INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, NO. 6, 301-304 (1972)

Electron Distribution in a Short A-Type Hydrogen Bond

PETER LINDNER* AND JOHN R. SABIN Quantum Theorv Project and Departments of Ph.ysics and Chemistry,

University of Florida, Gainesville. Florida 32601

The formal centrosymmetry of short A-type hydrogen bonds may arise from two situations [l]. The proton may have its equilibrium position at the bond midpoint, or it may randomly occupy two positions on either side of the bond center which are separated by a low energy barrier. As Ibers [2, 31 has shown, these two situations are not resolvable by diffraction methods, and thus the question of the symmetry of such bonds is particularly amenable to theoretical study. The situation is reflected in the seemingly contradictory results of X-ray and neutron diffraction studies on some hydrogen-bonded systems of this sort. For example, the X-ray study of potassium hydrogen mesotartrate [4] shows two maxima in the electron density, indicating an asymmetric hydrogen bond, while the structure determined by neutron diffraction [ S ] shows the hydrogen to be centrosymmetrically located.

Two possible explanations of this seeming contradiction have been offered by Speakman [ 11. The first suggestion involves a centrosymmetric hydrogen atom with the electron density in the short bond polarized by the electronegative neighbors. The second suggestion attributes the double peak in electron density to high-order terms in the X-ray analysis.

Some qualitative insight into this type of hydrogen bond can be obtained from a theoretical study of the valence electron density along the bond axis of such systems. Consequently, a semiempirical CND0/2 [6] calculation on the maleate ion (I) was carried out. This structure has many of the features of typical

* Permanent address : Quantum Chemistry Group, Uppsala University, Uppsala, Sweden.

@ 1972 by John Wiley & Sons, Inc. 301

302 P. LINDNER AND J . R. SABIN

A-type hydrogen bonds and can thus be considered as a good test model. Initial calculations were carried out at the experimental maleic acid geom-

etry [7]. In this structure the hydrogen is symmetrically located with 0-0 bond distance of 2.45 A.

The calculated potential for the hydrogen atom was found to be a shallow symmetric single minimum, with energy increase of 1.7 kcal/mole for 0.1 8, deviations of the proton from the bond center. The CNDO method is known to overestimate binding energies, indicating the calculated potential is probably too steep. Since the calculated potential is relatively flat at the minimum, it is expected that thermal motions of the hydrogen will be important in this case. The valence electron density for this system is nearly symmetric about the hydrogen bond axis in the molecular plane, and shows no evidence of local maxima off the bond axis, as reported by Kroon [4]. The charge densities are very similar to those obtained for other hydrogen-bonded systems by other methods [8].

In Figure la we show the part of the density relevant to our discussion. As expected, the density is almost constant in the immediate vicinity of the sym- metrically placed proton. We note that the method used (CNDO/2), besides various integral approximations, only utilizes a single 1s function on the hydrogen atom. Polarization of the hydrogen atom can be approached by inclusion of p orbitals [9]. Considering the expected degree of polarization and the form of 2s and 2p hydrogenic functions we believe, however, that any polarization effects would tend to flatten the density curve around the proton. Any possible sub- stantial maxima further out would be hidden by the high electron density around the oxygen atoms.

In an attempt to study any effects in elongated hydrogen bonds, we forced the 0 - H 4 distance to be 2.78 by opening the C-C-4 angles, while keeping all else constant. The potential in this case now shows a distinct double minimum form with a barrier height of 19 kcal/mole. Figure l b shows the charge density when the proton is kept in the symmetric position. In Figure lc the proton is moved to one of the minima points.

An idea of the change in charges on the atoms involved in the hydrogen bond can be obtained by a standard population analysis. The charge on the hydrogen atom changes from 0.72 in the case of the short bond (2.45 A) to 0.77 when the proton is in one of the minima for the long bond (2.78 A). The corresponding oxygen charges change from 6.48 in the short bond to 6.32 and 6.58 for the near and far oxygens, respectively, in the long bond.

In essence, we thus find that it is very unlikely that there exists a double peak in the electron density around a centrosymmetric proton in a short A-type hydrogen bond. The only situation where there could be a distinct double peak is in the case of a double potential minima (which show an experimental charge distribution composed of superimposing two curves similar to Figure lc). This is, however, not the general feature of a short hydrogen bond.

ELECTRON DISTRIBUTION 303

Figure 1. The electron density p ( X ) in arbitrary units vs the position X measured along the hydrogen bond from the bond center. Curve A : Roo = 2.45 A, H at the bond center. Curve B : R,, = 2.78 A, H at the bond center. Curve C : R,, = 2.78 A, H at the equilibrium

position, X = 0.325 A.

304 P. LINDNER AND J. R. SABIN

Acknowledgment

Acknowledgment is made to the donors of the Petroleum Research Fund administered by the American Chemical Society for partial support of one of us (JRS), and to the University of Florida Computer Center for a grant of computer time.

Bibliography

[ I ] See, for example, M. Currie and J. C. Speakman, J. Chem. SOC. (London) A 1970, 1923. [2] B. L. McGraw and J. A. Ibers, J. Chem. Phys. 39, 2677 (1963). [3] W. C. Hamilton and J. A. Ibers, Hvdrogen Bonding in Solids (Benjamin, New York, 1968). [4] J. Kroon, J. A. Kanters, and A. F. Peerdeman, Nature 229, 120 (1971). (51 J. Kroon, J. A. Kanters, and A. F. Peerdeman, Nature 232, 107 (1971). [6] For a good description of this method, see J. A. Pople and P. L. Beveridge, Appropximafe Molecular

[7] L. E. Sutton, Tables ofhreratomic Distances (Special Publication No. 1 I , The Chemical Society,

[8] See, for example, 1. Almof and 0. Martensson, Acta Chim. Scand. 25, 1413 (1971); M. Dryfus.

[9] For a simple illustrative example (H2) see, for example, S. Fraga and B. J. Ransik, J. Chem.

Orbital Theory (McGraw-Hill Book Co., New York, 1970).

London, 1958) p. 163.

B. Maigret, and B. Pullman, Theoret. Chim. Acta 17, 109 (1970).

Phys. 35, 1967 (1961).