1. (Communication between nuclei via bonding electrons)
COUPLING CONSTANT
(Communication between nuclei via bonding electrons)
Chemical shift
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2. Chemical shift
WHY ?
18-Nov-18

3. The magnetic dipole moment m of spin-half (1/2) nuclei may have two orientations in a magnetic field This will be discussed later when introducing the quantum mechanical concept) B0
”up” ”down”
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4. The spin-orientation of a neighboring nucleus affects
the magnetic field seen by the other nucleus
What will be the number of HA molecules in I and II ?
NA(I)  NA(II)
Boltzmann distribution
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5. How will the 1H-NMR spectrum of the following molecular
Exercise 3.0A
How will the 1H-NMR spectrum of the following molecular
fragments look like ? Discuss
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6. MOLECULAR STRUCTURE AND MR ( A QM-APPROACH)
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LECTURE IV
MOLECULAR STRUCTURE AND MR ( A QM-APPROACH)
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7. RETROSPECT SPIN-FUNCTION; |I,m>
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RETROSPECT
SPIN-FUNCTION; |I,m>
I; Spin quantum number (integer or half-integer)
m; -I, -I+1,…I-1, I
ORIENTATION OF A SINGLE SPIN IN AN EXTERNAL MAGNETIC FIELD.
CORRESPONDING SPIN-FUNCTIONS
|1/2, -1/2>
= b
()
|1,-1>
|1,0>
|1/2, 1/2>
= a
()
|1,1>
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8. (Quantum mechanical, Hamiltonian)
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ONE-SPIN SYSTEM (A-SYSTEM)
(I = ½, 1H, 13C, 31P, …..
NUCLEAR SPIN - MAGNETIC FIELD INTERACTION; ZEEMANN ENERGY)
EZ = -mA.BA
(Classical)
(Quantum mechanical, Hamiltonian)
NUMBER OF SPINS; 2 (=21),
SPIN FUNCTIONS; |f1> = |a> and f2 =|b>
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9. 11/18/2018
TRANSITION
Dm = + 1
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10. SPIN UP – SPIN DOWN, ……… SPIN…..………. !
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SPIN UP – SPIN DOWN, ……… SPIN…..………. !
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11. 11/18/2018
(ONE-SPIN SYSTEM)
(TWO-SPIN SYSTEM)
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12. 11/18/2018
OBSERVATION
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13. INTERACTION BETWEEN NUCLEI
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INTERACTION BETWEEN NUCLEI
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14. INDIRECT DIPOL-DIPOL COUPLING
(kvantemekanisk)
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15. INTRODUCE SHIFT OPERATOR
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INTRODUCE SHIFT OPERATOR
(Exercise 3.1)
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16. Select the following N trial spin-functions FN ( 2N = 22)
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Select the following N trial spin-functions FN ( 2N = 22)
F1 = a(A)a(B)
F2 = a(A)b(B)
F3 = b(A)a(B)
F4 = b(A)b(B)
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17. From basic quantum mechanics (QM)
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From basic quantum mechanics (QM)
(Exersice 3.1)
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18. 11/18/2018
What is Ĥ|fi>?
(Exercise 3.2)
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19. What functions are eigenfunctions ?
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(Exercise 3.3)
What functions are eigenfunctions ?
(Exercise 3.4)
Determine the total z-component of the spin operator Fz (= IzA + IzB). What can you conclude from this result?
How can we determine the two remaining energies E2 and E3 ?
(Exercise 3.5)
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20. Since E2 and E3 are now eigenvalues of the Hamiltonian, we may write:
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Since E2 and E3 are now eigenvalues of the Hamiltonian, we may write:
(Exercise 3.6)
Spin-function bb aa
cos q . ab +
sin ba -
ENERGI E 4
= 1/2 . ( n A + B
)+J AB /4 3
= C/2 -J 2
= - C/2-J 1
= -1/2
Show that the actual spin-functions are orthonormal. What is q ?
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21. How can we determine the signal intensity Iij ,
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How can we determine the signal intensity Iij ,
From basic QM
(Exercise 3.7)
TRANSITON
RESONANCE FREQUENCY
(Hz)
SIGNAL
INTENSITY 3 4 V
/2 - C/2 + J/2
1-sin2 q 2
V/2 + C/2 + J/2
1+sin2 1
V/2 +C/2 - J/2
V/2 - C/2 – J/2
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22. PROCEDURE TO DERIVE AN NMR SPECTRUM
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PROCEDURE TO DERIVE AN NMR SPECTRUM
1. CONSTRUCT AN ENERGY OPERATOR, HAMILTONIAN (Ĥ)
2. DETERMINE THE NUMBER (N) OF SPIN-FUNCTIONS ψN
(N = 2M, M IS THE NUMBER OF SPINS
3. DESIGN SOME INITIAL SPIN-FUNCTIONS fi ( i = 1,..N)
4. DETERMINE A BASIS SET OF EIGENFUNCTIONS yi (= aijfj) SUCH THAT |yi>= Ei|yi>
5. Ei DEFINES THE EIGENVALUES AND REPRESENT ENERGIES
6. CONSTRUCT AN ENERGY DIAGRAM AND DERIVE ALLOWED TRANSITION BETWEEN SPIN-STATES AND INTENSITIES
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23. 11/18/2018
RESONANSFREKVENSER
hn =DE FOR DmT = + 1
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24. 7A. WHAT IS THE INTENSITY (Iij) OF A RESONANCE
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7A. WHAT IS THE INTENSITY (Iij) OF A RESONANCE
BETWEEN LEVEL i AND j (Ei - Ej with Dm = mi-mj = + 1)
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25. Simulation of AB-spectra
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Simulation of AB-spectra
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26. 11/18/2018
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