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Second_Order_Spectra_10

# Second_Order_Spectra_10 - Second Order Spectra BCMB/CHEM...

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Second Order Spectra BCMB/CHEM 8190

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Second Order Spectrum Example: Acrylonitrile Twelve lines, all equal intensities • J AB = -2 Hz, δ C = 5.6 ppm • J AC = 11 Hz, δ B = 6.1 ppm • J BC = 16 Hz, δ A = 6.3 ppm Actual spectrum is more complex, field dependent N C 1 H C 1 H A 1 H B C B A AMX spectrum
Field dependence of second order spectra 60 MHz 90 MHz 250 MHz 490 MHz

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Line Intensities and Transition Probabilities What if spin system cannot be cleanly described as being in one state? ψ = c1 αα + c2 αβ + c3 βα + c4 ββ = j cj φ j What is the probability of being in one of the basis states? Probability in space is proportional to ψ * ψ . Hence, probability: ρ jj = c* j c j Similarly, c* k c k c* l c l is the probability of starting in k and ending in l If we know we start in k, c* k c k = 1, just need c l Schrodinger’s time dependent equation allows us to solve for dc j /dt by substituting k c k φ k , multiplying from left by φ l * and integrating: H ψ (t) = - i (h/2 π ) d( ψ (t))/dt
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