Polarizable continuum solvation models PCMs

We have reviewed some recent computational methodologies based on the combination of the TDDFT theory with the Polarizable Continuum solvation Model (PCM) to study chromophores in homogenous solutions. In particular we have considered... 

In the standard continuum solvation model, exemplified by the Polarizable Continuum Model (PCM) we developed in Pisa [9], the solute-solvent interaction energies are described by four Qx operators, each having a clearly defined physical nature. Each term gives a contribution to the solvation energy which has the nature of a free energy. The free energy of M in solution is thus defined as the sum of these four terms, supplemented by a fifth describing contributions due to thermal motions of the molecular framework ... 

The valence bond method with polarizable continuum model (VBPCM) method (55) includes solute—solvent interactions in the VB calculations. It uses the same continuum solvation model as the standard PCM model implemented in current ab initio quantum chemistry packages, where the solvent is represented as a homogeneous medium, characterized by a dielectric constant, and is polarizable by the charge distribution of the solute. The interaction between the solute charges and the polarized electric field of the solvent is taken into account through an interaction potential that is embedded in the... 

This chapter reviews the recent progress of the TDDFT when coupled to quantum mechanical (QM) continuum solvation models. Although the discussion will be focused on a specific family of solvation models, namely the family of methods known with the acronym PCM (Polarizable Continuum Model) [6], most of the results can be straightforwardly extended to other classes of implicit solvation models [7, 8],... 

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. 

Complementing the results obtained for the study of ground electronic states in solution, many computational studies indicate that approaches exploiting continuum solvation models are very effective tools for evaluating the solvent effect on the excited-state properties. Among continuum models, the polarizable continuum model (PCM) is probably the one most commonly used. In the following, we thus focus mainly on this method [78, 82]. 

We developed expressions for EOM-CCSD-PCM in the SS formalism, and a series of approximations to reduce the considerable computational cost of this approach. Christiansen and Mikkelsen originally developed the LR formalism for the CCSD wave function in solution for a simple continuum solvation model. Later, they extended it to their flavour of explicit polarizable solvation model. Cammi has also presented several interesting developments in this research area, including a rederivation of the LR-CCSD expressions for PCM, and we presented the first implementation of the method. Other examples of CC methods combined with (non-)polarizable solvation models [e.g., fixed point charges) are also available in the literature. ... 

CSM = continuum solvation model COSMO = conductorlike screening model COSMO-RS = generalization of COSMO to real solvents QC = quantum chemical PCM = polarizable continuum model SAS = solvent accessible surface SES = solvent excluding surface NPPA = average number of segments per full atom vdW = van der Waals, VWN = Vosko-Wilk-Nusair functional (see Density Functional Theory Applications to Transition Metal Problems). 

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. 

DFT was employed to study the mechanism of ammonolysis of phenyl formate in the gas phase, and the effect of various solvents on the title reaction was assessed by the polarizable continuum model (PCM). The calculated results show that the neutral concerted pathway is the most favourable one in the gas phase and in solution.24 The structure and stability of putative zwitterionic complexes in the ammonolysis of phenyl acetate were examined using DFT and ab initio methods by applying the explicit, up to 7H20, and implicit PCM solvation models. The stability of the zwitterionic tetrahedral intermediate required an explicit solvation by at least five water molecules with stabilization energy of approximately 35 kcalmol-1 25... 

The purpose of this chapter is to present an overview of the computational methods that are utilized to study solvation phenomena in NMR spectroscopy. We limit the review to first-principle (ab initio) calculations, and concentrate on the most widespread solvation model the polarizable continuum model (PCM), which has been largely described in the previous chapter of this book. 

The approach which will be reviewed here has been formulated within the framework of the quantum mechanical polarizable continuum model (PCM) [7], Within this method, the effective properties are introduced to connect the outcome of the quantum mechanical calculations on the solvated molecules to the outcome of the corresponding NLO experiment [8], The correspondence between the QM-PCM approach and the semi-classical approach will also be discussed in order to show similarities and differences between the two approaches. 

A significant recent advance in continuum SD has been achieved by combining the solvation response expressions in terms of the solvent s(cu) with quantum mechanical (QM) electronic structure methodology for solvated species. Specifically, the polarizable continuum model (PCM) [51], which was originally developed to predict the electronic structure of solutes in polar media, has been extended to nonequilibrium solvation [52]. A review by Mennucci [8] describes this extension of PCM and its application to the evaluation of S(t). The readers are referred to that article for the outline of the overall approach and for the details of the methods used. 

In this contribution we will first outline the formalism of the ONIOM method. Although ONIOM has not yet been applied extensively to problems in the solvated phase, we will show how ONIOM has the potential to become a very valuable tool in both the explicit and implicit modeling of solvent effects. For the implicit modeling of solvent, we developed the ONIOM-PCM method, which combines ONIOM with the Polarizable Continuum Method (PCM). We will conclude with a case study on the vertical electronic transition to the it state in formamide, modeled with several explicit solvent molecules. 

T. Vreven, B. Mennucci, C. O. da Silva, K. Morokuma and J. Tomasi, The ONIOM-PCM method Combining the hybrid molecular orbital method and the polarizable continuum model for solvation. Application to the geometry and properties of a merocyanine in solution, J. Chem. Phys., 115 (2001) 62-72. 

---