3Dielectric Continuum Solvation Models (CSM) solute molecule embedded in adielectriccontinuum,self-consistent inclusion of solvent polarisation(screening charges) into MO-calculation (SCRF)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 PCBorn 1920,Kirkwood 1934, Onsager1936- Rivail, Rinaldi et al.- Katritzky, Zerner et al.- Cramer, Truhlar et al. (AMSOL)- Tomasi et al. (PCM)electrondensity- Klamt, Schüürmann 1991COSMO =COnductor-like Screening Model:outlying chargeEffect minimized by COSMO- empirical finding: cavity radii should be about 1.2 vdW-radii- promising results for solvents water, alkanes, and a few other solventsBut CSMs are basically wrong and give a poor, macroscopic description of the solvent !
4COSMO as dielectric model in the QC-formalism exact dielectric boundary condition(E = electr. field, qi=single polarisation charge on segment iq=set of m polarisation charges)COnductorlikeScreeningMOdel-approx.: F = elektr. Pot.exact for electr. conductor: =; f()=(-1)/(+x)=1math. extremly simple calculation of the polarisationdielektric energy gainpotential F 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“
5Dielectric Continuum Solvation Models (CSM) solute molecule embedded in adielectriccontinuum,self-consistent inclusion of solvent polarisation(screening charges) into MO-calculation (SCRF)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 PCBorn 1920,Kirkwood 1934, Onsager1936- Rivail, Rinaldi et al.- Katritzky, Zerner et al.- Cramer, Truhlar et al. (AMSOL)- Tomasi et al. (PCM)electrondensity- Klamt, Schüürmann 1991COSMO =COnductor-like Screening Model:outlying chargeEffect minimized by COSMO- empirical finding: cavity radii should be about 1.2 vdW-radii- promising results for solvents water, alkanes, and a few other solventsBut CSMs are basically wrong and give a poor, macroscopic description of the solvent !
6Why are Continuum Solvation Models wrong for polar molecules in polar solvents?discrete permanant dipolesmainly reorientational polarizibilitylinear response requires Ereor << kTtypically Ereor ~ 8 kcal/mol !!!no linear response, no homogenityno similarity with dielectric theoryonly electronic polarizibilityhomogeneously distributedlinear response up to very high fieldsdielectric continuum theory shouldbe reasonably applicable
7state of ideal screening gas phaselatitudes ofsolvationwateralkaneshorizon ofCOSMO-RShorizon of gas-phase methodssolidstatebridge ofsymmetryHow to come to the latitudes of solvation?QM/MMCar-ParrinelloQuantum Chemistrywith dielectricsolvation modelslike COSMOor PCMMD / MCsimulationsnative home ofcomputational chemistry-OH-OCH3-C(=O)H-CarH-CarGroup contribution methodsUNIFAC, ASOG,CLOGP, LOGKOW, etc.simple, wellexplored solventsCOSMO-RSstate of ideal screeninghome of COSMOlogic
8Basic idea of COSMO-RS: Quantify interaction energies as local interactions of COSMO polarization charge densities s and s‘s‘sDEcontact = E(s,s‘)ss‘
91) Put molecules into ‚virtual‘ conductor (DFT/COSMO) COSMO-RS:2) Compress the ensemble to approximately right density3) Remove the conductor on molecular contact areas (stepwise) and ask for the energetic costs of each step.In this way the molecular interactions reduce to pair interactions of surfaces!+_s'>> 0<< 0(2)hydrogen bond(1)A thermodynamic averaging of many ensembles is still required!electrostat. misfitBut for molecules?Or just for surface pairs?ideal contact(3) specificinteractions
10Screening charge distribution on molecular surface COSMO-RSFor an efficient statistical thermodynamics reduce the ensemble of molecules to an ensemble of pair-wise interacting surface segments !Screening charge distribution on molecular surfacereduces to "s-profile"
11Screening charge distribution on molecular surface COSMO-RSA. Klamt, J. Phys. Chem., 99 (1995) 2224For an efficient statistical thermodynamics reduce the ensemble of molecules to an ensemble of pair-wise interacting surface segments !(same approximation as is UNIFAC)Screening charge distribution on molecular surfacereduces to "s-profile"
12Why do acetone and chloroform like each other so much? Because their s-profiles are almost complementary!
13Statistical Thermodynamics Replace ensemble of interacting molecules by anensemble S of interacting pairs of surface segmentsEnsemble 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:chemical potential of solute X in S:activity coefficients arbitrary liquid-liquid equilibriachemical potential of solute X in the gasphase: vapor pressuress-potential:affinity of solvent forspecific polarity scombinatorial contribution:solvent size effects
15Statistical Thermodynamics (more general reformulation) - define cluster “activity coeffs.“:and interaction parameters :- now the self-consistency equation reads:with QS(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.
16Extension of COSMOtherm to multi-conformations Many molecules have more than one relevant conformatione.g. salicylic acidCOSMOtherm can treat a compound as a set of several conformers- each conformer needs a COSMO calculation- conformational population is treated consistentlyaccording to total free energy of conformers (by external self-consistency loop)
17conformational effect in ortho-chlorophenols conformer1:prefererred inwater, alkohols,and specially inaprotic solvents(acetone)conformer0:prefererred ingas phase, non-hb-solvents, andin pure comp.prediction of activity coefficients and partition coefficients wouldfail to describe trends using only one conformer
18Conformational effects for glycerol lowest COSMO conformerall 3 donors are bound inone 6-ring and two 5-rings,also least polar conformer39% in octane9% in acetone2nd COSMO conformerEcosmo=+0.37 kcal/molEdiel =+2 kcal/mol1 free donor, two bound inone 6-ring and one 5-rings16% in octane8% in acetone7th COSMO conformerEcosmo=+1.3 kcal/molEdiel =+3.3 kcal/mol2 free donors, one boundin strong 6-ring(represents ~4 similarconformations)2% in octane41% in acetoneConclusions:- Conformational effects can be important for the detailedunderstanding of phase equilibriaIn most cases one conformation dominates in all phasesEffects are especially large for molecules with sub-optimalintramolecular 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 reliableregarding the energy differences between conformers andeven more between tautomers. Energy corrections may be required.partition coefficient betweenacetone and octane:logKAO = -3.3 (lowest conformer)logKAO = -4.0 (conformer ensemble)difference of 0.7 log-units ≈ 1 kcal/mol
19Extension of COSMOtherm to speciation COSMO-RS treats simple “single-contact“ associates very well,e.g. in alcohols:model works technically correctyields thermodynamically consistent resultsmore experience and validation required(an academic partner for a PhD thesis would be welcome)but it has no chance to automatically describe double-association:artificial segment D,which can only makeD-D contactsCOSMOtherm 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 ofmonomer and associate
20Residuals Limited by accuracy of DFT! alkanesalkenesalkinesalcoholsetherscarbonylsestersarylsdiverseaminesamidesN-arylsnitrilesnitrochlorowaterResults of parametrization based on DFT (DMol3: BP91, DNP-basis650 data17 parametersrms = 0.41 kcal/molA. 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/molResidualsLimited byaccuracy ofDFT!
21Applications to Phase Diagrams and Azeotropes Winner of theFirst IFPSC, 2002(AICHE/NIST)miscibility gap
22COSMO-RS Flow Chart of DFT/COSMO COSMOtherm Chemical Structure Phase DiagramsEquilibrium data:activity coefficientsvapor pressure,solubility,partition coefficientsQuantum ChemicalCalculation with COSMO(full optimization)s-potential of mixtures-profiles of compoundsideally screened moleculeenergy + screening chargedistribution on surfaceFast StatisticalThermodynamicsDatabase ofCOSMO-files(incl. all common solvents)other compoundss-profileof mixtureDFT/COSMOCOSMOtherm
25II.1 Vapor-Liquid Equilibria (III) Example : Prediction of azeotropes :AzeotropeNo Azeotrope
26II.1 Vapor-Liquid Equilibria (V) COSMOtherm is applicable where group contribution methods fail !(because of missing parameters). E.g. Fluorinated Solvents (HFCs):
27courtesy to Dr. C. Rose The calc. temperatures are more reliable than theexperimental data/ 27
28„Conformational analysis of cyclic acidic a-amino acids in aqueous solution - an evaluation ofdifferent continuum hydration models."by Peter Aadal Nielsen, Per-Ola Norrby, Jerzy W. Jaroszewski, and Tommy Liljefors, for JACSMethod Solvent rms rms (4 points) Max DevModel (kJ/mol) (kJ/mol) (kJ/mol)AM SM5.4APM SM5.4PAM SMHF/6-31+G* C-PCMHF/6-31+G* PB-SCRFAMBER* GB/SAMMFF GB/SABP-DFT/TZVP COSMO-RSCOSMO-RS was evaluated as a blind test !!!
29state of ideal screening How to come to the latitudes of solvation?COSMO-RSstate of ideal screeninghome of COSMOlogicQuantum Chemistrywith dielectricsolvation modelslike COSMOor PCMwaterlatitudes ofsolvationacetoneMD / MCsimulations-OH-OCH3-C(=O)H-CarH-CarGroup contribution methodsUNIFAC, CLOGP,LOGKOW, etc.horizon ofCOSMO-RSsolidalkanesbridge ofsymmetryQM/MMCar-Parrinellostatehorizon of gas-phase methodsnative home ofcomputational chemistrygas phase
30state of ideal screening COSMO (the long distance airplane):a dielectric continuum solvation modelpowered by DFT quantum mechanics(TURBOMOLE, DMol,GAUSSIAN,...)Glossary of COSMOxxx TerminologyCOSMO-RSstate of ideal screeninghome of COSMOlogicCOSMO-RS (flexible short distance airplane starting at the North Pole):a statistical thermodynamics method based on COSMO s-profilessimple, wellexplored solventsQuantum Chemistrywith dielectricsolvation modelslike COSMOor PCMwaterlatitudes ofsolvationCOSMO-RS(OLdenburg): (Gmehling, Grensemann)another spoiled COSMO-RS remake with technical standards of 1997 or lessCOSMOtherm:the name of the COSMO-RS programMD / MCsimulations-OH-OCH3-C(=O)H-CarH-CarGroup contribution methodsUNIFAC, ASOG,CLOGP, LOGKOW, etc.horizon ofCOSMO-RSCOSMObase:COSMO database for ~3500 compoundssolidCOSMO-SAC: (Lin/Sandler 2001)partly spoiled COSMO-RS remake with technical standards of 1997(available in ASPENTECH 12!)alkanesbridge ofsymmetryCOSMOfrag:High-Throughput s-profile generator(and chem-informatics engine)QM/MMCarr-Parrinellostatehorizon of gas-phase methodsCOSMOsim:Drug-similarity tool based on s-profilesCOSMOSPACE:the „exact“ thermodynamic equation (engine) of COSMO-RSnative home ofcomputational chemistrygas phaseCOSMOmic:Simulation tool for micelles and membranes
31From Quantum Chemistry to Fluid Thermodynamics: COSMO-RS/COSMOthermFrom Quantum Chemistry toFluid Thermodynamics:The basics ofCOSMO-RS theoryNow you should be well prepared for the COSMO-RS symposium.Enjoy the talks on the various aspects of COSMO-RS!Andreas KlamtCOSMOlogic GmbH&Co.KGLeverkusen, Germany