This paper shows that the Fermi hole of a reference electron can be so strongly localized to a given region of space, as to cause the conditional pair density for same-spin electrons to approach the one-electron spin density outside the region of localization and for a closed-shell system, the conditional pair density for both spins will approach the total density. Correspondingly, the Laplacian of the conditional pair density, whose local concentrations indicate the positions where the density of the remaining electrons are most likely to be found for a fixed position of a reference pair, approaches the Laplacian of the density. The Laplacian of the conditional pair density generated by a sampling of pair space by an α,β pair of reference electrons, exhibits a homeomorphism with the Laplacian of the electron density. This homeomorphism approaches an isomorphic mapping of one field onto the other, as the reference electron pair becomes increasingly localized to a given region of space. Thus the local charge concentrations (CCs) displayed by the Laplacian of the electron density, the local maxima in L(r)=−∇2ρ(r), signify the presence of regions of partial pair condensation, regions with greater than average probabilities of occupation by a single pair of electrons, as has been previously surmized on empirical grounds. This paper establishes a mapping of the essential aspects of electron pairing, determined in six-dimensional space, onto the three-dimensional space of the electron density. The properties of the conditional pair density enable one to determine which CCs of L(r) are coupled and represent the same localized pair of electrons. It is found that the pattern and properties of the electron localization domains predicted by the Laplacian of the conditional pair density differ in important aspects from those predicted by ELF, the electron localization function.
The unexpected greater Lewis acidity of BCl(3) than BF(3) with respect to strong bases such as NH(3) has been the subject of much discussion. A number of explanations have been proposed, among which the most popular and most widely quoted is that stronger back-donation from fluorine than from chlorine decreases the availability of the otherwise empty 2p orbital on boron from accepting an electron pair from a base. In contrast, toward weak bases such as CO, BF(3) is a stronger Lewis acid than BCl(3). We have reinvestigated the relative acid strengths of BF(3) and BCl(3) toward Lewis bases by calculating geometries and atomic charges for the following adducts: BF(3).NH(3), BF(3).N(CH(3))(3), BF(3).OH(2), BF(3).O(CH(3))(2), BCl(3).NH(3), BCl(3).N(CH(3))(3), BCl(3).OH(2), and BCl(3).O(CH(3))(2). Our results show that the halogen ligands remain close-packed throughout the formation of an adduct and that the bond lengths increase accordingly. It takes more energy to lengthen the short strong BF bonds than the longer weaker BCl bonds and it is for this reason that BCl(3) is a stronger Lewis acid than BF(3) toward a strong base such as NH(3). In contrast, in the formation of a complex with a weak base such as CO, the BX(3) is barely distorted from planarity and so the acidity of BF(3) is greater than that of BCl(3) because the charge on boron is greater in BF(3) than BCl(3).
Calculations at the B3PW91/6-311+G(2d,p) level of theory have been performed on a series of chlorofluoropropanes in order to account for the chemistry of the molecules CF 2 ClCF 2 CH 3 and CF 2 ClCF 2 CD 3 , chemically activated in the gas phase, which form novel elimination products, CF 3 CFdCH 2 or CF 3 CFdCD 2 , formally a 1,3-HCl or DCl elimination together with a 1,2-fluorine migration. The proposed mechanism involves an initial 1,2-FCl rearrangement, with an activation energy of 62.5 kcal/mol, giving CF 3 CFClCH 3 , which is 3.3 kcal/mol lower in energy than CF 2 ClCF 2 CH 3 . Subsequently CF 3 CFClCH 3 eliminates HCl with a barrier height of 55.4 kcal/mol. This mechanism accounts for both the unimolecular kinetics and the small kinetic isotope effect. A concerted transition geometry has been characterized for the 1,2-FCl rearrangement of each molecule of the type CF 2 ClCXFCY 3 , where X and Y are H, D, or F; in each case the rearrangement leads to a more thermodynamically stable rearrangement product CF 3 CXClCY 3 .
Chemically activated CF2ClCHFCH3 and CF2ClCHFCD3 molecules were prepared with 94 kcal mol-1 of vibrational energy by the recombination of CF2ClCHF and CH3(CD3) radicals at room temperature. The unimolecular reaction pathways were 2,3-FH(FD) elimination, 1,2-ClF interchange and 1,2-ClH elimination; the interchange produces CF3CHClCH3(CF3CHClCD3) with 105 kcal mol-1 of vibrational energy. Rate constants for CF2ClCHFCH3 [CF2ClCHFCD3] were (3.1+/-0.4)x10(6) s-1 [(1.0+/-0.1)x10(6) s-1] for 2,3-FH [FD] loss, (1.5+/-0.2)x10(6) s-1 [(8.3+/-0.9)x10(5) s-1] for 1,2-ClF interchange, and (8.2+/-1.0)x10(5) s-1 [(5.3+/-0.6)x10(5) s-1] for 1,2-ClH [DCl] loss. These correspond to branching fractions of 0.55+/-0.06 [0.43+/-0.04] for 2,3-FH [FD] loss, 0.29+/-0.03 [0.35+/-0.04] for 1,2-ClF interchange, and 0.16+/-0.02 [0.22+/-0.02] for 1,2-ClH [ClD] loss. Kinetic-isotope effects were 3.0+/-0.6 for 2,3-FH [FD] loss, 1.6+/-0.3 for 1,2-ClH loss, and 1.8+/-0.4 for 1,2-ClF interchange. The CF3CHClCH3 (CF3CHClCD3) molecules formed by 1,2-FCl interchange react by loss of HCl [DCl] with rate constants of (5.6+/-0.9)x10(7) s-1 [(2.1+/-0.4)x10(7)] s-1 for an isotope effect of 2.7+/-0.4. Density functional theory was employed to calculate vibrational frequencies and moments of inertia for the molecules and for the transition-state structures. These results were used with RRKM theory to assign threshold energies from comparison of computed and experimental unimolecular rate constants. The threshold energy for ClF interchange is 57.5 kcal mol-1, and those for HF and HCl channels are 2-5 kcal mol-1 higher. Experiments with vibrationally excited CF2ClCF2CF3, CF2ClCF2CF2Cl, and CF2ClCF2Cl, which did not show evidence for ClF interchange, also are reported.
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