The Chemical Shift

The applied magnetic field induces electron circulation about the nucleus of the hydrogen atom. This generates a small, local magnetic field around the proton that is opposed to applied magnetic field. The induced field shields the nucleus from the applied field. 

Relaxation. The return of an ensemble of spins to the equilibrium distribution of spin state populations. 

Spin-lattice relaxation. Syn T, relaxation. Relaxation involving the interaction of spins with the rest of the world (the lattice). 

Chemical shift (8). The alteration of the resonant frequency of chemically distinct NMR-active nuclei due to the resistance of the electron cloud to the applied magnetic field. The point at which the integral line of a resonance rises to 50% of its total value. 

The one-dimensional NMR spectrum shows amplitude as a function of frequency. To generate this spectrum, an ensemble of a particular NMR-active nuclide is excited. The excited nuclei generate a signal that is detected in the time domain and then converted mathematically to the frequency domain by using a Fourier transform. 

The Chemical Shift. - Having established that the Larmor frequency is a characteristic for each nucleus depending on y and H0, we must consider a minor perturbation in the observed value of v0 brought about by relatively small changes in the magnetic field experienced by a nucleus in a diamagnetic material, caused by the immediate chemical environment of the nucleus, namely the chemical shift, a, given by 

Equation 7 shows that the Larmor frequency, or resonance frequency, of a nucleus depends on the magnitude of the empirical constant, y. As Table 2 shows, y differs greatly from isotope to isotope and so the resonance frequency of each isotope, at a given external magnetic field strength, is very different. This means that only one isotope is studied directly in an NMR experiment there is no interference problem of one element being confused with another in NMR spectroscopy, as is possible with other analytical methods. 

The induction of electronic magnetic moments by an external field in materials that ordinarily have no inherent magnetic moment is termed diamagnetism, and occurs in all substances. Those substances in which only such induced moments may occur are called diamagnetic. 

Spin resonance data for some common nuclei  

Isotope Spin I in multiples of hlln Magnetic moment, /r, in multiples of the nuclear magneton (ehjAnmc) Magnetogyric ratio (y/10 rad-T -s ) 

Measurement of line positions in NMR spectra according to equation 18 requires use of a reference line. Experimentally, this means that a reference compound giving a sharp line(s) separate from sample resonances must be included in the NMR tube. For example, sodium 4,4-dimethyl-4-silapentane (DSS) is useful for many H-NMR 

NMR is a valuable structural tool because the observed resonance frequency vq depends on the molecular environment as well as on y and Bq. The electron cloud that surrounds the nucleus also has charge, motion, and, hence, a magnetic moment. The magnetic field generated by the electrons alters the Bq field in the microenvironment around the nucleus. 

The actual field present at a given nucleus thus depends on the nature of the surrounding electrons. This electronic modulation of the Bq field is termed shielding, which is represented quantitatively by the Greek letter a. The actual field at the nucleus becomes B]ocai and may be expressed as Bq(1 - cr), in which the electronic shielding ct normally is positive. The variation of the resonance frequency with shielding has been termed the chemical shift. 

By substituting B]ocai for oq. 1-2, the expression for the resonance frequency in terms of shielding becomes 

The chemical shift may be expressed as the distance from a chemical reference standard by writing eq. 1-3 twice—once for an arbitrary nucleus i as 

The distance between the resonances in the NMR frequency unit (Hz, or cycles per second) then is given by the formula 

In the following sections we describe the chemical factors that control the appearance of NMR spectra. The discussion will set the stage for the exploration of powerful techniques that make use of radiofrequency pulses and form the basis for all modern applications of NMR in biochemistry. 

We need to understand the moiecuiar origins of the local magnetic field experienced by nuclei to see how careful analysis of the NMR spectrum reveals details of the structure of a biological molecule and its environment. 

Because cr varies with the environment, different nuclei (even of the same element in different parts of a molecule) come into resonance at different frequencies. 

The chemical shift of a nucleus is the difference between its resonance frequency and that of a reference standard. The standard for protons is the proton resonance in tetramethylsilane, Si(CH3)4, commonly referred to as TMS, which bristles with protons and dissolves without reaction in many solutions. Other references are used for other nuclei. For C, the reference frequency is the resonance in TMS, and for it is the resonance in 85 per cent H3P04(aq). The separation of the resonance of a particular group of nuclei from the standard increases with the strength of the apphed magnetic field because the induced field is proportional to the applied field, and the stronger the latter the greater the shift. Chemical shifts are reported on the 5 scale, which is defined as 

In much of the literature that uses NMR, chemical shifts are reported in parts per million, ppm, in recognition of the factor of 10 in the definition. This practice is unnecessary. 

Measurement of the chemical shift. When a nucleus (or set of equivalent nuclei, see below) gives rise to a single absorption peak in the spectrum it is a simple matter to determine the chemical shift from a measurement of its separation from the reference peak. In -spectra when coupling of the nucleus results in a first order multiplet (see below) measurement of the separation from the reference peak must be made to the mid-point of the multiplet. In more complex spin-spin interactions it is not possible to determine directly the chemical shift by measurement in this way, and resort must be made to the application of mathematical methods of analysis. 

XH chemical shifts. More detailed chemical shift data for a wide range of proton environments is given in Appendix 3, Tables A3.1, A3.3 and A3.4. In particular the chemical shift values quoted in Table A3.1 show that an electronegative substituent in aliphatic systems causes a downfield shift the greater the electronegativity the more substantial the shift. When two substituents are attached to the same carbon atom there is a greater downfield shift, but not as great as the sum of the two substituents separately. The approximate position of absorption in such cases can be predicted on the basis of the empirical parameters shown in Appendix 3, Table A 3.2. 

The proton spectrum of phenylacetic acid (C6H5 CH2 C02H Fig. 3.47) exhibits three absorptions in the ratio 1 2 5 due to the carboxylic acid, methylene and phenyl protons respectively. The carboxylic acid proton has been offset by 

400 Hz so that it can be recorded on the chart which specifies a sweep width of 500 Hz. The actual absorption position of this proton, S 11.67, is calculated by adding the amount by which the absorption has been offset (400 Hz) to the position of absorption recorded on the chart (300 Hz), i.e. 700 Hz, and dividing by the operating frequency (60 MHz). 

Hybridisation of the carbon atom has a significant effect on the chemical shift sp3-hybridised carbon absorbs at high field (0-60p.p.m. downfield from TMS), sp2-carbon at low field (80-200 p.p.m.) and sp-carbon at intermediate values. The precise position of absorption of a particular atom is largely determined by the electronic effects of any substituents, and the fact that these are approximately additive enables fairly accurate predictions of chemical shifts to be made, provided that similar compounds of known structure are available for reference purposes. 

Actually, the nucleus senses a different field in different directions around it. Therefore, the shift is a tensorial quantity. Upon rotation in solution an average value a is obtained. The proton of CHCI3 will experience a smaller shielding constant because chlorine, being quite electronegative, will attract the electrons 

For fixed Bq, the frequency needed to have the transition will be larger for CHCI3 than for TMS. The difference in frequency is called chemical shift with respect to TMS. In this case the shift is positive  

We sometimes say that the CHCI3 proton resonates downfield (at a smaller external magnetic field) with respect to TMS, which in turn resonates upheld (at a larger external magnetic field) if we imagine to keep the frequency fixed and to vary the magnetic field. 

Under the above definition the chemical shift is expressed in frequency units (Hz) and depends on the external magnetic field, which then needs to be specified. It may be convenient to express the chemical shift as a pure number, i.e. divided by the frequency of the standard  

Unpaired electrons will have a preference for being aligned along the external magnetic field, in the absence of other restrictions. Therefore, their magnetic 

The NMR observable most commonly exploited in studies of solid acidity is the chemical shift. While some NMR observables (e.g., dipolar couplings) lend themselves to a more or less direct quantitative evaluation, the chemical shift must be interpreted. Changes in the 13C or 15N isotropic shifts of adsorbates are observed upon complexation with Brpnsted sites, and the same is true of the H shift of the Brpnsted site, but one is hard pressed to interpret such changes quantitatively in terms of a detailed structure of the adsorption complex or even the extent of proton transfer. 

Since many NMR studies of solid acids entail the observation of a chemical shift change in a probe molecule, reactant, intermediate, or product upon complexation with an acid site, there is an opportunity to fundamentally impact the application of NMR to solid acids by making better use of this information. We therefore review the salient parts of the chemical shift in some detail. Since some of the more visible controversies in NMR studies of solid acids regard carbenium ions and related electrophilic species, this treatment will use such ions as examples wherever possible. 

It is well known that electrons in atoms and molecules can shield the nucleus in part from the applied magnetic field and so alter its resonance frequency, 

The nuclear shielding is more precisely the second derivative of energy with respect to magnetic field (B) and nuclear magnetic moment (/u) (27). 

This nonsymmetric second-rank tensor can be decomposed to a symmetric (i.e., ay = o-ji) and an antisymmetric tensor through a symmetrization process (28). 

The variations in the positions of NMR absorptions, arising from electronic shielding and deshielding, are called chemical shifts. 

Chemical shift The difference (in parts per million) between the resonance 

A small amount of TMS is added to the sample, and the instrument measures the difference in magnetic field between where the protons in the sample absorb and where TMS absorbs. For each type of proton in the sample, the distance downfield of TMS is the chemical shift of those protons. 

Chemical shifts are measured in parts per million (ppm), a dimensionless fraction of the total applied field. By custom, the difference in field (the chemical shift) between the NMR signal of a proton and that of TMS is not measured in gauss, but in frequency units (hertz or Hz). Remember that frequency units and magnetic field units are always proportional in NMR, with v = The horizontal axis of the NMR spectrum is calibrated 

The chemical shift (in ppm) of a given proton is the same regardless of the operating field and frequency of the spectrometer. The use of chemical shifts to describe absorptions standardizes values for all NMR spectrometers. 

We have now seen that shielding and deshielding effects cause the absorptions of protons to have different chemical shifts along the JC-axis of NMR spectra. 

As we have also mentioned, chemical shifts are most often measured with reference to the absorption of the protons of TMS (tetramethylsilane). A small amount of TMS is usually added to the sample, and its signal establishes zero on the delta (5) scale. 

If this were all NMR had to offer, it would not be considered particularly useful in chemical investigations, since all one achieves is a costly and inconvenient estimate of the total hydrogen, fluorine, etc., content in a sample. In practice, all applications of NMR to chemistry are from three secondary phenomena the chemical shift the time-dependence of NMR phenomena and spin-spin coupling. These effects will now be discussed. 

From now on, unless otherwise indicated, we shall refer to protons and deal with PMR proton magnetic resonance) rather than with NMR. However, the principles are strictly analogous for all magnetic nuclei with / = 1/2. 

54 MHz in the same magnetic field is the closest resonance to that of H this is some 3,500,000 Hz away. It is apparent that the proton chemical shift range of about 1000 Hz is actually the fine structure of a single line. To put it pictorially, at a chart width where the chemical-shift range of protons corresponds to about 2 feet, the fluorine resonances will turn up 2 miles away the range will be found 48 miles away. 

The standard substance almost universally used is tetramethylsilane (Me4Si), commonly abbreviated as TMS. This standard was chosen because it gives rise to a single sharp line as a result of the identical environment of all the protons in the symmetrical molecule and because the chemical environment of protons in TMS is such that they resonate at a higher field than practically any other proton. Further, TMS is an inert, low-boiling liquid and can be easily removed from the sample after the spectrum has been run. Therefore, in practice, the procedure is nondestructive. The sample size required for examination by NMR, however, is relatively large, generally at least 10 mg, because of the inherently low sensitivity of the method. 

The chemical shift of any proton can be expressed in terms of Hz from TMS. By convention, the absence of a sign implies Hz to lower field, or down-field, from TMS, remembering at all times that field and frequency can be 

Observed position of peak (Hz) x 106 Operating frequency of instrument (Hz) 

The peak for acetone on a 200-MHz instrument occurs at 436 Hz, so the chemical shift is 2.18 8  

The absorption for the hydrogens of benzene appears 444 Hz downfield from TMS on an instrument that operates at 60 MHz. 

As discussed previously, the chemical shift of a hydrogen in a molecule is affected by the electrons surrounding it. The moving electrons generate their own small magnetic field that usually opposes the external magnetic field. The electrons shield the hy- 

Electronegative atoms deshield nearby hydrogens, resulting in a downfield shift. 

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Information from an n.m.r. spectrum is classified into the chemical shift, <5 (the relative shift from a standard [Me Si for H, CC13F for which is rendered independent of the field), and the coupling constants, J, which are determined directly from the spectra. 

Jameson C J and Mason J 1987 The chemical shift Multinuclear NMR ed J Mason (New York Plenum) oh 3... 

For a coupled spin system, the matrix of the Liouvillian must be calculated in the basis set for the spin system. Usually this is a simple product basis, often called product operators, since the vectors in Liouville space are spm operators. The matrix elements can be calculated in various ways. The Liouvillian is the conmuitator with the Hamiltonian, so matrix elements can be calculated from the commutation rules of spin operators. Alternatively, the angular momentum properties of Liouville space can be used. In either case, the chemical shift temis are easily calculated, but the coupling temis (since they are products of operators) are more complex. In section B2.4.2.7. the Liouville matrix for the single-quantum transitions for an AB spin system is presented. 

NMR spectra are basically characterized by the chemical shift and coupling constants of signals. The chemical shift for a particular atom is influenced by the 3D arrangement and bond types of the chemical environment of the atom and by its hybridization. The multiplicity of a signal depends on the coupling partners and on the bond types between atom and couphng partner. 

However, one of the most successfiil approaches to systematically encoding substructures for NMR spectrum prediction was introduced quite some time ago by Bremser [9]. He used the so-called HOSE (Hierarchical Organization of Spherical Environments) code to describe structures. As mentioned above, the chemical shift value of a carbon atom is basically influenced by the chemical environment of the atom. The HOSE code describes the environment of an atom in several virtual spheres - see Figure 10.2-1. It uses spherical layers (or levels) around the atom to define the chemical environment. The first layer is defined by all the atoms that are one bond away from the central atom, the second layer includes the atoms within the two-bond distance, and so on. This idea can be described as an atom center fragment (ACF) concept, which has been addressed by several other authors in different approaches [19-21]. 

A useful empirical method for the prediction of chemical shifts and coupling constants relies on the information contained in databases of structures with the corresponding NMR data. Large databases with hundred-thousands of chemical shifts are commercially available and are linked to predictive systems, which basically rely on database searching [35], Protons are internally represented by their structural environments, usually their HOSE codes [9]. When a query structure is submitted, a search is performed to find the protons belonging to similar (overlapping) substructures. These are the protons with the same HOSE codes as the protons in the query molecule. The prediction of the chemical shift is calculated as the average chemical shift of the retrieved protons. 

In such tables, typical chemical shifts are assigned to standard structure fragments (e.g., protons in a benzene ring). Substituents in these blocks (e.g., substituents in ortho, meta, or para positions) are assumed to make independent additive contributions to the chemical shift. These additive contributions are listed in a second series of tables. Once the tables are defined, the method is easy to implement, does not require databases, and is extremely fast. Predictions for a molecule with 50 atoms can be made in less than a second. On the other hand, it requires that the parent structure and the substituents are tabulated, and it considers no interaction... 

Neural networks can learn automatically from a data set of examples. In the case of NMR chemical shiffs, neural networks have been trained to predict the chemical shift of protons on submission of a chemical structure. Two main issues play decisive roles how a proton is represented, and which examples are in the data set. 

The descriptors are then submitted to previously trained and saved) neural networks, which give predictions for the chemical shifts. 

Another semiempirical method, incorporated in the VAMP program, combines a semiempirical calculation with a neural network for predicting the chemical shifts. Semiempirical calculations are useful for large molecules, but are not generally as accurate as ah initio calculations. 

Over the past decade it has been established that for various substituents the i C chemical shift increment is a constitutive property. This applies to many systems e.g. benzenes, alkanes and alkenes. The availability of over 200 allenes, randomly substituted with groups of different nature, enabled us to prove that in the case of allenes the chemical shift increment is a constitutive property too, thus establishing a convenient method for estimating i ( C) values for allenes. 

Using a multiple linear regression computer program, a set of substituent parameters was calculated for a number of the most commonly occurring groups. The calculated substituent effects allow a prediction of the chemical shifts of the exterior and central carbon atoms of the allene with standard deviations of l.Sand 2.3 ppm, respectively Although most compounds were measured as neat liquids, for a number of compounds duplicatel measurements were obtained in various solvents. 

In describing the chemical shifts of the exterior and central allene carbons, the substituent effect symbols depicted in Fig. 1 were used. 

The chemical shift can be calculated according the following equation ... 

The substituent effects on the chemical shift of the central carbon are given in Fig. 1 and are described by eg. 2 ... 

Making allowance for those effects gives a good correlation between the chemical shifts and the it- and/or tr-electron density of the carbon atom bearing the proton (133, 236,237). 

All the chemical shifts are expressed in 5 units ppm of applied field and TMS as reference peak. 

The chemical shifts of in natural abundance have been measured for thiazole and many derivatives (257,258). They are given in Tables 1-37 and T38. These chemical shifts are strongly dependent on the nature of the substituent CNDO/2 calculations have shown (184) that they correlate well with the ((t+tt) net charge of the atom considered. As a consequence, the order of the resonance signals is the same for protons and for carbon atoms. 

The NMR spectra of thiazoles show the same behavior as those of aromatic compounds, but the chemical shifts also depend on the two heteroatoms. 

The NMR determination in strongly acidic medium (trifluoroacetic acid) of the chemical shifts of the protons in the 4- or 5-position can be used to establish a reactivity scale. If the proton appears at low field, this indicates that this substitution site wiE be poorly or not at all nitrated (111). 

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