Stability of cascade search

Metal–Ligand Cooperative Reactivity in the (Pseudo)-Dearomatized PNx(P) Systems: The Influence of the Zwitterionic Form in Dearomatized Pincer Complexes

“…NICS(0) and NBO analyses have been employed to study the aromaticity of the relevant double-deprotonated PNP* pincer ligand, suggesting that the central pyridine ring is not aromatic, even though the ring has some significant contribution from the aromatic mesomeric form, enforced by the phosphorus-assisted hyperconjugation, i.e., lone pair C α‑P → σ* P‑CMe . The NICS analysis has been found to be useful in correlation with the activation energy and thermodynamic of the reactions, but it is noted that in comparison to NICS(0) iso NICS zz (1) based on the total contribution to the out-of-plane component of the NICS tensor is more reliable , when studying aromaticity, pseudoaromaticity, and antiaromaticity . The NICS zz (1) methodology has been proven to be extremely useful for identification of leading resonance structures and recognizing aromatic rings in complex polyaromatic hydrocarbons. ,, Moreover, the aromatic stabilization energy (ASE) correlates better with NICS(1) zz than with the NICS iso , given by equation E ASE = −0.604*NICS(1) zz , as suggested by von Ragué Schleyer et al based on the five-member ring analysis, even though the correlation between NICS and ASE for different ring sizes is not as straightforward. , …”

Каскадный Поиск Прообразов И Совпадений: Глобальная И Локальная Версии

“…В частности, были получены обобщения принципа Банаха неподвижной точки (принципа сжимающих отображений), а также ряда результатов Арутюнова [6], [7] о поиске и аппроксимации совпадений накрывающего и липшицева отображений метрических пространств. В [8]- [10] автором исследовались вопросы устойчивости предложенных методов каскадного поиска.…”