Quantum chemical approach for condensed-phase thermochemistry (IV): Solubility of gaseous molecules

Computation of rate coefficients in solutions based on transition state theory combined with a heuristically corrected polarizable continuum model: intermolecular Diels-Alder reactions as case studies

Transition state theory (TST) based on activation parameters computed using quantum mechanics calculations combined with the polarizable continuum model (QM/PCM) is a fundamental tool for investigating reaction rates in the liquid phase. In conventional QM/PCM methods, thermodynamic data and partition functions for a solute are often derived from a quasi-ideal gas treatment (IGT) widely implemented in commercially available computation packages. This approach tends to overestimate entropy because calculations of thermodynamic parameters in the liquid phase ignore hindered translational and rotational modes in real solutions. The present work formulated partition functions for more realistic solutes hindered by surrounding solvent molecules in conjunction with the basic QM/PCM concept. In addition, a configuration partition function for solute molecules at a standard concentration of 1 mol dm-3 was incorporated using a simple lattice model. The canonical partition function and thermodynamic functions were derived based on statistical thermodynamics for localized systems. Expressions for rate coefficients within TST were also derived with a consistent formalism based on the standard state selected in partition function calculations. The performance of the proposed method was assessed by predicting rate coefficients for three different Diels-Alder reactions and comparing these with experimental results. QM/PCM calculations at the G4//ωB97X-D/6-311++G(d,p)/IEF-PCM level of theory with corrections for the dispersion and repulsion energies were performed to obtain the electronic structures of stationary points on potential energy surfaces as a means of finding activation enthalpy, entropy and Gibbs energy values based on revised partition functions as well as predicting rate coefficients. The activation Gibbs energies obtained from our proposed method were lower than those obtained from the IGT method due to reasonable entropy computations. The proposed method overestimated the rate coefficients by one to two orders of magnitude compared to the experimental values, whereas the IGT method underestimated them by the same amount. This discrepancy arises because the proposed method calculates the partition function from the viewpoint of a localized system, whereas the IGT method calculates it from the viewpoint of a non-localized system. Given that actual liquids exist in a state between non-localized and localized systems, it is essential to formulate the partition function in a way that more accurately represents the liquid state.

Computation of entropy values for non-electrolyte solute molecules in solution based on semi-empirical corrections to a polarized continuum model

A simple heuristic model was developed for estimating the entropy of a solute molecule in an ideal solution based on quantum mechanical calculations with polarizable continuum models (QM/PCMs). A translational term was incorporated that included free-volume compensation for the Sackur-Tetrode equation and a rotational term was modeled based on the restricted rotation of a dipole in an electrostatic field. The configuration term for the solute at a given concentration was calculated using a simple lattice model that considered the number of configurations of the solute within the lattice. The configurational entropy was ascertained from this number based on Boltzmann's principle. Standard entropy values were determined for 41 combinations of solutes and solvents at a set concentration of 1 mol dm^-3 using the proposed model, and the computational values were compared with experimental data. QM/PCM calculations were conducted at the ωB97X-D/6-311++G(d,p)/IEF-PCM level using universal force field van der Waals radii scaled by 1.2. The proposed model accurately reproduced the entropy values reported for solutes in non-aqueous solvents within a mean absolute deviation of 9.2 J mol^-1 K^-1 for 33 solutions. This performance represents a considerable improvement relative to that obtained using the method based on the ideal gas treatment that is widely utilized in commercially available computation packages. In contrast, computations for aqueous molecules overestimated the entropies because hydrophobic effects that decrease the entropy of aqueous solutions were not included in the present model.

A simple heuristic approach to estimate the thermochemistry of condensed-phase molecules based on the polarizable continuum model

A simple model based on a quantum chemical approach with polarizable continuum models (PCMs) to provide reasonable translational and rotational entropies for liquid phase molecules was developed.