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:**

  * The ADFCRS-2018 database is updated.

  * The Densf calculation is enable when generating the ADF COSMO
    result file using the COSMO-RS Compound Task.


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.

[1] S.T. Lin and S.I. Sandler, *A Priori Phase Equilibrium Prediction
    from a Segment Contribution Solvation Model*,  Ind. Eng. Chem.
    Res. 41, 899 (2002)

[2] S. Wang, S.I. Sandler, C.C. Chen, *Refinement of COSMO-SAC and the
    Applications*,  Ind. Eng. Chem. Res. 46, 7275 (2007)

[3] C.M. Hsieh, S.I. Sandler, S.T. Lin, *Improvements of COSMO-SAC for
    vapor-liquid and liquid-liquid equilibrium predictions*,  Fluid
    Phase Equilib. 297, 90 (2010)

[4] R. Xiong, S.I. Sandler, R.I. Burnett, *An improvement to COSMO-SAC
    for predicting thermodynamic properties*,  Ind. Eng. Chem. Res.
    53, 8265 (2014)

[5] W.L. Chen, C.M. Hsieh, L. Yang, C.C. Hsu, S.T. Lin, *A Critical
    Evaluation on the Performance of COSMO-SAC Models for Vapor-Liquid
    and Liquid-Liquid Equilibrium Predictions Based on Different
    Quantum Chemical Calculations*,  Ind. Eng. Chem. Res. 55, 9312
    (2016)

[6] W.L. Chen, S.T. Lin, *Explicit consideration of spatial hydrogen
    bonding direction for activity coefficient prediction based on
    implicit solvation calculations*,  Phys.Chem.Chem.Phys. 19, 20367
    (2017)

[7] C.C. Chang, W.L. Chen, D.T. Wu, S.T. Lin , *Improved directional
    hydrogen bonding interactions for the prediction of activity
    coefficients with COSMO-SAC*,  Ind. Eng. Chem. Res. 57, 11229
    (2018)
