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The Direct COSMO-RS method (DCOSMO-RS):

In order to go beyond the pure electrostatic model a self consistent implementation of the COSMO-RS model the so-called "Direct COSMO-RS" (DCOSMO-RS) [177] has been implemented in ridft and dscf.

COSMO-RS (COSMO for Real Solvents) [178,179] is a predictive method for the calculation of thermodynamic properties of fluids that uses a statistical thermodynamics approach based on the results of COSMO SCF calculations for molecules embedded in an electric conductor, i.e. using f ($ \varepsilon$) = 1 . The liquid can be imagined as a dense packing of molecules in the perfect conductor (the reference state). For the statistical thermodynamic procedure this system is broken down to an ensemble of pair wise interacting surface segments. The interactions can be expressed in terms of surface descriptors. e.g. the screening charge per segment area ( σt = qt/at ). Using the information about the surface polarity σ and the interaction energy functional, one can obtain the so-called σ -potential ( μS(σ;T) ). This function gives a measure for the affinity of the system S to a surface of polarity σ . The system S might be a mixture or a pure solvent at a given temperature T . Because the parabolic part of the potential can be described well by the COSMO model, we substract this portion form the COSMO-RS potential:

$\displaystyle \tilde{{\mu}}_{S}^{}$(σ;T) = μS(σ;T) - (1 - f ($\displaystyle \varepsilon$))c0σ2.      

The parameter c0 can be obtained from the curvature of a COSMO-RS σ -potential of a nonpolar substance, e.g. hexane. Thus, the remaining part of the chemical potential of a compound i with mole fraction xi in the mixture S i can be expressed as:


μi$\displaystyle \sum^{m}_{{t=1}}$at$\displaystyle \tilde{{\mu}}_{S}^{}$(σ;T) + μiC, S + kT ln(xi).      

where the combinatorial term μiC, S accounts for effects due to the size and shape differences of the molecules in the mixture and at denotes the area of segment t . The kT ln(xi) can be skiped for infnited dilution. The free energy gained by the solvation process in the DCOSMO-RS framework is the sum of the dielectric energy of the COSMO model and the chemical potential described above:

Ediel, RS = $\displaystyle {\frac{{1}}{{2}}}$f ($\displaystyle \varepsilon$)$\displaystyle \bf q^{{\dagger}}_{}$$\displaystyle \bf\Phi^{{sol}}_{}$ + fpolμi = Ediel + fpolμi      

The factor fpol has been introduced to account for the missing solute-solvent back polarization. The default value is one in the current implementation. From the above expression the solvent operator $ \hat{{V}}^{{RS}}_{}$ can be derived by functional derivative with respect to the electron densityr:
$\displaystyle \hat{{V}}^{{RS}}_{}$ = - $\displaystyle \sum^{m}_{{t=1}}$$\displaystyle {\frac{{f(\varepsilon) q_t+q^{{\Delta}RS}_t}}{{\lvert {\bf r}_t -{\bf r} \rvert}}}$ = $\displaystyle \hat{{V}}^{{cos}}_{}$ - $\displaystyle \sum^{m}_{{t=1}}$$\displaystyle {\frac{{q^{{\Delta}RS}_t}}{{\lvert {\bf r}_t -{\bf r} \rvert}}}$.      

Thus, the solvation influence of the COSMO-RS model can be viewed as a correction of the COSMO screening charges qt . The additional charges denoted as qΔRSt can be obtained from $ \bf q^{{{\Delta}RS}}_{}$ = - $ \bf A^{{-1}}_{}$$ \bf\Phi^{{{\Delta}RS}}_{}$ , where the potential $ \bf\Phi^{{{\Delta}RS}}_{}$ arises from the chemical potential of the solute in the solvent:
φΔRSt = fpolat$\displaystyle \left(\vphantom{ \frac{\delta \tilde{\mu}_S}{\delta q}}\right.$$\displaystyle {\frac{{\delta \tilde{\mu}_S}}{{\delta q}}}$$\displaystyle \left.\vphantom{ \frac{\delta \tilde{\mu}_S}{\delta q}}\right)_{{q=q_t}}^{}$.      

In order to get a simple and differentiable representation of the COSMO-RS σ -potential μS(σ;T) , we use equally spaced cubic splines. An approximate gradient of the method has been implemented. DCOSMO-RS can be used in SCF energy and gradient calculations (geometry optimizations) with dscf, ridft, grad, and rdgrad. Please regard the restriction of the DCOSMO-RS energy explained in the keyword section 18.2.8. Because the DCOSMO-RS contribution can be considered as a slow term contribution in vertical exitations it does not have to be taken into account in response calculations. For the calculation of vertical excitation energies it is recommended to use the mos of a DCOSMO-RS calculation in a COSMO response calculation (see above).


next up previous contents index
Next: Keywords in the control Up: Treatment of Solvation Effects Previous: Vertical excitations and Polarizabilities   Contents   Index
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