5672
J. Phys. Chem. 1996, 100, 5672-5675
Ab Initio Studies of the GaH3-H2O, GaF3-H2O, and GaCl3-H2O Molecular Complexes Kimberly A. Grencewicz and David W. Ball* Department of Chemistry, CleVeland State UniVersity, CleVeland, Ohio 44115 ReceiVed: September 28, 1995; In Final Form: January 26, 1996X
We have performed Hartree-Fock ab initio calculations on GaH3-H2O, GaF3-H2O, and GaCl3-H2O to determine minimum-energy geometries, vibrational frequencies, and binding energies between the two molecular moieties. Qualitatively, the structures and binding energies were very similar to those for the corresponding aluminum complexes, and the binding energy was much larger than that for BF3-H2O. The potential energy surface as determined by rotation about the Ga-O bond shows some unusual features. An estimate of the basis set superposition error is also presented.
Introduction The electronics industry accounts for about 95% of the gallium used in the U.S. Fortunately, the metallic element is relatively easy to obtain at a high level of purity, in part due to its low melting point (30 °C). Both gallium and gallium suboxide, Ga2O, are used to make III-V semiconductors. Chemical vapor deposition is also a method used to make thin films of gallium-containing semiconductors, and there is consequently a lot of interest in how gallium molecules interact with other species. Trivalent gallium compounds are qualitatively similar to their aluminum counterparts.1 For example, the trifluoride is nonvolatile and has a high melting point, while the chloride is more volatile and exists as the dimeric Ga2Cl6 species in the gas phase. Gallium trihalides also act as Lewis acids, coordinating with lone electron pairs of Lewis bases to make stable complexes. However, because Ga is the first group IIIB element to have a filled d subshell, it actually interacts more strongly with donor atoms such as S (as for example in (CH3)2S) because of the ability for d-d orbital interactions.1 Therefore, comparisons of the Lewis acidity of compounds having group IIIB atoms as molecular centers can be tricky. We have been interested in understanding the behavior of trivalent group 13 compounds as Lewis acids. We have investigated experimentally2 and theoretically3 the structures, vibrations, and energies of interaction of the BF3-H2O complex, which had also been studied previously by Evans et al.4 (using theoretical methods) as well as by Hunt and Ault6 (using cryogenic matrix isolation techniques). We recently published a report6 on AlH3-H2O, AlF3-H2O, and AlCl3-H2O complexes. Hartree-Fock (HF) and second-order Møller-Plesset (MP2) calculations were performed using the 6-31G(d,p) basis exclusively, as the previous study on BF3-H2O had established that larger basis sets did not provide substantially different conclusions. The structures of all three complexes were qualitatively similar to that of BF3-H2O, with the water molecule bent ∼50° out of plane so as to eclipse two of the three substituents on the Al atom. Determination of the approximate charges on the hydrogens and on the X (X ) H, F, Cl) on aluminum showed that the reason for this structure was most likely Coulombic in nature. We showed that corrections for basis set superposition error were not as large as that found for AlX3 complexes (mostly hydrogen halide complexes) studied previously by others.7,8 X
Abstract published in AdVance ACS Abstracts, March 15, 1996.
0022-3654/96/20100-5672$12.00/0
We continue our investigation into aquo complexes of group 13 compounds by reporting here the optimized geometries, minimum energies, vibrational frequencies, and binding energies for GaH3-H2O, GaF3-H2O, and GaCl3-H2O. For the first time, we also include potential energy curves for the rotation of one molecule with respect to the other. We find generally that these results parallel those for the aluminum complexes but are slightly less bound if BSSE corrections are included. The potential energy diagrams provide a surprising result: while the diagrams for GaF3-H2O and GaCl3-H2O have a generally expected form, the one for GaH3-H2O is unusual. There have been several recent reports on theoretical calculations of gallium compounds and several on adducts with other species such as arsine (AsH3). However, we have been unable to find any previous investigations on water adducts of galliumcontaining molecules. Calculational Details Ab initio calculations were performed using the GAUSSIAN 92 program.9 The calculations were performed in the Windows environment on a 66 MHz 486 PC having 16 MB of RAM and ∼130 MB of available disk storage space or on a Cray Y-MP supercomputer for selected calculations. The basis set used for gallium was the (3333/333/3) basis, for oxygen and fluorine the (33/3) basis, and for chlorine the (333/33) basis of Huzinaga et al.10 The outermost valence basis function was split, and the recommended polarization functions were included, making the bases (3333/333/211) for gallium, (33/21/1) for oxygen and fluorine, and (333/321/1) for chlorine. We used this smallest Huzinaga polarization-function-containing basis set for calculational efficiency and did not sample the results using other, larger basis sets because our previous work3,6 showed little difference in the structure or binding energy if larger basis sets were used. The exponents and coefficients for hydrogen were taken from the 6-31G(d,p) basis set.11 The restricted Hartree-Fock method was used to determine minimum-energy geometries for the three aquo complexes and the individual molecules. D3h and C2V symmetries were imposed on the GaX3 and H2O individual molecule optimizations, respectively. For the GaF3-H2O and GaCl3-H2O, the Ga-X bonds and the O-H bonds were kept the same, as well as the X-Ga-X bond angles. This was done to improve calculational efficiency, and subsequent vibrational frequencies verified the true energy minimum character of the structures optimized under these conditions. However, when these restrictions were imposed on GaH3-H2O, vibrational frequency calcula© 1996 American Chemical Society
GaH3-H2O, GaF3-H2O, and GaCl3-H2O tions always showed at least one negative vibration. Therefore, in this case, the three Ga-H bonds were allowed to vary independently, as were the Ga-O-Hwater and O-GaHgallium hydride bond angles; under these conditions, optimized structures had no negative vibrational frequencies. The counterpoise method was used to estimate the magnitude of the basis set superposition error in the calculation of the binding energies. Finally, in order to determine how stable the optimum geometry was with respect to rotation of the two molecules about the Ga-O bonds, potential energy diagrams were generated by determining the single point energy of the molecule as the GaX3 was rotated with respect to the H2O in 10° increments. Since we expect distortions of the moieties to be slight as they rotate about each other, to speed the calculations only the rotation about the Ga-O bond was varied, structures were not reoptimized during the course of the potential energy scan.
J. Phys. Chem., Vol. 100, No. 14, 1996 5673
Figure 1. A general diagram of the optimized geometries of all of the GaX3-H2O complexes (X ) H, F, Cl). Specific structural parameters are listed in Table 1.
TABLE 1: Structural Parameters for Optimized GaH3-H2O, GaF3-H2O, and GaCl3-H2O (See Figure 1 for Atom Labels)a
Results and Discussion GaX3 and H2O. Initially, geometries of the individual GaX3 and H2O molecules were determined. The Ga-H, Ga-F, and Ga-Cl bond distances for the D3h molecules were 1.587, 1.708, and 2.113 Å, respectively. The C2V H2O molecule optimized with rOH ) 0.956 Å and RHOH ) 104.2°. GaH3 has yet to be isolated experimentally, although the dimeric species Ga2H6 was recently characterized in low-temperature inert gas matrices.12 The predicted 1.587 Å Ga-H bond distance is similar to the 1.577 and 1.586 Å bond distances predicted by Schwerdtfeger et al.13 using MP2 and quadratic configuration interaction (QCI) methods. It is also consistent with the 1.573 Å bond distance calculated by Duke, Hamilton, and Schaefer,14 who used a DZP basis set and HF-SCF methods. Ruda and Ping15 used effective core potentials and calculated a Ga-H bond distance of 1.582 Å, which is the same value found by Bock et al.16 using Huzinaga’s (433321/4321/4*) basis. Graves and Scuseria17 used a variety of methods and calculated Ga-H bond distances ranging from 1.5567 to 1.602 Å. Although there are no direct experimental measurements on GaH3 for comparison, the terminal Ga-H bond distance for Ga2H6, determined12 by electron diffraction, is 1.517 Å. (The bridging Ga-H has a 1.710 Å bond length.) There are less comparables for GaF3 and GaCl3. Schwerdtfeger et al.13 report 1.745 and 1.744 Å for the Ga-F bond distance (MP2 and QCI methods, respectively), which is slightly longer than our calculated 1.708 Å. Duke et al.14 report a 2.125 Å bond length for Ga-Cl, which is very close to our 2.113 Å. GaCl3 appears to be the only case where direct experimental evidence is available for comparison; Vogt et al.18 summarize previous work and also report their own electron diffraction data on GaCl3 vapors, finding a Ga-Cl bond length of 2.100 Å. Since H2O is such a frequent target of investigation, a detailed discussion of the calculated parameters will be omitted here, other than to acknowledge a good agreement with the experimentally determined structure (rOH ) 0.958 Å, RHOH ) 104.45°).19 Complex Geometries. A general diagram for the GaX3H2O complexes is shown in Figure 1. Since all three complexes have the same general geometry, this single diagram, shown from three different perspectives, is sufficient to illustrate the optimized structures of GaH3-H2O, GaF3-H2O, and GaCl3H2O. Since the structures of the complexes are qualitatively similar to those for the equivalent aluminum complexes, only one view of the complex is shown. (Those interested in the other perspectives of the general structure are referred to ref 6.)
r(Ga-O) r(O-H) r(Ga-X1) r(Ga-X2) r(Ga-X3) R(H1OH2) R(GaOH1) R(GaOH2) R(OGaX1) R(OGaX2) R(OGaX3) δ(X1-GaOH1) δ(X2-GaOH1) δ(X3-GaOH1) δ(Ga-HOH)
GaH3-H2O (X ) H)
GaF3-H2O (X ) F)
GaCl3-H2O (X ) F)
2.134 0.967 1.604 1.603 1.592 107.1 110.71 110.68 95.28 95.27 102.1 0.95 121.8 242.7 120.7
2.025 0.970 1.727 b b 108.1 112.6 b 98.0 b b -1.5 119.3 239.9 125.0
2.037 0.970 2.141 b b 108.7 115.1 b 99.1 b b -3.5 116.9 237.3 130.7
a δ ) dihedral angle. All r in angstroms; all R and δ in degrees. Bond lengths or bond angles that were constrained as equivalent in the geometry optimization.
b
Table 1 lists the structural parameters for the optimized complexes. Because for GaF3-H2O and GaCl3-H2O some of the bond distances and bond angles were defined using the same parameter, some of the parameters defined in the table are redundant for these complexes. With Ga-O distances of 2.0-2.1 Å, the two molecules in the complex are just slightly (∼0.1-0.2 Å) farther apart as were the water molecules and the AlX3 molecules and BF3. Such close values are a bit surprising considering the additional two electron shells the gallium atom contains, as well as the fact that the covalent radii from B to Ga differ by ca. 0.5 Å. Still, there is a noticeable trend to longer bonds to oxygen, perhaps only smaller than might be expected. Comparison of the structural parameters in Table 1 shows many similarities in the effects of complexation on the bond angles and distances. The Ga-X bonds all lengthen slightly, as do the O-H bonds of water. The GaX3 molecules distort slightly from planarity, as indicated by the >90° angle for the O-Ga-X angles. (If the GaX3 molecules had remained planar, this angle would be exactly 90°.) In the case of the GaH3H2O complex, two of the Ga-H bonds distort about 5° away from the water molecule, while the third distorts a full 12° away. This third hydrogen is the one that is not eclipsed by the water molecule, an effect that is probably due to the Coulombic attractions between the two types of eclipsing hydrogens. As with the previous water complexes, for all of the gallium complexes the water molecule is substantially tilted out of a potential molecular plane, bending over slightly so as to almost perfectly eclipse two of the three X substituents. Table 2, which lists the approximate charges on the hydrogen and X atoms, shows that the reason for this is almost certainly Coulombic.
5674 J. Phys. Chem., Vol. 100, No. 14, 1996
Grencewicz and Ball
TABLE 2: Approximate Charges on Atoms for GaX3-H2O Based on Mulliken Population Analysis charge complex
Ga
O
H
X
GaH3-H2O (X ) H) GaF3-H2O (X ) F) GaCl3-H2O (X ) Cl)
-0.04 +1.17 +0.77
-0.70 -0.71 -0.70
+0.44 +0.47 +0.48
-0.06 -0.46 -0.34
There are relatively high and opposite charges on the H atoms of water and the F and Cl atoms in the complexes. GaH3H2O is an unusual exception. The Mulliken population analysis indicates that the charge on the gallium atom is slightly negatiVe, suggesting that the major Coulombic attractions are between the hydrogens on the GaH3 (which have a slightly negative charge) and the hydrogens on the H2O (which have an obvious positive charge). Several of the optimized structural parameters are consistent with this charge distribution. The Ga-O bond is about 0.1 Å longer in GaH3-H2O than in GaF3-H2O or GaCl3-H2O, despite the smaller van der Waals radii on the X atoms on Ga in the complex. (Van der Waals radii of substitutents are know to effect structures of similar molecules.) Also consisent with this distribution is the angle that the H2O moiety makes with the Ga-O bond, which we have adopted as the molecule-fixed z axis for this series of studies. This angle, 120.7°, is much smaller than that in GaF3-H2O and GaCl3H2O. This indicates that the water molecule is tilted more toward the GaH3 moiety (since an angle of 180° would mean that the hydrogens of the H2O would be pointing directly away from the GaX3). We can justify this combination of structural parameters by suggesting that there are attractive forces between the hydrogens on the H2O and GaH3, but Very slight repulsive forces between the Ga and O atoms. The combination of these interactions would contribute to a longer Ga-O distance and a more pronounced tilt of the H2O with respect to the GaH3. Vibrational Frequencies. Table 3 lists the unscaled vibrational frequencies for the three gallium-water complexes, along with their approximate assignments. With very few exceptions, these assignments are Very approximate, since for most of the normal modes there is substantial movement of most of the atoms in the complex. There are no available experimental data for comparison; however, it is hoped that in the near future gasphase or matrix-phase measurements can be made. Energies. Using the electronic and thermal energies for the parent molecules and the complexes, we are able to determine the energy of binding between GaX3 and H2O. Table 4 summarizes those values. Without any basis set superposition error (BSSE) correction, the binding energies for the gallium complexes mimic the trend of, but are slightly higher than, those for the respective aluminum complexes. This is in apparent
contradiction to the accepted belief that aluminum halides bind more strongly than gallium halides to molecules having N or O atoms as the binding site.1 An estimation of the BSSE corrections for these complexes was made, since previous studies of aluminum halide-hydrogen halide complexes7,8 indicated that the BSSE correction could reduce the binding energy of the complex by up to 50%. Table 5 lists the calculated binding energy with and without BSSE. For all three complexes, the correction drops the calculated binding energy by about 20%. While this is proportionately more than the correction for the respective aluminum complexes, it is still much less than that for the hydrogen halide complexes reported by others.7,8 However, when BSSE corrections are included, the binding energies in the gallium complexes now drop below the BSSEcorrected binding energies of the corresponding aluminum complexes.6 These conclusions are thus consistent with the known binding trend of aluminum and gallium toward N- and O-containing ligands. It also illustrates the necessity of including such corrections in order to make proper conclusions for these systems. The trend in binding energies in the gallium complexes is understandable from several perspectives. A higher binding energy is seen for those complexes where the absolute magnitude difference in charge between Ga and O is seen. The more electronegative fluorine not only provides a more partially positive gallium but also participates in Coulombic interactions with the hydrogen atoms in water. In fact, if the binding were considered purely Coulombic, one would find that the fluorinehydrogen interaction accounts for 12-13% of the binding energy, or almost 20 kJ/mol. A question has arisen regarding the propensity for the water molecules to always eclipse two of the three X atoms on the gallium molecule (and similarly for BF3 and AlX3): how high is the potential energy barrier that directs the complexes to that same position? We therefore performed potential energy scans wherein we rotated the GaX3 360° in 10° increments and calculated the single point energy. (We did not reoptimize any structural parameters during the scan, for computational efficiency. Although such reoptimizations might change the exact energy values, lowering them somewhat, the major qualitative aspects of the potential energy surface would remain.) Plots of the potential energy diagram versus angle of torsion measured from the minimum-energy position are given in Figure 2. The plots for GaF3-H2O and GaCl3-H2O show expected behavior: as the water molecule rotates about the GaX3, there are similar energy minima at 120° and 240° from the optimum, as two different X atoms become eclipsed. (The fact that the other two minima do not go to exactly zero is because of a lack of symmetry in the optimized complex and from not
TABLE 3: Unscaled Vibrations (in cm-1) for GaH3-H2O, GaF3-H2O, and GaCl3-H2O GaH3-H2O
approx assgnt
GaF3-H2O
approx assgnt
GaCl3-H2O
approx assgnt
62 339 412 423 562 718 807 813 816 1793 1919 1935 1982 3855 3922
H2O/GaH3 wag Ga-O str H2O/GaH3 def H2O/GaH3 tilt H2O/GaH3 tilt H2O rock GaH3 bend o.o.p. GaH bend GaH3 rock HOH bend asym GaH str asym GaH str GaH str sym OH str asym OH str
86 145 148 189 219 235 424 543 695 722 810 811 1777 3825 3887
H2O/GaF3 wag H2O/GaF3 tilt H2O/GaF3 wag H2O/GaF3 tilt H2O/GaF3 tilt H2O/GaF3 def Ga-O str H2O rock H2O rock GaF3 rock sym GaF str asym GaF str HOH bend sym OH str asym OH str
46 125 132 147 156 165 396 410 463 475 512 713 1773 3822 3888
H2O wag GaCl2 bend H2O wag Ga-OH2 def H2O rock GaCl3 o.o.p. bend Ga-O str H2O wag/sym GaCl str H2O wag/asym GaCl str asym GaCl str H2O wag/asym GaCl str H2O rock HOH bend sym OH str asym OH str
GaH3-H2O, GaF3-H2O, and GaCl3-H2O
J. Phys. Chem., Vol. 100, No. 14, 1996 5675 electrostatic interactions between the Ga-O and H- - -X atoms in the complexes. But in the case of GaH3-H2O, the electrostatic interactions between the HH2O and HGaH3 atoms are not as strong, and another metastable conformation, a staggered conformation, is available at a slightly higher energy. The potential energy diagram indicates a rotational barrier of ca. 3 kJ/mol for GaH3-H2O, suggesting slightly hindered rotation. The well depth of the staggered metastable conformation is only ca. 1 kJ/mol. Conclusions
Figure 2. Potential energy curves for GaH3-H2O, GaF3-H2O, and GaCl3-H2O for rotation about the Ga-O bond. The angle of rotation on the abscissa is measured from the optimized dihedral angle.
TABLE 4: Energies and Energy Differences (Total Energy in hartrees; All Others in kJ/mol) E GaH3 H 2O GaH3-H2O GaF3 H 2O GaF3-H2O GaCl3 H 2O GaCl3-H2O
∆E
BE Ethermal ∆Ethermal (≡-∆Etot)
-1916.974 29 58.27 -75.580 12 65.84 -1992.590 75 -95.5 135.23 +11.12 -2212.079 54 30.56 -75.580 12 65.84 -2287.722 77 -162.6 106.17 +9.77 -3287.482 85 25.60 -75.580 12 65.84 -3363.118 66 -147.2 101.09 +9.66
84.4 152.9
The minimum-energy geometries of GaH3-H2O, GaF3-H2O, and GaCl3-H2O were calculated using HF ab initio methods and basis sets that included diffuse and polarization functions. The optimized geometries all had the water molecule tilted and positioned so that the hydrogens eclipsed two of the three X atoms attached to the gallium. Potential energy curves showed that while such a geometry was favored absolutely by GaF3H2O and GaCl3-H2O, the GaH3-H2O complex exhibited a metastable staggered conformation. The binding energies between the water and the trivalent gallium compounds were slightly higher than for the respective aluminum complexes, which is contrary to expectations. Finally, vibrational frequencies were calculated for all three complexes. The calculated binding energies are high enough that these complexes would be expected to form under appropriate conditions, in either the gas phase or the matrix phase. Acknowledgment. Some of these calculations (mostly on GaCl3-H2O) were performed using the resources of the Ohio Supercomputing Center in Columbus, OH, through Grant PFS183-3. References and Notes
137.6
TABLE 5: Comparison of Binding Energies (kJ/mol) with and without BSSE complex
without BSSE
with BSSE
GaH3-H2O GaF3-H2O GaCl3-H2O
84.4 152.9 137.6
66.6 124.9 110.2
reoptimizing the structure as the two molecules rotate with respect to each other.) Potential energy barriers of ca. 4 and 1 kJ/mol are predicted for GaF3-H2O and GaCl3-H2O, respectively. Therefore, at room temperature, we would expect slightly hindered rotation for GaF3-H2O and essentially free rotation for GaCl3-H2O, should such complexes ever be detected experimentally. The potential energy diagram for GaH3-H2O is unusual. It does not show the normal, tripartite shape as expected, but rather has a relative minimum when the water molecule is 180° rotated from its lowest-energy configuration. In such a position, the water molecule is in a staggered position relative to the H atoms of GaH3. While the unusual shape of the potential energy curve is in part due to our not reoptimizing some of the molecular parameters during the scan, the metastable staggered geometry is probably not an artifact. In our initial optimizations of the GaH3-H2O complex using equivalent Ga-H, etc., structural parameters, the geometry converged on a staggered conformation which yielded one negative frequency upon calculation of the vibrations. Attempts to find a metastable staggered conformation for the GaF3-H2O and GaCl3-H2O complexes were unsuccessful. We conclude from this that the eclipsed conformation for the GaF3-H2O and GaCl3-H2O are favored due to
(1) Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements; Pergamon Press: Oxford, 1984. (2) Ball, D. W.; Zehe, M. J. NASA Technical Memo 106422, Dec 1993. (3) Ball, D. W. J. Mol. Struct. (THEOCHEM) 1995, 331, 223. (4) Evans, D. G.; Yeo, G. A.; Ford, T. A. Faraday Discuss. Chem. Soc. 1988, 86, 55. (5) Hunt, R. L.; Ault, B. S. Spectrosc.: Int. J. 1982, 1, 45. (6) Ball, D. W. J. Phys. Chem. 1995, 99, 12786. (7) Scholz, G. J. Mol. Struct. (THEOCHEM) 1994, 309, 227. (8) Wilson, M.; Coolidge, M. B.; Mains, G. J. J. Phys. Chem. 1992, 96, 4851. (9) GAUSSIAN 92, Revisions B and D.2: Frisch, M. J.; Trucks, G. W.; Head-Gordon, M.; Gill, P. M. W.; Wong, M. W.; Foresman, J. B.; Johnson, B. G.; Schlegel, H. B.; Robb, M. A.; Replogle, E. S.; Gomperts, R.; Andres, J. L.; Raghavachari, K.; Binkley, J. S.; Gonzales, C.; Martin, R. L.; Fox, D. J.; Defrees, D. J.; Baker, J.; Stewart, J. J. P.; Pople, J. A. Gaussian, Inc., Pittsburgh, PA, 1992. (10) Huzinaga, S.; Andzelm, J.; Klobukowski, M.; Radzio-Andzelm, E.; Sakai, Y.; Tatewaki, H. Gaussian Basis Sets for Molecular Calculations; Elsevier: Amsterdam, 1984. (11) Hehre, W. J.; Ditchfield, R.; Pople., J. A. J. Chem. Phys. 1972, 56, 2257. Hariharan, P. C.; Pople, J. A. Theor. Chim. Acta 1973, 28, 213. Gordon, M. S. Chem. Phys. Lett. 1980, 76, 163. (12) Pulham, C. R.; Downs, A. J.; Goode, M. J.; Rankin, D. W. H.; Robertson, H. E. J. Am. Chem. Soc. 1991, 113, 5149. (13) Schwerdtfeger, P.; Heath, G. A.; Dolg, M.; Bennett, M. A. J. Am. Chem. Soc. 1992, 114, 7518. (14) Duke, B. J.; Hamilton, T. P.; Schaefer III, H. F. Inorg. Chem. 1991, 30, 4225. (15) Ruda, H. E.; Ping, J. G. Phys. ReV. B 1992, 46, 15936. (16) Bock, C. W.; Dobbs, K. D.; Mains, G. J.; Trachtman, M. J. Phys. Chem. 1991, 95, 7668. (17) Graves, R. M.; Scuseria, G. E. J. Chem. Phys. 1992, 96, 3723. (18) Vogt, N.; Haaland, A.; Martinsen, K. G.; Vogt, J. J. Mol Struct. 1994, 163, 515. (19) Lide, D. R. CRC Handbook of Chemistry and Physics, 71st ed.; CRC Press: Boca Raton, FL, 1990.
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