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J. Phys. Chem. 1996, 100, 16092-16097
Bonding, Electronic, and Vibrational Analysis of the Al-C2H4 Complex Using Density Functional Theory and Topological Method (ELF) M. E. Alikhani and Y. Bouteiller* Laboratoire de Spectrochimie Mole´ culaire (URA 508), UniVersite´ P. et M. Curie, Boıˆte 49, batiment F74, 4 Place Jussieu, Paris Cedex 05, France
B. Silvi Laboratoire de Chimie The´ orique (UPR 9070), UniVersite´ P. et M. Curie, Boıˆte 0137, batiment 2223, 4 Place Jussieu, Paris Cedex 05, France ReceiVed: NoVember 29, 1995; In Final Form: April 3, 1996X
The density functional theory (DFT) has been used to reexamine the Al-C2H4 complex because of discrepancies between the results of post-Hartree-Fock methods concerning the binding energy and the ordering of the metal-ligand stretching frequencies. In this study, equilibrium geometry, binding energy, and harmonic frequencies have been calculated using the 6-311G(2d,2p) basis set. It is shown that the Al-C2H4 complex has a C2V symmetry equilibrium structure and a 2B2 ground electronic state, which is strongly bound by -13.3 kcal/mol after BSSE correction (to be compared to the -16 kcal/mol experimental value). The bonding in the Al-C2H4 complex has been investigated by the electron localization function (ELF). The aluminumethylene bonding is found to be mostly electrostatic. The degree of weakening of the CdC double bond and the ordering of the two metal-carbon stretching modes have been discussed using a harmonic vibrational and force constant analysis and compared to the experimental results. Furthermore, a comparison of the shifting between the two wagging modes for complexed and free ethylene has allowed us, on the basis of isotopic substitutions, to reassign the symmetry of the only observed wagging mode (B2 instead of A1). We have also suggested the reassignment of the experimental band reported at 781 cm-1 from the B1 rocking mode to the A1 symmetric wagging one.
Introduction Aluminum atoms,1-5 as lithium atoms,6,7 are known to interact with ethylene to form π-bonded complexes. The knowledge of the molecular and electronic structure of such simple systems is important for understanding the nature of organometallic bonds and also for modeling the chemisorbed state of hydrocarbon molecules on these metals. During the last two decades, the Al-C2H4 complex has been experimentally characterized using various techniques.1-5 According to the three most important papers1,4,5 involving ESR and IR spectroscopies, the Al atom symmetrically binds to the ethylene molecule in a C2V structure, leading to a complex in the 2B2 electronic state with a binding energy of about 16 kcal/ mol. In parallel, since 1987 quantum chemical calculations have also been performed on this organometallic species using various methods.3,8-11 Xie and co-workers9 have performed ab initio calculations incorporating electron correlation effects through single and double configuration (CISD). They studied both σ-bonded (Cs structure, 2A′ electronic state) and π-type complexes (C2V structure, 2A1, 2B1, and 2B2 electronic states). At the DZ+P CISD level of theory, they clearly pointed out that the Al-C2H4 complex has a 2B2 electronic ground state with a binding energy of -10.1 kcal/mol while the 2B1 state is only very weakly bound (-1.3 kcal/mol) and the 2A1 state is unbound. At the same level of theory, they concluded that the Cs structure (2A′ electronic state) collapses to the C2V structure (2B2 state). They also calculated vibrational frequencies, but only for the natural isotopic species (Al-12C2H4). One year X
Abstract published in AdVance ACS Abstracts, August 1, 1996.
S0022-3654(95)03535-0 CCC: $12.00
later Gao and Karplus10 confirmed, at the UHF Moller-Plesset level, that the 2B2 electronic state (π-bonded geometry) is the ground state. More recently, Sanz et al.11 have studied the AlC2H4 complex at the CASSCF and second-order CI (SOCI) levels of theory with the DZ+P basis set. First, they calculated the 2B1 state to be more stable than the 2B2 one by 2.6 kcal/mol at the CASSCF level but reversed this conclusion at the SOCI level of calculation. Second, they also computed harmonic frequencies of the Al-12C2H4 complex with two methods (CASSCF and UMP2), but harmonic frequencies of the three isotopic species 12C/13C, H4/D4, and H4/H2D2 were reported only with the UHF/MP2 method. At both computational levels, there are contradictions between computed and experimental frequencies, especially in the case of the Al-C stretching motions, indicating that probably the potential energy surface of the AlC2H4 complex is not adequately enough described. To bring new elements for quantitative comparison between experiments and quantum chemical calculations, we have investigated the Al-C2H4 complex with the density functional theory (DFT). We have also carried out on this complex the electron localization function (ELF) to clarify the nature of the metal-ligand bonding. Methods of Calculation The DFT calculations have been performed with the Gaussian 92/DFT and the Gaussian 94/DFT quantum chemical packages.12 We have used Becke’s three-parameter functional13 for the exchange part and the nonlocal transformed correlation correction functional of Lee-Yang-Parr14 for the correlation one. The results have been carried out with the 6-311G(2d,2p) basis set of Pople and co-workers.15 © 1996 American Chemical Society
Bonding, Electronic, and Vibrational Analysis of Al-C2H4 TABLE 1: Equilibrium Geometry and Energy for the Al-12C2H4 Complex in the Ground Electronic State 2B2 parameter
DFT 6-311G(2d,2p)
CISDa DZ+P
CASSCFb DZ+P
exptc
rCC (Å) rCH (Å) rAl-C (Å) ∠HCH (deg) ∠CAlC (deg) ∠Θ (deg) EAl (au) Ecomplex (au) Ebinding (kcal/mol) ∆BSSE (kcal/mol) De (kcal/mol)
1.402 1.082 2.292 115.7 35.6 16.3 -242.386 366 -321.026 870 -14.2 0.95 -13.3
1.417 1.086 2.228 115.6 37.0 18.3
1.401 1.076 2.372 115.8 34.4 15.5
1.40 1.09 2.00 120.0 41.0 30.0
d
-11.6 -16d
a Reference 9. b Reference 11. c Reference 5, obtained by HFF. Reference 4.
Figure 1. Geometrical parameters of metal-ethylene complex in the C2V-symmetric equilibrium structure.
Results and Discussion 1. Geometry and Binding Energy. The geometrical parameters and the binding energy of Al-C2H4 are reported in Table 1. The structure and atom labeling are shown in Figure 1. Let us recall that the experimental geometrical parameters are determined by trial and error fitting in the harmonic force field (HFF) approximation.5 As shown in Table 1, the geometrical parameters of the C2H4 molecule are altered upon complexation with the Al atom. The equilibrium geometry of the complex, considered in the 2B2 ground electronic state (C2V symmetry), is quite accurately reproduced with the DFT method. Note that the present work confirms CISD9 and SOCI11 structural results. The experimental value proposed for the tilt angle (bending angle of CH2 groups with respect to the free planar molecule) is twice as large as that found by DFT, CISD, and SOCI methods (about 16°). The calculated HCH angle decreases by 1° with respect to the free molecule value. As for the Al-C distance, DFT, CISD, and SOCI results are close to each other, but the HFF value is at least 10% smaller than the quantum chemical one. Another significant change is the lengthening of the CdC double bond in the complex by comparison with the free molecule. The experimental estimate of this increase is +0.061 Å (+4.4%),5 to be compared with the +0.078 Å (+5.4%) DFT result. This bond length calculated with CISD and SOCI is 0.015 and 0.020 Å longer than the DFT value, respectively. The CH bond length is found to be very slightly shortened (
