NMR Exam Flashcards
What is I?
the spin quantum number
What are the three rules for I?
(1) I is a half integer when the mass number is odd
(2) I is an integer when the mass number is even
(3) I equals zero when the atomic number and mass number are both even
What is P?
angular momentum
What is ml?
magnetic quantum number
What is the range of ml?
ml ranges from -I to I in integer steps
Ex: if I = 3/2, ml = -3/2, -1/2, 1/2, 3/2
What is mu?
magnetic moment
What is gamma?
the gyromagnetic ratio - constant for each nuclide
What is the zeeman effect?
happens when I>0, nuclei exhibiting splitting of energy levels when placed in an external static magnetic field
What is the larmor frequency?
produced by magnets used for NMR
Energy level diagram for a given I
- on paper * (pg 1)
What does the energy level diagram for an AK system look like if gamma A > gamma K?
The K transitions are smaller energy requirements - alpha-beta is lower in energy than beta-alpha
What does the energy level diagram for an AK system look like if gamma A = gamma K?
The energy transitions are equal. alpha beta and beta alpha are at the same level
What does the energy level diagram for an AK system look like if gamma A < gamma K?
The A transitions are smaller energy requirements - alpha-beta is higher in energy than beta-alpha
What transitions are possible?
When the change in m = 1
alpha-alpha <–> alpha-beta
(1/2 + 1/2) (1/2 - 1/2) delta m = 1
alpha-alpha <–> beta-beta
(1/2 + 1/2) (-1/2 - 1/2) delta m = 2 (not allowed)
How are the transitions on an energy level diagram labeled?
1st letter is the the nucleus that is changing, the 2nd letter is what other nucleus is held constant at.
What does J - coupling equal?
The product of the ml values, so agreeing ml values (aa and bb) increase in energy, and disagreeing ml values (ab and ba) decrease in energy
How does magnetization evolve due to the pulse?
magnetization starts at thermal equilibrium on the z-axis, the pulse is to put the net magnetization on the x-y plane
How does magnetization evolve during acquisition?
Magnetizations oscillates back to thermal equilibrium, rotating from the starting point back up
How is the FID is determined from
the magnetization?
NMR spectroscopy a coil of wire is set up in an orientation such that magnetization
precessing in the xy-plane induces a current in the coil. The induced current is then measured over
time producing a signal called the free induction decay (FID)
How is the observed lineshape determined from the position of the magnetization at the start of acquisition?
If acquisition starts with extrema (max/min) the frequency domain will be an absorption model. If acquisition starts at zero the frequency domain will be a dispersion mode.
On the x-y plane which starting positions give what lineshape?
+y - down up dispersion
+x - positive absorption
-y - up down dispersion
-x - negative absorption
How does delta A change the acquired data?
changes where (in hertz) the frequencies are centered
Ex if delta A = 5 hz, the center will be at 5 hz instead of zero
How does J change the acquired data?
J changes where (in hertz) the frequencies stray from the centering
If J = 10 (no delta A)
Aa will be at +5 (J/2) herts and Ab will be at -5 (-J/2)
Calculate the matrix form of Iz x Ix
Iz = .5(1 0 0 -1)
Ix = .5(0 1 1 0)
Sketch a classical vector representation of the product
matrix stuff
What do the different places in a matrix correlate to?
P alpha alpha - - -
K alpha P alpha beta - -
A alpha ZQ P beta alpha -
DQ A beta K betta P beta beta
How do you determine the x, y, and z components from the matrix?
on the diagonal - the populations correlate to to the z-axis
if an imaginary number y-axis
if a real number x-axis
(positive and negative correlate to positive or negative on that axis)
design a pulse sequence to convert Az to Kx, when J = 50 hz and delta a and delta k are arbitrary, sketch the pulse sequence, write the product operator
do it
design a 2D pulse sequence to go form Az to Kx cos(omegaAt1) what is f1 and f2 in this case, sketch the pulse sequence and write the product operator
f1 is omega A
f2 is omega K
design a 2D pulse sequence to go from Az to Axcos(omegaKt1) what is f1 and f2 in this case, sketch the pulse sequence and write the product operator
f1 is omega K
f2 is omega A
Write a spin echo to remove theta on an A nucleus
pi pulse in A and K
Write a spin echo to remove phi on an A nucleus
pi pulse on K (opposite nucleus)
* if already antiphase stay antiphase, if together stay together
How is S/N impacted by the gyromagnetic ratio? What are the four main contributors?
Total: γ^(5/2) (for no polarization transfer)
from boltzmann distribution S ∝ γ
from magnetic moment S ∝ γ
from larmor frequency S ∝ γ
noise N ∝ γ^1/2
If there is polarization transfer how does the S/N change
γ*γ^3/2
where the first gamma is the boltzmanns factor from the starting nucleus, and the gamma to the three halves is the other components contribution and is the detected part if there is polarization transfer.
If removing theta…
pi pulse on both frames
If removing phi…
pi pulse on the opposite frame
How can polarization transfer improve the S/N of spectra when transferring magnetization from one nuclide to another to a lower value of γ?
1H is much more prevalent than 13C, so transferring the polarization from 1H to 13C greatly increases the signal acquired for 13C
Quantitative:
INEPT: γH = 4γC –> 4^3/2 = 8
HSQC: 8x better S/N –> 64 times faster
How does INEPT accomplish an improved 13C spectrum from transferring magnetization from attached 1H nuclei
Polarization transfer to enhance a signal from a less sensitive nuclide. Decoupling prevents the evolution of the J-coupling. Extra delay added to refocus antiphase components
How is a 2D spectrum acquired?
Series of FIDs are collected with a delay in the pulse sequence incremented between each one. The acquisition of each FID is given the time domain designation t2 called the direct dimension, the variable delay in the pulse sequence is given the time domain designation t1 and is called the indirect dimension.
How is a 2D spectrum processed?
Individual FIDs are acquired using a progession of values for a particular variable in the pulse sequcne. After a FT of each FID the signal amplitudes are modulated by the variable allowing for another FT point by point across the FIDs to put this information in the frequency domain
How is a 2D spectrum analyzed
<——————– f2 (related to t2)
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V
f1
(related to t1)
points will show when frequency increases or decreases
Compare and contrast HETCOR and HSQC
HETCOR - Heteronuclear Shift Correlation
- correlates signals that are spin coupled together (two different nuclei)
- the observable terms are the 2AzKx and 2AxKz components
- f1 is determined by the trig identity for the cos/sin multiplication (for theta and phi)
- f2 can be inferred from the product operator (2AxKz f2 in A, 2AzKx f2 in K)
HSQC
- an improvement on HETCOR based on further detecting the final magnetization on A instead of K
