Cosmosac Regression Presentation

8/11/2019 Cosmosac Regression Presentation

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Sigma profile generation with

conceptual segment approach

Md Rashedul Islam


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Outline

Background

Objective

Solvation thermodynamics

Conceptual segment idea

Sigma profile generation model formulation

Results and Discussion

Conclusion


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Background

A priori prediction of fluid phase equilibria and liquid phase non-

idealities are key factors in process and product development

Thermodynamic behavior is calculated/predicted based on group-

contribution methods, activity-coefficient models, and solvation-

thermodynamics

Solvation-thermodynamic approach predicts thermo-physical

properties based on molecular structure only


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Motivation

Among the solvation thermodynamic based models, COSMO-RS

and COSMO-SAC are the are well recognized

A key input to these models is so called Sigma Profile, i.e. ahistogram of charge density distribution over molecular surface

Typically -profile is generated using quantum mechanical

calculation

Interested researchers are intimated by the complexity of quantummechanical calculation to use COSMO-based model


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Objective We introduce conceptual segment based concept of NRTL-SAC

activity coefficient model

We select four reference solvents to represents hydrophobic,

solvation, polar, and hydrophilic conceptual segments

We generate -profile of any molecules from the linear

combination of -profile of four reference solvents

We identify the conceptual segment numbers from fitting availablesolubility date involving the molecules and four reference solvents

or their equivalents

We predict the solubility of three drug molecules to validate our

methodology


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Thermodynamic Background

Solubility Thermodynamics

Activity coefficient models:

UNIFAC

NRTL-SAC

COSMO-SAC

Theoretical structure of activity coefficient

=

+

=

= =+

: mole fraction of solute at saturation

: activity coefficient of solute

: heat of fusion of solute

T : melting temperature of solute

: solubility product constant


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NRTL-SAC model

A derivative of NRTL model

A practical thermodynamic framework for solubility modeling Surface interaction characteristics of a molecules are exploited

Qualitative parameters are identified from representative solvents:hydrophobic, polar, and hydrophilic

Due to multiple crystalline structure, multiple melting point or

latent heat of fusion may exist

Ksp is estimated through regression using experimental solubility

NRTL-SAC predicts solubility better than COSMO-SAC does


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Thermodynamic Background

Solubility Thermodynamics

Activity coefficient models:

UNIFAC

NRTL-SAC

COSMO-SAC

Theoretical structure of activity coefficient

=

+

=

= =+

: mole fraction of solute at saturation

: activity coefficient of solute

: heat of fusion of solute

T : melting temperature of solute

: solubility product constant


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Solvation Thermodynamic Model

Predict inter-molecular interactions based on molecularstructure

Characterize liquid phase non-ideality

Computational quantum mechanics is used to predict thermo-

physical properties

Models: COSMO-RS 1and COSMO-SAC2

COSMO-based models require sigma profile as input

Sigma profile is a molecular-specific distribution of surface-

charge density

1. Klamt et al2. Lin and Sandler


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COSMO-SAC Model

COSMO-SAC model predict thermo-physical properties based

on solvation free energy

Solvation free energy represents Gibbs free energy required

to bring a moving molecule from a fixed position in ideal state

to a fixed position in solution

Solvation free energy is related

to activity coefficient

Lin and Sandler, 2002


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Sigma Profile

Sigma profile is a measure of molecules dipole and higher

moment interaction with surrounding medium

Probability distribution of surface-charge density of a

molecule or a mixture, ()

-0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025

0

5

10

15

20

25

30

35

, e/Ang2

P()

*A(),Ang

2

Hexane

DMSO

Nitromethane

Water

Sigma profile of amixture is a weighted

average of the pure

components.


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Merits and Demerits of COSMO-SAC Model

Useful for priori estimates of thermo-physical properties of

new and unmeasured species

Predicts phase equilibria for new mixture

Merits

Sigma profile is highly subjected

to structural conformation

Over and under prediction of

solubility likely observed

Demerits


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Proposed Idea

Conceptual segment, i.e. X,Y+, Y-, and Z, idea from NRTL-SAC

is introduced into COSMO-SAC

Sigma profile is generated from the linear combination of

sigma profile of reference molecules

Like NRTL-SAC, reference molecules are hydrophobic, polar,

and hydrophilic

Cavity volume is calculated from the cavity volume and

conceptual segment parameters

X,Y+, Y-,Z are estimated from experimental solubility

Ksp value is also regressed if necessary


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Parameter Regression Algorithm

Non-linear regression is due to non-linearity of COSMO-SAC

Constrained optimization is employed for non-negativity of

sigma profile


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Proposed algorithm is implemented to predict the solubility of

three drug molecules: Caffeine, Aspirin, and Acetaminophen

For each drug, solubility is reported based on the sigma

profile from Virginia Tech(VT) database

Solubility of each drug is calculated from new sigma profile

and reported alongside VT results to demonstrate

improvement

For Acetaminophen, solubility in different binary solvent is

also predicted


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Caffeine

0

3

6

9

1215

18

21

24

27

-0.03-0.025-0.02-0.015-0.01-0.005 0 0.005 0.01 0.015 0.02 0.025 0.03

SigmaProfile,P()*Ai

(2)

Screening Charge Density, (e/2)

Sigma Profile of Caffeine

COSMOSAC VT

COSMOSAC-XYZ

Solvent Experimental solubility

N-HEXANE 3.94E-06

2-ETHOXYETHANOL 0.006779

1-OCTANOL 0.002455

1,4-DIOXANE 0.008204

N,N-DIMETHYLFORMAMIDE 0.012558

WATER 0.002247

ETHANOL 0.0017ETHYL-ACETATE 0.00409


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Caffeine

Regression ResultsHf & Tm Ksp

X 0 0Y+ 0.4296 0.4675Y- 1.2710 1.2044

Z 0.2553 0.1619Cavity volm 137.88 134.56

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01

Mo

delsolubility,xmodel

Experimental solubility, xexp

Caffeine: COSMOSAC Regression

Hf & Tm

Ksp

VT

Hexane

Water


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Aspirin

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

Modelsolubility,Xmodel

Experimental solubility, Xexp

Aspirin: COSMOSAC Regression

COSMOSAC VT

COSMOSACXYZ

Hf & TmRegression Results

Hf & Tm KspX 0.0357 0.0802

Y+ 0.0837 0.0845Y- 0.6555 0.6281Z 0.5716 0.5869

Cavity volm 74.04 79.10


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Acetaminophen (Paracetamol)

0

2

4

6

8

10

12

14

16

18

20

22

-0.03 -0.025 -0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02 0.025 0.03

SigmaProfile,P()*Ai(

2)

Screening Charge Density, (e/2)

Sigma Profile of Acetaminophen

COSMOSAC VTCOSMOSAC-XYZ

XYZKsp

SOLVENT Solubility Mole fractionWATER 17.39 0.002068

METHANOL 371.61 0.073012

ETHANOL 232.75 0.066232

ETHYLENE-GLYCOL 144.3 0.055935

1-PROPANOL 132.77 0.050135

ISOPROPYL-ALCOHOL 135.01 0.050941

N-BUTANOL 93.64 0.043897

1-PENTANOL 67.82 0.038043

1-HEXANOL 49.71 0.038014

1-HEPTANOL 37.43 0.0279671-OCTANOL 27.47 0.023118

ACETONE 111.65 0.041132

METHYL-ETHYL-KETONE 69.99 0.032308

METHYL-ISOBUTYL-KETONE 17.81 0.011663

TETRAHYDROFURAN 155.37 0.069000

1,4-DIOXANE 17.08 0.009857

ETHYL-ACETATE 10.73 0.006215

ACETONITRILE 32.83 0.008836

DIETHYL-AMINE 1316.9 0.389184

N,N-DIMETHYLFORMAMIDE 1012.02 0.328548

DIMETHYL-SULFOXIDE 1132.56 0.369225

ACETIC-ACID 82.72 0.031814

DICHLOROMETHANE 0.32 0.000180

CHLOROFORM

1.54 0.001215

CARBON-TETRACHLORIDE 0.89 0.000905

TOLUENE 0.34 0.000207


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Acetaminophen (Paracetamol)

Regression Results4 para. 5 para.

X 0.2980 0.6291Y+ 0.0379 0Y- 0 0

Z 1.3652 1.3142Ksp -3.5364

Cavity volm 82.43 125.75

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00

Modelsolubility,Xmodel

Experimental solubility, Xexp

Acetaminophen: COSMOSAC Regression

COSMOSAC VT COSMOSACXYZ XYZKsp


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Hydrophilic-hydrophilic pair

Methanol-water binary Ethanol-water binary


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polar-hydrophilic pair

Acetone-water binary 1,4-dioxane-water binary


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Results and DiscussionPolar-hydrophobic pair

Acetone-toluene binary


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Results and DiscussionHydrophilic-hydrophobic pair

Methanol-ethyl acetate binary Ethanol-ethyl acetate binary


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Conclusion

The proposed methodology offers a very simile and practical

approach to generate -profile This method generate -profile of any molecule in terms of

conceptual segment numbers

Conceptual segment numbers are in turn identified by fitting

against experimental solubility data in solvents of various nature

The methodology requires no knowledge of molecular structure nor

molecular conformation and no use of DFT calculations or quantum

chemistry packages

The generated -profile perform well in COSMO-based predictions

of thermophysical properties.


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Reference

Cosmosac Regression Presentation

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