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Acetylene as potential hydrogen-bond proton acceptor
Journal of Molecular Structure 615 (2002) 209–218 www.elsevier.com/locate/molstruc
Acetylene as potential hydrogen-bond proton acceptor Steve Scheinera,*, Sławomir J. Grabowskib a
Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322-0300, USA Institute of Chemistry, University of Białystok, 15-443 Białystok, Al. J. Pilsudskiego 11/4, Poland
b
Received 3 September 2001; revised 21 November 2001; accepted 21 November 2001
Abstract Ab initio calculations are used to assess the ability of the CxC triple bond in acetylene to act as proton acceptor to donor molecules HF, HCl, HCN and HCCH. The strength of the interaction energy varies from 3 kcal/mol for the strongest of these complexes FH· · ·HCCH, to 1 kcal/mol for the weakest (HCCH)2. The X– H bond of all donors undergoes the elongation characteristic of H-bonds, along with the red shift of its stretching frequency. In addition, electron density is transferred from the proton-acceptor molecule to the donor, and the bridging H becomes more positive. However, the magnitudes of these density shifts are larger than might be expected from a conventional H-bond. Opposite to a H-bond, the proton-accepting C atom loses density. Decomposition of the total interaction energy indicates the dominant role played by Coulombic attraction, as in a H-bond, but the exchange repulsion, charge transfer, and polarization terms are disproportionately larger than is typically seen in true H-bonds. q 2002 Elsevier Science B.V. All rights reserved. Keywords: CH/p; Red shift; Weak hydrogen bond; Energy decomposition; Distortion energy
1. Introduction During the early years of ab initio study of molecular interactions, work focused largely on strong interactions, due in large measure to the inability of early methods to treat weak interactions quantitatively. Continuing progress has expanded the range of interactions which can be investigated with reliability, enabling real advances to be made in our understanding of weak interactions [1]. The same situation exists with regard to the more specific case of hydrogen bonds. Conventional H-bonds of the sort where a proton donor OH or NH group approaches an acceptor atom like O or N, have been well studied * Corresponding author. Tel.: þ1-435-797-7419; fax: þ 1-435797-3390. E-mail address: [email protected] (S. Scheiner).
over the years, and their fundamental nature is understood. Recent advances have made it possible to investigate weaker interactions, which have some of the hallmarks of a conventional H-bond [2]. As an example, the last few years have seen a proliferation of ab initio studies of CH· · ·O interactions [3 –10], addressing the fundamental question as to whether it fits the criteria of a true H-bond. Rather than the traditional lone pairs of a protonacceptor atom like O or N, one is led to wonder whether the electron-rich environment of a CC multiple bond can function as a proton acceptor in a H-bond, viz. a so-called XH· · ·p bond. In particular, the triple CxC bond of a molecule like acetylene ought to serve as a particularly rich source of electrons, which has motivated a number of recent calculations concerning its ability to serve as proton acceptor. As an example, HF was taken as a proton
0022-2860/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 8 6 0 ( 0 2 ) 0 0 2 1 9 - 3
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donor and paired with systems containing CC multiple bonds, i.e. acetylene, ethylene, and benzene, as well as three and four-membered rings in 1997 [11]. The equilibrium geometries had the appearance of H-bonds, albeit weak ones. Atoms-in-molecules (AIM) analysis of the electron densities was also consistent with such a characterization, as was the observation of a small amount of electronic charge transferred between the two molecules. In the particular case of FH· · ·acetylene, the interaction energy was computed to be 3.1 kcal/mol at the MP2/6-311þ þ Gp p level. These results were largely confirmed the following year [12] which also added harmonic vibrational frequencies; zero-point vibrational corrections reduce the binding energy of the FH· · ·acetylene complex to 1.4 kcal/mol. The interaction was weakened by considering the CH of acetylene as the proton donor to another acetylene molecule by Novoa and Mota [6] whose AIM analysis suggested a H-bond here as well, even though the interaction energy is reduced to 1.2– 1.6 kcal/mol, depending upon basis set. Their data ˚ ) stretch of the CH further indicated a small (2 –3 mA bond of the donor acetylene upon formation of the dimer. Philp and Robinson [13] extended work on the acetylene dimer to consideration of the sensitivity of the interaction to an ‘offset’ of the proton donor, i.e. a ‘sliding’ parallel to the CC triple bond, as well as tilting the donor away from the perpendicular. Their results indicated that the interaction energy is reduced ˚, to half of its optimum value by a slide of about 1 A and is even less sensitive to a tilt. They found confirmation of these trends in a survey of crystals containing similar interactions. These authors concluded that the interaction in the acetylene dimer lies only on the borderlines of a true H-bond, and believed that the dispersion component of the interaction was likely to be comparable to the electrostatic term. Philp and Robinson also considered water as a proton donor to acetylene and computed a binding energy between 1.6 and 2.0 kcal/mol. The HCl molecule was more recently considered as a proton donor [14] to acetylene where the focus lied in comparison of the interaction energy with experiment. Their most accurate extrapolated value of De, including anharmonicity in the vibrational frequencies, was 1.5 kcal/mol, not far from an experimental value of 1.7. A more recent set of calculations [15]
includes not only HF and HCl, but also HBr as proton donors, yielding QCISD electronic binding energies of 3.7, 2.1, and 1.8 kcal/mol, respectively, as well as a full elucidation of vibrational frequencies in each complex. The present work refocuses on the properties of the acetylene molecule as a proton acceptor. Rather than consider just one donor molecule, or one type, a range of different sorts of molecules are taken as donors. HF and HCl represent strong proton donors, hydrogen halides. HCN is also a strong acid but differs in having a C atom as proton donor atom, which is thought to perhaps offer a different situation. The same theme of CH as proton donor group is taken up by HCCH, except that this molecule is a considerably weaker acid than the others. A variety of different aspects of the interaction are considered here. The binding energies are computed, as are the equilibrium geometries. Of some interest are the effects of the interaction upon the X –H bond of the proton donor molecule, its length and spectroscopic properties. This work also compares the sensitivity of the interaction energy of each complex to stretches and other distortions from equilibrium. We also evaluate which of these interactions can be considered as true H-bonds, using a number of electronic and energetic parameters as a litmus test.
2. Methods Ab initio calculations were carried out using the GAUSSIAN -98 set of codes [16] with its various built-in
basis sets. Standard notation was used for basis sets wherein þ signs indicate the presence of diffuse functions on non-hydrogen atoms (one þ ) or all atoms (double þ ); analogous meaning is attached to p signs and polarization functions. Aug-cc-pVDZ refers to a correlation-consistent polarized-valence double-zeta type of set. Electron correlation was included via the second-order Møller – Plessset (MP2) treatment [17,18], as well as by use of the B3LYP variant of density functional theory (DFT) [19,20]. Full geometry optimizations were carried out for each complex, and each resulted in a C2v T-shape, with the proton donor molecule lying perpendicular to the triple bond of acetylene, pointing toward the bond’s center.
S. Scheiner, Sł.J. Grabowski / Journal of Molecular Structure 615 (2002) 209–218 Table 1 Interaction energies (kcal/mol) calculated for complexes of various proton donors with HCCH. Counterpoise corrections of basis set superposition error are added
SCF
B3LYP MP2
Basis set
HF
HCl
HCN
HCCH
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þþ Gpp aug-cc-pVDZ 6-311þþ Gpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þþ Gpp aug-cc-pVDZ
3.09 2.93 2.87 2.70 2.71 2.86 3.98 3.22 3.44 3.30 3.31 3.14 3.72
1.69 1.39 1.41 1.44 1.38 1.48 2.08 2.16 1.83 1.78 1.89 1.91 2.72
1.87 1.58 1.59 1.58 1.52 1.63 1.73 2.07 1.79 1.73 1.80 1.81 2.21
0.83 0.71 0.71 0.69 0.72 0.72 0.79 1.08 0.95 0.92 1.05 1.10 1.38
3. Geometries and energetics The interaction energies computed for the complexes of the various donors with acetylene are reported in Table 1. The data in the top half of the table were evaluated at the SCF level. The values for the 6-31Gp basis set are somewhat inflated, when compared to the other data which are fairly consistent with one another. The correlated values in the lower half of the table are larger than their SCF correlates, due primarily to the influence of dispersion which is not present at the SCF level. Table 2 ˚ ) reported as distance Optimized intermolecular separations (A separating bridging H from center of CxC bond
SCF
B3LYP MP2
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þ Gpp aug-cc-pVDZ 6-311þ þ Gpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þ Gpp aug-cc-pVDZ
HF
HCl
HCN
HCCH
2.340 2.370 2.396 2.412 2.407 2.376 2.153 2.191 2.169 2.174 2.192 2.186 2.138
2.626 2.719 2.688 2.726 2.733 2.725 2.410 2.417 2.434 2.408 2.436 2.439 2.330
2.746 2.829 2.816 2.849 2.848 2.807 2.653 2.535 2.553 2.542 2.602 2.598 2.515
2.967 3.071 3.055 3.077 3.073 3.015 2.855 2.653 2.658 2.644 2.723 2.697 2.603
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There would appear to be a bit more sensitivity to basis set for the MP2 than for the SCF data. The B3LYP values, all computed with the 6311þ þ Gp p basis set, show greater variation from one donor to the next than does MP2. That is, the B3LYP/6-311þ þ G p p value for FH· · ·HCCH is 0.8 larger than the MP2 quantity, whereas the order is reversed for the acetylene dimer in the final column of the table. Perusal of Table 1 allows one to conclude that HF forms the most strongly bound complex with acetylene, with an interaction energy in excess of 3 kcal/mol. HF is followed by HCl and HCN, which are similar to one another, forming an interaction with acetylene of nearly 2 kcal/mol. HCCH is the weakest of the proton donors, bound to another acetylene molecule by around 1 kcal/mol. The effects of correlation upon the complexation energy can be elucidated as the difference between the SCF and MP2 values in Table 1. Excluding the augcc-pVDZ data for the moment, these correlation contributions are largest for the HF and HCl donors, lying in the range of 0.4 – 0.6 kcal/mol. Correlation is less significant for the two CH donors in the last two columns, amounting to 0.1 – 0.4 kcal/mol. This quantity is in fact larger for HCCH than for HCN in most cases, despite the weaker binding of the latter. As a result, correlation accounts for a greater fraction of the total binding energy in the acetylene dimer, as much as 35% for the 6311þ þ Gp p basis set. Not surprisingly, due to the nature of its formulation, the contribution of electron correlation to the total interaction is magnified in the case of the aug-cc-pVDZ basis set. The correlation contribution to the binding energy of acetylene dimer is 0.66 kcal/mol, accounting for nearly half of the total. The equilibrium separations are reported in Table 2 as the distance from the bridging proton to the midpoint of the CxC bond. These distances pretty well mirror the interaction energies in Table 1 in the sense that stronger binding tends to translate into a shorter intermolecular separation. Shortest in this collection is FH· · ·HCCH where the pertinent distance ˚ . The best correlated estimates for the HCl, is 2.2 A HCN, and HCCH donors are, respectively, 2.4, 2.6, ˚ , but with some residual uncertainty due to and 2.7 A lingering basis set sensitivity.
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Table 3 ˚ ) caused by Elongation of proton donating bond length (in mA complexation with HCCH
Table 5 Ratio of intensity in the complex/isolated subunit (for proton donating bond)
HF
HCl
HCN
HCCH
HF
HCl
HCN
HCCH
3.6 4.0 4.3 4.0 4.1 4.6 9.9 4.2 6.4 6.7 6.6 6.7 8.4
3.2 2.5 3.0 2.9 2.9 2.9 8.8 4.7 4.4 5.2 5.3 5.3 7.7
2.5 2.2 2.3 1.8 2.3 2.3 3.9 3.3 3.0 2.5 2.9 2.4 3.9
1.4 1.1 1.1 1.2 1.2 1.2 2.0 2.0 1.5 1.5 1.3 1.3 2.1
3.2 3.0 2.9 2.7 2.7 3.2 5.6 4.7 4.6 4.7 4.1 4.2 5.4
7.4 5.0 4.6 3.6 3.6 4.0 12.1 15.1 11.3 9.7 7.2 7.1 9.3
2.5 2.2 2.2 2.1 2.1 2.3 3.3 3.4 3.2 3.2 2.8 2.9 3.6
1.6 1.5 1.5 1.4 1.5 1.6 1.8 2.1 2.0 2.0 1.8 1.9 2.3
SCF
B3LYP MP2
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þ Gpp aug-cc-pVDZ 6-311þ þ Gpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þ Gpp aug-cc-pVDZ
4. Deformations of proton donor molecule The most notable geometric effect of the formation of an interaction of this type is the change in the length of the X – H bond of the proton donor molecule. In particular, significant elongations are observed in Hbonded systems. It is just such a stretch that is observed in the four systems of interest here, as witness the values reported in Table 3. The elongation ˚ , followed closely by is greatest for HF at about 7 mA HCl. The stretches are significantly smaller for the ˚ for HCN and 1 or 2 mA ˚ two CH donors, nearly 3 mA for HCCH. Table 4 Red shift in HX stretching frequency (in cm21) of proton donor caused by complexation with HCCH
SCF
B3LYP MP2
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þGpp aug-cc-pVDZ 6-311þ þGpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þGpp aug-cc-pVDZ
HF
HCl
HCN
HCCH
76 91 104 99 101 122 227 77 130 159 156 159 206
48 37 42 37 39 42 110 68 63 73 72 73 111
34 30 31 26 30 33 58 46 44 40 43 38 59
11 8 8 8 9 9 17 15 13 13 9 9 15
SCF
B3LYP MP2
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þþ Gpp aug-cc-pVDZ 6-311þþ Gpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þþ Gpp aug-cc-pVDZ
Along with the X – H stretch, it is characteristic of H-bonds that the stretching frequency of this bond be shifted to the red by the formation of the complex. The amount of this shift is listed in Table 4 for the various complexes. The pattern is very much like that observed in Table 3 in that longer stretches are associated with larger red shifts. This shift varies from as large as 206 cm21 for FH· · ·HCCH with the augcc-pVDZ basis set to only 9 cm21 for the acetylene dimer with some of the other large sets. The red shift is typically accompanied by an intensification of the band. This phenomenon is displayed in Table 5 as the ratio of the computed intensity in the complex to that in the isolated molecule. These data generally fall into the same pattern as those above in that stronger complexes are associated with a larger intensification. However, there is one interesting anomaly in that the ClH· · ·HCCH complex exhibits a surprisingly large effect, nearly double that of the very similar FH· · ·HCCH.
5. Intermolecular deformations The effects of stretching or contracting the H-bond are displayed in Fig. 1 where the interaction energy is plotted as a function of the distance separating the bridging hydrogen from the CxC midpoint. These curves show the expected trend of progressive deepening, accompanied by shorter equilibrium
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˚ ). Energies were calculated at the MP2/6-311þþ Gpp level, uncorrected Fig. 1. Interaction energies as a function of intermolecular separation (A for BSSE. Circles correspond to HF donor, open squares to HCN, and triangles to HCCH.
separation in the series HCCH , HCN , HF. All progress smoothly toward a long-distance asymptote. Another mode of distortion of these C2v equilibrium complexes might involve a bend of various sorts. One such bend, a ‘wag’ of sorts, is engendered by holding fixed the atom of the proton donor molecule that is furthest from the acceptor acetylene. Then the remainder of the donor molecule is rotated around that pivot atom, in the plane of the HCCH molecule, by an angle a. The sensitivity of the binding energy to this wagging motion is illustrated in Fig. 2 for the same three donor molecules. It appears that this motion is of large amplitude. Taking the FH· · ·HCCH molecule as an example, a wag of more than 308 is required to cut the binding energy in half. Another sort of wag is defined in a similar manner, except that the rotation of the donor molecule is perpendicular to the plane of the two molecules. The sensitivity of the binding energy to this out-of-plane wag, b, is reported in Fig. 3. The curves in Fig. 3 would appear somewhat flatter than those in Fig. 2, suggesting that the energy is less sensitive to out-of-plane than in-plane wags. Another type of distortion considered has to do
with the optimal geometry wherein the donor molecule lies directly along the perpendicular of the HCCH acceptor molecule that passes through its center. The donor molecule was allowed to ‘slide’ a distance d, parallel to the HCCH molecule, remaining perpendicular to the latter, but its distance from HCCH was optimized at each point. The effects of this sliding are depicted in Fig. 4 where the center of each curve corresponds to the equilibrium configuration. It is important to note that the binding energy is reduced by such a slide, buttressing the idea that the donor prefers to lie above the CxC midpoint, and not above either of the C atoms.
6. Nature of interaction In addition to geometry, energetics, and spectroscopic features, other hallmarks of a hydrogen bond involve distributions of electron density. For example, it is widely accepted that a certain amount of charge is shifted from the proton acceptor molecule to the donor upon H-bond formation. There are a number of ways
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Fig. 2. Interaction energies (in kcal/mol) as a function of a angle. Circles correspond to HF donor, open squares to HCN, and triangles to HCCH. Energies were calculated at the MP2/6-311þ þGpp level and are uncorrected for BSSE.
to measure this charge shift, two of which are reported in Table 6. The first, and in some ways more direct, is to sum up the atomic charges on each of the two molecules within the complex. As listed in the second column of Table 6, 33 me are transferred from HCCH to the HF molecule in FH· · ·HCCH. Slightly larger charge transfers are observed for HCl and HCCH, but the largest of all is associated with HCN which, in turn, forms the strongest complex with HCCH. These quantities are rather large when compared with
‘standard’ H-bonds. For example, a similar calculation of the water dimer reveals a charge transfer of 13 me [10]. Another indicator of the large amount of charge transfer in these complexes arises from the dipole moment of each complex. When this quantity is compared to the vector sum of the two isolated molecules (zero for HCCH), its enhancement in the complex is in part due to transfer of electron density from proton acceptor to donor. These enhancements
Fig. 3. Interaction energies (kcal/mol) as a function of beta angle. Circles correspond to HF donor, open squares to HCN, and triangles to HCCH. Energies were calculated at the MP2/6-311þ þGpp level and are uncorrected for BSSE.
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Fig. 4. Effect on interaction energy of sliding proton donor molecule parallel to HCCH. d is defined as the displacement distance between the proton donating molecule and a line perpendicular to acceptor HCCH, passing through the center of the CxC bond. Energies were calculated at the MP2/6-311þ þGpp level and are uncorrected for BSSE. Circles correspond to HF as donor, open squares to HCN, and triangles to HCCH dimer.
are listed in the last column of Table 6 and may be seen to vary between 0.274 D (for the acetylene dimer) and 0.582 D for FH· · ·HCCH. These two limits may be compared to the dipole enhancement of 0.41 D in the water dimer [10]. It is important to stress that in addition to density shifted from one molecule to the other, there are internal displacements of charge within each molecule which contribute to the dipole enhancement. For example, the FH· · ·HCCH complex shows the largest Dm, but a relatively small value of CT, which would Table 6 Dipole moment of complex relative to monomers and charge transferred from proton acceptor to donor molecule (MP2/6311þ þGpp level) Donor HF HCl HCN HCCH a
CTa (me) 33 36 52 38
suggest a good deal of its moment change comes from such internal charge rearrangements. Conversely, the small value of Dm for the HCCH dimer in the last row of Table 6 is likely composed largely of intermolecular charge transfer, as CT for this system is comparable to those of the other systems with a larger Dm. Hydrogen bonds are characteristically accompanied by a loss of electron density upon the bridging proton, while the donating and accepting atoms become more negatively charged. The complexes studied here also exhibit this increasingly Table 7 Change in natural population atomic charge (me) of atoms in complex relative to monomers (MP2/6-311þþ Gpp level)
Dm (D) 0.582 0.465 0.435 0.274
The sum of atomic charges of proton acceptor molecule (acetylene) within the complex.
Donor
DqH
DqXa
DqC
FH ClH NCH HCCH
42 59 26 44
29 223 3 2275
64 60 57 50
a
X refers to proton-donating atom F, Cl, or C.
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Table 8 Decomposition of interaction energies (kcal/mol) of various proton donors with acetylene using 6-311þ þGpp basis set. Geometries optimized at MP2 level
ES EX POL CT CORRa a
HF
HCN
HCCH
26.4 þ6.3 21.5 22.2 20.4
23.4 þ2.8 20.6 20.8 20.3
22.2 þ2.1 20.3 20.5 20.4
Corrected for BSSE.
positive charge on the bridging H, as evident by the positive entries in the second column of Table 7. In fact, these values are considerably larger than the 19 me change in the bridging hydrogen atomic charge in the water dimer. The changes in the charge of the proton-donating atom show quite a wide discrepancy, varying from the negligible change in the C of HCN to the very large negative change in the C atom of HCCH (275 me). Perhaps most interesting in Table 7 is the behavior of the C atom in the proton-accepting HCCH. Rather than become more negative, as characteristic of H-bonds, these atoms become more positive by some 50 (HCCH) to 64 (FH) me. When coupled with the comparably small shifts of density between molecules, this observation indicates a shift of electron density to the H atoms in the proton donor HCCH, i.e. away from the approaching donor molecule. It is hence fair to say that there are certain fundamental differences between these complexes and conventional H-bonds. Another window into the fundamental nature of the interaction arises from a decomposition of the total interaction energy into several ‘pieces’. Such a decomposition was used earlier to buttress the claim that methane and its fluorinated derivatives do in fact form genuine H-bonds with proton acceptors [10]. A similar energy decomposition, of the Morokuma variety [21], was carried out here for the complexes of interest. In summary, the electrostatic (ES) term represents the Coulombic interaction between the charge distributions of the two subunits, and the exchange energy (EX) corresponds approximately to steric repulsion between the two charge clouds. When the two molecules are permitted to distort the charge
clouds of their partners, one can extract polarization (POL) energy from the internal redistributions and charge transfer (CT) from density shifts from one molecule to the other. As a final component, the effects of electron correlation are contained in the CORR element. The results of an energy decomposition of the complexes of interest are reported in Table 8 where it may be seen that the electrostatic term makes the dominant attractive contribution, nearly counterbalanced by exchange repulsion. Charge transfer also makes a significant contribution to the attraction, followed closely by a slightly smaller polarization term. The final row indicates that the correlation contribution, while attractive in all cases, is fairly small, less than 0.5 kcal/mol. With the exception of the latter term, there is a clear pattern of diminishing magnitude as the proton donor is changed from HF to HCN to HCCH, consistent with the same trend in the total interaction energies. A comparison of the data in Table 8 with a classical H-bond such as the water dimer provides some illumination regarding the characterization of HCCH as a proton acceptor. The ES, EX, POL, CT, and CORR contributions to the binding energy of the water dimer are, respectively, 2 7.6, þ 4.2, 2 0.7, 2 0.9, and 2 0.3 kcal/mol. In many respects, these numbers are comparable to the data in Table 8, only larger in magnitude, as one would expect for the stronger interaction in the water dimer. One distinction arises in that whereas the exchange repulsion in the HCCH complexes is very nearly equal in magnitude to ES, the former is substantially smaller than the latter for (H2O)2. In a sense, the EX term is larger in the HCCH complexes than one might expect based on the water dimer as a model. The same might be said for POL and CT which are disproportionately large, compared to a conventional H-bond. On the other hand, the CORR contribution seems to be uniform across the board, with all complexes exhibiting a contribution of 0.3 – 0.4 kcal/mol. Summarizing the energy decomposition analysis, the complexes involving HCCH as proton acceptor would appear to be dominated by Coulombic attraction, as are conventional H-bonds, but they are also characterized by larger EX, POL, and CT contributions than are H-bonds of comparative strength.
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7. Conclusions HF forms the strongest complex with acetylene, followed by HCl and HCN, and then by HCCH. The interaction energies of these complexes are roughly 3, 2, 2, and 1 kcal/mol, respectively. The equilibrium separation between the bridging proton and the center ˚ for of the acetylene CxC bond increases from 2.2 A ˚ for the HCCH dimer. As a FH· · ·HCCH, up to 2.7 A consequence of the interaction, the covalent bond involving the bridging hydrogen is elongated in all cases. The stretches in the hydrogen halides are the ˚ ; shorter elongations of 1– largest, as much as 7 mA ˚ are observed in the two CH donors. Accom3 mA panying the latter bond stretch is a shift to the red of the associated stretching frequency. These shifts vary a great deal and are sensitive to the strength of the interaction, from a maximum of 200 cm21 for the strongest donor HF down to only about 10 cm21 for HCCH. The distance dependence of these interactions consists of a smooth progression to a long-distance asymptote, as in conventional H-bonds. The interaction energy is fairly insensitive to wagging the proton donor molecule either in the plane of the acceptor, or perpendicular to it. The donor prefers association with the center of the HCCH acceptor molecule; sliding the donor along the acceptor reduces the interaction energy quite steadily, and exhibits no evidence of any particular interaction with the C atoms per se. One sees evidence of a transfer of electron density from the acceptor molecule to the donor, characteristic of H-bonds. However, the amount of this transfer is disproportionately large in the HCCH complexes. Also larger than might be expected is the increase of positive charge on the bridging hydrogen. One feature exhibited by these complexes that is opposite from what is seen in conventional H-bonds has to do with the proton-acceptor atoms. The C atoms in HCCH become more positive in the complex, in contrast to the gain in density that is characteristic of a H-bond. Like a true H-bond, the largest contributor to the interaction energy in these HCCH complexes is the Coulombic attraction. Also in common are the signs of the exchange, polarization, and charge transfer terms. The magnitudes of these terms, however, are indicative of certain differences. The exchange
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repulsion is surprisingly large in the HCCH complexes, as are the polarization and charge transfer terms. The large magnitudes of the latter terms are consistent with the effects of the interaction upon the charge distribution mentioned above. In summary, then, pairing proton donors with the p cloud of acetylene, leads to an interaction which behaves in many respects like a true H-bond. On the other hand, there are certain differences, some of which are associated with a greater amount of electron density dislocation than is seen in H-bonds.
Acknowledgments We are grateful to Dr T. Kar for help with some of the calculations. This work was supported financially by NIH grant GM57936.
References [1] S. Scheiner, Molecular Interactions. From van der Waals to Strongly Bound Complexes, Wiley, Chichester, 1997, 359 pp. [2] G.R. Desiraju, T. Steiner, The Weak Hydrogen Bond in Structural Chemistry and Biology, Oxford, New York, 1999. [3] E.S. Kryachko, T. Zeegers-Huyskens, J. Phys. Chem. A 105 (2001) 7118. [4] R. Vargas, J. Garza, R.A. Friesner, H. Stern, B.P. Hay, D.A. Dixon, J. Phys. Chem. A 105 (2001) 4963. [5] M. Hartmann, S.D. Wetmore, L. Radom, J. Phys. Chem. A 105 (2001) 4470. [6] J.J. Novoa, F. Mota, Chem. Phys. Lett. 318 (2000) 345. [7] P. Hobza, Z. Havlas, Chem. Rev. 100 (2000) 4253. [8] I. Alkorta, I. Rozas, J. Elguero, J. Fluorine Chem. 101 (2000) 233. [9] E. Cubero, M. Orozco, P. Hobza, F.J. Luque, J. Phys. Chem. A 103 (1999) 6394. [10] Y. Gu, T. Kar, S. Scheiner, J. Am. Chem. Soc. 121 (1999) 9411. [11] I. Rozas, I. Alkorta, J. Elguero, J. Phys. Chem. A 101 (1997) 9457. [12] S.S.C. Ammal, P. Venuvanalingam, J. Chem. Phys. 109 (1998) 9820. [13] D. Philp, J.M.A. Robinson, J. Chem. Soc., Perkin Trans. 2 (1998) 1643. [14] P. C ¸ arc¸abal, V. Brenner, N. Halberstadt, P. Millie´, Chem. Phys. Lett. 336 (2001) 335. [15] S.A.C. McDowell, Phys. Chem. Chem. Phys. 3 (2001) 2754. [16] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D.
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C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Pittsburgh, PA, 1998. C. Møller, M.S. Plesset, Phys. Rev. 46 (1934) 618. J.A. Pople, R. Seeger, R. Krishnan, Int. J. Quantum Chem., Quantum Chem. Symp. 11 (1977) 149. A.D. Becke, J. Chem. Phys. 98 (1993) 5648. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. K. Morokuma, K. Kitaura, in: W.J. Orville-Thomas (Ed.), Molecular Interactions, vol. 1, Wiley, New York, 1980, p. 21.
Acetylene as potential hydrogen-bond proton acceptor Steve Scheinera,*, Sławomir J. Grabowskib a
Department of Chemistry and Biochemistry, Utah State University, Logan, UT 84322-0300, USA Institute of Chemistry, University of Białystok, 15-443 Białystok, Al. J. Pilsudskiego 11/4, Poland
b
Received 3 September 2001; revised 21 November 2001; accepted 21 November 2001
Abstract Ab initio calculations are used to assess the ability of the CxC triple bond in acetylene to act as proton acceptor to donor molecules HF, HCl, HCN and HCCH. The strength of the interaction energy varies from 3 kcal/mol for the strongest of these complexes FH· · ·HCCH, to 1 kcal/mol for the weakest (HCCH)2. The X– H bond of all donors undergoes the elongation characteristic of H-bonds, along with the red shift of its stretching frequency. In addition, electron density is transferred from the proton-acceptor molecule to the donor, and the bridging H becomes more positive. However, the magnitudes of these density shifts are larger than might be expected from a conventional H-bond. Opposite to a H-bond, the proton-accepting C atom loses density. Decomposition of the total interaction energy indicates the dominant role played by Coulombic attraction, as in a H-bond, but the exchange repulsion, charge transfer, and polarization terms are disproportionately larger than is typically seen in true H-bonds. q 2002 Elsevier Science B.V. All rights reserved. Keywords: CH/p; Red shift; Weak hydrogen bond; Energy decomposition; Distortion energy
1. Introduction During the early years of ab initio study of molecular interactions, work focused largely on strong interactions, due in large measure to the inability of early methods to treat weak interactions quantitatively. Continuing progress has expanded the range of interactions which can be investigated with reliability, enabling real advances to be made in our understanding of weak interactions [1]. The same situation exists with regard to the more specific case of hydrogen bonds. Conventional H-bonds of the sort where a proton donor OH or NH group approaches an acceptor atom like O or N, have been well studied * Corresponding author. Tel.: þ1-435-797-7419; fax: þ 1-435797-3390. E-mail address: [email protected] (S. Scheiner).
over the years, and their fundamental nature is understood. Recent advances have made it possible to investigate weaker interactions, which have some of the hallmarks of a conventional H-bond [2]. As an example, the last few years have seen a proliferation of ab initio studies of CH· · ·O interactions [3 –10], addressing the fundamental question as to whether it fits the criteria of a true H-bond. Rather than the traditional lone pairs of a protonacceptor atom like O or N, one is led to wonder whether the electron-rich environment of a CC multiple bond can function as a proton acceptor in a H-bond, viz. a so-called XH· · ·p bond. In particular, the triple CxC bond of a molecule like acetylene ought to serve as a particularly rich source of electrons, which has motivated a number of recent calculations concerning its ability to serve as proton acceptor. As an example, HF was taken as a proton
0022-2860/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 2 8 6 0 ( 0 2 ) 0 0 2 1 9 - 3
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donor and paired with systems containing CC multiple bonds, i.e. acetylene, ethylene, and benzene, as well as three and four-membered rings in 1997 [11]. The equilibrium geometries had the appearance of H-bonds, albeit weak ones. Atoms-in-molecules (AIM) analysis of the electron densities was also consistent with such a characterization, as was the observation of a small amount of electronic charge transferred between the two molecules. In the particular case of FH· · ·acetylene, the interaction energy was computed to be 3.1 kcal/mol at the MP2/6-311þ þ Gp p level. These results were largely confirmed the following year [12] which also added harmonic vibrational frequencies; zero-point vibrational corrections reduce the binding energy of the FH· · ·acetylene complex to 1.4 kcal/mol. The interaction was weakened by considering the CH of acetylene as the proton donor to another acetylene molecule by Novoa and Mota [6] whose AIM analysis suggested a H-bond here as well, even though the interaction energy is reduced to 1.2– 1.6 kcal/mol, depending upon basis set. Their data ˚ ) stretch of the CH further indicated a small (2 –3 mA bond of the donor acetylene upon formation of the dimer. Philp and Robinson [13] extended work on the acetylene dimer to consideration of the sensitivity of the interaction to an ‘offset’ of the proton donor, i.e. a ‘sliding’ parallel to the CC triple bond, as well as tilting the donor away from the perpendicular. Their results indicated that the interaction energy is reduced ˚, to half of its optimum value by a slide of about 1 A and is even less sensitive to a tilt. They found confirmation of these trends in a survey of crystals containing similar interactions. These authors concluded that the interaction in the acetylene dimer lies only on the borderlines of a true H-bond, and believed that the dispersion component of the interaction was likely to be comparable to the electrostatic term. Philp and Robinson also considered water as a proton donor to acetylene and computed a binding energy between 1.6 and 2.0 kcal/mol. The HCl molecule was more recently considered as a proton donor [14] to acetylene where the focus lied in comparison of the interaction energy with experiment. Their most accurate extrapolated value of De, including anharmonicity in the vibrational frequencies, was 1.5 kcal/mol, not far from an experimental value of 1.7. A more recent set of calculations [15]
includes not only HF and HCl, but also HBr as proton donors, yielding QCISD electronic binding energies of 3.7, 2.1, and 1.8 kcal/mol, respectively, as well as a full elucidation of vibrational frequencies in each complex. The present work refocuses on the properties of the acetylene molecule as a proton acceptor. Rather than consider just one donor molecule, or one type, a range of different sorts of molecules are taken as donors. HF and HCl represent strong proton donors, hydrogen halides. HCN is also a strong acid but differs in having a C atom as proton donor atom, which is thought to perhaps offer a different situation. The same theme of CH as proton donor group is taken up by HCCH, except that this molecule is a considerably weaker acid than the others. A variety of different aspects of the interaction are considered here. The binding energies are computed, as are the equilibrium geometries. Of some interest are the effects of the interaction upon the X –H bond of the proton donor molecule, its length and spectroscopic properties. This work also compares the sensitivity of the interaction energy of each complex to stretches and other distortions from equilibrium. We also evaluate which of these interactions can be considered as true H-bonds, using a number of electronic and energetic parameters as a litmus test.
2. Methods Ab initio calculations were carried out using the GAUSSIAN -98 set of codes [16] with its various built-in
basis sets. Standard notation was used for basis sets wherein þ signs indicate the presence of diffuse functions on non-hydrogen atoms (one þ ) or all atoms (double þ ); analogous meaning is attached to p signs and polarization functions. Aug-cc-pVDZ refers to a correlation-consistent polarized-valence double-zeta type of set. Electron correlation was included via the second-order Møller – Plessset (MP2) treatment [17,18], as well as by use of the B3LYP variant of density functional theory (DFT) [19,20]. Full geometry optimizations were carried out for each complex, and each resulted in a C2v T-shape, with the proton donor molecule lying perpendicular to the triple bond of acetylene, pointing toward the bond’s center.
S. Scheiner, Sł.J. Grabowski / Journal of Molecular Structure 615 (2002) 209–218 Table 1 Interaction energies (kcal/mol) calculated for complexes of various proton donors with HCCH. Counterpoise corrections of basis set superposition error are added
SCF
B3LYP MP2
Basis set
HF
HCl
HCN
HCCH
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þþ Gpp aug-cc-pVDZ 6-311þþ Gpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þþ Gpp aug-cc-pVDZ
3.09 2.93 2.87 2.70 2.71 2.86 3.98 3.22 3.44 3.30 3.31 3.14 3.72
1.69 1.39 1.41 1.44 1.38 1.48 2.08 2.16 1.83 1.78 1.89 1.91 2.72
1.87 1.58 1.59 1.58 1.52 1.63 1.73 2.07 1.79 1.73 1.80 1.81 2.21
0.83 0.71 0.71 0.69 0.72 0.72 0.79 1.08 0.95 0.92 1.05 1.10 1.38
3. Geometries and energetics The interaction energies computed for the complexes of the various donors with acetylene are reported in Table 1. The data in the top half of the table were evaluated at the SCF level. The values for the 6-31Gp basis set are somewhat inflated, when compared to the other data which are fairly consistent with one another. The correlated values in the lower half of the table are larger than their SCF correlates, due primarily to the influence of dispersion which is not present at the SCF level. Table 2 ˚ ) reported as distance Optimized intermolecular separations (A separating bridging H from center of CxC bond
SCF
B3LYP MP2
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þ Gpp aug-cc-pVDZ 6-311þ þ Gpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þ Gpp aug-cc-pVDZ
HF
HCl
HCN
HCCH
2.340 2.370 2.396 2.412 2.407 2.376 2.153 2.191 2.169 2.174 2.192 2.186 2.138
2.626 2.719 2.688 2.726 2.733 2.725 2.410 2.417 2.434 2.408 2.436 2.439 2.330
2.746 2.829 2.816 2.849 2.848 2.807 2.653 2.535 2.553 2.542 2.602 2.598 2.515
2.967 3.071 3.055 3.077 3.073 3.015 2.855 2.653 2.658 2.644 2.723 2.697 2.603
211
There would appear to be a bit more sensitivity to basis set for the MP2 than for the SCF data. The B3LYP values, all computed with the 6311þ þ Gp p basis set, show greater variation from one donor to the next than does MP2. That is, the B3LYP/6-311þ þ G p p value for FH· · ·HCCH is 0.8 larger than the MP2 quantity, whereas the order is reversed for the acetylene dimer in the final column of the table. Perusal of Table 1 allows one to conclude that HF forms the most strongly bound complex with acetylene, with an interaction energy in excess of 3 kcal/mol. HF is followed by HCl and HCN, which are similar to one another, forming an interaction with acetylene of nearly 2 kcal/mol. HCCH is the weakest of the proton donors, bound to another acetylene molecule by around 1 kcal/mol. The effects of correlation upon the complexation energy can be elucidated as the difference between the SCF and MP2 values in Table 1. Excluding the augcc-pVDZ data for the moment, these correlation contributions are largest for the HF and HCl donors, lying in the range of 0.4 – 0.6 kcal/mol. Correlation is less significant for the two CH donors in the last two columns, amounting to 0.1 – 0.4 kcal/mol. This quantity is in fact larger for HCCH than for HCN in most cases, despite the weaker binding of the latter. As a result, correlation accounts for a greater fraction of the total binding energy in the acetylene dimer, as much as 35% for the 6311þ þ Gp p basis set. Not surprisingly, due to the nature of its formulation, the contribution of electron correlation to the total interaction is magnified in the case of the aug-cc-pVDZ basis set. The correlation contribution to the binding energy of acetylene dimer is 0.66 kcal/mol, accounting for nearly half of the total. The equilibrium separations are reported in Table 2 as the distance from the bridging proton to the midpoint of the CxC bond. These distances pretty well mirror the interaction energies in Table 1 in the sense that stronger binding tends to translate into a shorter intermolecular separation. Shortest in this collection is FH· · ·HCCH where the pertinent distance ˚ . The best correlated estimates for the HCl, is 2.2 A HCN, and HCCH donors are, respectively, 2.4, 2.6, ˚ , but with some residual uncertainty due to and 2.7 A lingering basis set sensitivity.
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Table 3 ˚ ) caused by Elongation of proton donating bond length (in mA complexation with HCCH
Table 5 Ratio of intensity in the complex/isolated subunit (for proton donating bond)
HF
HCl
HCN
HCCH
HF
HCl
HCN
HCCH
3.6 4.0 4.3 4.0 4.1 4.6 9.9 4.2 6.4 6.7 6.6 6.7 8.4
3.2 2.5 3.0 2.9 2.9 2.9 8.8 4.7 4.4 5.2 5.3 5.3 7.7
2.5 2.2 2.3 1.8 2.3 2.3 3.9 3.3 3.0 2.5 2.9 2.4 3.9
1.4 1.1 1.1 1.2 1.2 1.2 2.0 2.0 1.5 1.5 1.3 1.3 2.1
3.2 3.0 2.9 2.7 2.7 3.2 5.6 4.7 4.6 4.7 4.1 4.2 5.4
7.4 5.0 4.6 3.6 3.6 4.0 12.1 15.1 11.3 9.7 7.2 7.1 9.3
2.5 2.2 2.2 2.1 2.1 2.3 3.3 3.4 3.2 3.2 2.8 2.9 3.6
1.6 1.5 1.5 1.4 1.5 1.6 1.8 2.1 2.0 2.0 1.8 1.9 2.3
SCF
B3LYP MP2
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þ Gpp aug-cc-pVDZ 6-311þ þ Gpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þ Gpp aug-cc-pVDZ
4. Deformations of proton donor molecule The most notable geometric effect of the formation of an interaction of this type is the change in the length of the X – H bond of the proton donor molecule. In particular, significant elongations are observed in Hbonded systems. It is just such a stretch that is observed in the four systems of interest here, as witness the values reported in Table 3. The elongation ˚ , followed closely by is greatest for HF at about 7 mA HCl. The stretches are significantly smaller for the ˚ for HCN and 1 or 2 mA ˚ two CH donors, nearly 3 mA for HCCH. Table 4 Red shift in HX stretching frequency (in cm21) of proton donor caused by complexation with HCCH
SCF
B3LYP MP2
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þGpp aug-cc-pVDZ 6-311þ þGpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þ þGpp aug-cc-pVDZ
HF
HCl
HCN
HCCH
76 91 104 99 101 122 227 77 130 159 156 159 206
48 37 42 37 39 42 110 68 63 73 72 73 111
34 30 31 26 30 33 58 46 44 40 43 38 59
11 8 8 8 9 9 17 15 13 13 9 9 15
SCF
B3LYP MP2
6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þþ Gpp aug-cc-pVDZ 6-311þþ Gpp 6-31Gp 6-31 þ Gp 6-31 þ Gpp 6-311 þ Gpp 6-311þþ Gpp aug-cc-pVDZ
Along with the X – H stretch, it is characteristic of H-bonds that the stretching frequency of this bond be shifted to the red by the formation of the complex. The amount of this shift is listed in Table 4 for the various complexes. The pattern is very much like that observed in Table 3 in that longer stretches are associated with larger red shifts. This shift varies from as large as 206 cm21 for FH· · ·HCCH with the augcc-pVDZ basis set to only 9 cm21 for the acetylene dimer with some of the other large sets. The red shift is typically accompanied by an intensification of the band. This phenomenon is displayed in Table 5 as the ratio of the computed intensity in the complex to that in the isolated molecule. These data generally fall into the same pattern as those above in that stronger complexes are associated with a larger intensification. However, there is one interesting anomaly in that the ClH· · ·HCCH complex exhibits a surprisingly large effect, nearly double that of the very similar FH· · ·HCCH.
5. Intermolecular deformations The effects of stretching or contracting the H-bond are displayed in Fig. 1 where the interaction energy is plotted as a function of the distance separating the bridging hydrogen from the CxC midpoint. These curves show the expected trend of progressive deepening, accompanied by shorter equilibrium
S. Scheiner, Sł.J. Grabowski / Journal of Molecular Structure 615 (2002) 209–218
213
˚ ). Energies were calculated at the MP2/6-311þþ Gpp level, uncorrected Fig. 1. Interaction energies as a function of intermolecular separation (A for BSSE. Circles correspond to HF donor, open squares to HCN, and triangles to HCCH.
separation in the series HCCH , HCN , HF. All progress smoothly toward a long-distance asymptote. Another mode of distortion of these C2v equilibrium complexes might involve a bend of various sorts. One such bend, a ‘wag’ of sorts, is engendered by holding fixed the atom of the proton donor molecule that is furthest from the acceptor acetylene. Then the remainder of the donor molecule is rotated around that pivot atom, in the plane of the HCCH molecule, by an angle a. The sensitivity of the binding energy to this wagging motion is illustrated in Fig. 2 for the same three donor molecules. It appears that this motion is of large amplitude. Taking the FH· · ·HCCH molecule as an example, a wag of more than 308 is required to cut the binding energy in half. Another sort of wag is defined in a similar manner, except that the rotation of the donor molecule is perpendicular to the plane of the two molecules. The sensitivity of the binding energy to this out-of-plane wag, b, is reported in Fig. 3. The curves in Fig. 3 would appear somewhat flatter than those in Fig. 2, suggesting that the energy is less sensitive to out-of-plane than in-plane wags. Another type of distortion considered has to do
with the optimal geometry wherein the donor molecule lies directly along the perpendicular of the HCCH acceptor molecule that passes through its center. The donor molecule was allowed to ‘slide’ a distance d, parallel to the HCCH molecule, remaining perpendicular to the latter, but its distance from HCCH was optimized at each point. The effects of this sliding are depicted in Fig. 4 where the center of each curve corresponds to the equilibrium configuration. It is important to note that the binding energy is reduced by such a slide, buttressing the idea that the donor prefers to lie above the CxC midpoint, and not above either of the C atoms.
6. Nature of interaction In addition to geometry, energetics, and spectroscopic features, other hallmarks of a hydrogen bond involve distributions of electron density. For example, it is widely accepted that a certain amount of charge is shifted from the proton acceptor molecule to the donor upon H-bond formation. There are a number of ways
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Fig. 2. Interaction energies (in kcal/mol) as a function of a angle. Circles correspond to HF donor, open squares to HCN, and triangles to HCCH. Energies were calculated at the MP2/6-311þ þGpp level and are uncorrected for BSSE.
to measure this charge shift, two of which are reported in Table 6. The first, and in some ways more direct, is to sum up the atomic charges on each of the two molecules within the complex. As listed in the second column of Table 6, 33 me are transferred from HCCH to the HF molecule in FH· · ·HCCH. Slightly larger charge transfers are observed for HCl and HCCH, but the largest of all is associated with HCN which, in turn, forms the strongest complex with HCCH. These quantities are rather large when compared with
‘standard’ H-bonds. For example, a similar calculation of the water dimer reveals a charge transfer of 13 me [10]. Another indicator of the large amount of charge transfer in these complexes arises from the dipole moment of each complex. When this quantity is compared to the vector sum of the two isolated molecules (zero for HCCH), its enhancement in the complex is in part due to transfer of electron density from proton acceptor to donor. These enhancements
Fig. 3. Interaction energies (kcal/mol) as a function of beta angle. Circles correspond to HF donor, open squares to HCN, and triangles to HCCH. Energies were calculated at the MP2/6-311þ þGpp level and are uncorrected for BSSE.
S. Scheiner, Sł.J. Grabowski / Journal of Molecular Structure 615 (2002) 209–218
215
Fig. 4. Effect on interaction energy of sliding proton donor molecule parallel to HCCH. d is defined as the displacement distance between the proton donating molecule and a line perpendicular to acceptor HCCH, passing through the center of the CxC bond. Energies were calculated at the MP2/6-311þ þGpp level and are uncorrected for BSSE. Circles correspond to HF as donor, open squares to HCN, and triangles to HCCH dimer.
are listed in the last column of Table 6 and may be seen to vary between 0.274 D (for the acetylene dimer) and 0.582 D for FH· · ·HCCH. These two limits may be compared to the dipole enhancement of 0.41 D in the water dimer [10]. It is important to stress that in addition to density shifted from one molecule to the other, there are internal displacements of charge within each molecule which contribute to the dipole enhancement. For example, the FH· · ·HCCH complex shows the largest Dm, but a relatively small value of CT, which would Table 6 Dipole moment of complex relative to monomers and charge transferred from proton acceptor to donor molecule (MP2/6311þ þGpp level) Donor HF HCl HCN HCCH a
CTa (me) 33 36 52 38
suggest a good deal of its moment change comes from such internal charge rearrangements. Conversely, the small value of Dm for the HCCH dimer in the last row of Table 6 is likely composed largely of intermolecular charge transfer, as CT for this system is comparable to those of the other systems with a larger Dm. Hydrogen bonds are characteristically accompanied by a loss of electron density upon the bridging proton, while the donating and accepting atoms become more negatively charged. The complexes studied here also exhibit this increasingly Table 7 Change in natural population atomic charge (me) of atoms in complex relative to monomers (MP2/6-311þþ Gpp level)
Dm (D) 0.582 0.465 0.435 0.274
The sum of atomic charges of proton acceptor molecule (acetylene) within the complex.
Donor
DqH
DqXa
DqC
FH ClH NCH HCCH
42 59 26 44
29 223 3 2275
64 60 57 50
a
X refers to proton-donating atom F, Cl, or C.
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Table 8 Decomposition of interaction energies (kcal/mol) of various proton donors with acetylene using 6-311þ þGpp basis set. Geometries optimized at MP2 level
ES EX POL CT CORRa a
HF
HCN
HCCH
26.4 þ6.3 21.5 22.2 20.4
23.4 þ2.8 20.6 20.8 20.3
22.2 þ2.1 20.3 20.5 20.4
Corrected for BSSE.
positive charge on the bridging H, as evident by the positive entries in the second column of Table 7. In fact, these values are considerably larger than the 19 me change in the bridging hydrogen atomic charge in the water dimer. The changes in the charge of the proton-donating atom show quite a wide discrepancy, varying from the negligible change in the C of HCN to the very large negative change in the C atom of HCCH (275 me). Perhaps most interesting in Table 7 is the behavior of the C atom in the proton-accepting HCCH. Rather than become more negative, as characteristic of H-bonds, these atoms become more positive by some 50 (HCCH) to 64 (FH) me. When coupled with the comparably small shifts of density between molecules, this observation indicates a shift of electron density to the H atoms in the proton donor HCCH, i.e. away from the approaching donor molecule. It is hence fair to say that there are certain fundamental differences between these complexes and conventional H-bonds. Another window into the fundamental nature of the interaction arises from a decomposition of the total interaction energy into several ‘pieces’. Such a decomposition was used earlier to buttress the claim that methane and its fluorinated derivatives do in fact form genuine H-bonds with proton acceptors [10]. A similar energy decomposition, of the Morokuma variety [21], was carried out here for the complexes of interest. In summary, the electrostatic (ES) term represents the Coulombic interaction between the charge distributions of the two subunits, and the exchange energy (EX) corresponds approximately to steric repulsion between the two charge clouds. When the two molecules are permitted to distort the charge
clouds of their partners, one can extract polarization (POL) energy from the internal redistributions and charge transfer (CT) from density shifts from one molecule to the other. As a final component, the effects of electron correlation are contained in the CORR element. The results of an energy decomposition of the complexes of interest are reported in Table 8 where it may be seen that the electrostatic term makes the dominant attractive contribution, nearly counterbalanced by exchange repulsion. Charge transfer also makes a significant contribution to the attraction, followed closely by a slightly smaller polarization term. The final row indicates that the correlation contribution, while attractive in all cases, is fairly small, less than 0.5 kcal/mol. With the exception of the latter term, there is a clear pattern of diminishing magnitude as the proton donor is changed from HF to HCN to HCCH, consistent with the same trend in the total interaction energies. A comparison of the data in Table 8 with a classical H-bond such as the water dimer provides some illumination regarding the characterization of HCCH as a proton acceptor. The ES, EX, POL, CT, and CORR contributions to the binding energy of the water dimer are, respectively, 2 7.6, þ 4.2, 2 0.7, 2 0.9, and 2 0.3 kcal/mol. In many respects, these numbers are comparable to the data in Table 8, only larger in magnitude, as one would expect for the stronger interaction in the water dimer. One distinction arises in that whereas the exchange repulsion in the HCCH complexes is very nearly equal in magnitude to ES, the former is substantially smaller than the latter for (H2O)2. In a sense, the EX term is larger in the HCCH complexes than one might expect based on the water dimer as a model. The same might be said for POL and CT which are disproportionately large, compared to a conventional H-bond. On the other hand, the CORR contribution seems to be uniform across the board, with all complexes exhibiting a contribution of 0.3 – 0.4 kcal/mol. Summarizing the energy decomposition analysis, the complexes involving HCCH as proton acceptor would appear to be dominated by Coulombic attraction, as are conventional H-bonds, but they are also characterized by larger EX, POL, and CT contributions than are H-bonds of comparative strength.
S. Scheiner, Sł.J. Grabowski / Journal of Molecular Structure 615 (2002) 209–218
7. Conclusions HF forms the strongest complex with acetylene, followed by HCl and HCN, and then by HCCH. The interaction energies of these complexes are roughly 3, 2, 2, and 1 kcal/mol, respectively. The equilibrium separation between the bridging proton and the center ˚ for of the acetylene CxC bond increases from 2.2 A ˚ for the HCCH dimer. As a FH· · ·HCCH, up to 2.7 A consequence of the interaction, the covalent bond involving the bridging hydrogen is elongated in all cases. The stretches in the hydrogen halides are the ˚ ; shorter elongations of 1– largest, as much as 7 mA ˚ are observed in the two CH donors. Accom3 mA panying the latter bond stretch is a shift to the red of the associated stretching frequency. These shifts vary a great deal and are sensitive to the strength of the interaction, from a maximum of 200 cm21 for the strongest donor HF down to only about 10 cm21 for HCCH. The distance dependence of these interactions consists of a smooth progression to a long-distance asymptote, as in conventional H-bonds. The interaction energy is fairly insensitive to wagging the proton donor molecule either in the plane of the acceptor, or perpendicular to it. The donor prefers association with the center of the HCCH acceptor molecule; sliding the donor along the acceptor reduces the interaction energy quite steadily, and exhibits no evidence of any particular interaction with the C atoms per se. One sees evidence of a transfer of electron density from the acceptor molecule to the donor, characteristic of H-bonds. However, the amount of this transfer is disproportionately large in the HCCH complexes. Also larger than might be expected is the increase of positive charge on the bridging hydrogen. One feature exhibited by these complexes that is opposite from what is seen in conventional H-bonds has to do with the proton-acceptor atoms. The C atoms in HCCH become more positive in the complex, in contrast to the gain in density that is characteristic of a H-bond. Like a true H-bond, the largest contributor to the interaction energy in these HCCH complexes is the Coulombic attraction. Also in common are the signs of the exchange, polarization, and charge transfer terms. The magnitudes of these terms, however, are indicative of certain differences. The exchange
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repulsion is surprisingly large in the HCCH complexes, as are the polarization and charge transfer terms. The large magnitudes of the latter terms are consistent with the effects of the interaction upon the charge distribution mentioned above. In summary, then, pairing proton donors with the p cloud of acetylene, leads to an interaction which behaves in many respects like a true H-bond. On the other hand, there are certain differences, some of which are associated with a greater amount of electron density dislocation than is seen in H-bonds.
Acknowledgments We are grateful to Dr T. Kar for help with some of the calculations. This work was supported financially by NIH grant GM57936.
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