J. Phys. Chem. 1987, 91, 2249-2253 ELECTRON ENERGY ( e V l
2.0
25
3.0
t 35 h
4 30
-0
lo
3.5
leads to a spread in Rydberg electron-N2 relative collision velocities. Nonetheless, the data demonstrate that the essentially free electron model can be applied to high-energy collisions.
4
I-
E
L 6
2249
7 8 9 IO II 12 13 KINETIC ENERGY ( k e V )
Figure 7. Cross section for collisional ionization in fast D(n)-N, collisions. The solid line shows the total cross section for free electron-N,
scattering at the same relative collision velocity. at energies of 6-1 3 keV. Measured cross section^'^ for reaction 11 are presented in Figure 7, together with the free electron scattering cross sections for the same relative collision ~elocities.~’ The Rydberg atom and free electron data are in excellent agreement, although no vibrational structure is evident in the Rydberg data because the orbital motion of the Rydberg electron (37) Kennedy, R. E. Phys. Rev. Left. 1979, 21, 1876.
Concluding Remarks Although this review has dealt only with the application of Rydberg atoms to studies of electron capture, it is now apparent that Rydberg atoms can be used to investigate a wide variety of subthermal electron collision processes. For example, measurements of Rydberg energy level shifts and broadening in the presence of a background gas can be related to the total free electron elastic scattering cross s e c t i ~ n . ~Inelastic ~ * ~ ~ scattering of the Rydberg electron can give rise to a number of interesting effects including the efficient, near-resonant interchange of energy of molecular rotation and energy of electronic excitation in Rydberg atom collisions with polar molecules.” Indeed, the use of Rydberg atoms as a tool to probe electron-scattering processes is in its infancy, and rapid development in this area should continue for many years. Acknowledgment. The research by the author and his colleagues described in this article is supported by the National Science Foundation under Grant No. PHY84-05945 and the Robert A. Welch Foundation. (38) See,for example, the article by F. Gounand and J. Berlande in ref 1.
(39) Matsuzawa, M. J. Phys. B 1975, 8, L382. (40) Kellert, F. G.; Smith, K. A.; Rundel, R. D.; Dunning, F. B.; Stebbings, R. F. J . Chem. Phys. 1980, 72, 3179.
ARTICLES Theoretical Studies on Solid Ammonia. 1. Electron Density Oscar E. Taurian and Sten Lunell* Department of Quantum Chemistry, Uppsala University, S - 751 20 Uppsala, Sweden (Received: September 16, 1986; In Final Form: December 15, 1986)
Ab initio MO-LCAO-SCF calculations of the electron density in solid ammonia have been carried out, using a 16-atom cluster surrounded by point charges as a model. A comparison with gaseous NH3 shows that the major changes induced by condensation to the solid state are (a) an increase of the polarity of the N-H bbnds and (b) a shift of charge away from the 3al lone pair orbital toward the regions between the N-H bonds, leading to a more spherical electron density distribution around the nitrogen nucleus, in agreement with experimental evidence from nuclear quadrupole resonance measurements.
I. Introduction Solid ammonia, NH3, possesses several features that makes it interesting for a theoretical study. Besides the well-known role of ammonia, e.g., in chemical industry, biochemistry, and astrophysics, it is together with water one of the simplest and most fundamental stable molecules known,and therefore has an intrinsic scientific interest for the study of basic physical and chemical properties. As a consequence, it has been very intensively studied from the experimental point of view. As with water, one of the most important characteristics of ammonia is its ability to form hydrogen bonds, which, e.g., in the condensed state manifests itself as “abnormally” high melting and boiling points. Crystallographic show that, in solid
ammonia, each NH3 molecule acts simultaneously as a triple hydrogen bond donor and a triple hydrogen bond acceptor. This is an unusual situation considering the fact that, according to a classical description, N H 3 has only one lone pair on the nitrogen atom and thus would be expected to accept only one hydrogen bond. From the point of view of electronic structure, the major qualitative change that an NH3molecule undergoes when it passes from the gaseous to the solid phase (the geometry of the molecule (1) Mark, H.; Pohland, E. 2.Krisf. 1925, 62, 532. (2) Olovsson, I.; Templeton, D. H. Acfa Crysfallogr. 1959, 22, 832. (3) Reed, J. W.; Harris, P. W. J . Chem. Phys. 1961, 35, 1730.
0022-3654/87/209 1-2249%01.SO10 0 1987 American Chemical Society
2250 The Journal of Physical Chemistry, Vola91, No. 9, 1987
changing only slightly) is in the character of the 3a1valence orbital. This orbital, being a nonbonding lone pair orbital in the free molecule, becomes responsible for the hydrogen bonding in the crystal. It is therefore expected that it will play a fundamental role in the change of properties of the molecule when passing from the gas to the solid. However, a certain experimental controversy exists about the effect on this orbital brought about by the hydrogen bond formation. This controversy is well illustrated by the following statements that appeared in the same year, in the same volume of the same journal: ”The major change from the gas phase to the solid state (Auger) spectrum is a significant lifetime broadening of the peaks involving the 3al-type molecular ~ r b i t a l ” . ~ “Thus the binding energies, the energy separation, the band widths, and the branching ratio (of UPS) of the two outermost bands of solid ammonia are not significantly different from the 3a1 and the l e molecular orbital states of gaseous ammonia; i.e., the intermolecular hydrogen bonding has not produced any detectable change in the electronic structure of the valence bands of NH3”.5 Hence it is interesting to make a careful theoretical study of different physical properties in the crystalline state and compare with the corresponding ones of the gaseous state, with particular attention to the bonding between the N atom of the N H 3 molecule and its three neighboring hydrogen bond donors. In this paper, we study the electron density distribution in solid ammonia. By performing a b initio calculations on the crystal and on the free molecules, we are also able to study separately the changes caused by condensation. 11. Theoretical Model The space group associated with solid ammonia is T4;’” hence the unit cell is cubic and deviates slightly from facecentered cubic. Four molecules are contained in the unit cell, see Figure 1, and they are placed on sites of C3 symmetry (cf. also Figure 1 of ref 2 and Figure 4 of ref 3). The principal axes of these molecules are parallel to the body diagonals of the cubic unit cell. As mentioned in the Introduction, each NH3 molecule accepts and donates three hydrogen bonds. All molecules in the crystal are crystallographically equivalent. In this study, the NH, crystal was represented by a central cluster, consisting of the four molecules which constitute its unit cell, surrounded by point charges placed at their atomic positions as determined by neutron diffraction3 and out to a distance of about 16 A. A total of 640 point charges were included. This model enables a very detailed description of the intramolecular and intermolecular bonding within the unit cell and at the same time accounts for the long-range structure of the crystal. One can notice that the adopted model treats the four molecules in the unit cell slightly inequivalently, while they are perfectly equivalent in the true crystal. The latter fact, however, does provide a valuable check on the accuracy of the model and will be discussed further below. All-electron a b initio MO-LCAO-SCF calculations were performed for the central 16-atom cluster, using the program system MOLECULE-ALCHEMY.~ The calculations were first done without any surrounding point charges, and then with these included. The magnitudes of the point charges were obtained by a Mulliken population analysis for the atoms in the cluster. These were used as initial values for the point charges representing the crystal, which were then recalculated iteratively by successive S C F calculations. The iterations were terminated when the changes in the point charges became less than 0.001 (cf. section IIIA). The basis sets used were the following: for N , Dunning’s’ double zeta [9s4p/4s2p] augmented with a 3d polarization function with (4) Larkins, F. P.; Lubenfeld, A. J. Electron Spectrosc. Relat. Phenom. 1979, 15, 137. ( 5 ) Campbell, M. J.; Liesegang, J.; Riley, J. D.; Leckey, R. C. G.; Jenkin, J. G. J. Electron Spectrosc. Relat. Phenom. 1979, 15, 83. (6) Almlof, J.; Bagus, P. S.; Liu, B.; MacLean, D.; Wahlgren, U. I.;
Yoshimine, U. IBM, San Jose Research Laboratory. (7) Dunning, T. H. J . Chem. Phys. 1970, 53, 2823.
Taurian and Lune11 a 2
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Figure 1. (a) Perspective view of the four NH3molecules in the unit cell of solid ammonia, along the (2, -1, 2) direction. (b) Perspective view along the (1, 1, 1 ) direction. TABLE I: Atomic Charges in the (NH3), Cluster Obtaiml by a Mulliken Population Analysis Comlwred with a Free N H I Molecde (NH,), cluster pt charge free environ (NH3)4 itern 1 itern 2 itern 3 free NH3 mol atom cluster N1 -0.680 -0.717 -0.721 -0.722 -0.620 -0.707 N2 -0.636 -0.715 -0.716 H1 +0.234 +0.250 +0.207 +0.248 +0.249 H2 +0.225 +0.235 +0.236 +0.236 H3 f0.203 +0.231 +0.233 +0.233 H4 +0.200 +0.232 +0.236 +0.237
+
~
exponent 0.902; and for H, Dunning’s7 double zeta [4s/2s] augmented with a 2p polarization function with exponent 0.735.
Theoretical Studies on Solid NH3
The Journal of Physical Chemistry, Vol. 91, No. 9, 1987 2251
The polarization functions of this basis are optimized for the free NH3 molecule.8 The calculations were performed on the BASF 7/75 computer of Uppsala University Data Center (UDAC). 111. Results and Discussion A. Charge Distribution. Table I shows the charges obtained from a Mulliken population analysis for the different atoms in the unit cell as well as for a free N H 3 molecule. Also shown in the table is the convergence of the iterative method described in section I1 for the determination of these charges. As mentioned above, the molecules in the unit cell, as well as the hydrogen atoms within each molecule, are not strictly equivalent in the computational model used. This is indicated by the numbering of the atoms in Figure 1, where atoms which are symmetry related in the model are given identical designations. The first column of Table I gives the results for a free (NH3)4cluster without any surrounding point charges. In the following iterations, it is surrounded by the 640 point charges representing the surrounding crystal, as described in section 11, these charges in each step being taken from the results of the preceding iteration. One can notice that significant differences exist between the nonequivalent atoms in the free cluster, where only the three H2 hydrogens are engaged in hydrogen bonds. When the surrounding point charges are included and self-consistency is achieved, however, these differences are strongly reduced. The nearequivalency of all molecules in the unit cell, once self-consistency is achieved for the point charges, irrespective of the description of their hydrogen bond environment, gives support to the model used. At the same time, it indicates that an electrostatic description of the hydrogen bonding in solid ammonia is satisfactory and that covalency and other effects have minor importance, which is typical for a relatively weak hydrogen bond. A comparison with the charges obtained in an equivalent calculation on a free NH3 molecule (Table I, last column) shows that the overall effect of the condensation is an increased polarity of the N-H bonds. Similar increases in bond polarity, compared to the gaseous state, have been observed also for water molecules in solid salt^^.'^ and is a logical consequence of the same electrostatic forces which determine the packing arrangement in the crystal. B. Electron Density Maps. A more detailed description of the charge distribution, and also of the effects of condensation, can be obtained from contour maps displaying the total deformation (difference) density and the double difference density, respectively. The former type of maps, shown in Figures 2a-4a, are obtained by substracting the electron densities of free (spherical) nitrogen and hydrogen atoms, placed a t the appropriate lattice positions, from the total calculated electron density of the crystal. They hence show the combined effects of intra- and intermolecular bonding, and will be strongly dominated by the former. In contrast, the much weaker intermolecular effects are shown by the double difference maps in Figures 2b-4b, in which the electron density of superposed free NH3 molecules (withthe same geometry as in the crystal), rather than free atoms, has been subtracted from the total density. (The term double difference density is conventionally used for this type of maps, since they also can be obtained as the difference between the deformation (difference) density of the crystal and the deformation densities of the free molecules.) Figure 2a shows the total deformation density of the crystal in a plane containing the acceptor atom N1 and the atoms N 2 and H 2 of one of the donor molecules (this plane is essentially identical with the plane of Figure la). The most prominent features of the map are, as expected, areas of positive deformation density in the N-H bonds and in the lone pair region of the nitrogen atom. Areas of negative deformation density, similar to those observed outside 0-H bonds but weaker (cf., e.g., ref ~
(8) Taurian, 0. E. Computer Phys. Commun. 1984, 33, 55. (9) Hermansson, K.; Lunell, S. Chem. Phys. Left. 1981, 80, 64; Acta Crystallogr., Sect. B 1982, B38, 2563. (10) Lunell, S . J . Chem. Phys. 1984, 80, 6185.
b
* H4
Figure 2. (a) Theoretical deformation density map of the unit cell of solid ammonia, in the Nl-H2-N2 plane. Contour interval 0.1 e/A3. Dashed lines denote negative levels. Zero contour omitted. (b) Double difference map, showing the charge rearrangement induced in the free NH3 molecules by the intermolecular interactions in the solid. Same plane as in (a). Contour interval 0.01 e/A3.
lo), are found outside the hydrogen atoms, in the direction of the hydrogen bonds and close to the nitrogen atom in the planes bisecting the N-H bonds. It can be observed that the positive deformation density in the lone pair region of N1 is concentrated in the region between the three incoming hydrogen bonds. The effects of the intermolecular (hydrogen bond) interactions in the solid state can be studied in detail in Figure 2b. (It should be noticed that the contour values here are a factor 10 weaker than in the deformation density, Figure 2a.) Aside from the evident loss of charge from the hydrogen atoms, reflected also in the Mulliken populations of Table I, the most pronounced result of the charge rearrangement is that electron density has been transferred from the lone pair region to regions around the nitrogen nucleus with negative or zero deformation density. (Actually, the region of zero deformation density close to the nitrogen nucleus
2252 The Journal of Physical Chemistry, Vol. 91, No. 9, 1987
H2
a
Taurian and Lunell H2
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Figure 3. (a) Deformation density in a plane passing through N1 and perpendicular to the (1, 1, 1) axis. (b) Double difference density in the same plane. Contours as in Figure 2.
Figure 4. (a) Deformation density in a plane perpendicular to the (1, 1, 1) axis but passing 0.159 A above N1. (b) Double difference density in the same plane. Contours as in Figure 2.
in the direction of the N-H bond in Figure 2a is slightly negative in the free N H 3 molecule.) This type of reduction of lone pair intensity in the solid phase compared to the free molecules, accompanied by a charge increase in directions with negative deformation density, has previously been observed by us in a number of oxygen-containing compounds, and seems to be a general feature accompanying the increase of negative charge of the atom carrying the lone pair, leading to a more spherical environment around the atomic nucleus in question.lO~llIt is in complete agreement with the experimentally observed decrease of the nuclear quadrupole coupling constant at 14Nin crystalline ammonia compared to the free molecule, being -4.08 M H z in the gaseous phase and -3.47 M H z in the crystalline phase.12 The fact that the hydrogen atom H1 lies only slightly outside the plane of Figure 2a makes the two molecules in the lower half of the diagram almost exactly equivalent. As can be seen, their deformation densities are very similar. Also their double difference maps are essentially identical, apart from the weakest contour, 0.01 e/A3, giving additional evidence that the model used treats all molecules in the unit cell in a balanced way. Figures 3a and 4a and 3b and 4b show the deformation densities and double difference densities, respectively, in planes perpendicular to the C3axis passing through N1. These planes are hence parallel to the plane of Figure l b (and also of Figure 2 of ref 2). The plane of Figure 3a,b passes through the nitrogen atom, whereas the plane of Figure 4a,b passes through the lone pair region, 0.159 A from the nitrogen atom. Figure 3a shows the charge accumulation in the N-H bonds, already noticed in Figure 2a, and also shows more clearly the distribution of negative deformation density in the directions bisecting these bonds. The deformation density is clearly dominated by the C,,symmetry of the free molecule, which is seen from both Figure 3a and Figure 4a, despite the lower C3symmetry of the hydrogen bond environment.
Figures 3b and 4b, which show the double difference density in the same planes, confirm the general principle, outlined above, of a charge reduction in the lone pair region and a buildup in regions of negative deformation density around the nitrogen atom. One can in this case also note a weak but clear tendency toward the lower C, symmetry of the surrounding crystal. The directions around N1 along which charge is built up can, however, be related neither to those of the Nl-H1 covalent bonds nor to those of the incoming H2-N 1 hydrogen bonds. Apparently, the charge rearrangement in the solid is determined both by the internal geometry of the N H 3 molecule and by the spatial arrangement of the surrounding hydrogen bond donors, their relative importance, as indicated by Figure 3b, being different close to the nitrogen nucleus and further away from it. We have in a previous paper discussed the lowering of lone pair peak density which in a number of experimental deformation density studies has been found to accompany hydrogen bonding and pointed out the importance of superposition of donor and acceptor deformation densities as a major cause of this lowering.1° This effect can be seen also in Figure 2a by comparing in more detail the two NH3 molecules in the lower half of the figure. Here, the lone pair peak height at N1, which is subject to superposition from the (three) neighboring H 2 atoms, is 0.8 e/A3, whereas the peak height is 0.9 e/A3 at N2, whose neighboring hydrogen bond donors are represented only as oint charges. This shows that the superposition effect is 0.1 e l l 3 in the former case. Likewise, a detailed comparison of the outer contours of the lone pairs reveals clearly lower deformation density outside N1. On the other hand, the *true" reduction in peak height in the solid is 0.08 e/A3 for both N 1 and N 2 (Figure 2b). The actual rearrangement effects and the superposition effects hence have similar magnitude is the present case, in contrast to the previously discussed NaHC2O4-H20,I0where the superposition effect was clearly dominant. The main reason for this difference is the much longer He-X bond length in solid ammonia, 2.37 A compared to 1.54 A in NaHC204.H20,which makes the superposition effect weaker. Probably, the unique arrangement in solid ammonia of one lone pair accepting three hydrogen bonds also makes the actual charge
(11) Taurian, 0. E.; Lunell, S.; Tellgren, R. submitted for publication in J . Chem. Phys. (12) Lehrer, S. S.; O'Konski, C. T. J . Chem. Phys. 1965, 43, 1941.
J. Phys. Chem. 1987,91, 2253-2258 rearrangement at the acceptor atom particularly large. For more normal hydrogen-bonded systems and bond lengths, the superposition effect should therefore be expected to account for most of the observable decrease in acceptor lone pair density in experimental deformation density maps. This is especially true at some distance from the acceptor atom, since the true density reduction mainly occurs within 0.3-0.5 A from the nucleus. Incidentally, the present results also illustrate the dominance of polarization effects over exchange repulsion (or closed-shell repulsion) around the acceptor atom. Thus, the density depletions at N 1 and N 2 are virtually identical, despite the fact that N 1 is subject to exchange repulsion from three neighboring hydrogen bond donors, while the neighbors of N 2 are represented only by point charges (cf. also ref 10).
IV. Conclusion The calculations show that the main changes in the free N H 3 molecules caused by condensation to the solid phase is, on the one
2253
hand, an enhanced polarity of the N-H bonds and, on the other hand, a shift of negative charge away from the lone pair region of the nitrogen atom, primarily toward the regions between the N-H bonds. As this charge mainly is transferred to regions of negative deformation density around the nitrogen nucleus, the net effect is a more spherical environment of this nucleus, in agreement with results of nuclear quadrupole resonance experiments on solid and gaseous ammonia. The clear effects observed in this paper on the 3al lone pair orbital may also explain the broadening of the Auger lines observed in ref 4.
Acknowledgment. This work was partially supported by a grant from the Swedish National Science Research Council (NFR). O.E.T. expresses his gratitude to the members of the Uppsala University Computer Center (UDAC), especially to Bertil Jansson, for he1 ful assistance during the course of the calculations, and to H. gren and C. Medina for stimulating discussions. Registry No. NH3, 7664-41-7.
8:
A Matrix Isolation Study of the Interaction between Water and the Aromatic ?r-Electron System Anders Engdahl and Bengt Nelander* Division of Thermochemistry, Chemical Center, University of Lund, S-221 00 Lund, Sweden (Received: October 1, 1986; In Final Form: January 14, 1987)
The interaction of water (H20,D20, HDO)with toluene, the xylenes, pseudocumene, mesitylene, pentamethylbenzene, and hexamethylbenzene in argon matrices has been studied with infrared spectroscopy. Interaction energy estimates are given. The shapes of the observed absorption bands suggest that water executes a complicated motion relative to the ring plane of the aromatic hydrocarbon. The infrared spectrum of the benzene-water complex has been recorded as a function of temperature in argon, krypton, and nitrogen matrices.
Introduction The interaction of water with ethylene,' benzene,2 and a series of simple olefins3 has recently been studied in this laboratory. Water forms a hydrogen bond with ethylene where one of its hydrogen atoms points toward the midpoint of the C = C The complex is quite weak; its dissociation energy is probably around 2 k ~ a l / m o l . ' * ~(Note the estimate of ref 1 includes zero-point vibration energies, but the estimate of ref 3 does not.) The dissociation energy increases when methyl groups are introduced next to the double bond. The dissociation energy of the tetramethylethylene-water complex is probably larger than that of the water dimer. The absorption band due to the stretching vibration of the water-OH bond engaged in the hydrogen bonding has a complicated shape. This was interpreted in ref 3 as the result of relative motions of the complex-forming molecules. Water forms a hydrogen bond with benzene, with one of its hydrogens pointing toward the midpoint of the benzene ring.2 The dissociation energy of the complex is probably close to that of the water-ethylene c o m p l e ~ . ~H?D~O forms a D bond to benzene or to an olefin. As was found for the water-olefin complexes, the absorption band due to the hydrogen-bonding OH stretch (OD stretch) has a complicated shape. However, the shape of the bonding OD band of H D O bound to benzene differs from the shapes of the conesponding O H and OD bands of H 2 0 and D20. For the water-olefin complexes, these three bands have closely similar shapes. It was suggested in ref 2 that these observations ( 1 ) Engdahl, A,; Nelander, B. Chem. Phys. Lett. 1985, 123, 49. (2) Engdahl, A.; Nelander, B. J . Phys. Chem. 1985, 89, 2860. (3) Engdahl, A.; Nelander, B. J. Phys. Chem. 1986, 90,4982. (4) Peterson, K. I.; Klemperer, W. J. Chem. Phys. 1986, 85, 725.
0022-3654/87/2091-2253$01.50/0
could be interpreted as evidence for a rapid interchange of the free and hydrogen-bonded proton (deuteron) in the H 2 0 (D,O)-benzene complex. Andrews and co-workers have studied the interaction between HF and a number of molecules related to the ones studied In most cases, they are able to observe the H F vibrations in addition to the shifted HF stretching vibration. This gives information about the shape of the potential energy surface close to the minimum. For the HF-benzene complex: Andrews et al. observe only one rather low HF libration band. They were therefore able to conclude that HF points to the center of the benzene ring and performs large-amplitude librations around its equilibrium position. The present investigation extends the studies of the interaction between water and unsaturated hydrocarbons to a series of methyl-substituted benzenes. We have also studied the benzene-water complex in krypton and nitrogen matrices and extended our previous study of water and benzene in argon over a larger temperature interval, using higher resolution.
Experimental Section The gas mixtures, except with penta- and hexamethylbenzene, were prepared with standard manometric techniques and sprayed on a CsI window kept at 17 K in a cryostat cooled by an Air Products CS208 refrigeration system. A benzene-HDO experiment in an argon matrix was run in a helium cryostat that has (5) Andrews, L. J . Phys. Chem. 1984,88, 2940. (6) Andrews, L.; Johnson, G. L.;Davis, S.R.J . Phys. Chem. 1985,89, 1706. (7) Patten, Jr., K. 0.;Andrews, L. J . Am. Chem. SOC.1985, 107, 5594. (8) Patten, Jr., K. 0.;Andrews, L. J . Phys. Chem. 1986, 90, 3910.
0 1987 American Chemical Society
