Double hump

There are eases where the aetivated eomplex exists as an unstable intermediate. This is observed in reaetion profile as a trough in the aetivated peak of the eurve. This produees a double hump and as the minimum in the trough is more marked, that is, as the intermediate beeomes more stable, it beeomes more diffieult to separate the intermediate from the reaetion mixture during the eourse of the reaetion. Figure 1-3 shows the eurve of an unstable intermediate. 

The H NMR spectra of acetic acid and acetamide are quite different. The OH proton generates a single sharp peak at room temperature, while the NHi protons generate a broad, double-humped peak that turns into two sharp peaks at lower temperatures. This suggests that the NH, protons occupy different chemical environments, while the OH proton occupies a single environment. 

Zweiheit, / duality, dualism couple. zwel-hdck(e)rig, a. two-humped, double-hump. 

Field Stabilization Energies, or LFSE s. The variation in LFSE across the transition-metal series is shown graphically in Fig. 8-6. It is no accident, of course, that the plots intercept the abscissa for d, d and ions, for that is how the LFSE is defined. Ions with all other d configurations are more stable than the d, d or d ions, at least so far as this one aspect is concerned. For the high-spin cases, we note a characteristic double-hump trace and note that we expect particular stability conferred upon d and d octahedral ions. For the low-spin series, we observe a particularly stable arrangement for ions. More will be said about these systems in the next chapter. 

In Fig. 8-13 are plotted lattice energies for MCI2 species. The metal ions are high-spin and lie in octahedral sites in the lattice. The double-hump form of the curve is obviously similar to that for the hydration energies we have just discussed. The reasons for the observed trend in lattice energy are virtually identical to those described for hydration energies. In one system, a metal(ii) ion is octahedrally coordinated by six water molecules within a liquid medium in the other, a metal(ii) ion is octahedrally coordinated by six chlorine atoms within a solid lattice. 

The graph shows what has become known as the "double-humped" appearance that reflects the fact that the ligand field stabilization energy for the aqua complexes begins at 0, increases to 12 Dq, then drops to 0 on going from d° to d5 and repeats the trend on going from d6 to d10 (see Table 17.4). 

The prominent feature of the triplet curve in the long-range region R > 1.8 A is a double-humped repulsive barrier. This is evidently associated with successive... 

The aqua ion Au(H20)4+ has not been characterized either in solution or in the solid state. Most of the substitution studies have involved the halide complexes AuXj and Au(NH3) (Ref. 319). A number of earUer generalizations have been confirmed. Rates are very sensitive to the nature of both entering and leaving ligands and bond formation and breaking are nearly synchronous. The double-humped energy profiles witnessed with Pd(II) and Pt(II) are not invoked the five-coordinate species resulting from an associative mechanism is the transition state ... 

The double-hump behavior depicted in Fig. 2 is usually rationalized in terms of the ligand field stabilization energy (LFSE). The LFSE is a function of the d configuration and the magnitude... 

For those systems we have studied so far, many classical ligand field features are successfully captured by LFMM e.g., the double hump variation of structural and thermodynamic properties due to the LFSE (73), o- (36,58,78) and -type (77) Jahn-Teller effects, the trans influence (21), and spin state effects (18,33,59). LFMM is equally at home with small molecules and large proteins and potential future coordination chemistry applications are enormous. 

In a study of the heats of formation of first row transition metal fluorides, AHf for K3CrF6 was found to be 2977 kJ mol-1.1062 The usual double-humped distribution of Ai7f vs. dn was... 

Figure 11.9 Schematic representation of the double humped fission harrier. Intrinsic excitations in the first and second minimum are shown along with the path of fission from isomeric states and ground-state spontaneous fission.

Cations of the first transition series do not conform to the smooth pattern for the lanthanide elements shown in fig. 6.1. This is illustrated in fig. 6.2a by the radii of divalent cations in oxides containing transition metal ions in high-spin states. There is an overall decrease of octahedral ionic radius from Ca2+to Zn2+, but values first decrease to V2+, then rise to Mn2+, decrease to Ni2+, and rise again to Zn2+. The characteristic double-humped curve shown in fig. 6.2a has... 

Figure 7.2 Heats of hydration of transition metal ions (a) M2+ ions (b) Nf ions. Filled circles experimental open circles CFSE deducted. Note that experimental values lie on double-humped curves when CFSE s (table 2.5) are deducted for each cation, the corrected values lie on smooth curves through the values for 3d°, 3d5 and 3d10 cations. [Sources of data George McClure, 1959 table 2.5.]...

Chapter 7 discusses some of the thermodynamic properties of transition metal compounds and minerals that are influenced by crystal field effects. The characteristic double-humped curves in plots of thermodynamic data for suites of transition metal-bearing phases originate from contributions from the crystal field stabilization energy. However, these CFSE s, important as they are for explaining differences between individual cations, make up only a small fraction of the total energy of a transition metal compound. In the absence of spectroscopic data, CFSE s could be evaluated from the double-humped curves of thermodynamic data for isochemical compounds of the first transition series. 

There are several other types of thermodynamic data that reflect the ligand field stabilization caused by splitting the d orbitals. For example, the lattice energies of the MC12 (where M is a +2 transition metal ion) compounds also show a double humped shape when plotted as shown in Figure 19.8. However, these types of data will not be discussed because the trends follow naturally from the principles that have already been presented. 

Kumar70 has prepared a series of 2//-1-benzopyrans with heteroaromatic groups annellated on the f, g, or h face. These compounds have enhanced optical density due to the phenyls at the 2-position being ortho substituted, an effect much like that observed in the 3,3-diaryl-3//- naphthol2,1 6]pyrans as shown in Section 2.2.2. It is interesting that the colored forms of many of these compounds have very broad, double-humped absorptions. An example of the visible spectrum of a representative compound is shown in Figure 3.20. 

One way of seeing these changes is to plot the experimental heats of hydration of the transition-metal ions against their atomic number. It is seen that in the case of both divalent and trivalent ions, the heats of hydration lie on double-humped curves (Fig, 2.48). 

Now, if the transition-metal ions had spherical charge distributions, then one would expect that with increasing atomic number toe would be a decreasing ionic radius and thus a smooth and monotonic increase of the heat of hydration as the atomic number increases. The double-humped curve implies therefore the operation... 

All the other transition-metal ions, however, should have contributions to their heats of hydration from the field stabilization energy produced by the effect of the field of the water molecules on the electrons in the 3d orbitals. It is these contributions that produce the double-humped curve of Fig. 2.54. If, however, for each ion, the energy corresponding to the water-field stabilization is subtracted from the experimental heat of hydration, then the resulting value should he on the same smooth curve yielded by plotting the heats of hydration of Mn and versus atomic number. This reasoning is found to be true (Fig. 2.54). 

---