I n this chapter, we concentrate on absorption of radio-frequency radiation bynuclei and the resulting transitions between energy levels, better known asnuclear magnetic resonance (NMR) spectroscopy. Felix Bloch and EdwardPurcell, both of the United States, first detected the phenomenon of nuclear mag-netic resonance in 1946. They shared the 1952 Nobel Prize for physics. Nuclearmagnetic resonance (NMR) spectroscopy was developed in the late 1950s and,within a decade, became the single most important technique available to chem-ists for the determination of molecular structure. Nuclear magnetic resonancespectroscopy gives us information about the number and types of atoms in a mol-ecule: for example, about hydrogens using IH-NMR spectroscopy, and about car-bons using 13C-NMR spectroscopy. It can also give us substantial information aboutthe connectivity of the atoms and, in many cases, can allow determination of thestructure of a molecule with no additional information.

13.1 Nuclear Spin StatesYou are already familiar from general chemistry with the conceRts that q) an elec-tron has a spin quantum number of t, with allowed values of +t and -2' and that(2) a moving charge has an associated magnetic field. In effect, an electron be-haves as if it is a tiny bar magnet and has a magnetic moment. The same effectholds for certain atomic nuclei.

Any atomic nucleus that has an odd mass number, an odd atomic number, orboth, also has a spin and a resulting nuclear magnetic moment. The allowed nuclearspin states are determined by the spin quantum number, 1, of the nucleus. A nucleuswith spin quantum number I has 21 + 1 spin states. Our focus in this chapter ison nuclei of IH and 13C, isotopes of the two elements most common to organiccompounds. Each has a nuclear spin quantum number of t and therefore has 2(t)+ 1 = 2 allowed spin states. Quantum numbers and allowed nuclear spin states for

Magnetic resonance imagingis a useful medical diagnostictool. Inset: a model of methylacetate. For a lH-NMR spec-trum of methyl acetate. seeFigure 13.5.

OUTLINE13.1 Nuclear Spin States13.2 Orientation of Nuclear

Spins in an AppliedMagnetic Field

13.3 Nuclear Magnetic"Resonance"

13.4 An NMR Spectrometer13.5 Equivalent Hydrogens13.6 Signal Areas13.7 Chemical Shift13.8 Signal Splitting and the

en + 1) Rule13.9 The Origins of Signal

Splitting13.10 Stereochemistry and

Topicity13.11 13C-NMR13.12 Interpretation of NMR

Spectra~ How To Solve NMR Spectral

Problems

Online homework for thischapter may be assignedin Organic OWL.

13.1 Nuclear Spin States 477

Table 13.1 Spin Quantum Numbers and Allowed Nuclear Spin States forSelected Isotopes of Elements Common to Organic Compounds

Element 10 2JI 12C 13C 14N 15N 160 19N 31p 32S

Nuclear spin1 1 1 1 1quantum number (1)"2 1 0 "2 1 "2 0 "2 "2 0

Number ofspin states 2 3 1 2 3 2 1 2 2 1

these nuclei and those ofother elements common to organic compounds are shown inTable 13.1. Note that 12e, 160, and 32S each have a spin quantum number of zero andonly one allowed nuclear spin state; these nuclei are inactive in NMR spectroscopy.

13.2 Orientation of Nuclear Spins in anApplied Magnetic Field

Note: the 51 unit for magneticfield strength is the tesla 1TI.A unit still in common use,however, is the gauss (G). Valuesof T and G are related by theequation 1 T = 104 G.

Within a sample containing IH and 13e atoms, the orientations of the nuclear mag-netic moments associated with their nuclear spins are completely random. Whenplaced between the poles of a powerful magnet of field strength .80, however, inter-actions between the nuclear spins and the applied magnetic field are quantized, withthe result that only certain orientations of nuclear magnetic moments are allowed.For IH and 13e nuclei, only two orientations are allowed as illustrated in Figure 13.1.By convention, nuclei with spin +~ are aligned with the applied magnetic field andare in the lower energy state; nuclei with spin -~ are aligned against the appliedmagnetic field and are in the higher energy state.

The most important NMR physical concept from the point of view of molecularstructure determination is that the difference in energy between nuclear spin statesfor a given nucleus is proportional to the strength of the magnetic field experiencedby that nucleus (Figure 13.2). We will come back to this concept several times inthis chapter. At an applied field strength of 7.05 T, which is readily available withpresent-day superconducting electromagnets, the difference in energy between nu-clear spin states for IH is approximately 0.120 J (0.0286 cal)/mol (corresponding toelectromagnetic radiation of 300 MHz). At 7.05 T, the energy difference in nuclearspin states for 13e nuclei is approximately 0.030J (0.00715 cal) Imol (correspondingto radiation of 75 MHz). Advanced commercial instruments now operate at fieldsmore than three times this value; the operating frequencies are proportional to thefield. Sensitivities are more than proportionally higher!

To put these values for nuclear spin energy levels in perspective, energies fortransitions between vibrational energy levels observed in infrared (IR) spectros-copy are 8 to 63 kJ (2 to 15 kcal) Imol. Those between electronic energy levelsin ultraviolet-visible spectroscopy are 167 to 585 kJ (40 to 140 kcal)/mol. Nucleartransitions involve only small energies, on the order of a few hundredths ofa calorie!

Figure 13.1IH and 13C nuclei with spin +~are aligned with the appliedmagnetic field, Eo, and are inthe lower spin energy state;those with spin -~ are alignedagainst the applied magneticfield and are in the higherspin energy state.

Higherenergy state

Lowerenergy state t

Spin -t(aligned againstthe applied field)

Spin +t(aligned withthe applied field)

478 Chapter 13 Nuclear Magnetic Resonance Spectroscopy

L0.120llm~

~I__.~~t:::=======-.:1=-.1Q~ I

0.0239llmol

-

Spin -t(aligned against theapplied field)

Spin +t(aligned with theapplied field)

Figure 13.2The energy differencebetween the allowed nuclearspin states increases linearlywith applied field strength.Values shown here are forIH nuclei.

1.41 T

Example 13.1

Eo (Tesla)7.05 T

Calculate the ratio of nuclei in the higher spin state to those in the lower spinstate, Nh/~, for IH at 25C in an applied field strength of 7.05 T.SolutionUse the equation given in Section 2.6B for the relationship between the difference inenergy states and equilibrium constant. In this problem, this relationship has the form

dCo = - RTln Nt,No,

The difference in energy between the higher and lower nuclear spin states inan applied field of 7.05 T is approximately 0.120 J/mol, and the temperature is25 + 273 = 298 K. Substituting these values in this equation gives

In Nt, = -dGo = -0.120Jmol-1 = -4.843 X 10-5No, RT 8.314JK I'mol I X 298K

Nh = 09999516 = 1.000000No,' 1.000048

From this calculation, we determine that, for every 1,000,000 hydrogen atoms in thehigher energy state in this applied field, there are 1,000,048 in the lower energy state.The excess population of the lower energy state under these conditions is only 48 permillion! What is important about this number is that the strength of an NMR signal isproportional to the population difference. As you will see, the greater this differencein populations, the stronger the signal will be, because more spins are flipping.

Problem 13.1Calculate the ratio of nuclei in the higher spin state to those in the lower spinstate, Nh/~, for 13C at 25C in an applied field strength of 7.05 T. The differencein energy between the higher and lower nuclear spin states in this applied field isapproximately 0.030J (0.00715 cal) Imol.

13.3 Nuclear Magnetic "Resonance"As we have seen, when nuclei with spin quantum number t are placed in anapplied magnetic field, a small majority of nuclear spins are aligned with theapplied field in the lower energy state. When nuclei in the lower energy spin stateare irradiated with a radio frequency of the appropriate energy, they absorb theenergy, and nuclear spins flip from the lower energy state to the higher energystate, the only other allowed spin state.

13.2 Nuclear Magnetic "Resonance" 479

Resonance in NMR spectroscopyThe absorption of electromagneticradiation by a precessing nucleusand the resulting "flip" of its nu-clear spin from the lower energystate to the higher energy state.SignalA recording in an NMR spectrumofa nuclear magnetic resonance.

Diamagnetic current in NMRThe circulation of electrondensity in a molecule in anapplied magnetic field.

To visualize the mechanism by which a spinning nucleus absorbs energy andthe meaning of resonance in this context, think of the nucleus as if it were reallyspinning. When an applied field of strength Bo is turned on, the nucleus becomesaligned with the applied field in an allowed spin energy state. The nucleus thenbegins to precess as shown in Figure 13.3(a) and traces out a cone-shaped surfacein much the same manner as a spinning top or gyroscope traces out a cone-shapedsurface as it precesses in the earth's gravitational field. We can express the rate ofprecession as a frequency in hertz.

If the precessing nucleus is irradiated with electromagnetic radiation at exactlythe precession frequency, then the two frequencies couple, energy is absorbed, andthe nuclear spin "flips' from spin state +i (with the applied field) to spin state -i(against the applied field) as illustrated in Figure 13.3(b). For lH in an applied mag-netic field of 7.05 T, the frequency of precession is approximately 300 MHz. ForlSC in the same field, it is approximately 75 MHz. Resonance in this context is theabsorption of electromagnetic radiation by a precessing nucleus and the resultingflip of its nuclear spin from the lower energy state to the higher energy state. Thespectrometer detects this absorption of electromagnetic radiation and records it as asignal. The process is quantized, so that only electromagnetic radiation of preciselythe correct frequency causes a nuclear spin to flip. Electromagnetic radiation of afrequency that is too low or too high is not absorbed.

Ifwe were dealing with lH nuclei isolated from all other atoms and electrons,any combination of applied field and electromagnetic radiation that produces asignal for one hydrogen nucleus would produce a signal for all hydrogen nuclei.In other words, hydrogens would be indistinguishable. Hydrogens in an organicmolecule, however, are not isolated; they are surrounded by electron density.

A key physical principle for NMR is that circulating electrons induce a magneticfield. This is the principle behind electromagnets and electric motors. The directionof electron movement dictates the orientation of the induced magnetic field. Ofequal importance to NMR, the converse is also true. An applied magnetic field in-duces electrons to circulate, and the orientation of the field dictates the direction ofcirculation. You will learn more details of these relationships in your physics classes.The important point for our purposes is that an applied magnetic field induces theelectron density in a molecule to circulate. The spin states of underlying nuclei are,in turn, influenced to a small but measurable degree by the magnetic field createdby the induced electron density circulation. The circulation of electron density in amolecule in an applied magnetic field is called a diamagnetic current

It turns out that a molecule's u-bonding electron density is induced to circu-late in a direction that creates a small magnetic field that directly upposes the appliedmagnetic field. As a result of the opposing magnetic fields, the nuclei within thecirculating electron density experience a magnetic field that is slightly smoJJ.er thanthe actual applied field. In other words, nuclei underneath circulating u-bonding

Figure 13.3The origin of nuclear mag-netic "resonance." (a) Preces-sion of a spinning nucleus inan applied magnetic field.(b) Absorption ofelectromag-netic radiation occurs whenthe frequency of radiationis equal to the frequency ofprecession.

B"Axis of precession~

Orbit of precession..-/

El ~radi'ectrornagneuc aUonof same frequency asprecession frequency

Axis of nuclear spin;spin +t

absorption of ~n~rgy;th~ nuclear spin flips

Bo

I

(b)

480 Chapter 13 Nuclear Magnetic Resonance Spectroscopy

Table 13.3 The Effect of Hybridizationon Chemical Shift

Type of Hydrogen(R = alkyl)

RCH3, ~CH2' R3CH~C=C(R)CHR2RC=CH

~C=CHR,R2C=CH2RCHO

Name ofHydrogen

AlkylAllylicAcetylenicVinylicAldehydic

ChemicalShift 6

0.8-1.71.6-2.62.0-3.04.6-5.79.5-10.1

of the explanation for the greater deshielding of vinylic hydrogens compared withalkyl hydrogens lies in the hybridization of carbon. Because a u-bonding orbitalof an sf-hybridized carbon has more s-character than a u-bonding orbital of ansp"-hybridized carbon (33% compared with 25%), an sf-hybridized carbon atomis more electronegative. Vinylic hydrogens are deshielded by this electronegativ-ity effect and their nuclei resonate farther downfield relative to alkyl hydrogens.Similarly, signals for acetylene and aldehyde hydrogens also appear farther down-field compared with alkyl hydrogens.

However, differences in chemical shifts of vinylic and acetylenic hydrogenscannot be accounted for on the basis of the hybridization of carbon alone. If thechemical shift ofvinylic hydrogens (a 4.6-5.7) were caused entirely by the hybrid-ization of carbon, then the chemical shift of acetylenic hydrogens should be evengreater than that of vinylic hydrogens. Yet the chemical shift of acetylenic hydro-gens is only a2.0 to 3.0. It seems that either the chemical shift of acetylenic hydro-gens is abnormally small or the chemical shift of vinylic hydrogens is abnormallylarge. In either case, another factor must be contributing to the magnitude of thechemical shift. Theoretical and experimental evidence suggest that the chemicalshifts of hydrogens bonded to 7T-bonded carbons are influenced not only by therelative electronegativities of the sf- and sjrhybridized carbon atoms but also bymagnetic induction from 7T bonds.

c. Diamagnetic Effects from TT BondsTo understand the influence of 7T bonds on the chemical shift of an acetylenichydrogen, imagine that the carbon-carbon triple bond is oriented as shown inFigure 13.9 with respect to the applied field. Because of magnetic induction, theapplied field induces a circulation of the 7T electrons, which in turn produces aninduced magnetic field. Given the geometry of an alkyne and the cylindrical na-ture of its 7T electron cloud, the induced magnetic field is shielding in the vicinity

Figure 13.9A magnetic field inducedin the 7T bonds of a carbon-carbon triple bond shields anacetylenic hydrogen and shiftsits signal upfield.

Induced flow ofelectrons in the 7Tsystem of an alkyne

Induced local magneticIt ~~field of the 7T electrons

is against the applied fieldat the hydrogen atoms;it requires lower frequency

V radiation to bring anacetylenic hydrogen~ nucleus into resonance.488 Chapter 13 Nuclear Magnetic Resonance Spectroscopy

Induced circulationof 1T electrons inan alkene

Applied field, Bo

~ Induced local magnetic~ field of the 1T electrons

reinforces the applied fieldat the hydrogen atoms;it requires higher frequencyradiation to bring a vinylichydrogen nucleus intoresonance.

Figure 13.10A magnetic field inducedin the 1T bond of a carbon-carbon double bond deshieldsvinylic hydrogens and shiftstheir signals downfield.

of the acetylenic hydrogen. Therefore, lower frequency electromagnetic radiationis required to make an acetylenic hydrogen nucleus resonate; the local magneticfield induced in the 'TT' bonds shifts the signal of an acetylenic hydrogen upfield toa smaller 8 value.

The effect of the induced circulation of 'TT' electrons on a vinylic hydrogen(Figure 13.10) is opposite to that on an acetylenic hydrogen. The direction ofthe induced magnetic field in the 'TT' bond of a carbon-carbon double bond isparallel to the applied field in the region of the vinylic hydrogens. The inducedmagnetic field deshields vinylic hydrogens and, thus, shifts their signal downfieldto a larger 8 value. The presence of the 'TT' electrons in the carbonyl group has asimilar effect on the chemical shift of the hydrogen of an aldehyde group.

The effects of the 'TT' electrons in benzene are even more dramatic than in al-kenes. All six hydrogens of benzene are equivalent, and its IH-NMR spectrum is asharp singlet at 87.27. Hydrogens bonded to a substituted benzene ring appear inthe region 8 6.5 to 8.5. Few other hydrogens absorb in this region; thus, aryl hy-drogens are quite easily identifiable by their distinctive chemical shifts, as much as2 ppm higher than comparably substituted alkenes.

That aryl hydrogens absorb even farther downfield than vinylic hydrogens isaccounted for by the existence of a ring current, a special property of aromaticrings (Figure 13.11). When the plane of an aromatic ring tumbles in an appliedmagnetic field, the applied field causes the 'TT' electrons to circulate around thering, giving rise to the so-called ring current. This induced ring current has as-sociated with it a magnetic field that opposes the applied field in the middle ofthe ring but reinforces the applied field on the outside of the ring. Thus, giventhe position of aromatic hydrogens relative to the induced ring current, theyare deshielded and come into resonance at a larger chemical shift.

Ring currentAn applied magnetic field causesthe 1T electrons of an aromaticring to circulate, giving rise to theso-called ring current and an asso-ciated magnetic field that opposesthe applied field in the middle ofthe ring but reinforces the appliedfield on the outside of the ring.

Inducedcirculation of1T electrons ina benzene ring

Induced local magnetic field of

iW the circulating 1T electrons/ reinforces the applied fieldat the hydrogen atoms; it~_....- requires higher frequencyradiation to bring aromatic"'\''';+-'f''~ hydrogen nuclei inID ~on~re

Applied field

Figure 13.11The magnetic field inducedby circulation of 7T electronsin an aromatic ring deshieldsthe hydrogens of the aromaticring and shifts their signaldownfield.

13.7 Chemical Shift 489

ChemicalConnections

Magnetic Resonance Imaging

The NMR phenomenon was discovered and explainedby physicists in the 1950s and by the 1960s, it had be-come an invaluable analytical tool for chemists. By theearly 1970s, scientists realized that imaging of parts ofthe body using NMR could be a valuable addition to di-agnostic medicine. Because the term "nuclear magneticresonance" sounds to many people as if the techniquemight involve radioactive material, health care person-nel call the technique magnetic resonance imaging(MRI). MRI has become so important, that in 2003, theNobel Prize for medicine or physiology was awarded toPaul Lauterbur and Peter Mansfield for their discover-ies that led to practical MRI.

The body contains several nuclei that, in principle,could be used for MRI. Of these, hydrogens, most ofwhich come from the hydrogens of water, triglycerides(Section 26.1), and membrane phospholipids (Section26.5) give the most useful signals. Phosphorus MRI isalso used in diagnostic medicine.

Computer-enhanced MRI scan ofa normal human brainwith pituitary gland highlighted.

Recall that in NMR spectroscopy, energy in theform of radio-frequency radiation is absorbed by nucleiin the sample. Relaxation time is a characteristic timeat which excited nuclei give up this energy and relax totheir ground state.

In 1971, it was discovered that relaxation of waterin certain cancerous tumors takes much longer thanthe relaxation of water in normal cells. Thus, if a relax-ation image of the body could be obtained, it might bepossible to identify tumors at an early stage. Subsequentwork demonstrated that many tumors can be identifiedin this way. Another important application of MRI is inthe examination of the brain and spinal cord. Whiteand gray matter are easily distinguished by MRI, whichis useful in the study of such diseases as multiple sclero-sis. Magnetic resonance imaging and x-ray imaging are,in many cases, complementary. The hard, outer layerof bone is essentially invisible to MRI but shows up ex-tremely well in x-ray images, whereas soft tissue is nearlytransparent to x-rays but shows up in MRI.

The key to any medical imaging technique is toknow which part of the body gives rise to which sig-nal. In MRI, spatial information is encoded usingmagnetic field gradients. Recall that a linear relation-ship exists between the frequency at which a nucleusresonates and the intensity of the magnetic field. InIH-NMR spectroscopy, we use a homogeneous mag-netic field, in which all equivalent hydrogens absorbat the same radio frequency and have the same chem-ical shift. In MRI, the patient is placed in a magneticfield gradient that can be varied from place to place.Nuclei in the weaker magnetic field gradient absorbat a lower frequency. Nuclei elsewhere in the strongermagnetic field absorb at a higher frequency. In a mag-netic field gradient, a correlation exists between theabsorption frequency of a nucleus and its position inspace. A gradient along a single axis images a plane.Two mutually perpendicular gradients image a linesegment, and three mutually perpendicular gradientsimage a point. In practice, more complicated proce-dures are used to obtain magnetic resonance images,but they are all based on the idea of magnetic fieldgradients.

13.10 Stereochemistry and Topicity 501

13.9 Calculate the index of hydrogen deficiency of these compounds.

~,->-L,~ Online homework for this chapter may be assigned in Organic OWL. indicates problems assignable in OWL.Red numbers indicate applied problems.

Interpretation of lH-NMR and 13C-NMR Spectra13.10 Complete the following table. Which nucleus requires the least energy to flip its

spin at this applied field? Which nucleus requires the most energy?

(b) Ascorbic acid (vitamin C), C6Hs0 6(d) Urea, CH4N20(f) Dopamine, CsH u N02

Applied Field Radio Frequency EnergyNucleus (tesla, T) (MHz) O/mol)

IH 7.05 30013C 7.05 75.519F 7.05 282

(a) Aspirin, C9Hs0 4(c) Pyridine, CsHsN(e) Cholesterol, C27H460

Section 13.11 13C-NMR 13C-NMR is like 1H-NMR, except the nuclear spins of13C nuclei are being analyzed.

- 13C-NMR spectra are commonly recorded in a hydrogen-decoupled instrumen-tal mode. In this mode, all 13C signals appear as singlets.

- The number of different signals in a 13C-NMR spectrum tell you how manynonequivalent carbon atoms are in a molecule.

- 13C-NMR chemical shifts tell you what kind of carbon atoms are present.

Section 13.12 Interpretation of NMR Spectra Four important types of structural information can be obtained from a IH-NMR

spectrum.- From the number of signals, we can determine the number of sets of equiva-

lent hydrogens.- From the integration of signal areas, we can determine the relative numbers of

hydrogens in each set.- From the chemical shift of each signal, we can derive information about the

chemical environment of the hydrogens in each set.- From the splitting pattern of each signal, we can derive information about the

number and chemical equivalency of hydrogens on the same and adjacent car-bon atoms, in other words the connectivities between different groups on themolecule.

Molecules in which substitution produces diastereomers are called diastereotopic.- Diastereotopic atoms are nonequivalent in all environments so they have dif-

ferent chemical shifts. These differences can lead to complex splitting of thesgnals of diastereotopic H atoms, especially those adjacent to a chiral center.

13.11 The natural abundance of 13C is only 1.1 %. Furthermore, its sensitivity in NMRspectroscopy (a measure of the energy difference between a spin aligned with oragainst an applied magnetic field) is only 1.6% that of IH. What are the relative sig-nal intensities expected for the IH-NMR and 13C-NMR spectra of the same sampleof Si(CH3)4?

Problems:13.09, 13.12-13.13,13.15-13.24, 13.28

Problems: 13.8, 13.27

PROBLEMS

512 Chapter 13 Nuclear Magnetic Resonance Spectroscopy Assignable in OWL

Ha = 1.0 ppmHb = 3.0 ppmHe = 6.0 ppmlab = 5.0 Hzlbc = 8.0 Hzlac = 1.0 Hz

13.27 The 13C-NMR spectrum of 3-methyl-2-butanol shows signals at 0 17.88 (CH3), 18.16(CH3), 20.01 (CH3), 35.04 (carbon-3), and 72.75 (carbon-2). Account for the factthat each methyl group in this molecule gives a different signal.

13.28 Sketch the NMR spectrum you would expect from a partial molecule with the follow-ing parameters.

Ascaridole

13.25 The percent s-character of carbon participating in a C-H bond can be establishedby measuring the 13C-1H coupling constant and using the relationship

Percent s-character = 0.2le3C - IH)The 13C-1H coupling constant observed for methane, for example, is 125 Hz, whichgives 25% s-character, the value expected for an sj/' hybridized carbon atom.(a) Calculate the expected 13C-1H coupling constant in ethylene and acetylene.(b) In cyclopropane, the 13C-1H coupling constant is 160 Hz. What is the hybridiza-

tion of carbon in cyclopropane?

13.26 Ascaridole is a natural product that has been used to treat intestinal worms. Explainwhy the two methyls on the isopropyl group in ascaridole appear in its IH-NMR spec-trum as four lines of equal intensity, with two sets of two each separated by 7 Hz.

Assignable in OWL Problems 519