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Estimating the pKa of phenols, carboxylic acids and alcohols from semi-empirical quantum chemical methods
Chemosphere, Vol. 38, No. 1, pp. 191-206, 1999 0 1998 Elsevier Science Ltd. All rights resewed 0045-6535/99/ $ - see front matter
Pergamon
PII:SOO45-6535(98)00172-6
ESTIMATING ALCOHOLS
THE
FROM
pK,
OF PHENOLS,
SEMI-EMPIRICAL
Mario Syracuse
Research
QUANTUM
ACIDS
CHEMICAL
AND
METHODS
J. Citra
Corporation
North
CARBOXYLIC
Syracuse,
6225 NY
Running
Ridge
Road,
13212
[email protected] (Received in USA 24 December 1997; accepted 8 April 1998)
ABSTRACT
Quantitative structure property relationships (QSPR) for the pK, of phenols, carboxylic acids and alcohols were developed from descriptors derived from semi-empirical molecular orbital theory quantum chemical calculations. A training set of compounds were used to refine the models and a validation set of appropriate chemicals were chosen to test the models. Correlation coefficients for the estimated versus observed pKa values were 0.96 for phenols, 0.84 for non-aromatic carboxylic acids, 0.89 for benzoic acids and 0.89 for alcohols. The results obtained by the quantum chemical method are compared to results obtained from linear free energy relationships (LFER) and the merits of each approach are discussed.,01998 ElsevierScienceLtd. Allrightsreserved INTRODUCTION The acid dissociation constant, which describes the extent to which a compound dissociates in aqueous solution, is a fundamental physical property of a chemical.
Differences in
adsorption, toxicology, solubility, bioconcentration and reactivity are common when comparing the properties of the ionized molecule to its neutral form[l].
Experimentally
determined pK, values are not always available from literature sources and often estimated values are employed in their place. Therefore, it is of interest to develop methods for estimating the pK, of ionizable compounds and use these methods to predict,,
191
192
the properties of a chemical in an aqueous environment. Most methods that are currently employed to estimate the pK,of
a compound have relied on using linear free energy
relationships (LFER). Perrin et a1[21. have reviewed the hundreds of equations that have been developed for accurately,predi&ing limited groups of structurally related chemicals through the use of Hammett c and Taft c* values. There are 2 computer programs developed that rely exclusively on LFER methodology to predict pKa(pKalc[3] and ACD/pKa[41).
Recently, a computer program was
developed by the U.S. EPA and the University of Georgia (SPARC[S]) to predict a variety of properties, including pK,, based on a combination of LFER, structure/activity relationship (SAR) and perturbed molecular orbital methods. The primary disadvantage of the purely LFER based approaches are the need to derive a vast number of fragment constants and correction factors which are used in the estimation methods.
Some researchers have
also criticized the use of LFER approaches on more philosophical grounds, arguing that the prediction of molecular properties by fragment constant methods lacks solid scientific basis[6,71.
A
more fundamental approach toward the prediction of pK, is a quantum mechanical method that does not rely on LFER methodology. Theoretically it is possible to calculate dissociation constants from first principles using quantum mechanical methods[81 .
Unfortunately these calculations are difficult for
large systems since they involve calculating very small differences in the energy of relatively large molecules[9,101. In order to obtain accurate enough energies to calculate solution phase dissociation constants, one must account for electron correlation at the ab initio or density functional level and consider the effects of solvation on the molecule.
Recently a
rigorous quantum mechanical method that calculates the pica of
193
In this method, electronic
molecules was publishedtI01.
structure calculations were performed with density functional theory and the electrostatic features were modeled through external charge distributions and continuum dielectrics.
The
reaction potential was computed by finite difference solutions to the Poisson-Boltzmann eguation that incorporated a selfconsistent field approach.
Even with this sophisticated approach
errors were observed in the calculation of the pK,[lOl. A less rigorous approach to this problem is to use a QSPR method that adopts quantum mechanical molecular orbital (MO) theory descriptors.
In a previous study, heats of formation,
highest occupied molecular orbital (HOMO) energies and partial atomic charges calculated by MNDO and AM1 semi-empirical methods were tested for correlation to experimentally determined pK, values[lll
.
The results of this study were encouraging in that
parameters calculated from semi-empirical methods could be used to estimate the pK, of fairly large molecules.
The authors of
this study determined that a high correlation existed between the pK, of phenols and the energy of the HOMO of the anionic species and the energy difference between the neutral phenol and the anion1111 .
We have also developed a method to predict the pK, of phenols, carboxylic acids and some simple alcohols based upon MO descriptors.
Rather than focus on energy differences between the
neutral and dissociated species, we have chosen descriptors associated with the neutral molecule in our calculations.
The
dissociation of an O-H bond is assumed to be highly dependent upon the charge density surrounding the oxygen and hydrogen atoms and the strength of the bond.
For this reason we have
investigated the relationship between pKa and the bond order of the O-H bond as well as the partial atomic charges of the oxygen
194
and hydrogen atoms involved in dissociation.
The results
indicate that a strong correlation exists between the pK, and partial atomic charges as well as the O-H bond order for phenols, alcohols and carboxylic acids.
Multiple linear regression
analysis provided useful equations that can be used to predict the pK, of chemicals based upon these parameters.
Although
different equations are used to predict the pK, of different classes of compounds, the need to parameterize and apply correction factors to multiple molecular fragments is avoided when adopting a MO approach as compared to LFER methods.
METHODS A data set of experimentally determined pK, values were collected from available sources[l21. Table 1 lists
all the
compounds used in the training set of this study. It is important to use caution when searching the literature for dissociation constants.
Often a molecule has more than 1 ionizable group and
quoted dissociation constants sometimes do not specify the site of ionization.
For consistency we have chosen the AM1
Hamiltonian[l31 to perform all computations.
All calculations
were performed on a 133 MHZ Gateway PC running the Microsoft Windows 95 operating system with 24 Mb of RAM and approximately 150 Mb of free hard disk space. The computational chemistry software ChemUltra with MOPAC 93 was used to build the molecules, perform the necessary geometry optimizations and compute all desired properties.
A gradient cutoff of 0.1 was used for all
geometry optimizations and the PRECISE keyword was invoked to increase the criteria for terminating the optimizations by a factor of 100.
Partial atomic charges of the oxygen atom,
hydrogen atom and G-H bond order involved in dissociation were used as chemical descriptors.
The charges were computed from
195
Table 1.
List of compounds
used in the training
set.
PHENOLS 2,4,6-trimethyl
4-methoxy-2-nitro
2,5-dichloro
4-methoxy-2,6-dimethyl
4-methyl-2,6-dichloro
4-chloro
4-butyl-2-methyl
I-nitro
5-methoxy-2-methyl
2,3,5-trimethyl
5-methoxy-2-nitro
4-bromo
2-hexyl
4-nitro-2,6-dimethyl
2-methylthio
2,6-dimethyl
2-methoxy-6-nitro
3-fluoro
2,4-dimethyl
2,6-dichloro
2-chloro-4-amino
5-methyl-2-nitro
3,5-dinitro
4-amino-2-chloro
2,4,5-trimethyl
2-methoxy-4-nitro
3-chloro
2,3-dimethyl
I-chloro-2-nitro
3-bromo
4-fluoro-2,6-dimethyl
2-nitro
2-chloro-4,5-dimethyl
P-amino
2,4,6-trichloro
4-methoxy-3-nitro
4-methoxy-3-methyl
4-bromo-2,6-dichloro
2-chloro-4-methyl
2,5-dimethyl
3-methoxy-4-nitro
2-fluoro
2-methoxy-6-methyl
2-chloro-6-nitro
2-chloro-6-methyl
3,4-dimethyl
2-chloro-4-nitro
3,4-dichloro
4-methoxy-2-methyl
3,4-dinitro
2-chloro
2-methoxy-4-methyl
2,5-dinitro
2-bromo
L-methyl
2,3-dinitro
2,4-dichloro-3,6-dimethyl
3,4,5-triethyl
4-methyl-2,6-dinitro
3-nitro
a-methyl
pentachloro
2,4-dichloro-3,5-dimethyl
I-methoxy
2-methyl-4,6-dinitro
3,5-dichloro
3,5-dimethyl
2,4-dinitro
6-methyl-2,4-dichloro
3-methyl
2,6-dinitro
3,5-dimethyl-2,4,6trinitro
3,4,5-trichloro
4-nitro-2,6-dichloro
2,3-dichloro
!-methoxy
4-chloro-3-methyl-2,6-dinitro
2,4-dichloro
S-amino
4-chloro-2,6-dinitro
2,6-dichloro-3,4-dimethyl
?-methoxy-S-methyl
2-chloro-4,6-dinitro
4-bromo-2-chloro
L-chloro-2,3-dimethyl
pentafluoro
4-chloro-3,5-dimethyl
L-fluoro
3-methyl-2,4,6-trinitro
2,4,6-trinitro
L-chloro-2,5-dimethyl
3-methylthio
4-chloro-3-methyl
!-amino
3-methoxy
4-methylthio
!-methoxy-3-methyl
6-methyl-2,4-dichloro
5-fluoro-2-nitro
I-chloro-2-methyl
2,4,6-trinitro-3-bromo
196
ALCOHOLS
methanol
2,2,2-trifluoro-1-(4-methoxyphenyl)ethanol
2-phenoxyethanol
l,l,l-trichloroathanol
prop-a-yne-l-01
2,2,2-trifluoro-1-(4-toluenejethanol
2-methoxyethanol
2,2,2-trifluoro-l-phenyl-ethanol
2-chloroethanol
2,2,2-trifluoro-l-(3-bromophenyl)-ethanol
2,2-dichloroethanol
2.2,2-trifluoro-1-(3-nitrophenylLethano1
2,2,3,3-tetrafluoro-l-propanol
2-mercapto-2-methyl-l-propanol
2,2,2-trifluoroethanol
2-mercaptoethanol
2-propanol-3,3,3-trifluoro-l-amino
2-propanol-1,1,1,3,3,3,-hexafluoro-2-methyl
2,2,2-trichloroethanol
2-propanol-1,1,1,3,3.3-hexafluoro
a-pro anal-1,1,1,3,3,3hexaf P uoro-2-trifluoromethyl
2-propanol-l,1,l-trichloro-3,3,3-trifluoro-2-trifluoromethyl
2-propanol-l,l,l-trichloro-
2-butanol
cyclopropenone-2-hydroxy-3-phenyl
2-mercapto-2-methyl-l-prop~ol
benzyl alcohol
CARBOXYLIC ACIDS fluoroacetic
trichloroacteic
trimethylacetic
malonic
trifluoroacetic
3-methyl-2-butenoic
chloroacetic
heptafluorobutanoic
tiglic
iodoacetic
cyclobutane
glycolic
-l,l-dicarboxcylic
bromoacetic
formic
2-heptenoic
2-chloropropionic
1-cyclohexene-1,2-dicarboxcylic
3-chloropropionic
3,3-difluoroacrylic
acetic
3-iodopropionic
2-iodopropionic
propionic
4,4,4-trifluoro
l-cyclohexene-1,2-dicarboxcylic
butanoic
phenyl acetic
2-bropmoropionic
isopentanoic
succinic
1,4,4-trinitrobutanoic
pentanoic
3-bromopropionic
Eumaric
hexanoic
lactic
zyclobutane l,l-dicarboxcylic
pelargonic
2-hydroxy-butanoic
butanoic
I-hydroxy-4,4,4-trinitrobutanoic
isohexanoic
4.4.dinitropentanoic
iichloroacetic
dodecanoic
mercaptoacetic
litroacetic
cyclobutane
cyclopentanecarboxylic
rrifluoroacrylic
isobutanoic
cyclohexanecarboxylic
I-hydroxy-3,3_dinitrobutanoic
trans-2-methy;cyclohexane carboxyliJc acrd
:richloroacrylic
cyclopropanecarboxylic
I-ethoxybenzoic acid
2,3-dimethylbenzoic
I-methoxybenzoic acid
2,4,6-trimethylbenzoic
!,4-dimethylbenzozc acid
2,6-dimethylbenzoic
xnzoic
2-chloro-4-methylbenzoic
BPWOIC
acid
l-methylcyclohexane carboxylic acid
acid
ACIDS acid
3,5-dinitrobenzoic
acid
acid
I-fluorobenzoic acid
2-iodo-4-methylbenzoic
!,5-dimethylbenzoic acid
2-fluorobenzoic acid
I-chlorobenzoic acid
2-bromo-4-methylbenzoic
:-chlorobenzoic acid
2-chloro-3-methylbenzoic
I-fluorobenzoic acid ',6-dinitrobenzoic acid :,4,6-trinitrobenzoic acid
acid acid
acid
acid
acid
2-chloro-4-nitrobenzoic
acid
2-chloro-5-nitrobenzoic
acid
acid
pentafluorobenzoic
acid
2,5-dinitrobenzoic
acid
2-chlorobenzoic acid
2,4-dinitrobenzoic
acid
2-chloro-6-nitrobcnzoic
2-bromo-6-nitrobenzoic
acid
acid
2-bromo-3-methylbenzoic
2,3-dinitrobenzoic acid
acid
2-iodo-3-methylbenzoic
acid
197
both Coulson and Mullikan population analysis and the results shown here reflect the Coulson charges.
The bond order of atoms
i-j is defined as the sum of the squares of the density matrix elements
connecting atoms i and j.
PHENOLS Figures la-lc show the correlation between the observed pK, of the phenols and the partial atomic charges on the oxygen atom (figure la), hydrogen atom (figure lb) and the O-H bond order (figure 1~).
All properties were calculated for the neutral
species. Multiple geometry optimizations were performed and the results are reported as an energy weighted average of properties computed for all of the optimized conformations. The highest correlation occurs for the atomic charge of the oxygen but the OH bond order and partial atomic charge on the hydrogen also show excellent correlation as well.
Multiple linear regression
analysis on this set of data yielded an r2 value of 0.96 and a regression derived equation given by;
pK,= 47.43 - 134.92x -61.42~ - 62.34~
(1)
where x represents the charge on the oxygen atom, y is the charge on the hydrogen atom and z is the O-H bond order.
These letters
will be used throughout the paper to represent these descriptors. To test the validity of this equation we used 15 phenols not included in the original training set and estimated the pKa of these compounds by eq. 1 and compared them to experimentally determined values.
We also included calculated values from the
commercially available programs pKalc and SPARC. given in table 2.
The results are
All three methods are in good agreement with
the experimental values although we note that the compounds used
198
PHENOLS
(a) I?
??
W
w
14
0.9533
z!!!!bL1 9
PKa
4
-0.26
-0.21
Oxygen
-1 CI.16
-
Charge
0.23
0.26
Hydrogen
0.33
b.66
Charge
0.66
0.9
0.92
0.94
OH Bond Order
ALCOHOLS
(4
-0.4
-0.2 Oxygen
(9)
0.1
0
0.15
0.2
Hydrogen
Charge
(f)
0.25
0.3
0.9
Charge
0.91
0.92
0.93
0.94
0.95
OH Bond Order
CAFtBOXYLlC ACIDS
(cl)
0)
A*=0.8006
_ b
4 PKa 2 0 -0.32
-0.3
-0.28
Oxygen
Charge
-Ok2
&I?2
0.24
0.26
0.28
_&9 0.9
0.91
0.92
0.93
OH Bond Order
BENZOK ACIDS
(i)
(k)
I
-0.3
-0.25 Oxygen
Charge
-0.2
0.22
0.23
0.24
Hydrogen
0.25
0.26
Charge
Figure 1. Correlation between pK, and the MO descriptors.
0.91
0.92
OH Bond Order
0.93
199 in
our validation set may have been included in the training set
of the commercially available programs.
A correlation
coefficient of 0.97 was obtained on the validation set using equation 1, while the pKalc and SPAKC!programs yielded rz values of 0.99.
Predicted
versus
experimental
pKa of test phenols.
Comuound
I 11.411 1 12.241
(2.4-di-t-butvlohenol 12,6-di-t-butvluhenol 2,6-di-t-butyl-4-bromophenol
11.291
11.81
12.251
12.271
11.75
11.68
11.47
10.83 12.23
11.641 11.71
2,6-di-t-butyl-4-methylphenol
12.55
12.56
12.32
2,6-di-t-butyl-4-methoxyphenol
12.48
12.5
13.48
12.15
2,4,6-tri-t-butylphenol
12.57
12.54
12.27
12.19
2,4,6_tripropylphenol
11.37
11.59
10.61
11.47
6-methyl-2-butylphenol
10.88
11.31
11.81
11.72 10.31
4-t-butvlohenol
10.25
10.22
10.14
10.121
10.051
10.081
2-t-butylphenol
11.08
10.85
10.56
11.24
2-methyl-4-t-butylphenol
10.54
10.6
10.35
10.59
2.6-diiodo-4-nitroohenol
4.34
3.46
5.11
3.32
0.091
0.161
0.221
-0.21
0.13
0.32
0.68
0.15
I
13-t-butylphenol
(2,4,6-trinitro-3-chlorophenol 2,4,6-trinitro-3-iodophenol
I
10.11
ALCOHOLS Figures Id-If show the correlation between the observed pK, of the alcohols and the partial atomic charges on the oxygen atom (figure Id), the hydrogen atom (figure le) and the O-H bond order (figure If).
Multiple linear regression analysis on the data
yielded an r2 value of 0.89 and a regression derived equation of;
pK,= -366.69 - 41.42x
+ 67.79y
+ 377.612
(2)
The lack of experimentally determined dissociation constants limited the size of the training set and not enough experimental data existed to develop a validation set of chemicals.
Equation
200
2 was used to predict the pKa of some alcohols and these values were compared to values predicted by the programs pKalc and SPARC.
The results are shown in table 3.
In general, good
agreement between equation 2 and the commercial programs are observed.
CARBOKYLIC AND BENZOIC ACIDS Figures lg-li show the correlation between the observed pK, and the 3 MO descriptors for the non-aromatic acids, while figures lj-11 show the correlation between the observed pK, of the benzoic acids and the MO descriptors.
We were unable to
obtain a reasonable fit from the data when the aliphatic acids and benzoic acids were simultaneously considered. Therefore, the non-aromatic compounds and the benzoic acids were treated separately and unique equations were derived for the pK,. Multiple linear regression analysis on the non-aromatic carboxylic acids yielded an r2 value of 0.84 and a regression derived equation given by;
pK,=
0.47 - 61.10x - 66.02~ +0.9Oz
(3)
Multiple linear regression analysis on the aromatic acids yielded
201
an r2 value of 0.89 and a regression derived equation given by;
PK, -284.41 - 35.17x - 235.70~ - 256.612
(4)
These equations were tested against representative carboxylic acids and benzoic acids for which experimental pK, values were available.
The results are shown in table 4 along with the pK,
values calculated by the commercially available programs. For the non-aromatic carboxylic acids, a correlation coefficient of 0.95 was obtained on the validation set using equation 3, while the pKalc and SPAFX programs yielded rz values of 0.99 and 0.97 respectively.
For the benzoic acids, a correlation coefficient
of 0.85 was obtained on the validation set using equation 4, while the pKalc and SPARC programs yielded rz values of 0.83 and 0.98 respectively.
I
Table
4.
benzoic
Predicted (ea. 4)
Vereue
experimental
pKa of the carboxylic
(eq. 3) and
I
acids.
I
/
2,2_dimethylpentanoic
acid
2-hydroxy-2-methylbutanoic 2-methyl-propanoic 2-methvloentanoic
acid acid
2,3-dimethoxybenzoic
acid
acid
pxalc
BPARC
Eqm. (3.4)
Experimental
5.2
4.88
4.56
5.0;
3.86
3.95
3.49
3.73
4.8
4.0
4.65
4.64
4.88
4.8
4.73
4.74
3.97
3.92
3.87
3.98
2,4-dimethylbenzoic
acid
4.08
3.99
4.15
4.22
2,3-dichlorobenzoic
acid
3.30
2.62
2.91
2.67
2,4-dichlorobenzoic
acid
3.49
2.73
3
2.75
2,5-dichlorobenzoic
acid
3.38
2.63
2.93
2.47
2,6-dichlorobenzoic
acid
2.6
1.92
2.84
1.59
3.5 dichlorobenzoic
acid
3.46
3.32
3.53
3.54
202
DISCUSSION The results indicate that eqs. 1-4 can be employed to estimate the pK, of phenols, carboxylic acids and alcohols with reasonable accuracy when compared to experimental values or the values predicted by LFER methods.
It is likely that similar
results can be obtained for other important classes of compounds such as amines. The primary advantage of employing the MO method, versus the LFER methods is that in order to obtain reliable estimates of pKa, the LFER methods must parameterize numerous fragments at different positions of the molecule.
Since there
are countless variations and combinations of fragments, this becomes an extremely difficult task as molecules become larger and more complex.
The weakness of this approach can be
illustrated by the results show in table 5.
In this example the
pKa of a fairly simple set of benzoic acids was estimated by the LFER program, pKalc, and compared to results obtained by the MO approach.
The benzoic acids contained a halogenated propyl group
and its position on the benzene ring was systematically altered. The estimated pK, was identical for all 9 possible combinations of the molecule shown in table 5 by the LFER method even though this is an extemely unlikely result. When Hammett (3 and Taft o* values are unavailable for a given fragment the LFER programs must use values from a similar fragment or estimate them from an existing algorithm.
The MO method yields different pKa values
and as expected the most acidic compounds are the ortho .1 substituted benzoic acids.
203
The primary disadvantage of using a molecular orbital theory QSPR method is that the results are extremely sensitive to the final optimized geometry of the molecule.
Since partial atomic
charges and bond orders are computed from the density matrix, these properties can have significantly different values when comparing one conformation to another.
In order to obtain
consistent and reproducible data, it is usually best to perform multiple geometry optimizations on a given compound in order to account for its properties over a wide range of conformations. Correlations between atomic charges and chemical reactivity are extensive throughout the field of chemistry.
One must keep
in mind that bond orders and partial atomic charges are purely conceptual entities that cannot be measured experimentally and their values
are dependent upon the semi-empirical method
employed or basis set used in the case of ab initio calculations. It is uncertain weather employing a higher level of theory to calculate these descriptors would make a profound difference in our results since partial atomic charges often fail to accurately reproduce experimentally determined dipole moments even if the charges were computed from ab initio calculations.
We initially
employed the Conductor-Like Screening Model (COSM0[14]) to account for solvation when calculating the MO descriptors but
204 abandoned
this approach
improvement
on the results
time to run these Since
parameterized
model
that significantly charge
models
partial yield this
achieved
to yield
these
little
significantly.
quantities, partial
we do not
atomic
Recently
calculated
dipole
charges
empirical
from semi-empirical
determined
of
initially
results.
level ab initio
charges
that
and the length
increasing
thermodynamic
experimentally
atomic
apparent
like AM1 were
alone
improve
than high
better
were
have been developed
that reproduce accurately
was being
methods
to reproduce
a solvation
it became
calculations
semi-empirical
expect
when
techniques
moments
calculations[l5].
more Using
from one of these models
correlations
with pK, than the charges
Quantum
mechanically
derived
studies
to predict
may
calculated
in
study.
CONCLUSIONS
QSPR
[71,
coefficient radical
with
parameterize structure
of organic
and equations
predicting
alcohols
the octanol/water
solubility[61
rate constants
methodology quickly
water
derived
multiple
accuracy
molecular
descriptors
are not currently
traditional
LFER methods,
approach
in this
to predict
for which
derived
accurate
no reliable
for
and
the need
While
to
quantitative
from quantum to supplant
mechanical the more
an alternative
of chemicals.
LFER
The
acids
avoiding
or in conjunction
methods
hydroxyl
are useful
carboxylic
they do represent
properties
field may yield
properties
in this study
sufficient
that can be used alone
procedures
molecules[l6,171.
while
in
partition
fragments.
relationships
have been used
and the gas-phase
the pKa of phenols,
reasonable
property
descriptors
with
Continuing
to predict
techniques
LFER work
physical
currently
exist.
205
REFERENCES 1) W.J. Lyman, W.F. Reehl and D.H. Rosenblatt, Handbook of Chemical Property Estimation Methods: Environmental Behavior of Organic Compounds. American Chemical Society, Washington, DC (1992). 2) D.D. Perrin, B. Dempsey and E.P. Serjeant, pKa Prediction for Organic Acids and Bases, Chapman and Hall, New York, NY (1981). 3) CompuDrug NA, Inc. pKalc Version 3.1, (1996). 4) ACD Inc.
ACD/pKa Version 1.0, (1997).
5) S.H. Hilal, L.A. Carreira and S.W. Karickhoff, Estimation of Chemical Reactivity Parameters and Physical Properties of Organic Molecules using SPARC. In Quantitative Treatments of Solute/Solvent Interactions: Theoretical and Computational Chemistry Vol. 1 p. 291-353. Elsevier, New York, NY, (1994). 6) N. Bodor and M.J. Huang, An Extended Version of a Novel Method for the Estimation of Partition Coefficients,
J. Phann Sci. 81,
272-281 (1992). 7) N. Bodor, Z. Gabanyi and C.K.
Wong, A New Method for the
Estimation of Partition Coefficients, 3783-3786
J. Am.
Chem.
Sot.
111,
(1989).
8) W.J. Hehre, L. Radom, P.V.R. Schleyer and J.A. Pople,
Ab
Initio Molecular Orbital Theory. John Wiley & Sons New York, NY (1986). 9) J.A. Pople, M. Head-Gordon, D.J. Fox, K. Raghavachari, and L.A. Curtis, Gaussian-l Theory: A General Procedure for Prediction of Molecular Energies,
J. Chem. Phys. 90, 5622-5630
(1989). 10) W.H. Richardson, C. Peng, D. Bashford, L. Noodleman and D.A. Case, Incorporating Solvation Effects Into Density Functional Theory: Calculation Of Absolute Acidities, Int. J. Quantum 61, 207-217 (1997).
Chem.
11) C. Gruber and V. Bub, Quantum-Mechanically Calculated Properties For the Development of Quantitative structure-Activity Relationships
(QSAR's). Pka Values of Phenols and Aromatic And
Aliphatic Carboxylic Acids, 12) E.P.
Chemosphere, 19, 1595-1609 (1989).
Sergeant and B. Dempsey, Ionization Constants of
Organic Acids in Aqueous Solution, IUPAC Chemical Database Series No. 23. 13)
Pergamon Press, New York, NY (1982).
M.J.S. Dewar, E.G. Zoebisch, E.F. Healy and J.J.P. Stewart,
Evaluation of AM1 Proton Affinities and Dependent Enthalpies, J. Am. Chem. Sot. 108, 8075-8085 (1986). 14) A. Klamt and G. Schuurmann, A New Approach to Dielectric Screening in Solvents With Explicit Expressions for the,Screening Energy and its Gradients, J. Chem. Sot. Perkin
Trans.
2, 799-805
(1993). 15) J.W. Storer, D.J. Giesen, C.J. Cramer and D.G. Truhlar, Class IV Charge Models: A New Semi-Empirical Approach in Quantum Chemistry, Comp-Aided
Mol. Des. 9, 87-110
(1995).
16) A. Klamt, Estimation of Gas-Phase Hydroxyl Radical Rate Constants of Organic Compounds From Molecular Orbital theory Calculations, Chemosphere
26, 1273-1289 (1993).
17) A Klamt, Estimation of Gas-Phase Hydroxyl Radical Rate Constants of Oxygenated Compounds Based on Molecular Orbital Theory Calculations Chemosphere
32, 717-726
(1996).
Pergamon
PII:SOO45-6535(98)00172-6
ESTIMATING ALCOHOLS
THE
FROM
pK,
OF PHENOLS,
SEMI-EMPIRICAL
Mario Syracuse
Research
QUANTUM
ACIDS
CHEMICAL
AND
METHODS
J. Citra
Corporation
North
CARBOXYLIC
Syracuse,
6225 NY
Running
Ridge
Road,
13212
[email protected] (Received in USA 24 December 1997; accepted 8 April 1998)
ABSTRACT
Quantitative structure property relationships (QSPR) for the pK, of phenols, carboxylic acids and alcohols were developed from descriptors derived from semi-empirical molecular orbital theory quantum chemical calculations. A training set of compounds were used to refine the models and a validation set of appropriate chemicals were chosen to test the models. Correlation coefficients for the estimated versus observed pKa values were 0.96 for phenols, 0.84 for non-aromatic carboxylic acids, 0.89 for benzoic acids and 0.89 for alcohols. The results obtained by the quantum chemical method are compared to results obtained from linear free energy relationships (LFER) and the merits of each approach are discussed.,01998 ElsevierScienceLtd. Allrightsreserved INTRODUCTION The acid dissociation constant, which describes the extent to which a compound dissociates in aqueous solution, is a fundamental physical property of a chemical.
Differences in
adsorption, toxicology, solubility, bioconcentration and reactivity are common when comparing the properties of the ionized molecule to its neutral form[l].
Experimentally
determined pK, values are not always available from literature sources and often estimated values are employed in their place. Therefore, it is of interest to develop methods for estimating the pK, of ionizable compounds and use these methods to predict,,
191
192
the properties of a chemical in an aqueous environment. Most methods that are currently employed to estimate the pK,of
a compound have relied on using linear free energy
relationships (LFER). Perrin et a1[21. have reviewed the hundreds of equations that have been developed for accurately,predi&ing limited groups of structurally related chemicals through the use of Hammett c and Taft c* values. There are 2 computer programs developed that rely exclusively on LFER methodology to predict pKa(pKalc[3] and ACD/pKa[41).
Recently, a computer program was
developed by the U.S. EPA and the University of Georgia (SPARC[S]) to predict a variety of properties, including pK,, based on a combination of LFER, structure/activity relationship (SAR) and perturbed molecular orbital methods. The primary disadvantage of the purely LFER based approaches are the need to derive a vast number of fragment constants and correction factors which are used in the estimation methods.
Some researchers have
also criticized the use of LFER approaches on more philosophical grounds, arguing that the prediction of molecular properties by fragment constant methods lacks solid scientific basis[6,71.
A
more fundamental approach toward the prediction of pK, is a quantum mechanical method that does not rely on LFER methodology. Theoretically it is possible to calculate dissociation constants from first principles using quantum mechanical methods[81 .
Unfortunately these calculations are difficult for
large systems since they involve calculating very small differences in the energy of relatively large molecules[9,101. In order to obtain accurate enough energies to calculate solution phase dissociation constants, one must account for electron correlation at the ab initio or density functional level and consider the effects of solvation on the molecule.
Recently a
rigorous quantum mechanical method that calculates the pica of
193
In this method, electronic
molecules was publishedtI01.
structure calculations were performed with density functional theory and the electrostatic features were modeled through external charge distributions and continuum dielectrics.
The
reaction potential was computed by finite difference solutions to the Poisson-Boltzmann eguation that incorporated a selfconsistent field approach.
Even with this sophisticated approach
errors were observed in the calculation of the pK,[lOl. A less rigorous approach to this problem is to use a QSPR method that adopts quantum mechanical molecular orbital (MO) theory descriptors.
In a previous study, heats of formation,
highest occupied molecular orbital (HOMO) energies and partial atomic charges calculated by MNDO and AM1 semi-empirical methods were tested for correlation to experimentally determined pK, values[lll
.
The results of this study were encouraging in that
parameters calculated from semi-empirical methods could be used to estimate the pK, of fairly large molecules.
The authors of
this study determined that a high correlation existed between the pK, of phenols and the energy of the HOMO of the anionic species and the energy difference between the neutral phenol and the anion1111 .
We have also developed a method to predict the pK, of phenols, carboxylic acids and some simple alcohols based upon MO descriptors.
Rather than focus on energy differences between the
neutral and dissociated species, we have chosen descriptors associated with the neutral molecule in our calculations.
The
dissociation of an O-H bond is assumed to be highly dependent upon the charge density surrounding the oxygen and hydrogen atoms and the strength of the bond.
For this reason we have
investigated the relationship between pKa and the bond order of the O-H bond as well as the partial atomic charges of the oxygen
194
and hydrogen atoms involved in dissociation.
The results
indicate that a strong correlation exists between the pK, and partial atomic charges as well as the O-H bond order for phenols, alcohols and carboxylic acids.
Multiple linear regression
analysis provided useful equations that can be used to predict the pK, of chemicals based upon these parameters.
Although
different equations are used to predict the pK, of different classes of compounds, the need to parameterize and apply correction factors to multiple molecular fragments is avoided when adopting a MO approach as compared to LFER methods.
METHODS A data set of experimentally determined pK, values were collected from available sources[l21. Table 1 lists
all the
compounds used in the training set of this study. It is important to use caution when searching the literature for dissociation constants.
Often a molecule has more than 1 ionizable group and
quoted dissociation constants sometimes do not specify the site of ionization.
For consistency we have chosen the AM1
Hamiltonian[l31 to perform all computations.
All calculations
were performed on a 133 MHZ Gateway PC running the Microsoft Windows 95 operating system with 24 Mb of RAM and approximately 150 Mb of free hard disk space. The computational chemistry software ChemUltra with MOPAC 93 was used to build the molecules, perform the necessary geometry optimizations and compute all desired properties.
A gradient cutoff of 0.1 was used for all
geometry optimizations and the PRECISE keyword was invoked to increase the criteria for terminating the optimizations by a factor of 100.
Partial atomic charges of the oxygen atom,
hydrogen atom and G-H bond order involved in dissociation were used as chemical descriptors.
The charges were computed from
195
Table 1.
List of compounds
used in the training
set.
PHENOLS 2,4,6-trimethyl
4-methoxy-2-nitro
2,5-dichloro
4-methoxy-2,6-dimethyl
4-methyl-2,6-dichloro
4-chloro
4-butyl-2-methyl
I-nitro
5-methoxy-2-methyl
2,3,5-trimethyl
5-methoxy-2-nitro
4-bromo
2-hexyl
4-nitro-2,6-dimethyl
2-methylthio
2,6-dimethyl
2-methoxy-6-nitro
3-fluoro
2,4-dimethyl
2,6-dichloro
2-chloro-4-amino
5-methyl-2-nitro
3,5-dinitro
4-amino-2-chloro
2,4,5-trimethyl
2-methoxy-4-nitro
3-chloro
2,3-dimethyl
I-chloro-2-nitro
3-bromo
4-fluoro-2,6-dimethyl
2-nitro
2-chloro-4,5-dimethyl
P-amino
2,4,6-trichloro
4-methoxy-3-nitro
4-methoxy-3-methyl
4-bromo-2,6-dichloro
2-chloro-4-methyl
2,5-dimethyl
3-methoxy-4-nitro
2-fluoro
2-methoxy-6-methyl
2-chloro-6-nitro
2-chloro-6-methyl
3,4-dimethyl
2-chloro-4-nitro
3,4-dichloro
4-methoxy-2-methyl
3,4-dinitro
2-chloro
2-methoxy-4-methyl
2,5-dinitro
2-bromo
L-methyl
2,3-dinitro
2,4-dichloro-3,6-dimethyl
3,4,5-triethyl
4-methyl-2,6-dinitro
3-nitro
a-methyl
pentachloro
2,4-dichloro-3,5-dimethyl
I-methoxy
2-methyl-4,6-dinitro
3,5-dichloro
3,5-dimethyl
2,4-dinitro
6-methyl-2,4-dichloro
3-methyl
2,6-dinitro
3,5-dimethyl-2,4,6trinitro
3,4,5-trichloro
4-nitro-2,6-dichloro
2,3-dichloro
!-methoxy
4-chloro-3-methyl-2,6-dinitro
2,4-dichloro
S-amino
4-chloro-2,6-dinitro
2,6-dichloro-3,4-dimethyl
?-methoxy-S-methyl
2-chloro-4,6-dinitro
4-bromo-2-chloro
L-chloro-2,3-dimethyl
pentafluoro
4-chloro-3,5-dimethyl
L-fluoro
3-methyl-2,4,6-trinitro
2,4,6-trinitro
L-chloro-2,5-dimethyl
3-methylthio
4-chloro-3-methyl
!-amino
3-methoxy
4-methylthio
!-methoxy-3-methyl
6-methyl-2,4-dichloro
5-fluoro-2-nitro
I-chloro-2-methyl
2,4,6-trinitro-3-bromo
196
ALCOHOLS
methanol
2,2,2-trifluoro-1-(4-methoxyphenyl)ethanol
2-phenoxyethanol
l,l,l-trichloroathanol
prop-a-yne-l-01
2,2,2-trifluoro-1-(4-toluenejethanol
2-methoxyethanol
2,2,2-trifluoro-l-phenyl-ethanol
2-chloroethanol
2,2,2-trifluoro-l-(3-bromophenyl)-ethanol
2,2-dichloroethanol
2.2,2-trifluoro-1-(3-nitrophenylLethano1
2,2,3,3-tetrafluoro-l-propanol
2-mercapto-2-methyl-l-propanol
2,2,2-trifluoroethanol
2-mercaptoethanol
2-propanol-3,3,3-trifluoro-l-amino
2-propanol-1,1,1,3,3,3,-hexafluoro-2-methyl
2,2,2-trichloroethanol
2-propanol-1,1,1,3,3.3-hexafluoro
a-pro anal-1,1,1,3,3,3hexaf P uoro-2-trifluoromethyl
2-propanol-l,1,l-trichloro-3,3,3-trifluoro-2-trifluoromethyl
2-propanol-l,l,l-trichloro-
2-butanol
cyclopropenone-2-hydroxy-3-phenyl
2-mercapto-2-methyl-l-prop~ol
benzyl alcohol
CARBOXYLIC ACIDS fluoroacetic
trichloroacteic
trimethylacetic
malonic
trifluoroacetic
3-methyl-2-butenoic
chloroacetic
heptafluorobutanoic
tiglic
iodoacetic
cyclobutane
glycolic
-l,l-dicarboxcylic
bromoacetic
formic
2-heptenoic
2-chloropropionic
1-cyclohexene-1,2-dicarboxcylic
3-chloropropionic
3,3-difluoroacrylic
acetic
3-iodopropionic
2-iodopropionic
propionic
4,4,4-trifluoro
l-cyclohexene-1,2-dicarboxcylic
butanoic
phenyl acetic
2-bropmoropionic
isopentanoic
succinic
1,4,4-trinitrobutanoic
pentanoic
3-bromopropionic
Eumaric
hexanoic
lactic
zyclobutane l,l-dicarboxcylic
pelargonic
2-hydroxy-butanoic
butanoic
I-hydroxy-4,4,4-trinitrobutanoic
isohexanoic
4.4.dinitropentanoic
iichloroacetic
dodecanoic
mercaptoacetic
litroacetic
cyclobutane
cyclopentanecarboxylic
rrifluoroacrylic
isobutanoic
cyclohexanecarboxylic
I-hydroxy-3,3_dinitrobutanoic
trans-2-methy;cyclohexane carboxyliJc acrd
:richloroacrylic
cyclopropanecarboxylic
I-ethoxybenzoic acid
2,3-dimethylbenzoic
I-methoxybenzoic acid
2,4,6-trimethylbenzoic
!,4-dimethylbenzozc acid
2,6-dimethylbenzoic
xnzoic
2-chloro-4-methylbenzoic
BPWOIC
acid
l-methylcyclohexane carboxylic acid
acid
ACIDS acid
3,5-dinitrobenzoic
acid
acid
I-fluorobenzoic acid
2-iodo-4-methylbenzoic
!,5-dimethylbenzoic acid
2-fluorobenzoic acid
I-chlorobenzoic acid
2-bromo-4-methylbenzoic
:-chlorobenzoic acid
2-chloro-3-methylbenzoic
I-fluorobenzoic acid ',6-dinitrobenzoic acid :,4,6-trinitrobenzoic acid
acid acid
acid
acid
acid
2-chloro-4-nitrobenzoic
acid
2-chloro-5-nitrobenzoic
acid
acid
pentafluorobenzoic
acid
2,5-dinitrobenzoic
acid
2-chlorobenzoic acid
2,4-dinitrobenzoic
acid
2-chloro-6-nitrobcnzoic
2-bromo-6-nitrobenzoic
acid
acid
2-bromo-3-methylbenzoic
2,3-dinitrobenzoic acid
acid
2-iodo-3-methylbenzoic
acid
197
both Coulson and Mullikan population analysis and the results shown here reflect the Coulson charges.
The bond order of atoms
i-j is defined as the sum of the squares of the density matrix elements
connecting atoms i and j.
PHENOLS Figures la-lc show the correlation between the observed pK, of the phenols and the partial atomic charges on the oxygen atom (figure la), hydrogen atom (figure lb) and the O-H bond order (figure 1~).
All properties were calculated for the neutral
species. Multiple geometry optimizations were performed and the results are reported as an energy weighted average of properties computed for all of the optimized conformations. The highest correlation occurs for the atomic charge of the oxygen but the OH bond order and partial atomic charge on the hydrogen also show excellent correlation as well.
Multiple linear regression
analysis on this set of data yielded an r2 value of 0.96 and a regression derived equation given by;
pK,= 47.43 - 134.92x -61.42~ - 62.34~
(1)
where x represents the charge on the oxygen atom, y is the charge on the hydrogen atom and z is the O-H bond order.
These letters
will be used throughout the paper to represent these descriptors. To test the validity of this equation we used 15 phenols not included in the original training set and estimated the pKa of these compounds by eq. 1 and compared them to experimentally determined values.
We also included calculated values from the
commercially available programs pKalc and SPARC. given in table 2.
The results are
All three methods are in good agreement with
the experimental values although we note that the compounds used
198
PHENOLS
(a) I?
??
W
w
14
0.9533
z!!!!bL1 9
PKa
4
-0.26
-0.21
Oxygen
-1 CI.16
-
Charge
0.23
0.26
Hydrogen
0.33
b.66
Charge
0.66
0.9
0.92
0.94
OH Bond Order
ALCOHOLS
(4
-0.4
-0.2 Oxygen
(9)
0.1
0
0.15
0.2
Hydrogen
Charge
(f)
0.25
0.3
0.9
Charge
0.91
0.92
0.93
0.94
0.95
OH Bond Order
CAFtBOXYLlC ACIDS
(cl)
0)
A*=0.8006
_ b
4 PKa 2 0 -0.32
-0.3
-0.28
Oxygen
Charge
-Ok2
&I?2
0.24
0.26
0.28
_&9 0.9
0.91
0.92
0.93
OH Bond Order
BENZOK ACIDS
(i)
(k)
I
-0.3
-0.25 Oxygen
Charge
-0.2
0.22
0.23
0.24
Hydrogen
0.25
0.26
Charge
Figure 1. Correlation between pK, and the MO descriptors.
0.91
0.92
OH Bond Order
0.93
199 in
our validation set may have been included in the training set
of the commercially available programs.
A correlation
coefficient of 0.97 was obtained on the validation set using equation 1, while the pKalc and SPAKC!programs yielded rz values of 0.99.
Predicted
versus
experimental
pKa of test phenols.
Comuound
I 11.411 1 12.241
(2.4-di-t-butvlohenol 12,6-di-t-butvluhenol 2,6-di-t-butyl-4-bromophenol
11.291
11.81
12.251
12.271
11.75
11.68
11.47
10.83 12.23
11.641 11.71
2,6-di-t-butyl-4-methylphenol
12.55
12.56
12.32
2,6-di-t-butyl-4-methoxyphenol
12.48
12.5
13.48
12.15
2,4,6-tri-t-butylphenol
12.57
12.54
12.27
12.19
2,4,6_tripropylphenol
11.37
11.59
10.61
11.47
6-methyl-2-butylphenol
10.88
11.31
11.81
11.72 10.31
4-t-butvlohenol
10.25
10.22
10.14
10.121
10.051
10.081
2-t-butylphenol
11.08
10.85
10.56
11.24
2-methyl-4-t-butylphenol
10.54
10.6
10.35
10.59
2.6-diiodo-4-nitroohenol
4.34
3.46
5.11
3.32
0.091
0.161
0.221
-0.21
0.13
0.32
0.68
0.15
I
13-t-butylphenol
(2,4,6-trinitro-3-chlorophenol 2,4,6-trinitro-3-iodophenol
I
10.11
ALCOHOLS Figures Id-If show the correlation between the observed pK, of the alcohols and the partial atomic charges on the oxygen atom (figure Id), the hydrogen atom (figure le) and the O-H bond order (figure If).
Multiple linear regression analysis on the data
yielded an r2 value of 0.89 and a regression derived equation of;
pK,= -366.69 - 41.42x
+ 67.79y
+ 377.612
(2)
The lack of experimentally determined dissociation constants limited the size of the training set and not enough experimental data existed to develop a validation set of chemicals.
Equation
200
2 was used to predict the pKa of some alcohols and these values were compared to values predicted by the programs pKalc and SPARC.
The results are shown in table 3.
In general, good
agreement between equation 2 and the commercial programs are observed.
CARBOKYLIC AND BENZOIC ACIDS Figures lg-li show the correlation between the observed pK, and the 3 MO descriptors for the non-aromatic acids, while figures lj-11 show the correlation between the observed pK, of the benzoic acids and the MO descriptors.
We were unable to
obtain a reasonable fit from the data when the aliphatic acids and benzoic acids were simultaneously considered. Therefore, the non-aromatic compounds and the benzoic acids were treated separately and unique equations were derived for the pK,. Multiple linear regression analysis on the non-aromatic carboxylic acids yielded an r2 value of 0.84 and a regression derived equation given by;
pK,=
0.47 - 61.10x - 66.02~ +0.9Oz
(3)
Multiple linear regression analysis on the aromatic acids yielded
201
an r2 value of 0.89 and a regression derived equation given by;
PK, -284.41 - 35.17x - 235.70~ - 256.612
(4)
These equations were tested against representative carboxylic acids and benzoic acids for which experimental pK, values were available.
The results are shown in table 4 along with the pK,
values calculated by the commercially available programs. For the non-aromatic carboxylic acids, a correlation coefficient of 0.95 was obtained on the validation set using equation 3, while the pKalc and SPAFX programs yielded rz values of 0.99 and 0.97 respectively.
For the benzoic acids, a correlation coefficient
of 0.85 was obtained on the validation set using equation 4, while the pKalc and SPARC programs yielded rz values of 0.83 and 0.98 respectively.
I
Table
4.
benzoic
Predicted (ea. 4)
Vereue
experimental
pKa of the carboxylic
(eq. 3) and
I
acids.
I
/
2,2_dimethylpentanoic
acid
2-hydroxy-2-methylbutanoic 2-methyl-propanoic 2-methvloentanoic
acid acid
2,3-dimethoxybenzoic
acid
acid
pxalc
BPARC
Eqm. (3.4)
Experimental
5.2
4.88
4.56
5.0;
3.86
3.95
3.49
3.73
4.8
4.0
4.65
4.64
4.88
4.8
4.73
4.74
3.97
3.92
3.87
3.98
2,4-dimethylbenzoic
acid
4.08
3.99
4.15
4.22
2,3-dichlorobenzoic
acid
3.30
2.62
2.91
2.67
2,4-dichlorobenzoic
acid
3.49
2.73
3
2.75
2,5-dichlorobenzoic
acid
3.38
2.63
2.93
2.47
2,6-dichlorobenzoic
acid
2.6
1.92
2.84
1.59
3.5 dichlorobenzoic
acid
3.46
3.32
3.53
3.54
202
DISCUSSION The results indicate that eqs. 1-4 can be employed to estimate the pK, of phenols, carboxylic acids and alcohols with reasonable accuracy when compared to experimental values or the values predicted by LFER methods.
It is likely that similar
results can be obtained for other important classes of compounds such as amines. The primary advantage of employing the MO method, versus the LFER methods is that in order to obtain reliable estimates of pKa, the LFER methods must parameterize numerous fragments at different positions of the molecule.
Since there
are countless variations and combinations of fragments, this becomes an extremely difficult task as molecules become larger and more complex.
The weakness of this approach can be
illustrated by the results show in table 5.
In this example the
pKa of a fairly simple set of benzoic acids was estimated by the LFER program, pKalc, and compared to results obtained by the MO approach.
The benzoic acids contained a halogenated propyl group
and its position on the benzene ring was systematically altered. The estimated pK, was identical for all 9 possible combinations of the molecule shown in table 5 by the LFER method even though this is an extemely unlikely result. When Hammett (3 and Taft o* values are unavailable for a given fragment the LFER programs must use values from a similar fragment or estimate them from an existing algorithm.
The MO method yields different pKa values
and as expected the most acidic compounds are the ortho .1 substituted benzoic acids.
203
The primary disadvantage of using a molecular orbital theory QSPR method is that the results are extremely sensitive to the final optimized geometry of the molecule.
Since partial atomic
charges and bond orders are computed from the density matrix, these properties can have significantly different values when comparing one conformation to another.
In order to obtain
consistent and reproducible data, it is usually best to perform multiple geometry optimizations on a given compound in order to account for its properties over a wide range of conformations. Correlations between atomic charges and chemical reactivity are extensive throughout the field of chemistry.
One must keep
in mind that bond orders and partial atomic charges are purely conceptual entities that cannot be measured experimentally and their values
are dependent upon the semi-empirical method
employed or basis set used in the case of ab initio calculations. It is uncertain weather employing a higher level of theory to calculate these descriptors would make a profound difference in our results since partial atomic charges often fail to accurately reproduce experimentally determined dipole moments even if the charges were computed from ab initio calculations.
We initially
employed the Conductor-Like Screening Model (COSM0[14]) to account for solvation when calculating the MO descriptors but
204 abandoned
this approach
improvement
on the results
time to run these Since
parameterized
model
that significantly charge
models
partial yield this
achieved
to yield
these
little
significantly.
quantities, partial
we do not
atomic
Recently
calculated
dipole
charges
empirical
from semi-empirical
determined
of
initially
results.
level ab initio
charges
that
and the length
increasing
thermodynamic
experimentally
atomic
apparent
like AM1 were
alone
improve
than high
better
were
have been developed
that reproduce accurately
was being
methods
to reproduce
a solvation
it became
calculations
semi-empirical
expect
when
techniques
moments
calculations[l5].
more Using
from one of these models
correlations
with pK, than the charges
Quantum
mechanically
derived
studies
to predict
may
calculated
in
study.
CONCLUSIONS
QSPR
[71,
coefficient radical
with
parameterize structure
of organic
and equations
predicting
alcohols
the octanol/water
solubility[61
rate constants
methodology quickly
water
derived
multiple
accuracy
molecular
descriptors
are not currently
traditional
LFER methods,
approach
in this
to predict
for which
derived
accurate
no reliable
for
and
the need
While
to
quantitative
from quantum to supplant
mechanical the more
an alternative
of chemicals.
LFER
The
acids
avoiding
or in conjunction
methods
hydroxyl
are useful
carboxylic
they do represent
properties
field may yield
properties
in this study
sufficient
that can be used alone
procedures
molecules[l6,171.
while
in
partition
fragments.
relationships
have been used
and the gas-phase
the pKa of phenols,
reasonable
property
descriptors
with
Continuing
to predict
techniques
LFER work
physical
currently
exist.
205
REFERENCES 1) W.J. Lyman, W.F. Reehl and D.H. Rosenblatt, Handbook of Chemical Property Estimation Methods: Environmental Behavior of Organic Compounds. American Chemical Society, Washington, DC (1992). 2) D.D. Perrin, B. Dempsey and E.P. Serjeant, pKa Prediction for Organic Acids and Bases, Chapman and Hall, New York, NY (1981). 3) CompuDrug NA, Inc. pKalc Version 3.1, (1996). 4) ACD Inc.
ACD/pKa Version 1.0, (1997).
5) S.H. Hilal, L.A. Carreira and S.W. Karickhoff, Estimation of Chemical Reactivity Parameters and Physical Properties of Organic Molecules using SPARC. In Quantitative Treatments of Solute/Solvent Interactions: Theoretical and Computational Chemistry Vol. 1 p. 291-353. Elsevier, New York, NY, (1994). 6) N. Bodor and M.J. Huang, An Extended Version of a Novel Method for the Estimation of Partition Coefficients,
J. Phann Sci. 81,
272-281 (1992). 7) N. Bodor, Z. Gabanyi and C.K.
Wong, A New Method for the
Estimation of Partition Coefficients, 3783-3786
J. Am.
Chem.
Sot.
111,
(1989).
8) W.J. Hehre, L. Radom, P.V.R. Schleyer and J.A. Pople,
Ab
Initio Molecular Orbital Theory. John Wiley & Sons New York, NY (1986). 9) J.A. Pople, M. Head-Gordon, D.J. Fox, K. Raghavachari, and L.A. Curtis, Gaussian-l Theory: A General Procedure for Prediction of Molecular Energies,
J. Chem. Phys. 90, 5622-5630
(1989). 10) W.H. Richardson, C. Peng, D. Bashford, L. Noodleman and D.A. Case, Incorporating Solvation Effects Into Density Functional Theory: Calculation Of Absolute Acidities, Int. J. Quantum 61, 207-217 (1997).
Chem.
11) C. Gruber and V. Bub, Quantum-Mechanically Calculated Properties For the Development of Quantitative structure-Activity Relationships
(QSAR's). Pka Values of Phenols and Aromatic And
Aliphatic Carboxylic Acids, 12) E.P.
Chemosphere, 19, 1595-1609 (1989).
Sergeant and B. Dempsey, Ionization Constants of
Organic Acids in Aqueous Solution, IUPAC Chemical Database Series No. 23. 13)
Pergamon Press, New York, NY (1982).
M.J.S. Dewar, E.G. Zoebisch, E.F. Healy and J.J.P. Stewart,
Evaluation of AM1 Proton Affinities and Dependent Enthalpies, J. Am. Chem. Sot. 108, 8075-8085 (1986). 14) A. Klamt and G. Schuurmann, A New Approach to Dielectric Screening in Solvents With Explicit Expressions for the,Screening Energy and its Gradients, J. Chem. Sot. Perkin
Trans.
2, 799-805
(1993). 15) J.W. Storer, D.J. Giesen, C.J. Cramer and D.G. Truhlar, Class IV Charge Models: A New Semi-Empirical Approach in Quantum Chemistry, Comp-Aided
Mol. Des. 9, 87-110
(1995).
16) A. Klamt, Estimation of Gas-Phase Hydroxyl Radical Rate Constants of Organic Compounds From Molecular Orbital theory Calculations, Chemosphere
26, 1273-1289 (1993).
17) A Klamt, Estimation of Gas-Phase Hydroxyl Radical Rate Constants of Oxygenated Compounds Based on Molecular Orbital Theory Calculations Chemosphere
32, 717-726
(1996).