Half-headed curved arrow

Double-headed arrow Full-headed curved arrow Half-headed curved arrow (fishhook)... 

To illustrate the movement of a single electron, use a half-headed curved arrow, sometimes called a fishhook. 

Two half-headed curved arrows are needed for two single electrons. 

Sample Problem 6.1 Use full-headed or half-headed curved arrows to show the movement of electrons in each equation. 

Full-Headed Curved Arrow Moves Two Electrons Half-Headed Curved Arrow Moves One Electron Electron Source Electron Sink Charge Is Conserved Direction of Electron Flow Good Arrow Pushing Habits Common Errors... 

A full-headed curved arrow indicates the movement of two electrons from the tail of the arrow to the head. A half-headed curved arrow indicates the shift of one electron likewise. The two ways that a bond can break are heterolytic (two electrons) or homolytic (one electron). Homolytic processes are unusual and will be treated separately in Chapter 11. 

A curved half-headed arrow indicates the movement of a single electron in the direction of the arrowhead... 

In chemical structures, the unpaired electron of a radical is represented by a dot. Radical mechanisms are depicted in one of two ways. Most commonly, each individual step of the mechanism is written without the use of arrows to show electron movement. The resulting series of equations shows the order of events, and it is assumed that one-electron transfers are taking place throughout. A second method uses curved, half-headed arrows ( - ) to show electron movement. The half-headed arrow is used to denote movement of a single... 

Curved arrowrs with full heads are used to describe the breaking of bonds and the formation of new ones in chemical reactions. Half-headed arrows are introduced to cover reaction situations where pairs of electrons forming bonds are supposed to move in different directions and join up in new pairings. 

Well develop the point in more detail later, but you might note for now that the movement of one electron in the symmetrical process is indicated using a half-headed, or "fishhook," arrow (a), whereas the movement of two electrons in the unsymmetrical process is indicated using a full-headed curved arrow (Ai). 

Figure 11. Antijunctions and mesojunctions. (a) A 949 knot drawn in a DNA context. Each of the nodes of this knot is shown to be formed from a half-turn of double helical DNA. The polarity of the knot is indicated by the arrowheads passing along it. Various enclosed areas contain symbols indicating the condensation of nodes to form figures. The curved double-headed arrow indicates the condensation of two half-turns into a full turn, the solid triangle indicates a three-arm branched junction, the empty square indicates a 4-strand antijunction, and the shaded square is a four-strand mesojunction. (b) Schematic drawings of 3-strand and 4-strand junctions, antijunctions, and mesojunctions shown as the helical arrangements that can flank a triangle or a square. Each polygon is formed from strands of DNA that extend beyond the vertices in each direction. The arrowheads indicate the 3 ends of the strands. The vertices correspond to the nodes formed by a half-turn of double helical DNA. Base pairs are represented by lines between antiparallel strands. Thin double-headed arrows perpendicular to the base pairs represent the axis of each helical half-turn. The lines perpendicular to the helix axes terminating in ellipses represent the central dyad axes of the helical half-turns. The complexes 33 and 44 correspond to conventional branched junctions. The complex 40 is a 4-strand antijunction. The complexes on the bottom row are mesojunctions, which contain a mix of the two orientations of helix axes.

Figure 12.10. The xy plane (9 = nil) of the unit sphere. The section of the positive half-sphere defined by eq. (12.8.13) is shown by the shaded regions (which include the tails of the curved arrows but not their heads). Poles of the proper rotations C2a, C2 b, and C2care shown by filled digons and the poles of the improper rotations /C2mj m = d, e, f, are indicated by unfilled digons.

Some atoms, even in covalent compounds, carry a formal charge, defined as the number of valence electrons in the neutral atom minus the sum of the number of unshared electrons and half the number of shared electrons. Resonance occurs when we can write two or more structures for a molecule or ion with the same arrangement of atoms but different arrangements of the electrons. The correct structure of the molecule or ion is a resonance hybrid of the contributing structures, which are drawn with a double-headed arrow () between them. Organic chemists use a curved arrow (O) to show the movement of an electron pair. 

If one electron comes from each of the atoms forming the new bond (the reverse of homolysis), there will be no change in formal charge (half of two shared electrons is equivalent to one attached to an individual atom). The combination of two chlorine atoms to form a chlorine molecule is shown in reaction (1.2e) the curved half-arrows show the movement of the electron from the chlorine atom (tail) to the position where the bond will be (head). 

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