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Lecture 32 General issues of spectroscopies. II (c) So Hirata, Department of Chemistry, University of Illinois at Urbana-Champaign. This material has been developed and made available online by work supported jointly by University of Illinois, the National Science Foundation under Grant CHE-1118616 (CAREER), and the Camille & Henry Dreyfus Foundation, Inc. through the Camille Dreyfus Teacher-Scholar program. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the sponsoring agencies.

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General issues of spectroscopies We will learn two types of spectroscopies: absorption/emission and scattering. We will learn their relationship to dipole moment and polarizability as well as perturbation theories.

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Absorption/emission versus scattering spectroscopy Absorption/emission spectroscopy: microwave, IR, and UV/vis absorption as well as fluorescence Scattering spectroscopy: Raman IRRaman

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Absorption spectroscopy One-photon process 1 st order perturbation theory

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Scattering (Raman) spectroscopy Two-photon process 2 nd order perturbation theory C. V. Raman Public domain image from Wikipedia

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Scattering (Raman) spectroscopy Rayleigh Anti-Stokes Raman (a hot band) Stokes Raman

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Scattering (Raman) spectroscopy Resonant Rayleigh Resonant Raman

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Quantum in nature Why is sky blue? Resonanc e Rayleigh scattering

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Quantum in nature Why is the Sun yellow? Resonanc e Rayleigh scattering

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Dipole moment and polarizability Absorption spectroscopies (such as IR spectroscopy) are related to the dipole moment and its changes. Scattering spectroscopies (such as Raman spectroscopy) are related to the polarizability and its changes. Polarizability – softness of wave function; the larger the polarizability, the more easily the wave function is distorted by external electric field to create an induced dipole.

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Dipole moment E0E0 E 0 + µE + + + + + + – – – – – – – – – First-order perturbation theory Electric field Perturbation Think of molecular length!

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Polarizability E0E0 E 0 + µE + αE 2 =E 0 + (µ+ αE)E + + + + + + – – – – – – – – – Second-order perturbation theory Induced dipole Think of molecular volume!

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Polarizability + + + + + + – – – – – – – – –

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Classical (Smekal) theory of Rayleigh and Raman scattering An oscillating electric field (incident photon) causes the molecule to have an induced dipole: Polarizability varies with molecular vibration; so does induced dipole:

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Absorption/emission versus Raman spectroscopies Absorption/emission occurs when molecular vibration, rotation, etc. alter dipole moment. The transition tends to transform as x, y, z. Raman occurs when molecular vibration, rotation, etc. alter polarizability. The transition tends to transform as xx, yy, zz, xy, yz, zx.

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Summary We have the general theories of absorption/emission spectroscopy and scattering (Raman) spectroscopy. We have learned the relationship between absorption/emission spectroscopies to dipole moment and that between scattering (Raman) spectroscopy and polarizability. We have made references to first- and second-order perturbation theories.

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Lecture 10 Harmonic oscillator (c) So Hirata, Department of Chemistry, University of Illinois at Urbana-Champaign. This material has been developed and.

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