Apparent surface charge models

The efficient construction of proper and sufficiently accurate segmentations of a molecular-shaped cavity is an important technical aspect of apparent surface charge models, because it has a strong influence on both the accuracy and speed of the calculations. Before going into details, some common features will be discussed. 

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. 

Most of the quantum chemical calculations of the nuclear shielding constants have involved two classes of solvation models, which belong to the second group of models (n), namely, the continuum group (i) the apparent surface charge technique (ASC) in formulation C-PCM and IEF-PCM, and (ii) models based on a multipolar expansion of the reaction filed (MPE). The PCM formalism with its representation of the solvent field through an ASC approach is more flexible as far as the cavity shape is concerned, which permits solvent effects to be taken into account in a more accurate manner. 

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 ... 

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. 

A different set of dynamical variables can be given by the use of continuum models based on the apparent surface charge approach (ASC). In the PCM (Aguilar et a/., 1993b Cammi and Tomasi, 1995a) the set of coordinates is reduced to a discrete number, related to the cavity shape and... 

The potential tot derives from all the sources present in the model, i.e. the solute and the apparent surface charges. Factor /e of eq.(37) reflects the boundary conditions of the electrostatic problem. The inclusion of this factor means that the gradient at sk is computed in the inner part of the surface element (the dielectric constant is e for the medium and 1 for the inner cavity space). 

This kind of analysis is easily shifted to BE-ASC models in which the polarization vector is substituted by the apparent surface charge in the representation of the solvent reaction field.In this framework, the previous partition of the polarization vector into fast and slow components leads to two corresponding surface apparent charges, c and the sum of... 

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. 

With respect to other QM continuum models, the PCM method represents of the interaction operator Vi l ) (i.e. of the solvent reaction potential Va) in terms of an apparent surface charge (ASC) charge distribution a spread on the boundary F of the cavity (C) hosting the solute M. 

ASC = apparent surface charges CRF = classical reaction field GAH = generalized atomic hybrids LO = localized orbital QM = quantum mechanics RISM = reference inter-acdon site model. 

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