Game of Frontier Orbitals: A View on the Rational Design of Novel Charge-Transfer Materials

Since the first application of frontier molecular orbitals (FMOs) to rationalize stereospecificity of pericyclic reactions, FMOs have remained at the forefront of chemical theory. Yet, the practical application of FMOs in the rational design and synthesis of novel charge transfer materials remains under-appreciated. In this Perspective, we demonstrate that molecular orbital theory is a powerful and universal tool capable of rationalizing the observed redox/optoelectronic properties of various aromatic hydrocarbons in the context of their application as charge-transfer materials. Importantly, the inspection of FMOs can provide instantaneous insight into the interchromophoric electronic coupling and polaron delocalization in polychromophoric assemblies, and therefore is invaluable for the rational design and synthesis of novel materials with tailored properties

A characterization of quasi-rational polygons

The aim of this paper is to study quasi-rational polygons related to the outer billiard. We compare different notions introduced, and make a synthesis of those.Comment: 15 pages, 9 figure

3. Bonaventura and Medieval Mysticism

Throughout the whole history of religious experience there have been two supplementary emphases, the rational and the non-rational, which have vied with each other for men\u27s allegiance. The Thomistic synthesis, with its stress on reason and how reason could prove the existence of God, was thought by many, including St. Bonaventura (1221-1274), to press too far the rational side of religion and thus to detract from the other side, which emphasizes the free g~it of faith, intuitive insight, and mystical experience. This rational emphasis, thought Bonaventura, could lead to intellectual pride and arrogance. It could also lead to a minimizing of that aspect of God which his Augustinian and Neoplatonic leanings led him to stress: the absolute sovereignty of God. [excerpt

Operational transconductance amplifier-based nonlinear function syntheses

It is shown that the operational transconductance amplifier, as the active element in basic building blocks, can be efficiently used for programmable nonlinear continuous-time function synthesis. Two efficient nonlinear function synthesis approaches are presented. The first approach is a rational approximation, and the second is a piecewise-linear approach. Test circuits have been fabricated using a 3- mu m p-well CMOS process. The flexibility of the designed and tested circuits was confirme

Synthesis with rational environments

Synthesis is the automated construction of a system from its specification. The system has to satisfy its specification in all possible environments. The environment often consists of agents that have objectives of their own. Thus, it makes sense to soften the universal quantification on the behavior of the environment and take the objectives of its underlying agents into an account. Fisman et al. introduced rational synthesis: the problem of synthesis in the context of rational agents. The input to the problem consists of temporal logic formulas specifying the objectives of the system and the agents that constitute the environment, and a solution concept (e.g., Nash equilibrium). The output is a profile of strategies, for the system and the agents, such that the objective of the system is satisfied in the computation that is the outcome of the strategies, and the profile is stable according to the solution concept; that is, the agents that constitute the environment have no incentive to deviate from the strategies suggested to them. In this paper we continue to study rational synthesis. First, we suggest an alternative definition to rational synthesis, in which the agents are rational but not cooperative. We call such problem strong rational synthesis. In the strong rational synthesis setting, one cannot assume that the agents that constitute the environment take into account the strategies suggested to them. Accordingly, the output is a strategy for the system only, and the objective of the system has to be satisfied in all the compositions that are the outcome of a stable profile in which the system follows this strategy. We show that strong rational synthesis is 2ExpTime-complete, thus it is not more complex than traditional synthesis or rational synthesis. Second, we study a richer specification formalism, where the objectives of the system and the agents are not Boolean but quantitative. In this setting, the objective of the system and the agents is to maximize their outcome. The quantitative setting significantly extends the scope of rational synthesis, making the game-theoretic approach much more relevant. Finally, we enrich the setting to one that allows coalitions of agents that constitute the system or the environment

OTA-based non-linear function approximations

The suitability of operational transconductance amplifiers (OTAs) as the main active element to obtain basic building blocks for the design of programmable nonlinear continuous-time networks is examined. The main purpose is to show that the OTA, as the active element in basic building blocks, can be efficiently used for nonlinear continuous-time function synthesis. Two efficient nonlinear function synthesis approaches are presented. The first approach is a rational approximation, and the second is a piecewise-linear approach. Test circuits have been integrated using a 3-μm p-well CMOS process. The flexibility of the designed and tested circuits is confirmed