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Lecture32Notes - Chem 120A Spring 2006 Approximation...

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Chem 120A Approximation Examples, part III 04/14/06 Spring 2006 Lecture 32 1 The Origin of the Chemical Shift In the last lecture we introduced spin interactions. These interactions can be modeled as perturbative terms to our Hamiltonian which will alter the wavefunctions and energy eigenvalues. In this lecture we will ignore spin-spin interactions and look at the interaction between the nuclear spin and an external magnetic field, B . In the presence of a magnetic field applied in the z-direction, B = B ˆ z the Hamiltonian for a hydrogen atom in the 1 s (ground) state is: H T ε 1 s - g n β N BI z + g n β N B σ I z - g β BS z (1) where g and g N are fundamental parameters determined either experimentally or by quantum electro- dynamics, g = 2 . 0023 and g N = 5 . 5855. The other constants are β = e ¯ h 2 m e c = 9 . 274 × 10 - 24 J / T and β N = m e M N β = 5 . 05079 × 10 - 27 J / T for Hydrogen. I z is the z-component of the nuclear spin, and S z is the z-component of the electron spin. Thus we see that the - g n β N BI z term describes the interaction of the nuclear spin with the magnetic field B and - g β BS z describes the interaction of the electron spin with the magnetic field. We will ignore the electron spin interaction (
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