A two-chromophore model for two-photon circular dichroism

A discussion of two-photon circular dichroism due to dissymmetrically placed chromophores is presented. Using quantum electrodynamics, expressions are derived for the differential rates or absorption associated with an electronic transition which is electric dipole forbidden to a one-photon interaction. A complex field formulation enables effective interaction operators to be derived which are formally equivalent to those arising in the theory of induced circular dichroism. For non-equivalent chromophores, it is shown that a coupling mechanism provides the necessary chiral discrimination, whilst for equivalent chromophores there is an additional contribution from an interference term which becomes more important as the chromophore separation is decreased.     

Ab initio derivative calculation of vibrational circular dichroism

The recent formalism of Stephens for the calculation of rotational strength in vibrational circular dichroism has been implemented, exploiting the analytical derivative technique for ab initio Hartree-Fock wavefunctions.     

Laser mass spectrometry with circularly polarized light: two-photon circular dichroism

Extensive studies of two-photon circular dichroism (TPCD) on 3-methylcyclopentanone are presented following the first TPCD experiment of gas phase molecules by Compton et al. [J. Chem. Phys.125 (2006) 144304]. (2 + 1)-Multiphoton ionization in a specially designed time-of-flight mass analyzer has been used to perform these studies. CD of two-photon transitions from the molecular ground state to low lying Rydberg states is strongly enhanced with respect to corresponding one-photon transitions in good agreement with Compton. Differences between CD values determined via the molecular ion and via fragment ions indicate strong molecular ion CD effects. This would be the first time that circular dichroism of isolated molecular ions has been measured.     

Ab initio study of the two-photon circular dichroism in chiral natural amino acids

Two-photon circular dichroism spectra calculated within an origin-invariant density functional theory approximation in the absorption region where the lowest electronic excited states appear are presented for all 19 essential amino acids in the gas phase. A comparison of intensities and characteristic features is made with the corresponding two-photon absorption and one-photon circular dichroism spectra for each species. Also, the contributions of the electric dipole, magnetic dipole, and electric quadrupole transitions to the rotational strengths are analyzed in some detail. The remarkable fingerprinting capabilities of the two-photon circular dichroism spectroscopy are highlighted.     

Ab initio study of the one- and two-photon circular dichroism of R-(+)-3-methyl-cyclopentanone

One- and two-photon circular dichroism spectra of R-(+)-3-methyl-cyclopentanone, a system that has been the subject of recent experimental studies of (2+1) resonance-enhanced multiphoton ionization circular dichroism, have been calculated with an origin-invariant density functional theory approximation in the region of the lowest electronic excited states, both for the gas phase and for a selection of solvents. A polarizable continuum model is used in the calculations performed on the solvated system. Two low-lying conformers are analyzed, and a comparison of the intensities and characteristic features is made with the corresponding two-photon absorption for each species, also for the Boltzmann-averaged spectra. The effect of the choice of geometry, basis set, and exchange-correlation functional is carefully analyzed. It is found that a density functional theory approach using the Coulomb attenuating method variant of Becke's three-parameter exchange and the Lee-Yang-Parr correlation functionals with correlation-consistent basis sets of double-zeta quality can reproduce the experimental electronic circular dichroism spectra very well. The features appearing in experiment are characterized in terms of molecular excitations, and the differences in the response of each state in the one- and two-photon processes are highlighted.     

Theoretical calculation of electronic circular dichroism of the rotationally restricted 3,8'-biflavonoid morelloflavone

Theoretical calculation of electronic circular dichroism (ECD) of the rotationally restricted 3,8'-biflavonoid (+)-morelloflavone using time dependent density functional theory (TDDFT), performed at 298 K at B3LYP-SCRF/6-31G*//B3LYP/6-31G* level with COSMO model, permitted unequivocal assignment of its 2R,3S absolute configuration. The experimentally observed Cotton effect (CE) around 290 nm is contributed by the acetophenone pi --> pi* transition of the ABC-flavanone moiety and the electronic transition within the DEF-flavone moiety, while another diagnostic positive CE around 350 nm is attributable to the electronic interaction between the ABC-flavanone moiety and the DEF-flavone moiety, as well as the electronic transition within the DEF-flavone moiety. The remarkable differences of the calculated ECD of its two rotamers indicate that the rotational restrictions significantly affect the ECD of 3,8'-biflavonoids. Empirical ECD rules derived from monomeric flavonoids may not be applicable to configurational assignment of complex 3,8'-biflavonoids. This study has provided new insights in interpreting the experimentally observed ECD spectra of this class of compounds.     

Ab initio calculation of the C/D ratio of magnetic circular dichroism

A procedure for calculating the magnetic circular dichroism C/D ratio from density functional theory calculations is discussed. The method is simplified considerably through the application of group theory and the irreducible-tensor method and only requires integrals of the magnetic dipole moment operator over a few orbitals and published tables of symmetry factors. The implementation of the method is tested through application to several small and medium-sized molecules.     

Ab initio calculation of electronic circular dichroism fortrans-cyclooctene using London atomic orbitals

Summary The second-quantization magnetic dipole operator that arises when London atomic orbitals are used as basis functions is derived. In atomic units, the magnetic dipole operator is defined as the negative of the first derivative of the electronic Hamiltonian containing the interaction with the external magnetic field. It is shown that for finite basis sets, the gauge origin dependence of the resulting magnetic dipole operator is analogous to that of the exact operator, and that the derived operator converges to the exact operator in the limit of a complete basis set. It is also demonstrated that the length expression for the rotatory strength in linear response calculations gives gauge-origin-independent results. Sample calculations ontrans-cyclooctene and its fragments are presented. Compared to conventional orbitals, the basis set convergence of the rotatory strengths calculated in the length form using London atomic orbitals is favourable. The rotatory strength calculated fortrans-cyclooctene agrees nicely with the corresponding experimental circular dichroism spectrum, but the spectra for the fragment molecules show little resemblance with that oftrans-cyclooctene.Dedicated to Prof. Jan Linderberg     

On the calculation of circular dichroism spectra using quantum wave-packet dynamics with an application to molecular dimers

Circular dichroism (CD) spectra are calculated from the Fourier transform of a time-correlation function. The latter can efficiently be evaluated by wave-packet propagation methods. This approach is similar to the time-dependent evaluation of absorption or Raman spectra. As an application, correlation functions and CD spectra for a molecular dimer are determined and compared to the case of absorption.     

Angular dependence of the scattering contribution to circular dichroism

The theory of the angular dependence of the difference between scattering of left- and right-circularly polarized light by optically active spheres is discussed. This difference is significant primarily in the forward scattering directions. It is shown that instrument geometry can markedly affect the observed circular dichroism spectrum of a suspension.     

Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism: calculation of B terms

Magnetically perturbed time-dependent density functional theory is applied to the calculation of the magnetic circular dichroism (MCD) B terms of closed shell molecules. Two approaches to evaluating B term parameters are described: a sum-over-states-type approach and an approach based on the direct solution of the matrix equations. The advantages and disadvantages and technical challenges of each approach are described. The interpretation of the parameters in terms of ground and excited state perturbations are discussed. Several applications of the methodology are described. Calculations of the MCD of ethene are used to compare the sum-over-states and direct solution approaches and to illustrate the potential for analysis. The other applications involving azabenzes, sulfur-nitrogen heterocycles and quinone molecules are compared with experiment and other theoretical calculations. For the most part, all important features of the observed spectra are reproduced.     

Vibrational circular dichroism in the mid-infrared

Vibrational circular dichroism (VCD) has been measured for the First tune in the CH₂ bending region down to 1250 cm^?1. This advance in technique was facilitated by the addition of a carbon-rod light source, a cooled HgCdTe detector, and signal averaging to our instrument.     

Induced circular dichroism of azulene

The π→π^* absorption bands of azulene show circular dichroism in the presence of (+)-nopinone.     

Photoacoustic detection of circular dichroism

An analysis is presented for an experimental technique involving the measurement of circular dichroism using polarization-modulated photoacoustic spectroscopy. The technique is referred to as photoacoustic circular dichroism (PACD). In the PACD experiment, a photoacoustic signal is induced by using polarization-modulated excitation light which is alternately left-and right-circularly polarized. Expression appropriate for analyzing the PACD experimental observables (signal strength and phase) in terms of sample circular dichroism are developed within the general framework of the Rosencwaig and Gersho model for the photoacoustic effect in solids and liquids. Calculations based on these expressions are reported and the applicability of PACD for measuring the circular dichronic properties of optically opaque samples is discussed.     

Magnetic vibrational circular dichroism of the haloforms

The magnetic vibrational circular dichroism of the three haloforms, CHCl₃ CHBr₃ and CHI₃, is presented. In the a¹ symmetry C-H stretch B₀/D₀ increases from <10^t̄6 to ≈ 3 × 10⁻⁵/cm⁻¹ from Cl to I. These values are correlated to ΔE for electronic excitation and to the methyl halide results.     

Exploring the ability of frozen-density embedding to model induced circular dichroism

In this study, we present calculations of the circular dichroism (CD) spectra of complexes between achiral and chiral molecules. Nonzero rotational strengths for transitions of the nonchiral molecule are induced by interactions between the two molecules, which cause electronic and/or structural perturbations of the achiral molecule. We investigate if the chiral molecule (environment) can be represented only in terms of its frozen electron density, which is used to generate an effective embedding potential. The accuracy of these calculations is assessed in comparison to full supermolecular calculations. We can show that electronic effects arising from specific interactions between the two subsystems can reliably be modeled by the frozen-density representation of the chiral molecule. This is demonstrated for complexes of 2-benzoylbenzoic acid with (-)-(R)-amphetamine and for a nonchiral, artificial amino acid receptor system consisting of ferrocenecarboxylic acid bound to a crown ether, for which a complex with l-leucine is studied. Especially in the latter case, where multiple binding sites and interactions between receptor and target molecule exist, the frozen-density results compare very well with the full supermolecular calculation. We also study systems in which a cyclodextrin cavity serves as a chiral host system for a small, achiral molecule. Problems arise in that case because of the importance of excitonic couplings with excitations in the host system. The frozen-density embedding cannot describe such couplings but can only capture the direct effect of the host electron density on the electronic structure of the guest. If couplings play a role, frozen-density embedding can at best only partially describe the induced circular dichroism. To illustrate this problem, we finally construct a case in which excitonic coupling effects are much stronger than direct interactions of the subsystem densities. The frozen density embedding is then completely unsuitable.