A computational protocol utilizing density functional theory calculations, including Poisson-Boltzmann implicit solvent and free energy corrections, is applied to study the thermodynamic and kinetic energy landscape of glycolaldehyde in solution. Comparison is made to NMR measurements of dissolved glycolaldehyde, where the initial dimeric ring structure interconverts among several species before reaching equilibrium where the hydrated monomer is dominant. There is good agreement between computation and experiment for the concentrations of all species in solution at equilibrium, that is, the calculated relative free energies represent the system well. There is also relatively good agreement between the calculated activation barriers and the estimated rate constants for the hydration reaction. The computational approach also predicted that two of the trimers would have a small but appreciable equilibrium concentration (>0.005 M), and this was confirmed by NMR measurements. Our results suggest that while our computational protocol is reasonable and may be applied to quickly map the energy landscape of more complex reactions, knowledge of the caveats and potential errors in this approach need to be taken into account.

Density functional theory calculations, including Poisson-Boltzmann implicit solvent and free energy corrections, are applied to study the thermodynamic and kinetic free energy landscape of formaldehyde oligomerization up to the C4 species in aqueous solution at pH 7. Oligomerization via C-O bond formation leads to linear polyoxymethylene (POM) species, which are the most kinetically accessible oligomers and are marginally thermodynamically favored over their oxane ring counterparts. On the other hand, C-C bond formation via aldol reactions leads to sugars that are thermodynamically much more stable in free energy than POM species; however, the barrier to dimerization is very high. Once this initial barrier is traversed, subsequent addition of monomers to generate trimers and tetramers is kinetically more feasible. In the aldol reaction, enolization of the oligomers provides the lowest energy pathway to larger oligomers. Our study provides a baseline free energy map for further study of oligomerization reactions under catalytic conditions, and we discuss how this will lead to a better understanding of complex reaction mixtures with multiple intermediates and products.

While previous research on the structural modes of gamelan gongs has revealed important insight into its unique acoustics, little attention has been dedicated to study the directionality of their acoustic radiation. This study compares high-angular resolution spherical directivity measurements of two Balinese gamelan gongs of different sizes. The directional characteristics are usually closely connected with measured structural modes at both low and high frequencies. However, the directivities of the large and small gong for the same structural mode shape are not always consistent, particularly at higher frequencies. Thus, changes in modal frequencies due to the scaling of the gongs do not always indicate similar acoustical radiation patterns.

No abstract

The directivity function of a played musical instrument describes the angular dependence of its acoustic radiation and diffraction about the instrument, musician, and musician’s chair. In this study, high angular resolution directivity data were acquired in an anechoic chamber of a muted trumpet being played by a seated musician. The chair height and horizontal displacement ensured that the geometric center of the instrument’s radiating region fell at the circular center of a computer-controlled semi-circular array of 36 microphones positioned at Δθ = 5° polar-angle increments. Azimuthal rotations progressed in Δφ = 5° increments, such that the measurements involved 2,521 unique positions over a sphere. Additional measurements at a position within the rotating reference frame facilitated post-processing. The musician played chromatic scales at each rotation position, and this process was repeated for straight, cup, and wow wow mutes in order to draw comparisons in the directivity patterns of each mute to the unmuted trumpet. Radiation behind the musician increased as a result of the mute, and mute-dependent changes to the directivity patterns primarily occurred above 1 kHz.