COSMO solvation model: Difference between revisions

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{{Short description|Computational model for solvent effects}}

[[Image:Pentaacrylat.png|thumb|COSMO surface of a pentaacrylate molecule (red = negative, green = positive equilibrium layer).]]

[[File:4-Nitrobenzoic-acid-elpot-3D-vdW.png|thumb|Charge density surface of 4-nitro-benzoicacid. Calculated with COSMO.]]

'''COSMO'''<ref name=":0" /><ref name=":1" /> (COnductor-like Screening MOdel) is a calculation method for determining the [[electrostatic]] interaction of a [[molecule]] with a [[solvent]]. COSMO is a dielectric continuum model<ref name=":0" /><ref name=":3">{{Cite journal |last=Herbert |first=John M. |date=2021-03-23 |title=Dielectric continuum methods for quantum chemistry |journal=WIREs Computational Molecular Science |volume=11 |issue=4 |doi=10.1002/wcms.1519 |arxiv=2203.06846 |s2cid=233629977 |issn=1759-0876}}</ref><ref>{{Cite book |last=Cramer |first=Christopher J. |title=Essentials of computational chemistry: theories and models |date=2004 |publisher=Wiley |isbn=0-470-09182-7 |edition=2nd |___location=Chichester, West Sussex, England |oclc=55887497}}</ref><ref>{{Cite book |last=Frank |first=Jensen |title=Introduction to computational chemistry |date=2017 |publisher=John Wiley & Sons |isbn=978-1-118-82599-0 |oclc=989360916}}</ref> (a.k.a. continuum solvation model). These models can be used in [[computational chemistry]] to model [[solvation]] effects. COSMO has become a popular method of these solvation models in recent years. The COSMO formalism is similar to the method proposed earlier by Hoshi et al.<ref name=":0" /><ref>{{Cite journal |last1=Hoshi |first1=Hajime |last2=Sakurai |first2=Minoru |last3=Inoue |first3=Yoshio |last4=Chûjô |first4=Riichirô |date=1987-07-15 |title=Medium effects on the molecular electronic structure. I. The formulation of a theory for the estimation of a molecular electronic structure surrounded by an anisotropic medium |journal=The Journal of Chemical Physics |volume=87 |issue=2 |pages=1107–1115 |doi=10.1063/1.453343 |bibcode=1987JChPh..87.1107H |issn=0021-9606}}</ref> The COSMO approach is based – as many other dielectric continuum models – on the surface segmentation of a molecule surface<ref name=":3" /> (usually referred to as 'solvent accessible surface' SAS approach).

InContinuum solvation models – such as COSMO the– solventtreat iseach treatedsolvent as a continuum with a [[permittivity]] ''&epsilon;<math>\varepsilon</math>'',. and therefore belongs to the "continuumContinuum solvation" group of models. As in all these models COSMO approximatesapproximate the solvent by a dielectric continuum, surrounding the solute molecules outside of a molecular cavity. The details of the cavity construction differ in different COSMO implementations. In most cases it is constructed as an assembly of atom-centered spheres with radii approximately 20% larger than the [[Van der Waals radius]]. For the actual calculation the cavity surface is approximated by segments, e.g., hexagons, pentagons, or triangles.

'''COSMO''' is the abbreviation for "'''CO'''nductor-like '''S'''creening '''MO'''del", a calculation method for determining the [[electrostatic]] interaction of a [[molecule]] with a [[solvent]].

Unlike other continuum solvation models, COSMO derives the polarization charges of the continuum, caused by the polarity of the solute, from a scaled-conductor approximation. If the solvent were an ideal conductor the [[electric potential]] on the cavity surface must disappear. If the distribution of the [[electric charge]] in the molecule is known, e.g. from quantum chemistry, then it is possible to calculate the charge ''<math>q''^*</math> on the surface segments. For solvents with finite dielectric constant this charge ''<math>q</math>'' is lower by approximately a factor ''&fnof;''<math>f(''&epsilon;''\varepsilon):</refmath>:

In COSMO the solvent is treated as a continuum with a [[permittivity]] ''&epsilon;'', and therefore belongs to the "continuum solvation" group of models. As in all these models COSMO approximates the solvent by a dielectric continuum, surrounding the solute molecules outside of a molecular cavity. The details of the cavity construction differ in different COSMO implementations. In most cases it is constructed as an assembly of atom-centered spheres with radii approximately 20% larger than the [[Van der Waals radius]]. For the actual calculation the cavity surface is approximated by segments, e.g., hexagons, pentagons, or triangles.

Unlike other continuum solvation models, COSMO derives the polarization charges of the continuum, caused by the polarity of the solute, from a scaled-conductor approximation. If the solvent were an ideal conductor the [[electric potential]] on the cavity surface must disappear. If the distribution of the [[electric charge]] in the molecule is known, e.g. from quantum chemistry, then it is possible to calculate the charge ''q''* on the surface segments. For solvents with finite dielectric constant this charge ''q'' is lower by approximately a factor ''&fnof;''(''&epsilon;''):</ref>

A., Klamt; G., Schüürmann (1992). "COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient". J. Chem. Soc. (Perkin Trans.2) 2 (5): 799–805. doi:10.1039/P29930000799. Retrieved 25 October 2015.</ref>

:<math>q = f(\varepsilon) q^*.</math>

The factor ''&fnof;''<math>f(''&epsilon;''\varepsilon)</math> is approximately

:<math>f(\varepsilon)=\frac{\varepsilon-1}{\varepsilon+x},</math>

where the value of <math>x</math> should be set to 0.5 for neutral molecules and to 0.0 for ions, see original derivation.<ref name=":1">{{Cite book|title=From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design|last=Klamt|first=Andreas|publisher=Elsevier|year=2005|isbn=9780444519948|___location=Boston, MA, USA}}</ref> The value of <math>x</math> is erroneously set to 0 in the popular C-PCM reimplementation of COSMO in Gaussian.

where the value of ''x'' is set to 0.5 based on theoretical arguments. Some re-implementations of COSMO use ''x''&nbsp;=&nbsp;0.

From the thus determined solvent charges ''<math>q''</math> and the known charge distribution of the molecule, the energy of the interaction between the solvent and the solute molecule can be calculated.

The COSMO method can be used for all methods in [[theoretical chemistry]] where the charge distribution of a molecule can be determined, for example semiempirical calculations, [[Hartree&ndash;Fock]]-method calculations or [[density functional theory]] (quantum physics) calculations.<ref name=":0">{{cite journal |last1=A.|first1=Klamt|last2=G.|first2=Schüürmann|date=1993|title=COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient|journal=J. Chem. Soc.|publisher=Perkin Trans.2|volume=2|issue=5|pages=799–805|doi=10.1039/P29930000799}}</ref>

==Variants and implementations==

COSMO has been implemented in a number of quantum chemistry or semi-empirical codes such as [[Amsterdam Density Functional|ADF]], [[GAMESS-US]], [[Gaussian (software)|Gaussian]], [[MOPAC]], [[NWChem]], [[TURBOMOLE]], and [[Q-Chem]]. A COSMO version of the [[polarizable continuum model]] PCM has also been developed {{Citation needed|date=April 2022}}. Depending on the implementation, the details of the cavity construction and the used radii, the segments representing the molecule surface and the <math>x</math> value for the dielectric scaling function <math>f(\varepsilon)</math> may vary –which at times causes problems regarding the reproducibility of published results.

==Comparison with other methods==

While models based on the [[multipole expansion]] of the charge distribution of a molecule are limited to small, quasi-spherical or ellipsoidal molecules, the COSMO method has the advantage (as many other dielectric continuum models) that it can be applied to large and irregularly formed molecular structures.

In contrast to the [[polarizable continuum model]] (PCM), which uses the exact dielectric boundary conditions, the COSMO method uses the approximative scaling function <math>f(\varepsilon)</math>. Though the scaling is an approximation, it turned out to provide a more accurate description of the so-called outlying charge, reducing the corresponding error. A method comparison<ref name=":2">{{Cite journal|last1=Klamt|first1=A.|last2=Moya|first2=C.|last3=Palomar|first3=J.|date=2015|title=A Comprehensive Comparison of the IEFPCM and SS(V)PE Continuum Solvation Methods with the COSMO Approach|doi=10.1021/acs.jctc.5b00601|journal=Journal of Chemical Theory and Computation|volume=11 |issue=9|pages=4220–4225|url=https://zenodo.org/record/1451619|pmid=26575917}}</ref> of COSMO and the integral equation formalism PCM (IEFPCM), which combines the exact dielectric boundary conditions with a reduced outlying charge error, showed that the differences between the methods are small as compared to deviations to experimental solvation data. The errors introduced by treating a solvent as a continuum and thus neglecting effects like hydrogen bonding or reorientation are thus more relevant to reproduce experimental data than the details of the different continuum solvation methods.

The COSMO method is more accurate for solvents with a higher permittivity because a solvent with infinite permittivity behaves like an ideal conductor. With water (''&epsilon;''&nbsp;&asymp;&nbsp;80) a very good accuracy is achieved. Nevertheless, with the choice of ''x''&nbsp;=&nbsp;0.5 even at low permittivities it is almost as accurate as a complete solution of the electrostatic equations, though at much lower numerical costs. Apart from the numerical effciciency, another big advantage of COSMO compared to other dielectric continuum methods is its huge reduction of the artifacts caused by the small part of the electron density reaching outside of the cavity, the so-called outlying charge errors.

==See also==

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==References==

{{reflist}}

1. ^{{cite journal |last=A.|first=Klamt|last2=G.|first2=Schüürmann|date=1992|title=COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient|url=http://pubs.rsc.org/en/content/articlepdf/1993/p2/p29930000799|journal=J. Chem. Soc.|publisher=Perkin Trans.2|volume=2|issue=5|pages=799-805|doi=10.1039/P29930000799|access-date=25 October 2015}}

==Further reading==

* {{cite journal | author = A. Klamt, G. Schüürmann | journal = [[Journal of the Chemical Society, Perkin Transactions 2]] | year = 1993 | doi = 10.1039/P29930000799 | title = COSMO: A new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient | pages = 799–805}}

[[Category:Computational chemistry]]