Partitioning nuclear

Fig. 3.4. A two-dimensional cross-section of the structure diagram for an ABC system. The full lines, denoting the catastrophe set, partition nuclear configuration space into its structural regions. The structure associated with each region is indicated by a representative molecular graph. The two broken lines indicate two possible reaction mechanisms for changing the structure A-B-C into the structure B-C-A.

Trapnell, D.W. and Hamrick, J.L., Partitioning nuclear and chloroplast variation at multiple spatial scales in the neotropical epiphytic orchid, Laelia rubescens, Molec. Ecol, 13, 2655, 2004. 

This method, introduced originally in an analysis of nuclear resonance reactions, has been extensively developed [H, 16 and F7] over the past 20 years as a powerful ab initio calculational tool. It partitions configuration space into two regions by a sphere of radius r = a, where r is the scattered electron coordinate. 

We now consider the connection between the preceding equations and the theory of Aharonov et al. [18] [see Eqs. (51)-(60)]. The tempting similarity between the structures of Eqs. (56) and (90), hides a fundamental difference in the roles of the vector operator A in Eq. (56) and the vector potential a in Eq. (90). The fomrer is defined, in the adiabatic partitioning scheme, as a stiictly off-diagonal operator, with elements (m A n) = (m P n), thereby ensuring that (P — A) is diagonal. By contiast, the Mead-Truhlar vector potential a arises from the influence of nonzero diagonal elements, (n P /i) on the nuclear equation for v), an aspect of the problem not addressed by Arahonov et al. [18]. Suppose, however, that Eq. (56) was contracted between (n and n) v) in order to handle the adiabatic nuclear dynamics within the Aharonov scheme. The result becomes... 

DFT methods compute electron correlation via general functionals of the electron density (see Appendix A for details). DFT functionals partition the electronic energy into several components which are computed separately the kinetic energy, the electron-nuclear interaction, the Coulomb repulsion, and an exchange-correlation term accounting for the remainder of the electron-electron interaction (which is itself... 

There are in principle also energy levels associated with nuclear spins. In the absence of an external magnetic field, these are degenerate and consequently contribute a constant term to the partition function. As nuclear spins do not change during chemical reactions, we will ignore this contribution. 

Bond, W. Leuze, R. "Feasibility Studies of the Partitioning of Commercial High-Level Wastes Generated in Spent Nuclear Fuel Reprocessing Annual Progress Report for FY-1974," ORNL-5012, Oak Ridge, Tennesse, January 1975. 

In Eq. (44), gei(T ) is the ratio of transition state and reactant electronic partition functions [31] and the rotational degeneracy factor = (2ji + l)(2/2 + 1) for heteronuclear diatomics, and will also include nuclear spin considerations in the case of homonuclear diatomics. 

The final expression is the classical limit, valid above a certain critical temperature, which, however, in practical cases is low (i.e. 85 K for H2, 3 K for CO). For a homonuclear or a symmetric linear molecule, the factor a equals 2, while for a het-eronuclear molecule cr=l (Tab. 3.1). This symmetry factor stems from the indistinguishable permutations the molecule may undergo due to the rotation and actually also involves the nuclear partition function. The symmetry factor can be estimated directly from the symmetry of the molecule. 

Fisher NS, Fowler SW, Boisson F, et al. 1999. Radionuclide bioconcentration factors and sediment partition coefficients in Arctic seas subject to contamination from dumped nuclear wastes. Environ Sci Technol33 1979-1982. 

Nuclear motion, the principle of least, and the theory of stereoelectronic control, 24, 113 Nucleophiles, partitioning of carbocations between addition and deprotonation. 35, 67 Nucleophilic aromatic photosubstitution, 11,225 Nucleophilic catalysis of ester hydrolysis and related reactions, 5,237 Nucleophilic displacement reactions, gas-phase, 21, 197... 

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