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The ethoxy and cyano groups are able to delocalize the radical ion in the transition state, thus stabilizing the radical center. The rate enhancement is due to the captodative effect. When R = H, the reaction has the largest energy of activation because the radical center is not stabilized by the captodative effect.
The first Dahlquist barrier states that a zero-stable and linear q-step multistep method cannot attain an order of convergence greater than q + 1 if q is odd and greater than q + 2 if q is even. If the method is also explicit, then it cannot attain an order greater than q (Hairer, Nørsett & Wanner 1993, Thm III.3.5).
This is more than the naive π-bond order of (for a total bond order of ) that one might guess when simply considering the Kekulé structures and the usual definition of bond order in valence bond theory. The Hückel definition of bond order attempts to quantify any additional stabilization that the system enjoys resulting from delocalization.
The Z group primarily affects the stability of the S=C bond and the stability of the adduct radical (Polymer-S-C•(Z)-S-Polymer, see section on Mechanism). These in turn affect the position of and rates of the elementary reactions in the pre- and main-equilibrium.
In the control system theory, the Routh–Hurwitz stability criterion is a mathematical test that is a necessary and sufficient condition for the stability of a linear time-invariant (LTI) dynamical system or control system. A stable system is one whose output signal is bounded; the position, velocity or energy do not increase to infinity as ...
The radical cyclization step usually involves the attack of a radical on a multiple bond. After this step occurs, the resulting cyclized radicals are quenched through the action of a radical scavenger, a fragmentation process, or an electron-transfer reaction. Five- and six-membered rings are the most common products; formation of smaller and ...
For higher degree polynomials the extra computation involved in this mapping can be avoided by testing the Schur stability by the Schur-Cohn test, the Jury test or the Bistritz test. Necessary condition: a Hurwitz stable polynomial (with real coefficients ) has coefficients of the same sign (either all positive or all negative).
The phosphinyl radicals synthesised by Lappert and co-workers were found to be stable at room temperature for periods of over 15 days with no effect from short-term heating at 360 K. [4] This stability was assigned to the steric bulk of the substituents and the absence of beta-hydrogen atoms.