hydrolysis of ticl4 - initial steps in the production of tio2

Hydrolysis of TiCl4: Initial Steps in the Production of TiO2

Tsang-Hsiu Wang, Alejandra M. Navarrete-Lopez, Shenggang Li, and David A. Dixon*Department of Chemistry, The UniVersity of Alabama, Shelby Hall, Box 870336,Tuscaloosa, Alabama 35487-0336

James L. GoleSchools of Physics and Mechanical Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0430

ReceiVed: March 5, 2010; ReVised Manuscript ReceiVed: May 26, 2010

The hydrolysis of titanium tetrachloride (TiCl4) to produce titanium dioxide (TiO2) nanoparticles has beenstudied to provide insight into the mechanism for forming these nanoparticles. We provide calculations ofthe potential energy surfaces, the thermochemistry of the intermediates, and the reaction paths for the initialsteps in the hydrolysis of TiCl4. We assess the role of the titanium oxychlorides (TixOyClz; x ) 2-4, y ) 1,3-6, and z ) 2, 4, 6) and their viable reaction paths. Using transition-state theory and RRKM theory, wepredicted rate constants including the effect of tunneling. Heats of formation at 0 and 298 K are predicted forTiCl4, TiCl3OH, TiOCl2, TiOClOH, TiCl2(OH)2, TiCl(OH)3, Ti(OH)4, and TiO2 using the CCSD(T) methodwith correlation consistent basis sets extrapolated to the complete basis set limit and compared with theavailable experimental data. Clustering energies and heats of formation are calculated for neutral clusters.The calculated heats of formation were used to study condensation reactions that eliminate HCl or H2O. Thereaction energy is substantially endothermic if more than two HCl molecules are eliminated. The resultsshow that the mechanisms leading to formation of TiO2 nanoparticles and larger ones are complicated andwill have a strong dependence on the experimental conditions.

Introduction

Titanium dioxide (TiO2) is technologically one of the mostimportant compounds formed by the group IVB transition-metalelements. It is widely used as a white pigment, catalyst support,and photocatalyst.1-4 At room temperature, bulk TiO2 exists inthree phases: rutile, anatase, and brookite.1 TiO2 as a photo-catalyst has been used for solar energy conversion and for theremoval of organic pollutants from wastewater.5-8 It is well-established that anatase TiO2 has a higher photocatalytic activitythan the rutile or brookite phases. For example, one of the mostactive commercial TiO2 photocatalysts, Degussa P25, is 60-80%anatase phase.9 The pure anatase phase is thermodynamicallyless stable than rutile at room temperature, and it can undergothermal conversion into the rutile phase in the temperature rangeof 700-800 °C.10

The most important commercial route for the production ofTiO2 nanoparticles and larger particles is based on the chloride-based process where purified TiCl4 is oxidized at high temper-ature (1200-1700 °C) and modest pressure (∼300 kPa), in anoxygen plasma or flame, as given by reaction 1a.11,12 Reaction1b corresponds to the same reaction for the formation of (TiO2)n

nanoparticles.

In the industrial combustion process, AlCl3 is added in smallquantities to the TiCl4 reactor feed to promote formation of the

rutile phase as otherwise the anatase phase is formed.13,14

Introduction of a small amount of water is important in theindustrial process to initiate the above reaction. The aqueoushydrolysis of TiCl4, as indicated in reaction 2a, representsanother process to produce nanostructured polycrystalline TiO2.15

This process can be run at room temperature. TiO2 nanoparticleshave also been generated by the vapor-phase hydrolysis of TiCl4

at temperatures in the range of 360-550 °C with the TiCl4

present at 1% or lower by volume (reaction 2b). This processcan yield anatase-phase particles because of the lower reactiontemperature.16 Reaction 2c represents the formation of TiO2

nanoclusters in the gas-phase hydrolysis.

TiO2 colloidal particles have been synthesized from titaniumisopropoxide in aqueous acid where the acid leads to chargingof the particles, which can enable the control of their growth.17

Nanocrystalline TiO2 films have also been synthesized by asol-gel method using reverse micelles formed by Triton X-100and water in cyclohexane with titanium isopropoxide as the

* To whom correspondence should be addressed. E-mail: [email protected].

TiCl4 + O2 f TiO2(s) + 2Cl2 (1a)

nTiCl4 + nO2 f (TiO2)n + 2nCl2 (1b)

TiCl4(g) + 2H2O(aq)98298 K

TiO2(s,rutile) + 4HCl(aq)

(2a)

TiCl4(g) + 2H2O(g)98630-830 K

TiO2(s,rutile) + 4HCl(g)

(2b)

nTiCl4(g) + 2nH2O(g) f (TiO2)n(g) + 4nHCl(g)(2c)

J. Phys. Chem. A 2010, 114, 7561–7570 7561

10.1021/jp102020h 2010 American Chemical SocietyPublished on Web 06/24/2010

reagent.18 An important issue is that both reactions 1b and 2care endothermic to produce small (TiO2)n nanoparticles in thegas phase. Therefore, one must partially oxidize or hydrolyzethe TiCl4 to build up an oxychloride/hydroxyoxychloride particlelarge enough so that the reaction thermodynamics begins toresemble that of the solid as evidenced in Table 1 for TiO2

clusters starting from Cl2 (reactions 1a and 1b) and in Table 2starting from H2O.19-22 The enthalpy and free energy in Table1 at 298 K show that, as the particle gets larger, the energy toform it decreases. At 1500 K, the structure of the individualparticle begins to play a more important role as the presence oflow-lying vibrational modes in the cluster can significantlycontribute to the entropy contribution to the free energy. In Table2, the addition of H2O leads to more exothermic (in terms ofthe free energy) reactions as the temperature increases, especiallyas the nanoparticle size gets larger, due to the release of moreHCl particles in the gas phase. The hydrolysis reaction to formrutile is overall exothermic, independent of whether the processtakes place with gas-phase reactants or in the aqueous phase.The gas-phase processes for the generation of TiO2 have beenmodeled in terms of the oxidation of TiClx radicals which thencluster to form (TiO2)n nanoparticles for large n.23 In anothercase, TiOCl2 has been suggested to be a key intermediate.24,25

West et al.26 have predicted the thermochemical parameters fora number of TiOxCly intermediates using density functionaltheory (DFT)27 with different functionals and with coupledcluster28 CCSD(T)29 calculations using modest basis sets. Thesedata were then used in kinetic models to predict the formationof TiO2 nanoparticles.14,30,31 The major reactions they studiedwere based on the thermal decomposition of TiCl4 to from theTiCl3 and Cl radicals. The compounds that we studied are similarto those given by Kraft and co-workers14,30,31 with the additionof the presence of hydroxyl groups, and their compounds couldalso play a role in the hydrolysis process.

Although the combustion approach to the synthesis of TiO2

particles has been used in industry for many years, the overallmechanism is still poorly understood. The goal of this work isto study the potential energy surface for the initial steps in thegas-phase hydrolysis of TiCl4, which may serve as an initiation

step in the combustion system and is relevant to the hydrolysismechanism as well. The formation of the species describedherein can be coupled with those based on the thermaldecomposition of TiCl4 in further studies of the formation ofTiO2 nanoparticles. For a number of species, the thermodynam-ics have been obtained at the coupled cluster CCSD(T) level atthe complete basis set (CBS) limit using approaches developedin our group in collaboration with Washington State Univer-sity.32 We have previously used such an approach to study thethermodynamic properties of TiO2 and other transition-metaloxide clusters.19 The focus of the current study is on the speciesformed by the reaction of H2O with TiCl4 and their subsequentclustering reactions.

Computational Methods

The potential energy surfaces were initially calculated at thedensity functional theory level with the B3LYP exchange-correlation functional33,34 and the aug-cc-pVDz/aug-cc-pVDZ-PP basis set described below. Equilibrium geometries andharmonic vibrational frequencies were calculated at the second-order Møller-Plesset perturbation theory (MP2) level forvarious structures on the potential energy surface using theGaussian 03 program.35 These calculations were done with theaug-cc-pVnZ basis sets36 for H and O, the aug-cc-pV(n+d)Zbasis sets for Cl,37 and the small core effective core potential(ECP) based aug-cc-pVnZ-PP basis sets19,38 for Ti with n ) Dand T. (We denote this combination of basis sets as aVnZ.)For the hydrates and transition states, the geometries calculatedat the MP2/aVTZ level were subsequently used in single-pointCCSD(T) calculations with the aVDZ, aVTZ, and aVQZ basissets. The geometries of TiCl4, TiCl3OH, TiOCl2, TiOClOH, andTiO2 were also optimized at the CCSD(T) level with the aVDZand aVTZ basis sets. The geometry calculated at the CCSD(T)/aVTZ level was then used in single-point CCSD(T)/aVQZcalculation. All of the CCSD(T) calculations were performedwith the MOLPRO 2006.1 program.39 The CCSD(T) energieswere then extrapolated to the CBS limit using a mixed Gaussian/exponential formula (eq 3).40 n ) 2, 3, and 4 for aVDZ, aVTZ,and aVQZ, respectively.

To predict thermochemical properties to high accuracy, it isnecessary to include additional corrections. For the complexeswith one Ti atom, the core-valence correlation corrections(∆ECV) were obtained at the CCSD(T)-DK/aug-cc-pwCVTZ-DK level.38 For the calculation of transition-metal compoundatomization energies, the core-valence calculations should becalculated at the CCSD(T)-DK level to achieve the bestaccuracy.19 In addition, we also account for relativistic effectsin atoms and molecules. The first is the spin-orbit correction(∆ESO), which lowers the sum of the atomic energies (decreasing∑D0) by replacing energies that correspond to an average overthe available spin multiplets with energies for the lowestmultiplets. This correction is required as most electronicstructure codes produce only spin multiplet averaged wavefunctions. The experimental ground-state atomic spin-orbitcorrections are ∆ESO(Ti) ) 0.64 kcal/mol, ∆ESO(Cl) ) 0.84kcal/mol, and ∆ESO(O) ) 0.22 kcal/mol.41 The second correctionis the scalar relativistic correction (∆ESR). As we already havesuch a correction for Ti through the use of the ECP, weevaluated ∆ESR for O and Cl as expectation values of the twodominant terms in the Breit-Pauli Hamiltonian, the mass-

TABLE 1: Reaction Enthalpy (∆H, kcal/mol) at 298 K forReactions 1a and 1ba

∆H298K ∆H1500K ∆G298K ∆G1500K

reaction 1b, n ) 1 114.2 110.8 103.7 64.9reaction 1b, n ) 2 105.4 103.0 96.6 64.3reaction 1b, n ) 3 86.6 85.5 77.8 44.4reaction 1b, n ) 4 66.7 66.7 65.1 59.8reaction 1a -43.4 -41.5 -39.0 -23.0

a Heats of formation for (TiO2)n from ref 19 and for TiCl4

(-182.4 kcal/mol) and TiO2(s,rutile) from ref 21.

TABLE 2: Reaction Enthalpy (∆H, kcal/mol) at 298 K forReactions 2a and 2ba

∆H298K ∆H700K ∆H1500K ∆G298K ∆G700K ∆G1500K

reaction 2c, n ) 1 141.4 140.8 139.4 121.8 95.7 44.8

reaction 2c, n ) 2 159.8 159.9 160.3 132.9 96.6 24.1

reaction 2c, n ) 3 171.7 172.8 174.8 135.8 86.8 -12.4

reaction 2c, n ) 4 175.5 177.4 181.2 137.7 85.8 -20.6

reaction 2b -16.2 -15.2 -12.8 -20.9 -27.8 -43.1

reaction 2ab -66.6 -51.0

a Heats of formation for (TiO2)n from ref 19 and for TiCl4

(-182.4 kcal/mol) and TiO2(s,rutile) from ref 21 unless notedotherwise. b Heats of formation from ref 22. If aqueous TiCl4 isused, then ∆H ) 1.3 kcal/mol and the reaction is essentiallythermoneutral.

E(n) ) ECBS + Be-(n-1) + Ce-(n-1)2(3)

7562 J. Phys. Chem. A, Vol. 114, No. 28, 2010 Wang et al.

velocity and one-electron Darwin (MVD) corrections, at theconfiguration interaction singles and doubles (CISD) level withthe aVTZ basis set at the MP2/aVTZ geometry. Our computedtotal atomization energy (∑D0) values were obtained with eq 4.

Given the known heats of formation at 0 K for the elements,∆Hf,0K(Ti) ) 112.4 ( 0.7 kcal/mol,42 ∆Hf,0K(Cl) ) 28.59 kcal/mol,21 ∆Hf,0K(O) ) 58.98 kcal/mol,21 and ∆Hf,0K(H) ) 51.63kcal/mol,21 we can derive ∆Hf,0K values for the molecules understudy. The heats of formation at 298 K can be obtained byfollowing the procedures outlined by Curtiss et al.43 Thetemperature dependence of the enthalpy and the entropycalculations were done in the rigid-rotor, harmonic oscillatorapproximation with hindered rotors treated as a vibration.44 Athigher temperatures, this may lead to modest errors in thethermodynamic properties due to the transition of a hinderedrotor to a free rotor.

The CCSD(T) method scales approximately as N7 with Nbasis functions, and large basis sets are required to reach theCBS limit. The approach described above for the CCSD(T)/CBS calculations has been used to predict a wide range ofthermodynamic properties to chemical accuracy.19,20,32,45 DFThas a much better scaling, scaling as N3 to N4 depending on theexchange-correlation functional, but is not as accurate as theCCSD(T)/CBS approach for the calculation of a broad rangeof thermodynamic properties including atomization energies.For small clusters with one Ti atom, accurate thermodynamicproperties can be calculated using the CCSD(T)/CBS approach,which is more reliable than similar DFT-based approaches.19,20,46

In addition, the CCSD(T)/CBS values can be used to benchmarkdifferent DFT functionals in the future. We avoided the use ofisodesmic and similar types of reaction energies as usedpreviously because of issues with the experimental heats offormation of similar Ti compounds and because there are sofew experimental values.47 For the larger clusters, we used thenormalized clustering energy method that we have previouslydeveloped19,20 for the prediction of the heats of formation oftransition-metal oxide clusters.

All calculations were performed on a Xeon- and Opteron-based Penguin Computing Linux cluster in our group, theItanium 2-based SGI Altix and the Opteron-based dense memorycluster Linux cluster at the Alabama Supercomputer Center, theXeon-based Dell Linux cluster at The University of Alabama,and the Opteron-based Linux cluster at the Pacific NorthwestNational Laboratory.

Results and Discussion

Geometries and Frequencies. The calculated Ti-X (X )Cl, O, OH) bond lengths at the CCSD(T)/aVTZ level forselected reactants, intermediates, and products are given in Table3. They are compared with available experimental values. Theelectronic states and symmetry labels for these molecules aregiven in Table 3 and will not be repeated hereafter. Theoptimized molecular structures for these molecules together withthose of the transition states are given in the potential energysurface plots (Figure 1). The total CCSD(T) energies, calculatedharmonic frequencies compared with the available experimentalvalues, and T1 diagnostics are given as Supporting Information.

The calculated Ti-Cl bond distance of 2.186 Å at theCCSD(T)/aVTZ level in TiCl4 is slightly longer (<0.02 Å) than

the gas-phase electron diffraction48 value of 2.170 Å. Lowerlevel calculations are also in agreement.49 The Ti-Cl bonddistances in TiCl3OH, TiOCl2, TiOClOH, TiCl2(OH)2, andTiCl(OH)3 are predicted to lengthen from that in TiCl4 with anincrease in the number of O atoms and with changes in thenumber of ligands bonded to the Ti atom. The Ti-Cl bonddistance in TiOCl2 of 2.234 Å calculated26 at the B97-1/6-311+G(d,p) level is shorter than our CCSD(T)/aVTZ value by∼0.02 Å. The calculated Ti-O bond distance in the series fromTiO2 to TiOClOH to TiOCl2 decreases as the number of ligandsincreases from two to three and Cl is substituted for OH. TheTi-O bond distance in TiOCl2 calculated at the B97-1/6-311+G(d,p) level26 is shorter than our CCSD(T)/aVTZ valueby ∼0.03 Å. The Ti-O bond distance in TiO2 has beenmeasured by Fourier transform microwave spectroscopy to be1.651 Å;50 the CCSD(T)/aVTZ calculations overestimate thisdistance by 0.015 Å.19 The Ti-OH bond distance increases by0.067 Å from TiCl3OH to TiOClOH.

The role of multireference character in the wave function canbe estimated from the T1 diagnostic51 for the CCSD calculation.The values for the T1 diagnostics are modest (<0.03), showingthat the wave function is dominated by a single electronconfiguration. TiO2 has a slightly larger T1 diagnostic but iswell-behaved on the basis of our recent work.19

Atomization Energies and Heats of Formation. The dif-ferent energetic components for the total atomization energies(TAEs) are given in Table 4. The core-valence corrections forthe Ti compounds are found to increase the TAEs by 1.3-4.8kcal/mol. The scalar relativistic corrections for the Ti compoundsare usually smaller than the core-valence corrections and arefound to decrease the TAEs by 0.7-2.0 kcal/mol.

The calculated heats of formation are also given in Table 4,and we use the values at 298 K in our discussion below unlessspecified otherwise. The estimated error bars for the calculatedheats of formation are (1.5 kcal/mol. Here we include ourestimates of the errors in the energy extrapolation, vibrationalfrequencies, and other electronic energy components, as wellas the error associated with the heat of formation of the Ti atombased on our recent work.20 The calculated heat of formationof TiCl4 is in good agreement with the experimental value20

considering the experimental error limits of (0.7 kcal/mol forboth ∆Hf(TiCl4) and ∆Hf(Ti). The calculated heat of formationof TiOCl2 is 11.4 kcal/mol more negative than the estimatedvalue of -130.4 kcal/mol.21 For TiOCl2, the calculated heat offormation by Green and co-workers26 at the B97-1/6-311+G(d,p)level of -142.9 ( 4.8 kcal/mol is in good agreement with our

ΣD0 ) ∆ECBS + ∆EZPE + ∆ECV + ∆ESR + ∆ESO

(4)

TABLE 3: Calculated and Experimental Ti-X (X ) Cl, O,OH) Bond Lengths (Å) at the CCSD(T)/aVTZ or MP2/aVTZLevels

molecule state method Ti-Cl Ti-O Ti-OH

TiCl41A1/Td CCSD(T)/aVTZ 2.186

exptla 2.170TiOCl2

1A1/C2V CCSD(T)/aVTZ 2.250 1.619B97-1/6-311+G(d,p)b 2.234 1.587

TiOClOH 1A′/Cs CCSD(T)/aVTZ 2.270 1.627 1.843TiO2

1A1/C2V CCSD(T)/aVTZc 1.666exptld 1.651

TiCl3OH 1A′/Cs MP2/aVTZ 2.192 1.7672.191

TiCl2(OH)21A/C1 MP2/aVTZ 2.213 1.784

1.775TiCl(OH)3

1A/C3 MP2/aVTZ 2.238 1.797Ti(OH)4

1A/S4 MP2/aVTZ 1.813

a Reference 48. b Reference 26. c Reference 19. d Reference 50.

Hydrolysis of TiCl4 J. Phys. Chem. A, Vol. 114, No. 28, 2010 7563

CCSD(T)/CBS value. These results suggest that the tabulatedheat of formation for TiOCl2 needs to be reevaluated.21 Thecalculated thermodynamic properties as a function of temper-ature for use in other modeling schemes are given in theSupporting Information.

Hydrolysis Potential Energy Surface. The calculated po-tential energy surfaces at 0 K of the hydrolysis of TiCl4 areshown in Figures 1 and 2. The initial reaction of water with

TiCl4 can be considered in two stages (Figures 1a and 2). Thefirst stage can be described by the overall reaction given asfollows, as shown in Figure 1a:

The second stage is the reaction of TiOCl2 with a second watermolecule shown in Figure 2:

Both overall reactions are substantially endothermic. The firstreaction step of the first stage

is only slightly endothermic by 2.5 kcal/mol at 0 K. The overallreaction free energy becomes more favorable as the temperatureincreases mostly due to the difference in the entropies of TiCl4

and TiCl3OH. At 700 K, the reaction will proceed to the rightwith Keq ≈ 5. This step starts with an exothermic Lewis acidbase addition of H2O to TiCl4, forming a stable complex.Complex formation is followed by a hydrogen transfer fromwater to a chlorine, leading to HCl elimination. The reactionbarrier for the H transfer from the complex is 18.8 kcal/molwith 8.2 kcal/mol due to the endothermicity (0 K) of the processrelative to the starting reactant complex and the formation of ahydrogen-bonded complex between HCl and TiCl3OH. Theoverall reaction is only weakly endothermic, so the reaction willproceed to a reasonable extent at the high processing temper-atures. Transfer of the second H atom from the OH group to asecond Cl atom to form the TiOCl2 ·HCl Lewis acid-basecomplex is endothermic by 33.4 kcal/mol, and the total barrierfor H transfer of 35.7 kcal/mol is predominantly due to theendothermicity of this reaction. HCl forms a strong Lewisacid-base complex with TiOCl2 with a (H)Cl-Ti dative bindingenergy of 17.0 kcal/mol. The overall endothermicity of theunimolecular reaction of TiCl3OH to form TiOCl2 + HCl showsthat the reaction will not likely proceed past the first protontransfer step. The effects of temperature on this step are notlarge in terms of the enthalpy or free energy.

A more likely process is that TiCl3OH reacts further withanother water molecule (Figure 1b):

This reaction is endothermic by only 4.2 kcal/mol at 0 K. Theentropy effects for this reaction are small, so there is only aslight decrease in the reaction free energy as the temperatureincreases. At equilibrium at 700 K, Keq ≈ 0.05, so the productTiCl2(OH)2 will be formed to some extent. As the prod-uct further reacts, Le Chatelier’s principle suggests that theproduct will continue to be formed. Again H2O forms a Lewisacid-base complex with the TiCl3OH, and there is a barrier of18.4 kcal/mol for transfer of the proton, leading to a hydrogen-bonded complex of HCl with TiCl2(OH)2. The hydrogen bondenergy is 2.5 kcal/mol.

TiCl2(OH)2 can further react with H2O to give a hydrogen-bonded complex as part of the following overall reaction:

Figure 1. Potential energy surfaces (kcal/mol) for reactions (a) TiCl4

+ H2O f TiOCl2 + 2HCl, (b) TiCl3OH + H2O, (c) TiCl2(OH)2 +H2O, and (d) TiCl(OH)3 + H2O. Key: black, ∆E from heats offormation at 0 K; crimson, ∆ECBS + ∆ECV + ∆EZPE; green, MP2/aVTZ+ ∆EZPE; blue, B3LYP/aVDZ + ∆EZPE; yellow, Ti; red, O; green, Cl;white, H.

TiCl4 + H2O f TiOCl2 + 2HCl (5)

TiOCl2 + H2O f TiO2 + 2HCl (6)

TiCl4 + H2O f TiCl3OH + HCl (5a)

TiCl3OH + H2O f TiCl2(OH)2 + HCl (7)

TiCl2(OH)2 + H2O f TiCl(OH)3 + HCl (8)


Reaction 8 is less favorable energetically than reactions 5and 7, and for this reaction at 700 K, Keq ≈ 8 × 10-3, so enoughproduct will be formed for the reaction to continue. Thiscomplex undergoes a hydrogen transfer with a barrier of 17.9kcal/mol to form a complex with HCl bonded to TiCl(OH)3

(Figure 1c). The H-bond energy is 4.6 kcal/mol, consistent withthe HCl being involved in two H bonds, one as an acceptorand one as a donor. The overall reaction is endothermic by 6.0kcal/mol at 0 K.

The final step is the reaction of TiCl(OH)3 with H2O:

It follows the same path of Lewis acid-base addition followedby H transfer with essentially the same energetics (Figure 1d).The final H-bond energy for the HCl with Ti(OH)4 is 5.2 kcal/mol. This reaction is the most endothermic for the hydrolysisreactions.

We can briefly summarize the reaction energetics for all stepsas (1) initial complex formation with a complexation energy ofabout 9 kcal/mol and (2) a hydrogen transfer step with a barrierof about 18 kcal/mol to form a complex with a HCl and the Tispecies with complexation energies of 2-4 kcal/mol and anoverall reaction endothermicity of 2-9 kcal/mol at 0 K. Thus,the hydrolysis of TiCl4 will not form TiOCl2 and HCl or TiO2

and HCl due to the large endothermicities inherent to theseprocesses. The overall reaction energies for each of the reactionsin the initial hydrolysis of TiCl4 are given in Table 5. Of course,any of the intermediates that are formed can react with otherspecies in the plasma, for example, any O or Cl atoms that areformed, or with themselves as discussed below.

For the following reactions, we used conventional transition-state theory (TST)52 and Rice-Ramsperger-Kassel-Marcus(RRKM) theory53 to predict the rate coefficients (k):

The predicted rates as a function of temperature are given inthe Supporting Information. The limiting rate constants fromRRKM theory in the temperature range (T) of 273-373 K andpressure range (P) of 380-1520 Torr and in the temperaturerange of 200-2000 K and pressure range of 760-2250 Torrare given in Table 6. The rate constant for the lower temperaturerange is essentially independent of pressure. The effect oftunneling52,54,55 on the rate constants at room temperature leadsto an increase of up to a factor of ∼2. We used the Skodje andTruhlar55 expression for the tunneling coefficient because itprovides a better approximation. The rate constants at atemperature of 1500 K more like that in the combustion reactorare quite fast and exhibit a dependence on pressure up to about3 atm. The reaction rates at 700 K representative of the high-temperature hydrolysis reaction process are also quite fast. Atthe higher temperatures used in the combustion or gas-phasehydrolysis processes, tunneling will not be important. Thereaction rates are comparable within an order of magnitude forthe displacement of HCl from tetracoordinate Ti at all temper-atures. Unimolecular reaction 6a is predicted to be substantiallyslower at 298 and 700 K but is predicted to be within an orderof magnitude of the other reactions at 1500 K. We also include

TABLE 4: Total Atomization Energies (∑D0,0K, kcal/mol) at 0 K and Heats of Formation at 0 and 298 K (∆Hf,0K and ∆Hf,298K,kcal/mol) Calculated at the CCSD(T) Level

molecule ∆ECBSa ∆EZPE

b ∆ECVc ∆ESR

d ∆ESOe ∑D0,0K

f ∆Hf,0Kg ∆Hf,298K

g ∆Hf,298K (exptl)

TiCl4 413.56 -3.65 3.32 -1.46 -4.00 407.78 -181.0 -181.5 -182.4 ( 0.7h

TiCl3OH 533.91 -10.27 3.88 -1.67 -3.38 522.47 -213.7 -214.5TiOCl2 375.57 -3.23 1.35 -1.17 -2.54 369.98 -141.4 -141.8 -130.4h

TiOClOH 490.09 -10.41 1.87 -1.32 -1.92 478.31 -167.7 -168.8TiO2

i 299.77 -3.26 2.92 -0.78 -1.08 297.57 -67.2 -67.8 -73.0 ( 3i

TiCl2(OH)2 653.35 -17.32 4.04 -1.86 -2.76 635.45 -244.7 -246.1TiCl(OH)3 770.77 -24.69 4.74 -2.00 -2.14 746.69 -273.9 -276.2Ti(OH)4 885.14 -31.81 4.34 -2.14 -1.52 855.01 -300.2 -303.2H2O 232.95 -13.44 0.34 -0.29 -0.22 219.34 -57.1 -57.8 -57.7978 ( 0.0096h

TiCl4 ·H2O 655.90 -19.22 3.89 -1.87 -4.22 634.48 -245.5 -247.2TS1 632.94 -15.24 4.05 -1.88 -4.22 611.60 -226.6 -228.2TiCl3OH ·HCl 644.14 -15.93 4.20 -1.90 -4.22 626.30 -237.3 -238.3HCl 107.40 -4.36 0.19 -0.23 -0.84 102.17 -21.9 -22.0 -22.06 ( 0.024i

TS2 495.63 -7.80 3.80 -1.50 -3.38 486.75 -178.0 -179.5TiOCl2 ·HCl 499.92 -8.95 2.98 -1.48 -3.38 489.09 -180.3 -181.0TiOCl2 ·H2O 640.95 -19.01 2.99 -1.64 -2.76 620.54 -229.7 -231.4

a CCSD(T)/CBS energies obtained using eq 3. b MP2/aVTZ. c CCSD(T)/aug-cc-pwCVTZ-DK. d Expectation value of the MVD operators onthe CISD/aVTZ wave function. e Experimental atomic spin orbit corrections from ref 41. f Equation 4. g See the text. h Reference 17. i Reference15.

Figure 2. Potential energy surface (kcal/mol) for TiOCl2 + H2O. Seethe Figure 1 caption for details.

TiCl(OH)3 + H2O f Ti(OH)4 + HCl (9)

TiCl4 ·H2O f TiCl3OH ·HCl (5b)

TiCl3OH ·H2O f TiCl2(OH)2 ·HCl (7a)

TiCl2(OH)2 ·H2O f TiCl(OH)3 ·HCl (8a)

TiCl(OH)3 ·H2O f Ti(OH)4 ·HCl (9a)


the TST rate constants assuming a bimolecular reaction (reac-tions 5a, 7, 8, and 9) at 298, 700, and 1500 K in Table 5 becausethe precomplexes may not have long lifetimes at the highertemperatures. Both the unimolecular and bimolecular reactionrates are substantial at T g 700 K.

TiOCl2 has been observed experimentally in some of thesystems,24,25 so we also studied the reaction of TiOCl2 with water(reaction 6). The first step as shown in the following reactionbegins with the formation of an initial Lewis acid-base complexwith a much larger complexation energy of 37.8 kcal/mol(Figure 2):

The hydrogen transfer reaction from the complex has a higherbarrier of 24.2 kcal/mol, and the resulting complex is a Lewisacid-base adduct of HCl with TiO(OH)Cl with a Lewisacid-base adduct bond energy of 16.1 kcal/mol. The overallreaction to form HCl + TiO(OH)Cl is endothermic by 9.2 kcal/mol at 0 K. The value of Keq at 700 K for reaction 6a is 4 ×10-3, which is large enough for some product to be formedwhich can be involved in further clustering reactions. There isno reaction barrier on the bimolecular energy surface other thanthe endothermicity of the reaction as the transition state forhydrogen transfer is below the energy of the reactants. At highertemperatures, the reaction will occur at the collision frequencyreduced by the appropriate exponential expression involving theendothermicity (a factor of 10-20 at 1500 K). The loss of thesecond HCl is highly endothermic as expected.

Titanium Oxychloride Hydroxide Species. We have notedabove that the formation of TiO2 nanoclusters must proceed byway of TixOyClz (or TixOyClz(OH)w) clusters as discussed in theIntroduction and have shown that it is possible to generate theintermediates needed for clustering reactions at the experimental

temperatures. Figure 3 shows the calculated molecular structureswith key geometry parameters for Ti2O3Cl2, Ti2O2Cl4, Ti2OCl6,Ti3O5Cl2, Ti3O4Cl4, Ti3O3Cl6, Ti4O6Cl4 and for a number ofTixOyClz(OH)w clusters. These molecules were optimized at theDFT level with the B3LYP, BP86,56,57 PBE,58,59 and PW9160,61

exchange-correlation functionals and the aVDZ basis set. Thegeometries obtained with the aVDZ basis set were then used insingle-point DFT energy calculations with the aVTZ basis set.The geometries obtained at the B3LYP/aVDZ level were alsoused in single-point energy calculations at the CCSD(T)/aVDZlevel.

In our previous work on TiO2 clusters,19 we studied theclustering energies of (TiO2)n (n ) 2-4) clusters, and we foundthat the normalized clustering energies at 0 K range from 60 to100 kcal/mol, increasing from the dimer to the tetramer. Thenormalized clustering energy is the average binding energy ofthe monomers in a cluster and for a (TiO2)n cluster with n Tiatoms, ∆Enorm,n is defined by the following equation:

For the TiO2 clusters previously studied, the CBS extrapolationeffect from the aVDZ basis set is small in contrast to the basisset extrapolation in the total atomization energies. We can thenuse the following equation to obtain the heat of formation of acluster where we are summing over the heats of formation ofthe monomers:

The advantage of this approach is that the normalized clusteringenergies (∆Enorm,n) are not strongly dependent on the basis set.19

TABLE 5: Calculated Reaction Energies (kcal/mol) and Rate Constants k (cm3/(molecule s)) from TST at 298, 700, and 1500 Kfor Bimolecular Reactions

reaction ∆H298K ∆H700K ∆H1500K ∆G298K ∆G700K ∆G1500K k(298 K)a k(700 K) k(1500 K)

TiCl4 + H2O f TS1 f TiCl3OH + HClb (5a) 2.7 3.5 4.9 0.7 -2.2 -9.7 2.0 × 10-3 3.0 × 102 5.0 × 104

TiCl3OH + H2O f TS3 f TiCl2(OH)2 + HClc (7) 4.1 4.8 6.3 4.4 4.3 3.3 5.1 × 10-4 3.4 × 101 4.3 × 103

TiCl2(OH)2 + H2O f TS4 f TiCl(OH)3 + HCld (8) 5.6 6.3 7.7 6.2 6.7 6.3 4.8 × 10-3 8.4 × 101 6.1 × 103

TiCl(OH)3 + H2O f TS5 f Ti(OH)4 + HCle (9) 8.7 9.4 10.8 9.4 10.0 10.1 3.5 × 10-3 1.3 × 102 1.3 × 104

TiOCl2 + H2O f TiOClOH + HCl (6a) 8.7 9.3 10.8 8.8 7.6 7.5 f f f

a The tunneling factors are not included in the rate constants. b Qtunnel(298 K) ) 2.38. c Qtunnel(298 K) ) 1.94. d Qtunnel(298 K) ) 1.65.e Qtunnel(298 K) ) 1.53. f There is no reaction barrier for the bimolecular reaction other than the reaction endothermicity.

TABLE 6: Calculated Rate Constants from TST (k∞, s-1) and the RRKM Rate Constant (s-1) at 298, 700, and 1500 K for theUnimolecular Reactions from the Precomplex to the Postcomplexa

reaction k∞(298 K) k∞(700 K) k∞(1500 K)

TiCl4 ·H2O f TS1 f TiCl3OH ·HClb 5.1 × 10-2 4.7 × 106 8.9 × 108

TiCl3OH ·H2O f TS3 f TiCl2(OH)2 ·HClc 3.0 × 10-2 2.0 × 106 6.2 × 108

TiCl2(OH)2 ·H2O f TS4 f TiCl(OH)3 ·HCld 1.9 × 10-2 9.9 × 105 4.3 × 108

TiCl(OH)3 ·H2O f TS5 f Ti(OH)4 ·HCle 3.5 × 10-1 2.1 × 107 1.8 × 109

TiOCl2 ·H2O f TS6 f TiOClOH ·HCl 3.1 × 10-6 4.0 × 104 1.4 × 108

reactionk(RRKM) (T ) 273-373 K,

P ) 380-1520 Torr)k(RRKM) (T ) 200-2000 K,

P ) 760-2250 Torr)

TiCl4 ·H2O f TS1 f TiCl3OH ·HCl k(T) ) (3.98 × 1012) exp(-19.0/RT) k(T,P) ) (5.0 × 1010)P0.36 exp(-17.8/RT)TiCl3OH ·H2O f TS3 f TiCl2(OH)2 ·HCl k(T) ) (1.26 × 1012) exp(-18.6/RT) k(T,P) ) (2.0 × 1010)P0.34 exp(-17.5/RT)TiCl2(OH)2 ·H2O f TS4 f TiCl(OH)3 ·HCl k(T) ) (5.01 × 1011) exp(-18.3/RT) k(T,P) ) (2.0 × 1010)P0.28 exp(-17.6/RT)TiCl(OH)3 ·H2O f TS5 f Ti(OH)4 ·HCl k(T) ) (1.58 × 1013) exp(-18.6/RT) k(T,P) ) (2.5 × 1010)P0.45 exp(-16.6/RT)TiOCl2 ·H2O f TS5 f TiOClOH ·HCl k(T) ) (1.26 × 1012) exp(-24.2/RT) k(T,P) ) (4.0 × 1010)P0.31 exp(-23.4/RT)

a The tunneling factors are not included in the rate constants. Activation energies in kcal/mol. b Qtunnel(298 K) ) 2.38. c Qtunnel(298 K) )1.95. d Qtunnel(298 K) ) 1.65. e Qtunnel(298 K) ) 1.53.

TiOCl2 + H2O f TiClOH + HCl (6a)

∆Enorm,n ) [nE(monomer) - E(cluster)]/n (10)

∆Hf,0K(cluster) ) ∑∆Hf,0K(monomer) - n∆Enorm,n

(11)


Thus, the heat of formation of the cluster can be calculated fromthe CCSD(T)/CBS heats of formation of the monomers and theCCSD(T)/aVDZ normalized clustering energies of the cluster,as given in eq 10.

Ti2O3Cl2, Ti2O2Cl4, and Ti2OCl6 are clusters with two Tiatoms that can be potentially formed in the oxidation of TiCl4

and involve only Cl and O as substituents. The calculated Ti-Clbond distance in Ti2O3Cl2 is longer than that of Ti2O2Cl4 andTi2OCl6. Most of the calculated Ti-O bond distances inTi2O3Cl2, Ti2O2Cl4, and Ti2OCl6 are longer than that of TiO2,and the Ti-O bond distance in these dimers increases as thenumber of oxygens increases. Previous work26 on the structuresof Ti2O3Cl2 and Ti2O2Cl4 at the B97-1/6-311+G(d,p) level

predicted the same trends observed in our study. The calculatedTi-Cl bond distances in Ti3O5Cl2 are longer than those in theclusters with three and four Ti atoms. The Ti-O bond distancein the trimers and tetramer are longer than the Ti-O bonddistance in TiO2. The Ti-O bond distance in the trimers andthe tetramer is similar to that of the dimers. Our calculationsshowed no significant dependence in the calculated geometrieson the choice of the DFT exchange-correlation functional.

The calculated clustering energies and heats of formation aregiven in Table 7. The calculated normalized clustering energyof Ti2O2Cl4 at the CCSD(T)/aD level is less exothermic thanthat of Ti3O3Cl6 by 8.8 kcal/mol. The calculated heat offormation at 298 K of Ti2O2Cl4, -370.6 kcal/mol, is in excellentagreement with the B97-1/6-311G(d,p) value26 of -370.9 kcal/mol. Our calculated heat of formation at 298 K of Ti2O3Cl2,-316.0 kcal/mol, is similar to the previously calculated value26

of -318.1 kcal/mol. For Ti3O4Cl4, our calculated value is lowerthan that of Green and co-workers26 by 3.3 kcal/mol.

A second set of dimers that involve OH as a substituent aswell can be generated as shown in Figure 3 and Table 7.Substitution of a OH for a Cl does not lead to much geometrychange in the core involving the Ti atoms. The Ti-O bridgebond distance increases by up to 0.03 Å. In most cases, theTi-O(H) bond distances are comparable to or slightly shorterthan a Ti-O(Ti) bond distance.

Cluster Reaction Energies. The clustering energies givenin Table 7 are in general highly exothermic,so condesationreactions of species such as Ti(O)Cl2 and Ti(O)Cl(OH) willreadily occur at the temperatures of interest. This leads toimportant oxygenated clusters that can serve as precursorsto TiO2 nanoparticles. We can use the calculated heats offormation to explore a range of additional condensationreactions coupled with elimination of H2O or HCl that maybe relevant to the formation of TiO2 nanoparticles asdemonstrated in Table 8. The reaction of TiCl3OH with itselfor with TiCl4 forms the dimer Ti2OCl6 in an exothermicreaction and releases either H2O or HCl. The dimer Ti2O2Cl4

can be formed either by reaction of TiCl3OH with itself orby the reaction of TiCl2(OH)2 with TiCl4. Both reactions areslightly endothermic on the enthalpy scale but will be nearlythermoneutral or exothermic on the free energy scale depend-ing on the temperature due to the formation of an additionalmolecule of HCl. The reaction of TiCl2(OH)2 with TiCl4 canalso form a single bridged cluster with elimination of HCl,and this reaction is slightly exothermic. The reactions ofTiCl(OH)3 are mostly exothermic if H2O is eliminated butare somewhat endothermic if two HCl molecules are elimi-nated. The reactions of Ti(OH)4 are exothermic, and thereaction of Ti(OH)4 with Ti(O)(OH)2 is highly exothermic.As expected, reactions that eliminate more than two HClmolecules to enhance oxygen atom incorporation in the dimerare substantially endothermic.

Basis Set Dependence and DFT Performance. The depen-dence of the relative energies on the basis set is given in theSupporting Information. There is only a small basis setdependence at the CCSD(T) level, so a reasonable potentialenergy surface can be obtained with a modest basis set.Figures 1 and 2 compare the ∆Etotal results and ∆ECBS + ∆ECV

results with the B3LYP/aVDZ results. The complexationenergies of H2O to a Ti calculated at the B3LYP/aVDZ levelare in general too small as compared to those calculated atthe CCSD(T) level. This arises because of the lack of formaldispersion energy treatments in the DFT functionals used inthis study and the difficulty that DFT can have in predicting

Figure 3. Optimized molecular structures for Ti2O3Cl2, Ti2O2Cl4,Ti2OCl6, Ti3O4Cl4, Ti3O5Cl2, Ti3O3Cl6, Ti4O6Cl4, TiO(OH)2, cis-Ti2O2Cl2(OH)2, trans-Ti2O2Cl2(OH)2, Ti2O2(OH)4, Ti2OCl5OH,Ti2OCl4(OH)2, Ti2OCl2(OH)4, Ti2O(OH)6, Ti2O2Cl(OH)3, and iso-Ti2O2Cl2(OH)2: yellow, Ti; red, O; green, Cl; white, H.


dative bond energies.45,62 These interactions are not dominatedby hydrogen bonding. The DFT functionals used mayunderestimate the reaction barriers as found in some of thehydrogen transfer reactions. The relative energies of TiCl4 ·H2O, TiCl3OH ·H2O, TiCl2(OH)2 ·H2O, TiCl3OH ·H2O, andTiOCl2 ·H2O calculated at the B3LYP/aVDZ level are greaterthan those at the CCSD(T) level for ∆ECBS + ∆ECV by 2.8,5.8, 4.8, 4.9, and 3.1 kcal/mol, respectively. Thus, DFT/B3LYP provides a qualitatively correct potential energysurface but not a quantitative one.

Conclusions

Coupled cluster [CCSD(T)] theory, Møller-Plesset per-turbation theory (MP2), and density functional theory (DFT)have been used to study the structural and energetic propertiesof the intermediates in the hydrolysis of TiCl4 and theformation of titanium oxychloride species (TixOyClz; x ) 2-4,y ) 1, 3-6, and z ) 2, 4, 6). The normalized clusteringenergies at 0 K for the ground state of (TiOCl2)n (n ) 2, 3)clusters range from 40 to 55 kcal/mol, increasing from thedimer to the trimer. The reaction energy of the condensationreactions is substantially endothermic if more than two HClmolecules are eliminated. In addition, we also predict thereaction paths for the initial steps of hydrolysis of TiCl4. Wepredict that the hydrolysis of TiCl4 will not form TiOCl2 andHCl or TiO2 and HCl due to the substantial endothermicitiesassociated with the formation of gas-phase TiO2. Usingtransition-state theory and RRKM theory, we predicted rateconstants including the effect of tunneling. The low-temper-

ature rate constant is independent of pressure, and the effectof tunneling on the rate constant is an increase of about afactor of 2 at 298 K. At higher temperatures, the predictedrate constants are large enough for the reactions to occurreadily and show that key oxygenated intermediates can beformed. The calculations show, at the temperatures relevantto the experimental conditions for the gas-phase hydrolysisof TiCl4 or the combustion of TiCl4 leading to TiO2 particles,that partially oxygenated Ti molecules can be generated.These molecules can condense to form partially oxygenatedTi clusters which are precursors to TiO2 nanoparticles. Ourcalculated data will enable the development of more detailedgas-phase mechanisms for the formation of TiO2 nanopar-ticles and larger particles which incorporate the hydrolysisof TiCl4. Within this framework, our calculations also showthat the reported values for the heat of formation of TiOCl2

should be remeasured.

Acknowledgment. This work was supported by the Na-tional Science Foundation (Grant CTS-0608896), through theNIRT program, and by the Chemical Sciences, Geosciencesand Biosciences Division, Office of Basic Energy Sciences,U.S. Department of Energy (DOE), under Grant DE-FG02-03ER15481 (Catalysis Center Program). D.A.D. also thanksthe Robert Ramsay Chair Fund of The University of Alabamafor support. Part of this work was performed in the MolecularSciences Computing Facility at the W. R. Wiley Environ-mental Molecular Sciences Laboratory, a national scientificuser facility sponsored by the DOE’s Office of Biological

TABLE 7: Calculated Heats of Formation (kcal/mol) of the Clusters and Reaction Energies (kcal/mol) at the CCSD(T)/aVDZ//B3LYP/aVDZ Level

reaction ∆H0K ∆H298K ∆H700K ∆H1500K ∆Hf,0K ∆Hf,298K

2TiOCl2 f Ti2O2Cl4 -86.3 -87.0 -85.7 -82.5 -361.9 -370.63TiOCl2 f Ti3O3Cl6 -155.9 -156.4 -153.5 -147.1 -580.1 -581.8TiOCl2 + TiO2 f Ti2O3Cl2 -105.7 -106.4 -105.1 -102.0 -314.3 -316.0TiOCl2 + 2TiO2 f Ti3O5Cl2 -203.7 -204.2 -201.4 -195.1 -479.5 -481.62TiOCl2 + TiO2 f Ti3O4Cl4 -200.9 -201.9 -199.2 -192.9 -550.9 -553.3TiOCl2 + TiCl4 f Ti2OCl6 -54.9 -55.2 -54.5 -52.9 -377.3 -378.52TiOCl2 + 2TiO2 f Ti4O6Cl4 -296.9 -298.4 -294.1 -284.5 -714.1 -717.6TiCl4 + TiOClOH f Ti2OCl5OH -58.6 -59.1 -57.0 -53.8 -407.8 -409.42TiOClOH f Ti2O2Cl2(OH)2 (cis) -92.2 -92.5 -90.9 -87.7 -427.6 -430.12TiOClOH f Ti2O2Cl2(OH)2 (trans) -93.2 -93.5 -92.1 -88.9 -428.6 -431.12TiOClOH f Ti2O2Cl2(OH)2 (iso) -91.1 -92.4 -90.9 -87.8 -426.5 -430.0Ti(OH)4 + TiO(OH)2 f Ti2O(OH)6 -55.1 -54.4 -52.6 -49.3 -552.7 -557.82TiO(OH)2 f Ti2O2(OH)4 -88.8 -88.7 -86.9 -83.5 -483.6 -487.8TiOClOH + TiO(OH)2 f Ti2O2Cl(OH)3 -91.5 -91.7 -93.1 -120.2 -456.6 -460.0

TABLE 8: Calculated Reaction Energies (kcal/mol)

reaction ∆H0K ∆H298K ∆H700K ∆H1500K

TiCl3OH + TiCl4 f Ti2OCl6 + HCl -4.7 -4.6 -4.9 -5.42TiCl3OH f Ti2OCl6 + H2O -7.3 -7.3 -6.2 -4.32TiCl3OH + TiCl4 f Ti2O2Cl4 + 2HCl 14.0 14.3 13.5 12.4TiCl2(OH)2 + TiCl4 f Ti2O2Cl4 + 2HCl 12.4 12.9 12.1 11.0TiCl2(OH)2 + TiCl4 f Ti2OCl5OH + HCl -4.7 -3.9 -3.4 -2.32TiCl2(OH)2 f Ti2O4 + 4HCl 145.1 146.3 143.4 138.12TiCl2(OH)2 f Ti2O2Cl4 + 2H2O 5.6 6.0 3.8 -0.1TiCl3OH + TiCl2(OH)2 f Ti2 O3Cl2 + 3HCl 77.7 78.4 76.6 73.42TiCl(OH)3 f cis-Ti2O2Cl2(OH)2 + 2H2O 6.5 6.7 3.5 -4.12TiCl(OH)3 f trans-Ti2O2Cl2(OH)2 + 2H2O 5.0 5.7 3.6 -0.22TiCl(OH)3 f iso-Ti2O2Cl2(OH)2 + 2H2O 6.2 6.8 4.7 0.82TiCl(OH)3 f Ti2O2(OH)4 + 2HCl 19.9 20.5 19.8 18.82TiCl(OH)3 f Ti2OCl2(OH)4 + H2O 107.5 108.0 107.1 105.2TiCl(OH)3 + TiCl4 f Ti2OCl4(OH)2 + HCl 49.1 50.2 50.8 51.92Ti(OH)4 f Ti2O(OH)6 + H2O -10.3 -9.2 -9.3 -9.62Ti(OH)4 f Ti2O2(OH)4 + 2H2O 2.3 3.0 1.0 -2.8Ti(OH)4 + TiO(OH)2 f Ti2O2(OH)4 + H2O -43.3 -42.9 -43.0 -43.2


and Environmental Research and located at Pacific NorthwestNational Laboratory, operated for the DOE by Battelle. Wethank Prof. K. A. Peterson of Washington State Universityfor providing the Ti basis set.

Supporting Information Available: Calculated geometryparameters for the molecules, CCSD(T)/aVnZ total energies(Eh) as a function of the basis set, calculated harmonicfrequencies for molecules at the MP2/aVTZ level, calculatedharmonic frequencies for Ti2O3Cl2, Ti2O2Cl4, Ti2OCl6,Ti3O4Cl4, Ti3O5Cl2, Ti3O3Cl6, and Ti4O6Cl4 at the B3LYP/aVDZ, BP86/aVDZ, PBE/aVDZ, and PW91/aVDZ levels, T1

diagnostics calculated at the CCSD(T)/aVQZ level, contribu-tions to the relative energies on the different potential energysurfaces, CCSD(T) relative energies for the potential energysurfaces as a function of the basis set, x, y, and z coordinatesof molecules at the MP2/aVTZ level (Å), complete potentialenergy surface for the hydrolysis of TiCl4 to produce TiO2

with different calculation methods (kcal/mol), and plots ofthe rate constant (k) vs temperature. This material is availablefree of charge via the Internet at http://pubs.acs.org.

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JP102020H


hydrolysis of ticl4 - initial steps in the production of tio2

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