1. Advanced Spectroscopy: Computation of Magnetic Vibrational Circular Dichroism

2. Basic idea of working with polarized light: We get more information than with unpolarized one
Example: ROA
Spectra from Charles University, Prague

3. vibrational/rotational
Chiroptical Methods
Natural Chirality
electronic
vibrational
ORD > 1848
V-ORD ?
ECD > 1960
VCD 1972/1995
CPL > 1960
ROA 1973/2005
Induced by a Magnet
vibrational/rotational
Faraday > 1845
V-MORD ?
MCD > 1930
MVCD 1981
MCPL
MROA

4. MVCD Experiment

5. MVCD Experiment RR (gas) MVCD Pure vibrational (liquid state) MVCD
Theory:
qualitative explanations
“A terms” only
cannot simulate spectra
modern approach needed
X not now !

6. Perturbation of Vibrational States in the Magnetic Field
nX, nY
n(+), n(-) B
(mixing and splitting)
but in solution: average
energy zero ….

7. Perturbation of Vibrational States in the Magnetic Field
nX, nY
n(+), n(-) B
(mixing and splitting)
How to imagine: nY nX - +
but in solution: average
energy zero …. -

8. Perturbation of Vibrational States in the Magnetic Field
nX, nY
n(+), n(-) B
(mixing and splitting)
How to imagine: nY
n(+) = nX + i nY + nX - +
but in solution: average
energy zero …. m -

9. Perturbation of Vibrational States in the Magnetic Field - Math

10. Perturbation of Vibrational States in the Magnetic Field - Math

11. Perturbation of Vibrational States in the Magnetic Field - Math
Second-order perturbation theory:

12. (cont.)
… molecule fixed frame

13. (cont.) … molecule fixed frame
… solution: isotropic (rotational) averages, e.g.
“Faraday’s B-term” of Stephens, but for vibrations

14. … but if Ejk = 0 ?
“Dirty” trick: spectral lines always broad, can introduce arbitrary perturbation
replace (1/E) by f(E)/2
E < 0

15. … but if Ejk = 0 ?
“Dirty” trick: spectral lines always broad, can introduce arbitrary perturbation
replace (1/E) by f(E)/2
E < 0
|E| > 0:
… no effect
E = 0:
f(E) = .
Shape does not depend on d

16. … closer look Equilibrium dipole APT APT derivatives AAT zero
AAT derivatives
harmonic part ... does not contribute to B-term
AAT derivatives are the leading term for MVCD

17. MVCD working equation APT, from Gaussian directly
AAT derivatives, from Gaussian numerically
vibrational (harmonic) frequencies,
from Gaussian directly

18. 1,3,5-chlorobenzene and triazine
B3LYP/ G**
signs and relative intensities agree
1440x 1440y 1600x y

19. tetraphenylporphyrin
B3LYP/ G**/6-31G**
non-degenerate states only, A and B terms in one shot

20. Summary We can simulate MVCD
May be useful to assign modes/study molecules
Measurement – MVCD cell

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