CPCM model

Solvatochromic shifts for cytosine have also been calculated with a variety of methods (see Table 11-7). Shukla and Lesczynski [215] studied clusters of cytosine and three water molecules with CIS and TDDFT methods to obtain solvatochromic shifts. More sophisticated calculations have appeared recently. Valiev and Kowalski used a coupled cluster and classical molecular dynamics approach to calculate the solvatochromic shifts of the excited states of cytosine in the native DNA environment. Blancafort and coworkers [216] used a CASPT2 approach combined with the conductor version of the polarizable continuous (CPCM) model. All of these methods predict that the first three excited states are blue-shifted. S i, which is a nn state, is blue-shifted by 0.1-0.2 eV in water and 0.25 eV in native DNA. S2 and S3 are both rnt states and, as expected, the shift is bigger, 0.4-0.6eV for S2 and 0.3-0.8 eV for S3. S2 is predicted to be blue-shifted by 0.54 eV in native DNA. 

As a second example, we have determined the influence of solvation on the steric retardation of SN2 reactions of chloride with ethyl and neopentyl chlorides in water, which has recently been studied by Vayner and coworkers [91]. In their study solvent effects were examined by means of QM-MM Monte Carlo simulations as well as with the CPCM model. Solvation causes a large increase in the activation energies of these reactions, but has a very small differential effect on the ethyl and neopentyl substrates. Nevertheless, a quantitative difference was found between the stability of the transition states determined using discrete and continuum treatments of solvation, since the activation free energies for ethyl chloride and neopentyl chloride amount to 23.9 and 30.4kcalmoF1 according to MC-FEP simulations, but to 38.4 and 47.6 kcal moF1 from CPCM computations. 

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. 

As mentioned above, we have considered the effect of bulk solvent (here water) on the electronic properties of Co(II) complex by the CPCM model. While this approach well reproduces non-specific solute-solvent interactions,... 

The properties of the Bernhard catalyst were studied by our group at the DFT (B3LYP) level.Geometries were fuUy optimized in gas phase with an SDD/6-31G basis set and their energies thereafter refined with an SDD/ 6-311+G basis set, including the solvation effects of water with the continuum CPCM model. The study focused on the influence of the protonation state of the postulated active species ([Ir (0)(X)(ppy)2] with... 

Bulk solvent described by the CPCM model, specific solvent effects considered by adding n = (4) water molecules in a metal coordination sphere. VE energies [eV], absorption wavelengths A. [nm]), oscillator strengths (f) and dipole moment p [Debyee]) are reported. All values are computed at... 

The percolation theory [5, 20-23] is the most adequate for the description of an abstract model of the CPCM. As the majority of polymers are typical insulators, the probability of transfer of current carriers between two conductive points isolated from each other by an interlayer of the polymer decreases exponentially with the growth of gap lg (the tunnel effect) and is other than zero only for lg < 100 A. For this reason, the transfer of current through macroscopic (compared to the sample size) distances can be effected via the contacting-particles chains. Calculation of the probability of the formation of such chains is the subject of the percolation theory. It should be noted that the concept of contact is not just for the particles in direct contact with each other but, apparently, implies convergence of the particles to distances at which the probability of transfer of current carriers between them becomes other than zero. 

For the small system involved in the water exchange on [Be(H20)4]2+, we evaluated the effect of an implicit and approximated explicit treatment of the bulk water while investigating water exchange on [Be(H20)4]2+. For the implicit treatment, the CPCM and PCM models were applied as implemented in Gaussian, and geometry optimizations and... 

A structural comparison of the calculated (B3LYP/6-311+G ) ts (transition state in the gas phase), ts-wc (transition state in the cluster of five extra water molecules), ts-CPCM (transition state within the CPCM-solvent model (B3LYP(CPCM)/6-311+G )) and ts-PCM (transition state optimized within the PCM-solvent model (B3LYP(PCM)/6-311+G )), shows no large differences (see Fig. 8), which is also valid for the precursor complexes (see Fig. 9). Modeling solvent effects shrinks in all cases the Be-0 bonds of the entering/leaving water molecules (159). 

While the transition states could all be confirmed as transition states, only the precursor in the gas phase pc, and for the water cluster approach pc-wc, was confirmed as a local minimum, and despite intensive search no minima could be found within the CPCM and PCM model approximation. 

While the MP2(full)/6-311+G 7/B3LYP/6-311+G energies show typical discrepancies, the application of the IPCM- and CPCM-solvent models dramatically lowers the energy for the intermediate and the transition states. The barriers of 2.8 and 1.8kcalmol 1 corroborate the experimental findings for an efficient formation of a water coordinated Li+ complex. 

Despite the simple form of Equation (1.83), the detailed formulation of an extended Lagrangian for CPCM is not a straightforward matter and its implementation remains challenging from the technical point of view. Nevertheless, is has been attempted with some success by Senn and co-workers [31] for the COSMO-ASC model in the framework of the Car-Parrinello ab initio MD method. They were able to ensure the continuity of the cavity discretization with respect to the atomic positions, but they stopped short of providing a truly continuous description of the polarization surface charge as suggested,... 

Table 1.2 Energy (kcal moC1) for the three molecules in Figure 1.8 in vacuo and in solution are reported. CPCM and DPCM indicate the calculations performed with the standard version of the models, sCPCM and sDPCM indicate the calculations where the geometry and the polarization are optimized simultaneously...

To account for indirect solvent effects, solvation models must allow for geometry optimizations and frequency calculations including the solute-solvent interactions. Indeed, many ab initio continuum solvation models and in particular those belonging to the family of the PCM [3] provide analytical first and second derivatives of the free energy with respect to the nuclear coordinates [4,5], In the following we shall present in detail the formalism for the derivatives in the PCM and Conductor-PCM (CPCM) [6] models. 

Keeping in mind the intrinsic features associated with the definition of the cavity in the most popular QM-SCRF methods, it can be questioned what is the influence of the fine details of the cavity definition on the computed solvation free energies. This question has been investigated in a recent study by Takano and Houk [61], who have examined the dependence of the solvation free energies estimated for a series of 70 compounds, including neutral and charged species, on both the choice of the cavity and the level of theory used in computations within the framework of the conductor-like polarizable continuum model (CPCM). The mean absolute deviation (MAD) between calculated... 

Y. Takano and K. N. Houk, Benchmarking the conductor-like polarizable continuum model (CPCM) for aqueous solvation free energies of neutral and ionic organic molecules, J. Chem. Theory Comput., 1 (2005) 70-77. 

In addition to SMx and the cluster-continuum model, other continuum models have also been used to study reactions in liquids, including the polarized continuum model [133-135] (PCM), the conductor-like screening model (COSMO [136] and COSMO-RS [137,138]), the generalized COSMO [139] (GCOSMO) model, conductorlike PCM [140] (CPCM), and isodensity PCM [141] (IPCM). 

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