Cundari Th.R. -- Computational Organometallic Chemistry-0824704789

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MP2 level of theory and are followed by hessian calculations to determine whether a particular structure is a minimum or a saddle point on the potential energy surface. If one is interested in determining a transition state for a chemical reaction, it is advisable to determine the minimum-energy path (MEP) that connects the transition state with the corresponding reactants and products. Especially for complex species, it is not always obvious what these connecting minima are without mapping out the MEP. The most common MEP algorithm is the second-order method developed by Gonzalez and Schlegel (17).

Because atomic titanium has low-lying electronic excited states, potential energy surfaces of Ti compounds, especially unsaturated compounds, often cross. When such crossings occur, nonradiative transitions can occur via spin-orbit coupling. In such cases, spin-orbit coupling probabilities must be evaluated. Such calculations usually are performed with MCSCF-based wavefunctions. In addition, relativistic effects can have a significant effect on chemical properties, even for compounds containing elements in the first transition series. Fortunately, new models have been developed to treat relativistic effects for all-electron basis sets (18).

One of the goals of computational inorganic chemistry is to perform elec- tronic-structure calculations on the specific system of interest, not on some simplified prototype. Improved hardware and software both contribute to achieving this goal. A particularly important development in this regard is scalable comput- ing—the use of multiple computer nodes to perform complex calculations. This capability has recently been enhanced by the development of a distributed data interface (DDI) (19) that permits a distributed parallel computer to look like a shared memory (SMP) computer to take maximum use of the aggregate memory and disk space. This method, which facilitates the prediction of structures at high levels of theory, can run on computers ranging from expensive ‘‘supercomputers’’ to networks of PCs.

All of the methods just outlined have been used for some of the chemistry discussed next, generally using the electronic structure program GAMESS (20) (General Atomic and Molecular Electronic Structure System). Coupled cluster calculations were performed using either ACES II (21) or Gaussian94 (22). Multireference CI calculations are commonly performed using the MOLPRO (23) code.

3. STRUCTURES AND POTENTIAL ENERGY SURFACES

3.1.TiX2

In the Group IVA analogs, CH2 has a triplet ground state, while SiH2 and the heavier congeners have singlet ground states, although such terminology is not particularly relevant to Pb. The low-lying states of TiH2 have been analyzed with state-averaged MCSCF wavefunctions and all-electron extended basis sets,

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followed by multireference configuration interaction (24). At this level of theory, several triplet states are found to lie within a 5-kcal/mol range, with the 3B1 state predicted to be the ground state. However, the 3A1 state is found to be only 1 kcal/mol higher in energy, so the ground state prediction may not be definitive. It is clear that the ground state is a triplet, since the lowest-energy singlet state is predicted to be nearly 1 eV above the ground state. The lowest quintet states are even higher in energy.

For all of the low-lying states, the H–Ti–H bend potential is very flat. All of these states are predicted to be mildly bent in C2v symmetry. These states are also susceptible to distortion along the asymmetric stretching mode to Cs symmetry with little energy expense. Although multireference wavefunctions are clearly necessary for a proper description of TiH2, it is interesting that the 1A1 structure is well reproduced by second-order perturbation theory, MP2. The latter level of theory also predicts TiCl2 to have a slightly bent triplet ground state (25).

An important divalent titanium species is titanocene, the Ti analog of ferrocene. While there have been a few experimental (26) or theoretical (27) studies of this species, none are definitive. On the experimental side, it is not clear whether the ground state is singlet or triplet, or indeed even whether the ground state species studied was the monomer. The only previous theoretical study of TiCp2 (Cp cyclopentadienyl) was an early semiempirical calculation that could not distinguish spin states. Since this is such an important compound, a series of MCSCF calculations have been initiated on TiCp2, in which all of the Ti valence electrons and orbitals are included in the active space. Preliminary results suggest that, like the simpler TiH2 and TiCl2 analogs, the ground state is a triplet (28).

3.2. Ti2H6

Superficially, Ti2H6 is a simple titanium analog of ethane and disilane. Indeed, early calculations on this species assumed that this is the case and therefore used single configuration, restricted Hartree-Fock (RHF)–based methods to predict its molecular and electronic structure (29). However, this assumption ignores the fact, discussed in Section 1, that Ti is an electron-deficient atom with more unoccupied valence d orbitals than the empty valence p orbitals in carbon or silicon. A careful examination of the electrons and orbitals in Ti2H6 reveals that one must treat this molecule as a potential diradical. This means the lowest state could either be an open-shell singlet or a triplet, depending on the extent of Ti–Ti bonding, but most assuredly not as a closed-shell singlet.

The calculations on Ti2H6 were performed (30) using a basis set of triple zeta plus polarization quality, including f functions on Ti. For the singlet states, both restricted open-shell Hartree–Fock (ROHF) and FORS MCSCF reference wavefunctions were used, while ROHF reference wavefunctions were used for the triplet states. In order to account for dynamic electron correlation and obtain

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reliable energetics, these reference wavefunctions were augmented by secondorder perturbation theory. For ROHFand MCSCF-based wavefunctions, this means RMP210 and MCQDPT216, respectively.

Five minima were found on both the singlet and triplet potential energy surfaces. All of these minima have hydrogens bridging the two titaniums, more reminiscent of diborane than ethane or disilane. The (µ-H)3 staggered and eclipsed structures that had previously been described by closed-shell RHF reference wavefunctions actually require at least a 2-electron, 3-orbital FORS MCSCF wavefunction for a qualitatively correct description. The analogous triplets require an ROHF wavefunction in which two degenerate states are averaged. All minima are predicted to be lower in energy than two separated TiH3 radicals, with binding energies in excess of 50 kcal/mol for the lowest-energy structures. The global minimum for Ti2H6 is found to be the triply bridged Cs triplet (3A″), but this species is only 0.3 kcal/mol lower in energy than the analogous 1A″ state. Doubly bridged D2h and quadruply bridged D4h (µ-H)4 species are only about 5 kcal/mol higher in energy than these Cs structures. For these more symmetric structures, the singlets are lower than the corresponding triplets by about 1.4 kcal/mol. The (µ-H)3 staggered and eclipsed singlets are more than 20 kcal/mol higher. The corresponding staggered and eclipsed triplets are much more stable than the singlets.

No Ti–Ti bonding is possible in the triplet minima, since the two unpaired electrons have the same spin. Somewhat more surprising is the fact that little Ti–Ti bonding is found in the singlet minima as well. In the (µ-H)3 C3v minima, both unpaired electrons reside on the less saturated Ti. The (µ-H)3 singlet and triplet Cs minima are purely diradical. Natural orbital analyses of the (µ-H)2 D2h and (µ-H)4 D4h singlet wavefunctions show a large amount of diradical character, although a slight bonding interaction is predicted in both of these singlets. This is reflected in the observation that these singlets are slightly lower in energy than the corresponding triplets. The lack of Ti–Ti bonding may be understood using the localized charge distribution (LCD) analysis (31). This analysis suggests that the lack of Ti–Ti bonding in the D2h isomer, where bonding should be most likely, is due to steric crowding, that is, unfavorable interactions of the bond with the surrounding molecule. Comparison of the calculated frequencies of Ti2H6 isomers with the experimental spectra of Chertihin and Andrews (32) suggests the presence of Ti2H6 in the matrix.

The D2h H2Ti(µ-H)2TiH2 structure is an excellent prototype for the many homodinuclear titanium(III) compounds known experimentally (33), such as titanocene dimer. Experimental evidence suggests either a Ti–Ti bond or a large singlet-triplet energy gap in this compound. Since the study of the Ti2H6 prototype predicts little Ti–Ti bonding and a small singlet-triplet splitting, it may be that the presence of the cyclopentadienyl rings and/or distortion of the bridge

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out of the molecular plane must significantly modify the electronic structure. This is the subject of ongoing calculations.

In dinuclear complexes comprising two metal centers, each with an unpaired electron, the interaction is said to be antiferromagnetic if singlet coupling of the electrons is favored over triplet coupling. If the reverse is true, the interaction is ferromagnetic (34). According to these definitions, D2h (µ-H)2 Ti2H6 is antiferromagnetic, with the isotropic exchange interaction J 250 cm 1, where

J 0.5 [E(singlet) E(triplet)].

In general, the magnitude and sign of the singlet-triplet energy gap is a measure of the isotropic exchange interaction, in the absence of spin-orbit coupling and magnetic dipole–dipole interactions. When the singlet-triplet splitting is very small, as is the case for Ti2H6, the normally subtle spin-orbit and magnetic effects can become important. Since EPR experiments are able to detect such subtle effects, and since these subtle effects have rarely been addressed using ab initio quantum mechanics methods, the excited-state energies and spin-orbit coupling matrix elements connecting the various states of Ti2H6 were calculated (35) using configuration interaction (CI) wavefunctions and the one-electron Zeff method (36). An overall ferromagnetic effect of 0.660 cm 1 is predicted on the ground-state singlet–first excited triplet energy gap. Future calculations will expand these studies to more complex bridged compounds.

3.3. Ti2X8 Compounds

TiH4 has a tetrahedral structure that is reminiscent of methane and silane. It is well represented by a single-configuration wavefunction and therefore a single, simple Lewis structure. However, in view of the foregoing discussion, one might (correctly) suspect that this is not the entire story of this ‘‘simple’’ molecule. Indeed, TiH4 is predicted (37) to dimerize with no energy barrier to Ti2H8. Since multireference wavefunctions are not necessary for this species, the calculations employed MP2 geometries, followed by single points at the coupled cluster, CCSD(T) level of theory. The exothermicity of the reaction 2TiH4 → Ti2H8 is estimated to be 40 kcal/mol. Both doubly and triply bridged dimers have been found, and the interconversion among the various isomers requires little energy.

Because bridged compounds such as Ti2H6 and Ti2H8 are important prototypes for more complex analogs, a systematic study of Ti2X8 species (X F, Cl, Br) was carried out (38). Geometry optimizations were performed at the MP2 level of theory, using effective core potentials, with a double zeta basis set augmented by polarization functions. The importance of higher-level dynamic correlation was explored using CCSD(T). Basis set effects were examined by single-point calculations that employed all-electron extended basis sets. Ti2F8

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is predicted to be a bound C2h dimer with two bridging bonds, lower in energy than the separated monomers by 10.5 kcal/mol. In contrast, Ti2Cl8 and Ti2Br8 are predicted to be weakly bound dimers with D3d symmetry, whose structures resemble associated monomers. This is consistent with experimental data, which suggests that solid-state TiF4 is a bridged polymer chain, whereas solid-state TiCl4 and TiBr4 remain molecular in structure. Ti2Cl8 is predicted to be bound by 4.9 kcal/mol at the CCSD(T)//MP2 level of theory. Coupled cluster calculations were not possible for the Br analog, but one can speculate that this species has a similar binding energy. Constrained optimizations along the dimerization pathway show that the formation of the F and Cl dimers occur with no energy barrier. Transition states with symmetrically equivalent bridging halides represent possible routes to halide exchange between monomers.

Dynamic correlation, at the MP2 level of theory, is very important for the prediction of accurate energetics for these species. While MP2 was not very important for the prediction of geometries for the fluorine dimer, it was essential for the geometry predictions for the heavier congeners. The effective core potential basis set overestimates the dimerization energy of TiF4 by about 4 kcal/mol, but it was quite reliable for the heavier species.

The LCD analysis was used to support the notion that the dimerization process is governed by a continuous competition between unfavorable endothermic monomer distortions and favorable exothermic monomer interactions. It was shown that the internal monomer energies indeed increase as the dimerization proceeds at the same time that the interaction between monomers drives the energy down. The net energy change along the dimerization path is a competition between these two. In the fluorine system, the favorable monomer interaction energy dominates, leading to a strongly bound dimer. In the chlorine and bromine systems, the two effects roughly cancel, so the net effect is a very weak binding.

3.4.H2TiCEH2

There has been a long-standing interest in the nature of multiple bonding between transition metals and main group elements (39). To quantitatively assess the nature of TiCC vs. TiCSi π bonding, the internal rotation process was studied for the molecules H2TiCCH2 and H2TiCSiH2 (40). Geometries were determined using MCSCF wavefunctions, optimizing the geometry of both the lowest singlet and lowest triplet states as a function of the angle between the TiH2 and EH2 (E C, Si) planes. Both effective core potentials and the triple zeta polarization (TZVP) basis set were used. In general, ECPs provided a good representation of the all-electron results. Final energetics were determined with the MC-QDPT2 method and the TZVP basis set. At the best level of theory, MC-QDPT2 with the TZVP basis set, the rotation barrier on the singlet surface is 15.8 kcal/mol for the carbon compound and 8.6 kcal/mol for the silicon species. To some degree

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this reflects the greater ability of C than Si to form π bonds, but note that due to the participation of the Ti d orbitals, there is significant π bonding at all rotation angles. Note also that the triplets for both species are minima at the twisted structure. Unlike the singlet states, the energy decreases for the triplets are very similar for C and Si.

Whereas the singlet remains below the triplet at all rotation angles for the carbon compound, the two curves cross in the silicon species,so the triplet is the ground state at the twisted structure. It is also interesting that the singlet TiC distance actually decreases upon rotation, whereas the TiSi distance increases, as expected. The origin of this behavior may be understood from the natural orbital occupation numbers (NOONs) for the π bonding orbitals. Normally, one expects this NOON to decrease from roughly 2.0 to roughly 1.0 as the π bond is broken. This behavior is just what is found for Si. In contrast, the NOON actually increases in the carbon case. This very likely reflects the greater ability of carbon to interact with the empty Ti d orbitals as the rotation occurs. So, while the rotation barrier cannot be equated with a π bond energy, the relative rotation barriers for C vs. Si do reflect the stronger π bonds formed by C. The determination of the total TiCSi and TiCC bond energies is in progress.

3.5. TiH3OH Decomposition

TiH3OH is the simplest prototype for a Ti–O bond. Therefore the thermal decomposition processes of this species is the simplest prototype for the chemical vapor deposition of titanium oxide. Titanol can dissociate by the following unimolecular routes (41):

TiH3OH → TiH2CO H2		(1)
→ HTiOH H2		(2)
→ TiH2	H2O	(3)
→ TiH3	OH	(4)
→ TiH4	O	(5)

In addition, one can have isomerization between the first two products. The ground electronic state of TiH3OH is a singlet, so the analysis of its decomposition pathways was performed on the singlet surface. All geometries for this reaction were determined using MCSCF wavefunctions with a triple zeta polarization (TZVP) basis set. Final energies were obtained using the CASPT2 method with the same basis set. The structure of the parent molecule is found to be C3v, with a linear Ti–O–H angle. Reactions (4) and (5) are predicted to proceed monotonically uphill, with no intervening barrier. At the MCSCF level of theory,

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the endothermicities for these reactions are 114.3 and 203.2 kcal/mol, respectively. Since these are very high-energy processes, they were not pursued further.

Reaction (2) is predicted to occur without barrier. The CASPT2 endothermicity, including zero-point vibrational corrections, is 30.9 kcal/mol. The endothermicity for the production of titanone, H2TiCO, is only 2.5 kcal/mol at the same level of theory, so this isomer is much lower in energy than HTiOH. However, there is an intervening barrier of 18.6 kcal/mol between TiH3OH and H2TiCO. [Note that the ground electronic state of HTiOH is a triplet, as is the case for TiH2. On the triplet surface, the relative stabilities of these two isomers is reversed.] For the remaining reaction (3), the production of water and TiH2, there is an intermediate complex in which the two products are weakly bound at about 55 kcal/mol above the reactant. The products are an additional 12.5 kcal/mol higher in energy. So, the lowest-energy decomposition path is clearly the one that leads to H2TiCO. Note also that the isomerization barrier from H2TiCO to HTiOH is 48 kcal/mol, so the lowest-energy route to the higherenergy isomer is directly from TiH3OH.

It is interesting to compare the electronic structure of H2TiCO with its main group analogs H2CCO and H2SiCO. The percentage decrease in bond length on going from the singly bound to the doubly bound species is about 7.5% for both the Ti and Si compound. In contrast, the percentage decrease for C is 14.6%, nearly twice as large. This reflects the much greater propensity for C to form double bonds. The TiCO and SiCO bonds are also much more polar than CCO: the Mulliken charges on the metal are 0.102 (C), 0.825 (Si), 0.713 (Ti).

3.6.Ti C2H6

Experimental studies of gas-phase reactions of first-row transition metal cations with simple alkanes provide valuable insight into the mechanism and energetics of C–H and C–C bond activation. Insertion of the metal into C–H or C–C bonds is common and leads eventually to elimination of H2 or small alkanes. Because C2H6 is the simplest alkane in which there is a competition between hydrogen and smaller alkane (i.e., methane) elimination, and since there have been several experimental gas-phase studies of Ti reactions with ethane (42), a comprehensive theoretical study of this reaction was initiated (43). The theoretical methods used include the B3LYP version (44) of density functional theory (DFT) with a valence triple zeta plus polarization basis set (TZVP), CCSD(T) with an extended basis set, and CASSCF MCQDPT2 using the TZVP basis set. The use of MCSCF-based wavefunctions proved to be essential, since parts of the potential energy surfaces are inherently multireference in nature. Geometries were determined using either B3LYP or CASSCF. Since Ti has low-lying doublet and quartet states, the potential exists for surface crossings, in which case spin-orbit coupling can become important. The spin-orbit coupling matrix elements were

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calculated with the CASSCF/TZVP basis set, using the full Breit–Pauli Hamiltonian (45).

The main questions addressed in this work were:

1.What is the nature of the adduct ions observed in the flow tube experiments?

2.Why are only the H2 elimination products, not CH4, observed at low energies?

3.Does the H2 elimination proceed by a 1,1- or a 1,2-mechanism?

4.How important are spin-orbit effects on the Ti C2H6 reaction?

It has been determined that both the H2 and CH4 reactions are initiated by the formation of an η3 coordinated Ti —C2H6 ion-induced dipole complex in the quartet state. Because the ground state of Ti is a quartet, whereas the C–H and C–C insertion products have ground-state doublets, doublet-quartet surface crossings occur, and the two reactions subsequently proceed on the doublet surface. So the nontrivial spin-orbit coupling predicted by these calculations plays an important role in the mechanism.

The net H2 elimination process is predicted to be nearly thermoneutral. The highest-energy transition state on this path has an energy requirement of 5–9 kcal/mol, depending on the level of theory employed. This may be contrasted with recent DFT results on Co and Fe mediated H2 elimination from C2H6. These latter calculations find a lower C–H insertion transition state, perhaps due to deeper wells corresponding to the initial M -ethane complexes. The calculations also predict that the 1,2-elimination is favored over the 1,1-elimination mechanism. The net CH4 elimination is predicted to be rather endothermic at all levels of theory, with a high C–C insertion barrier. This is consistent with the lack of experimental observation of CH4.

4. TITANIUM AS A CATALYST

Divalent titanium has been implicated as a catalyst in several reactions, including silane polymerization (1) and hydrosilation (2). Considerable theoretical effort has therefore been expended recently in analyzing the role of divalent titanium as a catalyst in the hydrosilation and bis-silylation reactions.

The hydrosilation reaction is the addition of a silane, R3Si–H to a CCC double bond, to form new carbon–silicon bonds. In the absence of a catalyst, this reaction occurs only with a very large (50–60 kcal/mol) barrier (46).

In order to assess several levels of theory, the first study was performed on the prototypical system SiH4 C2H4, using TiH2 as catalyst (46). These calculations were performed using the TZVP basis set, at the Hartree–Fock, MP2, and CCSD(T) levels of theory. It is very clear from a detailed analysis of the reaction path that correlation corrections are essential to obtain a reliable prediction of

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the energetics for this reaction. On the other hand, MP2 parallels the CCSD(T) calculations very well. This is an important result, since the MP2 calculations are affordable for larger species, while CCSD(T) would be out of the question. The key bottom line for this reaction is that the initial steps in the reaction, the formation of complexes between the catalyst and the two substrates, is so exothermic, nearly 70 kcal/mol at the highest level of theory, that all subsequent steps have barrier heights that are more than 30 kcal/mol below the starting reactants. The overall exothermicity for this reaction is predicted to be 28 kcal/mol.

With the foregoing results in hand, several additional reactions were considered with increasingly complex reactants and catalyst. The three reactions studied were:

TiH2 SiCl3H C2H4	(6)
TiCl2 SiCl3H C2H4	(7)
TiCp2 SiCl3H C2H4	(8)

where Cp is cyclopentadienyl. The calculations on these reactions (48) were made possible by two recent advances in theory and code development: the development of very effective parallel computer codes for MP2 gradients (19) and the development of much more efficient gradient and hessians for effective core potentials (49). Due to the size of these systems, using the TZVP basis set and CCSD(T) calculations would be prohibitively expensive.

Fortunately the unsubstituted work demonstrated that the MP2 level of theory is adequate for this reaction. To reduce the size of the basis set, ECPs were used for all elements except H and C. Effective core potentials are a very effective means for studying heavier elements, since they replace inner shells with more easily evaluated one-electron potentials leading to greater computational efficiency. To test the accuracy of ECPs they were used for Ti and Si in the unsubstituted reaction and checked against the previous all-electron results. The RMS difference in energy was shown to be 0.5 kcal/mol, which was deemed acceptable. Thus, ECPs were used in the substituted systems for all atoms except H and C, which remained all-electron.

The results for reactions (6)–(8) differ in detail, but not in substance, from those for the parent reaction just discussed. Initial formation of complexes formed between the catalyst and the substrates are consistently very exothermic, so all subsequent barriers are well below the starting reactants in energy. Thus there are no net barriers for any of these reactions. The overall exothermicities for these three reactions are 37.2 kcal/mol.

Bis-silylation is a more complex reaction in which a disilane adds across a CCC double bond, to form two new Si–C bonds:

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X3Si–SiX3 R2CCCR2 → X3Si–CR2–CR2–SiX3	(9)

A preliminary study (50) demonstrated that in the absence of a catalyst, this reaction has such a high barrier that it could not be a viable process. The most commonly used catalysts for bis-silylation are Pt and Ni phosphines. However, in view of the computational results, summarized earlier, on the hydrosilation reaction, the bis-silylation reaction has been studied, again using divalent Ti as a prototypical catalyst (51). Since this work is still in progress, only a very brief summary will be presented here. The reaction under consideration has R H and X Cl, with the TiCl2 catalyst. Geometries have been determined using both Hartree–Fock and MP2 methods. Two very important points have already emerged from this study. One is that, as for the hydrosilation reaction, correlation is essential for even a qualitatively sensible picture of the reaction. There are very large MP2 corrections relative to the Hartree–Fock results. The second important point is that effective core potentials faithfully reproduce the all-electron results at both the Hartree–Fock and MP2 levels of theory. This is important, since it means that ECPs are a viable, efficient alternative to the more expensive all-electron wavefunctions. It is advisable, however, to use the all-electron basis sets for first-row atoms such as carbon.

5.SUMMARY AND POTENTIAL FOR MATERIALS CHEMISTRY

Several titanium species are of interest due to their potential as materials with desirable properties or as materials precursors. One species that has generated considerable attention is the metallocarbohedrenes (met-cars), M8C12, first synthesized by the Castleman group (52). Although by far the most attention has been paid to M Ti, other met-cars have been synthesized. Although the experimental structure for these interesting species has yet to be determined, the overwhelming computational evidence favors the Td structure (53). Much more interesting than the met-car structure in the long run is the mechanism by which these species form and why the growth of these cage species stops at the Ti8C12 structure. The experiments are initiated by laser ablation of Ti metal in the presence of small hydrocarbons. Therefore, systematic calculations have been initiated in this laboratory to explore the building-up mechanisms that lead to the Ti8C12 structure (54,55).

It has been known for some time that SiO cage compounds, polyhedral oligomeric silsesquioxanes (POSS), are important three-dimensional materials for both lubricants and coatings (56). Very recently, there has been increasing interest in the titanium analogs of the POSS, both fully and partially substituted POSS. Important issues include the structure of the Ti cage compounds, their