Applied Spectroscop Ala-Arg-Pro-Tr-Asn-Phe-Cpa-Leu-NH 2 Cpa Ala Pro Guillermo Mona
What is Spectroscop? Without going into latin or greek, spectroscop is the stud of the interactions between light and matter. Here light refers to an sort of electromagnetic radiation, such as visible light, UV, IR, and radiowaves. Depending on the frequenc or wavelength of the radiation involved we will have different tpes of interactions with matter (molecules). The following chart shows the ranges (wavelengths), for different tpes of spectroscopies. γ-ras -ras UV VIS IR µ-wave radio 10-10 10-8 10-6 10-4 10-2 10 0 10 2 wavelength (λ, cm) As ou know, wavelength and frequenc are inversel proportional, so higher frequencies mean shorter wavelength.
Some background Also to remember throughout the course is the relationship between energ and frequenc. The two are related b one of the fundamental equations of quantum mechanics: E = h ν Therefore, the higher the frequenc, the higher the energ. In addition, and as said before, depending on the frequenc and wavelength we ll have different interactions with matter (molecules). The following is a brief list of these: E γ-ras/x-ras - inner shell electrons, nucleus UV/Vis - bonding electrons (valence electrons) IR - Bond length/angle/torsion vibrations NMR - Nuclear spin λ
Wh bother learning NMR? Structural (chemical) elucidation Natural product chemistr. Organic chemistr. Analtical tool of choice for snthetic chemists. Stud of dnamic processes Reaction kinetics. Stud of equilibrium (chemical or structural). Structural (three-dimensional) studies Proteins. DNA/RNA. Protein complees with DNA/RNA. Polsaccharides Drug design Structure Activit Relationships (SAR) b NMR Medicine - Magnetic Resonance Imaging (MRI) Finall, it s the biggest, meanest, most epensive piece of equipment ou ll see in our career at USP, and this is a great time to get our hands on it...
The gor details Absorption (or emission) spectroscop, as IR or UV. Detects the absorption of radiofrequencies (electromagnetic radiation) b certain nuclei in a molecule. Unfortunatel, some quantum mechanics are needed to understand it (a lot to reall understand it ). As opposed to the atomic mass or charge, the spin has no macroscopic equivalent. It eists, period... Onl nuclei with spin number (I) 0 can absorb/emit electromagnetic radiation. Even atomic mass & number I = 0 ( 12 C, 16 O) Even atomic mass & odd 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.
Background (continued) For 1 H, 13 C, 15 N, 31 P (biologicall relevant nuclei with I = 1 / 2 ): 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 nuclei is the magnetic moment (µ), which can be epressed as: µ = γ I h / 2ππ 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. The energ of a spin in a magnetic field will depend on the magnetic field, which we call, and µ:
Magnetic energ and populations When the field is applied, spins have to possible energ limits. In one we are in favor of the field, and in the other one we are against it. The energ is the dot product of the corresponding vectors: E = - µ. µ µ E α = - γ h / 4π E β = γ h / 4π The energ difference of the two levels, α and β, is: E = γ h / 2π The bigger, the larger the energ difference. Also, the population ratio between the two levels depends on E, and we can calculate it as a Boltmman distribution. The E for 1 H s at 400 MH ( = 9.4 T) is 4 10-5 Kcal / mol. N α / N β = e E / RT The N α / N β ratio is onl 1.000064. In one million spins we have a difference of just 64: NMR is ver insensitive when compared to UV or IR...
Magnetic energ, sensitivit, and frequenc Nuclei with larger γ will absorb/emmit more energ, and will therefore be more sensitive. Sensitivit is proportional to µ, to N α / N β, and to the magnetic flu of the coil, all of which depend on γ. In sum, sensitivit 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 onl due to γ. If we also take into account the natural abundance, 13 C (~1%) ends up being 6400 less sensitive than 1 H... Energ is related to frequenc (quantum mechanics...): E = h ν o E = γ h / 2π ν o = γ / 2π For 1 H s in normal magnets (2.35-18.6 T), the frequencies are between 100 and 800 MH. For 13 C, 1/4 of this γ-ras X-ras UV VIS IR µ-wave radio 10-10 10-8 10-6 10-4 10-2 10 0 10 2 wavelenght (cm)
Precession To eplain everthing in NMR we have to refer to rotation, and H are not the best units to do this. We define the precession or Larmor frequenc, ω o, in radians: ω o = 2πν πν o ω o = γ (radians) With what precession is ω o related to? One thing we left out of the mi was the angular momentum, L, asociated will all nuclei (magnetic or not). We can think of nuclei as small magnetied tops that spin on their ais: L µ After turning the magnet on we ll have two forces acting on the spins. One that tries to turn them towards, and the other that wants to maintain their angular momentum. The net result is that the nuclei spins like a top: ω o L µ
Precession (continued) Now we have to go against a concept used b lots of people to eplain NMR: Spins won t align with, no matter what their intiial orientation was. Spins pointing up and down don t eist! Spins will precess at the angle the were when we turned on the magnetic field : There are several magnetic fields acting on the spins. One is, which is constant in time and generates the precession at ω o. The others are fluctuating due to the molecular anisotrop and its environment, and make the spins tr all the possible orientations with respect to in a certain ammount of time. Orientations in favor of will have lower magnetic energ, and will be slightl favored. After a certain time (the longitudinal relaation, more later), a net magnetiacion (M o ) pointing in the direction of will develop.
Net magnetiation Where does the net magnetiation comes from? In order to figure it out we translate all the spins to the origin of the coordinate ssmem. We ll see something like this: We ll have a slight ecess of spins aligned with, but at an angle with respect to. The distribution is proportional to N α / N β. If we decompose the µ vectors in and <>, we get: = M o = 0 The net magnetiation is aligned with, and this is what we use in NMR.
NMR ecitation So far nothing happened. We have a little tube spinning in the magnet. To see something we have to move the sstem awa from equilibrium. That is, we have to perturb its 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 () How is that something that has a linear variation can be thought as circular field? A linear variation in is the linear combination of two counter-rotating circular fields: -ω o +ω o = +
For part of the period of oscillation: = + = + We go through ero and then it repeats = + Onl the one vector that rotates at +ω o (in the same direction of the precession of M o ) interacts with the bulk magnetiation. -ω o is the one normall used, but it s just a convention...
Now we throw M o on the mi... When the frequenc of the alternating current is ω o, the frequenc of the right vector of B 1 is ω o and we achieve a resonant condition. The alternating magnetic field and all the µ s interact, there s a torque generated, and the rotate. Since the all rotate the same ammount, the macroscopic effect is that M o rotates around the ais (in this case...), and we generate transverse magnetiation (M ): M o B 1 off B 1 (or off-resonance) M ω o ω o Since we altered the population ratio between energ levels (i.e., N / N α β ), the sstem absorbed energ and we altered the equilibrium... Since the individual spins keep precessing under the effect of, the transverse magnetiation M will rotate around the ais at the precession frequenc, ω o.
Detection of M and return to equilibrium In the absence of the eternal B 1, M will tr to go back to the ais (M o, equilibrium) b restoring the original N α / N β. distributiuon. We ll see the phsics that rule this phenomenon (relaation) later. M returns to the ais precessing on the <> plane (to damned hard to draw ): 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: M ω o Receiver coil () NMR signal