xvi FREQUENTLY USED SYMBOLS AND ABBREVIATIONS E/A, emission-absorption CIDNP net effect Jn residual internuclear coupling constant(Hz)observed EPL, echo planar imaging in an off-resonance decoupled spectrur EPR, electron ESR, electron spin resonance(same as EPR) exp, exponentiation on the base e k, rate constant for exchange k rate constant at coalescence FI, the FT of the evolution/mixing time parameter in a 2D NMR experiment F2. the FT of the detection time parameter in a 2D NMR L, number of lines(multiplicity)of a signal expenment FID, free induction decay time-domain signal FoV. field of view m,magnetic spin quantum number of a nucleus fp fraction of p-orbital character mr, magnetic spin quantum number of an electron f. fraction of s-orbital character M, net(macroscopic)magnetization vector FT. Fourier transformation Mo, net(macroscopic) magnetization vector at time zero Mr net(macroscopic)magnetization vector at time I Mrr component of the net(macroscopic) magnetization &(factor), signal position parameter in an EPR spectrum vector in the x, y plane G, standard-state free energy u, (I)magnetic moment of a nucleus; (2) parameter used Y. magnetogyric ratio of a nucleus to calculate the CIDNP net effect In the type of CIDNP net effect 1Hz, megahertz(10Hz) Im, the type of CIDNP multiplet effect MRI, magnetic resonance imaging Gr. magnetic field gradient GHz, gigahertz(10 Hz) n,(I)number of nuclei in an equivalent set;(2)mixing coefficient of an sp hybrid orbital h. Planck's constant N. number of neutrons in a nucleus n. signal intensity enhancement due to NOE v, frequency(Hz) HSC, 2D heteroscalar shift-correlated NMR spectrum Vav, average position(Hz) of two or more signals undergo- HET2DJ, 2D heteronuclear J-resolved experiment HETCOR, same as HSC Vo, operating frequency( Hz of an NMR spectrometer HOM2DJ, 2D homonuclear J-resolved experiment vo. operating frequency (MHz) of an NMR spectrometer HSC. 2D heteronuclear shift correlation VI, observing frequency in a double-resonance experiment Hz, unit of frequency(cycles per second) 2, "irradiating"frequency in a double-resonance experi VIn, signal halfwidth 1, magnetic spin of a nucleus in, signal halfwidth at the fast exchange limit INADEQUATE, ID and 2D NMR experiments to demon- NMR, nuclear magnetic resonance strate direct C-C connectivity NOE, nuclear Overhauser effect INEPT, insensitive nuclei enhanced by polarization trans- NoESY, a 2D COSY spectrum showing NOE interactions IoU. index of unsaturation o, angular frequency (rad s-) J, joules, a unit of energy J, internuclear coupling constant(Hz) P, population of a given state or energy level
FREQUENTLY USED SYMBOLS AND ABBREVIATIONS xvii ppm, parts per million facg acquisition time Pro-R, configuration of an atom about a prochiral center TE echo time Pro-S, configuration of an atom about a prochiral center Id, dwell time(s) PSR, paramagnetic shift reagent epr duration(us)of a pulse tr, B, pulse causing a 180 rotation around the r axis TR, repetition time (π/2)x,B1 pulse causing a9° rotation around the x’axis Iw, delay time T(Tesla), unit of magnetic field strength T absolute ure(K) q quartet(signal multiplicity) Tp, absolute rotating frame temperature T, spin-lattice (longitudinal)relaxation time of a nucleus TIp rotating-frame spin-lattice relaxation time T2, spin-spin( transverse)relaxation time of a nucleus r, internuclear distance T2p, rotating-frame spin-spin relaxation time R, (I)exchange ratio, k/Avo, (2)absolute configuration at Ti, effective spin-spin(transverse) relaxation time of a a chiral center; (3)spectroscopic resolution; (4)ideal nucleus gas constant TcP, cross-polarization time constant ROL, region of interest t, (I)old chemical shift scale; (2)lifetime(s) t correlation time of a nucleus 0. (I)angle between the internuclear vector and Bo.(2) s, singlet(signal multiplicity) dihedral (torsional) angle 5, (1)same as m (2)an atomic orbital TMS tetramethylsilane(intemal standard) S, absolute configuration at a chiral center TOCSY, total correlation 2D NMR spectroscopy o,(1)representing a plane of symmetry: (2)shielding constant; (3) parameter used in describing the CIDNP multiplet effect; (4)cylindrically symmetric bond or w, watt(measure of rf power) molecular orbital X. mole fraction S/N, signal-to-noise rat x,,z, Cartesian coordinate system in the laboratory frame SPl, selective population inversion of reference sp", hybridized atomic orbital with mixing coefficient n x',,, z, Cartesian coordinate system in the rotating frame SW, sweep(or spectral) width(Hz) of reference I, time(s) z axis, the axis of Bo, the external(applied)magnetic field triplet(signal multiplicity) Z atomic number
SPECTROSCOPY: SOME PRELIMINARY CONSIDERATIONS 1.1 WHAT IS NMR SPECTROSCOPY? Figure 1. 1. Notice that the wave is actually composed of two orthogonal (mutually perpendicular) waves that oscillate Nuclear magnetic resonance(NMR) spectroscopy is the exactly in phase with each other. That is, they both reach study of molecular structure through measurement of the peaks, nodes, and troughs at the same points. One of these interaction of an oscillating radio-frequency electromag- waves describes the electric field vector (E)of the radiation netic field with a collection of nuclei immersed in a strong oscillating in one plane(e. g, the plane of the page): the other external magnetic field. These nuclei are parts of atoms that, describes the magnetic field vector( B)oscillating in a plane in turn, are assembled into molecules. An NMR spectrum perpendicular to the electric field. Thus, both these fields therefore, can provide detailed information about molecular exhibit uniform periodic(e.g. sinusoidal)motion. The axis structure and dynamics, information that would be difficult, along which the wave propagates(the abscissa in Figure 1. 1) if not impossible, to obtain by any other method. can have dimensions of either time or length It was in 1902 that physicist P. Zeeman shared a Nobel The wave(s)pictured in Figure l I can be characterized by Prize for discovering that the nuclei of certain atoms behave strangely when subjected to a strong external magnetic field wo independent quantities, wavelength(i)and maximum amplitude(Eo and Bo in the figure). The intensity of a wave And it was exactly 50 years later that physicists F. Bloch and is proportional to the square of its amplitude. Knowing that E. Purcell shared a Nobel Prize for putting the so-called electromagnetic radiation travels with a fixed velocity c nuclear Zeeman effect to practical use by constructing the (3.00x 10 0 cm s-I in a vacuum), we can alternatively de first crude NMR spectrometer. It would be an understatement scribe the wave as having a frequency v, which is the inverse to say that, during the succeeding years, NMR has completely of the peak-to-peak time to in the figure revolutionized the study of chemistry and biochemistry, not to mention having a significant impact on a host of other areas. Nuclear magnetic resonance has become arguably the single (1.1) nost widely used technique for elucidation of molecular structure. But before we can begin our foray into NMR, need to review a few fundamental principles from physics where to is measured in seconds and v has units of cycle per second(cps or s-), now called hertz(Hz) in honor of the 1.2 PROPERTIES OF ELECTROMAGNETIC physicist H. Hertz. RADIATION Recognizing that the wave travels a distance i in time to ve can derive a second relationship All spectroscopic techniques involve the interaction of matter with electromagnetic radiation, so we should begin with a description of the properties of such radiation. The light rays C=-=入v (1.2) that allow our eyes to see this page constitute electromagnetic radiation in the visible region of the electromagnetic spec- Thus, the wavelength and frequency of a given wave trum. Each electromagnetic ray can be pictured as shown in independent quantities; rather, they are inversely
2 SPECTROSCOPY: SOME PRELIMINARY CONSIDERATIONS if abscissa scale is time if abscissa scale is length Figure I. Electromagnetic wave with electric vector E and magnetic vector B tional. Radiation of high frequency has a short wavelength, Since the strength of a chemical bond is typically around 400 while radiation of low frequency has a long wavelength w mol-l, radiation above the visible region in Table 1.I has The known electromagnetic spectrum (Table I 1)ranges sufficient energy to photodissociate(break )chemical bonds. from cosmic rays of extremely high frequency (and short while radiation below the visible region does not(see Table wavelength) to rf (radio-frequency)radiation of low fre- 1. 1). Of particular interest to us for NMR purposes is rf quency(and long wavelength). The narrow visible region in radiation, the same frequency range that carries communica the middle of the electromagnetic spectrum corresponds to tion signals to our radios and televisions. We will normally be radiation of wavelength 380-780 nm(I nm= 10-9m= 10-7 using radiation with frequencies of 200-750 MHz (I MHz cm)and frequency 4 x 10 4-8x 104Hz Our optic nerves do I0- Hz), at the low end of the energy scale in Table I.I. This, not respond to electromagnetic radiation outside this region. it will tum out, is exactly the amount of energy we will need In addition to its wave properties, electromagnetic radia- to perform NMR experiments tion also exhibits certain behavior characteristic of particles To summarize, if two photons possess the same energy. A particle, or quantum, of radiation is called a photon. Fo they correspond to waves(or wavelets)of the same frequency our purposes the most important particlelike property of a and the same maximum amplitude. The total intensity of an photon is its energy(). Each photon possesses a discrete electromagnetic beam is therefore the number of photons amount of energy that is directly proportional to its frequency delivered per secor (if we regard it as a wave). This relationship can be written I EXAMPLE 1.1 Derive the relationship between the E=hv (1.3) energy of a photon and its wavelength where h, Plancks constant, has values of 6.63 x 10- Js per 0 Solution: We can rearrange Eq (1. 2)tov=c/.Substi- photon. Alternatively, h can be expressed on a per-mole basis tuting for v in Eq (1. 3)gives through multiplication by Avogadro's number (6.02 x 10 mol-)and division by 10J(k)- to give h= 3. x 10-13kJ E=h hc s mol-(A mole of photons is referred to as an Einstein
1.3 INTERACTION OF RADIATION WITH MATTER: THE CLASSICAL PICTURE 3 TABLE 1.1 Electromagnetic Spectrum Radiation on Wavelength, A(nm) Frequency, v(Hz) Energy(kJ mol) Cosmic rays <103 >12×108 Gamma rays 3×108-3×10201.2×10-1.2×108 X-rays 10-10-13×1016-3×10181.2×104-1.2×105 Far ultraviolet 15×105-3×10166×102-1.2 UItraviolet 380-200 8×1034-15×10332×102-6×10 Visible 780-380 4×1014-8×10 1.6×102-3.2×102 3×104-780 10134×1014 4-1.6x102 Far infrared 3×10-3×104 1021013 044 Microwaves 3×10-3×105 1001012 4×10-3-04 Radio frequency 10-3×103 10°-100 4×10-7-4×10-3 It is perhaps worthwhile to mention that the velocity(v)of close to a perturbing particle. If the frequency of the radiation electromagnetic radiation decreases as it passes through a is unchanged, the scattering is described as elastic. However, ondensed medium(e. g, a liquid or solution). The ratio of its if the frequency has changed(inelastic scattering), this ind speed in a vacuum(c)to its velocity in the medium is called cates that there was a partial exchange of energy between the the index of refraction(n) of the medium photon and the particle. In the case of NMR spectroscopy we will be concerned (1. 4) only with absorption and emission of rf radiation. Quantum mechanics, the field of physics that deals with energy at the microscopic(atomic)level, allows us to define selection rules The magnitude of n for a given medium varies inversely with that describe the probability for a photon to be absorbed or the wavelength of radiation, but it is always greater than unity. emitted under a given set of circumstances. But even classical The energy of a photon(unless it is absorbed)is unaffected (i.e. pre-quantum-mechanical) physics tells us there is one by passage through the medium, so its frequency must also be requirement shared by all forms of absorption and emission unchanged [Eq(1.3)]. Therefore, its wavelength must have spectroscopy: For a particle to absorb(or emit)a photon, the decreased(to i')in order to preserve the relationship in Eq. particle itself must first be in some sort of uniform periodic motion with a characteristic fixed frequency. Most important, v=λv the frequency of that motion must exactly match the frequency of the absorbed (or emitted) photon where入'=λ/n=v/c Vmotion=Photon (1.5) 1.3 INTERACTION OF RADIATION WITH MATTER: THE CLASSICAL PICTURE This fact, which at first glance might appear to be an incred ible coincidence, is actually quite logical. If a photon is to be Now that we know something about electromagnetic radia- absorbed, its energy, which is originally in the form of the on, let us turn to the question of what factors control the oscillating electric and magnetic fields, must be transformed interaction of such radiation with particles of matter. The three into energy of the particle's motion. This transfer of energy main types of interactions of interest to spectroscopists are can take place only if the oscillations of the electric and/or absorption,emission, and scattering. When absorption oc- magnetic fields of the photon can constructively interfere with curs, the photon disappears and its entire energy is transferred the"oscillations"(uniform periodic motion)of the particle's to the particle that absorbed it. The resulting particle with this electric and/or magnetic fields. When such a condition exists, excess energy is said to be in an excited state. It can relax the system is said to be in resonance, and only then can the back to its ground state by emitting a photon, which carries act of absorption take place. By the way, do not confuse the off the excess energy. term resonance in this context with the concept of resonance Radiation is scattered when the direction of propagation (conjugation) of electrons used to describe the structure of of the photon is shifted by some angle, the result of passing molecules