Post on 31-Mar-2015
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!