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Compounds from the 2,2′-bipyridine molecular family were investigated for use as redox-active materials in organic flow batteries. For 156 2,2′-bipyridine derivatives reported in the academic literature, we calculated the redox potential, the pKa for the second deprotonation reaction, and the solubility in aqueous solutions. Using experimental data on a small subset of derivatives, we were able to calibrate our calculations. We find that functionalization with electron-withdrawing groups leads to an increase of the redox potential and to an increase of the molecular acidity (as expressed in a reduction of the pKa value for the second deprotonation step). Furthermore, calculations of solubility in water indicate that some of the studied derivatives have adequate solubility for flow battery applications. Based on an analysis of the phyisco-chemical properties of the 156 studied compounds, we down-select five molecules with carbonyl- and nitro-based functional groups, whose parameters are especially promising for potential applications as negative redox-active materials in organic flow batteries. [ABSTRACT FROM AUTHOR]

Solutions to the radial Schrödinger equation of a particle in a quantum corral are used to probe how the statistical correlation between the position, and the momentum of the particle depends on the effective potential. The analysis is done via the Wigner function and its Shannon entropy. We show by comparison to the particle-in-a-box model that the attractive potential increases the magnitude of the correlation, while a repulsive potential decreases the magnitude of this correlation. Varying the magnitude of the repulsive potential yields that the correlation decreases with a stronger repulsive potential. [ABSTRACT FROM AUTHOR]

Shannon entropies of the pair density, conditional entropies, and mutual information are studied in position and in momentum space for ground state neutral atoms and selected excited states at the Hartree-Fock level. We show that the mutual information, a measure of correlation, is larger in position space than in momentum space. This result also holds for a mutual information defined in terms of the exchange density; however, these quantities display much more structure than the corresponding ones based on the pair densities. The interpretation of this behavior is that exchange effects are smaller in momentum space than in position space in these systems. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011 [ABSTRACT FROM AUTHOR]

The sums of position- and momentum-space mutual information measures are used to examine the pairwise and higher-order statistical correlation in the ground states of N-particle coupled oscillators. Analytical expressions for these measures are shown to be related to the logarithmic interaction energies of these states, plus those of mirror states where the intensities of the one- and two-body potentials are interchanged, and the nature of the attractive or repulsive interaction is opposite to that in the original state. The measures separate the contributions from the interactions and those from the effective interactions due to marginalization into different terms. The pairwise mutual information sum is linearly related to the Shannon entropy sum in two particle systems, while the total correlation sum exhibits a similar relationship in three particle ones. In the latter instance, the interaction information sum can be related to entropy differences. This illustrates how entropy sums are connected to correlation measure sums in these systems. All measures approach zero with large N, when the magnitudes of the one- and two-body potentials are fixed. The pair mutual information and total correlation sums decay monotonically with N in the presence of an attractive potential and monotonically increase with a repulsive potential. On the other hand, the interaction information sum exhibits a minimum at small N, with an attractive potential. This is a consequence of the higher-order correlations governing behavior at smaller N while the pairwise ones dominate at larger N. Results are presented when the magnitude of the one-body potential is set to N.