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Do small carboxylic acids present intramolecular hydrogen bond?
Chemical Physics 323 (2006) 211–217 www.elsevier.com/locate/chemphys
Do small carboxylic acids present intramolecular hydrogen bond? Jose´ Manuel Hermida-Ramo´n, Ricardo A. Mosquera
*
Departamento de Quı´mica Fı´sica, Facultade de Quı´mica, Universidade de Vigo, Campus de Vigo, 36310-Vigo, Galicia, Spain Received 4 July 2005; accepted 26 August 2005 Available online 13 October 2005
Abstract The application of the quantum theory of atoms in molecules on charge electron distributions obtained at diverse computational levels indicates the lack of intramolecular hydrogen bond in the most stable conformers of small carboxylic acids. The theory is also applied to gain insight about the stabilization of the favoured conformation. Ó 2005 Elsevier B.V. All rights reserved. Keywords: QTAIM theory; Hydrogen bond; Acetic acid; Formic acid; Oxalic acid
1. Introduction It has been written that ‘‘hydrogen bond has such an ubiquitous influence in gaseous, liquid, and solid-state chemistry that its consequences were observed long before it was identified and given a name’’ [1]. Also, it has an eminent importance for the structure, function, and dynamics of chemical and biochemical systems that has led to keep it as an important research objective throughout a whole century. Nevertheless, and as this is an unfortunate rule affecting many fundamental chemical concepts, there is not a single definition of hydrogen bond (HB). More than 60 years ago Linus Pauling stated ‘‘Under certain conditions an atom of hydrogen is attracted by rather strong forces to two atoms instead of only one, so that it may be considered to be acting as a bond between them. This is called a hydrogen bond’’ [2]. This definition is probably the only classical view of HB that has not been outdated by the whole palette of hydrogen bonds known nowadays [3]. The quantum theory of atoms in molecules (QTAIM) [4], which has given physical insight about many chemical concepts, such as the definition of an atom, X, in a molecule as a closed quantum subsystem, has also been applied to establish rigorous criteria to decide about the existence *
Corresponding author. Fax: +34 986812382. E-mail address: [email protected] (R.A. Mosquera).
0301-0104/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.08.056
of HB in molecules and clusters [5,6]. The application of these criteria was successful to detect traditional HBs, such as those in creatine or carbomyl sarcosine [7], or unconventional HBs, such as the dihydrogen bonds [8,9], H p interactions [10], and O H–C interactions in dimers of methoxymethane [11] or formaldehyde [12]. Most of the assignment of HBs in molecules and clusters has been carried out upon geometrical considerations (comparison between H O distances and the summation of the corresponding van der Waals radii), on the basis of anomalous physical properties, energies, or through changes in the stretching frequency of the X-H bond. Thus, intramolecular HB (IHB) is still assumed to be present in many molecules where there is not such interaction, as pointed out by recent studies with the QTAIM framework carried out on the 1,2-diol moiety of glucopyranose [13], saturated 1,2-diols [14,15], and pinacols [15,16]. On the contrary, it has been confirmed using the same theory that IHB is present in ortho-hydroxybenzoic acids [16]. This work deals with the existence of IHB in the monomers of small carboxylic acids, i.e., formic (1), acetic (2), and oxalic (3). A class of compounds where IHB has been traditionally and ubiquitously assumed [17–20]. Nevertheless, since hydrogen bond is directional and the O@C–O bond angle tends to values close to 120°, the existence of a HB that forms a four-membered ring has also been considered not be very probable.
212
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
In this work, using the QTAIM, we check that IHB is not present within the COOH group of the above mentioned compounds (1-3). We also look for a QTAIM interpretation of the conformational stabilities of these compounds.
24 15 O
cis Z 4
Complete geometry optimisations with the 6-311++G** basis set were carried out at HF, MP2, and B3LYP levels using the Gaussian-98 program [21] for all the conformers of molecules 1-3. The corresponding electron charge densities were analysed within the framework of the QTAIM by means of the AIMPAC package [22] and MORPHY program [23,24]. This work makes use of the integrated atomic values of electron population, N(X), and total electron energy, E(X), and concentrates on the localization of bond and ring critical points (BCP and RCP, respectively), that are characterized by their position, rc, and electron charge density, q(rc). The relative minima of the laplacian of the electron charge density, $2q(r), around the oxygen atoms are employed to represent the position of the oxygen lone pairs, as they indicate the largest local concentration of the electron density [4]. We also make use of electron delocalization indexes, DIs, initially defined within the framework of this theory for HF wave functions [25,26] and recently extended for correlated wave functions, like MP2 [27,28]. Though in strict sense, the density of the Fermi hole cannot be defined within the framework of the DFT theory, recent calculations have shown that the numerical values of delocalization indexes obtained from Kohn– Sham spin-orbitals are very similar to those computed with HF wave functions [29].
C3
3. Results and discussion 3.1. Formic and acetic acids The conformational preference for the Z conformer of these compounds (Fig. 1) has been explained with two argumentations: (a) the presence of an IHB between H and O [30] and (b) preferential hyperconjugative p(O–H)– p*(C@O) interactions [31]. Nevertheless: (a) no BCP associated to a bond path between H1 and O4 atoms is present in the Z conformers of formic and acetic acid according to the charge densities obtained at the three computational levels here considered. Taking into account that 1,2ethanediol and catechol do not present IHB in the conformers [15], but a BCP associable to IHB appears for each of them when the H O distance is slightly reduced, we performed partial optimisations of the Z forms of formic and acetic acid fixing the H1 O4 interatomic distance at smaller values. No IHB connecting H1 and O4 was ob˚ in tained even when this distance was reduced to 1.5 A the Z arrangement (rising the molecular energy by more than 100 kJ mol 1). On the contrary, this kind of BCPs was found for the Z conformers of the corresponding per-
25 16
18 -58
C5
O2
H5
H1
-19 38
O4
-21 19
O4
H1 C3
11 -49
H 8 H7 -16
-16 15
C3
O2
3 -32
-33 27
12 H 6 -12
O4
H1
H5
2. Computational details
E
-12 28
15
C3
O2
24 -66
H6
C56
O2 H1
H8 H7
Fig. 1. Atom numbering and B3LYP/6-311++G** relative atomic electron populations (in a.u. multiplied by 103) and energies (shown in underlined italics in kJ mol 1) of the Z conformer of formic and acetic acid with regard to the corresponding E conformer. Relative total energies of the E conformer are: 22.7, 19.1 and 22.6 kJ mol 1 for formic acid (at respectively, HF, B3LYP, and MP2 levels) and 28.2, 24.8, and 28.2 kJ mol 1 for acetic acid.
acids, where the presence of one IHB leads to a five membered cyclic structure (Fig. 2). (b) No significant variation of DIs between Z and E conformers has been obtained with any of the charge densities here computed (shown in Table 1 for MP2). Accordingly, DIs do not support the explanation of the Z conformer stability based upon hyperconjugative delocalizations. Looking at the relative values of atomic populations, DN(X), and atomic energies, DE(X), of the Z conformer with regard to the E form (Fig. 1), we can observe that the preference for the Z forms is mainly due to the stabilization gained by C3 and O2 in these conformers, which exceeds the destabilization of O4, H1, and H5 (in formic acid) or O4, C5, H7, and H8 (in acetic acid). If we exclude the carbonyl oxygen (O4), we observe that DE(X) and DN(X) values present opposite signs. This means that an atom becomes stabilized in the Z form when its electron population is larger than in the E form (O4 being the exception). Thus, the stabilization gained by O2 and C3 in the Z conformers is related to the electron charge transferred from hydrogens (and C5 in acetic acid) to other atoms along the conformational interconversion. These transfer can be related to different repulsions experienced by the electron charge in each conformer. In particular, two facts give rise to larger atomic populations in C3 and O2 in Z conformers: (a) The important repulsions among the lone pairs of O2 and O4 in E, that spread their charge density on the rest of molecule, are practically suppressed in Z conformers. (b) The repulsions with other hydrogens represent the largest non-bonding interactions for H5 (and for the methyl group of C5 in acetic acid) in the E conformers. They are replaced by the repulsions with the lone pairs of O2 in
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
213
H 11 H 11
O O 56
O 22
O 45 C 33
O 22 C 44
H 54 H
O 33
H 65
a
b
Fig. 2. MORPHY plots of the electron charge density for the Z conformers of formic acid (a), and performic acid (b). Squares denote BCPs. The triangle observed in (b) is the RCP that corresponds to its cyclic structure due to the presence of IHB between H1 and O5.
Table 1 Relative values of the delocalization indexes, Dd, and localization index, Dk, of E conformers (with regard to Z conformers) of acetic and formic acids as obtained from MP2/6-311G** charge densitiesa X H1 O2 C3 O4 C5 (H5) H6 H7 H8
Dd(X,H1) 0.020 0.001 0.006 0.001 0.001 0.002 0.002
Dd(X,O2)
(0.019) (0.001) ( 0.003) ( 0.006)
0.007 ( 0.005) 0.010 ( 0.010) 0.005 (0.011) 0.002 0.001 0.001
Dd(X,C3)
Dd(X,O4)
0.008 (0.009) 0.005 (0.000) 0.002 0.001 0.001
Dd(X,X5)
0.005 (0.007) 0.001 0.001 0.001
0.005 0.004 0.004
Dd(X,H6)
0.000 0.000
Dd(X,H7)
0.002
Dk(X) 0.008 0.024 0.009 0.024 0.019 0.011 0.012 0.012
(0.006) ( 0.025) ( 0.006) ( 0.025) (0.028)
Values for formic acid are shown in parenthesis. a The maximum differences obtained with B3LYP and HF charge densities with regard to these values are smaller than 0.009 and 0.013 a.u., respectively (RMSs being 0.004 a.u. in both cases).
the Z conformers. The later are larger than the former, as can be inferred from interatomic distances and the position of the minima of $2q, and the values of q(r) at hydrogen nuclei and at $2q minima (Table 2). This explanation is in line with that recently proposed for the preference of gauche conformers in O–C–O anomeric units [32]. It has to be stressed that the three computational levels here employed produce the same qualitative explanations and that quantitative differences among them for N(X)
and E(X) values are small. Maximum differences are 0.005 a.u. between HF and B3LYP for DN(X) and 8 kJ mol 1 for DE(X) and reduce significantly for the two correlated methods (0.003 a.u. and 3.6 kJ mol 1, respectively). It is also worth to mention that the electron population at the carboxylic hydrogen is found always very small (never larger than 0.44 au) what agrees previous results obtained for hydroxyl hydrogens of alkanols [33].
Table 2 Comparison of distances and charge densities involved in the non-bonded interactions between hydrogen atoms and lone pairs (Lp) in E and Z conformers Z
HCOOH
CH3COOH
HF B3LYP MP2
HF B3LYP MP2
All values in a.u.
E
R(H1, LpO4)
q(H1)
q(LpO4)
R(H5, LpO2)
q(H5)
q(LpO2)
R(H1,H5)
q(H1)
q(H5)
R(LpO2,LpO4)
q(LpO2)
q(LpO4)
4.042 4.082 4.055
0.4244 0.4171 0.4083
0.9314 0.9280 0.9160
3.809 3.856 3.856
0.4385 0.4385 0.4272
0.9368 0.9332 0.9189
3.966 3.990 3.935
0.4334 0.4251 0.4160
0.4384 0.4377 0.4263
4.139 4.209 4.239
0.9376 0.9348 0.9207
0.9406 0.9358 0.9228
R(H1, LpO4)
q(H1)
q(LpO4)
R(H7, LpO2)
q(H7)
q(LpO2)
R(H1,H7)
q(H1)
q(H7)
R(LpO2,LpO4)
q(LpO2)
q(LpO4)
3.936 3.963 3.958
0.4263 0.4195 0.4095
0.9335 0.9376 0.9185
4.695 4.737 4.708
0.4282 0.4344 0.4203
0.9352 0.9312 0.9181
4.623 4.651 4.580
0.4357 0.4279 0.4182
0.4289 0.4353 0.4211
4.058 4.119 4.148
0.9373 0.9338 0.9204
0.9451 0.9419 0.9286
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
214
The partitioning of the electronic potential energy of every atom (Table 3), V(X), into interactions within the same basin, Vii(X), and with the remaining atoms, Vio(X), indicates that the stabilisation gained by O2 and C3 in the Z conformer is mainly due to the increase of the attractions with other nuclei. In fact, the balance of attractions, Vneo(X), and repulsions, Vee(X), experienced within their own basins in Z with regard to E is destabilizing for O2 in both acids and for C3 in acetic acid. The same trends are obtained at the three computational levels. This can be expressed more intuitively saying that the charge gained by O2 and C3 stabilizes the Z conformer, not because of the larger attractor of its basin, but for the proximity of other good attractors. O4 is the only case where the relative destabilization corresponds to a larger electron population in the Z conformer. The components of DV(O4) indicate this results from the increase of the electron–electron repulsions within the O4 basin, Vee(O4). The remaining atoms verify DN(X) Æ DE(X) < 0 and all those that are destabilized in the Z conformer (excluding H1 in formic acid) experience lower attractions by the other nuclei in it than in the E conformer. 3.2. Oxalic acid The five most stable conformers previously described in the literature [17,19,20] (Fig. 3) were optimised at the three computational levels here considered. We have investigated the presence of IHB in them looking for bondpaths connecting H and O atoms that are not connected in the Lewis structure. Such bondpaths are only observed, at the three computational levels here employed, for the tCc conformer (between H1 and O5). A bond path connecting H1 and O8 through a BCP for conformer tTc is obtained at the B3LYP level but not at the MP2 or HF ones. Finally, IHBs are not found for any of the remaining conformers at any of the computational levels here considered. These results were confirmed at the MP2/aug-cc-pVdZ//MP2/aug-ccpVdZ level. Therefore, the large set of IHBs proposed in the literature for the diverse conformers of oxalic acid is
-26(-16) O7
O7 H6
C3
O2
C4
O5
A
O5
C4 25(-28)
H6
B
-6(-24)
O2
-10(-1)
H1 O8
tTt
-2(28)
-26(75) C3
H1
7(-14)
O8
21(-17)
12(-19)
tTc (5.4, 8.3, 7.2)
17(-28)
O7
H1
2(-1)
0(6) 1(3) C 3 1(30) O5
O2
H6
-12(28)
C4
H6
O5 C4
C O8
O8
H1
C3 1(0) O7 -3(-5)
cCc (8.9, 13.2, 9.5)
D
cTc
O2
(6.0, 11.9, 8.6) 31(9) -12(19) H 6
O2 7(11)
O5
36(-64) C 4 8(-18)
H1 -13(8)
O8
C3 -16(47)
-23(-3)
O7
tCc (18.2, 18.5, 15.2)
Fig. 3. Conformers and atom numbering employed for oxalic acid. Relative energies (in kJ mol 1, after ZPVE correction, and with regard to the most stable conformer) computed, respectively, at the HF/6311++G**, B3LYP/6-311++G**, and MP2/6-311++G** levels, are shown in parenthesis. Relative (with regard to the conformer connected by the arrow, i.e., tTt for tTc) atomic electron populations (in a.u. multiplied by 103) and energies (in kJ mol 1 and underlined italics) are shown for every atom not related to other one by symmetry.
not verified by the QTAIM study. Regarding to the proposed classification [17] of intrafunctional and interfunctional IHBs, our study indicates that the corresponding intrafunctional BCPs do not appear even when important distortions of the geometry of the conformers are allowed (so large as those explored for formic and acetic acids). In contrast, interfunctional BCPs are observed for the charge densities computed (at any of the levels here considered) for geometries obtained by restricted optimisations of
Table 3 Variations experienced by the components of the atomic potential energy for the transformation of the E conformer into the Z one DVneo(X)
DVee(X)
DVii(X)
DVio(X)
HCOOH
H1 O2 C3 O4 H5
47 277 88 186 61
92 296 79 344 301
139 18 10 158 240
83 135 54 128 295
CH3COOH
H1 O2 C3 O4 C5 H6 H7/H8
67 353 181 186 158 28 33
241 842 351 361 309 112 159
173 489 169 175 151 84 126
250 623 268 144 191 108 156
All values in kJ mol
1
and computed from B3LYP charge densities.
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
the tTt and tTc conformations fixing the H1 O8 distance (and the symmetrical H6 O7 one for tTt) at values that are only slightly smaller than those obtained for the con˚ , rising the molecformers (for example from 2.11 to 2.05 A 1 ular energy only in 2.6 kJ mol , for the tTt conformer at the MP2 level, Fig. 4). The continuous evolution of the atomic and bond properties of the molecule when the O8 H1 distance is fixed at diverse values (shown in Fig. 5 for the tTt conformation) indicates that none of them experiences any important modification between the conformer and the structure where the bondpath associated to the IHB appears. So, although interfunctional IHBs are not formed in the tTt conformer yet (and probably not in tTc), both the electronic distribution and the molecular energy are very close to those presented in a conformation with IHBs, thus assuming two interfunctional IHBs in tTt and one in tTc is not a rough approximation. In fact, no atomic population of the conformer differs from the corresponding value in the structure with IHB by more than 0.003 a.u. (Fig. 5(b)). Differences in bond lengths and q(rc) are smal˚ and 0.008 a.u., respectively (Fig. 5(d) and ler than 0.013 A (c)). In contrast, the atomic energies (Fig. 5(a)) vary significantly between the conformer and the structure with a bondpath connecting O8 and H1. Thus, C3 results stabilized in 41 kJ mol 1 while O8 is destabilized in 29 kJ mol 1. In contrast, intrafunctional IHBs are far from being a reality in this molecule. The profile displayed by the molecular energy along this process for tTt (Fig. 5(a)) is basically due to the balance between the energy of carbon and oxygen atoms of the carbonyl groups. The former are stabilized by approaching O8 and H1 whereas the latter are destabilized. Also, the summations of the atomic charges for each C@O fragment and for each O–H fragment are nearly constant during the process (Fig. 5(b)), indicating that charge transferences take place within each group as the atoms involved in
hydrogen bond approach each other. Thus, every carbonylic oxygen gains more and more electron population from its attached carbon as the hydrogen approaches. In contrast, the direction of the electron charge transfer within the O–H groups changes when the H1 O8 distance is ˚ (Fig. 5(b)). around 2.35 A The origin for the sequence of conformational stabilities was studied considering the internal rotations detailed in Fig. 3 as A, B, C, and D. From this figure we can see that the rotation around the C4–O5 bond from the most stable conformer (tTt) diminishes the charge density in O7 and C3 (process A). We can also observe that the hydrogens gain electron charge from their attached oxygens. This reduces the O–H bond dipole moment in a conformer where these moments have a destabilizing interaction. The relative destabilization of tTc with regard to tTt is mainly due to C3 and O2 according to QTAIM atomic energies. When C4–O5 and C3–O2 are rotated simultaneously from the tTt (process B, Fig. 3) both hydrogens increase their electron population with charge taken from all the oxygens. The balance of atomic energies indicates a destabilization of O2, C3, C4, and O5, mainly due to a decrease of the attraction of their electron density by other nuclei that can be related with the general increase of bond lengths in this process. The rotation from cTc to cCc (process C) gives rise to a destabilizing interaction between C@O bond dipole moments that is reduced transferring electron charge from the most electronegative atom. The result is an almost isoenergetic transformation, where the most significant change is experienced in O2 and O5, which display the largest atomic destabilization and keep the same electron population. Looking at the partition of V(X) we observe Vii(X) rise substantially for these atoms, mainly due to an increase of the repulsions within each of these oxygen basins (Vii(O2) = 791 kJ mol 1, Vee(O2) = 785 kJ mol 1). This indicates a reorganization of their electron distributions.
H 15
H H 15 O 88
O 88 O O 23
O O 23
C 31
C 31
CC42
C C 42 O O 54
O O 54
O 77
O 77 H 66
H 66
a
215
b
Fig. 4. MORPHY plots of the electron charge density for the most stable conformer (tTt) of oxalic acid (a), where O8 H1 and O7 H6 distances are ˚ , and the geometry obtained by restricted optimization with those distances fixed at 1.900 A ˚ (b). Squares denote BCPs and triangles RCPs. 2.163 A
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
216 160
Molecule
120
O8+H1+O2
10 3 ΔN(Ω )/Δau
c)
C3
80
ΔE/ kJ mol-1
C3, C4 H1, H6 O2, O5 O7, O8
25
O8+H1
O8
40 0
15
5
-5
-40
-15
-80 -120
-25
1.8
2.0
2.2
2.4
2.6
R(O8...H1)=R(O7...H6) / A
a
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
R(O8...H1)=R(O7...H6) / A
b 120
40
R(C-C) 20
R(C-O)
90
R(O-H)
10 3ΔR/A
103Δr b/au
R(C=O) 0 -20 C-C -40
60
30
C-O C=O
-60
0
O-H O...H -30
-80 1.8
c
2.0
2.2
2.4
2.6
2.8
3.0
1.8
3.2
R(O8...H1)=R(O7...H6) / A
2.0
2.2
2.4
2.6
2.8
3.0
3.2
R(O8...H1)=R(O7...H6) / A
d
Fig. 5. Evolution of the main atomic properties of the tTt conformation with O8 H1 and O7 H6 distances as obtained from HF/6-311++G** charge densities. (a) variation of molecular and atomic energies; (b) variation of atomic populations; (c) variation of the charge density at the BCPs; and (d) variation of bond lengths. All values are relative to those in the tTt conformer but q(O H) which are absolute values.
Finally, the rotation around one C–O bond in cCc (process D) gives rise to a significant redistribution of the electron density accompanying the formation of an IHB between H1 and O5. Significant variations of E(X) and N(X) are observed for all the atoms. Main destabilizations in tCc correspond to O2 and C3, where the attractions of the electron density by other nuclei decrease, as a result of the general increase of bond lengths experienced by the molecule to allow the formation of the IHB. It has to be stressed that the only conformer that undoubtedly displays IHB is the most destabilized. The stability sequence can be explained assuming that the interaction between C@O bond dipoles and the repulsions between the lone pairs of the carbonylic oxygens play a leading role that stabilizes -T- conformers over -C- ones. The order among the three -T- conformers can be explained bearing in mind that two IHBs are about to be formed at the geometry of tTt, one at that of tTc, and none at cTc. Nevertheless, this rule cannot be applied for cCc and tCc where the energy released by the formation of IHB in the latter is not enough to compensate for the distortion of the geometry and the opposition of O–H bond dipoles achieves in cCc.
4. Conclusions The conformational preference of formic and acetic acids for the Z conformers is neither due to the presence of IHB nor to increased hyperconjugative delocalisations regarding to the E conformer. It is related to the effect of the lone-pair/lone-pair and lone-pair/hydrogen repulsions on the charge redistribution. They give rise to smaller electron population in atomic basins with weak attractors and larger electron population in others surrounded by better attractors in the Z conformer. Thus, the atomic energy of the C–O region becomes negative enough to compensate the destabilisation of the hydrogens that lose electron population. In a strict way IHB cannot be invoked as the explanation for the sequence of molecular energies in the conformers of oxalic acid. For this molecule IHB is only present in the least stable conformer, tCc, and probably in conformer tTc, where an IHB is only obtained with B3LYP calculations. Nevertheless, interfunctional BCPs between H and O atoms placed on different carboxyls are obtained after small distortions of the geometry of conformers tTt and tTc without any important modification of atomic or bond
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
properties. The sequence of stabilities can be related to interactions of bond dipole moments and repulsions between lone pairs, to the possibility of establishing interfunctional IHBs, and to the geometry distortions involved in IHB formation. Acknowledgements We thank Dr. Rodrı´guez-Otero for helpful comments at the 2nd GGG meeting, and CESGA for computational facilities. J.M.H.-R. thanks Xunta de Galicia for financial support as a researcher of the Isidro Parga Pondal program. References [1] G.A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997. [2] L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, 1939. [3] T. Steiner, Angew. Chem. Int. Ed. 41 (2002) 48. [4] R.F.W. BaderAtoms in Molecules – A Quantum Theory, vol. 22, Oxford University Press, Oxford, 1990. [5] M.T. Carroll, R.F.W. Bader, Mol. Phys. 65 (1988) 695. [6] U. Koch, P.L.A. Popelier, J. Phys. Chem. 99 (1995) 9747. [7] P.L.A. Popelier, R.F.W. Bader, Chem. Phys. Lett. 189 (1992) 542. [8] S.A. Kulkarni, J. Phys. Chem. A 102 (1998) 7704. [9] P.L.A. Popelier, J. Phys. Chem. A 102 (1998) 1873. [10] I. Rozas, I. Alkorta, J. Elguero, J. Phys. Chem. A 101 (1997) 9457. [11] A. Vila, R.A. Mosquera, J.M. Hermida-Ramo´n, J. Mol. Struct. (THEOCHEM) 541 (2001) 149.
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A. Vila, A.M. Gran˜a, R.A. Mosquera, Chem. Phys. 281 (2002) 11. R.A. Klein, J. Am. Chem. Soc. 124 (2002) 13931. R.A. Klein, J. Comput. Chem. 23 (2002) 585. M. Mandado, A.M. Gran˜a, R.A. Mosquera, Phys. Chem. Chem. Phys. 6 (2004) 4391. M. Mandado, A.M. Gran˜a, R.A. Mosquera, Chem. Chem. Lett. 400 (2004) 169. C. Cheng, S.-F. Shyu, Int. J. Quantum Chem. 76 (2000) 541. W.V.F. Brooks, C.M. Haas, J. Phys. Chem. 71 (1967) 650. P.D. Godfrey, M.J. Mirabella, R.D. Brown, J. Phys. Chem. A 104 (2000) 258. E.M.S. Mac¸oas, R. Fausto, M. Pettersson, L. Khriachtchev, M. Ra¨sa¨nen, J. Phys. Chem. A 104 (2000) 6956. M.J. Frisch et al., Gaussian-98 (Revision A.9), Gaussian, Inc., Pittsburgh, PA, 1998. R.F.W. Bader and co-workers, AIMPAC: A Suite of Programs for the Theory of Atoms in Molecules, McMaster University, Hamilton, Ontario, Canada L8S 4M1. MORPHY 98: A Suite of Programs for the Theory of Atoms in Molecules written by P.L.A. Popelier with a contribution from R.G.A. Bone, UMIST, England. P.L.A. Popelier, Chem. Phys. Lett. 288 (1994) 160. X. Fradera, M.A. Austen, R.F.W. Bader, J. Phys. Chem. A 103 (1999) 304. R.F.W. Bader, A. Streitwieser, A. Neuhaus, K.E. Laidig, K.E.P. Speers, J. Am. Chem. Soc. 118 (1996) 4959. Y.G. Wang, N.H. Werstiuk, J. Comput. Chem. 24 (2003) 379. Y.G. Wang, C.F. Matta, N.H. Werstiuk, J. Comput. Chem. 24 (2003) 1720. J. Poater, M. Sola`, M. Duran, X. Fradera, Theor. Chem. Acc. 107 (2002) 362. L. Turi, J.J. Dannenberg, J. Phys. Chem. 97 (1993) 12197. J.F. Marcoccia, I.G. Ciszmadia, M.R. Peterson, R.A. Poirier, Gazz. Chim. Ital. 120 (1990) 77. A. Vila, R.A. Mosquera, J. Chem. Phys., submitted. M. Mandado, A.M. Gran˜a, R.A. Mosquera, J. Mol. Struct. (THEOCHEM) 584 (2002) 221.
Do small carboxylic acids present intramolecular hydrogen bond? Jose´ Manuel Hermida-Ramo´n, Ricardo A. Mosquera
*
Departamento de Quı´mica Fı´sica, Facultade de Quı´mica, Universidade de Vigo, Campus de Vigo, 36310-Vigo, Galicia, Spain Received 4 July 2005; accepted 26 August 2005 Available online 13 October 2005
Abstract The application of the quantum theory of atoms in molecules on charge electron distributions obtained at diverse computational levels indicates the lack of intramolecular hydrogen bond in the most stable conformers of small carboxylic acids. The theory is also applied to gain insight about the stabilization of the favoured conformation. Ó 2005 Elsevier B.V. All rights reserved. Keywords: QTAIM theory; Hydrogen bond; Acetic acid; Formic acid; Oxalic acid
1. Introduction It has been written that ‘‘hydrogen bond has such an ubiquitous influence in gaseous, liquid, and solid-state chemistry that its consequences were observed long before it was identified and given a name’’ [1]. Also, it has an eminent importance for the structure, function, and dynamics of chemical and biochemical systems that has led to keep it as an important research objective throughout a whole century. Nevertheless, and as this is an unfortunate rule affecting many fundamental chemical concepts, there is not a single definition of hydrogen bond (HB). More than 60 years ago Linus Pauling stated ‘‘Under certain conditions an atom of hydrogen is attracted by rather strong forces to two atoms instead of only one, so that it may be considered to be acting as a bond between them. This is called a hydrogen bond’’ [2]. This definition is probably the only classical view of HB that has not been outdated by the whole palette of hydrogen bonds known nowadays [3]. The quantum theory of atoms in molecules (QTAIM) [4], which has given physical insight about many chemical concepts, such as the definition of an atom, X, in a molecule as a closed quantum subsystem, has also been applied to establish rigorous criteria to decide about the existence *
Corresponding author. Fax: +34 986812382. E-mail address: [email protected] (R.A. Mosquera).
0301-0104/$ - see front matter Ó 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2005.08.056
of HB in molecules and clusters [5,6]. The application of these criteria was successful to detect traditional HBs, such as those in creatine or carbomyl sarcosine [7], or unconventional HBs, such as the dihydrogen bonds [8,9], H p interactions [10], and O H–C interactions in dimers of methoxymethane [11] or formaldehyde [12]. Most of the assignment of HBs in molecules and clusters has been carried out upon geometrical considerations (comparison between H O distances and the summation of the corresponding van der Waals radii), on the basis of anomalous physical properties, energies, or through changes in the stretching frequency of the X-H bond. Thus, intramolecular HB (IHB) is still assumed to be present in many molecules where there is not such interaction, as pointed out by recent studies with the QTAIM framework carried out on the 1,2-diol moiety of glucopyranose [13], saturated 1,2-diols [14,15], and pinacols [15,16]. On the contrary, it has been confirmed using the same theory that IHB is present in ortho-hydroxybenzoic acids [16]. This work deals with the existence of IHB in the monomers of small carboxylic acids, i.e., formic (1), acetic (2), and oxalic (3). A class of compounds where IHB has been traditionally and ubiquitously assumed [17–20]. Nevertheless, since hydrogen bond is directional and the O@C–O bond angle tends to values close to 120°, the existence of a HB that forms a four-membered ring has also been considered not be very probable.
212
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In this work, using the QTAIM, we check that IHB is not present within the COOH group of the above mentioned compounds (1-3). We also look for a QTAIM interpretation of the conformational stabilities of these compounds.
24 15 O
cis Z 4
Complete geometry optimisations with the 6-311++G** basis set were carried out at HF, MP2, and B3LYP levels using the Gaussian-98 program [21] for all the conformers of molecules 1-3. The corresponding electron charge densities were analysed within the framework of the QTAIM by means of the AIMPAC package [22] and MORPHY program [23,24]. This work makes use of the integrated atomic values of electron population, N(X), and total electron energy, E(X), and concentrates on the localization of bond and ring critical points (BCP and RCP, respectively), that are characterized by their position, rc, and electron charge density, q(rc). The relative minima of the laplacian of the electron charge density, $2q(r), around the oxygen atoms are employed to represent the position of the oxygen lone pairs, as they indicate the largest local concentration of the electron density [4]. We also make use of electron delocalization indexes, DIs, initially defined within the framework of this theory for HF wave functions [25,26] and recently extended for correlated wave functions, like MP2 [27,28]. Though in strict sense, the density of the Fermi hole cannot be defined within the framework of the DFT theory, recent calculations have shown that the numerical values of delocalization indexes obtained from Kohn– Sham spin-orbitals are very similar to those computed with HF wave functions [29].
C3
3. Results and discussion 3.1. Formic and acetic acids The conformational preference for the Z conformer of these compounds (Fig. 1) has been explained with two argumentations: (a) the presence of an IHB between H and O [30] and (b) preferential hyperconjugative p(O–H)– p*(C@O) interactions [31]. Nevertheless: (a) no BCP associated to a bond path between H1 and O4 atoms is present in the Z conformers of formic and acetic acid according to the charge densities obtained at the three computational levels here considered. Taking into account that 1,2ethanediol and catechol do not present IHB in the conformers [15], but a BCP associable to IHB appears for each of them when the H O distance is slightly reduced, we performed partial optimisations of the Z forms of formic and acetic acid fixing the H1 O4 interatomic distance at smaller values. No IHB connecting H1 and O4 was ob˚ in tained even when this distance was reduced to 1.5 A the Z arrangement (rising the molecular energy by more than 100 kJ mol 1). On the contrary, this kind of BCPs was found for the Z conformers of the corresponding per-
25 16
18 -58
C5
O2
H5
H1
-19 38
O4
-21 19
O4
H1 C3
11 -49
H 8 H7 -16
-16 15
C3
O2
3 -32
-33 27
12 H 6 -12
O4
H1
H5
2. Computational details
E
-12 28
15
C3
O2
24 -66
H6
C56
O2 H1
H8 H7
Fig. 1. Atom numbering and B3LYP/6-311++G** relative atomic electron populations (in a.u. multiplied by 103) and energies (shown in underlined italics in kJ mol 1) of the Z conformer of formic and acetic acid with regard to the corresponding E conformer. Relative total energies of the E conformer are: 22.7, 19.1 and 22.6 kJ mol 1 for formic acid (at respectively, HF, B3LYP, and MP2 levels) and 28.2, 24.8, and 28.2 kJ mol 1 for acetic acid.
acids, where the presence of one IHB leads to a five membered cyclic structure (Fig. 2). (b) No significant variation of DIs between Z and E conformers has been obtained with any of the charge densities here computed (shown in Table 1 for MP2). Accordingly, DIs do not support the explanation of the Z conformer stability based upon hyperconjugative delocalizations. Looking at the relative values of atomic populations, DN(X), and atomic energies, DE(X), of the Z conformer with regard to the E form (Fig. 1), we can observe that the preference for the Z forms is mainly due to the stabilization gained by C3 and O2 in these conformers, which exceeds the destabilization of O4, H1, and H5 (in formic acid) or O4, C5, H7, and H8 (in acetic acid). If we exclude the carbonyl oxygen (O4), we observe that DE(X) and DN(X) values present opposite signs. This means that an atom becomes stabilized in the Z form when its electron population is larger than in the E form (O4 being the exception). Thus, the stabilization gained by O2 and C3 in the Z conformers is related to the electron charge transferred from hydrogens (and C5 in acetic acid) to other atoms along the conformational interconversion. These transfer can be related to different repulsions experienced by the electron charge in each conformer. In particular, two facts give rise to larger atomic populations in C3 and O2 in Z conformers: (a) The important repulsions among the lone pairs of O2 and O4 in E, that spread their charge density on the rest of molecule, are practically suppressed in Z conformers. (b) The repulsions with other hydrogens represent the largest non-bonding interactions for H5 (and for the methyl group of C5 in acetic acid) in the E conformers. They are replaced by the repulsions with the lone pairs of O2 in
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
213
H 11 H 11
O O 56
O 22
O 45 C 33
O 22 C 44
H 54 H
O 33
H 65
a
b
Fig. 2. MORPHY plots of the electron charge density for the Z conformers of formic acid (a), and performic acid (b). Squares denote BCPs. The triangle observed in (b) is the RCP that corresponds to its cyclic structure due to the presence of IHB between H1 and O5.
Table 1 Relative values of the delocalization indexes, Dd, and localization index, Dk, of E conformers (with regard to Z conformers) of acetic and formic acids as obtained from MP2/6-311G** charge densitiesa X H1 O2 C3 O4 C5 (H5) H6 H7 H8
Dd(X,H1) 0.020 0.001 0.006 0.001 0.001 0.002 0.002
Dd(X,O2)
(0.019) (0.001) ( 0.003) ( 0.006)
0.007 ( 0.005) 0.010 ( 0.010) 0.005 (0.011) 0.002 0.001 0.001
Dd(X,C3)
Dd(X,O4)
0.008 (0.009) 0.005 (0.000) 0.002 0.001 0.001
Dd(X,X5)
0.005 (0.007) 0.001 0.001 0.001
0.005 0.004 0.004
Dd(X,H6)
0.000 0.000
Dd(X,H7)
0.002
Dk(X) 0.008 0.024 0.009 0.024 0.019 0.011 0.012 0.012
(0.006) ( 0.025) ( 0.006) ( 0.025) (0.028)
Values for formic acid are shown in parenthesis. a The maximum differences obtained with B3LYP and HF charge densities with regard to these values are smaller than 0.009 and 0.013 a.u., respectively (RMSs being 0.004 a.u. in both cases).
the Z conformers. The later are larger than the former, as can be inferred from interatomic distances and the position of the minima of $2q, and the values of q(r) at hydrogen nuclei and at $2q minima (Table 2). This explanation is in line with that recently proposed for the preference of gauche conformers in O–C–O anomeric units [32]. It has to be stressed that the three computational levels here employed produce the same qualitative explanations and that quantitative differences among them for N(X)
and E(X) values are small. Maximum differences are 0.005 a.u. between HF and B3LYP for DN(X) and 8 kJ mol 1 for DE(X) and reduce significantly for the two correlated methods (0.003 a.u. and 3.6 kJ mol 1, respectively). It is also worth to mention that the electron population at the carboxylic hydrogen is found always very small (never larger than 0.44 au) what agrees previous results obtained for hydroxyl hydrogens of alkanols [33].
Table 2 Comparison of distances and charge densities involved in the non-bonded interactions between hydrogen atoms and lone pairs (Lp) in E and Z conformers Z
HCOOH
CH3COOH
HF B3LYP MP2
HF B3LYP MP2
All values in a.u.
E
R(H1, LpO4)
q(H1)
q(LpO4)
R(H5, LpO2)
q(H5)
q(LpO2)
R(H1,H5)
q(H1)
q(H5)
R(LpO2,LpO4)
q(LpO2)
q(LpO4)
4.042 4.082 4.055
0.4244 0.4171 0.4083
0.9314 0.9280 0.9160
3.809 3.856 3.856
0.4385 0.4385 0.4272
0.9368 0.9332 0.9189
3.966 3.990 3.935
0.4334 0.4251 0.4160
0.4384 0.4377 0.4263
4.139 4.209 4.239
0.9376 0.9348 0.9207
0.9406 0.9358 0.9228
R(H1, LpO4)
q(H1)
q(LpO4)
R(H7, LpO2)
q(H7)
q(LpO2)
R(H1,H7)
q(H1)
q(H7)
R(LpO2,LpO4)
q(LpO2)
q(LpO4)
3.936 3.963 3.958
0.4263 0.4195 0.4095
0.9335 0.9376 0.9185
4.695 4.737 4.708
0.4282 0.4344 0.4203
0.9352 0.9312 0.9181
4.623 4.651 4.580
0.4357 0.4279 0.4182
0.4289 0.4353 0.4211
4.058 4.119 4.148
0.9373 0.9338 0.9204
0.9451 0.9419 0.9286
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
214
The partitioning of the electronic potential energy of every atom (Table 3), V(X), into interactions within the same basin, Vii(X), and with the remaining atoms, Vio(X), indicates that the stabilisation gained by O2 and C3 in the Z conformer is mainly due to the increase of the attractions with other nuclei. In fact, the balance of attractions, Vneo(X), and repulsions, Vee(X), experienced within their own basins in Z with regard to E is destabilizing for O2 in both acids and for C3 in acetic acid. The same trends are obtained at the three computational levels. This can be expressed more intuitively saying that the charge gained by O2 and C3 stabilizes the Z conformer, not because of the larger attractor of its basin, but for the proximity of other good attractors. O4 is the only case where the relative destabilization corresponds to a larger electron population in the Z conformer. The components of DV(O4) indicate this results from the increase of the electron–electron repulsions within the O4 basin, Vee(O4). The remaining atoms verify DN(X) Æ DE(X) < 0 and all those that are destabilized in the Z conformer (excluding H1 in formic acid) experience lower attractions by the other nuclei in it than in the E conformer. 3.2. Oxalic acid The five most stable conformers previously described in the literature [17,19,20] (Fig. 3) were optimised at the three computational levels here considered. We have investigated the presence of IHB in them looking for bondpaths connecting H and O atoms that are not connected in the Lewis structure. Such bondpaths are only observed, at the three computational levels here employed, for the tCc conformer (between H1 and O5). A bond path connecting H1 and O8 through a BCP for conformer tTc is obtained at the B3LYP level but not at the MP2 or HF ones. Finally, IHBs are not found for any of the remaining conformers at any of the computational levels here considered. These results were confirmed at the MP2/aug-cc-pVdZ//MP2/aug-ccpVdZ level. Therefore, the large set of IHBs proposed in the literature for the diverse conformers of oxalic acid is
-26(-16) O7
O7 H6
C3
O2
C4
O5
A
O5
C4 25(-28)
H6
B
-6(-24)
O2
-10(-1)
H1 O8
tTt
-2(28)
-26(75) C3
H1
7(-14)
O8
21(-17)
12(-19)
tTc (5.4, 8.3, 7.2)
17(-28)
O7
H1
2(-1)
0(6) 1(3) C 3 1(30) O5
O2
H6
-12(28)
C4
H6
O5 C4
C O8
O8
H1
C3 1(0) O7 -3(-5)
cCc (8.9, 13.2, 9.5)
D
cTc
O2
(6.0, 11.9, 8.6) 31(9) -12(19) H 6
O2 7(11)
O5
36(-64) C 4 8(-18)
H1 -13(8)
O8
C3 -16(47)
-23(-3)
O7
tCc (18.2, 18.5, 15.2)
Fig. 3. Conformers and atom numbering employed for oxalic acid. Relative energies (in kJ mol 1, after ZPVE correction, and with regard to the most stable conformer) computed, respectively, at the HF/6311++G**, B3LYP/6-311++G**, and MP2/6-311++G** levels, are shown in parenthesis. Relative (with regard to the conformer connected by the arrow, i.e., tTt for tTc) atomic electron populations (in a.u. multiplied by 103) and energies (in kJ mol 1 and underlined italics) are shown for every atom not related to other one by symmetry.
not verified by the QTAIM study. Regarding to the proposed classification [17] of intrafunctional and interfunctional IHBs, our study indicates that the corresponding intrafunctional BCPs do not appear even when important distortions of the geometry of the conformers are allowed (so large as those explored for formic and acetic acids). In contrast, interfunctional BCPs are observed for the charge densities computed (at any of the levels here considered) for geometries obtained by restricted optimisations of
Table 3 Variations experienced by the components of the atomic potential energy for the transformation of the E conformer into the Z one DVneo(X)
DVee(X)
DVii(X)
DVio(X)
HCOOH
H1 O2 C3 O4 H5
47 277 88 186 61
92 296 79 344 301
139 18 10 158 240
83 135 54 128 295
CH3COOH
H1 O2 C3 O4 C5 H6 H7/H8
67 353 181 186 158 28 33
241 842 351 361 309 112 159
173 489 169 175 151 84 126
250 623 268 144 191 108 156
All values in kJ mol
1
and computed from B3LYP charge densities.
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
the tTt and tTc conformations fixing the H1 O8 distance (and the symmetrical H6 O7 one for tTt) at values that are only slightly smaller than those obtained for the con˚ , rising the molecformers (for example from 2.11 to 2.05 A 1 ular energy only in 2.6 kJ mol , for the tTt conformer at the MP2 level, Fig. 4). The continuous evolution of the atomic and bond properties of the molecule when the O8 H1 distance is fixed at diverse values (shown in Fig. 5 for the tTt conformation) indicates that none of them experiences any important modification between the conformer and the structure where the bondpath associated to the IHB appears. So, although interfunctional IHBs are not formed in the tTt conformer yet (and probably not in tTc), both the electronic distribution and the molecular energy are very close to those presented in a conformation with IHBs, thus assuming two interfunctional IHBs in tTt and one in tTc is not a rough approximation. In fact, no atomic population of the conformer differs from the corresponding value in the structure with IHB by more than 0.003 a.u. (Fig. 5(b)). Differences in bond lengths and q(rc) are smal˚ and 0.008 a.u., respectively (Fig. 5(d) and ler than 0.013 A (c)). In contrast, the atomic energies (Fig. 5(a)) vary significantly between the conformer and the structure with a bondpath connecting O8 and H1. Thus, C3 results stabilized in 41 kJ mol 1 while O8 is destabilized in 29 kJ mol 1. In contrast, intrafunctional IHBs are far from being a reality in this molecule. The profile displayed by the molecular energy along this process for tTt (Fig. 5(a)) is basically due to the balance between the energy of carbon and oxygen atoms of the carbonyl groups. The former are stabilized by approaching O8 and H1 whereas the latter are destabilized. Also, the summations of the atomic charges for each C@O fragment and for each O–H fragment are nearly constant during the process (Fig. 5(b)), indicating that charge transferences take place within each group as the atoms involved in
hydrogen bond approach each other. Thus, every carbonylic oxygen gains more and more electron population from its attached carbon as the hydrogen approaches. In contrast, the direction of the electron charge transfer within the O–H groups changes when the H1 O8 distance is ˚ (Fig. 5(b)). around 2.35 A The origin for the sequence of conformational stabilities was studied considering the internal rotations detailed in Fig. 3 as A, B, C, and D. From this figure we can see that the rotation around the C4–O5 bond from the most stable conformer (tTt) diminishes the charge density in O7 and C3 (process A). We can also observe that the hydrogens gain electron charge from their attached oxygens. This reduces the O–H bond dipole moment in a conformer where these moments have a destabilizing interaction. The relative destabilization of tTc with regard to tTt is mainly due to C3 and O2 according to QTAIM atomic energies. When C4–O5 and C3–O2 are rotated simultaneously from the tTt (process B, Fig. 3) both hydrogens increase their electron population with charge taken from all the oxygens. The balance of atomic energies indicates a destabilization of O2, C3, C4, and O5, mainly due to a decrease of the attraction of their electron density by other nuclei that can be related with the general increase of bond lengths in this process. The rotation from cTc to cCc (process C) gives rise to a destabilizing interaction between C@O bond dipole moments that is reduced transferring electron charge from the most electronegative atom. The result is an almost isoenergetic transformation, where the most significant change is experienced in O2 and O5, which display the largest atomic destabilization and keep the same electron population. Looking at the partition of V(X) we observe Vii(X) rise substantially for these atoms, mainly due to an increase of the repulsions within each of these oxygen basins (Vii(O2) = 791 kJ mol 1, Vee(O2) = 785 kJ mol 1). This indicates a reorganization of their electron distributions.
H 15
H H 15 O 88
O 88 O O 23
O O 23
C 31
C 31
CC42
C C 42 O O 54
O O 54
O 77
O 77 H 66
H 66
a
215
b
Fig. 4. MORPHY plots of the electron charge density for the most stable conformer (tTt) of oxalic acid (a), where O8 H1 and O7 H6 distances are ˚ , and the geometry obtained by restricted optimization with those distances fixed at 1.900 A ˚ (b). Squares denote BCPs and triangles RCPs. 2.163 A
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
216 160
Molecule
120
O8+H1+O2
10 3 ΔN(Ω )/Δau
c)
C3
80
ΔE/ kJ mol-1
C3, C4 H1, H6 O2, O5 O7, O8
25
O8+H1
O8
40 0
15
5
-5
-40
-15
-80 -120
-25
1.8
2.0
2.2
2.4
2.6
R(O8...H1)=R(O7...H6) / A
a
1.8
2.0
2.2
2.4
2.6
2.8
3.0
3.2
R(O8...H1)=R(O7...H6) / A
b 120
40
R(C-C) 20
R(C-O)
90
R(O-H)
10 3ΔR/A
103Δr b/au
R(C=O) 0 -20 C-C -40
60
30
C-O C=O
-60
0
O-H O...H -30
-80 1.8
c
2.0
2.2
2.4
2.6
2.8
3.0
1.8
3.2
R(O8...H1)=R(O7...H6) / A
2.0
2.2
2.4
2.6
2.8
3.0
3.2
R(O8...H1)=R(O7...H6) / A
d
Fig. 5. Evolution of the main atomic properties of the tTt conformation with O8 H1 and O7 H6 distances as obtained from HF/6-311++G** charge densities. (a) variation of molecular and atomic energies; (b) variation of atomic populations; (c) variation of the charge density at the BCPs; and (d) variation of bond lengths. All values are relative to those in the tTt conformer but q(O H) which are absolute values.
Finally, the rotation around one C–O bond in cCc (process D) gives rise to a significant redistribution of the electron density accompanying the formation of an IHB between H1 and O5. Significant variations of E(X) and N(X) are observed for all the atoms. Main destabilizations in tCc correspond to O2 and C3, where the attractions of the electron density by other nuclei decrease, as a result of the general increase of bond lengths experienced by the molecule to allow the formation of the IHB. It has to be stressed that the only conformer that undoubtedly displays IHB is the most destabilized. The stability sequence can be explained assuming that the interaction between C@O bond dipoles and the repulsions between the lone pairs of the carbonylic oxygens play a leading role that stabilizes -T- conformers over -C- ones. The order among the three -T- conformers can be explained bearing in mind that two IHBs are about to be formed at the geometry of tTt, one at that of tTc, and none at cTc. Nevertheless, this rule cannot be applied for cCc and tCc where the energy released by the formation of IHB in the latter is not enough to compensate for the distortion of the geometry and the opposition of O–H bond dipoles achieves in cCc.
4. Conclusions The conformational preference of formic and acetic acids for the Z conformers is neither due to the presence of IHB nor to increased hyperconjugative delocalisations regarding to the E conformer. It is related to the effect of the lone-pair/lone-pair and lone-pair/hydrogen repulsions on the charge redistribution. They give rise to smaller electron population in atomic basins with weak attractors and larger electron population in others surrounded by better attractors in the Z conformer. Thus, the atomic energy of the C–O region becomes negative enough to compensate the destabilisation of the hydrogens that lose electron population. In a strict way IHB cannot be invoked as the explanation for the sequence of molecular energies in the conformers of oxalic acid. For this molecule IHB is only present in the least stable conformer, tCc, and probably in conformer tTc, where an IHB is only obtained with B3LYP calculations. Nevertheless, interfunctional BCPs between H and O atoms placed on different carboxyls are obtained after small distortions of the geometry of conformers tTt and tTc without any important modification of atomic or bond
J.M. Hermida-Ramo´n, R.A. Mosquera / Chemical Physics 323 (2006) 211–217
properties. The sequence of stabilities can be related to interactions of bond dipole moments and repulsions between lone pairs, to the possibility of establishing interfunctional IHBs, and to the geometry distortions involved in IHB formation. Acknowledgements We thank Dr. Rodrı´guez-Otero for helpful comments at the 2nd GGG meeting, and CESGA for computational facilities. J.M.H.-R. thanks Xunta de Galicia for financial support as a researcher of the Isidro Parga Pondal program. References [1] G.A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997. [2] L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, 1939. [3] T. Steiner, Angew. Chem. Int. Ed. 41 (2002) 48. [4] R.F.W. BaderAtoms in Molecules – A Quantum Theory, vol. 22, Oxford University Press, Oxford, 1990. [5] M.T. Carroll, R.F.W. Bader, Mol. Phys. 65 (1988) 695. [6] U. Koch, P.L.A. Popelier, J. Phys. Chem. 99 (1995) 9747. [7] P.L.A. Popelier, R.F.W. Bader, Chem. Phys. Lett. 189 (1992) 542. [8] S.A. Kulkarni, J. Phys. Chem. A 102 (1998) 7704. [9] P.L.A. Popelier, J. Phys. Chem. A 102 (1998) 1873. [10] I. Rozas, I. Alkorta, J. Elguero, J. Phys. Chem. A 101 (1997) 9457. [11] A. Vila, R.A. Mosquera, J.M. Hermida-Ramo´n, J. Mol. Struct. (THEOCHEM) 541 (2001) 149.
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