COSMO-RS and COSMO-SAC parameters

The COSMO-RS and COSMO-SAC methods use general parameters and element-specific parameters. Each method has its own default parameter set, so selecting a method is sufficient to use its default parameters. This section lists which parameters are used by each COSMO-RS and COSMO-SAC method, their default values, and how to override them. Technical and accuracy parameters, such as convergence criteria, are listed separately. By default, the COSMO-RS method is used.

METHOD {COSMORS | COSMO-RS | COSMOSAC | COSMOSAC2013 |
        COSMOSAC2016 | COSMOSACDHB | COSMOSACDHB-MESP |
        COSMOSAC2010 | COSMOSAC2007}

COSMO-RS general parameters

METHOD COSMORS
CRSPARAMETERS
  {RAV         rav}
  {APRIME      aprime}
  {FCORR       fcorr}
  {CHB         chb}
  {SIGMAHBOND  sigmahbond}
  {AEFF        aeff}
  {LAMBDA      lambda}
  {OMEGA       omega}
  {ETA         eta}
  {CHORTF      chortf}
  {combi1998 | combi2005}
  {hb_all    | hb_hnof}
  {hb_temp   | hb_notemp}
End

The ADF combi2005 parameter set is the default for ADF calculations. The Klamt values can be found in Ref. [1]. See also Ref. [1] for the meaning of the parameters.

Table 3 COSMO-RS Parameters

Keyword	Symbol	ADF combi2005 (default)	ADF combi1998	Klamt	MOPAC PM6
		Ref. [2]	Ref. [2]	Ref. [1]
rav	\(r_{av}\)	0.400	0.415	0.5	0.400
aprime	a’	1510.0	1515.0	1288.0	1550.0
fcorr	\(f_{corr}\)	2.802	2.812	2.4	2.802
chb	\(c_{hb}\)	8850.0	8850.0	7400.0	8400.0
sigmahbond	\(\sigma_{hb}\)	0.00854	0.00849	0.0082	0.00978
aeff	\(a_{eff}\)	6.94	7.62	7.1	5.96
lambda	\(\lambda\)	0.130	0.129	0.14	0.135
omega	\(\omega\)	-0.212	-0.217	-0.21	-0.212
eta	\(\eta\)	-9.65	-9.91	-9.15	-9.65
chortf	\(c^\perp\)	0.816	0.816	0.816	0.816
combi1998 | combi2005		combi2005	combi1998	combi1998	combi2005
hb_all | hb_hnof		hb_hnof	hb_hnof	hb_hnof	hb_hnof
hb_temp | hb_notemp		hb_temp	hb_notemp	hb_notemp	hb_temp

chortf

See Ref. [1] for the definitions: \(\sigma_v^\perp = \sigma_v^0 - c^\perp \sigma_v\). See also the fast approximation section.

combi1998 | combi2005

Use combi1998 for the thermodynamically inconsistent combinatorial contribution to the pseudochemical potential, \(\mu_i^{comb}\), from Ref. [1]. Use combi2005 (default) for the thermodynamically consistent combinatorial contribution from Ref. [3]. See the combinatorial term.

hb_all | hb_hnof

Use hb_all to allow hydrogen bond interaction between H-atom segments and all other segments. Use hb_hnof (default) to allow hydrogen bond interaction only between H-atom segments bonded to N, O, or, F atoms and segments belonging to N, O, or F atoms.

hb_temp | hb_notemp

Use hb_notemp for the temperature-independent hydrogen bond interaction from Ref. [1]. Use hb_temp (default) for the temperature-dependent hydrogen bond interaction from Ref. [3]. See the temperature-dependent hydrogen bond interaction.

Links COSMO-RS GUI tutorial: set COSMO-RS parameters [1]

COSMO-RS element specific parameters

DISPERSION
  {H  dispH}
  {C  dispC}
  {N  dispN}
  {...}
End

The following table gives the element-specific COSMO-RS dispersion constants. These constants contribute to gas-phase pseudochemical potentials and vapor pressures. The ADF values are optimized for ADF calculations. The Klamt values can be found in Ref. [1]. The constants for F, Si, P, S, Br, and I in the ADF default parameter set were fitted to only a small number of experimental values or taken from Ref. [3].

Table 4 COSMO-RS Element Dispersion Parameters

element	ADF combi2005 (default)	ADF combi1998	Klamt
	Ref. [2]	Ref. [2]	Ref. [1]
H	-0.0340	-0.0346	-0.041
C	-0.0356	-0.0356	-0.037
N	-0.0224	-0.0225	-0.027
O	-0.0333	-0.0322	-0.042
Cl	-0.0485	-0.0487	-0.052
F	-0.026
Si	-0.04
P	-0.045
S	-0.052
Br	-0.055
I	-0.062

COSMO-RS element-specific dispersion parameters were not fitted for all elements in the periodic table.

Links COSMO-RS GUI tutorial: set COSMO-RS parameters [1]

COSMO-SAC general parameters

The ADF COSMO-RS program can use the COSMO-SAC models listed in the COSMO-SAC method table. A brief introduction to these models is available at here. For details, see the original references.

Table 5 COSMO-SAC Method Key

Method Key	GUI Label	Optimized with ADF Result Files	Reference
COSMOSAC | COSMOSAC2013	2013-ADF Xiong	Y	Ref. [4]
COSMOSAC2016	2016-ADF Chen	Y	Ref. [6]
COSMOSACDHB	DHB-ADF Chen	Y	Ref. [8]
COSMOSACDHB-MESP	DHB-ADF MESP	Y	Ref. [9]
COSMOSAC2010	2010 Hsieh	N	Ref. [5]
COSMOSAC2007	2007 Wang	N	Ref. [7]

Specifying a COSMO-SAC method key is sufficient to use the corresponding default parameter set from the COSMO-SAC Parameters Table. The SACPARAMETERS, EPSILON, and DISPERSION sections are optional and only override the parameters specified in them.

METHOD COSMOSAC
SACPARAMETERS
  {AEFF        aeff}
  {FDECAY      fdecay}
  {SIGMA0      sigma0}
  {RN          rn}
  {QN          qn}
  {AES         aes}
  {BES         bes}
  {COHOH       cohoh}
  {COTOT       cotot}
  {COHOT       cohot}
  {SIGMAHBOND  sigmahbond}
  {RAV         rav}
  {QS          qs}
  {rhbcut      rhbcut}
  {hb_temp   | hb_notemp}
End

Table 6 COSMO-SAC Parameters

Keyword	Symbol	2013-ADF Xiong	2016-ADF Chen	DHB-ADF Chen	DHB-ADF MESP	2010 Hsieh	2007 Wang
		Ref. [4]	Ref. [6]	Ref. [8]	Ref. [9]	Ref. [5]	Ref. [7]
aeff	\(a_{\mathrm{eff}}\)	6.4813	5.8447	5.8447	5.8447	7.25	7.25
fdecay	\(f_{\mathrm{decay}}\)		3.57	3.57	3.57	3.57	3.57
sigma0	\(\sigma_0\)	0.01233	0.007			0.007	0.007
rn	\(r\)		66.69	66.69	66.69	66.69	66.69
qn	\(q\)	79.532	79.53	79.53	79.53	79.53	79.53
aes	\(A_{\mathrm{ES}}\)	7877.13	5920.84	5920.84	5920.84	6525.69	8451.77
bes	\(B_{\mathrm{ES}}\)	0.0	1.3950 108	1.3950 108	1.3950 108	1.4859 108	0.0
cohoh	\(c_{\mathrm{OH-OH}}\)	5786.72	3551.10	33306.83	34234.17	4013.78	3484.42
cotot	\(c_{\mathrm{OT-OT}}\)	2739.58	1077.26	33306.83	34234.17	932.31	3484.42
cohot	\(c_{\mathrm{OH-OT}}\)	4707.75	3099.31	33306.83	34234.17	3016.43	3484.42
sigmahbond	\(\sigma_{\mathrm{hb}}\)			0.0063	0.0063
rav	\(r_{\mathrm{av}}\)	0.51
qs	\(q_{\mathrm{s}}\)	0.57
rhbcut	\(R_{\mathrm{cut}}^{\mathrm{HB}}\)			1.4432	1.3871
hb_temp | hb_notemp		hb_notemp	hb_notemp	hb_notemp	hb_notemp	hb_notemp	hb_notemp
omega	\(\omega\)		-0.212	-0.212	-0.212	-0.212	-0.212
eta	\(\eta\)		-9.00	-9.00	-9.00	-9.00	-9.00

Blank table entries indicate parameters that are not used by that COSMO-SAC model. The COSMO-SAC 2016-ADF Chen and COSMO-SAC DHB-ADF Chen parameter values used in AMS were reoptimized by Chen et al. for ADF COSMO result files and therefore differ from the original values in Ref. [6] and [8].

The parameter names from Ref. [7] were translated to the names used in Ref. [5] using: \(A_{\mathrm{ES}}=0.3 f_{\mathrm{pol}} a_{\mathrm{eff}}^{3/2} / (2 \epsilon_0)\), \(B_{\mathrm{ES}}=0\), and \(c_{\mathrm{OH-OH}} = c_{\mathrm{OT-OT}} = c_{\mathrm{OH-OT}} = c_{\mathrm{hb}}\).

hb_temp | hb_notemp

Use hb_notemp (default) for the temperature-independent hydrogen bond interaction from Ref. [7], [5] and [4]. Use hb_temp for the temperature-dependent hydrogen bond interaction described in temperature-dependent hydrogen bond interaction.

For COSMO-SAC 2013-ADF, the EPSILON block key sets element-specific epsilon constants contributing to vapor-pressure estimates and activity coefficients.

For COSMO-SAC methods other than COSMO-SAC 2013-ADF, the Dispersion block key sets the element-specific COSMO-RS dispersion constants used together with \(\omega\) and \(\eta\) in the COSMO-RS-like vapor-pressure estimate. These methods also use the OMEGA and ETA parameters in SACPARAMETERS:

METHOD COSMOSAC
SACPARAMETERS
  ...
  {OMEGA       omega}
  {ETA         eta}
End

COSMO-SAC element specific parameters

METHOD COSMOSAC2013
EPSILON
  {H  epsH}
  {C  epsC}
  {N  epsN}
  {...}
End

The following table gives the element-specific epsilon constants used only in COSMO-SAC 2013-ADF. These constants contribute to vapor-pressure estimates and activity coefficients.

Table 7 COSMO-SAC Element-Specific Epsilon Parameters

element	2013-ADF Xiong
	Ref. [4]
H	338.13
C.sp3	29160.92
C.sp2	30951.83
C.sp	20685.98
N.sp3	23488.54
N.sp2	22663.34
N.sp	6390.40
O.sp3-H	8527.06
O.sp3	8484.38
O.sp2	6736.85
O.sp2-N	12145.28
Cl	8435.13
F	82512.21
P	56067.81
S	45065.19
Br	62947.83
I	105910.88

COSMO-SAC element-specific epsilon parameters were not fitted for all elements in the periodic table.

Links COSMO-RS GUI tutorial: Expert option: set COSMO-SAC 2013-ADF parameters [1]

Technical and accuracy parameters

TECHNICAL
  {RSCONV rsconv}
  {SACCONV sacconv}
  {MAXITER maxiter}
  {BPCONV bpconv}
  {BPMAXITER bpmaxiter}
  {SOLCONV solconv}
  {SOLMAXITER solmaxiter}
  {SOLXILARGE solxilarge}
  {EHDELTAT ehdeltaT}
End

Table 8 Technical Parameters

Keyword	Default value	Description
rsconv	10-7 kcal/mol	Pseudochemical potential convergence criterion. Used only in COSMO-RS.
sacconv	10-7	Activity-coefficient convergence criterion. Used only in COSMO-SAC models.
maxiter	10000	Maximum number of cycles for pseudochemical potential or activity-coefficient calculations.
bpconv	10-6 bar	Convergence criterion for isobar or solvent boiling-point calculations.
bpmaxiter	40	Maximum number of cycles for isobar or solvent boiling-point calculations.
solconv	10-5 molar fraction	Convergence criterion for solubility calculations.
solmaxiter	40	Maximum number of cycles for solubility calculations.
solxilarge	0.99 molar fraction	Miscibility threshold for solubility calculations. Above this value, the mixture is considered fully miscible.
ehdeltaT	1.0 Kelvin	\(\Delta T\) used for numerical derivatives in excess-enthalpy calculations with the Gibbs-Helmholtz equation and enthalpy-of-vaporization calculations with the Clausius-Clapeyron equation.

Links COSMO-RS GUI tutorial: set COSMO-RS or COSMO-SAC 2013-ADF parameters [1]

References

[1] (1,2,3,4,5,6,7,8)

A. Klamt, V. Jonas, T. Bürger and J.C. Lohrenz, Refinement and Parametrization of COSMO-RS. J. Phys. Chem. A 102, 5074 (1998)

[2] (1,2,3,4)

C.C. Pye, T. Ziegler, E. van Lenthe, J.N. Louwen, An implementation of the conductor-like screening model of solvation within the Amsterdam density functional package. Part II. COSMO for real solvents. Can. J. Chem. 87, 790 (2009)

[3] (1,2,3)

A. Klamt, COSMO-RS From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design, Elsevier. Amsterdam (2005), ISBN 0-444-51994-7.

[4] (1,2,3,4)

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] (1,2,3,4)

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)

[6] (1,2,3)

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)

[7] (1,2,3,4)

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

[8] (1,2,3)

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)

[9] (1,2)

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)