Electronic and Molecular Structures of Polyheteroles: II. Aromaticity and Quinoidicity

Abstract

We study the dynamics of a few stochastic learning strategies for the 'Kolkata Paise Restaurant' problem, where N agents choose among N equally priced but differently ranked restaurants every evening, such that each agent tries to get dinner in the best restaurant (with each restaurant serving only one customer and the rest of the customers arriving there going without dinner that evening). We consider the learning strategies to be similar for all the agents, and assume that each follows the same probabilistic or stochastic strategy dependent on information about past successes in the game. We show that some 'naive' strategies lead to much better utilization of services than some relatively 'smarter' strategies. We also show that a service utilization fraction as high as 0.80 can result for a stochastic strategy, where each agent sticks to his past choice (independent of success achieved or not, with probability decreasing inversely in the past crowd size). The numerical results for the utilization fraction of the services in some limiting cases are analytically examined.

Tellurophenes with Delocalized π-Systems and Their Extended Valence Adducts

“…This is particularly true of tellurophene-containing π-conjugated materials, even though they have certain advantages relative to their lighter analogs due to the unique chemistry of tellurium. These advantages include red-shifted optical absorption properties, − unique solid-state supramolecular structures through tellurium–tellurium interactions, − and high polarizability. , …”

Polytellurophenes

“…Specifically, tellurophene has a narrow HOMO-LUMO gap and thus polytellurophenes have been predicted to have redshifted optical absorption properties. [31,32] Tellurium is a metalloid and forms strong Te-Te interactions. [33][34][35][36] Therefore, polytellurophenes should be capable of supramolecular interactions that lead to strong interchain electronic coupling and can further control the structure and properties.…”

“…Polytellurophenes, however, do have potential advantages as polymer semiconductors. Specifically, tellurophene has a narrow HOMO–LUMO gap and thus polytellurophenes have been predicted to have red‐shifted optical absorption properties 31, 32. Tellurium is a metalloid and forms strong Te–Te interactions 33–36.…”

Polytellurophenes with Properties Controlled by Tellurium‐Coordination

“…Specifically, tellurophene has a narrow HOMO-LUMO gap and thus polytellurophenes are predicted to have desirable light-absorption properties. [6] Tellurium is a metalloid with relatively large spin-orbit coupling, therefore polytellurophenes should have easily populated triplet excited states. [7] Indeed, there are some excellent examples of transition metal containing polymers that have these favorable properties.…”