Subject: pKa calc. Summary

From: "Emadeddin Tajkhorshid" <[email-masked]>
Date: Wed, 27 Nov 1996 14:27:22 +0100

Dear CCLers

It is the summary of the responses I got for my pKa calculation problem:
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Original Q:
I have calculated the energy (HF) of a set of protonated molecules and compared
them with the ones of non protonated species. After inclusion of vibrational
and thermal corrections you can get a figure which can be refered as 'proton
affinity' of the studied molecule. I want to know if there is any relationship
between this proton affinity and pKa of the molecule. Any comment in this
regard will be appreciated.
********************************************************************************

And the answers I got:
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Date: Mon, 25 Nov 1996 9:49:11 -0600 (CST)
From: YONG HUANG <[email-masked]>
To: [email-masked]
Subject: RE: CCL:pKa calculation

pKa and proton affinity (/\H) or basicity (/\G) have no relationship with each
other. This is not explicitly told in undergraduate courses in America.
However, we can safely say that the higher (lower) the pKa of MH, the higher
(lower) the proton affinity or basicity of M-, which is _the conjugate base of
MH_. Similarly, the higher proton affinity (basicity) of M, the less acidic MH+
is.

The above is from simple manipulation of chemical equations. On the other hand,
if you look at tables of acidity (or the negative trend of pKa) and basicity of
_the same_ species in a reference book, you'll find that _usually_ the more
acidic the less basic. But there's no guarantee. H2O is both less basic and
less
acidic than CH3OH in gas phase.

Yong
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Hi!

Whilst what you are saying is very interesting as far as it goes, it takes
no account of the entropic change on solvation.

The only method of which I am aware that will do this would be QM/MM
FEPT. This can be done at all levels of ab-initio theory - if you have a
big enough computer!  Hoever - I am begining to believe that it will give
reasonable results at AM1 level - and thus be do-able for small systems
- on a work-station.

Best wishes

Alex

 -------------------------------------------------------------------
|Alexander J Turner         [email-masked]                  |
|Post Graduate              |http://www.bath.ac.uk/~chpajt/home.html|
|School of Chemistry        |+144 1225 8262826 ext 5137             |
|University of Bath         |                                       |
|Bath, Avon, U.K.           |Field: QM/MM modeling                  |
 -------------------------------------------------------------------
*******************************************************************************

        Dear Emad,

        What you have here is a "gas phase pKa".  If you want the aqueous
pKa, you have to perform the calculations in solvent.  Some solvation
models are available, I'm not sure I really trust them, but you could try.

        Also, trying to calculate any kind of absolute pKa requires very
high levels, in my experience HF is not nearly good enough.  Something that
COULD be fairly reliable is calculating RELATIVE pKa from an isodesmic
comparison, eg:

        R3N  +  NH4+  <->  R3NH+  +  NH3

        Thus you could calculate values relative to one standard, this
should be good enough for most applications.  I recommend the book "Ab
initio molecular orbital theory" by Hehre, Radom, Schleyer, and Pople.
With an isodesmic comparison, you MIGHT get away with adding solvent
contributions as single point calculations for all species in the above
equation.  In my experience, the most reliable published methods for this
are the SMx models, available in many programs with semi-empirical
calculations, ie AM1-SM2 or PM3-SM3.  If you want to do it at the ab initio
level (not necessarily better), you could look into Tomasi's PCM-method.

        Regards,

        Per-Ola Norrby

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 *  Per-Ola Norrby
 *  The Royal Danish School of Pharmacy, Dept. of Med. Chem.
 *  Universitetsparken 2, DK 2100 Copenhagen, Denmark
 *  tel. +45-35376777-506, +45-35370850    fax +45-35372209
 *  Internet: [email-masked], http://compchem.dfh.dk/
*******************************************************************************

Hi!

Unless you have included an explicit solvation term for the products and
the reactants - and got at the delta - S then you don't really have an
estimation of pKa.

That is not to say that the above terms are not computable.

If someone comes up with a 'rule of thumb' way of getting pKa from the
proton affinity - I would love to here of it though.

Best wishes

Alex

 -------------------------------------------------------------------
|Alexander J Turner         [email-masked]                  |
|Post Graduate              |http://www.bath.ac.uk/~chpajt/home.html|
|School of Chemistry        |+144 1225 8262826 ext 5137             |
|University of Bath         |                                       |
|Bath, Avon, U.K.           |Field: QM/MM modeling                  |
 -------------------------------------------------------------------
*******************************************************************************

    Emad,

      I am very interested in this topic, in connection with a calculation
 for the pKa of coordinated water that I and a collaborator want to do.

      To get a pKa COMPLETELY ab initio requires that you also include the
 energetics of the solvated proton after dissociation, which is not a
 straightforward problem. It seems to me that it is more realistic to connect
 the computed proton affinities to shifts in pK from an experimental value.
 In our case, the exp. pKa of water is available, so by computing the shift
 in energy difference between the protonated and unprotonated forms of water
 for the isolated and complexed cases, you can compute a pK shift (the
 proton solvation contribution is the same in either case).

      The question is what level of theory needs to be applied to get
 decent estimates..

      Regards,

      Randy

All opinions expressed here are mine, not my employer's

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        Hi Alex,

>Whilst what you are saying is very interesting as far as it goes, it takes
>no account of the entropic change on solvation.

        Well, it does!  Some continuum solvation models (like the
Cramer-Truhlar models) calculate solvation free energies.  It's true that
many ab initio-based models only calculate the electrostatic contribution,
and for an isodesmic comparison that may actually be enough, but the SMx
models do give free energies of solvation.  Combining those with a normal
mode analysis for the remaining thermodynamic contributions should be a
very cost-effective way of getting the overall equilibrium free energies.

>The only method of which I am aware that will do this would be QM/MM
>FEPT. This can be done at all levels of ab-initio theory - if you have a
>big enough computer!  Hoever - I am begining to believe that it will give
>reasonable results at AM1 level - and thus be do-able for small systems
>- on a work-station.

        I'm very interested in QM/MM methods, but if you use them for FEP,
can you calculate any practical systems (say, 10-15 heavy atoms + a couple
of hundred water) this millenium, on ANY computer?  Also, FEP is only
theoretically defensible if you have a good description of the potential
energy surface at low energy non-stationary points, and we all know that
AM1 will give substantial errors even for relative energies of stationary
points.  Of course, as long as it works and gives good results, I wont
insist on a perfect theoretical background, but I'd like to see comparison
to experiment for a couple of hundred cases first.

        Regards,

        Per-Ola Norrby

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
 *  Per-Ola Norrby
 *  The Royal Danish School of Pharmacy, Dept. of Med. Chem.
 *  Universitetsparken 2, DK 2100 Copenhagen, Denmark
 *  tel. +45-35376777-506, +45-35370850    fax +45-35372209
 *  Internet: [email-masked], http://compchem.dfh.dk/
*******************************************************************************

Per Ola Norrby wrote :
>What you have here is a "gas phase pKa".  If you want the aqueous
>pKa, you have to perform the calculations in solvent.
Or another thing to do is to compare your calculations to experimental
gas phase pKa. In an article that will be published soon in the Journal
of Chemical Research, i compare calculated pKas with both solution and
gas phase pKas for carboxylic acids. The original reference for the gas
phase pKa determination was in the Canadian Journal of Chemistry, in 1970
but i dont remember the exact references. Maybe someone in the CCL
has it at hand or knows more recent references.
 I would be interested too
Regards,
--
Alexandre HOCQUET

Laboratorio de Cristalografía
Facultad de Ciencias Físicas
Universidad de Chile
Blanco Encalada, 2008
Santiago
Chile
fax : 56 2 696 73 59
email : [email-masked]
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A small point of clarification on this thread:
>
> >Whilst what you are saying is very interesting as far as it goes, it takes
> >no account of the entropic change on solvation.
>
>         Well, it does!  Some continuum solvation models (like the
> Cramer-Truhlar models) calculate solvation free energies.  It's true that
> many ab initio-based models only calculate the electrostatic contribution,
> and for an isodesmic comparison that may actually be enough, but the SMx
> models do give free energies of solvation.
>
   Even the electrostatic component of solvation as calculated by most
continuum models formally has the status of a free energy (it's just not ALL
of the free energy of solvation). That is because one usually invokes linear
response theory to account for the "cost" of solvent distortion in order to
solvate the solute, and that includes both enthalpic and entropic terms. So,
the Born formula, the Onsager formula, etc., all calculate free energies.
Several studies on the validity of linear response theory have appeared, and
the consensus seems to be that it works fine for solutes that do not
concentrate large amounts of charge over very small volumes (e.g., singly
charged atoms are OK, but doubly and higher charged atoms are not).
Naturally, however, there are some dissenters. In any case, SCRF models
almost always use a Hamiltonian that includes the cost of solvent distortion
and build a Fock operator to minimize the expectation value for that
Hamiltonian, the result then being a mixture of potential energy (from the
usual components of the Fock operator) and free energy (from the
solute/solvent mutual polarization).

   As for the rest of the free energy of solvation, the SMx models, and
modifications of other continuum models like Rivail/Rinaldi, Tomasi's PCM,
COSMO, etc., typically assume a proportionality between this quantity and
molecular surface area and by parameterization against experiment they
predict the full free energy of solvation -- THE ONLY PHYSICAL OBSERVABLE
since the components are not measureable with the possible exception of very
special systems where certain components must be zero. More complicated
approaches to estimating dispersion, cavitation, etc. have been proposed, but
in the absence of these properties being experimentally accessible, it is
difficult to decide whether they are worth the extra effort (opinions on
this subject vary).

Chris
--

Christopher J. Cramer
University of Minnesota
Department of Chemistry
207 Pleasant St. SE
Minneapolis, MN 55455-0431
--------------------------
Phone:  (612) 624-0859 || FAX:  (612) 626-7541
[email-masked]
http://pollux.chem.umn.edu/~cramer
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Many thanx to all people who replied me.

-- 
Emad
*********************************************************************
E. Tajkhorshid				
German Cancer Research Center; DKFZ  Tel: +49 6221 42 2339
Dept. Molecular Biophysics (0810)    FAX: +49 6221 42 2333
P.O.Box 101949			   Email: [email-masked]
69009 Heidelberg, FRG
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* A friend may well be reckoned a masterpiece of the nature (Emerson) *
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