9774
J. Phys. Chem. 1992,96, 9774-9781
(1 1) AlmlBf, J.; Faegri, K.,Jr.; Feyereism, M. W.; Fischer, T. H.; Korsell, K.;Ltithi, H. P. DISCO, a direct SCF and MP2 code. (12) Fletcher, R. Practical Methods of Optimization; Wiley: New York, 1980; Vol. 1. (1 3) Pulay, P. Mol. Phys. 1969, 17, 197. (14) Califano, S . Vibrationul Stares; Wiley: New York, 1976; Chapter 4. (15) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J. Am. Chem. Soc. 1979, 101, 2550. (16) Baker, J.; Hehre, W. J. J. Comput. Chem. 1991, 12, 606. (17) Frisch, M. J.; Head-Gordon, M.; Schlegel, H. B.; Raghavachari, K.; Binkley, J. S.;Gonzalez, C.; DeFrees, D. J.; Fox, D. J.; Whiteside, R. A.; Seem. R.: Melius. C. F.: Baker. J.: Kahn. L. R.: Stewart. J. J. P.: Fluder. E. fi.;Topiol, S.;Pople, J. A. Gaussian 88; Gaussian Inc.:' Pittsburgh, PA; 1988. (18) Amos, R. D.; Rice, J. E. CADPAC: The Cambridge Analytic Deriuatives Package; issue 4.2, Cambridge, 1990. (19) Carpenter, J. E.; Baker, J.; Hehre, W. J.; Kahn, S.D. The SPARTAN System, 1990.
(20) Hehre, W. J.; Stewart, R. F.; Pople, J. A. J . Chem. Phys. 1969. 51, 2657. (21) Binkley, J. S.;Pople, J. A.; Hehre, W. J. J . Am. Chem. Soc. 1980, 102, 939. (22) Francl, M. M.; Pietro, W.J.; Hehre, W. J.; Binkley, J. S.;Gordon, M . S.; DeFrm, D. J.; Pople, J. A. J . Chem. Phys. 1982, 77, 3654. (23) van Duijneveldt, F. B. IBM Publication RJ 945 (No. 16437). (24) Diercksen, G. H. F.; Krimer. W. Chem. Phys. Letr. 1970, 6, 419. (25) Dewar, M. J. S.;Thiel, W. J . Am. Chem. Soc. 1977, 99, 4899. (26) Allen, F. H.; Bellard, S.;Brice,M. D.; Cartwright, B. A.; Doubleday, A.; Higgs, H.; Hummelink, T.; Hummelink-Perrers, B. A.; Kennard, 0.; Mothmvell, W. D. S.;Rodgen, J. R.; Watson, D. A. Acta Crysfallop.,Secr. B 1979.35. 2331. (27)'Dunning, T. H. J . Chem. Phys. 1970, 53, 2823. (28) Sellers, H. Chem. Phys. Lett. 1991, 180, 461. (29) Fischer, T. H.; Ghosh, A.; AlmlBf, J.; Gassman. P. G. J . Am. Chem. Soc. (in press). (30) Head-Gordon,M.; Pople, J. A.; Frisch, M. J. Inr. J . Quantum Chem., Symp. 1989, 23, 291.
Structure, Spectra, and Stability of Ar2H+, Kr2HS,and Xe2H+: An Effective Core Potential Approach Jan Luodell**+and Henrik Kunttu*Si Departments of Physical Chemistry and Medical Chemistry, University of Helsinki, SF-001 70 Helsinki, Finland (Received: May 22, 1992)
The molecular properties of Ar2H+,Kr2H+,and Xe2H+are studied in their electronic ground states by ab initio methods using the effective core potential approach or all-electron methods employing the STO-3G* and 6-31G** Gaussian basis sets. Linear structures are obtained for these ions at all levels of computational theory. The lowest energy geometry is that where hydrogen is located between the rare gas atoms: for KrzH' and XeH', this structure is centrosymmetric &), whereas for Ar2H+some of the calculations show unequal Ar-H distances. The collinear Rg(Rg-H)' local minimum, possessing a " a 1 amount of charge delocalization among the rare gas atoms, was found to be 0.2-0.4 eV higher in energy. Predictions concerning the vibrational frequencies of the different structures are made. For all three species, the calculated us and U, frequencies support the experimental assignments. Based of the potential energy surface computed for Ar2H+,an isomerization mechanism involving the correlated motion of the nuclei is suggested as the origin of the observed thermal instability of these ions.
I. Introduction Ionic rare gas clusters have become the subject of a vigorously expanding field of research during the recent years. The advent of experimental procedures such as supersonic expansions and time-of-flight techniques has greatly enhanced the feasibility of experiments of high size selectivity.'" From the theoretical viewpoint, a significant computational effort toward a rigorous understanding of these systems at the microscopical level has been pursued.' Particularly, ionic clusters trapped in condensed phases provide a rather fascinating interface between isolation and continuous matter and, as such, enable a detailed insight to a wide variety of many-body interactions involved in chemical reaction dynamics in general. Moreover, the mundane issue of energy storage is closely tied to these highly energetic s p e c k 8 In the preceding paper, herein referred to as 1: we demonstrated that delocalized charge-transfer excitationsin solid xenon, multiply doped with atomic halogens (I, Br, C1) and hydrogen, lead to permanent charge separation by trapping of the positive charge. The trapped state was ascribed to.a triatomic Xe2H+molecular ion, a member of a larger family of ionic clusters of the form Xe,H+ recently described in the framework of diatomics in ionic systems (DIIS) by Last and George.Io In analogy with the isoelectronic species IHI-,"*'* the observed prominent progression of absorptions in the 700-1200-cm-' region was assigned to a u3 DeDartment of Phvsical Chemistry. *Department of Mkical Chemistry. I Permanent address: Department of Physical Chemistry, University of Helsinki, SF-00170 Helsinki, Finland.
+ nv1 (n = 0-4) progression of combination bands of a linear (Xe-H-Xe)+ ion of D,,h symmetry. Once this species was generated, its spectral features were found to be virtually insensitive to the type of halogen in the initial parent, HX (X = I, Br, Cl), molecule. The proposed geometry is, indeed, in deep contrast with the recent DIIS computation predicting a linear structure composed of a deeply bound XeH+ unit loosely bound to a essentially neutral Xe atom on the rare gas side.'O One of the most interesting findings presented in 1 is the observed decomposition of Xe2H+ in the dark at temperatures near 10 K. Quite interestingly, this process was observed for the protonated ion only. Although not completely understood, the dark decay of X%H+ absorptions was, a priori, ascribed to a tunneling mechanism involving the internal coordinate of the ion. The early matrix isolation data on Ar2H+ and Kr2H+showed the same kind of thermal in~tabi1ity.I~ Most of the theoretical approaches concerning ionic rare gas-hydrogen clusters limit themselves to a description of argon ~pecies?,~~.'~ The most recent ab initio treatment by Rosenkrane gives the optimized geometries of ArH+,Ar2H+,and Ar4H+using several h i s sets at different levels of computational theory. Also, predictions of the harmonic vibrational frequencies are given. Even for the triatomic ion, the optimized structure is not, however, stable at all levels of approximation. For the heavier rare gases, the current literature is more sparse, and ab initio investigations exist for the experimentally known diatomic KrH' and XeH+ ions only. Nevertheless, the detailed studies by Rosmus and co-workers'618 utilizing highly correlated SCEP/VAR (self-consistent electron pair approach yielding variational results) and SCEP/CEPA (coupled electron approach) methods are in excellent agreement
0022-3654/92/2096-9774$03.00/0 0 1992 American Chemical Society
Molecular Properties of Ar2H+,Kr2H+,and Xe2H+ TABLE I: Molecular Constants of Structure I (De,+) of Ar2H+at Different Levels of Theory basis set RArn, A h' 4H' E, au MP2/6-31G** HF/ECP MP2/ECP HF/ECP* MP2/ECP* MP2/ECP** MP2/WBP
1.4943 1.6271 1.6247 1.6052 1.6106 1.6104 1.5395
0.337 0.222 0.243 0.261 0.260 0.266 0.205
0.327 0.556 0.518 0.479 0.479 0.468 0.590
-1054.0038b -41.6857 -41.6977 -41.6928 -41.7366 -41.7443 -41.9195
'Partial charge on the individual atom. b A full ab initio treatment, electronic energy not comparable with the calculations utilizing the effective core potentials (see text for details).
with the experimental spectra and structure. The purpose of the present paper is 2-fold. First, the purpose is to provide a critical evaluation of the effective core potentials currently available for the rare gas atoms. Extensive ab initio calculations within the effective core potential approach are performed for Ar2H+,Kr2H+,and X@H+and compared with full ab initio treatments at the HF/STO-3G*, HF/6-31G**, and MP2/6-31G** levels. The issues of main interest here are the equilibrium structures, the vibrational spectra, and the distribution of the positive charge among the individual atoms. Second, in order to unravel the origin of the observed thermal decay of Rg2H+ absorptions in low-temperature matrices,dissociation energies are computed for the triatomic hydride ions. Finally, a potential energy surface along the hydrogen motion is presented for Ar2H'. The experimental results on the spectroscopy and dynamics of Ar2H+and Kr2H+isolated in solid Ar and Kr, respectively, will be reported in a forthcoming paper.lg
11. Computational Details Except for the STO-3G* and 6-31G** basis sets, an effective core potential approach with a restricted number of electrons was utilized in all computations. Two sets of effective core potentials were chosen for the present study, namely, the quasi-relativistic core potentials (LANLlDZ) introduced by Hay et a1.2h22and the relativistic core potentials (ECP) optimized by Christiansen and ~ o - w o r k e r s . ~The ~ - ~principal ~ difference between these core potentials is the number of electrons considered for the valence shell. In the ECP formalism, the accuracy of the calculation is improved by including a d subshell into the valence space of the heavier rare gases, Kr and Xe (total of 18 valence electrons), whereas the LANLlDZ approach describes all rare gas atoms with 8 valence electrons. For the sake of consistency, the Dun-
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9775 ning-Huzinaga valence double-{ (D95V)26*27 basis set was employed for hydrogen with both sets of core potentials. The calculations performed with these procedures will be hereafter referred to as LANLlDZ and ECP, respectively. The ECP basis set was further improved by including ptype polarization functions on Ar and Kr and d-type polarization functions on Xe. The scaling factors of the functions were op timized with respect to the energy minima of the diatomic rare gas hydride ions, RgH' (Rg = Ar, Kr, Xe). As wellcharacterized gas-phase s p e c i e ~ , ZRgH' ~ * ~ ~ions provide a good reference point between experiment and theory. The following factors were o b tained: ap(Ar)= 0.59, a,(Kr) = 1.88, and ad(Xe) = 0.34. This basis set will be referred to as ECP*. Furthermore, a second polarized basis set, ECP**, was designed by including two sets of polarization functions on the rare gas atoms with factors: apl(Ar)= 0.39, at(Ar) = 0.38, ap'(Kr)= 2.47, a:(Kr) = 0.77, adl(Xe) = 0.32, and q2(Xe) = 0.29. Also in this case,the scaling factors were obtained by minimizing the electronic energy of RgH'. Note that although the factors of the ppolarization functions on Kr are rather large, further optimization of d-polarization functions for Kr did not converge to a minimum in the total electronic energy. Finally, a recent developed balanced atomic basis set by Wallace et al.30was applied for Ar. This optimized Gaussian basis set includes d polarization within a relativistic core potential approach and will be referred to as WBP. Interelectronic correlation was considered via Morller-Plesset perturbation theory to the second order (MP2). All calculations were carried out using the GAUSSIAN 90 package of algorithms3' on CRAY X-MP/EA 432, CONVEX C 220, and V A X 8650 computers at the Centre for Scientific Computing (Espoo,Finland).
III. Results and Discussion Ar2H+. The geometry optimization for Ar2H+yielded three distinct linear minimum energy configurations, namely, a centrosymmetric (Ar-H-Ar)+ structure, an asymmetric (Ar-HAr)' structure with unequal Ar-H distances, and a collinear Ar-(Ar-H)+ structure possessing a minimal extent of delocalization of the positive charge. The molecular constants of these structures,referred to as structures 1-111, respectively, are collected in Tables I and 11. Our attempts to establish the existence of any nonlinear form of Ar2H+failed-even when optimization was started from a nuclear configuration recently proposed as the equilibrium structure of this ion.1° Note that although observed by mass spectrometry, there is no experimental input concerning the structure of Ar2H+ in the gas phase. As pointed out by
TABLE II: Molecular Constants of Structures I1 and IU of Ar2Ht at Different LeveLs of Theory basis set RAr(I)-H R.4r(2)-H P, D %I ) qAr(2) (ArI-H-Ar2)+ (Structure 11) HF/6-31G** 1.3364 1.8244 2.68 0.483 0.165 HF/LANLl DZ 1.4082 1.8774 0.167 2.32 0.390 1.5185 1.7080 0.98 0.333 MP2ILANLlDZ 0.237 HF/ECP** 1.4899 1.7484 1.39 0.328 0.196 HF/WBP 1.4304 1.7235 1.54 0.259 0.149 basis set RAI-A~ RAI-H P, D %I ) 4.w) Arl. ..(Ar2-H)' (Structure 111) HF/6-31G** 3.5326 1.2668 10.46 0.004 0.533 MP2/6-31G** 3.3101 1.2672 9.79 0.010 0.545 HF/LANLlDZ 3.7739 1.3156 12.05 0.001 0.463 MPZ/LANLlDZ 3.6800 1.3292 11.87 0.002 0.458 HF/ECP 5.0400 1.3711 15.69 0.0oO 0.357 MP2/ECP 4.8549 1.3702 15.25 0.0oO 0.357 HF/ECP* 3.6881 1.3396 12.00 0.007 0.425 MP2/ECP* 3.4842 1.3512 11.54 0.010 0.421 HF/ECP** 3.7614 1.3337 12.10 0.008 0.442 MP2/ECP8* 3.4962 1.3456 11.49 0.012 0.439 HF/WBP 3.6406 1.3058 11.49 0.001 0.348 MP2/WBP 3.4408 1.3072 1 1.oo 0.001 0.348 expt 1.2804b
4n
E, au
0.352 0.443 0.430 0.475 0.592 4n
-1053.6916' -41.4539 -4 1.5 160 -41.6971 -41.7088 E, au
0.462 0.445 0.535 0.540 0.643 0.643 0.568 0.569 0.550 0.550 0.652 0.651
-1053.6842' -1053.9886' -41.4458 -41.5080 -4 1.6722 -41.6832 -41.6843 -41.7250 -41.6904 -41.7339 -41.6974 -41.9036
' A full ab initio treatment. electronic energy not comparable with the calculations utilizing the effective A r e potentials (see text for details), *Experimental bond length of ArH' (ref 32).
9776
'%'
u
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992
1\
0.8
3k 0.6/
\
8
o)
0.4
\
2
0.2
/
0.0 -0.60
-0.40
-0.20
0.00
0.20
0.40
0.60
H displacement [i] Figure 1. Double minimum potential of Ar2H+obtained at the HF/631G**level. The x axis displays the relative position of hydrogen along the Ar-Ar internuclear axis with an origin at symmetric Ar-H distances. The Ar atom are fixed to their equilibrium positions (RAFh = 3.16 A) corresponding to the two equivalent minima. The solid point indicates the energy of the optimized saddle point (15 meV) at RArh = 3.06 A.
Rosenkrantz: the symmetric structure for ArzH+is obtained only at a fairly high level of theory: except for the ECP and ECP* basis sets, all of our SCF computations converged to asymmetric structure 11. Structure I is characterized by a Ar-H distance significantly larger than 1.28 A, which is experimentally determined for the diatomic ArH+ ion.32 In fact, the Ar-H separation in structure I is reasonably close to the 1.55-A CI-H equilibrium distance in HC12-,33a species isoelectronic with Ar2H+. For comparison, the equilibrium distance of the ground 22,state Arz+ is 2.48 A,34whereas the van der Waals separation in Arz is 3.76 A.35The given numbers would imply that trapping of structure I in an argon lattice would be associated with only moderate lattice distortions within the vicinity of the ionic center. The computed distribution of the positive charge in structure I rather consistently shows that ca. 50-60% of the charge resides on hydrogen. However, the calculation at the MP2/6-31G** level yielded a virtually uniform distribution of the charge among the individual atoms which, indeed, correlates with the somewhat tighter structure obtained at this level. The Ar-Ar separation in asymmetric structure I1 closely resembles that of the symmetric geometry, being -3.2 A. However, the two Ar-H distances differ significantly. This is, in fact, also clearly observed in the charge densities calculated for this geometry. Although the distribution of the excess positive charge shows quite severe variation between different theoretical approaches, all calculations yield a rather consistent picture where -80% of the charge is borne by the tighter Ar-H unit in structure 11. As shown in Figure 1, the two equivalent minima in structure I1 are separated by a maximum at the center of the Ar-Ar internuclear distance. The computed height of this barrier was found to be less than 20 meV (160 cm-I) at all levels of theory, showing a double minimum potential. It is interesting to note that, indeed, the potential energy surface for one-dimensional motion of hydrogen between the Ar centers has similarities with the C1+ HCl system, a member of the extensively studied family of vibrationally bound heavy-light-heavy (HLH) molecules. For the adiabatic ClHCl molecule existing on a minimum free potential energy surface, the saddle point energy is, however, an order of magnitude higher36than the values predicted by the present computations for Ar2H'. Furthermore, the experimental frequency of 903 cm-' for the asymmetric stretchl3.I9would place the zero-point energy of Ar2H+way above the barrier. The obvious implication would then be that, in fact, in this case optimization of the equilibrium structure by ab initio means resolves the locations of potential energy minima rather than gives the structure of the molecule: the real molecule possessing zero-point motions of the individual nuclei would still be symmetrical! Nevertheless, an interesting issue would be the extent of perturbation experienced by the u = 0 wave function due to the potential barrier located in the center of the potential well. This could, in principle, be one possible source for the anomalously strong coupling between v3 (asymmetric
Lundell and Kunttu stretch) and v 1 (symmetric stretch) observed for ArzH+,Kr2H+, and Xe2H+.9*'9 All calculations performed for Ar2H+indicate an existence of structure 111, Le., a tight ArH+ unit loosely bound to a neutral Ar atom on the Ar side of the diatomic. Depending on the level of theory, the total electronic energy of structure 111was found to be higher than that of structure I or structure I1 by 0.2-0.4 eV. The fact that the computations utilizing the effective core potential approach predict the Ar-H distance in structure I11 to exceed the bond length of ArH+, 1.28 A,32is purely due to the limited accuracy of the theory: calculations on ArH+ (not included in this paper) resulted in virtually identical Ar-H distances as obtained for structure 111. Also in this case, the 6-31G** basis set (SCF and MP2) predicts a considerably tighter and presumably more realistic structure. In conclusion, the weak k A r interaction seems to have a negligible effect on the deep (Ar-H)+ potential as well as on the charge distribution. In the Ar-(Ar-H)+ geometry, the positive charge is entirely borne by the ArH+ fragment. This has obviously a drastic influence on the dipole moment of this species: all of our calculations predict dipoles exceeding 10 D for structure 111. It is worth noting in this context that solvation of such a large dipole by host dielectric in the Ar matrix would have serious bearings with respect to the spectroscopy and energetics of this ion. The stability of ArzH+was investigated at the MP2/WBP level. According to this calculation, the (Ar-H-Ar)+ ArH+ Ar dissociation asymptote is characterized by De = 0.852 eV. This would mean significant stabilization of the triatomic ion with respect to ArH+, thus explaining the experimental observations, viz. the gas-phase detection of ArzH+, and the fact that ArH+ does not exist in solid Ar.I9 As already discussed, the second argon atom in the Ar...(Ar-H)+ structure carries a negligible fraction of the charge, reflected as a dissociation energy of only 14 meV for Ar detachment. The calculated De is, indeed, an order of magnitude smaller than that predicted for the proposed nonlinear geometry.I0 This discrepancy may be due to the weakness of the present calculations to accurately describe long-range interactions such as dispersion and polarization. The other dissociation limit, Le., the (Ar-H-Ar)' AT2 H+ proton abstraction, was found to involve a De for 3.727 eV. As will be discussed further, Ar2H+ is unique among the RgzH+ ions included in the present study since the Ar2 H+ asymptote is expected to lay below Arz+ H(2S). This conclusion is based on the fact that the adiabatic ionization potential of Arz (considering the 1.3-eV binding of the ground state Ar2+),14.4 eVP7exceeds that of hydrogen (13.6 eV). The given numbers would locate the Ar2+ + H(%) limit -0.8 eV higher in energy. A rather mundane issue concerning the dynamics of Ar2H+ in the Ar matrix is whether the obtained energetics is retained in the solid state as well. Note that the threshold for photoelectron emission in crystalline Ar is 13.9 eV.38 In order to search for the origin of the observed slow decay of Ar2H+absorptions in solid argon at temperatures near 10 K,I3J9 the potential energy surface along the hydrogen motion was computed at the HF/WBP level. In this scan, the Ar nuclei were frozen at their equilibrium positions, while the H position was used as a variable. As clearly seen in Figure 2, the perpendicular proton exit is prevented by a barrier exceeding the zero-point energy by almost 2 orders of magnitude. Nevertheless, only -0.3 eV of energy is needed for the hydrogen to access an equipotentialwhere essentially free rotation around one of the Ar atoms would be enabled (see the arrow in Figure 2). This equipotential, located 1.3 A from Ar, describes effectively the rotational contour of the ArH+ ion. Consequently, the motion of hydrogen along the 0.3-eV contour would be associated with simultaneous relaxation of the Ar-Ar coordinate. In order to establish the magnitude of this effect, hydrogen was frozen at a randomly chosen point P on the equipotential, whereas the Ar-Ar coordinate was released. The result of such a scan is shown in the inset of Figure 2, showing a rather drastic enlargening of the Ar-Ar separation. The origin of this effect where, indeed, hydrogen motion from its equilibrium position located between the Ar nuclei switches the Ar-Ar potential from a bound to purely repulsive one is a direct consequence
-
-
+
-
+
+
+
Molecular Properties of Ar2H+, Kr2H+, and Xe2H+
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9777
TABLE I V Harmonic Frequencies (cm-*) of Structures I1 and 111 of
2.0
Ar2W ~
n
basis set
Q
1.2
U
3 C
0.4
0
E a, 0 61
-0.4
-
Q 0 .A
-1.2
TI
I L."
-2.0
-1.2
-0.4
0.4
1.2
2.0
0.06 7
\e
I
3.1
0
Ar-Ar
distance [A]
F i i 2. Potential energy surface for Ar2H+at the HF/WBP level. The contours display the total electronic energy with respect to hydrogen position in two dimensions. The lowest energy contour represents 0.1 eV, while the others are drawn for 0.2 eV. The Cartesian displacement coordinatesrefer to an origin at the center of the Ar-Ar separation. The Ar atoms are frozen to positions (Itkh = 3.153 A) corresponding to the global minimum. The arrow indicates the lowest energy path for H exit. The inset shows relaxation of the Ar-Ar coordinate, while hydrogen is fixed at point P with ItArH= 1.33 A (see text for details).
TABLE IIk Harmonic Frequencies (cm-I) of Structure I of Ar2Ht basis set MP2/6-3 1G** HF/ECP MP2/ECP HF/ECP* MP2/ECP* MP2/ECP** MP2/WBP expt
a,,
ULV
334.9 244.5 250.0 256.3 257.6 259.2 287.8 236.7"
772.4 534.0 556.2 562.6 570.0 58 1.6 673.9
797.0 61 1.4 675.5 178.2 616.6 5 16.6 673.9 903.4'
"Reference 19. 'References 13 and 19.
of redistribution of the positive charge leading to localization of charge on the ArH+ fragment. The described process would eventually terminate to a potential energy minimum, i.e., structure I11 providing a significantly deeper well for the H atom. An interesting question is now whether the proposed model for the decay of (Ar-H-Ar)' could justify the experimental observation that the deuterated ion, (Ar-D-Ar)+, is stable in identical experimental conditi~ns.'~J~ As will be discussed later in this section, the present calculations place the frequency of the bending mode of Ar2H+in the 60&70O-cm-' region. Thus, the zero-point energy of this mode, obviously along the reaction coordinate in this model, would be only a fraction of the energy required for access to the reactive 0.3-eV equipotential region. Consequently, it would be essential to consider tunneling involving the bending mode with the given energetics. Considerably lower zero-point energy of the deuterated species combined with lower transmission probability for tunneling could, in principle, be the reason for the observed stability of (Ar-D-Ar)+.'3y'9 Note that isotopically selective decay of infrared absorptions is also clearly demonstrated for Kr2H+ and Xe2H+.9i19 A vibrational analysis was performed for the three structures of Ar2H+ (Tables I11 and IV). The calculations within the effective core potential approach locate the symmetric stretch (ug)
7r
~~
U
(Arl-H-Ar2)+ (Structure 11) HF/6-3 1G** 113.4 594.4 HF/LANLlDZ 153.8 525.8 MP2/LANLlDZ 171.0 619.1 HF/ECP* * 153.1 539.6 HF/WBP 162.2 588.7
1809.8 1274.0 521.0 718.7 1022.7
Arlo *(Ar2H)+(Structure 111) HF/6-31G** 43.2 96.7 MP2/6-31G** 64.9 132.1 HF/LANLlDZ 26.6 54.6 MP2/LANL1 DZ 32.1 68.8 HF/ECP 0.4 17.5 MP2/ECP 0.9 7.0 HF/ECP* 36.4 66.6 MP2/ECP* 54.7 105.6 HF/ECP** 33.9 70.1 MP2/ECP* * 54.5 108.4 HF/WBP 22.5 75.4 MP2/WBP 35.1 81.3 expt
2898.8 2886.7 2413.5 2344.8 2141.5 2176.8 2332.4 2285.1 2380.1 2325.6 2588.5 2600.0 27 10.5"
" w e for
O.O1 0.00
U
ArH+ according to ref 28.
of structure I quite consistently in the 250-29O-cm-' spectral region. Note that the ab initio prediction for the ground state Ar2+is rather similar, being 293 In a m r d with the tighter structure obtained at this level of theory, MP2/6-31G** predicts a somewhat higher harmonic frequency for the symmetric stretch of structure I. Consistently, the recent ab initio study by Rosenkrantz gives 338.4 and 325.5 cm-'for this mode at CI-Veillard and MP2-SGH levels, respectively.8 The experimental Ar matrix number, 336.7 cm-',19 should be used with some caution in the comparison between experiment and theory since sisnifcant matrix effects due to solvation of the positive charge by the host dielectric may be expected. There is no experimental input concerning the bending vibration (rU)of Ar2H+. Our computations for structure I would locate this vibration in the 600-700-cm-1 region. However, also in this case,the MP2/6-31G** calculation yielded a frequency considerably higher than the effective core potentials. Moreover, the previous CI-Veillard estimate for this mode is as high as 836 an-'.* The asymmetric stretch (uu)of structure I, Le., the motion of hydrogen between the Ar centers, suffers from a rather severe basis set dependence. Quite interestingly, all of our computations seem to underestimate the harmonic frequency of this mode if the comparison is made with the experimental Ar matrix frequency. An opposite trend is considered almost as a rule in ab initio calculations, and indeed, computations by Rosenkrantz predict frequencies exceeding 1100 cm-' for the asymmetric stretch.8 As already discussed, among the 12 different computational levels employed in the present study, 5 calculations predict structure I1 as the lowest energy geometry of Ar2H+. Although the Ar-Ar distance in structure I1 is virtually identical to that of structure I, the frequency of the symmetric stretch is reduced at all levels of theory. However, the bending frequency is essentially insensitive to the local symmetry, and quite similar numbers are obtained for both distinct structures concerning this mode. As shown in Figure 1, the potential barrier separating the two identical local minima of structure I1 is only a fraction of the zero-point energy of the asymmetric stretch. Thus, the vibrating ion samples the full width of the potential along the one-dimensional hydrogen motion at energies well above the local minima. However, the computation evaluates the force constant (the second derivative of the potential) at the bottom of the local well. The obtained force constant and the corresponding harmonic frequency would then be sensitive to the curvature of the potential within the vicinity of the local minimum. An obvious conclusion would then be that, in fact, the calculated frequency of the asymmetric stretch in structure I1 should be of only minor physical importance. The third structure, Le., Ar-(Ar-H)+ (structure 111), was considered as a diatomic ArH+ ion loosely bound to a neutral Ar atom
9778 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 TABLE V Molecular ComrtMb of Structure I (Doh)of KrzH' at Different Levels of Theory basis set R ~ HA , qKr' qH" E , au HF/STO- 3G * 1.6150 0.327 0.347 -5446.6738' c HF/LANLlDZ 1.7534 0.366 0.269 -35.9107d MPZ/LANLlDZ 1.7585 0.190 0.620 -488.5445 HF/ECP MP2IECP 1.7524 0.190 0.619 -488.5556 HF/ECP* 1.7123 0.242 0.516 -488.8908 MP2/ECP* 1.7107 0.242 0.516 -488.9714 HF/ECP** 1.6718 0.291 0.419 -488.9336 1.6794 0.290 0.420 -489.0783 MP2/ECP** "Partial charge on the individual atom. 'A full ab initio treatment, electronic energy not comparable with the calculations utilizing effective core potential. 'Unsymmetric structure I1 was obtained at this level with R ~ ( , ) - H = 1.6168 A, R ~ ( z ) - H = 1.9107 A, qfi(l) = 0.455, qKI(z) = 0.269, qH = 0.276, p = 1.76, E = -35.8628 au. dEight valence electrons considered for Kr.
with Ar-Ar separation comparable to the Ar-Ar van der Waals distance. This is consistent with the calculated spectrum consisting of a high-frequency asymmetric stretch and low-frequency symmetric stretch and bending modes related to soft, mostly dispersive forces. In fact, our calculations on the bare diatomic ArH' fragment (not included in this paper) yielded two practically identical frequencies. Except for the 6-31G** basis set, the computed frequencies for the asymmetric stretch are lower than the corresponding gas-phase frequency of ArH'. Kr2H+. The optimized structures and charge distributions for KrzH+are summarized in Tables V and VI. As in the case of ArzH', the lowest energy geometry of KrzH+ is that of D..h symmetry (structure I), and only the HF/LANLIDZ calculation converged to structure I1 possessing unequal Kr-H distances. The barrier separating the two local potential energy minima in structure I1 is, however, only 2 meV. The present calculations locate the Kr.-(Kr-H)+ configuration (structure 111) -0.3-0.4 eV above the structure I. The existence of any nonlinear minimum energy structure for Kr2H+could not be verified. We note that to the best of our knowledge, the present study is the first theoretical one on KrzH'. Although not observed in the gas phase, the first observation of KrzH+ in a Kr matrix is from 1972 by Bondybey and Pi1nente1.l~ The Kr-H distance in structure I clearly exceeds the 1.4212-A value experimentally determined for KrH'.32 We want to emphasize in this context that our calculations for the diatomic ion (not included in this paper) are in much better agreement with the experimental bond length than the corresponding computations for ArH+ which, indeed, significantly overestimate the Ar-H equilibrium distance. The equilibrium distance of the bound Kr2' ion is only 2.79 A,34whereas the van der Waals separation of the neutral dimer is 4.0 A.39 Hence, our estimate for the Kr-Kr distance in structure I is almost exactly the average of these limits. The computed distribution of the positive charge among the individual atoms in structure I again shows variation between different calculations. Nevertheless, most of the computations predict 40-60% of the positive charge to reside on hydrogen. However, the HF/STO-3G* calculation resulted in a charge
Lundell and Kunttu density in which the positive charge is virtually equally shared by the three atoms. This correlates with the somewhat shorter Kr-H distance obtained at this level. Structure I11 of KrzH+is effectively a deeply bound KrH' unit with a weak attraction to a second neutral Kr atom on the Kr side of the diatomic. The Kr-Kr distance in this structure is essentially identical to the van der Waals separation in the neutral Krz dimer, while the Kr-H separation resembles that of an isolated KrH+. As in most of the present calculations, the distribution of the excess positive charge is not stable with respect to the sophistication of the computation showing variation between 40% and 70% for the charge on hydrogen. The fact that the second Kr is essentially neutral has a drastic influence on the dipole moment of structure 111, and dipoles exceeding 10 D are predicted for this geometry. The stability of Kr2H+was investigated at the MP2/ECP** level. A dissociation energy of 0.74 eV was found for the krypton detachment, (Kr-H-Kr)' KrH' + Kr. This value is, indeed, quite similar to that computed for ArzH' and would predict KrzH+ as a stable gas-phase species. For comparison, in solid-state studies concerning the energetics of chargetransfer states between krypton and atomic fluorine, the triatomic Krz+F ionic state was located 0.8 eV below the lowest diatomic Kr+FstateemThe binding of the ground state Kr2' is 1.15 eV.37 The other dissociation limit, namely, the (Kr-H-Kr)' Krz + H+ proton abstraction, is not straightforward. This reaction was found to involve a dissociation energy of 3.85 eV, a value comparable to the experimental De = 4.29 eV of the diatomic KrH'.32 Due to the higher vertical ionization potential of Kr compared to H, the lowest energy dissociation asymptote would clearly be in this case KrH+ Kr H+. However, in the case of the triatomic ion, this limit may not be the lowest energy one. Instead, a simple comparison between the adiabatic ionization energy of the ground AZXC,, 2)u state of Krz+, 12.87 eV," and the vertical ionization potentiaiof hydrogen (13.6 eV) would, in fact, favor the Kr2' + H asymptote by -0.7 eV. This implies a dissociation energy of 3.12 eV for the exit of a neutral H atom from structure I. Note that the threshold for photoelectron emission in crystalline Kr is only 11.9 eV,38which would further favor this channel in the solid state. The binding of the neutral Kr atom in structure I11 is due to mostly weak dispersive forces. This is consistent with the low dissociation energy of 49 meV for the Kr...(Kr-H)' Kr + KrH' krypton detachment. The harmonic frequencies of structures I and I11 of KrzH+are given in Table VII. The calculations within the effective core potential approach locate the symmetric stretch of structure I in the 160-180-cm-' spectral region with only minor variation with respect to the different core potentials considered. However, also in this case, the full electronic treatment, HF/STO-3G*, yielded a considerably higher vibrational frequency, consistent with the uniform charge distribution and slightly tighter structure obtained at this level. The computed frequencies should be put in context with the experimental Kr matrix frequency of 155.4 cm-'and the 158.5-cm-l frequency obtained for the isoelectronic HBry ion in solid Kr.l2 The estimated o, for the ground state Krz+ is 177 c~n-'.'~Our calculationspredict a bending frequency quite similar to that of structure I of ArzH+ (see Table 111). Except for the HF/STO-3G* and MPZ/LANLlDZ calculations, the estimated
-
-
-
+
-
-
TABLE M: Molecular CoastMts of Structure III (Kr,. -Kr2-H+) of KrzH' basis set RKr-KI RKI-H P, D HF/STO-3G* 2.8918 1.4267 7.77 1.4490 4.0145 12.31 HF~LANLIDZ 1.4618 3.8885 12.03 MPZ/LANLIDZ 1.5191 3.9971 14.05 HF/ECP 1 SO96 3.6892 13.26 MP2/ECP 1.4312 4.5142 14.57 HF/ECP* 14.3 1.4346 4.4010 MP2/ECP* 1.3873 12.3 3.8120 HF/ECP** 1.4025 11.9 3.6326 MP2/ECP** 1.4212' expt
9KI(1)
qKr(2)
0.044
0.562 0.588 0.584 0.314 0.3 15 0.401 0.401 0.483 0.479
0.004
0.006 0.006 0.002 O.Oo0 O.OO0
0.006 0.009
qH 0.395 0.408 0.41 1 0.686 0.684 0.599 0.599 0.510 0.512
"A full ab initio treatment, electronic energy not comparable with the calculations utilizing effective core potentials. considered for Kr (see text for details). cExperimental bond length of KrH' (ref 32).
E , au -5446.6294' -35.8541' -35.8977@ -488.5332 -488.5436 -488.8788 -488.9561 4 8 8 . 9 210 -489.0620
'Eight valence electrons
The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 9779
Molecular Properties of Ar2H+, Kr2H+,and Xe2H+ TABLE W: hrmoaic Frequencies (cm-') of Structures I and III of Kr*H+ (KrH-Kr)' Krl-..(Kr2-H)+ (Structure 111) (Structure I) basis set HF/STO-3GS HF/LANLlDZ MPZ/LANLlDZ HF/ECP MP2/ECP HF/ECP* MP2/ECP* HF/ECP** MP2/ECP** expt
us
*U
uU
u
*
U
109.1 355.5 3039.2 20.9 73.7 2315.4 a 25.4 94.2 2245.9 175.2 632.6 458.3 6.4 40.2 1675.6 158.2 461.5 1005.4 19.2 67.9 1730.2 163.4 487.2 1029.9 2.9 17.4 1860.8 171.6 554.6 893.4 0.8 55.1 1869.7 174.8 580.9 1001.4 26.4 60.4 2060.7 183.7 602.4 911.5 38.5 93.2 2014.6 182.9 607.4 1078.7 2494.7d 155.4b 853.1'
271.8
827.3 1896.3
'Asymmetric structure I1 (see Table VI) with u = 106.4 cm-I, r = 586.7 cm-', and u = 727.9 cm-I. *Kr matrix numbers by Seetula et al. (ref 19). 'Reference 13 and 19. dwe for KrH' (ref 28).
TABLE Vm: Molecular Constants of Structure I Different Level0 of Theory basis set RXtH qX/ qH' HF/STO-3G* 1.8401 0.377 0.247 1.9265 0.464 0.072 HF~LANL 1DZ MP2/LANL 1DZ 1.9378 0.461 0.078 HF/ECP 2.0026 0.357 0.286 MP2/ECP 2.01 16 0.377 0.245 1.9244 0.268 0.465 HF/ECP* 1.9262 0.268 0.464 MP2/ECP* 1.9257 0.270 0.461 HF/ECP** 1.9187 0.269 0.462 MP2/ECP** ~~~~
of Xe2H+at
~
E, au -14325.9955b -30.6102' -30.650W -252.2045 -252.2007 -252.2293 -252.3685 -252.2307 -252.4009
'Partial charge on the individual atom. b A full ab initio treatment, electronic energy not comparable with the calculations utilizing effective core potentials. 'Eight valence electrons considered for Xe (see text for details).
frequency of the asymmetric stretch is subject to only minor basis set dependence, being between 900 and 1000 cm-I. Given the experimental Kr matrix frequency of 853 cm-I for this vibration,I3J9it is interesting to realize that while the present calculations tend to underestimate the frequency of this mode for Ar2H+,an opposite trend is observed for Kr2H+. However, as already discussed the expected matrix shifts would mean that only semiquantitative comparisons are afforded between theory and the current experimental numbers. For comparison, HBrc isolated in crystalline Kr has an asymmetric stretch near 687 cm-1.12The Kr-H stretching vibration in the loosely bound Kr-.(Kr-H)+ structure I11 can be safely assumed to resemble that of the bare KrH+ diatomic, having a harmonic frequency of 2494.7 cm-I.'* As seen in Table VII, the frequency of this vibration is rather sensitive to the basii set employed in the computation. The origin of this scatter between different calculations is evidently related to the instability of the charge distribution (see Table VI). In conclusion, all of the effective core potentials utilized for structure I11 have a common tendency to underestimate the Kr-H frequency if the we of KrH+ is used as a point of reference.
Xe2H+. The ab initio optimized structures of Xe2H+ are collected in Tables VI11 and IX. As in the case of the other hydride ions included in the present study, the centrosymmetric (Xe-H-Xe)+, structure I, was found to be that of the lowest energy, and none of the computations yielded a structure possesing unequal Xe-H distances. Depending on the effective core potentials employed in the calculations, the difference in the total electronic energy between structure I and the loose Xe-(Xe-H)+ structure I11 varies between 0.23 and 0.4 eV, whereas the full ab initio treatment at the HF/STO-3G* level predicts an energy difference of 0.9 eV. According to most of the computations, the X e H equilibrium distance is estimated as 1.92 A, which is, indeed, significantly larger then the experimental value of 1.6028 A determined for the diatomic XeH+ in the gas phaseaZ9For comparison, the ab initio prediction (with spin-orbit effects included) for R, of the ground state X%+ is 3.27 while the van der Waals distance of the neutral Xe2 dimer is 4.36 A.41 Thus, also in this case, triatomic structure I is characterized by a Rg-Rg separation between the ionic and neutral diatomic limits. It is interesting to note that the I-H equilibrium distance in the isoelectronic species, HI2-, is rather identical to our estimates for structure I of Xe2H+,being 1.94 The obvious shortcoming in the present calculations is the description of the charge distribution among the individual atoms. The computations utilizing the LANLlDZ formalism having eight electrons in the rare gas valence space predict a charge distribution where less than 10% of the excess positive charge is located on the hydrogen. This picture is, indeed, rather consistent with physical intuition based on the relatively large difference between ionization potentials of Xe and H. However, inclusion of the d subshell for the valence space of Xe increases the positive charge on hydrogen considerably. Finally, extension of the basis set by p- and d-type polarization functions leads to a picture where more than 45% of the charge resides on hydrogen. In fact, the ECP* and ECP** computations yielded charge distributions quite similar to those obtained for structure 1of Kr2H+ (see Table V). As shown in Table IX,structure I11 of Xe2H+is quite similar to those obtained for Ar2H+and Kr2H+,viz. a clearly localized XeH+ ion locaely bound to a virtually neutral Xe atom on the Xe side of the diatomic. In this respect, the present results agree well with the previous DIIS computations by Last and George.lo Note, however, that the DIIS formalism predicts structure I11 as the only stable nuclear configuration of XQH'. In order to investigate the effect of the neutral Xe atom on the diatomic potential, calculations were performed also for the bare diatomic ion. These computations (not included in this paper) yielded X e H equilibrium distances practically identical to those obtained for structure 111. Consistent with the fact that -5% of the positive charge is predicted to reside on hydrogen at this computational level, MP2/ECP** calculation yielded a X e X e distance slightly longer than the corresponding values obtained with the other core potentials. As discussed in the case of structure I, among the effective core potentials utilized in the present study, the LANLlDZ computations predict a considerably smaller fraction of the positive charge to be located on the hydrogen. The following estimates concerning the stability of Xe2H+are based on computations at the MP2/ECP** level. At this level,
-
-
TABLE I X Molecular Constants of Structure III (Xe,. .Xe2-H+) of Xe2H+ basis set HF/STO-3GL HF~LANL DZ ~ MP2ILANLlDZ HF/ECP MP2IECP HF/ECP* MP2/ECP* HF/ECP** MP2/ECP** expt
Rxtxc 3.5824 4.3282 4.1702 4.4688 4.4016 3.9190 3.7040 3.8991 3.6594
RXbH 1.6106 1.6120 1.6283 1.6993 1.7090 1.6257 1.642 1 1.6254 1.6407 1.6028'
w, D 9.53 12.26 11.86 13.86 13.70 10.36 9.64 10.05 9.24
4XC(l) 0.021 0.009 0.013 0.002 0.003 0.020 0.032 0.034 0.051
9XC(2) 0.698 0.157 0.750 0.575 0.575 0.428 0.424 0.420 0.413
qH 0.28 1 0.234 0.237 0.422 0.422 0.552 0.544 0.546 0.537
E, au -14325.9612' -30.60106 -30.6371' -252.1898 -252.2051 -252.2207 -252.3545 -252.2224 -252.3873
'A full ab initio treatment, electronic energy not comparable with the calculations utilizing effective core potentials. *Eight valence electrons considered for Xe (see text for details). 'Experimental bond length XeH' (ref 29).
9780 The Journal of Physical Chemistry, Vol. 96, No. 24, 1992 TABLE X Harmonic Frequencies (cm-I) of Structures I and In of Xe2H+ (Xe-H-Xe)+ Xel. .(Xe2-H)+ (Structure 111) (Structure I) basis set u. T., u., u T U HF/STO-3G* 195.1 755.2 1448.1 46.0 228.0 2787.3HF/LANLlDZ 136.9 624.4 301.7 18.0 93.0 2202.1 MPZ/LANLlDZ 132.6 617.1 618.4 23.2 119.7 2109.6 HF/ECP 127.2 491.8 862.6 10.4 59.4 1878.8 MP2/ECP 125.7 492.1 921.0 12.2 66.6 1840.0 HF/ECP* 135.3 544.6 278.6 37.0 151.8 2235.3 MP2/ECP* 135.2 541.2 736.1 58.4 210.1 2503.2 HF/ECP** 135.0 542.5 273.2 40.8 152.9 2234.6 MP2/ECP** 137.1 536.5 799.5 61.5 202.7 2158.8 2270.0 730.9' expt 11 1.9'
"Xe matrix numbers of ref 9.
b
~
of, XeH' (ref 29).
xenon detachment from centrosymmetric structure I was found to involve a dissociation energy of 0.846 eV. This energy is quite similar to the corresponding values obtained for Ar2H+and Kr2H+. The dissociation energy of the ground-state Xe2+dimer is 1.03 eV by experiment" and 0.79 eV by theory.34 Thus, Xe2H+ is clearly a stable gas-phase species. The other dissociation limit, namely, the (Xe-H-Xe)+ Xe2 + H+ proton exit, is characterized by a dissociation energy of 4.77 eV. However, applying the adiabatic ionization energy of Xe2 on its ground A2Z+(l,2)u state, 11.13 eV,37and the vertical ionization energy of H (13.6 eV) would locate the (Xe-H-Xe)' Xe2++ H(2S) asymptote to 2.30 eV (see discussion for Ar2H+and Kr2H+). The given number is clearly smaller than that obtained for Ar2H+ and Kr2H+. For comparison, the ab initio dissociation energy of XeH+ is 3.9 eV.'* The xenon detachment from structure 111, Xe(XeH)' Xe + XeH', involves as much as 0.22 eV of energy, which is, indeed, significantly more than the present estimates for structures I11 of Ar2H+and Kr2H'. Nevertheless, this is rather consistent with the observation that significant delocalization of the positive charge is predicted in the xenon species when employing the ECP* and ECP** basis sets (see Table IX). As a consequence of this somewhat dispersed charge distribution, a slightly shorter Xe-Xe equilibrium distance was obtained in these computations. On the contrary, the previous DIIS calculations yielded a charge distribution with 100% of the excess positive charge localized on the XeH+ subunit, consistent with a Xe-Xe distance as long as 4.46 A and a dissociation energy of 46 meV, only.1° The vibrational analysis for both stable structures of Xe2H+ is presented in Table X. As in the case for Ar2H+and Kr2H+, the harmonic frequency of the symmetric stretch of structure I shows only minor variation with respect to the different effective core potentials. The full ab initio treatment at the HF/STO-3G* level predicts, however, a considerably higher frequency for this mode. The experimental Xe matrix number of 1 is slightly smaller and rather similar to the ab initio predictions, 112-123 cm-I, for the ground state Xe2+.34The deviation between the present estimates and the experimental frequency is of the order of the expected matrix shift for an ionic species isolated in a polarizable medium like xenon. For comparison, the corresponding symmetric stretch of HI2- is observed near 117 and 109 cm-I in solid Kr and Xe, respectively.12 The bending frequency of structure I of Xe2H+ is quite similar to that obtained for Kr2H+. The harmonic frequency of the asymmetric stretch, i.e., the hydrogen motion between the heavy centers, shows significant variation between different theoretical approaches. Indeed, this is expected due to the observed variation in the computed distributions of the positive charge (see Table VIII). However, the computations including electron correlation yield frequencies reasonably close to the experimental Xe matrix value.
-
-
-
IV. Summary Ab initio calculations based on several effective core potentials available for rare gas atoms are reported for Rg2H+(Rg = Ar, Kr, Xe). For comparison, full ab initio treatments with STO-3G*
Lundell and Kunttu and &31G**basis sets are given. According to the present study, Ar2H+,Kr2H+, and XqH+ exist as stable linear gas-phase species, the nuclear configuration of the lowest electronic energy being that where hydrogen is located between Rg atoms. Most of the computations predict this structure to be centrosymmetric with Dmhsymmetry. This is, indeed, consistent with experimental low-temperature matrix data. In the case of Ar2H+,traces of a double minimum potential along the hydrogen coordinate between Ar centers were obtained at several levels of computational theory. However, the barrier separating the two equivalent minima was found to be too low to have any physical importance. Similar results were obtained in the previous ab initio work by Rosenkrantz.' The calculated u8 and u, frequencies support the experimental assignments in the matrix spectroscopy?J9 The calculations within the effective core potential approach would suggest the collinear Rg-.(Rg-H)+ structure to be 0.24.4 eV higher in energy. Furthermore, the (Rg-H-Rg)' --.L Rg RgH+ dissociation energy was found to be quite insensitive to the rare gas being -0.8 eV. For the looser Rg(Rg-H)+ structure, the detachment of the virtually neutral Rg atom is characterized by a dissociation energy ranging from 14 (Ar) to 220 meV (Xe). Proton abstraction was found to be the lowest energy channel for hydrogen exit for Ar2H+,while Kr2H+and Xe2H+yield Rg2+ H(2S) fragments. The dissociation energies of these reactions are, indeed, comparable with the bond energies of the diatomic RgH'. The computed potential energy surface for Ar2H+would suggest the (Rg-H-Rg)' Rg(Rg-H)+ isomerization as the possible origin for the experimentally observed decay of Rg2H+absorptions in low-temperature matrices. Finally, we conclude that the most severe shortcoming concerning the present calculations is the description of the partial charge on the individual atoms. This issue has rather serious bearings with respect to structure and especially the computed vibrational frequencies of the triatomic ions of concern. Thus, our predictions concerning the harmonic frequencies are only semiquantitative. The situation is worse in the case of modes involving hydrogen motion. Implementation of the highly correlated self-consistent electron pair approach (CEPA) would presumably increase the present computationalaccuracy, and such studies are underway in our laboratory. However, in order to afford rigorous comparisons between experiment and theory, experimental gas-phase data on these ions would be essential. Such studies are strongly encouraged.
+
+
-
Acknowledgment. We thank Profs. Pekka Pyykk6 and Markku Rfislnen for their help during the course of this work. References and Notes (1) Echt, 0.;Sattler, K.; Recknagel, E. Phys. Reu. Lett. 1981, 47, 1121. (2) Harris, I. A.; Kidwell, R. S.; Northby, J. A. Phys. Rev.Lett. 1984,53, 2390. (3) Levinger, N. E.; Ray, D.; Murray, K. K.; Mullin, A. S.; Schulz, C. P.; Lineberger, W. C. J. Chem. Phys. 1988, 89, 71. (4) Levinger, N. E.; Ray, D.; Alexander, M. L.; Lineberger, W. C. J . Chem. Phys. 1988, 89, 5654. ( 5 ) Nagata, T.; Hirokawa, J.; Kondow, T. Chem. Phys. Letr. 1991, 176, 526.
(6) Wei, S.; Shi, 2.;Castleman, A. W., Jr. J. Chem. Phys. 1991,94,8604. (7) For a up-to-date review, see: Last, I.; George, T. F.In Current Topics in Ion Chemistry and Physics; Ng, C . Y . , Baer, T.,Powis, I., Eds.; Wiley: New York. 1992 (in Dress): Vol. 1. (8) Rosenkraniz, M. Chem. Phys. Lett. 1990, 173, 378. (9) Kunttu, H.; Seetula, J.; Risinen, M.; Apkarian, V. A. J . Chem. Phys. 1992. 96. 5630.
(10) Last, I.; George, T. F. J . Chem. Phys. 1990, 93, 8925. (11) Ault, B. S. Acc. Chem. Res. 1982, 15, 103. (12) Risinen, M.; Seetula, J.; Kunttu, H. Submitted to J . Chem. Phys. (13) Bondybey, V. E.; Pimentel, G. C. J . Chem. Phys. 1972, 56, 3832. (14) Matcha, R. L.; Milleur, M . B. J . Chem. Phys. 1978, 69, 3016. (15) Potapov, S. G.; Sukhanov, L. P.; Gutsev, G. L. Rum. J. Phys. Chem. 1989, 63, 479. (16) Rosmus, P. Theor. Chim. Acta 1979, 51, 359. (17) Rosmus, P.; Reinsch, E. A. Z . Naturforsch. Teil A 1980, 35, 1066. (18) Klein, R.; Rosmus, P. Z . Naturforsch. Teil A 1984, 39, 349. (19) Seetula, J.; Risinen, M.; Kunttu, H. Manuscript in preparation. (20) Hay, P. J.; Wadt, W. R. J . Chem. Phys. 1985, 82, 270. (21) Wadt, W. R.; Hay, P. J. J. Chem. Phys. 1985, 82, 284. (22) Hay, P. J.; Wadt, W. R. J. Chem. Phys. 1985, 82, 299.
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9781
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Interactions between Cgoand Endohedral Alkali Atoms B. I. Dunlap,* Theoretical Chemistry Section, Code 6179, Naval Research Laboratory, Washington, D.C. 20375-5320
J. L. Ballester, Department of Physics, Emporia State University, Emporia, Kansas 66801
and P. P. Schmidt Chemistry and Materials Division, Office of Naval Research, Arlington, Virginia 22217-5000 (Received: June 22, 1992; In Final Form: September 11. 1992)
All-electron local-density-functional (LDF) total-energy calculations are used to study the interaction between icosahedral C , and endohedral lithium, sodium,and potassium ions and atoms. LDF potential energies as a function of radial displacement , suggest that the carbon shellalkali interaction is spherically symmetric from the center along the 5-fold and 3-fold axes of C to a good approximation. At equilibrium Li’, Na’, and K+ are displaced radially outward 1.4,0.7, and 0.0 A, respectively, from the center of the ball in the ground states of both the neutral and positively-charged complexes. Excited intramolecular chargetransfer states of the neutral molecules exist in which the endohedral alkali ion is neutralized. For these electronically excited neutral molecules the equilibrium position of the alkali atom is at or very near the center of the C, shell. A minimum in the spacing between totally-symmetric endohedral vibrational energy levels indicates a potential energy maximum at the center of the shell. The height of the potential energy maximum lies between the two corresponding vibrational energies.
I. Introduction At the fmt recognition that icosahedral Cso was experimentally important, the molecule was described as a ball and postulated to be able to trap atoms inside.’ Soon experimental evidence was found for trapping a lanthanum atom inside.2 The fact that certain atom-fullerene complexes could loose C2units only down to some endohedral-atom-dependentsize was further evidence that atoms could be trapped inside C, and C70.3With the advent of a method for making macroscopic amounts of these fullerenes: gas-phase collisions of Cso and C70with helium were shown to result in a helium atom being trapped i n ~ i d e . ~Collisions -~ can also trap a neon atom in bu~kminsterfullerene.~~~ Fullerenes with a single lanthanum atom inside (La@Cs2)10 and a dimer inside (La2@C8,,)I1 have been directly synthesized in macroscopic amounts. The electron-spin-resonance(ESR) hyperfine spectra of suggest a formal oxidative state La3+C823-for the molecule.12 X-ray photoelectron and ESR spectroscopies support this assignment and a similar assignment for Y@c82 in work that also suggests that other endohedral Y,C, species including Y&82 may be extractable.” These findings for ytterbium endohedral fullerene complexes have likewise been confirmed.I4 Given that both Y2c82 and L2c82 have been made, one would expect endo-
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hedral YLaCs2 to be synthesized, which it has.I5 Remarkably, the internal volume of the fullerenes is large enough that endohedral %&2 can also be made.’6J7 Studies of chemical reaction with oxygen show that these complexes are indeed endohedral.I8 Apparently C, with scandium, ytterbium, or lanthanum entrapped is too unstable or created in such low abundance that it cannot be extracted; however, endohedral FeCm can apparently be.2o While all fullerenes can apparently accept endohedral atoms, the Cso endohedral complex is most fascinating because Csois in many respects well approximated by a spherical ball. Aspects of its electronic structure can be viewed as arising from a potential that is slightly perturbed from having spherical ~ymmetry.~J~ The nodal structure of Csomolecular orbitals is strikingly similar to the nodal structure of spherical harmonics.22 It is natural to consider a single endohedral atom placed at the center of this approximate ball. The electronic response and structure of various atoms at the center of Cm have been computed by a number of worker~.~~-~I On the other hand, graphite is known to bind many different kinds of atoms including alkali atoms. Lithium-, sodium-, and potassium-intercalatedgraphite compounds can be made in which the alkali atoms not only chemisorb but migrate between the graphite sheet^.^^^^^ Photoemission studies of the initial stages of intercalation (alkali evaporation onto a 100 K graphite surface) 0 1992 American Chemical Society
