Determination of the hydrogen-bond basicity of weak and multifunctional bases: The case of lindane (γ-hexachlorocyclohexane)

Article abstract of DOI:10.1002/poc.688

We made use of four methods for determining the hydrogen-bond (HB) basicity of lindane (λ-hexachlorocyclohexane): (i) experimental Fourier transform IR measurement of a sum of individual 1:1 equilibrium constants for the formation of 1:1 4-fluorophenol-lindane hydrogen-bonded complexes in CCl₄; (ii) calculation of the overall HB basicity from octanol-water partition coefficients; (iii) correlation of the HB basicity of chloroalkanes with the electrostatic potentials around chlorine atoms; and (iv) correlation of the HB basicity of chloroalkanes with the computed enthalpy of their complexes with hydrogen fluoride. It is consistently found that lindane remains a weak HB base because multifunctionality cannot fully compensate for the electron-withdrawing inductive effects that chlorine atoms exert over one another. Actually, only five chlorine atoms behave as HB acceptors, one axial chlorine being deactivated by inductive effects. Stereoelectronic effects lead to the formation of three-centered hydrogen bonds. Copyright

Full text of DOI:10.1002/poc.688

JOURNAL OF PHYSICAL ORGANIC CHEMISTRY
J. Phys. Org. Chem. 2004; 17: 56–64
Published online 12 November 2003 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/poc.688
Determination of the hydrogen-bond basicity of
weak and multifunctional bases: the case of lindane
(c-hexachlorocyclohexane)
y
´ ˆ
Carole Ouvrard, Maryvonne Luc¸on, Jerome Graton, Michel Berthelot and Christian Laurence*
´
´
´
Laboratoire de Spectrochimie et Modelisation, EA 1149, FR CNRS 2465, Faculte des Sciences et des Techniques, Universite de Nantes,
`
2, rue de la Houssiniere, BP 92208, 44322 Nantes, Cedex 3, France
Received 17 March 2003; revised 2 June 2003; accepted 10 June 2003
ABSTRACT: We made use of four methods for determining the hydrogen-bond (HB) basicity of lindane
(ꢀ-hexachlorocyclohexane): (i) experimental Fourier transform IR measurement of a sum of individual 1:1
equilibrium constants for the formation of 1:1 4-fluorophenol-lindane hydrogen-bonded complexes in CCl4; (ii)
calculation of the overall HB basicity from octanol–water partition coefficients; (iii) correlation of the HB basicity of
chloroalkanes with the electrostatic potentials around chlorine atoms; and (iv) correlation of the HB basicity of
chloroalkanes with the computed enthalpy of their complexes with hydrogen fluoride. It is consistently found that
lindane remains a weak HB base because multifunctionality cannot fully compensate for the electron-withdrawing
inductive effects that chlorine atoms exert over one another. Actually, only five chlorine atoms behave as HB
acceptors, one axial chlorine being deactivated by inductive effects. Stereoelectronic effects lead to the formation of
three-centered hydrogen bonds. Copyright # 2003 John Wiley & Sons, Ltd.
KEYWORDS: hydrogen bonding; basicity; chloroalkanes; lindane; Fourier transform infrared spectrometry; octanol–water
partition coefficient; electrostatic potential
INTRODUCTION
Kx ¼ xcomplex=ðxchloroalkane ꢀ xphenol
Þ
ð2Þ
ð3Þ
ð4Þ
Kc ¼ Ccomplex=ðCchloroalkane ꢀ Cphenol
Þ
A growing body of experimental and theoretical evidence
confirms that weak hydrogen bonds (HBs) can play
important roles in chemistry and biology.1,2 Weak HBs
are obviously formed between weak HB donors and weak
HB acceptors, but might also occur when only one
partner is weak. This second category includes the inter-
action between fairly strong HB donors such as phenols
and weak HB acceptors such as haloalkanes.3–5 In the
present context, hydrogen-bond strength will be mea-
sured from 1:1 hydrogen-bond complexation constants6
(and, whenever possible, HB complexation enthalpies6).
We have recently measured7,8 these thermodynamic
properties for a number of chloroalkanes against 4-
fluorophenol in tetrachloromethane solution:
ꢀHꢁ ¼ RT2ð@lnKx=@TÞP
The mole-fraction equilibrium constant, Kx, the correct
one9 for obtaining the standard state-infinite dilution
enthalpy ꢀH ꢁ, is used10 in the calculation of the hydro-
gen-bonding term contributing to the octanol–water parti-
tion coefficient11 (see below). The molar-concentration
equilibrium constant, Kc, is generally used for defining the
Taft’s pKHB scale12 of hydrogen-bond basicity as log Kc.
Because of the strong inductive electron-withdrawing
effect of the chloro substituent,13 polychloroalkanes form
even weaker hydrogen bonds than monochloroalkanes,
and their HB acceptor strength becomes more difficult to
measure experimentally by the usual IR method.6 Addi-
tional methods must be employed in order to assess the
reliability of IR results. In this work, we shall calculate
the equilibrium constants of reaction (1) for polychlor-
oalkanes from their relationships with (i) octanol–water
partition coefficients,10 (ii) electrostatic potentials around
the chlorine atoms and (iii) computed enthalpies for
hydrogen-bonding complexation of hydrogen fluoride.14
These studies allow the issue of polyfunctionality in
hydrogen bonding to be addressed. Two extreme
situations, which we explain using the example of
--
R Cl þ 4-FC6H4OH
--
4-FC6H4OH ꢀ ꢀ ꢀ Cl R ð1Þ
Ð
*Correspondence to: C. Laurence, Laboratoire de Spectrochimie et
´
Modelisation, EA 1149, FR CNRS 2465, Faculte des Sciences et des
Techniques, Universite de Nantes, 2, rue de la Houssiniere, BP 92208,
´
´
`
44322 Nantes, Cedex 3, France.
E-mail: Christian.Laurence@chimie.univ-nantes.fr
yPresent address: Centre for Theoretical and Computational Chemistry,
University College London, 20 Gordon Street, London WC1H 0AJ,
UK.
Copyright # 2003 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 56–64

HYDROGEN-BOND BASICITY OF LINDANE
57
1,2,3-trichloropropane, are often encountered in solution
studies. In the first one, trichloroalkane is in excess [in
order to shift equilibrium (1) towards the hydrogen-
bonded complex] so that neither 2:1 nor 3:1 complexes
(phenol: trichloroalkane) can be significantly formed.
Three different 1:1 complexes (as shown from the elec-
trostatic potential map; see below) are mainly formed
according to the following equilibria of equilibrium
constants Kx,1–Kx,3:
complex is the major species, the overall equilibrium
constant17 is the product of three individual constants
corresponding to the stepwise formation of 1:1, 2:1 and
3:1 complexes.10,17 Since log ꢁKi ¼ ꢂ log Ki, the sum-
mation of the logarithm of the individual constants might
have some physical meaning.18 In neat water or neat
octanol, it is possible that each site of polyfunctional HB
acceptor solutes will be fully utilized. We have found10
that the hydrogen-bonding term contributing to the octa-
nol–water partition coefficient Pow of these multifunc-
tional solutes in linear solvation energy relationships19–24
is fairly well correlated with the sum of the log Kx values.
Provided that care is taken regarding family-dependent
behavior,10 we can use the Kx,i values [Eqns (2) and (5)–
(7)] corresponding to the 1:1 association in CCl4 of 4-
fluorophenol on each site.
The aim of this work was to determine the hydrogen-
bond basicity of lindane, a weak and multifunctional HB
acceptor. Lindane [1a,2a,3a,4e,5e,6e-hexachlorocyclohex-
ane or ꢀ-hexachlorocyclohexane (ꢀ-HCH)], is a well-
known insecticide used in agriculture25 and human ther-
apeutics.26 We also wanted to elucidate the structural basis
of its lipophilicity (i.e. octanol–water partition coefficient)
and hydrogen-bonding basicity, which are important prop-
erties of its transport to its target, its bioaccumulation and
its docking to receptors.27–29 Lastly, we wanted to revisit
the recent surprising finding that hexachlorocyclohexanes
are strong hydrogen-bond bases.30
Kx;1 ¼ xcomplex 1=xArOH ꢀ xClCH CHClCH Cl
ð5Þ
ð6Þ
2
2
Kx;2 ¼ xcomplex 2=xArOH ꢀ xClCH CHClCH Cl
2
2
Kx;3 ¼ xcomplex 3=xArOH ꢀ xClCH CHClCH Cl
ð7Þ
2
2
EXPERIMENTAL
In the usual IR method,6 one measures the equilibrium
mole fraction of hydrogen-bonded 4-fluorophenol, i.e.
the sum of the mole fractions of the three 1:1 complexes.
Chemicals and spectra
Therefore, the observed (measured) equilibrium constant
Tetrachloromethane, 4-fluorophenol, lindane, 1,2-di-
chloropropane, 1,2,3-trichloropropane, trans-1,2-dichlor-
ocyclohexane, 1,4-dichlorobutane, and 2-chloropropane
were commercial compounds purified as described else-
where.7,31 The Fourier transform (FT) IR spectrometer,
the cell and the method of measuring the IR wavenumber
shifts, upon hydrogen bonding, of the ꢂ(OH) band of
4-fluorophenol were described previously.7 The overlap
of the ꢂ(OH) bands of the free and hydrogen-bonded
4-fluorophenol was corrected using the Bruker Curve Fit
software, which enables overlapping bands to be mathe-
matically resolved into their Gauss–Lorentz components.
P
is the ratio
equal to the sum of the individual constants Kx,i:
xcomplex=xArOH ꢀ xClCH CHClCH Cl, which is
2
2
i
xcomplex 1 þ xcomplex 2 þ xcomplex 3
KxðobservedÞ ¼
xArOH ꢀ x
ClCH2CHClCH2Cl
X
¼ Kx;1 þ Kx;2 þ Kx;3
¼
Kx;i ð8Þ
i
P
P
We must point out that log i Kx;i ðlog i Kc;iÞ has no
thermodynamic meaning. Thus, the pKHB scale,12 and its
linear transform15 ꢁ2H, are ill-defined quantities for poly-
functional bases. However, in the case of n equivalent
basic functions, the statistically corrected quantity16
Determination of equilibrium constants and
enthalpies
P
log ð n Kx;iÞ ꢂ log n [i.e. an RTln(n) correction to the
i
Gibbs energy calculated from the measured equilibrium
constant] can be used for comparison with monofunc-
tional bases. In polychloroalkanes with equivalent chlor-
ine atoms, these statistically corrected quantities refer to
the hydrogen-bond basicity per chlorine atom.
Kx (at 25 ꢁC) and ꢀH ꢁ [Eqns (2) and (4)] were measured
from variations in the absorbance of the ꢂ(OH) band of
free 4-fluorophenol at 3614 cmꢂ1, with base mole frac-
tion (Kx) and with temperature (ꢀH ꢁ), as described
previously.7,8 Kx was calculated as illustrated in Table 1
for the example of lindane. The mean of four determina-
tions gave ꢂKx,i ¼ 12.8 ꢃ 1.1 (95%confidence level).
In the second situation, the 1,2,3-trichloropropane is
surrounded by a large excess of HB donor molecules and
takes part in multiple hydrogen bonding. If the 3:1
Copyright # 2003 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 56–64

58
C. OUVRARD ET AL.
Table 1. Mole fraction equilibrium constants for the 1:1
complexation of 4-fluorophenol with lindane in CCl4 at
25 ꢁC (four determinations)a
includes contributions arising from electronic (el), trans-
lational (tr), rotational (rot) and vibrational (vib) ener-
gies, and the ꢀPV ꢄ ꢂRT correction.
The binding energies of the complexes (ꢀEel) were
calculated without correcting the basis set superposition
error (BSSE), a spurious error introduced by the super-
molecule approach.33 The BSSE was assumed to be
almost constant in the series of closely related HF–
chloroalkane complexes.
0
1
2
3
4
xaꢁ
xbꢁ
4.41
0
4.53
227.3
4.41
226.5
4.45
4.41
230.1 224.0
0.838 0.830
3.47 3.44
0.98 0.97
229.1 223.1
22.0 22.0
12.3 12.7
Absorbance A 1.066
0.854
3.53
0.99
226.3
21.8
12.4
0.813
3.36
1.05
225.5
23.8
13.8
xa ¼ A="lb
xc ¼ xꢁa ꢂ xa
xb ¼ xꢁb ꢂ xc
% complexc
ꢂ Kx;i
The electrostatic potentials of chloroalkanes were
calculated on the molecular surface, around each chlorine
atom, with the HS95 program,34–36 using the Gaussian
archive file, and illustrated by means of the Molden
program.37 The molecular surface was defined by the
0.001 electron bohrꢂ3 contour of the electronic density.38
a
All mole fractions are multiplied by 104. xꢁa, xbꢁ; xa, xb and xc are
respectively the initial and equilibrium mole fractions of 4-fluorophenol
(acid a), lindane (base b) and complex (c).
b " ¼ 2416 cmꢂ1, l ¼ 1 cm.
c xc=xꢁa ꢀ 100. Percentage of hydrogen-bonded 4-fluorophenol.
RESULTS AND DISCUSSION
Computational methods
FTIR determination of hydrogen-bond basicity
Theoretical calculations were performed at the IDRIS
(Orsay) and CINES (Montpellier) supercomputer centers
using the Gaussian 98 suite of computer programs.32
The structures of the monomers HF and chloroalkanes
and the HF–chloroalkane complexes were optimized at
the B3LYP density functional theory level using the split-
valence plus polarization 6–31G(d,p) basis set. Harmonic
vibrational frequencies were computed at the same level
of theory, to distinguish equilibrium structures from
stationary point structures with imaginary vibrational
frequencies and to evaluate vibrational energies. In order
to obtain more accurate energies, single-point calcula-
tions were finally carried out by augmenting the basis set
with diffuse functions on non-hydrogen atoms, i.e. at the
B3LYP/6–31þG(d,p) level.
Table 2 presents the observed Kx (ꢂKx,i), the enthalpies
ꢀH ꢁ and the entropies ꢀS ꢁ for the complexation of
chloroalkanes with 4-fluorophenol in CCl4 [reaction (1)]
and the IR shifts ꢀꢂ(OH) of the 3614 cmꢂ1 band of 4-
fluorophenol. These new data are consistent with (and of
equivalent precision to) those of chloroalkanes measured
in our previous studies.7,8 They do indeed obey the
ꢀG(pKHB)/ꢀꢂ(OH) and ꢀH ꢁ/ꢀꢂ(OH) (Badger–Bauer
relationship) found previously.7,8 Figure 1 shows that the
correlation between the hydrogen-bond basicity per
chlorine atom, i.e. log (Kx/n), and the IR shifts ꢀꢂ(OH)
is obeyed by mono-, di- and trichloroalkanes.
The addition of these new data to those of Ref. 8
enables the existence of a relationship:
The enthalpies of complexation were calculated as the
difference between the quantity of the complex, treated as
a supermolecule, and the sum of the quantities of the
monomers.33 The enthalpy of complexation at 298.15 K,
given by
ꢀHꢁ ¼ ꢁꢀSꢁ þ constant
ð10Þ
between ꢀH ꢁ and ꢀS ꢁ (the compensation effect)39 to be
studied on a sample of eight mono- and dichloroalkanes.
However, since ꢀH ꢁ and ꢀS ꢁ are obtained from the
temperature dependence of log Kx, they are loaded with
ꢀHꢁ ¼ ꢀEel þ ꢀEtr þ ꢀErot þ ꢀEvib ꢂ RT
ð9Þ
Table 2. Equilibrium constants Kx, thermodynamic functions ꢀH ꢁ (kJ molꢂ1) and ꢀ Sxꢁ (J Kꢂ1 molꢂ1) and IR frequency shifts
ꢀꢂ(OH) (cmꢂ1) for hydrogen bonding of chloroalkanes to 4-fluorophenol in CCl4 at 25 ꢁC (FTIR determination)
Compound
Kx,observed
Kx,observed/na
ꢂꢀH ꢁ
ꢂꢀSꢁx;298
ꢀꢂðOHÞ
72
57
50
41
2-Chloropropane
5.15
7.26
6.52
5.00
5.31
12.8
5.15
3.63
3.26
2.50
1.77
7.57 ꢃ 0.78
6.25 ꢃ 0.26
5.75 ꢃ 0.15b
12.1 ꢃ 2.5c
4.4 ꢃ 0.9c,d
3.6 ꢃ 0.5c,e
1,4-Dichlorobutane
trans-1,2-Dichlorocyclohexane
1,2-Dichloropropane
1,2,3-Trichloropropane
Lindane
f
f
—
—
—
—
—
—
f
f
ꢅ29
f
f
ꢅ12
a n is the number of (assumed) equivalent chlorine atoms.
b Error limits of the slope in the regression analysis of the Van’t Hoff plot.
c Error limits of the intercept in the regression analysis of the Van’t Hoff plot.
d 10.2 when statistically corrected by ꢂR ln 2.
e 9.4 when statistically corrected by ꢂR ln 2.
f Too weak for a significant determination to be made.
Copyright # 2003 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 56–64

HYDROGEN-BOND BASICITY OF LINDANE
59
Hydrogen-bond basicity from octanol–water
partition coefficients
The equilibrium constant Pow for a solute partitioning
between wet octanol and water is known for a large
number of solutes.42 Fundamentally, ꢂRTlnPow measures
the differential of solute–octanol and solute–water mole-
cular interactions on the Gibbs energy scale. Attempts to
unravel and quantify the various interactions encoded in
the differential between wet octanol and water phases are
numerous. They all conclude19–24 that the two main terms
governing the partitioning are a hydrophobic volume term
and an opposing hydrophilic hydrogen-bond basicity term.
They also generally agreed22–24 that the HB acidity term
cancels out in the octanol–water solvation differential. We
have recently proposed10 the simple equation
Figure 1. Relationship between the thermodynamic
[log(Kx/n)] and the spectroscopic [ꢀꢂ(OH)] hydrogen-bond
basicity scales for one trichloro- (&), six dichloro- (*) and six
monochloroalkanes (*) (n ¼ 13, r ¼ 0.983)
log Pow ¼ 3:827V ꢂ 0:988ꢂꢃlog Kx þ 0:046
ð11Þ
for which the number of points n ¼ 266, r2 ¼ 0.986 and
the standard deviation from the regression s ¼ 0.20. In
this equation, the first term gathers contributions assumed
to be roughly collinear with volume V, i.e. the endoergic
solute cavity creation and the exoergic solute–solvent
dispersion and induction energies.43 The molecular vo-
lume V for any solute is calculated according to the
Abraham and McGowan algorithm.44 The second term
corresponds to the effective hydrogen-bond basicity. It
sums the HB basicities of the various HB acceptor sites of
the solute. We have found10 that this term can be
measured by the log Kx values of reaction (1). ꢃ is a
family-dependent term, which is required for employing
the simple log Kx values for 1:1 complexation in CCl4
towards a phenol to describe the solute hydrogen bonding
with bulk water and octanol, which is a much more
complex phenomenon. For haloalkanes, ꢃ ¼ 1.07 (Ref.
10) and the hydrogen-bond basicity of chloroalkanes can
be calculated from
Figure 2. Compensation law for the hydrogen-bonding
complexation of chloroalkanes with 4-fluorophenol in CCl4.
Data from Table 2 (*) and Ref. 8 (^)
correlated errors, which might cause the apparently good
relationship in Fig. 2 (squared correlation coefficient
r2 ¼ 0.947 for eight data points). We checked, by the
statistically correct method of Exner and Beranek,40 with
the program written by Ouvrard et al.,41 that there is a
true chemical dependence between ꢀH ꢁ and ꢀS ꢁ. We
find for chloroalkanes an isoequilibrium temperature
ꢁ ¼ 615 K. This ꢁ value satisfactorily stands within the
confidence interval (529–701 K) of the value (592 K)
found previously8 for a mixed sample of fluoro-,
chloro-, bromo- and iodoalkanes. The existence of
Eqn (10) indicates that the variation of ꢀG (i.e. log Kx)
is enthalpy dependent. Hence values of log Kx might be
calculated from energy-based descriptors of hydrogen-
bond basicity (see below).
The Kx value of lindane seems fairly precise:
Kx ¼ 12.8 ꢃ 1.1 at the 95% confidence level. However,
the low solubility of lindane in CCl4 (ca 0.25 dm3 molꢂ1),
and hence the low quantity of hydrogen-bonded 4-fluor-
ophenol (Table 1), and the overlap of the free and
hydrogen-bonded ꢂ(OH) bands [ꢀꢂ(OH) is only ca
12 cmꢂ1], make the mathematical decomposition of the
two bands rather hazardous and the correctness of our
result ill-defined. This requires the determination of the
hydrogen-bond basicity of lindane by other approaches.
ꢂ log Kx ¼ ½ꢂlog Pow þ 3:827V þ 0:046ꢆ=1:057 ð12Þ
Table 3 illustrates the application of Eqn (12) to a
training set of 20 mono- and dihaloalkanes, for which
41
7
reliable values of both Pow and ꢂlog Kx have been
measured. For dihaloalkanes, we assume the equivalence
of the two halogens and ꢂlog Kx can be calculated from
Kx(observed) by means of the equation
ꢂ log Kx ¼ n½log KxðobservedÞ ꢂ log nꢆ
ð13Þ
The differences (Table 3) between the values of
ꢂ log Kx calculated from log Pow and those calculated
from Kx measured by FTIR spectrometry, assuming the
equivalence of halogens in dihaloalkanes [Eqn (13)],
range from þ 0.22 (relative error 34%) to ꢂ 0.16 (relative
error 15%), and are fairly well distributed around zero
Copyright # 2003 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 56–64

60
C. OUVRARD ET AL.
Table 3. Comparison of the hydrogen-bond basicity of haloalkanes towards 4-fluorophenol in CCl4 calculated from log Pow
and measured by FTIR spectrometry
ꢂ log Kx
Solute
Log Paow
Vb
From log Pcow
From FTIRd
Difference
1-Fluoropentane
2-Chloropropane
1-Chlorobutane
Bromocyclohexane
2-Bromopropane
1-Bromobutane
1-Bromopentane
1-Bromopropane
Bromoethane
Iodoethane
Iodomethane
1,4-Dichlorobutane
1,3-Dichlorobutane
1,2-Dichloropropane
1,2-Dichloroethane
trans-1,2-Dichlorocyclohexane
1,3-Dibromopropane
1,2-Dibromoethane
1,3-Diiodopropane
1,2-Diiodoethane
2.33
1.90
2.64
3.20
2.14
2.75
3.37
2.10
1.61
2.00
1.51
2.24
2.00
2.02
1.47
3.21
2.37
1.96
3.02
2.71
0.931
0.654
0.795
1.020
0.706
0.847
0.988
0.706
0.565
0.649
0.508
0.917
0.776
0.776
0.635
1.090
0.881
0.740
1.048
0.907
0.85
0.61
0.42
0.71
0.58
0.51
0.43
0.61
0.57
0.50
0.45
1.24
0.96
0.94
0.95
1.00
0.99
0.87
0.98
0.76
0.95
0.71
0.60
0.75
0.71
0.67
0.65
0.63
0.61
0.54
0.54
1.08
0.98
0.80
0.80
1.03
0.96
0.76
0.98
0.72
þ0.10
þ0.10
þ0.18
þ0.04
þ0.13
þ0.16
þ0.22
þ0.02
þ0.04
þ0.04
þ0.09
ꢂ0.16
þ0.02
ꢂ0.14
ꢂ0.15
þ0.03
ꢂ0.03
ꢂ0.11
0
ꢂ0.04
a From Ref. 42.
b (cm3 molꢂ1)/100.
c From Eqn (12).
d This work and Ref. 7. The pKHB (log Kc) in Ref. 7 are converted into Kx by the equation log Kx ¼ pKHB þ 1.013, since Kx and Kc are related, for dilute CCl4
solutions, by Kx ꢄ Kc ꢇ 1000 d/M ꢄ Kc ꢇ 1000 ꢇ 1.58439/153.82 ꢄ 10.3 Kc, where d and M are respectively the density and the molecular weight of CCl4.
(with a mean of þ 0.03). These differences arise from
measurement errors of Pow and Kx(observed), model
errors [see above for the assumptions included in Eqn
(11)], and also the influence, not taken into account, of
stereochemical factors on the partition coefficient.45 Most
haloalkanes of the training set can exist in several conf-
ormations46 with different dipole moments, so the most
stable conformation(s) in the apolar solvent CCl4 may not
be the same as in water and octanol, which have much
higher dielectric permittivities.
Nevertheless, the results from the training set are
sufficiently encouraging that we may apply Eqn (12) to
lindane and other stereoisomers of known Pow.47 The
results are presented in Table 4. For lindane, the compar-
ison of ꢂlog Kx ¼ 2.24, calculated from log Pow, with
ꢂKx ¼ 12.8, measured by FTIR spectrometry, is not
possible without making assumptions. Assuming six
equivalently basic chlorines, we calculate [Eqn (13)]
ꢂlog Kx ¼ 1.97. With five equivalently basic chlorines
and one inert chlorine (see below), we have
ꢂlog Kx ¼ 2.04. Clearly, the two different thermody-
namic methods (octanol–water partition and hydrogen
bonding with a phenol in CCl4) give macroscopic values
of similar magnitude for the hydrogen-bond basicity of
lindane. However, a deeper view of the basicity of each
chlorine of lindane is needed at the molecular level. To
achieve this, we chose in the following to calculate the
electrostatic potentials around each chlorine atom of
lindane, its ꢄ, ꢁ and ꢅ isomers and, for comparison, a
training set of chloroalkanes.
Hydrogen-bond basicity from electrostatic
potentials
Table 4. Calculation of the hydrogen-bond basicity of four
stereoisomers of 1,2,3,4,5,6-hexachlorocyclohexane from
the octanol–water partition coefficient
The electrostatic potential V(r) created in the space around
a molecule by its nuclei and electrons is defined by
ð
ꢆðr0Þdr0
jr0 ꢂ rj
Isomer
Configuration Log Poaw
Vb ꢂ log Kxc
X
ZA
VðrÞ ¼
ꢂ
ð14Þ
ꢄ-HCH
ꢁ-HCH
ꢀ-HCH (lindane) a,a,a,e,e,e
a,a,e,e,e,e
e,e,e,e,e,e
3.80
3.78
3.72
4.14
1.580
1.580
1.580
1.580
2.17
2.19
2.24
1.85
jRA ꢂ rj
A
where ZA is the charge on nucleus A, located at RA, ꢆ(r)
is the electronic density function of the molecule and r0 is
a dummy integration variable. V(r) gives the interaction
energy between a proton located at r and the unperturbed
ꢅ-HCH
a,e,e,e,e,e
a Ref. 47.
b (cm3 molꢂ1)/100.
c Eqn (12).
Copyright # 2003 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 56–64

HYDROGEN-BOND BASICITY OF LINDANE
61
Table 5. Hydrogen-bond basicity, log Kx, minimum electrostatic potential on the molecular surface, Vs,min (kJ molꢂ1), most
stable conformer, and directionality ( ꢁ) of the spatial minimum of electrostatic potential, for chloroalkanes
Chloroalkane
Log Kx
ꢂVs,min
Directionalityc
Conformerd
1-Chloroadamantane
2-Chloro-2-methylpropane
Chlorocyclohexane
0.84
0.74
0.74
82.47
77.28
78.66
113.1
114.4
112.3
THHH
SCC
(axial)
SHH
PC
2-Chloropropane
1-Chloropentane
1,5-Dichloropentane
1-Chlorobutane
1,4-Dichlorobutane
trans-1,2-Dichlorocyclohexane
0.71
0.64
0.63a
0.60
0.54a
0.51a
75.14
74.43
67.78
73.93
62.01
56.19
113.2
112.2
110.5
111.9
111.3
111.2
0
PH PH
PC
0
0
PH PH
0
0
0
0
0
SH Cl SH Cl
(axial–axial)
PH PH
PCl(PCl)
0.50a
0.40a
0.40a
64.35
43.85
48.20b
108.9
110.5
111.9
0 0
1,3-Dichloropropane
1,2-Dichloroethane
1,2-Dichloropropane
0
PCl SHCl
a Log Kx,observed ꢂlog 2.
b Mean of two close values (see text).
c Defined by the Min—Cl—C angle. Min is the point of the molecular surface where Vs is minimum.
d Mizushima notation: type of substitution of the carbon atom is specified by P (primary), S (secondary) or T (tertiary). The subscript indicates the atom(s) in
antiperiplanar position towards the chlorine atom.
charge distribution of the molecule. A (partially) positive
hydrogen to be shared in a hydrogen bond will be
attracted to those regions where V(r) is negative, which
are usually associated with the lone pairs of the more
electronegative atoms, such as N, O, F and Cl.
conformations known for chloroalkanes.46,54,55 We
checked that the electrostatic potential is not generally
greatly affected by changes in molecular conformation.56
However, when a conformation brings two chlorines into
spatial proximity, a significantly more negative Vs,min is
found in the region between the two atoms. We chose to
report in Table 5 the electrostatic potentials calculated
from the most stable (from electronic energy) conforma-
tion. This choice is somewhat arbitrary, but dictated by
our ignorance of the population of various conformers in
CCl4. Also reported are (i) the log Kx for hydrogen
bonding to 4-fluorophenol, statistically corrected by
log 2 when two equivalent (quasi-equivalent in the case
of 1,2-dichloropropane) chlorine atoms are present, and
(ii) the directionality of the Vs minimum on the molecular
surface. This Vs,min directionality agrees fairly well with
the directionality of the hydrogen bond to chlorine atoms
found in theoretical calculations31,33,57 or in hydrogen-
bonded contacts in crystal structures.1,31,58
The hydrogen-bond basicity has been shown48 to be
quantitatively related to the magnitudes of the most
negative electrostatic potentials computed on the mole-
cular surface, Vs,min, for a group of 33 HB acceptors of
various types. Better correlations have been obtained by
treating different chemical classes separately, e.g. aro-
matic N-heterocycles,49 nitriles50 or amines.51 A ratio-
nale for these good family-dependent correlations
between the Gibbs energy of complexation (i.e. pKHB
or log Kx) and electrostatic potential is (i) the family-
dependent relationship between the enthalpy and entropy
of association (see above), (ii) the dominant part of the
energy of association is in most cases the electrostatic
contribution52 and (iii) other contributing terms may
fortunately cancel out53 or be constant or be related to
the electrostatic term for a family of structurally homo-
geneous HB acceptors.
Using the data set of Table 5, we find a good linear
relationship between Vs,min and log Kx, given in Fig. 3 and
We calculated Vs,min at the B3LYP/6–31 þ G(d,p)//
B3LYP/6–31G(d,p) level for 11 chloroalkanes that have
either a single chlorine HB acceptor or two equivalent
chlorine HB acceptors. We added 1,2-dichloropropane to
this sample because we calculate almost equal Vs,min
values on each chlorine ( ꢂ 48.33 and ꢂ 48.07 kJ molꢂ1).
). We could not add 1,2,3-trichloropropane, which shows
three different Vs,min values ( ꢂ 70.16, ꢂ 48.87 and
ꢂ 44.77 kJ molꢂ1; see Table 6). It should be noted that
most studied compounds are conformationally flexible.
We did not fully explore the potential energy surface but,
where it was deemed necessary, we optimized the geo-
metries of various input conformations. The most stable
geometries found always agree with the experimental
Figure 3. Correlation of the hydrogen-bond basicity scale,
log(Kx/n), with the minimum electrostatic potential, Vs,min, on
the molecular surface, located on the chlorine atoms
Copyright # 2003 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 56–64

62
C. OUVRARD ET AL.
Table 6. Calculation of individual (log Kx,i), and overall
(ꢂlog Kx,i) hydrogen-bond basicities of polychloroalkanes,
from electrostatic potentials Vs,min (kJ molꢂ1); comparison
with the overall hydrogen-bond basicity calculated from the
octanol–water partition coefficient
the map for lindane (Plate 1) shows well the subtle
stereoelectronic interactions between the six negative
chlorine and the six positive hydrogen atoms situated
around the carbon ring. These interactions produce (i)
one axial chlorine with Vs,min ꢄ 0, i.e. without the ability to
attract the positive hydrogen of the hydroxyl of water,
octanol or 4-fluorophenol, and (ii) five negative relative
minima situated between the five remaining chlorines,
because of the overlap of lone-pair electron densities.
Polychloroalkane ꢂVs,min Na Log Kx,i ꢂlog Kx,i ꢀb
ꢄ-HCH
60.71
57.03
40.50
1
2
2
0.53
0.49
0.31
2.11
0.06
ꢁ-HCH
ꢀ-HCH (lindane)
48.42
63.30
55.60
34.50
6
2
2
1
0.39
0.56
0.47
0.24
2.35 ꢂ0.17
Hydrogen-bond basicity from similarities
between HF and 4-fluorophenol
hydrogen-bonded complexes
2.29 ꢂ0.05
ꢅ-HCH
54.27
50.17
41.76
70.17c
48.87d
44.77e
2
2
2
0.46
0.41
0.32
Lamarche and Platts14 have recently shown, on a set of 40
HB acceptors including one chloroalkane, that the pKHB
scale (i.e. log Kx) could be correlated with the hydrogen-
bond binding energy, enthalpy, and Gibbs energy (ꢀEel,
ꢀH ꢁ and ꢀG ꢁ) of their hydrogen-bonded complexes with
hydrogen fluoride (r2 ¼ 0.906, 0.910 and 0.927 respec-
tively), calculated at the B3LYP/6–31þG(d,p)//B3LYP/6–
31þG(d,p) level. As a last approach to the HB basicity of
lindane, we also use in the following the model of HF
complexes for calculating ꢂlog Kx,i of lindane.
For this purpose, we first established a relationship
between the experimental Gibbs energies (i.e. log Kx) of
4-fluorophenol complexes and the computed enthalpies
of HF complexes for the family of chloroalkanes. As
shown by Lamarche and Platts,14 the best correlation (i)
comes from computed ꢀG ꢁ and (ii) seems family-in-
dependent. However, it must be taken into account that,
through the entropy, ꢀG ꢁs are affected by an error of
calculation. This is because, for weak hydrogen bonds,
such as in chloroalkanes–HF complexes, there are a
number of vibrational modes of very low frequency,
hence very anharmonic.59 Since vibrational frequencies
are computed under the harmonic approximation,60 the
error affecting the vibrational entropy may be large.
The error in the computed enthalpies must be smaller
since, unlike the vibrational entropy, low frequencies
contribute little to the zero-point vibrational energy.33
In any case, we restricted the relative comparison be-
tween experimental ꢀG ꢁ (4-fluorophenol complexes)
and computed ꢀH ꢁ (HF complexes) to the family of
chloroalkanes and, according to the similarity principle,
model and/or calculation errors are expected to be fairly
small and/or constant.
2.37 ꢂ0.53
1.42 ꢂ0.27f
1,2,3-Trichloro-
propane
1
1
1
0.64
0.41
0.37
a
Number of equivalent (relative) minima on the electrostatic potential
surface.
b Difference between ꢂlog Kx,i calculated from log Pow (Table 4) and from
Vs,min
.
c Absolute minimum located between Cl1 and Cl2 in Cl1CH2CHCl2CH2Cl3.
d Minimum located on Cl3 atom.
e Minimum located on Cl1 atom.
f From a measured log Pow value of 2.27 (A. J. Leo, personal communica-
tion) and the volume V ¼ 89.9 cm3 molꢂ1/100, Eqn (12) yields ꢂlog
Kx,i ¼ 1.15.
Eqn (15), where numbers in parentheses are standard
deviations on the slope and intercept, respectively:
logðKx=nÞ ¼ 1:06ðꢃ0:12ÞðꢂVs;min=100Þ ꢂ 0:11ðꢃ0:08Þ
n ¼ 12; r2 ¼ 0:893; s ¼ 0:05
ð15Þ
This correlation can be used to predict the hydrogen-
bond basicity of polychloroalkanes with equivalent chlor-
ine acceptors (e.g. ꢁ-HCH) and, most importantly, with
inequivalent chlorine acceptors. In this case, Vs,min is
computed on the molecular surface around one chlorine
acceptor, or between two chlorine acceptors when their
spatial proximity creates a zone of high electron density
(as illustrated in Plate 1). The log Kx,i values predicted by
Eqn (15) are then summed to give a prediction for the
overall hydrogen-bond basicity, ꢂlog Kx,i. The results of
these calculations for ꢄ-, ꢁ-, ꢀ-, and ꢅ-HCH, and 1,2,3-
trichloropropane are given in Table 6. Agreement with
ꢂlog Kx,i calculated from octanol–water partition coeffi-
cients (as illustrated in Table 4) is good, with relative
differences between values predicted by the two methods
ranging from 0 to 7% for all compounds except ꢅ-HCH,
for which the difference is higher (22%).
Table 7 gives the results of B3LYP/6–31þG(d,p)//
B3LYP/6–31G(d,p) calculations of the enthalpies of
complexation of five chloroalkanes with HF. The geome-
try of these complexes is illustrated in Plate 2. The
equilibrium complex can be described as a cyclic struc-
ture with a predominant F—Hꢀ ꢀ ꢀCl hydrogen bond
distorted by secondary C—Hꢀ ꢀ ꢀF hydrogen bonds (si-
milar structures were found at the MP2/6–31þG(d,p)
level for the complexes of HF with chloromethanes57).
Advantages of the electrostatic potential method are the
possibility of calculating individual complexation con-
stants and of obtaining molecular knowledge about the
electrostatic origin of hydrogen-bond basicity, through an
analysis of the electrostatic potential map. For example,
Copyright # 2003 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17: 56–64

Plate 1. Molecular electrostatic potential maps of lindane (ꢀ-HCH) and ꢁ-HCH. The isodensity surface of 0.001 e bohrꢂ3
shows five relative minima [Vs,min ¼ ꢂ63.30 (a), ꢂ55.60 (b), and ꢂ34.50 (c) kJ molꢂ1] for lindane and six equivalent minima for
ꢁ-HCH (Vs,min ¼ ꢂ48.42 kJ molꢂ1). The electrostatic potential is colour coded from red (Vs,min < 0) to blue (Vs,min > 0)
Copyright # 2003 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17

Plate 2. B3LYP/6–31G(d,p) geometries of hydrogen-bonded complexes of hydrogen fluoride with 1-chloroadamantane (1),
2-chloro-2-methylpropane (2), 2-chloropropane (3), 1-chlorobutane (4) and 1,2-dichloroethane (5)
Plate 3. Superimposed B3LYP/6–31G(d,p) geometry of the five 1:1 three-centered hydrogen-bonded complexes of lindane
with hydrogen fluoride. Only three 1:1 complexes (a, b, c) have different geometries (in agreement with the electrostatic
potential map of Plate 1)
Copyright # 2003 John Wiley & Sons, Ltd.
J. Phys. Org. Chem. 2004; 17

HYDROGEN-BOND BASICITY OF LINDANE
63
Table 7. Calculation of the individual (log Kx,i), and overall
(ꢂlog Kx,i) hydrogen-bond basicity of lindane, from the
B3LYP/6–31þG(d,p)//B3LYP/6–31G(d,p) computed enthal-
pies of 1:1 complexations with hydrogen fluoride, ꢀH ꢁ
methods give fairly concordant results since ꢂ Kx,i ranges
from 12 to 15 and ꢂlog Kx,i between 1.6 and 2.3 (see
Table 8). We cannot conclude, as in a recent study,30 that
lindane ‘can be regarded as a reasonably strong HB base,
comparable in strength to aliphatic amines, and not far
short of amides,’ because the log Kx values of ethylamine,
triethylamine and N,N-diethylacetamide (3.18, 2.99, and
3.48, respectively) are higher by an order of magnitude.
According to our results, lindane can be described as a
weak HB acceptor. Each chlorine of lindane is individu-
ally a weaker acceptor than the chlorine of monochlor-
ocyclohexane (comparing the values 0.24–0.56 in Table 6
or 0.06–0.40 in Table 7 with the value 0.74 of c-C6H11Cl
in Table 5), because of the electron-withdrawing induc-
tive effect that chlorine atoms exert over one another. The
overall HB basicity of lindane is raised to 1.6–2.3 by
virtue of its multifunctionality (five active chlorine ac-
ceptors), but still does not attain the values of common
strong monofunctional HB bases.
(kJ molꢂ1
)
Chloroalkane
ꢂꢀH ꢁ
Log Kx
Training set
Comput.
13.71
12.58
11.14
10.14
6.43
Comput.
5.83
6.48
Exp.
0.84
0.73
0.71
0.60
0.39a
Est.b
0.36
0.40
0.06
1.58c
1-Chloroadamantane
2-Chloro-2-methylpropane
2-Chloropropane
1-Chlorobutane
1,2-Dichloroethane
Lindane
1:1 complex a
1:1 complex b
1:1 complex c
0.67
ꢂlog Kx,i
a Statistically corrected by ꢂlog 2.
b Estimated from Eqn (16).
c Taking into account two equivalent complexes a, two equivalent b and one
c.
These computed enthalpies correlate well with log Kx,
according to the equation
Acknowledgments
log Kx ¼ ꢂ0:060ðꢃ0:005ÞꢀHꢁ þ 0:016ðꢃ0:051Þ
The authors gratefully acknowledge the IDRIS (Institut
´
du Developpement et des Ressources en Informatique
Scientifique) and the CINES (Centre Informatique
n ¼ 5; r2 ¼ 0:982; s ¼ 0:03
ð16Þ
This correlation can be used to predict the HB basicity of
lindane. In the optimized structures of 1:1 HF–lindane
complexes, we find only five stable complexes (the axial
chlorine of Vs,min ꢄ 0 does not give any complex, as
expected), of which only three are different. These
complexes are three-centered as shown in Plate 3. These
observations are coherent with the electrostatic potential
map of lindane, which shows five relative minima, each
situated between two proximal chlorines. The log Kx,i
values predicted by Eqn (16) are then summed to give a
prediction for the overall HB basicity, ꢂ log Kx,i. The
results of these calculations are given in Table 7.
´
National de l’Enseignement Superieur) for a grant of
computer time, Dr J. Y. Le Questel for help with calcula-
tions and Mr A. Planchat for help with FTIR measure-
ments.
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