Self-consistent isodensity PCM

The original PCM method uses a cavity made of spherical regions around each atom. The isodensity PCM model (IPCM) uses a cavity that is defined by an isosurface of the electron density. This is defined iteratively by running SCF calculations with the cavity until a convergence is reached. The self-consistent isodensity PCM model (SCI-PCM) is similar to IPCM in theory, but different in implementation. SCI-PCM calculations embed the cavity calculation in the SCF procedure to account for coupling between the two parts of the calculation. 

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. 

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., J. Phys. Chem., 100,16098 (1996)]. The isodensity value 0.0004 electrons/bohr is commonly used, but other values have also been recommended [C.-G. Zhan and D. M. Chipman, J. Chem. Phys., 109, 10543 (1998)]. Since the solute s electronic wave function changes in each SCRF iteration, the size of the molecular cavity changes in each IPCM iteration. In the IPCM method, Pint is calculated from apparent surface charges. The self-consistent isodensity PCM (SCIPCM) method is a refinement of the IPCM method Foresman and Frisch, Chapter 10), which allows geometry optimization and vibrational-frequency calculations to be done for the solute molecule in solution. 

The cluster-continuum moder iUuslrated in scheme 1 was used to simulate the most common electrolytes of LIBs. The supra-molecular cluster applied to the inner ring (scheme 1) incorporates the mutual effect between salt and solvent molecules by including the first solvation shell of the salt. Due to the minor effect that the salt anion XT has on the reductive behavior of solvent molecules coordinated with Li, XT and the surrounding solvent molecules are not discussed in the current chapter. The bulk solvent effect in the second ring of scheme 1 is treated by polarized continuum models, such as PCM, conductor-like PCM (CPCM), isodensity PCM (IPCM), and self-consistent isodensity PCM (SCl-PCM), which were developed on the basis of the Onsager reaction field theory and are recognized to provide reliable results for systems without specific interactions such as hydrogen bond. 

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]. 

Over the years, many workers have addressed the problem of choice of cavity and the reaction field. Tomasi s polarized continuum model (PCM) defines the cavity as a series of interlocking spheres. The isodensity PCM (IPCM) defines the cavity as an isodensity surface of the molecule. This isodensity surface is determined iteratively. The self-consistent isodensity polarized continuum model (SQ-PCM) gives a further refinement in that it allows for a full coupling between the cavity shape and the electron density. 

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. 

---