Polarizable continuum model geometry optimization

H. Li and J. H. Jensen, Improving the accuracy and efficiency of geometry optimizations with the polarizable continuum model new energy gradients and molecular surface tessellation, J. Comput. Chem., 25 (2004) 1449-1462. 

Barone V, Cossi M, Tomassi J (1998) Geometry optimization of molecular structures in solution by the polarizable continuum model. J Comput Chem 19 404-417... 

Although many satisfactory VCD studies based on the gas phase simulations have been reported, it may be necessary to account for solvent effects in order to achieve conclusive AC assignments. Currently, there are two approaches to take solvent effects into account. One of them is the implicit solvent model, which treats a solvent as a continuum dielectric environment and does not consider the explicit intermolecular interactions between chiral solute and solvent molecules. The two most used computational methods for the implicit solvent model are the polarizable continuum model (PCM) [93-95] and the conductor-like screening model (COSMO) [96, 97]. In this treatment, geometry optimizations and harmonic frequency calculations are repeated with the inclusion of PCM or COSMO for all the conformers found. Changes in the conformational structures, the relative energies of conformers, and the harmonic frequencies, as well as in the VA and VCD intensities have been reported with the inclusion of the implicit solvent model. The second approach is called the explicit solvent model, which takes the explicit intermolecular interactions into account. The applications of these two approaches, in particular the latter one will be further discussed in Sect. 4.2. 

Embedded quantum/classical calculations were used to study the epoxidation reaction of styrene catalyzed by Mn-porphyrins. Optimized geometries were obtained for the Mn-porphyrin, reaction intermediates, and transition state structures along the proposed reaction path. A polarizable continuum model (PCM) was used to study solvent effects, with dichloromethane as the solvent. While it has been shown previously that the concerted intermediate between the oxidized porphyrin and the alkene is the lowest energy configuration, a transition state to directly form the concerted intermediate without the prior formation of a radical could not be found. A stepwise mechanism, in which a radical intermediate is formed before the concerted intermediate, is proposed. 

The polarizable continuum model (PCM) by Tomasi and coworkers [77-79] was selected to describe the effects of solvent, because it was used to successfully investigate the effect of solvent upon the energetics and equilibria of other small molecular systems. The PCM method has been described in detail [80]. The solvents and dielectric constants used were benzene (s = 2.25), methylene chloride (g = 8.93), methanol (g = 32.0), and water (g = 78.4). Full geometry optimizations were carried out for the discrete and PCM models. To simultaneously account for localized hydrogen bonding and bulk solvation effects, PCM single-point energy calculations have been conducted on stationary points of the acrolein and butadiene reaction with two waters explicitly... 

Geometry optimization and absorption peak prediction were performed by the Gaussian 03 program 3 the geometries of all compounds were optimized by B3LYP/6-31+G(d,p) level of theory, and absorption peaks were predicted by TD-B3LYP/6-31+G(d,p). We also applied the Polarizable Continuum Model (PCM) to solvent effect of DMSO (e=46.7) on the geometry optimization and prediction of absorption peaks. 

The original PCM method uses atomic spheres with radii 1.2 times the van der Waals radii to define the molecular cavity. The isodensity polarizable continuum model (IPCM) is a modification of the PCM that defines the surface of the molecular cavity as a contour surface of constant electron probability density of the solute molecule M [J. B. Foresman et al., J. Phys. Chem., 100,16098 (1996)]. The isodensity value 0.0004 electrons/bohr is commonly used, but other values have also been recommended [C.-G. Zhan and D. M. Chipman, J. Chem. Phys., 109, 10543 (1998)]. Since the solute s electronic wave function changes in each SCRF iteration, the size of the molecular cavity changes in each IPCM iteration. In the IPCM method, Pint is calculated from apparent surface charges. The self-consistent isodensity PCM (SCIPCM) method is a refinement of the IPCM method Foresman and Frisch, Chapter 10), which allows geometry optimization and vibrational-frequency calculations to be done for the solute molecule in solution. 

Bond distances in A, valence and dihedral angles in polarizable continuum model, PCM Results using the MOx geometry optimized in a... 

All calculations were performed within the Kohn-Sham framework. Geometries of all radical species were optimized in solvent at the B3LYP/6-311-l-G(d,p) level of theory [29-31] using both the polarizable continuum model through the integral equation formalism (lEF-PCM), as implemented in Gaussian09 [32], and the conductor-like screening model (COSMO), as implemented in MOLPRO... 

Additionally, for flexible molecules, the presence of multiple conformations may require the consideration of solvent effects, mainly if experimental data in polar solvents are to be reproduced. The relative energies of conformers and their chiroptical properties can be largely affected by solvent effects, and thus, in some cases, the inclusion of either the polarizable continuum model (PCM) or the conductor-like screening model (COSMO) since geometry optimization steps may be beneficial." ... 

Alternatively, reaction field calculations with the IPCM (isodensity surface polarized continuum model) [73,74] can be performed to model solvent effects. In this approach, an isodensity surface defined by a value of 0.0004 a.u. of the total electron density distribution is calculated at the level of theory employed. Such an isodensity surface has been found to define rather accurately the volume of a molecule [75] and, therefore, it should also define a reasonable cavity for the soluted molecule within the polarizable continuum where the cavity can iteratively be adjusted when improving wavefunction and electron density distribution during a self consistent field (SCF) calculation at the HF or DFT level. The IPCM method has also the advantage that geometry optimization of the solute molecule is easier than for the PISA model and, apart from this, electron correlation effects can be included into the IPCM calculation. For the investigation of Si compounds (either neutral or ionic) in solution both the PISA and IPCM methods have been used. [41-47]... 

---