Journal of Molecular Structure (Theochem) 577 (2002) 219±228
www.elsevier.com/locate/theochem
Topological and NBO analysis of hydrogen bonding interactions
involving C±H´´ ´O bonds
Gladis L. Sosa a, NeÂlida M. Peruchena a, RubeÂn H. Contreras b, Eduardo A. Castro c,*
a
Facultad de Ciencias Exactas y Naturales y Agrimensura, UNNE, Corrientes, Argentina
Departamento de FõÂsica, Facultad de Ciencias Exactas y Naturales UBA, Ciudad Universitaria, PabelloÂn I, NuÂnÄez,
Buenos Aires 1154, Argentina
c
Departamento de QuõÂmica, CEQUINOR, Facultad de Ciencias Exactas, UNLP, C.C. 962, La Plata 1900, Argentina
b
Received 1 June 2001; accepted 29 June 2001
Abstract
Ab initio calculations are used to analyze the effect of C±H´ ´ ´O hydrogen bonding interactions on the C±H bond length.
Methane derivatives, CH42n Xn (where n ˆ 1; 2; 3 for X ˆ F and n ˆ 1 for X ˆ NO2 ) are taken as proton donors and H2O as
acceptor. The topological properties of electronic charge density are analyzed employing the Bader's Atoms In Molecules
(AIM) theory. A good correlation between the structural parameters and the properties of charge density is found. Then, using
the Natural Bond Orbitals (NBO) approach, the effects of charge transfer interactions on the behavior of the C±H bond are
investigated. It is found that the competitive effects between intermolecular nO ! s…C±H† p and intramolecular nF ! s…C±H† p
of charge transfer interactions in the CH42nFn/H2O systems causes a decrease of the s (C±H) p antibond occupation number, and
concomitantly, a contraction of the corresponding C±H bond. In the NO2CH3/H2O system, the only charge transfer interaction,
the n O ! s…C±H† p intermolecular interaction cause a increase of the s (C±H) p antibond occupation number which entails a
slight lengthening of the corresponding C±H bond. q 2002 Elsevier Science B.V. All rights reserved.
Keywords: Bader's AIM theory; Hydrogen bonding; NBO; Intermolecular interactions; Charge transfer
1. Introduction
When the vibrational spectra (determined by
Raman or IR spectroscopy) of a free X±H group
and a X±H´ ´ ´Y traditional hydrogen bond are
compared, generally is observed that the X±H stretching vibration n s undergoes a substantial shift towards
a lower frequency and the band-width and the n s
intensity increase [1±3]. For this reason, the lengthen-
* Corresponding author.
E-mail address: [email protected]
(E.A. Castro).
ing of the covalent X±H bond is often used like test
for the presence of a hydrogen bond [4].
Other useful test for the presence of a hydrogen
bond is based in NMR spectroscopy. Previously it
was reported that the proximity of a C±H bond to
an atom bearing lone pairs may yield either an
increase or a decrease in the corresponding 1J(CH)
coupling parameter [5]. While in the ®rst case a slight
shortening of the C±H bond length is calculated, in
the second case a slight lengthening of that C±H bond
length is obtained. A model system for the former is
the molecular complex H3C±H´ ´ ´FH, and that for the
latter is the N ; C±H¼OH 2 : This founding have
been rationalized as originating in hydrogen bond
0166-1280/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved.
PII: S 0166-128 0(01)00670-4
220
G.L. Sosa et al. / Journal of Molecular Structure (Theochem) 577 (2002) 219±228
Table 1
Selected geometric parameters and interaction energies calculated in the complexes 1±4. The corresponding C±Ha bond lengths in the isolated
compounds are given between parentheses
Ê)
d(C±Ha) (A
Ê)
d(Ha´ ´´O) (A
Ê)
d(C´´´O) (A
EBSSE (kcal/mol) a
a
1
2
3
4
1.0809 (1.0829)
2.5952
3.6761
21.0562
1.0773 (1.0801)
2.4316
3.5089
22.1428
1.0743 (1.0767)
2.2958
3.3701
23.4901
1.0813 (1.0808)
2.3274
3.4087
22.9433
The EBSSE values are corrected for BSSE resorting to the counterpoise correction.
interactions. Afonin et al. [6,7], have also rationalized
an increase in a 1J(C(sp 2)±H) coupling as originating
in a hydrogen bond interaction with a close F atom.
Satonaka et al. [8,9], have explained a similar increase
in a formyl 1J(CH) coupling as originated in a
OyC±H¼OyC hydrogen bond type.
It is also known that the magnitude 1J(CH)
coupling constant depends upon its stereochemical
relationships to vicinal lone electron pairs. For
instance, there is an difference of approximately
10 Hz in 1J(CH) coupling constants at the anomeric
centres of anomeric pairs of glycosides [10]. This
difference is attributed in the literature to the charge
transfer interactions, nX ! s Cp ±H ; which seem to
cause a lengthening and a weakening of axial C±H
bond which entails a decrease in the corresponding
1
J(CH) [11±16]. It can thus be expected that the
phenomenon of charge transfer also in¯uences on
the C±H bond length in the C±H´ ´ ´O interactions.
The C±H´ ´ ´O interactions frequently occur in
biological structures. They participate in a wide
variety of processes, such as the molecular recognition drug-receptor, immune response and in the architecture and function of biological systems [17±20].
The study of their structural characteristics has a
fundamental interest since they could help to elucidate
the complex nature of biological processes.
In the previous work, we have veri®ed the existence
of bonding interactions of the C±H´ ´ ´O type which
show, respectively, a lengthening and a shortening
of the C±H bond [21]. In the present work, we investigated the origin of this different behaviors of the C±
H bond in a series of substituted methanes forming
complexes with the water. The bonding characteristic
of these systems are investigated by means of the
Bader's Theory of Atoms in Molecules (AIM) [22].
Subsequently, the charge transfer effects on the C±
H´ ´ ´O interactions is analyzed by means of Weinhold's Natural Bond Orbitals (NBO) technique of
decomposition [23,24].
2. Methods
The geometries of the different complexes studied
were optimized at the HF/6-31G pp level, resorting to
the supermolecule approach. It has been shown in the
literature that this level of theory reproduce reliable
and consistent data on hydrogen bonding interactions
[25±28]. The binding energies were calculated at the
RHF/6-31111G pp level of theory and corrected for
basis set superposition error by the counterpoise
procedure [29]. It must be noted however, that the
purpose of this study is not the rigorous calculation
of the interaction energies. On the other hand, since
that the results obtained keep a good qualitative agreement with those informed by other authors [30,31], we
could consider that possible calculations at a higher
theory level would not change signi®cantly the main
conclusions of this work.
The electronic densities and NBO analyzes [32]
were also calculated at the RHF/6-31111G pp level.
All the calculations were carried out with the gaussian 94 package of computer programs [33]. The
topological properties of the charge density were
computed with the aimpac software [34].
3. Results and discussion
3.1. Energetics and geometries
The interaction energies of the complexes CFH3/
H2O (1), CF2H2/H2O (2), CF3H/H2O (3) and
NO2CH3/H2O (4) as computed at indicated level and
G.L. Sosa et al. / Journal of Molecular Structure (Theochem) 577 (2002) 219±228
Fig. 1. Geometrical arrangements of the complexes studied. In
complex 1, X122 ˆ H and X3 ˆ F: In complex 2, X1 ˆ H and
X223 ˆ F: In complex 3, X123 ˆ F: In complex 4, X1 ˆ NO2
and X223 ˆ H:
corrected for basis set superposition error by the
counterpoise procedure, are reported in Table 1. We
have also included the C´ ´ ´O, Ha´´ ´O intermolecular
distances and the C±Ha bond lengths. The values in
parentheses correspond to the isolated compounds. It
is worth stressing that the geometries of the
complexes were fully optimized with the single
restriction of a linear H-bond, i.e. the C±H´ ´ ´O
angle was taken to be 1808. In the absence of such a
restriction, some of the complexes optimized to
geometries that are not relevant to this study. Fig. 1
shows the geometric arrangement of the complexes
studied. In all cases Ha denotes the hydrogen atom
involved in the C±H´ ´´O interaction.
From Table 1, it can be seen that the binding
energies lie in the range between 1.05 and 3.49 kcal/
mol. In good agreement with the binding energies
reported by other authors for the complexes 1±3, it
is found an increment (in absolute value) of about
1.0 kcal/mol for each F atom [30,31]. Whereas the
value obtained for complex 4 is around 0.5 kcal/mol
lower than for complex 3. These results indicate that
the stability of these C±Ha´´ ´O interactions increase in
the order 1 , 2 , 4 , 3. Consistently, it is observed a
Ê in the C´ ´ ´O intermolecular
contraction of about 0.3 A
distance on going from the complex 1 to complex 3. It
must also be noted that this equilibrium separation,
Ê , is well inside the
which varies from 3.37 to 3.67 A
Ê , based on a
interval quoted by Desiraju of 3.0±4.0 A
survey of over 100 structures [35]. On the other hand,
all the C±Ha´´ ´O bonds obey the geometrical criteria
statistic of Taylord and Kennard [36].
When the C±Ha bond lengths in the complexes
and the isolated compounds are compared it is
observed that the complexation yields a shortening
of the C±Ha bond in the ¯uorosubstituted
compounds (1±3). The amount of the bond length
reduction increase on going from complex 1
Ê ) to complex 2 (0.0028 A
Ê ) and decrease
(0.0020 A
221
Ê ). These results
again in the complex 3 (0.0024 A
Ê
are in line with the contraction of 0.0006 A
previously reported for the system CH4/H2O [21].
It is worth noting that this trend is opposite to that
observed in the complex 4, where the C±Ha bond
likewise in conventional hydrogen bonds, underÊ ). Also in line with
goes a lengthening (0.0005 A
Ê previously reported
the lengthening of 0.0097 A
for the system NCH/H2O [21].
Furthermore, it is important to point out that the
behavior of the C±Ha bond was also examined in
the systems CH2 yCH2 =H2 O; CFHyCH2 =H2 O;
CH3OH/H2O CHCl3/H2O, ®nding in each case that
the C±Ha bond results shorter in the complexes
than in the CH2 yCH2 ; CFHyCH2 ; CH3OH and
CHCl3 isolated compounds. These results, in addition to those found in the literature [4,25], suggest
that the opposed trends observed in the C±Ha bond
lengths is not related directly to the hybrid character of the carbon atom neither with the strength of
the interaction. It is worth stressing that the
changes in the C±Ha bond length are insensitive
to basis set [5,31]. As we will see next, these
results are consistent with the topological properties
of charge density at the bond critical points.
3.2. Topological analysis
Different studies have pointed out that formation of
hydrogen bonds is associated with the appearance of a
bond critical point between the hydrogen atom and the
acceptor atom, which are linked by the concomitant
bond path [26±28,37]. This critical point has typical
properties of a closed-shell interaction: the value of
electron density at the bond critical point, r (rc), is
relatively low, the relationship, ul 1u/l 3 is ,1 and the
Laplacian of the electron density, 7 2 r…rc †; is positive
indicating that the interaction is dominated by the
contraction of charge away from the interatomic
surface toward each nuclei (see Figs. 2±5). As can
be seen in Table 2, these conditions are ful®lled in
the Ha´ ´´O bond critical points for the complexes 1±4.
The electron density at the bond critical point ranges
from 0.006 to 0.011 a.u., which compares fairly well
with the values reported for different hydrogen
bonded complexes, where this quantity was found to
vary from 0.002 to 0.034 a.u. [25,28]. Similarly, the
Laplacian of the electron density ranges from 0.022 to
222
G.L. Sosa et al. / Journal of Molecular Structure (Theochem) 577 (2002) 219±228
Fig. 2. Display of the gradient vector ®eld of the charge density for
the complex 3. Each line represents a trajectory of 7r…r†: A nucleus
acts as an attractor of the 7r…r† ®eld, that is, all the trajectories in
some open neighborhood of a nucleus terminate at that nucleus.
These trajectories are lines of steepest ascent through the charge
density. An atom is the union of an attractor and its basin. Basins of
neighboring atoms are separated by trajectories that terminate at a
bond critical point (denoted by solid circles). A pair of lines of
steepest ascent originate at each critical point and terminate, one
to each, at the neighboring nuclei. They de®ne the atomic interactions lines±lines (bond paths) along which r is a maximum with
respect to any neighboring line.
0.044 a.u. and it also compares satisfactorily with
previous results that vary from 0.016 to 0.139 a.u.
[25,28].
From Table 2, it can also be observed that the
Fig. 3. Display of the gradient vector ®eld of the charge density for
the complex 4.
Fig. 4. Contour map of the Laplacian of r (r), for the complex 3 with
the bonds path linking the C, Ha and O nuclei and bond critical point
superimposed. The solid contour lines correspond to negative
values of 7 2 r…r†; the dashed ones to positive values. Starting at a
zero contour, contour values change in steps of ^2.10 n, ^4.10 n,
^8.10 n with n beginning at 23 an increasing in steps of unity. Note
that the C±Ha bond critical point occurs at a region of charge
concentration (region of negative values of 7 2 r† while the Ha´´´O
bond critical point is found in a region of charge depletion concentration (region of positive values of 7 2 r†:
density and the Laplacian of charge density at the
Ha´ ´´O bond critical point increases on going from
complex 1 to complex 3. This increment is consistent
with the contraction of the intermolecular distance
discussed above, and indicates that there is a progression toward stronger interactions as ¯uoride atoms are
added to the proton donor. In the complex 4 the value
of density is identical to that found in the complex 3,
Fig. 5. Contour map of the Laplacian of r (r), for the complex 4 with
the bonds path linking the C, Ha and O nuclei and bond critical point
superimposed. The solid contour lines correspond to negative
values of 7 2 r…r†; the dashed ones to positive values. Starting at a
zero contour, contour values change in steps of ^2.10 n, ^4.10 n,
^8.10 n with n beginning at 23 an increasing in steps of unity. Note
that the C±Ha bond critical point occurs at a region of charge
concentration (region of negative values of 7 2 r† while the Ha´´´O
bond critical point is found in a region of charge depletion concentration (region of positive values of 7 2 r†:
1
Bond
r (rc)
7 2r (r)
l1
l2
l3
ul 1u/l 3
C±Ha
0.3003 (0.2966)
21.1501 (21.1233)
20.8352
20.7911
0.4762
1.7539
2
Ha´´´O
0.0063
0.0221
20.0062
20.0055
0.0338
0.1834
C±Ha
0.3159 (0.3113)
21.2747 (21.2358)
20.9180
20.8940
0.5372
1.7089
3
Ha´´´O
0.0087
0.0315
20.0091
20.0082
0.0488
0.1865
C±Ha
0.3264 (0.3221)
21.3749 (21.3248)
20.9819
20.9818
0.5888
1.6676
4
Ha´´´O
0.0113
0.0440
20.0129
20.0116
0.0685
0.1883
C±Ha
0.2943 (0.2919)
21.1093 (21.0866)
20.8085
20.7861
0.4853
1.6660
Ha´´´O
0.0113
0.0407
20.0123
20.0116
0.0646
0.1904
G.L. Sosa et al. / Journal of Molecular Structure (Theochem) 577 (2002) 219±228
Table 2
Analysis of C±Ha and Ha´´´O bond critical points in the complexes 1±4 (The values corresponding to the isolated compounds are given between parentheses. All quantities are in
atomic units. Symbols are explained in the text)
223
224
G.L. Sosa et al. / Journal of Molecular Structure (Theochem) 577 (2002) 219±228
Table 3
Change of atomic properties on C, Ha, and O atoms in complexes 1±
4 (All quantities are in atomic units. Symbols are explained in the
text)
DN (V )
DE (V )
DV (V )
DuMu (V )
Dv (V )
V
1
2
3
4
Ha
C
O
Ha
C
O
Ha
C
O
Ha
C
O
Ha
C
O
20.047
0.024
0.012
0.0172
20.0124
20.0143
0.0371
20.0875
20.0629
20.022
0.000
0.016
23.559
1.073
0.200
20.055
0.040
0.018
0.0205
20.0266
20.0180
0.0444
20.1583
20.0976
20.025
0.014
0.019
24.844
1.336
20.809
20.065
0.054
0.024
0.0259
20.0420
20.0245
0.0559
20.2170
20.1370
20.026
0.068
0.024
26.816
1.344
21.837
20.064
0.030
0.020
0.0243
20.0145
20.0216
20.0458
20.0999
20.1184
20.027
0.012
0.032
26.558
1.437
22.111
while the Laplacian is slightly smaller. Thus, as it has
been found by other authors [25±28,38±39], r (rc) and
7 2 r…rc † at the intermolecular bond exhibit an
approximate linear relationship with the strength of
the interaction.
This interaction with the base atom, Ha´ ´ ´O, is to be
contrasted with that found in the C±Ha bond of the
acid which exhibits the characteristic of a shared
interaction, i.e. the value of electron density at the
bond critical point is relatively large, the relationship
ul1 u=l3 is .1, and the Laplacian of the charge density
is negative indicating that the electronic charge is
concentrated in the internuclear region (see Figs. 2±
5). In Table 2, the properties calculated at this bond
critical point are reported. The values within parentheses correspond to the isolated compounds. It is worth
noting that in line with the contraction of the C±Ha
bond, the density at the corresponding bond critical
point, increase upon complexes 1±3 formation (by
0.0037, 0.0046 and 0.0043 a.u., respectively).
However, when complex 4 is formed the electronic
density also increases, in spite of the fact that bond C±
Ha undergoes a stretch, although this increment is the
lower one (0.0024 a.u.). A similar trend upon
complexation is also observed in the changes in the
charge density Laplacian.
In addition to the local topological properties at
the bond critical points, a set of atomic integrated
properties have been considered to be indicative of
hydrogen bonding [26,28]. They are referred to the
hydrogen atom and are determined by integration of
the given quantity over the atomic basin. Such
properties are the atomic charge (q), the energy of
the atom (E), the energy potential intra-atomic (V),
the dipolar polarization (M), and the atomic volume
(v). Previously has been reported [21] that in addition
to the usual study of hydrogen parameters, it is
important to analyze also the atomic properties of
the acceptor (O) and donor (C) atoms. In Table 3,
the changes in the atomic properties on C, H and O
atoms are reported. It is worth stressing that the
changes are calculated subtracting the property
value of the atom in the isolated compound to the
value of the corresponding property in the complex.
A careful consideration of these results, allow us to
make the following comments.
The hydrogen atom loses charge in all cases
(denoted as a decrease of the electronic population
…DN , 0††; in amounts ranging from 0.047 e for the
weakest complex (1) to 0.065 e for the strongest
complex (3). As a consequence of this loss of electronic charge, the change in V(H), which denotes the
potential energy of interaction of the charge density
within the basin of the H atom with its own nucleus, is
positive in the complexes 1±3. In the complex 4,
however DV(H) is ,0. While the change of atomic
energy, DE, is positive in all cases indicating that the
H atom is unstabilized. It must be mentioned that no
exception has been found for DE…H† is ,0 in previous
studies. Also, as a consequence of the loss of their
nonbonded density, the hydrogen atom [28] undergoes a reduction in the atomic polarization and in
the atomic volume …DuMu; Dv , 0†: More importantly,
in agreement with the results reported by Carroll and
Bader [26], the changes DN, DE and Dv on hydrogen
atom is roughly correlated with the strength of the
interaction.
The acceptor (O) and donor (C) atoms gain charge
…DN , 0† in all cases, being the charge gained by
C atom considerably greater than the charge gained
by O atom. It can also be observed that there is a rough
correlation between the decrease in volume of the
C atom and increasing DN: As a result of the gain
of electronic charge, the C and O atoms are stabilized
…DV and DE , 0† in the complexes. The volume of the
C atom, as it has been found for the system CH4/H2O
G.L. Sosa et al. / Journal of Molecular Structure (Theochem) 577 (2002) 219±228
225
Table 4
p
antibonds and the nO and nF lone pairs, with their corresponding orbital
NBO analysis of complexes 1±4: occupation numbers for the s CH
energies E. The same parameters calculated for the isolated compounds are given between parenthesis (The NBO analyses carried out at HF/631111G pp basis set level. All quantities are in atomic units)
p d
s Cha
Es pCHa
p d
s CHo
Es pCHo
n1F
E1F
n2F
E2F
n3F
E3F
n1O
E1O
n2O
E2O
1a
2b
3c
0.01301 (0.01328)
0.62324 (0.61653)
0.01345 (0.01328)
0.64988 (0.61653)
1.99599 (1.99592)
21.34820 (21.35484)
1.98015 (1.97866)
20.61842 (20.62605)
1.97921 (1.97866)
20.61809 (20.62605)
1.99777 (1.99798)
20.87913 (20.90165)
1.99570 (1.99718)
20.54900 (20.50752)
0.02592 (0.02708)
0.61903 (0.57497)
0.02652 (0.02708)
0.58329 (0.57497)
1.99500 (1.99484)
21.38735 (21.39790)
1.97874 (1.97720)
20.65010 (20.66229)
1.96074 (1.95962)
20.64294 (20.65533)
1.99762 (1.99798)
20.81382 (20.90165)
1.99513 (1.99718)
20.62892 (20.50752)
±
±
4a
0.03820 (0.04104)
0.59971 (0.53887)
1.99395 (1.99369)
21.42320 (21.43859)
1.96780 (1.96575)
(20.69074) 20.67310
1.95754 (1.95644)
20.66973 (20.68753)
1.99733 (1.99798)
20.53355 (20.90165)
1.99507 (1.99718)
20.92484 (20.50752)
±
±
±
±
±
±
0.00601 (0.00316)
0.63939 (0.59760)
0.00423 (0.00421)
0.62413 (0.61238)
1.99761 (1.99798)
20.75661 (20.90165)
1.99420 (1.99718)
20.69825 (20.50752)
a
Both hydrogen atoms are equal due to symmetry reasons.
F and F 0 are equal due to symmetry reasons.
c
F, F 0 and F 00 are equal due to symmetry reasons.
d
p
p
s CHa
denotes occupation numbers of the antibonds involved in the C±Ha´´ ´O interaction and s CHo
denotes the occupation number of the
other antibonds.
b
[21], increase in all cases, while the volume of the O
atom increase slightly in the complex 1 and decrease
in the complexes 2±4. A decrease in the volume of O
atom, although considerably larger, has also been
found in the system NCH/H2O, …dv…O† ˆ
211:11 a:u:† [21]. The results discussed shown that
the complexation leads, in all cases, to a net attractive
interaction of C d 2 ±H d 1´ ´´O d 2 type.
Table 5
The second-order perturbation energies E (2) (donor ! acceptor)
involving the s (C±Ha) p antibond in the 1±4 complexes. The corresponding values in isolated compounds are given between parenthesis (The NBO analyses carried out at the HF/6-31111G pp basis set
level. Energies in kcal/mol)
E (2)n ! s p
p
n1O ! s CHa
p
n2O ! s CHa
p
n2F ! s CHa
p
n2F ! s CHo
p
n3F ! s CHa
p
n3F ! s CHo
a
b
c
1
0.12
1.19
8.27 (±)
2.21 c (6.71)
± (8.94)
6.54 c (2.24)
2a
0.23
1.95
6.69 (7.24)
6.94 (7.24)
1.54 (1.88)
1.97 (1.88)
3b
±
2.83
8.44 (9.59)
±
±
±
4
0.21
2.65
±
±
±
±
F and F 0 are equal due to symmetry reasons.
F, F 0 and F 00 are equal due to symmetry reasons.
p
The same interaction energy with the other antibond s CHo
.
3.3. Natural bond orbitals analysis
It is important to recall that in the NBO analysis the
electronic wavefunction is interpreted in terms of a set
of occupied Lewis and a set of unoccupied non-Lewis
localized orbitals [23]. Delocalization effects can be
identi®ed from the presence of off-diagonal elements
of the Fock matrix in the NBO basis. The strengths of
these delocalization interactions, E (2), are estimated
by second-order perturbation theory.
In Table 4, the NBO occupation numbers for the
s (C±H) p antibonds, the oxygen lone pairs, nO, the
¯uorine lone pairs, nF, and their respective orbital
energies, e are reported. Ha denotes the hydrogen
atom involved in the C±H´ ´ ´O interaction and Ho
denotes the others hydrogen atoms. The secondorder perturbation energies E (2) (donor ! acceptor)
that involve the s (C±H) p antibonds are given in
Table 5. The data are referenced to the values for
the isolated molecules (numerical data between
parentheses). It is worth stressing that, as it is usual,
the orbital energies, e , are reported in ua, while the
second-order perturbation energies E (2) are reported in
kcal/mol.
226
G.L. Sosa et al. / Journal of Molecular Structure (Theochem) 577 (2002) 219±228
Table 6
Analysis of F±Ha and Ha´´´N bond critical points in the complex
FH´´´NH3 (All quantities are in atomic units)
FH´ ´´NH3
Bond
Ê)
D (A
r (rc)
7 2r (r)
l1
l2
l3
F±Ha
0.9183 (0.9006)
0.3584 (0.3922)
23.1552 (23.3639)
22.6433
22.6433
2.1313
Ha ±N
1.8373 (±)
0.0343 (±)
0.1336 (±)
20.0519
20.0519
0.2172
When the NBO results for the isolated compounds
are compared, it can be seen that the s (C±H) p antibonds occupation number in the ¯uoromethanes, is
fairly high (ranges from 0.01328 to 0.04104 e).
Besides, the occupation number of these antibonds
increase in the order CH3F , CH2F2 , CHF3, being
the increment around 0.014 e for each F atom. Their
orbitals energies increase in this same order. It is
important also to note that the F lone pairs occupation
number, n2F and n3F differ from the ideal occupation
by an important amount. These results can be rationalized in terms of the charge transfer interactions
between orbitals. As can be seen in Table 5, the F
lone pairs, n2F and n3F participate as donors and the
s (C±H) p antibonds as acceptors in strong intramolecular charge transfer interactions, n F !
s…C±H† p : The sum E (2) terms corresponding to these
interactions can be considered to be the total charge
transfer energy, ET(2) and it was found to be 8.94,
18.24, and 28.77 kcal/mol for CH3F, CH2F2, and
CHF3, respectively. An increment of about 10 kcal/
mol for each F atom. In the nitromethane molecule,
due to the absence of these strong intramolecular
interactions, the s (C±Ha) p antibond occupation
number is substantially minor (0.00316 e) than in
the ¯uoromethanes.
The most signi®cant results arise when the changes
upon complexation are analyzed. Perusal of the results
in Tables 4 and 5, allows us to make the following
comments:
In all cases the s (C±Ha) p antibonds participate as
acceptors and oxygen lone pairs as donors in intermolecular charge transfer interactions, n O ! s…C±H a †p ;
being the interaction n1O ! s…C±H a †p smaller than
the interaction n2O ! s…C±H a †p : As result, the n2O
occupation number diminishes with respect to its
value in the water molecule (by 0.00169, 0.00241,
0.00211 and 0.00335 e for the complexes 1, 2, 3 and
4, respectively), while the n1O occupation number
remains practically invariant.
In the complexes 1, 2 and 3, the total charge transfer energy, ET(2) corresponding to the intramolecular
interactions, nF ! s…C±H a †p ; decrease by 0.67, 1.78
and 3.45 kcal/mol, respectively. Consistently, the F
lone pairs, n2F and n3F occupation numbers, (n2F plus
n3F on each F atom) increase (by 0.00204, 0.00266 and
0.00315 e respectively). These results suggest that the
nO ! s…C±H a †p intermolecular interaction, inhibits
the intramolecular charge transfer from ¯uorine lone
pairs to the s (C±Ha) p antibond causing a corresponding decrease (about 0.0003, 0.0012 and 0.0028 e,
respectively) in the occupation number of this antibond. It is important to note that the charge lost by
oxygen lone pairs plus the charge lost by s (C±Ha) p
antibond is comparable to the charge gain by F lone
pairs. These changes are accompanied by a contraction of the C±Ha bond.
A opposite trend is found upon complex 4 formation, where the s (C±Ha) p antibond occupation
number increases notably, ca. twice the value for the
isolated CH3NO2 molecule (from 0.00316 to
0.00601 e). This increment is comparable to the
decrease of the oxygen lone pairs, nO occupation
number. Whereas that the intermolecular interaction
of charge transfer, n O ! s…C±H a †p (2.86 kcal/mol) is
of similar magnitude to that found in the complex 3
(2.83 kcal/mol). These results can be rationalized by
considering that in 4, it is the only interaction of
charge transfer to the s (C±Ha) p antibond, and the
competitive effect aforementioned is not observed in
this complex. It is in line with the slight lengthening of
the C±Ha bond.
Finally, it is of interest to compare these results
with those obtained on a conventional hydrogen
bond. For this purpose, the complex between ammonia and hydrogen ¯uoride, H3N´ ´´HF was chosen. The
bonding characteristics of this complex were investigated by Carroll and Bader [27] and con®rm the topological data reported here. In Table 6, the F±Ha bond
distance, N´ ´ ´Ha intermolecular distance and the topological properties in the corresponding bond critical
points are given. These results shown that the F±Ha
Ê upon complexation.
bond is lengthened by 0.0077 A
Consistently, the charge density in this bond critical
G.L. Sosa et al. / Journal of Molecular Structure (Theochem) 577 (2002) 219±228
Table 7
NBO analysis of H3N/HF complex and H3N; HF isolated
p
compounds: occupation numbers for the s HF
antibond and the nN
lone pair, with their corresponding orbital energies E (in atomic
p
units). The second order perturbation energy E …2† nN ! s FH
is
expressed in kcal/mol (The NBO analyses carried out at HF/631111G pp level of theory)
p
s FH
Es pFH
n1N
E1N
p
E …2† nN ! s FH
H3N
H3N/HF
HF
± ±
± ±
1.99728
20.50572
±
0.03100
0.76400
1.96695
20.55662
22.57
0.00000
0.74134
± ±
± ±
±
point decrease (from 0.3922 to 0.3584 a.u.) and the
Laplacian, 7 2 r…rc †; results less negative (it varies
from 23.3639 a.u. in the isolated compound to
23.1552 a.u. in the complex). The strength of the
hydrogen bond (EBSSE ˆ 11:04 kcal=mol calculated
with 6-31111G pp basis set [27]) is clearly re¯ected
in the intermolecular distance N´ ´´Ha, which is considÊ ) than in the complexes 1±4,
erably shorter (1.8373 A
and in the values more larger of the topological properties at the N´ ´´Ha intermolecular bond critical point
(r…rc † ˆ 0:0343 a:u:; 7 2 r…rc † ˆ 0:1336 a:u:).
The results of the NBO analysis on the complex
H3N´ ´´HF and the H3N and HF isolated compounds
are compared in Table 7, where the occupation
numbers of the N lone pair, nN, of s (F±H) p antibond,
their respective orbital energies and the second-order
perturbation energy, E (2), corresponding to the intermolecular interaction n N ! s…F±H a †p are given. It is
also worth to note that this intermolecular interaction
is notably higher (22.6 kcal/mol) than those found in
the 1±4 complexes. As a consequence, the occupation
number of s (F±H) p antibond increase considerably
upon complexation (from 0.000 to 0.0310 e). While
the occupation number of N lone pair decrease by
0.0303 e. This result suggests that all the charge lost
by N lone pair of the base is gain by the s (F±H) p
antibond of the acid.
4. Conclusions
The analysis of the charge density has shown that
all systems studied in this paper satisfy the indicative
criteria of hydrogen bonding interactions. Besides, a
227
good correlation between the binding energy, intermolecular distance, C´ ´ ´O, and the charge density at
the bond critical point has been found.
The NBO analysis reveals that in the ¯uoromethanes, there are strong intramolecular interactions
of charge transfer from F lone pairs to the s (C±H) p
antibonds. As a consequence, the occupation number
of these antibonds is fairly high. Upon complexes
formation, a charge transfer from the lone pair of
the oxygen of the base (H2O) to the s (C±Ha) p antibond is also produced. At the same time, a signi®cant
decrease of the intramolecular interactions is also
observed. C±Ha These results indicate that the intermolecular charge transfer inhibits the intramolecular
charge transfer from the F lone pairs to the s (C±Ha) p
antibond, causing a decrease of occupation number of
this antibond and concomitantly a contraction of the
C±Ha bond.
In the NO2CH3/H2O system, where there is no the
competitive effects between the intra and intermolecular interactions, the charge transfer from the
oxygen lone pair to the s (C±Ha) p antibond leads to
a notable increase of the occupation number of the
antibond and as they also occur in the `Bands of
Bohlmann' [40,41] the corresponding C±Ha bond is
lengthened. A similar result has been found in the
strong H3N´ ´´HF hydrogen bond, where the charge
transfer from nitrogen lone pair to the s (F±Ha) p antibond also causes a notable increment in the occupation number of this antibond and consistently the Ha ±
F bond is lengthened and weakened, as is seen
re¯ected in the change of the charge density in the
corresponding bond critical point. This seem to be
the explanation to the behavior of X±H bond generally observed in the X±H´ ´´Y conventional hydrogen
bonds. At present more evidences and additional
theoretical support for these conclusion is in progress
in our laboratory. Results will be presented elsewhere
in the forthcoming future.
References
[1] A. Hadzi, S. Bratos, in: P. Schuster, G. Zundel, C. Sandorfy
(Eds.), The Hydrogen Bond. Recent Developments in Theory
and Experiments, Vibrational Spectroscopy of the Hydrogen
BondNorth-Holland, Amsterdam, 1976, pp. 565±611.
[2] C. Sandorfy, Top. Curr. Chem. 120 (1984) 41.
[3] P. Marechal, in: H. Rarajczak, W.J. Orville-Thomas (Eds.),
228
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
G.L. Sosa et al. / Journal of Molecular Structure (Theochem) 577 (2002) 219±228
Molecular Interactions, Vibrational Spectroscopy of Hydrogen Bonded Complexes in the Gaseous Phase, vol. 1, Wiley,
New York, 1980, pp. 231±272.
T. Steiner, J. Chem. Soc., Perkin Trans. 2 (1995) 1315.
C. Vizioli, M.C. Ruiz de AzuÂa, C.G. Giribet, R.H. Contreras,
L. Turi, J.J. Dannenberg, I.D. Rae, J.A. Weigold, M. Malagoli,
R. Zanasi, P. Lazzaretti, J. Phys. Chem. 98 (1994) 8858.
A.V. Afonin, M.A. Andriyankov, Zh. Org. Khim. 24 (1988)
1034.
A.V. Afonin, M.V. Sigalov, S.E. Korustova, I.A. Aliev, A.V.
Vashchenko, B.A. Tro®mov, Magn. Reson. Chem. 28 (1990)
580.
H. Satonaka, K. Abe, M. Hirota, Bull. Chem. Soc. Jpn. 60
(1987) 953.
H. Satonaka, K. Abe, M. Hirota, Bull. Chem. Soc. Jpn. 61
(1988) 2031.
S. Perlin, B. Casu, Tetrahedron Lett. (1969) 2921.
S. Wolfe, B.M. Pinto, V. Varma, R.Y.N. Leung, Can. J. Chem.
68 (1990) 1051.
E. Juaristi, G. Cuevas, A. Vela, J. Am. Chem. Soc. 116 (13)
(1994) 5796.
J.E. Anderson, A.J. Bloodworth, J. Cai, A.G. Davies, N.A.
Tallant, J. Chem. Soc., Chem. Commun. (1992) 1689.
K.B. Wiberg, V.A. Walters, W.P. Dailey, J. Am. Chem. Soc.
107 (1985) 4860.
S. Cieplak, J. Am. Chem. Soc. 103 (1981) 4540.
A.S. Cieplak, B.D. Tait, C.R. Johnson, J. Am. Chem. Soc. 111
(1989) 8447.
G.A. Jeffrey, W. Saenger, Hydrogen Bonding in Biological
Structures, Springer, Berlin, 1991.
T. Steiner, W. Saenger, J. Am. Chem. Soc. 115 (1993) 4540.
W. Saenger, Principles of Nuclei Acid Structure, Springer,
Berlin, 1984.
Z.S. Derewenda, U. Derewenda, P.M. Kobos, J. Mol. Biol.
241 (1994) 83.
G.L. Sosa, N.M. Peruchena, R.H. Contreras, E.A. Castro, J.
Mol. Struct. (Theochem) 401 (1997) 77±85.
[22] R.F.W. Bader, Atoms in Molecules. A Quantum Theory,
Oxford Science Publications/Clarendon Press, London, 1990.
[23] A.E. Reed, L.A. Curtis, F.A. Weinhold, Chem. Rev. 88 (1988)
899.
[24] F.A. Weinhold, J. Mol. Struct. (Theochem) 398 (1997) 181.
[25] P.L.A. Popelier, R.F.W. Bader, Chem. Phys. Lett. 189 (1992)
542.
[26] M.T. Caroll, R.F.W. Bader, Mol. Phys. 65 (1988) 695.
[27] M.T. Caroll, C. Chang, R.F.W. Bader, Mol. Phys. 63 (1988)
387.
[28] U. Koch, P.L.A. Popelier, J. Phys. Chem. 99 (1995) 9747.
[29] S.F. Boys, F. Bernardi, Mol. Phys. 19 (1970) 553.
[30] J.J. Novoa, F. Mota, Chem. Phys. Lett. 166 (1997) 23±30.
[31] Y. Gu, T. Kar, S. Scheiner, J. Am. Chem. Soc. 121 (1999)
9411.
[32] E.D. Glendening, A.E. Reed, J.A. Carpenter, F. Weinhold,
NBO VersioÂn 3.1.
[33] M.J. Frisch, G.W. Trucks, H.B. Schlegel, P.M.W. Gill, G.B.
Johnson, M.A. Robb, J.R. Cheeseman, T.A. Keith, G.A. Peterson, J.A. Montgomery, K. Raghavachari, M.A. Al-Laham,
V.G. Zakrzewski, J.V. Ortiz, J.B. Foresman, J. Cioslowski,
B.B. Stefanov, A. Nanayakkara, M. Challacombe, C.Y.
Peng, P.Y. Ayala, W. Chen, M.W. Wong, J.L. Andres, E.S.
Replogle, R. Gomperts, R.L. Martin, D.J. Fox, J.S. Binkley,
D.J. Defrees, J. Baker, J.J.P. Stewart, M. Head-Gordon, C.
Gonzalez, and J.A. Pople, gaussian 94, (Revision D.1),
Gaussian, Inc., Pittsburgh PA, 1995.
[34] F.W. Blieger-KoÈnig, R.F.W. Bader, T.H. Tang, J. Comput.
Chem. 3 (1982) 317.
[35] G.R. Desiraju, Acc. Chem. Res. 24 (1991) 290.
[36] R. Taylor, O. Kennard, J. Am. Chem. Soc. 104 (1982) 5063.
[37] R.F.W. Bader, H. EsseÂn, J. Chem. Phys. 80 (1984) 1943.
[38] R.J. Boyd, S.C. Choi, Chem. Phys. Lett. 120 (1985) 80.
[39] R.J. Boyd, S.C. Choi, Chem. Phys. Lett. 129 (1986) 62.
[40] F. Bohlmann, Angew. chem. 69 (1957) 641.
[41] F. Bohlmann, Chem. Ber. 91 (1958) 2157.