Half arrow

Historically, ethylene potymerization was carried out at high pressure (1000-3000 atm) and high temperature (100-250 °C) in the presence of a catalyst such as benzoyl peroxide, although other catalysts and reaction conditions are now more often used. The key step is the addition of a radical to the ethylene double bond, a reaction similar in many respects to what takes place in the addition of an electrophile. In writing the mechanism, recall that a curved half-arrow, or "fishhook" A, is used to show the movement of a single electron, as opposed to the full curved arrow used to show the movement of an electron pair in a polar reaction. 

Another example of an acid is hydrogen cyanide, HCN, which transfers its proton to water when it dissolves to form the solution known as hydrocyanic acid, HCN(aq). However, only a small fraction of the HCN molecules donate their protons, and so we classify HCN as a weak acid in water. We write the proton transfer reaction with equilibrium half-arrows ... 

Our analysis of the changes in the SC wavefunction along the reaction path strongly suggests that the two n bonds on the butadiene fragment and the ethene ti bond break simultaneously, and that the formation of the two new a bonds that close the cyclohexene ring and of the cyclohexene n bond also takes place almost in parallel. If we wish to express all of this using full- or half-arrows, it would be most appropriate to use half-arrows, as in scheme B from the Introduction ... 

At the RHF level of theory, which uses a wavefunction that is relatively straightforward to interpret, the subtle differences between the half- and full-arrow reaction schemes would remain well-hidden within the doubly-occupied, usually delocalized orbitals. While it can be argued that the application of an orbital localization procedure could produce a semblance of the SC description for the 1,3-dipolar cycloaddition of fulminic acid to ethyne, the double-occupancy restriction makes it impossible to obtain the analogue of a half-arrow SC mechanism using an RHF wavefunction. 

Figure 6. Molecular orbital energy level diagram for [ Mo( and related complexes. The half-arrows designate...

Figure 2. A stable DNA-branched junction. The junction shown is composed of four strands of DNA, labeled with Arabic numerals arms are labeled with Roman numerals. The 3 end of each strand is indicated by the half-arrows. Each strand is paired with two other strands to form a double helical arm. There is no homologous twofold sequence symmetry flanking the central branch point, thereby stabilizing its position.

Figure 27-10 Organization of the globin genes on human chromosomes 11 and 16. The composition of the various embryonic, fetal, and adult hemoglobins is also indicated. Closed boxes indicate active genes and open boxes pseudogenes. The triangles ( ) indicate Alu repetitive sequences and their orientation. The shaded boxes indicate Kpn repeat sequences and the half-arrows their respective orientation. The Kpn sequence between the e and 7° genes in fact consists of two tandemly linked Kpn repeats. From Karlsson and Nienhuis196 and Proudfoot.197...

The second formula means merely that the HC1 molecule is a resonance hybrid between the ionic molecule H+Cl" and the molecule with the purely covalent bond, the direction of the arrow giving the direction in which the electrons have, on the average, been displaced (66). As, however, such an arrow is used by others (57), for indicating a coordinate link (semipolar double bond) caused by a lone electron pair of the donor atom, which likewise produces a dipole with its positive end on the donor side and its negative one on the acceptor side, the author suggests that the symbol — be used for the normal covalent bond, which, by resonance with an ionic structure, possesses a dipole. The point of this half arrow also indicates the direction of the negative end of the dipole. The full arrow — will then be reserved for the coordinate link. Both links play their roles in chemisorption, and it may be useful for the purposes of this article to introduce relatively simple symbols. According to this principle HC1 should be formulated as H—1-Cl. 

Orbital diagrams assign electrons to individual orbitals so the energy state of individual electrons may be found. This requires knowledge of how electrons occupy orbitals within a subshell. Hund s rule states that before any two electrons occupy the same orbital, other orbitals in that subshell must first contain one electron each with parallel spins. Electrons with up and down spins are shown by half-arrows, and these are placed in lines of orbitals (represented as boxes or dashes) according to Hund s rule, the Aufbau principle, and the Pauli exclusion principle. Below is the orbital diagram for vanadium ... 

Most chemists still tend to think about the structure and reactivity of atomic and molecular species in qualitative terms that are related to electron pairs and to unpaired electrons. Concepts utilizing these terms such as, for example, the Lewis theory of valence, have had and still have a considerable impact on many areas of chemistry. They are particularly useful when it is necessary to highlight the qualitative similarities between the structure and reactivity of molecules containing identical functional groups, or within a homologous series. Many organic chemistry textbooks continue to use full and half-arrows to indicate the supposed movement of electron pairs or single electrons in the description of reaction mechanisms. Such concepts are closely related to classical valence-bond (VB) theory which, however, is unable to compete with advanced molecular orbital (MO) approaches in the accurate calculation of the quantitative features of the potential surface associated with a chemical reaction. 

The orbitals remain associated with the same carbon atom throughout the reaction, but with a recoupling of the corresponding electron spins. As in the case of the Diels-Alder reaction, it seems appropriate to label the changes as homolytic , as might be represented using half-arrows as ... 

Notice the fishhook-shaped half-arrows used to show the movement of single unpaired electrons. Just as we use curved arrows to represent the movement of electron pairs, we use these curved half-arrows to represent the movement of single electrons. These halfarrows show that the two electrons in the Cl—Cl bond separate, and one leaves with each chlorine atom. 

A half arrow indicates the displacement of a single electron. Note that when the heteroatom corresponds to an oxygen atom, the positively charged oxygen in this last cation is isoelectronic with nitrogen and thus forms three covalent bonds. 

One-electron shifts are represented in diagrams by curly half-arrows ( I) to distinguish them from two-electron processes in polar reactions, which are shown by full-headed arrows ( >). 

An alternative treatment is offered by Bader s AIM approach which can be used to extract potentially very useful information from the changes in the total electronic density of the reacting system. However, it is not straightforward to transcribe this information into, say, a reaction scheme that makes use of full and half-arrows which any chemist would find easy to understand. 

The changes in the SC orbitals and spin-coupling mode during the course of the reaction strongly suggest that the best schematic representation of the Diels-Alder reaction between cw-butadiene and ethene is through a homolytic mechanism, in which six half-arrows indicate the simultaneous breaking of the... 

Notice that in the last step we have put in only half the mechanism - we shall generally do this from now on as it is clearer (p. 1022). There is nothing wrong with putting in another set of half-arrows going the other way if you want to. 

This convention may also be used for ligands in which o-bonds are coordinated in a side-on fashion, such as the H-H bond in complexes of dihydrogen (i.e. r 2-H2)5 or the saturated C-H bonds in agostic interactions.6 The p symbol and locants for agostic interactions are placed separately from other locants at the end of the ligand name. In Example 30 the agostic bond is denoted by a half arrow. 

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