Magnetic Field (B) A photon generates both an electric and a magnetic field A current passing through a wire also generates both an electric and a magnetic field B (T) = |B| =  o I/(2  r) permittivity of vacuum:  o = 4  x T m amp -1 I = current (amp) r = distance from wire (m)  Magnetic Spectroscopy Zeeman Spectroscopy: A magnetic field will eliminate degeneracy of various m ℓ quantum states. e.g. An 1 S → 1 P transition will be split into 3 bands. ESR Spectroscopy: (microwave region) Applies to an molecule with unpaired electrons (e.g. radicals & TM cpds). Hold frequency constant and vary B. Position of transition depends on interactions with adjacent nuclear spins.

Zeeman Spectroscopy Look at the 1 S → 1 P electronic transition in an atom (e.g. He 1s → 2P transition) ℓ = 0 to ℓ = 1 1S1S 1P1P EE no magnetic field 1S1S 1P1P EE With magnetic field L = 0 and M L = 0 L = 1 and M L = -1, 0, +1 (degenerate) L = 1 and M L = -1, 0, +1 (split) ← M L = -1 ←M L = +1 M L = 0 →

ESR Spectroscopy (microwave region) ΔE = g e μ B B 0 g e = B = 0 B ≠ 0

As an example of how hν = g e μ B B 0 can be used, consider the case of a free electron, which has g e = , [1] and the simulated spectrum shown at the right in two different forms. For the microwave frequency of MHz, the predicted resonance position is a magnetic field of about B 0 = h ν / g e μ B = tesla = 3350 gauss, as shown. Note that while two forms of the same spectrum are presented in the figure, most EPR spectra are recorded and published only as first derivatives. [1] Because of electron-nuclear mass differences, the magnetic moment of an electron is substantially larger than the corresponding quantity for any nucleus, so that a much higher electromagnetic frequency is needed to bring about a spin resonance with an electron than with a nucleus, at identical magnetic field strengths. For example, for the field of 3350 G shown at the right, spin resonance occurs near MHz for an electron compared to only about 14.3 MHz for 1 H nuclei. (For NMR spectroscopy, the corresponding resonance equation is hν = g N μ N B 0 where g N and μ N depend on the nucleus under study.)magnetic moment

Proton NMR Spectroscopy Spin (I) = ½ Possible orientations = 2I + 1 = 2  E mag = g N  N B M I g N = unitless constant related to magnetic moment = for proton  N = nuclear magneton B = magnetic field strength M I = nuclear spin angular momentum quantum # B tot = B (1-  )  = shielding constant  = chemical shift  (ppm) = (  TMS –  nuc ) x 10 6

Proton NMR Spectroscopy Spin (I) = ½ Possible orientations = 2I + 1 = 2  E mag = g N  N B M I B tot = B (1-  )  = shielding constant  = chemical shift  (ppm) = (  TMS –  nuc ) x 10 6 spin-spin coupling – splits absorption into multiple values like Zeeman selection rules do not allow spin-spin coupling of Hs on same C atom … but do allow coupling of Hs on adjacent Cs. example 16.12: methane – ethane - propane doublet = 1:1 triplet = 1:2:1 quadruplet = 1:3:3:1

hν = g N μ N B 0 NMR Spectroscopy: (radio wave region) Applies to nuclei that have a total spin (I) Application of a magnetic field splits energy levels according to M I values. Position of transition depends on interactions with adjacent nuclear spins.  B = -  B  = shielding constant (no units) B o is constant and vary frequencyB tot = B o (1 –  ) nucleusSpin, IgNgN 1H1H½ He½ Li B 3/ C½ F½ P½

 E =  B/I  = magnetic moment like dipole moment for magnetic rather than charge Isotope Natural % Abundance Spin (I) Magnetic Moment (μ)* Magnetogyric Ratio (γ) † 1H1H / H2H , B81.173/ C1.1081/ , O0.0375/ , F100.01/ , Si4.7001/ , P100.01/ ,840 * μ in units of nuclear magnetons = JT -1 † γ in units of 10 7 rad T -1 sec -1  = spin

Continuous Wave NMR

Increasing Magnetic Field Strength improves resolution

Pulsed Fourier Transform Spectroscopy Relaxation time (T 1 )

Relaxation Time T 1 = spin-Lattice Relaxation or longitudinal relaxation The time it takes for a fraction of the spins to re-equilibrate after a pulse. Sample is ready to be pulsed again. Relaxation Time T 2 = transverse relaxation The time it takes for pulsed nuclei precessing in sync to fall out of synchronization. T 2 is typically shorter that T 1 and related to linewidths of NMR lines.

1D NMR – magnetic field is constant – vary emr, at E = h =  E the nucleus will absorb emr resulting in NMR spectra. The chemical shift (relative value of ) and splitting pattern is dependent on the chemical environment of the proton. 2D NMR – Main magnetic field is constant (B 0 ) A 2 nd magnetic field (B 1 ) ┴ to (B 0 ) Relaxation time – fraction of time required after pulse for nuclear spins to return to their original equilibrium distribution values. Boltzman Distribution Function N 2 /N 1 = e -  E/kT. NOE – Nuclear Overhauser Effect – Through space interactions that influence the relaxation time of neighboring protons. Used for 2D NMR structure determination of proteins.

fMRI A techniques that monitors the NMR signal of water in a specific area of the brain – 64 MHz with 1.5T instrument The water signal is influenced by the Fe center of Hemoglobin deoyHb is paramagnetic and shifts the water signal. Since the signal is spread out over a greater range the spectrum records this as a reduction in signal intensity relative to oxyHb.

BOLD Blood Oxygen Flow Dependence Baseline brain activity = normal blood flow Active areas of brain ↑metabolic activity This causes ↑glucose metabolism and ↑O 2 release and ↑[deoxyHb] Body responds by increasing blood flow to area for 4-5s – mechanism ? ↑blood volume = ↑(oxyHb/deoxyHb) = ↑(H 2 O NMR signal)

NMR signal intensity time Control – no cognitive activity Noise or normal fluctuations in signal intensity NMR signal intensity time Cognitive activity in specific brain area Increase in deoxyHb Increase in oxyHb due to blood flow (BOLD) Blood Oxygen Flow Dependence 4-5s