Double-headed arrows

Combinations of the Above. Note that arrows are used to show movement of electrons. An arrow always follows the motion of electrons and never of a nucleus or anything else (it is understood that the rest of the molecule follows the electrons). Ordinary arrows (double-headed) follow electron pairs, while single-headed arrows follow unpaired electrons. Double-headed arrows are also used in pericyclic reactions for convenience, though in these reactions we do not really know how or in which direction the electrons are moving. 

Many types of cirrows cire used in organic chemistry, and each of them conveys information about the particular reaction. These arrows include the resonance arrow, equilibrium arrow, reaction arrow, double-headed arrow, and singleheaded cirrow. 

The anisotropy of the product rotational state distribution, or the polarization of the rotational angular momentum, is most conveniently parametrized tluough multipole moments of the distribution [45]. Odd multipoles, such as the dipole, describe the orientation of the angidar momentum /, i.e. which way the tips of the / vectors preferentially point. Even multipoles, such as the quadnipole, describe the aligmnent of /, i.e. the spatial distribution of the / vectors, regarded as a collection of double-headed arrows. Orr-Ewing and Zare [47] have discussed in detail the measurement of orientation and aligmnent in products of chemical reactions and what can be learned about the reaction dynamics from these measurements. 

To deal wifh circumslances such as fhe bonding m ozone fhe nolion of resonance befween Lewis sfrucfures was developed According fo fhe resonance concepf when more fhan one Lewis sfrucfure may be written for a molecule a single sfrucfure is msuf ficienl fo describe if Ralher fhe frue sfrucfure has an eleclron dislribulion fhaf is a hybrid of all fhe possible Lewis sfrucfures fhaf can be written for fhe molecule In fhe case of ozone fwo equivalenf Lewis sfrucfures may be wriffen We use a double headed arrow fo represenf resonance befween fhese fwo Lewis sfrucfures... 

If IS imporfanf fo remember fhaf fhe double headed resonance arrow does not mdi cate a process m which fhe fwo Lewis sfrucfures mferconvert Ozone for example has... 

Fig. 6. Discharge behavior of a battery where is the open circuit voltage (a) current—potential or power curve showing M activation, ohmic, and M concentration polarization regions where the double headed arrow represents polarization loss and (b) voltage—time profile.

The double-headed arrow is used to separate resonance structures. 

One way to explain this situation is to assume that each of the bonds in S02 is intermediate between a single and a double bond. To express this concept, two structures, separated by a double-headed arrow, are written... 

In stoichiometric and non-stoichiometric mechanistic equations, a double-headed arrow (— ) indicates that the reaction involves more than one mechanistic step. 

Because all three bonds are identical, a better model of the nitrate ion is a blend of all three Lewis structures with each bond intermediate in properties between a single and a double bond. This blending of structures, which is called resonance, is depicted in (9) by double-headed arrows. The blended structure is a resonance hybrid of the contributing Lewis structures. A molecule does not flicker between different structures a resonance hybrid is a blend of structures, just as a mule is a blend of a horse and a donkey, not a creature that flickers between the two. 

FIGURE 18.5 (a) The atoms in neighboring straight-chain alkanes, represented by the tubelike structures, can lie close together. Ibl Fewer of the atoms of neighboring branched alkane molecules can get so close together overall, and so the London forces (represented by double-headed arrows) are weaker and branched alkanes are more volatile. 

This is the form employed by the carbohydrate databank CarbBank, and is preferred for most purposes. Each symbol for a monosaccharide unit is preceded by the anomeric descriptor and the configuration symbol. The ring size is indicated by an italic / for furanose or p for pyranose, etc. The locants of the linkage are given in parentheses between the symbols a double-headed arrow indicates a linkage between two anomeric positions. In CarbBank, omission of a/p, D/L, or ftp means that this structural detail is not known. 

The double-headed arrow is intended to imply the existence of a resonance hybrid a stmcture with an electronic distribution intermediate between the two shown. Every instmctor knows the hazards of this portrayal. Firstly, the doubleheaded arrow is misinterpreted by some students to mean either (i) that there is an equilibrium condition involving the two different species, or (ii) that flipping occurs between the two species. A second problem is demonstrated by those students who ask Are these not the same If we rotate one of the molecules by 60°, we see that they are identical . We can hypothesise that the latter problem may be exacerbated by the tendency of textbooks (and probably teachers) to talk about these two different resonance stmctures as though we are referring to two different molecules - when, in fact, we are talking about different electron distributions in just one molecule. It seems so important for instractors to refer to just one set of six carbon atoms joined by ct bonds, and then to discuss alternative distributions of the six TT electrons within that system. 

Most of the examples of chemical equations presented in Table 4.1 include an arrow ( ) symbol. This implies a direction to the chemical change represented this is a process of reactant(s) becoming produces). However, sometimes students meet reactions where an equality sign (=) or a double-headed arrow symbol is... 

Which of these options is the best Lewis structure Actually, no single Lewis structure by itself is an accurate representation of NO3. Any single structure of the anion shows nitrate with one NDO double bond and two N— O single bonds. In Section 9 1, we show that single and double bonds between the same types of atoms have different lengths and different energies. In contrast, experiments show that the three nitrate N—O bonds are identical. To show that the nitrate N—O bonds are all alike, we use a composite of the three equivalent Lewis structures. These are traditionally called resonance structures. Resonance stmctures are connected by double-headed arrows to emphasize that a complete depiction requires all of them. 

The two candidates are equivalent Lewis structures, so the best depiction of H2 PO4 shows two resonance structures connected by a double-headed arrow. 

C15-0084. Consider the exothermic reaction AC -b B AB -b C. (a) Draw an activation energy diagram for this reaction, (b) Label the energies of reactants and products, (c) Show A reaction by a double-headed arrow, (d) Show a for the forward reaction by a single-headed arrow, (e) Label and draw a molecular picture of the activated complex. 

These difficulties have led to the convention of representing molecules that cannot adequately be written as a single classical structure by a combination of two or more classical structures, the so-called canonical structures, linked by a double-headed arrow. The way in which one of these structures can be related to another often being indicated by curved arrows, the tail of the curved arrow indicating where an electron pair moves from and the head of the arrow where it moves to ... 

We shall, however, subsequently write canonical structures, e.g. (19a) and (19b), linked by a double-headed arrow, but without curved arrows. These will be reserved for indicating a real movement of electron pairs, i.e. as happens during the forming, and breaking, of bonds in the course of a real reaction. 

Fig. 8.1 Wong s evolutionary map shows possible relationships between code words. The codons in boxes correspond to today s code words (compare Table 8.1). The codons for Asp and Glu in dotted boxes refer to these amino acids in a very early evolutionary stage of the genetic code. Single-headed arrows refer to the biosynthetic relationships between precursor and product, while double-headed arrows refer to reciprocal formation possibilities. All pairs of codon units (irrelevant of whether they are linked by single- or double-headed arrows) differ only in one single base change (Wong, 1975)...

Along the edges of the square there are mathematical operations. The Fourier transform describes the relation between the left and the right side of the square. Thus, on the left side we find the functions of physical space, and the reciprocal space is found on the right side. Double-headed arrows show that the path from the left to the right side is reversible. Unfortunately, reversion is impossible after we have moved from the top to the bottom of the square - and the scattering intensity I (s) is located in the lower right corner of the square. 

Resonance structures or resonance contributors are connected by double-headed arrows (<- ) => the real molecule, radical, or ion is a hybrid of all of them. 

The situation is illustrated in Figure 46-13. The actual voltage is a continuous, linear physical phenomenon. The values represented by the output of the A/D converter, however, can only take discrete levels, as illustrated. The double-headed arrows represent the error introduced by digitizing the continuous physical voltage at various points. The error cannot be greater than 1/2 the difference between representing adjacent levels of the converter if the voltage increases beyond 1/2 the difference between levels, then the conversion will provide the next step s representation of the value. 

Figure 46-13 The actual voltage is a continuous, linear function. The values represented by the output of the A/D converter, however, can only take discrete levels. The double-headed arrows represent the error introduced by digitizing the continuous physical voltage at various points.

Heating of isopropanol under conventional reflux conditions, with 2,4,6-trimethyl-benzoic acid and a catalytic amount of sulfuric acid, afforded the corresponding isopropyl ester in only 2% conversion after 28 h. With the MBR, the product was isolated in 56% yield after 1 h at 148°C[26] (Scheme 2.1 - please note that in all schemes herein, the use of a double headed arrow does not imply a balanced equation). 

Fig. 18 Free energy profiles for the solvent extraction of copper, where L is Acorga P50. The profile shows the free energy of a site on the liquid/liquid interface. All higher-order rate constants are reduced to first-order rate constants by using the concentrations of reactants in either phase. The free energy lost in each cycle can be seen from the difference between 0 and the 10%, 50% and 80% extraction lines on the right of the diagram. The double-headed arrows indicate the rate-limiting free energy difference.

Fig. 25 Free energy profiles for stripping copper out of the organic phase. Note that the rate-limiting step, indicated by the double-headed arrow, has the reactant and the transition state in different cycles with respect to the vacant site.

Figure 7.6 Fingerprint texture of lyotropic cholesteric double-headed arrow corresponds to pitch.

Fig. 1. An ultrathin section of an untreated fresh protoplast with 4% uranyl acetate and 0.4% lead citrate. A line profile of gray level (below) was taken along the double-headed arrow through the Golgi cistemae (G) and the endoplasmic reticulum (ER). (From ref. 40.)...

It is wrong (but common) to see a reversible reaction written with a double-headed arrow, as A B. Such an arrow implies resonance, e.g. between the two extreme valence-bond structures of Kekule benzene. 

Figure 11.11 shows there are some molecules which can legitimately be drawn in several different ways using Lewis structures, each conforming to the octet rule. These are resonance structures, and are equally valid, but the true structure is a hybrid of the two or more possible structures. This is indicated by the double-headed arrow, where the electrons are moved, but the atoms stay in position. However, in this example, the carbon oxygen bonds are of equal length - they do not rapidly interconvert from one version to another. The true... 

Although aspartate and alanine have been identified in the description above as the amino group donor , the Keq for transaminase reactions is close to 1.0 so both reactions are, as indicated by the double-headed arrows, are easily reversible. Glutamate could just as easily act as the amino group donor if either reaction proceeds from right to left, resulting in the formation of alanine or aspartate respectively. 

To communicate the bonding in SO2 more accurately, chemists draw two Lewis structures and insert a double-headed arrow between them. Each of these Lewis structures is called a resonance structure. Resonance structures are models that give the same relative position of atoms as in Lewis structures, but show different places for their bonding and lone pairs. 

The double headed arrow is used in the field of chemistry to indicate that a reaction is an equilibrium reaction. That is, the reaction does not proceed completely to the left or to the right. 

---