Car-Parrinello simulation of NH3 adsorbed on the MgO(100) surface

CHEMICAL

30 August 1996

PHYSICS LETTERS ELSEVIER

Chemical Physics Letters 259 (1996) 7 - 1 4

,

Car-Parrinello simulation of NH 3 adsorbed on the MgO(100)surface Walter Langel Fachbereich Chemie, Universitht Siegen, D 57068 Siegen. Germany Received 29 March 1996; in final form 25 June 1996

Abstract

The Car-Parrinello method has been applied the adsorption of ammonia on regular (100) surfaces of solid magnesium oxide. One N H 3 molecule was positioned on a surface consisting of three layers with four Mg and four O atoms in each. The samples were first subjected to simulated annealing up to temperatures in the range of 50-300 K and then to a free molecular dynamics run covering time intervals of 2 - 3 ps. N H 3 is physisorbed on the surface. The N atom is bound to the Mg but not centered above it, The dynamics of the NH 3 molecule are discussed in terms of three modes, a stochastic reorientation of the molecule around its figure axis, a nutation around an axis vertical to the figure axis, and the N - H stretching modes. The calculation confirms recent inelastic neutron scattering results, which indicate rotation-translation coupling and a low barrier to the rotational motion.

1. I n t r o d u c t i o n Magnesium oxide is a widely used high-temperature ceramic material. It crystallizes in well defined cubes o f rocksalt structure. The most stable surface of M g O is the (100) plane. The adsorption of small molecules on this surface is of considerable interest for several applications such as catalysis. Cluster calculations [1] aim at modelling the catalytic activity of metal atoms such as Li in the M g O matrix, In inelastic neutron scattering (INS) experiments, rotational tunnelling modes of adsorbed probe molecules are readily observed. The vast majority of the data is interpreted in terms of a single particle rotation of a molecule or a molecular group in a fixed external hindrance potential ([2] and references

therein). Due to the interaction with the surface these transition energies in general only amount to a small fraction of the corresponding free rotation energy. In the case of C H 4 [3] the transitions occur at 0 . 0 5 - 0 . 4 5 meV. (According to standard conventions neutron energy transfers will be given in meV and IR frequencies in c m - ~.) The correlated three-dimensional C H 4 r o t o r has a transition energy o f 2 B c n 4 .~- 1.31 meV, and the downshift was described by a single particle rotation with a barrier of 10.5 meV. INS experiments on NH 3 adsorbed on the (100) M g O surface revealed a nearly free rotation. The energy of the lowest transition is 0.61 m e V for isolated molecules and decreases to about 0.44 meV at higher coverages. These values are close to the energy o f BNH 3 = 0.782 m e V for the one-dimen-

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W. Langel/Chemical Physics Letters 259 (1996) 7-14

sional free rotor [4]. A total of five transitons were found, and the single particle rotation model did not allow a consistent description of all observed shifts, Havighorst and Prager [5] adopted an elegant formalism which had been developed in Refs. [6,7]. It provides a coupled motion consisting of a rotation of the molecule around its figure axis and an eccentric rotation of the molecule around a spatially fixed axis. For NH 3 on MgO this axis is vertical to the surface through the adjacent Mg atom, and this description is equivalent to the coupling of the rotational mode with translational modes of the Nil 3 molecule parallel to the surface. The shift of the molecular centreof-gravity with respect to this axis comes out from the model as 0.126 ,~ [5]. The barrier heights A 1 and A 2 for the rotation around the figure axis and the off-centre rotation, respectively, are 4.25 meV and 2.6 ixeV for isolated molecules, and increase to 14.6 meV and 7.76 p,eV if intermolecular interaction is present. The small values of these potential parameters seem to be in severe disagreement with IR absorption data [8-11 ] on this system which reveal hydrogen bonding between the ammonia H-atoms and the surface oxygen. This observation is consistent with observations on related systems such as H 2 0 on MgO ([12,13] and references therein), and should result in a strong anisotropy of the adsorption potential, A number of static calculations has been published o n NH 3 on MgO. The density functional approach [14] shows that positions of adsorbed NH 3 with its N atom linked to a surface Mg and the H atoms pointing outwards are energetically more favorable than those with the H atoms directed towards the surface, The highest adsorption energy is reported for the NH 3 figure axis in the z direction through a surface Mg. The contributions of such highly symmetric geometries to the real situation are in general overestimated in static calculations, since entropy effects cannot be taken into account. It was shown, however, that an inclined position of the NH 3 with the N atom displaced and two H atoms pointing to two surface oxygens also has a considerable adsorption energy [14]. Borve discusses a similar inclined geometry on Li-doped MgO [1]. Extensive calculations using empirical potentials [15] and periodic Hartree-Fock programs [16] confirm that the N atom points towards a surface Mg.

No consistent description of the IR spectra of N H 3 has been achieved from a normal coordinate analysis of these results, since at least the umbrella mode of NH 3, v 2, is highly anharmonic. This problem has been circumvented by rescaling the frequencies of the four normal modes of N H 3 by different factors. Moreover, no satisfying description of the dynamics of hydrogen bonds is possible in the harmonic approach, to which static schemes are restricted [13]. Here ab initio molecular dynamics simulations are reported on NH 3 adsorbed on a (100) MgO surface employing the scheme successfully tested [12,13], where the adsorption of H 2 0 hydrolysis both on perfect and defective surfaces, as well as the vibrational properties of the chemisorbed species, have been simulated. It was found that defects, in particular steps, play a crucial role in the hydrolysis process. Hydrogen bonding in the system was correctly reproduced by the calculation, which could account for the broadening and the strong red-shift of the O-H-stretching mode and confirmed the ad hoc model of adiabatic coupling [ 17,18]. In contrast to specific models such as adiabatic coupling the Car-Parrinello method is a general scheme for the interpretation of a vast number of experiments. For the present work the interest in this method consists in reconciling data as obtained from different spectroscopic methods. Static methods which aim at high-precision energy calculations of single atomic geometries do not include thermal motion. The evaluation of experimental quantities such as structure and dynamics from these calculations is severely constrained by initial guesses and simplifying models. A shortcoming of the Car-Parrinello approach with respect to the cited experimental data is that the ionic motion is described on the basis of classical mechanics, and that an interpretation of the tunnelling data is a priori impossible. However, lowtemperature tunnelling through a barrier is always correlated with a thermally activated motion across the same barrier at higher temperatures, which manifests itself in the classical trajectories. The layout of the paper is as follows. In Section 2 a short review of the calculation is given. Section 3 is subdivided into two parts treating the adsorption geometry and the dynamics. Section 4 contains a conclusion.

W. Langel / Chemical Physics Letters 259 (1996) 7-14

2. Details of the calculation The adaptation of the Car-Parrinello method to the H 2 0 - M g O system and pseudopotentials for Mg, O and H have been laid out [13]. For oxygen and hydrogen the Vanderbilt potentials from Refs. [12,13] have been adopted, and for nitrogen a new pseudopotential has been generated using the same method. The total energy of the nitrogen atom converged as well as had been observed for oxygen, and a cutoff energy of 25 Ryd for the plane wave basis was sufficient. For Mg a standard norm-conserving pseudopotentiai [ 19] was used instead. As in Refs. [ 12,13], a gradient correction was applied to the exchange energy of the electrons, Since it was intended to compare the results of the present simulation to neutron scattering data [4], the calculation was restricted to the perfect (100) type surface. Neutron scattering is not sensitive to minor quantities of adsorbed NH 3 on defects, since the signal roughly scales with the number of scattering centres. A (001) plane was generated by a slab oriented perpendicular to the z direction consisting of three (001) planes of 4 Mg and 4 0 atoms each. Cyclic boundary conditions in x and y direction were used to simulate an extended surface. In the xy plane the cell axis were in the (l 10) and ( - 110) direction. On top of the third layer one NH 3 molecule was positioned. It has been noted [20] that a three layer film is the thinnest sample, in which the charge densities of the atoms in the center layer are similar to those found in the bulk. The distance from the top of the upper layer to the top of the column is 3 lattice constants or about 12.7 ,~. This large free volume is needed to decouple each slab from its periodically repeated images in the z direction. The cell dimensions thus were 5.94 × 5.94 × 16.9 ,~3. Formally, one NH 3 on the MgO slab corresponds to a 2 × 2 adsorption layer with one out of four Mg atoms covered by a NH 3 molecule, since, in contrast to cluster calculations [1], the interaction of the adsorbed molecule with its next neighbours is taken into account by means of the cyclic boundary conditions. However, the surface in the supercell only contains 4 Mg and 4 0 atoms, and the next neighbours of the adsorbed NH 3 are its images rather than independently orientating molecules. For the IR data

9

in Refs. [8,11] coverages of 0.2 to 0.5 molecule Nil 3 per surface Mg were specified. Havighorst and Prager analyzed their data on the basis of isolated molecules. In the frame of their model an increase in the coverage does not affect the translation-rotation coupling and the eccentricity of the motion, but only induces an increase in the absolute barrier heights AI and A 2 [4]. The interaction of neighboring NH 3 molecules may result in a relaxation of their respective orientations, which cannot be modelled in the present approach. After guessing an initial nuclear configuration, the corresponding electronic charge densities were optimized starting from arbitrary wavefunctions by a steepest descent method. Using this converged electronic configuration, the optimized structures were determined by simulated annealing. Typically this meant heating the system during 5000 time steps from 3 K to a temperature between 50 and 300 K by rescaling ion velocities. Runs will be referred to by this final annealing temperature. After the annealing, which caused significant thermal fluctuation of all atomic coordinates a further run of 15000 steps was started without temperature control. The time step in all dynamic runs was 7 au or 0.169 fs, the tx parameter of the Car-Parrinello Lagrangian was 1100 au. This choice yielded a satisfactory energy conservation for all runs. The simulations thus cover time intervals of 2-3 ps. Due to the small system size, large fluctuations in the kinetic energy were observed. After heating up it varied usually by about a factor of two during the run. It could be seen, however, that crucial structure parameters, like the distance of the adsorbed molecule from the surface, were not drifting but fluctuating around a constant average value. The time intervals and cell sizes accessible to the present simulations are, however, too small for the observation of effective thermalization between different normal modes of the system, even in the case of anhannonic systems. Therefore, the results may to some extent reflect the choice of the initial conditions of the simulation. As the description of bulk MgO and of O - H bonds has been checked already [13], preliminary tests concentrated on the N atom and on NH 3. A pair potential acting between N and H was calculated, which describes in a satisfying way the bond dis-

W. Langel/ Chemical Physics Letters 259 (1996) 7-14

10

(~1)

3. Results

NH3I' i~

NHa a)

~--~/"~° 1

b)

,zanY' , ~ ~

O

23~J

Mg

',2~-ao

2" 22

2~5~2

2.~ w

Results were obtained from six free runs, which started from samples heated to temperatures of 50, 80, 100, 150, and 300 K (two runs). In none of the runs was dissociation of NH 3 observed. This is similar to the situation when adsorbing H20 on (001) MgO [12]. In general dissociation of NH 3 on MgO only occurs in the presence of metal atoms such as Li substituting lattice Mg [1]. In recent work on highly disperse MgO [22] absorptions above 3700 cm - 1 have been assigned to dissociated NH 3. I assume that this dissociation can only occur at highly active defects. Two different initial geometries were chosen. In two runs (I00 K and 300 K) the N H 3 molecule was positioned about 4 A above the MgO surface and had strongly deformed H - N - H angles between 80 and 140°. After a complicated relaxation pathway taking about 0.8 ps including a rotation of the molecule around an axis parallel to the surface a stable adsorption geometry of the N H 3 w a s attained, which is depicted in Fig. la and will be referred to as

~.J 2.1 w

O

O

Mg

O

(1(2~) ~ y Fig. 1. NH 3 on MgO: (a) H-bonded config I, (b) non H-bonded

configII.

tance of NH and the curvature around the minimum [21]. The bond angles and lengths of the free NH 3 molecule are close to the experimental values (Table 1). The calculated frequencies are lower than the observed ones by about 6-12%, which is a typical systematic error of the density functional aproach [13]. The consistent behaviour of all normal modes, including the umbrella mode v 2, indicates that the dynamics of the N H 3 molecule is correctly described,

Table I Numerical results for NH 3 in the gas phase and physisorbed on MgO. The calculated frequencies are unscaled

free NH 3 molecule this work experimental NH 3 on the MgO(001) surface this work, config I free O - H H-bonded this work, config II

N - H bond length

H - N - H angle

N - M g distance

M g - N - H angle

(.~)

(deg)

(~)

(deg)

1.04 1.014[27]

108.3 107.2[27]

1.03 1.1 1.22 [1] 1.03

114

2.2

84 100-130

111

2.27 [1] 2.3 2.4411]

106

2.55 [16] ~l

v3

v2

~'4

(cm - l )

(cm - i )

(cm - ' )

(cm - ' )

free NH 3 molecule this work static calculation [16] experimental

2930 3759 3307

3050 3955 3414

NH 3 on the MgO(001) surface this work, config I1 experimental [ 11]

2990 3270

3120 3360

890 620 950

940 1065-1080

1500 1820 1627

1500 1600-1630

W. Langel / Chemical Physics Letters 259 (1996) 7-14

config I. One N - H group of the NH 3 molecule is aligned to an M g - O bond in the surface, the N atom pointing to the Mg. The respective hydrogen atom approaches the adjacent O atom within 1.5 A, inducing an elongation of the corresponding N - H bonds from 1.03 to 1.1 A. The H - N - H angles are slightly larger than in the free molecule due to the attraction of ammonia H and surface O. The N-H..O angle is close to 180°, and the O - H distance is only 1.6 ,~. Comparison with the results of the M g O - H 2 0 system shows that this geometry is typical for hydrogen bonding. Due to this hydrogen bond the molecule is strongly inclined with respect to the N - M g axis. The distance between the Mg and the O is elongated due to the interaction with the N H 3 molecule. A similar configuration has been proposed by Borve [1]. The N - M g distance is similar to the Mg-O bond length in the crystal. The N atom is close to a surface Mg but not precisely vertically above it, the shift in the xy plane amounting to about 0.7 .~. In the strictly vertical position one of the three M g - N - H angles would decrease significantly below 90 ° due to the attraction between the H and the surface O. Results for the M g - O - H angle in H 2 0 on MgO [12,13] suggest that this may be energetically unfavorable. A further four runs started from configurations in which not only the electronic wavefunctions were equilibrated but also the nuclear positions were relaxed (config II, 50 K, 80 K, 150 K, and the second 300 K run, Fig. lb). As in config I, the N atom points to the surface, but all O - H distances are always greater than about 2.5 A and none of the N - H bonds was significantly stretched. Thus no significant hydrogen bonding is found in this geometry, and the molecular axis was only slightly inclined. NH 3 was still not in a vertical position on top of the MgO, the shift being only 0.2-0.3 A in this configuration. The M g - N distance is slightly relaxed here with respect to config I (2.3 versus 2.2 ,~, Table 1). In Ref. [1] values of 2.27 and 2.44 fk are quoted for inclined and vertical positions, respectively, In Ref. [14] two similar configuration were considered, one with NH 3 centered vertically above a surface Mg and one, in which the NH 3 molecule was strongly inclined with two H atoms directed towards two surface oxygens. Both configurations are ener-

11

05 04 5 .~ ~03 b) config fl -~

~o.2 :~

~

~01

~

-

-

-

-

-

]

a) c

2000

2500

3000

3500

/cm-1 Fig. 2. Density of states of the N - H stretching mode for the T= 100 K simulations. (a) H-bonded config 1, (b) config I1

without H-bondcontribution.

getically more favorable than those with the hydrogen atoms directed towards the surface. The first structure corresponds to config II, but config I is an intermediate case of the geometries studied in Ref. [14]. The figure axis of the molecule is indeed inclined, but only one H atom points towards a surface O.

3.1. Dynamics In this section the motions of the adsorbed NH 3 molecule are extracted from the dynamic simulations and compared with experimental data for the N - H stretching modes and for the rotational tunnelling and nutation of the NH 3 molecule. The calculated densities of states in the IR range for config II are similar to those of the free NH 3 molecule. The N - H stretch is clearly split into two major components (Fig. 2b), which are assigned to u~ and v 3, and no significant contributions of hydrogen bonding to these spectra was found, in agreement with structural considerations. In contrast, hydrogen bonding is reflected in the calculated densities of states of config I, since a broad intensity is found extending from 3000 down to 2400 cm -1 (Fig. 2a). The experimental studies on the IR spectra of adsorbed NH 3 on dehydroxylated MgO are consistent [8-11 ]. Both the broadened and slightly shifted modes of the free molecule and the spectrum of the

12

W. Langel / Chemical Physics Letters 259 (1996) 7-14

180 gO c) o

-g0

-18°0

½ t / ps

Fig. 3. Angles of orientation with respect to the (1, - 1, 0) direction for the T = 100 K run (config I) as a function of simulation time: (a) projection of the N-H1 bond onto the xy plane (see Fig. 4), (b) projection of the N - M g bond onto the xy

plane, (c)as (b), but anglesdividedby -3.

hydrogen bond were found when adsorbing NH 3 on dehydroxylated MgO (Fig. 2 in Ref. [11]). There is no obvious correlation between coverage and amount of hydrogen bonding (Fig. 1 in Ref. [8]). In each simulation run the NH 3 molecule started a continuous rotational motion during annealing. The occurrence of rotation at higher temperatures is consistent with the experimental low-temperature tunnelling spectra of isolated molecules [4]. Here the corresponding thermally activated rotational diffusion is revealed by the simulation. This motion is composed of two rotations, one of the H atoms around the molecular figure axis and one of the whole molecule around the z axis through the adjacent Mg (dashed-dotted lines in Fig. 1). They are traced evalU byoxy n planeatingthe lengths of the projections the of the connections from the surface Mg atom to the N atom and to the centre of the three H atoms on the xy plane, respectively, as a function of time. In the runs with config I and in the run with config II at 50 K these two rotations are correlated (compare Fig. 3): - the centre of mass characterized by the N atom always rotates in the r e v e r s e s e n s e from the H atoms, - the modulus of the centre of mass angular velocity is always three times greater than that of the internal rotation, This correlated motion is explained on the basis of Fig. 4 which represents a snapshot of the calcu-

lated trajectory where N and one H (HI) are aligned to the (1, - 1, z) direction. This corresponds to the time interval around 1.5 ps in Fig. 3. An energetically equivalent position can be obtained by rotating the N atom by + 90° around the z axis, and simultaneously the H-triangle by - 3 0 ° around the NH 3 figure axis. Now H2 is pointing towards an oxygen and H1 is rotated by - 3 0 °, which corresponds to the situation at t = 2.1 ps in Fig. 3. The system is not stable in this orientation, N-H2 in the (1, 1, z) direction, but oscillates back, passing through the original configuration at t = 2.6 ps and reaches a third equivalent orientation with N-H3 aligned along the ( - 1, - 1, z) direction (t = 3-3.3 ps). Projected into a plane parallel to the surface this is the motion modelled in the rotation-translation coupling model [6], which was applied to the tunnelling spectra [5]. The potential surface used there provides four minima for the position of the N atom and three minima for the position of the H atoms, which are correlated to the position of the N atom. The correlated motion proceeds along a valley of this surface, i.e. avoids crossing of the large barrier A I. From the tunnelling experiment alone it was deduced that the three protons of the NH 3 molecule are redistributed over four preferred positions at the comer of a square (Fig. 3 of Ref. [5]), but the orientation of this square with respect to the MgO surface could not be assigned. The simulation shows

~

~,.~\ /, ""2× ~ J ~ N /7" O ~ ~ / )+f 9~ 0, ~~ ~' ~ O - . ~ - - ~ ~ _ ~ ""

.~. .

~

~ ,,~.,

~\~ ~

Fig. 4. Config I, looking from z direction. The adsorption site consists of one Mg in the centre and four surface O atoms coordinated to it. The N - M g connection is aligned in (1, - 1, z) direction, as well as one of the N - H bonds (N-H1). A neighbouring energy minimum is attained by aligning N - M g in (1, 1, z) direction, i.e. rotating the N atom by + 90* around the symmetry axis of the site on the large circle. At the same time the NH 3 rotates on the small circle in opposite sense by - 3 0 * around its figure axis for aligning the N-H2 bond 1~(1, 1, z) direction.

W. Langel / Chemical Physics Letters 259 (1996) 7-14

15

1 config I ~ . ~ ~ ~ "

N ~'. .-z ~ C~0.5 ~'" . . . . :,. %.

o.

a

100 K

daa a

.~. *~ 00

signal thus is tentatively assigned to this nutation. Further INS experiments should be carried out in order to reproduce the tunnelling transition and the l0 meV feature in the same experiment on the same sample. The calculated spectra for the nutations in config I and II are similar (Fig. 5). The main difference is that the equilibrium orientation for this nutation in config II is only inclined by about 10° with respect to the z axis, so that oscillations through the vertical orientation are observed.

®°

.'-. •

13

'

160 K

*¢.~ _ * * ~ _ ~ E / meV

Fig. 5. Low-frequency vibrations in simulation and thermal neutron spectra. (a) Spectra of the N atom translations in x and y directions for config If, (b) as (a), config l, (c) neulron energy loss spectrum of NH 3 on MgO [23], T = 40 K, (d) neutron energy gain spectrum of NH 3 on MgO [24], T = 100 K, (e) as (d), T = 160 K.

that the H atoms are attracted by the four O atoms around the central Mg, to which the N is linked. The correlation of the two rotations is strict in the case of config I even at 300 K, since there the O..H attraction is strong. For config II the correlation exists in the 50 K run but not in the 80, 150, and 300 K runs. At higher temperatures the thermal motion overrides the small O..H attraction in this configuration. The evaluation of absolute attraction energies and barrier heights from the present calculation is not obvious, since the total potential energy, which comes out of the calculation, cannot be split up into pair interactions, In addition to the tunnelling spectra, two earlier INS experiments on a sample of NH 3 on disperse MgO powder [23,24] revealed a broad but intense feature around 10 meV (Fig. 5). A low-frequency nutation of the molecules in the simulation is found in the same spectral range at about 13 meV. It is identified here by evaluating the spectrum of the linear motions of the N atom in x and y direction but will also involve a motion of the hydrogen atoms which is seen in the neutron spectrum. The neutron

4. Conclusion The present calculation allows us to describe the physisorption of NH 3 on MgO and to reproduce experimental data from various approaches. Some calculations treat the NH 3 molecule by classical molecular dynamics on the basis of empirical pair potentials [15,25]. This approach w i l l n o t b e s u f f i c i e n t to describe the interference of hydrogen bonds which are essential for the understanding of the adsorption of molecules such a s NI--I 3 and H 2 0 on metal oxides. Two adsorption geometries were stable under the conditions of the simulation. In both, the N of the NH s points towards a surface Mg but in one the H-atoms are not interacting strongly with the surface, whereas the other has strong O..H hydrogen bonding. The rotation-translation coupling which has been postulated ad hoc for explaining the level spacing in the INS rotational tunnelling experiment, is confirmed by an independent approach. As the surface and the molecule have four- and three-fold symmetries, respectively, only one proton at a time can be attracted by the surface oxygen, leading to an asymmetric position of the N atom. The four preferred sites of the protons, which have been postulated earlier, are related to this O..H attraction. The present simulation cannot cover a sufficiently large time interval to establish the stability of one or the other adsorption configurations. The tunnelling data indicate weak attraction of the NH 3 protons and the surface O atoms since the eccentricity is rather small. It is overestimated by the calculation, but

14

W. Langel // Chemical Physics Letters 259 (1996) 7-14

config II fits much better. The experimentally observed correlation of the two rotations around the molecular figure axis and the vertical axis through

the surface Mg can be reproduced in both configurations at the low temperatures of t u n n e l l i n g experiments.

The IR experiments which clearly favour the hyd r o g e n - b o n d e d config I have all b e e n performed at room temperature. Recent experimental work on H 2° on MgO has revealed dramatic changes in the IRspectra w h e n reducing the temperature [26]. It thus

cannot be excluded that strong hydrogen bonding occurs at higher temperatures, whereas at low tern-

perature the absence of hydrogen bonds enables nearly free rotation.

Acknowledgement I thank Dr. Markus Havighorst and Dr. Michael Prager, Jtilich, for m a n y fruitful discussions and the

Deutsche Forschungsgemeinschaft for a Heisenberg Fellowship. The calculations were performed on an I B M 6000/350 workstation of the Fachbereich C h e m i c der Universit~it Siegen.

Refel'ence$ [1] K.J. Bcrve, J. Chem. Phys. 96 (1992) 6281. [2] M. Prager and A. Heidemann, Compilation of rotational tunnelling data, Chem. Rev., submitted for publication. [3] J.Z. Larese, J.M. Halstings, L. Passell, D. Smith and D. Richter, J. Chem. Phys. 95 (1991) 6997. [4] M. Havighorst, M. Prager and G. Coddens, Chem. Phys. Letters 222 (1994) 113.

[5] M. Havighorst, M. Prager and G. Coddens, Chem. Phys. Lett., this issue; M. Havighorst, Ph.D. Thesis, RWTH, Aachen (1995). [6] M. Kolarschik, Thesis, FAU, Erlangen (1995). [7] P. Schiebel, A. Hoser, W. Prandl, G. Heger, W. Paulus and P. Schweiss, J. Phys. C 6 (1994) 10989. [8] A.J. Tench and D. Giles, J. Chem. Soc. Faraday Trans. 1 68 (1972) 193. [9] S. Coluccia, E. Garbone and E. Borello, J. Chem. Soc. Faraday Trans. 1 79 (1983) 607. [1o] R. Echterhoff and E. KnSzinger, Surface Sci. 230 (1990) 237. [11] S. Coluccia, S. Lavagnino and L. Marchese, J. Chem. Soc. Faraday Trans. I83 (1987)477. [12] w. Langel and M. Parrinello, Phys. Rev. Lett. 73 (1994) 504. [13] W. Langel and M. Parrinello, J. Chem. Phys. 103 (1995) 3240. [14] S. Pugh and M.J. Gillan, Surface Sci. 320 (1994) 331. [15] S. Picaud, A. Lakhlifi and C. Girardet, J. Chem. Phys. 98 (1993) 3488. [16] A. Allouche, F. Cor~ and C. Girardet, Chem. Phys. 201 (1995) 59, 72. [17] S. Bratos, J. Chem. Phys. 63 (1975) 399; S. Bratos and H. Ratajczak, J. Chem. Phys. 76 (1982) 77. [18] S.A. Barton and W.R. Thorson, J. Chem. Phys. 71 (1979) 4262. [19] R. Stumpf, X. Gonze and M. Scheffler, A list of separable, norm conserving, ab initio pseudopotentials, Research Report of the Fritz-Haber Institute (1990). [20] C.A. Scamehorn, A.C. Hess and M.I. McCarthy, J. Chem. Phys. 99 (1993) 2786. [21] S.N. Suchard, ed., Spectroscopic data, Vol. 1. Heteronuclear diatomic molecules (IFI Plenum, New York, 1975). [22] K.-H. Jacob, Ph.D. Thesis, GHS, Siegen (1992). [23] w. Langel, K.-H. Jacob and J. Tomkinson, unpublished results. [24] W. Langel, W. Schuller and G. Kearley, unpublished results. [25] D. Paschek and A. Geiger, Proceedings of the 1st European Conference on Computational Chemistry, Nancy (1994). [26] J. Heidberg, B. Redlich and D. Wetter, Ber. Bunsenges. Physik. Chem. 99 (1995) 1333. [27] K.-H. Hellwege, ed., Landolt-BSrnstein, Vol. 7. Structure data of free polyatomic molecules (Springer, Berlin, 1976).