Surfaces polarizable continuum model

The Polarizable Continuum Model (PCM) employs a van der Waals surface type cavity, a detailed description of the electrostatic potential, and parameterizes the cavity/ dispersion contributions based on the surface area. The COnductor-like Screening... 

It is relatively straightforward to implement the polarizable continuum model (PCM) via Eq. (39).11 12,105,117 The potential of the reaction field, VCT(r), is due to the ostensible (virtual) charge distribution o(r) on the cavity surface, which in turn is related to the potential Vsoiutc(r) that arises from the nuclei and electrons of the solute molecule, Eq. (2). Since the latter is likely to be further polarized by VCT(r), thus affecting Vs0,utc(r), iteration to self-consistency is needed,105,106 as already has been pointed out. (However Montagnani and Tomasi suggest that this often has little practical consequence.)118... 

S. Hofinger and O. Steinhauser, Making use of Connolly s molecular surface program in the isodensity adapted polarizable continuum model, J. Chem. Phys., 115 (2001) 10636-10646. 

H. Li and J. H. Jensen, Improving the accuracy and efficiency of geometry optimizations with the polarizable continuum model new energy gradients and molecular surface tessellation, J. Comput. Chem., 25 (2004) 1449-1462. 

A more sophisticated description of the solvent is achieved using an Apparent Surface Charge (ASC) [1,3] placed on the surface of a cavity containing the solute. This cavity, usually of molecular shape, is dug into a polarizable continuum medium and the proper electrostatic problem is solved on the cavity boundary, taking into account the mutual polarization of the solute and solvent. The Polarizable Continuum Model (PCM) [1,3,7] belongs to this class of ASC implicit solvent models. 

The sharp dielectric surface was implemented for the Polarizable Continuum Model (PCM) for the first time by Bonaccorsi et al. [9] and further developed by Hoshi etal. [10] The only requirements for the employment of the PCM is a knowledge of the constitutive parameters of the system geometry of the dielectrics and corresponding dielectric constants. The same model has been subsequently revisited in 2000 [11] supplemented with the modelling of nonelectrostatic interactions (see later). 

The most sophisticated methods developed to date to treat solvent effects in electronic interactions and EET are those reported by Mennucci and co-workers [47,66,67], Their procedure is based on the integral equation formalism version of the polarizable continuum model (IEFPCM) [48,68,69], The solvent is described as a polarizable continuum influenced by the reaction field exerted by the charge distribution of the donor and acceptor molecules. In the case of EET, it is the particular transitions densities that are important. The molecules are enclosed in a boundary surface that takes a realistic shape as determined by the molecular structure. 

L. Bondesson, L. Frediani, H. Agren, B. Mennucci, Solvation of N3- at the water surface The polarizable continuum model approach. J. Phys. Chem. B 110, 11361 (2006)... 

Moving now to QM/continuum approaches, we shall limit our exposition to the so-called apparent surface charges (ASC) version of such approaches, and in particular to the family known with the acronym PCM (polarizable continuum model) [11], In this family of methods, the reaction potential Vcont defined in Eq. (1-2) has a form completely equivalent to the Hel part of the Z/qm/mm operator defined in Eq. (1-4), namely ... 

The Polarizable Continuum Model (PCM)[18] describes the solvent as a structureless continuum, characterized by its dielectric permittivity e, in which a molecular-shaped empty cavity hosts the solute fully described by its QM charge distribution. The dielectric medium polarized by the solute charge distribution acts as source of a reaction field which in turn polarizes back the solute. The effects of the mutual polarization is evaluated by solving, in a self-consistent way, an electrostatic Poisson equation, with the proper boundary conditions at the cavity surface, coupled to a QM Schrodinger equation for the solute. 

The most serious limitation remaining after modifying the reaction field method as mentioned above is the neglect of solute polarizability. The reaction field that acts back on the solute will affect its charge distribution as well as the cavity shape as the equipotential surface changes. To solve this problem while still using the polarizable continuum model (PCM) for the solvent, one has to calculate the surface charges on the solute by quantum chemical methods and represent their interaction with the solvent continuum as in classical electrostatics. The Hamiltonian of the system thus is written as the sum of the Hamilton operator for the isolated solute molecule and its interaction with the macroscopic... 

In this work we present a study of the potential energy surfaces (PES) for some simple chemical processes in aqueous solution, combining the polarizable continuum model (PCM) with the CASSCF methodology and interpreting the results in a valence bond (VB) formalism. 

Low-cost continuum models are often used to assess bulk solvation effects. The polarizable continuum models (PCM) [20] are continuum solvation models in which the solvent effects are described with induced surface charges. In a PCM calculation, the solutes can be modeled with ab initio methods or force fields, or both. In a combined QM/EFP/PCM calculation [21], the EFP induced dipoles and PCM induced charges are iterated to self-consistency as the QM wavefunction converges. 

The PCM Method. Accurate ab initio calculation of solvent effects requires use of a molecular shape more realistic than spherical or ellipsoidal shapes. In the polarizable-continuum model (PCM) of Miertus, Scrocco, and Tomasi, each atomic nucleus in the solute molecule M is surrounded by a sphere of radius 1.2 times the van der Waals radius of that atom. The cavity region is taken as the volume occupied by these overlapping atomic spheres. (Recall the van der Waals molecular surface— Section 15.8.)... 

The original PCM method uses atomic spheres with radii 1.2 times the van der Waals radii to define the molecular cavity. The isodensity polarizable continuum model (IPCM) is a modification of the PCM that defines the surface of the molecular cavity as a contour surface of constant electron probability density of the solute molecule M [J. B. Foresman et al.,/. Phys Chem., 100,16098 (19%)]. iscxlensity value of 0.0004 electrons/bohr is reconunended, since it gives molecular volumes that agree with experimental values of where is the molar volume of the liquid solute... 

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