pKa=0.8

p =p (1+ ) +p (1+q)+pk qa 1 2 3

2

József Szegezdi* and Ferenc Csizmadia ChemAxon Ltd.Máramaros köz 3/a, 1037 Budapest, Hungary.:*corresponding author, e-mail: jszegezdi@chemaxon.com

Introduction

Fig.1. Scheme of K calculationp a

Prediction of dissociation constant using microconstants

Calculation of pKaCalculation of pKa

The -th macro ionization constant of a multiprotic molecule

can be calculated with the next expression.

i Ka,i

A new method for predicting the aqueous ionization constants(p ) of organic molecules has been developed. The method is

based mainly on empirically calculated partial charges.Hydrogen bonds are also parameterized and taken into accountwithin the calculation.

Predicted and experimental values are in good correlation(r =0.95, s=0.72, n=1670) for common organic compounds andpharmaceutical molecules.

Ka

2

where,

=1...

is the number of ionizable atoms in the molecule.

is the proton concentration of the aqueous solution

is the concentration of the -th microspecies released

protons from the fully protonated molecule

is the concentration of the -th microspecies released

( ) protons from the fully protonated molecule.

and are calculated from the micro ionization

constants

i

c

c

c c

N

N

j i

k

i

k

[H ]

-1

+

( )

( -1)

( ) ( 1)

j

k

j k

i

i

i i-

a

Observable macro ionization constants are obtained from theconcentration distribution of the microspecies at a given pH.e.g. is shown.Ka,2

Fig.2. Ionization steps of 2-carboxylic-3-amino-pyrazine

Input molecule

Assign ionization sites to the molecule

Generating all microspecies

Calculation of partial charge distribution of microspecies

Calculation of micro ionization constant p of microspeciesKa

Calculate ratio of microspecies

Calculate macro ionization constant pKa

Setting hydrogen bond interactions

Altogether 2 = 16 microspecies can be formed in aqueoussolution. Their concentration depends on the micro ionizationconstants s and the solution's pH. When molecules have a

tendency to form tautomers we should consider the most stableisomer during p calculation.

4

'k

K

a

a

Fig.3. Tautomer forms of aspergillic acid

It is generally true that 2 -1 microspecies can be formed from amolecule containing ionizable sites. Calculation of the relativeconcentration of microspecies requires 2 -1 microconstants .Ratios can be calculated if micro ionization constants areavailable.

The micro ionization constant (p ) value is calculated from the

partial charge distribution and the atomic polarizability ofmicrospecies using empirical linear or non-linear equations.

N

N

N

k

1

2,3

a

Example for p - partial charge relationkaExample for p - partial charge relationka

The next figure shows the p - partial charge distribution of a

basic oxygen atom in pyridine N-oxide. (para-NH has the

largest p and ortho-NO , the smallest).

k

k

a

2

a 2

The p , as a function of the partial charge ( ) is obtained

through linear regression analysis using the quadratic funtionform.

k qa

where p , p and p are regression coefficients1 2 3

-4

-2

0

2

4

0.65 0.7 0.75 0.8

1+ partial charge

pK

ae

xp

.

Fig.4. The basic k v. the partial charge of oxygen atomp a

Presented at American Chemical Society National Meeting. Mar 28 - Apr 1, 2004updated, April 15th, 2004.

0

5

10

15

20

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2

pka

non-linearnon-linear linear

q: (partialcharge)

Sometimes non-linear regression analysis according to theregression equation,

p =p exp(p q)+p q+p

provides a better fit than a quadratic equation. The examplebelow is the p charge relation of substituted pyrrole

derivatives.

k

K

a 1 1 2 3

a

References

1. Csizmadia, F.; Tsantili-Kakoulidou, A.; Panderi, I.; Darvas, F.,,86, 866-871

2. Gasteiger, J.; Marsili, M.: , , 36, 32193. Miller, K.J.; Savchik, J.A., , , 101, 7206-7213

J.Pharm. Sci.Tetrahedron

J.Am.Chem.Soc.

19971980

1979

Modeling of the intramolecular hydrogen bond (IHB)Modeling of the intramolecular hydrogen bond (IHB)

Fig.6. Example for the parameterization of the IHB in picolinicacid.

It seems to be generally true that the micro ionization constant-partial charge relation has three separable ranges. The majorityof data fall into the linear domain range, however very weak orvery strong acids or bases are in the non-linear domain.

Explanation of this phenomenon is beyond the scope of thispresentation.

where,

is the -th micro ionization constant, predicted with Marvin

is the -th observed macro ionization constant

k

K

i

,i

i

i*a

k*i is the -th micro ionization constant which is calculated

from the equilibrium equations and *

i

K a,i

The -th macro ionization constant * is a function of the four

micro ionization constants * 's.

i K ,

k

a

.

i

i

(and additional two relation for K* ,2)a

The optimized values of * 's are calculated from the non-linear

equation set of * 's. (Four equations and four variables.)

k

Ki

ia,

The change of the -th micro ionization constant due to the

IHB, is obtained from the relation:

=a + b or =c + d

Where a,b,c d are regression parameters

i k

k q k q

�

�

�

� �

i

i i

= -

Different picolinic acid derivatives result in different values,

depending on the partial charge of nitrogen (acceptor) and

hydroxyl group (donor). as a function of partial charge of

donor or acceptor is obtained with linear regression

analysis.

�k k k

k

k

q q

i i i

i

i

*

donor acceptor

i donor i i acceptor i

i i i, i

When the IHB is detected in a molecule is used instead of

within Marvin.

'= +

Where c and d are regression coefficients

k k

k k k

'

i i

i i i�

The change of caused by the IHB is approximately

proportional to the partial charge difference between theacceptor and donor atoms.

Ka,i

i i

idonoracceptoria, d)qq(c ���� iK

Input n molecules and their observed K* ’sa

Calculate all with non-linear equ. solverk*i

Predict the IHB free with Marvinki

Calculate �k for alli = k* - k ii i

Calculate �k = aq + b ii i i with regression analysis for all

Fig.7. Scheme for the parameterization of the internal hydrogenbond

Test of p calculationsKaTest of p calculationsKa

After a preliminary data preparation, altogether 1670molecules were used for testing the performance of the p

calculation model. Observed p data are taken from the

PhysProp database.

Certain CH acid derivatives, molecules with ether type oxygenand some tautomeric compounds were excluded from thetesting. (We are working on the prediction of these types ofmolecules.) Several erroneous structures were also omitted.

K

Ka

a

-10.00

0.00

10.00

20.00

-10.00 0.00 10.00 20.00

pKa exp.

pK

ap

red

. Fig 7. Predictedvs. ExperimentalpK (n=1670,

r =0.95, s=0.72)a

2

y=0.98 p +0.12Ka,exp

Implementation

All calculations performed using Marvin version 3.4.pre1Calculation Plugins available through ChemAxon’s Marvin andJChem software suites (100% Java)

Hardware and software requirements: any system running JavaRuntime Environment 1.1 or above.

Fig.5. Some typical IHB's

Marvinimplementationshowingpredicted p ’s

and microspeciesdistribution chart

Ka