Advanced Spectroscopy Computation of Magnetic Vibrational Circular Dichroism

Advanced Spectroscopy: Computation of Magnetic Vibrational Circular Dichroism

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

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

MVCD Experiment

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

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

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

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

Perturbation of Vibrational States in the Magnetic Field - Math

Perturbation of Vibrational States in the Magnetic Field - Math

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

(cont. ) … molecule fixed frame

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

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

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

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

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

1, 3, 5 -chlorobenzene and triazine - B 3 LYP/6 -311++G** - signs and relative intensities agree 1440 x 1440 y 1600 x 1600 y

tetraphenylporphyrin - B 3 LYP/6 -311++G**/6 -31 G** - non-degenerate states only, A and B terms in one shot

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

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