Molecular pairing

Rahman T S, Knox R S and Kenkre V M 1979 Theory of depolarization of fluorescence in molecular pairs Chem. Phys. 44 197-211... 

Knox R S and Gulen D 1993 Theory of polarized fluorescence from molecular pairs Photochem. Photobiol. 57 40-3... 

In Eq. (4-215), ky is an empirical interaction parameter specific to an i-J molecular pair. When i = J and for chemically similar species, ky = 0. Otherwise, it is a small (usually) positive number ev uated from minimal PVT data or in the absence of data set equal to zero. 

At the simplest level the orientational correlation of molecular pairs can be characterised by the averages of the even Legendre polynomials Pl(cos J ij) where is the angle between the symmetry axes of molecules i and j separated by a distance r. This correlation coefficient is denoted by... 

In the crystal of 7 OEt, two molecules form a molecular pair as is the case in the crystal of 7 OMe. Considering the intermolecular distances between the ethylenic double bonds (3.714 and 3.833 A within the pair, and 4.734 and 4.797 A between the pairs), each molecule can react only with its partner in the molecular pair and not with any molecule of another pair. Since paired molecules are related by centrosymmetry, two pairs of facing ethylenic double bonds should be equal in photoreactivity, affording two... 

Great simplification is achieved by introducing the hypothesis of independent reaction times (IRT) that the pairwise reaction times evolve independendy of any other reactions. While the fundamental justification of IRT may not be immediately obvious, one notices its similarity with the molecular pair model of homogeneous diffusion-mediated reactions (Noyes, 1961 Green, 1984). The usefulness of the IRT model depends on the availability of a suitable reaction probability function W(r, a t). For a pair of neutral particles undergoing fully diffusion-con-trolled reactions, Wis given by (a/r) erfc[(r - a)/2(D t)1/2] where If is the mutual diffusion coefficient and erfc is the complement of the error function. 

An approach, similar to that employed in the analysis of tartrate mixtures, has been used for the chiral discrimination of amino acid (M/j/s) mixtures, using an amino acid of defined configuration as reference (S). The proton-bound trimers [S2-M H]+ form [S M H]+ and [S2H]+ fragments upon CID or MIKE decay (equations (9)-(12)). With two independent measurements of the fragmentation ratio [S-M-H] /[S2H] from either [S2-M -H] and [52-M5-H]" , the differences in binding energies can be determined. The relative gas phase basicities (GB) of the molecular pairs [S-M] and [S2] can be derived from equations (13) and (14). 

Tab. n.5 Matched molecular pair analysis of the effect of substituent on aqueous solubility... 

In typical organic crystals, molecular pairs are easily sorted out and ab initio methods that work for gas-phase dimers can be applied to the analysis of molecular dimers in the crystal coordination sphere. The entire lattice energy can then be approximated as a sum of pairwise molecule-molecule interactions examples are crystals of benzene [40], alloxan [41], and of more complex aziridine molecules [42]. This obviously neglects cooperative and, in general, many-body effects, which seem less important in hard closed-shell systems. The positive side of this approach is that molecular coordination spheres in crystals can be dissected and bonding factors can be better analyzed, as examples in the next few sections will show. 

DFT for the pair energies in the coordination shell of the nitroguanidine crystal. The picture is instructive because the molecular pairs where uncorrected DFT gives the worst errors (pairs E and L) are dispersion-dominated stacked pairs. Not only are total energies nearly identical in DFT/D and PIXEL, but also the dispersion contributions are nearly identical, lending mutual support to the evaluation of the sum of Coulombic-polarization and repulsion terms in the two methods, as well as further validation to the PIXEL parameterization. 

The set of equations (3.7-3.9) shows that the sign and magnitude of the second virial coefficient provides information on how the behaviour of the macromolecular solution deviates from that of the thermodynamically ideal state, thus reflecting the nature and intensity of the inter-molecular pair interactions (both biopolymer-biopolymer and biopolymer-solvent) (Prigogine and Defay, 1954 Tanford, 1961 Ogston 1962 ... 

Now, let us consider a system where an achiral molecule (A) and a chiral molecule (C) have a fixed mutual orientation. An electronic transition of the achiral molecule from the ground state z(0> to the excited state Aa, higher in energy by E0a, has a zero-order (non-perturbed) electric dipole moment po0 and an orthogonal magnetic dipole moment ma0. These moments are increased in the molecular pair (A -C) by first-order dynamic coupling as ... 

With so many uncertainties, it is hardly surprising that the difficulties inherent in a successful application of the diffusion equation (or molecular pair analysis) to recombination probability experiments are very considerable. Chemically induced dynamic polarisation (Sect. 4) is a fairly new technique which may assist in the study of recombination of radicals following their diffusive separation from the solvent cage. 

A Critique of the Diffusion Equation and Molecular Pair Treatments... 

The diffusion equation analysis is discussed in Sect. 2. It has been used very much more frequently in studies of diffusion-limited reactions rates than the analysis based on molecular pair behaviour, which is discussed in Sect. 3. This is probably because the diffusion equation approach is rather more direct, clear and versatile than the molecular pair analysis (furthermore, time-dependent Green s functions are required for the molecular pair approach). Besides, the probability that a molecular pair will reencounter one another is often derived from a diffusion equation analysis in any case and under these circumstances the two approaches are identical. 

As an example of the application this work, Kapral [285] and Pagistas and Kapral [37] have considered the reaction rate between iodine atoms (or some other similar species) effectively distributed uniformly in solution. They compared their calculations with those of the diffusion equation analysis and with the molecular pair approach rather than compare rate coefficients, Kapral [285] compared the rate kernels (which are approximately the time derivatives of rate coefficients). Over long times, these kinetic theory and molecular pair rate kernels both reduce to the typical form of the Smoluckowski rate kernel. However, with parameters such as R — 0.43 nm and D = 6 x 10 9m2s 1, the time beyond which the rate kernels of kinetic theory and the Smoluchowski theory are in reasonably close agreement is 20 ps, a time much longer than the velocity... 

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