COSMO-SAC 2013-ADF, 2016-ADF, DHB-ADF

On the basis of the framework of COSMO-RS, Lin and Sandler [1] suggested a variation, the COSMO-SAC (where SAC denotes segment activity coefficient) model by invoking a necessary thermodynamic consistency criterion. Although there are differences, COSMO-RS and COSMO-SAC share some similarities. Over time, several improvements have been made to the COSMO-SAC model, particularly in the treatment of electrostatic interaction and hydrogen bonding interaction:

  • In Ref. [2], a Gaussian-type probability for determining the hydrogen bonding \(\sigma\)-profile \(\left( P^{hb}(\sigma) \right)\) is introduced. This version is called here the COSMO-SAC 2007 method.

  • In Ref. [3], temperature dependence is introduced into the electrostatic interaction, and \(P^{hb}(\sigma)\) is differentiated into \(P^{OH}(\sigma)\) and \(P^{OT}(\sigma)\). This revised COSMO-SAC model is called here the COSMO-SAC 2010 method.

Note: The parameters of the COSMO-SAC 2007 and COSMO-SAC 2010 methods have not been optimized for use with ADF COSMO result files.

COSMO-SAC 2013-ADF

The COSMO-SAC 2013-ADF method used in ADF is the one developed by Xiong et al., which is described in detail in Ref. [4]. The COSMO-SAC 2013-ADF parameters in Ref. [4] were optimized for use with ADF COSMO result files. COSMO-SAC 2013-ADF is an improved COSMO-SAC method compatible to ADF and different than previous COSMO-SAC methods. The main difference compared to previous COSMO-SAC methods is that the COSMO-SAC 2013 model includes a dispersion contribution in the mixture interaction.

COSMO-SAC 2016-ADF

In Ref. [5] COSMO-SAC model parameters were optimized by Chen et al. for different quantum mechanical calculations. The authors of Ref. [5] also reoptimized the revised COSMO-SAC model [3] parameters for quantum mechanical calculations with ADF, which will be called here the COSMO-SAC 2016-ADF method.

COSMO-SAC DHB-ADF

Instead of differentiating the \(P^{hb}(\sigma)\) into \(P^{OH}(\sigma)\) and \(P^{OT}(\sigma)\), a directional hydrogen bond (DHB) approach was introduced in Ref. [6], leading to the development of the COSMO-SAC(DHB) model. This model constrains hydrogen bond segments within a cutoff radius around the hydrogen bond center (hbc), which is determined using VSEPR theory and molecular geometry. The parameters were reoptimized by Chen et al. for use with ADF, which will be called here the COSMO-SAC DHB-ADF method.

COSMO-SAC DHB-MESP

In Ref. [7] an improved directional hydrogen bond approach was developed. The new scheme determines the hbc through the local minima of the molecular electrostatic potential (MESP), computed from the Densf calculation. Unlike the VSEPR-based approach, which is limited to chemical species with distinct hybridization characteristics, this new method is applicable to all types of chemical species. This improved approach will be referred to as the COSMO-SAC DHB-ADF MESP method.

Note

The COSMO-SAC DHB-MESP method requires the hydrogen bond center derived from the Densf calculation. To use this model, ensure that:

ADF Implementation of the COSMO-SAC Model

The ADF COSMO-RS program can calculate activity coefficients using any of the COSMO-SAC model version described above. Like in the COSMO-RS method, pure compound vapor pressures can be given as input, for example, if experimental values are available. In case of the COSMO-SAC 2013-ADF model, if these values are not specified then the pure compound vapor pressure will be calculated according to the COSMO-SAC 2013-ADF model. However, for all other COSMO-SAC models, if these values are not specified then the pure compound vapor pressures will be approximated using a method similar as in the COSMO-RS method.

The COSMO-SAC 2013 model includes a dispersion contribution in the mixture interaction. This dispersion contribution is a complicated expression which also depends on the liquid molar volume of the pure compounds and on the molar volume of the mixture. The molar volume of the mixture is calculated from the pure compound liquid molar volumes assuming ideal mixing. In the input for the ADF COSMO-RS program one include for each compound the experimental pure compound liquid density (kg/L), from which the program can calculated the pure compound liquid molar volumes. If this density is not given the pure compound liquid molar volume will be calculated from its COSMO volume. Note that in the calculations with the COSMO-SAC 2013-ADF model in Ref. [4] often experimental pure compound liquid molar volumes were used.

The complete set of parameters used in different COSMO-SAC models can be found at the COSMO-RS program section.

The governing equations for various property calculations are summarized in the Calculation of Properties section.

References