Is there an anisotropy factor (g factor) for TDDFT Abs and CD calculations?

Question

Experimentally, anisotropy factor is calculated by dividing the CD spectra by the absorbance spectra multiplying by a factor of 32980 (in order to get a nondimensional quantity)

Theoretical calculations can be performed via TDDFT to obtain rotatory and oscillatory strengths, obtaining excitations for each case and adjusting, for each excitation, a curve, obtaining then the "theoretical absorbance/CD spectra".

How can then we define a theoretical anisotropy factor, does it have sense? Should another calculation be performed?

Would you divide both adjusted curves or divide the corresponding excitations, adjusting a new set of curves to what you get?

Any clues?

Answer 1

One approach would be to divide the corresponding excitations as you mention. I would avoid adjusting curves to the absorbance and CD spectra first then dividing, as you would be introducing too many tunable parameters. This being said, the more common approach in the literature is to calculate the g_abs directly as the ratio of rotational strength to dipole strength at each transition, then fit a curve such as a sum of gaussians etc. Rotatory strength is given by; $$ R_{0n} = Im\{\mathbf{\mu_{0n}.m_{0n}}\}$$ Here $ \mathbf{\mu_{0n}}$ and $m_{0n}$ are the electric and magnetic transition dipole moments. This is often called the Rosenfeld equation, and is valid for isotropic samples, which most calculations of CD are concerned with. In most cases g_abs is then calculated approximately as $g_{abs}= \frac{4R}{D}$, where D is the dipole strength ($|\mu_{0n}|^{2} + |m_{0n}|^{2}$). For more theoretical details see Wakabayashi et al., J. Phys. Chem. A 2014, 118, 27, 5046–5057 or Molecular Light Scattering and Optical Activity by Laurence Barron. Some quantum chemical calculation programs give you the rotatory strength tensor, for Gaussian 09 it is given amongst the output under Excited states from <AA,BB:AA,BB> singles matrix: in the log file. Then there are a couple of ways of calculating R from this, which are given as R(velocity) and R(length), which are explained in Pederson and Hansen, Chem. Phys. Lett., 246 (1995) 1-8. The velocity method is, as I understand it, more suited to this problem.