Slab models of rutile TiO2 (110) surface: DFT and DFT+U calculations

The F2B slab model weakens the oscillations and calculations on F2B model quickly converge. However, the F2B model leads to artificial narrowness of band gap. Besides, when the number of layers increases, surface energy obtained from all three slab models approaches similar values. In particular, values of surface energy from DFT calculations converge to the experimental range for all three slab models.
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Slab models of rutile TiO2 (110) surface: DFT and DFT+U calculationsCite this paper: Vietnam J. Chem., 2023, 61(5), 563-570 Research articleDOI: 10.1002/vjch.202200153 Slab models of rutile TiO2 (110) surface: DFT and DFT+U calculations Tran Thi Thoa1, Trang Thuy Nguyen2, Hoang Van Hung1*, Nguyen Thi Minh Hue1* 1 Faculty of Chemistry and Center for Computational Science, Hanoi National University of Education, 136 Xuan Thuy, Cau Giay, Hanoi 10000, Viet Nam 2 Key Laboratory for Multiscale Simulation of Complex Systems, University of Science, Vietnam National University – Hanoi, 19 Le Thanh Tong, Hoan Kiem, Hanoi 10000, Viet Nam Submitted August 18, 2022; Revised October 3, 2022; Accepted August 2, 2023Abstract The dependence of rutile TiO2 (1 1 0) surface’s structural and electronic properties on the number of layers has beencarefully investigated with DFT and DFT+Ud,p approaches using three slab models. We have found that oscillations ofsurface energy, electronic properties from DFT calculations on the three models are stronger than those fromcorresponding DFT+Ud,p calculations. The even-odd fluctuations were demonstrated to relate to over delocalization ofelectrons, especially electrons in Ti 3d orbitals. The Ud,p corrections in DFT+Ud,p enabled to restrict the oscillations. TheF2B slab model weakens the oscillations and calculations on F2B model quickly converge. However, the F2B modelleads to artificial narrowness of band gap. Besides, when the number of layers increases, surface energy obtained fromall three slab models approaches similar values. In particular, values of surface energy from DFT calculations convergeto the experimental range for all three slab models. Keywords. Rutile (1 1 0) surface, surface energy, atomic displacements, band gap, DFT, DFT+Ud,p.1. INTRODUCTION calculations are the same, surface energy obtainedA (1 1 0) surface is the thermodynamically most from different slab models converged to differentstable crystal face of rutile TiO2 and gains a lot of values instead of the same or similar values. Forattention of scientists.[1] Structural and electronic example, in the study of H. Perron et al., convergedproperties of the surface play crucial roles in variety surface energy received the value of 0.50 J/m2 forof applications such as photocatalysis, sensors, fully relaxing all atom (FR), whereas 0.60-0.70 J/m2photovoltaics.[2-4] Although a wide number of was shown in the model which one or two internalcalculations based on DFT with local density layers are fixed to bulk atomic positions (FIL).[16] Theapproximation (LDA) and generalized gradient discrepancy of 0.13 J/m2 in converged surface energyapproximation (GGA) were published, most obtained was also seen between fixed bottom layer (F2B) and(1 1 0) surface energy has large deviation from FR models with 12 layers.[17]experimental observation. Experimental surface Furthermore, it is known that the DFT methodenergy of rutile (1 1 0) surface was recorded about underestimates band gap of rutile TiO2. This is0.28-0.38 J/m2.[5] Difference in the experimental consequence of self-interaction errors (SIE). One ofsurface energy values of a solid derivates from not effective and economical methods to deal with theonly mistakes and different performing conditions of limitation is using DFT+U method. Depend on eachthe contact angle measurements, kind of measuring specific purpose, U should be taken different values.liquids used in the contact angle but also objectively For example, for defective systems of TiO2 such as Odifferent mathematical formulas in methods of vacancies or Ti interstitials, Ud = 3-6 eV is good fordetermining surface energy.[6,7] Meanwhile, describing defective states.[18,19] Meanwhile, forcalculations with LDA reported large surface energy, composite of TiO2, Ud value could be choose to be 6nearly 0.89 J/m2.[8,9] Results of surface energy from eV,[20] even 9 eV.[21] Our previous work demonstratedGGA are smaller but still far from experimental that the combination of Ud and Up corrections helpsvalues, 0.74 J/m2 (PBE),[10] 0.73 J/m2 (GGA of simultaneously increase the band gap and decreasePerdew and Wang),[11] 0.57 J/m2 (PBE),[12,13] 0.47 discrepancy of lattice constants of rutile TiO2 bulk inJ/m2 (PBE).[14,15] Besides, when all parameters in comparison with DFT approach.[22] We found that a563 Wiley Online Library © 2023 Vietnam Academy of Science and Technology, Hanoi & Wiley-VCH GmbH 25728288, 2023, 5, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/vjch.202200153 by Readcube (Labtiva Inc.), Wiley Online Library on [01/05/2024]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons LicenseVietnam Journal of Chemistry Nguyen Thi Minh Hue et al.pair of Ud = 7 eV, Up = 10 eV was one of the best Optimization the rutile TiO2 bulk with the DFTpairs for calculations on the bulk. If the DFT+Ud,p is method obtained lattice constants, a = 4.644 Å, c =applied to rutile ...