13_lecnotes_rwf

13_lecnotes_rwf - MIT Department of Chemistry 5.74, Spring...

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MIT Department of Chemistry 5.74, Spring 2004: Introductory Quantum Mechanics II Instructor: Prof. Robert Field 5.74 RWF Lecture #13 13 – 1 Polyads, a, a , N Readings : Chapter 9.4.4 - 9.4.9, The Spectra and Dynamics of Diatomic Molecules , H. Lefebvre-Brion and R. Field, 2 nd Ed., Academic Press, 2004. Last time: () two level problem with complex E j 0 . strong coupling limit V 2 >> δε 2 + δΓ 2 /4 : if either δε = 0 or δΓ = 0, the two quasi-eigenstates have the same width. Otherwise no major surprises. weak coupling limit V 2 << δε 2 δΓ 2 /4 : if δε = 0 we get no level repulsion and no level-width sharing. Big surprise! Quantum beats between two decaying quasi-eigenstates. I( t ) expressed in terms of 8 parameters (I + , I , Γ + , Γ , I QB , Γ QB , ω QB , φ QB ) obtained from 6 dynamical parameters ( δε , δΓ , Γ , V , I A , I B ). H Today: begin study of vibrational dynamics, leading eventually to replacement of the quantum mechanical eff by a classical mechanical H eff . Tricks to get A without use of Trace( Αρ ( t )). Polyatomic Molecule Vibration 3 N 6 = ψ V = φ v j product basis set 12 v ψ vv 3 N 6 j = 1 3 N 6 H = h j + coupling terms j = 1 1243 4 H 0 could also include diagonal anharmonicities 0 / E = h ω j ( v j + ) (traditionally ω is in cm –1 units, E = hc ω ( v + 1/2), and ω is not in j radians/s) coupling terms have the form k ijk QQ Q + { quartic } + { quintic } +… i j ij ,, cubic most important Enormous number of undeterminable anharmonic force constant terms.
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5.74 RWF Lecture #13 13 – 2 matrix element scaling and selection rules h a scaling = 2 π c µω j a /2 { v a j highest power term /2 } (and similarly for P a j ) v j + n v j Q selection rule n = a , a – 2, … – a µ and ω j must be generalized from single oscillator (diatomic molecule) form via a Wilson force constant geometry F , G
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This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

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13_lecnotes_rwf - MIT Department of Chemistry 5.74, Spring...

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