Advanced Spectroscopy: Computation of Magnetic Vibrational Circular Dichroism

Advanced Spectroscopy:Computation of Magnetic Vibrational Circular Dichroism

Basic idea of working with polarized light:We getmore informationthan with unpolarized one Example: ROA Spectra from Charles University, Prague

Chiroptical Methods Natural Chirality Induced by a Magnet

MVCD Experiment

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 !

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

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

Perturbation of Vibrational States in the Magnetic Field n(+),n(-) nX, nY B (mixing and splitting) How to imagine: nY n(+) = nX + inY + nX - + 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 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 E < 0 … no effect |E| > 0: f(E) = . E = 0: Shape does not depend on d

… closer look APT derivatives Equilibrium dipole APT AAT 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 • B3LYP/6-311++G** • signs and relative intensities agree 1440x 1440y 1600x 1600y

tetraphenylporphyrin • B3LYP/6-311++G**/6-31G** • 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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Advanced Spectroscopy: Computation of Magnetic Vibrational Circular Dichroism