Electron pairs, conservation

There is a small class of processes for which correlation effects on relative energies should cancel so that an HF description may be sufficient. These are conformational processes and electron pair conserving reactions such as isodesmic reactions or homodesmotic reactions involving just first row atoms provided effects described under point 2 are not significant. 

If we know the moles of A and the number of reaction units associated with A and B, then we can calculate the moles of B. Note that a conservation of reaction units, as defined by equation 2.3, can only be applied between two species. There are five important principles involving a conservation of reaction units mass, charge, protons, electron pairs, and electrons. 

Quantitative Calculations The stoichiometry of complexation reactions is given by the conservation of electron pairs between the ligand, which is an electron-pair donor, and the metal, which is an electron-pair acceptor (see Section 2C) thus... 

Conservation of electron pairs for the titration reaction requires that Moles EDTA = moles Ca +... 

The principle of the conservation of electron pairs is easily extended to other com-plexation reactions, as shown in the following example. 

Finally, quantitative problems involving multiple analytes and back titrations also can be solved by applying the principle of conservation of electron pairs. 

Conservation of electron pairs for the three titrations requires that for Titration 1 moles Ni = moles EDTAl (Fe, Cr masked)... 

Cyclooctatetraene (COT) —> Semibullvalene (SB) Photorearrangement. Irradiation of COT yields semibullvalene [97], in spite of the fact that this photochemical reaction is forbidden by orbital conservation mles. The Longuet-Higgins loop for this system actually predicts that this should happen, although the reaction is phase preserving. (Fig. 42). This is another example of type C loop (Fig. 11). Only six of the eight electrons re-pair as COT transforms to SB. The reaction is made possible by the fact that COT valence isomerization, a phase-inverting reaction (four electron-pair Hiickel system), takes place simultaneously. One expects to produce in the reaction a COT isomer, that can be detected solely by proper substitution. 

Comparisons between reactants and transition states (required for calculation of absolute activation energies) also typify situations in which the total number of electron pairs is not likely to be conserved. These will be considered separately in Chapter 9. 

Closely related is the need for correlated models to account for absolute activation energies. Here too, bonds are being made or broken and the number of electron pairs may not be conserved. 

Heterolytic Bond Dissociation. A process in which a bond is broken and a cation and anion result. The number of electron pairs is conserved, but a non-bonding electron pair has been substituted for a bond. 

FIGURE 19-9 IMADH ubiquinone oxidoreductase (Complex I). Complex I catalyzes the transfer of a hydride ion from NADH to FMN, from which two electrons pass through a series of Fe-S centers to the iron-sulfur protein N-2 in the matrix arm of the complex. Electron transfer from N-2 to ubiquinone on the membrane arm forms QH2, which diffuses into the lipid bilayer. This electron transfer also drives the expulsion from the matrix of four protons per pair of electrons. The detailed mechanism that couples electron and proton transfer in Complex I is not yet known, but probably involves a Q cycle similar to that in Complex III in which QH2 participates twice per electron pair (see Fig. 19-12). Proton flux produces an electrochemical potential across the inner mitochondrial membrane (N side negative, P side positive), which conserves some of the energy released by the electron-transfer reactions. This electrochemical potential drives ATP synthesis. 

How is a concentration gradient of protons transformed into ATP We have seen that electron transfer releases, and the proton-motive force conserves, more than enough free energy (about 200 lcJ) per mole of electron pairs to drive the formation of a mole of ATP, which requires about 50 kJ (see Box 13-1). Mitochondrial oxidative phosphorylation therefore poses no thermodynamic problem. But what is the chemical mechanism that couples proton flux with phosphorylation ... 

An isodesmic reaction92 is a formal reaction, in which the number of electron pairs as well as formal chemical bond types are conserved while the relationships among the bonds are altered. A subclass of the isodesmic reactions is the class of bond separation energies, in which all formal bonds of a molecule are separated into two-heavy-atom molecules containing the same type of bonds. Stoichiometric balance is achieved for the bond separation energies by adding an appropriate number of one-heavy-atom hydrides to the left side of the reaction92. 

So diat charge is conserved, anionic bases upon reaction with a proton give neutral conjugate acids neutral bases upon reaction with a proton give positively charged conjugate acids. Occasionally shared pairs of electrons can be given up to a proton such as when olefins react with acids. In such cases n electrons are die electron pair which forms a bond to the proton. 

The formation of a bond between two atoms can proceed by one of the atoms donating an electron pair and die other atom accepting the electron pair. As before, charge must be conserved and die loss and gain in electrons by the donor... 

Another common feature of free-radical reactions is that they tend to be chain processes. Since any chemical reaction must exhibit conservation of spin, the reaction of a free radical widi a closed-shell (fully electron paired) molecule must result in the production of a new free-radical species which can participate in subsequent free-radical reactions. The series of free-radical reactions leading to product is often a cyclic process in which the initial free radical is produced once again in die last step of the cycle so that the reaction sequence starts over again. The process is termed a chain reaction because each step of the process is linked directly to die preceding step. 

An indirect means of dealing with the correlation problem when the molecule is too large to be treated by advanced methods such as the G2 is to include it in a reaction (often hypothetical) in which the reactants and products are similar in terms of one or more of several electronic and structural factors, e.g. number of electron pairs, types of bonds, atom environments, etc. [15,20,21], It is hoped that in computing AH(298 K) for such a process, the errors for the reactants and products will largely cancel. The desired AHf can then be obtained if the AHf of all of the other species are known. There are several categories of such reactions isogyric ones conserve the number of electron pairs, isodesmic maintain unchanged... 

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