Diffusivity eigen

This approximation was denoted initially by the acronym IQG [34] and later on by IP (Independent Pairs) [35]. It gave satisfactory results in the study of the Beryllium atom and of its isoelectronic series as well as in the BeH system. The drawback of this approximation is that when the eigen-vectors are diffuse, i.e. there is more than one dominant two electron configuration per eigen-vector, the determination of the corresponding nj is ambiguous. In order to avoid this problem the MPS approximation, which does not have this drawback, was proposed. 

A normal proton transfer was defined by Eigen as one whose rate in the thermodynamically favourable direction was diffusion-controlled (Eigen, 1964). By use of relaxation techniques Eigen was able to show that many proton transfers involving oxygen and nitrogen acids and bases were in this category. If the reactions (5) of an acid (HA) with a series of bases (B-) shows normal proton-transfer behaviour, the rate coefficients in the forward... 

Importantly, carbonic anhydrase II is one of the most efficient biological catalysts known and it catalyzes the hydration of CO2 with a turnover rate of 10 sec at 25 C (Khalifah, 1971 Steiner et al, 1975). With kcaJKm = 1.5 X 10 sec carbonic anhydrase II is one of a handful of enzymes for which catalysis apparently approaches the limit of diffusion control. Since transfer of the product proton away from the enzyme to bulk solvent comprises a kinetic obstacle [an enzyme-bound group with ap/C, of about 7 cannot transfer a proton to bulk solvent at a rate faster than 10 sec (for a review see Eigen and Hammes, 1963)], the observed turnover rate of 10 sec" requires the participation of buffer in the proton transfer. 

And the best estimate of the eigen-functions ipn is obtained by minimising the variational integral, and is given by E . This well-known procedure can be extended from the Schrodinger equation to the diffusion equation, since, in effect, both are diffusion equations [499]. 

From the diffusion equation (9), the lowest eigen-function in the spherical volume is... 

The rate coefficient can be directly related to the current of the diffusing species up to the reaction radius R, but it is much more conveniently related to the relaxation of the lowest eigen-function... 

Ultrafast proton transfer. The diffusion-controlled limit for second-order rate constants (Section A3) is 1010 M 1 s 1. In 1956, Eigen, who had developed new methods for studying very fast reactions, discovered that protons and hydroxide ions react much more rapidly when present in a lattice of ice than when in solution.138 He observed second-order rate constants of 1013 to 1014 M 1 s These represent rates almost as great as those of molecular vibration. For example, the frequency of vibration of the OH bond in water is about 1014 s . The latter can be deduced directly from the frequency of infrared light absorbed in exciting this vibration Frequency v equals wave number (3710 cm-1 for -OH stretching) times c, the velocity of light (3 x 1010 cm s ). 

Most of the pKd values of free radicals have been determined by pulse radiolysis, and it is therefore useful to recall, how fast pK equilibria become established. In general, the reaction of H+ with an acid anion is practically diffusion-controlled [reaction (2) k ranging between 5 x 109 dm3 mol1 s1 and 5 X 1010 dm3 mol"1 s 1 (Eigen et al. 1964 Perrin et al. 1981)]. The same holds for the deprotonation of an acid by OH [reaction (3)]. The rates of reaction (4) can be calculated from the pKa value taking into account that Kw = [H+] x [OH ] = 1014 mol2 dm 6. 

Whereas base-induced deprotonation at a heteroatom is very fast (practically diffusion-controlled), deprotonation at carbon is generally much slower (Eigen et al. 1964, 1965). Thus, this type of 02 -elimination is observed at higher pH values compared to the reactions discussed before. The elimination of HO2 is subject to steric restrictions, but the OH -induced 02 -elimination is not, and at high pH all hydroxycyclohexadienylperoxyl radicals eliminate 02 bringing the phenolate yield close to 100% [reactions (9) and (14)/(15)] competing reactions (see below) are thereby suppressed. 

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