Andreas Klamt

COSMOlogic GmbH&Co.KG

Leverkusen, Germany

From Quantum Chemistry to Fluid Thermodynamics:

The basics of COSMO-RS theory

gas phase

latitudes ofsolvation

water

alkanes

horizon ofCOSMO-RS

horizon of gas-phase methods

solid

phasebridge ofsymmetry

Thermophysical data prediction methods

Quantum Chemistrywith dielectric

solvation models like PCM

or COSMO

quantumchemistry

-OH

-OCH3

-C(=O)H

-CarH-CarH -C

arH-Car

-Car -Car

Group contribution methodsCLOGP, …, Benson, Joback,UNIFAC, ASOG, etc.

simple, well explored solvents

fitted parameters: CLOGP:~ 1500UNIFAC: ~5000 +50% gaps

≠

Car-Parrinello

MD / MCforce-fieldsimulations

MD/MC

softbiomatter

Dielectric Continuum Solvation Models (CSM) Dielectric Continuum Solvation Models (CSM)

-Born 1920, -Kirkwood 1934, Onsager1936 - Rivail, Rinaldi et al.

- Katritzky, Zerner et al.- Cramer, Truhlar et al. (AMSOL)

- Tomasi et al. (PCM)

- promising results for solvents water, alkanes, and a few other solvents

- empirical finding: cavity radii should be about 1.2 vdW-radii

solute molecule embedded in a dielectric continuum,self-consistent inclusion of solvent polarisation

(screening charges) into MO-calculation (SCRF)

But CSMs are basically wrong and give a poor, macroscopic description of the solvent !

- Klamt, Schüürmann 1991

COSMO = COnductor-like Screening Model:

21

1)(

)(

f

conductorfdielectric

Density Functional Theory (DFT)is appropriate level of QC!COSMO almost as fast as gasphase!programs: TURBOMOLE,

DMol3, Gaussian03, ...up to 25 atom:< 24 h on LINUX PC

electron density

outlying chargeEffect minimized by COSMO

i

pol

i

X

i

i

i nqEEs

q*)(

14

qAf

qf

X

poli

Xi

)(0

)()(0

PDPPBABP

AqEtttf

XXfXdiel

211

2)(

1

2)(

21 *

qE Xidiel *2

1

COSMO as dielectric model in the QC-formalism

PBX

exact dielectric boundary condition(E = electr. field, qi=single polarisation charge on segment i q=set of m polarisation charges)

COnductorlikeScreeningMOdel-approx.: = elektr. Pot.exact for electr. conductor: =; f()=(-1)/(+x)=1

math. extremly simple calculation of the polarisation

dielektric energy gain

potential is a linear function of density (of nuclei and electrons)

The dielectric energy is a bilinear form of the density. Hence it is formally analogous to the Coulomb terms (nuclei-nuclei, nuclei-electrons und electron-electron) COSMO can be directly integrated into the energy operator (Fock- or Kohn-Sham operator) direct convergence to the self-consistent state in thedielectric continuum (small speed-up of SCF!!!)

advantages of COSMO: - math. simplicity, small storage requirements - numerical stability - low sensitivity with respect to “Outlying Charge“

Dielectric Continuum Solvation Models (CSM) Dielectric Continuum Solvation Models (CSM)

-Born 1920, -Kirkwood 1934, Onsager1936 - Rivail, Rinaldi et al.

- Katritzky, Zerner et al.- Cramer, Truhlar et al. (AMSOL)

- Tomasi et al. (PCM)

- promising results for solvents water, alkanes, and a few other solvents

- empirical finding: cavity radii should be about 1.2 vdW-radii

solute molecule embedded in a dielectric continuum,self-consistent inclusion of solvent polarisation

(screening charges) into MO-calculation (SCRF)

But CSMs are basically wrong and give a poor, macroscopic description of the solvent !

- Klamt, Schüürmann 1991

COSMO = COnductor-like Screening Model:

21

1)(

)(

f

conductorfdielectric

Density Functional Theory (DFT)is appropriate level of QC!COSMO almost as fast as gasphase!programs: TURBOMOLE,

DMol3, Gaussian03, ...up to 25 atom:< 24 h on LINUX PC

electron density

outlying chargeEffect minimized by COSMO

Why are Continuum Solvation Models Why are Continuum Solvation Models wrong for polar molecules in polar solvents? wrong for polar molecules in polar solvents?

-only electronic polarizibility-homogeneously distributed-linear response up to very high fields

dielectric continuum theory should

be reasonably applicable

-discrete permanant dipoles -mainly reorientational polarizibility

-linear response requires Ereor << kT

- typically Ereor ~ 8 kcal/mol !!!

no linear response, no homogenity

no similarity with dielectric theory

gas phase

latitudes ofsolvation

water

alkanes

horizon ofCOSMO-RS

horizon of gas-phase methods

solid

statebridge ofsymmetry

How to come to the latitudes of solvation?

QM/MMCar-Parrinello

Quantum Chemistrywith dielectric

solvation models like COSMO

or PCM

MD / MCsimulations

native home of computational chemistry

-OH

-OCH3

-C(=O)H

-CarH-CarH -C

arH-Car

-Car -Car

Group contribution methodsUNIFAC, ASOG,CLOGP, LOGKOW, etc.

simple, well explored solventsCOSMO-RS

state of ideal screening home of COSMOlogic

‘

‘

Econtact = E(‘)

Basic idea of COSMO-RS: Quantify interaction energies as local interactions of COSMO polarization charge densities and‘

1) Put molecules into ‚virtual‘ conductor (DFT/COSMO)

COSMO-RS:COSMO-RS:

++++

++

____ _

'

' << 0(1)

(2) hydrogen bond

electrostat. misfit

ideal contact

3) Remove the conductor on molecular contact areas (stepwise) and ask for the energetic costs of each step.

2) Compress the ensemble to approximately right density

(3) specificinteractions

2)'(2

')',( effmisfit aG

}',0min{)()',( 2hbhbeffhb TcaG

In this way the molecular interactions reduce to pair interactions of surfaces!

A thermodynamic averaging of many ensembles is still required!

But for molecules?

Or just for surface pairs?

Water

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020 [e/A2]

pw

ater

(s)

(am

ou

nt

of

su

rfa

ce

)

Screening charge distribution on molecular surface reduces to "-profile"

COSMO-RS COSMO-RS

For an efficient statistical thermodynamics reduce the ensemble of molecules to an ensemble of pair-wise interacting surface segments !

0

5

10

15

20

25

-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020

[e/A2]

pX(

)

Water

Methanol

Acetone

Benzene

Chloroform

Hexane

Screening charge distribution on molecular surface reduces to "-profile"

A. Klamt, J. Phys. Chem., 99 (1995) 2224COSMO-RS COSMO-RS

For an efficient statistical thermodynamics reduce the ensemble of molecules to an ensemble of pair-wise interacting surface segments !

(same approximation as is UNIFAC)

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Mole fraction of acetone (1)

ln(g

)

Acetone (calculated)

Chloroform (calculated)

Acetone (experiment, Rabinovichet al.)

Chloroform(experiment,Rabinovich et al.)

Aceton (experiment, Apelblat etal.)

Chloroform (experiment, Apelblatet al.)

0

5

10

15

20

25

-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020

[e/A2]

pX(

)

Acetone

Chloroform

Because their Because their -profiles are -profiles are almost complementary!almost complementary!

Why do acetone and chloroform Why do acetone and chloroform like each other so much?like each other so much?

• Replace ensemble of interacting molecules by an ensemble S of interacting pairs of surface segments• Ensemble S is fully characterized by its -profile pS() pS() of mixtures is additive! -> no problem with mixtures! • Chemical potential of a surface segment with charge density is exactly(!) described by:

kT

EpdkT S

SS

)'()',(exp''ln)( int

chemical potential of solute X in S:

SS

XXS AkTpd ln

kTXX

XS

XS /)(exp g

activity coefficients arbitrary liquid-liquid equilibria

0)( g

Xringel

XXCOSMO

Xvac

XGas nAEE

chemical potential of solute X in the gasphase: vapor pressures

Statistical ThermodynamicsStatistical Thermodynamics

combinatorial contribution:solvent size effects

)( el

combXS

,g

i

iii

ii

S areax

pxp

)()(

-potential:affinity of solvent forspecific polarity

-profiles -profiles and and

-potentials of -potentials of representative liquidsrepresentative liquids

-0.50

-0.30

-0.10

0.10

0.30

0.50

0.70

-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020 [e/A2]

X (

) [k

J/m

ol

A2]

Water

Methanol

Acetone

Benzene

Chloroform

Hexane

hydrophobicity

affinity for HB-donors

affinity for HB-acceptors

0

5

10

15

20

25

-0.020 -0.015 -0.010 -0.005 0.000 0.005 0.010 0.015 0.020

[e/A2]

pX(

)

Water

Methanol

Acetone

Benzene

Chloroform

Hexane

- define cluster “activity coeffs.“: and interaction parameters :

- now the self-consistency equation reads:

withS(i) being the normalized composition of the ensemble S with respect to clusters. This eq. is similar to the UNIQUAC eq. but gS(j) on r.h.s.

Statistical Thermodynamics Statistical Thermodynamics (more general reformulation)(more general reformulation)

kT

ii S

S

)(exp)(

g

m

jSSS jijji ),()()()( 1 gg

kT

jiEji

),(exp),(

...),(),,;,,(),;,())();(();( jivdWjjjiiihbjjiimf eeEenenEnnEjdidEjiE

Extension of COSMOtherm to multi-conformations

COSMOtherm can treat a compound as a set of several conformers- each conformer needs a COSMO calculation - conformational population is treated consistently according to total free energy of conformers (by external self-consistency loop)

Many molecules have more than one relevant conformation

e.g. salicylic acid

conformational effect in ortho-chlorophenols

0

2

4

6

8

10

12

14

16

18

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2

phenol

2-chlorophenol0

2-chlorophenol1

4-chlorophenol

2,6-dichlorophenol

prediction of activity coefficients and partition coefficients wouldfail to describe trends using only one conformer

conformer1:prefererred in water, alkohols,and specially in aprotic solvents (acetone)

conformer0:prefererred in gas phase, non-hb-solvents, and in pure comp.

-profiles of glycerol conformers

0

2

4

6

8

10

12

14

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

h2oglycerol4_cosmoc01

glycerol2_cosmoc02glycerol3_cosmoc04glycerol1_cosmoc05glycerol0_cosmoc03

glycerol3_cosmoc05glycerol3_cosmoc03

z

Conformational effects for glycerollowest COSMO conformerall 3 donors are bound in one 6-ring and two 5-rings,also least polar conformer39% in octane 9% in acetone

2nd COSMO conformer Ecosmo=+0.37 kcal/mol Ediel =+2 kcal/mol1 free donor, two bound in one 6-ring and one 5-rings 16% in octane 8% in acetone

7th COSMO conformer Ecosmo=+1.3 kcal/mol Ediel =+3.3 kcal/mol2 free donors, one bound in strong 6-ring(represents ~4 similar conformations) 2% in octane41% in acetone

partition coefficient between acetone and octane:

logKAO = -3.3 (lowest conformer)logKAO = -4.0 (conformer ensemble)

difference of 0.7 log-units ≈ 1 kcal/mol

Conclusions:

- Conformational effects can be important for the detailed understanding of phase equilibria

- In most cases one conformation dominates in all phases

- Effects are especially large for molecules with sub-optimal intramolecular HBs in solvents having strong HB acceptors, but a deficit of HB-donors.

-Tautomers can be considered as a kind of conformers.

-Unfortunately the DFT level of QC is not always reliable regarding the energy differences between conformers and even more between tautomers. Energy corrections may be required.

Extension of COSMOtherm to speciationCOSMO-RS treats simple “single-contact“ associates very well,e.g. in alcohols:

but it has no chance to automatically describe double-association: artificial segment D,which can only make D-D contacts

COSMOtherm now can treat dimers and other strong associates (or reaction products?) as pseudo-conformers and thus can treat speciation in combination with VLE- two adjustable parameters for the enthalpy and entropy difference of monomer and associate

-model works technically correct-yields thermodynamically consistent results-more experience and validation required(an academic partner for a PhD thesis would be welcome)

a) DGhydr (in kcal/mol)

-11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3

-2

-1

0

1

2

b) log Pvapor (in bar)-4 -3 -2 -1 0 1 2

-2

-1

0

1

2

c) log KOctanol/Water

-2 -1 0 1 2 3 4 5 6-2

-1

0

1

2

d) log KHexane/Water

-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7-2

-1

0

1

2

e) log KBenzene/Water

-4 -3 -2 -1 0 1 2 3 4 5-2

-1

0

1

2

f) log KEther/Water

-3 -2 -1 0 1 2 3-2

-1

0

1

2

alkanes alkenes alkines alcohols ethers carbonyls esters aryls diverse amines amides N-aryls nitriles nitro chloro water

Results of parametrization based on DFT (DMol3: BP91, DNP-basis

650 data17 parametersrms = 0.41 kcal/mol

A. Klamt, V. Jonas, J. Lohrenz, T. Bürger, J. Phys. Chem. A, 102, 5074 (1998)

meanwhile:COSMOtherm2.1_0104 with Turbomole BP91/TZVPrms = 0.33 kcal/mol

Res

idua

ls

Limited by accuracy of DFT!

Applications to Phase Diagrams and AzeotropesApplications to Phase Diagrams and Azeotropes

Binary mixture of Butanol(1) and Heptane (2)

at 50° C

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0x

y Calculated

Experiment

Binary mixture of Butanol(1) and Heptane (2)

at 50° C

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

x1 Mole fraction of 1-butanol (1)

ln(

)

1-Butanol (calculated)

n-Heptane (calculated)

1-Butanol (experiment)

n-Heptane (experiment)

Binary mixture of ethanol (1) and benzene (2)

at 25° C

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0x

yCalculated

Experiment

Binary Mixture of 1-butanol (1) and water

at 60° C

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0x

y

Calculated

Experiment

miscibility gap

Winner of theFirst IFPSC, 2002

(AICHE/NIST)

sigma-profiles

0

2

4

6

8

10

12

14

-0.02 -0.01 0 0.01 0.02

screening charge density [e/A²]

vanillin

w ater

acetone

sigma-potential

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

-0.02 -0.01 0 0.01 0.02

Chemical Structure

Quantum ChemicalCalculation with COSMO

(full optimization)

-profiles of compounds

other compounds

ideally screened moleculeenergy + screening charge distribution on surface

DFT/COSMO COSMOtherm

-profile of mixture

-potential of mixture

Fast Statistical Thermodynamics

Equilibrium data:activity coefficientsvapor pressure,solubility,partition coefficients

Phase Diagrams

Database of COSMO-files

(incl. all common solvents)

Flow Chart of COSMO-RS Binary Mixture of

Butanol and Water at 60° C

0.0

0.2

0.4

0.6

0.8

1.0

0.0 0.2 0.4 0.6 0.8 1.0x

y Calculated

Experiment

miscibility gap

COSMOtherm Graphical User Interface

0

150

300

450

600

750

900

1050

1200

1350

1500

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Mole fraction of octane

H^

E [

J/m

ol]

H-Excess ( experimentaldata of octane + 2-methylpyridine )

H-Excess ( calculateddata of octane + 2-methylpyridine )

H-Excess ( experimentaldata of octane + 1-octyne )

H-Excess ( calculateddata of octane + 1-octyne )

H-Excess ( experimentaldata of octane +cyclopentanol )

H-Excess ( calculateddata of octane +cyclopentanol )

Example : Prediction of azeotropesazeotropes :

II.1 Vapor-Liquid Equilibria (III)II.1 Vapor-Liquid Equilibria (III)

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x1, y1

p [

kPa]

Liquid

Liquid + Vapour

Vapour2-methylpropane (1) + ethanenitrile (2) at T=358 [K]

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x1

ln(g )

2-methylpropene (1) + ethanenitrile (2) at T=358 [K]

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x1, y1

p [

kPa]

Liquid

Liquid + Vapour

Vapour

2-methylpropene (1) + ethanenitrile (2) at T=358 [K]

0

0.5

1

1.5

2

2.5

3

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x1

ln(g )

2-methylpropane (1) + ethanenitrile (2) at T=358 [K]

AzeotropeAzeotropeNo AzeotropeNo Azeotrope

COSMOtherm is applicable where group contribution

methods fail !

(because of missing parameters). E.g. Fluorinated

Solvents (HFCHFCs):

II.1 Vapor-Liquid Equilibria (V)II.1 Vapor-Liquid Equilibria (V)

400

900

1400

1900

2400

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x1, y1

PV

AP [

kP

a]

HFC-32 (1) + HFC-143a (2)

T=263.15 K

T=273.15 K

T=283.15 K

T=293.15 K

T=303.15 K

T=313.15 K

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x1, y1

PV

AP [

kPa]

HFC-143a (1) + HFC-236fa (2)

T=283.11 K

T=298.16 K

T=313.21 K

CH2

FF

HFC-32

FF

F

CH3

HFC-143a

FF

F

F

FF

HFC-236fa

Blind Test on Isomeres

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

x1

y1

COSMOtherm

exp.

ideal (y=x)

The non-ideality of the isomere mixture was exactly predicted by COSMOtherm

/ 27

143.00

144.00

145.00

146.00

147.00

148.00

149.00

150.00

0 0.2 0.4 0.6 0.8 1

x1,y1

T[°C

]

Calculation

Measurement

The calc. temperatures aremore reliable than the experimental data

courtesy to Dr. C. RoseO

ON

O

NO

+

„Conformational analysis of cyclic acidic -amino acids in aqueous solution - an evaluation of

different continuum hydration models."by Peter Aadal Nielsen, Per-Ola Norrby, Jerzy W. Jaroszewski, and Tommy Liljefors, for JACS

Method Solvent rms rms (4 points) Max Dev Model (kJ/mol) (kJ/mol) (kJ/mol)AM1 SM5.4A 4.6 5.6 9.2PM3 SM5.4P 13.6 16.2 20.5AM1 SM2.1 7.4 9.0 16.7HF/6-31+G* C-PCM 3.1 3.8 5.9HF/6-31+G* PB-SCRF 4.7 5.8 8.8AMBER* GB/SA 13.2 16.2 24.3MMFF GB/SA 18.5 19.9 31.4

BP-DFT/TZVP COSMO-RS 2.2 2.6 4.8COSMO-RS was evaluated as a blind test !!!

gas phase

latitudes ofsolvation

water

acetone

alkanes

horizon ofCOSMO-RS

horizon of gas-phase methods

solid

statebridge ofsymmetry

How to come to the latitudes of solvation?

QM/MMCar-Parrinello

-OH

-OCH3

-C(=O)H

-CarH-CarH -C

arH-Car

-Car -Car

Group contribution methodsUNIFAC, CLOGP, LOGKOW, etc.

Quantum Chemistrywith dielectric

solvation models like COSMO

or PCM

MD / MCsimulations

native home of computational chemistry

COSMO-RS

state of ideal screening home of COSMOlogic

gas phase

latitudes ofsolvation

water

alkanes

horizon ofCOSMO-RS

horizon of gas-phase methods

solid

statebridge ofsymmetry

Glossary of COSMOxxx Terminology

QM/MMCarr-Parrinello

Quantum Chemistrywith dielectric

solvation models like COSMO

or PCM

MD / MCsimulations

native home of computational chemistry

-OH

-OCH3

-C(=O)H

-CarH-CarH -C

arH-Car

-Car -Car

Group contribution methodsUNIFAC, ASOG,CLOGP, LOGKOW, etc.

simple, well explored solventsCOSMO-RS

state of ideal screening home of COSMOlogic

COSMO (the long distance airplane):a dielectric continuum solvation modelpowered by DFT quantum mechanics (TURBOMOLE, DMol,GAUSSIAN,...)

COSMO-RS (flexible short distance airplane starting at the North Pole):a statistical thermodynamics method based on COSMO -profiles

COSMOtherm:the name of the COSMO-RS program

COSMOSPACE:the „exact“ thermodynamic equation (engine) of COSMO-RS

COSMO-SAC: (Lin/Sandler 2001)partly spoiled COSMO-RS remake with technical standards of 1997(available in ASPENTECH 12!)

COSMO-RS(OLdenburg): (Gmehling, Grensemann)another spoiled COSMO-RS remake with technical standards of 1997 or less COSMObase:

COSMO database for ~3500 compounds

COSMOfrag:High-Throughput -profile generator(and chem-informatics engine)

COSMOsim:Drug-similarity tool based on -profiles

COSMOmic:Simulation tool for micelles and membranes

Andreas Klamt

COSMOlogic GmbH&Co.KG

Leverkusen, Germany

From Quantum Chemistry to Fluid Thermodynamics:

The basics of COSMO-RS theory

Now you should be well prepared for the COSMO-RS symposium.Enjoy the talks on the various aspects of COSMO-RS!