1. NMR Theory
There are 2 variables in NMR: an applied magnetic field B0, and the frequency ( ) of radiation required for resonance, measured in MHz.

2. Effect of B0 on resonance frequency
NMR spectrometers are designated according to the frequency required to make protons resonate. The modern standard is 300 MHz. However, manufacturers are actively pursuing stronger magnets. 900 MHz is currently as high as it gets.

3. Schematic of an NMR

4. Resonance Frequency
Different nuclei resonate at greatly different ν : on a 300 MHz instrument (1H = 300 MHz) 13C resonates at 75 MHz.
The same type of nucleus also absorbs at slightly different ν, depending on its chemical environment.
Exact frequency of resonance = “chemical shift”
The strength of the magnetic field actually felt by a nucleus (Beff) determines its resonance frequency.
Electron clouds shield the nucleus from the magnet
Circulation of electrons in π orbitals can generate local magnetic fields that influence Beff
Modern NMR spectrometers use a constant magnetic field strength B0, and pulse a broad range of frequencies to bring about the resonance of all nuclei at the same time.

5. Chemical Shift Peaks on NMR spectrum = “resonances “.
Chemical shift is measured in ppm
ppm = ν in Hz relative to ref peak/instrument ν in MHz.
Protons absorb between 0-10 ppm. C-13 nuclei absorb between ppm.
Reference peak = 0 ppm = (CH)4Si = tetramethylsilane (TMS). TMS is an inert compound that gives a single peak at higher frequency than most typical NMR peaks.

6. Electronic Shielding More electron density = more shielding
Less electron density = less shielding

7. Shielding in Spectrum

8. 1H NMR Interpretation Number of Resonances Chemical Shifts
Integrations
Splitting Patterns
Exchangeable Protons

9. Number of Resonances

10. Stereochemistry
Watch out when you have rings and/or double bonds! To determine equivalent protons in cycloalkanes and alkenes, always draw all bonds to hydrogen.

11. Number of Signals in a Cyclic Compound
Proton equivalency in cycloalkanes can be determined similarly.
Types of NMR relationships:
1. chemically equivalent
2. coincidentally equivalent
3. non-equivalent, enantiotopic
4. non-equivalent, diastereopic
5. non-equivalent.
Use substitution criterion to decide.

12. Chemical Shift - Local Diamagnetic Shielding

13. Induced Anisotropic Shielding - Benzene
In a magnetic field, the six  electrons in a benzene ring circulate around the ring creating a ring current.
The magnetic field induced by these moving electrons reinforces the applied magnetic field in the vicinity of the protons.
The protons feel a stronger magnetic field and thus are deshielded. A higher frequency is needed for resonance.

14. Induced Anisotropic Shielding - Alkenes
In a magnetic field, the loosely held  electrons circulate creating a magnetic field that reinforces the applied field in the vicinity of the protons.
Since the protons now feel a stronger magnetic field, they require a higher frequency for resonance. Thus the protons are deshielded and the absorption is downfield.

15. Induced Anisotropic Shielding - Alkyne
In a magnetic field, the  electrons of a carbon-carbon triple bond are induced to circulate, but in this case the induced magnetic field opposes the applied magnetic field (B0).
Thus, the proton feels a weaker magnetic field, so a lower frequency is needed for resonance. The nucleus is shielded and the absorption is upfield.

16. Summary of pi electron effects

17. Characteristic Shifts

18. Integrations
The integration of each resonance is proportional to the number of absorbing protons.
The integral ratios tell us the ratios of the protons causing the peak.
Strategy - find a peak that you can assign unambiguously and set its integral at the appropriate number of Hs.

19. Splitting Patterns
Consider the spectrum below:

20. Theory of spin-spin splitting
Spin-spin splitting occurs only between nonequivalent protons on the same carbon or adjacent carbons.
Let us consider how the doublet due to the CH2 group on BrCH2CHBr2 occurs:

21. Triplet Let us now consider how a triplet arises:
When placed in an applied magnetic field (B0), the adjacent protons Ha and Hb can each be aligned with () or against () B0.
Thus, the absorbing proton feels three slightly different magnetic fields—one slightly larger than B0, one slightly smaller than B0, and one the same strength at B0.

22. Triplet

23. Peak ratios in a multiplet.
Doublet – The two spin states of the proton causing splitting are nearly equally populated (because the energy difference is so small). Therefore a doublet is has a peak ratio of 1:1.
Triplet - Because there are two different ways to align one proton with B0, and one proton against B0—that is, ab and ab—the middle peak of the triplet is twice as intense as the two outer peaks, making the ratio of the areas under the three peaks 1:2:1.
Higher – use Pascals triangle

24. Multiplet names

25. Rules for predicting splitting patterns
Equivalent protons do not split each other’s signals.
A set of n nonequivalent protons splits the signal of a nearby proton into n + 1 peaks.
Splitting is observed for nonequivalent protons on the same carbon or adjacent carbons.
If Ha and Hb are not equivalent, splitting is observed when:

27. Nuclear Magnetic Resonance Spectroscopy
1H NMR—Spin-Spin Splitting
Whenever two (or three) different sets of adjacent protons are equivalent to each other, use the n + 1 rule to determine the splitting pattern.