14_580ln_fa08

14_580ln_fa08 - MIT OpenCourseWare http:/ocw.mit.edu 5.80...

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MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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5.80 Lecture #14 Fall, 2008 Page 1 of 7 pages Lecture #14: Definition of Angular Momenta and | A α M A . Evaluation of H ROT We want to be able to set up effective Hamiltonian models for rotation-vibration-electronic structure of diatomic molecules with non-zero electronic angular momenta. The important terms in H are H ROT = B(R) R 2 H SO = ( ) s i a r i ˆ i ·ˆ i electrons * a convenient basis set for evaluating matrix elements of H ROT and H SO HUND’S CASE A * A z , A ± , and A Z , A ± and A 2 operators and | A α M A basis functions * H eff and van Vleck Corrections to H eff * Limiting cases where H eff is approximately diagonal and energy levels are expressed in terms of a pattern-forming rotational quantum number like J(J + 1), N(N + 1), R(R + 1). (Example in next lecture for 2 and 2 + states.) * effects of accidental degeneracies — perturbations. Angular Momenta R nuclear rotation L e orbital angular momentum S e spin R + L + S  J total angular momentum N angular momentum. exclusive of spin J S = R + L J total electron angular momentum = L + S a See H. Lefebvre-Brion/R. W. Field, pages 72-81. All angular momenta can be defined by their commutation rules.
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5.80 Lecture #14 Fall, 2008 Page 2 of 7 pages A i ,A j = + i ε ijk A k k ε ijk +1 for x, y, z in cyclic order –1 for non-cyclic 0 repeated coordinator Above is a “normal” Commutation Rule which is applicable for all SPACE components of J , L , S , R , N , J a and all body components of L , S (but not J , R , N ) .  involve
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14_580ln_fa08 - MIT OpenCourseWare http:/ocw.mit.edu 5.80...

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