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Andreas Klamt COSMOlogic GmbH&Co.KG Leverkusen, Germany From Quantum Chemistry to Fluid Thermodynamics: The basics of COSMO-RS theory

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gas phase latitudes of solvation water alkanes horizon of COSMO-RS horizon of gas- phase methods solid phase bridge of symmetry Thermophysical data prediction methods Quantum Chemistry with dielectric solvation models like PCM or COSMO quantum chemistry -OH -OCH3 -C(=O)H -CarH -Car Group contribution methods CLOGP, …, Benson, Joback, UNIFAC, ASOG, etc. simple, well explored solvents fitted parameters: CLOGP:~ 1500 UNIFAC: ~ % gaps Car-Parrinello MD / MC force-field simulations MD/MC soft biomatter

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Dielectric Continuum Solvation Models (CSM) -Born 1920, -Kirkwood 1934, Onsager 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 adielectric 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: Density Functional Theory (DFT) is appropriate level of QC! COSMO almost as fast as gasphase! programs: TURBOMOLE, DMol 3, Gaussian03,... up to 25 atom:< 24 h on LINUX PC electron density outlying charge Effect minimized by COSMO

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COSMO as dielectric model in the QC-formalism exact dielectric boundary condition (E = electr. field, q i =single polarisation charge on segment i q=set of m polarisation charges) CO nductorlike S creening MO del -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 the dielectric continuum (small speed-up of SCF!!!) advantages of COSMO: - math. simplicity, small storage requirements - numerical stability - low sensitivity with respect to Outlying Charge

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Dielectric Continuum Solvation Models (CSM) -Born 1920, -Kirkwood 1934, Onsager 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 adielectric 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: Density Functional Theory (DFT) is appropriate level of QC! COSMO almost as fast as gasphase! programs: TURBOMOLE, DMol 3, Gaussian03,... up to 25 atom:< 24 h on LINUX PC electron density outlying charge Effect minimized by COSMO

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Why are Continuum Solvation Models 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 E reor << kT - typically E reor ~ 8 kcal/mol !!! no linear response, no homogenity no similarity with dielectric theory

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gas phase latitudes of solvation water alkanes horizon of COSMO-RS horizon of gas- phase methods solid state bridge of symmetry How to come to the latitudes of solvation? QM/MM Car-Parrinello Quantum Chemistry with dielectric solvation models like COSMO or PCM MD / MC simulations native home of computational chemistry -OH -OCH3 -C(=O)H -CarH -Car Group contribution methods UNIFAC, ASOG, CLOGP, LOGKOW, etc. simple, well explored solvents COSMO-RS state of ideal screening home of COSMOlogic

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E contact = E( ) Basic idea of COSMO-RS: Quantify interaction energies as local interactions of COSMO polarization charge densities and

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1) Put molecules into virtual conductor (DFT/COSMO) COSMO-RS: (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) specific interactions 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?

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Screening charge distribution on molecular surface reduces to " -profile"COSMO-RS For an efficient statistical thermodynamics reduce the ensemble of molecules to an ensemble of pair-wise interacting surface segments !

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Screening charge distribution on molecular surface reduces to " -profile" A. Klamt, J. Phys. Chem., 99 (1995) 2224COSMO-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)

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Because their -profiles are almost complementary! Why do acetone and chloroform like each other so much?

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Replace ensemble of interacting molecules by an ensemble S of interacting pairs of surface segments Ensemble S is fully characterized by its -profile p S ( ) p S ( ) 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 equilibria chemical potential of solute X in the gasphase: vapor pressures Statistical Thermodynamics combinatorial contribution: solvent size effects -potential: affinity of solvent for specific polarity

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-profiles -profilesand -potentials of -potentials of representative liquids representative liquids hydrophobicity affinity for HB-donors affinity for HB-acceptors

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- define cluster activity coeffs.: and interaction parameters : - now the self-consistency equation reads: with S (i) being the normalized composition of the ensemble S with respect to clusters. This eq. is similar to the UNIQUAC eq. but S (j) on r.h.s. Statistical Thermodynamics (more general reformulation)

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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

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conformational effect in ortho-chlorophenols prediction of activity coefficients and partition coefficients would fail 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.

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Conformational effects for glycerol lowest COSMO conformer all 3 donors are bound in one 6-ring and two 5-rings, also least polar conformer 39% in octane 9% in acetone 2 nd COSMO conformer E cosmo =+0.37 kcal/mol E diel =+2 kcal/mol 1 free donor, two bound in one 6-ring and one 5-rings 16% in octane 8% in acetone 7 th COSMO conformer E cosmo =+1.3 kcal/mol E diel =+3.3 kcal/mol 2 free donors, one bound in strong 6-ring (represents ~4 similar conformations) 2% in octane 41% 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.

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Extension of COSMOtherm to speciation COSMO-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 )

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alkanes alkenes alkines alcohols ethers carbonyls esters aryls diverse amines amides N-aryls nitriles nitro chloro water Results of parametrization based on DFT (DMol 3 : BP91, DNP-basis 650 data 17 parameters rms = 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/TZVP rms = 0.33 kcal/mol Residuals Limited by accuracy of DFT!

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Applications to Phase Diagrams and Azeotropes miscibility gap Winner of the First IFPSC, 2002 (AICHE/NIST)

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Chemical Structure Quantum Chemical Calculation with COSMO (full optimization) -profiles of compounds other compounds ideally screened molecule energy + screening charge distribution on surface DFT/COSMOCOSMOtherm -profile of mixture -potential of mixture Fast Statistical Thermodynamics Equilibrium data: activity coefficients vapor pressure, solubility, partition coefficients Phase Diagrams Database of COSMO-files (incl. all common solvents) Flow Chart of COSMO-RS

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COSMOtherm Graphical User Interface

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azeotropes Example : Prediction of azeotropes : II.1 Vapor-Liquid Equilibria (III) Azeotrope No Azeotrope

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COSMOtherm is applicable where group contribution methods fail ! HFC (because of missing parameters). E.g. Fluorinated Solvents (HFCs): II.1 Vapor-Liquid Equilibria (V)

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/ 27 The calc. temperatures are more reliable than the experimental data courtesy to Dr. C. Rose

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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 PM3 SM5.4P AM1 SM HF/6-31+G* C-PCM HF/6-31+G* PB-SCRF AMBER* GB/SA MMFF GB/SA BP-DFT/TZVP COSMO-RS COSMO-RS was evaluated as a blind test !!!

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gas phase latitudes of solvation water acetone alkanes horizon of COSMO-RS horizon of gas- phase methods solid state bridge of symmetry How to come to the latitudes of solvation? QM/MM Car-Parrinello -OH -OCH3 -C(=O)H -CarH -Car Group contribution methods UNIFAC, CLOGP, LOGKOW, etc. Quantum Chemistry with dielectric solvation models like COSMO or PCM MD / MC simulations native home of computational chemistry COSMO-RS state of ideal screening home of COSMOlogic

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gas phase latitudes of solvation water alkanes horizon of COSMO-RS horizon of gas- phase methods solid state bridge of symmetry Glossary of COSMOxxx Terminology QM/MM Carr-Parrinello Quantum Chemistry with dielectric solvation models like COSMO or PCM MD / MC simulations native home of computational chemistry -OH -OCH3 -C(=O)H -CarH -Car Group contribution methods UNIFAC, ASOG, CLOGP, LOGKOW, etc. simple, well explored solvents COSMO-RS state of ideal screening home of COSMOlogic COSMO (the long distance airplane): a dielectric continuum solvation model powered 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(OL denburg ) : (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

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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!

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