COSMO method

There are many technical details involved in SCRF calculations, many of which the user can control. Readers of this book are advised to use the default values as much as possible unless they have carefully examined the original literature and tested their modifications. PCM methods are generally more accurate than the Onsager and COSMO methods. 

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

Smooth COSMO solvation model. We have recently extended our smooth COSMO solvation model with analytical gradients [71] to work with semiempirical QM and QM/MM methods within the CHARMM and MNDO programs [72, 73], The method is a considerably more stable implementation of the conventional COSMO method for geometry optimizations, transition state searches and potential energy surfaces [72], The method was applied to study dissociative phosphoryl transfer reactions [40], and native and thio-substituted transphosphorylation reactions [73] and compared with density-functional and hybrid QM/MM calculation results. The smooth COSMO method can be formulated as a linear-scaling Green s function approach [72] and was applied to ascertain the contribution of phosphate-phosphate repulsions in linear and bent-form DNA models based on the crystallographic structure of a full turn of DNA in a nucleosome core particle [74],... 

The COSMO method is a solution of the Poisson equation designed primarily for the case of very high e [190], It takes advantage of an analytic solution for the case of a conductor (e = ). The difference between (l--)for the case of e = 80 and e = °°is only 1.3%, so this is a good approximation for water. Its use for the treatment of nonpolar solvents with e 2 depends on further approximations which have not yet been sufficiently tested to permit an evaluation of their efficacy. 

In this book I will try to explain the different steps of the entire COSMO-RS method in detail, and give various examples of applications. For this purpose, we will start with the COSMO method in the next chapter. 

The effect of different heteroatoms on the ring opening of substituted three-membered rings was investigated at the B3LYP/TZV+P level of theory.115 Two specific water molecules were included in the calculations and the COSMO method was used to include the bulk solvent. With the methyl thiolate nucleophile, thiirane was... 

There are currently three different approaches for carrying out ASC-PCM calculations [1,3]. In the original method, called dielectric D-PCM [18], the magnitude of the point charges is determined on the basis of the dielectric constant of the solvent. The second approach is C-PCM by Cossi and Barone [24], in which the surrounding medium is modelled as a conductor instead of a dielectric. The third, IEF-PCM method (Integral Equation Formalism) by Cances et al the most recently developed [16], uses a molecular-shaped cavity to define the boundary between solute and dielectric solvent. We have to mention also the COSMO method (COnductorlike Screening MOdel), a modification of the C-PCM method by Klamt and coworkers [26-28], In the latter part of the review we will restrict our discussion to the methods that actually are used to model solute-solvent interactions in NMR spectroscopy. 

The designed molecular complexes of the reactants, products, and transition states were optimized using the Becke3LYP functional of the DFT technique and the COSMO method. The used basis set is the same as in the previous in vacuo model. The single point energy determination was performed with the CCSD(T) method and the 6-31++G(d,p) basis set within the COSMO formalism. The active space contained all of the orbitals except those belonging to frozen core electrons (Is of the O and N atoms inner electrons of Pt and Cl were covered within the ECP approach). 

All new compounds were fully characterized by spectroscopic data. UV-visible absorption spectra were measured with a Varian Cary 50 spectrophotometer. Spectroscopic measurements were done by using spectral grade solvents at 25 °C. Semi-empirical MO calculations were carried out with the AMI-COSMO method in the MOP AC package (MOPAC2000 ver. 1.0, Fujitsu Ltd, Tokyo, Japan, 1999). 

Solving the system of linear equations (Eq. (21)) would give induced charges qs for a solute in a conductor (sw = oo). The COSMO method assumes that the induced charges of a solute inside a dielectric with dielectric constant sw are equal to... 

The COSMO method is also interesting as the basis of a very successful COSMO-RS method, which extends the treatment to solvents other than water [27,28]. The COSMO method is very popular in quantum chemical computations of solvation effects. For example, 29 papers using COSMO calculations were published in 2001. However, we are not aware of its use together with MM force fields. Compared with the BE method, COSMO introduces one more simplification, that of Eq. (22). On the other hand, the matrix A in Eq. (21) is positively defined [25], which makes solution of the system of linear equations simpler and faster. Also, because both A and B matrices contain only electrostatic potential terms, their computation in quantum chemistry is easier than calculation of the electric field terms in Eq. (12). Another potential benefit is that the long-range electrostatic potential contribution is easier to expand into multipoles than the electric field needed in BE methods, which may benefit linear-scaling approaches. 

Quantum-Mechanical Continuum Solvation Models. Several ab initio continuum solvation models were discussed in Section 15.22. One can calculate AG, , by such SCRF methods as the dipole-in-a-sphere, the multipole expansion, or the PCM methods using semiempirical methods such as AMI or PM3 instead of an ab initio electronic-structure method. Thus the program MOPAC-93 implements the PCM calculation of solvent effects with semiempirical methods and the program AMPAC 6.0 implements the COSMO method. 

An alternative method for the description of solute-continuum electrostatic interaction has been developed as based on the notion that the electrostatic equations referring to the boimdary smface between the solute and dielectric mediiun can be substantially simplified if to assume that the solvent is a homogeneous ideally conducting medium. Within this method (called the COSMO method), the electrostatic screening energy of a solute is given by the following equation (in matrix form) ... 

The COnductor-like Screening MOdel (COSMO) is a method that computes the electrostatic interaction of the analyzed molecule with a certain solvent by considering the dielectric continuum surrounding the solute molecule outside of molecular cavities (Klamt and Schuiirmann 1993). The COSMO method can be used by all methods that compute the net atomic charges in analyzed molecules, for example, the semiempirical quantum mechanics method PM6. 

FIGURE 4 Typical structural model of the aralkyl hydroperoxides - Et NBr complexes with combined action of the cation, anion and the solvent molecule obtained by AMI/ COSMO method. 

TABLE 3 Values of Mi°(ROOH), A °(ROOHADq i AH° for the aralkyl hydropero-xides obtained with AMl/COSMO method. 

Continuum solvation models (QM/CSM), viii COSMO method, viii Coupled eluster Bruckner double (BD), 10 Coupled cluster linear response equations, 30 Coupled cluster linear response functions, 24 Coupled cluster method (CC), 6, 8, 20, 30, 31 Coupled cluster quadratic response functions, 31... 

Figure 8. Visualization of the screening charges on the COSMO surface obtained for the DPNO radical in water. The plots were generated employing (a) the COSMO correction, (b) the D-COSMO-RS approach, (c) the supermolecule approach in combination with the COSMO method, and (d) a difference plot of the screening charges from COSMO and D-COSMO-RS. Positive screening charges are given in red. Reproduced with permission from [133]. Copyright 2006, American Chemical Society.

Fig. 8.6 Energy profiles in aqueous solution by the PEG method (Apeg. closed circles), and the COSMO method (Acosmo. closed triangles), and in the isolated state at PM3 (Vs(PM3), opened circles) level of theory along the reaction coordinate R(N1-H5) according to the EEG method (Reproduced with permission from Nagaoka et al. [9]. Copyright 2006 American chemical society)...

Figure 12 shows the behavior of the supermolecule and supermolecule -I- COSMO methods as a function of number of solvent molecules. (Note that there are several possibilities for the radical-pair clusters. The energies reported were the... 

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