Origin_of_Chemical_Shifts_10

Origin_of_Chemical_Shifts_10 - Origin of Chemical Shifts...

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Origin of Chemical Shifts BCMB/CHEM 8190
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Empirical Properties of Chemical Shift υ i (Hz) = γ B 0 (1- σ i ) /2 π σ i , shielding constant dependent on electronic structure, is ~ 10 -6 . Measurements are made relative to a reference peak (TMS). Offsets given in terms of δ in parts per million, ppm, + downfield. δ i = ( σ ref - σ i ) x 10 6 or δ i = (( υ i - υ ref )/ υ ref ) x 10 6 Ranges: 1 H, 2 H, 10 ppm; 13 C, 15 N, 31 P, 300 ppm; 19 F, 1000 ppm
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Ramsey’s Equation for Chemical Shift • Additional Reference: G.A. Webb, in “Nuclear Magnetic Shielding and Molecular Structure”, J.A. Tossel, ed. Nato Adv. Sci. Series (1993) 1-25 • Physical origin: moving charges experience a force perpendicular to the trajectory. Hence electrons precess. • Circulating current gives an opposing field. F = - (e/c) v x B 0 B 0 e - v F r B’ = -(e/c) (r x v) / r 3 = -e (r x p) / r 3 (cm) But, we actually need to treat electrons at QM level
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Some Quantum Mechanics Fundamentals Expectation values correspond to observables: O = < ψ | O | ψ > = ψ * O ψ d τ O - an operator, ψ - a wave function (electronic or spin) Examples, wave functions: ψ = 1s, 2s, 2p 1 , 2p 0 , 2p -1 …… (electronic wave functions) ψ = α , β (one spin ½ ), αα , αβ , βα , ββ (two spins ½ ) All are solutions to Schrodinger’s equation: H ψ = E ψ They are normalized: < ψ | ψ > = ψ * ψ d τ = 1 Examples, Operators: Hamiltonian operator is special: < ψ | H | ψ > = E Zeeman Hamiltonian for nuclei in a magnetic field: H z = - μ B 0 , E z = < α |- μ B 0 | α > Begin with classical expression: substitute QM operators μ z = γ I z (h/2 π ) (magnetic moment) E z = < α |-( γ h/2 π ) I z B 0 | α > = - ½ γ (h/2 π ) B 0 < α *| α > = - ½ γ (h/2 π )B 0
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Quantum Expression for B’ • Have QM operator for linear momentum: p 0 = i(h/(2 π ))( /
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Origin_of_Chemical_Shifts_10 - Origin of Chemical Shifts...

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