摘要:

GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date 1907 1907 1910 191 1 1912 1913 1913 1913 1914 1914 1915 1916 1916 1917 1917 1917 1918 1918 1918 1919 1919 1920 1920 1920 1920 1921 1921 1921 1921 1922 1922 1923 1923 1923 1923 1923 1924 1924 1924 1924 1924 1925 1925 1926 1926 1927 1927 1927 1918 Subject Osmotic Pressure Hydrates in Solution The Constitution of Water High Temperature Work Magnetic Properties of Alloys Colloids and their Viscosity The Corrosion of Iron and Steel The Passivity of Metals Optical Rotary Power The Hardening of Metals The Transformation of Pure Iron hfethods and Appliances for the Attainment of High Temperatures in a Refractory Materials Training and Work of the Chemical Engineer Osmotic Pressure Pyrometers and Pyrometry The Setting of Cements and Plasters Electrical Furnaces Co-ordination of Scientific Publication The Occlusion of Gases by Metals The Present Position of the Theory of Ionization The Examination of Materials by X-Rays The Microscope : Its Design, Construction and Applications Basic Slags : Their Production and Utilization in Agriculture Physics and Chemistry of Colloids Electrodeposition and Electroplating Capillarity The Failure of Metals under Internal and Prolonged Stress Physico-Chemical Problems Relating to the Soil Catalysis with special reference to Newer Theories of Chemical Action Some Properties of Powders with special reference to Grading by The Generation and Utilization of Cold Alloys Resistant to Corrosion The Physical Chemistry of the Photographic Process The Electronic Theory of Valency Electrode Reactions and Equilibria Atmospheric Corrosion.First Report Investigation on Oppau Ammonium Sulphate-Nitrate Fluxes and Slags in Metal Melting and Working Physical and Physico-Chemical Problems relating to Textile Fibres The Physical Chemistry of Igneous Rock Formation Base Exchange in SoiIs The Physical Chemistry of Steel-Making Processes Photochemical Reactions in Liquids and Gases Explosive Reactions in Gaseous Media Physical Phenomena at Interfaces, with special reference to Molecular Atmospheric Corrosion. Second Report The Theory of Strong Electrolytes Cohesion and Related Problems Laboratory Elutriation Orientation Volume Trans. 3 3 6 7 9 9 9 10 10 11 12 12 13 13 13 14 14 14 14 15 15 16 15 16 16 17 17 17 17 18 18 19 19 19 19 19 20 20 20 20 20 21 21 22 22 23 23 24 aDale 1928 1929 1929 1929 1930 1930 1931 1932 1932 1933 1933 1934 1934 1935 1935 1936 1936 1937 1937 1398 1938 1939 1939 1940 1941 1941 1942 1943 1944 1945 1945 1946 1946 1947 1947 1947 1947 1948 1948 1949 1949 1949 1950 1950 1950 1950 1951 1951 1952 1952 1952 1953 1953 1954 1954 GENERAL DISCUSSIONS OF THE FARADAY SOCIETY Subject Homogeneous Catalysis Crystal Structure and Chemical Constitution Atmospheric Corrosion of Metals.Third Report Molecular Spectra and Molecular Structure Optical Rotatory Power Colloid Science Applied to Biology Photochemical Processes The Adsorption of Gases by Solids The Colloid Aspects of Textile Materials Liquid Crystals and Anisotropic Melts Free Radicals Dipole Moments Colloidal Electrolytes The Structure of Metallic Coatings, Films and Surfaces The Phenomena of Polymerization and Condensation Disperse Systems in Gases : Dust, Smoke and Fog Structure and Molecular Forces in (a) Pure Liquids, and (b) Solutions The Properties and Functions of Membranes, Natural and Artificial Reaction Kinetics Chemical Reactions Involving Solids Luminescence Hydrocarbon Chemistry Volume 24 25 25 25 26 26 27 28 29 29 30 30 31 31 32 32 33 33 34 34 35 35 The Electrical Double Layer (owing to the outbreak of war the meeting was abandoned, but the papers were printed in the Transnctions) 35 The Hydrogen Bond 36 The Oil-Water Interface 37 The Mechanism and Chemical Kinetics of Organic Reactions in Liquid Systems 37 The Structure and Reactionsof Rubber Modes of Drug Action 39 Molecular Weight and Molecular Weight Distribution in High Polymers.(Joint Meeting with the Plastics Group, Society of Chemical Industry) 40 The Application of Infra-red Spectra to Chemical Problems 41 Oxidation 42 Dielectrics 42 A Swelling and Shrinking 42 B Electrode Processes Disc. 1 The Labile Molecule 2 Surface Chemistry. (Jointly with the Societk de Chimie Physique at Colloidal Electrolytes and Solutions The Interaction of Water andPorous Materials The Physical Chemistry of Process Metallurgy Crystal Growth 5 Chromatographic Analysis 7 38 Bordeaux.) Published by Butterworths Scientific Publications, Ltd. Trans. 43 Disc. 3 4 Lipo-Proteins 6 Heterogeneous Catalysis 8 Physicochemical Properties and Behaviour of Nuclear Acids Trans. 46 Spectroscopy and Molecular Structure and Optical Methods of 10- vestigating Cell Structure Disc.9 Electrical Double Layer Trans. 47 Hydrocarbons Disc. 10 The Size and Shape Factor in Colloidal Systems Radiation Chemistry 12 11 The Physical Chemistry of Proteins 13 The Reactivity of Free Radicals 14 The Equilibrium Properties of Solutions of Non-Electrolytes 15 The Physical Chemistry of Dyeing and Tanning 16 17 Coagulation and Flocculation 18 The Study of Fast ReactionsGENERAL DISCUSSIONS OF THE FARADAY SOCIETY Date 1955 1955 1956 1956 1957 1957 1958 1958 1959 1959 1960 1960 1961 1961 1962 1962 Subject Microwave and Radio-Frequency Spectroscopy Physical Chemistry of Enzymes Membrane Phenomena Physical Chemistry of Processes at High Pressures Molecular Mechanism of Rate Processes in Solids Interactions in Ionic Solutions Configurations and Interactions of Macromolecules and Liquid Crystals Ions of the Transition Elements Energy Transfer with special reference to Biological Systems Crystal Imperfections and the Chemical Reactivity of Solids Oxidation-Reduction Reactions in Ionizing Solvents The Physical Chemistry of Aerosols Radiation Effects in Inorganic Solids The Structure and Properties of Ionic Melts Inelastic Collisions of Atoms and Simple Molecules High Resolution Nuclear Magnetic Resonance For current availability of Discussion volumes, see back cover. Volume 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

ISSN:0366-9033    

DOI:10.1039/DF962340X001

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

I. NUCLEAR MAGNETIC RESONANCE IN DIAMAGNETIC MATERIALS The Theory of Chemical Shifts BY J. A. POPLE* Dept. of Chemistry, Carnegie Institute of Technology, Pittsburgh 13, USA. Received 14th June, 1962 This paper describes the main features of a new molecular orbital theory of the diamagnetic currents induced in a molecule by an external magnetic field with particular emphasis on the inter- pretation of chemical shifts in nuclear resonance experiments. For noxwyclic molecules, these currents are reduced to atomic components which may be calculated from approximate 1.c.a.o. molecular orbitals. Local diamagnetic anisotropies are predicted for carbon-carbon double and triple bonds and the carbonyl group, but not for carbon-carbon single bonds. The theory is applied to carbon and hydrogen chemical shifts in some simple organic compounds.1. INTRODUCTION For molecules without unpaired electrons, chemical shifts of nuclear resonance frequencies due to magnetic screening arise from orbital electronic currents induced by the external magnetic field. These currents also give rise to the diamagnetic polarization of the molecule. In fact, if the external magnetic field is Ho, the total magnetic moment of the induced currents is XmHO where xm is the (molecular) dia- magnetic susceptibility, while the secondary magnetic field due to these same currents at a particular nucleus A is (-aAHo), a* being the corresponding magnetic screening constant. The total field experienced by nucleus A determining the n.m.r. frequency is then A complete understanding of the diamagnetic currents, therefore, should lead to a full interpretation of the diamagnetic susceptibility and the screening constants of all nuclei in the molecule.Ideally, theie should be a unified theory of the two phenomena. For a molecule with no particular symmetry, the induced magnetic moment and the secondary fields at the nuclear positions will not be parallel to the primary field and will depend on the orientation of the molecule. This means that the quantities Xm and aA are really tensors with three principal values and axes. Experi- ments on fluid media measure only the mean of these three values. To develop a systematic theory of the diamagnetic properties of large molecules, it is necessary to break down the total current distribution into components which can be carried over from one molecule to another.For non-cyclic systems, where there is no possibility of interatomic ring currents flowing round a closed loop of bonds, this decomposition can be done on an atomic basis, the total current flow being a superposition of local currents in each atom. b alternative, proposed in * Ford Visiting Professor 1961-62. Permanent address : Basic Physics Division, National Physical Laboratory, Teddmgton, Middlesex, England. H A = Ho(l -oA). (1.1) 78 THEORY OF CHEMICAL SHIFTS some work on diamagnetism,I is to treat the total flow as a superposition of circula- tions in individual chemical bonds. This, however, leads to difficulties in handling non-bonding electrons and, in any case, is unsuited for detailed numerical calcula- tions which are most conveniently based on an atomic orbital approximation. For cyclic molecules such as benzene and other aromatic compounds, account must also be taken of the ring currents due to the mobile ;rt-electrons.These lead to additional, highly anisotropic contributions to the diamagnetic susceptibility2 In principle, ring currents may also occur in non-aromatic cyclic molecules such as cyclohexane, but the more localized nature of the bonding electrons will make them smaller and there is as yet no theoretical or experimental estimate of their magnitude. If an atomic decomposition is used and the aromatic ring currents treated separ- ately, the total molar susceptibility can be written in the form where into two parts Here x$ is a diamagnetic (negative) contribution which is the susceptibility atom A would have if its electrons all circulated freely about the direction of the magnetic field with the Larmor angular frequency u) = eH12me.For an isolated spherical atom, this is the only contribution and the molar atomic susceptibility is given by the Langevin formula is a sum over atoms. The atomic contribution X* can be further split A XA = xdA+xpq (1.3) Ne2 6mc d = where ?is the mean square distance of electron i from the nucleus. For an atom in a molecule, however, this circulation cannot occur freely because of the hindering effect of the electric fields due to other atoms and so a second paramagnetic (positive) contribution xf has to be added. The calculation of this hindering effect requires a quantum-mechanical study of the electronic wave functions in a magnetic field.The theory of chemical shifts can also be developed in terms of an atomic break- down of diamagnetic currents as first suggested by Saika and Slichter.3 The total screening constant for atom A is then written the interpretation of the various terms being as follows. is the contribution to the secondary magnetic field at nucleus A due to the diamagnetic Langevin-type currents on the atom A itself. For an isolated spherical atom, it is the only contribution and is given explicitly by the Lamb formula, (1) e2 - Cp = --+-yl, 3mc which is the analogue of (1.4). (2) c p is the contribution due to the paramagnetic-type currents on atom A which give the susceptibility term $. Such terms were first calculated for fluorine atoms by Saika and Slichter 3 who showed that they were much more sensitive to chemical structure than uy.The total variation of o p from F2 to a highly ionic system is of the order of 10-3. For most other atoms, variations in this term willJ. A. POPLE 9 give the main contribution to chemical shifts. The principal exception is hydrogen, where the absence of low-lying atomic p-orbitals will make this paramagnetic term much smaller. is the contribution to the screening of atom A by the atomic circulations on atom B. If the magnetic effects of these neighbouring currents are treated in a dipole approximation, this term involves only the local anisotropy of the local sus- ceptibility on the atom B.59 6 If atom A is on or near the axis of high diamagnetism of B, there will be an increase in average screening (om>O).The effect falls off as the inverse cube of the AB distance and is unlikely to exceed 10-5 in magnitude. (4) Finally CTA, ring is the contribution to the screening due to ring currents which cannot be localized on any atom. The magnitude is usually less than 2 x 10-6, but it plays an important part in determining the proton spectra of aromatic compounds.7~ 8 Further development of the theory of chemical shifts along these lines requires the detailed calculation of the components of the electronic currents. The theory of aromatic ring currents has been widely developed in molecular orbital terms,9 but less attention has been paid to the intra-atomic parts. Recently, a molecular orbital theory of diamagnetism of non-cyclic molecules has been proposed 10 which accounts for some of the principal features of observed susceptibilities and which also makes certain predictions about anisotropies.In the following sections we shall apply this theory to the calculation of chemical shifts, illustrating its applica- tion to experimental data on hydrogen and carbon. (3) 2. A GENERAL MOLECULAR ORBITAL THEORY OF CHEMICAL SHIFTS In its simplest form, the molecular orbital theory of diamagnetism can be de- veloped in terms of an independent-electron model, the motion of each being deter- mined by a one-electron Hamiltonian, 2m where A is the magnetic vector potential and V a suitably averaged effective electro- static potential. For a molecule in an external magnetic field H with a single magnetic nucleus with magnetic moment p at the origin, A is given by A(r) = -&Hxr+pxr/r3. (2.2) In the presence of the magnetic field, the molecular orbitals may be written approximately as a linear combination of atomic orbitals (1.c.a.o.) : where xp is a gauge-dependent atomic orbital 4 , being the normal atomic orbital and A, the value of the vector potential at the nuclear position of 4,.By treating the terms in the Hamiltonian involving A as a perturbation, it is possible to calculate the change in individual molecular orbital energies and hence the total magnetic susceptibility and the screening constant. This procedure is essentially that used by London9 in the theory of aromatic ring currents and later modified by Pople 11 and McWeeny 12 to handle chemical shifts. Here it is proposed to use the method for all electrons in the molecule instead10 THEORY OF CHEMICAL SHIFTS of just the mystem.For organic-type molecules, the atomic orbitals used will be Is for hydrogen and Is, 2, 2pz, 2py and 2pz for carbon, nitrogen, oxygen and fluorine. Molecules with heavier atoms will not be considered in this paper. The reduction to intra-atomic terms is accomplished by neglecting certain integrals involving atomic orbitals on more than one atom. This involves a series of approx- imations which are discussed in detail in ref. (10). Once this is done, the various atomic contributions to the susceptibility can be picked out immediately and X* written in the form (1.3).The diamagnetic part ~2 arises from the gauge-factor modification of the atomic orbitals (2.4); the paramagnetic part comes from the changes in the 1.c.a.o. coefficients. These changes are equivalent to the mixing of the ground and certain excited states of the molecule by the magnetic field. Ex- plicitly the formulae for x$ and xpA are (in the z-direction) and In these formulae the various Ppv elements are components of the charge-density and bond-order matrix for the unperturbed molecule, the sum being over occupied molecular orbitals. In the expression (2.5) for the diamagnetic part, ( x 2 + ~ 2 ) ~ ~ is the mean value of (x2fy2) for the atomic orbital #p referred to its own nucleus. The paramagnetic part (2.6) has been simplified by the assumption that the excitation energies needed in the perturbation theory formula can be replaced by an average value AE.This enables the result to be expressed in terms of Ppv matrix for the molecular ground state. PZAZB is the ele- ment of the matrix for the 2px atomic orbitals on atoms A and B. If A = B, it is the charge density in 2pXA and if A+B, it is the bond order between the two atomic orbitals. For the magnetic screening constant a*, the theory gives an expression of the type (1.5) with the following explicit expressions for the components : (i) LOCAL DIAMAGNETIC CURRENTS This is similar to the Lamb formula (1.6) and is easily calculated if 1.c.a.o. molecular orbitals are known. (ii) LOCAL PARAMAGNETIC CURRENTS where (r-3&, is the meanvalue of Y-3 for the 2p atomic orbitals.The direct pro- portionality to the local paramagnetic contribution x,^ should lead to a correlation of the chemical shift with diamagnetic susceptibility data for atoms with 2p electrons.J . A. POPLE 11 The (r-3) proportionality factor makes the local paramagnetic contribution large and it is likely to be dominant in the application to carbon, nitrogen, oxygen and fluorine. (iii) CURRENTS ON NEIGHBOURING ATOMS aAB = - JJN - '&;b(3R,,R,p - R&5m,J/R; (2.10) where a, p are tensor suffxes and RB, (a = x, y , z) are the components of the vector from nucleus A to nucleus B. If the susceptibility on atom B is isotropic (x$ = xBG,~), this formula gives zero, so the contribution is frequently referred to as the neighbour anisotropy e - e c t . If the local susceptibility tensor on atom B is axially symmetric, (2.10) reduces to 596 where AxR (= $- x:) is the anisotropy of the susceptibility and YB is the angle between the axis of anisotropy and the AB internuclear line.(iii) RING CURRENTS To describe interatomic ring currents in aromatic compounds, the matrix element of the unperturbed Hamiltonian between 2pn atomic orbitals on neighbouring atoms (that is the resonance integrals p ) must be retained in the theory. The expression for a*$ ring is then equivalent to that derived by McWeeny.12 aS oAB = +(AxB)(l -3 cos2 yB)/RiN, (2.11) 3. ATOMIC CONTRIBUTIONS TO CHEMICAL SHIFTS IN ORGANIC MOLECULES The preceding formulae have been used to make approximate estimates of atomic contributions to the diamagnetic susceptibility for some of the more important organic groups.10 These calculations were based on localized molecular orbitals for bonds and an average electronic excitation energy of 10 eV (with some correc- tions for known states of lower energy).In this section, we shall discuss the cor- responding contributions to the chemical shifts of hydrogen and carbon nuclei. For atoms other than hydrogen, the paramagnetic contribution $ is most sensitive to electronic structure and estimates of the relative shifts of carbon and the neighbour anisotropy effect for hydrogen can be made by considering this term only. (i) CARBON-CARBON SINGLE BONDS The theory with completely localized non-polar bonding molecular orbitals predicts that all carbon atoms in saturated compounds have the same x$ (+ 6.46 x 10-6) and are isotropic.Accordingly, all carbon atoms in unstrained paraffins should have the same chemical shift. In fact, such resonances are spread over a range of about 30p.p.m. to low field (low 0) from methane. These shifts are not yet satisfactorily interpreted ; they may be connected with some delocal- ization of the bonding electrons. Since the carbon atoms are predicted to be isotropic, calculated chemical shifts for all paraffinic hydrogens are the same. Again there is a spread of = 1.5 p.p.m. to low field from methane in the experimental data, but this may be due to changing electron density. Some authors have postulated an intrinsic diamagnetic anisotropy for the carbon- carbon single bond.13 Among other things, this would explain the higher screening of axial protons in cyclohexane and related systems.However, in this approxi- mate a priori theory no such anisotropy is calculated. a(-CH)<a(-CH2)<a(-CHJ)<a(CH4),12 THEORY OF CHEMICAL SHIFTS (ii) CARBON-CARBON DOUBLE BONDS For ethylene and other olefins, the theory predicts larger xf terms on the carbon atoms, but only if the magnetic field is perpendicular to the C=C bond and in the plane of the other nuclei (for ethylene). This additional contribution arises from the mixing of o-+n and n-w excited states with the ground state by the magnetic field. It is in qualitative agreement with the observed low diamagnetism of olefins (the constitutive correction for C=C in the Pascal scheme is large and positive) and the low field shift of the carbon resonance from ethane. The additional para- magnetic term Ax," (relative to saturated carbon) is anisotropic (fig.1). From the H H \ / +4.3 C=C t FIG. 1 .-Additional contribution to carbon molar atomic susceptibility (units of 10-6) and direction for ethylene. Value quoted for single carbon atom relative to ethane. theoretical estimate of its magnitude, chemical shifts relative to methane or ethane can be calculated for both carbon and hydrogen (table 1) using eqn. (2.9) and (2.1 1). TABLE CALCULATED CHEMICAL SHIFTS (p.p.m.) FOR ETHYLENE (RELATIVE TO ETHANE) DUE TO ADDITIONAL CARBON PARAMAGNETIC TERMS AND OBSERVED VALUES Calc. Obs. carbon - 46 - 120' 14 hydrogen - 2.1 - 4.211 *approximate value for comparable larger compounds. Data for ethylene and ethane un- available.The calculated shifts are in the correct direction but in both cases somewhat smaller than the observed values. This is comparable with the calculation of the Pascal constitutive correction for the carbon-carbon double bond which also gave a low value.10 The predicted diamagnetic anisotropy of the carbon-carbon double bond should have other consequences on proton shifts. Protons on or close to the axis of low dia- magnetism (fig. l) such as the protons furthest from the double bond in cyclopentene CHZ H H wilI be shifted to low field. This is confirmed by the measurements of Wiberg and Nist,l6 who found a shift of -0.39 p.p.m. for these protons relative to cyclopentane. Also protons which approach a carbon-carbon double bond from above or below (out of the nuclear plane) should show small high field shifts.(iii) CARBON-CARBON TRIPLE BONDS The acetylene molecule is predicted to have a high diamagnetic anisotropy with high diamagnetism along the molecular axis.59 10 This implies a high field shift for the protons due to the neighbour anisotropy effect. The observed position slightly to low field of ethane (-0.6 p.p.m.) can be interpreted as a cancellation of this with3. A. POPLE 13 a low field shift due to reduced charge density on the hydrogen atoms. The mean of the three atomic susceptibilities on each carbon atom is predicted to be the same as for a saturated carbon; this is consistent with the small Pascal constitutive cor- rection. Accordingly, the carbon shift should be close to that of the paraffins.In practice, it lies at an intermediate position between singly and doubly bonded carbon. (iv) ALLENES Calculations on the allene molecule H \ C=C=C-H2 / H are of some interest, as they give an additional paramagnetic term Ax," which is twice as large on the central atom as on the two end atoms. This is because the additional term in the plane of a double bond (fig. 1) occurs for both directions perpendicular to the C=C=C axis for the central atom, but only for one direction for the end atoms. The carbon resonance of the central atom should therefore, be shifted to low field relative to the end atoms; in fact, it should give the lowest field carbon signal for any hydrocarbon. Separations of this kind have been observed in a number of allene derivatives by Friedel and Retcofsky." They find a chemical shift of about 130 p.p.m.which may be compared with a calculated value of 40p.p.m. using a method comparable to that applied above to ethylene. Again, the calculated shifts are too small. (V) CARBONYL GROUPS Application of the theory with simple approximate molecular orbitals for the carbonyl group leads to an interpretation of the low diamagnetism of aldehydes and ketones (large positive constitutive correction) and also predicts anisotropies on the carbon and oxygen atoms.10 Table 2 summarizes the paramagnetic terms $. TABLE 2.-cALCuLATED PARAMAGNETIC CONTRIBUTIONS TO THE ATOMIC MOLAR SUSCEPTIBILITIES FOR THE CARBONYL GROUP (units of 10-6) C \ r' P = O I-.+ 6-46 10-76 6.46 x 0 10.83 1 o*oo 4.3 1 (The diamagnetic parts x$ will be more isotropic.) On the carbon atom there is an excess paramagnetic term in the y-direction which is comparable to that for carbon atoms in the C=C group.The excess term on the oxygen in the y direction can be interpreted similarly. The high paramagnetic term on oxygen in the x-direction aiises from the low-lying n-n* excited state, which is mixed with the ground state by a magnetic field in this direction. The anisotropies shown in table 1 for both atoms lead to negative (low field) contributions to the screening of aldehyde protons. The total calculated neighbour * I am indebted to Dr. G. Friedel of the Bureau of Mines, Pittsburgh, U.S.A., for permission to quote this unpublished data.14 THEORY OF CHEMICAL SHIFTS anisotropy shift is -2-6 p.p.m. of which - 2.2 p.p.m. comes from carbon. This is insufficient to explain the full shift of about -8 of the aldehyde resonance relative to paraffinic hydrogen. It may be that the theory underestimates the anisotropies in the carbonyl group, just as it underestimates the Pascal constitutive correction.10 Some low field shift is to be expected, however, for the charge distribution in the molecule, the carbon atom bearing a considerable net positive charge. 1 Hameka, J. Chent. Physics, 1961, 34, 1996. 2 Selwood, Magnetochemistry (Interscience, New York, 1943). 3 Saika and Slichter, J. Chem. Physics, 1954, 22, 26. 4 Lamb, Physic. Ren, 1941, 60, 817. SPople, Pr-oc. Roy. SOC. A, 1957, 239, 550. 6 McConnell, J. Chem. Physics, 1957, 27, 226. 7 Pople, J. Chem. Physics, 1956, 24, 1 1 11. SBernstein, Schneider and Pople, Proc. Roy. SOC. A , 1956, 236, 515. 9 London, J. Physique Rad., 1937, 8, 397. 10 Pople, J. Chem. Physics, 1962, to be published. 11 Pople, Mol. Physics, 1958, 1, 175. 12 McWeeny, Mol. Physics, 1958, 1, 311. 13 Bothnerly and Naar-Colin, Ann. N. Y. Acad. Sci., 1958, 70, 833. 14 Holm, J. Chem. Physics, 1957, 26, 707. 15 Schneider, Bernstein and Pople, J. Chem. Physics, 1958, 28, 601. 16 Wiberg and Nist, J. Amer-. Chem. SOC., 1961, 83, 1226.

ISSN:0366-9033    

DOI:10.1039/DF9623400007

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Theory of the Chemical Shift in Aromatic Heterocycles BY G. G. HALL,* A. HARDISSON * AND L. M. JACKMAN I>ept. of Mathematics, and Dept. of Chemistry (Organic Chemistry Research Laboratories), Imperial College, London, S. W.7 Received 7th June, 1962 An extension of the self-consistent form of the molecular orbital theory, to enable the chemical shifts associated with ring currents in aromatic molecules to be calculated, is discussed. The theory is used to predict the shifts of the aromatic protons in aza derivatives of alternant hydrocarbons and the results of the self-consistent calculations are compared with those of the Huckel theory. Calcula- tions for some other molecules are also presented and used to discuss the different effects of a hetero- atom on ring current. The ring current contributions to diamagnetic anisotropy are also tabulated. A ring current is induced among its mobile electrons when a conjugated mole- cule having at least one ring is subjected to a magnetic field.This current produces two effects which enable it to be observed, the diamagnetic anisotropy and the chemical shift. Unfortunately, both effects are influenced by other contributions and the calculated ring current contributions can be compared with experiment only when due account has been taken of these other effects. In general, the chemical shift is a more useful indicator of ring current than the anisotropy, partly because it is easier to isolate the ring current contribution 1 and partly because there are experimental results for each proton.The development of a theory of ring current using the self-consistent form of molecular orbital theory with the external magnetic field and the nuclear magnetic dipole treated as perturbations has been given recently 2 and described in relation to earlier theories by the present authors.3 Their paper also discussed a number of heterocycles and showed that the differences between the self-consistent results and the Hiicltel ones could become large and significant. This contrasts with the alternant hydrocarbons for which the results are almost the same. This discussion is continued in the present paper and some general conclusions drawn about the factors governing ring current. EFFECTS O F NITROGEN SUBSTITUTION In table 1 is given the calculated chemical shifts, due to ring current, for pyridine, pyrimidine and S-triazine.These are expressed as ratios to the corresponding effect in benzene and, since these are single ring systems, the same ratio is found for the ring current contribution to the diamagnetic anisotropy. Since the value of the electronegativity parameter 6~ is not precisely known the calculations have been repeated for thee possible values of &. This also facilitates the general dis- cussion of substitution. Two main effects can be seen in table 1. First, the ring current decreases as increases. This is due to the increased localization of electrons on the nitrogens and is parallel to the increase in formal charge there. It is least in pyridine, which has only one hetero-atom and greatest in S-triazine which * present address : Department of Mathematics, University of Nottingham.t present address : Department of Chemistry, University of Melbourne, Australia. 1516 CHEMICAL SHIFT I N HETEROCYCLES has three. The second effect is that the self consistent results for & = 0.2 show a ring current larger than in benzene. This can be attributed to larger value of PCN, which is 1.076 PCC, and increases the ring current. In the Huckel theory the first effect always predominates. To demonstrate that this B effect is genuine the cal- culation was repeated for pyridine with the same & and PCN equal to PCC. The result is 0.99 which is now less than benzene and also less than the Huckel value. TABLE 1.-cALClJLATED CHEMICAL SHIFTS AND DIAMAGNETIC ANISOTROPIES (RELATIVE TO BENZENE) IN PYRIDINE, PYR~MIDINE AND S-TRIAZINE pyridine pyrimidine S-triazine % Huckel S.C.F. Hiickel S.C.F.Huckel S.C.F. 0.20 1.00 1-02 0.99 1 -03 0.98 1 -04 0.50 0.98 0.99 0.95 0.96 0.90 0.89 0.80 0.96 0.95 0.87 0.83 0.76 0.67 The chemical shifts and diamagnetic anisotropies of the more elaborate hetero- cycles 4-( 1 -1ndenylidene)- 1 methyl- ly4-dihydropyridine (I) and cyclazine (11) are shown in table 2. For purposes of calculation, (I) is assumed to be planar. The results for (I) show that the chemical shift is considerably reduced from the benzene TABLE 2.-cALCULATED CHEMICAL SHIFTS AND DIAMAGNETIC ANISOTROPIM (RELATIW TO BENZENE) IN HETEROCYCLES (I) AND OI) chemical shifts T II ak 1 -02 1-52 2.02 position A B C D A B C D A B C D Huckel S.C.F.Hiickel S.C.F. 0.79 0-36 1.41 1.44 0.81 0.38 1.51 1.54 1-20 1.22 1.08 1.09 0.70 0.27 1.44 1-47 0.72 0.29 1-55 1.59 1-31 1-36 1.19 1.M 0-61 0.21 1.46 1.48 0.64 0-22 1-58 1-61 1.39 1-45 1.27 1-33 diamagnetic anisoiropies I II Huckel S.C.F. Hlickel S.C.F. 2-28 1.49 2.53 2-58 2.15 1.33 2-69 2-78 2-04. 1-20 2.80 2.89 value. This is due to the combined effect of the nitrogen, with its large value of 6iY and the substituent. The large difference between the Hiickel results and the self-consistent ones, already mentionedy3 is again to be noted. The effect of an increase in the electronegativity of a group attached to a ring is to counteract more and more the localizing effect of a nitrogen in the ring and hence to increase the ring current. (This effect is illustrated in table 2 of the previous paper.3) The experimental shifts4 suggest that there is virtually no ring current and hence that the planar model is incorrect.One explanation might be that the steric effect of the hydrogens attached to the two rings would produce a large twist about the inter-ring bond. This non-planarity would require a smaller p for the inter-ring bond and hence a smaller ring current. The results for (II) show an effect of nitrogen substitution which is of a quite different character. For this molecule the increase in produces a steadyG. G. HALL, A. HARDISSON AND L. M. JACKMAN 17 increase in the chemical shift and also a reduction in the range of values for the different protons. This can be explained by the fact that, as 6, increases, the molecule approaches closer to the 10 electron ring formed by the peripheral carbons because two electrons are becoming localized on the central nitrogen.To confirm z? A I 1 & C 0 U A Q; m FIG. 1. this interpretation the hypothetical molecule whose configuration is the same as this periphery was calculated. The results agree well with those obtained by extra- polating the results in table 2 to an infinite value for i3i. Effects of this kind can be expected in similar polycyclic molecules provided that the periphery is of Huckel type with (4n+2) electrons. Such perimeters have singlet ground states and are diamagnetic with large ring currents. THE PERINAPHTHENYLIUM ION The calculated chemical shifts and diamagnetic anisotropy of the perinaph- thenylium ion (111) are shown in table 3.It is hoped that experimental shifts will be available soon. One feature of this molecule is that the self-consistent results show much larger effects than the Huckel ones. This is in striking contrast with TABLE 3.<ALCULATED CHEMICAL SHIFTS AND DIAMAGNETIC AMSOTROPES (RELATIVE TO BENZENE) N THE PERINAPHTHENYLIUM ION chemical shifts diamagnetic anisotropies position Hiickel S.C.F. Hiickel S.C.F. A 0.77 0.92 2.01 2.41 B 0.85 1 -02 the corresponding results for the single ring systems discussed above. It agrees, however, with the results for (11) though the effect there is much smaller. The probable reason is that the central carbon, which has a negative charge of 0.024 in the self-consistent treatment and is neutral in the Huckel treatment, is increasing the ring current by making the periphery more nearly of type (4n + 2). One of us (A. H.) has to thank the C.S.I.C. of Madrid for a grant and we are indebted to the English Electric Company and staff of the DEUCE Department for computing facilities. 1 Elvidge and Jackman, J. Chem. Suc., 1961, 859. 2 Hall and Hardisson Proc. Roy. Suc., A, 1962, 268, 328. 3 Hall, Hardisson and Jackman, Tetrahedron, 1962, 268, 328. 4 Boyd and Jackman, unpublished results,

ISSN:0366-9033    

DOI:10.1039/DF9623400015

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Proton Chemical Shifts and Electron Densities BY B. P. DAILEY, ALBERT GAWER AND W. C. NEIKAM Dept. of Chemistry, Columbia University, New York 27, New York Received 15th June, 1962 Difficulty has been experienced in demonstrating empirically the theoretically expected linear relation betweer, chemical shifts and electron densities. The proton and C13 shifts for the aromatic ions are influenced appreciably by polar solvent effects and by " ring-current " shifts. When these are corrected for, a roughly linear relation between chemical shift and electron density is established. When this relation is applied to the azulene shifts, the poor correlation with calculated electron densities may be due to errors in spectral analysis or flaws in the calculations. The n.rn.r. spectra of substituted benzenes give results which correlate with the expected 71 electron densities reasonably well in the para position, although there are unexplained perturbations.In the ortho position a large extra shift is observed. Additional information on these problems obtained from new studies of cyclohexyl and cyclopropyl derivatives, substituted benzenes, and from a series of nitrogen heterocycles will be discussed. In the Ramsey equation,l proton chemical shifts are divided into a diamagnetic term dependent on the electrostatic potential produced at the proton by the mole- cular electrons and a second-order paramagnetic term which depends on the electronic excitation energies. The equation is too complex and requires too much detailed information to be used explicitly. However, many investigators have been attracted by the possibility of demonstrating an empirical correlation of chemical shifts with electron densities, at least for systems where the second-order paramagnetic term can be kept small and roughly constant.Unfortunately there are few chemical systems where the relative electron densities are reliably known. In this connection the aromatic hydrocarbon ions are of great interest because they have a known amount of charge which is symmetrically distributed about the ring. The chemical shift data for (C#S)-, (C7H7)+, and (CgH#- are summarized in table 1. TABLE. 1 .-CHEMICAL SHIFT-ELECTRON DENSITY RATIOS FOR HYDROCARBON IONS ion obs. chem. shift d corr. for 8 con. for charge shift from benzene solvent shift ring current benzene from ratio dhi*y C ~ H F ~ +1.731 +1.60 +1*43 +a200 7.15 C7H$" -1.87 -1.70 -1.59 -a143 11-13 C B H ~ - ~ +1*575 +1.48 +2.42 +a250 9-70 aver.9-33 (a) Fraenkel, Carter, McLachlan and Richards, J. Amer. Chem. Soc., 1960, 82, 8546. (6) Katz and Straws, J. Chem. Physics, 1960, 32, 1873. Unfortunately, the experimentally obtained chemical shifts, measured from a benzene reference, include two additional effects which must be taken into account if we are to obtain the factor of proportionality between charge density and chemical shift. The first of these effects involves differences in chemical shift due to induced " ring currents " in the aromatic ions. The aromatic hydrocarbon ions will have ring currents with different shielding effects than those of benzene because their rings are of different size, because their protons are at different distances from the centre of the ring, and because the rotating currents have different magnitudes.18B. P. DAILEY, A. GAWER A N D W. C. NEIKAM 19 The relation between theoretical and experimental ring current chemical shifts has been recently reviewed. Using the procedure outlined there, the ring current chemical shift for an aromatic hydrocarbon ion is given by the relation where KO is the entry in Johnson and Bovey's tables 2 for the appropriate proton- ring centre distance, a1 is the radius of the ring in question, ab is the radius of the benzene ring, 11 is the ratio of the ring current intensities for the ion and benzene, and 0.63 is the empirical constant found by Jonathan, Gordon and Dailey.3 These calculations are summarized in table 2.TABLE 2.-&NG CURRENT CORRECTIONS IN AROMATIC HYDROCARBON IONS distance of K COrr. ring centre KB x e)' no* ,z2m proton from I KIX 0.63 5 1-627A 1.228 6/6 -744 6 1.784 1-500 6/6 -946 7 1 -929 1.678 6/6 1-055 8 2.101 1.797 10/6 1.885 A second important correction arises from the presence of solvent effects on the chemical shift. The ion pairs involved in these measurements have large dipole moments and are soluble only in rather polar solvents. The data of Lumbroso, Wu and Dailey 4 indicate that electric field and polarizability effects resulting from aligned dipoles will give rise to chemical shifts which in table 3 are seen to be as large as 0.1 to 0.4 p.p.m. The entries in this table are the chemical shifts at infinite dilution in the individual solvents minus the chemical shift in the gas phase corrected for the van der Waals shift which was taken to be the average shift of methane and ethane TABLE 3.AOLVENT EFFECT DATA FOR ETHYL AND METHYL DERIVATIVES (CzHsIzO (CzHhN (,u = 1.15) (p = 0.8) group CH3 CH3CHz CH3CHz CH3CH2 CH3CH2 CH3CH2 molecule dipole CH3CN CzHsCN C2HsBr CzHd solvent moment proton ( p = 3.5) (p = 3.5) o( = 2.01) ( p = 1.87) cyclo- hexane ( p = 0) + 8.6 +0.7 + 8-6 +2.7 + 3-6 $0.5 - 0.2 - 0.9 - 3.0 -1.5 -3.4 dioxane ( p = -4) +10*2 -64 + 8.9 -3.4 + 5.5 -3.0 + 2.3 - 8-9 -10.3 -8.7 -8.7 CClJ (P = 0) +13.3 +0.9 + 8.5 -0.5 + 1.3 -1.2 - 3.1 - 4.7 - 6.7 acetone ( p = 2.75) 3-20-9 -1.0 +18.7 +la5 $13.3 +6.2 +13.7 -10-7 -6.0 - 6 4 at infinite dilution in the solvent. The solvent effect is largest for the most polar solute in the most polar solvent.The angle of orientation between the electric dipoles of solute and solvent also seems to be an important variable. The solvent effect corrections applied in table 1 are necessarily rather arbitrary but enable us to put an upper limit on the corrected chemical shifts. With the calculated n electron charges and the corrected chemical shifts, we can derive three separate values of the chemical shift-electron density ratio. The average value is 9-3 p.p.m./electron charge, but the agreement among the individual values is poor. A similar calculation has been made by Spiesecke and Schneider 5 for two of these ions, and by MacLean and Mackor 6 for the carbonium ions of methyl substituted benzenes. All of these calculations involve assumptions about ring currents.MacLean and Mackor use a somewhat arbitrary figure of 1.87 p.p.m. for the chemical shift from benzene to that for a proton bonded to an sp2 carbon atom. The use of accurate internuclear distances and the empirical factor 0-63 brings these results into fair agreement (8.8) with those reported above.20 PROTON CHEMICAL SHIFTS Another interesting situation is represented by the molecule azulene where a number of molecular orbital calculations have been made of the pattern of electron densities in the five- and seven-membered rings. The n.m.r. spectrum of azulene has been analyzed by Spiesecke and Schneider 7 and also in our laboratory. Un- fortunately, the assignment of chemical shifts to protons attached to the seven- membered ring is somewhat ambiguous.Again it is necessary to correct the ob- served chemical shifts for ring current effects. These corrections were calculated using the same procedure as above, and the calculations are summarized in table 4. TABLE 4.-&NG CURRENT CORRECTIONS IN AZULENE position 1: K i K&,m I&&, I: K i K&=r I&orr & &g 1, 3 2.262A 1.699 1.228 1.412 3.771 A 05045 0.6694 0.716 -2128 -0.396 2 2.262 1.699 1.228 1.412 4.660 0.2703 0.3587 0.383 -1.795 -0.186 6 5.080 0.2082 0.1505 0173 2.682 1.264 1.678 1.793 -1.966 -0.294 5, 7 4.578 0.2847 0.2058 0.237 2.682 1.264 1.678 1.793 -2030 -0.334 4, 8 3.175 0.8212 0.5937 0.683 2.682 1.264 1.678 1.793 -2476 -0.615 (1) I distance in A of ring proton from centre of ring ; (2) Kb obtained for this distance from Johnson and Bovey tables ; (3) &(as or,,, /abe,ne)2 ; (4) 15Kcon = 1.150 Kam; (5) I7&orr = 1.069 Kcom; (6) UAZ = I ~ K ~ ~ ~ f 1 7 K ~ ~ ~ ; (7) 0.63 (u,+=- 1.5).In table 5 the spectral data of Spiesecke and Schneider are corrected for ring current effects and the chemical shifts divided by 9.3 to obtain charge differences from benzene at the various positions. They are then compared to various calculated TABLE CH CHEMICAL SHIFTS AND ELECTRON DENSITIES IN AZULENE Streit- position 6H corrected for - 160 and Parr vEscFd wiesera ring current proton chem. shift SH 'H 6% HMOs scFb PariserC p.p.m. p.p.m. 2 -*583 --4OO +so43 f.023 -so47 +.003 +so21 -404 -so48 3, 1 -*067 +*333 -a036 -*061 -*173 --049 -so96 -*061 -*118 4,8 -*945 ---333 +a036 +*033 +-145 +-092 +.121 +-063 +-095 5,7 +.280 +.617 -so66 -*041 +.014 --034 -049 -*009 +*025 6 -*170 +*I33 -.014 f.038 +.130 +*062 +*052 +a039 +a084 (a) Streitwieser, Molecular Orbital Theory for Organic Chemists (John Wiley and Sons, Inc., New York, 19611, p.457. (b) Julg, J. chim. Physique, 1955, 52, 377. (c) Pariser, J. Chem. Physics, 1956,25, 1112. (d) Brown and Heffernan, Austral. J. Chem., 1960, 13, 38. eleotron density differences. Except for position 6, there is rough qualitative agree- ment between the " observed " densities and those calculated by Pariser and Parr, or the SCF method. Since the proton shift at position 6 is of a different sign than the C13 shift and since its assignment is somewhat doubtful, it is possible that a correct spectral assignment would produce improved agreement.The more recent calculations of Brown and Streitwieser also give the wrong sign for the density shift at position 2 where the spectral assignment is unambiguous. Another series of molecules with varying charge densities for which a number of calculations of electron density have been carried out is made up of the nitrogen heterocyclic molecules. The chemical shifts of some dozen of these molecules have been measured with respect to a benzene reference under comparable conditions. Unfortunately, calculations with identical parameters have not yet been completed for the majority of these molecules. Table 6 presents the available data for four of them, namely pyridine, quinoline, isoquinoline, and pyrimidine.Again there is rough qualitative agreement between " observed " and calculated patterns of electronB. P. DAILEY, A. GAWER AND W. C. NEIKAM 21 density. However, in view of the various complexities and uncertainties involved, it seems premature to conclude at this time that measurements of chemical shifts give an accurate and unambiguous measure of electron density. TABLE 6.-CHEMCAL SHIFTS AND ELECTRON DENSITIES IN THE NITROGEN HETEROCYCLES molecule position 6, from benzene d COIT for ring ? cum. P pyridine 2 - 1.30 p.p.m. - 1.30 p.p.m. -86 3 + -15 + -15 1.016 4 - -27 - -27 -97 quinoline 2 -1.565 - 1.38 *85 3 + 0033 + -21 1 *02 4 - -683 - 014 -985 isoquinoline 1 - 1.917 - 1.38 085 3 -1.231 - 1-04 * 89 4 - ,267 + -27 1 ~ 0 3 pyrimidine 2 -1.917 - 1.917 079 4 -1.382 - 1.382 a 8 5 5 + 0100 + -100 1.01 (a) Veillard and Pullman, Cumpt.rendu, 1961, 253, 2277. (b) Adams, Thesis (Illinois Institute of Technology, 1961). (c) Lowdin, J. Chem. Physics, 1951, 19, 1323. calc. .905a a970 ~ 8 2 9 ~ 1.038 a907 -825b a907 1 *009 *84= -87 1.01 1-05 Numerous studies have been made of chemical shifts in substituted benzenes, including the work of Spiesecke and Schneider at Ottawa and the recently completed work of Martin 8 in this laboratory. For a large group of para disubstituted benzenes, Martin found that the accurately measured chemical shifts obeyed the following relation where 6 is the chemical shift of a proton ortho to substituent R1 and meta to sub- stituent R4? do and dm are characteristic ortho and meta shielding parameters, and the y’s are empirical constants.The parameters obtained by Martin are listed in table 7 6 = dO(R1) + Y(Rl)d?n(R4), TABLE 7.-sUBSTlTuENT PARAMETERS IN PARA-DISUBSTITUTED BENZENES substituent NH2 OCH3 CH3 c1 Br I NO2 CN CHO COCH3 COCl 0.768 0477 0.1 83 O*OOO -0.159 - 0.363 - 0.955 - 0.27 - 0.54 - 0.64. - 0.83 d,, P.P.m. 0.27 1 0.108 0.107 0.065 0.134 0.265 -0.155 - 0.100 -0.195 - 0.091 -0.156 Y 0.70 0.67 0.9 1 1-00 1 -03 1-10 1 -20 and compared to those obtained by Spiesecke and Schneider in table 8. Somewhat similar results were also obtained by Diehl.9 As pointed out by Spiesecke and Schneider, in the para position the proton, F, and C13 chemical shifts all correlate well with the Hammett sigma reactivity constants. It is possible that all of these properties depend in a similar manner on the electron density on the carbon atom para to the substituent.However, the zero point of these various parameters is not identical. The shifts for chlorine, for example, may be positive in one case and22 PROTON CHEMICAL SHIFTS negative in another. This would indicate at least one other important contribution to the chemical shift even in the para position. In the ortho position, although there is a rough correlation between ortho and para shifts, there is definite evidence that other factors are important. Spiesecke and Schneider have suggested that this may be due to the magnetic anisotropy of the substituent group, but this has not been well supported by quantitative calculations. The meta shifts are small, and they do not seein well correlated with the expected pattern of electron densities.TABLE COMPARISON OF SHIELDING PARAMETERS DERIVED FROM PARA-DISUBSTITUTED BENZENES TO CHEMICAL SHIFTS OF MONOSUBSTlTUTED BENZENES substituent ortho shift d0 meta shift dm para shift derived dp NH2 0-75 0.768 OCH3 0.43 0.477 CH3 0.183 Cl - 0.02 0.000 Br - 0.22 -- 0.1 59 I -040 -0.363 NO2 -0.93 -0.955 CHO -0.58 -0.54 0.20 0.271 0.04 0.1 08 0-107 0.03 0.065 0.09 0.134 0.25 0.265 -0.21 -0.155 -0.21 -0.195 0-63 0.67 0-37 0.41 0.12 0-16 0-03 0.07 0.03 0-07 -0.33 -0.29 -0.28 -0.24 0.16 a (a) mean chemical shift of toluene ring protons. It is difficult to calculate the contribution of magnetic anisotropy to chemical shift since almost no accurate experimental measurements of magnetic anisotropies have been made except for a few aromatic hydrocarbons. Nevertheless, consider- able evidence has accumulated to indicate that important contributions to the chemical shift exist which are due neither to electron density nor to magnetic anisotropy.One such study is that of Cavanaugh and Dailey 10 on the chemical shifts in alkyl halides. Their data are summarized in table 9. It is evident that there is an incre- ment in chemical shift in going from the methyl to ethyl to the isopropyl derivative which is closely proportional to the number of C-C bonds. There seems to be no plausible way of accounting for these " C-C bond shifts " in terms of molecular anisotropy. TABLE 9.-cHEMICAL SHLFTS OF SOME ALKYL DERIVATIVES (Shifts to Lower Field in c/sec at 60 Mclsec from a Methane Reference) methyl ethyl isoprop yl prowl substituent - a gas a gas B gas a a B i F Cl Br I OH CN COOH -0- -S- CHO NH2 - s2- NO, NO2 F H C6H5 240 254 69 170 163 195 193 66 78 235 79 195 95 50 148 139 189 187 86 88 239 90 187 100 50 116 111 176 178 99 100 241 100 176 99 48 190 202 57 223 56 196 78 42 105 92 127 117 65 65 147 67 124 89 53 111 128 56 141) 59 125 87 46 127 144 59 160 61 142 85 44 181 186 189 198 55 61 200 51 183 79 42 112 114 136 143 61 66 162 61 132 82 45 117 108 134 54 I30 54 127 85 45 134 151 52 171 48 143 72 42 147 67 144 89 48 256 70 296 69 249 93 49 244 235 249 81 150 78 243 107 48 243 0 38 67 41B.P . DAILEY, A. GAWER AND W . C. NEIKAM 23 In a more recent study in this laboratory an attempt was made to study these various effects by determining the chemical shifts of the a protons in a series of monosubstituted cyclohexanes.At room temperature there is a rapid conversion of each of the two conformers of these derivatives into the other, so that a weighted average chemical shift is observed. It was necessary to freeze, where possible, each sample into separate, non-interchanging conformers in order to determine the indi- vidual chemical shifts shown in table 10. In table 1 1 is presented a calculation of the C-C bond shift for the cyclohexyl derivatives. The agreement with the values TABLE 1o.-cHEMICAL SHZFTS OF SOME CYCLOHEXANE DERIVATIVES AND THE POPULATION OF THE EQUATORIAL CONFORMERS clsec at 60 Mc/sec reference TMS substituent equatorid ez$ axial-equat.% POP equil., 26°C equatorla1 difference conformer proton OH 232 196 36 205 7.1 c1 264 221 43 232 21.5 Br 276 229 47 239 23.1 I 283 239 44 252 24.0 NO;! - (254) 253 -0 NH2 - (148) 150 -0 TABLE 11 .-c< BOND SHIFTS IN CYCLOHEXYL DERIVATIVES 'I 11-1 ethyl isopropyl I average - 2 c-c c-c substituent methyl axial- shift equat. c-4. bond- bond- cy&,hexyl bond-slft shift Shift OH 203 214 5.5 12 16 NH2 147 170 11.5 17 18 c1 183 243 30 25 33 Br 161 253 46 41 46 I 129 261 66 60 63 obtained for ethyl and isopropyl derivatives is quite good. The presence of the additional atoms in the cyclohexane ring makes it appear qualitatively as if the ct proton felt the influence of the magnetic anisotropy of the C-C bonds. One actually observes an increasing shielding for axial protons and a decreased shielding for equatorial protons.Quantitatively, however, this requires an implausibly large value for the anisotropy of a C-C bond. Anomalous chemical shifts are also found in three-membered ring systems. The central methylene group in propane would appear to have an electronic environment similar to the protons in cyclopropane. Their relative chemical shifts, however: are rather surprising. The propane methylene protons, for propane infinitely dilute in CC14, are found at 80 c/sec from the tetramethylsilane reference. The cyclopropane protons occur at over 1 p.p.m. to higher field at 13-3 clsec from TMS. Since the change in H-C-H bond angle (from 110" to 118') suggests an increase in the s character of the carbon bonding orbital, one would expect a lower electron density about the H atoms in cyclopropane as compared to propane.The suggestion that this upfield shift is due to a " ring current " in cyclopropane does not agree very well with the rather nonaromatic nature of the molecule. Further- more, the angle between the C-H bond and the plane of the ring is such that the expected ring current shift would not only be very small but would be in the wrong direction.24 PROTON CHEMICAL SHIFTS It is of interest to see if this shift to high field on ring closure would hold for other small ring systems. One interesting comparison is to compare chemical shifts for a series of substituted epoxides with those obtained for an analogous series of sub- stituted methyl ethers.The data obtained are presented in tables 12 and 13. Since TABLE 12.-CHEM[CAL SHIFTS FOR ETHERS AND EPOXIDES MEASURED FROM TETRAMETHYLSILANE ether CH34-CHzX epoxides X X H3 H Z HB H A H X OCH3 195.5 264.0 180.0 176.2 202.0 4 H 194 194 154.7 154-7 154.7 197.5 262.7 168.5 156.0 216.5 176.0 208.4 COOH 205.3 239.7 1792 c1 207.8 322.9 169.5 a 165-1 a 294-0 CN 205-7 247.9 181.4 18 6.7 210.0 (a) dilute CC14 solution : all other epoxides are from the data of Swalen. TABLE. 13.-Rwc CLOSURE s m IN SUBSTITUTED EPOXIDES substituent H~-HAB H2-ffx aver. ( 1 9 ) H 39 39 39 OCH3 17.5 62 40 32 30 COOH 28 c1 41 29 35 CN 22 38 30 35 46 40-5 4 a propane-cyclopropane shift is 40 clsec. one compares methyl protons for the substituted ethers with methylene protons on the epoxide, we actually observe the difference between a shift to higher field due to ring closure and a shift to lower fields due to the substitution of C-C for C-H. This overall shift in the propane+cyclopropane case is 40 c/sec. For the various substituents listed in table 13 the overall ring closure shift varies from 17.5 to 62 clsec up field. We may conclude by saying that the empirical relation between chemical shifts and electron densities is not yet firmly established. A number of other contributions to the chemical shift exist, and these contributions can be accurately estimated in only a few cases. The numerous instances in the literature where n.m.r. data have been used to establish molecular electron densities and molecular conformations must be reviewed quite carefully. 1 Ramsey, Physic. Rev., 1950, 78, 699. 2 Johnson and Bovey, J. Chem. Physics, 1958,29, 1012. 3 Jonathan, Gordon and Dailey, J. Chem. Physics, 1962,36, 2443. 4 Lumbroso, Wu and Dailey, J. Chem. Physics, to appear. 5 Spiesecke and Schneider, Tetrahedron Letters, 1961, 468. 6 MacLean and Mackor, J. Chenz. Physics, 1961,34,2208. 7 Spiesecke and Schneider, J . Chem. Physics, 1961, 35, 731. 8 Martin, NMR Spectra of Disubstituted Benzenes, Thesis (Columbia University, New York, 10 Cavanaugh and Dailey, J. Chem. Physics, 1961,34, 1099, 1962). 9 Diehl, Helv. chim. Acta, 1961, 44, 829,

ISSN:0366-9033    

DOI:10.1039/DF9623400018

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Long-Range Spin Coupling in Organomercury Compounds BY S. BROWNSTEIN Division of Applied Chemistry, National Research Council, Ottawa, Canada Received 9th April, 1962 Proton resonance spectra have been obtained of many compounds of the type CH30RHgX, where R is an organic radical and X is chloride, bromide, iodide or acetate. The proton-199Hg spin couplings are tabulated and discussed in terms of R and X. No hindrance to rotation about the carbon-carbon bonds is observed, contrary to previous reports. Extensive measurements have been made of proton-proton spin-coupling and theories have been postulated which give good agreement with the experimental results.132 Spin coupling of protons to heavy metal atoms is much larger, frequently does not attenuate regularly with an increasing number of chemical bonds between the coupled nuclei and often changes sign along the hydrocarbon chain3-6.The aim of this investigation was to obtain a more extensive body of data to aid in under- standing the mechanism of proton-heavy atom spin coupling. The proton resonance spectra of methoxyethylmercuric acetate and hydroxide have been reported.7 Although the authors report many extra lines, this may be attributed to the weaker magnetic field and poorer resolution available to them. Many of the lines due to the 199Hg spin-coupled satellites would be situated adjacent to the principal peaks under the conditions of their spectra. Hindered rotation about the carbon-carbon bond in methoxyethylmercuric iodide has been postulated from an examination of its infra-red spectrum.* However the proton resonance spectrum of this compound, along with all the others reported in this paper, may be most easily explained if free rotation is assumed.EXPERIMENTAL The proton resonance spectra were obtained on a Varian Associates high-resolution spectrometer operating at 56.4 Mc, and with the samples at approximately 26°C. Some of the compounds were dissolved in carbon tetrachloride containing 1 % tetramethylsilane. Concentrated or saturated solutions were necessary to obtain a good signal-to-noise ratio for the satellite peaks. Some of the spectra were obtained on the pure liquids in which case the methoxyl group or the terminal methyl group were used as a secondary standard. For these compounds no error is listed beside the appropriate peak in table 1.From cross- checks with other peaks it appears that this procedure does not introduce any error greater than that in determining the peak positions. Chemical shifts are reported in parts per million to low field of tetramethylsilane, and spin-coupling constants in clsec. The spectra were calibrated by superposition of audio- frequency side bands generated by a Hewlett Packard model 200J audio oscillator. The modulation frequency was determined to 0.1 c/sec with a frequency counter. Methoxyethylmercuric iodide was prepared as previously reported.8 An analysis for mercury yielded 51.3 % compared with the theoretical of 51.9 %. The general procedure followed to prepare the compounds used in this investigation was to bubble the appropriate olefin in excess, into a methanol solution of mercuric acetate.Aliquots of the resultant solutions were evaporated to obtain the acetates. By addition of an equal volume of a methanolic solution of potassium halide to an aliquot of the original reaction mixture, a precipitate of the alkylmercuric halide was obtained. This was filtered if a solid, or separated 2526 LONG-RANGE SPIN COUPLING N 0 -ti s -H N 0 -ti x N NN 0 00 N 0 $I 4 3 x x N 0 4 N x 3 2 4 '? m m 0 T s sf N N 9 0 3 1 - H c.l 0 -H \o 0 4 P4 0 8 2 2 $ 1 4 * * s * N N 8 000 N N Q 9 + I + s 31 m u" fa fl e 0 0 4 -ti fl N N 0 0 0 4 4 - H k f 00 0 x 1 e 0 $I N H 64 s u I O=U I x" I Y u I u O=Q I 57 u 0- H r4 m x" u d-S. BROWNSTEIN 27 if a liquid, and dried under vacuum before spectra were obtained.Most of the compounds were unstable to light and heat. This instability increased with increasing atomic weight of halogen and with increasing length of carbon chain. For this reason it was not possible to prepare iodides using olefins larger than ethylene. The spectra of the compounds were obtained shortly after preparation, and following this analyses were performed for mercury. The results of the analyses agreed with the theoretical composition within a few per cent, but were consistently low due to decomposition of the organo-mercury compounds. Best agreement was obtained with the most stable compounds. The proton resonance spectra sometimes showed acetate ion, water or methanol as impurities, generally in quite low concentrations. The corresponding compounds could not be prepared with perfluoro- olefins either by the method just described, or by heating in an autoclave under pressure.DISCUSSION The chemical shifts for the protons in the compounds studied are listed in table 1, and the spin couplings in table 2. The spectrum of 2-methoxychloromercuripropane, representative of those obtained, is shown in fig. 1. Except for treatment of the non- equivalent CH;! protons as an AB system the spectra may be satisfactorily analyzed 1864 74 ~ 110.3 9 L FIG. 1 by first-order perturbation theory. This does not ordinarily allow an assignment of relative signs to the spin-coupling constants. Under certain circumstances it is possible to determine the relative signs even when first-order perturbation is applic- able? However, these conditions are not met in the present results.Proton double resonance would be required to determine the relative signs of the mercury-proton spin couplings in these compounds at the magnetic field strength employed.5 Despite the lack of signs, certain conclusions may still be drawn about the variation in spin coupling with structure. No satellite peaks due to proton-199Hg spin coupling were observed for methoxy- ethylmercuric iodide under conditions similar to those for which these peaks were readily obtained with the corresponding chloride, bromide and acetate. It is con- cluded that rapid exchange is occurring between iodomercuri and methoxyethyl species. Such exchange has previously been observed in organomercury compounds 10 and in other metal alkyls.SJ1 Such exchange was not observed in any of the other compounds investigated.Spin coupling between 199Hg and the protons on the carbon atom attached directly to mercury are within about 10 c/sec of the value 215 c/sec, regardless of the structure28 LONG-RANGE SPIN COUPLING u" 2 I m B 2 F4 $I d d N d $I z 0 0 cl 0 N 00 ccr m $I N m N N -H d $1 M Q\ N * N $1 N -ti 8 N m Y 8 I o=u I 0 I 3 I x" I /\ u -u " N$ u 0 m k Y I . ' 8 8S. BROWNSTEIN 29 of the alkyl chain or the identity of the substituent X. Spin coupling to the protons on the p carbon atom shows a greater variation with X, but no trend is discernible. However, there is a marked increase in the coupling constant for CH compared with CH2. No spin coupling to the protons on the y carbon atom is observed in the propyl compounds but a spin coupling constant of 21 c/sec, independent of X, is observed with the sec.-butyl compounds, These results may be rationalized if we assume that the spin coupling is a function of the dihedral angle between the mercury- carbon bond and the bond between the /? carbon atom and a proton or methyl group attached to it.A similar relationship has been proposed for long-range proton- proton spin coupling.12 It has been assumed that the spin coupling is a minimum for a dihedral angle of 180" and gradually increases as the angle approaches 60O.12 To explain the present results one must further assume no conformational prefer- ence about the a-p carbon bond when only protons and a methoxyl group are attached to the carbon atom.Methyl groups attached to this carbon are assumed to be located as far from the mercury atom as possible. This is shown in fig. 2. The +++ Hg Hg Hg AVERAGE H = looo AVERAGE H = 60° AVERAGE CH, = 120° 11 CH,= 180° FIG. 2.-Average dihedral angle smaller average dihedral angle then corresponds to the larger observed spin couplings. However, if the above conformational preferences are assumed to be true, the larger spin couplings are also associated with a smaller average distance between the coupled nuclei. Direct interaction through space, as has been proposed for some fluorine- fluorine coupling,l3 would also explain the results. Both these hypotheses must be considered quite speculative. The proton-proton spin couplings are similar to those usually observed for alkyl groups. No unusual effects are observed in the proton chemical shifts. 1 Karplus, J. Chem. Physics, 1959,30, 11. 2 Gutowsky, Karplus and Grant, J. Chem. Physics, 1959,31, 1278. 3 Dessy, Flautt, Jaffe and Reynolds, J. Chem. Physics, 1959,30, 1422. 4 Narasimhan and Rogers, J. Chem. Physics, 1961, 34, 1049. 5 Maher and Evans, Proc. Chem. SOC., 1961,208. 6 Stafford and Baldeschwieler, J. Amer. Chem. SOC., 1961,83, 4473. 7 Cotton and Leto, J. Amer. Chem. SOC., 1958,80, 4823. 8 Kreevoy and Ditsch, J. Amer. Chem. SOC., 1960, 82,6124. 9 Narasimhan and Rogers, J . Chem. Physics, 1959,31,1430. lo Reutov, Smolina and Kalyavin, Dokludy Akad. Nuuk. S.S.S.R., 1961,139,389. 11 Brownstein, Smith, Ehrlich and Laubengayer, J. Amer. Chem. Soc., 1960, 82, 1000. 12 Bothner-By and Naar-Colin, J. Amer. Chem. SOC., 1962,84,743. 13 Petrakis and Sederholm, J. Chem. Physics, 1961, 35, 1243.

ISSN:0366-9033    

DOI:10.1039/DF9623400025

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Measurement of J Coupling Using Spin Echo Techniques BY J. G. POWLES AND J. H. STRANGE Physics Dept., Queen Mary College (University of London), Mile End Road, London E.l Received 25th June, 1962 The spin echo method of measuring indirect spin-spin coupling and chemical shifts from the modulation of the echo amplitude is described. and compared with the steady state method. The hitherto unobserved small variation with temperature of the J coupling in acetaldehyde and in methyl alcohol is explained in terms of thermally excited internal molecular motion and angle dependent J coupling. The double J coupling in the methyl formamides is discussed. The absence of effects due to coupling to non-resonant nuclei is illustrated for fluorobenzene, the methyl formamides and ammonia. The effect of proton exchange on the signal from methyl alcohol may allow a closer study of the exchange process than by steady-state methods.The indirect couplings between nuclei, J, and the chemical shifts, S, are usually measured by delineation of the absorption spectrum by use of a small probing radio frequency field and by sweeping the field or the frequency. Actually the hyperfine splitting was first observed at almost the same time by steady state and by transient methods.1 Hahn and Maxwell 2 showed that the modulation ofcertain transient signals could be explained by couplings of the form hJ 11 .12 which also explain the steady state multiplet spectra. However, the transient method proved to be less attractive because the signals are not as straightforward to interpret and the electronic techniques are less familiar.In addition it proved not too difficult and not pro- hibitively expensive to produce magnetic fields of the requisite homogeneity and stability. Consequently the transient method was almost abandoned. Only one paper 3 was published after Hahn and Maxwell. It is noted that the transient wiggle beat method 4 requires the high resolution magnetic field. Recently we took up the method again 5 since it was realized 6 that techniques have considerably improved and more importantly, the original method employed a particularly unfortunate pulse sequence as explained below. echo method is of interest for the following reasons. It does not require a high resolution magnet (our " resolution " is 100 mG). It is possible in some cases to measure J to higher accuracy than with con- ventional high resolution equipment.The limitation to improvement in accuracy of measurement is not an arbitrary field inhomogeneity or stability. One gets automatic decoupling from non-resonant nuclei (non-resonant nuclei can be coupled in but this has not been exploited 7). Some effects, such as proton exchange and isomeric conversion behave differentIy in transient measurements and so a closer study may be possible than by high resolution spectroscopy alone. It is always sensible to study an effect in as many different ways as possible. principal disadvantages of the method are : It is usually difEcult to interpret the results in terms of J and 6 values. 30J . G. POWLES A N D J .H . STRANGE 31 (ii) In echoes, interactions described by magnetic fields tend to be removed, thus effects due to 6 tend to disappear. (However, this may have the ad- vantage of simplifying the transient and, in any case, 6 is easier to measure than J ) . (iii) The apparatus is not as yet available commercially. (iv) Decoupling of identical chemically shifted sets of nuclei is not possible. (v) The equivalent of double quantum experiments are probably not possible. We hope to show by the examples given below that the echo method is of con- siderable interest in an increasing number of special cases. cos nJt cos x(d2 + J2)*t (S2 + J 2 ) EXPERIMENTAL In the spin echo method, one applies a series of pulses of intense radio frequency field at the resonant frequency which can turn the nuclear magnetization by a certain angle, in our case by 90" or by 180".For a sample in a static inhomogeneous field and for spacing 2 between the 90" and 180" pulses, a nuclear signal, an echo, appears at time 22. We study the amplitude E of this echo. It is attenuated by decay of transverse magnetization (T2) and by self-diffusion in the inhomogeneous field ( T D ) by the factor exp - [t/T2+ t3/Ti] where t is the time of echo. In the original ex- periment, a go", 2, 90" sequence was usedzb but there was excessive decay due to self-diffusion which in practice meant that barely one cycle of J could be observed. It was suggested that a go", 2, 180", 22, 180", . . . sequence be used 6 since this tends to remove self-diffLision effects 8 and incidentally gives the considerable experimental advantage of a series of echoes and hence values of E(t) in one shot. For non-zero J and 6 the echo amplitude is modulated.For a go", 2, 90" sequence for an AB case, the amplitude of the echo at time t is 2 . (2) For a go", 2, 180" sequence we have 6 cos nJt+ ~ sin nJt sin n(a2 + J2)*t + (d2 + J2)+ Both expressions depend on both J and 6. It is of interest to consider the AX case, i.e., J/6 < 1 ; these then become E(t) = + I 1 -4(1- cosnJt)(l -cosnnSt) 1 (1') and E(t) = I cos nJt 1 (2') This illustrates the considerable simplification in using 180" pulses if one is interested in J. In fact for a go", z, 180", 22, 180°, 22, . . ., sequence the amplitude of the nth echo (at t = 2127) for AX is 5 also E(t) = 1 cos nJt I (2") It is easy to show that the echo amplitude for AnMmXz, etc., is given by taking the steady state spectrum, collapsing by removing all the chemical shifts and then taking the Fourier transform of the collapsed spectrum.(It should be noted that the Fourire32 J BY SPIN ECHOES transform of the steady state spectrum is the Bloch decay in a homogeneous field, which is quite different.) Thus, for AX3 we have E,(t) = (1/16) [ 15 cos nJt + cos 3nJt 1, (3) which it so happens is not very different from (2”) for AX and we have exploited this in a study of a series of AX3 and almost A B 3 cases. We have not yet been able to calculate En(t) for AB. However, we have the result up to and including E4(t) 5- 9 and Strange has found that these fit the general formula En(t) = I (1 - r/2) cos n(J-2)t + (- l)n(r/2) cos n(J+Z)t I .. . r = 1 - [ 1 - 2L2 sinZn(J2+ S ~ ) + Z ] / [ 1 -L2 sin22n(J2 + S2)32]3, L = I J 1/(J2+82)+ (4) where and 2 is given by the equation sin 2nZz = L sin 2n(J2+62)%. We have tested this semi-empirical formula for the AB case of 2-bromo-5-chloro- thiophene. At our resonant frequency of 20.8 Mc/sec this has J/6=1. We shall report this in detail elsewhere. Eqn. (4) is also of interest since it allows an important correction of eqn. (2”) and more complicated cases. It will be noted that eqn. (4) reduces to (2”) if sin 27~(62+J2)% = 0. (This corresponds roughly to the fact that the first and second, or third and fourth, lines of the AB spectrum have a separation J independent of 6.) Thus, by choosing the echo spacing z judiciously we can remove the correc- tion terms to eqn.(2”) and considerably simplify the determination of J when the condition J/6< 1 is not well obeyed. Since we are hoping to measure J to 3-0.01 c/sec we find that the correction is important even when J/S is as small as 0-01 as for example, in methyl formate discussed below. We believe that eqn. (4) can be used with some confidence also for cases approaching AB3, since we note that the second term in (3) is not only small but has zeros with cos nJt. The correction seems to operate sensibly for acetaldehyde which for us has J/6 = 0.018 and for methyl alcohol where J/6 e0.15. We are able in most cases to almost remove the effect of self diffusion attenuation so that the decay of the echo amplitude in the figures is mainly due to T2, i.e., they correspond to the unavoidable natural line width and so one can observe amplitude modulation out to effective T2’s of order 5 sec.The effective T2 for a go”, z, 90” sequence would be about 0-2 sec. In favourable cases we can measure J with a standard deviation of k0-01 c/sec and are able to detect a J down to about 0.2 c/sec. We worked at the rather low frequency of 20-8 Mc/sec because the apparatus was available. Operation at a higher frequency, say 60 Mc/sec, would reduce the values of J/d and make the interpretation much simpler, as for steady state spectra. It would increase considerably the number of molecules that could be studied without undue labour. We have observed echo modulation in a great number of molecules,5~ 9-11 but we only report those cases where the echo method has done more than merely con- firm the steady state measurements.SMALL VARIATIONS OF J COUPLING WITH TEMPERATURE We have studied a number of molecules for which the J coupling in the literature, usually given to k0.1 c/sec, did not appear to depend on temperature. We have ignored those cases where, due to isomerism for instance, as in propionaldehydeFIG. 5.--Echo modulation pattern in N-methyl formamide at 24°C. Total sweep is 1.5 sec. This fits eqn. (6). FIG. 6.--Echo pattern with no modulation for dry liquid ammonia at 23°C. with N14 gives the steady state triplet for the same sample shown in the upper right corner. were effective in the echo experiment alternate echoes would have almost zero amplitude.The J interaction If it Total $weep is 0.25 sec.FIG. 3.-Echo modulation pattern in l,l-dichloroethane at 22'C. Total sweep is 1.5 sec. FIG. 4.-Echo modulation pattern in methyl formate at 22°C. Total sweep is 4 sec. [To face page 33J . G . POWLES AND J. H. STRANGE 33 the J values vary considerably with temperature since this can be studied quite easily by steady state methods. All the molecules below are of A X 3 or AB3 type. (a) ACETALDEHYDE CH3CHO We have reported elsewhere 12 the variation in J coupling with temperature shown in fig. 1. We have J/S = 0.01 8. The variation in observed J i s due to changes with temperature in the averaging over J(4), the coupling of the methyl to the aldehyde proton, due to a three-well sinusoidal potential. If we write a) J(4) = a,, cos n4 n=O (5) the experimentally observed average value (J>T determines a0 and a3.We find for acetaldehyde a0 = +2-54 c/sec and a3 = 20.69 cfsec. The large a3, the cos 3# term, is surprising in view of the theoretical result for ethane,l3 that J(4) approxim- ates to (c1+ c2 cos24) for which indeed no temperature dependence of (.I> is expected. 8 3.0 2.9 2 \ .!3 Q E-4 v 2-43 -100 - 58 0 50 2.7 temperature in "C are from ref. (15). FIG. 1 .-Variation of observed J coupling with temperature in acetaldehyde.12 Circled points Our results suggest that J(4) might go quite negative for some values of #. In carry- ing out the analysis 12 we used the information that the internal barrier in acetalde- hyde is sinusoidal with height 1.16 kcal/mole.l4 Our calculations show that for our accuracy an appreciable variation of <J)T in the usual liquid temperature range will only be found when the internal barrier is of order 1 kcal/mole, supposing a suitable J(4) exists.Steady state methods had in fact indicated the variation of J with temperature in acetaldehyde 15 but with insufficient accuracy for this to be claimed. If our inter- pretation is accepted the J value +(Jt + 2J,) which is the average value without thermal vibration? even zero point vibration? is 3-23 c/sec and this is the value to be com- pared with theory. The observed value at 25°C is 14 % lower! B34 J BY SPIN ECHOES (b) METHYL ALCOHOL CH30H We have J/6-0.15. The correction described in the experimental section is rather important.We knew the internal barrier to be 1.07 kcal/mole 16 so we were not surprised to find the variation of (J)T with temperature shown in fig. 2. Above -20°C proton exchange becomes important and this is discussed in another connection below. It is interesting that in this case (J)T increases with temperature. This means that a3 and a0 have opposite signs in methyl alcohol whereas they are the same in acetaldehyde. Using the theory developed for acetaldehyde12 we estimate a0 = +5-9 c/sec and a3 = f 1.8 clsec. Thus again the cos 34 term is important. temperature in "C FIG. 2.Variation of observed J coupling with temperature in pure methyl alcohol. Above -220°C J appears to fall due to proton exchange. The open points are for methyl alcohol+acetone 23 in which the exchange is slowed. (c) I,~-DICHLOROETHANE CH3CHC12 We have J/6 = 0.074.The echo modulation is shown in fig. 3. There is possibly a decrease in (J)T over the range -120°C to 100°C of about 2 %. This is con- sistent on our theory with the fact that the internal barrier to rotation of the methyl group is probably considerably greater than 1 kcal/mole. (d) 1,I 1 &TETRA C H LOR0 P RO PANE CH3CHClCCl3 We have J/6 = 0.11. A preliminary investigation shows no variation of <J)T with temperature. (e) METHYL FORMATE HCOOCH3 We have J/6 = 0.009. This compound illustrates the value of the method for small J values, J = 0.815+0-01 c/sec as illustrated in fig. 4. No variation in <J)T in the range - 110°C to 25°C has yet been observed probably because J itself is so small.The barrier is " suitable ", 1-19 kcal/mole.22J . G . POWLES AND J . H. STRANGE 35 CASES WITH MORE THAN ONE J COUPLING We have shown 12 that for ABX with JAB = 0 the echo modulation is given by the collapsed spectrum method.5 We give two examples approximating to this situation. (a) N-METHYL FORMAMIDE 0 CH3 \ \ / C-N 2 1 This is ABX3, J / 6 ~ 0 - 0 0 8 . H/ ‘ € 3 3 We see no effect of J13 since J13/&3> 1. (The high resolution spectrum’ similarly does not give J13 except with spin decoupling.17) The remaining two couplings 4 2 and J23, should give an echo amplitude modulation, En(t) = 1/5 I 3 cos nJl2t cos nJ23t +~0~3nJl2t + c o s % J ~ ~ ~ 1. (6) The experimental result in fig. 5 fits eqn. (6), with 3 % “loading”,5 with J12 = 1.0+0.1 c/sec and J 2 3 = 4.9+0.1 c/sec.The steady state results using N14 decoup- ling are J12 = 0.9 c/sec and J23 = 4.9 c/sec.17 We have ignored coupling to N14, which has a considerable effect on the steady state spectrum, because this coupling is ineffective as discussed below. We found it useful in this case to “ load ” the signal with known proportions of dissolved water, which simply adds a known constant term inside eqn. (6). This enables one to check compliance with the equation more precisely and is a useful trick when interpreting complex modulation patterns, (6) N,N-DIMETHYL FORMAMIDE 0 CH3 2 \ / C-N CH3 3 / \ 1 H This is A&X, J / 6 ~ 0 . 0 0 6 . Using the collapsed spectrum method we expect an echo modulation pattern given by, En(t) = 1/7 I 6 cos n%(J12+J13)t cos n&(J12-J13)t ~0~3nJ23t fcos’nJ12t COS371J13t 1.(7) We only see the dominant first term and find I J12kJ13 I = 1.10&0.05 c/sec, I J12qJ13 I ~ 0 . 2 c/sec, according as J12 and J13 have the same or opposite signs. J23 qO.2 c/sec. of J 2 3 is observed. There is, therefore, some discrepancy in this case. The steady state results are J12 = 0.8 c/sec and J13 = 0.4 c/sec 179 18 and no effect ABSENCE OF COUPLING TO NON-RESONANT NUCLEI If the pulses are only applied to one set of resonant nuclei any coupling to a set of non-resonant nuclei will be ineffective. This coupling can in fact be shown up if we also pulse the other set of nuclei, or even only irradiate them.7 We have not yet exploited this effect for measuring J couplings between non-resonant nuclei.36 J BY SPIN ECHOES (a) FLUOROBENZENE C6&F The steady state proton spectrum of fluorobenzene is dominated by the doubling due to H1-F19 coupling of about 6 c/sec.It has also been observed in a free pre- cession experiment.20 A 6 clsec modulation is certainly not observed in the echo pattern; the slight modulation found can be ascribed to the proton interactions only. (b) N-METHYL FORMAMIDE AND N,N-DIMETHYL FORMAMIDE We have already mentioned that in the analyses for these molecules we ignored the H1N14 coupling, which considerably affects the steady state spectrum, and yet obtained a satisfactory result. (C) AMMONIA We have prepared dry liquid ammonia and observed the triplet high resolution proton signal as shown in fig. 6. For the same sample there is no echo modulation as shown in fig.6, thus illustrating the effective N14 decoupling. MEASUREMENT OF CHEMICAL SHIFT To avoid giving the impression that the echo method can only measure J we point out that by use of go", z,90° pulse sequences S can be measured even if J<6, e.g., using eqn. (1'). Since 6 is usually greater than 10 clsec little difficulty with self- diffusion attenuation is experienced. We have not reported 6 values determined by our method since they can be as easily determined by steady state methods. We have already discussed 2-bromo-5-chloro-thiophene which is an AB case and for which we get both 6 and J in these and earlier 5 experiments. We recall that in order to apply the condition sin 2n(62+J2)3 = 0 we have to know 6. This was usually measured for the examples given in this paper by steady state methods.It is interesting to note that the condition above can be found experimentally by the echo experiment. If only the order of magnitude of 6 is known it can be determined quite accurately at the same time as J. As a matter of fact the experimentally required variation of z with temperature to get good modulation patterns in methyl alcohol drew our attention to a considerable variation of 6 in this liquid with temperature. PROTON EXCHANGE EFFECTS It is well known that proton exchange, if fast enough compared with J, can cause a collapse of the multiplet structure. One of the simplest examples is methyl alcohol. By following the changes in the multiplet structure an estimate can be made of the exchange rate and its variation with temperature, with an appropriate model of the exchange process.21 The corresponding effect on the echo amplitude modulation is that first the apparent J value decreases (as for the steady state spectrum) and this is shown in fig.2. With increasing temperature the modulation disappears. In the steady state method only one experiment can be performed, namely, the study of the line shape as a function of temperature. In the echo experiment we have another variable, the pulse spacing. We find that the echo amplitude modula- tion varies considerably with echo spacing particularly in the intermediate region. The effect is quite similar to the breaking-up of the diffusion process by the use of multiple echoes.8 The analysis of the effect is rather complicated and will be pre- sented elsewhere.We find we can observe modulation due to J coupling in spite of exchange to a temperature some 10°C higher than by the steady state method.J . G . POWLES AND J . H. STRANGE 37 Moreover, our more detailed experimental data lead us to expect that we shall be able to make a more severe check on the validity of models for proton exchange. Rather similar considerations should apply to the suppression or variation of J coupling by isomeric conversion processes at rates comparable to J but we have not yet found a simple example of this. We thank Mr. D. Green for measuring high resolution spectra of the substances used and Dr. K. Krinicki and Dr. D. Cutler for help in the preparation of samples. J. H. S. held a D.S.I.R. Post-graduate Studentship during this work. 1 (a) Proctor and Yu, Physic. Reu., 1950, 78, 471. (b) Gutowsky and McCall, Physic. Rev., 2(a) McNeil, Slichter and Gutowsky, Physic. Rev., 1951, 84, 1245. (b) Hahn and Maxwell, 3 Crawford and Foster, Can. J. Physics, 1956, 34, 653. 4 Bknk, Denis and Exterman, Physica, 1951, 17, 308. 5 Powles and Hartland, Proc. Physic. Sac., 1961, 77, 273. 6 Powles, Reports Progr. Physics, 1959, 22,433. 7 Emshwiller, Hahn and Kaplan, Physic. Rev., 1960, 118,414. * Carr and Purcell, Physic. Reu., 1952, 88, 415 ; 1954, 94, 630. 9 J. H. Strange, private communication. 1951, 82, 748. Physic. Rev., 1951, 84, 1246 ; 1952, 88, 1070. 10 A. Hartland, private communication. 11 Powles and Hartland, 1960, Report of 9th Colloque AMPERE, p. 474. 12 Powles and Strange, MoZ. Physics, 1962, 5, 329. 13 Karplus, J. Chem. Physics, 1959,30, 11. 14 Kilb, Lin and Wilson, J. Chem. Physics, 1957, 26, 1695. 15 Abraham and Pople, Mul. Physics, 1960, 3, 609. 16 Wilson, Adv. Chem. Physics, 1959,2, 367. 17 Baldeschwieler and Randall, Chem. Rev., 1962, 00, OOO. 18 Fraenkel and Franconi, J. Amer. Chem. Soc., 1960,82,4478. 19 Bak, Shoolery and Williams, J. Mol. Specf., 1958, 2, 525. 20 Elliott and Schumacher, J. Chem. Physics, 1957, 26, 1350. 21 Kaplan, J. Chem. Physics, 1958, 28, 278. 22 Curl, J. Chem. Physics, 1959, 30, 1529. 23 R. J. Abraham, private communication.

ISSN:0366-9033    

DOI:10.1039/DF9623400030

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Possibilities for High-Resolution Nuclear Magnetic Resonance Spectra of Crystals BY E. R. ANDREW AND R. G. EADES Dept. of Physics, University College of North Wales, Bangor, Caernarvonshire. Received 15th June, 1962 The observation of high-resolution n.m.r. spectra in liquids is possible because rapid molecular tumbling removes the dipolar broadening which in solids obscures the fine structure. It is shown that rapid rotation of solid specimens about an axis inclined at an angle 54" 44' to the direction of the applied magnetic fieId can achieve the same end. Some experimental results are reviewed and a short discussion is given of factors affecting the residual line-width. For proton and fluorine resonances it may prove difficult to achieve speeds of macroscopic rotation which are high enough to be useful.The alternative approach of a fixed specimen placed in a rotating magnetic field is therefore discussed, and the construction of a practical system is outlined. The paper closes with a discussion of nuclear cross-relaxation induced by specimen rotation in solid phosphorus pentachloride. THE ROTATING SPECIMEN METHOD High-resolution nuclear magnetic resonance spectra of the kind much studied in liquids are not normally observed with solid specimens. The relatively strong magnetic dipolar interactions between the nuclei overlay and obscure the finer features arising from differing chemical shifts and electron-coupled interactions. In liquids the dipolar broadening is largely removed by the rapid random rotational and trans- lational motions of the molecules.Each term in the truncated dipolar Hamiltonian contains the angular factor (3 cos20if- l), where 0$, is the angle between a typical internuclear vector rgj and the applied magnetic field Ho; the isotropic average of this factor over times of order of the spin-spin relaxation time T2 is small, when the correlation time zc of the random motion is much less than Tz, as is usually the case with liquids. We have approached the problem of removing the dipolar broadening in solids by rapid macroscopic rotation of the sample. The truncated dipolar Hamiltonian is = c ( p l .pj-3pizpjz)4(3 c o s * ~ , j - i ) r ; 3 . (1) i,3 If the specimen is rotated with uniform angular velocity cl>, about an axis inclined at angle a to €30, then Oij is time-dependent and (1) may be conveniently expanded as 3pizpj3 sin2 y i j cos (20,t + 4,j)rG3. (4) 2 1 is the mean truncated dipolar interaction.S i ( t ) is the time-dependent part of the interaction, which generates side-spectra at integral multiples of mr on either 38E. R. ANDREW AND R. G. EADES 39 side of the central resonance. Comparison of (1) and (3) shows that the central line should have the same shape as that of the static specimen when Ho is directed along the axis used in rotation experiments, but reduced in width by a factor 4(3 cos2a- 1). The second moment of this central line should be reduced by a factor $(3 cos2a- 1)2. These features have been verified in experiments using 23Na resonance in sodium chloride.1-3 The method applies equally to monocrystalline or polycrystalline specimens.Particular interest centres on the use of an angle a of 54" 44' (cos-1 l/J3), for which the dipolar breadth is small. Rapid rotation about an axis inclined at this particular angle largely removes the dipolar broadening just as isotropic motion removes it for a liquid. Whena, greatly exceeds the static line-width the side spectra generated by the time-dependent perturbation (4) move well out and become un- observably weak, as for a liquid, leaving only the narrowed central line. Finer structure, if present, should now be observable. Plastic air-driven rotors of the type developed by Henriot and Huguenard4 and by Beams 5 have been used to rotate solids up to 3 kc/sec. The specimen is placed in a capsule mounted on the rotor, spinning freely inside the radio-frequency coil.Experimental rotors of the kind developed by Lowe6 have been spun at speeds up to 8.5 kc/sec. On theoretical grounds the criterion for spectral narrowing is that the rate of rotation must be comparable with the static line-width. In practice this is found to be the case, and in particular cases the spectrum begins to break up when the rate of rotation is about a quarter of the line-width defined by the interval between derivative turning points. In order to exceed the line-width with the speeds of rotation available, the first experiments were done with 23Na and 31P resonances since these nuclei have lower magnetic moments than protons or 19F nuclei, and therefore generate much smaller dipolar broadening. With phosphorus pentachloride two sharp chemically-shifted lines were obtained.7 The two lines arise from the two types of ion PCli and PCl; of which the crystal is composed in equal numbers. It has been checked that the separation is proportional to the applied field, and it is large enough to enable the lines to be separated in a strong field even without spinning.The shifts, relative to 85 % orthophosphoric acid, the usual phosphorus standard, form a monotonic sequence with those for PC15 in carbon disulphide solution and liquid PC13 : PC13 (-215 p.p.m.), PCl; (-96 p.p.m.), PC15 (+80 p.p.m.), PCl; (+281 p.p.m.). THE RESIDUAL SPECTRAL LINE-WIDTH Factors which determine the residual breadth of lines narrowed by rapid rotation with a = 54" 44' include the following.FIELD 1NHOMOGENEITY.-when recording high-resolution n.m.r. spectra of liquids, the specimens are rotated for the specific purpose of reducing the effect of field inhomogeneity. In our case the specimens are being rotated anyway and the result is largely to remove broadening due to inhomogeneity in planes normal to the axis of rotation, leaving only the inhomogeneity along the axis. This residual inhomo- geneity can be made very small, as with liquids. RESIDUAL DIPOLAR BROADENING.-on1Y in the limit of infinitely rapid random isotropic motion is dipolar broadening entirely removed for a liquid. Similarly here, only in the limit of an infinitely rapid rate of macroscopic rotation is dipolar broadening entirely removed for a solid. Random nuclear spin exchanges cause the magnetic environment of a given nucleus to change in the course of each rota- tion of the specimen.As the period of rotation becomes shorter in relation to T2 the loss of phase coherence decreases and the resonance line becomes narrower.40 HIGH RESOLUTION N.M.R. SPECTRA OF CRYSTALS Clough 8 and Clough and Gray 9 have applied the statistical approach of Anderson and Weiss,lO Anderson 11 and Kubo and Tomita 12 to this problem. With certain simplifying assumptions they find that the residual dipolar breadth is approximately 3w;/8w?, where col is the r.m.s. width of the line when the specimen is at rest. I n order to reduce the width to a few c/sec the rate of rotation must therefore be some five to ten times the r.m.s. width. having I>+ is proportional to the component aEJ& of the electric field gradient tensor, where the z axis is along the direction of Ho.If the principal axes of the electric field gradient tensor at the site of a given nucleus are the Cartesian set XI, Yl, Z1, then QUADRWOLAR BROADENING.-The first-order quadrupole splitting for nuclei where A,, 12, 2 3 are the direction cosines of HO with respect to the axes XI, Yl, 2 1 . If the crystal is rotated about an axis making an angle a with Ho, and angIes v1, v2 and v3 with XI, Yl, 21, then R1 = cos a cos v1 + sin a sin v1 cos (art+ $), (6) with similar equations for 12 and 13. It follows that the average value of A? over the rotational motion is - d: = cos2a cos2v1 ++ sin% sin2v,. (7) Thus, when a = cos-1(1/$) = 54" 44', we find that The mean value of aEJ3.z is thus trace (tensor), which is zero since div E is zero ; the result applies to all nuclear sites.Rapid rotation about this axis is therefore as effective as isotropic motion in removing first-order quadrupoIe splitting and broadening. This result is similar to that for the removal of dipolar broadening since the dipolar interaction can also be expressed as a traceless second rank tensor. For nuclei which, in a perfect crystal, have a non-cubic site, this removal of first- order quadrupole splitting will often be academic since the quadrupole coupling constants are typically 105-106 clsec, and therefore much higher than accessible rates of rotation. However, for imperfect cubic crystals, removal of first-order broadening should be observable.Second-order quadrupole broadening will, how- ever, not be removed by the rotation, though in general it will be reduced. Rapid rotation generates radial stresses in solid specimens and may generate some residual quadrupolar broadening even in crystals which show no quadrupolar broadening when at rest. CHEMICAL smT.-The chemical shift, and its counterpart in metals, the Knight shift, is a second rank tensor Q. In liquids and gases the rapid random reorientation of the molecules ensures that only the isotropic mean value of the shift is observed for each type of nucleus. However, in solids the anisotropic component of the shift can lead, for monocrystalline specimens, to a dependence of the spectral lines on the orientation of the crystal with respect to Ho,13 and, for polycrystalline speci- mens, to a broadening of the spectrum.14~ 15 The value of the shift for a particular nucleus can be expressed as where 01, 0-2, 03 are the principal values of the chemical shift tensor, and 21, A2, A3 are now the direction cosines of Ho relative to the principal axes of this tensor.0 = afo, +~;a, -+ Rig3, (9)E. R. ANDREW AND R. G . EADES 41 When the specimen is rotated about an axis making an angle a with Ho, and angles v1, v2 and v3 with the principal axes of the tensor, eqn. (6) and (7) again apply, and when a = 54" 44', we again have (8) with the result Under these conditions each nucleus will thus display its isotropic mean shift as in a liquid ; for polycrystalline specimens any broadening due to anisotropy is removed from the central line.INDIRECT NUCLEAR SPIN-SPIN INTERACTIONS.-Electron-coupled nuclear spin-spin interactions are responsible for the multiplet structure encountered in the high- resolution spectra of liquids. The interaction has the form 11 . f .P2, where $ is a second rank tensor, so that the observed multiplets are described by the scalar JII .I2, where J = 4 trace /. However, in solids both the isotropic and the aniso- tropic parts of the tensor must be taken into account and can lead to observable broadening.16917 The scalar interaction is invariant to rotation, and those features of the spectrum which originate from this term will be unchanged by macroscopic rotation of the specimen. However, as with the chemical shift, the anisotropic part of the tensor is removed by rapid rotation at angle 54" 44' just as it is removed by isotropic reorientation in liquids.SPIN-LATTICE RELmTIoN.-If there is a strong spin-lattice relaxation mechanism operating, as for example in a metal, an important contribution to the residual breadth may come from the reciprocal of the short spin-lattice relaxation time TI. 0 = 3 trace a. THE ROTATING MAGNETIC FIELD APPROACH High resolution n.m.r. spectra of solids would be of particular value with specimens which are not significantly soluble in any suitable solvent, and which cannot be melted without decomposition. Moreover even for compounds which can be rendered into fluid form, there is interest in comparing the behaviour in the different phases. However, it seems probable that many of the applications which would be of greatest value are concerned with proton and 19F resonances, and here there is the difficulty that the spectra of static specimens are typically 20-60 kc/sec wide.A rotation rate of this order is therefore required. It seems unlikely with present techniques that mechanical rotation of specimens of sufficient size will achieve speeds much above 10 kc/sec, and only in specially favourable cases is such a speed likely to produce more than marginal effects with proton and fluorine resonances. In order to avoid the problem of very high speed mechanical rotation we are exploring an alternative approach. It is, of course, the motion of the nuclei relative to their magnetic environment which causes spectral narrowing, and this can either be achieved by motion of the nuclei in a fixed applied magnetic field, as we have been discussing so far, or by placing a static specimen containing the nuclei in a magnetic field which is rotating.Since the nuclei are gyroscopes the behaviour of fixed nuclei in a rotating field is not precisely equivalent to that of rotating nuclei in a fixed field. Nevertheless if, as in our case, the rate of rotation of the field is much less than the Larmor frequency, the nuclear moments will follow the rotating field adiabatically and the two situations are then effectively equivalent. The requirement therefore is for a stable and uniform strong magnetic field HO rotating at a frequency of order 50 kclsec with the magnetic vector inclined at an angle 54" 44' to the a x i s of rotation.Such a field can be produced by the superposition of fields applied along three mutually orthogonal directions : a static field of H&/3 along the z direction, and alternating fields of amplitude J ~ H ~ along the x and y directions having their phases in quadrature. Iron cannot be42 HIGH RESOLUTION N.M.R. SPECTRA OF CRYSTALS used at these frequencies and the use of ferrites raises problems of geometrical design which may well be soluble but which we have initially thought better to avoid. With Mr. R. C. Gupta we are therefore developing a system with three mutually orthogonal Helmholtz-type pairs of coils to generate a rotating field of about a kilogauss. CROSS-RELAXATION INDUCED BY ROTATION In the course of the work on phosphorus pentachloride, mentioned earlier, a new effect of cross-relaxation induced by rotation was found.The two types of phosphorus nucleus have different spin-lattice relaxation times differing by a factor of ten. Mr. V. T. Wynn has found values of approximately 6 sec and 0.6 sec for the PCli and PC1; resonances respectively. The resonance spectra of the two types of nuclei do not overlap and an exchange of energy between the two systems is there- fore not possible since the spin-exchange perturbation is not secular. However, it was noticed by Dr. Bradbury that when the specimen is rotated at a frequency just equal to the separation between the resonance lines, the saturation properties of the two lines, which previously were very different, became almost identical, and both systems of nuclei relax with the shorter relaxation time.The spin-exchange term in the dipolar Hamiltonian (1) contains the angular factor (3 cos26ij- I) which is time-dependent when the crystal is rotated. As expansion of this factor in (4) shows, terms periodic in ci), and 20.1~ appear, so that there are now secular com- ponents in the spin-exchange perturbation when the rate of rotation is equal to the difference between the Larmor frequencies of the two types of nuclei, or to half that difference. Calculation shows that the spin-exchange transition probability is of the order Tg1. Since T2 is a few msec, energy can be transferred between the two systems in times short compared with T I , the whole assembly of phosphorus nuclei relaxing together towards equilibrium with the lattice through the more efficient mechanism of the PC1g groups. 1 Andrew, Bradbury and Eades, Arch. Sci. Geneva, 1958, 11,223. 2 Andrew, Bradbury and Eades, Nature, 1958,182, 1659. 3 Andrew, Bradbury and Eades, Nature, 1959,183, 1802. 4Henriot and Huguenard, Compt. rend., 1925,180, 1389; J. Physique Rad., 1927,8,433. 5 Beams, Rev. Sci. Instr., 1930, 1, 667; J. Appl. Physics, 1937, 8, 795. 6 Lowe, Physic. Rev. Letters, 1959, 2, 285. 7 Andrew, Bradbury, Eades and Jenks, Nature, 1960, 188, 1096. 8 Clough, Bull. Ampere, 1960, 9, fascicule special, 374. 9 Clough and Gray, Proc. Physic. SOC., 1962,79,457. 10 Anderson and Weiss, Rev. Mod. Physics, 1953, 25, 269. 11 Anderson, J. Physic. SOC. Japan, 1954, 9, 3 16. 12 Kubo and Tomita, J. Physic. SOC. Japan, 1954, 9, 888. 13 Lauterbur, Physic. Rev. Letters, 1958, 1,343. 14 Ragle, J. Chem. Physics, 1961,35, 753. 15BIoembergen and Rowland, Acta Met., 1953, 1,731. 16 Ruderman and Kittel, 1954, Physic. Rev., 1954, 96, 99. 17 Bloembergen and Rowland, Physic. Rev., 1955,97,1679.

ISSN:0366-9033    

DOI:10.1039/DF9623400038

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

High Resolution N.M.R.-Instrumentation : Recent Advances and Prospects BY R. ERNST AND H. PRIMAS Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, Zurich, Switzerland Received 18th June, 1962 The recent advances of n.m.r.-instrumentation will be reviewed and some new types of equip- ment will be described. New stabilizers for n.m.r.-spectrometers, double resonance devices and high-resolution spectrometers with high magnetic field strength sre discussed. By increasing the signal-to-noise ratio essentially over the present usage exciting new applications of n.m.r. -spectroscopy will become feasible. As an example the proton resonance spectroscopy with just a few micrograms of complex organic substances will be sketched and its importance to biology will be stressed.1. INTRODUCTION In spite of the rapid progress in the field of high resolution n.m.r.-spectroscopy we are of the opinion that there is still plenty of room for essential improvements of the instrumentation and even for completely new developments. It is to be expected that in the next few years we will have available significantly improved n.m.r.-spectrometers and that the chemists will therefore be able to extend the range of n.m.r.-spectroscopy to problems outside the range of present possibilities. Some exciting new applications seem to become feasible. We would expect that the future development in n.m.r.-instrumentation will just continue the trend of the last few years with special concentration on the follow- ing topics : (i) enhancement of the sensitivity of n.m.r.-spectrometers by quite a large factor ; (ii) increasing the resolution, (iii) improving the stability of the instruments, (iv) developments of auxiliary methods and the hereto necessary devices which allow to get more information than from the usual n.m.r.-spectra or to get some part of the information in a more convenient and understandable form, (v) developments of spectrometers of greater versatility, (vi) developments of really foolproof instruments.Of course, these points are not all independent of each other and several are even contradictory. A technical review of the state of the art at the end of 1959 was given at another place 1 and we will restrict ourselves here to the more recent improvements that are partially already realized and partially still in the state of further development of great promise.2. HIGH-FIELD N.M.R.-SPECTROMETERS AND THEIR PROBLEMS It is well known that it is often possible to simplify the appearance of n.m.r.- spectra by increasing the field strength of the magnetic field. There exist two 4344 HIGH RESOLUTION N.M.R. INSTRUMENTATION classes of phenomena, those which are independent of the magnetic field strength (spin-spin-coupling, internal rotation, line width) and those proportional to the magnetic field strength (chemical shift). Only with very high fields can the first class of phenomena be easily separated from the second. The usual magnets used for high-resolution n.m.r.-spectroscopy are electromagnets with iron pole tips. The very high homogeneity of such magnets is due to the fact that iron has at moderate field strengths a high permeability and therefore the pole faces are almost exactly equipotential surfaces.The criterion of “ high ” and “ low ” field strength for a magnet with ferromagnetic material is its saturation field strength, i.e., for pure iron 21-62 kgauss, whilst the highest known saturation fields are 2 to 3 kgauss higher with alloys of the type of Permendur (50 % Fe+ 50 % Co). With iron electromagnets of conventional construction a rather abrupt change of the field configuration occurs at about 12 kgauss (fig. 1) which spoils B &GI FIG. 1 .-Inhomogeneity against field strength. (a) for a typical electromagnet of conventional construction ; (b) for an electromagnet with correctly designed pole tips which avoid any local saturation.(r = radial distance from the centre). B~(v) = B(l +r2b2+ . . .) (2.1) the homogeneity of the higher fields. With certain tricks, such as cycling of the magnet, it is possible to extend the useful range of an iron electromagnet for high- resolution n.m.r. to 15 kgauss or even more. Such procedures can be extremely useful but we have to pay for it : we lose the versatility of the instrument because there is usually a sharp optimum of the field strength for maximal resolution. Further, any cycling procedure reflects the irreversible behaviour of the ferromagnetic material and is therefore inherently not stable. A theoretical and experimental study 2 has elucidated this strange behaviour of electromagnets of conventional construc- tion over 12 kgauss. We could show that these phenomena are entirely due to local saturation effects that must appear with the usual cylindrical or conical pole tips.According to a somewhat simplified theory there is just one pole form that avoids any local saturation at any field strength. It was found that this theoretical curve has to be realized with an extreme accuracy to get a completely flat magnetic field with the same pole tips for any field strength from 0 to 22 kgauss. Further, with carefully selected pure iron any cycling effect can be avoided.R. ERNST AND H. PRIMAS 45 Such spectrometers are nowadays a reality and the extension to field strengths of up to 30 kgauss is in the stage of detailed investigation. At least it should be possible to work with a reduced resolution (enough e.g., for 13C-n.m.r.) at fields up to 30 kgauss even with pole tips of iron.Permendur would be preferable, of course, but there are still severe technological difficulties. It is not easy to speculate on the future of magnetic fields essentially over 30 kgauss for n.m.r.-work. It seems not completely impossible to use magnets of con- ventional construction for certain special n.m.r.-investigations at field strength up to 100 kgauss. But it is to be expected that such investigations will, in consequence of the great expense necessary, be restricted to highly specialized laboratories such as the M.I.T. National Magnet Laboratory and that these magnets will not come into general use. Progress in the development of magnets with superconducting material is so ex- citing that it is tempting to speculate on a possible application for n.m.r.-spectros- copy.It seems possible that a resolution of 1 : 106 can be achieved at a field strength of 60kgauss and with newer materials perhaps even over 100kgauss. But now- adays it is still unknown whether it will be possible to get the necessary time stability for such a resolution and whether it may eventually be feasible to shim such a field to even higher homogeneities. 3. STABILITY OF N.M.R.-SPECTROMETERS Besides all the problems of homogeneity of the polarizing magnetic field the time stability of this field is the most difficult problem in the construction of a high- resolution n.m.r.-spectrometer. The approved principle of pre-stabilization of the magnet current and fine stabilization with a flux-stabilizer seems still to be the best solution.A flux-stabilizer needs a d.c.-amplifier of an extremely good zero-point stability. The use of a galvanometer amplifier for this purpose is now superseded by the use of special mechanical chopper amplifiers which are much more robust, very easy to handle and which give an essentially better zero-point stability than any galvanometer.3 Even with the best flux-stabilizer there are still appreciable residual field fluctu- ations that restrict the measuring accuracy and the measuring time. With a flux- stabilizer alone it is not possible to get automatically a reliable calibration of the spectra which, of course, would be very convenient for precise routine n.lz1.r.- measurements.It is evident that the phenomena of nuclear magnetic resonance itself is predestinated for a field-stabilizer of excellent long-time stability and suitable for an absolute and automatic calibration of the spectra. This idea is almost as old as the invention of the n.m.r. phenomena itself. A high resolution n.m.r.- spectrometer stabilized with a second n.m.r.-probe was for the first time described in 1957 by Baker and Burd.4 The construction of a n.m.r.-stabilizer with a second probe was brought to perfection in the commercial routine instrument A-605, a specific proton resonance spectrometer with precalibrated paper and a calibration accuracy which should fulfil most requirements of routine measurements of the organic chemist. There is a second approach to the construction of a n.m.r.-stabilizer which is technically more complicated but which allows a still greater improvement in the long-term stability of the magnetic field.Evidently the stability of a spectrometer with two spacially separated probes-one for measuring purposes and one for the stabilizer-can be only as good as the field between the probes is constant, i.e., this type of stabilizer is inherently not of absolute stability but susceptible to external disturbances. Such troubles can be avoided if only one single probe is used.46 HIGH RESOLUTION N.M.R. INSTRUMENTATION Nowadays it is customary to use an internal standard (e.g., a few % TNS for proton resonance spectra) and this suggests the use of just this internal reference for the signal for the n.m.r.-stabilizer.This idea was first realized in 19606 and proved to give excellent results. With a high-resolution 25 Mc proton resonance spectro- meter we could achieve a long-term stability of better than 3 parts in 1Olor.in.s. (or better than 1, 5 parts in lO9p.t.p.) over several days. With such excellent long-term stability it is, of course, easy to get n.m.r.-spectra automatically calibrated with extreme accuracy. Further, there is no longer any limitation of the measuring time. There is no difficulty in extending the measuring time over days and to getting 1 I I I I I I 4 5 4 3 2 9 p.p.m. from t.m.s. FIG. 2.-N.m.r.-spectrum of 0.085 mg hydroxyprogesterone. IH-spectrum at 25 Mc ; RC-time constant = 50 sec ; sweep rate = 1 p.p.m./h. in this manner an increased sensitivity by a factor 10 to 50.On account of practical considerations one often does not wish to extend the measuring time over, say, 14 h (taking spectra overnight) but even this time gives an enhancement of the signal- to-noise ratio of a factor of 10 compared with the usual measuring time of some minutes. Fig. 2 shows the very first application of this method : the proton reson- ance spectrum of 0.085 mg of a steroid. In spite of the low frequency of 25 Mc the signal-to-noise ratio still allows a useful discussion of the spectrum. 4. EQUIPMENT FOR DOUBLE RESONANCE EXPERIMENTS BETWEEN LIKE NUCLEI Double resonance experiments and very similar experiments with multiple quantum transitions allow us to get more information from a spin system than the usual n.m.r.-measurements and-what is often even more important-under certain conditions we are able to get this information in a much simpler form. Such decoupling experiments between unlike nuclei or between like nuclei with a big dif- ference in chemical shift have been well known for some years and are rather easily realizable.But the extension of double resonance methods to nuclei with only small differences in chemical shift imposes some difficulties on the apparatus side. Using a n.m.r.-stabilizer with an internal standard this problem can be easily over- come and we could show that it is possible to decouple proton resonance lines which are just a few c/sec apart. Fig. 3 shows a principal scheme of such an apparatus.R . ERNST AND H.PRIMAS 47 The exact theory of double-resonance experiments with a two-spin system with strong coupling shows7 that one has to be very careful in the interpretation of a double resonance spectrum with strong coupling. The large direct and indirect Bloch-Siegert shift makes a straightforward evaluation of the chemical shift values complicated. The complications by the direct Bloch-Siegert effect can be eliminated if one works under symmetrical irradiation conditions.8 For a simple double resonance experiment this means that one has to use two double-resonance frequencies which are symmetrical with respect to the measuring frequency. This can be achieved simply by amplitude modulation of the measuring frequency. p1 record e r FIG. 3.-Schematic diagram for double-resonance equipment with an n.m.r.-stabilizer.w = measuring frequency ; w+ Aw = frequency of the n.m.r.-stabilizer ; w + Sw = double resonance frequency. N.m.r. experiments with multiple quantum transitions give similar information to a double resonance experiment. The ideal universal n.m.r.-spectrometer of the future should have the facilities for using high-frequency fields with high field strength together with very stable leakage and modulation systems. 5. SENSITIVITY OF N.M.R.-SPECTROMETERS The sensitivity of an n.m.r.-spectrometer is defined as the ratio of the signal-to- noise voltages at the output of the instrument. If the noise sources consist entirely of the Johnson- and the Shot-noise of the input circuit the optimal linear filter to achieve a maximal sensitivity is determined by the van Vleck-Middleton-criterion2 The maximal sensitivity Y is then given by a relation of the following form :48 HIGH RESOLUTION N.M.R.XNSTRUMENTATION Apart from the factor 09 the frequency dependence of Y is determined by the series- resistance r of the receiving coil, the noise-factor F of the preamplifier and the con- nection receiving coil-preamplifier. Y is, therefore, a complicated function of the frequency which can be approximated by &YO. It is, therefore, possible to increase the sensitivity considerably by increasing the frequency of the high-frequency field (e.g. from 20 to 100 Mc by a factor of 11). Further the sensitivity is proportional to a geometric factor g determined by the dimensions of the receiver coil and the probe.It can be shown that it is possible to increase the sensitivity of most present n.m.r.-spectrometers by a factor of 5-10 by the proper optimization of the receiver coil and of the connection between receiver coil and preamplifier and by the choice of an appropriate preamplifier tube. There can be given iterative methods for the optimization of the factors dJ'F It is seen from (5.1) that the sensitivity can be increased by reducing the sweep rate a. But a smaller sweep rate affords simultaneously a higher time stability of the frequency and of the magnetic field. This implies the necessity of a n.m.r.- stabilizator. An improvement of the sensitivity by a factor of about 10 in relation to the usual measuring time of some minutes is possible. It is to be remembered that the usual measuring conditions are far from stationary conditions.Therefore, the field strength of the high-frequency field has to be lowered for smaller sweep rates to prevent saturation effects. In this way the sensitivity will be decreased by some amount especially if the relaxation time TI is very long. By the combination of some of these improvements it is therefore easy to exceed the sensitivity of all present n.m.r.-spectrometers by at least a factor of 100. This is, of course, of greatest importance for the biologists and the organic chemists as it means a reduction in the analyzable amount of a substance to less than a hundredth of the present minimum amount. 6. DESCRIPTION OF A NEW UNIVERSAL N.M.R.-SPECTROMETER It is impossible to combine in one single instrument the wishes of a pure chemist who likes a simple and foolproof instrument, suitable for routine investigations and those of a physical chemist who prefers a universal spectrometer of maximum efficiency and versatility.So it is unavoidable that in the future we will have two rather different types of n.m.r.-spectrometers. We restrict ourselves here to a short description of a new universal n.m.r.-spectrometer, developed during the last few years in our laboratory. The first criterion in the design of our new system was a reasonable compromise between the maximum possible field strength suitable for high-resolution n.m.r. and the expenses a research laboratory of physical chemistry can afford. According to a criterion of Klerklo there is a logarithmic dependence between the quotient Y/v (Y = volume of the copper and iron of the magnet, v = volume of the field space) and the maximum possible field strength obtainable with such a magnet This means that the weight of a magnet is increasing exponentially with the maximal possible field strength.We decided that a weight of 5 tons (everything included) would make a fine research magnet at a not yet astronomically high price. This magnet was designed to give a resolution of a few parts in lo9 for the usual n.m.r.-probes but we intend to use also much larger probes with only slightly re- duced resolution. These conditions have given the volume of the field space to about 600 to 800 cm3. With a gap of 30 mm we can achieve a field of 20 kgauss with an (cf.fig. 4).R. ERNST A N D H . PRIMAS 49 input power of only 2.7 kW. But the magnet can dissipate 20 kW with a rise in temperature of only a few degrees so that we can get a field strength over 30 kgauss with a gap of 25 mm and a somewhat reduced homogeneity, but still suitable e.g., for 13C investigations. Thanks to the very carefully designed pole tips this magnet shows the same high degree of homogeneity in the whole range of 0 to over 22 kgauss without the necessity of changing the pole tips and without cycling. It is clear that today a high-voltage magnet is an anachronism. Our electromagnet is a transistor-regulated high-current magnet with directly water cooled hollow conductors. Such a magnet shows a much better thermal behaviour which is of utmost importance for a stable operation.log (V/4 FIG. 4.-Maximum field strength B achievable with a magnet of volume Y and a field space u (according to Klerk 10). a = high performance magnet ; b = low performance magnet. Because the use of an n.m.r.-stabilizer is not possible nor convenient for all types of experiments? we used a flux-stabilizer with a drift stability of about 1 part in 1010 per second and additional devices to allow all kinds of sweep and modulation methods. For the most precise measurements a n.m.r.-stabilizer with internal standard will be added. Facilities for n.m.r.-experiments with any nuclei are a matter of course. It is clear that such a universal instrument cannot be a very compact unit nor an extremely simple instrument. We preferred to use a system of standardized units built around the central part of the system, the high performance magnet.7. EXAMPLES OF NEW APPLICATIONS OF N . M . R . In regard to the applications of the n.m.r.-spectroscopy in chemistry the most significant progress is the gain of sensitivity. In the following we will present as examples some new experiments which, as a result of insufficient sensitivity, were not previously realizable and which are now under investigation in our laboratory.50 HIGH RESOLUTION N.M.R. INSTRUMENTATION Preliminary results with our new n.m.r.-spectrometer constructed especially for The necessary number of moles M to get a signal-to-noise ratio V with a sweep high sensitivity suggest that it will be possible to get the following sensitivities : 8 rate a in rad sec-2 and a longitudinal relaxation time TI is given by c is dependent on the magnetic field strength B and on the nuclear P, kgauss c, mole sec) for 1H for 1 X 7 3 6 ~ 10-9 1 8 ~ 10-7 1 4 12 x 10-9 5~ 10-7 21 7~ 10-9 3~ 10-7 28 5~ 10-9 2~ 10-7 ( 7 4 species : 13C-RESONANCE WITH NATURAL ABUNDANCE : It is well known that n.m.r.-spectroscopy with W-resonance can supply valuable information about the structure of organic molecules.The chemical shifts of the W-lines are much more sensitive to small chemical changes in the environment as those of the 1H-lines. A universal method would permit work with the natural abundance of 13C of 1.1 %. Together with the relatively small magnetic moment of 13C this means that the necessary sensitivity of the n.m.r.-spectrometer has to be very high.ExampZe.-13C-resonance with natural abundance. Molecular weight, 100; relaxation time, TI = I sec; sweep rate, 1 rad sec-2; To get a signal-to-noise ratio of 4, 11 mg of this substance would be necessary. A further application of W-spectroscopy would be as a tracer method for marked molecules in organic chemistry and in biochemistry. The radioactive tracer isotope 14C could be replaced by the stable isotope 13C. A great advantage of 13C is that for an analysis it is not necessary to disintegrate the molecule. magnetic field, 21 kgauss. BIOCHEMICAL PROBLEMS WITH LARGE MOLECULES : With a n.m.r.-spectrometer of extreme sensitivity it is now possible to examine solutions of very low concentrations or of solutions of macromolecules.This is important for biological solutions and, e.g., for the analysis of polypeptides and other complicated molecules. ExampZe.--1H-resonance. Molecular weight, 4000 ; relaxation time, TI = 1 sec ; sweep rate, 1 rad sec-2 ; magnetic field, 21 kgauss. To get a signal-to-noise ratio of 4 0.12 mg of this substance would be necessary. This is equivalent to a solution of 0-4 % in our usual spherical probes of diameter 4 mm. With a smaller sweep rate the necessary amount could be further diminished. PHOTOMAGNETISM: Another useful application of the very high sensitivity of our spectrometer is the detection of paramagnetic triplet states with n.m.r. by observation of the Line broadening on illumination of the probe under examination with suitable light. There are, of course, a great many further applications in any chemical problem where only very small amounts of substance are available.t 1 Primas, Arndt, and Ernst, Z. Instr., 1959, 67, 293 ; 1960, 68, 8 ; 1960, 68, 21 ; 1960, 68, 55. 2 to be published in NucZear Instruments and Methods. 3 A high resolution n.m.r.-spectrometer with a chopper-type flux-stabilizer was constructed in 1961 in our laboratory and exceeds the performance of any galvanometer-type stabillzer by far (unpublished, some preliminary details can be found in ref. (1)). 4 Baker arid Burd, Rev. Sci. Instr., 1957, 28, 313. 5 Varian Associates, Palo Alto, California. 6A short communication was given at the 5th European Congr. MoZ. Spectr. in June 1961. 7 to be published in Mol. Physics. 8 Ernst, Thesis, 1962 (Swiss Federal Institute of Technology). 9 Goldman, Injormatiun Theory, p. 233 (Constable, 1953). 10 de KIerk, Ned. Naiuurk., 1960, 26, 65. de Klerk and Gorter, Appl. Sci. Res. B, 8,265.

ISSN:0366-9033    

DOI:10.1039/DF9623400043

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

Valence Bond Studies of Internuclear Coupling BY H. s. GUTOWSKY AND CYNTHIA JUAN No yes Chemical Laboratory, University of Illinois, Urbana, Illinois Received 18th June, 1962 Two studies are reported which involve valence bond calculations of internuclear coupling. The first, of the proton spectra for the -CH2CH2- bridges in (2,2) metacyclophane, shows con- clusiveIy that the relative signs of the geminal and vicinal proton coupling constants are opposite, which disagrees with the theoretical prediction that both are positive. In this compound, the C-CH2-CH2-C groups are locked in position with the dihedral angle between alkyl C-C-C bonds slightly less than the symmetrical, staggered 60". A complete analysis of the A2X2 and A2B2 type proton spectra, at 60 and 15 Mc/sec leads to the following assignments : JFH = f12.3, JFH (the coupling of the " central " pair of gauche protons) = i-3-2, = 112-0, and JFH = rt4.0, all f0-1 clsec.A second related study is concerned with an interpretation for the additivity of substituent contributions to the 13C-H coupling constant. Each atom or group X is assigned a characteristic " affinity " for s character in the carbon hybrid orbital of the C-X bond. The additivity can be derived if the s character is distributed among the four carbon orbitals in accord with the relative s affinities of the four substituents, provided that the total s character is conserved. The valence bond approach used with this model gives a linear relation between the s character of the carbon hybrid orbital involved in a C-H bond and the observed 13C-H coupling constant (JCH = 500 ah).Valence-bond methods have been used to calculate internuclear coupling con- stants for non-bonded 1 and also for directly bonded nuclei? For non-bonded nuclei, the a-electron contribution to the coupling has been expressed in terms of deviations of the molecular electronic structure from perfect pairing.1 Such calcula- tions for protons predicted the geminal coupling JgE to be + 12.5 c/sec in methane,1 and subsequent, more approximate, calculations 3 for vicinal protons in the HCCH ethanic fragment gave the trans coupling JFw to be about + 9.2 c/sec and the gauche J,", + 1.7 clsec. These magnitudes agree well with experiment except that the trans vicinal constants observed for ethanic groups 4 (and also the cis and trans constants for ethylene 3) are often about 50 % larger than predicted. Usually, only the magni- tudes of J have been obtained from experiment; but increasing attention is being given to the importance of their relative signs. Several substituted ethylenes have been reported 5 9 6 in which the sign of JZE (1 to 3 c/sec) is opposite to, and also the same as, that of JzF (5 to 11 c/sec) and J t s s (12 to 18 clsec).These results are com- patible with the valence-bond calculations for the CH2 fragment,s which neglect substituent and n-electron effects, and which predict that JgE should become negative for HCH bond angles larger than about 120°.53 7 Similarly, there are substituted ethanes in which the sign of the vicinal coupling JF (1 to 3 c/sec) is opposite to and also the same as, that ofJFH (10 to 16-5 c/sec).49 6 Again, the results seem compatible with the calculated dependence of the coupling upon the dihedral angle 4, because substituent effects were neglected and tetrahedral HCC angles were assumed.3 A more troublesome question has been raised by relative sign determinations, in diethyl sulphite 8 and in several dioxolane derivatives,g which conflict with the pre- dictions ~3 that large values of Jgg and J$F should both be positive.However, the 52 JZF N 9 C O S ~ 4 - 0.3, (1)H . S . GUTOWSKY AND C. JUAN 53 compounds studied are such that substituent effects, angular distortions and motional averaging are important, and their neglect in the theoretical treatment might be responsible for the apparent discrepancies in the relative signs.Therefore, we have made a detailed study of the proton spectrum of the -CH2CH2- groups in (2,2) metacyclophane,lo the conformation of which is given in fig. 1. This compound avoids the uncertainties of the cases reported earlier 899 because an x-ray structural determination of the solid11 has shown that the methylene groups are locked in virtually symmetrical, staggered positions, with tetrahedral bond angles. Nonethe- less, opposite signs are found for the large trans and geminal constants, in agreement with the previous experiments 8 9 9 and disagreeing with the theoretical predictions that both are positive.193 This disagreement may result either from inaccurate molecular wave functions or from the approximations made in calculating the coup- ling of the non-bonded nuclei, and both aspects require further theoretical study.FIG. 1.-The structure of (2,2) metacyclophane and the conformation of the -CHzCH2- “ bridges” whose proton spectra were analyzed. The protons in the -CH2CH2- groups are labelled A and B, and symbols are defined for the coupling constants. Thus far, the valence bond calculations for directly bonded nuclei appear to be more reliable. In this case, deviations from perfect pairing are relatively unimportant? and further simplification results when the coupling depends mainly on the Fermi contact term as in the 13C-H group.2 A number of theoretical and experimental studies indicate that JCH is determined by the carbon orbital hybridization and by the polarity of the C-H bond.29 12913 In fact JCH has been employed as a simple measure of orbital hybridization.More recently, attention has been turned to the effects of substituents upon JCH, and several interesting empirical relationships have been discovered,l4~ 15 the most basic of which is probably the linear additivity of group contributions to JCH in substituted methanes.14 We have found that this relation can be derived by assuming that a substituent changes the hybridization of the carbon 2s orbital in a characteristic fashion.16.17 Substituent effects have also been noted for H-H coupling in hydrocarbons. In particular, more or less linear relations have been found between the electronegativity of the substituent and the geminal and/or vicinal coupling constants in substituted ethylenes 18-20 and ethanes.21 As yet, no detailed, theoretical interpretation of these effects appears to have been advanced.However, it seems very probable that the effects of substituents upon JCH are related directly, or at least indirectly, to those for JHH. If our model is correct for the effect of X upon JCH in CHXYZ or CH2=CHX groups, it should contribute to a better understanding of JHH, inasmuch as the latter is also affected by the hybridization of orbitals in the C-H bonds. RELATIVE SIGNS OF J g z , JBHH AND J)IH A sample of (2,2) metacyclophane was provided for our experiments by Wilson, Boekelheide, and Griffin.10 The high resolution proton spectra were observed at54 INTERNUCLEAR COUPLING room temperature using 10 % solutions in CCle Spectra at 60 Mc/sec were observed with Varian Associates HR-60 and A-60 spectrometers.The 15.083 Mc/sec spectrum was obtained through the courtesy of Dr. J. N. Shoolery at Varian Associates, where it was observed with a V-4300 spectrometer system. The general procedure used to determine the magnitudes and relative signs of the coupling constants in the -CH2CH2- group is the following.22 At a resonance frequency of 60 Mc/sec, the chemical shift v06 between the A2 and B2 sets of protons, defined in fig. I, is sufficiently large that the quite simple observed spectrum is a good approximation to the A2X2 type. From it, the magnitudes of v06 and of the four coupling constants are determined readily, as well as the relative signs for each of two pairs of coupling constants.In part, the 60 Mc/sec spectrum is easy to analyze because it is insensitive to one of the relative signs. However, the latter becomes important at lower resonance frequencies, where the spectrum is of the A2Bz type. Therefore, the magnitudes and signs obtained from the 60 Mc/sec spectrum were used to calculate 15.083 Mclsec spectrum for the remaining relative sign permutations, and comparison of these with the observed spectrum completes the analysis. It is convenient to use the parameters where the coupling constants are defined in fig. 1. These four constants have three relative signs which we wish to establish. In terms of the parameters K, L, M and N, which we treat as positive quantities except for Kin the one circumstance noted below, the relative signs of each pair of coupling constants in eqn.(2) is determined by the relative values of the corresponding two parameters. Thus, if N> L, Jg and Jgem have the same sign ; and if N t L , the opposite. Identical relations involving K and M hold for Jt and J g . In addition, the spectrum is sensitive to the actual relative signs of K = (Jt+Jgt) and N = (Jg+Jgem). Whether the observed spectrum is fitted by K positive or negative, while treating N as positive, determines the third relative sign. If K negative applies, then the constant of largest magnitude in K is of opposite sign to the constant of largest magnitude in N, while they are of the same sign for a positive K. Finally, the magnitudes of the coupling constants are obtained by means of eqn.(2) from the numerical (positive) values for K, L, M, and N ; however, the spectrum alone does not tell which constant is which within each pair and supplemental in- formation about the relative magnitudes of the constants is required to complete the assignment. THE 60 Mc/sec SPECTRUM The proton spectrum observed at 60 Mc/sec is given in fig. 2. As a first approxi mation it is of the A2X2 type, with " mirror image " A2 and X2 multiplets whose centres are separated by [(v06)2+ N2]*. In general, each A2Xz multiplet has ten lines, two quartets and a doublet with a common centre. The outer splitting of one quartet is K, and of the other, M, while the central splittings are (Kz+L2)*-K and (Mz+L2)*--M, respectively. The lines of the doublet are the strongest transitions ; their splitting is N.In the observed spectrum, the A2 and Xz multiplets have two rather broad, very strong lines at the centre, with two weaker lines at each side. Therefore, the inner lines of the two quartets are not resolved from the strong N- doublet, and only the outer lines of the quartets are visible. Thus, the -8 clsec splitting of the strong centre pair of lines undoubtedly is N. Also, the outer splittings of the two quartets are - 9 and - 15 c/sec but at this point it is uncertain which is K and which is M. These values, in combination with the expressions for the centralH. S. GUTOWSKY AND C . JUAN 55 splitting of the two quartets and their observed values of -8 c/sec, give an unam- biguous value for L of 15+2 c/sec. Also, the separation between the centres of the two multiplets is approximately the chemical shift, which gives v06 = 60.3 c/sec.The values of the parameters were refined by varying them systematically, com- paring the resulting calculated spectra 23 with experiment, and then interpolating. In this manner, the following best-fit, numerical values were obtained : v06 = 59-1, N = 8.0, L = 16.0, and More important, the spectra calculated for the four possible permutations show that although the spectrum observed at 60 Mc/sec is too insensitive to the sign of K for its determination, the asymmetry in the splittings p and q in fig. 2 is governed by the relative magnitudes of K and M. In order to have p <q as observed, it is necessary to have K> M,22 which requires that K be 15-5 and M, 9.1 c/sec.K or M = 9.1 or 15.5, all in c/sec. L I I I I I 0 clsec FIG. 2.-The spectrum observed at 60 Mclsec for the -CHzCH2- group protons in (2,2) meta- cyclophane. This spectrum is fitted by v08 = 59.1, N = 8.0, L = 16.0, M = 9.1 and r t K = 15.5 c/sec. Spectra calculated for interchanged values of K and M have p >q, rather than p < q as observed. THE 15.083 Mc/sec SPECTRUM Figure 3 includes the spectrum observed at 15.083 Mc/sec and also spectra cal- culated for the two remaining sign permutations, K = k 15.5 c/sec. There is ex- cellent agreement between experiment and the spectrum calculated for K = - 15-5 c/sec, and very poor agreement for K = 15.5 c/sec. Therefore, the parameters which apply to the -CH2CHz- group are : K = - 15.5 c/sec, N = 8.0 c/sec, h!f = 9.1, L = 16.0. (3) Upon combining these results with the definitions in eqn.(2) we find from N and L that Jg and Jgem are 12.0 and 4.0 or 4.0 and 12.0 c/sec. Moreover, they are of opposite signs because N<L. From Kand M, Jt and Js. are 12-3 and 3.2 c/sec or the reverse. Also, they are of the same sign because K> M. (Here, both K and M must be treated as positive quantities.) Also K and N actually have opposite signs so the largest constant of the K, M pair (12-3 c/sec) is of opposite sign to the largest constant of the N, L pair (12.0 c/sec).56 INTERNUCLEAR COUPLING The assignment is completed by introducing the inequality I Jt 1 > I Jgt I , which is known with certainty from the nmr studies of substituted ethanesP.6 and the inequality I Jgem I > I Jg 1 which is equally certain from the experimental results 4 6 for substituted ethanes in Combination with those on Jgem in methane 1 and substi- tuted methanes.5 The final assignment is JyH = & 12.3 c/sec, .JF = 43.2, J!& = T 12.0 c/sec, JfH = k4.0 with probable errors of about 40.1 c/sec in the numerical values. A B I $1 I II I In I I1 II I ll A 0 (4) I[ I, I , I 1 I 1 I a I0 20 clsec FIG. 3.-The left-hand spectrum is that observed at 15083 Mclsec for the -CH2CHr group protons in (2,2) metacyclophane.The line spectra at the right were caIculated for the two sign permutations not differentiated by the 60 Mc/sec spectrum, i.e. for K = f 15.5 clsec. The spectrum for K positive disagrees with the wings and the central portion of the observed spectrum.COMMENTS The closeness of the 12.0+0.1 c/sec value found for Jgz to the 12.4+0.6 c/sec observed in methane 1 indicates that the former is not affected by angular distortion and substituent effects. The small difference between the 3-2 and 4-0c/sec values for JF and J," is consistent with a C-C-C-C dihedral angle of slightly less than the 60" for a symmetric, staggered -C&CH2- group, as is suggested by the X-ray data for the solid.11 Also, this could account for the value of 12.3 c/sec for JFH being smaller than most found for substituted ethanes.697 Therefore, our finding of large values of opposite sign for JCHH and .Ig%, as well as the less conclusive earlier studies,s* 9 show that either the calculation on CH4 1 or that on the ethanic (and probably also on the ethylenic) fragment 3 is in error.Which of the calculations is most likely to be in error, if not both, is another question. In some ways, the calcula- tions for the HCCH fragment present the best opportunities for error. These calcula- tions are more complex than for CH4 (or CH2), and it is possible for example that the non-neighbouring-atom exchange integrals should not have been neglected.3 A more direct approach to the question would be to determine the sign of JvF andlor Jgz with respect to JCH for there is little doubt but that it is positive.2.17 Such relative sign determinations could help decide which of the JHH calculations to redo first. Fortunately, the relative signs of JCH, J g z and can be determined by the sort of approach used here and also by double resonance methods, either on 13C en- riched (2,2) metacyclophane or other appropriate compounds.H. S.GUTOWSKY A N D C. JUAN 57 In fact, analysis of the 3 1 P and proton spectra observed for diphosphine H2PPH2 has given results,24 related to our problem. For this compound, JgE and Jpp were found to have values of 108.2 and 12 c/sec, respectively, and to be of the same sign, opposite to that of J z (cis and trans) which has values of 10.5 and 6.8 c/sec. By analogy to the results of the HCCH calculations,3 it was assumed24 that was positive in diphosphine, which, of course, made J p p and Jzz negative. A negative value for JPP is surprising because the coupling between directly bonded atoms due to the usually dominant contact term is positive.In view of the present findings it may be somewhat more plausible to take Jpp as positive, which leads to Jgg positive and JF (cis and trans) negative, at least in the diphosphine case. EFFECTS OF SUBSTITUENTS UPON JCH Malinowski has reported 14 that to a very good approximation the W-H coup- ling constant in substituted methanes, CHXYZ, is an additive property of the sub- stituents. This additivity has been expressed in two equivalent forms 149 17 employing different definitions of the " substituent parameters ". What is perhaps a better formulation may be obtained by returning to the basic experimental fact, namely,14.17 JcH(CHXYZ) = Jc,(CH,X) +JcH(CH,Y)+Jc,(CH,Z)-2Jc,(CH,), ( 5 ) and noting that it may be written as where, by definition JcH(CHXYZ) = Jc~(cH4) + 6~ + 8y + 82, Sx = Jm(CH3X) - JCH(CH4).In other words, each substituent X contributes a characteristic term &, to JcH(CHXYZ), which is independent of the other substituents. There are two general approaches to the theoretical interpretation of this empirical result. Previous work 2,129 13 is consistent with JCH being determined by the carbon orbital hybridization and the C-H bond polarity. Therefore, one can seek to derive eqn. (6) on the basis of hybridization and/or polarity changes produced in the C-H bond by the substituent. Or one can investigate the other contributions, such as n-electron and orbital polarization terms, which X could make to JCH without affecting materially the C-H bond. We are concerned here with the first approach. VALENCE BOND FORMULATION FOR JCH The general expression for JNN consists of several terms.25 However, in this paper we consider only the Fermi contact term which is dominant for the 13C-H coupling, at least in CH4,2 The symbols used above have their usual meanings.In the ground state wave function Y?o deviations from perfect pairing are not important for the coupling of directly bonded nuclei.2 We use the separated eIectron pair wave function, (9) y o = (8 !>-+I (- ~ ~ p ~ c \ y , x ~ ~ , ~ ~ ~ ~ ~ ~ ~ , ~ ~ i c l , , ~ ~ , ~ ~ with where ur(i,j) is of the valence bond form with inclusion of ionic terms,58 INTERNUCLEAR COUPLING In the latter, 4a, . . . q5d are carbon atomic orbitals ; &, . . . & are atomic orbitals on the atoms bonded to the carbon, and q is the normalization constant.The co- efficients of the ionic terms are il, and 1,. Substituting YO into eqn. (8) and using the Dirac identity S k Sj = (+)(2P&- l), in which P,& is an operator interchanging the spins of electrons k andj, one obtains We assume the four carbon hybrid orbitals to be formed from one 2 orbital and three 2p orbitals, e.g. where the s character, a&, a$, etc., of the orbitals depends on the groups or atoms H, X, Y or Z bonded to the carbon. Substituting 4 d , and #h = Is, into eqn. (12), one finds that +d = O~HS + (1 - ~1H')'p~ a d = a , ~ + (1 - aX2)'pG*, (13) where q - = (2 + (2 + &AH)[aiS: + (1 - ai)sg f 2aH(1- aG)'s,sp] + 4(& + AH) x [aHSs f (1 - ai)'sp] + 2; + 1;). (15) 2340) is the 2s wave function of carbon evaluated at the carbon nucleus, and l s ~ ( 0 ) is the corresponding quantity for the hydrogen 1s function.S8 and Sp are the over- lap integrals between the hydrogen 1s atomic orbital and the 2s and 2p carbon atomic orbitals, respectively. In eqn. (15) for q-2, i l ~ is much less than Ac, because the electronegativity of C is greater than that of H, so AH is neglected and the coefficient of the ionic contribution to the wave function is hereafter denoted by ~ c - H . Eqn. (14) leads to JCH = (Aq2/AE)ai = J,ai clsec, (16) where A is a collection of constants, and JO is 500c/sec, as determined from the observed value 129 13 of 125 clsec for Jc~(cH4). This value for JO is consistent with the valence bond theory inasmuch as Karplus and ($ant2 obtained a reasonable value of 0-374 for ilc-~, using the same approach, with JCH = 124 clsec, in combina- tion with an estimate of AE and calculations of the overlap integrals from Hartree- Fock functions.Eqn. (16), depending upon the sensitivity of AE and q2 to sub- stituents, affords an attractive semi-empirical way to obtain the s character of bonding orbitals from coupling constants. For the substituted methanes, or other classes of closely related compounds, one would expect AE to be very nearly constant. This follows from the fact that it is approximately twice the bond energy,;! which varies by only a few percent for C-H bonds. The constancy of q2 depends upon its sensitivity to il and a&. These dependences can be calculated relatively simply and directly by means of eqn.(15). For the C-H bond, q 2 was found 17 to be insensitive to the value of a&, the total change being only 0.2 % over a range of cx& from 0-24 to 0-45. q2 is also relatively insensitive to Ac-H. Substituents are expected to change the electronegativity of the C atom by at most 0.1 to 0.2 units according to estimates of effective electronegativities by proton chemical shift measurements.26 The empirical values of AB-H, AC-H and AN-H given by Karplus and Grant,2 indicate that an increase in electronegativity of the carbon by 0.2 units would change &!-H from 0.374 to about 0.44. This corresponds to a decrease in q 2 to about 0.95 @(CH4)H. S. GUTOWSKY AND C. JUAN 59 However, the increase in LC-H is accompanied by an increase of Zeff for the 2s and 2p electrons of carbon which leads to a decrease in the overlap integrals Ss, Sp, and to an increase in q2.Thus, the effects tend to cancel, and even though a&, &-R, and the overlap integrals all change with the substituents, q 2 is expected to remain about the same for the substituted methanes. This leads to JO zz 500 c/sec and the linear relation in eqn. (16) between JCH and a:. THE ADDITIVITY OF SUBSTITUENT EFFECTS The additivity relation observed by Malinowski 14 can be derived by means of eqn. (16) providing one assumes that the substituents redistribute the carbon 2s orbital among the four bonds in a particular manner. First of all, the 2s character must be conserved, that is Secondly, each atom or group X is assigned a " characteristic affinity for s character ", AX.Let AX be measured with respect to H so that AX is positive if the " s affinity " of X is less than H and negative if greater than H. Consider the four bonds to be four equivalent interconnected potential wells of possibly different depths. The difference in the depths of the wells for X and H is defined as AX. The 2s orbital will distribute itself among the wells to give a common 2s level, because of their interconnection. Moreover, this common 2s level, and the content of each well, can be obtained very readily via eqn. (17), i.e. by the assumption that the sum of the 2s content of the four wells is unity. In CH4 or CX4 the four wells are all of the same depth so that 2s character is distributed equally among them, and a2 = $. In CH3X, the H wells are deeper than that of X by the amount AX which is distributed equally among four bonds so an H well will have (+)Ax 2s character more than an H well in CH4.In general, the H well in CHXYZ will have [(i) AX + ($) Ay + (t) Az)] 2s character more than an H well in CH4. Expressed mathematically, this means that for CH3X a;+a;+a;+c!; = 1. (17) a$(CH3X) = ai(CH4) + (+)Ax or (+)Ax = a&(CH,X) - &(CH4), (18) &(CHXYZ) = ai(CH4) + (+)(Ax + Ay + Az). (19) (+)AXJO = JCH(CH3X) - JCH(CH4) 6X, (20) JcH(CHXYZ) = JcH(CH4) + + 6, + 6z. (6) ag(CHXYZ) = ($)(I +Ax+Ay+Az)-Ax. (21) and for CHXYZ, By means of eqn. (16), c!& can be eliminated from eqn. (18), giving which in turn converts eqn. (19) into the observed additivity relation, eqn. (6) In addition, a general equation, similar to eqn.(19), may be written for the s character of the carbon orbital in the C-X bond, COMPARISON WITH EXPERIMENT Experimental values 2314 of JcH(CH3X) and the resulting AX obtained from them by means of eqn. (20) are given in table 1 for a number of substituents. The AX tend to follow the electronegativity of X, being negative for electropositive substituents (- 0-096 for Al) and positive for electronegative (+ 0-2 for the halogens). However, at least another factor is important because for substituents with the same electro- negativity, AX is larger for those which have the greater number of lone pair electrons.60 INTERNUCLEAR COUPLING Moreover, AX is virtually the same for the four halogens in spite of their large range of electronegativity.Qualitatively, the AX values are consistent with charge and spin correlation effects 17 in CH3X, but their detailed significance remains to be determined. TABLE l.-SUBSTITUENT PARAMETERS Ax OBTAINED FROM JCH OBSERVED IN SOME CH3X COMPOUNDS CH3X A12(CH3)6 113 CH4 125 CH3CH3 126 CH34 126 CH3CHO 127 CH3CH2Br 128 CH3CH2C1 128 CH3COOH 130 CH3CHCl2 131 CH-jNHCH3 132 Si(CH314 118 CH3CH2I 132 a& 0.226 0.236 0.250 0-252 0.252 0.254 0-256 0.256 0.260 0.262 0.264 0.264 Ax - 0.096 - 0.056 0.000 + 0.008 + 0.008 +0.016 + 0.024 + 0.024 + 0.040 + 0.048 + 0.056 + 0.056 CH3X CH~CECH 132 CH3NH2 CHqCClq 133 134 136 138 138 141 143 149 150 151 152 a& 0.264 0.266 0.268 0.272 0.276 0.276 0.282 0.286 0.298 0.300 0.302 0-304 + 0.056 + 0.064 + 0.072 + 0.088 +0.104 +Oslo4 $0.128 +0.144 3-0-192 + 0.200 + 0.208 +0.216 The effects of substituents upon a& are additive to within an accuracy of 2 % for about 20 polysubstituted rnethanes.14.17 This may be seen in fig.4 where the observed coupling constants JCH are plotted against olz values predicted by means of eqn.(19) from the AX values in table 1. Also plotted in fig. 4 are the JCH values observed 129 139 27 for the 16 unsaturated hydrocarbons listed in table 2. The calcula- tions carried out for the methanes were extended to JCH in these sp2 and sp hybridized TABLE 2.-J(33 OBSERVED IN HYDROCARBONS WITH Sp2 AND Sp HYBRIDIZATION, AND VALUES " PREDICTED " FOR C& IN ETHYLENES USING THE Ax VALUES FROM SUBSTITUTED METHANES compound JCHc/sec a h compound JCHc/sec a& naphthalene benzene mesitylene cyclohexene ethylene CHCl=WH2 (cis) CHCl=WH2 (trans) (CH3)2C=C=13CH2 157 159 160 166 1 70 157 160 161 CH2=CC12 166 CH2=13CHCl 195 cis CHClSHCl 198 trans CHClSHCl 199 CClZ-CHCl 201 CH3C=13C-H 248 &kS3C-H 251 H--C-C<=C-H 259 0.349 0.402 0-408 0.408 0-41 6 SP SP SP compounds. Using AC-H = 0-374 and the overlap integrals28 appropriate to the C-H bond distances in ethylene and acetylene, we find y2 for these two compounds to be 0.987 y2 (CH4) and 0-977 y2 (CH4) respectively.Moreover, y2/AE for ethylene and acetylene is affected no more by substituent effects than it is for the methanes. Hence JCH E 500a& for sp2 and sp hybridized carbon, as well as for sp3, except for possible effects of the n electrons. There does not appear to be any simple way of estimating the substituent effects upon a& for the cyclic and acetylenic compounds, so the " pure " sp2 and sp values of -4 and 3 are used without correction in fig.4. The resulting points scatter somewhat more than those for the polysubstituted methanes, but the agreement with the theoretical line is still good. a& can be estimated for the substituted ethylenes by using the AX values obtained from the methanes. The main difference is that there are three cr bonds instead ofH. S. GUTOWSKY AND C. JUAN 61 four. Also, the substituent CYZ in CYZ = CHX has no counterpart in the methanes. However, it seems reasonable to use ACEYZ (methane) for ACYZ (ethylene). On this basis the s character for a monosubstituted ethylene is given by (22) which with eqn.(16) gives rise to c ~ ( C H ~ = 13CHX) = (+)[1+ ACH2 +Ax] = 0&CH2 = CH2) + (+)Ax, J ~ H ( C H ~ = 13CHX) = Jc~(cH2 = CH,)+($)[J,,(CH,X) -JcH(CHJ]. (23) Values of a& predicted by means of eqn. (22) are listed for eight substituted ethylenes in table 2 and plotted, as open circles, in fig. 4 against the observed JCH. FIG. 4.-Observed JCH values plotted against predicted values of ah. The straight line is JCH = 500 a$ c/sec, upon which all points would fall if the methods for predicting rx$ were sufficiently accurate. The points for sp2 and sp hybridization are from table 2, with no corrections for sub- stituent effects. The open circles are for the substituted ethylenes in table 2, for which a& was predicted using the A, values obtained from substituted methanes.The other points represent polysubstituted methanes for which I& was predicted by eqn. (19). It may be seen that these data are consistently 5 to 10 clsec below the theoretical line. It seems likely that this discrepancy may result from a n electron contribution to JCH. An estimate 17 of J& for ethylene gives a value of -2.6 clsec, which is of the same sign and magnitude as the discrepancy. A less satisfactory feature of our results is their relation to observed bond angles. The '' interorbital " angles 29 corresponding to the hybridization parameters obtained from JCH data are consistently smaller than the observed H-C-Y and X-C-X angles. In the methyl halides, CH3X, the calculated H-C-X angles are about 102" while those observed are 107" ; and for CH2X2 the calculated X-C-X angles are 100" and the observed, 112".In other words the a& values appear to be too large. These differences, at least in part, could reflect deviations from orbital following 30 of62 INTERNUCLEAR COUPLING the same nature as those found in CH2C12 for which both the H-GH and the Cl-C-Cl bond angles are greater than tetrahedral. Also, part of the substituent effect, 6x, may result from other than a change in a;. Interactions between electrons in the C-X bond and those in C--H can contribute to J m , without affecting aE2 and have the required additivity. The values for 6x range from - 12 to f27 c/sec compared to the 125c/sec value for JCH in methane itself. Even relatively small non-a& effects of about 5 c/sec would materially improve the picture.Such contribu- tions might come from the neglected 01 and 0 2 terms 2 and/or from overlap terms 15 which were assumed to be negligible in our calculation of the Fermi contact inter- action. Further studies of this question as well as of the nonadditivity of substituent effects found for JS~H in silanes 16917 are indicated. 140 I50 JCH (CH3X) C/S~C relation between JCH observed in CH3X and JHH observed in CHz=CHX. The three sets of points are for JP-, JF and J g z , from top to bottom. RELATION OF JCH TO .@ AND Jgg Both JCH and JHH in hydrocarbons depend upon the electron density at the proton and on the carbon orbital hybridization so one would expect there to be some relation between the coupling constants. Such a relation is implicit in the fact that JcR(CH~X)~~ and J~H(CH~=CHX),~~ 18919 cis, trans and geminal, individually have an approxi- mately linear dependence on the electronegativity of X. This may be seen in fig.5, where the three proton-proton coupling constants observed in a number of substituted ethylenes are plotted against the corresponding JCH(CH~X). The scatter is con- siderable but there is nonetheless a general linear correlation between JCH and each of the three types of JHH. It is noteworthy that the scatter comes mainly from the JCH values, which indicates that there are interactions affecting JCH which do not contribute significantly to JHH. Another point of interest is that all three types of J=H increase while JCH decreases, based upon the arbitrary assignment of JtZs as positive.A decrease in JCH implies a decrease in the s character of the C-H bond. In turn, this would tend to decreaseH. S . GUTOWUKY AND C. JUAN 63 the C-C-H bond angle. And, according to valence bond calculatioiis of JHH in the HCCH fragment,3 this would increase both Jzp and JES, as observed. It is surprising to find virtually the same dependences upon JCH for all three types of JHH in spite of the different structural features and magnitudes involved, particularly for J,"ef;t. These similar slopes in fig. 5 may be accidental; nonetheless they are one of many features of internuclear coupling which remain to be explained. Acknowledgment is made to donors of The Petroleum Research Fund, adminis- tered by the American Chemical Society, for partial support of this research.The work also was supported by the Office of Naval Research. 1 Karplus, Anderson, Farrar and Gutowsky, J. Chem. Physics, 1957, 27, 597. Karplus and Anderson, ibid., 1959, 30, 6. 2 Karplus and Grant, Proc. Nat. Acad. Sci., 1959, 45, 1269. See also Gutowsky, McCall and Slichter, J. Chem. Physics, 1953, 21, 279, for an earlier discussion of the coupling of directly bonded nuclei and its dependence upon the perfect pairing structure. 3 Karplus, J. Chem. Physics, 1959, 30, 11. 4 Gutowsky, Belford and McMahon, J. Chem. Physics, 1962, 36, 3353, and prior work cited SGutowsky, Karplus and Grant, J. Chem. Physics, 1959, 31, 1278. Barfield and Grant, J. 6 Banwell, Sheppard and Turner, Spectruchim, Acta, 1960, 16, 794. Banwell and Sheppard, 7 Gutowsky, Mochel and Somers, J.Chem. Physics, 1962,36,1153. 8 Kaplan and Roberts, J. Amer. Chem. Soc., 1961,83,4666. 9 Fraser, Lemieux and Stevens, J. Amer. Chem. Soc., 1961, 83, 3901. 10 Wilson, Boekelheide and Griffin, J. Amer. Chem. SOC., 1960, 82, 6302. 11 Brown, J. Chem. Soc., 1953, 3278 12 Muller and Pritchard, J. Chem. Physics, 1959, 31, 768, 1471. Muller, ibid., 1962, 36, 359. 13 Shoolery, J. Chem. Physics, 1959, 31, 1427. 14 Malinowski, J. Amer. Chem. Suc., 1961, 83,4479. 15 Malinowski, Pollara and Larmann, J. Amer. Chem. SOC., 1962, 84, 2649 ; we wish to thank 16 Gutowsky and Juan, J. Amer. Chem. Suc., 1962, 84, 307. 17 Juan and Gutowsky, J. Chem. Physics, 1962, 37, 2198. 18 Sheppard and Turner, Proc. Roy. SOC. A , 1959, 252, 506. 19 Cohen, Sheppard and Turner, Pruc. Chem. SOC., London, 1958, 118. 20 Waugh and Castellano, J. Chem. Physics, 1961, 35, 1900. 21 Glick and Bothner-By, J. Chem. Physics, 1956, 25, 362. 22 Grant, Hirst and Gutowsky, J. Chem. Physics, 1963, 38, 470. This reference reviews in considerable detail the nature and analysis of A2B2 and A2X2 spectra in general and serves as a basis for the approach used on (2, 2) metacyclophane. A fuller account of the latter is given by Gutowsky and Juan, J. Chem. Physics, 1962, 37, 120. 73 These calculations were made with the University of Illinois electronic digital computer, IIliac, using a programme written by Dr. Ger,eva G. Belford for the general 6-spin system. We are indebted to the staff of the Digital Computer Laboratory for their assistance. there for substituted ethanes. Chem. Physics, 1962, 36, 2054. Mol. Physics, 1960, 3, 351. See also the results on epichlorohydrin by Reilly and Swalen, J. Chem. Physics, 1961, 35, 1522. Dr. Malinowski for sending us a copy of the manuscript prior to publication. 24 Lynden-Bell, Trans. Faraday Soc., 1961, 57, 888. 25 Ramsey, Physic. Rev., 1953, 91, 303. 26 Dailey and Shoolery, J. Amer. Chem. Suc., 1955, 77, 3977. 27 Lauterbur, J. Chem. Physics, 1957, 26, 217. 28 Kotani et al., Table of Molecular Integrals (Maruzen and Co., Tokyo, 1955). 29 Coulson, Valence (Clarendon Press, Oxford, 1952), p. 194. 30 Linnett and Wheatley, Trans. Faraday SOC., 1949, 45, 33, 39. Whipple, Stewart, Reddy and Goldstein, ibid., 1961,34,2136, and Snyder and Roberts, J. Amer. Chem. Suc., 1962, 84 (in press).

ISSN:0366-9033    

DOI:10.1039/DF9623400052

出版商:RSC    

年代:1962

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. J. Guy (Universite' de Paris) said : I would like to mention that in my labora- tory, we have tried to calculate the mean screening constant a, using a variation method (with J. R. Didry and Mlle. F. Cabaret). The appropriate equations are the following, (additivity of orbital contributions), + where @ko is the kth unperturbed molecular orbital while Gk: must be an acceptable solution of - b + 3 + v2(@koGk) - Gkv2(@ko) = - 2v (@kork). (3) Eqn. (2) and (3) are not valid for degeneracy of @ko but other analogous relations (although less simple) are then available. On the other hand, we have also to perform the integration of (2) with Gk vectors which are only approximate : adjustment of parameters is practically obtained by testing the mean susceptibilities which are also --+ known by and We now give a table showing some of the results obtained.THEORETICAL NUMERICAL RESULTS FOR a (p.p.m.) .=27.41 (free rotation) '-..27-46 (fixed configuration) H2, 27.03 ; CH4, 27-64 C2H6:' CM3--Ck2-CH3,27-18 ; (CH&Cfi, 26-95 ; C2H2,26*38 (free rotation) (free rotation) NUMERICAL RESULTS FOR (P.P.M) methane-hydrogen + 0.61, methane-ethane + 0-23, methane-propane + 0-46, methane-isobutane + 0.69, ethane-propane + 0.23, ethane-isobutane + 0.46, propane-isobutane + 0.23, methane-acetylene + 1 -26. For the details of these calculations, the following papers must be consulted: Cornpt. rend., 1961, 252, 1296, 2854 and 3439 ; 1961,253, 422 and 2902; J. Physique Rad., 1962,23,65 and 258. The last but one of these papers indicates how to set up " isoscreenhg diagrams ".1 see papers with Tillieu and Baudet, as J. Chem. Physics, 1956, 24, 1117; Ann. Physique, 1957, 2, 471, 631 ; Cornpt. rend., 1954, 239, 1203, and other works published in J. Physique Rad., J. Chim. Physique and Compt. rend. 64GENERAL DISCUSSION 65 Dr. D. W. Davies (Rijsuniversiteit te Groningen) said: I should like to make two comments on Dr. Pople’s theory, given in his paper here and in two other papers.1 Dr. Pople stresses the importance of the paramagnetic contribution x p to the suscepti- bility of a diamagnetic molecule. He discusses his values of x p in relation to the constitutive corrections in the Pascal scheme. For methane, ammonia, and water, however, experimental values of x p are known from measurements of rotational magnetic moments.2 The values for xp obtained from Dr.Pople’s theory, and the experimental values are shown in the first and second columns of the table. TABLE 1 1 O6XP -106Xd molecule calc. expt. calc. expt. me thane 6.46 9.3 28.4, 29.0 26.7 f0.8 ammonia 6-46 4 3 18.8 20.6 f0.8 water 5-39 1.46 12.5 14.46 Dr. Pople’s theory is, no doubt, more applicable to larger molecules than these ; but the much greater variation of the experimental x p compared to the theoretical xp suggests that the detailed conclusions of the theory must be treated with caution. My second comment concerns his suggestion that his theory gives better results for xp than for the diamagnetic contribution to the susceptibility xd. Most workers on diamagnetic susceptibilities have come to the opposite conclusion : that it is not too difficult to calculate xd, but that the use of the mean energy approximation makes the calculation of xp very uncertain. In support of the general view, I give calculated and experimental values 3 of Xd in the third and fourth columns of the table.The calcula- tions are much more elaborate than those on the basis of Dr. Pople’s theory ; but the results suggest that it is possible to get good theoretical values for ~ 6 . I know of no satisfactory perturbation method calculation of xp for these molecules. I suggest, therefore, that Dr. Pople might find it easier to improve his calculations of ~d than Prof. Dr. A. Bother-By (Universitiit Miinchen) said : Many papers have appeared dealing with the possible influence of near-by carbon-carbon single bonds on the chemical shift of a proton.When we originally suggested this concept, we were concerned at the magnitude of the diamagnetic anisotropy required to produce the shifts which could be explained on this basis. The work of others (Dailey, Narasimhan and Rogers, Musher, Ziircher, inter aZii) has demonstrated, that if all of the effect of alkyl substitution is to be produced by this mechanism, the required value of the magnetic anisotropy is so large as to imply a paramagnetism along the bond axis. This, together with the non-additivity often encountered in such systems strongly suggests that other mechanisms are at work. It is reasonable, however, that some fraction of the effect may be produced by this means : C-C bonds and C-H bonds are not identical, and a carbon atom substituted with some H’s and some C’s cannot be completely magnetically isotropic.A fairer comparison of the shift in aldehyde protons would be with the a-protons in alcohols-such a comparison would partially cancel the effect of the electro- negative oxygen substituent. The observed shift would then be about 5.0-5.5 p.p.m., or about twice that calculated, as with the other cases. Prof. J. I. Musher (Harvard University) said: As has been shown by Dr. Ziircher, and I would show by a priori calculations, it appears that AXC-H must not be neglected for magnetic shielding. In these long-chain crystalline paraffins there are two C-H of XP* 1 Pople, J. Chem. Physics, 1962, 37, 53, 60. 3 Banyard, J. Chem. Physics, 1960,33, 832 ; 1961, 34, 338.C 2 Weltner, J. Chern. Physics, 1958, 28,477.66 GENERAL DISCUSSION bonds for each C-C bond oriented effectively perpendicular to the chain. Were the sign of AXC-H the same as that of Axc-c as indicated by theory (although opposed to the above cited experimental work) and were the two Ax’s of comparable magnitude, then Dr. Pople’s conclusion of A ~ c - c negative does not follow from the measurement of the crystal magnetic anisotropy. Dr. D. W. Davies (Rijsuniversiteit te Groningen) said: In connection with the anisotropy of carbon-carbon single and double bonds, I should like to draw attention to some remarks made by Hoarau in his thesis.1 He pointed out that there is no paramagnetic contribution to the total magnetic susceptibility along the axis of a single bond X I I ; but there is a contribution to the susceptibility at right-angles to this axis xl.Thus, if the diamagnetic contributions to the susceptibfities in the two directions are nearly equal, I xL I < I X I I I . This is in agreement with the experi- mental observations of the Cotton-Mouton effect, mentioned by Dr. Pople. Hoarau also pointed out that the paramagnetic contribution for p-electrons in double bonds decreases the absolute value of the susceptibility in the plane of the a-bonds. Dr. R. F. Ziircher (Ciba Ltd., Bash) said: In his calculations, Dr. Pople found no anisotropy of the magnetic susceptibility of the carbon-carbon single bond. Dr. Tillieu,2 who made a variational calculation, obtained a value of 1.2 p.p.m.for this quantity. The experimental workers in this field give values between about 2 and 5 p.p.m. There is only one point of agreement : the anisotropy of the diamagnetic susceptibility of the carbon-carbon single bond, if it exists, seems to be positive. In this situation perhaps another consideration might help. The well-known equation of Kirkwood 3 connecting the electron polarizability a with the magnetic susceptibility x has been extended by Gans and Mrowka 4 to express the principal susceptibilities as a function of the principal polarizabilities, and vice versa. With the help of these equations, the mean bond polarizabilities and susceptibilities, and two equations for the combined electric and magnetic anisotropies it is possible to determine by a least-squares treatment the longitudinal and transverse polarizabilities and susceptibilities of the carbon-carbon and carbon-hydrogen bond.5 Values of these quantities calculated by different methods, generally compare favourably.The anisotropy of the magnetic susceptibility of the G C bond turns out to be about 1 p.p.m. At the same time an appreciable magnetic anisotropy of the C - € 3 bond is obtained. The Gans-Mrowka equations indicate clearly that if the electron polarizabfity of a bond is anisotropic the magnetic susceptibility must be, also, or more precisely that the direction of largest diamagnetic susceptibility must be perpendicular to the one with largest electron polarizability. The rather low value for the anisotropy of the susceptibility of the C-C bond makes it possible-as Dr.Pople has pointed out- that other effects such as ring currents in saturated cyclic compounds, differences in electronegativity, electric bond dipoles and the magnetic anisotropy of the C-H bond, which may also contribute to the difference in chemical shifts, must be taken into consideration in an empirical calculation. In many cases, besides, it is doubtful whether the so-called dipole approximation used in the empirical calculations of bond anisotropies is justified. Dr. R. J. Abraham (Liverpool University) said: The chemical shift difference be- tween methyland methylene protons has been considered previously as due to a “ C-C bond shift ”, i.e., due to the anisotropy of the C-C bond. This may equally we11 be 1 Hoarau, Thesis (Masson, Paris, 1956), p.23. 2 Tillieu, Ann. Physique, 1957, 2, 471, 631. 4 Gans and Mrowka, Schriften Konigsberger GeIehrten Ges. Naturw. KI., 1935, 12, 1. 5 Ziircher, J. Chem. Physics, in press. 3 Kirkwood, Physik. Z., 1932, 33, 57.GENERAL DISCUSSION 67 considered as a methyl group shift, in which the methyl group affects the proton chemical shifts of the neighbouring methylene groups by a Van der Waals type of interaction. This was shown to be the only mechanism to satisfactorily account for the effect of methyl substitution in some steroid molecules. Dr. J. I. Mushes (Harvard University) said: I would just like to point out the difficulty involved in obtaining quantitative results from Dr. Pople’s elegantly derived theory. It stems from the following two approximations, both of which could be easily reinstated into the theory.These are (i) the neglect of overlap and its con- sequence, the neglect of all integrals between wave functions on two centres; and (ii) treating nearest neighbour electron distributions in a dipolar approximation. The errors involved are significant essentially for proton and lithium shielding and to demonstrate them I will discuss the series of molecules H2, HF, and HCl. For all of these, Dr. Pople’s method gives essentially 20.6 &- 2.0 x 10-6 using a Wang wave function for the hydrogen, and Slater orbitals to calculate Ax on the halides. To illustrate my objections, I perform a nearly exact calculation on H2 using the Wang-Heitler-London wave function and Ramsey’s formalism. Let, for the general HX case, I ) = (I H) + I X)) I X’ .. . ), where I H} is the usual shielded Slater 1s a.0. centred on the proton whose shielding we are calculating and I X} is the bonding a.0. centred on the second nucleus (for H2 the 1s a.0. on the other proton), both of which are normalized, including overlap. I X‘ , . . ) is the function for the remaining X electrons. There are two shielding operators whose matrix elements we must find, one for Lamb term shielding and one for high-frequency term shielding, such that a,,(R) = aL(R)+aHF(R), where R is arbitrary and determines the gauge. There are three such pairs of integrals (H 1 a, I H), (H I a, I X) and (XX’ . . . I B,, I X’X). For Hz, if we choose R = 0 for the first two of these and R = RH-x for the third, then all matrix elements of aHF(R) vanish exactly.Furthermore (X 1 & ( R H ~ ) I X) also nearly equals zero since H is essentially outside the cloud of X. Thus there are two remaining integrals as shown in the table where the shielding contributions are listed symbolically and the two terms which for X # H are also tabulated for the halides. molecule <H I ~L(o) I H) <H I:.W I X> C <x I ~ L ( R ) I x> C <x I am^) I x> exp t . X X H2 12.5 12.5 0 0 262x 10-6 HF 12.5 11.7 small ? 22.7 HCl 14 negative large positive ? L Y J Pople, dipole <1 \ Y J Pople, dipole N 1.2 30-7 What this attempts to show most schematically is : (i) H2 : Half of the H2 shielding comes from an overlap term as different from Pople who has the first term 20.6 and the second, zero.Note the agreement with the Newel1 wave function result cited as ‘‘ experimental ” is excellent. The closed shell approximation gives a nearly exact result. Incidentally note that the high-frequency term calculated by Ramsey as 5-9 x 10-6 is given by - (X I a L ( 0 ) I X), or 6.4 x 10-6. (ii) HF : Once overlap is included the dipole approximation also gives a very good result. Note that RH-F = 0-9 A while (r2)* = 0.5 A. (iii) HC1: Including overlap makes the result even worse in the dipole approxima- tion, in either case the error being 15 x 10-6. Clearly here the last two terms must be calculated exactly, the significant one being (X I aL I X> because RHC~ = 1.2 A while (r2)* = 1 A. For HI, R = 1.6 A and <r2)* = 2.4 A.68 GENERAL DISCUSSION What I have done is essentially the same as the variational methods of Das and Bersohn, and Tillieu and Guy, by minimizing the Lamb terms and hence the high- frequency term except that rather than minimize it once for the entire bond wave function, I do it separately for each pair of integrals.Thus I can calculate the proton shielding in H2 (Ramsey’s calculation uses the experimental aHF) by hand in approxi- mately five minutes! This also gives immediately the isotopic shift. The justifica- tion and exposition of the procedure will be published shortly. It is formally similar to that of Hameka, and the error in both cases is the same. Dr. J. A. Pople (Nut. Physic. Lab., Teddington) said: I should like to make two further points about diamagnetic anisotropies and their relation to proton chemical shifts. The first concerns the origin of the diamagnetic anisotropy of aromatic compounds of the type studied by Prof.Dailey. The high diamagnetism of these compounds perpendicular to the molecular planes is usually attributed to inter- atomic ring currents, the n-electrons circulating in closed conjugated paths. How- ever, this is not the only possible mechanism and the theory described in my paper suggests anisotropy in ethylene itself, an axis of low diamagnetism existing in the molecular plane. Anisotropy is found experimentally in non-cyclic conjugated systems such as the carbonate and nitrate ions; a comparable theory provides a quantitative interpretation of this. If the theory is applied to benzene, it predicts that a substantial contribution to the total anisotropy (about 30 %) arises from intra-atomic circulations of this kind.Since the local anisotropies due to this factor will vary from atom to atom, the theory of proton shifts may need some modification. My second point concerns the local anisotropy in saturated hydrocarbons where the present situation is rather unsatisfactory. It is commonly supposed from n.m.r. data that the local anisotropy for a carbon-carbon single bond is positive. However, this appears to be inconsistent with the known experimental fact 1 that long-chain paraffinic compounds have their axis of greatest diamagnetism in the chain direction. Prof. Musher is correct in his suggestion that this paradox could be resolved by assigning a positive anisotropy also to the carbon-hydrogen bond.The principal drawback, however, is that rather large values would be required for both. On a bond additivity basis (assuming tetrahedral angles) the difference between the susceptibility along the chain axis and the mean susceptibility perpendicular to the chain axis (per methylene group) is + A ~ c c - AXCH. Lonsdale’s data 1 suggest that this is about - 1.3 x 10-6. Moritz and Sheppard 2 find from proton shifts that AXCC- AXCH = +4.2 x 10-6. The anisotropies required to fit both pieces of data are AXCC = + 11.0 x 10-6; AXCH = + 6.8 x 10-6. Clearly, further theoretical and experimental work is required. In reply to the remarks by Dr. Davies, the breakdown into diamagnetic and paramagnetic parts in my theory is on an atomic basis and not for the whole mole- cule as in the original Van Vleck treatment.Thus, the paramagnetic terms may not be compared directly with rotational magnetic moments. The calculation of such moments would be an interesting application, but the structure of the theory would require some modification. In reply to Dr. Musher’s second comment, I agree that the approximations in my theory lead to difficulties in obtaining good apriori quantitative results for small molecules. The hydrogen molecule is a particularly poor case for the neglect of differential overlap, because the neighbouring atom is so close. For the hydrogen 1 Lonsdale, Proc. Roy. SOC. A, 1939, 171, 541. 2 Moritz and Shepparcl, MoZ. Physics, 1962, 5, 361.GENERAL DISCUSSION 69 halides, there will be a substantial variation in the Lamb term because of the relative charge densities on the hydrogen atoms.The differences between the proton shifts in the whole series could be attributed to this. Prof. Dr. A. Bother-By (Universitiit Miinchen) said : It is tempting for the chemist to construct additive schemes for the calculation of chemical shifts, and a number of reasonably successful schemes have been proposed (Shoolery, Primas, inter alii). The schemes mostly run into trouble when there is an accumulation of several polar and/or polarizable substituents on one carbon, e.g., chloroform or the branched alkyl halides. The simple additive schemes also fail, in such cases, for the cal- culation of other molecular properties such as dipole moment, or molar refraction.The reason is that the polar groups polarize the polarizable groups, which in turn polarize other groups, etc. and non-linear behaviour is observed. The interactions can be calculated from sets of relations such as Pi = Moi + aizpjkj, where pi is the electric moment in bond i, Moi is the moment it would have in the absence of other polar groups, at is the bond polarizability of i, kj is a geometric factor equal to (cos 0 - 3 cos # cos $)/r3, which can be calculated if the molecular geometry is known, and the sum j is taken over all the groups present in the mole- cule. Such a set of relations correlates well the dipole moments measured for alkyl halides in the gas phase. In view of the good correlation observed between chemical shift of a-protons in the alkyl halides, and molecular electric moment (Bothner-By and Naar, 1958), similar relations must be obtainable for shielding, and should give a better fit, with no increase in disposable parameters (the a's are obtained from experiment). Dr.E. L. Mackor (KoninklijkelShell-Lab., Amsterdam) said : The chemical shifts of a number of hydrogen-bonded species, dissolved in hydrogen fluoride at -7O"C, have been determined recently by Dr. MacLean and myself. They are HF - 7.5 p.p.m. (C6H12) HF? - 22 H30+ - 9.4 H20. C2HSf - 8.9 HO . C(CH3); - 13.2 H2F+ -13 (+20°C). The shifts of the positive ions were determined directly from their distinct n.m.r. signals. The shift of the HF: ion could be inferred from the displacement of the HF peak upon the addition of small amounts of bases such as NaF, H20, acetone and ethanol.In the positive ions the hydrogens experience a charge shift in addition to the hydrogen-bond shift, both to lower field. The shift to low field of the added proton in acetone, as compared with the one in H3O+ and the H20f group of ethanol, seems to indicate that the proton attached to the oxygen atom lies in the y direction of the xy plane.1 It would then feel a considerable paramagnetic contribution.1 The smallness of the chemical shift of the HFT ion is puzzling. First, the electron density in the hydrogen atom cannot be expected to be much lower than that in HF.2 Secondly, it is difficult to see how a large paramagnetic shift could arise in the ion. Preliminary susceptibility measurements in KHFz single crystals have not revealed an 1 See table 2 in Pople, this Discussion.2 CIementi, J. Chern. Physics, 1961, 34, 1468. Bessis and Bratoz, J. Chim. Physique, 1960, 57, 769. Ransil, Rev. Mod. Physics, 1960, 32, 245.70 GENERAL DISCUSSION anisotropy in the susceptibility larger than 10 %. Moreover, the molar diamagnetic susceptibility value seems to conform to Pascal’s rules. Qualitatively, the smallness of the magnetic shielding is in line with the exceptionally small FHF distance of 2-26 A. Dr. E. W. Randall (Queen Mary College, London) said: In attempts to correlate electron densities with chemical shifts, paramagnetic contributions to the chemical shift are usually ignored, at least for the lighter nuclei. There is some evidence, however, that in heterocyclic compounds such a contribution is important.Measure- ments of the N14 chemical shifts by double-resonance studies on pyridine, pyridinium ion, ammonia and the ammonium ion have been interpreted in terms of a large para- magnetic effect in pyridine for which the n+n excitation energy is relatively low.1 N14 shifts measured by single resonance methods have, indeed, been correlated with the n+n excitation energies in a way that proves that differences in the shifts are due mainly to changes in the paramagnetic part of the Ramsey equation.2 Such changes may also be of importance in determining the chemical shift of the a-protons of the pyridine molecule, and of the 2 protons of pyridine I-oxides.1 It seems dangerous therefore, to deal only with the diamagnetic contribution to the chemical shift, even for protons, in those molecules where there is a small electronic excitation energy, e.g., aromatic heterocycles.Electron-density calculations in such molecules may, therefore, be more suspect than usual. Dr. R. J. Abraham (Liverpool University) said: Proton resonance studies of the effect of meso methylation in the porphyrin and benzene rings demonstrated the existence of a new mechanism affecting proton chemical shifts in aromatic compounds. This was a decrease in the aromatic ring current on the introduction of a methyl substituent. Dr. E. L. Mackor (Koninkl~kelShell-Lab., Amsterdam) said: There is a tendency to correlate charge densities in carbon atoms in conjugated systems, as obtained from chemical shift data, with electron charge densities calculated in the n-electron approxi- mation.Our results indicate that the differences in the calculated values are much larger than those in the measured ones. There is a good reason why the measured excess charge is more evenly distributed. Both the C13 and the proton shifts are determined by the overall excess charge on the carbon atom. The n-electron density is not the sole determining factor, however, because an alternating n-electron density in the molecule is accompanied by a polariza- tion of the cr-core.3 Thus the “ measured ” excess charge is necessarily more evenly distributed. Large excess charges are found in the aromatic ions of odd-alternant systems ;4 for instance, in the proton complex of benzene a unit charge is distributed over five conjugated carbon atoms and this leads to considerable proton shifts (2-3 p.p.m.).The following diagram gives the charge distribution based on the chemical shift data, (a), calculated with the simple Huckel method (b) and the s.c.f. method (c). It is seen that the correspondence is poor. *25 -33 -33 (4 (4 (4 1 Baldescheieler and Randall, Proc. Chem. Soc., 1961, 303. 2 Phillips, private communication. 3 Colpa, MacLean and Mackor, Tetrahedron, in press. 4 MacLean and Mackor, Mol. Physics, 1961, 4,241.GENERAL DISCUSSION 71 Prof. A. R. Ubbelohde ( h p e r i d College, London) said : Dr. Powles’ interpretation of the weak temperature coefficient of the observed J coupling in acetaldehyde seems plausible. However, even in the absence of water this molecule readily forms various association polymers and also probably packs into non-crystallizable clusters in the liquid.The consequent rearrangements in the acetaldehyde molecule may themselves be sufficient to modify the J coupling. The extent of such association will certainly be temperature dependent and this effect would be difficult to segregate from other sources of temperature dependence of about the same order of magnitude. Dr. J. I. Musher (Harvard University) said : I would like to say that I believe some of the difficulties involved in correlating Jc~~-H’s with hybridization and the questions of angles between bond orbitals to be due to neglecting the change in the J with ionic character of the bond and the arbitrary assumption of orthogonality of a.o.’s on the carbon atom.It has been assumed that if a m.0. or v.b. function represents a C-H bond with a sp3 a.0. on the carbon then the polar contribution will also be in an sp3 a.0. I would contend that this is not necessarily the case since there is nothing sacred about such hybridization in the first place unless all the carbon a.o.’s, not the bond orbitals, are doubly occupied (C4-). In other words, one can form four tetrahedrally oriented sp hybrids (incidentally giving greater overlap than sp3) from one 2s function and one 2p function as long as each of these orbitals will be singly occupied (with random spin) which is the case when bond orbitals are formed. Thus for carbon a.o.’s and the bond orbitals are formed by The only problem is that the four bonds are not even nearly orthogonal which means that the Slater determinants do not adequately describe the total wave function.The usual methods are not satisfactory and the non-independence of the bond orbitals implies that the spins of the bonds are correlated giving rise to a spin correlation energy depending on the atomic overlaps. Note that the Pauli principle is not violated in the BO picture since (neglecting overlap) each $i has densities of 3 in each of the m, states. Thus, the 4fS has a density of + in each m, state from each $i giving a total of 1 as allowed. There is an experimental inkling of at least the partial necessity of such an approach. Goldstein showed that linear correlations exist between the proton shielding CJH and JC-H both for ethylene derivatives and for methyl derivatives.Depending on the exact relationship of CJH with polar character one can derive the differential hybridiza- tion in this part of $. In the simplest model of C J H G C ~ ~ , ap$Jap& can be easily calculated indicating almost purely sp character for the ethylene derivatives. Note that the three C-H bonds in methyl derivatives rehybridize identically and indepen- dently, not being concerned about their lack of orthogonality. The critical conclusion of such rough ideas is that there is no need for other bonds to ‘‘ follow ” the rehybridiz- ation of a given bond by orthogonalizing its a.o.’s relative to the bond’s a.0. and thus bond angles do not have to change merely because of the rehybridization of a given individual bond. Prof. E. R. Andrew (University College of North Wales, Bungor) said : For complete- ness I wish to mention a third method of removing dipolar broadening, which is not discussed in our paper, and which is being investigated in Bangor by Mr.S. Clough. The method is based on an observation made by Redfield 1 some years ago. He had 1 Redfield, Physic. Rev., 1955, 98, 1787.72 GENERAL DISCUSSION found that the n.m.r. dispersion signal does not saturate so severely as the absorption signal. In order to give a satisfactory statistical mechanical treatment of the nuclear system in the presence of a strong radiofrequency field H I , Redfield showed that the system must be considered in a frame of reference rotating with the radio-frequency field. He further showed that if an audio-frequency magnetic field, of angular frequencyoa, was applied perpendicular to the effective field Her in the rotating frame, there should be a resonant saturation of the dispersion signal whenw, = YHer.He observed this rotating saturation resonance for the particular case in which the radio- frequency was adjusted to exact resonance so that the angle @ between the effective field Her (which is now just H I ) and the main field Ho is 90". He predicted that the dipolar breadth of this rotating saturation resonance should be less than that for a normal low-power absorption resonance spectrum by a factor 3 1 3 cos2 0 - 1 1. When 0 is 90" the observed narrowing was rather more than the factor half predicted by this expression. However, if an experiment is carried out just off resonance with H I so adjusted that 0 has the value 54"44', the dipolar broadening should be suppressed.Prof. Dr. A. Bother-By (Universitat Miinchen) said : Eqn. (3) in the paper of Dr. Andrews and Dr. Eades must also hold for individual molecules which are cylindrical and rotate rapidly about their long axes. This suggests that some inter- esting experiments might be done with macromolecules, such as DNA or helical peptides, by causing a preferential alignment of their long axes at the " magic angle " to the permanent field. The rapid rotational reorientation about the long axis should cause a sharpening of the lines. Correct orientation of the long axis might be achieved by flow methods, for example. I would be interested to know whether anyone has done or is contemplating such experiments? Prof.E. R. Andrew (Univ. of N. Wales) said : As Dr. Bothner-By suggests a marked reduction in dipolar breadth should result from molecular rotation about an axis inclined at the "magic angle" to the applied field. It does not matter whether the rotation is produced mechanically or by reorientation of the molecules within the material so far as the intramolecular dipolar broadening is concerned ; however, in the latter case, the intermolecular dipolar broadening is only partially reduced, and this might limit the resolution obtainable. I do not know of any experiments which have been carried out of precisely the type mentioned by Dr. Bothner-By, though there have been experiments of a related character on liquid cry st als . Dr. A. C. M. Finch (Leicester University) said: As the matter of conventions has been mentioned, may I make a plea that in reporting chemical shifts in this Discussion and elsewhere, authors should say from what reference and in what direction the shift is. There are two conventions for reporting the direction of chemical shift. One, adopted for instance by Pople, Schneider and Bernstein in their book 1 is that shifts to greater field (and therefore to a lower frequency) than that required for resonance of the reference, be positive. The opposite convention (namely, that shifts from the resonance of the reference to higher frequency, and hence to lower field, be positive) is adopted for instance by Varian Associates for their scale 6 in p.p.m. from tetra- methylsilane.2 This convention was used also by Tiers 3 in constructing his scale of z-values by subtracting the chemical shift from ten. Hence 7-values are made to be similar in sign to the first convention. 1 Pople, Schneider, and Bernstein, High Resolution Nuclear Magnetic Resonance, (McGraw-Hill, 2 Bhacca, Johnson, and Shoolery, H&h Resohtion N.M.R. Spectra Catalog, (Varian Associates, 3 Tiers, J. Amer. Clzem. Suc., 1958, 62, 1151. 1959), 89. Palo Alto, Calif., 1962).GENERAL DISCUSSION 73 Sometimes the two conventions are confused ; shifts are reported in c/sec, and the sign is determined by whether the resonance occurs at fields greater (positive) or smaller (negative) than that of the reference compound, although the resonant frequency at fixed field would be smaller or bigger respectively. This practice has been used without explanation, for instance, by MacLean and Mackor,l and by Philips and co-workers in this Discussion. It is strictly incorrect, and most confusing to one entering the field. Shifts to lower field, expressed in clsec, are positive. 1 MacLean and Mackor, Mol. Physics, 1960, 3, 223 ; 1961, 4, 241 ; J. Chem. Physics, 1961, 34, 2207, 2208.

ISSN:0366-9033    

DOI:10.1039/DF9623400064

出版商:RSC    

年代:1962

数据来源: RSC