Enthalpies of formation of N-substituted pyrazoles and imidazoles

Article abstract of DOI:10.1021/jp992244f

Accurate experimental enthalpies of formation measured using static bomb combustion calorimetry, the "vacuum sublimation" drop calorimetry method, and the Knudsen-effusion method are reported for the first time for four azoles: 1-methylimidazole (1MeIMI), 1-methylpyrazole (1MePYR), 1-benzylimidazole (1BnIMI), and 1-benzylpyrazole (1BnPYR). These values and those corresponding to imidazole (1HIMI), pyrazole (1HPYR), 1-ethylimidazole (1EtIMI), 1-ethylpyrazole (1EtPYR), 1-phenylimidazole (1PhIMI), and 1-phenylpyrazole (1PhPYR) are compared with theoretical values using the G2(MP2) and the B3LYP/6-311*G(3df,2p)//6-31G(d) approaches. In general, there is a very good agreement between calculated and experimental values for the series of N-substituted imidazoles, while the agreement is less good for the series of the N-substituted pyrazoles. Experimentally, the gap between the enthalpies of formation of imidazoles and pyrazoles decreases significantly upon N-substitution, while the theoretical estimates indicate that this decrease is smaller.

Full text of DOI:10.1021/jp992244f

9336
J. Phys. Chem. A 1999, 103, 9336-9344
Enthalpies of Formation of N-Substituted Pyrazoles and Imidazoles
Otilia M o´ * and Manuel Y a´ n˜ ez
Departamento de Qu ´ı mica, C-9, UniVersidad Aut o´ noma de Madrid, Cantoblanco, E-28049 Madrid, Spain
Mar ´ı a Victoria Roux,* Pilar Jim e´ nez, and Juan Z. D a´ valos
Instituto de Qu ´ı mica F ´ı sica “Rocasolano”, C.S.I.C., Serrano, 119, E-28006 Madrid, Spain
Manuel A. V. Ribeiro da Silva,* Maria das Dores M. C. Ribeiro da Silva,
M. Agostinha R. Matos, and Luisa M. P. F. Amaral
Centro de InVestiga c¸ ao em Qu ´ı mica, Department of Chemistry, Faculty of Science, UniVersity of Porto,
Rua do Campo Alegre, 687, P-4169-007 Porto, Portugal
Ana S a´ nchez-Migall o´ n
Facultad de Qu ´ı mica, UniVersidad de Castilla-La Mancha, E-13071 Ciudad Real, Spain
Pilar Cabildo and Rosa Claramunt
Departamento de Qu ´ı mica Org a´ nica y Biolog ´ı a, Facultad de Ciencias, UNED, Senda del Rey, s/n,
E-28040 Madrid, Spain
Jos e´ Elguero
Instituto de Qu ´ı mica M e´ dica, C.S.I.C., Juan de la CierVa, 3, E-28006 Madrid, Spain
Joel F. Liebman
Department of Chemistry and Biochemistry, UniVersity of Maryland, Baltimore County,
Baltimore, Maryland 21250
ReceiVed: June 30, 1999; In Final Form: September 13, 1999
Accurate experimental enthalpies of formation measured using static bomb combustion calorimetry, the
“
vacuum sublimation” drop calorimetry method, and the Knudsen-effusion method are reported for the first
time for four azoles: 1-methylimidazole (1MeIMI), 1-methylpyrazole (1MePYR), 1-benzylimidazole
1BnIMI), and 1-benzylpyrazole (1BnPYR). These values and those corresponding to imidazole (1HIMI),
(
pyrazole (1HPYR), 1-ethylimidazole (1EtIMI), 1-ethylpyrazole (1EtPYR), 1-phenylimidazole (1PhIMI),
and 1-phenylpyrazole (1PhPYR) are compared with theoretical values using the G2(MP2) and the B3LYP/
6-311*G(3df,2p)//6-31G(d) approaches. In general, there is a very good agreement between calculated and
experimental values for the series of N-substituted imidazoles, while the agreement is less good for the series
of the N-substituted pyrazoles. Experimentally, the gap between the enthalpies of formation of imidazoles
and pyrazoles decreases significantly upon N-substitution, while the theoretical estimates indicate that this
decrease is smaller.
Introduction
The purpose of this work is to study the substituent effects
through the nitrogen atom in diazoles (imidazoles and pyrazoles)
comparatively to the effect of the same substituents through
the carbon atom in benzenes. If benzenes 1 are the paradigm of
an aromatic molecules, azoles are the simplest representatives
of stable aromatic structures bearing N-substituents. Pyrroles
being rather unstable compounds, N-substituted imidazoles 2
and pyrazoles 3 were selected.
of formation. The five R groups are H, CH3 (Me, methyl), C2H5
Et, ethyl), CH2C6H5 (Bn, benzyl), and C6H5 (Ph, phenyl). They
(
The selected approach is a combination of experimental
determinations and high-level ab initio calculations of enthalpies
correspond to the more important classes of substituents:
aliphatic (methyl and ethyl), benzylic, and aromatic.
1
0.1021/jp992244f CCC: $18.00 © 1999 American Chemical Society
Published on Web 11/03/1999

Enthalpies of Formation of Pyrazoles and Imidazoles
J. Phys. Chem. A, Vol. 103, No. 46, 1999 9337
Experimental Section
standard deviation of the mean. 1BnIMI is a hygroscopic solid,
and frequent NMR analyses were made in order to confirm the
sample did not contain water.
The heats of formation of the N-unsubstituted pairs (1HIMI
and 1HPYR) were already known when we started this study.
Those of the N-ethyl pairs (1EtIMI and 1EtPYR) and N-phenyl
1
Calorimetry. The combustion experiments were performed
with two static bomb calorimeters I and II from Porto and
Madrid, respectively. The apparatus and procedure have been
2
pairs (1PhIMI and 1PhPYR) have been published or are in
3
press. The results concerning the remaining four compounds
8
described. Benzoic acid (Bureau of Analysed Samples, Ther-
are described below.
mochemical Standard, BCS-CRM-190 p and BCS-CRM-190
c) were used for calibration of calorimeter I. Their specific
Synthesis and Purity Control. N-Methylimidazole (1MeI-
MI) is a commercial product (Aldrich 33,609-2, purity > 99%,
water < 0.03%). It was redistilled twice over freshly prepared
sodium wire (in the following procedures, sodium always means
freshly prepared sodium wire) in an argon atmosphere (bp )
-1
energies of combustion are (26431.8 ( 3.7) J g and (26432.3
-
1
(
3.8) J g , respectively, under certificate conditions. The
calibration results were corrected to give the energy equivalent
(calor) corresponding to the average mass of water added to
the calorimeter, 3119.6 g. From eight calibration experiments,
ꢀ
471 K/760 mmHg). N-Methylpyrazole (1MePYR) was prepared
using two different procedures. The first one proceeds by mixing
pyrazole (20.4 g, 0.30 mol) and methyl iodide (20.6 g, 0.15
mol). The mixture was stirred at 323 K during 2 h. After that,
to purify the residue was distillated twice using a B u¨ chi Glass
Oven model B-580 (390-400 K/760 mmHg) giving a final yield
of 80% of a colorless product with boiling temperature bp )
-
1
ꢀ
(calor) ) (15911.2 ( 1.5) J K was used for 1-methylimid-
azole and also from eight calibration experiments ꢀ(calor) )
-
1
(
1
15908.3 ( 1.0) J K was used for 1-methylpyrazole and
-benzylpyrazole where the uncertainties quoted are the standard
deviations of the means. For all experiments, ignition was made
at T ) (298.150 ( 0.001) K. Combustion experiments were
3
97 K/760 mmHg. The second procedure uses phase transfer
3
made in oxygen at 3.04 MPa, with 1 cm of water added to the
catalysis without solvent conditions; pyrazole (0.07 mol), finely
grounded potassium hydroxide (0.14 mol), and tetra-n-butyl-
bomb. The liquids 1MeIMI, 1MePYR, and 1BnPYR were
burnt in sealed polyester bags made of Melinex, using the
-
4
ammonium bromide (TBAB, 35 × 10 mol), were sonicated
with an ultrasonic cleaning bath (50 W, 200 MHz) for 15 min.
Methyl iodide (0.07 mol) was added at 273 K, and the reaction
was stirred for 6 h. Distillation of reaction crude afforded a
mixture of water and 1MePYR. After removal of water, the
product was dried over sodium hydroxide and distilled twice at
9
technique described by Skinner and Snelson, who determined
the specific energy of combustion of dry Melinex as ∆cu° )
-
1
-
(22902 ( 5) J g . That value was confirmed in Porto
laboratory. The mass of Melinex used in each experiment was
corrected for the mass of water (0.0032), and the mass of carbon
dioxide produced from it was calculated using the factor
760 mmHg over sodium in an argon atmosphere using a Vigreux
9
previously reported. The electrical energy for ignition was
column (bp ) 398-403 K): yield 80%; bp ) 401 K/760
determined from the change in potential difference across a
capacitor when discharged through the platinum ignition wire.
mmHg; lit. bp ) 398 K/760 mmHg.4 N-Benzylimidazole
(
(
1BnIMI) was prepared using the second procedure; imidazole
0.07 mol), potassium tert-butoxide (0.077 mol), and tetra-n-
1
0
For the cotton-thread fuse, the empirical formula CH1.686O0.843,
∆
-1
cu° ) 16 250 J g , was used and the value of ∆cu° confirmed.
-
4
butylammonium bromide (TBAB, 35 × 10 mol) were mixed
and submerged in an ultrasonic cleaning bath (50 W, 200 MHz)
for 15 min. Benzyl chloride (0.07 mol) was added at 273 K,
and the reaction was stirred at room temperature for 1 h. The
The amount of substance used in each experiment was deter-
mined from the total mass of carbon dioxide produced after
allowance for that formed from the cotton thread fuse and
Melinex.
3
mixture was extracted with dichloromethane (2 × 30 cm ). After
The energy equivalent of the calorimeter II was determined
from the combustion of benzoic acid, NIST standard reference
sample 39i, having a massic energy of combustion under the
removal of the solvent, the product was distilled three times
over sodium in an argon atmosphere using a Vigreux column
(fraction 390-400 K/0.7 mmHg): yield 85%; bp ) 395 K/0.7
-
1
5
conditions specified on the certificate of -(26434 ( 3) J g .
From 10 calibration experiments, ꢀ(calor) ) (14316.9 ( 2.0) J
mmHg; mp ) 346 K; lit. mp ) 345 K. N-Benzylpyrazole
1BnPYR) was prepared analogously; pyrazole (0.07 mol),
finely grounded potassium hydroxide (0,084 mol), and tetra-n-
(
-
1
K , where the uncertainty quoted is the standard deviation of
the mean. The energy of combustion of the 1-benzylimidazole
was determined by burning the solid sample in pellet form in
-
4
butylammonium bromide (TBAB, 35 × 10
sonicated with an ultrasonic bath for 15 min. Benzyl chloride
0.07 mol) was added at 273 K, and the reaction was stirred at
mol) were
3
oxygen inside the bomb, with 1 cm of added water. As a result
(
of the relatively high vapor pressure of 1BnIMI and its
hygroscopicity, the pelleted compound was enclosed in poly-
ethene bags. Under these conditions no carbon or CO were
found. The initial temperature was 296.95 K. The energy of
reaction was always referred to the final temperature T ) 298.15
K. The massic energy of combustion and empirical formula of
room temperature for 48 h. The mixture was extracted with
3
dichloromethane (2 × 30 cm ). After removal of solvent, the
product was distilled two times over sodium in an argon
atmosphere using a Vigreux column: yield 90%; bp ) 378 K/8
mmHg; lit. bp ) 393 K/15 mmHg.6
Determination of purity was assessed by GC for the liquid
compounds and by DSC using the fractional fusion technique
-1
1
polyethene are -(46371 ( 4) J g and C0.961H2.000. All samples
were weighed with a Mettler AT-21 microbalance and correc-
tions of apparent mass to mass were made. After disassembly
of the calorimeter, the bomb gases were slowly released and
the absence of CO was checked with Dr a¨ ger tubes (sensitivity
7
for solid 1BnIMI. The mass fraction of impurities for the four
-
3
compounds was 5 × 10 . 1-Benzylimidazole was studied by
DSC over the temperature range between T ) 270 K and T )
3
49 K and no phase transitions was found.
MeIMI, 1MePYR, and 1BnPYR are hygroscopic liquids.
-
6
levels were approximately 1 × 10 mass fraction).
1
The corrections for nitric acid formation were based on -59.7
Although the handling of samples was performed under nitrogen,
the average ratios of the mass of carbon dioxide recovered after
combustion to that calculated from the mass of sample were
-
1
-3
kJ mol for the molar energy of formation of 0.1 mol dm
1
1
HNO3(aq) from N2(g), O2(g), and H2O(l).
1
1
MeIMI (0.9969 ( 0.0006), 1MePYR (0.9928 ( 0.0014), and
BnPYR (0.9996 ( 0.0002), where the uncertainties are the
The densities at T ) 298.15 K for 1MeIMI, 1MePYR, and
1BnPYR were measured using an Anton Paar DMA 02D

9
338 J. Phys. Chem. A, Vol. 103, No. 46, 1999
M o´ et al.
(1)
-
3
-3
2
densimeter, respectively, as 1.030 g cm , 0.9929 g cm , and
1
calibrated pycnometer d ) 1.22 g cm . An estimated pressure
coefficient of specific energy, (δu/δp)T ) - 0.2 J g MPa
at T ) 298.15 K, a typical value for most organic compounds,
was assumed. For each compound, the massic energy of
combustion, ∆cu°, was calculated by the procedure given by
Hubbard et al.12
W ) 0.0147(l/r) + 0.3490(l/r) + 0.9982
a
-
3
.078 g cm . The density of 1BnIMI was measured with a
-
3
r being the radius of the effusion orifice. The vapor pressures
-
1
-1
were calculated using
1
/2
p ) (∆m/W at)(2πRT/M)
(2)
a
A differential scanning calorimeter (Perkin-Elmer Pyris 1)
equipped with an Intracooler unit was used in this research in
order to measure the heat capacities of all the compounds as
well as to control the purity of solid 1BnIMI. Its temperature
scale was calibrated by measuring the melting temperature of
the recommended high-purity reference materials: n-octadecane,
octadecanoic acid, benzoic acid, tin, and indium.13 The power
scale was calibrated with high-purity indium (mass fraction:
where p is the vapor pressure, ∆m the mass loss during the
22
time t, W the Clausing coefficient of the Knudsen-cell orifice,
a
a the area of the effusion orifice, R the gas constant, T the
thermodynamic temperature, and M the molar mass of the
studied compound. The molar masses used for the elements were
2
3
those recommended by the IUPAC in 1995.
Computational Details
13
>
0.99999) as reference material.
Heat capacities were calculated following the method de-
The geometries of pyrazole and imidazole as well as those
of their N-methyl, N-ethyl, N-phenyl, and N-benzyl derivatives
were optimized at the B3LYP/6-31G(d) level, which was shown
to yield quite reliable geometries for these kinds of systems.24
The B3LYP approach is a density functional hybrid method
which combines the Becke’s three parameter nonlocal hybrid
scribed in ref 14. Synthetic sapphire and benzoic acid were used
as standard materials15 for checking all the process. The
complete temperature range for determination of the heat
capacities was divided into three intervals of approximately 40
K, overlapping by 15 K from one interval to another. The heat
capacity values were the average of four experiments done for
each interval of temperature. Fresh samples of mass of ap-
proximately 8-12 mg were scanned using a heating rate of 0.17
2
5
exchange potential with the nonlocal correlation functional
2
6
of Lee, Yang, and Parr.
The harmonic vibrational frequencies were evaluated at the
same level of theory in order to confirm that the stationary points
found corresponded to local minima of the potential energy
surface and to evaluate the zero-point energies (ZPE), which
-
1
K s and a sensitivity of 0.008 W full scale. All the samples
were handled under nitrogen atmosphere. The accuracy of the
molar heat capacities was between 0.01 and 0.02 Cp,m and the
standard deviations of the mean of the experimental results were
2
7
were scaled by the empirical factor 0.98.
To obtain reliable energetics, the final total energies were
obtained in single-point calculations at the B3LYP/6-311+G-
(
0.07 for 1MeIMI, (0.09 for 1MePYR, (0.10 for 1BnIMI,
and (0.06 for 1BnPYR.
(
3df,2p) level, which usually yields thermodynamic properties
The enthalpies of vaporization of 1MeIMI, 1MePYR, and
28
29
as proton affinities and enthalpies of formation in fairly good
agreement with experimental values. In this respect, it should
be mentioned that, recently, Curtiss et al. have shown that
the B3LYP density functional method, when used together with
a 6-311+G(3df,2p) basis set expansion yields, for a large set
of compounds, calculated enthalpies of formation with an
average absolute deviation equal to 13.0 kJ mol . This set
includes the 55 molecules which define the so-called G2 neutral
test set and 93 new molecules. A better performance is achieved
when using the different G2 approaches, among which the G2
formalism is the most reliable yielding an average absolute
deviation of 6.6 kJ mol . The performance of the more
economic G2(MP2) and G2(MP2,SVP) methods is a little worse,
but still quite good with average absolute deviations of 8.1 and
1
BnPYR were measured using a method similar to that used
for sublimation of solids, the “Vacuum sublimation” drop
2
9
16
microcalorimetric method which was previously tested in the
Porto laboratory.17 Samples, about 7-11 mg of each liquid
compound, contained in a thin glass capillary tube sealed at
one end, were dropped, at room temperature, into the hot
reaction vessel, in a high-temperature Calvet microcalorimeter
held at T ) 371 K (1MeIMI), 363 K (1MePYR), and 386 K
-1
(1BnPYR) and then removed from the hot zone by vacuum
vaporization. The observed enthalpies of vaporization were
corrected to T ) 298.15 K, using the value of
-
1 29
To
∫
C°p,m(g) dT
298.15K
-
1
29
8
.5 kJ mol , respectively. Unfortunately, although these
18
procedures can be currently used for systems of the size of
imidazole and pyrazole, they become prohibitively expensive
for derivatives where the substituent is a phenyl or a benzyl
group. Hence, for the sake of consistency, we will use for all
the derivatives included in this study the B3LYP/611+G(3df,-
estimated by the Benson’s group method, using values from
Stull et al. The microcalorimeter was calibrated in situ for
1
9
these measurements using the reported enthalpy vaporization
of undecane.20
Knudsen-Effusion Method. The vapor pressure for 1BnIMI
2
p)//B3LYP/6-31G(d) approach. To asses the reliability of this
was determined by the Knudsen-effusion method, using the
technique and procedure described previously.21 The apparatus
approach, these values will be compared with those obtained
at the G2(MP2) level for the smaller systems, namely, imidazole
and pyrazole and their N-methyl and N-ethyl derivatives. All
these calculations have been carried out using the Gaussian-94
consists, essentially, of a stainless steel sublimation chamber
immersed in a thermoregulated water jacket and connected to
-
4
a high-vacuum system (p ) 1 × 10 Pa). The Knudesn cell
was weighed after each experiment in order to determine the
mass of sublimed material. The weighings were reproducible
to within ( 0.000002 g. The membrane for the effusion
measurement of vapor pressure was a tantalum foil, thickness
l ) (0.021 ( 0.004) mm. The area of the effusion orifice was,
3
0
series of programs.
Results and Discussion
Thermodynamic Part. Results for a typical combustion
experiment of each compound are given in Table 1, where
∆m(H2O) is the deviation of the mass of water added to the
calorimeter from 3119.6 g, and ∆UΣ is the correction to the
-
3
2
22
a ) (3.47 ( 0.02) × 10 cm ; the Clausing coefficient Wa
(0.980 ( 0.004) was found from the expression
)

Enthalpies of Formation of Pyrazoles and Imidazoles
J. Phys. Chem. A, Vol. 103, No. 46, 1999 9339
TABLE 1: Typical Combustion Experiments for
N-Imidazole and N-Pyrazole Derivatives at T ) 298.15 K
TABLE 4: Experimental Molar Heat Capacities Cp,m of
N-Imidazole and N-Pyrazole Derivatives
1
MeIMI
1MePYR 1BnIMI
1BnPYR
T
K
C
p,m
T
K
C
p,m
T
K
C
p,m
J K- mol-1
1
J K-1 mol-1
J K-1 mol-1
m(CO
2
)/g
1.45176
0.60321
0.06675
1.48565
0.62995
0.05713
1.75225
m′(cpd)/g
0.44368 0.57585
0.06359
1-methylimidazole
m′′(melinex)/g
m′′(polyethene)/g
m′′′(fuse)/g
278.1
283.1
288.2
293.3
298.15
303.4
308.4
176.36
178.44
180.40
182.22
183.90
185.46
186.88
313.4
318.4
323.4
328.4
333.4
338.4
343.4
188.17
189.34
190.37
191.27
192.05
192.70
193.22
348.4
353.3
358.3
363.2
368.1
370.1
193.62
193.89
194.04
194.07
196.81
197.15
0.05389
0.00343
1.25902
15911.2
16.00
0.00257
1.31287
15908.3
15.88
0.00290
1.36967
∆
T
ad/K
1.2637
14253.1 15908.3
16.06
ꢀ
(calor)/(J K-1)
1
ꢀ
f
/(J K-
)
15.71
-0.1
∆
m(H
∆U(IBP)/J
U(HNO )/J
U(ign.)/J
/J
2
O)/g
-0.2
0.0
a
-
20050.93 20905.28 17981.4 21809.30
1
-methylpyrazole
∆
∆
∆
∆
∆
∆
-
3
68.95
0.68
12.98
1528.77
67.70
1.10
13.44
1308.32
38.8
50.8
8.6
41.91
0.77
13.67
1456.35
2
2
2
2
2
3
3
78.1
82.1
87.2
92.3
98.15
02.4
07.4
167.20
169.24
171.18
172.36
173.28
174.69
176.90
312.4
317.4
322.4
327.4
332.4
337.4
342.4
177.59
179.24
180.28
182.85
184.46
185.09
186.26
347.4
352.3
353.3
362.2
367.1
370.1
188.23
190.01
193.93
197.50
201.79
203.10
U
Σ
U(melinex)/J
U(polyethene)/J
U(fuse)/J
2498.8
55.70
41.74
47.10
-
1
∆
c
u°/J g
30477.83 30913.69 34789.0 35165.88
a
∆
U(IBP) already includes the ∆U(ign.).
1
-benzylimidazole
2
2
2
2
78.1
83.1
88.2
93.3
169.51
173.25
177.35
181.73
182.10
303.4
308.4
313.4
318.4
323.5
184.23
188.43
190.95
195.37
200.07
328.4
333.4
337.4
207.25
217.33
235.77
TABLE 2: Individual Values of the Massic Energy of
Combustion ∆ u° of N-Imidazole and N-Pyrazole Derivatives
at T ) 298.15 K
c
1
MeIMI
1MePYR
1BnIMI
1BnPYR
298.15
∆u°/J g-1
1-benzylpyrazole
-
2
2
2
2
2
3
3
3
3
80.0
85.0
90.0
95.0
98.15
00.0
05.0
10.0
15.0
254.74
255.77
257.05
258.56
259.61
260.27
262.15
264.18
266.33
320.0
325.0
330.0
335.0
340.0
345.0
350.0
355.0
360.0
268.58
270.88
273.23
275.58
277.92
280.22
282.44
284.57
286.57
365.0
370.0
375.0
380.0
385.0
390.0
392.0
288.42
290.09
291.55
292.78
293.74
294.42
294.61
3
3
3
3
3
3
3
0477.83
0510.95
0478.11
0513.12
0505.60
0465.06
0483.43
30947.30
34790.60
34758.20
34789.00
34790.90
34759.40
34795.10
35165.88
35174.13
35158.72
35150.28
35165.03
35166.70
35178.04
30913.03
30910.50
30913.69
-
〈∆
c
u°〉/(J g-1)a
34780.5 ( 7.0
3
0490.6 ( 7.2
30921.1 ( 8.7
35165.6 (3.5
a
TABLE 5: Vapor Pressures of 1-Benzylimidazole
Mean value and standard deviation of the mean.
Ta/K
t /s
b
∆m /mg
c
pd/Pa
10 δp /p
2
e
TABLE 3: Derived Standard (p° ) 0.1 MPa) Molar
2
2
61.96
65.24
25200
16560
18840
13560
18480
15420
2.20
2.04
3.78
3.91
7.38
9.41
0.595
0.846
1.39
2.01
2.79
4.31
-0.2
-0.3
0.2
Energies of Combustion, ∆ U°, Standard Molar Enthalpies
c
m
of Combustion, ∆ H°, and Standard Molar Enthalpies of
c
m
Formation, ∆ H°, for N-Imidazole and N-Pyrazole
269.94
273.78
2
f
m
Derivatives at T ) 298.15 K
-2
76.51
4
-
∆ U°(cd)
- ∆ H°(cd)
∆ H°(cd)
f m
c
m
c
m
281.66
-2
-
1
-1
-1
kJ mol
kJ mol
kJ mol
a
Temperature. b Time lengh of the experiment. c Mass of sublimed
substance. d Vapor pressure. e Fractional deviations of the experimental
vapor pressures from the values computed using the eq 4.
1
MeIMI
MePYR
BnIMI
BnPYR
2503.4 ( 3.8
2538.8 ( 1.5
5502.4 ( 3.4
5563.3 ( 1.6
2504.6 ( 3.8
2540.0 ( 1.5
5506.1 ( 3.1
5567.0 ( 1.6
73.1 ( 3.8
108.5 ( 1.6
141.9 ( 3.4
202.8 ( 2.1
1
1
1
-
1
K, respectively, -(285.830 ( 0.042) kJ mol and -(393.51
-
1
32
standard state. The remaining quantities are as previously
described.
( 0.13) kJ mol , were used.
1
2
The molar heat capacities for the liquids 1-methylimidazole,
-methylpyrazole, and 1-benzylpyrazole were measured from
1
∆
U(IBP) ) -{ꢀ(calor) + ∆m(H O)c (H O,l) + ꢀ }∆T +
2
p
2
f
ad
T ) 280 K to the temperature of the vaporization and, for the
solid 1-benzylimidazole, from T ) 280 K to near its melting
temperature T ) 338 K. The temperatures were corrected by a
program that includes the calibrations of temperature and power
scales of the DSC apparatus, being the obtained values given
in Table 4.
ꢀi(T - 298.15) + ꢀ (298.15 - T - ∆T ) + ∆U (3)
i
f
i
ad
ign
The individual results of all combustion experiments, together
with the mean value and its standard deviation, are given for
each compound in Table 2.
Table 3 lists the derived standard molar energies and
enthalpies of combustion and the standard molar enthalpies of
formation for the four compounds at T ) 298.15 K. In
accordance with normal thermochemical practice, the uncertain-
ties assigned to the standard molar enthalpies of combustion
are, in each case, twice the overall standard deviation of the
mean and include the uncertainties in calibration31 and in the
values of auxiliary quantities.
The results of our Knudsen-effusion experiments are sum-
marized in Table 5.
An equation of the type
-
1
log(p/Pa) ) -B(T/K) + A
(4)
was fitted to the results of Table 5 by the least-squares method.
The quantities δp/p are the fractional deviations of the experi-
mental vapor pressures from those computed using eq 4. The
To derive ∆ H°(l) from - ∆ H°(l), the standard molar
f
m
c
m
-
3
enthalpies of formation of H2O(l) and CO2(g), at T ) 298.15
highest error for the vapor pressure, p, in Table 5 is 5 × 10 p,

9340 J. Phys. Chem. A, Vol. 103, No. 46, 1999
M o´ et al.
Figure 1. B3LYP/6-31G* optimized geometries of the N-substituted azoles showing the relative orientation of the substituents with respect to the
azole ring.
TABLE 6: Molar Enthalpies of Vaporization and
SCHEME 1
g,T
Sublimation ∆ ∆H° at Various Temperatures T, for
cd
m
N-Imidazole and N-Pyrazole Derivatives (p° ) 0.1 MPa)
g
cd
∆
H°
m
g,T
cd
kJ mol
T
no. of
expts
T
K
∆
∆H°
∫
C° (g)dT (298.15 K)
m
298.15K p,m
-
1
-1
-1
kJ mol
kJ mol
1
1
1
1
MeIMI
MePYR
BnIMI
5
6
8
9
371 71.9 ( 1.3
363 54.4 ( 1.3
298 102.1 ( 0.4
386 92.6 ( 2.0
7.16
6.36
64.7 ( 1.3
48.0 ( 1.3
102.1 ( 0.4
73.8 ( 2.0
Geometries. Although a detailed description of the optimized
geometries of the N-substituted azoles investigated is not the
aim of this paper, we have considered it of interest to outline
the most significant features.
BnPYR
18.79
TABLE 7: Derived Standard (p° ) 0.1 MPa) Molar
Enthalpies of Formation, ∆ H°, of N-Imidazole and
N-Pyrazole Derivatives at T ) 298.15 K
f
m
For the ethyl derivatives, we have initially considered two
alternative conformers, namely, 1EtIMI1, 1EtIMI2, 1EtPYR1,
and 1EtPYR2, which differ in the relative position of the methyl
group of the substituent with respect to the azole ring (See
Scheme 1). In all cases, both conformers evolve to yield a sole
equilibrium conformation, 1EtIMI and 1EtPYR, respectively,
in which the methyl group is almost perpendicular to the plane
of the azole (see Figure 1). Also interestingly, the local structure
of the substituent is rather similar for both imidazole and
pyrazole, the NCC angle (R in Figure 1) being in both cases
around 114°. An almost identical NCC bond angle is predicted
for both the N-benzyl pyrazole (1BnPYR) and the N-benzyl
imidazole (1BnIMI). In these last two cases, the relative
orientation of the benzene ring with respect to the azole ring is
rather similar for both compounds. Actually, in both cases the
CCNC dihedral angle (â in Figure 1) is close to 117°.
-
1
g
cd
-1
-1
∆fH°(cd)/kJ mol
∆ H°/kJ mol
∆ H°(g)/kJ mol
m
m
f
m
1
1
1
1
MeIMI
MePYR
BnIMI
73.1 ( 3.8
108.5 ( 1.6
141.9 ( 3.4
202.8 ( 2.1
64.7 ( 1.3
48.0 ( 1.3
102.1 ( 0.4
73.8 ( 2.0
137.8 ( 4.0
156.5 ( 2.1
244.1 ( 3.4
276.6 ( 2.9
BnPYR
computed as the sum of the estimated errors of all quantities in
eq 3. The parameters A and B for this equation are (16.40 (
0
.06) and -(5332.9 ( 18.7), respectively. The enthalpy of subli-
mation corresponding to the mean temperature 〈T〉 ) 316.67 K
of this experimental range is given in Table 6, and it has been
calculated from the corresponding B value. The uncertainty
assigned to the value of ∆ Hm is based on the standard devia-
tion of the B value. The enthalpy of sublimation at T ) 298.15
K has been computed using the same equation as in ref 33,
where Cp°,m (cr) has been determined by DSC and C° (g) has
been calculated using the group contribution scheme of Rihani.
The results of measurements of the enthalpies of vaporization
and sublimation are given in Table 6. Uncertainties for enthal-
pies of vaporization are twice the standard deviation of the mean.
The derived enthalpies of formation, in both condensed and
gaseous phases, for 1MeIMI, 1MePYR, 1BnIMI, and 1BnPYR
are summarized in Table 7.
Computational Part. Total and relative energies as well as
the zero-point vibrational energies of the compounds included
in this study are given in Table 8.
g
cr
p,m
34
Our results also show that the N-phenyl derivatives, namely
1PhPYR and 1PhIMI, differ in the relative orientation of the
phenyl group. Although neither in 1PhPYR nor in 1PhIMI,
the phenyl group is coplanar with the azole ring, for 1PhPYR
the calculated torsional angle is 20.5°, for the corresponding
imidazole is almost twice this value (39.8°), due to a strong
repulsive interaction between the hydrogen of the benzene ring
and the CH group of the azole. It is worth noting that these
torsional angles are in good agreement with the experimental
3
5
values, 25° for 1PhPYR and 40° for 1PhIMI.

Enthalpies of Formation of Pyrazoles and Imidazoles
J. Phys. Chem. A, Vol. 103, No. 46, 1999 9341
TABLE 8: Total Energies (E, in hartrees), Zero-Point Energies (ZPE; in hartrees), and Relative Energies (∆E, in kJ mol-1) for
N-substituted Azoles
G2(MP2)
B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d)
compound
E
∆E
E
ZPE
∆E
imidazole (1HIMI)
pyrazole (1HPYR)
-225.82659
-225.80865
-265.04689
-265.03177
-304.27450
-304.25979
0.0
46.9
0.0
39.7
0.0
-226.29940
-226.28242
-265.62131
-265.60672
-304.95039
-304.93602
-457.41959
-457.40494
-496.74408
-496.72943
0.07126
0.07140
0.09913
0.09908
0.12784
0.12783
0.15224
0.15224
0.18106
0.18115
0.0
44.8
0.0
38.1
0.0
37.7
0.0
38.5
0.0
1
1
1
1
1
1
1
1
MeIMI
MePYR
EtIMI
EtPYR
PhIMI
PhPYR
BnIMI
BnPYR
38.5
38.5
TABLE 9: Enthalpies of Formation of N-Substituted Azolesa
calcd using
atomization energies
calcd using quasiisodesmic
reactions 9-13
calcd using quasiisodesmic
reactions 14-18
compound
G2(MP2)
B3LYPb
G2(MP2)
B3LYPb
G2(MP2)
B3LYPb
experimental
imidazole (1HIMI)
pyrazole (1HPYR)
136.0
183.3
128.5
168.2
99.2
123.4
168.2
125.1
176.6
108.8
146.4
287.9
326.4
284.5
323.0
132.2
179.1
132.6
172.4
101.7
140.2
131.8
176.6
138.5
176.6
115.9
153.6
275.7
314.2
269.4
307.9
132.9 ( 0.6
179.4 ( 0.8
137.8 ( 4.0
156.5 ( 2.1
110.8 ( 4.3
132.6 ( 3.3
264.7 ( 4.3
291.4 ( 4.5
244.1 ( 3.4
276.6 ( 2.9
163.2
145.2
116.3
162.3
153.1
141.8
306.7
293.3
1
1
1
1
1
1
1
1
MeIMI
MePYR
EtIMI
EtPYR
PhIMI
PhPYR
BnIMI
BnPYR
138.9
a
All values in kJ mol-1 at 298.15 K. b Values obtained at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) level of theory.
-
1
Calculated Enthalpies of Formation. The enthalpies of
formation of the azoles under investigation were initially
calculated from the corresponding atomization reactions, fol-
lowing the procedure outlined in ref 29. In this procedure, the
enthalpy of formation of a AxByHz molecule at 0 K in the
gaseous state is given by
kJ mol ) is smaller than the average absolute deviation reported
in ref 29 for this method. On the other hand it is worth noting
that this theoretical approach reproduces well the trends along
the series. The enthalpy of formation of the methyl derivative
is predicted to be slightly higher than that of the unsubstituted
parent compound while the enthalpies of formation of the ethyl
and the phenyl derivatives are smaller or sizeably larger,
respectively, than that of imidazole, in agreement with the
experimental evidence. As expected, the largest deviation, as
mentioned above, is found for the N-benzyl derivative which
is the largest system. This finding is consistent with the
∆fH°(A B H ,0 K) ) x∆ H°(A,0 K) + y∆ H°(B,0 K) +
m
x
y
z
f
m
f
m
z∆ H°(H,0 K) - ΣD (5)
f
m
0
where ΣD0 is the calculated atomization enthalpy, and ∆ H°-
f
m
3
6
(
A,0 K), ∆ H°(B,0 K), ∆ H°(H, 0 K) the experimental enthal-
conclusions of Petersson et al. in the sense that, when this
method is used, the errors tend to be proportional to the size of
the molecules.
f
m
f
m
pies of formation of the isolated atoms at 0 K.
The corresponding enthalpies of formation at 298.15 K in
the gaseous state are calculated by correction to ∆ H°(0 K) as
The deviations found when atomization energies are used can
be significantly reduced if appropriate isodesmic reactions are
used. In an isodesmic reaction, the number of bonds between
each pair of atom types is preserved. Hence, if the error in the
calculated bond energy was about the same in both sides of the
reaction, the overall error in the calculated reaction enthalpy
would be drastically reduced. The next condition to be fulfilled
is that the heats of formation of the different molecules which
participate in the reaction, but the one whose heat of formation
is unknown, should be known as accurately as possible.
For imidazole and pyrazole, these isodesmic reactions would
be
f
m
follows:
∆fH°(A B H ,298.15 K) ) ∆ H°(A B H ,0 K) +
m
x
y
z
f
m
x
y
z
[
H°(A B H ,298.15 K) - H°(A B H ,0 K)] -
m x y z m x y z
x[H°(A,298.15 K) - H°(A,0 K)] - y[H°(B,298.15 K) -
m
m
st
m
H°(B,0 K)] - z[H°(H,298.15 K) - H°(H,0 K)] (6)
m
st
m
m
st
where the heat capacity correction for the AxByHz molecule is
made using the B3LYP/6-31G(d) harmonic frequencies for the
vibrational energy, and adding 3/2RT for the translational energy,
3
/2RT for the rotational energy (RT for linear molecules) and
the PV term. For the elements the heat capacity corrections are
for the standard states of the elements and were the same as
those listed in ref 29.
C N H (1HIMI) + 3CH + 2NH f
3
2
4
4
3
3
CH NH + CH CH + CH NH (7)
3 2 2 2 2
The corresponding calculated enthalpies of formation for the
imidazoles are given in Table 9. It can be seen that both the
G2(MP2) and the B3LYP/6-311+G(3df,2p) estimates, using
atomization energies, are in a reasonably good agreement with
the experimental values. Actually, if the larger N-phenyl and
N-benzyl derivatives are discarded, the average deviation (11.6
C N H (1HPYR) + 3CH + 2NH f
3
2
4
4
3
CH CH + CH NH + CH CH + CH NH + NH NH (8)
3
3
3
2
2
2
2
2
2
However, these reactions do not fulfill the aforementioned
conditions in the sense that the enthalpy of formation of the

9342 J. Phys. Chem. A, Vol. 103, No. 46, 1999
M o´ et al.
Surprisingly, the agreement is much worse if we use the same
isodesmic reactions to estimate the enthalpies of formation of
the corresponding N-substituted pyrazoles. As illustrated in
Table 8, the theoretical scheme used predict the energy gap
between N-substituted imidazoles and N-substituted pyrazoles
-1
to be only slightly smaller (ca. 38 kJ mol ) than that estimated
-
1
for the unsubstituted parent compounds (44.8 kJ mol ) and
sizeably larger than the gap observed between their experimental
-
1
enthalpies of formation (ca. 21 kJ mol ). It is worth noting
that this gap is only nicely reproduced for the couple imidazole/
pyrazole but is clearly overestimated for the N-substituted
derivatives. A possible origin for this disagreement is the
inadequacy of the isodesmic reactions 9-13 for the particular
case of pyrazoles, which present a N-N linkage, which does
not exist in the case of imidazoles. Very likely, HCN is not a
good reference compound in this particular cases and should
be replaced by hydrazine (H2N-NH2).
Figure 2. Linear correlation between calculated and experimental
enthalpies of formation [∆
It is not easy in this case to accommodate the total number
of atoms when one of the reference systems is hydrazine. Hence,
the only quasiisodesmic reactions we found reasonable are
f
∆ H°(cal.) ) (1.10 ( 0.05)∆ H°(exp.) -
f m f m
-
1
2
(
13.5 ( 10.2) kJ mol , R ) 0.984] for the N-substituted imidazoles
(b) and N-substituted pyrazoles (2). For imidazoles, the calculated
values were obtained through the use of the quasiisodesmic reactions
9
-13, while for pyrazoles, the quasiisodesmic reactions 14-18 were
C N H (1HPYR) + CH f N H + 2C H
2
3
2
4
4
2
4
2
used.
-1
∆rH°(298.15 K) ) 464.0 kJ mol (14)
m
CH2NH species is not accurately known. In fact, there are, at
least, five experimental values for the enthalpy of formation of
methylenimine, and these are scattered over ca. 40 kJ mol
C N H (1MePYR) + C H f N H + 3C H
2
4
2
6
2
4
2
4
2
-
1
-
1
∆ H°(298.15 K) ) 574.0 kJ mol (15)
r m
-
1 37
(
∼90 ( 20 kJ mol ). Our theoretically estimated value at
C N H (1EtPYR) + C H f N H + 3C H + C H
4
-1
5
2
8
3
6
2
4
2
2
2
the G2 level (86.2 kJ mol ) is similar to that reported by Pople
-1
-
1 38
at the same level (86 kJ mol ) and by Jursic using DFT
∆ H°(298.15 K) ) 669.4 kJ mol (16)
r m
-
1 39
methods (84 kJ mol ). In view of this difficulty, we decided
to use instead the following reactions:
C N H (1PhPYR) + C H f N H + 6C H
2
9
2
8
3
8
2
4
2
-1
∆rH°(298.15 K) ) 1261.5 kJ mol (17)
m
C N H (1HIMI) + CH f 2HCN + C H
6
3
2
4
4
2
C N H (1BnPYR) + C H f N H + 6C H
2
-
1
10
2
10
2
6
2
4
2
∆rH°(298.15 K) ) 128.9 kJ mol (9)
m
-1
∆rH°(298.15 K) ) 1254.4 kJ mol (18)
m
C N H (1MeIMI) f 2HCN + C H
4
4
2
6
2
-
1
The enthalpies of formation obtained are now in much better
agreement with the experimental values, with only the exception
of the unsubstituted parent compound. Unfortunately, these
results are not conclusive, since although the agreement with
the experimental values is better, this seems to be a consequence
of the fact that all the heats of formation, including that of the
parent compound, are smaller, while what the experimental
results actually indicate is that the substituent effects are not
quantitatively equal in imidazoles and pyrazoles. For instance,
if we consider the N-methyl derivatives, the experimental values
show that while the methyl substitution effect is negligibly small
for the imidazole, it is sizeably large for the pyrazole, and this
fact is not reproduced by the theoretical calculations, indepen-
dently of the quasiisodesmic reactions used. In this respect, it
is important to mention that both situations are found for other
systems. For instance, while the methyl substitution effect on
∆rH°(298.15 K) ) 183.3 kJ mol (10)
m
C N H (1EtIMI) f 2HCN + C H
6
5
2
8
3
-
1
∆rH°(298.15 K) ) 174.5 kJ mol (11)
m
C N H (1PhIMI) + CH f 2HCN + 3C H + C H
4
9
2
8
4
2
2
2
-
1
∆rH°(298.15 K) ) 804.6 kJ mol (12)
m
C N H (1BnIMI) f 2HCN + 4C H
2
1
0
2
10
2
-
1
∆rH°(298.15 K) ) 913.0 kJ mol (13)
m
that we shall call from now on quasiisodesmic.
The energies of the different molecules which are involved
in these processes were also obtained at the B3LYP/6-311+G-
(3df,2p)//B3LYP/6-31G(d) level, and their experimental enthal-
4
0
the heat of formation of benzene is quite large [∆ H° (ben-
f m
pies of formation were taken from Lias et al.
-
1
-1 40
zene) ) 82.4 kJ mol , ∆ H° (toluene) ) 50.2 kJ mol ], the
same effect on the heat of formation of hydrazine is negligibly
small [∆ H° (NH2NH2) ) 95.4 kJ mol , ∆ H° (CH3NHNH2)
95.4 kJ mol ].
The first question we need to answer is whether our
f
m
The calculated enthalpies of formation obtained through the
use of these quasiisodesmic reactions are now in much better
agreement with the experimental values (see Table 9). It can
be observed that the largest absolute deviation, excluding the
-
1
f
m
f
m
-
1 40
)
-
1
largest derivatives, is only 5 kJ mol . Even for the largest
-
1
theoretical scheme is able to reproduce this different behavior.
For the particular case of benzene and toluene, we have chosen
the following isodesmic reactions:
derivatives, this absolute deviation (25.3 kJ mol ) is almost
half that obtained when atomization energies are used. The very
good agreement between calculated and experimental values is
clearly reflected in the goodness of the linear correlation between
both sets of values (see Figure 2).
-1
C H f 3C H ∆ H°(298.15 K) ) 605.0 kJ mol (19)
6
6
2
2
r
m

Enthalpies of Formation of Pyrazoles and Imidazoles
J. Phys. Chem. A, Vol. 103, No. 46, 1999 9343
TABLE 10: Application of the Hess’s Lawa
C H + CH f 3C H + C H
6
7
8
4
2
2
2
-
1
quasiisodesmic
∆rH°(298.15 K) ) 615.5 kJ mol (20)
m
R1
reactions 9-13 experimental experimental experimental
PYR-IMI PYR-BENb IMI-BEN
b
substituents
PYR-IMI
From the enthalpies of these reactions, we could estimate the
enthalpies of formation of benzene and toluene to be 79.1 kJ
H
Me
Et
Ph
Bn
44.8
38.1
37.7
38.5
38.5
39.5
46.5 ( 1.4
18.7 ( 6.1
21.8 ( 7.6
26.7 ( 8.8
32.5 ( 6.3
29.2
96.8
106.1
102.7
110.0
137.6
110.6
50.3
87.4
80.9
83.3
105.0
81.4
-
1
-1
mol and 59.0 kJ mol , which are in fairly good agreement
-
1
with the experimental values (82.4 and 50.2 kJ mol , see
previously).40
average
For the particular case of hydrazine and methylhydrazine
we have used, as before, the procedure based on their atomi-
a
All values in kJ mol-1 at 298.15 K. b Benzene, toluene, ethylben-
zene, biphenyl, and diphenylmethane data from ref 20.
-
1
zation energies. The results obtained, 84.1 kJ mol and 88.3
-
1
kJ mol , respectively are also in nice agreement with the
experimental values, and clearly predict a rather small substitu-
ent effect.
This is a simple consequence of the Hess’s law which states
that the differences (24-26) must be constant, i.e., that the
slopes should be 1:
In summary, the experimental enthalpies of formation of the
N-substituted imidazoles are very well reproduced by our
calculations, but the agreement for the particular case of
pyrazoles is worse. This is so because while the theory predicts
that substituent effects on the enthalpies of formation are rather
similar for imidazoles and pyrazoles, the experimental values
show that this effect is larger for pyrazoles than for imidazoles.
Unfortunately from our study the origin of this small discrepancy
is not clear.
1
1
[R -IMI] - [R -PYR] ) const ≈ 29
(24)
(25)
(26)
IP
1
1
[R -PYR] - [R -BEN] ) const ≈ 111
PB
1
1
[
R -IMI] - [R -BEN] ) const ≈ 81
IB
The value of these constants depends on the isodesmic or
quasiisodesmic reactions selected, but not on R . However, an
1
examination of these differences (Table 10) shows large
fluctuations, even for calculated values (although in this case it
affects only the 1H derivatives). We have no explanation for
these anomalies which seem to affect mainly the 1H and 1Bn
substituents.
Conclusions
Accurate experimental enthalpies of formation measured
using static bomb combustion calorimeter, “vacuum sublima-
tion” drop calorimeter method, and Knudsen-effusion method
have been reported for 1MeIMI, 1MePYR, 1BnIMI, and
Acknowledgment. This work has been partially supported
by the DGES Projects PB 96-0001-C03-03, PB96-0067, and
PB96-0927-C02-01. A generous allocation of computational
time at the Centro de Computaci o´ n Cient ´ı fica de la Facultad
de Ciencias (CCCFC) de la UAM is also gratefully acknowl-
edged. Thanks are due to Junta National de Investiga c¸ a˜ o
Cient ´ı fica e Tecnol o´ gica (JNICT), Lisbon, Portugal and Consejo
Superior de Investigaciones Cient ´ı ficas (CSIC), Madrid, Spain,
for a joint research project CSIC/JNICT. Financial support from
the Praxis XXI, Project 2/2.1/qui/54/94, is acknowledged.
L.M.P.F.A. thanks Funda c¸ aˆ o para a Ci eˆ ncia e Tecnologia,
Lisbon, Portugal for the award of a postdoctoral fellowship
1
BnPYR. For the series of N-substituted imidazoles, these
values, together with those reported in the literature, are in very
good agreement with the corresponding theoretical estimates
obtained using the B3LYP/6-311*G(3df,2p)//6-31G(d) approach,
when the appropriate quasiisodesmic reactions are used. The
agreement is slightly worse when the corresponding atomization
energies are used. The agreement between experimental and
calculated values is worse for the series of the N-substituted
pyrazoles, in particular as far as the differences with respect to
the analogous imidazoles are concerned. Experimentally, the
gap between the enthalpies of formation of imidazoles and
pyrazoles decreases significantly upon N-substitution, while
the theoretical estimates indicate that this decrease is signifi-
cantly smaller. The origin of this small discrepancy is not at all
clear.
(Praxis XXI/BDP/16319/98). J.F.L. acknowledges funding from
“
Dow Chemical Company” for partial support of his thermo-
chemical studies.
References and Notes
1
1
The example here reported, R -IMI vs R -PYR, is a
particular case of the more general problem of substituent
effects. Concerning the problem addressed in the Introduction,
i.e., the comparison of effects through the nitrogen (diazoles)
vs effects through the carbon (benzenes),40 the results for five
substituents (H, Me, Et, Ph, and Bn) show that these effects
are approximately the same (slopes of the regression lines
between 1.01 and 1.13).
(
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