From owner-chemistry@ccl.net Tue Feb 7 13:31:01 2017 From: "Ernest Chamot echamot\a/chamotlabs.com" To: CCL Subject: CCL: Entropy of a Bimolecular System Message-Id: <-52625-170207124811-13612-hO/lB6JTkucFc1AZvSs7jw]|[server.ccl.net> X-Original-From: Ernest Chamot Content-Type: multipart/alternative; boundary="Apple-Mail=_8D6C1CBE-CBF4-4891-B115-A867FF2E0795" Date: Tue, 7 Feb 2017 11:48:03 -0600 Mime-Version: 1.0 (Mac OS X Mail 10.2 \(3259\)) Sent to CCL by: Ernest Chamot [echamot%%chamotlabs.com] --Apple-Mail=_8D6C1CBE-CBF4-4891-B115-A867FF2E0795 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset=utf-8 Hi All, I seem to have argued myself into a state of confusion: I guess I just = don=E2=80=99t really understand the entropy of a bimolecular system. I can calculate the enthalpy of a molecule with any number of methods, = and so long as I also do an IR or frequency calculation, I can also get = the entropy, and ultimately the free energy of the molecule. So if I am = considering the equilibrium of a dissociation reaction, I can get the = heat of reaction by modeling all three species, and subtracting the = enthalpy of the reactant from the sum of the enthalpies of the products. = But how do I calculate the free energy of reaction? I can=E2=80=99t just add up the individual free energies, can I? = Isn=E2=80=99t the entropy of the pair of product molecules different = > from just the sum of the two individual entropies? Since there are two = separate molecules in the same frame of reference, there should be an = additional 6 degrees of freedom for the second molecule, even at = infinite separation. Or do these all have a correspondence with a = vibrational mode in the original reactant molecule? Doesn=E2=80=99t = there need to be an additional term or factor: ln(2), or angular = momentum, or something? (I=E2=80=99m interested in the overall reaction, not with the two = product molecules still bound together in some intermediate complex. = Otherwise I could just model that.) Thanks for any help. EC Ernest Chamot Chamot Labs, Inc. http://www.chamotlabs.com --Apple-Mail=_8D6C1CBE-CBF4-4891-B115-A867FF2E0795 Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset=utf-8 Hi All,

I seem to have argued myself into a state of = confusion: I guess I just don=E2=80=99t really understand the entropy of = a bimolecular system.

I can calculate the enthalpy of a molecule with any number of = methods, and so long as I also do an IR or frequency calculation, I can = also get the entropy, and ultimately the free energy of the molecule. =  So if I am considering the equilibrium of a dissociation reaction, = I can get the heat of reaction by modeling all three species, and = subtracting the enthalpy of the reactant from the sum of the enthalpies = of the products. But how do I calculate the free energy of = reaction?

I = can=E2=80=99t just add up the individual free energies, can I? =  Isn=E2=80=99t the entropy of the pair of product molecules = different from just the sum of the two individual entropies?  Since = there are two separate molecules in the same frame of reference, there = should be an additional 6 degrees of freedom for the second molecule, = even at infinite separation.  Or do these all have a correspondence = with a vibrational mode in the original reactant molecule? =  Doesn=E2=80=99t there need to be an additional term or factor: =  ln(2), or angular momentum, or something?

(I=E2=80=99m interested = in the overall reaction, not with the two product molecules still bound = together in some intermediate complex. Otherwise I could just model = that.)

Thanks = for any help.

EC


Ernest Chamot
Chamot Labs, = Inc.
http://www.chamotlabs.com

= --Apple-Mail=_8D6C1CBE-CBF4-4891-B115-A867FF2E0795-- From owner-chemistry@ccl.net Tue Feb 7 14:33:01 2017 From: "Torsten Bruhn torsten.bruhn_-_mail.uni-oldenburg.de" To: CCL Subject: CCL: SpecDis 1.70 Message-Id: <-52626-170207143224-10752-jUeM7HpEtDb3J95ldP4UaQ[a]server.ccl.net> X-Original-From: "Torsten Bruhn" Date: Tue, 7 Feb 2017 14:32:21 -0500 Sent to CCL by: "Torsten Bruhn" [torsten.bruhn-*-mail.uni-oldenburg.de] Hi all, we released a new version of SpecDis, a tool to compare calculated and experimental CD spectra (UV/ECD, IR/VCD). It is free and there are version for Windows and Linux (GTK2). For details on the changes have a look at https://specdis-software.jimdo.com/ The layout has been changed significantly UV/ECD or IR/VCD are handled in one tab now. We added a peak picking tool and SpecDis calculates g factors now. Furthermore, the work flow for Boltzmann weighting has been improved and the similarity algorithms have been changed so that they produce even more reliable values. There are many more changes, they are all listed in the download section. If you have any suggestions please send me an email, every constructive feedback is welcome. Cheers, Torsten From owner-chemistry@ccl.net Tue Feb 7 16:53:01 2017 From: "David Mannock dmannock ~~ yahoo.com" To: CCL Subject: CCL: Entropy of a Bimolecular System Message-Id: <-52627-170207155310-19013-iHI0HYKTODdV/qMgqQjOJA^^^server.ccl.net> X-Original-From: David Mannock Content-Type: multipart/alternative; boundary="----=_Part_2785071_372096695.1486500062517" Date: Tue, 7 Feb 2017 20:41:02 +0000 (UTC) MIME-Version: 1.0 Sent to CCL by: David Mannock [dmannock[a]yahoo.com] ------=_Part_2785071_372096695.1486500062517 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Ernest, I suggest you look at an old but fundamental paper by Lumry & Rajen= der 1970 and go through the list 0f 625 citations some of which examine the= mathematical modeling of these relationships in biomolecular reactions. Th= is is a big monograph that took me quite a while to photocopy many years ag= o as I recall. Enjoy! Dave=20 http://onlinelibrary.wiley.com/doi/10.1002/bip.1970.360091002/abstract=20 On Tuesday, February 7, 2017 12:45 PM, Ernest Chamot echamota/chamotlab= s.com wrote: =20 Hi All, I seem to have argued myself into a state of confusion: I guess I just don= =E2=80=99t really understand the entropy of a bimolecular system. I can calculate the enthalpy of a molecule with any number of methods, and = so long as I also do an IR or frequency calculation, I can also get the ent= ropy, and ultimately the free energy of the molecule. =C2=A0So if I am cons= idering the equilibrium of a dissociation reaction, I can get the heat of r= eaction by modeling all three species, and subtracting the enthalpy of the = reactant from the sum of the enthalpies of the products. But how do I calcu= late the free energy of reaction? I can=E2=80=99t just add up the individual free energies, can I? =C2=A0Isn= =E2=80=99t the entropy of the pair of product molecules different from just= the sum of the two individual entropies? =C2=A0Since there are two separat= e molecules in the same frame of reference, there should be an additional 6= degrees of freedom for the second molecule, even at infinite separation. = =C2=A0Or do these all have a correspondence with a vibrational mode in the = original reactant molecule? =C2=A0Doesn=E2=80=99t there need to be an addit= ional term or factor: =C2=A0ln(2), or angular momentum, or something? (I=E2=80=99m interested in the overall reaction, not with the two product m= olecules still bound together in some intermediate complex. Otherwise I cou= ld just model that.) Thanks for any help. EC Ernest ChamotChamot Labs, Inc.http://www.chamotlabs.com =20 ------=_Part_2785071_372096695.1486500062517 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Ernest, I suggest you look at an old but fundamental= paper by Lumry & Rajender 1970 and go through the list 0f 625 citation= s some of which examine the mathematical modeling of these relationships in= biomolecular reactions. This is a big monograph that took me quite a while= to photocopy many years ago as I recall. Enjoy! Dave



On Tuesday, February 7, 2017 12:45 PM, Ernest Chamot echamota/c= hamotlabs.com <owner-chemistry(!)ccl.net> wrote:

=
Hi All,<= div class=3D"yiv4878580470">
I seem to have argued myself i= nto a state of confusion: I guess I just don=E2=80=99t really understand th= e entropy of a bimolecular system.

I can calculate th= e enthalpy of a molecule with any number of methods, and so long as I also = do an IR or frequency calculation, I can also get the entropy, and ultimate= ly the free energy of the molecule.  So if I am considering the equili= brium of a dissociation reaction, I can get the heat of reaction by modelin= g all three species, and subtracting the enthalpy of the reactant from the = sum of the enthalpies of the products. But how do I calculate the free ener= gy of reaction?

I can=E2=80=99t just add up the indiv= idual free energies, can I?  Isn=E2=80=99t the entropy of the pair of = product molecules different from just the sum of the two individual entropi= es?  Since there are two separate molecules in the same frame of refer= ence, there should be an additional 6 degrees of freedom for the second mol= ecule, even at infinite separation.  Or do these all have a correspond= ence with a vibrational mode in the original reactant molecule?  Doesn= =E2=80=99t there need to be an additional term or factor:  ln(2), or a= ngular momentum, or something?

(I=E2=80=99m int= erested in the overall reaction, not with the two product molecules still b= ound together in some intermediate complex. Otherwise I could just model th= at.)

Thanks for any help.

EC


Ernest Chamot
Chamot Labs, Inc= .
http://www.chamo= tlabs.com



=
------=_Part_2785071_372096695.1486500062517-- From owner-chemistry@ccl.net Tue Feb 7 18:44:00 2017 From: "David Sherrill prof.david.sherrill_-_gmail.com" To: CCL Subject: CCL: Georgia Tech Summer Theory Program Message-Id: <-52628-170207141916-6119-lhunEpu6RgRWGw1Rx1sXKw_._server.ccl.net> X-Original-From: David Sherrill Content-Type: text/plain; charset=UTF-8 Date: Tue, 7 Feb 2017 14:19:08 -0500 MIME-Version: 1.0 Sent to CCL by: David Sherrill [prof.david.sherrill:_:gmail.com] Georgia Tech will host its annual Summer Theory Program as part of its NSF-sponsored Research Experiences for Undergraduates (REU) program in chemistry and biochemistry. The ten-week program runs from May 21 to July 28 and is open to students who will be in their junior or senior years during the next academic year. Theory students will work with Professors David Sherrill, Jean-Luc Bredas, or Ken Brown in the areas of electronic structure theory, organic electronics, or quantum computing. The research experience is supplemented by an introductory lecture series in theoretical chemistry. Successful applicants will receive a stipend of $5000, a travel allowance, and housing. Further details are available at http://vergil.chemistry.gatech.edu/opp/summer.html and http://ww2.chemistry.gatech.edu/reu/ Participants supported by the NSF must be US citizens or permanent residents of the US. The deadline for applications is February 15. From owner-chemistry@ccl.net Tue Feb 7 19:20:01 2017 From: "Tymofii Nikolaienko tim_mail---ukr.net" To: CCL Subject: CCL: Entropy of a Bimolecular System Message-Id: <-52629-170207161350-23971-J6IxD3bc30Lh6oxdeYuzrQ%a%server.ccl.net> X-Original-From: Tymofii Nikolaienko Content-Type: multipart/alternative; boundary="------------9E69627C6164E4ED3C31FC3C" Date: Tue, 7 Feb 2017 23:13:25 +0200 MIME-Version: 1.0 Sent to CCL by: Tymofii Nikolaienko [tim_mail-,-ukr.net] This is a multi-part message in MIME format. --------------9E69627C6164E4ED3C31FC3C Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Dear Ernest, why not consider the reactants and/or the products as a collection of (the same!) N atoms, and not distinguish different molecules - in fact, this is the point of view taken by electronic structure software ? In this case, before, after and even during the reaction the total number of atoms is N, it is constant and, likewise, the _total_ number of their degrees of freedoms is constant and equal to 3*N. Note that even when we have two molecules, we can still make frequency calculation for their complex, and there will be some frequencies corresponding to mutual movements of the molecules (which can in fact be hindered rotations or other motions which are displayed as vibrations only due to the made harmonic approximation). Please, excuse me if I have misunderstood your question... Best regards, Tymofii On 07.02.2017 19:48, Ernest Chamot echamota/chamotlabs.com wrote: > Hi All, > > I seem to have argued myself into a state of confusion: I guess I just > don’t really understand the entropy of a bimolecular system. > > I can calculate the enthalpy of a molecule with any number of methods, > and so long as I also do an IR or frequency calculation, I can also > get the entropy, and ultimately the free energy of the molecule. So > if I am considering the equilibrium of a dissociation reaction, I can > get the heat of reaction by modeling all three species, and > subtracting the enthalpy of the reactant from the sum of the > enthalpies of the products. But how do I calculate the free energy of > reaction? > > I can’t just add up the individual free energies, can I? Isn’t the > entropy of the pair of product molecules different from just the sum > of the two individual entropies? Since there are two separate > molecules in the same frame of reference, there should be an > additional 6 degrees of freedom for the second molecule, even at > infinite separation. Or do these all have a correspondence with a > vibrational mode in the original reactant molecule? Doesn’t there > need to be an additional term or factor: ln(2), or angular momentum, > or something? > > (I’m interested in the overall reaction, not with the two product > molecules still bound together in some intermediate complex. Otherwise > I could just model that.) > > Thanks for any help. > > EC > > > Ernest Chamot > Chamot Labs, Inc. > http://www.chamotlabs.com > > --------------9E69627C6164E4ED3C31FC3C Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: 8bit

Dear Ernest,

why not consider the reactants and/or the products as a collection of (the same!) N atoms, and not distinguish different molecules -
in fact, this is the point of view taken by electronic structure software ?

In this case, before, after and even during the reaction the total number of atoms is N, it is constant and, likewise,
the _total_ number of their degrees of freedoms is constant and equal to 3*N.

Note that even when we have two molecules, we can still make frequency calculation for their complex,
and there will be some frequencies corresponding to mutual movements of the molecules (which can in
fact be hindered rotations or other motions which are displayed as vibrations only due to the made harmonic
approximation).

Please, excuse me if I have misunderstood your  question...


Best regards,
Tymofii



 

On 07.02.2017 19:48, Ernest Chamot echamota/chamotlabs.com wrote:
Hi All,

I seem to have argued myself into a state of confusion: I guess I just don’t really understand the entropy of a bimolecular system.

I can calculate the enthalpy of a molecule with any number of methods, and so long as I also do an IR or frequency calculation, I can also get the entropy, and ultimately the free energy of the molecule.  So if I am considering the equilibrium of a dissociation reaction, I can get the heat of reaction by modeling all three species, and subtracting the enthalpy of the reactant from the sum of the enthalpies of the products. But how do I calculate the free energy of reaction?

I can’t just add up the individual free energies, can I?  Isn’t the entropy of the pair of product molecules different from just the sum of the two individual entropies?  Since there are two separate molecules in the same frame of reference, there should be an additional 6 degrees of freedom for the second molecule, even at infinite separation.  Or do these all have a correspondence with a vibrational mode in the original reactant molecule?  Doesn’t there need to be an additional term or factor:  ln(2), or angular momentum, or something?

(I’m interested in the overall reaction, not with the two product molecules still bound together in some intermediate complex. Otherwise I could just model that.)

Thanks for any help.

EC


Ernest Chamot
Chamot Labs, Inc.


--------------9E69627C6164E4ED3C31FC3C-- From owner-chemistry@ccl.net Tue Feb 7 19:55:01 2017 From: "Eric Hermes erichermes^-^gmail.com" To: CCL Subject: CCL: Entropy of a Bimolecular System Message-Id: <-52630-170207162232-24306-zNNzGpzlb1RE0yOBwZPWIg() server.ccl.net> X-Original-From: Eric Hermes Content-Transfer-Encoding: 8bit Content-Type: text/plain; charset="UTF-8" Date: Tue, 07 Feb 2017 15:22:24 -0600 Mime-Version: 1.0 Sent to CCL by: Eric Hermes [erichermes[#]gmail.com] EC, You are on the right path. First, it is important to understand how free energies of gas-phase species are calculated. I would suggest reading the relevant chapters of McQuarrie's Statistical Mechanics (5 through 8 in my version) or Hill's Introduction to Statistical Thermodynamics (5 through 9). The free energy of a gas-phase molecule has contributions from the electronic degrees of freedom, translation, rotation, and vibration.  Typically, the free energy from electronic degrees of freedom is assumed to be the potential energy plus an entropic term arising from multiplicity. This comes from the assumption that excited electronic states are thermally inaccessible, but this assumption breaks down if the system has low-lying excited states or is metallic. The translational free energy is typically calculated using the particle-in-a-box picture and employing the ideal gas approximation. In your case, this is where the confusion arises. If you treat the bimolecular system as a single system with only three degrees of translational freedom, you are going to massively underestimate the amount of entropy. Instead, you must consider them as two separate non- interacting systems with three degrees of translational freedom each. The rotational free energy is typically calculated by employing the rigid rotor approximation. If you treat your bimolecular system as a single system, you will also be calculating this value incorrectly, as a system composed of two non-bonded molecules is not a rigid rotor. The vibrational free energy is typically calculated by employing the harmonic oscillator approximation. For this, the second derivative matrix of the energy (the Hessian) is calculated and diagonalized. The eigenvalues of the Hessian correspond to vibrational frequencies and the eigenvectors the corresponding normal modes. The Hessian is 3N dimensional, and since there are only 3N-6 vibrational modes (3N-5 if the molecule is linear), the 6 lowest frequency modes are typically discarded -- these should correspond to some linear combination of translational and rotational modes. If you treat your bimolecular system as a single system, you will likely have an additional 6 low frequency modes corresponding to additional rotations or intermolecular translations. In summary, make sure you are accounting for each species degrees of freedom correctly: 1 electronic, 3 translational, 3 rotational (2 if linear), and 3N-6 vibrational (3N-5 if linear) modes per molecule. Also, remember that the resulting free energy is the free energy at the standard state, typically 298 K and 1 atm. Eric On Tue, 2017-02-07 at 11:48 -0600, Ernest Chamot echamota/chamotlabs.com wrote: > Hi All, > > I seem to have argued myself into a state of confusion: I guess I > just don’t really understand the entropy of a bimolecular system. > > I can calculate the enthalpy of a molecule with any number of > methods, and so long as I also do an IR or frequency calculation, I > can also get the entropy, and ultimately the free energy of the > molecule.  So if I am considering the equilibrium of a dissociation > reaction, I can get the heat of reaction by modeling all three > species, and subtracting the enthalpy of the reactant from the sum of > the enthalpies of the products. But how do I calculate the free > energy of reaction? > > I can’t just add up the individual free energies, can I?  Isn’t the > entropy of the pair of product molecules different from just the sum > of the two individual entropies?  Since there are two separate > molecules in the same frame of reference, there should be an > additional 6 degrees of freedom for the second molecule, even at > infinite separation.  Or do these all have a correspondence with a > vibrational mode in the original reactant molecule?  Doesn’t there > need to be an additional term or factor:  ln(2), or angular momentum, > or something? > > (I’m interested in the overall reaction, not with the two product > molecules still bound together in some intermediate complex. > Otherwise I could just model that.) > > Thanks for any help. > > EC > > > Ernest Chamot > Chamot Labs, Inc. > http://www.chamotlabs.com > > From owner-chemistry@ccl.net Tue Feb 7 20:30:01 2017 From: "Michael K. Gilson mgilson^^^ucsd.edu" To: CCL Subject: CCL: Entropy of a Bimolecular System Message-Id: <-52631-170207163810-26337-irNF9CJ5flXG6+syao41SQ]-[server.ccl.net> X-Original-From: "Michael K. Gilson" Content-Type: multipart/alternative; boundary="------------8E88ECF8D33AE5430DA00B95" Date: Tue, 7 Feb 2017 13:37:54 -0800 MIME-Version: 1.0 Sent to CCL by: "Michael K. Gilson" [mgilson##ucsd.edu] This is a multi-part message in MIME format. --------------8E88ECF8D33AE5430DA00B95 Content-Type: text/plain; charset=utf-8; format=flowed Content-Transfer-Encoding: 8bit Hi Ernest, You should be able to get the free energy for the energy well of interest by applying the rigid rotor harmonic oscillator (RRHO) approximation. Then just subtract the free energies. Since most quantum codes use a 1 atm gas phase standard state for the translational partition function, the result will be a binding free energy referenced to this pressure. If you are using a continuum solvent model to get at binding in solution, then you'll likely want to convert to the standard solution concentration of 1 mole/liter. Since an ideal gas at 1 atm is 1 mole/22.4 liters, the correction is DG_1M = -RT ln (22.4) + DG_1atm, where the subscripts indicate the standard concentration. Of course you can then get the entropy of binding by subtracting the enthalpy from this free energy. The way to conceptualize this is that the thermochem is giving you the chemical potential of each species (AB, A and B for A and B binding) for an ideal gas or solution at the chosen standard concentration (or pressure for the gas phase). Note that the binding entropy depends on the choice of standard concentration: the more dilute the standard state, the greater the entropy loss of binding. For more details, it may be useful to look over papers from several groups (e.g., mine, Grimme's) that describe the use of quantum methods to compute host-guest binding free energies. Hope this helps! Mike On 2/7/2017 9:48 AM, Ernest Chamot echamota/chamotlabs.com wrote: > Hi All, > > I seem to have argued myself into a state of confusion: I guess I just > don’t really understand the entropy of a bimolecular system. > > I can calculate the enthalpy of a molecule with any number of methods, > and so long as I also do an IR or frequency calculation, I can also > get the entropy, and ultimately the free energy of the molecule. So > if I am considering the equilibrium of a dissociation reaction, I can > get the heat of reaction by modeling all three species, and > subtracting the enthalpy of the reactant from the sum of the > enthalpies of the products. But how do I calculate the free energy of > reaction? > > I can’t just add up the individual free energies, can I? Isn’t the > entropy of the pair of product molecules different from just the sum > of the two individual entropies? Since there are two separate > molecules in the same frame of reference, there should be an > additional 6 degrees of freedom for the second molecule, even at > infinite separation. Or do these all have a correspondence with a > vibrational mode in the original reactant molecule? Doesn’t there > need to be an additional term or factor: ln(2), or angular momentum, > or something? > > (I’m interested in the overall reaction, not with the two product > molecules still bound together in some intermediate complex. Otherwise > I could just model that.) > > Thanks for any help. > > EC > > > Ernest Chamot > Chamot Labs, Inc. > http://www.chamotlabs.com > > -- Michael K. Gilson, M.D., Ph.D. Professor, Skaggs School of Pharmacy and Pharmaceutical Sciences Co-Director, UCSD Center for Drug Discovery Innovation U. C. San Diego 9500 Gilman Drive Pharmaceutical Sciences Building, Room 3224 La Jolla, CA 92093-0736 Voice: 858-822-0622 Fax: 858-822-7726 http://gilson.ucsd.edu http://www.bindingdb.org http://drugdiscovery.ucsd.edu http://drugdesigndata.org --------------8E88ECF8D33AE5430DA00B95 Content-Type: text/html; charset=utf-8 Content-Transfer-Encoding: 8bit
Hi Ernest,

You should be able to get the free energy for the energy well of interest by applying the rigid rotor harmonic oscillator (RRHO) approximation. Then just subtract the free energies. Since most quantum codes use a 1 atm gas phase standard state for the translational partition function, the result will be a binding free energy referenced to this pressure. If you are using a continuum solvent model to get at binding in solution, then you'll likely want to convert to the standard solution concentration of 1 mole/liter. Since an ideal gas at 1 atm is 1 mole/22.4 liters, the correction is DG_1M = -RT ln (22.4) + DG_1atm, where the subscripts indicate the standard concentration. Of course you can then get the entropy of binding by subtracting the enthalpy from this free energy. 

The way to conceptualize this is that the thermochem is giving you the chemical potential of each species (AB, A and B for A and B binding) for an ideal gas or solution at the chosen standard concentration (or pressure for the gas phase). Note that the binding entropy depends on the choice of standard concentration: the more dilute the standard state, the greater the entropy loss of binding.

For more details, it may be useful to look over papers from several groups (e.g., mine, Grimme's) that describe the use of quantum methods to compute host-guest binding free energies.

Hope this helps!
Mike

On 2/7/2017 9:48 AM, Ernest Chamot echamota/chamotlabs.com wrote:
Hi All,

I seem to have argued myself into a state of confusion: I guess I just don’t really understand the entropy of a bimolecular system.

I can calculate the enthalpy of a molecule with any number of methods, and so long as I also do an IR or frequency calculation, I can also get the entropy, and ultimately the free energy of the molecule.  So if I am considering the equilibrium of a dissociation reaction, I can get the heat of reaction by modeling all three species, and subtracting the enthalpy of the reactant from the sum of the enthalpies of the products. But how do I calculate the free energy of reaction?

I can’t just add up the individual free energies, can I?  Isn’t the entropy of the pair of product molecules different from just the sum of the two individual entropies?  Since there are two separate molecules in the same frame of reference, there should be an additional 6 degrees of freedom for the second molecule, even at infinite separation.  Or do these all have a correspondence with a vibrational mode in the original reactant molecule?  Doesn’t there need to be an additional term or factor:  ln(2), or angular momentum, or something?

(I’m interested in the overall reaction, not with the two product molecules still bound together in some intermediate complex. Otherwise I could just model that.)

Thanks for any help.

EC


Ernest Chamot
Chamot Labs, Inc.

 



-- 
Michael K. Gilson, M.D., Ph.D.
Professor, Skaggs School of Pharmacy and Pharmaceutical Sciences
Co-Director, UCSD Center for Drug Discovery Innovation
U. C. San Diego
9500 Gilman Drive
Pharmaceutical Sciences Building, Room 3224
La Jolla, CA 92093-0736
Voice: 858-822-0622
Fax: 858-822-7726
http://gilson.ucsd.edu
http://www.bindingdb.org
http://drugdiscovery.ucsd.edu
http://drugdesigndata.org
--------------8E88ECF8D33AE5430DA00B95-- From owner-chemistry@ccl.net Tue Feb 7 23:10:00 2017 From: "Hao-Bo Guo guohaobo::gmail.com" To: CCL Subject: CCL: Entropy of a Bimolecular System Message-Id: <-52632-170207230618-20215-fBht3qFGN25AyEERTNH8gw..server.ccl.net> X-Original-From: Hao-Bo Guo Content-Type: multipart/alternative; boundary=001a1146c75033041e0547fcfc4c Date: Tue, 7 Feb 2017 23:06:11 -0500 MIME-Version: 1.0 Sent to CCL by: Hao-Bo Guo [guohaobo ~ gmail.com] --001a1146c75033041e0547fcfc4c Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: quoted-printable Hi Mr Ernest, I think I do not really understand the entropy, too. The entropy that you mentioned, I think, is the thermodynamic entropy defined in statistical mechanics, which is the sum of electronic, rotational, translational and vibrational components. Except the vibrational term that is derived via the frequency calculations, the other terms are directly obtained from the ensemble that the system belongs to. Entropy is additive, and the biomolecules are different only in the total number of atoms as well as electrons. Nevertheless, the above approach does not really address why entropy is so significant. Entropy should be equivalent to uncertainty, it is a statistical quantity and is better estimate through probability of the states of the interested systems. This is exactly what Claude Shannon had defined from his equation, which ultimately formulated the information technology we appreciate today. The Shannon entropy can be equivalent to the thermodynamic entropy multiplied with kbTln(2), where KB is the Boltzmann's constant and T the temperature. This relationship is often traced back to the Maxwell's Demon proposed some 150 years ago by James Clerk Maxwell. The connection between information and thermodynamic entropy had been experimentally confirmed: Erasure of information of 1 bit leads to dissipation of heat of kbTln(2)---heat from information transmission and computations. Thanks, Hao-Bo Guo On Feb 7, 2017 2:37 PM, "Ernest Chamot echamota/chamotlabs.com" < owner-chemistry###ccl.net> wrote: Hi All, I seem to have argued myself into a state of confusion: I guess I just don=E2=80=99t really understand the entropy of a bimolecular system. I can calculate the enthalpy of a molecule with any number of methods, and so long as I also do an IR or frequency calculation, I can also get the entropy, and ultimately the free energy of the molecule. So if I am considering the equilibrium of a dissociation reaction, I can get the heat of reaction by modeling all three species, and subtracting the enthalpy of the reactant from the sum of the enthalpies of the products. But how do I calculate the free energy of reaction? I can=E2=80=99t just add up the individual free energies, can I? Isn=E2=80= =99t the entropy of the pair of product molecules different from just the sum of the two individual entropies? Since there are two separate molecules in the same frame of reference, there should be an additional 6 degrees of freedom for the second molecule, even at infinite separation. Or do these all have a correspondence with a vibrational mode in the original reactant molecule? Doesn=E2=80=99t there need to be an additional term or factor: ln(2), or a= ngular momentum, or something? (I=E2=80=99m interested in the overall reaction, not with the two product m= olecules still bound together in some intermediate complex. Otherwise I could just model that.) Thanks for any help. EC Ernest Chamot Chamot Labs, Inc. http://www.chamotlabs.com --001a1146c75033041e0547fcfc4c Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable
Hi Mr Ernest,
I think I do not really un= derstand the entropy, too.=C2=A0

The entropy that you mentioned, I think, is the thermodynamic ent= ropy defined in statistical mechanics, which is the sum of electronic, rota= tional, translational and vibrational components. Except the vibrational te= rm that is derived via the frequency calculations, the other terms are dire= ctly obtained from the ensemble that the system belongs to. Entropy is addi= tive, and the biomolecules are different only in the total number of atoms = as well as electrons.

Ne= vertheless, the above approach does not really address why entropy is so si= gnificant. Entropy should be equivalent to uncertainty, it is a statistical= quantity and is better estimate through probability of the states of the i= nterested systems. This is exactly what Claude Shannon had defined from his= equation, which ultimately formulated the information technology we apprec= iate today. The Shannon entropy can be equivalent to the thermodynamic entr= opy multiplied with kbTln(2), where KB is the Boltzmann's constant and = T the temperature.=C2=A0

This relationship is often traced back to the Maxwell's Demon proposed= some 150 years ago by James Clerk Maxwell. The connection between informat= ion and thermodynamic entropy had been experimentally confirmed: Erasure of= information of 1 bit leads to dissipation of heat of kbTln(2)---heat from = information transmission and computations.=C2=A0
Thanks,
Hao-Bo Guo

On Feb 7, 2017 2:37 PM, "Ernes= t Chamot echamota/chamotlabs.com"= ; <owner-chemistry###ccl.net> wrote:
Hi All,

I seem to have argue= d myself into a state of confusion: I guess I just don=E2=80=99t really und= erstand the entropy of a bimolecular system.

I can= calculate the enthalpy of a molecule with any number of methods, and so lo= ng as I also do an IR or frequency calculation, I can also get the entropy,= and ultimately the free energy of the molecule.=C2=A0 So if I am consideri= ng the equilibrium of a dissociation reaction, I can get the heat of reacti= on by modeling all three species, and subtracting the enthalpy of the react= ant from the sum of the enthalpies of the products. But how do I calculate = the free energy of reaction?

I can=E2=80=99t just = add up the individual free energies, can I?=C2=A0 Isn=E2=80=99t the entropy= of the pair of product molecules different from just the sum of the two in= dividual entropies?=C2=A0 Since there are two separate molecules in the sam= e frame of reference, there should be an additional 6 degrees of freedom fo= r the second molecule, even at infinite separation.=C2=A0 Or do these all h= ave a correspondence with a vibrational mode in the original reactant molec= ule?=C2=A0 Doesn=E2=80=99t there need to be an additional term or factor: = =C2=A0ln(2), or angular momentum, or something?

<= div>(I=E2=80=99m interested in the overall reaction, not with the two produ= ct molecules still bound together in some intermediate complex. Otherwise I= could just model that.)


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