NMR Spectroscopy Part I: Basic concepts of 1H and 13C NMR

1. NMR SpectroscopyPart I: Basic concepts of 1H and 13C NMR 1

2. General overview NMR spectroscopy has emerged as the penultimate spectroscopic method for organic structural analysis Currently, the development of novel NMR methods is in its “golden age” with some of the 2-D methods entering their maturation period as routine spectroscopic methods A typical NMR sample consists of 5-10 mg of sample, with which a full analysis of 1H, 13C, ADEPT, 1H-1H COSY, 1H-13C COSY, NOESY could be done in a few hours on a high-field instrument Important spin-offs of NMR spectroscopy include a host of medical and security imaging equipment 2

3. NMR Spectroscopy Nuclear Spin States The sub-atomic particles within atomic nuclei possess a spin quantum number just like electrons As with electrons, the nucleons are organized in energy levels Just as when using Hund’s rules to fill atomic orbitals with electrons, nucleons must each have a unique set of quantum numbers The total spin quantum number of a nucleus is a physical constant, I For each nucleus, the total number of spin states allowed is given by the equation: 2I + 1 3

4. NMR Spectroscopy Nuclear Spin States Observe that for atoms with no net nuclear spin, there are zero allowed spin states All the spin states of a given nucleus are degenerate in energy 4

5. NMR Spectroscopy Nuclear Magnetic Moments A nucleus contains protons, which each bear a +1 charge If the nucleus has a net nuclear spin, and an odd number of protons, the rotation of the nucleus will generate a magnetic field along the axis of rotation Thus, a nucleus has a magnetic moment, m, generated by its charge and spin A hydrogen atom with its lone proton making up the nucleus, can have two possible spin states, degenerate in energy 5

6. Nuclear Spin States In the presence of an externally applied magnetic field, these two spin states are no longer degenerate in energy The spin opposed orientation is slightly higher in energy than the spin aligned orientation 6

7. Absorption of Energy The energy difference between the two non-degenerate spin states in the presence of an applied magnetic field is quantized At low B0 is easy to surmise that the potential energy of the spin opposed state would be low, and as B0 grows in strength, so would the potential energy Thus, with increasing strength of B0, DE between the two spin states also increases 7

8. NMR Spectroscopy Absorption of Energy From theory we have already discussed, we say that a quantum mechanical particle can absorb a photon of energy equal to DE and become promoted to the higher state This energy is proportional to the frequency of the photon absorbed, and in the case of nuclear spin, is a function of the magnetic field applied: DE = hn = f (B0) Every nucleus has a different ratio of m to angular momentum (each has a different charge and mass) – this is referred to as the magnetogyric ratio, g DE = hn = f (gB0) Angular momentum is quantized in units of h/2p, thus: DE = hn = g (h/2p)B0 8

9. Absorption of Energy Solving for the frequency of EM radiation we are observing: DE = n = (g/2p) B0 For a bare hydrogen nucleus (H+), g = 267.53 (106 radians/T·sec) In a field strength of 1 Tesla, DE = 42.5 MHz (for our discussion, at 1.41 T, DE = 60 MHz) DE = hn = f (B0) This energy difference corresponds to the highly weak radio frequency region of the EM spectrum – with wavelengths of >5 meters equal to < 0.02 cal·mol-1 9

10. Mechanism of absorption – nuclear magnetic resonance What we are actually observing for DE is the precessional or Larmor frequency (w) of the spinning nucleus – this is analogous to a spinning toy top precessing as a result of the influence of the earth’s magnetic field: 10

11. NMR Spectroscopy Mechanism of absorption – Nuclear Magnetic Resonance When a photon of n = 60 MHz encounters this spinning charged system (a bare proton) the two can couple and change the spin state of the proton 11

12. NMR Spectroscopy Mechanism of absorption – Nuclear Magnetic Resonance The energy difference corresponding to 60 MHz (DE = hn) is 2.39 x 10-5 kJ mol-1 (tiny) – thermal energy at room temperature (298 oK) is sufficient to populate both energy levels The energy difference is small, so rapid exchange is occurring between the two populations, but there is always a net excess of protons in the lower energy state From the Boltzman distribution equation we can calculate the population of each energy state: Nupper/Nlower = e-DE/kT = e-hn/kT @ 298 oK the ratio is 1,000,000 / 1,000,009 ! There is an excess population of 9 nuclei in the lower energy state! 12

13. Mechanism of absorption – Nuclear Magnetic Resonance As the applied B0 increases, exchange becomes more difficult and the excess increases: In each case, it is these few nuclei that allow us to observe NMR When radio radiation is applied to a sample both transitions upward and downward are stimulated – if too much radiation is applied both states completely equilibrate – a state called saturation – no NMR signal can be observed 13

14. NMR Spectroscopy Chemical Shift Spectroscopic observation of the NMR phenomenon would be of little use if all protons resonated at the same frequency The protons in organic compounds are not bare nuclei, they are surrounded by an s -orbital of containing an electron shared with an electron in a hybridized orbital of another atom to form a covalent bond In the presence of an external magnetic field, an induced circulation of electrons opposite to that of a proton is observed since the two are of opposite charges This induced circulation generates a magnetic field in opposition to the applied magnetic field – a local diamagnetic current 14

15. NMR Spectroscopy Chemical Shift Since the magnetic field “felt” by the proton within this electron cloud is lowered, the resonance condition frequency is also lowered This effect of lowering the energy of transition by a cloud of electrons is called diamagnetic shielding or shielding The opposite effect – if electron density is removed from the vicinity of the proton is called deshielding 15

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18. NMR Spectroscopy Chemical Shift The effect of electrons on a 1.41 T magnetic field is negligible, but measurable Compare the resonance frequencies for the protons in fluromethane vs. chloromethane CH3F CH3Cl The stronger inductive w/d of electrons by fluorine reduces the resonance frequency by 72 Hz (not MHz) compared to an operating frequency of the instrument at 60 MHz @ 1.41 T – barely 1 part per million (ppm) There needs to be a reference “proton” by which these “chemical shifts” can be related - the best candidate would be a completely deshielded proton (H+) which does not exist in the solution phase 18

19. NMR Spectroscopy Chemical Shift NMR spectroscopists chose the other end of the spectrum- a proton that was more shielded than any other known proton (at the time) – those in tetramethylsilane (TMS) The 12 chemically identical protons in TMS were used as the standard zero for an NMR spectrum The resonance frequency of any proton to be studied (since all were less shielded) would be at parts per million of the operating frequency of the instrument greater than this zero This allowed NMR instruments of varying field (and thus operating frequency) strengths to use the same scale Here’s how: 19

20. Chemical Shift In an applied field of 1.41 T, the resonance frequency for a typical proton is 60 MHz, at 2.35 T it is at 100 MHz – a ratio of 5/3 Thus, for a given proton, the shift in Hz from the TMS standard should be 5/3 greater in the 100 MHz instrument compared to the 60 MHz Since these are simple ratios, we can simply factor out the effect of field strength by defining d, or chemical shift to be d = (shift from TMS in Hz) (spectrometer frequency in MHz) …or ppm of the instruments operating frequency 20

21. Continuous-Wave (CW) Instrument An NMR spectrometer needs to perform several functions: Generate a high (>1 Tesla) magnetic field to split the energy levels of the spin states enough to: Create an excess nuclei population large enough to observe Make the radio n that correspond to the transition be observable Ensure that the field is homogeneous (shimming) Vary either the applied field or the radiofrequency (RF) to observe different nuclei at their various energies of transition Receive the faint signal of the relaxation of the excited nuclei to their ground state Process the signal into a usable spectrum vs. a reference 21

22. Continuous-Wave (CW) Instrument: 22

23. How it works (CW NMR): The sample is placed in a 5 mm solution cell or tube (experimental aspects we will cover shortly) in the center of a large permanent or electromagnet A RF oscillator coil at 90° to the sample generates a radio signal at the operating frequency of the instrument (60 MHz for a 1.41 T field) The overall magnetic field is varied by a small electromagnet capping the poles of the larger field magnet Remember: DE = n = (g/2p) B0, so variations of either magnetic field or frequency will cover the observed spectral width if the other is held constant As with older dispersive IR instruments, the sweep of magnetic fields is simultaneous with the movement of the chart paper 23

24. How it works (CW NMR): As a particular proton population comes into resonance, a second receiver coil at 90° to the transmitter coil will pick up the change in orientation of nuclear spin This is recorded by the chart as a voltage response, proportional to the size of the proton population that generated the resonance One artifact of CW instruments is that the relaxation of the protons is slower than the movement (sweep) of the chart paper This causes the ringing effect – a decreasing oscillation of the signal after the spectrometer has moved past a given resonance CW instruments operate by bringing each individual population of protons into resonance individually. 24

25. Limitations- CW NMR: Since the spectrum is collected once, the sample must possess enough protons to give a suitable excess population that can be observed – need a concentrated sample Due to the limitations of the relatively low magnetic field (CW instruments top out at 60-90 MHz) the coupling constants for JHH are relatively large compared to the spectral width – so only simple molecules can be observed and their structures elucidated For nuclei of lower magnetogyric ratios, g, or natural abundance (13C most specifically) the ratio of radio noise to signal is high 25

26. Pulsed Fourier Transform (FT) Instrument First, what is a Fourier Transform? Fourier transforms interconvert mathematical functions in the frequency domain to the time domain: For purposes of this discussion, we will black box the actual calculations and derivations of these functions, but we need to understand what they do 26

27. Pulsed Fourier Transform (FT) Instrument If we feed two simple oscillating equations into a FT, here are the results: 27

28. NMR Spectroscopy Pulsed Fourier Transform (FT) Instrument In the FT instrument, all proton populations are excited simultaneously by a short, intense burst of RF energy Due to a variation of the Heisenberg Uncertainty Principle, even if the RF generator is set at 90 MHz, if the duration of the pulse is short, the radio waves do not have time to establish a solid fundamental frequency This can be illustrated by the following cartoon, showing the combination of a short pulse being added to a step function: 28

29. Pulsed Fourier Transform (FT) Instrument If this short pulse is converted into the frequency domain by a FT: Observe that we have a continuum of frequency content centered at the operating frequency of the instrument We will talk more about the effects of pulse time and width when we discuss advanced 1-D and 2-D NMR 29

30. Pulsed Fourier Transform (FT) Instrument For now, if a sample containing one unique population of hydrogens was excited over tp by a pulse, it would then “relax” back to its original spin state As each nuclei relaxes it will emit RF radiation of a given frequency; since different nuclei will relax at different rates, the signal decays over time This emission is recorded by the spectrometer as a free-induction decay or FID 30

31. Pulsed Fourier Transform (FT) Instrument The actual frequency of the FID is the interference signal of the relaxing protons superimposed with the frequency of the RF source Conversion of this decay signal by FT back into the frequency domain gives us the actual n of resonance for the proton being observed Again to due Heisenburg and other factors, NMR signals are not single lines, but a Lorentzian shaped continuum of lines centered at the n of the signal 31

32. Pulsed Fourier Transform (FT) Instrument Advantages: Since all nuclei are excited and observed simultaneously, the pulse can be repeated after each relaxation period (for 1H, about 10 seconds) and the resulting signals added together Because we are observing weak radiofrequency signals in a sea of RF noise for dilute samples (or those observed once as in CW NMR) noise becomes an issue If several to hundreds of FIDs are added together, signals will tend to constructively add together and become more pronounced; since noise is random, it will tend to destructively add and become less pronounced Signal to noise ratio improves as a function of the square root of the scans (FIDs) performed: S/N = f (n) 32

33. A typical 1H NMR is recorded from -2 to 15 d (ppm); what is typically reported is the region from 0 to 10 d Remember, if a proton is shielded (e- circulation reduces “felt” magnetic field) DE for the transition is lowered and the signal is near the high field or upfield region of the spectrum (right) If the proton is deshielded (e- circulation doesn’t reduce the “felt” magnetic field) DE for the transition is raised and the signal is near the low field or downfield region of the spectrum (left) 33

34. The number of signals observed will be equal to the number of unique populations of chemically equivalent protons To determine if two protons are chemically equivalent, substitute “X” for that each respective hydrogen in the compound and compare the structures If the two structures are fully superimposible (identical) the two hydrogens are chemically equivalent; if the two structures are different the two hydrogens were not chemically equivalent A simple example: p-xylene 34

35. The position (v) of each resonance is dependant on the electronic environment around the proton – chemical shift as a result of local diamagnetic shielding There are three principle effects that contribute to local diamagnetic shielding: Electronegativity Hybridization Proton acidity/exchange 35

36. Local Diamagnetic Shielding - Electronegativity Electronegative groups comprise most organic functionalities: -F -Cl -Br -I -OH -OR -NH2 -NHR -NR2 -NH3+ -C=O -NO2 -NO -SO3H -PO3H2 -SH -Ph -C=C and most others In all cases, the inductive w/d of electrons of these groups decreases the electron density in the C-H covalent bond – proton is deshielded – higher DE of transition 36

37. Local Diamagnetic Shielding - Electronegativity Protons bound to carbons bearing electron withdrawing groups are deshielded based on the magnitude of the withdrawing effect – Pauling electronegativity: 37

38. Local Diamagnetic Shielding - Electronegativity The magnitude of the withdrawing effect is cumulative: The magnitude of the withdrawing effect is reduced by distance, as the inductive model suggests 38

39. NMR Spectroscopy Local Diamagnetic Shielding - Hybridization The hybridization of the carbon the proton is bound exerts a strong electronic effect The greater the s-character, the more tightly bound the electrons are to carbon, raising its effective electronegativity (sp = 50% s, sp2, 33% s and sp3 25% s) 39

40. NMR Spectroscopy Local Diamagnetic Shielding - Proton Acidity/Exchange If an organic molecule that possesses hydrogen atoms of low pKA are dissolved in a deuterated solvent that also has a low pKA, the “visible” protons will exchange with “deuterium” from solvent and become “invisible” to the NMR spectrometer Such studies are useful, if it is desired to see which H-atoms on an organic are acidic! 40

41. NMR Spectroscopy Local Diamagnetic Shielding - Proton Acidity/Exchange Due to H-bonding effects, the resonance for certain functional groups (esp. –OH and –NH2) can change drastically dependent on concentration and the extent of the H-bonding Just as in IR spectroscopy, peaks corresponding to these resonances are broad and often undefined – observing a continuum of bond strengths/electron densities about the observed proton The correlation tables for the position of such protons tend to be broad and unreliable: Acid –OH 10.5-12.0 d Phenol –OH 4.0-12.0 d Alcohol –OH 0.5-5.0 d Amine –NH2 0.5-5.0 d Amide –NH2 5.0-8.0 d Enol CH=CH-OH >15 d 41

42. NMR Spectroscopy Some observed 1H resonances can not be fully explained by local diamagnetic shielding effects Magnetic Anisotropy – literally “magnetic dissimilarity” For example, by our hybridization model, a proton bound to an sp2 C should be observed at lower d than a proton bound to an sp C 42

43. NMR Spectroscopy Magnetic Anisotropy – This effect is primary due to the fact that there is an additional effect of circulating electrons, observed in p-systems In benzene, the 6-p-orbitals overlap to allow full circulation of electrons; as these electrons circulate in the applied magnetic field they oppose the applied magnetic field at the center – just like the circulation of electrons in the 1-s orbital about hydrogen – at the middle!: 43

44. NMR Spectroscopy Magnetic Anisotropy – On the periphery of the ring, the effect is opposite – the magnetic effect reinforces the applied B0, and DE becomes greater – deshielding effect 44

45. NMR Spectroscopy Magnetic Anisotropy – This theory can easily be tested by the observation of large aromatic systems that possess protons inside the ring (now a shielding effect): Or over a ring system: 45

46. NMR Spectroscopy Magnetic Anisotropy – In alkynes, a similar situation (to the central protons in large aromatic systems) arises where the terminal proton is in the region of maximum shielding 46

47. NMR Spectroscopy General Correlation Chart – 1H NMR Due to the three effects on local diamagnetic shielding, in conjunction with the effect of magnetic anisotropy 1H NMR chemical shifts are variable Avoid using hard and fast rules (tables of numbers) Instead, start from the general correlation table and deduce structural features based on the effects just discussed After a structural inference has been made, then use the more specific correlation tables to confirm the analysis 47

48. NMR Spectroscopy General Correlation Chart – 1H NMR Here are the general regions for 1H chemical shifts: 48

49. NMR Spectroscopy Spin-spin splitting – 1H NMR The magnetic effects of nuclei in close proximity to those being observed have an effect on the local magnetic field, and therefore DE Specifically, when proton is close enough to another proton, typically by being on an adjacent carbon (vicinal), it can “feel” the magnetic effects generated by that proton On any one of the 108 of these molecules in a typical NMR sample, there is an equal statistical probability that the adjacent (vicinal) proton is either in the + ½ or – ½ spin state If there is more than one proton on an adjacent carbon – all the statistical probabilities exist that each one is either + ½ or – ½ in spin The summation of these effects over all of the observed nuclei in the sample is observed as the spin-spin splitting of resonances 49

50. Spin-Spin Splitting Consider the spectrum of ethyl alcohol: Why does each resonance “split” into smaller peaks? 50

51. Spin-Spin Splitting The magnetic effects of nuclei in close proximity to those being observed have an effect on the local magnetic field, and therefore DE Specifically, when proton is close enough to another proton, typically by being on an adjacent carbon (vicinal), it can “feel” the magnetic effects generated by that proton On any one of the 108 of these molecules in a typical NMR sample, there is an equal statistical probability that the adjacent (vicinal) proton is either in the + ½ or – ½ spin state If there is more than one proton on an adjacent carbon – all the statistical probabilities exist that each one is either + ½ or – ½ in spin The summation of these effects over all of the observed nuclei in the sample is observed as the spin-spin splitting of resonances 51

52. Spin-Spin Splitting Recall, we are observing the frequency (E = hn) where a proton goes into resonance 52

53. Spin-Spin Splitting In solution we are not looking at a single molecule but about 108 On some molecules the proton being observed may be next to another proton of spin + 1/2 : 53

54. Spin-Spin Splitting On some molecules the proton being observed may be next to another proton of spin – 1/2 : 54

55. Spin-Spin Splitting Observe what effect this has on an isolated ethyl group: The two methylene Ha protons have three neighbors, Hb, on the adjacent methyl carbon Each one of these hydrogens can be + ½ or – ½ , and since we are not looking at one molecule, but billions, we will observe all combinations 55

56. Spin-Spin Splitting The first possibility is that all three Hb protons have a + ½ spin; in this case the three protons combine to generate three small magnetic fields that aid B0 and deshield the protons – pushing the resonance for Ha slightly downfield (the magnetic field of a proton is tiny compared to B0) 56

57. Spin-Spin Splitting The second possibility is that two Hb protons have a + ½ spin and the third a - ½ ; in this case the two protons combine to enhance B0 and the other against it, a net deshielding; there are 3 different combinations that generate this state 57

58. Spin-Spin Splitting The third possibility is that two Hb protons have a –½ spin and the third +½; here, the two protons combine to reduce B0 and the other enforce it, a net shielding effect; there are 3 different combinations that generate this state 58

59. Spin-Spin Splitting The last possibility is that all three Hb protons have a – ½ spin; in this case the three protons combine to oppose B0, a net shielding effect; there is one combination that generates this state 59

60. Spin-Spin Splitting The result is instead of one resonance (peak) for Ha, the peak is “split” into four, a quartet, with the constituent peaks having a ratio of 1:3:3:1 centered at the d (n) for the resonance 60

61. Spin-Spin Splitting Similarly, the Hb protons having two protons, on the adjacent carbon each producing a magnetic field, cause the Hb resonance to be split into a triplet 61

62. Spin-Spin Splitting Rather than having to do this exercise for every situation, it is quickly recognized that a given family of equivalent protons (in the absence of other spin-coupling) will have its resonance split into a multiplet containing n+1 peaks, where n is the number of hydrogens on carbons adjacent to the carbon bearing the proton giving the resonance – this is the n + 1 rule 62

63. 1H NMR—Spin-Spin Splitting Common patterns: 63

64. 1H NMR—Spin-Spin Splitting 64

65. NMR Spectroscopy Spin-spin splitting – 1H NMR Consider this: the basis for spin-spin splitting is that protons on adjacent carbons exert their own magnetic fields with or opposite the applied magnetic field – because all alkyl protons are in roughly the same chemical environment (sp3 orbital – 1s H orbital) their magnetic influence is similar Due to free rotation in open chain compounds, the distance effect of the magnetic influence is averaged The n+1 rule works in these simple alkyl cases ONLY! propyl -CH2- triplet -CH2- sextet -CH3 triplet 65

66. NMR Spectroscopy Spin-spin splitting – 1H NMR The amount of influence exerted by a proton on an adjacent carbon is observed as the difference (in Hz) between component peaks within the multiplet it generates. This influence is quantified as the coupling constant, J In complex spectra, you can determine which groups of protons are exerting magnetic influence on another group by comparing J values. For the ethyl group this is easily observed: 66

67. Spin-spin splitting – 1H NMR For alkyl chains, typical 3JHH values are on the order of 6-8 Hz Since J’s are generated by the magnetic influence within a molecule they are independent of the instrument frequency. This leads to the observation on high-field FT-NMR spectrum of the multiplets appearing narrower – cleaning up the appearance of the spectrum Remember 1 d (ppm) on a 60 MHz spectrum is 60 Hz, whereas 1 d is 300 Hz on a 300 MHz spectrum 67

68. NMR Spectroscopy Spin-spin splitting – 1H NMR The next level of complexity (which we will cover in detail in Chapter 5) is when protons on adjacent carbons exert different J’s than one another. Consider the ethylene fragment: 68

69. NMR Spectroscopy Spin-spin splitting – 1H NMR For ethylene we would then observe three chemically distinct resonances with spin-spin splitting exerted by the other two protons: J couplings: 69

70. NMR Spectroscopy Spin-spin splitting – 1H NMR Similar behavior is observed with aromatic rings; since the ring structure is fairly rigid and electronic effects are conducted over a longer distance, J – couplings are observed across the ring system: 70

71. NMR Spectroscopy Spin-spin splitting – 1H NMR For our initial treatment of 1H NMR the alkenyl, aromatic and the following J values should be learned: 71

72. Intensity of Signals—Integration The area under an NMR signal is proportional to the number of absorbing protons An NMR spectrometer automatically integrates the area under the peaks, and prints out a stepped curve (integral) on the spectrum The height of each step is proportional to the area under the peak, which in turn is proportional to the number of absorbing protons Modern NMR spectrometers automatically calculate and plot the value of each integral in arbitrary units The ratio of integrals to one another gives the ratio of absorbing protons in a spectrum; note that this gives a ratio, and not the absolute number, of absorbing protons 72

73. NMR Spectroscopy Integration – 1H NMR Like instrumental chromatography, in NMR spectroscopy, the area under a peak (or multiplet) is proportional to the number of protons in the sample that generated that particular resonance The NMR spectrometer typically will print this information on the spectrum as an integral line (stepped line on the spectrum below) The height of the integral is proportional to that proton population; by comparing the ratios of the integrals on an NMR spectrum you can determine the number of protons as a least common multiple of these ratios 73

74. NMR Spectroscopy Integration – 1H NMR For example observe the integration of the ethanol spectrum below: 74

75. Intensity of Signals—Integration 75

76. Intensity of Signals—Integration 76