Isodensity polarizable continuum model

Values in acetonitrile calculated by the isodensity polarizable continuum model. 

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... 

A full quantum-mechanical description of the Menshutkin reaction has been obtained for gas phase and solution by using density functional theory (DFT) and the self-consistent isodensity polarizable continuum model (SCI-PCM). Ammonia and pyridine were the nucleophiles and methyl chloride and methyl bromide, the electrophiles. In the gas phase an initial dipole complex intermediate is followed by a transition state leading to an ion pair. In the solvent-effect calculations, the dipole complex disappears with both cyclohexane and DMSO. The transition state is stabilized compared with the gas phase. The ion-pair product is strongly stabilized and in DMSO it is dissociated into free ions. 

Fig. 5 Oxidation potentials calculated at the HF/6-31 + G (d, p) level for three solvation models isodensity polarizable continuum model (IPCM), polarizable continuum model (PCM), and solvation model based on density (SMD). Experimental oxidation potentials (EXP) are from the literature. Reproduced with permission [91]. Copyright 2011 American Chemical Society...

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. 

In this thesis, the models that have been used for all the calculations are the widely known polarizable continuum model (PCM) [79], and the recently developed SMD model [80]. These two models define the cavity for the solute as the union of a series of interlocking spheres centered on the atoms and differ only in that the latter includes the radii and non-electrostatic terms as suggested by Truhlar and coworkers. Other variants of the PCM model are, for example, the Isoelectronic-PCM (IPCM), which uses a static isodensity surface for the cavity, and its improved version self-consistent isodensity-PCM (SCI-PCM) [81]. 

In the IPCM calculations, the molecule is contained inside a cavity within the polarizable continuum, the size of which is determined by a suitable computed isodensity surface. The size of this cavity corresponds to the molecular volume allowing a simple, yet effective evaluation of the molecular activation volume, which is not based on semi-empirical models, but also does not allow a direct comparison with experimental data as the second solvation sphere is almost completely absent. The volume difference between the precursor complex Be(H20)4(H20)]2+ and the transition structure [Be(H20)5]2+, viz., —4.5A3, represents the activation volume of the reaction. This value can be compared with the value of —6.1 A3 calculated for the corresponding water exchange reaction around Li+, for which we concluded the operation of a limiting associative mechanism. In the present case, both the nature of [Be(H20)5]2+ and the activation volume clearly indicate the operation of an associative interchange mechanism (156). 

Over the last years, the basic concepts embedded within the SCRF formalism have undergone some significant improvements, and there are several commonly used variants on this idea. To exemplify the different methods and how their results differ, one recent work from this group [52] considered the sensitivity of results to the particular variant chosen. Due to its dependence upon only the dipole moment of the solute, the older approach is referred to herein as the dipole variant. The dipole method is also crude in the sense that the solute is placed in a spherical cavity within the solute medium, not a very realistic shape in most cases. The polarizable continuum method (PCM) [53,54,55] embeds the solute in a cavity that more accurately mimics the shape of the molecule, created by a series of overlapping spheres. The reaction field is represented by an apparent surface charge approach. The standard PCM approach utilizes an integral equation formulation (IEF) [56,57], A variant of this method is the conductor-polarized continuum model (CPCM) [58] wherein the apparent charges distributed on the cavity surface are such that the total electrostatic potential cancels on the surface. The self-consistent isodensity PCM procedure [59] determines the cavity self-consistently from an isodensity surface. The UAHF (United Atom model for Hartree-Fock/6-31 G ) definition [60] was used for the construction of the solute cavity. 

Alternatively, reaction field calculations with the IPCM (isodensity surface polarized continuum model) [73,74] can be performed to model solvent effects. In this approach, an isodensity surface defined by a value of 0.0004 a.u. of the total electron density distribution is calculated at the level of theory employed. Such an isodensity surface has been found to define rather accurately the volume of a molecule [75] and, therefore, it should also define a reasonable cavity for the soluted molecule within the polarizable continuum where the cavity can iteratively be adjusted when improving wavefunction and electron density distribution during a self consistent field (SCF) calculation at the HF or DFT level. The IPCM method has also the advantage that geometry optimization of the solute molecule is easier than for the PISA model and, apart from this, electron correlation effects can be included into the IPCM calculation. For the investigation of Si compounds (either neutral or ionic) in solution both the PISA and IPCM methods have been used. [41-47]... 

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