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COSMO-RS
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<h2 id="basic-principles">Basic principles</h2> <p>The below description is a simplified overview of the COSMO-RS version published in 1998. </p> <h3>Assumptions</h3> <ol><li>The liquid state is incompressible</li> <li>All parts of the molecular surfaces can be in contact with each other</li> <li>Only pairwise interactions of molecular surface patches are allowed</li></ol> <p>As long as the above assumptions hold, the chemical potential μ in solution can be calculated from the interaction energies of pairwise surface contacts. </p> <h3>COSMO-RS equations</h3> <p>Within the basic formulation of COSMO-RS, interaction terms depend on the screening charge density σ. Each molecule and mixture can be represented by the histogram p(σ), the so-called σ-profile. The σ-profile of a mixture is the weighted sum of the profiles of all its components. Using the interaction energy Eint(σ,σ') and the σ-profile of the solvent p(σ'), the chemical potential μs(σ) of a surface piece with screening charge σ is determined as: </p> μ s ( σ ) = − k T ln ∫ p s ( σ ′ ) e − E i n t ( σ , σ ′ ) − μ s ( σ ′ ) k T d σ ′ {\displaystyle \mu _{s}(\sigma )=-kT\ln \int p_{s}(\sigma ')e^{-{\frac {E_{int}(\sigma ,\sigma ')-\mu _{s}(\sigma ')}{kT}}}d\sigma '} <p>Due to the fact that μs(σ) is present on both sides of the equation, it needs to be solved iteratively. By combining the above equation with px(σ) for a solute x, and adding the σ-independent combinatorial and dispersive contributions, the chemical potential for a solute X in a solvent S results in: </p> μ s x = μ c o m b x + E d i s p + ∫ p x ( σ ) μ s ( σ ) d σ {\displaystyle \mu _{s}^{x}=\mu _{comb}^{x}+E_{disp}+\int p^{x}(\sigma )\mu _{s}(\sigma )d\sigma } <p>In analogy to activity coefficient models used in chemical engineering, such as <a href="/facts/Non-random_two-liquid_model/CaHzNBRT">NRTL</a>, <a href="/facts/UNIQUAC/VtYVwpIj">UNIQUAC</a> or <a href="/facts/UNIFAC/Kcv3bL78">UNIFAC</a>, the final chemical potential can be split into a combinatorial and a residual (non ideal) contribution. The interaction energies Eint(σ,σ') of two surface pieces are the crucial part for the final performance of the method and different formulations are used within the various implementations. In addition to the liquid phase terms a chemical potential estimate for the ideal gas phase μgas has been added to COSMO-RS to enable the prediction of vapor pressure, free energy of solvation and related quantities. </p> <h3>Interaction energy (Residual)</h3> <p>The residual part is the sum of three different contributions, where Emisfit and Ehb are part of Eint and Edisp is added directly to the chemical potential. </p> <h4>Electrostatic interaction</h4> E m i s f i t ( σ ) = α 2 ( σ + σ ′ ) 2 {\displaystyle E_{misfit}(\sigma )={\frac {\alpha }{2}}(\sigma +\sigma ')^{2}} <p>In the Emisfit expression α is an adjustable parameter and σ and σ' refer to the screening charge densities of the two surface patches in contact. This term has been labeled "misfit" energy, because it results from the mismatch of the charged surface pieces in contact. It represents the Coulomb interaction relative to the state in a perfect conductor. A molecule in a perfect conductor (COSMO state) is perfectly shielded electronically; each charge on the molecular surface is shielded by a charge of the same size but of opposite sign. If the conductor is replaced by surface pieces of contacting molecules the screening of the surface will not be perfect any more. Hence an interaction energy from this misfit of σ on the surface patches will arise. </p> <h4>Hydrogen bonding energy</h4> E h b ( σ ) = c h b ( T ) max [ 0 , σ a c c − σ h b ] min [ 0 , σ d o n + σ h b ] {\displaystyle E_{hb}(\sigma )=c_{hb}(T)\max[0,\sigma _{acc}-\sigma _{hb}]\min[0,\sigma _{don}+\sigma _{hb}]} <p>In the Ehb expression σacc and σdon are the screening charge densities of the hydrogen bond acceptor and donor respectively. The hydrogen bonding threshold σhb and the prefactor chb are adjustable parameters. The max[] and min[] construction ensures that the screening charge densities of the acceptor and donor exceeds the threshold for hydrogen bonding. </p> <h4>Dispersion (van der Waals energy)</h4> E d i s p = ∑ k γ k A k {\displaystyle E_{disp}=\sum _{k}\gamma _{k}A_{k}} <p>The COSMO-RS <a href="/facts/Van_der_Waals_force/jyGU8Vh9">dispersion</a> energy of a solute depends on an element (k) specific prefactor γ and the amount of exposed surface A of this element. It is not part of the interaction energy but enters the chemical potential directly. </p> <h3>Parameters</h3> <p>Though the use of quantum chemistry reduces the need for adjustable parameters, some fitting to experimental data is inevitable. The basic parameters are α, chb, σhb as used in the interaction energies, and one general parameter for the effective contact area. In addition, one adjustable van der Waals parameter γ per element is required. All parameters either are general or element specific, which is a distinctive feature of COSMO-RS as compared to <a href="/facts/Group_contribution_method/29UR7szr">group contribution methods</a> like UNIFAC. </p> <h2 id="implementations">Implementations</h2> <p>The original streamline of COSMO-RS was continuously developed and extended by A. Klamt in his company COSMOlogic (now part of BIOVIA), and the most advanced software for COSMO-RS is the COSMOtherm software, now available from BIOVIA. They also offer a huge database (COSMObase) with more than 12000 COSMO files. COSMOtherm proved its prediction accuracy by delivering the most accurate physicochemical property predictions in the recent <a href="/facts/SAMPL_Challenge/YgQzSbaF">SAMPL5 and SAMPL6 challenges</a>. </p><p>LVPP maintains an open sigma-profile database with COSMO-SAC ("Segment Activity Coefficient") parameterizations.<a class="footnote-ref" id="fnref:12" href="#fn:12"><sup>12</sup></a><a class="footnote-ref" id="fnref:13" href="#fn:13"><sup>13</sup></a> </p><p><a href="/facts/Gaussian_(software)/QGQaJ7ug">Gaussian (software)</a> cannot compute σ-profiles, but can produce .cosmo input files for COSMO-RS/Cosmotherm via the keyword scrf=COSMORS. </p><p>SCM licenses a commercial COSMO-RS implementation in the Amsterdam Modeling Suite, which also includes COSMO-SAC, UNIFAC and QSPR models.<a class="footnote-ref" id="fnref:14" href="#fn:14"><sup>14</sup></a> </p> <h2 id="see-also">See also</h2> <ul><li><a href="/facts/UNIFAC/Kcv3bL78">UNIFAC</a></li> <li><a href="/facts/UNIQUAC/VtYVwpIj">UNIQUAC</a></li> <li><a href="/facts/MOSCED/hcNLK8sc">MOSCED</a></li> <li><a href="/facts/Non-random_two-liquid_model/CaHzNBRT">NRTL</a></li></ul> <h2 id="references">References</h2> <ol> <li id="fn:1"><p>"Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena", A. Klamt, J. Phys. Chem., 99, 2224-2235 (1995), DOI: 10.1021/j100007a062 <a href="http://pubs.acs.org/doi/abs/10.1021/j100007a062" target="_blank">http://pubs.acs.org/doi/abs/10.1021/j100007a062</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li> <li id="fn:2"><p>Klamt, Andreas. (2007). COSMO-RS : from quantum chemistry to fluid phase thermodynamics and drug design. Elsevier. ISBN 978-0-08-045553-2. OCLC 1226672539. <a href="978-0-08-045553-2" target="_blank">978-0-08-045553-2</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li> <li id="fn:3"><p>Klamt, Andreas; Eckert, Frank; Arlt, Wolfgang (2010-06-15). "COSMO-RS: An Alternative to Simulation for Calculating Thermodynamic Properties of Liquid Mixtures". Annual Review of Chemical and Biomolecular Engineering. 1 (1): 101–122. doi:10.1146/annurev-chembioeng-073009-100903. ISSN 1947-5438. PMID 22432575. <a href="https://dx.doi.org/10.1146/annurev-chembioeng-073009-100903" target="_blank">https://dx.doi.org/10.1146/annurev-chembioeng-073009-100903</a> <a href="#fnref:3" class="footnote-back-ref">↩</a></p></li> <li id="fn:4"><p>"COSMO: A New Approach to Dielectric Screening in Solvents with Explicit Expressions for the Screening Energy and its Gradient", A. Klamt and G. Schüürmann, J. Chem. Soc. Perkin Trans. II 799-805 (1993) doi:10.1039/P29930000799 <a href="//doi.org/10.1039/P29930000799" target="_blank">//doi.org/10.1039/P29930000799</a> <a href="#fnref:4" class="footnote-back-ref">↩</a></p></li> <li id="fn:5"><p>"Conductor-like Screening Model for Real Solvents: A New Approach to the Quantitative Calculation of Solvation Phenomena", A. Klamt, J. Phys. Chem., 99, 2224-2235 (1995), DOI: 10.1021/j100007a062 <a href="http://pubs.acs.org/doi/abs/10.1021/j100007a062" target="_blank">http://pubs.acs.org/doi/abs/10.1021/j100007a062</a> <a href="#fnref:5" class="footnote-back-ref">↩</a></p></li> <li id="fn:6"><p>"Refinement and Parametrization of COSMO-RS", A. Klamt, V. Jonas, T. Bürger and J. C. W. Lohrenz, J. Phys. Chem. A 102, 5074-5085 (1998), doi:10.1021/jp980017s <a href="//doi.org/10.1021/jp980017s" target="_blank">//doi.org/10.1021/jp980017s</a> <a href="#fnref:6" class="footnote-back-ref">↩</a></p></li> <li id="fn:7"><p>"A Priori Phase Equilibrium Prediction from a Segment Contribution Solvation Model", S.-T. Lin and S.I. Sandler, Ind. Eng. Chem. Res., 41 (5), 899–913 (2002), doi:10.1021/ie001047w <a href="//doi.org/10.1021/ie001047w" target="_blank">//doi.org/10.1021/ie001047w</a> <a href="#fnref:7" class="footnote-back-ref">↩</a></p></li> <li id="fn:8"><p>"Performance of a Conductor-Like Screening Model for Real Solvents Model in Comparison to Classical Group Contribution Methods", H. Grensemann and J. Gmehling, Ind. Eng. Chem. Res., 44 (5), 1610–1624 (2005), doi:10.1021/ie049139z <a href="//doi.org/10.1021/ie049139z" target="_blank">//doi.org/10.1021/ie049139z</a> <a href="#fnref:8" class="footnote-back-ref">↩</a></p></li> <li id="fn:9"><p>"Infinite Dilution Activity Coefficients for Trihexyltetradecyl Phosphonium Ionic Liquids: Measurements and COSMO-RS Prediction", T. Banerjee and A. Khanna, J. Chem. Eng. Data, 51 (6), 2170–2177 (2006), doi:10.1021/je0602925 <a href="//doi.org/10.1021/je0602925" target="_blank">//doi.org/10.1021/je0602925</a> <a href="#fnref:9" class="footnote-back-ref">↩</a></p></li> <li id="fn:10"><p>"An implementation of the conductor-like screening model of solvation within the Amsterdam density functional package. Part II. COSMO for real solvents", C.C. Pye, T. Ziegler, E. van Lenthe, J.N. Louwen, Can. J. Chem. 87, 790 (2009), doi:10.1139/V09-008 <a href="//doi.org/10.1139/V09-008" target="_blank">//doi.org/10.1139/V09-008</a> <a href="#fnref:10" class="footnote-back-ref">↩</a></p></li> <li id="fn:11"><p>"On the influence of basis sets and quantum chemical methods on the prediction accuracy of COSMO-RS", R. Franke, B. Hannebauer, Phys. Chem. Chem. Phys., 13, 21344-21350 (2011), doi:10.1039/C1CP22317H <a href="//doi.org/10.1039/C1CP22317H" target="_blank">//doi.org/10.1039/C1CP22317H</a> <a href="#fnref:11" class="footnote-back-ref">↩</a></p></li> <li id="fn:12"><p>"LVPP sigma-profile database + COSMO-SAC parametrizations: lvpp/sigma". LVPP. 30 October 2019. Retrieved 6 November 2019. <a href="https://github.com/lvpp/sigma" target="_blank">https://github.com/lvpp/sigma</a> <a href="#fnref:12" class="footnote-back-ref">↩</a></p></li> <li id="fn:13"><p>Ferrarini, F.; Flôres, G. B.; Muniz, A. R.; Soares, R. P. de (2018). "An open and extensible sigma-profile database for COSMO-based models". AIChE Journal. 64 (9): 3443–3455. doi:10.1002/aic.16194. ISSN 1547-5905. S2CID 103011443. <a href="/wiki/Doi_(identifier)" target="_blank">/wiki/Doi_(identifier)</a> <a href="#fnref:13" class="footnote-back-ref">↩</a></p></li> <li id="fn:14"><p>"COSMO-RS: predict activity coefficients, logP, VLE from DFT data". Software for Chemistry & Materials. Retrieved 6 November 2019. <a href="https://www.scm.com/product/cosmo-rs/" target="_blank">https://www.scm.com/product/cosmo-rs/</a> <a href="#fnref:14" class="footnote-back-ref">↩</a></p></li> </ol>