J. Phys. Chem. 1995,99, 6457-6460
6457
Theoretical Study of C W . 0 Hydrogen Bonds in H20-CH3F, H20-CH2F2, and H~O-CHFJ Ibon Alkorta* and Sergio Maluendes? Molecular Research Institute, 845 Page Mill Road, Palo Alto, California 94304 Received: October 14, 1994; In Final Form: February 9, 1995@
Ab initio methods have been used to study the CH.. 0 hydrogen bond between H20 and CH3F, CH2F2, and CHF3. The calculations have been carried out using the 6-31G**, 6-311G**, 6-311++G**, and 6-31G** basis sets at the MP2 and MP4 levels of theory. Interaction energies include basis set superposition error adjustments. The results show that the strongest CH. 0 hydrogen bond is the bisector one with the lone pairs on the oxygen. The inclusion of each additional fluorine results in a systematic strengthening of the hydrogen bond by 1 kcaymol as well as in the shortening of the hydrogen bond distance by 0.1 A.
Introduction
Hydrogen bonds of the type X-H-.*Y, where X and Y are heteroatoms, play an important role in determining the structure and activity of biological molecules. Extensive experimental and theoretical effort has been done to study this type of interaction.' Nonstandard hydrogen bonds, as the ones of the types XH- * *Ar,3,4and XH. C,5have been described in the CH. * literature. In this article, a theoretical study of the CHq.0 hydrogen bonds has been carried out using model systems. This kind of hydrogen bond usually presents an electronegative atom attached to the "CH' carbon which is responsible for the electron deficiency of the hydrogen involved in the hydrogen bond. Crystallographic and spectroscopic studies have provided very strong evidence for the existence of CH- -0 hydrogen bonds6 Systematic searches of the Cambridge Structural Database7have indicated that these interactions are very frequent in the solid and recent investigations have shown their importance in the determination of crystal p a ~ k i n g . ' ~ . ' ~ From a theoretical point of view, several authors have addressed these interactions. Kollman et a l . I 4 predicted the existence of the NH3-CHF3 complex before it was experimentally chara~terized.'~Several systems in which HCN, H2C0, and HCCH act as proton donors have been studied with a minimal basis set by Vishveshwara.I6 The frequencies and vibrational properties of (HCNh and NH3-HCN have been calculated at the SCF level and compared to the experimental ones.I7 The minimum of the nitromethane dimer has been found to be a cyclic C2h structure, with two weak hydrogen bonds at the MP4 level of theory.'* A shallow minimum has been found in a recent study of the interaction between phenol and waterI9 in which the water molecule interacts exclusively with one hydrogen of the aromatic ring. Several of the minima found in the conformational analysis of 1,2-dimethoxyethane are stabilized by attractive intramolecular CH. 0 hydrogen bonds.*O Finally, the CH. -0 hydrogen bonds of HCN and HCCH with H20, H2C=O, and 0 3 have been studied by Turi and Dannenberg.2' Since the strength of these hydrogen bonds is expected to be small, the steric and electronic effects could play a very different *Actual address and author to whom correspondence should be addressed: Instituto de Quimica MBdica, Juan de la Cierva, 3, Madrid28006, Spain. e-mai:
[email protected]; fax: 01 1-34-1-564 48 53. +Actualaddress: IBM Research, Almaden Research Center, 650 Harry Road, San Jose, Califomia 95120. Abstract published in Advance ACS Abstracts, April 1, 1995. @
role from that in standard hydrogen bonds. As a model of more complex systems, the interaction between water and the different methyl fluorides has been studied. As a fist step, three different approaches of the water to the CH3F have been studied at the MP2/6-31G** level. The minima found at this level have been confirmed by MP2/6-31 lG**, MP2/6-31 l++G**, and MP4/ 6-3 1G** calculations. Additionally, the interaction between H20 and CH2F2 and CHF3 has been studied to determine the influence in the hydrogen bond of the electronegativity of the atoms attached to the carbon. In all the cases, the optimal distances and minima energies have been characterized in the BSSE corrected surface. Methods
Ab initio calculations have been performed with the HONDO 8 program22 using the standard 6-31G**,23 6-31 1G**,24 and 6-3 11++G**25 bases sets at the second- and fourth-order Moller-Plesset perturbation theory levels (MP2 and MP4).26 Experimental geometries of the isolated molecule^,^^-^^ determined using microwave spectroscopy, have been used in the intermolecular energy computations. The interaction energies have been corrected for the inherent basis set superposition error (BSSE) using the Boys-Bemardi counterpoise technique.31 Thus, the interaction energies have been calculated as the difference between the dimer energy and the sum of the monomer energy calculated in the full basis set, with "ghost" orbitals for the missing monomers. In order to simplify the study of these interactions, a linear geometry of the C-Hl.a-0 has been adopted based on the best disposition found theoretically and experimentally for CH* *X'O-' and standard hydrogen bonds.32 For the smaller system, H20-CH3F, three different approaches of the water molecule to the hydrogen responsible for the hydrogen bond (Hl) have been studied (Figure 1). In the first approach (Figure lA), the lone pairs on oxygen have been positioned sharing the hydrogen bond with H1. In the other two approaches, one of the lone pairs of the oxygen is pointing directly to the H1 (Figure 1, B and C). Additionally, in order to study most of the possible dispositions that the water could adopt in the interaction with the a hydrogen of CH3F, the water molecule has been rotated around several axes centered in the oxygen for each approach, as shown in Figure 2. For the H20-CH2F2 and H20-CHF3 interactions, two approaches, similar to A and B in the HIO-CH~F system, have
QQ22-3654/95/2Q99-6457$09.Q~/Q 0 1995 American Chemical Society
Alkorta and Maluendes
6458 J. Phys. Chem., Vol. 99, No. 17, 1995
TABLE 1: Interaction Energy (MP2/6-31G**) between H2O and CHJF in Approach A as a Function of the Rotation around the a, b, and c Axes (0-H1 Distance = 2.51 A)
H
\ /"
H &H I
angle" E (kcal/mol)
Approach A
"A:
95 100 103 105 107 110 115 120 125 127 130 140
H
A,
H&o
H
Approach B
HAH H
I
b. h axis
a. a axis
H
H
H
H%
/
-1.37 -1.40 -1.40 -1.40 -1.40 -1.40 -1.38 -1.34 -1.30 -1.26' -1.23 -1.07
the three approaches studied. In the left side, a Newman projection of the orientation, looking through the C-Hl**.O bond, is shown. (In approach B, x represents a dummy atom, bisector to the H-0-H, used to define the orientation in Table 2a, Table 6, and Table 7).
a
I50 160 170 180
-0.4 1 -0.64 -0.83 -0.97 - I .08
90 100 1IO 120 130 140 150 160 170 180
-1.15 -1.21 - 1.24 - 1.26 - I .25"
TABLE 2: Interaction Energy (MP2/6-31G**) between H2O and CHJF in Approach B as a Functiop of the Rotation around the a Axis (0-H1 Distance = 2.55 A) angle"
E (kcal/mol)
angle"
E (kcal/mol)
115 120 125 128
- 1.30 - 1.32 - 1.34 - 1.35"
I30 135 140
- 1.35 - 1.36 - 1.35
Angle defined as X-0-H1.
w2
-1.21 -1.21 -1.21 - I .22 - 1.23 - 1.24 - 1.25 - 1.26 - 1.26 - 1.26'
90 100 1 IO 120 130 140
a Defined as HW 1 -0-H1. Angle generated by the water plane and the plane defined by H 1 -C-F. Starting point.
H
Approach C Figure 1. Relative orientation of the H20 molecule to the CH3F in
"
c. c axis
angleb E (kcal/mol) angleh E (kcal/mol)
Starting point.
TABLE 3: Energetic and Geometric Values Obtained for the Minima Found for the H~O-CHJFSystem with Different Methods
C
~
Figure 2. Rotation studied for each approach shown in Figure 1.
-Approach
B
method
energy (kcal/mol)
0-H
I
distance (A)
MP2/6-3 1G** MP2/6-311G** MP2/6-3 1 1++G** MP4/6-3 1G**
Approach A -1.41 - 1.46 - 1.49 - 1.35
2.5 1 2.5 1 2.55 2.5 1
MP2/6-31G** MP2/6-3 1 1G** MP2/6-31 l++G** MP4/6-3 1G**
Approach B - 1.35 - 1.39 -1.38 - 1.30
2.55 2.60 2.60 2.55
~~~~~~~~
H,,-O-H I angle (den) 105 107 105 105
electronic cloud of the fluorine seems to be responsible for this fact. The other two approaches, which do not have this repulsive interaction, have similar interaction energies in the -1 - 5 I , I . I minimum regions (1.26 kcal/mol at 2.5 1 8, in approach A and 1.35 kcaVmol at 2.55 8, in approach B). 2 2.2 2.4 2.6 2.8 3 The additional variables studied do not provide a significant distance O....Hl (A) lowering of the interaction energy (Tables 1 and 2). Only the Figure 3. Interaction energies for the CHaF-H20 system in the three rotation of the water molecule around the a axis in approach A approaches studied. (The fixed angles used for these calculations are the HWl-0-HI angle equal to 127' in approach A, the X-0-HI increases the interaction energy (1.41 kcaVmo1). This movement angle equal to 128' in approach B, and the HW 1-0-H 1 angle equal produces an enlargement of the distance between the lone pairs to I I 1' in approach C.) on oxygen and the fluorine atom and, at the same time, locates the hydrogen atom outside the plane defined by the lone pairs been studied. In these cases, only the influence of rotating the and the oxygen. water molecule around the a axis has been treated. The results obtained with more extended basis sets (6-311G** and 6-3 1l++G**) or higher level of theory (MP4). are very Results and Discussion similar to the ones note previously (Table 3). The interaction energies lie in the range of 1.46 to 1.35 kcaVmol for approach CH3F-H20 System. The interaction energy for the three studied approaches shows a very flat surface surrounding the A and between 1.39 and 1.30 kcaVmo1 for approach B. In all minima which are located at 2.50-2.55 8, between 0 and H1 the cases, approach A is slightly more stable and the hydrogen (Figure 3). From the three approaches, C is the least energetibond distance is shorter than the ones of approach B when a cally favored. The gauche disposition that is observed in this similar basis set and level of theory are compared. All these approach between one of the lone pairs on oxygen and the facts indicate that MP2/6-3 1G** calculations could be consid-
Theoretical Study of CH0.0 Hydrogen Bonds
c
-
J. Phys. Chem., Vol. 99, No. 17, 1995 6459
1-
-0.5
*--- Approach A Approach B
\
m
I
Approach A Approach B
~
--+-
-2
1
-2.2
x
z
1\
/
-2.4
W
-2.5
'
2
, 2.2
2.4
I
1
I
2.6
2.8
3
-3.2
2
0-8' !
2.2
ered adequate to evaluate the interaction energy of larger systems as the ones treated later. These results show the existence of two minima in the interaction surface with very similar energies. One corresponds to the configuration where one of the lone pairs of the oxygen is pointing directly at the hydrogen. However, the interaction is slightly more favorable if both lone pairs share their contribution to the hydrogen bond. A similar result was found for the H20-HCNt6s2' and H20-HCCH systems2' in which the most favorable interaction were those with the hydrogen bonds linear to the bisector of the lone pairs on oxygen. The value of the interaction energy at the minimum, approximately 1.4 kcdmol, is very similar to the calculated energy for other weak hydrogen bonds33 and for the hydrogen bond between water and benzene (1.78 k~al/mol).~ Other parameters that indicate the existence of this hydrogen bond are the calculated charge transfer (0.010 e) and bond order of the hydrogen bond (0.017). An additional parameter that have been used to characterized the hydrogen bonds has been the comparison of the distances between the atoms involved and their corresponding van der Waals radius. In this respect, the distance observed in this case is only slightly shorter than the sum of the van der Waals radius of both atoms as defined by Pauling or B ~ n d iwhich , ~ ~ indicates that this interaction is at the limit to be considered as a hydrogen bond. These results indicate a weak hydrogen bond, in which the short-range directional effect of the nonbonding electron pairs on the oxygen can have a similar importance to that of the longer range dipole-dipole intera~tion.~~ CHzFz-HzO and'CHF3-H20 Systems. The inclusion of additional fluorine atoms on the carbon results in a shortening of the optimal interaction distance and an increase in the interaction energy (Figures 4 and 5). In these systems, approach A corresponds to the more stable interaction. As observed in the case of the H20-CH3F system, conformations in which one of the lone pairs on oxygen is in gauche position with a fluorine atom are unfavorable. This repulsive interaction occurs once in approach B for the H20-CH2F2 system and twice for the same approach for the H20-CHF3 system. The influence in the interaction energy of rotating the water molecule around the a axis in approach A (Tables 4 and 5) is minimum, since, in the case of the H20-CH2F2 system, an interaction energy slightly better than the initial one is found at 120' (Table 4), and, in the H2O-CHF3 system, the initial energy is not improved (Hwl-0-HI angle equal to 137') (Table 5 ) .
2.4
1
I
2.6
2.8
3
Distance O....Hl (A)
Distance O....Hl (A)
Figure 4. Interaction energies for the CH2F2-H20 system in the two approaches studied. (The fixed angles used for these calculations are the HWI-0-H1 angle equal to 127' in approach A and the X-OH1 angle equal to 128' in approach B.)
I
N'
1
Figure 5. Interaction energies for the CHF3-H20 system in the two approaches studied. (The fixed angles used for these calculation are the HW1-0-H1 angle equal to 127' in approach A and the X-OHI angle equal to 128" in approach B.) TABLE 4: Interaction Energy (MP2/6-31G**) between H20 and CHzFz in Approach A as a Function of the Rotation around the a Axis (0-H1 Distance = 2.39 A) angle" E (kcaYmo1) angle" E (kcaYmol) 110 115 120 125
-2.08 -2.12 -2.13 -2.12
Angle defined as HW1-0-H1.
127 130 135 140
-2.1 1' -2.09 -2.04 - 1.97
'Starting point.
TABLE 5: Interaction Energy (MP2/6-31G**) between H2O and CHF3 in Approach A as a Function of the Rotation around the a Axis (0-H1 Distance = 2.28 A) anglea E (kcaYmol) angle" E (kcaymol) ~
~~
110 115 120 125 a
-2.96 -3.06 -3.13 -3.16
Angle defined as HW1-0-H1.
127 130 135 140
-3.16' -3.16 -3.13 -3.06
'Starting point.
TABLE 6: Interaction Energy (MP2/6-31G**) between HzO and CH2F2 in Approach B as a Function of the Rotation around the a Axis (0-H1 Distance = 2.45 A) angle" E (kcaYmol) angle" E (kcaYmol) 120 125 128 130 135 a
- 1.86 - 1.92 - 1.95' - 1.98 -2.02
Angle defining as X-0-H1.
140 150 I60 170 180
-2.05 -2.08 -2.10 -2.1 1 -2.12
Starting point.
TABLE 7: Interaction Energy (MP2/6-31G**) between H20 and CHF3 in Approach B as a Function of the Rotation around the a Axis (0-H1 Distance 2.35 A) angle" E (kcaymol) angle" E (kcaYmol) 120 128 130 140 a
-2.62 -2.79' -2.83 -2.96
Angle defined as X-0-H1.
150 160 170 180
-3.05 -3.10 -3.13 -3.14
Starting point.
However, in approach B (Tables 6 and 7), the rotation around the a axis increases the interaction energy until the water molecule reaches a disposition similar to the one in approach A. This is reasonable if we take into account that this movement eliminates the gauche interaction between the lone pairs on oxygen and the fluorines.
6460 J. Phys. Chem., Vol. 99, No. 17, 1995
The energetic values of the minimum are 2.11 and 3.16 kcal/ mol, located at 2.39 and 2.28 8, of distance between HI and 0 for the H~O-CH~FZ and H2O-CHF3 systems, respectively. The last value is very similar to the experimental one found in the NH3-CHF3 complex (2.31 In these geometries, the distances between the oxygen and the hydrogen (Hl) are clearly below the sum of each van der Waals radii, and the values of the charge transfer and bond order are larger than in the previous system: 0.013 e and 0.021 for H~O-CHZF~ and 0.016 e and 0.024 for H2O-CHF3, indicating that these interactions can clearly be considered as hydrogen bonds. Finally, using published data for the H20-CH4 system, an optimal distance of 2.676 8, and interaction energy of 0.59 kcal/ mol,36 and the values described here, it is clear that in these systems the inclusion of each additional fluorine represents a shortening in the optimal interaction distance of about 0.1 8, and an increase in the interaction energy of 1 kcdmol. These results are in good agreement with a statistical analysis of the CH.. 0 hydrogen bond distances of chloroalkyl compounds in the solid state.37
Conclusion The C H * . 0 hydrogen bonds on the HzO-CH~F, H20CH2F2, and H20-CHF3 systems have been studied including the BSSE correction on the interaction energy at the MP2/631G** level. Our studies indicate that the preferred disposition is the one in which the direction of the hydrogen bond is bisector to the lone pairs on oxygens. The disposition in which the hydrogen is in the direction of one of the lone pairs of the oxygen is not a minimum in two of the systems. This shows the particularities of these hydrogen bonds when compared with stronger ones in the gas p h a ~ e . ~The ~ . inclusion ~~ of each additional fluorine atom affects the hydrogen bond by shortening its distance by 0.1 8, and by increasing its strength by 1 kcall mol. The calculated interaction energies for these systems indicate that these kinds of hydrogen bonds can contribute to define the 3D structure of organic molecules and specially to define stable crystal packing. Recent experimental results support the latter idea and have shown that these forces are able to maintain a dimer structure in solution similar to the one found in the solid state.I2 References and Notes (1) Scheiner, S. In Reviews in Computational Chemistry; Boyd, D. B., Lipkowitz, K. B., Ed.; VCH Publishers: New York, 1991; Vol. 2, pp 165218. (2) Desiraju, G. R. Acc. Chem. Res. 1991,24, 290-296. (3) Rodhamn, D. A.; Suzuki, S.; Suenram, R. D.; Lovas, F. J.; Dasgupta, S.; Goddard, W. A., III; Blake, G. A. Nature 1993,362,735-737. Atwood, J. L.; Hamada, F.; Robinson, K. D.; Om, W. G.; Vincent, R. L. Nature 1991, 349, 683-684. Al-Juaid, S. S.; Al-Nasr, A. K. A.; Eaborn, C.;
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