Beyond the Rosenfeld Equation: Computation of Vibrational Circular Dichroism Spectra for Anisotropic Solutions

Abstract

The difference in absorption of left and right circularly polarized light by chiral molecules can be described by the Rosenfeld equation for isotropic samples. It allows the assignment of the absolute stereochemistry by comparing experimental and computationally derived spectra. Despite the simple form of the Rosenfeld equation, its evaluation in the infrared regime remained challenging, as the contribution from the magnetic dipole operator is zero within the Born− Oppenheimer (BO) approximation. In order to resolve this issue, "beyond BO" theories had to be developed, among which Stephen's magnetic field perturbation (MFP) approach offers a computationally easily accessible form. In this work, optical activity is discussed for cylindrically symmetric solutions, which cannot be described anymore by Rosenfeld's equation due to broken spherical symmetry. Mathematical properties of natural and electric-field induced anisotropies are discussed on the basis of the gauge-independent theoretical framework of Buckingham and Dunn. The issue of achiral noise arising from external field perturbations is considered, and potential remedies are introduced. Natural anisotropic vibrational circular dichroism (VCD) equations are solved numerically by applying the MFP approach within the Hartree−Fock (HF) formalism. Properties of anisotropic VCD spectra are discussed for R-(+)-methyloxirane and (1S,2S)-cyclopropane-1,2-dicarbonitrile. In particular, by using a group theoretical argument, a gauge-independent lower bound for the quadrupole contribution of C 2 -symmetric molecules can be identified, which allows the importance of additional quadrupole terms in anisotropic VCD spectra calculation to be assessed.

Concentration Dependence of a Hydrogel Phase Formed by the Deprotonation of the Imidazole Side Chain of Glycylhistidylglycine

“…Note that anisotropic networks were reported for the gel phases of cationic GAG . Anisotropy is known to cause birefringence effects that influence recorded VCD and IR spectra. , While newer instruments are capable of correcting birefringence effects, the spectrometer model used in this study does not fully eliminate them. Thus, to probe for the influence of birefringence on the recorded spectra, we recorded the spectra for three different orientations of the sample termed R1, R2, and R3, which differ by ca.…”

“…26 Anisotropy is known to cause birefringence effects that influence recorded VCD and IR spectra. 40,41 While newer instruments are capable of correcting birefringence effects, the spectrometer model used in this study does not fully eliminate them. Thus, to probe for the influence of birefringence on the recorded spectra, we recorded the Concentration of deprotonated GHG calculated as a function of pH by means of eq 1 for 75 mM (green short dash), 175 mM (red long dash), and 300 mM (black line) total GHG concentration.…”

Comparative rotatory power of bent and twisted polyynes

“…Increasingly, chiroptics has extended its purview to organized systems where the wave vector of the incident light mixes the moments in some directions. 33,[38][39][40][41][42][43][44][45] The scalar product of cross products of the wave vector and the transition dipole moments determines the sign of the response in oriented systems. These values are equal and opposite for some optically active, non-enantiomorphous point groups.…”

“…m is proportional to optical activity only applies to the spatial average measured for molecules rapidly randomly reorienting. Increasingly, chiroptics has extended its purview to organized systems where the wave vector of the incident light mixes the moments in some directions 33,38–45 . The scalar product of cross products of the wave vector and the transition dipole moments determines the sign of the response in oriented systems.…”

Vibrational Circular Dichroism Spectroscopy of Chiral Molecular Crystals: Insights from Theory

“…Recently, Sidler et al. showed how significant quadrupolar contributions to VCD can become in anisotropic solutions, which opens up a range of possible new applications [2, 81] …”