Gibbs free energy profiles

Figure 2-1 shows the Gibbs free energy profile of a binary system, where G on the y-axis represents the Gibbs free energy of the system and X on the x-axis represents the mole fraction of the desired compound. Specifically, the first component in this system can be the desired compound, and the second component can simply be the solvent. Both temperature and pressure are maintained constant in this case. 

Fio. 10. Gibbs free energy profiles for the formation of tyrosyl adenylate and pyrophosphate, as defined in Eq. (2), by wild-type (energy levels in dashed lines) and mutant (energy levels in solid lines) tyrosyl-tRNA synthetases, using standard states of 1 W for tyrosine, ATP, and pyrophosphate. [Reprinted with permission from Ref. (25/).]... 

Scheme 3 Condensed Gibbs free-energy profile (kcal mol ) of the complete catalytic cycle of the co-oligomerization of 1,3-butadiene and ethylene catalyzed by zerovalent bare nickel complexes affording linear and cyclic Cio-olefins, focused on viable routes for individual elementary steps. The favorable [Ni (ri -frans-butadiene)2(ethylene)] isomer of the active catalyst species lb was chosen as reference. Activation barriers for individual steps are given relative to the favorable stereoisomer of the respective precursor (given in italics)...

Scheme 8 The Gibbs free energy profile for the reaction of H2 with the iridium thiolate complex. All the relative free energies are in kcal/mol...

Scheme 17 Gibbs free energy profiles of reactions 1-5 over the cluster model 4g without adsorbing formald are in kcal moP ...

Fig. 5. 33 Potential energy (underlined data) and Gibbs free energy profile (in kcal mol ) at 298.15 K for the reductive decomposition process of Li (PS) calculated at B3PW91/6-311++G...

Scheme 7.3 Gibbs free-energy profile of the ring-opening cross-metathesis of norbornene with alkenes. The free energies were calculated at the B3LYP/LANL2DZ level of theory, and are in kcal mol [37].

Scheme 7.6 Gibbs free-energy profiles of the two lowest energy trans reaction pathways [E-proximal and E-distal) for the initiation of ROMP of 3-methyl-Z-cyclooctene.

Figure 6 The potential energy (underlined data) and Gibbs free energy profile at 298.15 K for the reductive decomposition paths of (PC)2Li (VC) (left) and (EC)2Lr(VC) (right, italic data) with B3PW91/6-311++G(d,p)//B3PW91/6-31G(d) method. The favorable paths are 39—>40, followed by two competitive paths, a and c. Reproduced from [15, 31] with permission of Amer. Chem. Soc.

Figure 8.10 Calculated Gibbs free energy profile (kJ mol ) for the palladium-catalyzed allyllc C-H alkylation using DFT/B3LYP-D3.

Figure 17.8 Computed Gibbs free energy profiles for the stereoselectivity-controlling C-C bond formation step in (a) enamine pathway involving a Houk-List transition...

Figure 3.12 Gibbs free energy profiles for acetylene cyclotrimerization by Crfllj/SiOj cluster model. The Gibbs free energies are calculated at 298.15 K, 1 atm as default in Gaussian09. Also shown are the total energies in parentheses. The triplet reaction pathway is depicted in gray, while the quintet parts are in black. Energies are in kcal/mol and relative to 1C plus the corresponding number of acetylenes.

As shown in Scheme 3.6, the first reaction pathway firom lE lead to the cycHc product 1,2,4-TMB through either an intermolecular [4-p2] cycloaddition pathway on potential energy surface (PES)—Tla or an insertion and reductive ehmination pathway PES—Tib. The Gibbs free energy profiles are depicted in Fig. 3.14. The key intermediate 4Ea is formed through direct insertion of a second methylacetylene into the three-membered ring in 2Ea... 

The Gibbs free energy profile for the reaction pathways by model L, a simple monovalent cationic species Cr(I), is shown in Fig. 3.17. The liberation of 1-butene was prohibited by showing two successive activation... 

Figure 3.18 Gibbs free energy profile of model Cr(l) /DME at 298.15 K. The solid line in black shows the metallacycle growth pathway the dotted line in gray shows 1-butene elimination pathway the solid line in gray shows 1-hexene elimination pathway via two-step route the dotted line in black shows 1-hexene elimination pathway via p-agostic hydrogen shift. Energy differences (kcal/mol) are expressed with respect to 1L corrected for the corresponding number of ethylene molecules. Energy barriers are indicated in italics and heat absorption is shown in parentheses.

The Gibbs free energy profile of the reaction pathway by model Q was shown in Fig. 3.19. The coordination of the first ethylene to the unsaturated chromium center in the sextet ground state is sHghtly exoergic by 1.0 kcal/mol, which is followed by an endoergic coordination process of... 

Figure 13.12 Gibbs free energy profiles of the reactions between f(( ArO)3N)U" j and n-BuCCH. See color plate section...

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