Polarizable Continuum Model linear-response

PCM-LR Polarizable Continuum Model Linear Response method... 

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]. 

R. Cammi and J. Tomasi, Nonequilibrium solvation theory for the polarizable continuum model - a new formulation at the SCF level with application to the case of the frequency-dependent linear electric-response function, Int. J. Quantum Chem., (1995) 465-74 B. Mennucci, R. Cammi and J. Tomasi, Excited states and solvatochromic shifts within a nonequilibrium solvation approach A new formulation of the integral equation formalism method at the self-consistent field, configuration interaction, and multiconfiguration self-consistent field level, J. Chem. Phys., 109 (1998) 2798-807 R. Cammi, L. Frediani, B. Mennucci, J. Tomasi, K. Ruud and K. V. Mikkelsen, A second-order, quadratically... 

Abstract The computational study of excited states of molecular systems in the condensed phase implies additional complications with respect to analogous studies on isolated molecules. Some of them can be faced by a computational modeling based on a continuum (i.e., implicit) description of the solvent. Among this class of methods, the polarizable continuum model (PCM) has widely been used in its basic formulation to study ground state properties of molecular solutes. The consideration of molecular properties of excited states has led to the elaboration of numerous additional features not present in the PCM basic version. Nonequilibrium effects, state-specific versus linear response quantum mechanical description, analytical gradients, and electronic coupling between solvated chromophores are reviewed in the present contribution. The presentation of some selected computational results shows the potentialities of the approach. 

R. Cammi, B. Mennucci, Linear response theory for the polarizable continuum model B. J. Chem. Phys. 110, 9877 (1999)... 

S. Comi, R. Cammi, B. Mennucci, J. Tomasi, Electronic excitation energies of molecules in solution within continuum solvation models Investigating the discrepancy between state-specific and linear-response methods, Formation and relaxation of excited states in solution A new time dependent polarizable continuum model based on time dependent density functional theory. J. Chem. Phys. 123, 134512 (2005)... 

Here, we provide the theoretical basis for incorporating the PE potential in quantum mechanical response theory, including the derivation of the contributions to the linear, quadratic, and cubic response functions. The derivations follow closely the formulation of linear and quadratic response theory within DFT by Salek et al. [17] and cubic response within DFT by Jansik et al. [18] Furthermore, the derived equations show some similarities to other response-based environmental methods, for example, the polarizable continuum model [19, 20] (PCM) or the spherical cavity dielectric... 

Other Work on Water-Related Systems. Sonoda et al.61 have simulated a time-resolved optical Kerr effect experiment. In this model, which uses molecular dynamics to represent the behaviour of the extended medium, the principle intermolecular effects are generated by the dipole-induced-dipole (DID) mechanism, but the effect of the second order molecular response is also include through terms involving the static molecular / tensor, calculated by an MP2 method. Weber et al.6S have applied ab initio linear scaling response theory to water clusters. Skaf and Vechi69 have used MP2/6-311 ++ G(d,p) calculation of the a and y tensors of water and dimethylsulfoxide (DMSO) to carry out a molecular dynamics simulation of DMSO/Water mixtures. Frediani et al.70 have used a new development of the polarizable continuum model to study the polarizability of halides at the water/air interface. 

R. Cammi and J. Tomasi, Int. J. Quantum Chem., 29, 465 (1995). Nonequilibrium Solvation Theory for the Polarizable Continuum Model A New Formulation at the SCF Level with Application to the Case of the Frequency-Dependent Linear Electric Response Function. 

The problem of the description of the excited states within the Polarizable Continuum Model leads to two non-equivalent approaches, the approach based on the linear response (LR) approach, and the state specific (SS) approach, as already said in the Introduction. Each approach has advantages and disadvantages. The LR approach is computationally more convenient, as it gives the whole spectrum of the excited states of interest in a single calculation, but is physically biased. In fact, in the LR approach the solute-solvent interaction contains a term related to the one-particle transition densities of the solute connecting the reference state adopted in the LR calculation, which usually corresponds to the electronic groimd state, to the excited electronic state. The SS approach is computationally more expensive, as it requires a separate calculation for each of the excited states of interest, but is physically im-biased. In fact, in the SS approach the solute-solvent interaction is determined by the effective one-particle electron density of the excited state. 

Since pNA and most of the chromophores of interest have large dipole moments an important feature of the continuum models is the introduction of the reaction field. The pNA molecule at the centre of the cavity in the continuum induces a polarization on the surface of the cavity, which produces the reaction field acting on the central molecule. This reaction field changes the dipole moment of the pNA molecule via the linear polarizability. A self consistent procedure is required in which the effects of the reaction field and also the effects of the applied macroscopic fields modified by the internal field factors are included in a self-consistent determination of the molecular response within a specified quantum mechanical model. 

The application of the Lorentz-Lorenz equation gives a convincing demonstration of the general similarity of the linear response in gas and liquid but its application in the liquid introduces an approximation which has not yet been quantified. A more precise objective for the theory would be to calculate the frequency dependent susceptibility or refractive index directly. For a continuum model this may lead to a polarizability rigorously defined through the Lorentz-Lorenz equation as shown in treatments of the Ewald-Oseen theorem (see, for example Born and Wolf, plOO),59 but the polarizability defined in this way need not refer to one molecule and would not be precisely related to the gas parameters. 

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