An enthalpic scale of hydrogen-bond basicity. 3. Ammonia, primary, secondary, and tertiary amines

Article abstract of DOI:10.1021/jo050535g

A reliable enthalpic scale of hydrogen-bond acceptor strength (basicity) is built for aliphatic amines by means of a new infrared method, from the temperature variation of hydrogen-bond equilibrium constants. Enthalpies of hydrogen bonding to a reference hydrogen-bond acceptor, 4-fluorophenol, have been determined in CCl₄ and/or C2C1₄ for ammonia and 68 primary, secondary, and tertiary amines. The scale spans from -23.8 kJ mol ^-1 for i-Pr₂NCH(Et)₂ to -39.4 kJ mol ^-1 for Et₃N. This large variation is mainly explained by the basicity-enhancing electronic effects of alkyl groups, which can be overcompensated by dramatic basicity-decreasing steric effects. Relationships between ΔH° and the change in electronic energy or the infrared shift of the OH stretching upon hydrogen bonding are studied and found useful in the prediction of the hydrogen bond enthalpies of amines with several hydrogen-bond acceptor sites. A careful statistical analysis of the enthalpy-entropy relationship shows an isoentropic tendency. The entropies of 65% of hydrogen-bonding reactions between aliphatic amines and 4-fluorophenol have a mean value of -55.1 ± 4.2 J K^-1 mol^-1. Amines excluded from the isoentropic set are mainly severely hindered ones. The hydrogen-bond enthalpic scale can be useful in measuring the electrostatic character of Lewis bases.

Full text of DOI:10.1021/jo050535g

An Enthalpic Scale of Hydrogen-Bond Basicity. 3.
Ammonia, Primary, Secondary, and Tertiary Amines
Je´roˆme Graton,* Michel Berthelot, Franc¸ois Besseau, and Christian Laurence
Laboratoire de Spectrochimie et Mode´lisation, EA 1149, FR CNRS 2465, Faculte´ des Sciences et des
Techniques, Universite´ de Nantes, 2, rue de la Houssinie`re, BP 92208, 44322 Nantes, Cedex 3, France
Jerome.Graton@univ-nantes.fr
Received March 16, 2005
A reliable enthalpic scale of hydrogen-bond acceptor strength (basicity) is built for aliphatic amines
by means of a new infrared method, from the temperature variation of hydrogen-bond equilibrium
constants. Enthalpies of hydrogen bonding to a reference hydrogen-bond acceptor, 4-fluorophenol,
have been determined in CCl4 and/or C2Cl4 for ammonia and 68 primary, secondary, and tertiary
amines. The scale spans from -23.8 kJ mol-1 for i-Pr2NCH(Et)2 to -39.4 kJ mol-1 for Et3N. This
large variation is mainly explained by the basicity-enhancing electronic effects of alkyl groups,
which can be overcompensated by dramatic basicity-decreasing steric effects. Relationships between
∆H° and the change in electronic energy or the infrared shift of the OH stretching upon hydrogen
bonding are studied and found useful in the prediction of the hydrogen bond enthalpies of amines
with several hydrogen-bond acceptor sites. A careful statistical analysis of the enthalpy-entropy
relationship shows an isoentropic tendency. The entropies of 65% of hydrogen-bonding reactions
between aliphatic amines and 4-fluorophenol have a mean value of -55.1 ( 4.2 J K-1 mol-1. Amines
excluded from the isoentropic set are mainly severely hindered ones. The hydrogen-bond enthalpic
scale can be useful in measuring the electrostatic character of Lewis bases.
Introduction
ever, in 1974, the data of Arnett et al.5 indicated that
“in general, a straight line correlation between ∆H° and
∆S° does not hold although a trend is clear”. Another
debated correlation is the Badger-Bauer correlation6,7
of the hydrogen-bond enthalpy with the infrared shift of
the XH stretching frequency upon complexation. It has
been supported by some workers8-18 and challenged by
Despite the importance of hydrogen bonding through-
out chemistry1 and biochemistry,2 there is a serious
dearth of reliable hydrogen-bond enthalpies. It is critical
to find good enthalpies of hydrogen bonding between
hydrogen-bond donors and acceptors in a number of
cases. For example, reliable experimental values of
enthalpy are necessary for comparison with quantum-
chemical calculations of the energy of the hydrogen bond.3
Also there is a need of good values for testing the
extrathermodynamic relationship4 between enthalpy and
entropy of hydrogen bond formation. In 1960, Pimentel
and McClellan1 proposed a monotonic relationship be-
tween ∆H° and ∆S° for hydrogen bond formation. How-
(5) Arnett, E. M.; Mitchell, E. J.; Murty, T. S. S. R. J. Am. Chem.
Soc. 1974, 96, 3875-3891.
(6) Badger, R. M.; Bauer, S. H. J. Chem. Phys. 1937, 5, 839-851.
(7) Badger, R. M. J. Chem. Phys. 1940, 8, 288-289.
(8) Joesten, M. D.; Drago, R. S. J. Am. Chem. Soc. 1962, 84, 3817-
3821.
(9) Gramstad, T. Spectrochim. Acta 1963, 19, 497-508.
(10) Neerinck, D.; Lamberts, L. Bull. Soc. Chim. Belg. 1966, 75,
473-483.
(11) Neerinck, D.; Lamberts, L. Bull. Soc. Chim. Belg. 1966, 75,
484-497.
(12) Barakat, T. M.; Nelson, M. J.; Nelson, S. M.; Pullin, A. D. E.
Trans. Faraday Soc. 1966, 62, 2674-2684.
(13) Epley, T. D.; Drago, R. S. J. Am. Chem. Soc. 1967, 89, 5770-
5773.
(14) Purcell, K. F.; Stikeleather, J. A.; Brunk, S. D. J. Am. Chem.
Soc. 1969, 91, 4019-4027.
(15) Drago, R. S.; Epley, T. D. J. Am. Chem. Soc. 1969, 91, 2883-
2890.
* To whom correspondence should be addressed. Ph: (+33)(0)2 51
12 56 63. Fax: (+33)(0)2 51 12 55 67.
(1) Pimentel, G. C.; McClellan, A. L. The Hydrogen Bond; Free-
man: San Francisco, 1960.
(2) Jeffrey, G. A.; Saenger, W. Hydrogen Bonding in Biological
Structures; Springer-Verlag: Berlin, 1991.
(3) Scheiner, S. Hydrogen Bonding: A Theoretical Perspective;
Oxford University Press: New York, 1997.
(4) Liu, L.; Guo, Q. X. Chem. Rev. 2001, 101, 673-695.
10.1021/jo050535g CCC: $30.25 © 2005 American Chemical Society
Published on Web 09/07/2005
7892
J. Org. Chem. 2005, 70, 7892-7901

Enthalpic Scale of Hydrogen-Bond Basicity
many others.5,19-27 At last, opinion is divided about
whether the enthalpy or the Gibbs energy is the best
parameter for measuring basicity.28 Gutmann,29 Drago,30
and Maria and Gal31 chose the enthalpy for building
Lewis basicity scales. However, in the field of hydrogen-
bond basicity most scales are based on Gibbs energies,32-35
a choice possibly dictated by the lack or inaccuracy of
enthalpy data.
In parts 1 and 2 of this series we have reported an
enthalpic scale of hydrogen-bond acceptor strength, i.e.,
hydrogen-bond basicity, for halogen (F, Cl, Br, and I)36
and sulfur bases.37 In this work we extend the scale to
nitrogen bases, more precisely to aliphatic amines.
A number of studies5,20,38-47 have been devoted to the
enthalpies of hydrogen bonding between amines and
hydrogen-bond donors. Unfortunately, they suffer from
various shortcomings. First, they are often concerned
with a restricted sample of amines. Second, they are not
homogeneous, being relative to different hydrogen-bond
donors (alcohols,39,45 phenol,38,40,47 4-fluorophenol,5,20 4-ni-
trophenol,43 and other substituted phenols44) in different
5,20,38,39
solvents (c-C6H12,41-44 CCl4,
C2Cl4,40 and pure
base5,20). At last, when obtained from the variation of the
equilibrium constant with temperature, they are deter-
mined on a too-restricted range of temperature: 40,40
30,38 and even only 1547 or 10 °C.43 Since the error in
enthalpy is inversely related to the temperature range
of van’t Hoff plots,48 the precision and/or correctness of
most data might not be sufficient. In summary, literature
data do not at present allow construction of an extensive,
homogeneous, and reliable enthalpic scale of hydrogen-
bond basicity of aliphatic amines.
We present here a set of thermodynamic data on
aliphatic amines contrasting with these results. We have
first selected a diversified sample of 69 amines (ammonia,
9 primary, 26 secondary, and 33 tertiary amines) includ-
ing alkylamines of different chain length and chain
branching, cyclic and bicyclic amines of various ring size,
diamines, a tetramine, and amines substituted with
various electron-withdrawing groups (F, Cl, CHdCH2,
Ph, and CtCH). Thus, we have been able to extend the
hydrogen-bond enthalpic scale of aliphatic amines over
15 kJ mol-1. Second, for the purpose of homogeneity, we
have used 4-fluorophenol and CCl4 as standard hydrogen-
bond donor and solvent, respectively. The use of C2Cl4, a
solvent very close to CCl4,49 has occasionally been neces-
sary owing to the reaction of few amines with CCl4.50 At
last, to decrease the error in enthalpy (and entropy), the
temperature dependence of equilibrium constants has
been carried out over 60 °C (-5 to +55 °C) in CCl4 and
over 75 °C (-5 to +70 °C) in C2Cl4. Under these
conditions, the reaction studied will be
(16) Vogel, G. C.; Drago, R. S. J. Am. Chem. Soc. 1970, 92, 5347-
5351.
(17) Drago, R. S.; O’Bryan, N.; Vogel, G. C. J. Am. Chem. Soc. 1970,
92, 3924-3929.
(18) Sherry, A. D.; Purcell, K. F. J. Am. Chem. Soc. 1972, 94, 1853-
1857.
(19) West, R.; Powell, D. L.; Whatley, L. S.; Lee, M. K. T.; Schleyer,
P. v. R. J. Am. Chem. Soc. 1962, 84, 3221-3222.
(20) Arnett, E. M.; Joris, L.; Mitchell, E.; Murty, T. S. S. R.; Gorrie,
T. M.; Schleyer, P. v. R. J. Am. Chem. Soc. 1970, 92, 2365-2377.
(21) Becker, E. D. Spectrochim. Acta 1961, 17, 436-447.
(22) Powell, D. L.; West, R. Spectrochim. Acta 1964, 20, 983-991.
(23) Singh, S.; Murthy, A. S. N.; Rao, C. N. R. Trans. Faraday Soc.
1966, 62, 1056-1066.
(24) Gramstad, T.; Sandstrom, J. Spectrochim. Acta, Part A 1969,
25, 31-38.
CCl4 (C2Cl4)
F-C6H4OH + NRR′R′′ {- 5 to + 55 (70) °C
}
(25) Rossarie, J.; Gallas, J. P.; Binet, C.; Romanet, R. J. Chim. Phys.
Phys.-Chim. Biol. 1978, 75, 63-73.
F-C6H4OH‚‚‚NRR′R′′
(26) Goralski, P. J. Chem. Soc., Faraday Trans. 1993, 89, 2433-
2435.
(27) Abraham, M. H.; Prior, D. V.; Schulz, R. A.; Morris, J. J.; Taylor,
P. J. J. Chem. Soc., Faraday Trans. 1998, 94, 879-885.
(28) Jensen, W. B. The Lewis Acid-Base Concepts: An Overview;
Wiley: New York, 1980.
With these extensive and hopefully reliable data in
hand, we have analyzed a number of problems related
to the thermodynamics of hydrogen bonding, namely, the
prevision of enthalpies of amines bearing a second
hydrogen-bond acceptor site by means of quantum-
chemical calculations,3 the domain of validity of the
enthalpy-infrared shift relationship,6,7 the existence of
the enthalpy-entropy relationship,4 and the usefulness
of hydrogen-bond enthalpies to compare the strength of
bases.28-31
(29) Gutmann, V. Electrochim. Acta 1976, 21, 661-670.
(30) Drago, R. S. Coord. Chem. Rev. 1980, 33, 251-277.
(31) Maria, P. C.; Gal, J. F. J. Phys. Chem. 1985, 89, 1296-1304.
(32) Gurka, D.; Taft, R. W. J. Am. Chem. Soc. 1969, 91, 4794-4801.
(33) Taft, R. W.; Gurka, D.; Joris, L.; Schleyer, P. v. R.; Rakshys, J.
W. J. Am. Chem. Soc. 1969, 91, 4801-4808.
(34) Abraham, M. H.; Duce, P. P.; Prior, D. V.; Barratt, D. G.; Morris,
J. J.; Taylor, P. J. J. Chem. Soc., Perkin Trans. 2 1989, 1355-1375.
(35) Abraham, M. H.; Grellier, P. L.; Prior, D. V.; Morris, J. J.;
Taylor, P. J. J. Chem. Soc., Perkin Trans. 2 1990, 521-529.
(36) Ouvrard, C.; Berthelot, M.; Laurence, C. J. Phys. Org. Chem.
2001, 14, 804-810.
Computational Methods
(37) Laurence, C.; Berthelot, M.; Evain, K.; Illien, B. Can. J. Chem.
2005, 83, 138-145.
Electronic Structure Calculations. These calculations
were performed using the Gaussian 98 package51 supported
on a 300 MHz bi-pentium II personal computer. The hydrogen-
(38) Gramstad, T. Acta Chem. Scand. 1962, 16, 807-819.
(39) Lamberts, L.; Zeegers-Huyskens, T. J. Chim. Phys. Phys.-Chim.
Biol. 1963, 60, 435-441.
(40) Horak, M.; Sara, V.; Moravec, J. Collect. Czech. Chem. Commun.
1972, 37, 1990-1992.
(48) Wiberg, K. B. In Physical Organic Chemistry; Wiley: New York,
1964; p 378.
(41) Shah, S. B.; Murthy, A. S. N. Ind. J. Chem. 1976, 14A, 100-
103.
(49) Reichardt, C. Solvents and Solvent Effects in Organic Chemistry;
Wiley-VCH: Weiheim, 2003.
(42) Shah, S. B.; Murthy, A. S. N. Ind. J. Chem. 1976, 14A, 104-
106.
(50) Stevenson, D. P.; Coppinger, G. M. J. Am. Chem. Soc. 1962,
84, 149-152.
(43) Libus, W.; Mecik, M.; Sulek, W. J. Solution Chem. 1977, 6, 865-
879.
(51) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.;
Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.
J.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels,
A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.;
Cossi, M.; Cammi, R.; Menucci, B.; Pomelli, C.; Adamo, C.; Clifford,
S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma,
K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.;
Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Liu, G.; Liashenko, A.;
Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith,
(44) Kogowski, G.; Scott, R. M.; Filisko, F. J. Phys. Chem. 1980, 84,
2262-2265.
(45) Spencer, J. N.; Wolbach, W. S.; Hovick, J. W.; Ansel, L.;
Modarress, K. J. J. Solution Chem. 1985, 14, 805-814.
(46) Dwivedi, P. C.; Banga, A. K.; Sharma, N. Spectrochim. Acta,
Part A 1986, 42A, 623-629.
(47) Orban, M.; Kiss, A.; Barcza, L. J. Chem. Soc., Perkin Trans. 2
1987, 1815-1817.
J. Org. Chem, Vol. 70, No. 20, 2005 7893

Graton et al.
bond enthalpy ∆H° in CCl4 is the sum (eq 1) of ∆Eel, the change
∆H° ) ∆Eel + ∆Etr + ∆Erot + ∆Evib + ∆pV + ∆H° (solv)
(1)
in the electronic energy upon hydrogen bonding; ∆Etr, ∆Erot
,
and ∆Evib, the changes in the translational, rotational, and
vibrational energies, respectively, which can be calculated in
vacuo; and of a solvation term, ∆H° (solv). In this work we
have focused on the calculation of ∆Eel, which is the term
explaining the greatest part of the variance of ∆H°.3 We have
treated the amine-water complex as a supermolecule.3 This
method introduces a basis set superposition error (BSSE)3 that
was accounted for by the counterpoise procedure.52 Fragment
relaxation energy terms were also taken into account to
estimate BSSE.53 Geometries were optimized and electronic
energies were calculated at the B3LYP/6-311+G(d,p) level of
theory.3 At a similar level, Rablen et al.54 have reached a
reliably accurate description of hydrogen-bonded complexes of
small organic molecules with water.
Statistics of the Enthalpy-Entropy Correlation. The
linear dependence of enthalpy and entropy within a series of
related reactions (here, hydrogen bonding of 4-fluorophenol to
a series of amines) must not be studied under the form of eq
2, because ∆H° and ∆S° are loaded with correlated errors when
they are obtained from van’t Hoff plots (eq 3).
FIGURE 1. IR determination of the enthalpy and entropy of
hydrogen bonding of 4-fluorophenol (0.003 mol L-1) to N,N′-
dimethylpiperazine (0.01 mol L-1) in CCl4. The absorbance of
the sharp OH band of free 4-fluorophenol at 3614 cm-1
decreases with decreasing temperature (+55 to -5 °C), with
a concomitant increase of the broad OH band of the complex
at about 3000 cm-1
.
where.36,58 It is adapted from the UV method first
proposed by Joesten and Drago.59 An important advan-
tage of IR over UV is that the free 4-fluorophenol signal
(at 3614 cm-1) is not overlapped by the hydrogen-bonded
4-fluorophenol absorption (shifted to lower frequencies)
nor by the amine NH bands (also at lower frequencies).
Thus the equilibrium concentration of free 4-fluorophenol
is directly obtained by reading the free OH band absor-
bance and applying the Beer-Lambert law.
Let us recall important steps of the IR method on the
example of the hydrogen bonding between 4-fluorophenol
and N,N′-dimethylpiperazine in CCl4. The formation of
an 1:1 hydrogen-bonded complex can be represented by
equilibrium 5. Very low concentrations (ca. 3 × 10-3 mol
∆H° ) â∆S° + constant
(2)
(3)
- ∆H°
c 1
∆S°
c
ln Kc )
+
R
T
R
Exner55 has achieved a statistically correct solution by return-
ing to the original experimental quantities, ln Kc and T. By
substituting ∆S° from eq 2 into eq 3 one obtains eq 4.
∆H°
R
ln Kc ) -
(T-1 - â-1) + constant
(4)
In the coordinates ln Kc and T -1, eq 4 represents a family
of straight lines with different slopes (-∆H°/R) intersecting
at one point at T ) â (the isoequilibrium temperature). A linear
dependence in the coordinates ∆H° and ∆S° is thus math-
ematically, but not statistically, strictly equivalent to the
constraint of a common point of intersection in the coordinates
ln Kc and T -1. Thus, we have used the IKR program56 written
by Ouvrard et al.57 in order to test several hypotheses:
whether the van’t Hoff lines are parallel (â-1 f ∞, isoenthalpic
reactions), intersect at â-1 ) 0 (isoentropic reactions), intersect
at any other â-1 value (isoequilibrium relationship), or do not
intersect (no valid relationship between ∆H° and ∆S°).
L-1) of 4-fluorophenol and a 3-fold excess of the diamine
are necessary for preventing self-association of 4-fluo-
rophenol and the significant formation of a 2(phenol):
1(amine) complex, respectively. The spectra of such a
single solution were recorded at five temperatures be-
tween -5 and + 55 °C and are shown in Figure 1. The
method requires the preliminary determination of the
absorption coefficient temperature dependence (eq 6,
Results
Determination of Enthalpy and Entropy. Accurate
enthalpy and entropy measurements are done by follow-
ing the absorbance of a single solution of 4-fluorophenol
and amine in CCl4 and/or C2Cl4 as a function of temper-
ature. Our IR method has been fully described else-
ꢀ(t) ) ꢀ(25) - 0.624(t - 25)
(6)
temperature t/°C). The absorbance and concentration
data, as well as the equilibrium constants Kc calculation
(relative to molar concentrations), at the various tem-
peratures are reported in Table 1. The enthalpy and
T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.;
Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian
98, Revision A.9; Gaussian, Inc.: Pittsburgh, PA, 1998.
(52) Boys, S. F.; Bernardi, F. Mol. Phys. 1970, 19, 553-566.
(53) Xantheas, S. S. J. Chem. Phys. 1996, 104, 8821-8824.
(54) Rablen, P. R.; Lockman, J. W.; Jorgensen, W. L. J. Phys. Chem.
A 1998, 102, 3782-3797.
(55) Exner, O. Prog. Phys. Org. Chem. 1973, 10, 411-82.
(56) IKR program; http://www.sciences.univ-nantes.fr/spectro/
publicat.htm#P17.
(57) Ouvrard, C.; Berthelot, M.; Lamer, T.; Exner, O. J. Chem. Inf.
Comput. Sci. 2001, 41, 1141-1144.
entropy relative to molar concentrations, ∆H° and ∆S°,
c
are obtained from the slope and intercept ofc the ln Kc
versus 1/T van’t Hoff plot (eq 3) as ∆H° ) -32.0 ( 0.3
c
kJ mol-1 and ∆S° ) -65.6 ( 0.8 J K-1 mol-1 (the
c
(58) Graton, J.; Berthelot, M.; Gal, J. F.; Laurence, C.; Lebreton,
J.; Le Questel, J. Y.; Maria, P. C.; Robins, R. J. Org. Chem. 2003, 68,
8208-8221.
(59) Joesten, M. D.; Drago, R. S. J. Am. Chem. Soc. 1962, 84, 2037-
2039.
7894 J. Org. Chem., Vol. 70, No. 20, 2005

Enthalpic Scale of Hydrogen-Bond Basicity
TABLE 1. Determinations of the Enthalpy and Entropy of Hydrogen Bonding of N,N′-dimethylpiperazine to
a
4-fluorophenol in CCl4
temp (°C)
-4.6
3.09
9.6
3.04
24.9
2.98
39.4
2.93
54.1
2.88
Ca0
Cb0
10.38
10.21
10.02
9.85
9.67
absorbance A
ꢀ (L mol-1 cm-1
Ca ) A/ꢀl
Cc
0.137
257.3
0.53
0.220
248.4
0.88
0.318
238.9
1.33
0.392
0.446
)
229.8
220.6
1.70
1.23
8.61
2.02
0.86
8.81
2.56
2.16
1.66
Cb
7.82
616.3
8.05
302.6
8.37
Kc (L mol-1
)
148.7
83.6
∆S° ) -65.6 ( 0.8 J K-1 mol-1
48.2
thermodynamic parameters
∆H° ) -32.0 ( 0.3 kJ mol-1
;
c
c
a All concentrations in mmol L-1. Ca0 and C0b are the initial concentrations of the acid 4-fluorophenol and the base N,N′-
dimethylpiperazine, respectively. Ca, Cc, and Cb are the equilibrium concentration of the free 4-fluorophenol, the hydrogen-bonded
4-fluorophenol (complex) and the free base, respectively. The equilibrium constant Kc is given by Kc ) Cc/CaCb. The thermodynamic
parameters in the table are the mean of two determinations.
precision of the results is taken from the error limits of
the slope and intercept in the regression analysis of
squared correlation coefficient r2 ) 0.9995 for n ) 10
data, 2 determinations and 5 temperatures). The Gibbs
energy, relative to molar concentrations, is obtained from
eq 7:
and ∆G° gives the entropies to ( 10%, i.e., ( 6 J K-1
mol-1 for the mean value (57 J K-1 mol-1) of the studied
set.
Only one comparison can be made with literature
results. For hydrogen bonding of 4-fluorophenol to cyclo-
propylamine in CCl4, a calorimetric method gives20 ∆H°
) -31.4 ( 1.2 kJ mol-1. This value compares very well
with our value of -31.9 kJ mol-1 obtained by a van’t Hoff
∆Gc°,298 ) - 298.15R ln Kc(25 °C) ) -12.5 kJ mol-1
method with an estimated error of (0.9 kJ mol-1
.
(7)
Table 2 presents 81 values of Gibbs energies, ∆G′°
,
enthalpies, ∆H°, and entropies, ∆S′x°,298, for the hyxd,2r9o8-
gen bonding of 4-fluorophenol to 69 amines in CCl4 and/
or C2Cl4. Results of measurements in C2Cl4 are reported
in parentheses. Data are sorted in four subseries: am-
monia, primary, secondary and tertiary amines. Amines
in each subseries are arranged in order of decreasing
-∆H°.
It should be noted that this result can be controlled by
comparison with the value calculated from pKHB (log Kc),
obtained in our previous work60 as the average of five
determinations in which the amine concentration was
varied in order to complex various quantities of 4-fluo-
rophenol. From pKHB ) 2.1860 we obtain ∆G′°
)
- 298.15R ln 10 pKHB ) -12.4 kJ mol-1. The two cv,2a9l8ues
match perfectly. A more systematic comparison made on
a sample of 75 amines between ∆G′°, obtained in our
previous works60-62 from “the concentration variation
method”, and ∆G°, obtained in this work from the
“temperature variation method”, shows a strong correla-
tion (r ) 0.995) between the two sets. Moreover the
regression coefficient and the intercept of eq 8, not
significantly different from unity and zero, respectively,
confirm that the two sets of Gibbs energies match very
satisfactorily.
The enthalpies, entropies, and Gibbs energies of eqs 3
and 7 were first calculated on the molar concentration
scale, since the Kc unit is L mol-1. However Hepler64 has
shown that the ∆H° value relative to molarity is not the
c
correct “standard-state infinite dilution” ∆H°. The ther-
modynamically correct value must be calculated from Kx
relative to mole fraction, which is related to Kc by eq 9
Kx ) Kcnj
(9)
for dilute solutions. The number of moles of solvent per
liter, nj, are 10.3 for CCl4 and 9.74 for C2Cl4. ∆H° is then
∆G° ) 0.994(( 0.011) ∆G′°+ 0.18 (( 0.26)
related64 to ∆H° by eq 10, where R is the coefficient of
c
c
c
n ) 75, r ) 0.995, s ) 0.25 kJ mol-1
,
∆H° ) ∆H° - RRT2
(10)
c
Fisher test ) 7403 (8)
thermal expansion of the solvent. For CCl4 and C2Cl4 at
298 K the corrections amount to 0.9 and 0.8 kJ mol-1
respectively. Kx values lead to standard Gibbs energies
∆G° ) -RT ln Kx and entropies ∆S° ) (∆H° - ∆G°)/T
From concentration, absorbance, and temperature er-
rors, the maximum relative error in Kc is estimated63 to
be (8%, corresponding to a maximum error of (0.25 kJ
mol-1 in ∆G°. From slope errors and the repetition of
measurements we estimate63 the maximum error in ∆H°
to be (0.9 kJ mol-1. The propagation of errors in ∆H°
thaxt differ from ∆G° and ∆S° by -5.8 kJ mol-1 and
x
x
c
c
+16.4 J K-1 mol-1, respectively, in CCl4 at 298 K and by
-5.6 kJ mol-1 and + 16.4 J K-1 mol-1, respectively, in
C2Cl4 at 298 K.
(60) Graton, J.; Besseau, F.; Berthelot, M.; Raczynska, E. D.;
Laurence, C. Can. J. Chem. 2002, 80, 1375-1385.
(61) Graton, J.; Laurence, C.; Berthelot, M.; Le Questel, J.-Y.;
Besseau, F.; Raczynska, E. D. J. Chem. Soc., Perkin Trans. 2 1999,
997-1001.
(62) Graton, J.; Berthelot, M.; Laurence, C. J. Chem. Soc., Perkin
Trans. 2 2001, 2130-2135.
(63) Graton, J. Ph.D. Thesis, University of Nantes, 2001.
If one wants to compare ∆G° and ∆S° of diamines 17,
29, 41, 42, 54, and 56 and tetramine 68 to those of
monoamines, statistical corrections -RT ln n and -R ln
n (n being the number of equivalent nitrogen atoms) must
(64) Hepler, L. G. Thermochim. Acta 1981, 50, 69-72.
J. Org. Chem, Vol. 70, No. 20, 2005 7895

Graton et al.
TABLE 2. Thermodynamic Functions ∆G, ∆H (kJ mol-1), and ∆S (J K-1 mol-1) and IR Shifts ∆ν(OH) (cm-1) for
Hydrogen Bonding of Aliphatic Amines to 4-Fluorophenol in CCl4 and in C2Cl4; Belonging to the Isoentropic Set Is
Precised
-∆H°
CCl4 C2Cl4
-∆S°
-∆G°
x,298
∆ν(OH)a
isoentropic
set
x,298
CCl4
53.1
C2Cl4
CCl4
C2Cl4
CCl4
1
ammonia
31.49
15.65
276
yes
Primary Amines
35.10
2
3
methylamine
56.8
18.20
356
359
359
349
354
324
310
284
244
(yes)
yes
cyclohexylamine
t-butylamine
34.26
34.20
51.1
19.03
18.49
4
52.7
yes
5
ethylamine
33.84
31.06
51.0
49.2
18.63
16.38
yes
yes
yes (no)
yes
no (yes)
yes (yes)
6
n-butylamine
33.70
32.35
31.88
28.18
26.88
52.2
54.1
54.9
45.8
56.9
18.14
16.23
15.50
14.53
9.92
7
benzylamine
8
cyclopropylamine
propargylamine
2,2,2-trifluoroethylamine
9
30.63
26.10
53.1
53.9
14.77
10.00
10
Secondary Amines
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
2,2,6,6-tetramethylpiperidine
pyrrolidine
37.23
70.3
16.26
422
no
(yes)
yes (yes)
no
36.09
35.80
53.1
55.0
20.26
19.40
piperidine
34.80
35.97
35.74
35.67
35.63
35.56
35.38
35.21
51.7
62.9
57.7
51.0
55.8
59.3
56.2
55.7
19.38
17.21
18.53
20.48
18.99
17.87
18.62
18.60
404
396
398
402
407
401
395
402
diisopropylamine
diethylamine
azetidine
yes
yes
N,N′-dimethylethylenediamine
di-n-butylamine
N-methylbutylamine
N-methylcyclohexylamine
dimethylamine
N-methyltertiobutylamine
hexamethyleneimine
N-methylisopropylamine
N-methylphenetylamine
N-methylethylamine
N-methylallylamine
N-methylbenzylamine
piperazine
2-phenylpyrrolidine
tetrahydroisoquinoline
diallylamine
2-(3-fluorophenyl)-pyrrolidine
N-methylpropargylamine
2-(3-trifluoromethylphenyl)-pyrrolidine
dichloroethylamine
yes
yes
yes
yes
35.13
56.2
18.37
(yes)
yes
35.09
35.08
35.01
34.92
34.69
34.07
56.1
55.0
55.6
57.4
53.7
55.9
18.36
18.69
18.43
17.82
18.67
17.41
406
400
395
394
394
374
yes
yes
yes
yes
yes
33.54
35.03
58.4
55.9
16.12
18.38
(yes)
yes (yes)
yes
33.32
33.27
52.0
55.2
17.82
16.82
386
381
33.10
52.2
17.54
(yes)
yes
yes
yes (no)
yes
yes
32.80
31.09
31.01
30.47
30.23
58.3
53.1
53.0
56.2
59.0
15.42
15.26
15.21
13.72
12.65
356
361
336
348
330
29.90
49.0
15.30
Tertiary Amines
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
triethylamine
39.35
38.40
37.68
35.66
39.01
38.06
35.49
34.79
76.4
73.9
55.4
60.6
54.8
16.57
14.41
21.05
19.18
17.00
21.53
17.43
18.46
429
430
444
446
no (no)
no
yes (yes)
yes
no
yes
tri-n-butylamine
80.5
55.8
55.3
quinuclidine
tropane
N,N,N′,N′-tetramethylethylenediamine
N,N,N′,N′-tetramethylhexane-1,6-diamine
N-methylpyrrolidine
N,N-dimethylcyclohexylamine
N,N-dimethylisopropylamine
N-butylpyrrolidine
N,N-dimethylethylamine
3-chloroquinuclidine
N-methylpiperidine
35.15
59.0
17.57
415
(yes)
yes
34.75
34.67
34.53
34.47
34.11
34.04
34.03
33.89
33.60
33.48
33.20
33.13
32.93
32.87
32.84
32.79
32.58
32.45
32.18
31.01
30.83
29.27
56.1
55.9
57.3
54.6
57.6
54.4
70.8
74.0
71.4
52.4
47.9
61.4
55.1
57.2
53.8
64.0
65.0
59.8
56.1
63.8
49.7
48.7
18.03
18.00
17.43
18.19
16.94
17.81
12.91
11.81
12.31
17.84
18.92
14.83
16.52
15.82
16.81
13.70
13.19
14.61
15.47
12.01
16.01
14.75
433
425
426
418
394
421
419
414
419
409
417
387
402
401
399
386
375
397
400
372
383
367
yes
yes
yes
yes
yes
1,2,2,6,6-pentamethylpiperidine
N,N-diisopropylethylamine
N-ethyldicyclohexylamine
trimethylamine
no
no
no
yes
diazabicyclooctane
35.12
31.33
52.4
55.3
19.49
14.84
no (yes)
no (yes)
yes
N,N-dimethylbenzylamine
N,N′ dimethylpiperazine
3-chloromethyl-1-methylpiperidine
N,N-dimethylallylamine
N-methyl-2-phenylpyrrolidine
triallylamine
yes
yes
no
no
N,N-dimethylamino-propyl chloride
4-chloro-N-methylpiperidine
N-methyl-2-(3-fluorophenyl)-pyrrolidine
N-methyl-1,2,3,4-tetrahydro-isoquinoline
N,N-dimethylpropargylamine
no
yes
no
no
30.29
51.4
14.97
no (yes)
7896 J. Org. Chem., Vol. 70, No. 20, 2005

Enthalpic Scale of Hydrogen-Bond Basicity
Table 2. (Continued)
-∆H°
CCl4 C2Cl4
Tertiary Amines (Continued)
-∆S°
-∆G°
x,298
∆ν(OH)a
isoentropic
set
x,298
CCl4
C2Cl4
CCl4
C2Cl4
CCl4
66
67
68
69
N-methyl-2-(3-trifluoromethylphenyl)-pyrrolidine
N,N-diisopropylisobutylamine
29.26
27.15
26.15
23.83
60.6
65.8
43.2
67.1
11.18
7.51
13.25
3.82
368
392
335
no
no
no (no)
no
hexamethylenetetramine
28.03
48.7
13.50
N,N-diisopropyl-3-pentylamine
a IR shifts from this work for NH3 and primary amines, ref 62 for secondary amines, and ref 60 for tertiary amines.
TABLE 3. Change in Electronic Energy (kJ mol-1) upon
Hydrogen Bonding of Water to Amines in Vacuo: H2O +
NRR′R′′ h HOH‚‚‚NRR′R′′
be applied to the Gibbs energy and the entropy respec-
tively, to put these thermodynamic functions on a per
nitrogen basis.
a
no.
amine
-∆Eel
Determination of OH Frequency Shift. The OH
stretching band of methanol at 3644 cm-1 is shifted to
lower wavenumbers upon hydrogen bonding to amines
in CCl4. The IR shifts, ∆ν(OH), are given in Table 2. More
reliable shifts are obtained with methanol as standard
hydrogen-bond donor than with 4-fluorophenol.60 Values
of secondary and tertiary amines are those measured in
previous works.60,62 Values of NH3 and primary amines
have been measured for this work.
10
8
trifluoroethylamine
cyclopropylamine
propargylamine
trimethylamine
ammonia
23.03
26.44
26.45
26.93
27.39
28.51
28.90
27.64
28.56
29.43
29.69
9
53
1
21
2
40
13
11
39
dimethylamine
methylamine
tropane
piperidine
pyrrolidine
quinuclidine
a Corrected for BSSE.
Discussion
demanding amines spanning a (rather) wide enthalpic
range of 11 kJ mol-1. The results of our B3LYP/6-311+G-
(d,p)//B3LYP/6-311+G(d,p) calculations are presented in
Table 3.
Quantum-Mechanical Prediction of Hydrogen
Bonding Enthalpies. The case of amines with a second
hydrogen-bond acceptor site X is very common in chem-
istry and biochemistry. These amines form two different
1:1 complexes with equilibrium constants K(N) and K(X)
(insofar as an amine excess prevents the formation of a
2:1 complex). The experimental method gives the equi-
librium concentration of hydrogen-bonded 4-fluorophenol,
i.e., the sum of the concentration of the two 1:1 com-
plexes. Therefore, the measured equilibrium constant is
the sum of the individual constants, K(N) + K(X). As the
derivative with respect to temperature, d{ln[K(N) +
K(X)]}/dT, has no thermodynamic meaning, we cannot
determine experimentally the individual enthalpies,
∆H(N) and ∆H(X). Theoretically, a reliable absolute
calculation of the hydrogen-bond enthalpy of 4-fluorophe-
nol with a large and flexible molecule, in CCl4 at 298 K,
would be a very costly and time-consuming process.65 We
therefore sought an alternative method to predict ∆H(N)
values using the techniques of quantum chemistry, with
the ultimate aim of estimating ∆H(N) for any molecule
purely from its structure.
We find a good correlation (eq 11) between ∆H°298 and
- ∆H2°98 (4-FC6H4OH, amines, CCl4) )
1.54[-∆Eel (H2O, amines,in vacuo)] - 8.97
n ) 11, r ) 0.941, s ) 1.09 kJ mol-1, F ) 70 (11)
∆Eel since 92% (squared r) of the variance of ∆H° is
298
explained by ∆Eel. The greater than unity slope can be
explained by the greater hydrogen-bond donor strength
of 4-fluorophenol compared to that of water,35 while the
nonzero intercept comes from the neglect of nuclear
motions and solvation.
We may wonder if the agreement would be improved
by taking account of solvation effects. However, the
disregard of solvation effects has already been justified
since (i) PCM (polarizable continuum model) calculations
(65) We have tried an absolute calculation in vacuo of the enthalpy
of the 4-fluorophenol-cyclopropylamine complex. The CPU time on
Opteron 2.4 GHz or Pentium 2.2 GHz processors is the following:
B3LYP/6-31+G(d,p) geometry optimization of monomers and four
putative dimers, ca. 100 h; B3LYP/6-31+G(d,p) frequency calculations,
ca. 12 h; MP2/6-311+G(3df,2p) electronic energy calculations of
monomers and the most stable dimer, ca. 9 h; BSSE calculation, ca.
18 h. The MP2/6-311+G(3df,2p)//B3LYP/6-31+G(d,p) result is ∆H° )
-36.32 kJ mol-1. This compares well with the experimental value of
-31.88 kJ mol-1, if one attributes the difference of 4.44 kJ mol-1 to
the solvation enthalpy (for comparison the experimental CCl4 solvation
In their theoretical study of hydrogen-bonded com-
plexes of small organic molecules with water, Rablen et
al.54 found that their in vacuo calculated hydrogen bond
energies were satisfactorily correlated with the experi-
mental CCl4 solution hydrogen-bond basicity parameter
H 35
â2
.
This parameter is a linear transformation of the
Gibbs energy of 4-fluorophenol hydrogen-bonded com-
plexes.35 We therefore investigated if a relationship might
be found between (i) the experimental enthalpies of
4-fluorophenol-amine complexes in CCl4 and (ii) the
calculated electronic energy change (corrected for BSSE)
for the hydrogen bonding of water with amines in vacuo.
For doing this, we have selected 11 low-computationally
enthalpy of the methanol-triethylamine complex is +6.7 kJ mol-1
:
Hirano, E.; Kojima, K. Bull. Chem. Soc. Jpn. 1966, 39, 1216-1220).
Thus, a CPU time of ca. 6 days is required to reach a chemically
significant result in vacuo for a small complex (12 heavy atoms).
Therefore, a reliable absolute calculation on a significant sample of
larger and more flexible amines in the presence of solvent seems
unlikely to be achieved today in our laboratory. Consequently, we have
turned to the calculation of a simple quantum-mechanical descriptor
of enthalpy (vide infra).
J. Org. Chem, Vol. 70, No. 20, 2005 7897

Graton et al.
do not improve the agreement between the hydrogen-
bond energies of 4-fluorophenol complexes in CCl4 solu-
tion and HF complexes in vacuo,66 and (ii) it was observed
that the relative strength of hydrogen-bond acceptors
does not change on going from the gas phase to a
nonpolar solution.54,67,68
The enthalpy of hydrogen bonding of 4-fluorophenol to
amines in CCl4 can then be estimated, through eq 11,
from the change in the electronic energy of the reaction
H2O + NRR′R′′ h HOH‚‚‚NRR′R′′, calculated in vacuo.
Let us illustrate the method in the case of N-methylmor-
pholine 71. N-Methylmorpholine forms simultaneously
two 1:1 complexes, OH‚‚‚O 71a and OH‚‚‚N 71b, with
FIGURE 2. ∆H° versus ∆ν(OH) plot for the hydrogen bonding
of OH donors with (O) nitriles (DMAA is trans-dimethylami-
noacrylonitrile), (]) pyridines (Cl2pyr and Me2pyr are 3,5-
dichloro- and 3,5-dimethylpyridines respectively), ([) ammo-
nia, (b) secondary amine 33, and (9) tertiary amine 62. Data
are from Table 2, ref 54, and unpublished works.
If one tries to define a family as a series of compounds
with a common hydrogen-bond acceptor atomic site, e.g.,
the nitrogen atom of nitriles, pyridines, and amines, one
observes in Figure 2 that nitriles and pyridines draw two
different lines. In fact trans-dimethylaminoacrylonitrile
and 3,5-dichloropyridine have nearly the same enthalpy
(dashed line a in Figure 2), but the frequency shift is
55% higher in the pyridine. Also NH3, 3,5-dimethylpy-
ridine, a secondary amine 33, and a tertiary amine 62
have very close enthalpies (dashed line b in Figure 2)
but quite different frequency shifts.
If we limit a family to those hydrogen-bond acceptors
with a common atomic site in the same hybridization
state, this definition holds for nitriles (sp nitrogen) and
pyridines (sp2 nitrogen) as shown in Figure 2 but not for
amines (sp3 nitrogen). For 80 amines the correlation
coefficient is only 0.745, i.e., only 55% of the variance of
∆H° is explained by ∆ν(OH).
OH donors, and there is no simple experimental method
for measuring the hydrogen-bond enthalpy of each site
(vide supra). The calculation of ∆Eel corresponding to the
formation of 71b (R ) H) makes it possible to estimate
∆H° for the formation of 71b (R ) C6H4F). We find ∆Eel
) -25.14 kJ mol-1 and, from eq 11, ∆H° ) -30.2 kJ
mol-1. This estimated value agrees well with the experi-
mental values of N,N′-dimethylpiperazine and N-meth-
ylpiperidine: the basicity (minus the enthalpy) decreases
when the electronegativity of the γ ring atom increases
from carbon to nitrogen to oxygen:
Prediction of Hydrogen Bonding Enthalpies from
OH IR Shifts. Since the Badger and Bauer observation6,7
that the change in OH stretching frequency correlates
with self-association energies of alcohols or energies of
intramolecular hydrogen bonds, there has been a con-
tinuing controversy5,8-27 concerning how well the spectral
change reflects the interaction magnitude. Actually, there
is a tremendous advantage to be gained if reliable
spectroscopic indications of the strength of interaction
can be found. Instead of the day(s) required for a van’t
Hoff measurement, the answer could be found in the time
required to run a spectrum. Moreover many systems that
do not possess the physical properties needed for a van’t
Hoff study could be investigated this way. Such is the
very common case of hydrogen-bond acceptors with
several sites (vide supra).
A careful analysis of amines shows that primary,
secondary, and tertiary amines draw three different lines
in the Badger-Bauer graph as shown by eqs 12-14
-∆H°(NH2R) ) 6.8((0.5)[∆ν(OH)/100] + 10((2)
n ) 12; r ) 0.970; s ) 0.77 kJ mol-1; F ) 158 (12)
-∆H°(NHRR′) ) 7.6 ((0.5)[∆ν(OH)/100] + 5((2)
n ) 29; r ) 0.944; s ) 0.65 kJ mol-1; F ) 223 (13)
-∆H°(NRR′R′′) ) 9.5((0.9)[∆ν(OH)/100] - 5((4)
n ) 38; r ) 0.859; s ) 1.6 kJ mol-1; F ) 102 (14)
It seems now accepted5,11,12,36,37 that the validity of the
relationship between ∆H° and ∆ν(OH) is limited to series
of similar donor groups hydrogen-bonded to bases with
common acceptor atoms, i.e., the Badger-Bauer relation-
ship is family-dependent. But how must a family be
exactly defined in the Badger-Bauer context?
and Figure 3 (for the sake of clarity secondary amines
are not shown). Ammonia does not obey the eq 12 of
primary amines (standing 3 kJ mol-1 above the line) and
constitutes a family per se. For primary and secondary
amines the quality of correlations 12 and 13 is enough
to make a good estimation of ∆H°, since the standard
errors of the estimate, 0.67 and 0.64 kJ mol-1, are within
the experimental error (0.9 kJ mol-1). Such is not the
case of tertiary amines for which s reaches almost twice
the experimental error. We find the greatest deviation
for the severely hindered tertiary amine i-BuN-i-Pr2 67,
(66) Lamarche, O.; Platts, J. A. Chem. Eur. J. 2002, 8, 457-466.
(67) Le Questel, J.-Y.; Berthelot, M.; Laurence, C. J. Phys. Org.
Chem. 2000, 13, 347-358.
(68) Marco, J.; Orza, J. M.; Notario, R.; Abboud, J.-L. M. J. Am.
Chem. Soc. 1994, 116, 8841-8842.
7898 J. Org. Chem., Vol. 70, No. 20, 2005

Enthalpic Scale of Hydrogen-Bond Basicity
FIGURE 3. ∆H° versus ∆ν(OH) plot for the hydrogen bonding
of OH donors with ([) ammonia, (2) primary amines, and (9)
tertiary amines. Hindered tertiary amines are located below
(67), on (50-52) or above (38) the regression line.
FIGURE 4. T∆S° versus ∆H° plot; h and s are the range of
∆H° and T∆S° values, respectively.
value of -∆H implies stronger bonding, with a more
restricted configuration in the complex, hence a greater
order, leading to a larger value of -∆S”) is not valid. Also,
the reaction is clearly neither isoenthalpic nor isoentropic
since the ranges h and s of enthalpy and entropy
variation (Figure 4) amount, respectively, to ca. 20 and
5 times the experimental errors in ∆H° and ∆S°. If we
refer to the lead compound NH3 1, alkylation increases
-∆H° by 7.9 kJ mol-1 in the case of three ethyl substit-
uents on nitrogen (Et3N 37) and decreases -∆H° by 7.7
kJ mol-1 in the case of two isopropyl and a 3-pentyl
substituents (i-Pr2NCHEt2 69). This double mechanism
of alkyl substituents has been carefully studied in our
previous work37,60,62 and explained by the polarizability
effect (basicity-enhancing) and the steric effect (basicity-
decreasing). The balance of these effects gives to Et3N,
an archetype amine, the strongest enthalpy of our set.
The enthalpy-entropy relationship is better under-
stood if we split the sample of 69 amines into three sets.
The first set is an isoentropic one. It is constructed
starting from the lead compound, NH3, which has ∆S° )
-53.1 J K-1 mol-1. There are 42 amines having entropies
equal to that of NH3 plus or minus an arbitrary starting
range of 3 J K-1 mol-1, i.e., between -50.1 and -56.1 J
K-1 mol-1. With the help of the IKR program and the
included statistical tests,56,57 we can enlarge this iso-
entropic set step by step toward higher and lower
entropies. At the 95% confidence level we find that 53
amines form an isoentropic set with a mean value of
-55.1 J K-1 mol-1 and a tolerance supported by statistics
of ca. (4.2 J K-1 mol-1, not so far from the experimental
error. The belonging or not of each of 69 amines to the
isoentropic set is given in Table 2. It is seen that the so-
defined isoentropic set includes ammonia, 9 primary
amines (75%), and 25 secondary amines (86%) but only
19 tertiary amines (50%).
which stands 4.5 kJ mol-1 below the line of eq 14.
However, the influence of steric effects on the validity of
the Badger-Bauer relationship does not appear clear-
cut since, among the tertiary amines designed as hin-
dered in our previous work,60 some are found above (n-
Bu3N 38), on (EtN-i-Pr2 51, EtN-c-Hex2 52 and 2,2,6,6-
tetramethylpiperidine 50), or below (i-BuN-i-Pr2 67) the
regression line. A better criterion appears to be a certain
rigidity of the molecule since all bicyclic and most cyclic
tertiary amines satisfactorily obey eq 14 (mean absolute
deviation ) 0.7 kJ mol-1).
In summary, a necessary condition of validity of the
Badger-Bauer relationships is the existence of a common
atomic site in a common state of hybridization. This
condition is not sufficient for sp3 hybridized nitrogen
bases, for which ammonia and primary, secondary, and
tertiary amines form four distinct families. Some rigidity
of the molecular skeleton around nitrogen appears to be
a last criterion in order that tertiary amines follow the
Badger-Bauer relationship.
The usefulness of the Badger-Bauer relationship can
be illustrated by the example of morpholine, a secondary
amine for which no enthalpy can be measured owing to
the presence of oxygen, a second hydrogen-bond acceptor
site. From the ν(OH‚‚‚N) band in the IR spectrum of the
complex with methanol, we get ∆ν(OH) ) 360 cm-1 and,
from eq 13, ∆H° ) -32.0 kJ mol-1, a value that agrees
with those of piperazine and piperidine (vide supra):
Relation between ∆H° and ∆S°. The ∆H° and ∆S°
of Table 2 have been calculated from a set of 688
equilibrium constants Kc. The statistical analysis, with
the IKR program,56,57 of the relationship between ∆H°
and ∆S° in the (ln Kc, T -1) coordinates shows, for all
688 data points, that the hydrogen bonding of 4-fluo-
rophenol to amines in CCl4 (C2Cl4) (i) is not isoenthalpic,
(ii) is not isoentropic, and (iii) does not follow a compen-
sation law (eq 2).
These statistical conclusions are trivial since they can
be deduced from a direct examination of a plot of -∆H°
versus -T∆S°. It is seen in Figure 4 that the compensa-
tion law suggested by Pimentel and McClellan (“a higher
The second set contains 17 amines excluded from the
isoentropic set because of a too-high entropy value. It
consists mainly of tertiary amines such as n-Bu3N 38,
1,2,2,6,6-pentamethylpiperidine 50, i-Pr2NEt 51, c-Hex2-
NEt 52, i-Pr2N-i-Bu 67, and i-Pr2NCH(Et)2 69 and of a
few secondary amines such as 2,2,6,6-tetramethylpiperi-
dine 11 and i-Pr2NH 14. In these amines the nitrogen is
hindered by long and/or branched alkyl chains. Clearly
the increase of entropy beyond the mean isoentropic
value is caused by the steric effect of alkyl groups. The
restricted access of the OH group to the nitrogen lone
J. Org. Chem, Vol. 70, No. 20, 2005 7899

Graton et al.
pair leads to a greater order of the complex and to a
larger value of the entropy.
The third set corresponds to nine amines having a too-
low entropy value compared to the mean isoentropic
value. No clear structural reasons are found to explain
these weak values. We only remark that most of these
amines show significant differences between CCl4 and C2-
Cl4. Six of these nine amines have been studied in both
solvents, and only one, hexamethylenetetramine 68,
keeps both entropy values too weak to join the isoentropic
set.
Hydrogen Bond Enthalpies as Lewis Basicity
Parameters. It is well-known that the electronic Lewis
definition of bases as electron pair acceptors is more
general than the protonic Bro¨nsted definition.28 In return
it becomes more difficult to achieve the building of a
quantitative scale of Lewis basicity that would be as
general as the GB69 or pKa70 scales of proton basicity. This
comes from the fact that, in the Lewis definition, there
is no Lewis acid that can be naturally chosen and
exploited as a reference, in the same manner as the
proton. In fact, there are so many kinds of chemical bonds
(e.g., dative bond a,71 hydrogen bond b,1 halogen bond
c,72 or back-bonding d71) that can be formed during the
FIGURE 5. Plot of the enthalpy of hydrogen bonding of
4-fluorophenol with Lewis bases, ∆H° (4-FC6H4OH), versus the
enthalpy of complexation of diiodine, ∆H° (I2), to the same
bases. The two enthalpic scales appear quasi-orthogonal (n )
62, r2 ) 0.32).
which the electron acceptor and donor are the hydrogen-
bond donor and acceptor, respectively. This raises the
question whether the hydrogen-bond enthalpies can be
useful as a Lewis basicity parameter.
In the language of frontier molecular orbitals, we need
to find a charge-controlled76 and a frontier-controlled76
term (or electrostatic and covalent terms in the language
of other models30,73) in order to quantify the strength of
intermolecular bonds. Since the hydrogen bond is mainly
electrostatic in character,3 the charge-controlled (elec-
trostatic) term might be furnished by the hydrogen-bond
enthalpy of the kind measured in this work. An experi-
mental substitute for the frontier-controlled (covalent)
term is more difficult to find. We have previously shown78
that the enthalpy of diiodine complexation (reaction c)
measures a kind of basicity quite different from the
hydrogen-bond basicity. There is indeed a greater amount
of charge transferred from the base to dihalogens than
to hydrogen-bond donors.79
The two enthalpic scales, ∆H° (I2 complexation) and
∆H° (4-FC6H4OH complexation) are under construction
in our laboratory. Here, we want only to show that the
two scales encode quite different information on the
strength of bases. We have selected 62 bases for which
both enthalpies of complexation are available (this and
previous works).37,78,80 This selection covers a wide range
of enthalpies both for diiodine (45.9 kJ mol-1 from
benzene to n-Bu3N) and 4-fluorophenol (33.3 kJ mol-1
from thiophene to Et3N). There is also a great variety of
complexation sites (π, O, CO, PO, SO, NO, Nsp, Nsp2,
Nsp3, S, CS, PS, and PSe). We find that the correlation
coefficient between ∆H° (I2 complexation) and ∆H° (4-
FC6H4OH complexation) is only 0.569, i.e., only 32% of
the variance of one scale is explained by the other (Figure
5).
creation of a Lewis acid-base complex, that attempts to
31
choose one reference Lewis acid, such as SbCl529 or BF3
in order to construct a quantitative scale of Lewis basicity
have given scales of limited validity only. Further work
has shown that at least two parameters are necessary73
for measuring the strength of Lewis bases and various
double parameter empirical scales have been pro-
posed.30,73,74 Valence-bond,75 molecular orbital,76 and
density functional theories77 have supported the quan-
tification of Lewis base strength from two theoretical
descriptors.75-77
Among reactions a-d, the interaction b between the
hydrogen-bond acceptor NH3 and the hydrogen-bond
donor 4-fluorophenol points hydrogen-bond donors XH to
a particular class of Lewis acids. In a hydrogen bond
there is a (small) charge transfer from the base to the
antibonding σ*(XH) orbital,3 so the formation of a hy-
drogen bond constitutes a Lewis acid-base reaction in
(69) Hunter, E. P. L.; Lias, S. G. J. Phys. Chem. Ref. Data 1998,
27, 413-656.
(70) Perrin, D. D. Dissociation Constants of Organic Bases in
Aqueous Solution. (Pure and Applied Chemistry); Butterworth: Lon-
don, 1965.
(71) Murrell, J. N.; Kettle, S. F. A.; Tedder, J. M. The Chemical
Bond; Wiley: New York, 1978.
(72) Ouvrard, C.; Le Questel, J. Y.; Berthelot, M.; Laurence, C. Acta
Crystallogr., Sect. B 2003, 59, 512-526.
(73) Maria, P. C.; Gal, J. F.; De Franceschi, J.; Fargin, E. J. Am.
Chem. Soc. 1987, 109, 483-492.
(74) Kamlet, M. J.; Gal, J. F.; Maria, P. C.; Taft, R. W. J. Chem.
Soc., Perkin Trans. 2 1985, 1583-1589.
(78) Laurence, C.; Queignec-Cabanetos, M.; Dziembowska, T.;
Queignec, R.; Wojtkowiak, B. J. Am. Chem. Soc. 1981, 103, 2567-
2573.
(79) Alkorta, I.; Rozas, I.; Elguero, J. J. Phys. Chem. A 1998, 102,
9278-9285.
(80) El Ghomari, M. J. Ph.D. Thesis, University of Nantes, 1996.
(75) Mulliken, R. S.; Person, W. B. Molecular Complexes; Wiley:
New York, 1969.
(76) Klopman, G. J. Am. Chem. Soc. 1968, 90, 223-234.
(77) Pearson, R. G. J. Am. Chem. Soc. 1985, 107, 6801-6806.
7900 J. Org. Chem., Vol. 70, No. 20, 2005

Enthalpic Scale of Hydrogen-Bond Basicity
In summary, the enthalpic scale of hydrogen-bond
basicity will be useful for the measurement of the
electrostatic character of Lewis acid-base reactions.
Further experimental work is in progress in our labora-
tory for extending this scale to a large variety of Lewis
bases.
studied, because these reactions show an isoentropic
tendency. Amines excluded from the isoentropic set are,
mainly, severely sterically hindered ones. The separation
of enthalpy and entropy is thus useful for fully under-
standing the hydrogen-bond acceptor strength of amines.
Hydrogen-bond enthalpies are quasi-orthogonal to
diiodine complexation enthalpies. This supports the
different electrostatic/covalent characters of diiodine and
hydrogen-bond donors. The enthalpic scale of hydrogen-
bond basicity might be useful for the measurement of the
electrostatic character of Lewis acid-base reactions.
Conclusions
We have constructed an extensive and reliable scale
of hydrogen-bond enthalpies for ammonia, primary,
secondary, and tertiary amines. This scale is useful per
se since hydrogen bonding interactions constitute an
important class of acid-base reactions and the most
characteristic chemical property of amines is their ability
to act as bases.81
Hydrogen-bond enthalpies are correlated to electronic
interaction energies and, through family-dependent re-
lationships, to infrared frequency shifts. These correla-
tions are useful for extending our primary enthalpic scale
to amines bearing more than one hydrogen-bond acceptor
site. This situation is frequently encountered in chem-
istry, biochemistry, and pharmaceutical chemistry since
the amine function is widely present in the structure of
neurotransmitters, drugs, medicines, and alkaloids. We
have recently shown58 that the determination of the
hydrogen bond affinity of each site of the alkaloids
nicotine and nornicotine is useful for understanding their
lipophilicity and molecular recognition and the thermo-
dynamics of the nicotinic pharmacophore.
Experimental Section
Chemicals. Solvents (CCl4 and/or C2Cl4), amines, 4-fluo-
rophenol, and methanol were carefully purified and dried
according to procedures published elsewhere.58,60-62
Spectra. Infrared (IR) absorbances of the stretching OH
band of 4-fluorophenol in CCl4 (3614 cm-1, absorption coef-
ficient ꢀ ) 238 L mol-1 cm-1 at 25 °C) and/or C2Cl4 (3612 cm-1
,
ꢀ ) 234 L mol-1 cm-1 at 25 °C) and IR shifts of the stretching
OH band of methanol (3644 cm-1 in CCl4) have been measured
as described elsewhere.58,60,62 IR shifts ∆ν(OH) are generally
known to (5 cm-1, but the accidental presence of the base
elongation bands, such as the νas(NH2), νs(NH2), ν(NH), or ν-
(≡CH) bands, near the maximum of the broad ν(OH‚‚‚N) band
cause larger errors.
A Peltier thermoelectric device regulates the 1 cm path
length cell temperature to (0.2 °C from -5 to +55 °C in CCl4
(-5 to +70 °C in C2Cl4). The effective temperature is measured
inside the cell with a calibrated thermocouple.
Supporting Information Available: Z-matrix coordi-
nates and B3LYP/6-311+G(d,p) electronic energies of B3LYP/
6-311+G(d,p) optimized structures of 12 hydrogen-bonded
complexes and their monomers. This material is available free
of charge via the Internet at http://pubs.acs.org.
Enthalpies and Gibbs energies give the same order of
hydrogen-bond basicity of amines for 65% of the reactions
(81) Roberts, J. D.; Caserio, M. C. Basic Principles of Organic
Chemistry; W. A. Benjamin, Inc.: New York, 1964; Chapter 19.
JO050535G
J. Org. Chem, Vol. 70, No. 20, 2005 7901