J. Phys. Chem. 1996, 100, 12277-12279
12277
On the Molecular and Electronic Structures of the H3TiTiH3 Species Ame´ rica Garcı´a† and Jesus M. Ugalde* Fakultatea Kimika, Euskal Herriko Unibertsitatea, P.K. 1072, 20080 Donostia, Euskadi, Spain ReceiVed: December 20, 1995; In Final Form: April 5, 1996X
An ab initio molecular orbital study has been carried out for the H3TiTiH3 molecule. Geometries have been obtained using the second-order perturbation theory with a triple-ζ plus polarization basis set. Additivity of correlation and basis set effects has been used to estimate relative energies. Only two bridged structures, with eclipsed and staggered shapes, respectively, have been found to be stable. These two isomers are nearly degenerate in energy and lie 22.2 kcal/mol below two TiH3 units.
1. Introduction Two-electron three-center electron-deficient bridges have been the subject of many theoretical and experimental studies.1 Recently, Kudo and Gordon2 have reported on the increasing propensity of titanium to form two-electron three-center TiH-X bonds, where X goes from right to left in the third period of the periodic table. In particular, for the H3TiSiH3 two minima are found on its ground state potential energy surface: one is an open staggered structure and the other is a structure with three Ti-H-Si two-electron three-center peripheral bonds and no central Ti-Si bond. Moreover, the latter isomer turned out to be the most stable when electron correlation effects were taken into account. We would like, in the present work, to discuss the molecular and electronic structures of the H3TiTiH3 species. We shall show that one basic structural feature of this molecule is its three skeletal Ti-H-Ti electron-deficient brigades. 2. Methods Geometries for the species studied in this work were optimized at the HF level of theory and then reoptimized using the second-order Møller-Plesset perturbational theory (MP2).3 Frequencies were evaluated at the former level and used to assess that all species were true minima, as well as to estimate the zero-point vibrational energy (ZPVE) corrections. The basis set used in the present work for the titanium is the triple-ζ valence of Scha¨fer, Huber, and Ahlrichs,4 supplemented by the two 4p polarization functions optimized by Wachters5 for excited states. For the hydrogens we have used the 3-11G(p) of Krishnan et al.6 This set will be hereafter referred to as TZVP. Cartesians coordinates of all the optimum structures and their IR and Raman frequencies and intensities are given in Tables 1 and 2, respectively, of the supporting information. The additivitiness of the basis set and electron correlation effects7 were used to improve the energies. Thus, the corrections due to the deficiencies in the basis set were estimated by calculating the MP2 energy with a large basis set. Namely, the TZVP basis set of the titanium atom has been augmented with a diffuse s function (with an exponent 0.36 times that of the most diffuse s function on the original set) and one diffuse d function (optimized by Hay).8 The effects of f functions were accounted for adding three uncontracted f functions, including both the tight and diffuse exponents, as recommended.9 For † On leave from Dpto. de Quı´mica, Fac. de Ciencias Nat. y Mat., Universidad de Oriente, Avenida Patricio Lumumba S/N, 90500, Santiago de Cuba, Cuba. X Abstract published in AdVance ACS Abstracts, June 15, 1996.
S0022-3654(95)03779-8 CCC: $12.00
the hydrogen atom the 311G(p) basis set has been supplemented with one p function. This basis set will be hereafter referred to as TZVP+G(3df,2p). Next, we calculate the contributions of successive improvements in the method, to obtain the CCSD(T)/TZVP+G(3df,2p) energies, by the following additivity scheme:
E[CCSD(T)/TZVP+G(3df,2p)] ) E[MP4/TZVP]+∆E[CCSD(T)/TZVP]+ ∆MP2 + HLC + ZPVE with
∆E[CCSD(T)/TZVP] ) E[CCSD(T)/TZVP] - E[MP4/TZVP] ∆MP2 ) E[MP2/TZVP+G(3df,2p)] - E[MP2/TZVP] where HLC is the empirical high-level correlation correction of Curtiss et al.10 These calculations were performed using GAMESS11a and Gaussian94/DFT.11b In addition, we have explored the bonding characteristics by means of both the natural bond orbital (NBO) analysis12 and the Bader’s topological analysis of the electron charge density.13 The former was carried out with the NBO code,14 as implemented on the Gaussian 94/DFT, and the latter with the AIMPAC series of programs.15 3. Results and Discussion The geometries of the two stable structures found on the MP2/ TZVP potential energy surface are shown in Figure 1. It is worth mentioning that both structures have the three hydrogens of one of the titaniums, turned inside. Structures a and b of the H3TiTiH3, discussed in this paper, differ in the relative orientation of the triangles defined by the terminal hydrogens 3, 4, and 5 and the bridged hydrogens 6, 7, and 8 (see Figure 1). Thus, structure a has a staggered-like shape, while structure b has an eclipsed-like shape. Nevertheless, both structures are found to belong to the C3V symmetry point group. Open, both staggered and eclipsed structures have been reported previously for related compounds H3TiX, with X ) CH3,2,16,17 NH2,2 OH,2 SiH3,2 PH2,2 and SH.2 However, attempts to locate analogous open structures for the H3TiTiH3 on the MP2/TZVP potential energy surface failed because of the collapse to structures a or b in Figure 1. The three bridge hydrogens (Hb) of both staggered and eclipsed structures are almost equidistant from both of the titaniums. Namely, for the staggered structure the bond length between the Hb and the terminal titanium atom (Tit) is only 0.21 Å shorter than the bond length between the Hb and the © 1996 American Chemical Society
12278 J. Phys. Chem., Vol. 100, No. 30, 1996
Garcı´a and Ugalde TABLE 1: Atomic NBO Coefficients of the Two-Electron Three-Center Ti-H-Ti Molecular Orbitals and, in Parentheses, Their Corresponding Hybridization Pattern, from the MP2/TZVP Molecular Wave Function coefficient
Figure 1. MP2/TZVP of (a) staggered and (b) eclipsed structures with SCF geometries in parentheses. Bond lengths are given in angstroms and bond angles in degrees.
isomer
occupancy
Ti1
Ti2
H
eclipsed
1.911
1.915
eclipsed
1.950
0.39 (s, 31.29) (p, 0.41) (d, 68.28) 0.39 (s, 29.24) (p, 0.47) (d, 70.29) 0.36 (s, 32.97) (p, 0.62) (d, 66.41)
0.85 (s, 99.75) (p, 0.25)
eclipsed
0.35 (s, 11.87) (p, 1.21) (d, 86.92) 0.35 (s, 11.99) (p, 1.24) (d, 86.76) 0.32 (s, 12.27) (p, 1.64) (d, 86.09)
bond
F(rc)
∇2F(rc)
H(rc)
Ti-Ti
0.0441 (0.0483) 0.1116 (0.1083) 0.0793 (0.0817) 0.0538 (0.0558)
0.1795 (0.1455) -0.0009 (0.0261) 0.2147 (0.2274) 0.1572 (0.1264)
-0.0048 (-0.0080) -0.0528 (-0.0492) -0.0233 (-0.0244) -0.0066 (-0.0089)
Ti-Hb direct Ti-Hb
central titanium (Tic) atom. For the eclipsed structure this difference is 0.20 Å, a trend akin to that found for the H3TiSiH3 species.2 Similarly, the bond lengths and angles between the terminal hydrogens (Ht) and the central titanium of both the staggered and eclipsed structures are nearly alike, as shown in Figure 1. The distance between the two Ti atoms is predicted to be 2.54 Å for the staggered structure and 2.54 Å for the eclipsed one, at the MP2/TZVP level of theory. Although it has been claimed that, in noncubic isomers of the Ti8C12+ met-car,18 single covalent bonds exist between Ti atoms separated by 2.90 Å, we shall argue below that for the species studied in this paper, there is no such Ti-Ti single covalent bond. Effects of the electron correlation on the optimum structures
0.88 (s, 99.72) (p, 0.28)
TABLE 2: Bonding Properties, in au, of the Bond Critical Points of the Eclipsed and Staggered (in Parentheses) Isomers of the Bridged H3TiTiH3, at the MP2/TZVP Level of Theory
Ti-Ht
Figure 2. Countour (each contour separated by 0.05 au-3/2) plots of LMO’s in H3TiTiH3. Orbitals of the eclipsed and staggered structures are on the left- and right-hand sides, respectively. In each case, the Ti-H terminal bond is shown at the top, the Ti-H-Ti two-electron three-center bond in the middle, and the 3d lone pair on the bottom.
0.85 (s, 99.70) (p, 0.30)
can also be appreciated from Figure 1. In general, at the MP2/ TZVP level of theory, all bond distances lengthen with respect to those at the RHF/TZVP level by amounts not exceeding 0.1 Å. Analysis of the localized molecular orbital (LMO) contour diagrams, shown in Figure 2 for both the eclipsed and staggered isomers, sheds some insight into the nature of the bonding. The interesting point is that there is no LMO that corresponds to a Ti-Ti bond for neither of the two bridged isomers of the H3TiTiH3 . Instead, we have found a 3d lone pair associated with the terminal Ti atom and three two-electron three-center TiHb-Ti bonding LMO’s, which keep the two Ti atoms at a calculated separation of ∼2.5 Å, a distance even shorter than that considered as an average Ti-Ti single bond,19 namely, 2.90 Å. The three central Ti terminal hydrogen bonding LMO’s are regular σ bonds, as expected. This picture comes along with the natural bond orbital analysis of Weinhold et al.12 Thus, we have been able to find three doubly occupied two-electron three-center Ti-Hb-Ti bonds, which are summarized in Table 1, for both the eclipsed and staggered structures. Their inspection reveals that these bonding molecular orbitals are formed by a linear combination of sd hybrids on the titaniums and the s atomic orbital of the bridge hydrogen atom. We have been unable to find any TiTi bonding natural bond orbital. However, for both of the structures a lone pair, of the 3d nature, has been characterized. This lone pair is doubly occupied and associated with the terminal titanium atom, in full agreement with the highest energy occupied molecular orbital, as discussed in the preceding paragraph. According to the natural bond orbital energies, the twoelectron three-center bonds are more energetic than the central titanium terminal hydrogen bonds by 51.8 kcal/mol for the staggered isomer and by 44.8 and 52.4 kcal/mol for the eclipsed and for the two staggered Ti-H-Ti bonds, respectively, of the eclipsed isomer, at the MP2/TZVP level. In both cases the
H3TiTiH3 Species
J. Phys. Chem., Vol. 100, No. 30, 1996 12279
TABLE 3: MP4/TZVP Base Level and CCSD(T)/TZVP+G(3df,2p) Energies, in hartrees, and Corrections, in mhartrees, to the Base Level Energy for TiH3 and H3TiTiH3 Isomers TiH3 staggered eclipsed
MP4/TZVP
∆E[CCSD(T)/TZVP]
∆MP2
ZPVE
HLC
E[CCSD(T)/TZVP+G(3df,2p)]
-850.120 66 -1700.393 88 -1700.400 11
-6.63 -7.76 -6.63
-101.39 -72.35 -71.84
16.15 34.53 35.77
-29.66 -77.19 -77.19
-850.242 19 -1700.516 65 -1700.519 69
HOMO corresponds to the terminal titanium lone pair, which lies 33.5 and 46.8 kcal/mol, for the staggered and eclipsed isomers, respectively, above the terminal hydrogen central titanium natural bond. Insight into the nature of the molecular bonding can also be gained by analyzing the electron charge density. Thus, we have collected in the Table 2 the salient features of Bader’s topological analysis of the electron charge density. Notice that the Bader’s analysis predicts a Ti-Ti covalent bond for both isomers, as evidenced by the existence of a bond critical point at rc, with a negative value of the energy density. Closer inspection of the small values of the electron density at the TiTi bond critical points of both isomers puts forward that the geometry constraints, imposed by the three angular two-electron three-center Ti-H-Ti bonds, could result in a marginal overlap of the tails of the electron densities of the two titaniums, which could be suggestive of a weak dative interaction from the lone pair of the terminal titanium to the vacant 3d orbitals of the central titanium, although such an interaction is not found by the other two methods, the natural bond orbital analysis and the inspection of the LMO’s. Otherwise, the topological bonding properties of the Ti-H bonds predict two kinds of hydrogen atoms, one set of three terminal hydrogens and one set of three bridged hydrogens, in accord with the discussion of the preceding paragraphs. Energies shown the Table 3 indicate that the eclipsed isomer of H3TiTiH3 is slightly more stable than the staggered isomer. At our highest level of theory, i.e., CCSDT/TZVP+G(3df,2p), the energy difference is 1.9 kcal/mol. Also, from Table 3, one can see that the eclipsed H3TiTiH3 lies 22.2 kcal/mol lower in energy than the two units of TiH3, which is indicative of the stability of the dimer. Finally, one should observed that the additive corrections to the base level energy have a remarkable effect on the relative energies. Thus, at the MP4/TZVP base level, the energy difference between the two isomer of the H3TiTiH3 is 3.9 kcal/mol, the eclipsed isomer being the more stable, and the energy difference between the dimer and two units of TiH3 rises up to 99.6 kcal/mol. 4. Conclusions Our calculations predict that the H3TiTiH3 molecule exists as two nearly energy degenerate bridged eclipsed and staggered isomers. The bridged eclipsed isomer is found to be 1.9 kcal/ mol more stable than the bridged staggered isomer and 22.2 kcal/mol more stable than the two TiH3 units. This is suggestive of the stability of the H3TiTiH3 molecule and of the strength of the three two-electron three-center Ti-H-Ti bonds. The highest occupied molecular orbital of both isomers corresponds
to the 3d lone pair associated with the terminal titanium atom. This should be regarded as a basic site. Hence, it could determine their initial reaction stage toward electrophilic attack. Acknowledgment. This research has been supported by the University of the Basque Country (Euskal Herriko Unibertsitatea) and the Basque Government (Eusko Jaurlaritza), Grant No. GV/203.215-49/94. A.G. thanks the Spanish Agencia de Cooperacio´n Iberoamericana (AECI) for a grant. The authors are grateful to Dr. X. Lo´pez for many useful suggestions. Supporting Information Available: Cartesian coordinates at the RHF/TZVP and MP2/TZVP levels of theory (Table I) and harmonic vibrational frequencies and infrared and Raman intensities at the HF-TZV level of theory (Table II) for eclipsed and staggered H3TiTiH3 (2 pages). Ordering information is given on any current masthead page. References and Notes (1) Trinquier, G.; Malrieu, J.-P. J. Am. Chem. Soc. 1991, 113, 8634, and references therein. (2) Kudo, T.; Gordon, M. S. J. Phys. Chem. 1995, 99, 9340. (3) Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople; J. A. Ab Initio Molecular Orbital Theory; Wiley-Interscience: New York, 1986. (4) Scha¨fer, A.; Huber, C.; Ahlrichs, R. J. Chem. Phys. 1994, 100, 5829. (5) Wachters, A. J. H. J. Chem. Phys. 1970, 52, 1033. (6) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. (7) Ignacio, E. W.; Schlegel, H. B. J. Comput. Chem. 1991, 12, 751. (8) Hay, P. J. J. Chem. Phys. 1971, 66, 4377. (9) Raghavachari, K.; Trucks, G. W. J. Chem. Phys. 1989, 91, 1062. (10) Curtiss, L. A.; Raghavachari, K.; Pople, J. A. J. Chem. Phys. 1993, 98, 1293 (11) Frish, M. J.; Trucks, G. W.; Schlegel, H. B.; Gill, P. M. W.; Johnson, B. G.; Robb, M. A.; Cheeseman, J. R.; Keith, T. A.; Petersson, G. A.; Montgomery, J. A.; Raghavachari, K.; Al-Laham, M. A.; Zakrzewski, V. G.; Ortiz, J. V.; Foresman, J. B.; Croslowski, J.; Stefanov, B. B.; Nanayakkara, A.; Challacombe, M.; Peng, C. Y.; Ayala, P. Y.; Chen, W.; Wong, M. W.; Andres, J. L.; Replogle, E. S.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Binkley, J. S.; Defrees, D. J.; Baker, J.; Stewart, J. P.; HeadGordon, M.; Gonzalez, C.; Pople, J. A. Gaussian 94, Revision A.1; Gaussian, Inc.: Pittsburgh, PA, 1995. (12) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899. (13) Bader, R. F. W. Atoms in Molecules. A Quantum Theory; Clarendon Press: Oxford, 1990. (14) Glendening, E. D.; Reed, A. E.; Carpenter, J. E.; Weinhold, F. NBO, Version 3.1, as implemented in Gaussian 94. (15) Biegler-Konig, F. W.; Bader, R. F. W.; Tang, T. H. J. Comput. Chem. 1980, 27, 1924. (16) Dobbs, K. D.; Hehre, W. J. J. Am. Chem. Soc. 1986, 108, 4663. (17) Williamson, R. L.; Hall, M. B. J. Am. Chem. Soc. 1988, 110, 4428. (18) Khan, A. J. Phys. Chem. 1995, 99, 4923. (19) Huber, K. P.; Herzberg, G. Constants of Diatomic Molecules; Van Nostrand Reinhold Co.: New York, 1979; p 642.
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