Theoretical investigation of C–H H–B dihydrogen bonded
complexes of acetylenes with borane-trimethylamine
Prashant Chandra Singh, G. Naresh Patwari
*
Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India
Abstract
Formation of C–H H–B dihydrogen bonded complexes of acetylene, ﬂuoroacetylene, chloroacetylene, and cyanoacetylene with borane-trimethylamine were investigated with MP2 and B3LYP methods using 6-311++G(d,p) and aug-cc-pVDZ basis sets. The stabilization energies ranged from 6–20 kJ mol 1. NBO analysis predicts transfer of charge from r B–H bonding orbital to r* C–H anti-bonding
orbital. It was also found that the lowering of the C–H stretching frequencies of acetylene moiety in the dihydrogen bonded complex does
not correlate with other hydrogen bonded complexes, indicating that the supposition of dihydrogen bonding as another type of hydrogen
bonding (r and p) may be incorrect.
1. Introduction
Over the past few years several cases of hydrogen bonds
involving unconventional donors and/or acceptors have
been reported [1]. For instance, hydrogen bonds in which
p bond electrons act as acceptors [2] and also hydrogen
bonds involving C–H groups as donors [3] have been well
documented. Yet another important class of unconventional hydrogen bonds are the interaction of oppositely
charged hydrogen atoms, which can be generically represented as E–H(d ) (d+)H–X, wherein E and X are atoms
which are less and more electronegative than hydrogen,
respectively. This favorable interaction between oppositely
charged hydrogens has been termed as Ôdihydrogen bondingÕ [4,5]. Apart from metal hydrides, borane-amines have
played crucial role in understanding dihydrogen bonding.
Notable are the investigation of dihydrogen bonding in
BH3NH3 [6–9] and its complexes with molecules containing
acidic hydrogens [10–12]. MikamiÕs group has reported the
formation of B–H H–X (X = O, N) dihydrogen bonded
complexes in the gas phase [13].
The ability of C–H bonds to form hydrogen bonds has
been fairly well recognized, albeit weaker than the conventional hydrogen bonds [3]. This information can be extrapolated to infer the formation of dihydrogen bonds
involving CH groups. Recently, Grabowski et al. [14] have
reported the formation of dihydrogen bonded complexes
between acetylene and several hydrides, such as LiH,
BeH2, and HBeF. Further, to the best of our knowledge,
reports on C–H H–B dihydrogen bonds are extremely
sparse [15], and thus provides the impetus for investigating
of C–H H–B type dihydrogen bonded systems. In this
Letter, we report the formation of dihydrogen bonded
complexes of borane-trimethylamine (BTMA) with acetylene and F, Cl, CN substituted acetylenes. Along with the
energetic aspects of the interaction, structural and spectroscopic markers were computed using a high level of theory.
Comparison with other hydrogen bonded complexes of
acetylene is also presented.
2. Methodology
Theoretical methods employed in this report are
MP2(FC) and DFT-B3LYP, both of which include electron correlation, using 6-311++G(d,p) and aug-cc-pVDZ
6
basis sets. It has been shown in several instances that the
inclusion of polarization and diﬀuse functions on heavy
atoms improves the description of hydrogen bonding [16].
Since dihydrogen bonding is essential an interaction, analogous to hydrogen bonding, between a pair of oppositely
charged hydrogen atoms, polarization and diﬀuse functions have been added on hydrogen as well. The equilibrium structures of the monomers and the complexes were
calculated and the nature of stationary point obtained
was conﬁrmed by calculating the vibrational frequency at
the same level of theory. The calculated vibrational frequencies were scaled by 0.958, 0.958, 0.951, and 0.96 for
B3LYP/6-311++G(d,p),
B3LYP/aug-cc-pVDZ,
and
MP2/6-311++G(d,p),
MP2/aug-cc-pVDZ
methods,
respectively. The scaling factors were adapted to match
the experimental C–H stretching frequencies of acetylene
[17]. According to Kim et al. [18] 100% of BSSE correction
often underestimates the interaction energy and 50% correction is a good empirical approximation. The interaction
energies, reported herein, are corrected for the scaled zero
point vibrational energy (sZPVE) and 50% BSSE
correction.
It is well known that Mulliken charges are not adequate
to explain the bonding in various situations, therefore
molecular electrostatic potential (MEP) derived charges
as well as charges from the natural population analysis
(NPA) have also been obtained. The topographical analysis of the electron density distribution has been carried
using Atom in Molecules approach [19]. Further, to get
more insights about the lowering of the C–H stretching frequency of the donors upon complex formation, natural
bond analysis (NBO) has also been carried out [20]. All
the calculations reported here were carried out using
GAUSSIAN 98 [21].
3. Results and discussion
˚ , twice the van der
The H H distance of less than 2.4 A
˚ ), is the most
Waals radius of the hydrogen atom (1.2 A
used geometrical criterion to identify the formation of
dihydrogen bonds. However, due to electrostatic nature
of the (di)hydrogen bonding, van der Waals cutoﬀ criteria
is strongly criticized, as electrostatic interaction acts
beyond this distance [22]. Moreover, it has been reported
recently that for C–H bonds, the van der Waals radius of
˚ [23]. Howhydrogen atom is marginally greater than 1.2 A
ever, to be inline with the existing reports in the literature,
˚ as the cutoﬀ of the formation of
we have considered 2.4 A
dihydrogen bonds. Fig. 1 depicts the calculated structure of
acetylene-BTMA complex at MP2/aug-cc-pVDZ level of
theory, which has a pair of symmetrically bifurcated
˚ . Further,
dihydrogen bonds, with H H distance of 2.27 A
the acetylene-BTMA complex was also investigated at
MP2/aug-cc-pVTZ level. In this case the geometry changes
marginally with respect to MP2/aug-cc-pVDZ level and the
˚ . All the
H H distance is slightly elongated by 0.007 A
other complexes form similar structures and Table 1 lists
Fig. 1. MP2/aug-cc-p VDZ calculated structure of acetylene-BTMA
complex. Hydrogen atoms are depicted in grey, symbols B, C, and N
correspond to boron, carbon and nitrogen atoms, respectively, and the
˚.
distances are given in A
the relevant intermolecular geometrical parameters. Further, for all the complexes the B–H H angles are the
range of 92–97°, while C–H H angles, comparatively
more linear, are in the range of 146–151°. The present
results are in accord with those reported elsewhere [5–13].
Table 1 also lists the stabilization energies corrected for
sZPVE and 50% BSSE for various dihydrogen bonded
complexes. It is apparent from Table 1 that for all the
complexes the MP2 stabilization energies are higher than
the corresponding DFT-B3LYP value. This can be attributed to the neglect of the dispersion energy contribution
in the DFT-B3LYP method, which can be signiﬁcant for
complexes involving C–H groups. The highest stabilization
energies are obtained at MP2/aug-cc-pVDZ level of theory,
are in agreement with the shortest distances obtained at the
same level. It can also be seen from Table 1 that the stabilization energy increases with the substitution of ﬂuoro,
chloro, and cyano groups, in that order, respectively. For
instance at MP2/aug-cc-pVDZ level the stabilization
energy of acetylene-BTMA complexes is 14.2 kJ mol 1
increases to 20.6 kJ mol 1 in the case of cyanoacetylene
complex, while the ﬂuoro- and chloro-acetylenes taking
intermediate values of 14.8 and 16.2 kJ mol 1, respectively.
In order to understand the nature of H H interaction
in various complexes, we carried out charge analysis using
molecular electrostatic potential (MEP) method as well as
the natural population analysis (NPA) scheme at MP2/
aug-cc-pVDZ level and the results are presented in Table
2. In the case of acetylene-BTMA complex, the MEP
charge on the acetylenic hydrogen is +0.236, while the
two interacting hydrogens of BH3 group show a negative
charge 0.254 AU. The NPA results show that the acetylenic
hydrogen has a positive charge of 0.246 AU, while the
interacting hydrogens of borane have a negative charge is
0.082 AU, thus conﬁrming the formation of dihydrogen
bond between two oppositely charged hydrogen atoms.
The same trend continues for all the complexes with positive charged acetylenic hydrogen interacting with two negative charged hydrogens of BH3 group forming a pair of
symmetrically bifurcated dihydrogen bonds.
7
Table 1
˚ ), B–H H and C–H H angles (°) and stabilization energies, DE, (kJ mol 1) for various dihydrogen bonded complexes of
Optimized H H distances (A
BTMA
B3LYP/6-311++G(d,p)
B3LYP/aug-cc-pVDZ
MP2/6-311++G(d,p)
MP2/aug-cc-pVDZ
C2H2–BTMA
H H
B–H H
C–H H
DE
2.40
98.5
150.7
6.0
2.37
97.5
152.3
6.9
2.32
97.0
143.9
11.4
2.27
95.2
146.1
14.2
FC2H–BTMA
H H
B–H H
C–H H
DE
2.36
98.2
153.2
6.8
2.29
97.4
152.6
7.6
2.33
96.7
147.6
12.2
2.23
94.7
148.5
14.8
ClC2H–BTMA
H H
B–H H
C–H H
DE
2.35
98.0
152.9
7.3
2.29
97.2
152.8
8.0
2.34
96.7
143.8
12.5
2.22
94.7
146.6
16.2
NCC2H–BTMA
H H
B–H H
C–H H
DE
2.25
93.1
153.0
12.9
2.19
92.4
152.3
13.6
2.21
96.6
146.1
17.5
2.14
94.0
146.6
20.6
Table 2
MEP and NPA charges on interacting acetylenic and borane hydrogens in
all the four complexes calculated at MP2/aug-cc-pVDZ level of theory
MEP
NPA
CH
C2H2–BTMA
FC2H–BTMA
ClC2H–BTMA
NCC2H–BTMA
BH
+0.236
+0.347
+0.258
+0.284
0.254
0.257
0.249
0.215
CH
BH
+0.246
+0.259
+0.261
+0.255
0.082
0.070
0.081
0.072
The bonding pattern of dihydrogen bonded complexes
can be analyzed by the topographical study of electron density. In the present case, the critical points of electron density distribution were obtained, characterized by the rank
and trace of the Hessian matrix. A (3, 1) bond critical
point with positive Laplacian for the electron density distribution at the bond critical point indicates the non-covalent
interaction. However, in the case of very strong hydrogen
and dihydrogen bonds, which are often partly covalent in
nature, have negative values of Laplacian of electron density at the BCPs [24]. Table 3 lists the electron density and
their Laplacian for the present complexes. The electron
density and its Laplacian range from 0.002 to 0.04 and
0.02 to 0.15 a.u., respectively, and are in the range accept-
able for hydrogen [25] and dihydrogen bonds [26]. Further,
the BCPs between the two interacting hydrogens in all the
complexes are of the (3, 1) type, with positive values for
the Laplacian of the electron density. It is clearly evident
from the charge and critical point analysis that in all the
complexes the interaction is between two oppositely
charged hydrogen atoms thus conﬁrming the formation
of dihydrogen bonds.
Further, natural bond orbital (NBO) analysis was also
carried out at B3LYP/aug-cc-pVDZ level using structures
optimized at MP2/aug-cc-pVDZ level. This is due to the
fact that the natural bond orbital (NBO) analysis yields
reliable values only with either HF or DFT methods, since
the wavefunction is completely deﬁned [27]. Table 3 also
lists the changes in the electron occupancies, relative to
the monomer, for both donor r B–H bonding orbital
and the acceptor r* C–H bonds anti-bonding orbital.
Clearly, the donor orbital looses the occupancy and the
acceptor gains, implying charge transfer from r B–H bonding orbital to r* C–H bonds anti-bonding orbital. Consequently the C–H bond is weakened resulting in lowering its
stretching frequency.
It is well known that the donor X–H bond is elongated
due to the formation of hydrogen bond. In the case of
Table 3
Electron density at the critical points (CP), Laplacian of electron density between H H contacts and the changes in the electron occupancy in the
bondinga and anti-bondingb orbitals of the donor and the acceptors, respectively, in various complexes
Nature of CP
q(r)
D2q(r)
C2H2–BTMA
(3,
1)
0.0084
0.0287
0.00248
0.00520
0.00040
FC2H–BTMA
ClC2H–BTMA
NCC2H–BTMA
(3,
(3,
(3,
1)
1)
1)
0.0089
0.0091
0.0101
0.0304
0.0310
0.0361
0.00292
0.00303
0.00492
0.00656
0.00656
0.00996
a
b
r BH is the donor NBO.
r* CH is the acceptor NBO.
DDonor occupancy
DAcceptor occupancy
8
Table 4
C–H stretching frequenciesa and their shiftsb in various complexes of acetylenes with BTMA
B3LYP/6-311++G(d,p)
B3LYP/aug-cc-pVDZ
MP2/6-311++G(d,p)
MP2/aug-cc-pVDZ
C2H2–BTMA
3243 (3275) 32
3358 (3374) 16
3232 (3274) 42
3353 (3373) 20
3257 (3288) 31
3355 (3373) 18
3252 (3292) 40
3357 (3375) 18
FC2H–BTMA
ClC2H–BTMA
3284 (3345) 61
3273 (3337) 64
3273 (3349) 76
3267 (3343) 76
3302 (3357) 55
3287 (3342) 55
3288 (3368) 80
3279 (3355) 76
NCC2H–BTMA
3246 (3322) 76
3236 (3328) 92
3247 (3321) 74
3238 (3333) 95
a
b
The values given in parenthesis are for the monomer.
Shifts are italicized.
example, MikamiÕs group has shown for several hydrogen
bonded complexes of phenol that the lowering of the O–
H stretching vibration of the phenol moiety is linearly correlated to the proton aﬃnity of the acceptor [28,29]. To
ascertain whether the linear correlation holds for hydrogen
bonded complexes of acetylene, the structures and vibrational frequencies of hydrogen bonded complexes of acetylene with water, methanol, dimethylether, ammonia,
trimethylamine, and N,N-dimethyl-ethylamine were calculated at MP2/6-311++G(d,p) level and are listed in Table
5. Fig. 2 shows the plot of total lowering of C–H stretching
frequencies [R(DmCH)] of acetylene in hydrogen bonded
complexes with water, methanol, ammonia, trimethylamine, and N,N-dimethyl-ethylamine against the gas-phase
proton aﬃnities of the acceptors. It is evident from Fig. 2
that the lowering of C–H stretching frequencies of the acetylene moiety is linearly correlated with proton aﬃnities of
the bases. In order to set the conﬁdence limit, using the calculated R(DmCH) of 98 cm 1 for the acetylene-dimethylether
complex (Table 5), the proton aﬃnity of dimethylether is
estimated to be 780 kJ mol 1 (Fig. 2, m), which is in very
good agreement with the experimental value of
792.3 kJ mol 1 [30]. Further, from the same correlation,
using R(DmCH) of 49 cm 1 for the dihydrogen bonded acetylene-BTMA complex, the proton aﬃnity of BTMA can be
estimated as 690 kJ mol 1 (Fig. 2, n).
Recently, we had used the linear correlation between the
lowering of the O–H stretching vibration of the phenol
moiety in various hydrogen bonded complexes and estimated the proton aﬃnity of BTMA as 710 kJ mol 1 [31].
BTMA complexes with the acetylenes, we have examined
the changes in the bond lengths and the stretching frequencies of the C–H groups. In the case of acetylene-BTMA
complex the maximum elongation of the interacting C–H
˚ ) is observed at MP2/aug-cc-pVDZ level,
bond (0.004 A
while the other C–H bond of acetylene showed marginal
˚ . On the acceptor side the two interelongation of 0.001 A
˚ , and the
acting B–H bonds are elongated by 0.001 A
non-interacting B–H bond shortens by same amount. In
the case of ﬂuoro-, chloro-, and cyano-acetylene complexes
with BTMA, the elongation of C–H bonds are 0.006, 0.006,
˚ , respectively, at MP2/aug-cc-pVDZ level of
and 0.007 A
theory. The natural consequence of the elongation of the
C–H bonds is lowering of its stretching frequency. The
vibrational spectroscopy of the donor groups in the
hydride stretching region has been one of the major experimental tool to characterize hydrogen bonds [1]. Table 4
lists the C–H stretching frequencies of acetylenes and the
shifts upon dihydrogen bonded complex formation. Once
again, in all the cases the lowering of the C–H stretching
frequency is higher when calculated using aug-cc-pVDZ
basis set. Also, as expected the lowest shifts are observed
for acetylene-BTMA and highest for cyanoacetyleneBTMA complex, while the ﬂuoro- and chloro-acetylene
complexes take intermediate values.
The two most important factors that inﬂuence the structure and energetics of hydrogen bonding are: (1) the acidity
of the donor; (2) the proton aﬃnity of the acceptor. Therefore, for a given donor the stabilization energy should be
proportional to the proton aﬃnity of the acceptor. For
Table 5
C–H stretching frequencies (in cm 1) of acetylene and its complexes calculated at MP2/6-311++G(d,p) level of theory
C2H2
C2H2–BTMA
C2H2–C2H2
C2H2–H2O
C2H2–MeOH
C2H2–MeOMe
C2H2–NH3
C2H2–NMe3
C2H2–NEtMe2
a
b
c
1
m1
m3
Dm1
Dm3
R(Dm)
PA/kJ mol
3373
3355
3365
3353
3350
3348
3347
3339
3338
3288
3257
3275
3246
3230
3215
3197
3117
3124
–
–
–
–
690.0a, 836.8b
641.4c
691.0c
754.3c
780a, 792.3c
853.6c
948.9c
960.1c
Estimated using linear correlation in Fig. 2.
G2 proton aﬃnity from [31].
Gas phase proton aﬃnities from [30].
18
08
20
23
25
26
34
35
31
13
42
58
73
91
171
164
49
21
62
81
98
117
205
199
9
Acknowledgments
NMe3
200
NEtMe2
Σ(∆ν)CH / cm
-1
150
Financial support from CSIR (Grant No. 01(1902)/03/
EMR-II) and BRNS (Grant No. 2004/37/5/BRNS/398)
are gratefully acknowledged.
NH3
References
MeOMe
100
MeOH
H2O
50
BTMA
C2H2
650
700
750
800
850
900
950
Proton Affinity / kJmol-1
Fig. 2. Plot of total lowering of the C–H stretching frequencies R(Dm) of
acetylene moiety in various hydrogen bonded systems vs proton aﬃnities
of the acceptors (h) The straight line is linear least-squares ﬁt to the data
points, excluding the MeOMe (m) and BTMA (j). From the ﬁt, the
proton aﬃnities of MeOMe and BTMA can be estimated as 780 and
690 kJ mol 1, respectively.
The estimated values of proton aﬃnity of BTMA, in both
the cases (690 and 710 kJ mol 1) are much lower than the
calculated value of 836.8 kJ mol 1 using G2 method [31],
which is know to predict the proton aﬃnities with an accuracy of ±10 kJ mol 1 [32–34]. From these results, one can
straightforwardly infer that the linear correlation between
frequency shifts and the proton aﬃnities involving hydrogen bonded species grossly underestimates the proton aﬃnities of the dihydrogen bonded species. This implies that
such a correlation does not hold for dihydrogen bonded
complexes and re-emphasizes our earlier assertion [31] that
the premise of the dihydrogen bond being another type of
hydrogen bond (r and p) might be incorrect.
4. Conclusions
In summary, acetylene and ﬂuoro, chloro, and cyano
substituted acetylenes form dihydrogen bonded complex
with borane-trimethylamine, with H H contact distances
˚ and stabilization energies in the range of 6–
less than 2.4 A
20 kJ mol 1. The stabilization energy increases with the
substitution of ﬂuoro, chloro, and cyano groups, in that
order, respectively. The molecular electrostatic potential
derived charge, natural population, natural bond order,
atoms in molecules analysis support the formation of C–
H H–B dihydrogen bonds. Using the linear correlation
between the lowering of the C–H stretching frequencies
of acetylene and proton aﬃnities of bases, in various
hydrogen and dihydrogen bonded complexes, the proton
aﬃnity of borane-trimethylamine was estimated as
690 kJ mol 1, a value much lower than the G2 value of
836.6 kJ mol 1. It can be concluded from the results presented here that dihydrogen bonded complexes cannot be
correlated along with the hydrogen bonded complexes.
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