SLIDE 1
NMR spectrum
NMR spectrum of 1,1,2 trichloroethane
Two different types of H
Signals from both alkanes are split
Integrals are in 2:1 ratio
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Nuclear Magnetic Resonance NMR spectrum NMR spectrum of 1,1,2 - - PowerPoint PPT Presentation
Nuclear Magnetic Resonance NMR spectrum NMR spectrum of 1,1,2 - - PowerPoint PPT Presentation
Nuclear Magnetic Resonance NMR spectrum NMR spectrum of 1,1,2 trichloroethane Two different types of H Signals from both alkanes are split Integrals are in 2:1 ratio Molecular Spectroscopy CEM 484 2 Spin-spin coupling
SLIDE 2
SLIDE 3
Spin-spin coupling
Spin-spin coupling responsible for multiple signals.
For example, the single H atom experiences three different magnetic fields
The external static field
The induced field by valence electron motion (chemical shift)
Local field due to protons on adjacent carbon
Add a term to the Hamiltonian.
Ĥ = Ĥ1
nz + Ĥ2 nz + Ĥ(1-2) ss
Ĥ1 and Ĥ2 result from zeeman effect, much greater than ss.
Treat ss as a perturbation
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SLIDE 4
Wavefunction
Distinguishable protons.
Four different eigenstates for the nuclear Zeeman portion
- f Hamiltonian.
Ψ1 = a(1) a(2)
Ψ2 = a(1) b(2)
Ψ3 = b(1) a(2)
Ψ4 = b(1) b(2)
Operate on the respective wavefunction with the Hamiltonian to determine state energies.
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SLIDE 5
Energies (1)
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SLIDE 6
Energies (2)
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SLIDE 7
Energies (3)
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SLIDE 8
Spin-spin coupling
Spin-spin hamiltonian
Ĥss = hJ12/hbar2*I1*I2
J12 spin coupling constant
Wavefunctions are not eigenstates of Ĥss so they are treated using perturbation theory
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SLIDE 9
Spin-spin coupling (1)
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SLIDE 10
Spin-spin coupling (2)
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SLIDE 11
Spin-spin coupling (3)
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SLIDE 12
Spin-spin coupling
Energy level diagram with spin-spin coupling.
Only four different transitions are allowed.
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SLIDE 13
Indistinguishable protons
Why do indistinguishable protons not show a splitting?
Consider dichloromethane.
Need symmetric and antisymmetric wavefunctions
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SLIDE 14
Indistinguishable protons (1)
Apply same Hamiltonian to the system
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SLIDE 15
Indistinguishable protons (2)
Apply same Hamiltonian to the system
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SLIDE 16
Indistinguishable protons (3)
Spin-spin coupling
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SLIDE 17
Indistinguishable protons (4)
Spin-spin coupling
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