Semicontinuum (Cluster-Continuum) Modeling of Acid-Catalyzed Aqueous Reactions: Alkene Hydration

Limited ionicity in poor protic ionic liquids: Association Gibbs energies

Protic ionic liquids (PILs), made from anhydrous mixtures of Bronsted acids HA and bases B (HA + B → BH⁺ + A^-), occasionally suffer from limited ionicity. In cases of "poor" PILs (<10% ionicity, e.g., using carboxylic acids), past simulations have hinted that ion-pair association, more than incomplete proton transfer, is at fault. To improve upon the Fuoss equation for predicting the degree of ion pairing, new electrostatic equations (including induced dipoles) are presented, for ion-pair and other associations that occur in anhydrous amine/carboxylic acid mixtures. The equations present the association Gibbs energies ΔG_A (and thus the association constants K_A) as functions of three fundamental properties: the acid/base mixing ratio (n = x_A/x_B), the HA-to-B proton-transfer strength (ΔpK_a,ε=78), and the dielectric constant (relative permittivity) of the mixture (ε). Parameter values were obtained from fits to constant-dielectric quantum chemistry data (obtained and presented here). These ΔG_A functions were then used to predict ΔG_ioniz values for the net ion-generating (autoionization) equilibrium in carboxylic acid/amine mixtures: 2B(HA)_n⇄B(HA)_n-dHB⁺+A(HA)_n+d-1 ^-, where n = x_A/x_B and d = degree of disproportionation. The agreement with experiment was excellent, demonstrating that these equations could have useful predictive power.

Intermolecular Interactions of Pyrene and Its Oxides in Toluene Solution

In this work, the conformer-rotamer ensemble sampling tool (CREST), with the underlying semiempirical GFN2-xtb method, was used for automated geometry exploration of the homodimers of pyrene, pyrene-4,5-dione, and pyrene-4,5,9,10-tetraone, along with the heterodimer of pyrene and pyrene-4,5,9,10-tetraone. Geometries and energies of the dimers were further refined at the ωB97X-D4/def2-TZVP level of theory, both in the gas phase and in toluene solution. Computations in solution were handled using the CPCM (conductor-like polarizible continuum model) and SMD (solvation model based on density) models. Two previously unidentified pyrene-homodimer conformations were identified, and the effects of oxidation on the geometries and energies of dimerization were explored; in general, oxidation leads to stronger intermolecular interactions and decreased solubility in toluene. For selected dimers, DLPNO-CCSD(T)/cc-pVTZ/SMD(Toluene) energies were determined at the DFT geometries and illustrated the accuracy of the ωB97X-D4 approach, with an MAD of 1.47 kJ/mol.

Challenges in predicting ΔrxnG in solution: The chelate effect

Gibbs energies for reactions involving aqueous ions are challenging to predict due to the large solvation energies of such ions. A stringent test would be the ab initio reproduction of the aqueous-phase chelate effect, an entropic effect in reactions of very small enthalpy changes. This paper examines what is required to achieve such a reproduction for the paradigmatic reaction M(NH3)42+ + 2 en → M( en)22+ + 4 NH3 ( en = 1,2-ethylenediamine), for which ΔrxnG* and ΔrxnH* are −2.3 and +1.6 kcal mol−1, respectively, if M = Zn. Explicit solvation via simulation was avoided in order to allow sufficiently accurate electronic structure models; this required the use of continuum solvation models (CSMs), and a great deal of effort was made in attempting to lower the relative errors of ΔsolvG*[M(NH3)42+] vs ΔsolvG*[M( en)22+] from the CSMs available in Gaussian software. CSMs in ADF and JDFTx software were also tested. A uniform 2.2 kcal mol−1 accuracy in ΔrxnG* for all three metal-atom choices M = {Zn, Cd, Hg} was eventually achieved, but not from any of the known CSMs tested, nor from cavity size reoptimization, nor from semicontinuum modeling: post facto solvation energy corrections [one per solute type, NH3, en, M(NH3)42+, M( en)22+] were needed. It is hoped that this study will aid (and encourage) further CSM development for coordination-complex ions.