Laser-Evaporated Aluminum Atom Reactions with Halogen Molecules

Department of Chemistry, University of Virginia, Charlottesville, Virginia 22901. Matthew Neurock. Department of Chemical Engineering, School of Engin...
0 downloads 0 Views 361KB Size
J. Phys. Chem. 1996, 100, 7317-7325

7317

ARTICLES Laser-Evaporated Aluminum Atom Reactions with Halogen Molecules. Infrared Spectra of AlXn (X ) F, Cl, Br, I; n ) 1-3) in Solid Argon Parviz Hassanzadeh, Angelo Citra, and Lester Andrews* Department of Chemistry, UniVersity of Virginia, CharlottesVille, Virginia 22901

Matthew Neurock Department of Chemical Engineering, School of Engineering & Applied Science, UniVersity of Virginia, CharlottesVille, Virginia 22901 ReceiVed: October 16, 1995; In Final Form: February 9, 1996X

Reactions of laser-evaporated aluminum atoms with molecular fluorine, chlorine, bromine, and iodine in excess argon during condensation onto a CsI window at 11 ( 1 K produced the AlXn (X ) F, Cl, Br, I and n ) 1-3) and Al2X6 molecules, which were characterized by infrared absorption spectroscopy. Low laser power favored the primary reaction product AlX and AlX2 transient species over the more stable secondary reaction product AlX3 molecules. Chlorine and bromine isotopic structures substantiated the molecular identifications and vibrational assignments. DFT calculations were done for the AlCln and AlBrn series to support the vibrational assignments. Possible Al2Cl4 structures were also explored by DFT calculations, and evidence is presented for a distorted Cl2AlCl2Al structure. The present study provides further evidence for transient aluminum dihalide radicals for the four halogens.

Introduction Aluminum is an important structural material and a component in solid propellants, and thus its chemical reactions have been the subject of a great deal of investigation. Spectroscopic studies of aluminum halide intermediate species are limited due to their further reactivity. Transient aluminum halides are conventionally produced from the reaction of resistively heated elemental aluminum with aluminum trihalides or with halogen molecules. Vibrational spectroscopy of the aluminum monohalides1-7 and the stable aluminum trihalides and dialuminum hexahalides7-17 is well-known. Matrix infrared spectra of AlF,3,5,6 AlF36,8 AlCl,4,5,7,8 AlCl3,10-13 AlBr,4 AlBr3,14,15 AlI3,15 and dialuminum hexahalides11,15-20 have been reported. However, infrared spectra of the divalent aluminum halide radicals, except for aluminum dichloride,7,8 have not been reported. On the other hand, infrared spectra of the transient hydrides AlH, AlH2, and AlH3 have been studied by four groups,21-24 the infrared spectrum of HAlOH has been studied by one group,25 and ESR spectra have been reported for AlH2, HAlOH, and Al(OH)2.26,27 Furthermore, the chemistry of AlCl2 and AlBr2 has been explored,7 and donor-stabilized Al2Br2 and Al2Br4 have recently been prepared.28 Quantum chemical calculations have been done for the aluminum fluoride29-34 and aluminum chloride35-38 molecular species studied here. DFT calculations were performed for AlCl, AlCl2, AlCl3, and Al2Cl4 structures to support vibrational assignments. Analogous calculations were done for AlBr, AlBr2, and AlBr3. Laser evaporation has proven to be an effective technique for producing atomic vapor for reaction with other precursors X

Abstract published in AdVance ACS Abstracts, April 1, 1996.

S0022-3654(95)03065-6 CCC: $12.00

such as halogens. We have previously reported FTIR studies of the reaction products of the laser-evaporated boron atoms with halogens39 and aluminum atoms with oxygen40 and hydrogen23 in solid argon. The present investigation presents the results of similar studies of aluminum atom and halogen molecule reactions with particular emphasis on the novel aluminum dihalide radical intermediates. Experimental Section The vacuum system and the chamber for matrix-isolation experiments have been described previously.41 A closed-cycle refrigerator (CTI Cryogenics, Model 22) was used to cool the substrate CsI window to 11 ( 1 K as monitored by a diode indicator on the refrigerator cold stage. Argon/reagent gas samples were deposited continuously at 2-3 mmol/h for 2-6 h periods. The laser ablation method has been described previously.39,40,42-44 The fundamental (1064 nm) of a Qswitched Nd:YAG (Quanta-Ray DCR-11) laser was focused on the aluminum (Aesar, 99.998%) target, which was epoxy glued to a 6 mm o.d. glass rod and rotated at 1 rpm. Typically laser energies of 10-50 mJ/pulse at the target with pulse duration of 10 ns gave sufficient aluminum atoms for observation of reaction product absorptions. Fourier transform infrared (FTIR) spectra were recorded on a Nicolet 5DXB instrument at 2 cm-1 resolution with an accuracy of better than 0.5 cm-1 and a Nicolet 60SXR instrument at 0.25 and 0.5 cm-1 resolutions with an accuracy of better than 0.1 cm-1 to resolve isotopic splittings. Matrix samples were temperature cycled to allow diffusion and reaction of trapped species by monitoring spectrum, temperature of cold stage, and dynamic pressure in the vacuum system. Annealing cycles were done to three successively higher temperatures over 2-4 min periods with dynamic system pressure rising from 10-7 © 1996 American Chemical Society

7318 J. Phys. Chem., Vol. 100, No. 18, 1996

Hassanzadeh et al. TABLE 1: Infrared Absorption Bands for the Reaction Products of the Laser-Ablated Aluminum with Molecular Fluorine in Solid Argon annealinga absorption (cm )

T < 35 K

T < 45 K

assignment

975.0 947.0 944.0 931.7 928.7 887.5 860.7 784.7 776.9 772.0 755.3 430.1

+ + + + + + + -

+/0 + + + +/0 -

Al2F6 (B1u) AlF3 (ν3) site site AlF3 (ν3) site AlF2 (ν3) unidentified Al2F6 (B2u) site AlF AlF AlF2 (ν1) (AlF)2

-1

a Annealing behavior: +, grow; -, decrease; +/0, slight grow or no change.

Figure 1. Infrared spectra of the Al + F2 reaction products in solid argon at 11 ( 1 K in the 1000-700 cm-1 region with aluminum laserablated at 50 mJ/pulse: (a) after a 21/2 h codeposition of fluorine/argon (1:800); (b) after a 11/2 h codeposition of fluorine/argon (1:400); (c) after a 11/2 h codeposition of fluorine/argon (1:100).

Torr to between 10-6 and 10-5 Torr. Presented spectra show sharp bands which clearly demonstrate that no significant argon loss or reagent clustering occurred during these temperature cycles. Sample (solid argon) vapor pressure measurements suggest that first, second, and third temperature cycles employed here allowed the matrix sample to reach temperatures near 22, 27, and 32 ( 2 K. Reagents fluorine (Matheson) and chlorine (Matheson) were handled in a passivated stainless manifold; bromine (Mallinckrodt) was purified by vacuum distillation and then transferred into a 3 L stainless steel can and diluted with argon. Solid iodine (Fisher) was placed in a 3 L glass bulb and diluted with 100-200 Torr of argon. Results Aluminum atom reactions with molecular halogen precursors will be described for different laser powers, halogen/argon concentrations, and reaction geometries, and DFT calculations for the AlCln and AlBrn species will be presented. Fluorine. A 1:400 mixture of fluorine/argon (F2/Ar) was codeposited at 11 ( 1 K with laser-evaporated aluminum atoms. The Al-F stretching region is shown in Figure 1, and new bands are listed in Table 1. Oxygen contamination in the system is not significant as attested by the lack of Al2O absorption at 992 cm-1.40 The annealing behavior of the observed bands is shown in Figure 2. The 772.0 and 776.9 cm-1 bands decreased on first annealing and vanished on higher annealing along with a weaker band at 430.1 cm-1. The 887.5 and 755.3 cm-1 bands decreased together on annealing to 27 K and vanished at 32 ( 2 K. The bands at 947.0 and 931.7 cm-1 with a shoulder at 928.7 cm-1 increased on first and second annealing and decreased thereafter. In another experiment with a 1:100 mixture of F2/Ar, the band intensity distribution changed (Figure 1). The intensity of the bands at 975.0, 947.0, 931.7, and 784.7 cm-1 increased relative to other absorptions.

Figure 2. Infrared spectra of the Al + F2 reaction products in solid argon at 11 ( 1 K in the 1000-700 cm-1 region: (a) after a 11/2 h codeposition of fluorine/argon (1:400) with aluminum laser ablated at 50 mJ/pulse; (b) after annealing at 22 ( 2 K; (c) after annealing at 27 ( 2 K; (d) after annealing at 32 ( 2 K.

Finally, the F2/Ar concentration was diluted to 1:800, and the reaction was confined to occur on the matrix surface by laser ablating the aluminum inside a glass tube which was extended to a few millimeters from the cold window.39 The intensity of the 776.9 and 772.0 cm-1 bands increased by a factor of 2 over the 887.5 and 755.3 cm-1 bands and by a factor of 3-4 over the 947.0 and 931.7 cm-1 bands; the 975.0 and 784.7 cm-1 bands previously observed with higher fluorine/ argon concentration did not appear (Figure 1a). Chlorine. Codeposition of laser-ablated aluminum atoms with a 1:400 mixture of chlorine/argon (Cl2/Ar) onto a cold window at 11 ( 1 K produced major bands at 619.2 cm-1 (with a shoulder at 615.6 cm-1), 563.6 cm-1 (with shoulders at 561.3 and 558.2 cm-1), 461.0 cm-1 (with a shoulder at 457.2 cm-1) and 455.3 cm-1 (with a shoulder at 450.2 cm-1) and a weak absorption at 496.8 cm-1; longer sample deposition also

IR Spectra of AlXn in Solid Ar

J. Phys. Chem., Vol. 100, No. 18, 1996 7319

Figure 3. Infrared spectra of the Al + Cl2 reaction products in solid argon at 11 ( 1 K in the 645-400 cm-1 region after 3 h codepositions of chlorine and aluminum laser-ablated at 50 mJ/pulse: (a) chlorine/ argon (1:400) with aluminum ablated inside an extended glass tube; (b) chlorine/argon (1:400) with open aluminum target; (c) chlorine/ argon (1:100) with open target; (d) infrared absorption spectrum at 0.5 cm-1 resolution in the 570-550 cm-1 region.

TABLE 2: Infrared Absorption Bands for the Reaction Products of Laser-Ablated Aluminum and Molecular Chlorine in Solid Argon annealinga absorption (cm )

T < 35 K

T < 40 K

assignment

619.2 619.2 615.6 610.2 607.6 600.0 596.0 563.6 561.3 558.2 529.0 496.8 492.3 482.7 461.0 457.2 sh 455.3 450 sh 421.7

+ + + + + + + + + + + +

+ + + + + + + +

Al2Cl6 (ν8) AlCl3 (ν3) AlCl3 (ν3) (Cl2AlCl2Al) (Cl2AlCl2Al) AlCl3--N2 complexb AlCl3--N2 complexb Al35Cl2 (ν3) Al35Cl37Cl (ν3) Al37Cl2 (ν3) (Cl2AlCl2Al) AlO2 site AlO2 Al2Cl6 (ν16) Al35Cl2 (ν1) Al35Cl37Cl (ν1) Al35Cl Al37Cl Al2Cl6 (ν13)

-1

a

Annealing behavior: +, grow; -, decrease. b Reference 11.

produced weak absorptions at 529.0, 482.7, and 421.7 cm-1. The spectrum after 3 h sample deposition is shown in Figure 3; the annealing behaviors are shown in Figure 4. The 619.2, 615.6 cm-1 as well as the 610.0, 600.0, 529.0, and 482.7 cm-1 absorptions grew on annealing, whereas the 563.6, 561.3 cm-1 and the 455.3, 450.2 cm-1 bands decreased stepwise on annealing. The 496.8 cm-1 AlO2 band grew on annealing as

Figure 4. Infrared spectra of the Al + Cl2 reaction products in solid argon at 11 ( 1 K in the 645-400 cm-1 region: (a) after 3 h codeposition of chlorine/argon (1:400) with aluminum laser ablated inside an extended glass tube at 50 mJ/pulse; (b) after annealing at 22 ( 2 K; (c) after annealing at 27 ( 2 K; (d) after annealing at 32 ( 2 K.

reported.40 The 461.0 and 421.7 cm-1 absorptions followed the 563.6 and 482.7 cm-1 bands, respectively. In a similar experiment the aluminum target was positioned inside a glass tube such that the evaporated aluminum atoms could react with the chlorine just on the surface. As shown in Figure 3b, the major bands were produced in different intensity ratios; particularly the 563 cm-1 absorption dominated all other bands. In another experiment a 1:100 mixture of Cl2/Ar was used, and the relative intensity of the bands changed to the order 619.2 > 563.6 > 496.8 ≈455.2 > 461.0 > 482.7 (Figure 3). Several experiments were carried out with laser energies of 10, 20, and 40 mJ/pulse at the target and with chlorine/argon concentrations of 1:400 and 1:600, and spectra were recorded at 0.25 and 0.5 cm-1 instrumental resolutions to resolve the chlorine isotopic patterns. The best results were obtained with 40 mJ/pulse, chlorine/argon ratio of 1:400, a resolution of 0.5 cm-1, and a short period of sample deposition. Under such conditions the 563.5 cm-1 band was resolved into a 9:6:1 triplet structure at 563.6, 561.3, and 558.2 cm-1 (Figure 3d). Bromine. A 1:800 mixture of bromine/argon (Br2/Ar) was codeposited with aluminum vapor using a laser energy of 10 mJ/pulse at the target. The spectrum after a 2 h sample deposition (Figure 5) revealed three major bands at 508.4, 457.8, and 357.9 cm-1 with relative band intensities in the order of 457.8 > 357.9 > 508.4 cm-1. After 5 h sample deposition, the 457.8 cm-1 band grew by a factor of 3, the 508.4 cm-1 band grew by a factor of 2, the 357.9 cm-1 band grew slightly, and new weak bands appeared at 408.6 and 397.7 cm-1. After first annealing, all bands became sharper or grew slightly, and new absorptions appeared at 431.6, 498.6, and 494.5 cm-1. Annealing the second time caused the 457.8 and 357.9 cm-1 bands to decrease, the 508.4 cm-1 band intensity remained unchanged, the 431.6, 498.6, 494.5, 408.6, and 397.7 cm-1

7320 J. Phys. Chem., Vol. 100, No. 18, 1996

Hassanzadeh et al.

Figure 5. Infrared spectra of the Al + Br2 reaction products in solid argon at 11 ( K in the 530-330 cm-1 region: (a) after a 2 h codeposition of bromine/argon (1:800) with aluminum laser ablated at 10 mJ/pulse; (b) after a 21/2 h more codeposition; (c) after annealing at 22 ( 2 K; (d) after annealing at 27 ( 2 K; (e) after annealing at 32 ( 2 K.

TABLE 3: Infrared Absorption Bands for the Reaction Products of the Laser-Ablated Aluminum and Molecular Bromine in Solid Argon annealinga absorption (cm-1)

T < 35 K

T < 40 K

assignment

508.4 498.6 494.5 481.9 458.4 457.8 457.2 431.6 408.6 397.7 380.0 357.9 348.3

+ appears appears appears appears + + appears -

+/0 + + + + +/0 +/0 + -

AlBr3 (ν3) Al2Br6 (ν8) Al2Br6 (ν8) (Br2AlBr2Al) Al79Br2 (ν3) Al79Br81Br (ν3) Al81Br2 (ν3) (Br2AlBr2Al) unidentified unidentified Al2Br6 (ν16) AlBr (AlBr2(ν1))

a Annealing behavior: +, grow; -, decrease; +/0, slight grow or no change.

bands grew. The 431.6 cm-1 absorption dominated this set of bands, and a new set of bands at 490.7 and 481.9 cm-1 appeared. Upon final annealing, the 508.4 cm-1 absorption decreased, the 457.8 and 357.9 cm-1 bands vanished, and the 408.6 and 397.7 cm-1 bands remained intact; however, the 431.6, 498.6, 494.5, 490.7, and 481.9 cm-1 bands increased. Several experiments were carried out with different laser energies and bromine/argon concentrations. With a laser energy of 25 mJ/pulse at the target and a bromine/argon ratio of 1:800, the spectral features were the same as those described earlier, except that the 408.6 cm-1 band intensity was comparable to the 508.4 and 357.9 cm-1 band intensities. Increasing the

Figure 6. Infrared absorption spectra in the 460-290 cm-1 region after 6 h codepositions of iodine and aluminum in excess argon at 11 ( K: (a) iodine/argon (1:800) with aluminum laser ablated at 10 mJ/ pulse; (b) iodine/argon (1:800) with aluminum laser ablated at 40 mJ/ pulse; (c) iodine/argon (1:400) with aluminum laser ablated at 10 mJ/ pulse; (d) iodine/argon (1:400) with aluminum laser ablated at 40 mJ/ pulse.

concentration of bromine/argon to 1:400 with a low laser energy of 10 mJ/pulse at the target changed the relative intensity of the bands in the order of 508.4 > 457.8 > 357.9 cm-1. A higher laser energy of 35 mJ/pulse at the target with a bromine/argon ratio of 1:400 further enhanced the relative intensity of the bands in the order 508.4 > 457.8 > 357.9 cm-1; the major absorptions which grew after annealing to higher temperatures in the experiments with 10 mJ/pulse of laser energy and bromine/argon ratio of 1:800 were readily observed on initial sample deposition. Several spectra were recorded at high resolution in an attempt to resolve the bromine isotopic structure for the 457.8 cm-1 band. The best spectra were obtained at a low laser energy of 10 mJ/pulse at the target, a dilute concentration of bromine/ argon of 1:1000, and a short period of sample deposition. After first annealing, a partially resolved 1:2:1 triplet pattern at 458.4, 457.8, and 457.2 cm-1 was observed (full width at halfmaximum ) 1.5 cm-1). Iodine. A dilute mixture of iodine in argon (1:800) was codeposited with laser-evaporated aluminum atoms using a laser energy of 10 mJ/pulse at the target for 6 h (Figure 6). The spectra revealed two major bands at 301.9 and 385.9 cm-1, which grew slightly on first annealing and decreased thereafter, and a weak band at 435.0 cm-1, which grew on second annealing and decreased slightly on higher temperature annealing; the 495.8 cm-1 AlO2 band and a new band at 446.8 cm-1 with a satellite at 443.6 cm-1 appeared on first annealing. Additional new bands appeared at 423.4 and 366.5 cm-1 upon second annealing and increased on further annealing. Another experiment was done with 40 mJ/pulse at the target and dilute I2/Ar concentration (1:800); the spectra before and

IR Spectra of AlXn in Solid Ar

J. Phys. Chem., Vol. 100, No. 18, 1996 7321

TABLE 4: Infrared Absorption Bands for the Reaction Products of the Laser-Ablated Aluminum and Molecular Iodine in Solid Argon

TABLE 5: DFT Calculated and Observed Parameters for the AlCl, AlCl2, and AlCl3 Molecules species

annealinga absorption (cm )

T < 30 K

T < 45 K

assignment

AlCl

495.8 446.9 443.6 435.0 423.4 385.9 366.5 301.9

+ appears appears 0 0 + 0 +

+ + + + + + -

AlO2 (I2AlI2Al)b (I2AlI2Al) site AlI3 (ν3) Al2I6 AlI2 (ν3) (I2AlI2Al) AlI

AlCl2

-1

a Annealing behavior: +, grow; -, decrease; 0, no change. b Could be due to AlI3 complex.

after annealing were similar to the low laser power and dilute iodine experiment except that the upper absorptions (385.9 and 435.0 cm-1) were slightly more intense than the 301.9 cm-1 band (Figure 6b). A similar experiment was carried out with a lower laser energy of 10 mJ/pulse at the target and a higher concentration of I2/Ar (1:400); the 385.9 cm-1 band was the only major band, and traces of 301.9 and 435 cm-1 bands were also detected (Figure 6). The 385.9 cm-1 band intensity increased 80% on photolysis with 254 nm light for 30 min. The annealing behavior described earlier was also observed. Finally, a higher laser energy of 45 mJ/pulse at the target and the higher I2/Ar concentration (1:400) were used; major bands were produced in higher yield and with relative intensity of 385.9 > 301.9 > 435.0 cm-1. Calculations. DFT calculations were performed on a variety of aluminum chloride structures using the DeGauss program developed by Cray Research Inc.45 This employs Gaussian basis sets to solve the single-particle Kohn-Sham equations.46 The local spin density exchange-correlation potential is represented by the Vosko-Wilk-Nusair potential.47 Nonlocal gradient corrections to the exchange and correlation are determined within the SCF cycle using the correlation and exchange potentials developed by Becke and Perdew, respectively.48,49 DFT-optimized TZVP quality (73111/6111/1) basis sets were used for both aluminum and chlorine. All SCF calculations converged to within 5 × 10-7 hartrees on the SCF energy, and all structures were optimized to within 8 × 10-4 hartrees/Å. Second derivatives, force constants, and frequencies were all determined numerically using the harmonic oscillator approximation. Finally, all calculations used the 27Al and 35Cl isotopes of aluminum and chlorine. Structures were optimized, and vibrational frequencies were calculated for AlCl, AlCl2, and AlCl3. These results are summarized in Table 5 with experimental observations in brackets where available. It is apparent that the calculated bond lengths for the monoand trichloride are longer by 0.048 and 0.026 Å, respectively. No such data are available for the dichloride, but considering the fact that the calculated vibrational frequency follows the same trend as that for AlCl and AlCl3, it is likely that the AlCl2 bond length is too large by 0.03-0.05 Å. The degenerate stretching frequency for AlCl3 is broken due to a slight inequivalence between the three calculated Al-Cl bond lengths. The error in the calculated vibrational frequencies for these molecules increases as the size increases, from just 7 cm-1 for the diatomic to roughly 30 cm-1 for the trichloride, all below the observed values. A previous study of AlCl2 and AlCl3 at the HF/6-31G* level gave stretching frequencies 20-25 cm-1 too high.38 Despite these inaccuracies, the DFT results for these three molecules are very useful as they allow us to estimate the

bond length (Å)

2.178, 2.160a [2.130 gas]c 2.131 118.3 2.109a

AlCl3

bond angle (deg)

2.094 2.077c 2.077a [1.068 gas]e

frequencies (cm-1) 448.6 (119)b [477.4 gas]c [455.2 matrix] 543.4(164), 438.7(47), 150.8(7), 587.7, 480.1a

[115 ( 3 matrix] [563.6, 461.0 matrix] 120 594.2 (177), 593.6 (177) e′ 364.4 (0) a1′, 156.2 (36) a2′′, 135.5 (7), 121.9 (9) e′ 120 628, 382, 204, 148d 120 642.3, 399.5, 213.5, 156.6a 120 [616, 375, 214, 151 gas]f [619.2 matrix]

a HF/6-31G*, ref 37. b DFT calculated intensities (km/mol). c Reference 1. d Scaled HF, ref 38. e Spiridonov, V. P.; Ermolayeva, L. I. High Temp. Sci. 1981, 14, 285. f Tomita, T.; Sjogren, C. E.; Kaleboe, P.; Papatheodoru, G. N.; Rytler, E. J. Raman Spectrosc. 1983, 14, 415.

TABLE 6: DFT Calculated Al2Cl4 Geometries and Energies relative SCF energy energies (hartrees) (kJ/mol) Cl2AlCl2Al (Cs) Cl2AlCl2Al (C2V) Cl2AlAlCl2 (D2d) AlCl3AlCl (“C3V”) Cl2AlAlCl2 (D2h) Cl3AlAlCl (C3V) ClAlCl2AlCl (C2V)

-2326.1715 -2326.1706 -2326.1690 -2326.1687 -2326.1593 -2326.1545 -2326.1091

0.0 2.3 6.5 7.3 32.0 44.6 163.7

notes stable geometry one imaginary frequency three imaginary frequencies stable geometry three imaginary frequencies stable geometry stable geometry

errors involved in calculations on the larger Al2Cl4 species and to take this into account when using calculated frequencies to make assignments. In addition to the simple monoaluminum halides, DFT calculations were performed on a number of Al2Cl4 geometrical isomers to determine structural characteristics and to predict infrared spectra. The semiempirical MNDO method has previously been used to estimate the relative stabilities of several structures, and it was found that the Cl2AlCl2Al (C2V) structure was the most stable.7 The DFT calculations reproduced the same order of stability for a selected sample of these conformers, the C2V form being considerably lower in energy than other structures. The results of the DFT calculations are summarized in Table 6. However, three of these structures, the C2V, D2h, and D2d isomers, were found to have imaginary vibrational frequencies, indicating that these are not stable geometries. The nature of the imaginary mode calculated for the C2V structure suggested that a deviation of the ring from a planar to a puckered conformation would be favorable. When the geometry of this structure is optimized, the result is a stable molecule of Cs symmetry with the lowest energy of all the Al2Cl4 conformers investigated in this study. The calculated structural and vibrational attributes are detailed in Figure 7 and Table 7. The C3V structure is also a stable geometry, and its parameters are also given in Figure 7 and Table 7. One additional geometry not investigated previously was also calculated, the ClAlCl2AlCl (C2V) “boat structure”, which is found to be a stable molecule, as in the Cs structure, with very high energy. This is a puckered central ring with the thermal chlorines angled upward. Finally, DFT calculations were done for AlBr, AlBr2, and AlBr3 using DZVP basis sets (63321/5321/41) for Br and (6321/ 521/1) for Al, and the results are summarized in Table 8. Comparison of the calculated and gas phase1 bond lengths for AlBr suggests that the DFT values are too long by approximately 0.06 Å; note, however, the trend in decreasing calculated bond

7322 J. Phys. Chem., Vol. 100, No. 18, 1996

Hassanzadeh et al.

Figure 7. Al2Cl4 structures.

TABLE 7: Frequencies and Intensities Calculated for Cl2AlCl2Al (Cs) and AlCl3AlCl (“C3W”) by DFT Cl2AlCl2Al (Cs) freq (cm

-1)

AlCl3AlCl (“C3V”)

int (km/mol)

freq (cm-1)

int (km/mol)

160 180 90 20 151 6 20 4 1 4 0 1

585 437 415 333 238 196 174 171 132 119 107 83

197 97 95 1 126 11 11 9 10 4 5 5

572 490 377 318 260 193 190 160 133 116 99 50

TABLE 8: DFT Calculated and Observed Parameters for the AlBr, AlBr2, and AlBr3 Molecules species AlBr AlBr2 AlBr3

a

bond length (Å)

bond angle (deg)

frequencies (cm-1)

350.8 (95)a [375.4 gas]b [357.9 matrix] 446.6 (152), 322.4 (29), 95.4 (2) [457.8, 348.3 matrix] 2.259, 2.255 120.0 ( 0.3 489.7 (155), 485.2 (155) e′ 220.3 (0) a1 145.3 (15) a2′′ 83.1 (2), 81.4 (2) e′ [503, 176, 123, 83 gas]c [508.4 matrix]

2.355 [2.295 gas]b 2.299 120.9

DFT calculated intensities (km/mol). b Reference 1. c Reference 15.

lengths and increasing calculated frequencies in the series AlBrAlBr2-AlBr3. As with AlCl3, the calculated bond lengths in AlBr3 are not exactly the same. Discussion The new absorptions produced from the reaction of aluminum atoms with halogen molecules will be identified for each halogen. Fluorine. Four major bands were observed on deposition of Al and F2, namely 947.0, 887.5, 772.0, and 755.3 cm-1

(Figure 1). On annealing, the latter three bands decreased and the 947.0 cm-1 band increased as did weaker bands at 975.0 and 784.7 cm-1 (Figure 2), which forms the basis for the following assignments. Stable Species AlF3 and Al2F6. The bands at 947.0 and 931.7 cm-1 grow on annealing and are favored as the fluorine concentration is increased. These bands are 2 cm-1 blue-shifted from the antisymmetric stretching vibrational mode ν3(e′) for the thermally evaporated AlF3 molecule trapped in solid argon.6 The splitting in the absorption is most likely as a result of different trapping sites for the molecules, although the possibility of removal of degeneracy due to matrix environment or a molecule perturbed by a neighboring species cannot be ruled out. A subsequent matrix study9 has questioned the former assignment to AlF3, but the observation of gas phase AlF3 at 945 or 935 cm-1 in two studies50,51 supports the Snelson assignment.6 Finally, the present method of forming AlF3 avoids aggregation with undecomposed Al2F6 as a complication in the spectra, and the good agreement with Snelson and a MP2 frequency33 calculation (946 cm-1) reinforces this assignment to isolated AlF3 in solid argon. The 975.0 and 784.7 cm-1 bands grow on annealing and are favored at higher fluorine concentration. These bands are within 2 cm-1 of the strongest vibrations of Al2F6 in solid argon,6 which supports the identification of both AlF3 and Al2F6 in the present experiments. Transient Species AlF and AlF2. The 772.0 and 776.9 cm-1 bands are dominant at very low concentration of fluorine and decrease on annealing, which are indicative of a primary reaction product. These bands are assigned to the fundamental of diatomic AlF trapped in two different matrix sites. This is in agreement with the previously reported AlF spectrum in solid argon at 772 cm-1 with a site at 778 cm-1 which was produced from the reaction of HF with aluminum heated to 1300 K3 and with the argon matrix value of 776 cm-1 observed from the codeposition of aluminum vapor with AlF3.6 The MP2 calculated frequency is slightly lower at 746 cm-1.33 Both are redshifted from the gas phase value of 793 cm-1 deduced from an emission study.1 Finally, a weak band at 430.1 cm-1 corresponds to the strongest infrared absorption of (AlF)2 in solid argon.3 The sharp 887.5 and 755.3 cm-1 bands track together under all experimental conditions and are favored over the AlF3 bands at lower fluorine concentration. These bands decrease on annealing and belong to a new transient species other than AlF in these experiments. The AlF3 and AlF vibrational frequencies are higher by an average factor of 1.6 than their chlorine analogues AlCl3 and AlCl (to be discussed next). If the AlCl2 absorption frequencies are multiplied by this factor, values of 898 and 738 cm-1 are predicted for the antisymmetric and symmetric stretching vibrational modes of AlF2, which are in good agreement with the observed 887.5 and 755.3 cm-1 bands. Quantum chemical calculations at the UMP2 level33 predict a 2A radical with 118 ( 1° valence angle and modes at 886 and 1 745 cm-1 just below the values assigned here to AlF2, which strongly supports the present first experimental evidence for the AlF2 free radical. Annealing produces a weak band at 860 cm-1, which could be due to aggregated AlF2. Chlorine. The major products appear at 619.2, 563.6, 461.0, and 455.3 cm-1 on codeposition of Al and Cl2 (Figure 3a,b). On annealing, the 455.3 cm-1 band decreases more than the 563.6 and 461.1 cm-1 bands while the 619.2 cm-1 band increases, and bands grow at 607.2, 600.0, 529.0, 482.7, and 421.7 cm-1. Stable Species AlCl3 and Al2Cl6. The 619.2, 615.6, 482.7,

IR Spectra of AlXn in Solid Ar and 421.7 cm-1 bands are present in all experiments, grow on annealing, and are favored over the other bands as the chlorine concentration is increased. The 619.2 and 615.6 cm-1 bands are in excellent agreement with the antisymmetric stretching vibration of natural chlorine isotopic AlCl3 in solid argon.8-11,12 Furthermore, the 421.7, 482.7 cm-1 and part of the 619.2 cm-1 bands which grow on annealing are in good agreement with the ν13 ) 422.1 cm-1, ν16 ) 482.6 cm-1, and ν8 ) 620.3 cm-1 vibrational modes of Al2Cl6 in solid argon16 and are slightly shifted from the gas phase values of 420, 484, and 625 cm-1.19 The 496.8 cm-1 band, which grows on annealing, behaves like AlO2 and is appropriately assigned.40 The bands at 600-596 cm-1 also grow on annealing and were observed in the earlier thermal work.7,8 These bands are probably due to aggregated AlCl3 or the reaction products of AlCl3 with other species such as Cl2 or N2.11 Transient Species AlCl and AlCl2. The 455.3 and 450.0 cm-1 absorptions show a 3:1 intensity ratio in all experiments, which is in agreement with the natural abundance of chlorine isotopes for a single chlorine-containing species. These absorptions are favored over the AlCl3 bands at lower concentration of chlorine and gradually diminish on annealing characteristic of a primary transient species. The chlorine isotopic ratio of R35/37 ) 455.3/450.0 ) 1.011 78 is in agreement with the calculated value of 1.012 02 for an AlCl harmonic oscillator. These vibrational frequencies are also in good agreement with the reported argon matrix value for diatomic AlCl and the present 448.6 cm-1 DFT calculated value.4,7,8 The 563.6 cm-1 band is the strongest absorption at relatively lower concentration of chlorine and decreases on annealing, which are characteristic of primary transient species. This band is resolved into a clear 9:6:1 triplet pattern at 563.6, 561.3, and 558.2 cm-1 indicative of involvement of two equivalent chlorine atoms in the vibration. The 563.6 cm-1 band is assigned to the antisymmetric (ν3) stretching vibration mode of AlCl2. This observation, especially the resolved 9:6:1 triplet structure, confirms the previous assignment of this band recorded at 2 cm-1 resolution after codeposition of a mixture of Cl2/Ar with resistivity heated aluminum.7,8 The valence angle upper limit calculated from the G-matrix element for the antisymmetric stretching mode predicts a 115 ( 3° value. The 461.0 cm-1 absorption which follows the 563.6 cm-1 band in all experiments and annealing processes is also in the appropriate region for the symmetric stretching mode of AlCl2. Furthermore, the molecule HAlCl2 has Al-Cl2 stretching modes at 579 and 481 cm-1, just 15-20 cm-1 higher than the 563.6 and 461.0 cm-1 AlCl2 stretching modes.52 The 461.0 cm-1 band was observed in the thermal Al + Cl2 studies7,8 and assigned to the ν1 mode of AlCl2.8 The observation of the symmetric stretching mode ν1 is in accord with a bent molecule as determined from the isotopic splittings in the ν3 fundamental. These assignments are in agreement with HF calculations37 which predict 588 and 481 fundamentals for the 2A1 state AlCl2 radical. Furthermore, the present DFT calculations predict bands at 543 and 439 cm-1 for AlCl2 just 20-25 cm-1 below the observed values. Al2Cl4. The bands that grow on annealing at 610 and 529 cm-1 at the expense of AlCl2 could be due to aggregated AlCl2 or Al2Cl4 species. The most stable Cl2AlCl2Al species is predicted to have strong Al-Cl stretching modes at 572 and 490 cm-1, and the slightly higher energy species AlCl3AlCl is calculated to have strong bands at 585 and 437 cm-1. Since the present DFT calculations predict AlCl, AlCl2, and AlCl3 20-25 cm-1 too low, the Cl2AlCl2Al species should absorb at higher wavenumbers by at least 20-25 cm-1 than the DFT

J. Phys. Chem., Vol. 100, No. 18, 1996 7323 calculations predict. Accordingly, the 610 and 529 cm-1 bands that grow on annealing are tentatively assigned to the Cl2AlCl2Al species calculated here. Bromine. Sharp bands at 508.4, 457.8, and 357.9 cm-1 dominate the deposition spectra (Figure 5a,b). Annealing produces other bands at 498.6, 481.9, 431.6, and 380.0 cm-1. Stable Species AlBr3 and Al2Br6. The 508.4 cm-1 band dominated the other bands at higher concentration of Br2/Ar and higher laser power where dissociation of molecular to atomic halogen increases; this band is also stable on second annealing and decreases thereafter and is in excellent agreement with the doubly degenerate antisymmetric (ν3) stretching vibrational mode of AlBr3 in solid argon.14 Similar to the Al + Cl2 experiments, the 498.6 and 380.0 cm-1 bands grow on annealing and are in agreement with the Al-Br stretching vibrations (ν16) and (ν8) for Al2Br6.20 Transient Species AlBr and AlBr2. The 357.9 cm-1 band is favored at low laser power, dilute concentration of bromine, and decreases gradually on annealing, which suggests involvement of a transient species. This band is assigned to the fundamental of diatomic AlBr, which is red-shifted from the 375.4 cm-1 value deduced from gas phase studies,1 and is in perfect agreement with the 357 cm-1 value reported for AlBr in an argon matrix4 produced from the reaction of HBr with the resistivity evaporated aluminum from a Knudsen cell. The 457.5 cm-1 band dominates the AlBr and AlBr3 absorptions at lower bromine concentration, and as the bromine concentration increases, its intensity compared to the 508.4 cm-1 band of AlBr3 decreases. The 457.5 cm-1 band decreases stepwise on annealing, which suggests that it belongs to a primary reaction product. This band shows a partially resolved 1:2:1 triplet pattern indicative of two identical bromine atoms and is assigned to the antisymmetric stretching vibrational mode (ν3) of the AlBr2 radical. This assignment is further supported by the peak position and the patterns observed for AlXn (X ) F, Cl and n ) 1-3). An upper limit angle of 106° is estimated from the bromine isotopic structure. Finally, the weaker 348 cm-1 band that tracks with the 458 cm-1 band on annealing could be due to the ν1 fundamental of AlBr2 radical, but more evidence is needed for such an assignment. Al2Br4. Two remaining bands that grow together on annealing at 481.9 and 431.6 cm-1 are in the same relative position in the AlBrn system as the 610.2 and 529.0 cm-1 bands in the AlCln system. The 481.9 and 431.6 cm-1 bands are tentatively assigned to the analogous Br2AlBr2Al species. Note that this presumably distorted C2V species is distinctly different from the donor-stabilized R2Al2Br4 species reported recently;28 the latter species lacks the strong diagnostic (AlBr2Al) ring stretching band at 431.6 cm-1, which differentiates between the R2Al2Br2 species and the product observed here. Iodine. Sharp bands at 385.9 and 301.9 cm-1 dominate the deposition spectra (Figure 6), and a weak 435.0 cm-1 band is enhanced at highest laser power and I2 concentration. Annealing decreases the 385.9 and 301.9 cm-1 bands and increases 366.5, 423.4, 435.0, and 446.9 cm-1 bands. Stable Species AlI3 and Al2I6. The 435.0 cm-1 absorption is favored with higher laser power and I2 concentration. This band is assigned to the antisymmetric stretching vibrational mode (ν3) of AlI3 although it falls just above the gas phase band reported for this species (427 cm-1).14 Gas phase Al2I6 is reported to have its strongest absorption (ν8) at 423 cm-1; the 423.5 cm-1 band appears on second annealing, and it is assigned to the strongest band of Al2I6. The 446.9 cm-1 band appears on annealing to 25 K along with AlO2 before much change occurs in any of the AlIx species. This band is most likely due

7324 J. Phys. Chem., Vol. 100, No. 18, 1996

Hassanzadeh et al.

to an AlI3 complex with I2 or N2, but other assignments cannot be ruled out. Transient Species AlI and AlI2. The 301.9 and 385.9 cm-1 absorptions are the major bands in the most dilute experiments, and they decrease on annealing while other bands such as 435.0 cm-1 increase. This suggests that the former bands belong to the primary reaction products and the latter absorption to stable final reaction products. The 301.9 cm-1 band is in good agreement with the fundamental of AlI and is red-shifted from the gas phase value of 314.1 or 314.3 cm-1 deduced from electronic and microwave studies.1,2 The 385.9 cm-1 band also belongs to a transient species and is located between the AlI and AlI3 absorptions similar to the other AlX2 radical absorptions and is thus assigned to the antisymmetric stretching vibrational mode (ν3) of the AlI2 radical. Al2I4. Two bands that grow on annealing at 446.9 and 366.5 cm-1 (not shown in Figure 6) at the expense of AlI and AlI2 remain to be identified. The 366.5 cm-1 band falls below AlI2 in just the same relationship as the strongest band tentatively assigned above to Br2AlBr2Al and Cl2AlCl2Al and a like tentative assignment to I2AlI2Al is suggested. The higher 446.9 cm-1 band could be due to the same species or an AlI3 complex. Reaction Mechanisms. In the previously reported reaction of chlorine with resistively evaporated aluminum atoms,7,8 the AlCl3, AlCl2, and AlCl bands were observed, which suggests that excess kinetic energy40 in the laser-ablated Al atoms is not necessary for this reaction. Although laser-ablated Al has been shown to insert into O2,40 the present observation of AlX2 radicals could arise from Al + X2 insertion or combination of X + AlX. The primary abstraction reaction (1) is exothermic

Al + X2 f AlX + X

(1)

by 61 kcal/mol for chlorine, based on bond energies,1 and the insertion reaction is expected to be considerably more exothermic. The combination reaction (2) will no doubt proceed rapidly.

X + AlX f AlX2

(2)

Further secondary reaction of AlX with X2 produces the trihalide

AlX + X2 f AlX3

(3)

which is favored at higher halogen concentration. On annealing to allow diffusion and reaction of trapped species, AlX and AlX2 diminish, AlX3 grows then decreases with increasing annealing temperature, and Al2X6 bands increase. Clearly the more stable dimer is formed:

2AlX3 f Al2X6

(4)

Another possible dimer Al2X4 can be formed from 2AlX2 or AlX3 + AlX in reactions 5 on diffusion and reaction of trapped species.

2AlX2 f X2AlX2Al

(5a)

AlX3 + AlX f AlX3AlX

(5b)

Since O4- was detected in similar experiments with oxygen,40 the role of charged species in these experiments must be considered. There are no additional higher frequency absorptions that might be due to cations, and the most likely molecular anion is this system, X2-, is infrared silent. Since the major products with thermal and laser-ablated Al + Cl2 reactions are

the same, it must be concluded that charged species do not make a significant contribution to the observed spectrum. Conclusion Laser-evaporated aluminum atoms react with molecular halogens to produce the AlX, AlX2, and AlX3 molecules where the initially formed AlX and AlX2 transients dominated the reaction products at lower laser powers and halogen concentrations. Higher thermal energy of the aluminum atoms generated by laser evaporation in comparison with the resistivity heated aluminum method favored the insertion reaction of the aluminum atom into the halogen-halogen bond as was shown by the higher yield of the AlX2 over AlX and AlX3 species. These experiments provide further evidence for aluminum dihalide radicals. Stepwise formation of these radicals from elemental aluminum and the infrared-inactive molecular halogen eliminated the usual spectral interferences from the strong bands of the AlX3 and Al2X6 precursors. Excellent agreement between observed ν3 and ν1 modes for AlF2, AlCl2, and AlBr2 and values from quantum chemical calculations provides strong support for these assignments. Further DFT calculations on Al2Cl4 species give evidence for tentative identification of the Cl2AlCl2Al isomer. The halogen bond to aluminum clearly increases in strength with increase in oxidation state. This is shown by the increase in frequencies AlCl < AlCl2 < AlCl3, the increase in AlCl force constants AlCl (1.86 mdyn/Å) < AlCl2 (2.40 mdyn/Å) < AlCl3 (2.74 mdyn/Å),11 and the decrease in calculated37 Al-Cl bond lengths AlCl (2.160 Å) > AlCl2 (2.109 Å) > AlCl3 (2.077 Å). Acknowledgment. We gratefully acknowledge financial support from the N.S.F Grant CHE 91-22556. A.C. is a visiting graduate student from the University of Southampton. References and Notes (1) Huber, K. P.; Herzberg, G. Molecular Spectra and Molecular Structure; Van Nostrand Reinhold: New York, 1979; Vol IV. (2) Wyse, F. C.; Gordy, W. J. Chem. Phys. 1972, 56, 2130. (3) Ahlrichs, R.; Zhengyan, L.; Schnockel, H. Z. Anorg. Allg. Chem. 1984, 519, 155. (4) Schnockel, H. Z. Naturforsch. 1976, B31, 1291. (5) Schnockel, H. J. Mol. Struct. 1978, 50, 267. (6) Snelson, A. J. Phys. Chem. 1967, 71, 3202. (7) Olah, G. A.; Farooq, O.; Farnia, S. M. F.; Bruce, M. R.; Clouet, F. L.; Morton, P. R.; Prakash, G. K. S.; Stevens, R. C.; Bau, R.; Lammertsma, K.; Suzer, S.; Andrews, L. J. Am. Chem. Soc. 1988, 110, 3231. (8) Samsonov, E. D.; Osin, S. B.; Shevel’kov, V. F. Russ. J. Inorg. Chem. 1988, 33, 1598. (9) Yang, Y. S.; Shirk, J. S. J. Mol. Spectrosc. 1975, 54, 39. (10) Lesiecki, M. L.; Shirk, J. S. J. Chem. Phys. 1972, 56, 4171. (11) Schnockel, H. Z. Anorg. Allg. Chem. 1976, 424, 203. (12) Beattie, I. R.; Blayden, H. E.; Ogden, J. S. J. Chem. Phys. 1976, 64, 909. (13) Shirk, J. S.; Shirk, A. E. J. Chem. Phys. 1976, 64, 910. (14) Pong, R. G. S.; Shirk, A. E.; Shirk, J. S. J. Chem. Phys. 1979, 70, 525. (15) Sjoegren, C. E.; Klaeboe, P.; Ryther, E. Spectrochim. Acta 1984, 40A, 457. (16) Tranquille, M.; Fouassier, M. J. Chem. Soc., Faraday Trans. 2 1980, 76, 26. (17) Beattie, I. R.; Gilson, T.; Ozin, G. A. J. Chem. Soc. A 1969, 813. (18) Adams, D. M.; Churchill, R. G. J. Chem. Soc. 1970, 697. (19) Klemperer, W. J. Chem. Phys. 1956, 24, 353. (20) Nakamoto, K. Infrared and Raman Spectra of Inorganic and Coordination Compounds; John Wiley & Sons: New York, 1986, and references therein. (21) Parnis, J. M.; Ozin, G. A. J. Phys. Chem. 1989, 93, 1215. (22) Kurth, F. A.; Eberlein, R. A.; Schnockel, H. G.; Downs, A. J.; Pulham, C. R. J. Chem. Soc., Chem. Commun. 1993, 1302. (23) Chertihin, G. V.; Andrews, L. J. Phys. Chem. 1993, 97, 10295. (24) Pullumbi, P.; Mijoule, C.; Manceron, L.; Bouteiller, Y. Chem. Phys. 1994, 185, 13.

IR Spectra of AlXn in Solid Ar (25) Hauge, R. H.; Kauffman, J. W.; Margrave, J. L. J. Am. Chem. Soc. 1980, 102, 6005. (26) Knight, L. B., Jr.; Cobranchi, S. T.; Gregory, B. W.; Earl, E. J. Chem. Phys. 1987, 86, 3143. (27) Knight, L. B., Jr.; Woodward, J. R.; Kirk, T. J.; Arrington, C. A. J. Phys. Chem. 1993, 97, 1304. (28) Mocker, M.; Robl, C.; Schnockel, H. G. Angew. Chem., Int. Ed. Engl. 1994, 33, 862, 1754. (29) Dyke, J. M.; Kirby, C.; Morris, A.; Gravenor, B. W. J.; Klein, R.; Rosmus, P. Chem. Phys. 1984, 99, 289. Klein, R.; Rosmus, P. Theor. Chim. Acta 1984, 66, 21. (30) Hirst, D. M. J. Mol. Spectrosc. 1987, 121, 189. Wang, M. W.; Radom, L. J. Phys. Chem. 1990, 94, 638. (31) Cramer, C. J. J. Mol. Struct. (THEOCHEM) 1991, 235, 243. (32) Scholz, G.; Schoffel, K.; Jensen, V. R.; Bache, φ.; Ystenes, M. Chem. Phys. Lett. 1994, 230, 196. (33) Gutsev, G.; Les, A.; Adamowicz, L. J. Chem. Phys. 1994, 100, 8925. (34) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital Theory; Wiley: New York, 1986. (35) Curtiss, L. A. Int. J. Quantum Chem. 1978, 94, 7099. (36) Alvarenga, A. D.; Saboungi, M.-L.; Curtiss, L. A.; Grimsditch, M.; McNeil, L. E. Mol. Phys. 1994, 81, 409. (37) Wilson, M.; Coolidge, M. B.; Mains, G. J. Phys. Chem. 1992, 96, 4851.

J. Phys. Chem., Vol. 100, No. 18, 1996 7325 (38) Ystenes, M.; Rytter, E.; Manzel, F.; Brockner, W. Spectrochim. Acta 1994, 50A, 233. (39) Hassanzadeh, P.; Andrews, L. J. Phys. Chem. 1993, 97, 4910. (40) Andrews, L.; Burkholder, T. R.; Yustin, J. T. J. Phys. Chem. 1992, 96, 10182. (41) (a) Mielke, Z.; Brabson, G. D.; Andrews, L. J. Phys. Chem. 1991, 95, 75. (b) Brabson, G. D.; Mielke, Z.; Andrews, L. J. Phys. Chem. 1991, 95, 79. (42) Andrews, L.; Burkholder, T. R. J. Phys. Chem. 1991, 95, 8554. (43) Burkholder, T. R.; Andrews, L. J. Chem. Phys. 1991, 95, 8697. (44) Hassanzadeh, P.; Andrews, J. J. Phys. Chem. 1992, 96, 9177. (45) DGauss, UniChem 2.3, Cray Research Inc., Mendota Heights, MN. (46) Andzelm, J.; Wimmer, E. J. Chem. Phys. 1991, 96, 1280. (47) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200. (48) Becke, A. D. Phys. ReV. A 1988, 38, 3098. Becke, A. D. J. Chem. Phys. 1988, 88, 2537. (49) Perdew, J. P. Phys. ReV. B 1986, 33, 8822. (50) McCory, L. D.; Paule, R. C.; Margrave, J. L. J. Phys. Chem. 1963, 67, 1086. (51) Buehler, A.; Marrau, E. P.; Stauffer, J. L. J. Phys. Chem. 1967, 71, 4139. (52) Schnockel, H. J. Mol. Struct. 1978, 50, 275.

JP953065A