molecules
    Received: November 2, 2014 | Accepted: November 21, 2014 | Web Released: November 29, 2014 CL-140997 Highlight Review Recent Progress inQuinoidal Singlet Biradical Molecules Takashi Kubo Department of Chemistry, Graduate School of Science, Osaka University, 1-1 Machikaneyama, Toyonaka, Osaka 560-0043 (E-mail: kubo@chem.sci.osaka-u.ac.jp) Takashi Kubo was born in Yamaguchi, Japan, in 1968. He graduated from Osaka University in 1991, received M.Sc. in 1993 under the guidance of Professor Ichiro Murata, and received Ph.D. in 1996 under the guidance of Professor Kazuhiro Nakasuji.After working at Mitsubishi Chemical Co., he joined Professor Nakasuji’s group at Department of Chemistry, Graduate School of Science, Osaka University in 2000 as Assistant Professor. In 2006 he served as Associate Professor. Since 2006 he is Professor of Graduate School of Science, Osaka University. He received the Bulletinof the Chemical Society of Japan Award in 2001. His research interests are structural and physical organic chemistry, mainly the syntheses and properties of polycyclic aromatic compounds with open-shell character, and the development of multifunctional materialsusing a cooperative proton- and electron-transfer system. Chem. Lett. 2015, 44, 111–122 | doi:10.1246/cl.140997 © 2015 The Chemical Society of Japan | 111 Abstract Ph Ph Ph Ph Elusive nature inspin state isafeature of singlet biradical Ph Ph Ph Ph molecules and arises from the weak coupling of unpaired 2 l i i li i f i e ectrons. Th shgh ght rev ew ocuses on recent advances n i i i i ’ f l f experimental approaches for elucidating the electronic structure F gure 2.
    [Show full text]
  • Appendix a Mathematical Operations
    Appendix A Mathematical Operations This appendix presents a number of mathematical techniques and equations for the convenience of the reader. Although we have attempted to sum­ marize accurately some of the most useful relations, we make no attempt at rigor. A bibliography is included at the end of this appendix. A-1 COMPLEX NUMBERS A complex quantity may be represented as follows: u = x + iy = re+i<l> (A-I) where i 2 = -1, x, y, r, and cp are real numbers and ei<l> = cos cp + i sin cpo One refers to x and y as the real and the imaginary components, respectively of u, whereas r is the absolute magnitude of u, that is, r = lui. cp is called the phase angle. The complex conjugate of u, viz., u*, is obtained by changing the sign of i wherever it appears; that is, u* = x - iy. The relation between complex numbers and their conjugates is clarified by representing them as points in the "complex plane" (Argand diagram, see Fig. A-I). The abscissa is chosen to represent the real axis (x), and the ordinate the imaginary axis 391 392 ELECTRON SPIN RESONANCE Imaginary axis u iy ~E2---------t-- Real axis u' Fig. A-l Representation of a point u and of its complex conjugate u* in complex space (Argand diagram). (y). Note that the real component of u is equal to one-half the sum of u and u*; the product of u and its complex conjugate is the square of the absolute magnitude, that is, (A-2) A-2 OPERATOR ALGEBRA A-2a.
    [Show full text]
  • Aggregation-Induced Radical of Donor-Acceptor Organic Semiconductors
    Aggregation-Induced Radical of Donor-Acceptor Organic Semiconductors Zhongxin Chen,1 Yuan Li*,1 Weiya Zhu,1 Zejun Wang,1 Wenqiang Li,1 Miao Zeng,1 Fei Huang*1 1 Institute of Polymer Optoelectronic Materials and Devices, State Key Laboratory of Luminescent Materials and Devices, South China University of Technology, Guangzhou 510640, P. R. China * Correspondence author: celiy@scut.edu.cn, msfhuang@scut.edu.cn Abstract Narrow bandgap donor-acceptor organic semiconductors are generally considered to show closed-shell singlet ground state and their radicals are reported as impurities, polarons, charge transfer state monoradical or defects. Herein, we reported the open-shell singlet diradical electronic ground state of two diketopyrrolopyrrole-based compounds Flu-TDPP and DTP- TDPP via the combination of variable temperature NMR, variable temperature electron spin spectroscopy (ESR), superconducting quantum interference device magnetometry, and theoretical calculations. It is observed that the quinoid-diradical character is significantly enhanced in aggregation state because of the limitation of intramolecular rotation. Consequently, we propose a mechanism of aggregation-induced radical to understand the driving force of the open-shell diradical formation of DTP-TDPP based on the ESR spectroscopy test in different proportions of mixed solvents. Our results demonstrate the thermally-excited triplet state for donor-acceptor organic semiconductors, providing a novel view to comprehend the intrinsic chemical structure of donor-acceptor organic semiconductors, as well as the potential electronic transition process between ground state and excited state. 1 Introduction In the recent more than 30 years, organic semiconductors (OSCs) exhibited great application potential in organic light-emitting diodes (OLEDs),1, 2 organic photovoltaics (OPVs),3, 4 organic field-effect transistors (OFETs),5-7 organic photodetectors (OPDs)4 and other organic electronic devices8.
    [Show full text]
  • OXIDE and SEMICONDUCTOR MAGNETISM
    OXIDE and SEMICONDUCTOR MAGNETISM J. M. D. Coey Physics Department, Trinity College, Dublin 2 Ireland. 1. Single-ion effects 2. Collective Effects 3. Examples www.tcd.ie/Physics/Magnetism Boulder July 2003 1 Some references: Magnetic oxides: D. J. Craik (editor) Wiley-Interscience 1975 Magnetism and the chemical bond: J. B. Goodenough Wiley-Interscience 1963 Introduction to ligand field theory. C. Ballhausen McGraw Hill 1962 Mineralogical applications of crystal-field theory. R. G. Burns CUP 1993 (2nd ed.) Point charge calculations of energy levels of magnetic ions in crystalline electric fields. M. T. Hutchings Solid State Physics 16 227 - 73 (1964) Boulder July 2003 2 1. Single-ion effects 1.1 Ubiquity of oxides. Oxide structures. Octahedral and tetrahedral sites. Magnetic ions – 3d, 4d, 4f. 1.2. Electronic structure of free ions (summary). Hund’s rules. g- factors. Paramagnetic susceptibility. 1.3. Ions in solids. Crystal field. Crystal field Hamiltonian. One-electron states. 3d t2g and eg states. Notation. 2p-3d hybridization. One- electron energy-level diagrams in different symmetry. Quenching of orbital moment. Many-electron states. Orgel and Tanabe-Sugano diagrams. 1.4. Crystal field and anisotropy. Single-ion anisotropy. Determination m of Bn . Boulder July 2003 3 1.1 Ubiquity of Oxides Earth’s crust is composed almost entirely of oxides — rocks, economic minerals, water. Composition in atomic % 2- Oxygen (O ) is most abundant Fe O followed by silicon (Si4+) and Si aluminium (Al3+). Al3+ Al Crust is mostly composed of Fe aluminosilicates. Mg Iron (Fe2+/Fe3+) is most O2- Si4+ Ca abundant magnetic element. It is K 40 times as abundant as all other magnetic elements Na together.
    [Show full text]
  • A COMPARATIVE STUDY of the ATOMIC TERM SYMBOLS of F3 and F11 CONFIGURATION P
    ACPI Acta Chim. Pharm. Indica: 2(1), 2012, 32-45 ISSN 2277-288X A COMPARATIVE STUDY OF THE ATOMIC TERM SYMBOLS OF f3 AND f11 CONFIGURATION P. L. MEENA*, P. K. JAIN, N. KUMAR and K. S. MEENA Department of Chemistry, M. L. V. Govt. College, BHILWARA (Raj.) INDIA (Received : 13.10.2011; Revised : 30.10.2011; Accepted : 31.10.2011) ABSTRACT The term is a particular energy state and term symbol is a label to energy state. The importance of these term symbols has been emphasized in connection with the spectral and magnetic properties of complexes and metal free ions and also provide information about the energy of atomic electrons in orbital’s and total spin, total orbital and grand total momenta of whole atom and electronic configuration. Russell-Saunders (L-S) coupling and j-j coupling schemes are important schemes for determination of terms and term symbols of the atoms and ions of inner transition elements in which electrons are filled in a f sub-shell with azimuthal quantum number 3. The determination of terms and term symbols for fn configuration is very difficult work since there are seven orbital’s in f-sub shell which give large number of microstates. In this proposed work computation is done for calculating all possible terms and term symbols regarding for f3 and f11 configurations without any long tabulation with mental exercise and a comparative study was carried out between the f3 and f11 terms and term symbols. The possible microstates and spectroscopic terms calculated for f3 and f11 configuration (ions M+3) are 364 and 17.
    [Show full text]