Polarizable continuum model reaction field

C. S. Pomelli, A tessellationless integration grid for the polarizable continuum model reaction field, J. Comput. Chem., 25 (2004) 1532-1541. 

The most common approach to solvation studies using an implicit solvent is to add a self-consistent reaction field (SCRF) term to an ab initio (or semi-empirical) calculation. One of the problems with SCRF methods is the number of different possible approaches. Orozco and Luque28 and Colominas et al27 found that 6-31G ab initio calculations with the polarizable continuum model (PCM) method of Miertius, Scrocco, and Tomasi (referred to in these papers as the MST method)45 gave results in reasonable agreement with the MD-FEP results, but the AM1-AMSOL method differed by a number of kJ/mol, and sometimes gave qualitatively wrong results. 

It is relatively straightforward to implement the polarizable continuum model (PCM) via Eq. (39).11 12,105,117 The potential of the reaction field, VCT(r), is due to the ostensible (virtual) charge distribution o(r) on the cavity surface, which in turn is related to the potential Vsoiutc(r) that arises from the nuclei and electrons of the solute molecule, Eq. (2). Since the latter is likely to be further polarized by VCT(r), thus affecting Vs0,utc(r), iteration to self-consistency is needed,105,106 as already has been pointed out. (However Montagnani and Tomasi suggest that this often has little practical consequence.)118... 

Organometallic systems such as porphyrines have been investigated because of the possibility to fine tune their response by functionalization[105-107]. Systems of increased the dimensionality have been of particular interest [108-111], Concomitant to the large effort to establish useful structure-to-properties relationships, considerable effort has now been put to investigate the environmental effects on TPA[112-114], For example, the solvent effect has been studied for a small linear push-pull chromophore using a self-consistent reaction field (homogeneous solvation) method employing a spherical cavity and an internal force field (IFF) method[l 12] in another study the polarizable continuum model has been employed to calculate the relevant quantities to obtain the TPA cross-section in the limit of a two-state model[113] Woo et al. made a critical study of experimental comparison of TPA cross-sections in different solvents[114]. 

The most sophisticated methods developed to date to treat solvent effects in electronic interactions and EET are those reported by Mennucci and co-workers [47,66,67], Their procedure is based on the integral equation formalism version of the polarizable continuum model (IEFPCM) [48,68,69], The solvent is described as a polarizable continuum influenced by the reaction field exerted by the charge distribution of the donor and acceptor molecules. In the case of EET, it is the particular transitions densities that are important. The molecules are enclosed in a boundary surface that takes a realistic shape as determined by the molecular structure. 

The Polarizable Continuum Model (PCM)[18] describes the solvent as a structureless continuum, characterized by its dielectric permittivity e, in which a molecular-shaped empty cavity hosts the solute fully described by its QM charge distribution. The dielectric medium polarized by the solute charge distribution acts as source of a reaction field which in turn polarizes back the solute. The effects of the mutual polarization is evaluated by solving, in a self-consistent way, an electrostatic Poisson equation, with the proper boundary conditions at the cavity surface, coupled to a QM Schrodinger equation for the solute. 

The most serious limitation remaining after modifying the reaction field method as mentioned above is the neglect of solute polarizability. The reaction field that acts back on the solute will affect its charge distribution as well as the cavity shape as the equipotential surface changes. To solve this problem while still using the polarizable continuum model (PCM) for the solvent, one has to calculate the surface charges on the solute by quantum chemical methods and represent their interaction with the solvent continuum as in classical electrostatics. The Hamiltonian of the system thus is written as the sum of the Hamilton operator for the isolated solute molecule and its interaction with the macroscopic... 

The Polarizable Continuum Model (PCM), in its original version, uses a quantum description of the solute molecule, an SE molecular cavity, and the ASC approach to determine the reaction field. The quantum mechanical calculation is performed using two nested cycles in the internal cycle the charges [Eq. (7.16)] are calculated from the distribution while on the external cycle an improved solute charge distribution Pm is determined. 

A many-body perturbation theory (MBPT) approach has been combined with the polarizable continuum model (PCM) of the electrostatic solvation. The first approximation called by authors the perturbation theory at energy level (PTE) consists of the solution of the PCM problem at the Hartree-Fock level to find the solvent reaction potential and the wavefunction for the calculation of the MBPT correction to the energy. In the second approximation, called the perturbation theory at the density matrix level only (PTD), the calculation of the reaction potential and electrostatic free energy is based on the MBPT corrected wavefunction for the isolated molecule. At the next approximation (perturbation theory at the energy and density matrix level, PTED), both the energy and the wave function are solvent reaction field and MBPT corrected. The self-consistent reaction field model has been also applied within the complete active space self-consistent field (CAS SCF) theory and the eomplete aetive space second-order perturbation theory. ... 

SCC-DFTB self-consistent charge-density functional tight binding SCRFPCM self-consistent reaction field polarizable continuum model SIBFA sum of interactions between fragments ab initio computed... 

The extension of continuum solvation modes to evaluate vibrational frequencies of molecular systems in solution was pioneered by RivaU and co-workers in the 1980s [150] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium. Further extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [151-153] in the framework of the polarizable continuum model (PCM). Wang et al. [154] used an ab initio self consistent reaction field (SCRF) Onsager model to compute vibrational frequencies at different levels of... 

In the present example, the electronic QM computations have been performed with the DFT/N07D model while the effect of the methanol solvent has been included by means of the polarizable continuum model, where the solvent is represented by a homogeneous dielectric polarized by the solute, placed within a cavity built as an envelope of spheres centered on the solute atoms [ 154] (see Chapter 1 for details). The solvent has been described in the nonequilibrium hmit where only its fast (electronic) degrees of freedom are equilibrated with the excited-state charge density while the slow (nuclear) degrees of freedom remain equilibrated with the ground state. This assumption is well suited to describe the broad features of the absorption spectrum in solution due to the different time scales of the electronic and nuclear response components of the solvent reaction field [89]. 

Solvent effects may be treated using several models self-consistent reaction field (SCRF) (Karelson et aL 1986, 1993 Kirkwood 1934 Tapia and Goscinski 1975), polarizable continuum model (PCM) (Cammi and Tomasi 1995 Miertui et al. 1981 Tomasi and Persico 1994 Tomasi et al. 2005), surface and simulation of volume polarization for electrostatics (SS(V)PE) (Chipman 1997, 2000, 2002), and conductor-like screening model (COSMO) (Baldridge and Klamt 1997 Klamt 1995 Klamt and Schiiurmann 1993). 

During the last 40 years it has been possible to witness an important evolution on the way the environment around a solute molecule is described. The reaction field approach, the effect a continuous dielectric medium has on the charge distribution of a molecule that polarizes back the dielectric and generates a reaction potential, is a standard scheme to consider the solvent effects on many molecular properties. Most modem continuum models obtain through a self-consistent cycle the wave function of the molecule affected by the reaction potential thus the self-consistent reaction field acronym (SCRF). Solvatochromic effects have been more or less successfully explained using from Onsager s to more refined models like Nancy SCRF [44], Tomasi s polarizable continuum model (PCM) [45], Cramer and Tmhlar s SMx models [46]. 

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