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**From Quantum Chemistry to Fluid Thermodynamics:**

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

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**Thermophysical data prediction methods**

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

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**Dielectric Continuum Solvation Models (CSM)**

solute molecule embedded in a dielectric continuum, 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 PC Born 1920, Kirkwood 1934, Onsager1936 - Rivail, Rinaldi et al. - Katritzky, Zerner et al. - Cramer, Truhlar et al. (AMSOL) - Tomasi et al. (PCM) electron density - Klamt, Schüürmann 1991 COSMO = COnductor-like Screening Model: outlying charge Effect minimized by COSMO - empirical finding: cavity radii should be about 1.2 vdW-radii - promising results for solvents water, alkanes, and a few other solvents But CSMs are basically wrong and give a poor, macroscopic description of the solvent !

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**COSMO as dielectric model in the QC-formalism**

exact dielectric boundary condition (E = electr. field, qi=single polarisation charge on segment i q=set of m polarisation charges) COnductorlikeScreeningMOdel-approx.: F = elektr. Pot. exact for electr. conductor: =; f()=(-1)/(+x)=1 math. extremly simple calculation of the polarisation dielektric energy gain potential 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 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)**

solute molecule embedded in a dielectric continuum, 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 PC Born 1920, Kirkwood 1934, Onsager1936 - Rivail, Rinaldi et al. - Katritzky, Zerner et al. - Cramer, Truhlar et al. (AMSOL) - Tomasi et al. (PCM) electron density - Klamt, Schüürmann 1991 COSMO = COnductor-like Screening Model: outlying charge Effect minimized by COSMO - empirical finding: cavity radii should be about 1.2 vdW-radii - promising results for solvents water, alkanes, and a few other solvents But CSMs are basically wrong and give a poor, macroscopic description of the solvent !

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**Why are Continuum Solvation Models **

wrong for polar molecules in polar solvents? 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 only electronic polarizibility homogeneously distributed linear response up to very high fields dielectric continuum theory should be reasonably applicable

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**state of ideal screening**

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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**Basic idea of COSMO-RS: Quantify interaction energies as **

local interactions of COSMO polarization charge densities s and s‘ s‘ s DEcontact = E(s,s‘) s s‘

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

COSMO-RS: 2) Compress the ensemble to approximately right density 3) 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. misfit But for molecules? Or just for surface pairs? ideal contact (3) specific interactions

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**Screening charge distribution on molecular surface**

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

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**Screening charge distribution on molecular surface**

COSMO-RS A. Klamt, J. Phys. Chem., 99 (1995) 2224 For 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 surface reduces to "s-profile"

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

Because their s-profiles are almost complementary!

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**Statistical Thermodynamics**

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: chemical potential of solute X in S: activity coefficients arbitrary liquid-liquid equilibria chemical potential of solute X in the gasphase: vapor pressures s-potential: affinity of solvent for specific polarity s combinatorial contribution: solvent size effects

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**representative liquids**

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

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**Statistical 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.

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**Extension of COSMOtherm to multi-conformations**

Many molecules have more than one relevant conformation e.g. salicylic acid 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)

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**conformational effect in ortho-chlorophenols**

conformer1: prefererred in water, alkohols, and specially in aprotic solvents (acetone) conformer0: prefererred in gas phase, non- hb-solvents, and in pure comp. prediction of activity coefficients and partition coefficients would fail to describe trends using only one conformer

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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 2nd COSMO conformer Ecosmo=+0.37 kcal/mol Ediel =+2 kcal/mol 1 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/mol 2 free donors, one bound in strong 6-ring (represents ~4 similar conformations) 2% in octane 41% in acetone 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. 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

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**Extension of COSMOtherm to speciation**

COSMO-RS treats simple “single-contact“ associates very well, e.g. in alcohols: model works technically correct yields thermodynamically consistent results more 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 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

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**Residuals Limited by accuracy of DFT!**

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 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**

Winner of the First IFPSC, 2002 (AICHE/NIST) miscibility gap

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**COSMO-RS Flow Chart of DFT/COSMO COSMOtherm Chemical Structure**

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

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**COSMOtherm Graphical User Interface**

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

Example : Prediction of azeotropes : Azeotrope No Azeotrope

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

COSMOtherm is applicable where group contribution methods fail ! (because of missing parameters). E.g. Fluorinated Solvents (HFCs):

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**courtesy to Dr. C. Rose The calc. temperatures are**

more reliable than the experimental data / 27

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**„Conformational analysis of cyclic acidic a-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) AM SM5.4A PM SM5.4P AM 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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**state of ideal screening**

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

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**state of ideal screening**

COSMO (the long distance airplane): a dielectric continuum solvation model powered by DFT quantum mechanics (TURBOMOLE, DMol,GAUSSIAN,...) Glossary of COSMOxxx Terminology COSMO-RS state of ideal screening home of COSMOlogic COSMO-RS (flexible short distance airplane starting at the North Pole): a statistical thermodynamics method based on COSMO s-profiles simple, well explored solvents Quantum Chemistry with dielectric solvation models like COSMO or PCM water latitudes of solvation COSMO-RS(OLdenburg): (Gmehling, Grensemann) another spoiled COSMO-RS remake with technical standards of 1997 or less COSMOtherm: the name of the COSMO-RS program MD / MC simulations -OH -OCH3 -C(=O)H -CarH -Car Group contribution methods UNIFAC, ASOG, CLOGP, LOGKOW, etc. horizon of COSMO-RS COSMObase: COSMO database for ~3500 compounds solid COSMO-SAC: (Lin/Sandler 2001) partly spoiled COSMO-RS remake with technical standards of 1997 (available in ASPENTECH 12!) alkanes bridge of symmetry COSMOfrag: High-Throughput s-profile generator (and chem-informatics engine) QM/MM Carr-Parrinello state horizon of gas- phase methods COSMOsim: Drug-similarity tool based on s-profiles COSMOSPACE: the „exact“ thermodynamic equation (engine) of COSMO-RS native home of computational chemistry gas phase COSMOmic: Simulation tool for micelles and membranes

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**From Quantum Chemistry to Fluid Thermodynamics:**

COSMO-RS/COSMOtherm 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! Andreas Klamt COSMOlogic GmbH&Co.KG Leverkusen, Germany

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