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
Introduction
Mean Signed Error (MSE) of Atomization Energy in kJ/mol
• 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:
o How accurate is B97-1 for the Ti-O-Cl species?
o Are there more accurate DFT methods for these species?
350
300
250
200
150
100
50
0
-50
-100
-150
Mean Unsigned Error of Bond Length in pm
5
Green: Pure DFT
Blue: Hybrid DFT
Purple: Double-hybrid DFT
4
Blue: Hybrid DFT
Purple: Double-hybrid DFT
3
2
Mean Unsigned Error of Vibrational Freq. in cm-1
50
Benchmark Calculations
25
• 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
350
300
Green: Pure DFT
Blue: Hybrid DFT
Purple: Double-hybrid DFT
250
Conclusions
200
Density Functional Theory Calculations
𝐸𝐷𝐹𝑇 𝜌 = 𝐸𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝜌 + 𝐸𝑒𝑙𝑒𝑐𝑡𝑟𝑜𝑠𝑡𝑎𝑡𝑖𝑐 𝜌 + 𝐸𝑥𝑐 (𝜌)
• 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-1 MUE 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.
150
100
50
•
“Pure” DFT with exchange and correlation depending on 𝜌
𝐸𝑥𝑐 = 𝐸𝑥𝑐 (𝜌) = 𝐸𝑥 (𝜌) + 𝐸𝑐 (𝜌)
BLYP, BP86, BPW91, LSDA, M06-L, PBE, PW91, TPSS
0
0
•
Hybrid DFT with some Hartree-Fock exchange included
𝐸𝑥𝑐 = 𝐸𝑥𝑐 (𝜌) + 𝑎𝑥 ∆𝐸𝑥 ,
where ∆𝐸𝑥 = 𝐸𝑥 (𝐻𝐹)−𝐸𝑥 (𝜌).
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)
𝐸𝑥𝑐 = 𝐸𝑥𝑐 (𝜌) + 𝑎𝑥 ∆𝐸𝑥 + 𝑎𝑐 ∆𝐸𝑐 ,
where ∆𝐸𝑥 = 𝐸𝑥 (𝐻𝐹)−𝐸𝑥 (𝜌),
∆𝐸𝑐 = 𝐸𝑐 (MP2)−𝐸𝑐 (𝜌).
B2PLYP, mPW2PLYP
Eight Methods with the Smallest MUE of Atomization Energy in kJ/mol
50
25
Blue: Hybrid DFT
Purple: Double-hybrid DFT
0
The 6-311+G(d) basis sets are used in all DFT calculations.
Pure vs. Hybrid DFT: MUE of Atomization Energy in kJ/mol
Ti-O-Cl species studied
150
2Cl
1O
1O
3O
2 (D∞h)
3TiCl (D )
2
∞h
3TiO (C )
∞v
1TiO (C )
2
2v
3TiO Cl (C )
2 2
2v
3O
2 (D∞h)
2TiCl (C )
3
3v
2TiOCl (C )
s
1TiO ring (C )
2
2v
1Ti O (D )
2 2
2h
1Ti
2TiCl
3Ti
(C∞v)
1TiCl (T )
4 d
1TiOCl (C )
2
2v
1TiO (D )
2
∞h
3Ti O (D )
2 2
2h
1Cl
2 (D∞h)
1TiCl (D )
2
∞h
1TiO (C )
∞v
3TiOCl (C )
2
2v
1TiO Cl (C )
2 2
2v
1Ti O (D )
2 4
2h
100
50
0
Green: Pure DFT
Blue: Hybrid DFT
References
1. 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.
2. R. Shirley, W. Phadungsukanan, M. Kraft, J. Downing, N.E. Day, P. Murray-Rust, Firstprinciples thermochemistry for gas phase species in an industrial rutile chlorinator,
Journal of Physical Chemistry A. 114 (2010) 11825.
3. 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.
4. 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.
5. M. Wloch, J.R. Gour, P. Piecuch, Extension of the renormalized coupled-cluster
methods exploiting left eigenstates of the similarity-transformed Hamiltonian to openshell systems: A benchmark study, Journal of Physical Chemistry A. 111 (2007) 11359.
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