13-1 nuclear magnetic resonance chapter 13. 13-2 molecular spectroscopy nuclear magnetic resonance...

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Nuclear Magnetic Nuclear Magnetic ResonanceResonance

Chapter 13Chapter 13

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Molecular SpectroscopyMolecular Spectroscopy

Nuclear magnetic resonance (NMR) Nuclear magnetic resonance (NMR) spectroscopyspectroscopy:: a spectroscopic technique that gives us information about the number of certain types of atoms and their environment in a molecule.

Most commonly, about the number and types of:• hydrogen atoms using 1H-NMR spectroscopy

• carbon atoms using 13C-NMR spectroscopy The NMR study in Chem 3020 will be restricted to

these two types of atoms.

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13.1 13.1 Nuclear Spin StatesNuclear Spin States An electron has a spin quantum number of 1/2

with allowed values of +1/2 and -1/2. • This spinning charge creates an associated

magnetic field, in effect, an electron behaves as if it is a tiny bar magnet and has what is called a magnetic moment.

The same effect holds for certain atomic nuclei.• Any atomic nucleus that has an odd mass

number, an odd atomic number, or both has a net nuclear spin and a resulting nuclear magnetic moment.

• The allowed nuclear spin states are determined by the spin quantum number, I, of the nucleus.

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Nuclear Spin States, Table 13.1Nuclear Spin States, Table 13.1

• A nucleus with spin quantum number II has 22II + 1 + 1 spin states; if I = 1/2, there are two allowed spin states.

• Table 13.1 gives the spin quantum numbers and allowed nuclear spin states for selected isotopes of elements common to organic compounds.

1H 2H 12C 13C 14N 16O 31P 32SElement

Nuclear spinquantum number (I )

Number ofspin states

1/2 1 0 0 01/2 1

2 3 1 2 3 1

1/2

2 1

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13.2 13.2 Nuclear Spins in BNuclear Spins in B00

• Within a collection of 1H and 13C atoms, nuclear spins are completely random in orientation.

• When placed in a strong external magnetic field of strength Bo (or Ho), however, interaction between nuclear spins and the applied magnetic field is quantized, with the result that only certain orientations of nuclear magnetic moments are allowed.

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Nuclear Spins in BNuclear Spins in B00

• for 1H and 13C, only two orientations are allowed (Fig 13.1)

BB00

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Nuclear Spins in BNuclear Spins in B00

In an applied field strength of 7.05T (Tesla), which is readily available with present-day superconducting electromagnets, the difference in energy between nuclear spin states for: • 1H is approximately 0.120 J (0.0286 cal)/mol, which

corresponds to electromagnetic radiation of 300 MHz (300,000,000 Hz).

• 13C is approximately 0.030 J (0.00715 cal)/mol, which corresponds to electromagnetic radiation of 75MHz (75,000,000 Hz).

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Nuclear Spin in BNuclear Spin in B00

• The energy difference between allowed spin states increases linearly with applied field strength.

• Values shown here are for 1H nuclei (Fig 13.2)

BB00

300 MHz300 MHz60 MHz60 MHz

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13.3 13.3 Nuclear Magnetic ResonanceNuclear Magnetic Resonance

• When nuclei with a spin quantum number of 1/2 are placed in an applied field, a small majority of nuclear spins are aligned with the applied field in the lower energy state.

• The nucleus begins to precess and traces out a cone-shaped surface, in much the same way a spinning top or gyroscope traces out a cone-shaped surface as it precesses in the earth’s gravitational field.

• We express the rate of precession as a frequency in hertz.

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Nuclear Magnetic ResonanceNuclear Magnetic Resonance

If the precessing nucleus is irradiated with electromagnetic radiation of the same frequency as the rate of precession:• the two frequencies couple,

• energy is absorbed, and

• the nuclear spin is flipped from spin state +1/2 (with the applied field) to -1/2 (against the applied field).

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• The origin of nuclear magnetic “resonance” (Fig 13.3)

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ResonanceResonance:: in NMR spectroscopy, resonance is the absorption of electromagnetic radiation by a precessing nucleus and the resulting “flip” of its nuclear spin from a lower energy state to a higher energy state.

RelaxationRelaxation: : a loss of energy when the higher energy state returns to the lower energy state.

The instrument used to detect this coupling of precession frequency and electromagnetic radiation records it as a signal.• Signal:Signal: A recording in an NMR spectrum of a

nuclear magnetic resonance.

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13.4 13.4 NMR SpectrometerNMR Spectrometer

(Fig 13.4)

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NMR SpectrometerNMR Spectrometer

Essentials of an NMR spectrometer are a powerful magnet, a radio-frequency generator, and a radio-frequency detector

The sample is dissolved in a solvent, most commonly CDCl3 or D2O, and placed in a sample tube which is then suspended in the magnetic field and set spinning

Using a Fourier transform NMR (FT-NMR) spectrometer, a spectrum can be recorded in about 2 seconds

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• If we were dealing with 1H nuclei isolated from all other atoms and electrons, any combination of applied field and radiation that produces a signal for one 1H would produce a signal for all 1H. The same is true of 13C nuclei.

• But hydrogens in organic molecules are not isolated from all other atoms; they are surrounded by electrons, which are caused to circulate by the presence of the applied field.

• The circulation of electrons around a nucleus in an applied field is called diamagneticdiamagnetic currentcurrent and the nuclear shielding resulting from it is called diamagnetic shielding.diamagnetic shielding.

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NMR SpectrumNMR Spectrum 1H-NMR spectrum of methyl acetate (Fig 13.5)

• Downfield:Downfield: the shift of an NMR signal to the left on the chart paper; downfield requires lower energy.

• Upfield:Upfield: the shift of an NMR signal to the right on the chart paper; upfield requires higher energy.

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NMR: cycles/sec (Hertz) vs ppm (NMR: cycles/sec (Hertz) vs ppm (• The difference in resonance frequencies among

the various hydrogen nuclei within a molecule due to shielding/deshielding is generally very small.

• The difference in resonance frequencies for hydrogens in CH3Cl compared to CH3F under an applied field of 7.05T is only 360 Hz, which is 1.2 parts per million (ppm) compared with the irradiating frequency (ppm is also called

360 Hz300 x 106 Hz

1.2= 1.2 ppm

106=

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NMR Reference SignalNMR Reference Signal

• Signals are measured relative to the signal of the reference compound tetramethylsilane (TMS).

• For a 1H-NMR spectrum, signals are reported by their shift from the 12 H signal in TMS.

• For a 13C-NMR spectrum, signals are reported by their shift from the 4 C signal in TMS.

• Chemical shift (Chemical shift ():): the shift in ppm of an NMR signal from the signal of TMS.

Tetramethylsilane (TMS)

CH3

Si CH3

CH3

CH3

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13.5 13.5 Equivalent HydrogensEquivalent Hydrogens

Equivalent hydrogens:Equivalent hydrogens: These have the same chemical environment.• A molecule with 1 set of equivalent hydrogens

gives 1 NMR signal.

H3C

C C

CH3

H3C CH3

CH3CCH3 ClCH2CH2Cl

Propanone(Acetone)

1,2-Dichloro-ethane

Cyclopentane2,3-Dimethyl-2-butene

O

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Equivalent HydrogensEquivalent Hydrogens

• A molecule with 2 or more sets of equivalent hydrogens gives a different NMR signal for each set.

CH3CHCl

Cl ClC C

CH3

H H

O

Cyclopent-anone

(2 signals)

1,1-Dichloro-ethane

(2 signals)

(Z)-1-Chloro-propene

(3 signals)

Cyclohexene (3 signals)

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13.6 13.6 Signal Areas (integration)Signal Areas (integration) Relative areas of signals are proportional to the

number of H giving rise to each signal. Modern NMR spectrometers electronically

integrate and record the relative area of each signal (Fig 13.7).

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ChemicalChemicalShiftsShifts11H-NMRH-NMR

RCH2OR

(CH3)4Si

ArCH3

RCH3

RC CH

RCCH3

ROHRCH2OH

ArCH2R

O

O

RCH2RR3CH

R2NH

RCCH2R

R2C=CRCHR2

R2C=CHR

RCH

O

RCOH

O

RCH2ClRCH2BrRCH2I

RCH2F

ArHO

O

R2C=CH2

RCOCH3

RCOCH2R

ArOH

9.5-10.1

3.7-3.9

3.4-3.6

Type of Hydrogen

0 (by definition)

Type of Hydrogen

Chemical Shift ()

1.6-2.62.0-3.0

0.8-1.01.2-1.41.4-1.7

2.1-2.3

0.5-6.0

2.2-2.6

3.4-4.0

Chemical Shift ()

3.3-4.0

2.2-2.52.3-2.8

0.5-5.0

4.6-5.05.0-5.7

10-13

4.1-4.73.1-3.3

3.6-3.84.4-4.5

6.5-8.5

4.5-4.7

13.7 13.7 Chemical Shift - Chemical Shift - 11H-NMRH-NMR

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Chemical Shift - Chemical Shift - 11H-NMR, Fig. 13.8H-NMR, Fig. 13.8

(Fig 13.8)

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A. A. Chemical Shift, Table 13.2Chemical Shift, Table 13.2 Depends on (1) electronegativity of nearby atoms, (2)

the hybridization of adjacent atoms, and (3) diamagnetic effects from adjacent pi bonds.

Electronegativity: inductive effect deshields

CH3OH

CH3F

CH3Cl

CH3BrCH3I

(CH3)4C(CH3)4Si

CH3-XElectroneg-ativity of X

Chemical Shift ()

4.03.5

3.1

2.82.5

2.1

1.8

4.263.47

3.05

2.68

2.16

0.86

0.00

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B.B. Chemical Shift, Table 13.3 Chemical Shift, Table 13.3 Hybridization of adjacent atoms: Greater “s”

character in the hybrid holds shared electrons closer to carbon

RCH3, R2CH2, R3CH

R2C=CHR, R2C=CH2

RCHO

R2C=C(R)CHR2

RC CH

Allylic

Type of Hydrogen(R = alkyl)

Name ofHydrogen

Chemical Shift ()

Alkyl

Acetylenic

Vinylic

Aldehydic

0.8 - 1.7

1.6 - 2.6

4.6 - 5.7

9.5-10.1

2.0 - 3.0

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C.C. Chemical Shift Chemical Shift Diamagnetic effects of pi bonds:

• A carbon-carbon triple bond shields an acetylenic hydrogen and shifts its signal upfield (to the right) to a smaller value.

• A carbon-carbon double bond deshields vinylic hydrogens and shifts their signal downfield (to the left) to a larger value.

RCH3

R2C=CH2

RC CH

Type of H Name

Alkyl

VinylicAcetylenic

0.8- 1.0

4.6 - 5.72.0 - 3.0

Chemical Shift ()

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Chemical ShiftChemical Shift

• Magnetic induction in the pi bond of a carbon-carbon double bond (Fig 13.10):

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• Magnetic induction of the pi electrons in an aromatic ring (Fig. 13.11).

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• Magnetic induction in the pi bonds of a carbon-carbon triple bond (Fig 13.9):

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Chemical Shift and IntegrationChemical Shift and Integration

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13.8 13.8 Signal Splitting; the (Signal Splitting; the (nn + 1) Rule + 1) Rule

NMR Signals: NMR Signals: not all appear as a single peak. Peak:Peak: The units into which an NMR signal

appears: singlet, doublet, triplet, quartet, etc. Signal splitting:Signal splitting: Splitting of an NMR signal

into a set of peaks by the influence of neighboring nonequivalent hydrogens.

((nn + 1) rule: + 1) rule: If a hydrogen has n hydrogens nonequivalent to it but equivalent among themselves on the same or adjacent atom(s), its 1H-NMR signal is split into (n + 1) peaks.

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Signal Splitting (n + 1)Signal Splitting (n + 1)

• 1H-NMR spectrum of 1,1-dichloroethane (Fig 13.12)

CH3-CH-ClCl

For these hydrogens, n = 1;their signal is split into(1 + 1) = 2 peaks; a doublet

For this hydrogen, n = 3;its signal is split into(3 + 1) = 4 peaks; a quartet

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13.9 13.9 Origins of Signal SplittingOrigins of Signal Splitting

Signal coupling:Signal coupling: An interaction in which the nuclear spins of adjacent atoms influence each other and lead to the splitting of NMR signals.

Coupling constant (J):Coupling constant (J): The separation on an NMR spectrum (in hertz) between adjacent peaks in a multiplet. • A quantitative measure of the influence of the

spin-spin coupling with adjacent nuclei.

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Origins of Signal SplittingOrigins of Signal Splitting

(Fig 13.13)

Ha and Hb are non-equivalent

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Origins of Signal SplittingOrigins of Signal Splitting

• Because splitting patterns from spectra taken at 300 MHz and higher are often difficult to see, it is common to retrace and expand certain signals.

• 1H-NMR spectrum of 3-pentanone; expansion more clearly shows the triplet/quartet (Fig 13.14).

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Signal Splitting (n + 1)Signal Splitting (n + 1)

ProblemProblem: Predict the number of 1H-NMR signals and the splitting pattern of each.

CH3CCH2CH3

O

CH3CH2CCH2CH3

O

CH3CCH(CH3)2

O

(a)

(b)

(c)

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Coupling Constants, Table 13.4Coupling Constants, Table 13.4

Coupling constant (J):Coupling constant (J): the distance between peaks in a split signal, expressed in hertz.• J is a quantitative measure of the magnetic

interaction of nuclei whose spins are coupled.

8-11 Hz

8-14 Hz 0-5 Hz 0-5 Hz6-8 Hz

11-18 Hz 5-10 Hz 0-5 Hz

CCHa

C C

HbHaC

Hb

C

Ha

Hb

Ha

Hb

Ha

Hb HbHa

Hb

Ha

C CHaHb

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A.A. Origins of Signal Splitting Origins of Signal Splitting

(Fig 13.15)

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Signal SplittingSignal Splitting Pascal’s Triangle:

• As illustrated by the highlighted entries, each entry is the sum of the values immediately above it to the left and the right (Fig 13.16).

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B.B. Physical Basis for ( Physical Basis for (nn + 1) Rule + 1) Rule Coupling of nuclear spins is mediated through

intervening bonds.• H atoms with more than three bonds between

them generally do not exhibit noticeable coupling.

• For H atoms three bonds apart, the coupling is referred to as vicinal coupling (Fig 13.17).

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Signal Splitting (n + 1) exampleSignal Splitting (n + 1) example

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Coupling ConstantsCoupling Constants

• An important factor in vicinal coupling is the angle between the C-H sigma bonds and whether or not it is fixed.

• Coupling is a maximum when is 0° and 180°; it is a minimum when is 90° (Fig 13.18).

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C.C. More Complex Splitting Patterns More Complex Splitting Patterns

• Thus far, we have observed spin-spin coupling with only one other nonequivalent set of H atoms.

• More complex splittings arise when a set of H atoms couples to more than one set H atoms.

• A tree diagram shows that when Hb is adjacent to nonequivalent Ha on one side and Hc on the other, coupling gives rise to a doublet of doublets.

(Fig 13.19)

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More Complex Splitting PatternsMore Complex Splitting Patterns

• If Hc is a set of two equivalent H, then the observed splitting is a doublet of triplets.

(Fig 13.20)

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D.D. More Complex Splitting Patterns More Complex Splitting Patterns

• Because the angle between C-H bond determines the extent of coupling, bond rotation is a factor.

• In molecules with relatively free rotation about C-C sigma bonds, H atoms bonded to the same carbon in CH3 and CH2 groups generally are equivalent.

• If there is restricted rotation, as in alkenes and cyclic structures, H atoms bonded to the same carbon may not be equivalent.

• Nonequivalent H on the same carbon will couple and cause signal splitting, this type of coupling is called geminal coupling.geminal coupling.

(Fig 13.21)

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• In ethyl propenoate, an unsymmetrical terminal alkene, the three vinylic hydrogens are nonequivalent (Fig 13.22).

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• A tree diagram for the complex coupling of the three vinylic hydrogens in ethyl propenoate.

(Fig 13.23)

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• Cyclic structures often have restricted rotation about their C-C bonds and have constrained conformations (Fig 13.24).

• As a result, two H atoms on a CH2 group can be nonequivalent, leading to complex splitting.

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• A tree diagram for the complex coupling in 2-methyl-2-vinyloxirane (Fig 13.25).

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F.F. More Complex Splitting Patterns More Complex Splitting Patterns Complex coupling in flexible molecules:

• Coupling in molecules with unrestricted bond rotation often gives only m + n + I peaks.

• That is, the number of peaks for a signal is the number of adjacent hydrogens + 1, no matter how many different sets of equivalent H atoms that represents.

• The explanation is that bond rotation averages the coupling constants throughout molecules with freely rotation bonds and tends to make them similar; for example in the 6- to 8-Hz range for H atoms on freely rotating sp3 hybridized C atoms.

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• simplification of signal splitting occurs when coupling constants are the same (Fig 13.26).

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• An example of peak overlap occurs in the spectrum of 1-chloropropane.

• The central CH2 has the possibility for 12 peaks (a quartet of triplets) but because Jab and Jbc are so similar, only 5 + 1 = 6 peaks are distinguishable.

(Fig 13.28)

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13.10 13.10 Stereochemistry & TopicityStereochemistry & Topicity Depending on the symmetry of a molecule,

otherwise equivalent hydrogens may be:• homotopic

• enantiotopic

• diastereotopic The simplest way to visualize topicity is to

substitute an atom or group by an isotope; is the resulting compound:• the same as its mirror image

• different from its mirror image

• are diastereomers possible

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Stereochemistry & TopicityStereochemistry & Topicity Homotopic atoms or groups:

• Homotopic atoms or groups have identical chemical shifts under all conditions.

Achiral

H

C

H

Cl

Cl

H

C

D

Cl

Cl

Dichloro-methane(achiral)

Substitution does not produce a stereocenter;therefore hydrogensare homotopic.

Substitute one H by D

Achiral

H

C

H

Cl

Cl

H

C

D

Cl

Cl

Dichloro-methane(achiral)

Substitution does not produce a stereocenter;therefore hydrogensare homotopic.


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Stereochemistry & TopicityStereochemistry & Topicity Enantiotopic groups:

• Enantiotopic atoms or groups have identical chemical shifts in achiral environments.

• They have different chemical shifts in chiral environments.

Chiral

H

C

H

Cl

F

H

C

D

Cl

F

Chlorofluoro-methane(achiral)


Substitution produces a stereocenter;

therefore, hydrogens are enantiotopic. Both hydrogens are prochiral; one is pro-R-chiral, the other is pro-S-chiral.Chiral

H

C

H

Cl

F

H

C

D

Cl

F

Chlorofluoro-methane(achiral)


Substitution produces a stereocenter;

therefore, hydrogens are enantiotopic. Both hydrogens are prochiral; one is pro-R-chiral, the other is pro-S-chiral.

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Stereochemistry & TopicityStereochemistry & Topicity Diastereotopic groups:

• H atoms on C-3 of 2-butanol are diastereotopic.

• Substitution by deuterium creates a chiral center.

• Because there is already a chiral center in the molecule, diastereomers are now possible.

• Diastereotopic hydrogens have different chemical shifts under all conditions.

H OH

HH

H OH

HD

Chiral

Substitute one H on CH2 by D

2-Butanol(chiral)

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Stereochemistry & TopicityStereochemistry & Topicity The methyl groups on carbon 3 of 3-methyl-2-

butanol are diastereotopic. If a methyl hydrogen of carbon 4 is substituted

by deuterium, a new chiral center is created.• Because there is already one chiral center,

diastereomers are now possible.

• Protons of the methyl groups on carbon 3 have different chemical shifts.

OH

3-Methyl-2-butanol

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Stereochemistry and TopicityStereochemistry and Topicity 1H-NMR spectrum of 3-methyl-2-butanol:

• The methyl groups on carbon 3 are diastereotopic and appear as two doublets (Fig 13.29).

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13.11 13.11 1313C-NMR SpectroscopyC-NMR Spectroscopy Each nonequivalent 13C gives a different signal.

• A 13C signal is split by the 1H bonded to it according to the (n + 1) rule .

• Coupling constants of 100-250 Hz are common, which means that there is often significant overlap between signals, and splitting patterns can be very difficult to determine.

The most common mode of operation of a 13C-NMR spectrometer is a hydrogen-decoupled mode.

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1313C-NMR SpectroscopyC-NMR Spectroscopy In a hydrogen-decoupled mode, a sample is

irradiated with two different radio frequencies.• One to excite all 13C nuclei.

• A second broad spectrum of frequencies to cause all hydrogens in the molecule to undergo rapid transitions between their nuclear spin states.

On the time scale of a 13C-NMR spectrum, each hydrogen is in an average or effectively constant nuclear spin state, with the result that 1H-13C spin-spin interactions are not observed; they are decoupled.

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1313C-NMR: C-NMR: 11H coupled and decoupledH coupled and decoupled

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1313C-NMR SpectroscopyC-NMR Spectroscopy

• Hydrogen-decoupled 13C-NMR spectrum of 1-bromobutane:

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Chemical Shift - Chemical Shift - 1313C-NMRC-NMR

RCH3RCH2R

R3CH

R2C=CR2

RC CR

R3COR

RCH2Cl

RCH2BrRCH2I

R3COH

RC

RCNR2

O

RCH, RCRO O

RCCOHO

RCORO

0-40

110-160

165 - 180

160 - 180

165 - 185

180 - 215

40-80

40-80

35-80

25-65

65-85

100-150

20-6015-5510-40

Type of Carbon

ChemicalShift ()

ChemicalShift ()

Type of Carbon

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Chemical Shift - Chemical Shift - 1313C-NMRC-NMR

(Fig 13.31)

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13.12 13.12 The DEPT MethodThe DEPT Method In the hydrogen-decoupled mode, information on

spin-spin coupling between 13C and hydrogens bonded to it is lost.

The DEPT method is an instrumental mode that provides a way to acquire this information.• Distortionless Enhancement by Polarization Distortionless Enhancement by Polarization

TransferTransfer (DEPT):DEPT): An NMR technique for distinguishing among 13C signals for CH3, CH2, CH, and quaternary carbons.

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The DEPT MethodThe DEPT Method The DEPT methods uses a complex series of

pulses in both the 1H and 13C ranges, with the result that CH3, CH2, and CH signals exhibit different phases:• Signals for CH3 and CH carbons are recorded as

positive signals.

• Signals for CH2 carbons are recorded as negative signals.

• Quaternary carbons give no signal in the DEPT method.

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Isopentyl acetateIsopentyl acetate• 13C-NMR: (a) proton decoupled and (b) DEPT

(Fig 13.32)

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13.13 13.13 Interpreting NMR SpectraInterpreting NMR Spectra

A.A. AlkanesAlkanes • 1H-NMR signals appear in the range of 0.8-1.7.

• 13C-NMR signals appear in the considerably wider range of 10-60.

B.B. AlkenesAlkenes • 1H-NMR signals appear in the range 4.6-5.7.

• 1H-NMR coupling constants are generally larger for trans vinylic hydrogens (J= 11-18 Hz) compared with cis vinylic hydrogens (J= 5-10 Hz)

• 13C-NMR signals for sp2 hybridized carbons. appear in the range 100-160, which is downfield from the signals of sp3 hybridized carbons.

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Interpreting NMR SpectraInterpreting NMR Spectra

• 1H-NMR spectrum of vinyl acetate (Fig 13.33)

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C.C. AlcoholsAlcohols 1H-NMR O-H chemical shifts often appears in the

range 3.0-4.0, but may be as high as 0.5. • 1H-NMR chemical shifts of hydrogens on the

carbon bearing the -OH group are deshielded by the electron-withdrawing inductive effect of the oxygen and appear in the range 3.0-4.0.

D.D. EthersEthers • A distinctive feature in the 1H-MNR spectra of

ethers is the chemical shift, 3.3-4.0, of hydrogens on carbon attached to the ether oxygen.

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• 1H-NMR spectrum of 1-propanol (Fig. 13.34)

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E.E. Aldehydes and ketonesAldehydes and ketones• 1H-NMR: Aldehyde hydrogens appear at

9.5-10.1.

• 1H-NMR: -hydrogens of aldehydes and ketones appear at 2.2-2.6.

• 13C-NMR: Carbonyl carbons appear at 180-215.

G.G. AminesAmines• 1H-NMR: Amine hydrogens appear at 0.5-

5.0 depending on conditions.

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Interpreting NMR SpectraInterpreting NMR Spectra F.F. Carboxylic acidsCarboxylic acids

• 1H-NMR: Carboxyl hydrogens appear at 10-13, lower than most any other hydrogens .

• 13C-NMR: Carboxyl carbons in acids and esters appear at 160-180 (Fig 13.35).

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Spectral Problem 1; molecular formula C5H10O

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Spectral Problem 1Spectral Problem 1

molecular formula Cmolecular formula C55HH1010OO

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Spectral Problem 2; molecular formula C7H14O

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Spectral Problem 2Spectral Problem 2

molecular formula C7H14O

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NuclearNuclear

Magnetic Magnetic ResonanceResonance

End Chapter 13End Chapter 13

13-1 nuclear magnetic resonance chapter 13. 13-2 molecular spectroscopy nuclear magnetic resonance...

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