Infrared Spectroscopy and Extensions FTIR Raman VCD The

Infrared Spectroscopy and Extensions: (FT)IR, Raman, VCD

The Harmonic Approximation revision Any molecule – vibrational energy: Wavefunction:

Infrared absorption (today: almost exclusively FTIR) older: dispersion spectrometers

IR: measurement modes

IR: basic nomenclature Energy (Multiple) excited states, |0, 0, 4, 0, . . . 0> (Multiple) excited states, |0, 0, 1, 1, . . . 0> (Mono) excited states, |0, 0, 1, 0, . . . 0> Ground state, |0, 0, . . . 0> Overtones Fundametal Hot transitions bands. Combination transitions

Typical Spectra transmitance (%), T = I/I 0 absorbance, A = log(I/I 0)

Spectral intensities absorbance band area - dipole strength - need to develop transition electric dipole matrix element (integral)

Spectral intensities zero for i f dipole derivatives most important (“molecule = TV antenna”) zero for fundamental modes

Computation of IR intensities Atomic polar tensor (“dipole derivatives”) “S-matrix”, Cartesian coordinatenormal mode transformation matrix

VCD Spectroscopy - chiral molecules - more information than IR - absolute configuration, conformation

Computation of VCD Intensities VCD band area - rotation strength - electrons shift - need to develop also magnetic dipole moment - electrons rotate

VCD intensities zero for i f el. part zero for BO approximation !!! zero for fundamental modes magnetic dipole (momentum) derivatives most important (“molecule = more than TV antenna”)

Computation of VCD intensities “S-matrix”, Cartesian coordinatenormal mode transformation matrix Atomic axial tensor (“magnetic dipole derivatives”) MPF theory, 1985 (Philip Stephens)

Computation of VCD intensities -AAT – usually analytical at DFT - potentially origin dependent – use GIAO -Gaussian: #B 3 LYP/6 -31 G** FREQ=VCD

Raman Scattering -CV Raman, 1926 - two-photon event virtual state hv hv’ Excited state, |0, 0, 1, 0, . . . 0> Ground state, |0, 0, . . . 0>

Raman Scattering

Raman Scattering hv hv’ molecule = “ oscillating induced dipole”

Computation of Raman Intensities (transition) polarizability I 180 = k[7 (i) + (i) ],

Computation of Raman Intensities (transition) polarizability in Placzek (BO) approximation polarizability derivatives Actual intensity expressions complicated, e. g. I 180 = k[7 (i) + (i) ],

Computation of Raman Intensities polarizability derivatives -numerically/analytically - third-order property Gaussian: #B 3 LYP/6 -31 G** Freq=Raman

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