Directionality of Inter- and Intramolecular OHO Hydrogen Bonds: DFT

The latest IUPAC definition of the hydrogen bond includes directionality as its key feature. ... packing in the solid state, so investigation of direc...
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Directionality of Inter- and Intramolecular OHO Hydrogen Bonds: DFT Study Followed by AIM and NBO Analysis Irena Majerz* Faculty of Chemistry, University of Wroclaw, Joliot-Curie 14, 50-383 Wroclaw, Poland ABSTRACT: The directionality of inter- and intramolecular OHO hydrogen bonds has been compared. For intramolecular bridges it is determined by an orbital formed in the proton transfer process. For intermolecular bonds, the hydrogen-bonded proton is attached to two lone pairs of the acceptor and the OHO angle is not fixed but can change in a broad range. Depending on the OHO angle, the interaction changes continuously from electrostatic interaction to strong OHO hydrogen bond.

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INTRODUCTION The hydrogen bond is an interaction of intermediate strength between covalent bonds and van der Waals interactions. Being responsible for the geometry of a single molecule as well as the interaction in liquids and molecular packing in crystals, hydrogen bonding is important in biology, chemical reactions, and material sciences. For this reason it has been intensively investigated for many years. From the very beginning the main features of selectivity, cooperativity, stoichiometry, and directionality have been found as common for all hydrogen bonds. Directionality is expressed by a fixed hydrogen bond angle and is an essential feature that differentiates the weak hydrogen bond from van der Waals and electrostatic interaction. The latest IUPAC definition of the hydrogen bond includes directionality as its key feature.1,2 The hydrogen bond is always directional, whereas electrostatic interactions usually are not characterized by directionality,3,4 and some directional character of electrostatic interaction is not very common. Even for the strong dipole−dipole interaction many possible relative orientations can be considered. From the beginning of the hydrogen-bond investigation it was generally assumed that hydrogen bridges are linear. Precise determination of the proton position revealed that that particular hydrogen bond is characterized by a fixed angle not necessarily equal to 180°.5−7 Checking the directionality can be used as a method of differentiation of electrostatic and specific interaction.8−10 Directionality is also related to the hydrogen bond strength. The stronger intermolecular hydrogen bonds are more linear. The preferred value of the angle donor−proton−acceptor for the strongest OHO hydrogen bond is close to 180°. The weaker the hydrogen bond the broader the range of the hydrogen bond angle.11 Directionality of the hydrogen bond is connected with mutual orientation of the donor and acceptor. © 2012 American Chemical Society

The proton is accepted by the region of the molecule with high electron density, so the preferable direction for the proton is the lone pair of the acceptor.12,13 Analysis of the lone pair’s direction can suggest a structure of the hydrogen-bonded complex that can be very far from the real structure, so this simple explanation of the hydrogen bond directionality was not sufficient, and the symmetry and energy of orbitals should also be taken into account.14 When the relation of the hydrogen-bond angle and hydrogen-bond strength is very well-known for the intermolecular hydrogen bond, the intramolecular hydrogen-bond angle seems to be fixed by the molecular geometry that determines the location of the proton donor against the proton acceptor. An examination of the Cambridge Structural Database15 (CSD) showed that although for intermolecular OHO hydrogen bonds the linear geometry of the hydrogen bridge is preferred, every value of the hydrogen-bond angle can be found, and there is no relation between the hydrogen-bond strength expressed by the O···O distance and the OHO angle.16 For the neutron structures with intramolecular OHO hydrogen bond the relation between the OHO angle and O···O distance is seen.16 Additionally, for molecules representative of interand intramolecular hydrogen bonds, the dependencies of potential energy surfaces for the proton motion along the hydrogen bridge at different OHO values were investigated.16 For intermolecular hydrogen bond independent of the OHO angle the proton can be moved from donor to acceptor, keeping its valency constant17 and equal to 1. For an intramolecular hydrogen bond there is a preferred value of the OHO angle of about 158°,2 for which the proton can be Received: January 30, 2012 Revised: July 7, 2012 Published: July 9, 2012 7992

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moved along the hydrogen bridge and its valency at every point on the way from donor to acceptor is 1. This observation suggests the different importance of the hydrogen bond directionality for inter- and intramolecular hydrogen bonds, and for a particular O···O distance of intramolecular hydrogen bond, a special value of OHO angle is expected. To investigate this problem in detail for a typical complex with intermolecular OHO hydrogen bond, the dimer of acetic acid (ACETAC03),18 and a typical example of intramolecular OHO hydrogen bond, the molecule of benzyloacetone (BZOYAC01),19 the geometry and electron densities have been investigated at different OHO angles. Previously for these compounds the potential energy surfaces of different OHO angles were investigated.14

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CALCULATIONS The crystal structure data determined by neutron diffraction were taken from the CSD database.15 DFT calculations have been carried out with the B3LYP/6-311++G** method using the Gaussian 03 program package.20 It was demonstrated previously that the B3LYP level of theory is very reliable for predicting hydrogen-bonding interactions.21−23 The crystallographically determined coordinates were used as starting points for geometry optimization at the OHO values kept constant from 100° to 180° with 5° steps. The AIM analysis with the AIM2000 program24 was used to check the existence of hydrogen bonds in the investigated molecules. NBO analysis25 was performed using the ADF program.

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RESULTS AND DISCUSSION 1. Neutron Structures of Intramolecular OHO Hydrogen Bonds. The directionality of the hydrogen bond determines the conformation and packing in the solid state, so investigation of directionality of the OHO hydrogen bond must start by analyzing the OHO values in crystals. The relation of OHO angle and O···O bridge length published previously16 showed that in intermolecular bridges the O···O and OHO change independently. For intramolecular hydrogen bonds a correlation between these values exists. To investigate the correlation of O···O and OHO in intramolecular hydrogen bonds, the CSD is examined once again. The searching of intramolecular OHO hydrogen bridges has been done without any restriction concerning the O···O distance and OHO angle. The search has been limited to the neutron structures for which the proton position is determined precisely. Results of the CSD examination are shown in Figures 1−3. In Figure 1a is presented correlation of both OH distances. The points representing the experimental structures can be divided into two groups. The first group contains structures located appreciably near the BORC (bond order coordinate) curve. This theoretical curve proposed by Pauling17 reflects the relation between both OH’s when the proton moves from donor to acceptor keeping its valency constant and equal to 1. Other experimental points are located very far from the BORC curve. In these structures, illustrated by the example in Figure 1a, the distances of the proton to oxygen atoms are shorter than the van der Waals radii sum, but the interaction is not a OHO hydrogen bond and the oxygen atoms are not a proton donor and proton acceptor. In these structures the proton is linked by the covalent bond to the carbon atom that determines its valency. The CH forms a bifurcated interaction and both

Figure 1. Correlation for intramolecular OHO hydrogen bonds (a) between OH distances. Blue curve, bond order coordinate (BORC). The molecule (AHGLPY12) represents the interactions that are not a typical hydrogen bond. The error bars for OH changes from 0.0001 (AJOHEM, IRETII) to 0.002 Å (DHNAPH17). (b) Correlation between OHO and O···O. The points located appreciably near the BORC (full dots) are separated from points out of the BORC (empty circles). For the empty points the correlation of O···O distance with OHO angle can be described by a polynomial: O···O = −0.0005(OHO)2 + 0.1219(OHO) − 4.0872, R2 = 0.9565. The error bar for O···O changes from 0.0001 Å (AJOHEM, GADBAP) to 0.008 Å (MEMANP11) Å, for an OHO angle from 0.001° (AJOHEM) to 0.07° (DHNAPH17).

oxygen atoms play the role of the proton acceptor. In the structures out of the BORC curve, the interactions of proton with oxygen atoms do not fulfill the criterion of constant valency and therefore are not typical. This statement does not mean that any interaction between the proton and both oxygen atoms does not exist. For the first group of structures, a strong directional interaction dominates the strong hydrogen bond, which is close to covalent, and the interaction in the second group has the character of a rather weak interaction. The classification of the structures in Figure 1a is confirmed by the correlation of the O···O distance with the OHO angle (Figure 1b). Strong intramolecular OHO hydrogen bonds are gathered in the lower part of the correlation when weaker interactions are represented by longer O···O distances and form a correlation in the upper part of the diagram. To check if this classification is reflected in the statistics of the hydrogen bond geometry parameters, the histograms of 7993

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Figure 2. Histograms of O···O and OHO of neutron structures with an intramolecular OHO hydrogen bond. The upper diagrams contain all neutron intramolecular OHO structures from the CSD, in the lower diagrams only structures located at bond order coordinate curves are included.

the hydrogen bonds out of the BORC curve does not eliminate all the bonds with low OHO angle. It can be expected that nontypical OHO hydrogen bonds are characterized by the very low value of the OHO angle, but the lower part of the histogram contains numerous groups of compounds with an angle below 120°. It is known for intermolecular hydrogen bonds that their strengthening is connected with linearization.26−28 In the case of intramolecular hydrogen bonds, elimination of the weak hydrogen bonds that are far from the BORC curve is not connected with a preference for more linear hydrogen bridges. Spreading of the points in the correlations of experimental structures hides the effect caused by changes in the hydrogen bridge entirely. To reproduce the relation between OHO and O···O not influenced by the packing effects in the crystal theoretical methods have been used. For the dimer of acetic acid (ACETAC03),18 a typical complex with an intermolecular hydrogen bond, and benzyloacetone (BZOYAC01),19 a typical compound with an intramolecular hydrogen bond, the structures have been optimized with the OHO angle kept constant starting from 100° to 180° with steps of 5°. Both investigated compounds are shown in Scheme 1. In Figure 3 the points for experimental neutron structures with intramolecular OHO hydrogen bonds that fulfill the criterion of constant valency equal to 1 are compared with the results of optimization of the acetic acid dimer and benzyloacetone. To reproduce correctly the molecules in crystal, the periodic calculation model would be more correct than optimization of a single molecule. In the case of investigation of systematic trends, calculation for single

Figure 3. Comparison of experimental neutron structures with an intramolecular OHO hydrogen bond for which the OH bond distances are located appreciably near the bond order coordinate curve with theoretical correlations of O···O with OHO for benzyloacetone (◇) and the dimer of acetic acid (△).

O···O and OHO for intramolecular hydrogen bond are investigated (Figure 2). In the upper part of the histograms all neutron structures are included. The lower part of the histogram contains only the structures located appreciably near the BORC curve. Reproduction of the classification from Figure 1 causes elimination of the hydrogen bonds longer than 2.9 Å, but it appears that the classification is more complex than elimination of a group of compounds with long distances. Elimination of 7994

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The correlations of experimental structures shown in Figures 1−3 allow dividing the intramolecular hydrogen bonds into classes. The correlation in Figure 1 separates nontypical interactions from the typical hydrogen bond with constant proton valency equal to 1. In the group of compounds with typical hydrogen bonds confirmed by theoretical correlation, except intramolecular hydrogen bonds, also included are structures located at the correlation typical for intermolecular hydrogen bond. The last differentiation is connected with the location of the proton against the acceptor. Change of the OHO angle is connected with change of the O···O distance, which reflects the hydrogen bond strength. In addition, the location of the proton in the hydrogen bridge is sensitive to the OHO angle. At 175° and 180° in both investigated compounds, the proton is shifted to the acceptor. Changes of the hydrogen bond influence the lengths of other bonds in the molecule. These changes for the dimer of acetic acid are limited to the CO and CC bonds. In benzyloacetone, the whole chelate ring formed by the hydrogen bond is sensitive to the hydrogen bond strength. It was shown30 that the presence of the methyl group in the neighborhood of the hydrogen bond, as in benzoylacetone, can influence the proton transfer in the hydrogen bridge. For very short hydrogen bonds, the proton transfer degree is very sensitive to the environment, and the proton dynamics in short hydrogen bonds can be coupled to other internal degrees of freedom and to the crystal field. This observation was confirmed by comparison of the proton location in the short hydrogen bond in tetraacetylethane, benzoylacetone, and citrinin.30 This effect is not seen in the optimization of the single molecule of benzyloacetone at different values of the OHO angle performed in this work. Geometrical parameters of the dimer of acetic acid and benzyloacetone are collected in Tables 1 and 2, respectively. 2. Atom in Molecules Analysis of the OHO Hydrogen Bonds. The experimental and theoretical values of O···O and OHO in Figures 1−3 cover a very broad range. If there is no doubt that in the case of short, linear O···O the interaction is a typical hydrogen bond, for low OHO and long bridge lengths, a question about the character of the interaction arises. The smooth shape of the theoretical curves in Figure 3 does not categorize the investigated compounds into typical hydrogen

Scheme 1. Molecular Structure and Atom Numbering of the Dimer of Acetic Acid (ACETAC03) and Benzyloacetone (BZOYAC01)

molecules can better reproduce effects caused by change of geometric parameters that are not masked by crystal packing influences. It was shown that results of the single molecule calculations can be compared with the solid-state results,27 so theoretical calculation can be used as an additional tool in investigation of the systematic trends and individual effects. The experimental points reflecting the solid-state structures in Figure 3 are not located precisely at the theoretical correlation performed for the single molecule in a vacuum, but the experimental points confirm the trend expressed by the theoretical curve. It is characteristic that the correlation of OHO angle with bridge length for intra- and intermolecular hydrogen bonds is different. Although for both types of hydrogen bridges strengthening of the hydrogen bond is expressed by shortening of the O···O distance, this dependency is more significant for intramolecular hydrogen bonds. Experimental points referring to typical intramolecular hydrogen bonds confirm the theoretical correlation, but there is a group of compounds that are located close to the curve describing the correlation for intermolecular hydrogen bonds. In all of these, the proton acceptor is out of the plane passing through the donor and other atoms of the chelate ring formed by the hydrogen bond.

Table 1. Geometry of the Optimized Structures of the Dimer of Acetic Acid OHO, deg

O1H, Å

O2···H, Å

O1···O2, Å

C1O1, Å

C2O2, Å

C1O3, Å

C2O4, Å

C1C4, Å

C2C3, Å

100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180

0.9700 0.9707 0.9717 0.9726 0.9738 0.9750 0.9764 0.9777 0.9791 0.9805 0.9817 0.9829 0.9839 0.9847 0.9847 0.9841 0.9834

2.8145 2.6386 2.4936 2.3681 2.2653 2.1766 2.0963 2.0300 1.9718 1.9231 1.8835 1.8498 1.8231 1.8036 1.8013 1.8110 1.8248

3.1321 3.0381 2.9698 2.9156 2.8785 2.8501 2.8247 2.8078 2.7936 2.7837 2.7775 2.7719 2.7682 2.7666 2.7763 2.7927 2.8081

1.3485 1.3475 1.3466 1.3458 1.3452 1.3445 1.3438 1.3432 1.3425 1.3418 1.3414 1.3409 1.3404 1.3400 1.3398 1.3399 1.3402

1.2081 1.2085 1.2090 1.2095 1.2102 1.2109 1.2115 1.2122 1.2128 1.2135 1.2140 1.2145 1.2149 1.2p152 1.2152 1.2148 1.2145

1.2086 1.2090 1.2094 1.2098 1.2102 1.2106 1.2111 1.2115 1.2119 1.2123 1.2126 1.2129 1.2131 1.2133 1.2131 1.2126 1.2121

1.3576 1.3568 1.3560 1.3552 1.3541 1.3532 1.3522 1.3514 1.3504 1.3497 1.3489 1.3483 1.3478 1.3475 1.3477 1.3483 1.3488

1.5051 1.5056 1.5058 1.5060 1.5062 1.5063 1.5063 1.5064 1.5065 1.5066 1.5067 1.5067 1.5068 1.5069 1.5071 1.5074 1.5076

1.5021 1.5020 1.5018 1.5015 1.5013 1.5010 1.5006 1.5002 1.4999 1.4995 1.4992 1.4989 1.4986 1.4984 1.4980 1.4978 1.4977

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Table 2. Geometry of the Optimized Structures of Benzyloacetone OHO, deg

O1−H, Å

O2···H, Å

O1···O2, Å

O1C1, Å

O2C3, Å

C1C2, Å

C2C3, Å

100 105 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180

0.9702 0.9715 0.9732 0.9753 0.9778 0.9808 0.9843 0.9884 0.9935 0.9998 1.0067 1.0194 1.0294 1.0389 1.3868 1.3579 1.3399

2.4021 2.3116 2.2218 2.1374 2.0554 1.9772 1.8994 1.8191 1.7407 1.6679 1.6018 1.5233 1.4682 1.4219 1.0459 1.0530 1.0579

2.7424 2.7295 2.7134 2.6984 2.6815 2.6638 2.6420 2.6132 2.5820 2.5521 2.5243 2.4848 2.4608 2.4403 2.4236 2.4087 2.3977

1.3512 1.3478 1.3445 1.3412 1.3381 1.3351 1.3327 1.3313 1.3301 1.3287 1.3276 1.3237 1.3224 1.3216 1.2701 1.2740 1.2770

1.2248 1.2263 1.2278 1.2295 1.2311 1.2329 1.2351 1.2377 1.2409 1.2444 1.2479 1.2541 1.2585 1.2627 1.3191 1.3195 1.3202

1.3595 1.3605 1.3615 1.3625 1.3635 1.3647 1.3661 1.3681 1.3706 1.3736 1.3763 1.3824 1.3864 1.3903 1.4408 1.4418 1.4430

1.4622 1.4593 1.4560 1.4529 1.4500 1.4471 1.4449 1.4437 1.4428 1.4414 1.4406 1.4364 1.4353 1.4346 1.3878 1.3915 1.3944

bonds and electrostatic interaction. A separate group of compounds with the OHO below 120° in Figure 2 suggests two groups of compounds with different types of interaction. To answer the question at which value of OHO the interaction can be treated as a hydrogen bond, the atom in molecules (AIM) analysis can be used. This method, on the basis of the value of electron density at the bond critical point and the electron density paths, delivers criteria for the existence of the hydrogen bond. According to refs 28−33, a hydrogen bond exists if the electron density at the bond critical point is more than 0.002 au and the Laplacian of electron density is higher than 0.004 au. These criteria are fulfilled for all theoretical structures of the dimer of acetic acid and benzyloacetone. Another criterion for when an interaction can be called a hydrogen bond is important for benzyloacetone. It is that the bond critical point must be remote from a ring critical point in the chelate ring formed by the intramolecular hydrogen bond. At the distance shorter than 0.002 Å both critical points coalesce. For every theoretical structure of acetic acid dimer and benzyloacetone also this criterion is fulfilled. The next criterion is the presence of an electron density path linking proton with acceptor and a bond critical point located on it. Finally, the electron density paths linking proton and acceptor cannot be very bent. In Figure 4 theoretical structures of the dimer of acetic acid and benzyloacetone at different OHO with bond critical points and electron density paths are presented. For OHO equal to 100° (Figure 4a,e), the proton is located out of the O···O direction, so formation of the hydrogen bond is not possible. Although the distance of proton to the chelate ring plane is 0.736 Å and the geometry does not exclude the hydrogen-bond existence, the proton is located out of the electron density path between the bridge oxygen atoms. The path linking both oxygen atoms represents an electrostatic interaction but not a hydrogen bond. At OHO of 120° the bond path links the acceptor with the bond critical point on the OH bond and the proton is still out of the electron density path. Finally, the structures with OHO of 125° are typical for the hydrogen bond, so starting from this OHO value the interaction in both the dimer of acetic acid and benzyloacetone fulfills all criteria of a hydrogen bond. The electron density path passes from the proton to acceptor. Starting from this OHO value, the proton is

Figure 4. Molecular graphs of both investigated compounds at OHO equal to 100° (a, e), 120° (b, f), 125° (c, g), and 170° (d, h). Large circles correspond to attractors attributed to atomic positions: gray, H; black, C; red, O. Small circles are attributed to critical points: red, bond critical point; yellow, ring critical point.

very close to the O···O, and for benzyloacetone the distance of proton to the chelate ring plane is 0.270 Å. The AIM analysis of the structures with different OHO values performed for the acetic acid dimer and bezyloacetone is not sufficient to determine a general cutoff value for all OHO hydrogen bonds. The bond paths calculated for theoretical structures at different OHO are in agreement with the categorization of the OHO angles shown in the histograms in Figure 2. There is a separate group of compounds with low OHO values from 90° to 120° and the AIM analysis shows that the interaction in 7996

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these compounds is not a hydrogen bond. To form the hydrogen bond the OHO angle must be higher than 125°. For all compounds from lower histograms in Figure 2, the points characterizing the hydrogen bonds are located appreciably near the BORC curve (Figure 1a). Among them are also included the compounds with the OHO lower than 120°. The weak, nondirectional interaction which is not a hydrogen bond does not influence the OH bond significantly, and the proton valency is equal 1 as in the OH bond. The electron densities at bond critical points representing the bonds other than these in the hydrogen bridge are sensitive to the proton transfer similarly to other previously investigated compounds with interand intramolecular hydrogen bonds.34−38 3. Natural Bond Orbital Analysis of the OHO Hydrogen Bonds. To investigate the changes of electron density under the hydrogen bond formation and proton transfer which changes with the OHO angle for both investigated compounds, natural bond orbital (NBO) analysis has been performed. The idea of natural bond orbitals was proposed by Loewdin.39 This method reproduces the molecular orbital according to the Lewis concept40 of localized, doubly occupied orbitals in one- or two- centered regions, which represent chemical bonds and lone pairs. The orbitals should represent the highest percentage of electron density, and for typical organic molecules it is above 99%, which confirms the Lewis structure. If the charge distribution is far from the typical Lewis structure, localized molecular orbitals (NLMO) should be used.41 The percentage of NBO orbital in the NLMO is a measure of delocalization and deviation of the orbitals from the Lewis structure. Another feature of NLMO is the contribution of the atom orbitals not directly engaged in the bond or the lone pairs and sometimes remote from the molecular orbitals. It can be expected that the most significant changes caused by moving of the hydrogen-bonded proton are connected with changes of the OH bond. The NBO OH bond orbital in both investigated compounds is typical, composed of oxygen and hydrogen valence hybrids, and the σOH bond for OHO equal to 100° and 180° in the dimer of acetic acid are expressed as σOH = 0.8717(sp3.36)O + 0.4901(s)H and σOH = 0.8815(sp2.80)O + 0.4716(s)H, respectively. The continuous change of the bond is connected with an increase of its ionic character and polarization of the bond when the proton moves to the acceptor. The analogous OH bond in benzyloacetone is very similar and at 100° can be described as σOH = 0.8748(sp3.49)O + 0.4846(s)H. The occupancy of the OH NBO is slightly higher for the dimer of acetic acid (1.9866 at 100°) then in case of benzyloacetone (1.9772 at 100°). The changes in the OH bonding NBO orbital under proton transfer are better illustrated by the percentage of hydrogen and oxygen hybrids shown in Figure 5. Polarization of the OH bond in benzyloacetone is higher and more sensitive to the proton transfer than in the dimer of acetic acid. Other orbitals that should change under proton moving from donor to acceptor are the lone pairs of the bridge oxygen atoms. In Figure 6 are shown the NLMO orbitals representing the lone pairs of the dimer of acetic acid. Analogous orbitals of benzyloacetone are depicted in Figure 7. It is very characteristic that the NBO orbitals representing the lone pairs are strongly delocalized. If participation of the parent NBO in the NLMO for typical organic component is about 99%, in the dimer of acetic acid orbitals it is about 98% for orbitals a and c, about 90% for orbital b, and 92% for orbital d (Figure 6). Delocalization of the lone pairs of the dimer of acetic acid

Figure 5. Participation of proton (a) and oxygen (b) hybrids in the NBO orbital representing the OH bond: benzyloacetone (●) and the dimer of acetic acid (○).

Figure 6. NLMO representing lone pairs of proton donor and proton acceptor in the dimer of acetic acid at the OHO angle equal to 135°.

does not change with the proton moving from donor to acceptor. When delocalization of the lone pairs of proton donor and acceptor for the dimer of acetic acid is higher than in typical organic molecules, delocalization in benzyloacetone is even more significant. The NLMO shown in Figure 7a, contains 98.9% of the parent NBO orbital. This value for orbitals b, d, and e is about 94%, 98.6%, and 92.2% respectively. Occupancy of the lone pair orbitals, which for the dimer of acetic acid is about two electrons, for the orbitals of benzyloacetone is equal 1.98, 1.87, 1.97, and 1.85 for orbitals a, b, d, and e, respectively. It is very characteristic that in benzyloacetone at the OHO angle of about 155° the orbitals of OH bond disappear and a new orbital on the donor oxygen atom arises (Figure 7c). 7997

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Figure 7. NLMO lone pair orbitals on proton donor and proton acceptor in benzyloacetone at the OHO angle equal to 155°.

Delocalization of this orbital is very significant, about 78%, and occupancy is very low, about 1.6 electrons. For benzyloacetone delocalization of all lone pairs on the proton, the donor and acceptor are sensitive to the proton transfer. Participation of the parent NBO in NLMO for the lone pairs of donor and acceptor is shown in Figure 8a. Delocalization of the donor lone pair is constant until the hydrogen bond is formed and above the OHO of 120° increases. Delocalization of the acceptor lone pair increases in full range of the OHO values. The new orbital formed on the donor oxygen atom at 150° is extremely delocalized and its delocalization decreases with the proton transfer. In an intramolecular hydrogen bond the hydrogen bridge is a part of the chelate ring formed by the hydrogen bond and other atoms connected to the aromatic ring, so with delocalization of the electrons in the lone pairs delocalization of other NLMO orbitals participating in the chelate ring also increases. In Figure 9, delocalization of the CC double bonds is shown. A similar picture can be prepared for CO bonds. Delocalization of the orbitals in the chelate ring confirms the idea of a resonance-assisted hydrogen bond.42−45 Formation of the chelate ring containing the mobile proton in the hydrogen bridge and aromatic or double bonds is connected with possible polarization of the electrons when the proton moves from the donor to the acceptor. Transfer of the proton from donor to acceptor is connected with changes not only of the lone pairs of the proton donor but also in participation of the hydrogen s orbital in the delocalization of the lone pairs of acceptor. Figure 10 presents the correlations of participation of the proton orbital in both acceptor lone pairs for inter- and intramolecular hydrogen bonds. For the dimer of acetic acid, the participation of the orbital of hydrogen engaged in the hydrogen bond is limited to 1% and is comparable in both orbitals of the oxygen acceptor. For the intramolecular hydrogen bond in benzyloacetone, the contribution of the proton is higher only for one of the orbitals. The highest participation of the proton appears in the lone pair of the acceptor, which is included in the chelate ring. For an intramolecular OHO hydrogen bond, the proton

Figure 8. Participation of the NBO orbitals in NLMO orbitals of proton donor and proton acceptor of benzyloacetone.

Figure 9. Participation of NBO orbitals in NLMO orbitals of CC bonds of the chelate ring of benzyloacetone.

transfer is connected with formation of the new orbital on the proton donor which arise for an OHO angle of about 155°. This value for benzyloacetone is in agreement with the experimental neutron structure value (153° 19) and with the estimated OHO, for which the proton in hydrogen bridge can move with constant valency (158° 16). The obtained value of the OHO angle is characteristic just for the benzyloacetone molecule. Correlation between OHO and O···O16 suggests that for other molecules with an intramolecular OHO hydrogen bond the OHO typical for formation of a new orbital can be different, but this conclusion must be supported by more detailed calculations performed for different molecules with 7998

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action has hydrogen bond character if the OHO angle is higher than 125°. (3) The intramolecular OHO hydrogen bond is realized at the OHO angle at which an additional orbital on donor atom can be formed. With the feature of an intramolecular hydrogen bond is connected the presence of a preferred OHO value and the correlation of OHO with O···O. For benzyloacetone the OHO value equals 155° but correlation of O···O and OHO suggests that this value is not common for all intramolecular hydrogen bonds. (4) Directionality of the OHO intramolecular hydrogen bond is determined by the direction of the acceptor electron pair. For an intermolecular hydrogen bond the direction of the hydrogen bond is not precisely determined, because the proton is accepted equally by both lone pairs of the acceptor. For an intramolecular OHO hydrogen bond the proton is accepted by one of the acceptor lone pairs, which determines the direction of hydrogen bond.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 48-71-315-28-16. Fax: 04871-328-23-48. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS I thank the Wroclaw Centre for Networking and Supercomputing for generously granting the required computer time.

Figure 10. Participation of the hydrogen orbital in NLMO lone pairs of the proton acceptor for (a) the dimer of acetic acid and (b) benzyloacetone.

intramolecular OHO hydrogen bonds. Participation of the proton in this orbital is about 20% and slightly decreases when proton moves to the acceptor. Comparison of the acceptor orbitals in inter- and intramolecular OHO hydrogen bonds shows the main difference between both of them. In an intramolecular OHO hydrogen bond, the proton is transferred to one of the acceptor orbitals, which determines the direction of the hydrogen bond. In an intermolecular OHO hydrogen bond, the proton transfer is not determined by the acceptor lone pair direction, because it is transferred in comparable amount to both lone pairs of the acceptor. This conclusion confirms the previous observation of directionality of the hydrogen bond in water dimer and in water−hydroxide ion.46

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REFERENCES

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CONCLUSIONS

(1) For intramolecular OHO hydrogen bonds the theoretical, sigmoidal dependency of the O···O distance and OHO angle has been confirmed by experimental neutron structures. From this correlation must be excluded the experimental points that do not fulfill the proton constant valency rule and those with a nonplanar chelate ring. (2) Taking into account the geometry of the complex, it is not possible to recognize if the complex is formed by a hydrogen bond or by an electrostatic interaction. The AIM method delivers criteria for existence of the hydrogen bond. For investigated complexes the inter7999

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The Journal of Physical Chemistry A

Article

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