Lecture 32General 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.

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.

Absorption/emission versus scattering spectroscopy Absorption/emission spectroscopy:

microwave, IR, and UV/vis absorption as well as fluorescence

Scattering spectroscopy: Raman

IR Raman

Absorption spectroscopy

One-photon process1st order perturbation theory

Scattering (Raman) spectroscopy

Two-photon process2nd order perturbation theory

C. V. RamanPublic domain image from

Wikipedia

Scattering (Raman) spectroscopy

RayleighAnti-Stokes

Raman(a hot band)

Stokes Raman

Scattering (Raman) spectroscopy

ResonantRayleigh

ResonantRaman

Raman

Quantum in nature

Why is sky blue?

Resonance Rayleigh scattering

Quantum in nature

Why is the Sun yellow?

Resonance Rayleigh scattering

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.

Dipole moment

E0 E0 + µE

+ + + + + + + + + + + +

– – – – – – – – –

(0)* (0)0 0ˆx x d

First-order perturbation theory

Electric fieldPerturbation

Think of molecular

length!

Polarizability

E0

E0 + µE + αE2

=E0 + (µ+ αE)E

+ + + + + + + + + + + +

– – – – – – – – –

Second-order perturbation theory

Induced dipole

Think of molecular volume!

Polarizability

+ + + + + + + + + + + +

– – – – – – – – –

(0)* (0) (0)* (0)0 0

(0) (0)0

ˆ ˆk k

xyk k

x d y d

E E

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:

0 0cos t

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.

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.