# AMBER Archive (2008)Subject: Re: AMBER: Explanation of the energy unit ?

From: Marek Malý (maly_at_sci.ujep.cz)
Date: Mon Sep 08 2008 - 15:15:43 CDT

Hi Gustavo,

As I see you just repeated my interpretation (pls see my last contribution
in detail)
so of course that I have to agree with your opinion regarding to
[kcal/mol] unit understanding.

Regarding to Carlos reaction I only noticed that Carlos sentence:

"...that is that the energy reported does not depend on how
many molecules you are measuring/simulating."

is not probably valid.

which is true since from my simple exmple with H2O follows that
energy in [kcal/mol] unit depends on number of simulated molecules H2O and
constant is only number E/N where E is the energy and N number of H2O
molecules.

From this point of view unit [kcal/mol] behave quite the same like another
energy units
like "J", "kcal", "eV" and if I am not wrong Carlos wanted to show that
this not true,
that [kcal/mol] behave differently.

But maybe that I didn't understand above Carlos sentence well.

I think that the interpretation of [kcal/mol] unit is now clear to all :))
but
still is here question (at least on my side) why was this special unit
introduced.

Marek

Dne Mon, 08 Sep 2008 21:07:28 +0200 Gustavo Seabra
<gustavo.seabra_at_gmail.com> napsal/-a:

> Hi Marek,
>
> Carlos point is indeed valid. What you are missing here is that the
> results you get are for one mole *of your system*, whatever it is. If
> you system has N1 molecules of water, then the results in kcal/mol
> mean y kcal in 1 mole * N1 molecules of water. Obviously, the results
> from a different number of water molecules in your system will have to
> be different. Of course, then, E1/N1 should be approximately equal to
> E2/N2, and that's what your results show.
> (http://physics.ujep.cz/~mmaly/UnitDiscussion/)
>
> Gustavo.
>
> On Mon, Sep 8, 2008 at 3:02 PM, Marek Malý <maly_at_sci.ujep.cz> wrote:
>> Dear Carlos,
>>
>> if I understood well (and seems to me that Prof. Case confirmed that
>> yes),
>>
>> "...that is that the energy reported does not depend on how
>>>
>>> many molecules you are measuring/simulating."
>>
>> is not probably valid.
>>
>> It means that if I simulate for simplicity N1 molecules of H2O with the
>> total energy of this system E1[kcal/mol] and
>> than I simulate N2 molecules of H2O (under the same physical conditions
>> like
>> in first case) with the total energy
>> E2[kcal/mol] than if N1 is different from N2 than also E1 will be
>> different
>> from E2.
>> In other words reported numbers E1,E2 are not energies of one mol of
>> H2O in
>> given conditions but:
>>
>> E1 = energy of N1 x NA molecules = N1 moles of H2O measured in [kcal]
>> E2 = energy of N2 x NA molecules = N2 moles of H2O measured in [kcal]
>>
>> This conclusion should be OK if the results from previous communication
>> is
>> OK.
>> Also my experiences agree with the conclusion that we should think
>> mole
>> of "whole systems" and not about one mole of molecules when we would
>> like
>> interpret
>> unit [kcal/mol].
>>
>> So I think this is probably different for example from the molar heat
>> capacity of water which
>> really gives me the heat which is necessary to add to one mole of H2O
>> molecules to cause increase
>> 1K in temperature.
>>
>> The hypothesis that we should think about energy one mole of "whole
>> systems"
>> some subunits i.e. "molecules" in interpretation of [kcal/mol] unit is
>> clear
>> also from the fact, that in practice we are often dealing
>> with heterogenous, complex systems where you can not say: "This system
>> is
>> composed of N of one type molecules, hence is resonable to deal
>> with energy of one mole of this molecules in given conditions."
>>
>> Here:
>>
>> http://physics.ujep.cz/~mmaly/UnitDiscussion/
>>
>> are results from 3 simulations of H2O in Materials Studio. All under the
>> same conditions.
>> There are 3 cases: 100,200,300 molecules of H2O. It is pretty seen that
>> the
>> energies
>> measured in [kcal/mol] are in all three cases different.
>>
>> I think that similar results (at least qualitatively) gives us
>> calculation
>> of the same
>> systems in Amber.
>>
>> Marek
>>
>>
>>
>>
>>
>>
>> Dne Mon, 08 Sep 2008 16:56:48 +0200 Carlos Simmerling
>> <carlos.simmerling_at_gmail.com> napsal/-a:
>>
>>> your questions aren't quite clear, but if you mean why are the units
>>> in per mole, it's because it is much easier (both in experiment and
>>> computation) to deal with units that are intensive rather than
>>> extensive, that is that the energy reported does not depend on how
>>> many molecules you are measuring/simulating.
>>>
>>>
>>> On Mon, Sep 8, 2008 at 11:01 AM, Marek Malý <maly_at_sci.ujep.cz> wrote:
>>>>
>>>> Dear Prof. Case,
>>>>
>>>> made me sure that my interpretation of
>>>> the [kcal/mol] unit is OK.
>>>>
>>>> The second part of my question:
>>>>
>>>> "The sense (background) of this "strange" unit" is unfortunately still
>>>>
>>>>
>>>>
>>>> http://en.wikipedia.org/wiki/Units_of_energy
>>>>
>>>>
>>>> since in computational(and probably not only computational) chemistry
>>>> is
>>>> this (at least it seems to me)
>>>> energy unit standard. So maybe it would be worth to spend some time
>>>> the
>>>> right
>>>> interpretation and some background. Of course I do not mean that it is
>>>> for you
>>>> personally :)), but for anybody who knows the right answers.
>>>>
>>>> I think that could be interesting to answer question:
>>>> "What was the reason for introducing energy unit which gives me
>>>> energy of
>>>> NA
>>>> my systems in [kcal] or in another
>>>> words what was the reason to introduce energy unit which is NA times
>>>> smaller
>>>> than [kcal] ?"
>>>>
>>>> Is it because the relevant energies expressed using this small unit
>>>> are
>>>> usually "nice" numbers like 30.56, 400.78 and
>>>> not numbers like 30.56 * 10^-n ... which should appear using any other
>>>> energetical unit or is there some
>>>> deeper background ? I think that there should be some deeper
>>>> background
>>>> since there is use precisely Avogadro
>>>> constant in relationship with [kcal].
>>>>
>>>>
>>>> Marek
>>>>
>>>>
>>>>
>>>>
>>>> Dne Mon, 08 Sep 2008 00:12:22 +0200 David A. Case
>>>> <case_at_biomaps.rutgers.edu>
>>>> napsal/-a:
>>>>
>>>>> On Sat, Sep 06, 2008, Marek Malý wrote:
>>>>>>
>>>>>> Let's assume that we have some molecular system Y and we for
>>>>>> example
>>>>>> calculate the total energy of this system. Lets say that result is
>>>>>> X[kcal/mol].
>>>>>>
>>>>>> My only interpretation is that X is the energy in [kcal] of NA
>>>>>> systems
>>>>>> Y.
>>>>>> So if I want energy of one system Y in [kcal] it is X/NA. Where NA
>>>>>> is
>>>>>
>>>>> This is correct. 1 cal = 4.184 J (exactly). See wikipedia (or other
>>>>> places) for a discussion of its history and use.
>>>>>
>>>>> ...dac
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