Conditional bond state probability

The probability for a conformation of an unperturbed chain of n C-C bonds on the underlying diamond lattice can be expressed in terms of the probability for state r) at the second bond and the conditional probability for state 7] at bond i (2 < i < n), given state at the preceding bond. These probabilities, which are usually denoted by p,/ 2 and q , respectively, are extracted from 2 of Eq. (4.1) using the conventional partial derivatives [35,36]. Then the probability, p, for a specified conformation of the entire chain is ... 

When the transfer reaction competes successfully with further insertion, as in the case of nickel, dimerization becomes the dominant transformation. When metal hydride elimination, in turn, is slow relative to insertion, polymeric macromolecules are formed. Ligand modification, the oxidation state of the metal, and reaction conditions affect the probability of the two reactions. Since nickel hydride, like other metal hydrides, catalyzes double-bond migration, isomeric alkenes are usually isolated. 

Since the donor strength of duroquinone is rather small, the capacity of the nickel atom in stabilizing two duroquinone molecules by dative n bonding is probably limited. The situation is similar to that in the nickel complexes of the 1,1-dicyano- and 1,1,2-tricyanoethylenes which also form only 1 1 complexes (Section IV, B, 3). During thermal decomposition of (XX) monomeric, coordinately unsaturated Ni(duroquinone) is formed. This species is evidently very reactive and rapidly associates to (XXI). It may be trapped in the monomeric state if generated in the presence of electron donors such as cyclic dienes and some phosphines. Under these conditions new complexes of composition olefin-Ni(0)-duroquinone and (phosphine)2-Ni(0)-duroquinone are formed (55, 56, 57). 

The reactant R2 can also be considered to be a solvent molecule. The global kinetics become pseudo first order in Rl. For a SNl mechanism, the bond breaking in R1 can be solvent assisted in the sense that the ionic fluctuation state is stabilized by solvent polarization effects and the probability of having an interconversion via heterolytic decomposition is facilitated by the solvent. This is actually found when external and/or reaction field effects are introduced in the quantum chemical calculation of the energy of such species [2]. The kinetics, however, may depend on the process moving the system from the contact ionic-pair to a solvent-separated ionic pair, but the interconversion step takes place inside the contact ion-pair following the quantum mechanical mechanism described in section 4.1. Solvation then should ensure quantum resonance conditions. 

Reaction of aldehydes and ketones with iminoboranes has been widely investigated. Conditions for the [2 + 2]-cycloaddition between XBNR and R R"CO are relatively good stability of the iminoborane and lack of enolic protons in the oxo compound [Eq. (46)] 14, 19). Relatively less stable iminoboranes, but in some cases the stable ones too, may react with 0X0 compounds by a total opening of the B=N triple bond [Eq. (43)], presumably via a [2 + 2]-cycloaddition [Eq. (42)] (Section V,D). A relatively stable iminoborane and a ketone containing enolic protons may yield an open-chain product, probably through a six-membered cyclic transition state [Eq. (46b)] 19). 

These estimations engage the assumption that any additional effects due to bending vibrations will tend to contribute relatively weakly to the isotope effect. In fact, however, the above estimates are probably only ball park estimates, in that coupling of molecular vibrations of multiatomic molecules is ignored Another key point is that a covalent bond need not be completely broken in the transition state, and two isotopic isomers may behave slightly differently in the transition state. Jencks discusses this matter as well as the problem of nonlinear transition states, a condition that takes into account the fact that bending frequencies often lessen the developed magnitude of isotope effects. 

Nitrenes,239 R—N, are the nitrogen analogs of carbenes, and most of what we have said about carbenes also applies to them. Nitrenes are too reactive for isolation under ordinary conditions. Alkyl nitrenes have been isolated by trapping in matrices at 4 K,24n while aryl nitrenes, which are less reactive, can be trapped at 77 K.241 The ground state of NH, and probably of most nitrenes,242 is a triplet, though nitrenes can be generated in both triplet and singlet states. In additions of EtOOC—N to C=C double bonds two species are involved,... 

The Ufson-Roig matrix theory of the helix-coil transition In polyglycine is extended to situations where side-chain interactions (hydrophobic bonds) are present both In the helix and in the random coil. It is shown that the conditional probabilities of the occurrence of any number and size of hydrophobic pockets In the random coil can be adequately described by a 2x2 matrix. This is combined with the Ufson-Roig 3x3 matrix to produce a 4 x 4 matrix which represents all possible combinations of any amount and size sequence of a-helix with random coil containing all possible types of hydrophobic pockets In molecules of any given chain length. The total set of rules is 11) a state h preceded and followed by states h contributes a factor wo to the partition function 12) a state h preceded and followed by states c contributes a factor v to the partition function (3) a state h preceded or followed by one state c contributes a factor v to the partition function 14) a state c contributes a factor u to the partition function IS) a state d preceded by a state other than d contributes a factor s to the partition function 16) a state d preceded by a state d contributes a factor r to the partition function. 

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