18078
J. Phys. Chem. 1996, 100, 18078-18082
Molecular Structures and Harmonic Vibrational Frequencies of M2O3 (M ) Ga, In, Tl) Edet F. Archibong* and Richard Sullivan Department of Chemistry, Jackson State UniVersity, 1400 Lynch Street, Jackson, Mississippi 39217 ReceiVed: May 30, 1996; In Final Form: September 18, 1996X
The structures of Ga2O3 have been studied using the SCF, MP2, QCISD(T), and B3LYP methods with oneparticle basis sets of at least triple-ζ plus double-polarization quality. The V-shaped (C2V) structure was found to be the most stable isomer of Ga2O3, with the linear OGaOGaO (inversion transition state) structure lying about 3 kcal/mol above the former at the QCISD(T)/TZ2P level. The results show that inclusion of electron correlation is very important in determining the energy difference between the V-shaped C2V isomer and the linear D∞h form. The calculated harmonic vibrational frequencies, especially the isotopic ratios obtained with the MP2/TZ2P+f and B3LYP/TZ2P+f models, when compared to the available experimental IR data reinforce our prediction that Ga2O3 is a V-shaped planar system with C2V symmetry. Furthermore, calculations at the Hartree-Fock and MP2 levels using ab-initio relativistic effective core potential and a double-ζ valence basis set predict In2O3 and Tl2O3 as linear systems. Computed geometrical parameters, harmonic vibrational frequencies, and isotopic ratios are provided for the linear OMOMO (M ) In, Tl) to complement future experimental studies on these systems.
Introduction The chemistry of the group 13 oxides is characterized with many interesting structural features and a fascinating periodproperty relationship. The recent experiments involving the reactions of pulsed-laser evaporated B, Al, Ga, and In atoms with molecular oxygen1-3 resulted in unambiguous identification of some group 13 metal oxides, exhibiting remarkable structural similarities and a number of noticeable differences. For example, linear OMO species and MOM suboxides (M ) B, Al, Ga, In) are principal products in the reaction of these group 13 elements with oxygen. These linear oxides, with the exception of OGaO and OInO, were established by ab-initio calculations4-8 as the global minimum structures on the singlet potential energy surfaces of the MO2 and M2O systems. Moreover, while a cyclic structure was established as a lowlying energy minimum structure on the PES of AlO2 using abinitio techniques,6 accurate ordering of the energies of the linear OMO (M ) Ga, In) relative to the cyclic and the bent MO2 forms remains unknown. Our recent computational studies9,10 of the structures and harmonic vibrational frequencies of M2O2 (M ) Al, Ga, In, Tl) concluded that the most stable isomer of Al2O2 at the CCSD(T)/TZ2P+f level is a cyclic D2h form, even though the existence of this cyclic isomer in matrix experiments is uncertain and still remains a controversial subject.2,11-15 On the other hand, the linear MOMO (C∞V) found in matrix experiments3 was established as the global minimum for Ga2O2, In2O2, and Tl2O2, with the cyclic D2h form of Ga2O2 lying about 3 kcal/mol above the linear structure at the QCISD/TZ2P+f level.9 Considerable efforts have been devoted to elucidate the structures and vibrational frequencies of M2O3 (M ) B, Al) experimentally,1,2,14,16-19 and via computational methods.2,7,8,21,22 After several extensive investigations, many of which are conflicting, very recent studies1,8 have firmly established that B2O3 molecule is V-shaped (C2V symmetry), in agreement with earlier infrared (IR) studies.16,17 Similarly, Al2O3 has been confirmed as a linear OAlOAlO with some ionic character.2,7 However, the reports of experimental and computational X
Abstract published in AdVance ACS Abstracts, November 1, 1996.
S0022-3654(96)01571-7 CCC: $12.00
investigations of the molecular structures and vibrational frequencies of M2O3 (M ) Ga, In, Tl) are scarce. In fact, we found only one article on the infrared studies of matrix-isolated Ga2O3 and In2O3.3 Based on analogies with the extensively studied OAlOAlO isomer, the IR bands observed at 979.4 and 826.0 cm-1 in argon matrices were assigned3 to the linear OGaOGaO and OInOInO, respectively. Though the analysis of the data collected from matrix isolation studies suggests a linear structure for the M2Ox (M ) Al, Ga; x ) 2, 3) system, the information we gathered from computing the molecular structures of Al2O2 and Ga2O2,9,10 for example, indicates the possible existence of isomers which are nearly isoenergetic or even more stable than the linear forms suggested from experimental studies. Thus, the cardinal objective of this study is to elucidate the molecular structure of Ga2O3 using traditional ab-initio and the density functional theory (DFT) methods. As noted above, it is well established experimentally and computationally that B2O3 molecule has a V-shaped structure (C2V symmetry) and Al2O3 is a linear (D∞h) system. Examination of the potential energy surface of the next member of this series, Ga2O3, is imperative and timely. This study shed light on the question of whether Ga2O3 is isostructural with OAlOAlO as suggested by experimental data or resembles B2O3 (V-shaped, C2V symmetry). Furthermore, in anticipation of definitive future experimental studies, we report the structures and harmonic vibrational frequencies of In2O3 and Tl2O3. In short, the purpose of this paper is to report ab-initio calculations of the structures and harmonic vibrational frequencies of M2O3 (M ) Ga, In, Tl) for comparison with experimental data, where available, and also to provide structural information which might be useful in future experimental studies on these species. To our knowledge there are no published reports on the ab-initio calculations of the structures and vibrational frequencies of M2O3 (M ) Ga, In, Tl). And this study is a continuation of our investigation of the molecular structures and bonding in model systems containing heavy elements of groups 13 and 14.9,10,23,24 Computational Methods The one-particle basis sets employed for Ga2O3 are designated as TZ2P and TZ2P+f. The TZ2P consists of Huzinaga’s Ga© 1996 American Chemical Society
Structures and Frequencies of M2O3 (M ) Ga, In, Tl)
J. Phys. Chem., Vol. 100, No. 46, 1996 18079 TABLE 1: Absolute Energies (hartrees), Zero-Point Energies,a ZPE (kcal/mol), and Relative Energies (kcal/mol) for the Ga2O3 Isomers (1-4) abs energy 1-C2V(0) 2-D∞h(2) 3-C2V(2) 4-D3h(0) 1-C2V(0) 2-D∞h(2) 3-C2V(2) 4-D3h(0)
Figure 1. Geometries of the selected M2O3 isomers (M ) Ga, In, and Tl).
[4333/433/4] and O[43/3] contracted basis sets25 loosely uncontracted to Ga[433111/43111/4] and O[4111/111] and augmented with two sets of five-membered d-type polarization functions with exponent ζd(Ga) ) 0.336 and 0.091 and ζd(O) ) 2.704 and 0.535, respectively. Addition of a single set of uncontracted seven-membered f-type polarization functions26 (ζf ) 0.167) on Ga gives the [6s5p3d1f/4s3p2d] set labeled as TZ2P+f. The calculations for In2O3 and Tl2O3 were performed using Dunning’s [4s2p] set27 on oxygen and relativistic effective core potentials for In and Tl, with the outer ns2np1 (In) and (n - 1)d10ns2np1 (Tl) explicitly treated with associated double-ζ basis sets.28 Geometry optimizations were carried out at the Hartree-Fock level using analytical gradients. Utilizing the SCF geometries and force constants, the structures were reoptimized at the second-order Moller-Plesset perturbation (MP2) level. Further geometry optimizations were carried out for the two lowestenergy structures of Ga2O3 using quadratic configuration interaction in the space of single and double substitutions (QCISD), with the effect of connected triple excitations included perturbatively [QCISD(T)]. The QCISD method can be regarded as an approximation to the coupled cluster (CCSD) method in the same space.29 The harmonic vibrational frequencies were obtained from analytic second-derivative methods at the SCF and MP2 levels. In all the post-SCF calculations, 21 lowest molecular orbitals in Ga2O3 were kept doubly occupied. In the density functional theory calculations, we use the B3LYP hybrid functional30 of the form
AExSlater + (1 - A)ExHF + BExBecke + CEcLYP + (1 - C)EcVWN where the respective terms are the Slater exchange, the HartreeFock exchange, Becke’s gradient correction to exchange,31 the correlation functional of Lee, Yang, and Parr,32 and the VoskoWilk-Nusair correlation functional.33 The constants A, B, and C are those determined by Becke by fitting heats of formation. All calculations were carried out using the GAUSSIAN 92/DFT program.34 Results and Discussion Ga2O3. At the initial stage of this study, attention was focused primarily on the OGaOGaO linear arrangement (suggested from experimental work) with the aim of computing the unavailable geometrical parameters and to correlate the computed infrared (IR) vibrational frequencies with those obtained from matrix isolation studies. However, the vibrational frequency analyses at the SCF and post-SCF levels indicate that linear OGaOGaO is a transition state structure. Consequently, other isomers of Ga2O3 depicted in Figure 1 were considered
1-C2V(0) 2-D∞h(2) 3-C2V(2) 4-D3h(0) 1-C2V(0) 2-D∞h(2) 3-C2V(2) 4-D3h(0) 1-C2V 2-D∞h 1-C2V(0) 2-D∞h(2) 3-C2V(2) 4-D3h(0) 1-C2V(0) 2-D∞h(2) 3-C2V(2) 4-D3h(0)
rel energy
ZPE
SCF/TZ2P 0.00 6.27 0.19 6.14 13.82 5.81 66.19 6.79 SCF/TZ2P+f -4067.061 984 0.00 6.17 -4067.061 901 0.05 6.09 -4067.042 703 12.10 5.79 -4066.968 638 58.58 6.84 MP2/TZ2P -4067.969 692 0.00 6.05 -4067.966 177 2.21 5.81 -4067.904 758 40.75 5.28 -4067.854 535 72.26 5.44 MP2/TZ2P+f -4067.987 602 0.00 5.87 -4067.984 253 2.10 5.69 -4067.926 952 38.06 5.25 -4067.892 828 59.47 5.58 QCISD(T)/TZ2P -4067.918 924 0.00 -4067.913 565 3.36 B3LYP/TZ2P -4071.497 308 0.00 5.90 -4071.494 001 2.08 5.59 -4071.459 545 23.70 5.14 -4071.387 771 68.74 4.51 B3LYP/TZ2P+f -4071.503 280 0.00 5.84 -4071.500 402 1.81 5.56 -4071.468 442 21.86 5.13 -4071.405 494 61.36 4.86 -4067.055 251 -4067.054 955 -4067.033 227 -4066.949 770
rel energy + ∆ZPE 0.00 0.06 13.49 66.71 0.00 -0.03 11.72 59.25 0.00 1.97 39.98 71.65 0.00 1.92 37.44 59.18
0.00 1.77 22.94 67.35 0.00 1.53 21.15 60.38
a Imaginary frequencies are neglected in calculating the zero-point energies. The values in parentheses denote the number of imaginary vibrational frequencies.
in addition to the linear form. One of the structures examined is that of B2O3, that is, a “V” form having C2V symmetry (see structure 1 in Figure 1). At all theoretical levels, the optimized geometry of structure 1 has positive definite Hessian, whereas the linear OGaOGaO structure 2 possesses one doubly degenerate (πu) imaginary frequency and is an inversion transition state to the bent (1-C2V) form. In Table 1, we present the absolute and relative energies for the stationary points corresponding to the four selected structures of Ga2O3. The results in Table 1 show that, at the SCF/TZ2P+f level, 1 and 2 have nearly the same energy, while 3 and 4 lie 12 and 59 kcal/mol above 1. The results also indicate that electron correlation favors structure 1 over structure 2. Consequently, the energy difference between the V-shaped structure 1 and the linear structure 2 increases to 2 kcal/mol at the MP2 level and to 3 kcal/mol at the QCISD(T)/TZ2P level. To have greater confidence in the energy difference between structures 1 and 2, a higher level of computational study may be required. However, limited computational resources prevent us from perfoming calculations beyond the QCISD(T)/TZ2P for Ga2O3. It should also be noted that the DFT results reported in Table 1 also indicate that the C2V structure 1 is more stable than the linear OGaOGaO form. Inspection of the table shows that the relative energies predicted by the B3LYP approximation are generally lower than the corresponding MP2 and QCISD(T) values. Since the relative energies of 3 and 4 rule them out as the lowest-energy structure of Ga2O3, they will not be discussed further. Table 2 contains selected geometrical parameters for the V-shaped structure 1-C2V and the linear OGaOGaO structure
18080 J. Phys. Chem., Vol. 100, No. 46, 1996
Archibong and Sullivan
TABLE 2: Selected Geometrical Parameters for the V-Shaped (1-C2W) and Linear (2-D∞h) Structures of Ga2O3 (Bond Lengths in Å and Bond Angles in deg) isomer 1-C2V
2-D∞h
ra rb θc θd ra rb
SCF/TZ2P
SCF/TZ2P+f
MP2/TZ2P
MP2/TZ2P+f
QCISD(T)/TZ2P
B3LYP/TZ2P
1.725 1.631 154.0 179.6 1.719 1.631
1.727 1.633 161.4 179.0 1.723 1.633
1.759 1.659 131.0 178.1 1.739 1.659
1.768 1.661 129.1 177.3 1.744 1.660
1.759 1.667 132.3 178.7 1.739 1.667
1.754 1.653 135.4 177.7 1.737 1.652
B3LYP/TZ2P+f 1.758 1.654 136.6 177.0 1.741 1.654
TABLE 3: Harmonic Vibrational Frequencies (cm-1) and Infrared Intensities (in Parentheses, km/mol) of the V-Shaped (1-C2W) and Linear (2-D∞h) Structures of Ga2O3 SCF/TZ2P
SCF/TZ2P+f
MP2/TZ2P
MP2/TZ2P+f
B3LYP/TZ2P
B3LYP/TZ2P+f
comments
a1 a1 a1 a1 a2 b1 b2 b2 b2
1035 (3) 411 (20) 223 (76) 46 (20) 169 (0) 237 (102) 1130 (476) 965 (27) 169 (5)
1026 (2) 370 (16) 222 (95) 36 (18) 172 (0) 228 (116) 1131 (511) 959 (17) 171 (2)
1010 (8) 494 (10) 200 (23) 66 (11) 159 (0) 213 (43) 1036 (290) 895 (103) 160 (7)
1-C2V 1001 (9) 491 (11) 186 (26) 54 (12) 147 (0) 192 (49) 1022 (270) 870 (109) 137 (7)
978 (5) 465 (11) 198 (27) 67 (13) 157 (0) 210 (49) 1023 (287) 874 (84) 156 (5)
973 (5) 451 (14) 198 (30) 67 (14) 158 (0) 206 (56) 1016 (291) 866 (86) 154 (5)
69Ga 16O 2 3
a1 a1 a1 a1 a2 b1 b2 b2 b2
990 (3) 398 (16) 216 (71) 44 (18) 164 (0) 227 (94) 1080 (427) 911 (29) 164 (4)
982 (2) 360 (13) 214 (89) 34 (16) 167 (0) 218 (107) 1080 (460) 906 (21) 166 (2)
966 (8) 472 (8) 195 (21) 63 (10) 154 (0) 203 (40) 993 (268) 844 (91) 155 (7)
958 (9) 469 (10) 182 (24) 52 (11) 142 (0) 184 (45) 979 (251) 824 (95) 133 (7)
936 (5) 444 (10) 193 (25) 64 (11) 153 (0) 201 (45) 981 (261) 824 (76) 151 (5)
931 (5) 432 (12) 193 (27) 64 (13) 153 (0) 197 (52) 973 (264) 816 (78) 149 (4)
69Ga 18O 2 3
σg+ σg+ σu+ σu+ πg πu πu
1034 (0) 334 (0) 1155 (544) 974 (13) 169 (0) 229 (107) 38i
1026 (0) 331 (0) 1145 (547) 963 (10) 174 (0) 224 (120) 30i
1009 (0) 315 (0) 1097 (560) 954 (15) 160 (0) 185 (54) 77i
2-D∞h 1000 (0) 311 (0) 1084 (558) 942 (14) 159 (0) 163 (64) 87i
972 (0) 312 (0) 1085 (491) 912 (19) 147 (0) 168 (59) 87i
967 (0) 308 (0) 1075 (492) 905 (18) 153 (0) 163 (67) 84i
69Ga 16O 2 3
σg+ σg+ σu+ σu+ πg πu πu
990 (0) 329 (0) 1103 (489) 921 (17) 164 (0) 219 (98) 36i
982 (0) 326 (0) 1093 (493) 911 (14) 169 (0) 214 (110) 28i
966 (0) 311 (0) 1048 (502) 901 (19) 155 (0) 178 (49) 73i
957 (0) 306 (0) 1036 (501) 890 (18) 154 (0) 156 (58) 83i
930 (0) 301 (0) 1036 (440) 862 (22) 143 (0) 161 (54) 78i
926 (0) 304 (0) 1026 (442) 856 (21) 149 (0) 156 (62) 79i
69Ga 18O 2 3
2-D∞h. The results in the table show the usual bond lengthening effect of electron correlation when a decent one-particle basis set is used. In general, the increase in the SCF bond lengths of 1 and 2 is not more than 0.04 Å at the MP2 and QCISD(T) levels. Furthermore, the bond distances computed with the B3LYP method are longer than the SCF ones but shorter than their MP2 and CCSD(T) counterparts. A close inspection of Table 2 reveals some finer points about the structures of 1 and 2. At all levels of theory the terminal GaO (rb in Figure 1) bond lengths in 1 and 2 are shorter than the interior OGa (ra in Figure 1). Specifically, rb is shorter than ra for 1 and 2 by 0.09 and 0.07 Å, respectively, at the QCISD(T)/TZ2P level. Similar shortening of the terminal MO bond compared to the interior OM (M ) B, Al) was also found in B2O3 and Al2O3. Note that while the terminal GaO bond distance is virtually the same for structures 1 and 2 at a given level of theory, the interior OGa bond distance is generally longer in structure 1. The effects of electron correlation on the GaOGa (θc) angle of 1 should also be noted. At the SCF/TZ2P+f level, for example, the GaOGa angle is 161.4°. However, using the same basis set, the angle decreases to 129.1° and 136.6° at the MP2 and B3LYP levels, respectively. Thus, unlike the B2O3 system for which it was reported22 that electron correlation had no effect
on the geometrical parameters of a similar V-shaped structure 1, the geometrical parameters of Ga2O3 (especially the central GaOGa angle) appear to be sensitive to the level of theory employed. Computed harmonic vibrational frequencies are a very important source of information for the analysis of experimental infrared data. In particular, the importance of isotopic shifts and mixed isotopic multiplets for the identification of “troublesome” systems cannot be overemphasized.1-3 Experimentally, Ga2O3 has been suggested3 as having a linear OGaOGaO (D∞h) structure similar to that of well-characterized OAlOAlO. In the Ga2O3 ablation experiment, the band observed3 at 979.4 cm-1 exhibits a 1.0433 oxygen isotopic ratio and was assigned as antisymmetric Ga-O stretching. In Table 3, we summarize our computed harmonic vibrational frequencies and infrared intensities for structure 1 (C2V symmetry) and also for the linear OGaOGaO (2, D∞h). Also included in the table are the frequencies referring to the isotopomer 18O69Ga18O69Ga18O. Note that the harmonic vibrational frequencies reported in Table 3 are not scaled. First, our results show that 2 is in fact a transition state; characterized by one doubly degenerate imaginary frequency of πu symmetry. Using the TZ2P+f results, the strong band (σu+ mode) at 1145 cm-1 (547 km/mol), 1084
Structures and Frequencies of M2O3 (M ) Ga, In, Tl)
J. Phys. Chem., Vol. 100, No. 46, 1996 18081
TABLE 4: Bond Lengths (Å), Harmonic Vibrational Frequencies (cm-1), and Intensities (in Parentheses, km/mol) of the Linear (D∞h) Structures of the In2O3 and Tl2O3 SCF OInOInO ra(O-In) rb(In-O) freq (int) σg+ σg+ σu+ σu+ πg πu πu σg+ σg+ σu+ σu+ πg πu πu
MP2
comments 115In 16O 2 3
1.840 1.803
1.870 1.793
679 (0) 228 (0) 951 (396) 661 (11) 105 (0) 232 (88) 66 (54)
838 (0) 217 (0) 888 (311) 836 (258) 95 (0) 170 (76) 56 (25)
647 (0) 226 (0) 901 (353) 627 (11) 101 (0) 220 (81) 63 (48)
796 (0) 215 (0) 842 (327) 793 (189) 92 (0) 161 (70) 53 (22)
115In 18O 2 3
cm-1 (558 km/mol), and 1075 cm-1 (492 km/mol) at the SCF, MP2, and B3LYP levels, respectively, correspond to the inplane antisymmetric Ga-O stretch. This result appears to agree with the experimental data taking into consideration that calculated harmonic vibrational frequencies are expected to be higher than the experimental vibrational frequencies. However, the agreement between the computed and experimental isotopic ratio is not very impressive. Specifically, the isotopic (16O/ 18O) ratio computed for the σ + mode is 1.0472, 1.0465, and u 1.0470 at the SCF, MP2, and B3LYP levels compared to experimental value of 1.0433. The disagreement in the observed and computed isotopic ratio for the linear isomer, coupled with the fact that the linear form is a transition state at all levels of theory employed, led to the consideration of 1 as a possible gas phase equilibrium structure for Ga2O3. Next consider the harmonic vibrational frequencies computed for the 1-C2V isomer. Using the TZ2P+f basis set, the MP2 and B3LYP models predict an intense antisymmetric Ga-O stretch at 1022 cm-1 (270 km/mol) and 1016 cm-1 (291 km/ mol), respectively. Good agreement with the experimental value of 979 cm-1 is observed if the respective MP2 and B3LYP values are scaled by 0.96 to give 981 and 975 cm-1. More importantly, the 16O/18O ratios calculated for this band is 1.0434 and 1.0436 at the MP2 and B3LYP levels, in excellent agreement with experimental value of 1.0433. The information obtained from the computed harmonic vibrational frequencies of isomers 1 and 2 (in particular the 16O/18O isotopic ratio) combined with the relative energies in Table 1 leads to a definite gas phase equilibrium structure for Ga2O3 as a V-shaped molecule with a C2V symmetry. In2O3 and Tl2O3. Investigation of structures 1-4 in Figure 1 for In2O3 and Tl2O3 shows that the linear OMOMO (M ) In, Tl) is the most stable isomer for both systems. All geometry optimizations beginning with the C2V V-shaped structure 1 always converged to the linear form. The results of geometry optimizations at the SCF and MP2 levels, including the harmonic vibrational frequencies, are briefly summarized in Table 4. First consider OInOInO. The MP2 results listed in Table 4 show that the interior O-In and the terminal In-O bond distances are 1.870 and 1.793 Å, respectively. The MP2 model also predicts two intense stretching modes at 888 and 836 cm-1 with 16O/18O isotopic ratio of 1.0546 and 1.0542, respectively. Scaling the most intense band at 888 cm-1 by 0.93 results in a perfect agreement with the band observed at 826 cm-1.
SCF OTlOTlO ra(O-Tl) rb(Tl-O) freq (int) σg+ σg+ σu+ σu+ πg πu πu σg+ σg+ σu+ σu+ πg πu πu
MP2
comments 205Tl 16O 2 3
2.003 1.969
2.010 1.908
571 (0) 169 (0) 901 (885) 539 (182) 103 (0) 178 (61) 53 (13) 542 (0) 167 (0) 852 (785) 509 (165) 98 (0) 169 (55) 50 (11)
205Tl 18O 2 3
Next consider Tl2O3. Geometrical parameters and IR vibrational frequency data are not available in the literature for this system to our knowledge. We present in Table 4 computed geometrical parameters at the SCF and MP2 levels, and unscaled harmonic vibrational frequencies at the SCF level for linear OTlOTlO, as a reference for future studies on this system. The interior O-Tl and terminal Tl-O bond lengths are 2.010 and 1.908 Å, respectively. Tl is the largest member of group 13, and as expected, the bond distances in OTlOTlO are longer than those in OInOInO. Our computed harmonic vibrational frequencies indicate a very strong antisymmetric Tl-O stretch at 901 cm-1 with an 16O/18O isotopic ratio of 1.0575; scaling by 0.9 suggests an 811 cm-1 fundamental. Thus, we predict that a strong antisymmetric TlO stretch could be detected for OTlOTlO around 800 cm-1 with an 16O/18O isotopic ratio of about 1.0575. Comparison of the most stable geometries for the M2O3 (M ) B, Al, Ga, In, Tl) reveals some interesting pattern. B2O3 is V-shaped (C2V symmetry) and Al2O3 is linear (D∞h) as reported in past studies.1,2,7,8,14,16-19,21,22 The results of this work indicate that Ga2O3 appears to be isostructural with B2O3, while In2O3 and Tl2O3 are linear. Nemukhin and Weinhold have explained the difference in the geometries of B2O3 and Al2O3 in terms of elementary hybridization concepts.8 The authors noted that while the formal Lewis structures are similar for B2O3 and Al2O3, the bonding hybrids of the central oxygen have significant higher p character in B2O3 with the consequence that the central BOB angle (corresponding to θc in Figure 1) is somewhat bent rather than linear. Furthermore, Ault rationalized35 the different geometries of M2X3 (M ) B, Al; X ) O, S) in terms of electronegativity differences.36 The latter report35 concluded that the bonding in B2S3, Al2S3, B2O3, and Al2O3 is roughly 7%, 22%, 44%, and 63% ionic in character, respectively. Al2O3 with the most ionic character is linear, while B2S3, Al2S3, and B2O3 adopt the V-shaped geometry. In the same vein, using the Allred-Rochow scale,37 we find the difference in electronegativity of M and O to be 1.5, 2.0, 1.7, 2.0, and 2.1 for M ) B, Al, Ga, In, and Tl, respectively. Consequently, based on Pauling’s procedure for approximating the percentage ionic character of a bond,36 the amount of ionic character of the M-O bonds in Ga2O3, In2O3, and Tl2O3 is approximately 51%, 63%, and 66%. And the general trend in the geometries of the M2O3 appears to be that species with the most ionic in character (when M ) Al, In, and Tl; M-O has greater than 60% ionic character) are linear, while the less ionic ones (when M ) B, Ga; M-O
18082 J. Phys. Chem., Vol. 100, No. 46, 1996 has 44% and 51% ionic character, respectively) are angular and essentially flexible, with a very small inversion barrier around the central oxygen atom. Conclusions Experimentally, Ga2O3 and In2O3 have been tentatively interpreted3 as linear D∞h systems. However, the results presented in this paper, in contrast to the earlier assignment, suggest that Ga2O3 is a planar V-shaped species of C2V symmetry. The linear isomer was found to be a transition state at all levels of theory employed. The intense antisymmetric stretching mode predicted at 1022 cm-1 (MP2/TZ2P+f) for the V-shaped isomer exhibit an 16O/18O isotopic ratio of 1.0434. The latter ratio matches the observed isotopic ratio of 1.0433 better than the isotopic ratio of 1.0465 computed for the most intense stretching mode of the linear structure. The QCISD(T)/TZ2P model employed for Ga2O3 predicts interior OGa bond distance of 1.759 Å, terminal GaO bond distance of 1.667 Å, and a central GaOGa angle of 132°. Ga2O3 appears to be a flexible system; the lowest bending mode (a1) of the V-shaped structure is very small (less than 70 cm-1 at all levels employed), and the computed energy barrier for the inversion motion is 3.4 kcal/mol at the QCISD(T)/TZ2P level. In the case of In2O3, our computed harmonic vibrational frequencies correlate well with experiment, and the combined information presented in Table 4 supports the early assignment3 of In2O3 as a linear system. For future experimental studies on Tl2O3, our results suggest that this system is isostructural with In2O3, and a very intense IR band is predicted at about 800 cm-1 with an 16O/18O isotopic ratio of 1.0575. Acknowledgment. This work was supported in part by NSF/ EPSCOR Grant No. 94-4-756-01. We thank the Mississippi Center for Supercomputing Research for generous allotment of computer time. References and Notes (1) Burkholder, T. R.; Andrews, L. J. J. Chem. Phys. 1991, 95, 8697. (2) Andrews, L.; Burkholder, T. R.; Yustein, J. T. J. Phys. Chem. 1992, 96, 10182. (3) Burkholder, T. R.; Yustein, T. J.; Andrews, L. J. J. Phys. Chem. 1992, 96, 10189. (4) Masip, J.; Clotet, A.; Ricart, J. M.; Illas, F.; Rubio, J. Chem. Phys. Lett. 1988, 144, 373. (5) Bencivenni, L.; Pelino, M.; Ramondo, F. J. Mol. Struct. (THEOCHEM) 1992, 253, 109. (6) Nemukhin, A. V.; Almlof, J. J. Mol. Struct. (THEOCHEM) 1992, 253, 101.
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