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Assessment of density functional theory methods for the Ti-O- Cl species

Assessment of density functional theory methods for the Ti-O- Cl species Doug DePrekel, Phu Vo, Kevin Ngo, and Yingbin Ge* Department of Chemistry, Central Washington University, Ellensburg, WA 98926. Mean S igned Error (MSE) of Atomization Energy in kJ/ mol. Introduction

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Assessment of density functional theory methods for the Ti-O- Cl species

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  1. Assessment of density functional theory methods for the Ti-O-Cl species Doug DePrekel, Phu Vo, Kevin Ngo, and Yingbin Ge* Department of Chemistry, Central Washington University, Ellensburg, WA 98926 Mean Signed Error (MSE) of Atomization Energy in kJ/mol • Introduction • Titanium oxide (TiO2) nanoparticles are widely used as a surface support in contaminant remediation , photo-catalysis , and dye-sensitized solar cell manufacturing. • The production of TiO2 nanoparticles via the oxidation of titanium tetrachloride (TiCl4) is important; yet its mechanism is little known. Experimental data are limited. Study of Ti-O-Cl thermochemistry is challenging. • B97-1 density functional theory (DFT) calculations have been carried out to obtain the thermochemical and kinetic data of Ti-O-Cl species.1-2 Yet questions remain: • How accurate is B97-1 for the Ti-O-Cl species? • Are there more accurate DFT methods for these species? Mean Unsigned Error of Bond Length in pm Green: Pure DFT Blue: Hybrid DFT Purple: Double-hybrid DFT Blue: Hybrid DFT Purple: Double-hybrid DFT Mean Unsigned Error of Vibrational Freq. in cm-1 • Benchmark Calculations • CR-CC(2,3)3-5: left eigenstate completely renormalized coupled cluster singles, doubles, and non-iterative triples • CR-CC(2,3)/cc-pVTZ optimized geometry • <0.5 pm error in bond length; <0.5o error in bond angle • CR-CC(2,3)/cc-pVTZ vibrational frequencies • CCSD(T)/cc-pVQZ singlet point energy • <5-10 kJ/mol error (chemical accuracy) Mean Unsigned Error (MUE) of Atomization Energy in kJ/mol Green: Pure DFT Blue: Hybrid DFT Purple: Double-hybrid DFT • Conclusions • B97-1 is reasonably accurate for the Ti-O-Cl species with 32 kJ/mol MUE in atomization energy, 3.9 pm MUE in bond length, and 24 cm-1MUE in vibrational frequency. • B3LYP is more accurate with 22 kJ/mol MUE in atomization energy, 2.5 pm MUE in bond length, and 25 cm-1 MUE in vibrational frequency. • Hybrid DFT methods are significantly more accurate than the corresponding pure ones for the Ti-O-Cl species. • Hybrid DFT methods are much faster and as accurate as the double-hybrid ones. • Density Functional Theory Calculations • “Pure” DFT with exchange and correlation depending on • () + () • BLYP, BP86, BPW91, LSDA, M06-L, PBE, PW91, TPSS • Hybrid DFT with some Hartree-Fock exchange included • where = )). • B3LYP, B3P86, B3PW91, B97-1, B97-2, M06, M06-2x, M06-HF, PBE0, TPSSh • Double-hybrid DFT with some HF exchange and some MP2 correlation included (slow) • , • where = )), • = )). • B2PLYP,mPW2PLYP • The 6-311+G(d) basis sets are used in all DFT calculations. References R.H. West, G.J.O. Beran, W.H. Green, M. Kraft, First-principles thermochemistry for the production of TiO2 from TiCl4, Journal of Physical Chemistry A. 111 (2007) 3560. R. Shirley, W. Phadungsukanan, M. Kraft, J. Downing, N.E. Day, P. Murray-Rust, First-principles thermochemistry for gas phase species in an industrial rutile chlorinator, Journal of Physical Chemistry A. 114 (2010) 11825. P. Piecuch, M. Wloch, Renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian, Journal of Chemical Physics. 123 (2005) Art. No. 224105. P. Piecuch, M. Wloch, J.R. Gour, A. Kinal, Single-reference, size-extensive, non-iterative coupled-cluster approaches to bond breaking and biradicals, Chemical Physics Letters. 418 (2006) 467. M. Wloch, J.R. Gour, P. Piecuch, Extension of the renormalized coupled-cluster methods exploiting left eigenstates of the similarity-transformed Hamiltonian to open-shell systems: A benchmark study, Journal of Physical Chemistry A. 111 (2007) 11359. Eight Methods with the Smallest MUE of Atomization Energy in kJ/mol Blue: Hybrid DFT Purple: Double-hybrid DFT Pure vs. Hybrid DFT: MUE of Atomization Energy in kJ/mol Ti-O-Cl species studied 2Cl 1O 3O 1Ti 3Ti1Cl2 (D∞h) 1O2 (D∞h) 3O2 (D∞h) 2TiCl (C∞v) 1TiCl2 (D∞h) 3TiCl2 (D∞h) 2TiCl3 (C3v) 1TiCl4 (Td) 1TiO (C∞v) 3TiO (C∞v) 2TiOCl (Cs) 1TiOCl2 (C2v) 3TiOCl2 (C2v) 1TiO2 (C2v) 1TiO2 ring (C2v) 1TiO2 (D∞h) 1TiO2Cl2(C2v) 3TiO2Cl2(C2v) 1Ti2O2(D2h) 3Ti2O2(D2h) 1Ti2O4(D2h) Green: Pure DFT Blue: Hybrid DFT • Acknowledgements • CWU Office of Graduate Studies and Research Travel Grant • CWU College of the Sciences Faculty Development Fund • CWU startup and CBA fund • CWU Department of Chemistry

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