Supermolecule-polarizable continuum

Heard, G. L., Yates, B. F. Hybrid supermolecule-polarizable continuum approach to solvation application to the mechanism of the Stevens rearrangement. J. Comput. Chem. 1996, 17, 1444-1452. 

The acid-catalysed, neutral, and base-catalysed hydrolysis of seven lactones was studied using a hybrid supermolecule polarizable continuum model (PCM) approach including six explicit water molecules. DFT and ab initio methods were used to analyse the features of the various possible hydrolysis mechanisms of -propiolactone, j0-butyrolactone, j0-isovalerolactone, diketene, y-butyrolactone, 2(5//)-furanone, and... 

TD-DFT) they calculated the transition energies and dipole moments for NMA both in vacuum and in an aqueous solution. Moreover, in the treatment of the solvent they compared two different approaches, i.e., a polarizable-continuum method (COSMO) and a supermolecule approach. For the latter, the authors performed molecular-dynamics calculations using a force-field model and, subsequently, extracted a cluster containing the solute and 3 water molecules that form hydrogen bonds to the solute. Averages over 90 such configurations were ultimately determined. 

In their study of the photodissociation of formic acid, Tian and Fang compared the gas-phase reaction with that of an aqueous solution. For the solvent they used a combined model with a supermolecule treatment of the solute plus the nearest water molecules together with a polarizable continuum model for the long-range solvent effects. They could demonstrate that the explicit treatment of water molecules closest to the solute was important for the theoretical study of the photoabsorption process. 

Such a treatment is not possible and one has to restore to approximations. We discussed some of those in section II. They could, as a first approximation, be split into three dilferent classes. In one set of approximations the solvent was treated within a simplified, parameterized approach. Thereby, the structure of the solvent was retained. As an alternative, the solvent could be approximated as a polarizable continuum that would respond to the presence of the solute but otherwise was without any internal structrue. These two types of approaches are coined explicit and implicit methods, respectively. Finally, a full quantum-mechanical treatment of either a smaller, finite supermolecule or an infinite, periodic supercell could be carried through. 

The effect of the solvent is usually modelled either by the use of the Onsager s self consistent reaction field (SCRF) [20] or by the polarizable continuum method (PCM) [21]. With regard to the relative stability of cytosine tautomers in aqueous solution, these methods provided results [14,15] which, in spite of some discrepancies, are in reasonable agreement with experimental data [3]. However, continuum-based methods do not explicitly take into consideration the local solvent-solute interaction which is instead important in the description of the proton transfer mechanism in hydrogen-bonded systems. A reasonable approach to the problem was recently proposed [22,23] in which the molecule of interest and few solvent molecules are treated as a supermolecule acting as solute, while the bulk of the solvent is represented as a polarizable dielectric. 

In summary, the supermolecule approach and polarizable continuum methods were used in concert to obtain solvation energies which take into account both specific solvent-solute effects and the electrostatic contribution to solvation. The... 

In Eq. (6) Ecav represents the energy necessary to create a cavity in the solvent continuum. Eel and Eydw depict the electrostatic and van-der-Waals interactions between solute and the solvent after the solute is brought into the cavity, respectively. The van-der-Waals interactions divide themselves into dispersion and repulsion interactions (Ed sp, Erep). Specific interactions between solute and solvent such as H-bridges and association can only be considered by additional assumptions because the solvent is characterized as a structureless and polarizable medium by macroscopic constants such as dielectric constant, surface tension and volume extension coefficient. The use of macroscopic physical constants in microscopic processes in progress is an approximation. Additional approximations are inherent to the continuum models since the choice of shape and size of the cavity is arbitrary. Entropic effects are considered neither in the continuum models nor in the supermolecule approximation. Despite these numerous approximations, continuum models were developed which produce suitabel estimations of solvation energies and effects (see Refs. 10-30 in 68)). 

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