PCM induced charges

PB see Poisson-Boltzmann PCM, 2, 266, 271, 275 PCM induced charges, 3,181 PDB see Protein Data Bank PDBbind, 2,161... 

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 EFP induced dipoles and PCM induced charges may be described by a supermatrix equation [22] ... 

The matrix p is a combined set of the external electrostatic fields that represent the effects of the QM field on the EFP polarizability tensors and the PCM potential, while w is a combined set of induced dipoles and surface charges. The physical meaning of the supermatrix equation (3) is that the EFP induced dipoles and PCM induced charges are uniquely determined by the external field and potential therefore, the right hand side of Eq. (3) involves only the external field /potential, and the left side involves only the induced EFP dipoles and PCM charges. The interactions among the induced dipoles and charges are implicitly described with the matrix B. The supermatrix Eq. (3) can be solved either with direct inversion or various iterative methods. 

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. 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

All these effects are considered in a more consistent and general way in the PCM framework, where the coupling between the induced electronic charge distribution (not limited to the dipolar component but described by the QM wavefunction) and the external medium is represented by the reaction potential produced by the apparent charges, while the boundary effect on the Maxwell field is represented by the matrices m . 

Within the DPM the specific contributions due to the polarizable and structured environment will lead to two different sorts of corrections (i) contributions due to the static multipole moments (here partial charges) and (ii) contributions due to the induced polarization in the environment. In contrast, for the PCM only contributions due to the induced polarization in the solvent are relevant. 

Implemented as outlined above, the PCM seems to correctly account for the main non-additive effects for cations in water. Except for cations like NH4 where exchange seems the principal source of non additivity [133], they are basically polarization of water in the electric field of the cation and electron transfer from water to the cation. A second water molecule nearby reduces both these effects, giving a less deep potential well in the effective two-body potential compared to the strictly two-body one. In the PCM picture, a distribution of negative charge on the cavity, due to the polarization of the dielectric continuum induced by the cation, decreases the electric field of the cation and hence both water polarization and electron transfer from water to the cation. 

The gradients (both forces and torques) of the polarization energy in a combined EFP/PCM calculation have been derived and implemented [22]. It is found that all of the energy gradient terms can be formulated as simple electrostatic forces and torques on the induced dipoles and charges as if they were permanent static dipoles and charges, in accordance with the electrostatic nature of these models. Geometry optimizations can be performed efficiently with the analytic... 

Regarding the additional solvent-induced matrices, here we anticipate, but without giving any detail, some of the features exploited by the PCM method to describe solute-solvent electrostatic interactions which will be better described later, j and y are two one-electron matrices collecting the electrostatic interactions between each solute electronic elementary charge distribution XmXi/ the nuclei-induced ASCs, and between solute nuclear charges and the electron-induced ASCs, respectively, while Xj, (P) is the matrix defining the same kind of interactions but, this time, between the solute electrons and the ASCs they generate. 

The D, matrix can be associated to the D matrix of PCM whose elements give the normal components of the field the ASCs induce on the center of the tesserae, while the S, matrix is strictly related to the B matrix of COSMO giving the potential of the apparent charges on the center of the tesserae. 

For solvation of small molecules, the polarizable continuum model (PCM) and its variants have been widely used for calculation of solvation energy. The conductor-like PCM (CPCM) model gives a concise formulation of solvent effect, in which the solvent s response to the solute polarization is represented by the presence of induced surface charges distributed on the solute-solvent interface. In this formulation, no volume polarization (extension of solute s electron distribution into the solvent region) is allowed. The induced surface charge counterbalances the electrostatic potential on the interface generated by the solute molecule. 

Equation (11.20) is the primary PCM equation. It must be discretized for actual computation (see Section 11.2.2), but then given the solute s electrostatic potential evaluated at the surface discretization points, this equation can be solved for the induced surface charge at those points (i.e.,the discretized a). In an MM/PCM calculation, the electrostatic solvation energy is then immediately available via a discretized version of Eq. (11.3), although in QM applications the surface charge must be included in the next self-consistent field (SCF) iteration, and the SCF procedure is iterated until both the electron density and the surface charge have reached mutual self-consistency. 

As other QM continuum models, the PCM model requires the solution of two coupled problems an electrostatic classical problem for the determination of the solvent reaction potential Va induced by the total charge distribution and a quantum mechanical problem for the determination of the wavefunction I of the solute described by the effective QM Hamiltonian (1.1). The two problems are nested and they must be solved simultaneously. 

The PCM method is one of the best known of such models. In essence, it involves the generation of a solvent cavity from spheres centered at each atom in the solute the polarization of the solvent is represented by means of virtual point charges mapped onto the cavity surface and proportional to the derivative of the solute electrostatic potential at each point, calculated from the molecular wavefunction. The point charges are then included into the one-electron Hamiltonian, and therefore they induce a polarization of the solute. An iterative procedure is performed until the wavefunction and the point charges are self-consistent. 

The basis of the PCM approach to the local field relies on the same assumption as in the classical approaches that is, it is assumed that the effective field experienced by a molecule in the cavity is the sum of the reaction and cavity fields. The former is related to the dielectric polarization induced from the solute charge distribution, whereas the cavity field depends on the dielectric polarization induced by the applied field once the cavity has been created. 

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