= I, (I - 1), (I - 2),, -I

Transcription

1 NMR spectroscop Absorption (or emission) spectroscop, as IR or UV. Detects the absorption of radiofrequencies (electromagnetic radiation) b certain nuclei in a molecule. Onl nuclei with spin number (I) 0 can absorb/emit electromagnetic radiation. Even atomic number & even mass I = 0 ( 12 C, 16 O) Even atomic mass & odd atomic number I = whole integer ( 14 N, 2 H, 10 B) Odd atomic mass I = half integer ( 1 H, 13 C, 15 N, 31 P) The spin states of the nucleus (m) are quantied: m = I, (I - 1), (I - 2),, -I Properl, m is called the magnetic quantum number.

2 Background (continued) For 1 H, 13 C, 15 N, 31 P (biologicall relevant nuclei) then: m = 1/2, -1/2 This means that onl two states (energ levels) can be taken b these nuclei. Another important parameter of each particular nucleus is the magnetic moment (µ), which can be epressed as: µ = γ I h / 2π It is a vector quantit that gives the direction and magnitude (or strength) of the nuclear magnet h is the Planck constant γ is the gromagnetic ratio, and it depends on the nature of each nuclei. Different nuclei have different magnetic moments.

3 Effect of a magnetic field (for I = 1/2) In the ground state all nuclear spins are disordered, and there is no energ difference between them. The are degenerate: = γ h / 4π Since the have a magnetic moment, when we appl a strong eternal magnetic field (B o ), the orient either against or with it: B o There is alwas a small ecess of nuclei (population ecess) aligned with the field than pointing against it.

4 Energ and populations Upon application of the eternal magnetic field we create an energ difference between nuclei aligned and against B o : β B o = 0 B o > 0 α E = h ν Each level has a different population (N), and the difference between the two is related to the energ difference b the Boltmann distribution: N α / N β = e E / kt The E for 1 H at 400 MH (B o = 9.5 T) is Kcal / mol N α / N β = The surplus population is small when compared to UV or IR.

5 Energ and sensitivit The energ (for a single spin) is proportional to the magnetic moment of the nuclei and the eternal magnetic field: E = - µ. B o E (up) = γ h B o / 4π --- E (down) = - γ h B o / 4π E = γ h B o / 2π This has implications on the energ (i.e., the intensit of the signal and sensitivit) that each nuclei can absorb: Bigger magnets (bigger B o ) make more sensitive NMR instruments. Nuclei with larger γ absorb/emit more energ and are therefore more sensitive. Sensitivit is proportional to µ, to N α - N β, and to the coil magnetic flu, which are all dependent on γ. Therefore, it is proportional to γ 3. γ 13 C = 6,728 rad / G γ 1 H = 26,753 rad / G 1 H is ~ 64 times more sensitive than 13 C just because of the γ If we consider natural abundance, 13 C (~1%) ends up being 6400 times less sensitive...

6 Energ and frequenc Since energ is related to frequenc, we can do some insightful math E = h ν E = γ h B o / 2π ν = γ B o / 2π For 1 H in normal magnets ( T), this frequenc is in the MH range. For 13 C, 1/4 of that γ-ras -ras UV VIS IR µ-wave radio wavelength (cm) To eplain certain aspects of NMR, we need to refer to circular motion. H are not the best units to do so. We define the precession or Larmor frequenc, ω: ω = 2πν ω o = γ B o (radians)

7 Precession and spinning tops What precession is ω o associated with? One thing that we left out from the mi is the angular momentum, l, which is associated with all nuclei: l Crudel, we can think of the nuclei as being spinning around its ais. If we now consider those nuclei that have also a non ero µ, we have little spinning atomic magnets. Now, if we bring about a big B o, there will be an interaction between µ and B o that generates a torque. No matter which is the original direction of µ, it will tend to align with B o : µ B o or... µ B o

8 Precession (continued) Since the nuclei associated with µ is spinning due to l, there are two forces acting on it. One that wants to bring it towards B o, and one that wants to keep it spinning. µ ends up precessing around B o : ω o µ B o The best wa to picture it is to imagine a spinning wooden top under the action of gravit.

9 Bulk magnetiation We see the effects on macroscopic magnetiation, M o, which is directl proportional to the population difference (N α - N β ), in which contributions from different µs have been averaged: M o B o B o We can decompose each little µ in a contribution and an <> plane contribution. The components in the <> plane are randoml distributed and cancel out. For the ones in, we get a net magnetiation proportional to N α - N β. Since this is (more or less) the situation in a real sample, we will from now on use M o in all further descriptions/eamples. There is an important difference between a µ and M o. While the former is quantied and can be onl in one of two states (α or β), the latter tells us on the whole spin population. It has a continuous number of states.

10 NMR ecitation So far, nothing happened. We need to do something to the sstem to observe an kind of signal. What we do is take it awa from this condition and observe how it goes back to equilibrium. This means affecting the populations... We need the sstem to absorb energ. The energ source is an oscillating electromagnetic radiation generated b an alternating current: B 1 = C * cos (ω o t) M o B 1 i Transmitter coil () B o

11 Resonance When the frequenc of the alternating current is ω o, we achieve a resonant condition. The alternating magnetic field and M o interact, there is a torque generated on M o, and the sstem absorbs energ : M o B 1 off B 1 (or off-resonance) M ω o ω o Since the sstem absorbed energ, the equilibrium of the sstem was altered. We modified the populations of the N and N α β energ levels. Again, keep in mind that individual spins flipped up or down (a single quanta), but M o can have a continuous variation.

12 Return of M o to equilibrium (and detection) In the absence of the eternal B 1, M will tr to go back to M o (equilibrium) b restoring the same N α / N β distribution. This phenomenon is called relaation. M returns to the ais precessing on the <> plane: equilibrium... M o M ω o The oscillation of M generates a fluctuating magnetic field which can be used to generate a current in a coil: Receiver coil () M ω o NMR signal

13 NMR Instrumentation An NMR machine is basicall a big and epensive FM radio. B o N S Magnet B 1 Frequenc Generator Recorder Detector Magnet - Normall superconducting. Some electromagnets and permanent magnets (EM-360, EM-390) still around. Frequenc generator - Creates the alternating current (at ω o ) that induces B 1. Continuous wave or pulsed. Detector - Subtracts the base frequenc (a constant frequenc ver close to ω o ) to the output frequenc. It is lower frequenc and much easier to deal with. Recorder - XY plotter, oscilloscope, computer, etc., etc.

14 Continuous Wave ecitation It s prett de mode, and is onl useful to obtain 1D spectra. The idea behind it is the same as in UV. We scan the frequencies continuousl (or sweep the magnetic field, which has the same effect - ω = γ B), and record successivel how the different components of M o generate M at different frequencies (or magnetic fields). ω o or B o time ω o or B o

15 Fourier Transform - Pulsed ecitation The wa ever NMR instrument works toda. The idea behind it is prett simple. We have two was of tuning a piano. One involves going ke b ke on the keboard and recording each sound (or frequenc). The other, kind of brutal for the piano, is to hit it with a sledge hammer and record all sounds at once. We then need something that has all frequencies at once. A short pulse of radiofrequenc has these characteristics. To eplain it, we use another black bo mathematical tool, the Fourier transformation: It is a transformation of information in the time domain to the frequenc domain (and vice versa). S(ω) = s(t) e -iωt dt s(t) = 1/2 π S(ω) e iωt dt - If our data in the time domain is periodical, it basicall gives us its frequenc components. Etremel useful in NMR, where all the signals are periodical. -

16 Fourier Transform of simple waves We can eplain (or see) some properties of the FT with simple mathematical functions: For cos( ω * t ) FT ω ω For sin( ω * t ) FT ω ω The cosines are said to give absorptive lines, while sines give dispersive lines.

17 Back to pulses Now that we master the FT, we can see how pulses work. A radiofrequenc pulse is a combination of a wave (cosine) of frequenc ω o and a step function: * = t p This is the time domain shape of the pulse. To see the frequencies it reall carr, we have to anale it with FT: FT ω o The result is a signal centered at ω o which covers a wide range of frequencies in both directions. Depending on the pulse width we have wider (shorter t p ) or narrower (longer t p ) ranges. Remember that f 1 / t.

18 Pulse widths and tip angles The pulse width is not onl associated with the frequenc range (or sweep width), but it also indicates for how long the ecitation field B 1 is on. Therefore, it is the time for which we will have a torque acting on the bulk magnetiation M o : M o t p θ t B 1 M θ t = γ * t p * B 1 As the pulse width for a certain flip angle will depend on the instrument (B 1 ), we will therefore refer to them in terms of the rotation we want to obtain of the magnetiation. Thus, we will have π / 4, π / 2, and π pulses.

19 Some useful pulses The most commonl used pulse is the π / 2, because it puts as much magnetiation as possible in the <> plane (more signal can be detected b the instrument): M o π / 2 M Also important is the π pulse, which has the effect of inverting the populations of the spin sstem... M o π -M o With control of the spectrometer we can basicall obtain an pulse width we want and flip angle we want.

20 1D Pulse sequences We now have most of the tools to understand and start analing pulse sequences. Vectors: M o 90 pulse M acquisition Shorthand: According to the direction of the pulse, we ll use 90 or 90 (or 90 φ if we use other phases) to indicate the relative direction of the B 1 field in the rotating frame. The acquisition period will alwas be represented b an FID for the nucleus under observation (the triangle). n

21 Relaation phenomena So far we haven t said anthing about the phenomena that brings the magnetiation back to equilibrium. Relaation is what takes care of this. There are two tpes of relaation, and both are time-dependent eponential deca processes: Longitudinal or Spin-Lattice relaation (T 1 ): It works for the components of magnetiation aligned with the ais (M ). - Loss of energ in the sstem to the surroundings (lattice) as heat. - Dipolar coupling to other spins, interaction with paramagnetic particles, etc... Transverse or Spin-Spin relaation (T 2 ): It acts on the components of magnetiation ling on the <> plane (M ). - Spin-spin interactions dephase M - Also b imperfections in the magnet homogeneit (fanning out). - Cannot be bigger than T 1.

22 Free Induction Deca (FID) Now, we are interested in analing the signal that appears in the receiver coil after putting the bulk magnetiation in the <> plane (π / 2 pulse). We said earlier that the sample will go back to equilibrium () precessing. In the rotating frame, the frequenc of this precession is ω - ω o. The relaation of M o in the <> plane is eponential. Therefore, the receiver coil detects a decaing cosinusoidal signal (single spin tpe): ω = ω o M ω - ω o > 0 M time time

23 FID (continued) In a real sample we have hundreds of spin sstems, which all have frequencies different to that of B 1 (or carrier frequenc). Since we used a pulse and effectivel ecited all frequencies in our sample at once, we will se a combination of all of them in the receiver coil, called the Free Induction Deca (or FID): t1 sec The FT of this signal gives us the NMR spectrum:

24 Data processing - Window functions Now we have the signal in the computer, properl sampled. There are some things we can do now a lot easier, and one of them is filtering. The real information in the FID is in the first section. As M decas, we have more and more noise: Good stuff Mostl noise t1 sec The noise is generall high frequenc, and that is wh NMR spectra have this jagged baseline. What if we could filter all the signals that were higher than a certain frequenc? We use digital filtering. Intuitivel, it means multipling the FID b a function that makes the noise at the end smaller: 1

25 Window functions (continued) In this case, it is called eponential multiplication, and has the form: F(t) = 1 * e - ( LB * t ) or F(t) = 1 * e - ( t / τ ) Wh is that this removes high frequenc noise? Actuall, we are convoluting the frequenc domain data with the FT of a decaing eponential. The FT of this function is a Lorentian shaped peak with a width at half-height proportional to the rate of deca, or line broadening (LB), in H. LB Convolution makes the contribution of everthing with a WAHH thinner than LB smaller in the spectrum (the scale here is bogus ). If we use an LB with the opposite sign, the eponential grows instead of decaing, letting signals with narrower widths to pass, improving resolution but lowering signal to noise ratio.

26 Sensitivit and resolution enhancement For the following raw FID, we can appl either a positive or negative LB factor and see the effect after FT: t1 sec LB = 5.0 H LB = -1.0 H t1 sec t sec FT FT

27 Chemical shifts If each tpe of nucleus has its characteristic ω o at a certain magnetic field, wh is NMR useful? Depending on the chemical environment we have variations on the magnetic field that the nuclei feels, even for the same tpe of nuclei. It affects the local magnetic field. B eff = B o - B loc --- B eff = B o ( 1 - σ ) σ is the magnetic shielding of the nucleus. Factors that affect it include neighboring atoms, aromatic groups, etc., etc. The polariation of the bonds to the observed nuclei are also important. As a crude eample, ethanol looks like this: HO-CH 2 -CH 3 low field ω o high field

28 The NMR scale (δ, ppm) We can use the frequenc scale as it is. The problem is that since B loc is a lot smaller than B o, the range is ver small (hundreds of H) and the absolute value is ver big (MH). We use a relative scale, and refer all signals in the spectrum to the signal of a particular compound. δ = ω - ω ref ω ref ppm (parts per million) The good thing is that since it is a relative scale, the δ in a 100 MH magnet (2.35 T) is the same as that obtained for the same sample in a 600 MH magnet (14.1 T). Tetramethl silane (TMS) is used as reference because it is soluble in most organic solvents, is inert, volatile, and has 12 equivalent 1 Hs and 4 equivalent 13 Cs: CH 3 H 3 C Si CH 3 CH 3 Other references can be used, such as the residual solvent peak, dioane for 13 C, or TSP in aqueous samples for 1 H.

29 Scales for different nuclei For protons, ~ 15 ppm: Acids Aldehdes Aromatics Amides Alcohols, protons α to ketones Olefins Aliphatic ppm For carbon, ~ 220 ppm: 15 C=O in ketones Aromatics, conjugated alkenes Olefins 2 0 TMS Aliphatic CH 3, CH 2, CH ppm 210 C=O of Acids, aldehdes, esters Carbons adjacent to alcohols, ketones 0 TMS

30 Coupling Constants The energ levels of a nucleus will be affected b the spin state of nuclei nearb. The two nuclei that show this are said to be coupled to each other. This manifests in particular in cases were we have through bond connectivit: 1 H 1 H 1 H 13 C one-bond three-bond Energ diagrams. Each spin now has two energ sub-levels depending on the state of the spin it is coupled to: αβ I S ββ I αα The magnitude of the separation is called coupling constant (J, H). Coupling patterns are crucial to identif spin sstems in a molecule and to the determination of its chemical structure. S βα J (H) I S