Polarisable continuum model

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

J. L. Rivail and D. Rinaldi, Liquid-state quantum chemistry computational applications of the polarisable continuum models, in J. Leszczynski (ed.), Computational Chemistry, Reviews of Current Trends, World Scientific, Singapore, 1995, pp 139-174. 

C. Curutchet, M. Orozco, F. J. Luque, B. Mennucci and J. Tomasi, Dispersion and repulsion contributions to the solvation free energy comparison of quantum mechanical and classical approaches in the polarisable continuum model, J. Comput. Chem. 27 (2006) 1769-1780. 

Another VB study of S 2 identity reactions has been reported by Song, Wu, Hiberty and Shaik. These authors applied the BOVB method on its own and within the VBPCM framework (VB coupled with a polarised continuum model) to the reactions... 

A theoretical study based on MP2/6-31+G(d,p) and HF/6-31G(d) ab initio quantum mechanical calculations coupled with Langevin dipoles (LD) and polarised continuum (PCM) solvation models have been carried out by Florian and Warshel [387] to achieve a first systematic study of the free energy surfaces for the hydrolysis of methylphosphate in aqueous solution. The important biological implication of this work is the fact that since the energetics of both the associative and the dissociative mechanics are not too different, the active sites of enzymes can select either mechanism depending on the particular electrostatic environment. This conclusion basically means that both mechanisms should be considered, and this fact seems to contradict some previous studies which have focused on phosphoryl transfer reactions. 

This is a theoretical study using ab initio quantum mechanics in combination with a polarisable continuum model (PCM) for the solvent. The theoretical approach is satisfactory both for the determination of stractures and energetic in the ground and transition states the latter refer to the transfer of a proton from water coordinated in the first, to water in the second coordination sphere. The reactions studied are ... 

A weakness of the Polarised Continuum Model is the arbitrary choice of radii in defining the cavity. The Isodensity Polarised Continuum Model was developed[54] to avoid this problem. 

In the Isodensity Polarised Continuum Model the cavity is based on an isosurface of the total electron density calculated at the level of theory being employed. Only the electron density describing the isosurface is required to fully specify this model instead of the set of radii for the spheres used in the Polarised Continuum Model. The cavity is derived entirely from the electronic environment. In the present study, the isosurface W is defined by the 0.001 electrons/Bohr density envelope. 

For the Isodensity Polarised Continuum Model we have studied the variation of the cavity volume, defined by the isodensity surface, together... 

Lactone enolate nucleophiles react with allyl carbonates in the presence of [Pd2(dba)3]-CHCl3, 2,2 -bis(diphenylphosphino)-l,l -binaphthyl (BINAP), and LiCl in THF at -78 °C, giving the product in high yields (70-99%) and in an enantio-(85-97%) and diastero-selective manner (>95% when an enantionmerically pure lactone enolate is used). B3LYP/6-31+G calculations in the gas phase and the 0 PCM (polarisable continuum model) model in solution can be used to predict the major diastereomer when an enantiomerically pure lactone enolate reacts. This suggests that the reaction occurs when the LiCl—lithium enolate adduct reacts with an allylPd(BINAP) complex. LiCl is crucial in the reaction. 

As mentioned in the introduction, elimination of the explicit (atomistic) part of the solvent leads to the conventional polarisable continuum model, in which the solute creates a cavity in the bulk (continuous) solvent, whose shape follows the movement of solute atoms and whose reaction field responds to the electrostatic potential created by the solute wave-function. Note that under such circumstances the solute electron density penetrates the solvent boundary originating the so-caUed escaped charge effects, whose treatment requires more sophisticate descriptions of electrostatic contributions (e.g. the so-called integral equations formalism, lEF [12, 13, 15]). 

Spectropolarimetric monitoring is being carried out on the Anglo-Australian telescope by Cropper et al. (1987). The initial continuum polarisation was about 0.8%, but this subsequently decreased. However, the polarisation in the lines, particulary in the absorption component of Ha has increased sharply. Since the polarisation is determined by the interstellar dust, the shape of the supernova fireball and the scattering processes in the photosphere, these results are difficult to interpret However, they can provide us with very useful modelling constraints. 

As soon as we consider the molecular nature of a material, we realise that the internal electric field will vary from point to point as a consequence of the interaction of fields from the dipoles which are induced on each molecule by the applied field, although the space-average electric field over a volume large in comparison with molecular size (this is equivalent to the classical electric field based on a continuum model) may still be uniform. The field acting on an individual polarisable entity like an atom or molecule is called the local field Eh, and it is an important concept in linking observable bulk behaviour of a material with the properties of its constituent atoms or molecules. 

Continuum models can be directly interfaced with atomistic or coarse grain models using a two-way embedded interface. In this scheme, the atomistic or CG model is embedded within a continuum model. Implicit solvent methods, in which an atomistic or CG model of a solute is embedded within a continuum model of the solvent, are popular and well-established examples of this type of interface. Implicit solvent models represent the solvent as a dielectric continuum, and allow the electrostatics of the atomistic or CG solute to polarise the continuum, which then results in an electrostatic reaction field that returns to interact with the solute. Implicit solvent models have been reviewed in detail many times before, and enable the dynamic transfer of electrostatic information across the atomistic/ continuum or CG/continuum interfaces. Recently, new multiscale continuum methods have been developed that allow for the dynamic transfer of mechanical and hydrodynamic information across these interfaces. One example is the work by Villa... 

Treating the protein atoms as well as the surrounding solvent molecules explicitly constitutes the main alternative to continuum models. This obviously incurs a much heavier computational cost and simplified solvent models have been introduced to reduce it. The Langevin dipole (LD) model [299] is such an example here each molecule is represented by a polarisable point dipole, assumed to obey the Langevin polarisation law, located on a 3D grid with a cubic unit shell. This model has been progressively improved and recently used in free energy simulation calculations [370, 371]. 

In the seventies, most of the 37 papers (8-24) that we report are quantum chemical calculations, mainly on H502+ (8-14,20) or H30+(14-20) and a few on larger clusters with n=4-6 (8,9). However these last calculations are not accurate, obtained either from semi-empirical methods (8) or with small basis sets (DZ, 4-31G) and at the SCF level in ab initio calculations (9). The first accurate Cl calculations definitely establish the pyramidal geometry of the oxonium ion (15,16). The first ab initio determination of the barrier in H502+ appeared in 1970 (10). An attempt was made to study the effect of Cl on this barrier (11) and the abnormal polarizability of H502+ (12). At the end of this decade appeared the first Cl ab initio calculation on the excited states of H30+ (19) and the first CNDO calculations on excited states of larger clusters (20). In parallel to these quantum chemistry studies, a kinetic model (21) treats large systems with n=20 and 26, a polarisation model (22) is proposed, and a study on the liquid uses a continuum model (23). 

The polarisation term can be a major contributor to the free energy of solvation of a solute, and a variety of schemes have been devised to incorporate such effects where the solvent is modelled as a continuum. We shall discuss these methods in more detail in Sections 11.9-11,12. 

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