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SOME CALCULATIONS of NMR CHEMICAL SHIFTS a Thesis SOME CALCULATIONS OF NMR CHEMICAL SHIFTS A Thesis submitted to the UNIVERSITY OF SURREY in partial fulfilment of the requirements for the Degree of Master of Philosophy By HUSAM MOHEMMED SAID ABID Department of Chemical Physics (Spectroscopy Section) University of Surrey Guildford March 1980 ProQuest Number: 10797503 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. uest ProQuest 10797503 Published by ProQuest LLC(2018). Copyright of the Dissertation is held by the Author. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code Microform Edition © ProQuest LLC. ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 4 8 1 0 6 - 1346 2 ABSTRACT Some calculations of the 13C and 15N shielding constant are carried out using CNDO/S and INDO/S procedures within the GIAO-MO framework described by Pople. These are compared with the experimental results, in the form of 13C chemical shifts with respect to benzene and in the form of 15N chemical shifts with respect to nitromethane,: C H 3N 0 2 . In Chapter one, several current theories of magnetic shielding are briefly reviewed. Chapter two presents a survey of various semi-empirical molecular orbital treatments of magnetic shielding constant. The approximations introduced and the MO theory used are also described in Chapter two. Chapter three presents 13C, 15N and 19F chemical shifts and their anisotropies were calculated. A reasonable correlation between the calculated and experimental ch.emiteal shifts, compared by means of least square fit, is obtained for most of the molecules considered. 3 ACKNOWLEDGEMENT I wish to acknowledge Dr. G. A. Webb, under whose supervision the project was carried out, for his continuous fruitful suggestions and discussions. Many thanks to P. G. Abdul Ahad, B. Na Lamphun and D. J. Reynolds for their valuable assistance during all the stages of the project. I am thankful for the help provided by Angela Steele in typing the thesis. Finally, the award of Scholarship from the Iraqi Government is gratefully acknowledged. 4 To my family 5 . CONTENTS Page ABSTRACT 2 ACKNOWLEDGEMENT 3 CHAPTER ONE: THEORIES OF NUCLEAR MAGNETIC SHIELDING 7 1.1. Introduction. 8 1.2. General considerations of nuclear shielding. 9 1.3. Molecular orbital theory. I3 1.4. Coupled Hartree-Fock perturbation theory. I7 1.5. Gauge Invarient Molecular orbital methods. 20 CHAPTER TWO: SEMI-EMPIRICAL M.O. METHODS APPLIED TO THE CALCULATION OF NUCLEAR SCREENING .23 2.1. Introduction. 24 2.2. Pople’s (GIAO) Approach. * 24 2.3. Calculation using All-Valence electron LCAO-SCF-M.0. theory. 32 2.4. CNDO Methods. 36 2.5. INDO Method. 44 2.6. Uncoupled Hartree-Fock Method. 49 2.7. Finite Perturbation Method. 31 2.8. The evaluation of the molecular coulomb and exchange integrals. 52 2.9. Some computational details. 55 CHAPTER THREE: THE RESULTS OF SOME CALCULATIONS OF THE SCREENING TENSOR AND ITS ANISOTROPY FOR SOME FIRST ROW NUCLEI. 56 3.1. Carbon Chemical Shifts. 57 3.1.1. Introduction. 57 3.1.^. Results and discussion of 13C chemical shifts in different molecules. 58 3.1.2.1. 13C Chemical shifts of cyclohexenone. 58 3.1.2.2. 13C Chemical shifts of alkyl and phenyl perchlorates and pyridine molecules. 62 6 Page 3.1.2.3* 13C Chemical shifts of anthrquinones molecules, 62 3.1,2.4. 13C Chemical shifts of some polycyclic atomatic compounds and their amino derivatives. 68 3.1.3. Carbon-13 shielding anisotropies of some simple organic molecules. 72 3.1.4. The variation of the shielding constant with twist angle about single bonds in conjugated systems. 76 3.2. Nitrogen chemical shifts. 111 3.2.1. Introduction. 111 3.2.2. Results and discussion. 111 3.2.3. Fluorine-15 shielding anistropies of some simple organic molcules. 116 3.3. Conclusions. 116 REFERENCES 119 CHAPTER ONE THEORIES OF NUCLEAR MAGNETIC SHIELDING 1.1. Introduction Nuclear shielding provides a basis for an understanding of nuclear and electronic environments occurring within and about the nucleus. It is possible to obtain a good knowledge of the electronic distribution and structure of a molecule by studying the nuclear magnetic resonance spectra of several different nuclei in that molecule. In recent years significant developments in experimental technique have led to the routine measurement of chemical shifts, especially for rare nuclei such as 13C and 15N. The identification of structural conformation of the species present in a given sample by comparison of the experimental and calculated shieldings has thus been extended to less common nuclei. The theoretical estimates of nuclear screening are usually based upon an isolated molecule as a model, however most experimental chemical shifts are reported for liquid samples in which solvent effects may be present. Therefore, theoretical values of magnetic shielding are not exactly necessarily expected to reproduce experimental values even if the calculations are accurate. The current widespread interest in theories of carbon (1 2 ) and nitrogen chemical shifts is reflected by reviews. 9 Both Ab initio and semi-empirical molecular orbital calcula­ tions have provided significant advances in the understanding of the major factors determining carbon and nitrogen chemical shifts. For large molecules, semi-empirical methods are more practical at present. 9 New instrumentation and techniques have made possible the measurement of shielding anisotropies. Since the anisotropy is a difference between tensor components, it does not need a reference point and thus can readily be compared with various theoretical treatments. The large body of experimental data.for l3C and 15N nuclei (1 3 4 5 6 } available'- > > > » ;lead us to present some theoretical results. The values of chemical shifts screening constants and their anisotropies are given in ppm. 1.2. General considerations of nuclear shielding: For a molecule held fixed in a uniform magnetic field B0 , the magnetic shielding of any one of its nuclei can be described by a second rank tensor a whose components are defined by the expression: B = - o . B 0 (1.1) where B is the secondary magnetic field at the nucleus of interest created by the currents induced in the electronic system by S0.a is the screening constant usually expressed in ppm. The total magnetic field experienced by a nucleus, 6 , is the vector Sum of the applied magnetic field §0 and the induced field B. § — § 0 a.S0 (1 .2) 10 If two nuclei A and B of the same isotope have shielding constants cr^, and aB at the same value of B0 , then the chemical, shift is 6AB aA aB (1.3) A general theory of chemical shifts in closed shell ( 7 8 } molecules was originated by Ramseyv * 'by using second order perturbation theory. This gave the first treatment of the calculation of the nuclear screening constant of a molecule. The electronic Hamiltonian describing a closed; shell molecule in the presence of a magnetic field B, and nuclear , *)■ . magnetic moment p is: H (S,yA) = |m Z [f VK - e lK(r)f + $(r) (1.4) • K h 7 Where (1- V,-)Is is the linear momentum of the kth electron, V(r) is the electrostatic potential energy function for the electrons and XK(r) is the vector potential describing the total magnetic field at the position of electron k and is given by: 1 K = 4 § x (rK- r0) + (PA x rK)/|rK3| (1.5) Where is the distance from the kth electron to the In nucleus in question. r0 is the separation between this 11 nucleus and the origin of the vector potential. The second order perturbation energy is expressed as: E^2^(S,ua ) = i Ocz$ Btt yA g (1.6) “3=1 Where “ and 3 are used to indicate cartisian coordinates x, y and z. cr^ are the elements of the shielding tensor for a given nucleus A which possesses a nuclear magnetic moment pA , B is the applied magnetic field, aa^ is expressed as a second partial derivative of the energy with respect to the corresponding component of § and yA as: = 32E (2)(S.uA )/3Bo:SyA6 ..... yA = § = o (1.7) (9) The components of cr^ are given; J °o:g -= a«gd + a=gdg + a°=BP + ®ccgPg (1 .8 ) dec pec where the & terms are gauge-dependent. The diamagnetic term is a positive term depending largely on the electronic density near the nucleus. The paramagnetic term is a negative term and. its accurate calculation is difficult, since it requires knowledge of the energies and wave functions of all the excited states of the molecule concerned. The paramagnetic contribution of the total shielding for a nucleus in a molecule is intimately related to the components of the spin rotation interaction tensor. The terms on the right-hand side of equation (1.8) are defined by: (1.9) :gd = 4? Is <0I S rK 3(rK 6 = B " rK« rK 3 > 10> K dg _ e 2 < 0 I Z rK 3(r0ocr K3 - r0 r 6a 3)|0> ( 1. 10) 4tt 2m a = 6 P = " i t l i 2 * [ < 0 h r K 3 L K = l n > < n l 2 l k 6 | o > n K .K + <0| z LKg|n><n| j rK 3LK<r |0> ] (En-E0 ) 1 TU '2 ac=BPg = 4? Is* E 8y«r 0Y £ [< 0 I K rK 3LKa|nxn|s Pk5 |0> n (1.12) +<0 |£ Pk5|n><n | £ rK 3LKO:|0>] (En-E0 ) 1 where yQ is the permeability of free space, e,m are respectively the electronic charge and mass, rK is the distance of the kth electron from the nucleus under consideration, JK (.= rK x h/i^K ) is the orbital!-angular ;.
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