From owner-chemistry@ccl.net Sat Apr 8 04:46:00 2017 From: "Andreas Klamt klamt^^^cosmologic.de" To: CCL Subject: CCL:G: Thermodynamic Data & Solvation - Calculation Questions: Message-Id: <-52733-170408044449-23436-Q/GEDb3XjfzlBllfq5urCA(!)server.ccl.net> X-Original-From: Andreas Klamt Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset=utf-8 Date: Sat, 8 Apr 2017 10:44:37 +0200 MIME-Version: 1.0 Sent to CCL by: Andreas Klamt [klamt-.-cosmologic.de] Hi together, it is surely true that the most fundamental way to separate H and TS is doing a temperature derivative. But that requires that the free energy has the correct temperature dependence. Please note that the 2nd derivatives in solution, if calculate from a continuum solvation model, are not the true vibrational frequencies. It is pure fiction to assume that in this way you would end up the correct enthalpy and entropy. In COSMO-RS we have a consistent, although not completely ab initio (no practically usable solvation model is completely ab initio!), scheme for temperature and mixture dependent free energies, and thus for H and TS. Best regards Andreas Am 07.04.2017 um 09:12 schrieb adon cumi adonmage- -gmail.com: > Sent to CCL by: adon cumi [adonmage .. gmail.com] > HI TO ALL! > > > The most *robust* way of separating enthalpic and entropic > contributions would be to calculate the full value of the free energy > at a variety of different temperatures, then numerically evaluating > dG/dT to find the entropy > > The JAGUAR program from SCHRODINGER Inc. It provide a tool via > jaguar-->single point energy-->vibrational frequencies. in the tab > below you should be able to increment the temperature to do your > "dG/dT" ! > > BEST REGARDS, > > 2017-04-06 17:08 UTC+02:00, Eric Hermes erichermes**gmail.com > : >> Sent to CCL by: Eric Hermes [erichermes!^!gmail.com] >> Dr. Mielczarek, >> >> As always, the free energy of a species is defined with respect to some >> choice of reference state, such that for a reaction of the form: >> >> (1) A + B -> C >> >> with a standard state free energy of reaction ΔG°, one can write the >> equilibrium constant as: >> >> (2) Keq = exp[-ΔG°/(kB T)] = a_C / (a_A a_C) >> >> Where a is the *activity* of a species. In the case of an ideal gas, >> the activity is simply the density divided by the *standard state* >> density: >> >> (3) a = ρ/ρ° >> >> The numerical value of Keq then depends on choice of reference state, >> but the equilibrium densities do not. Eq. 2 satisfies this requirement. >> One can show that the free energy of a species at an *arbitrary* >> reference state is given by: >> >> (4) G = G° + kB T ln[ρ/ρ°] >> >> This is *general*, but you can show that for an ideal gas the >> expression derives from the translational entropy. >> >> Now, when we are discussing free energy of solvation, the reaction >> becomes: >> >> (5) A_g -> A_soln >> >> Which of course brings with it changes to both the enthalpy and the >> entropy. These issues are *orthogonal* to the reference state issue, >> though. The standard state for species in the gas phase is usually >> taken to be 1 bar (occasionally 1 atm is chosen instead), but the >> standard state for species in *solution* is typically chosen to be 1 M, >> which is very different! With these choices of reference state, the >> free energy of solvation ΔG°solv can be used to calculate the >> equilibrium constant like this (using P for pressure to visually >> distinguish from the density ρ): >> >> (6) Keq = exp[-ΔG°solv/(kB T)] = (ρ_A/(1 M)) / (P_A / (1 bar)) >> >> As before, the numerical value of Keq depends on the choice of >> reference state, but the equilibrium density and pressure do not. >> >> So, if your goal is to determine the equilibrium properties of a >> solvation process, then you do not need to be concerned about the >> choice of reference state -- you need to be *aware* of it in order to >> calculate the properties directly, but whichever choice you make you >> will get the same answer. On the other hand, if you wish to compare >> your free energies of solvation to experimental values, you should most >> definitely ensure that the value you are calculating uses a reference >> state of 1 M for solution-phase species and 1 bar for gas-phase >> species. >> >> In the case of SMD, by default it will use the *same* reference state >> for the gas-phase and solution-phase species. The actual value of the >> reference state is irrelevant, as ΔGsolv has the same value for any >> choice of reference state so long as the reactants and products have >> the *same* reference state (if you are not convinced, stare at eqs 2, >> 3, and 4 in the context of eq 5 until you believe me :) ). >> >> This means you can arbitrarily say what reference state ΔGsolv is at, >> say 1 bar, for both reactants and products. Then, if you want to >> calculate ΔG°solv (the *experimental* standard state value), you just >> need to use eq 4: >> >> (7) ΔGsolv = Gsoln - G°gas (we choice a reference state of 1 bar) >> (8) Gsoln = G°soln + kB T ln[(1 bar / (kB T))/1 M] (ideal gas law) >> (9) ΔG°solv = G°soln - G°gas = ΔGsolv - kB T ln[(1 bar / (kB T))/1 M] >> >> Note that you would have gotten the *exact same result* if you had >> arbitrarily chosen a reference state of 1 M instead for ΔGsolv (if you >> don't believe me, try it yourself -- start with ΔGsolv = G°soln - >> Ggas). >> >> --- >> >> Now, as to your point about the entropy of solution phase species -- >> I'm not sure the paper you are linking is making the claim you are >> saying it does. It is an *unarguable fact* that (at the typical choice >> of standard states) a species in solution has less entropy than the >> same species in the gas phase. This *must* be the case because the >> molecules in an ideal gas are non-interacting, uncorrelated, and >> undergoing ballistic motion, whereas in solution molecules are *caged* >> by the solvent and undergoing diffusive motion, which means they have >> significantly less freedom of motion. >> >> The paper you link talks about *vibrational* motion, which is going to >> be *significantly* less perturbed by the presence of solvent. The >> *vast* majority of entropy for gas-phase species comes from >> translational motion, not vibrational motion. >> >> --- >> >> Finally, I'm not sure SMD is well-suited to give a *breakdown* of >> enthalpic and entropic terms to the free energy of solvation. The >> procedure you discuss will get *some* of that breakdown, but ultimately >> several contributions to ΔGsolv are all entangled with one another. >> >> What I mean by that is if you simply perform two *single point* >> calculations on the same species, one with and one without SMD >> correction, the difference in the potential energies between those two >> calculations will include a mixture of enthalpic and entropic effects. >> >> Doing the full thermodynamic calculations (i.e. doing a frequency >> calculation and reading the thermodynamic data printed in the Gaussian >> output file) will give you a *full* estimate for ΔGsolv. But, in both >> calculations (with and without SMD) the calculated enthalpic and >> entropic contributions are arising from the same set of approximations >> -- harmonic oscillator for vibration, rigid rotor for rotation, and >> *ideal gas* for translation. >> >> This works because the *potential energy* difference between the >> systems is parameterized such that the free energy difference >> calculated by Gaussian is a good approximatino of the total free energy >> of solvation. Since the enthalpy and entropy calculated by Gaussian for >> both calculations are using the same approximations, they will have >> very similar (but not identical!) values. All of those complicated >> factors such as the loss of translational entropy due to solvation are >> baked into the *electronic energy* that is calculated by the SMD >> method. >> >> The most *robust* way of separating enthalpic and entropic >> contributions would be to calculate the full value of the free energy >> at a variety of different temperatures, then numerically evaluating >> dG/dT to find the entropy. However, SMD as implemented in Gaussian is >> not temperature-dependent, so you cannot actually do this. There are >> other continuum solvation models developed by Cramer and Truhlar which >> do have temperature-dependence, which would allow you to do this, but >> as far as I can tell they are not included in Gaussian. >> >> --- >> >> I hope this answers all of the questions that you had. Please let me >> know if anything I said was unclear or you want additional assistance. >> >> Eric Hermes >> >> On Thu, 2017-04-06 at 06:24 +0000, MIELCZAREK Detlev Conrad detlev- >> conrad.mielczarek-.-ifpen.fr wrote: >>> Sent to CCL by: MIELCZAREK Detlev Conrad [detlev- >>> conrad.mielczarek]^[ifpen.fr] >>> Dear CCL, a question on thermodynamic data & solvation from me, maybe >>> you can help me. >>> >>> So, the basic problem for me is, that I am calculating/want to >>> calculate thermodynamic data (Hf, S - hence also dG) in solvation, >>> using implicit solvation models, SMD with a COSMO cavity to be >>> specific. For my application, these should be accurate enough. (So no >>> molecular dynamics simulations etc.) >>> >>> Solvation models are normally parametrised for dGsolv - so this value >>> can be extracted from the quantum chemistry calculation as the >>> difference in the calculated Gibbs Free Enthalpy. >>> Hf can calculated easily in the gas phase, and a re-optimisation of >>> the structure with solvation should capture the majority of the >>> impact of solvation on the enthalpy. (Which is dominated by molecular >>> structure.) >>> (I guess there is the case of stabilisation and complexes, such as >>> are reported for water. However this is currently beyond the scope of >>> my work.) >>> >>> The topic of solvation has been discussed previously on the CCL here: >>> http://www.ccl.net/chemistry/resources/messages/2011/12/01.001-dir/ >>> http://www.ccl.net/chemistry/resources/messages/2011/10/06.005-dir/ >>> http://www.ccl.net/chemistry/resources/messages/2014/05/01.004-dir/ >>> And there is the book "Essentials of Computational Chemistry Theories >>> and Models" from Professor Cramer with a section on phase change (the >>> source of my confusion). >>> >>> Specifically, the discussion concerning the energy change related to >>> the state conversion causes me some grief. >>> >>> On the one hand, the CCL responses read as if this should be applied >>> in the case of any phase change, but then others suggest this is >>> applicable only if the process is a second order reaction and thus >>> the total number of mols changes? - The latter view seems to agree >>> with the book... >>> >>> So if I have compound A in both the gas and liquid phase (from a >>> quantum chemistry calculation), do I need to account for the phase >>> change/change of state or not? Or is it something that can be >>> included in the parametrisation of the solvation model/the quantum >>> chemistry code already? >>> >>> Just to add more confusion to the topic: I have trialled a commercial >>> product which gives the Gibbs Enthalpy of Solvation in kcal/mol for >>> mol/L concentrations and using a very low end/fast functional, it >>> gives values similar to when a correction term is added... on the >>> other hand, where available, the calculated values without correction >>> agree with the published values in the SMD paper: http://pubs.acs.org >>> /doi/abs/10.1021/jp810292n (Supplementary Data) >>> >>> In addition, a regular computational chemistry calculation sees very >>> little (virtually no) difference in the entropy between the gaseous >>> and solvated phase. This would agree with the CCL-linked paper here h >>> ttp://pubs.acs.org/doi/abs/10.1021/jp205508z . But this would clash >>> with the common expectation that entropy in the liquid phase is >>> reduced... >>> >>> Hence, I would highly appreciate if someone knowledgeable in the >>> field of solvation could guide me onto the correct track. >>> >>> Detlev Conrad Mielczarek >>> Scientific Visitor/Post Doctorant >>> IFP Energies nouvelles >>> France >>> >>> www.ifpenergiesnouvelles.fr >>> >>> __________________________ >>> Avant d'imprimer, pensez à l'environnement ! Please consider the >>> environment before printing ! >>> Ce message et toutes ses pièces jointes sont confidentiels et établis >>> à l'intention exclusive de ses destinataires. Toute utilisation non >>> conforme à sa destination, toute diffusion ou toute publication, >>> totale ou partielle, est interdite, sauf autorisation expresse. IFP >>> Energies nouvelles décline toute responsabilité au titre de ce >>> message. This message and any attachments are confidential and >>> intended solely for the addressees. Any unauthorised use or >>> dissemination is prohibited. IFP Energies nouvelles should not be >>> liable for this message. >>> __________________________ >>> >>> >>> >>> -= This is automatically added to each message by the mailing script >>> =- >>> To recover the email address of the author of the message, please >>> change>> Conferences: http://server.ccl.net/chemistry/announcements/conference >>> s/> > > -- -------------------------------------------------- Prof. Dr. Andreas Klamt CEO / Geschäftsführer COSMOlogic GmbH & Co. KG Imbacher Weg 46 D-51379 Leverkusen, Germany phone +49-2171-731681 fax +49-2171-731689 e-mail klamt_+_cosmologic.de web www.cosmologic.de [University address: Inst. of Physical and Theoretical Chemistry, University of Regensburg] HRA 20653 Amtsgericht Koeln, GF: Prof. Dr. Andreas Klamt Komplementaer: COSMOlogic Verwaltungs GmbH HRB 49501 Amtsgericht Koeln, GF: Prof. Dr. Andreas Klamt