Theoretical and Experimental Studies on the Bond Dissociation

The structures and bond dissociation energies (BDEs) for Al(methane)+, ... Al(ethane)+ have been determined by using both Fourier-transform ion cyclot...
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8786

J. Phys. Chem. 1996, 100, 8786-8790

Theoretical and Experimental Studies on the Bond Dissociation Energies of Al(methane)+, Al(acetylene)+, Al(ethene)+, and Al(ethane)+ Detlef Sto1 ckigt,*,† Joseph Schwarz,‡ and Helmut Schwarz*,‡ Max-Planck-Institut fu¨ r Kohlenforschung, Abteilung Massenspektrometrie, Kaiser Wilhelm-Platz 1, D-45470 Mu¨ lheim an der Ruhr, Germany, and Institut fu¨ r Organische Chemie der Technischen UniVersita¨ t Berlin, Strasse des 17. Juni 135, D-10623 Berlin, Germany ReceiVed: January 2, 1996; In Final Form: March 6, 1996X

The structures and bond dissociation energies (BDEs) for Al(methane)+, Al(acetylene)+, Al(ethene)+, and Al(ethane)+ have been determined by using both Fourier-transform ion cyclotron resonance (FTICR) mass spectrometry and the ab initio post-HF methods MP2, MP4, and QCISD(T) with split valence basis sets plus polarization and diffuse functions, i.e., 6-31G(d,p), 6-311+G(d,p), and 6-311+G(3df,2p). The ab initio results indicate the following 300 K data: BDE(Al+-methane) ) 5.2, BDE(Al+-acetylene) ) 13.2, BDE(Al+ethene) ) 13.6, BDE(Al+-ethane) ) 8.4, (end-on), and BDE(Al+-ethane) ) 8.5 kcal/mol (side-on). According to the results of the FTICR experiments, the Al+-ligand BDE values increase in the following order: Al+-CH4 < Al+-C2H6 < Al+-C2H4 < Al+-C2H2.

Introduction

Experimental Section

An important feature in understanding organometallic reactions and homogeneous and/or heterogeneous catalysis concerns the energetics of the bond-making and -breaking processes that occur at coordinatively unsaturated metal centers. Of particular interest are organometallic and “zeolithic” aluminum compounds due to their role in important applications such as metal-organic chemical vapor decomposition1 or heterogeneous2 and homogeneous3 catalysis, respectively. It has been stated repeatedly that more direct structure/reactivity information on “cation-like” catalytic centers is highly desirable in order to develop catalysts for industrial applications.4 Techniques as diverse as matrix isolation5 or ion-molecule reactions6 have been used recently, and not surprisingly, theoretical investigations7-9 have been employed in order to characterize metal-ligand bonds. As a continuation of our previous studies on small cationic aluminum complexes,8 here we will focus on the determination of the bond dissociation energies (BDEs) of methane, acetylene, ethene, and ethane to Al+ (1S) and the electronic and structural properties of the metal-ligand binding. These systems are of particular interest with regard to (i) the linear correlation of proton affinities and BDE(Al+-L) values reported earlier for a number of ligands L,8,10 (ii) being the key steps in many organometallic reactions, and (iii) serving as model systems for more complex processes. Recently, theoretical11 and experimental12 results have been presented with regard to the interaction of transition-metal ions with L ) methane, acetylene, ethene, and ethane. In the present article, a combination of ab initio quantum chemical approaches and Fourier-transform ion cyclotron mass spectrometry will be used to determine the 300 K BDEs of Al+-L complexes (L ) methane, acetylene, ethene, ethane) by conducting equilibrium measurements8c,d,13 (eq 1) and employing bracketing techniques14 (eq 2).

Gas-phase experiments were performed by using a Spectrospin CMS 47X Fourier-transform ion cyclotron resonance mass spectrometer15 which is equipped with an external ion source.16 The standard procedures have been described previously.8,15,17 For the generation of Al(L)+ (L ) C2H2, C2H4, C2H6), laserdesorbed18 Al+ was reacted with β-butyrolactone yielding Al(CO2)+ that was carefully isolated.19 Subsequently, CO2 was exchanged by acetylene, ethene, or ethane in order to result in the Al(L)+ complex, respectively. Double resonance and collision-induced dissociation20 experiments were performed as described previously.15,17

Al(L)+ + L′ a Al(L′) + L

(1)

Al(L)+ + L′ f Al(L′) + L

(2)

Computational Details The quantum chemical calculations have been performed on a Digital DEC 3000/300 workstation by using the GAUSSIAN 94 program package.21 Following the recommendation of Durant and Rohlfing22 concerning the Gaussian2 (G2) procedure,23 we have employed the quadratic configuration interaction method including single and double excitations with a perturbational treatment of the triple excitations in conjunction with the 6-31G(d,p) split valence basis set (QCISD(T)/6-31G(d,p)) in order to determine the geometrical parameters. More reliable results concerning the energies were obtained by evaluating the relative stabilities with the use of larger polarized basis sets including diffuse functions as well, i.e., 6-311+G(d,p) and 6-311+G(3df,2p) and by further single-point MP4(SDTQ) and QCISD(T) calculations on the QCISD(T)/6-31G(d,p) calculated geometry. The MP2(FU)/6-31G(d,p) level of theory was used in order to determine the vibrational frequencies (scaled24 by 0.94) and zero-point vibrational energies (ZPVEs, scaled24 by 0.96). The relative stabilities discussed in the text are given in kcal/mol. The accuracy is expected to be of the order of (2 kcal/mol.23 The bond lengths are given in angstroms and bond angles in degrees. Only singlet species are considered in this study.25,26 Results and Discussion

†

Max-Planck-Institut fu¨r Kohlenforschung Mu¨lheim (Ruhr). ‡ Technische Universita ¨ t Berlin. X Abstract published in AdVance ACS Abstracts, May 1, 1996.

S0022-3654(96)00060-3 CCC: $12.00

A. Theoretical Results. In Scheme 1, conceivable modes for the Al+ coordination to the respective ligands L are shown.11d © 1996 American Chemical Society

Bond Dissociation Energies of Al+-L Complexes

J. Phys. Chem., Vol. 100, No. 21, 1996 8787

SCHEME 1

a

b

Figure 1. HF/6-31G(d,p) (normal), MP2(FU)/6-31G(d,p) (italic), and QCISD(T)/6-31G(d,p) (bold) optimized geometries for Al(methane)+ (1), Al(acetylene)+ (2), Al(ethene)+ (3), and the Al(ethane)+ isomers (4) (end-on) and (5) (side on).

For L ) methane, only the (η3) C3V symmetrical complex corresponds to a minimum structure according to the frequency analysis of both the HF/6-31G(d,p) and MP2(FU)/6-31G(d,p) levels of theory. The (η2) C2V Al(CH4)+ complex possesses one negative eigenvalue of the force constant matrix indicating the movement of the aluminum ion from one plane of the methane tetrahedron to another. Further, for the (η1) C3V compound two imaginary frequencies are found. Considering the coordination of acetylene to Al+, only the (η2)CC C2V geometry corresponds to a minimum structure on the singlet potential energy surface (PES).27 In the case of the Al+ interaction with ethene, the two C2V isomers (η2)HH and (η2)′HH are characterized by one imaginary frequency for each at the HF/6-31G(d,p) and MP2(FU)/6-31G(d,p) levels with the corresponding vector components pointing to the rotation of the ethene ligand. However, the (η2)CC C2V Al(C2H4)+ complex corresponds to a true minimum. Additionally, both the (η3) C3V and the (η3) Cs Al(ethane)+ complexes correspond to minima on the respective singlet PES of Al+/C2H6 in contrast to the (η2) Cs geometry.28 Other minimum structures of the Al(L)+ ions have not been detected. The QCISD(T)/6-31G(d,p) optimized geometries of (η3) C3V Al(methane)+ (1A1) (1), (η2)CC C2V Al(acetylene)+ (1A1) (2),

(η2)CC C2V Al(ethene)+ (1A1) (3), “end-on” (η2) C3V Al(ethane)+ (1A1) (4), and “side-on” (η3) Cs Al(ethane)+ (1A′) (5) are shown in Figure 1.29 The corresponding absolute energies and the calculated BDE values at 300 and 0 K including ZPVEs are listed in Table 1. The five species (1-5) have been located as true minima; i.e., the frequency analysis only confirmed the presence of real frequencies. Compared to the MP2 and QCISD(T) calculations with the 6-31G(d,p) basis set, the Hartree-Fock approximation results in 20-60% lower BDE values.30 As expected, consistent results within (10% have been always obtained by using the post-HF methods. The QCISD(T)/6-31G(d,p) geometries of the aluminum complexes deviate from the experimental values of the free ligands31 by less than (5%. Similarly, the differences in the geometrical parameters of 1-5 considering the various methods also amount to less than (5%. However, with the increase of the BDE values as noted above, the Al+-L distances decrease by using the post-HF methods. Additionally and not quite unexpectedly, the BDE values increase with the size and flexibility of the basis sets. Concerning the Al+-L binding characteristics of the species 1-5, an NBO analysis32 has been performed.33 The major component (ca. 40%) responsible for the stability of the Al(CH4)+ complex 1 was found to be the donor-acceptor interaction of the Al+ s-orbital and the σ*(C-H)-MO of the opposite CH bond. It is followed by the σ(C-H)-MO donation of the same bond into an empty p-orbital of Al+ (ca. 15%

TABLE 1: Summary of Absolute Energies (hartrees) and Zero-Point Vibrational Energies (ZPVEs, in millihartrees) of the Aluminum Complexes method

Al(methane)+ (1) (1A1)

Al(acetylene)+ (2) (1A1)

Al(ethene)+ (3) (1A1)

HF/6-31G(d,p) ZPVE MP2(FU)/6-31G(d,p) ZPVE QCISD(T)/6-31G(d,p) MP4(SDTQ)/6-31G(d,p)a MP4(SDTQ)/6-311+G(d,p)a MP4(SDTQ)/6-311+G(3df,2p)a QCISD(T)/6-311+G(d,p)a QCISD(T)/6-311+G(3df,2p)a

-281. 857 695 47. 866 -282. 064 087 47. 055 -282. 087 230 -282. 084 728 -282. 117 229 -282. 147 428 -282. 119 667 -282. 149 596

-318. 492 929 29. 796 -318. 802 753 27. 131 -318. 823 786 -318. 822 229 -318. 866 553 -318. 915 378 -318. 867 555 -318. 915 367

-319. 711 338 55. 767 -320. 039 484 53. 549 -320. 070 415 -320. 067 292 -320. 109 900 -320. 162 193 -320. 112 757 -320. 164 212

a

Single-point calculation on the QCISD(T)/6-31G(d,p) geometry.

Al(ethane)+ (end-on) (4) (1A1)

Al(ethane)+ (side-on) (5) (1A1)

-320. 896 052 79. 474 -321. 251 893 77. 689 -321. 286 800 -321. 283 940 -321. 331 218 -321. 385 525 -321. 333 900 -321. 387 627

-320. 895 080 79. 217 -321. 251 120 77. 217 -321. 285 950 -321. 283 117 -321. 330 655 -321. 385 158 -321. 333 306 -321. 387 232

8788 J. Phys. Chem., Vol. 100, No. 21, 1996

Sto¨ckigt et al.

TABLE 2: Theoretically Predicted BDE Values of Al(methane)+ (1), Al(acetylene)+ (2), Al(ethene)+ (3), and the Al(ethane)+ isomers 4 (1A1) (end-on) and 5 (1A′) (side-on) in kcal/mol method

Al(methane)+ (1) (1A1)

Al(acetylene)+ (2) (1A1)

Al(ethene)+ (3) (1A1)

Al(ethane)+ (end-on) (4) (1A1)

Al(ethane)+ (side-on) (5) (1A1)

HF/6-31G(d,p) MP2(FU)/6-31G(d,p) QCISD(T)/6-31G(d,p) MP4(SDTQ)/6-31G(d,p)a MP4(SDTQ)/6-311+G(d,p)a MP4(SDTQ)/6-311+G(3df,2p)a QCISD(T)/6-311+G(d,p)a QCISD(T)/6-311+G(3df,2p)a ab initio (300 K)b ERc BSSEd

1.8 3.8 3.4 3.5 3.6 5.3 3.4 5.2 5.5 4.9 0.1

11.2 14.3 13.5 13.9 11.3 13.5 11.0 13.2 13.1 7.4 0.3

11.6 14.7 13.5 14.0 11.7 14.0 11.3 13.6 13.9 7.9 0.3

3.0 6.5 5.8 6.0 6.3 8.7 6.1 8.4 8.1 7.6 0.4

2.6 6.3 5.5 5.8 6.3 8.7 6.0 8.5 8.8 9.1 0.4

a Single-point calculation on the QCISD(T)/6-31G(d,p) geometry. b QCISD(T)/6-311+G(3df,2p)//QCISD(T)/6-31G(d,p) corrected for the enthalpy changes obtained at the MP2(FU)/6-31G(d,p) level. c ER is the estimated contribution of the charge-induced polarization. For details, see ref 11d. d Counterpoise correction according to ref 39 by using the QCISD(T)/6-311+G(3df,2p) basis set.

contribution). Additionally, the three identical CH bonds also donate electrons to the higher lying empty AOs of Al+. Concerning the bonding situation of the end-on Al(ethane)+ (4) complex, a similar situation compared to 1 is observed; i.e., the Al+ s-orbital donates to the σ*(C-C)-MO (40%) accompanied by the σ(C-H)-MO donation into an empty p-orbital of Al+ (ca. 10% contribution). With regard to the side-on Al(ethane)+ coordinated species 5, electron donation (i) from the σ(C-H)-MOs (originating from the CH bonds directed toward Al) to the p-orbitals of Al+ together with (ii) the interaction of the Al+ s-orbital and the σ*(C-H)-MOs of the CH bonds lying in the Al, C, C plane constitute the dominating (ca. 70%) bonding interaction. Completely different results are obtained for the Al(acetylene)+ (2) and Al(ethene)+ (3) complexes. For 2, the σ-donation of the CC π-bond into the empty p-orbital is responsible for ca. 80% of the BDE value. A smaller contribution is to be noticed for the π-donation of the other π-MO (ca. 10%). The Al+ back donation into the π*-MO of the CC bond is negligible. The σ-donation of the CC π-bond into the empty p-orbital of Al+ is also the most important component for ion 3 amounting to almost 90% of the Al+-ethene bond. Additionally, the Al+ back donation into the π*-MO of the CC bond is also negligible. Besides the orbital analysis given above another approach for the characterization of a M+-L bond has been suggested.11d Accordingly, the dominating factors of a M+-L bond are (i) charge-induced dipole interactions, (ii) charge-quadrupole interactions, (iii) polarization of the charge on the metal, and (iv) charge transfer. In the case of M ) Al, charge transfer33 and the polarization of the charge on the metal are almost negligible. The charge-induced polarization data (ER), given in Table 2, indicate that ER is the by far dominating part in the complexes 1, 4, and 5 (ca. 95%). Considering L ) acetylene and ethene, the effect is smaller and the charge-quadrupole interactions come into play. The theoretical predictions of the general trend in bond strengths of the Al+-L complexes can be summarized in a row of increasing BDE (Table 2, QCISD(T)/6-311+G(3df,2p) data, given in kcal/mol at 0 K in parentheses):34

CH4 (5.2) < C2H6 (8.4 and 8.5) < C2H2 (13.2) < C2H4 (13.6) B. Equilibrium and Bracketing Experiments. The relative BDE values were determined (i) by applying the kinetic method described in ref 8d and (ii) by using the indirect equilibration of Al(C2H2)+/Al(C2H4)+ and appropriate corrections of the ∆G values with the ab initio calculated -T∆S term (see Table 3).

TABLE 3: Results of the Equilibrium Measurements According to Eq 1 (T ) 300 K) and of the Bracketing Measurements According to Eq 2 (b) Equilibrium Measurements Results p(C2H2)/ p(C2H2)a

Al(C2H2)+/ Al(C2H4)+

∆Gb

-T∆Sc

∆H

1.0/1.4 1.0/1.0

1.0/0.6 1.0/0.4

+0.5 +0.5

-0.1 -0.1

+0.4 +0.4

(b) Bracketing Experiments Results

}

L/L′

does eq 2 apply?d

C2H2/CH4 C2H4/CH4 C2H6/CH4 C2H4/C2H6 C2H4/C2H2 C2H6/C2H2 C2H6/C2H4 C2H2/C2H4

no no no no yes, kR ) kcoll yes, kR ) kcoll yes, kR ) kcoll slow, kR < kcoll

consequence BDE(Al+-L′) < BDE(Al+-L) BDE(Al+-C2H4) < BDE(Al+-C2H2) BDE(Al+-C2H6) < BDE(Al+-C2H2) BDE(Al+-C2H6) < BDE(Al+-C2H4) BDE(Al+-C2H2) ≈ BDE(Al+-C2H4)

a Relative partial pressures. b The experimental uncertainty amounts to 0.5 kcal/mol. c The entropy term (∆S) is derived from MP2(FU)/631G(d,p) calculations. d Concerning kcoll, see ref 35. kR is the experimentally determined rate constant.

From this it follows that at 300 K ethene is by 0.4 ( 0.5 kcal/ mol less strongly bound to Al+ as compared with acetylene. From the bracketing techniques (eq 2) the following information is available: (i) At 300 K BDE(Al+-CH4) has to be the smallest values since the complex Al(CH4)+ cannot be produced from any of the complexes by ligand exchange reactions. (ii) The ethane ligand in Al(C2H6)+ can be replaced by acetylene and ethene at the collision rate, whereas (iii) the reverse reaction of Al(C2H4)+ with ethane does not occur. (iv) Additionally, acetylene does expel ethene from Al(C2H4)+ near the collision rate.35 The set of experimental data for the BDE values (at 300 K) on Al(L)+ can be ordered with the following trend of increasing BDE(Al+-L) values: CH4 < C2H6 < C2H4 < C2H2. C. Discussion. The theoretically predicted BDE values of the Al(L)+ complexes (L ) methane, acetylene, ethene, ethane) are summarized in Table 2. Compared to the literature data of several transition-metal ion complexes, the BDE values for the aluminum ions are in general lower. For example (0 K data), BDE(Co+-CH4) ) 22.9 ( 0.7,12c BDE(Co+-CH4) ) 21.4 ( 1.4,12e and BDE(Co+-C2H6) ) 28.0 ( 1.6 kcal/mol12c have been determined experimentally. Furthermore, BDE(Fe+C2H6) ) 15.3 ( 1.4,12d 17.9 ( 3,12g and 10 ( 5,11a BDE(Ni+C2H6) ) 28.7 ( 312g as well as BDE(Cu+-CH4) ) 14.836a or 18.1,36b BDE(Fe+-CH4) ) 13.7 ( 0.8,36c BDE(Zr+-C2H2) ) 59 ( 3,37 and BDE(Nb+-C2H2) ) 57 ( 3 kcal/mol37 have been reported. In addition, Siegbahn et al. calculated BDE(Ru+-

Bond Dissociation Energies of Al+-L Complexes C2H4) ) 26.8, BDE(Rh+-C2H4) ) 34.9, and BDE(Pd+-C2H2) ) 30.7 kcal/mol.38 We consider two effects to be responsible for the differences of the absolute BDE data of the Al+ and other M+ complexes (M ) transition metal). From the MO approach, i.e., the population analysis by using either the NBO or the Mulliken scheme, the interacting orbitals appear to be not the same in these two systems. The “classical” π-MO back-bonding from Al+ to the empty antibonding orbitals of the ligand L does not exist due to unoccupied π-orbitals of Al+. The second component results from the Pauli repulsion due to the filled Al+ s-orbital, resulting in an increased Al+-L distance and a less efficient overlap of bonding orbitals. The latter point affects also the ER data; i.e., an increased Al+-L distance diminishes the charge-induced polarization of the ligand. With regard to 2 and 3, the discrepancy of the Al+-L bond dissociation energy ordering yielded by the theoretical and experimental investigations cannot be ascribed to a basis set superposition error (BSSE,39,40 see Table 2). Still, the ab initio results predict ethene to be bonded more strongly to Al+ compared to acetylene in contrast to the experimental data. However, preliminary data resulting from density-functional and Hartree-Fock hybrid methods, i.e., the B3LYP functional, indicate a small improvement toward the reproduction of the experimental data.41 In addition, since the QCISD(T)/6-311+G(3df,2p) calculations are expected to be accurate by (2 kcal/ mol,23 the incorrect ordering in BDE data is within the error limits.42 Conclusions At 300 K the bond dissociation energies of the ground state complexes Al(L) + (L ) methane, acetylene, ethene, ethane) have been determined in a combined theoretical and experimental approach. The obtained values43 at 300 K are BDE(Al+-methane) ) 6 ( 2, BDE(Al+-acetylene) ) 13 ( 2, BDE(Al+-ethene) ) 13 ( 2, and BDE(Al+-ethane) ) 9 ( 2 kcal/mol for the side-on and 8 ( 2 kcal/mol for the end-on isomer. Contrary to the findings on the respective transitionmetal complexes, the aluminum complexes are characterized by (i) only one stable isomer for each Al(L)+ adduct except L ) ethane, (ii) almost exclusive (L ) methane and ethane) or dominating (L ) acetylene and ethene) electrostatic bonding interactions, and therefore, (iii) smaller BDE(Al+-L) values compared to BDE(M+-L). Acknowledgment. Continuous financial support by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie is acknowledged. D.S. acknowledges the Computer Group of the Max-Planck-Institut fu¨r Kohlenforschung in Mu¨lheim (Ruhr) for the generous allocation of CPU time. References and Notes (1) (a) Miller, L. M.; Coleman, J. J. CRC Crit. ReV. Solid State Mater. Sci. 1988, 15, 1. (b) Williams, J. O. Angew. Chem. AdV. Mater. 1989, 101, 1136. (c) Stringfellow, G. B. Organometallic Vapor Phase Epitaxy: Theory and Practice Academic Press: New York, 1989. (d) Cowly, A. H.; Jones, R. A. Angew. Chem. 1989, 101, 1235. (2) (a) Sauer, J. Chem. ReV. 1989, 89, 199. (b) Kassab, E.; Farguet, J.; Allevena, M.; Evleth, E. M. J. Phys. Chem. 1993, 97, 9034. (c) Kramer, G. J.; van Santen, R. A. J. Am. Chem. Soc. 1995, 117, 1766. (d) Haase, F.; Sauer, J. J. Am. Chem. Soc. 1995, 117, 3780. (3) Selected references: (a) Ziegler, K.; Holzkamp, E.; Breil, H.; Martin, H. Angew. Chem. 1955, 67, 541. (b) Natta, T. Macromol. Chem. 1955, 16, 213. (c) Sishta, S.; Hathorn, R. M.; Marks, T. J. J. Am. Chem. Soc. 1992, 114, 1112. (d) Pellececchia, C.; Grassi, A.; Immirzi, A. J. Am. Chem. Soc. 1994, 116, 1160 and references therein. (4) Chem. Eng. News 1993, 71 (May 31), 27.

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(b) Pople, J. A.; Scott, A. P.; Wong, M. W.; Radom, L. Isr. J. Chem. 1993, 33, 345. (25) Test calculations indicate the corresponding triplet species to be more than 80 kcal/mol higher in energy compared to the singlet ones. For example, the singlet-triplet gap of Al+ amounts to 106.9 kcal/mol.26 For more detailed discussions, see ref 8. (26) Moore, C. E. Atomic Energy LeVels; NSRDS-NBS 35; National Standards Reference Data Series; U.S. National Bureau of Standards: Washington, DC, 1971.

8790 J. Phys. Chem., Vol. 100, No. 21, 1996 (27) A σ-bound complex with Al-C distances on the order of 1.6-1.8 Å was not detected; see also ref 8b. However, note the predicted existence of an s-bound Sc(acetylene)+ complex (Bauschlicher, C. W., Jr.; Langhoff, S. R. J. Phys. Chem. 1991, 95, 2278 and ref 11a). (28) With regard to the Co(CH4)+ complexes, the (η2) C2V form was found to be a more stable minimum structure compared to the (η3) C3V coordination mode. The contrary findings for Co+ and Al+ may result from the dominating charge-induced polarization effects; see below and ref 11d. Similar aspects may be expected considering the Co(C2H6)+ and Al(C2H6)+ isomers; however, a frequency analysis of Co(C2H6)+ is not reported in ref 11d. (29) The respective data of the free ligands can be obtained from the authors upon request. (30) See, for example: Hehre, W. J.; Radom, L.; v. R. Schleyer, P.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (31) For experimental data on the structures of methane, acetylene, ethene, and ethane, see: Johnson, B. G.; Gill, P. M. W.; Pople, J. A. J. Chem. Phys. 1993, 98, 5612. (32) The NBO analysis was carried out on the optimized HF/6-31G(d,p), MP2(FU)/6-31G(d,p), and QCISD(T)/6-31G(d,p) wave functions, whereas the latter results are taken throughout the discussion: Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899. NBO is included in: Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. GAUSSIAN 94, NBO Version 3.1. (33) Additionally, the Mulliken charges for Al+ at the QCISD(T)/631G(d,p) level have been evaluated and amount to qAl(1) ) 0.954, qAl(2) ) 0.820, qAl(3) ) 0.813, qAl(4) ) 0.932, and qAl(5) ) 0.933. (34) By using the Uppal-Staley relationship,8c,8d,10 one obtains (BDE data in parentheses given in kcal/mol): CH4 (0.5) < C2H6 (9) < C2H2 (14) < C2H4 (15).

Sto¨ckigt et al. (35) The collision rate, kcoll, has been calculated according to the method described in: Su, T.; Chesnavich, W. J. J. Chem. Phys. 1982, 76, 5183. (36) (a) Hill, Y. D.; Freiser, B. S.; Bauschlicher, C. W., Jr. J. Am. Chem. Soc. 1991, 113, 1507. (b) Berthier, G.; Cimiraglia, R.; Daoudi, A.; Mestdagh, H.; Rolando, C.; Suard, M. J. Mol. Struct.: THEOCHEM 1992, 154, 43. (c) Schultz, R. H.; Armentrout, P. B. J. Phys. Chem. 1993, 97, 596. (37) Ranatunga, D. R. A.; Freiser, B. S. Chem. Phys. Lett. 1995, 233, 319. (38) Siegbahn, P. E. M.; Blomberg, M. R. A.; Svensson, M. J. Am. Chem. Soc. 1993, 115, 1952. (39) van Duijneveldt, F. B.; van Duijneveldt-van de Rijdt, J. G. C. M.; van Lenthe, J. H. Chem. ReV. 1994, 94, 1873. (40) (a) Schwarz, J.; Heinemann, C.; Schwarz, H. J. Phys. Chem. 1995, 99, 11405. (b) Heinemann, C.; Schwarz, J.; Koch, W.; Schwarz, H. J. Chem. Phys. 1995, 103, 4551. (41) BDE(Al(C2H2)+)/BDE(Al(C2H4)+) ) 16.7/16.4 kcal/mol (basis set: 6-31G(d,p)), 12.6/12.8 (6-311+G(d,p)), and 13.7/13.7 (6-311++G(3df,2p)). (42) An even more pronounced effect has been obtained for Fe(N2)+ and Fe(Xe)+ as is discussed in ref 40. (43) The error limits originate from the theoretical and experimental results: The QCISD(T)/6-311+G(3d,2p) method is effectively the same as G2; the latter was shown to yield accurate data within (2 kcal/mol.22 The uncertainty of the kinetic method and the equilibrium measurements are expected to be smaller than (2 kcal/mol due to cancellation of errors40a and the negligible influence of pressure determinations, respectively.

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