KEVIN C. GROSS,1 PAUL G. SEYBOLD,1 CHRISTOPHERM. HADAD2
1Department of Chemistry, Wright State University, Dayton, Ohio 45435
2Department of Chemistry, The Ohio State University, Columbus, Ohio 43210
International Journal of Quantum Chemistry, Vol. 90, 445–458 (2002) © 2002 Wiley Periodicals, Inc.
Introduction
 Any definition of atomic charge in a molecule is immensely
useful in its ability to correlate with the experimental properties
such as pKa of a compound.
 A good correlation between aqueous acidity and easily calculated
gas-phase properties is especially convenient if the atomic charge
method is practical for rapid evaluation.
 For substituted anilines and phenols, the charges on the
functional group heavy atom (e.g., N in – NH2 or the O- of the
OH) and on the acidic hydrogens(e.g., in –NH3+ or OH) can
serve as good regression parameters in determination of the pKa
of the compound.
Introduction
 In the phenol series, the –OH group pKa varies with
substitution, increasing with electron-donating group (EDGs)
and decreasing with electron-withdrawing groups (EWGs).
 Three population analysis were examined for their ability to
generate charges that correlate with the experimental pKa’s for a
series a para and meta monosubstituted anilines and phenols.



the Mulliken charge Q(H+) Mul,
the natural population charge Q(H+) NPA
electrostatic-potential Q(H+) ESP
 Geometry optimizations were carried out at the 6-31G(D) level
for each compound.
Definitions
Mulliken Analysis
Divides overlap population equally between the two atoms of a bond
and thus has advantage of simplicity. However, its results vary with
the basis set employed inducing sometimes unnatural and ineffective
results.
Natural Population Analysis (NPA)
The analysis of the electron density distribution in a molecular system
is based on the orthonormal natural atomic orbitals. Natural
populations, ni(A) are the occupancies of the natural atomic orbitals
which rigorously satisfy the Pauli exclusion principle: 0 < ni(A) <2.
Electrostatic Potential Analysis (ESP)
Assigns point charges to the atomic centers in order to best
reproduce the electrostatic potential.
Aniliniums
m-Amino
p- Amino
m- Methoxy
p- Methoxy
m- Nitro
p-Nitro
Phenols
m- Amino
p-Amino
m- Methoxy
p- Methoxy
m- Nitro
p- Nitro
Compounds used to verify the effectiveness of
estimating pKa using different atomic charge
methods.
4-tert-amylphenol
4-phenylphenol
4-ethylphenol
4-hydroxybenzaldehyde
Results
Plots of the averaged amoni-group hydrogen
pKa vs. charge using several charge definitions
for a series of monosubstituted aniliniums: the
Mulliken charge Q(H+) Mul, the natural
population charge Q(H+) NPA, and the
electrostatic-potential Q(H+) ESP.
7
6
5
pKa
4
3
2
1
0
0.465
0.47
0.475
0.48
7
7
6
6
5
5
4
4
3
3
pKa
pKa
Q(H+) Mul
2
2
1
1
0
0
0.472 0.474 0.476 0.478
0.4
0.41
0.42
Q(H+) ESP
0.43
0.48
Q(H+) NPA
0.482 0.484
Results
12
Plots of the phenolic hydrogen pKa vs. charge using
several charge definitions for a series of
monosubstituted phenols: Q(H+) Mul, Q(H+) NPA,
and Q(H+) ESP. and Q(H+) ESP.
10
pKa
8
6
4
2
0
0.45
0.455
0.46
0.465
0.47
12
12
10
10
8
8
pKa
pKa
Q(H)Mul
6
6
4
4
2
2
0
0.485
0
0.49
0.495
Q(H) NPA
0.5
0.505
0.44
0.445
0.45
Q(H)ESP
0.455
0.46
Results
10.2
10.09
10
4-tert-amylphenol
4-ethylphenol
4-phenylphenol
4-hydroxybenzaldehyde
10.04
9.8
9.73
9.6
pKa
9.4
9.2
9
8.8
8.6
Plots of the phenolic hydrogen pKa vs.
charge using several charge definitions
for a series of the para
monosubstituted phenols as indicated
on the graphs: Q(H+) Mul, Q(H+)
NPA, and Q(H+) ESP.
8.58
8.4
0.454000 0.456000 0.458000 0.460000 0.462000 0.464000
Q(H)Mul
10.2
10.09
10.2
10
9.8
10.04
9.73
9.4
9.2
9.2
8.8
8.6
8.6
8.58
0.45
0.455
Q(H)ESP
0.46
0.465
4-tert-amylphenol
4-ethylphenol
4-phenylphenol
4-hydroxybenzaldehyde
9
8.8
8.4
0.445
9.73
9.6
9.4
9
10.04
9.8
pKa
pKa
9.6
10
4-tert-amylphenol
4-ethylphenol
4-phenylphenol
4-hydroxybenzaldehyde
10.09
8.4
0.49
8.58
0.492
0.494
0.496
Q(H) NPA
0.498
0.5
Results
These plots indicate the effectiveness
of determining pKa values through
different atomic charge methods by
using the actual experimental values
(known) and the training set of data
points.
12
10
pKa
8
6
Actual experimental
values
4
2
Training set of data
0
points (phenols)
0.450000 0.455000 0.460000 0.465000 0.470000
Q(H)Mul
12
12
10
10
8
pKa
pKa
8
6
6
4
Actual experimental values
4
Actual experimental values
2
Training set of data points
(phenols)
2
Training set of data points
(phenols)
0
0.44
0.445
0.45
0.455
Q(H)ESP
0.46
0.465
0
0.485
0.49
0.495
Q(H) NPA
0.5
0.505
Conclusion
 NPA and Mulliken charges are observed to be quite
useful and effective measures in correlating with
the observed pKa’s of the known compound.
 ESP produced less effective results for the succesful
correlation with the observed pKa’s as indicated by
the regression results.
 Atomic charges methods are very useful for rapid
evaluation and determination of the pKa for
anilines and phenols as observed experimentally.
Thank You