Radical stabilization: Synthesis and decomposition of a β-ketodiazene

The synthesis and decomposition of bis(1,1-dimethyl-2-oxo-2-phenylethyl)diazene ($\text{7e}$) is described. The presence of a carbonyl group adjacent to a radical center greatly enhances the radical stability.     

Branch-and-cut approaches for chance-constrained formulations of reliable network design problems

We study solution approaches for the design of reliably connected networks. Specifically, given a network with arcs that may fail at random, the goal is to select a minimum cost subset of arcs such the probability that a connectivity requirement is satisfied is at least $1 - \epsilon $ , where $\epsilon $ is a risk tolerance. We consider two types of connectivity requirements. We first study the problem of requiring an $s$ - $t$ path to exist with high probability in a directed graph. Then we consider undirected graphs, where we require the graph to be fully connected with high probability. We model each problem as a stochastic integer program with a joint chance constraint, and present two formulations that can be solved by a branch-and-cut algorithm. The first formulation uses binary variables to represent whether or not the connectivity requirement is satisfied in each scenario of arc failures and is based on inequalities derived from graph cuts in individual scenarios. We derive additional valid inequalities for this formulation and study their facet-inducing properties. The second formulation is based on probabilistic graph cuts, an extension of graph cuts to graphs with random arc failures. Inequalities corresponding to probabilistic graph cuts are sufficient to define the set of feasible solutions and violated inequalities in this class can be found efficiently at integer solutions, allowing this formulation to be solved by a branch-and-cut algorithm. Computational results demonstrate that the approaches can effectively solve instances on large graphs with many failure scenarios. In addition, we demonstrate that, by varying the risk tolerance, our model yields a rich set of solutions on the efficient frontier of cost and reliability.     

A branch-and-cut decomposition algorithm for solving chance-constrained mathematical programs with finite support

We present a new approach for exactly solving chance-constrained mathematical programs having discrete distributions with finite support and random polyhedral constraints. Such problems have been notoriously difficult to solve due to nonconvexity of the feasible region, and most available methods are only able to find provably good solutions in certain very special cases. Our approach uses both decomposition, to enable processing subproblems corresponding to one possible outcome at a time, and integer programming techniques, to combine the results of these subproblems to yield strong valid inequalities. Computational results on a chance-constrained formulation of a resource planning problem inspired by a call center staffing application indicate the approach works significantly better than both an existing mixed-integer programming formulation and a simple decomposition approach that does not use strong valid inequalities. We also demonstrate how the approach can be used to efficiently solve for a sequence of risk levels, as would be done when solving for the efficient frontier of risk and cost.     

Some results on the strength of relaxations of multilinear functions

We study approaches for obtaining convex relaxations of global optimization problems containing multilinear functions. Specifically, we compare the concave and convex envelopes of these functions with the relaxations that are obtained with a standard relaxation approach, due to McCormick. The standard approach reformulates the problem to contain only bilinear terms and then relaxes each term independently. We show that for a multilinear function having a single product term, this approach yields the convex and concave envelopes if the bounds on all variables are symmetric around zero. We then review and extend some results on conditions when the concave envelope of a multilinear function can be written as a sum of concave envelopes of its individual terms. Finally, for bilinear functions we prove that the difference between the concave upper bounding and convex lower bounding functions obtained from the McCormick relaxation approach is always within a constant of the difference between the concave and convex envelopes. These results, along with numerical examples we provide, give insight into how to construct strong relaxations of multilinear functions.     

Excitonic luminescence of hemiporphyrazines

Metal-free hemiporphyrazine (HpH(2)) is a notoriously insoluble material possessing interesting photophysical properties. Here we report the synthesis, structure, and photophysical properties of an octahedral zinc trans-ditriflate hemiporphyrazine complex "HpH(2)Zn(OTf)(2)" that contains a neutral hemiporphyrazine ligand. The photophysical properties of hemiporphyrazine are largely unaffected by introduction of zinc(II) triflate, but a dramatic increase in solubility is observed. HpH(2)Zn(OTf)(2) therefore provides a convenient model system to evaluate the impact of aggregation on the photophysical properties of hemiporphyrazine. Soluble aggregates and crystalline materials containing planar hemiporphyrazines exhibit relatively strong absorbance of visible light (450-600 nm) and red luminescence (600-700 nm). Hemiporphyrazine monohydrate (HpH(2)·H(2)O), in contrast, has a nonplanar "saddle-shaped" conformation that exhibits very little absorbance of visible light in solution or in the solid state. Upon photoexcitation at 380 nm, HpH(2)Zn(OTf)(2) and HpH(2) exhibit multiwavelength emissions centered at 450 and 650 nm. Emissions at 450 nm are highly anisotropic, while emissions at 650 nm are fully depolarized with respect to a plane-polarized excitation source. Taken together, our results suggest that excitonic coupling of aggregated and crystalline hemiporphyrazines results in increased absorbance and emission of visible light from S(0) ? S(1) transitions that are usually symmetry forbidden in isolated species. In contrast to previously proposed theories involving excited-state intramolecular proton transfer, we propose that the multiple-wavelength luminescent emissions of HpH(2)Zn(OTf)(2) and HpH(2) are due to emissive S(1) and S(2) states in aggregated and crystalline hemiporphyrazines. These results may provide a better understanding of the nonlinear optical properties of these materials in solution and in the solid state.