Molecular Spectra and Molecular Structure - Lec 28S

Lecture # 28 Supplement Contents A. “On the Relation of Child and Lawton’s Harmonically Coupled Anharmonic-Oscillator Model and Darling-Dennison Coupling” by K. Lehmann . . . . . . . . . . . . . . . 1 B. “The C-H Overtone Spectra of Acetylene: Bend/Stretch Interactions Below 10,000 cm−1 ,” by B. C. Smith and J. S. Winn . . . . . . . . . . . . . . . . . . . . . . . . . . 2 “The High-Resolution Visible Overtone Spectrum of Acetylene” by G. J. Scherer, K. K. Lehmann, and W. Klemperer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 “Local and Normal Vibrational States” by M. S. Child and R. T. Lawton . . . . . . 4 C. D. A. “On the Relation of Child and Lawton’s Harmonically Coupled Anharmonic-Oscillator Model and Darling-Dennison Coupling” by K. Lehmann Kevin K. Lehmann, “On the Relation of Child and Lawton’s Harmonically Coupled Anharmonic-Oscillator Model and Darling-Dennison Coupling,” J. Chem. Phys. 79(2), 1098 (1983). SUMMARY In a recent publication, M. S. Child and R. T. Lawton [Faraday Discuss. 71, 273 (1981)] presented an approximate model for two identical, coupled anharmonic oscillators. It is the purpose of this letter to show that the effective Hamiltonian of that model can be transformed into a special case of the familiar Darling-Dennison [B. T. Darling and D. M. Dennison, Phys. Rev. 57, 128 (1940)] resonance Hamiltonian. 1 Page 2 B. “The C-H Overtone Spectra of Acetylene: Bend/Stretch Interac­ tions Below 10,000 cm−1,” by B. C. Smith and J. S. Winn B. C. Smith and J. S. Winn, “The C-H Overtone Spectra of Acetylene: Bend/Stretch Interactions Below 10,000 cm−1 ,” J. Chem. Phys. 89(8), 4638-4645, (1988). SUMMARY High resolution FT-IR spectra of C2 H2 have been obtained from 1800 to 10,000 cm−1 . Over 1600 rovi­ brational transitions belonging to 30 vibrational bands were assigned and analyzed yielding band ori­ gins and rotational constants. Band centers from this and other studies were used to calculate various stretch/stretch and bend/stretch anharmonic coupling constants. Several resonances of the type between ν3 and (ν2 + ν4 + ν5 )0 were analyzed, and an unperturbed value of ν3 was determined. This was combined with other data to obtain ωm , xm , and λ in the local mode basis. x-K relations were imposed to yield the normal mode constants for ν1 and ν3 . Treatment of Darling-Dennison resonances in the first two overtone manifolds led to reassignments of previously reported spectra and to the discovery of a Fermi resonance involving overtones of ν3 and states containing ν1 , ν2 , and 2ν40 . Calculated rotational constants and in­ tensity data confirm the assignments and interactions treated in the vibrational analysis. Treatment of these resonances significantly improved the agreement between calculated and observed transition wave numbers, providing a coherent picture of acetylene C-H stretch dynamics below 10,000 cm−1 . Page 3 C. “The High-Resolution Visible Overtone Spectrum of Acetylene” by G. J. Scherer, K. K. Lehmann, and W. Klemperer G. J. Scherer, K. K. Lehmann, and W. Klemperer, “The High-Resolution Visible Overtone Spectrum of Acetylene,” J. Chem. Phys. 78(6), 2817-2832 (1983). SUMMARY Direct, gas-phase overtone spectra of states corresponding to five and six quanta of C-H stretch have been obtained for four isotopically substituted acetylenes in the region 14,900-18,500 cm−1 . Peak positions of individual rotation-vibration lines were determined to a precision of about 0.003 cm−1 . A total of 39 bands are analyzed: 16 for 12 C2 H2 ; 14 for 13 C2 H2 ; five for 12 C13 CH2 ; and four for 12 C2 HD. The rotational structure of the bands is fit to a semirigid rotor Hamiltonian. However, the bands suffer from severe rotational perturbations, with typical matrix elements being on the order of 0.3 cm−1 or less. The error in the determined band origins varies between 0.001 and 0.1 cm−1 , depending on the degree of perturbation. Precision rotational constants are also determined for the observed bands. The vibrational term values cannot be adequately explained in terms of the usual slightly anharmonic normal mode expansion. Even though acetylene represents an intermediate case between the local mode and normal mode limits, the simple local mode theory described by Child and Lawton [M. S. Child and R. T. Lawton, Faraday Discuss. 71, 273 (1981)] can be used to rationalize many aspects of the spectrume.g., the splitting of the states � � �� � �005g 011 and ��005u 011 is found to be only 0.44 cm−1 . The intermediate character of acetylene is seen upon single deuterium substitution. The state corresponding to five quanta of 12 C-H stretch shifts about 100 cm−1 to the blue, a result which is certainly anomalous from the point of view of intuitive local mode theory. The band origins for the observed Σ-Σ transitions for all four acetylenes studied are found to be in good agreement with the results of a recent variational calculation [L. Halonen, M. S. Child and S. Carter, Mol. Phys. 47, 1097 (1982)]. It is also observed that the anharmonic shifts of the sequence band transitions are quite large — for the v = 5 overtone band, the sequence bands are shifted 74 cm−1 for the Πg bend and 39 cm−1 for the Πu bend. Page 4 D. “Local and Normal Vibrational States” by M. S. Child and R. T. Lawton M. S. Child and R. T. Lawton, “Local and Normal Vibrational States: a Harmonically Coupled Anharmonic­ oscillator Model,” Farad. Disc. of the Chem. Soc. 71, 273-285 (1981). SUMMARY Analysis of previous calculations indicates that the observation of an irregular overtone/combination spec­ trum implies increasingly close local-mode near-degeneracies in the higher overtone states. This behavior is accurately reproduced by a model of two harmonically coupled anharmonic oscillators, when the an­ harmonicity parameter exceeds the coupling strength, the effect being independent of the momentum or potential origin of the coupling. The same model reproduces familiar normal-mode behavior in the oppo­ site limit. Applications of the model indicate local-mode behavior for H2 O and C2 H2 and normal mode features for C2 D2 and SO2 , the dominant inter-bond coupling in all cases except H2 O being due to cross­ terms in the kinetic-energy operator. In H2 O such momentum coupling is combined with an approximately equal potential coupling contribution.