ARTICLE pubs.acs.org/JPCA
Charge-Assisted Intramolecular Hydrogen Bonds in Disubstituted Cyclohexane Derivatives A. J. Lopes Jesus†,‡,* and J. S. Redinha‡ † ‡
Faculty of Pharmacy, University of Coimbra, 3004-295 Coimbra, Portugal Department of Chemistry, University of Coimbra, 3004-535 Coimbra, Portugal
bS Supporting Information ABSTRACT: In this paper, the N+H 3 3 3 N, N+H 3 3 3 O, and OH 3 3 3 O charge-assisted intramolecular hydrogen bonds (CAHBs) are investigated using different theoretical approaches. Monocharged cyclohexyldiamines (CHDA), aminocyclohexanols (ACHO), and cyclohexanediols (CHDO) are used as model compounds. Geometry optimizations at the MP2/aug-cc-pVDZ level are used to find the equilibrium structures for all possible H-bonded conformers. CAHBs are characterized geometrically and spectroscopically, and their energy is evaluated by means of homodesmic reactions. By comparison with the neutral forms, the presence of the charge is found to have a deep influence on the geometric and energetic H-bond parameters. In addition, these parameters are strongly dependent on the type of the groups involved as well as on their relative position in the cyclohexyl ring. For the systems under study, the H-bond energies vary from 23 to 113 kJ mol1, being classified from moderate to strong H-bonds. These H-bonds are also characterized by the application of the NBO and AIM theories. NBO analysis reveals that the energy corresponding to the charge transfer between the lone-pairs of the electron donor group and the antibonding orbitals of the acceptor group represents an important contribution in the H-bond stabilization. From the application of the AIM theory it is possible to see that these H-bonds possess some covalence which varies according to the type and relative position of the intervenient groups.
1. INTRODUCTION Hydrogen bonding (H-bonding) is a type of interaction of utmost importance in all branches of science.14 The nature of hydrogen bonds is complex since they occupy an intermediate position between covalent, ionic, and van der Waals interactions.5 Indeed, they are orientationally dependent but neither as rigid as the electron share bonding nor as lithe as the ionic or van der Waals forces. The strength of most H-bonds fall between 10 and 40 kJ mol1,6 which means that they are stronger than the dispersion forces but weaker than covalent or ionic bonds. In an XH 3 3 3 Y bond, the hydrogen atom is attracted by Y. Hence, the distance between H and Y, although larger than the covalent one (XH), gets short enough to give to this interaction a hybrid covalentionic resonance structure.7 The H-bonding features, associated with the ubiquity of the polar molecules in nature, allow this interaction to play an important role in many fields. For example, the structure and behavior of various biomacromolecules, such as proteins and nucleic acids, as well as the drug action, are elucidative examples of its importance in the biological molecular recognition processes.4,810 Furthermore, the properties of water, the most important liquid in living organisms, are governed by H-bonding.3 H-bonds wherein the donor group has a positive charge or the acceptor group a negative one are called charge-assisted (CAHBs),7,1115 ionic,16 or low-barrier hydrogen bonds.17,18 The latter designation accounts for the low potential barrier height for the proton transfer process between the donor and acceptor atoms. As it will be seen later on, the presence of the charge increases considerably their strength, making them to fall r 2011 American Chemical Society
into the category of moderate (1763 kJ mol1) or strong (63167 kJ mol1) hydrogen bonds.1 The CAHBs control a great variety of processes involving molecules with groups exhibiting acidbase properties. For example, in solution, they are responsible for the molecular self-assemblies into clusters, growing to ionic crystals.16 The structure of the “proton sponges” is characterized by the existence of two basic nitrogen atoms attached to a relatively rigid organic core. Due to the high basicity, one of the nitrogen atoms gains a proton in acidic media, giving rise to a strong N+H 3 3 3 N intramolecular H-bond.1 Because of their strength and directionality, this type of interactions has relevance in crystal engineering.19 Owing to the importance of the inter- and intramolecular CAHBs in many processes, some papers on their nature have been published in literature.15,2025 In the present work, geometric, vibrational and thermodynamic data, together with those provided by natural bond orbital (NBO) and atoms-in-molecules (AIM) theories, are used to get a deep insight into the N+H 3 3 3 N, N+H 3 3 3 O, and OH 3 3 3 O intramolecular CAHBs. As model compounds, we have chosen the 1,2-, 1,3-, and 1,4-isomers of the following disubstituted cyclohexane derivatives: cyclohexyldiamimes (CHDA), cyclohexanediols (CHDO), and aminocyclohexanols (ACHO). With this group of molecules, important aspects about these interactions can be pointed out, namely the effect of the charge, nature of the groups involved, and their relative position. Received: June 30, 2011 Revised: October 23, 2011 Published: October 25, 2011 14069
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Table 1. Relative Gibbs Energies (ΔG) and Geometrical Parameters Calculated at the MP2/aug-cc-pVDZ Level of Theory for the H-Bonded Conformers of the Charged CHDA, CHDO, and ACHO Isomersa molecule
ΔG/ kJ mol1
t12CHDA
15.18
1.960
c12CHDA
17.50
1.895
c13CHDA
0.00
H 3 3 3 Y/ Å
X 3 3 3 Y/ Å
XH/ Å
XH 3 3 3 Y/°
2.649
1.051
120.2
2.617
1.055
122.4
1.663
2.660
1.088
149.7
2.225
2.950
1.023
126.5 158.2
Cyclohexyldiamines
c14CHDA
10.21
1.612
2.668
1.104
(2.96) b
(3.24) b
(1.028) c
Cyclohexanediols t12CHDO
19.29
1.861
2.622
1.002
130.2
c12CHDO
13.80
1.782
2.571
1.008
132.3
c13CHDO
0.00
c14CHDO
17.32
1.499
2.515
1.054
160.0
1.969
2.810
0.972
143.4 165.1
1.451
2.500
1.070
(2.89) b
(3.17) b
(0.968) c
Aminocyclohexanols t2ACHO c2ACHO
15.00 17.90
2.093 2.015
2.629 2.588
1.034 1.035
109.7 112.1
c3ACHO
0.00
1.741
2.630
1.047
139.9
2.173
2.927
1.021
129.1 153.3
c4ACHO
14.65
1.662
2.649
1.056
(2.89) b
(3.24) b
(1.028) c
Figure 1. Some optimized conformers (MP2/aug-cc-pVDZ) of the disubstituted cyclohexane derivatives considered in the present work, showing the different intramolecular CAHBs and different geometrical arrangements of the functional groups. Intramolecular H-bonds are represented by dotted lines.
Table 2. Hydrogen Bond Energies (ΔEH‑bond) Estimated from Homodesmic Reaction1
Cyclohexyldiaminesa
a
Values in italic were computed for the neutral forms. b Sum of the van der Waals atomic radii given by Bader:53 1.34, 1.62, and 1.55 Å for H, N, and O, respectively. c X-H distances taken from the optimized geometries (MP2/aug-cc-pVDZ) of protonated cyclohexylamine and neutral cyclohexanol.
2. CALCULATIONS AND MOLECULES Geometry optimizations without constrains of previously selected conformations were conducted using the MP2 approximation method26,27 and the aug-cc-pVDZ basis set.28 Harmonic vibrational frequencies at the B3LYP/cc-pVDZ level were also performed to confirm the absence of imaginary frequencies in the optimized stationary points, obtain the vibrational frequencies, and also to account for the thermal corrections at 298.15K. All electronic structure calculations were executed with the Gaussian 03W program package.29 In order to give a deeper insight into the nature of the intramolecular CAHBs, NBO and AIM theories have been applied. The NBO calculations used the MP2-optimized structures and were performed with the NBO 5.0 program30 implemented in the GAMESS software package, version 22-Feb-2006 (R5).31 Regarding the AIM analysis, identification and characterization of bond critical points (BCP) was carried out with the program EXTREME.32,33 The molecules considered in the present study were the cis (c) and trans (t) isomers of the monocharged CHDA, CHDO, and ACHO. Only the structures with the functional groups adopting a configuration and orientation able to form an intramolecular hydrogen bond have been optimized. This reduced the number of starting conformations to fifteen, one conformer for each
ΔEH‑bond/kJ mol1
molecule
t12CHDA
52.88
c12CHDA
57.30
c13CHDA c14CHDA
75.43 85.46 Cyclohexanediols 83.86
t12CHDO c12CHDO
89.54
c13CHDO
101.80
c14CHDO
113.51 Aminocyclohexanols
a
t2ACHO
22.93
c2ACHO c3ACHO
34.44 46.50
c4ACHO
51.94
Values taken from ref 38.
isomer, except in c12CHDA, c12CHDO, and c2ACHO which exhibit two H-bonded conformers.
3. MOLECULAR GEOMETRY AND RELATIVE ENERGIES In Table 1 are given the values of the Gibbs energy computed for the conformers under consideration and the structural parameters commonly used to characterize the intramolecular H-bonds. Figure 1 displays the optimized geometries of some conformers, illustrating the different CAHBs and the different relative positions of the substituents. As it has been referred above, c12CHDA, c12CHDO, and c2ACHO exhibit two intramolecularly hydrogen-bonded conformers. Since they are conformationally and energetically similar, only the values computed for one of them are shown in Table 1. 14070
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Table 3. Calculated (B3LYP/aug-cc-pVDZ) IR Wavenumbers and Intensities (I) for the XH Stretching Vibration and Donor Group Torsion and Frequency Shift (Δν and Δτ) Relative to the Free Groupa NH3+ or OH torsion
XH stretching vibration molecule
wavenumber/cm1
Δν/cm1
I/Km mol1
wavenumber/cm1
Δτ/cm1
I/Km mol1
t12CHDA
2940.5
465.3
245.0
305.1
118.6
23.9
c12CHDA c13CHDA
2855.4 2355.1
550.4 1050.7
347.1 955.1
307.8 345.7
121.3 159.2
40.8 10.6
2127.4
1278.4
1210.7
411.9
225.4
Cyclohexyldiamines
c14CHDA
(3405.8)
(68.4)
(186.5)
8.6 (0.1)
Cyclohexanediols t12CHDO
3195.5
504.4
277.1
781.9
510.7
45.6
c12CHDO
3067.0
632.9
329.6
837.7
566.5
53.7
c13CHDO
2395.1
1304.8
1244.4
1009.2
738.0
26.5
c14CHDO
2257.0
1442.9
1465.0
1113.3
842.1
(3699.9)
(17.9)
(271.2)
28.8 (99.9)
Aminocyclohexanols t2ACHO
3236.9
453.3
73.7
226.1
39.6
c2ACHO
3217.4
472.8
95.7
217.7
31.2
8.5
c3ACHO
2990.4
699.8
175.6
287.5
101.0
18.7
2814.3
875.9
620.6
385.9
199.4
26.2
(68.4)
(186.5)
c4ACHO
(3405.8)
8.3
(0.1)
a
Values in parentheses correspond to the calculated wavenumbers and intensities of the XH stretching and NH3+ or OH torsion vibrations for the groups unperturbed by hydrogen bonding, which were obtained from vibrational calculations at the B3LYP/aug-cc-pVDZ level carried out on cyclohexylamine and cyclohexanol.
A common manifestation used to confirm the presence of a H-bond is the effect produced on the geometry of the donor and acceptor groups. It is well-known that the establishment of an XH 3 3 3 Y bond lengthens the XH distance and shortens the H 3 3 3 Y and X 3 3 3 Y distances relatively to the sum of the van der Waals radii. In addition, to reach a maximum strength, the XH direction has to make with the H 3 3 3 Y line an angle as close as possible to 180°, although significant interactions can be found for angles >110°.34 The values of the geometrical parameters given in Table 1 show that all conformers are stabilized by the formation of an intramolecular hydrogen bond. To see the effect of the charge on the H-bond geometry, the values tabled for 1,3-derivatives are compared against those obtained for the corresponding neutral forms. As can be seen, the presence of the charge decreases the H 3 3 3 Y distance by 2025%, increases the XH distance by 38% and increases the XH 3 3 3 Y angle by 818%. The better geometrical arrangement of the functional groups to form an H-bond is ordered as follows: CHDOs > CHDAs > ACHOs. Within each cyclohexane derivative this interaction becomes more favorable as the donor and acceptor are more apart in the cyclohexyl ring. In general, for the three disubstituted derivatives, structures with more favorable geometry to establish an H-bond have a lower Gibbs energy. The only exceptions to this trend are the 1,4disubstituted isomers that despite a smaller H 3 3 3 Y distance and larger XH 3 3 3 Y angle are not the most stable structures. The reason is the stronger distortion on their geometry. In fact, the formation of an H-bond in the 1,4-isomers requires the cyclohexyl ring to adopt a twist-boat (TB) conformation (Figure 1), which increases the energy by about 2529 kJ mol1.35 CAHBs
play in some isomers a decisive role on the conformational changes of the charged species comparatively to their neutral counterparts. In neutral disubstituted cyclohexane derivatives the equatorial configuration is generally preferred over the axial and the cyclohexyl ring adopts a chair conformation.36,37 However, when one of the groups is charged, the increased stabilization arisen from the hydrogen bond leads to pronounced conformational modifications. For example, neutral c13CHDA is preferentially diequatorial while the corresponding monocharged form is diaxial.36,38 Also, in the most stable conformer of the neutral c14CHDA the cyclohexyl ring is in the chair conformation whereas in the monoprotonated specie it acquires a twist-boat conformation, as referred above.36,38 Such conformational variations have also been described for the anionic cyclohexanediols.39
4. CHARGE-ASSISTED HYDROGEN BOND PROPERTIES The data supplied by the MP2 calculations give evidence for the existence of an intramolecular CAHB which determines the energy and geometry of the molecules under investigation. A thermodynamic, spectroscopic and electronic characterization of the CAHBs using different methodologies is now presented. 4.1. Determination of the H-Bond Energy. The H-bond energy is a valuable property not only for its characterization, but also to estimate the role it plays in various processes, such for example in hydration. In the case of an intermolecular H-bond, it can be quantified theoretically through the difference between the energy of the complex and the sum of the energies of the isolated monomers. However, in an intramolecular H-bond no such strategy can be followed. Various estimation schemes have thus been proposed to estimate the intramolecular H-bond 14071
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Table 4. NBO Results Characterizing the Interaction of LP(Y) with σ*(XH) and σ(XH) Orbitals: p Character of the LP Orbitals, Occupancy of the σ*(XH) Orbital, Integral Overlaps, |Si,j*| and |Si,j|, Second Order Stabilization Energies, E(2) i,j* , and Steric Exchange Repulsion Energies, E(st)a i,j 1 E(2) i,j* /kJ mol
1 E(st) i,j /kJ mol
molecule
LP (%p)
σ*(XH) occupancy
t12CHDA
80.9
0.03675
0.2723
70.33
0.2164
56.11
c12CHDA
80.8
0.04492
0.3121
90.17
0.2379
70.12
|Si,j*|
|Si,j|
Cyclohexyldiamines
c13CHDA
79.1
0.09306
0.5137
247.19
0.3294
150.58
c14CHDA
79.1
0.11175
0.5466
305.14
0.3480
173.47
t12CHDO
34.1
0.04036
Cyclohexanediols 0.0469
7.61
0.0275
1.17
99.6
0.0176
0.04
0.0185
0.08
97.8
0.2641
74.01
0.2070
-81.66 c12CHDO
c13CHDO
0.0631
11.70
0.0340
1.67
99.8
0.0156
0.00
0.0149
0.08
97.0
0.2995
98.80
0.2279
63.93
0.1153
-110.50 34.39
0.0284
65.52 1.46
34.4
0.05025
44.7
0.10337
99.4
0.0355
2.55
0.0144
0.12
86.0
0.4789
309.23
0.3054
151.50
0.1499
41.30
0.0395
2.38
99.7
0.0013
0.33
0.0033
2.09
84.3
0.5123
372.00
0.3277
-346.17 c14CHDO
49.83 50.52
46.1
0.12029
153.08
-413.63
177.19 181.66
Aminocyclohexanols t2ACHO
56.5
0.01184
96.8
0.0931
8.91
0.0862
9.04
0.0937
8.70
0.0834
10.13
0.1062
11.67
0.0959
0.1197
13.81
0.1044
-17.61 c2ACHO
59.1
0.01458
94.1
19.17
-25.48 c3ACHO
81.8
0.03870
71.2 c4ACHO
84.3
0.05334
68.4
15.52 26.73
0.0801
8.62
0.0460
3.72
0.3327
100.37 -108.99
0.2198
72.97 9
0.0521
6.90
0.0101
0.29
0.3995
150.37
0.2535
76.69
-157.27 a
11.21
5
(st) Values in italic refer to the sum of the E(2) i,j* or Ei,j values computed for the different lone pairs.
energy.2,4044 A quite popular one is based on the comparison of the energy between a conformation wherein the H-bond is retained with another one where it is broken. Alternatively, it can be calculated as the energy variation of isodesmic/homodesmic reactions. A thorough discussion on the strengths and weaknesses of these two and other approaches is given elsewhere.43 In this work the H-bond energy has been estimated by considering the following homodesmic reaction: R 1 CY H þ H CY R 2 f R 1 CY R 2 þ H CY H ðIÞ
ðIIÞ
ðIIIÞ
ðIVÞ
ð1Þ wherein CY stands for the cyclohexyl ring, R1 represents the proton donor group (NH3+ or OH), and R2 is the proton
acceptor group (NH2, OH, or O). Structure III corresponds to the optimized geometry of the hydrogen-bonded conformer, and I, II, and IV are obtained from III by replacing R2, R1, or both, by hydrogen atoms, respectively. The electronic energy values of these three structures were evaluated by optimizing (MP2/augcc-pVDZ) the internal coordinates involving the substituting hydrogen atoms, and freezing all the others. This procedure ensures that the energy variation of reaction 1 is related to the intramolecular H-bond formation. The estimated H-bond energies (ΔEH‑bond) are given in Table 2. To obtain the enthalpy of the H-bond formation (ΔHH‑bond), corrections for the translational, rotational, and vibrational energies have to be calculated for the products and reagents. This can be done for fragment III but not for I, II, and IV since they are not minima in the potential energy surface. 14072
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The Journal of Physical Chemistry A In general, no significant differences are expected between the translational and rotational energies of the reagents and products. On the contrary, some vibration modes are affected by the H-bond, giving different contributions to the vibrational energy. In any case, in relative terms, the correction due to such variations is expected to be small. To check the reliability of the application of homodesmic reaction 1, it has been used in some conformers where an H-bond is not found to exist. Negative and positive energy variations with mean values of 6 and 4 kJ mol1, respectively, have been obtained. This means that other attractive/repulsive interactions besides H-bond (e.g., ion-dipole interactions)38 are likely to be included in the energy variations calculated from (1). Nevertheless, considering the order of magnitude of the values shown in Table 2, one can say that this methodology gives a reasonable estimation for the energy of CAHBs under study. The intramolecular H-bond strength in monoprotonated α,ωalkyldiamines was quantified by comparing the energy of the H-bonded conformations with fully distended structures wherein no such interaction exists.45 Values of 48, 75, and 85 kJ mol1 have been estimated for ethanediamine, 1,3-propanediamine and 1,4-butanediamine, respectively. These figures are in good agreement with those reported in this work for cyclohexyldiamines with the same relative position of the amino groups. Unfortunately, we are not aware of values estimated for the energy of the NH3+ 3 3 3 OH or OH 3 3 3 O H-bonds to be compared with our results. The computed H-bond energies given in Table 2 span over a wide range of values. The ordering of these energies among and within the three classes of substituents is in agreement with the geometrical data inserted in Table 1. The N+H 3 3 3 OH is the weakest H-bond with values of ΔEH‑bond falling between 23 (t2ACHO) and 52 kJ mol1 (c4ACHO). For the same relative position of the two functional groups, the substitution of OH by NH2 decreases the hydrogen bond energy by about 30 kJ mol1. The strongest interaction if found for OH 3 3 3 O, with energies varying from 84 to 114 kJ mol1. According to the guiding values proposed for the classification of the H-bonds based on the energy,1 these intramolecular CAHBs can be included into the moderate (17 to 63 kJ mol1) or strong (63 to 167 kJ mol1) categories. Just to have an idea about the energetic effect due to the presence of a charge at the H-bond partners, similar calculations have been carried out for the neutral 1,3-disubstituted conformers. The values estimated for ΔEH‑bond were found to be 3.7, 7.8, and 14.8 kJ mol1 for c3ACHO, c13CHDA, and c13CHDO, respectively. These figures lead to the conclusion that, in fact, the charge has a strong effect on the CAHB energy. 4.2. Infrared Spectroscopy. Valuable information on H-bonding can be obtained from infrared spectroscopy. One of the most significant spectral manifestations of this interaction is the displacement of the XH stretching vibration toward lower frequencies (Δν), and an increase of its intensity.46 Although not so pronounced, a blue shift of the torsional vibration of the donor group (Δτ) is generally observed.47,48 The wavenumbers and intensities of these vibrational modes were calculated at the B3LYP/aug-cc-pVDZ level and the values are displayed in Table 3. To be used as reference, similar calculations have been done on the charged cyclohexylamine and neutral cyclohexanol. The magnitude of the red-shift and intensity of the XH stretching vibration clearly confirms the existence of relatively
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Figure 2. Contour plots of preorthogonalized NBOs in t2ACHO (A) and c14CHDO (B) showing the most relevant LP(Y) f σ*(XH) interaction. Circled crosses represent the atomic positions. The outermost contours are at 0.032 au and the contour interval is 0.05 au.
strong hydrogen bonds. In addition, the values of both parameters are very sensitive to structural variations, being particularly large in the nonvicinal isomers of CHDAs and CHDOs, in agreement with the geometric and energetic data. The OH and NH3+ torsional modes do not involve a specific bond but rather the whole group. As consequence of the hydrogen bond formation this vibration is coupled with the torsion vibration of the acceptor group (NH2 or OH). The coupling becomes stronger as the H-bond strength increases. Attempts have been made to estimate the enthalpy of the H-bond formation from the shift of the stretching or torsional modes. Various empirical correlations relating Δν or Δτ with ΔH have been proposed, from simple direct proportionality relationships to more complex expressions.4648 These correlations would be very useful as far as one could quantify the H-bond strength from a simple determination of a band shift. However, in the present case, the values of ΔH estimated from the application of these relationships were found to be underestimated relatively to those of ΔEH‑bond given in Table 2 (see the Supporting Information). This is particularly noticeable in the values obtained from Δτ. 4.3. Natural Bond Orbital (NBO) Theory. 4.3.1. Orbital Interactions. According to the NBO theory, the XH 3 3 3 Y H-bonded complex results from the electron transfer from the Y lone-pairs, LP(Y), to the antibonding XH orbital, σ*(XH). This process is represented as LPðYÞ f σðXHÞ ð2Þ The electron delocalization from a filled (i) to an unfilled (j*) orbital lowers the energy of the former, thereby contributing to the structure stabilization. This energy decrease, E(2) i,j* , can be estimated by the second-order perturbation theory.49 However, the compression of the electrons into a smaller spatial volume, as consequence of H-bonding, gives rise to a steric repulsive energy 50,51 The global stabilizing between the i and j filled orbitals, E(st) i,j . effect of the orbital interactions depends on the balance of the effects just referred. Naturally, it becomes stronger as the (st) energy difference between |E(2) i,j* | and |Ei,j | increases. The molecular stabilization due to H-bonding can be also evaluated from 14073
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Table 5. Natural Charges of the Atoms Involved in the Hydrogen Bond and Hybrid Composition of the σ(XH) Orbital a σ(XH) hybrid composition
natural atomic charges molecule
QX
QH
Δneb
t12CHDA
0.79570
0.50472
0.50244
0.95344
0.8760
0.4823
3.08
c12CHDA
0.81497
0.50586
0.50406
0.95824
0.8783
0.4781
3.04
QY
aX
aH
λX
Cyclohexyldiamines
c13CHDA
0.84148
0.51199
0.51425
0.95874
0.8923
0.4514
2.65
c14CHDA
0.84217
0.50648
0.51053
0.94854
0.8956
0.4448
2.62
(0.76539)
(0.46094)
(0.91114)
(0.8279)
(0.5608)
(3.29)
t12CHDO
0.88193
0.54125
0.53876
1.05386
0.8872
0.4614
3.32
c12CHDO c13CHDO
0.89285 0.93152
0.54229 0.56675
0.54046 0.56771
1.06050 1.03733
0.8899 0.9102
0.4561 0.4141
3.16 2.48
0.56480
Cyclohexanediols
0.93508
0.56305
(0.80455)
(0.47774)
t2ACHO
0.77356
0.49241
0.48878
0.83356
c2ACHO
0.78995
0.49510
0.49146
0.83580
c3ACHO
0.80871
0.50972
0.50810
0.86056
0.8781
0.81374
0.51108
0.51086
(0.76539)
(0.46094)
c14CHDO
1.02872
0.9135
0.4069
2.49
(1.05725)
(0.8606)
(0.5092)
(3.89)
0.8665
0.4991
3.24
0.8679
0.4967
3.20
0.4785
2.87
Aminocyclohexanols
c4ACHO
0.85426
0.8822
0.4709
2.80
(0.80455)
(0.8279)
(0.5608)
(3.29)
a
Values in parentheses are the natural atomic charges when the atoms are not involved in a H-bond and were taken from NBO calculations performed in cyclohexylamine and cyclohexanol. b Electron population reduction on the hydrogen atom estimated from eq 5.
the overlap integrals for the attractive (Si,j*) and repulsive (Si,j) interactions. The ratio (Si,j*/Si,j)2 is sometimes taken as a measure of the H-bond stabilizing effect.49 The results of the NBO calculations are displayed in Table 4. In CHDAs one lone-pair is involved in the charge transfer process, while in CHDOs three lone-pairs act as donors; they are designated as LP1, LP2 and LP3 according to the order they appear in Table 4. LP1 has a predominantly s character which decreases as the interaction with the acceptor increases. LP2 is almost a pure p orbital; although it is more diffuse than LP1, the relative disfavorable donoracceptor orientation makes the values of E(2) i,j* to be vanishingly small. LP3 is predominantly p and it is strongly overlapped with σ*(OH), being therefore the dominant contribution in the LP(O) f σ*(OH) orbital interaction. Regarding ACHOs, the role of the two oxygen lone-pairs in the donoracceptor process is dependent on the relative position of the two functional groups: in the vicinal isomers they have identical contributions while in the nonvicinal ones LP2 is a stronger donor than LP1. In Figure 2 are displayed some contour plots showing the maximum overlap of LP(Y) with σ*(XH) in the weakest (t2ACHO) and stronger (c14CHDO) H-bonds. The values of E(2) i,j* displayed in Table 4 show a large variation among the structures under consideration, ranging from 18 to 414 kJ mol1. Such wide range indicates that they are strongly dependent on the nature of the groups, as well as on their relative position in the cyclohexyl ring. The order of magnitude of the values point out the high strength of the CAHBs in most of the conformers. Another conclusion taken from the donoracceptor energy values is the higher charge transference in the homonuclear CAHBs than in the heteronuclear one. Within the homonuclear interactions this effect is stronger in OH 3 3 3 O than in N+H 3 3 3 N. It is also to be noted that when the groups are more apart the charge transference increases substantially.
Both effects make the donoracceptor interaction to be particularly strong in the nonvicinal CHDAs and CHDOs, thus explaining the more favorable geometric and energetic H-bond parameters computed for these structures. The comparison of the figures obtained for E(2) i,j* with those estimated for the ΔEH‑bond (Table 2) reveals that the formers are, in most cases, largely overtimated to be taken as the hydrogen bond energy. Really, the electron delocalization involving i and j* orbitals is accompanied by other orbital interactions, in particular the repulsion between i and j. In principle, a better estimative of the H-bond energy can be achieved by including the effect of the pairwise steric energies, which are also inserted in Table 4. In fact, (st) the values obtained by summing E(2) i,j* with Ei,j are much closer to those estimated for ΔEH‑bond. The remainder energy is attributed to other interaction energy components, namely the electrostatic and dispersive energies, according to the H-bond energy decomposition approaches that have been proposed by several authors, as for example that of Morokuma.52 4.3.2. Repolarization of the σ(XH) Orbital. The occupation of the σ*(XH) orbital by electron transfer from LP(Y) induces a repolarization/rehybridization of the σ(XH) orbital to maximize any LP(Y) σ*(XH) overlap. As it is explained following, this process reduces the electron population at the shared hydrogen atom, thereby increasing its positive charge. Writing the σ(XH) NBO as function of its natural hybrid orbitals (NHOs) we have σðXHÞ ¼ aX ðspλ ÞX þ aH ðsÞH
ð4Þ
where aX and aH are the polarization coefficients of the hybrids and λ the hybridization label. Considering that the donor orbital is complete and that nt electrons are transferred to the acceptor orbital, the number of electrons at the hydrogen atom is given by 14074
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Table 6. Selected Topological Properties (in a.u.) at the H 3 3 3 Y BCPs, RCPs, and CCPs RCP/CCPa
BCP molecule
F
rF2
rY
rH
F
rF2
Cyclohexyldiamines t12CHDA
0.034209 0.024091 1.2642 0.6980 0.026963 0.037025
c12CHDA c13CHDA
0.039033 0.026797 1.2342 0.6620 0.028810 0.040655 0.063187 0.029193 1.1408 0.5221 0.018191 0.024694 0.008255 0.009436 0.008148 0.010140
c14CHDA
0.071548 0.026087 1.1181 0.4936 0.011788 0.015143 0.011614 0.015563
Figure 3. Molecular graphs for the optimized (MP2/aug-cc-pVDZ) conformers of t2ACHO (A) and c14CHDO (B). For better visualization, H-bond BCPs, RCPs, and CCPs are indicated by letters b, r, and c, respectively.
0.011471 0.015563 Cyclohexanediols t12CHDO
0.037978 0.027362 1.2067 0.6587 0.032874 0.039610
c12CHDO 0.044626 0.031946 1.1672 0.6178 0.035767 0.044569 c13CHDO 0.080253 0.035710 1.0478 0.4521 0.023581 0.032021 0.009514 0.011349 0.009486 0.011938 c14CHDO 0.090401 0.029464 1.0270 0.4244 0.015031 0.019834 0.014598 0.020121 0.014581 0.020137 Aminocyclohexanols t2ACHO c2ACHO
0.022249 0.021707 1.2676 0.8460 0.021324 0.028838 0.025693 0.024462 1.2356 0.7932 0.018492 0.025109
c3ACHO
0.042368 0.036628 1.1450 0.5970 0.015990 0.022680 0.007790 0.009049 0.007748 0.009556
c4ACHO
0.050973 0.040285 1.1154 0.5483 0.011264 0.014544 0.010855 0.014967 0.010854 0.014986
a
Values in italic refer to the cage critical point (CCP).
the following expression:49 Δne ¼ 2ðaHf 2 aHb 2 Þ þ nt ð1 aHb 2 Þ
ð5Þ
aHb and aHf are the NHOs polarization coefficients for σ(XH) when the group is bonded and free, respectively. The first term of eq 5 is the number of electrons withdrawn from the hydrogen atom due to σ(XH) repolarization, while the second is the number of electrons donated to σ*(XH). Since the weight of first term overcomes that of the second, globally, the number of electrons at H decreases. The values computed for the polarization coefficients, hybrid labels and natural charges (Q ) are presented in Table 5. The values of these parameters in a free XH bond were taken from the monosubstituted cyclohexanes (cyclohexylamine and cyclohexanol) and are inserted in parentheses in the same table. The repolarization of the σ(XH) bond turns it more polarized toward X and the σ*(XH) antibond more polarized toward H. This decreases the steric exchange repulsion between LP(Y) orbital and the H terminus of σ(XH) and the amplitude of σ*(XH) near H, thus favoring the overlap.49 The electron depletion at the hydrogen atom estimated from eq 5, Δne, is in close agreement with the values of the natural
charges taken from the NBO analysis output (see Table 5). The values of Q H found for the systems we are studying prove that it is a sensitive parameter in the hydrogen bond diagnose. The charge increase at the hydrogen atom, as consequence of the H-bond formation, ranges from +0.0438 in t2ACHO to +0.0890 in c13CHDO and its variation with ΔEH‑bond is approximately linear. 4.4. AIM Theory. The AIM theory, developed by Bader and co-workers,53 has been used to establish H-bonding criteria. According to this theory, the formation of a hydrogen bond requires the existence of a (3,-1) bond critical point (BCP) along the H 3 3 3 Y bond path. The values of the electron density at the critical point (FBCP) ant its Laplacian (r2FBCP) are important quantities to characterize H-bonding in respect with strength and nature. Popelier established that in such interactions the values of FBCP are in the range 0.002 to 0.04 au, while those of r2FBCP are positive, falling between 0.02 and 0.15 au.54,55 Another important criterion is the existence of mutual penetration of the H and Y atoms, i.e., r0H > rH and r0Y > rY, where rH and rY are to the distances from the nuclei of H and Y to BCP, whereas r0H and r0Y correspond to the nonbonded radii. The values of r0H, r0N and r0O estimated by Bader are 1.34, 1.62, and 1.55 Å, respectively.53 The values of the topological properties at the BCP are summarized in Table 6 for the structures under analysis. The sequence of the H-bond strength based on the values of FBCP, either within or among the series of compounds, follows that established from the other approaches. Moreover, the variation of FBCP with the estimated H-bond energy yields a good linear correlation. In the nonvicinal CHDAs and CHDOs, as well as in c4ACHO, the values of FBCP exceed the limits proposed by Popelier. This means that these criteria do not account for systems with so strong H-bonds, particularly CAHBs. As expected, for all structures, a pronounced mutual penetration between Y an H is observed. Indeed, the differences between r0H + r0Y and rH + rY vary from 0.91 Å in 2ACHO to 1.6 Å in c14CHDO, following the hydrogen bond strength sequence. As can be seen from the molecular graphs displayed in Figure 3, the formation of a five to seven-membered ring caused by the H-bond creates one or two ring critical points (RCP). Additionally, a cage critical point is present in structures wherein the functional groups occupy the 1,3- or 1,4-positions. The values of the electron density and Laplacian at the RCPs and CCPs are also included in Table 6. The positive values of r2FBCP at the BCP lead us to include the CAHBs into the category of closed-shell interactions. A more detailed picture about the nature of these bonds can be drawn from the virial theorem equation relating r2FBCP with the 14075
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Table 7. Energy Densities (au) at the H 3 3 3 Y BCP molecule
VBCP
GBCP
HBCP
t12CHDA
0.02550
0.02480
0.00071
c12CHDA
0.02971
0.02825
0.00146
Cyclohexyldiamines
c13CHDA
0.05660
0.04289
0.01370
c14CHDA
0.06807
0.04708
0.02099
t12CHDO
0.03254
0.02995
0.00259
c12CHDO
0.03931
0.03563
0.00368
c13CHDO c14CHDO
0.09170 0.10977
0.06370 0.06961
0.02799 0.04015
t2ACHO
0.02004
0.02087
c2ACHO
0.02305
0.02375
0.00071
c3ACHO
0.03777
0.03720
0.00057
c4ACHO
0.04791
0.04410
0.00381
Cyclohexanediols
Aminocyclohexanols 0.00083
topological energetic parameters at the BCP:53,56 1 2 ∇ FBCP ¼ 2GBCP þ VBCP 4
ð6Þ
GBCP represents the electron kinetic energy density at the BCP which is always positive, while VBCP is the electron potential energy density at that point which is always negative. The signal of r2FBCP depends on the relative values of both terms. Cremer et al.57 used the signal and magnitude of the total electron energy density at the BCP (HBCP), given by HBCP = GBCP + VBCP, to go deeper into the nature of hydrogen bonds. This approach has been followed by other authors.58,59 HBCP > 0 means that the interaction is predominantly electrostatic, and HBCP < 0 indicates a significant covalent character. As the bond strength increases HBCP becomes more and more negative, i.e., the covalence of the bond increases too. The energy densities calculated for the different structures and presented in Table 7 show that in the ACHOs vicinal isomers the values of HBCP are small and positive, which means that the H-bonds in these molecules are predominantly electrostatic. In the remaining structures they are negative, thus indicating the existence of a certain covalence which is particularly notorious in the nonvicinal isomers of CHDAs and CHDOs. These results are consistent with the stronger LP(Y) f σ*(XH) charge transference found in latter isomers by NBO analysis. The CO bond in the CHDOs may exhibit an intermediate character between single and double. Using the values of FBCP at the BCP computed for cyclohexanol (neutral and charged forms) and cyclohexanone, and the equation proposed by Bader53 relating the bond order with FBCP, a value of 1.37 have been calculated for the CO bond. A similar Figure (1.34) has been found by applying the Pauling correlation between bond order and bond length.60,61 This is an indication that a significant double bond character is found to exist; that is, the OH 3 3 3 O interaction, besides charged-assisted is also resonance-assisted.
5. CONCLUDING REMARKS ON THE NATURE OF CAHBs Insight into CAHBs and their global effect on the structure and energy of the monoprotonated cyclohexane diderivatives
were pointed out by different research methods. Computational calculations at the MP2 level allowed for the determination of the energy values for the conformations stabilized by intramolecular H-bonds. Quantification of the H-bond strength was performed by calculations of the energy variation for homodesmic reactions. Besides the geometric and thermodynamic data, an interpretation of the CAHBs based on the NBO and AIM theories was carried out. Insight into the electrostatic-covalent nature of these interactions was obtained from these methods. The results collected from each method allow for the establishment of an identical sequence of the H-bond strength of the isomers under consideration. The energy of the intramolecular CAHBs in the monoprotonated cyclohexane diderivatives falls between 22.93 kJ mol1 (t2ACHO) and 113.51 (c14CHDO). Such high energy values for this type of interaction show the strong influence of the charge at the acceptor or donor groups on the H-bond stabilization. These internal bonds originate pronounced structure modifications in some molecules relative to the neutral forms: in the c13 isomers the configuration of the amino groups changes from diequatorial to diaxial; the cyclohexyl ring in the c14 isomers acquires a twist-boat conformation in the charged species. Among the substituents, the CAHBs are ordered as follows: ACHO , CHDA < CHDO. The homonuclear CAHBs are stronger than the heteronuclear ones. This conclusion in agreement with the findings reported by some other authors.7,11,62 As explained by Gilli,7 the difference between homo and heteronuclear H-bonding depends on the ratio between the forms involved in the XH 3 3 3 Y T XH 3 3 3 Y+ resonance system. The resonance increases, and consequently the structure stability, as X is similar to Y. Besides the influence of the chemical similitude between X and Y, resonance is also dependent on the XH 3 3 3 Y geometry. As the groups are more apart, the XH 3 3 3 Y angle tends to 180°, which increases the H-bond symmetry and favors the resonance stabilization. Three reasons account for the energy difference between the OH 3 3 3 O and N+H 3 3 3 N homonuclear CAHBs: higher electronegativity of the oxygen atom; a more effective donor acceptor orbital overlaps in the former because two electron lone-pairs are involved; some resonance-assisted effect in the former. An open question about the hydrogen bond interaction is the understanding of its nature. The application of the NBO and AIM theories allows concluding that the H-bonds we are dealing with have electrostatic-covalent hybrid behavior, varying among and within the groups of derivatives. They are predominantly electrostatic in the vicinal ACHOs. On the other hand, those existing in the nonvicinal CHDAs and nonvicinal CHDOs have an accentuated covalent character.
’ ASSOCIATED CONTENT
bS
Supporting Information. Hydrogen bond enthalpies estimated from stretching and torsion vibration frequencies. This material is available free of charge via the Internet at http:// pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. 14076
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