[gmx-users] Excess Heat of mixing

[Michael Brunsteiner]

Hi Amninder,

DeltaU_mix = <U_AB> - <Um_A> * N_A - <Um_B> * N_B

<U_AB> ... average total intermolecular energy of the blend
<Um_A> ... the average interaction energy of a single molecule of type A in a pure sample of A
<Um_B> ... the average interaction energy of a single molecule of type B in a pure sample of B
N_A ... the number of molecules of type A in the blend
N_B ... the number of molecules of type B in the blend

usually people write H (enthalpy) instead of U (internal energy) ... as enthalpy is what you
get from experiments ... however the latter is simpler to calculate from MD results and
in most cases DeltaU  and DeltaH are very close, i.e., the difference (the Delta pV term) is
smaller than your overall error bars, and you can stick with U.


With the above eqns ... if you have a mixing ratio of 100% A and 0% B then your mixing energy
will be zero, as expected, because now <U_AB> = <Um_A> * N_A (the "blend" is now pure A),
and N_B and consequently N_B <Um_B> are zero. the same goes for 0% A and 100% B ...


an open question (and i agree that there is quite some confusion in the literature about this - 

not in a single paper I read (NOR in google) is this discussed explicitely) is: do we want to include the 

INTRA-molecular contributions to the various Us or not, and if so, all of them or just the intra-molecular 

non-bonded interactions?
In practice the answer probably depends on the type of mixture you consider (and perhaps on the force
field you use) ... often the RELATIVE energy differences you get when comparing different mixing ratios
(or even different compounds) are pretty similar, whether you include intra-molecular contributions or not
... however you might see non-neglegible differences if you have fairly flexible molecules whose conformation
is systematically different in the pure phase versus the blend/mixture. In the first case you probably want
to stick with inter-molecular contributions only since the error-contribution from poor sampling of the
intra-molecular contributions might be larger than the error you introduce by neglecting
these contributions altogether. However, if you do this you need to be careful regarding the evaluation of

<U_AB> , <Um_A> and <Um_B>. If you have electrostatic long range interactions (i.e. you use Ewald
or PME) you might need to perform multiple reruns with part of the charges turned off to get the true
intermolecular energies, instead of just using energy groups and the output of g_energy! ... if you don't
know how to do this .... there are a few discussions in this mailing list regarding this topic!


hope that helps... feel free to contact me if anything i wrote is unclear!

cheers
michael

I have tried everything...even most the results in literature are not consistent to each other...actually I became more confused after reading literature..I am hoping that some one must've calculated for water-alcohol mixtures and explained in detail Sent from my iPhone On 03-Jul-2014, at 8:42 PM, Justin Lemkul <jalemkul at vt.edu> wrote: >>>On 7/3/14, 12:17 AM, AMNINDER SINGH wrote: >>Dear People, >>>>I am trying to calculate heat of mixing of two solvents using inter molecular energies. >>>>I have calculated heat of vaporization of both solvents in pure form and results are in agreement with  experimental and theoretical data. >>>>But, I can't find a right equation to calculate heat of mixing. >>>>Any help will be highly appreciated. >>Have you tried Google? >>-Justin >>-- >================================================== >>Justin A. Lemkul, Ph.D. >Ruth L. Kirschstein NRSA Postdoctoral Fellow >>Department of Pharmaceutical Sciences >School of
 Pharmacy >Health Sciences Facility II, Room 601 >University of Maryland, Baltimore >20 Penn St. >Baltimore, MD 21201 >>jalemkul at outerbanks.umaryland.edu | (410) 706-7441 >http://mackerell.umaryland.edu/~jalemkul >>==================================================


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