C566lecture3_000 - C566 Master Lecture Notes Lecture 3...

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C566 Master Lecture Notes Lecture 3 Corrections to the Rigid Rotor approximation “Large” Correction for vibration-rotation coupling (not complete separability of vibrational and rotational coordinates) <R>, <R 2 > varies with vibrational quantum number, . B = B e e ( + ½) e is the “vibration-rotation interaction constant,” determined empirically, B e / e ~ 10 2 Finer Correction for Centrifugal stretching- Breakdown of rigid-rotor approximation happens when molecules distorts (elongates) at high rotational energies. B R -2 , so B drops as J increases. F(J) = BJ(J+1) D[J(J+1)] 2 And D varies with vibrational level, too. D = D e + e ( + ½), correction is very small. FROM CRC HANDBOOK: B e e D e CO 1.931 cm -1 0.0175 cm -1 6.12 x 10 -6 cm -1 H 35 Cl 10.59 0.3072 5.32 X 10 -4 cm -1 HCl distorts more with rotation than CO. ______________________________________________________________________ Spectroscopic line positions including centrifugal correction term: F(J ) F(J ) = 2B(J +1) 4D(J +1) 3 Note- if no prime is indicated in the expression, it means J , the lower state quantum number. R e
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With values of both D e and B e , dissociation energy, harmonic frequency, and anharmonic correction term can be approximated. [See the paper I handed out last week, Zack and Ziurys, J. Mol. Spec., 257 , 213-216 (2009).] Vibrational Spectroscopy of Diatomic Molecules See Chapter 6 of Hollas Near R = R e , we can expand the vibrational potential energy function in a Taylor series: V(R) = V(R e ) + (dV/DR)| Re (R R e ) + (2!) -1 (d 2 V/dR 2 )| Re (R R e ) 2 + … At R e , the potential is a minimum, and because it is a minimum, the first derivative is also zero. Truncating the expansion after the 2
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C566lecture3_000 - C566 Master Lecture Notes Lecture 3...

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