A configurational and conformational study of aframodial and its diasteriomers via experimental and theoretical VA and VCD spectroscopies

In this work we present the experimental and theoretical vibrational absorption (VA) and the theoretical vibrational circular dichroism (VCD) spectra for aframodial. In addition, we present the theoretical VA and VCD spectra for the diasteriomers of aframodial. Aframodial has four chiral centers and hence has 2⁴ = 16 diasteriomers, which occur in eight pairs of enantiomers. In addition to the four chiral centers, there is an additional chirality due to the helicity of the entire molecule, which we show by presenting 12 configurations of the 5S,8S,9R,10S enantiomer of aframodial. The VCD spectra for the diasteriomers and the 12 configurations of one enantiomer are shown to be very sensitive not only to the local stereochemistry at each chiral center, but in addition, to the helicity of the entire molecule. Here one must be careful in analyzing the signs of the VCD bands due to the ‘non-chiral’ chromophores in the molecule, since one has two contributions; one due to the inherent chirality at the four chiral centers, and one due to the chirality of the side chain groups in specific conformers, that is, its helicity. Theoretical simulations for various levels of theory are compared to the experimental VA recorded to date. The VCD spectra simulations are presented, but no experimental VCD and Raman spectra have been reported to date, though some preliminary VCD measurements have been made in Stephens’ lab in Los Angeles. The flexible side chain is proposed to be responsible for the small size of the VCD spectra of this molecule, even though the chiral part of the molecule is very rigid and has four chiral centers. In addition to VCD and Raman measurements, Raman optical activity (ROA) measurements would be very enlightening, as in many cases bands which are weak in both the VA and VCD, may be large in the Raman and/or ROA spectra. The feasibility of using vibrational spectroscopy to monitor biological structure, function and activity is a worthy goal, but this work shows that a careful theoretical analysis is also required, if one is to fully utilize and understand the experimental results. The reliability, reproduceability and uniqueness of the vibrational spectroscopic experiments and the information which can be gained from them is discussed, as well as the details of the computation of VA, VCD and Raman (and ROA) spectroscopy for molecules of the complexity of aframodial, which have multiple chiral centers and flexible side chains. Festschrift in Honor of Philip J. Stephens’ 65th Birthday.     

Conservative methods for the Toda lattice equations

We are concerned with the numerical integration of the Todalattice equations by using different conservative methods. Numericalexperiments suggest that the global error for isospectral schemesdecreases exponentially with time but it is almost constantfor either symplectic or more general integrators. We providea theoretical explanation for these experimental findings.