Free enthalpy of activation

Finally from the logarithmic form of the Eyrlng equation, the free enthalpy of activation, AG, of rotation of the dimethylamino group at the coalescence temperature (318 K) can be calculated ... 

Apparently, the 1H NMR spectra of 1 //-azepines are invariant over substantial temperature ranges.61 However, temperature dependence has been noted69 in the 13CNMR spectra of some 1 -acyl-1 //-azepines, and is attributed to hindered rotation about the N-CO bond rather than to ring-inversion phenomena AG free enthalpies of activation for hindered rotation of 62-66 kJ moP1 have been calculated. E/Z-rotamcr ratios for l-aroyl-l//-azepines have been assessed and show a slight preference for the -rotamer 22 however, an X-ray structural analysis of l-(4-bromobenzoyl)-2-methyl-3.5,7-triphenyl-l//-azepine demonstrates that in the crystal state it is exclusively in the E configuration.22... 

The salient points in this diagram are (i) the rate-determining step in the interconversion 55 6 is the bond-making (or bond-breaking) between the secondary C+ and CO (ii) the rate of carbonylation of the secondary pentyl ion 10 (and presumably also of other secondary acyclic alkyl cations) in FHSO3—SbFs has a free-enthalpy of activation of about... 

The isomerization of 5 to 7 and 8 involves a chain-branching type rearrangement (lOis ll) (Brouwer and Oelderik 1968) and has a free-enthalpy of activation of about 22 kcal mole . This result, combined with the data of Fig, 2, the free-enthalpy of activation of 17 kcal mole for the rearrangement 9-i ll (Brouwer and Hogeveen, 1972), and an estimated difference in free-enthalpy of about 0-8 kcal mole between 10 and 11 constitutes the basis for the free-enthalpy diagram in Fig. 3. 

From Fig. 4 it is seen that the free-enthalpy of activation for the rearrangement of tertiary butyl to secondary butyl cation is 30-4 — 3.9 = 26-5 kcal mole . As the reverse rearrangement has been found by direct observation to have JG cl7-18 kcal rnole" (Saunders et al., 1968), it follows that the difference in stabilization between tertiary and secondary butyl cations is indeed 9 + 1 kcal mole . This value is in excellent agreement with a previous experimental value of 10 + 1 kcal mole (Brouwer and Hogeveen, 1972). 

Table 5. Thermal decomposition of hydrocarbons R1R2R3C-CR1R2R3. Temperature T for X f2 = 1 h, free enthalpy of activation AG at 300 °C and strain enthalpy F,sa...

As a result of the small, but apparent single bond character of the triafulvene C3/C4 bond and the good stabilization of the transition state of the rotation established earlier, rotation around this bond should be lower in energy in comparison to simple ethylene derivatives183. In fact, 1H-NMR spectra of several types of asymmetrically substituted triafulvenes 219-224 proved to be temperature-dependent and showed reversible coalescence phenomena at definite temperatures diagnostic for internal rotation processes. These were characterized by the free enthalpy of activation AG at the coalescence point of appropriate substituent signals61. ... 

Dynamic NMR spectroscopic measurements indicate, that the free enthalpies of activation of 57 and 59 are 10.2 kcal/mol and 11.9 kcal/mol, respectively. Similar conformational behavior is exhibited by the [2.2](2,5)heterophanes 43, 61, and 62. The thiophene-containing hetero-phanes 61 and 62 8b82) are conformationally rigid up to 200 °C and are not subject to ring inversion, whereas the furanophane 43 is conforma-... 

Here, the decrease of the free enthalpy of activation for process (9) is attributed to an increase in N-basicity of the porphyrin ligands from [36a] to [36h]. However, the standard deviations of the AG values for [36c-36f] would also allow a different ordering of these four complexes. Although not proven by equilibrium measurements, the (TRP) ligands are always regarded as less basic than the (OEP) ligand (131, 135). 

Tab. 5 Diffusion coefficient, heterogeneous rate constant ks, collision number Zheti free enthalpy of activation DG j and standard free enthalpy of activation DG 298 for the reduction of 10 M a-l<4SiWi2O40 in DMF containing 0.1 M LiCl04 (taken from Ref 49)...

Such equilibria depend on the temperature T(K) and the free enthalpy of activation AG (Fig. 3.9). The rate constant kT of isomerization is given by the Eyring equation (3.9) [107] ... 

The calculation of these data requires the temperature dependence of kr [107] the energy of activation can then be obtained as the slope of a logfcr versus IjT plot according to eq. (3.12). However, the measurement of kr = f (T) is more difficult and includes more errors than the determination of kr at or near 7[. by using eqs. (3.10) and (3.11) [107,108], For this reason it is usually preferable to determine the numerically more accurate free enthalpy of activation, AGjc, from the temperature dependent NMR spectra according to eq. (3.9 a). 

The maximum of the Gibbs free enthalpy between the ground states of substrate and product forms the Gibbs free enthalpy of activation with the energy difference AG7, which determines the rate constant of the reaction, like every catalyst, an enzyme decreases the value of AG and thus accelerates the reaction. (An agent increasing the value of AG7 is termed an anti-catalyst .)... 

A different derivation starts with the total Gibbs free enthalpy of activation AG f between substrate and enzyme, which consists of the energetically negative (i.e.,... 

Abstract Enantioselection in a stoichiometric or catalytic reaction is governed by small increments of free enthalpy of activation, and such transformations are thus in principle suited to assessing dendrimer effects which result from the immobilization of molecular catalysts. Chiral dendrimer catalysts, which possess a high level of structural regularity, molecular monodispersity and well-defined catalytic sites, have been generated either by attachment of achiral complexes to chiral dendrimer structures or by immobilization of chiral catalysts to non-chiral dendrimers. As monodispersed macromolecular supports they provide ideal model systems for less regularly structured but commercially more viable supports such as hyperbranched polymers, and have been successfully employed in continuous-flow membrane reactors. The combination of an efficient control over the environment of the active sites of multi-functional catalysts and their immobilization on an insoluble macromolecular support has resulted in the synthesis of catalytic dendronized polymers. In these, the catalysts are attached in a well-defined way to the dendritic sections, thus ensuring a well-defined microenvironment which is similar to that of the soluble molecular species or at least closely related to the dendrimer catalysts themselves. 

The aim of catalyst recycling and the exploitation of possible constructive interactions between catalytic sites underlie the rapidly growing field of stereoselective dendrimer catalysis. Since enantioselection is governed by small increments in the free enthalpy of activation, such transformations are particularly suited to assessing dendrimer effects , which result from the immobilization of catalysts. 

This ratio is governed by AAG — the difference of Free Enthalpy of activation... 

In Fig. 2a the free enthalpies of activation AG (300 °C) of the thermolysis reactions of symmetrical hexaalkylethanes 11 (Cq—Cq series) — the weakest bond connects two quaternary carbons — are plotted against their ground state strain Hs as obtained from MM2 calculations 14 32 37>. The large range of stability differences encompassed by this series is easily judged from the scale on the right side of Fig. 2 in which is given for each compound the temperature at which the half-life is 1 h. 

The high quality (r = —0.987) of the linear correlation in Fig. 2 a, for which Eq. (1) is given in the caption, is quite surprising for several reasons. In particular, because free enthalpies of activation AG are correlated with strain enthalpies Hs despite the fact that there is neither an isoentropic (AS = const.)41) nor an isokinetic relationship (AH aAS ) 41) within this series. Indeed AS varies from 13 to 26 entropy units14). In a kind of Exner test42) it was shown, however, that the order of decreasing AG (T) values is independent of temperature and therefore significant for structural interpretation 14). 

A brief comment is in place here, to avoid any confusion between the thermodynamic terms stable/unstable and the kinetic descriptors labile/ inert. Inert complexes simply have no suitable low-energy pathway for the reaction available, or, in other words, the free enthalpy of activation (AGt) is very high even if there are more (thermodynamically) stable products. A stable complex has a large positive free enthalpy of reaction (AG°) for its decomposition (702). This is illustrated in Fig. 1. Quite often, however, the terms inert/labile are replaced by kinetically stable/unstable. For an interesting essay on the different meaning of the simple term stable in the chemistry and physics community, see Ref. 103. 

Experimentally, free enthalpies of activation (AG n) corresponding to rotational barriers around C—N bonds of variously substituted enamines have been obtained from a linear correlation, represented by equation 7. This was derived from a relation of the... 

Free Enthalpies of Activation (AG ) of Acetamides Having a Five- or Six-membered Bing ... 

---