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DOI: 10.1002/ijch.201600099

Doped 1D Nanostructures of Transition-metal Oxides:First-principles Evaluation of Photocatalytic SuitabilityYu. F. Zhukovskii,*[a] S. Piskunov,[a] O. Lisovski,[a, b] D. Bocharov,[a] and R. A. Evarestov[c]

1. Introduction

Proper choice of alternative energy sources for wide ap-plications in modern technology and everyday life is oneof the urgent research problems, because deposits of tra-ditional fossil fuels (coal, gas, oil, etc.) run out at an ex-treme rate, while their restoration rate is obviously inferi-or. Dissociation of water molecules under the influenceof solar light on semiconductor electrodes immersed inelectrolyte is found to be a promising process for the pro-duction of hydrogen fuel, and is extraordinarily friendlytowards the environment. In addition, hydrogen possessesa high energy density of ~237 kJ mol@1.[1]

Photocatalytic H2 production, often considered as arti-ficial photosynthesis, is an attractive and challenging re-search topic in the field of chemistry and renewableenergy.[1–3] Moreover, the only combustion product of hy-drogen is water, while traditional H2 production technolo-gies (e.g., steam reforming) are accompanied by the re-lease of CO2 and/or other undesirable side products.

A number of metal-oxide semiconductors were pro-posed and intensively studied as possible candidates forphotoelectrochemical water splitting catalysts (e.g.,SrTiO3, TiO2, ZnO, WO3, PbO, Fe2O3, CuO, andCu2O).[2,4–7] The major limitation for solar light conversionby photocatalysis relates to the band-gap position in cor-

responding photocatalytic materials. According to dataon the solar irradiation spectrum (at the level of EarthQssurface), the theoretical maximum degree of solar energyconversion for a catalyst with a 3.2 eV wide band gap isapproximately 1 %. For efficient water splitting undervisible light, the optimum band gap is estimated to be inthe interval of 2.0–2.2 eV (with conversion of solarenergy ~15 %),[8, 9] which is small enough to absorb a sig-nificant amount of visible sunlight, but at the same time,

Abstract : The splitting of water molecules under the influ-ence of solar light on semiconducting electrodes is a cleanand renewable source for the production of hydrogen fuel.Its efficiency depends on the relative position of the band-gap edges or the induced defect levels with a proper bandalignment relative to the redox H+/H2 and O2/H2O poten-tials. For example, TiO2 and ZnO bulk, as well as thick slabs(whose band gaps are ~3.2–3.4 eV), can be active only forphotocatalytic applications under UV irradiation (possessing~1% solar energy conversion efficiency). Nevertheless, byadjusting the band gap through formation of nanostructuresand further doping, the efficiency can be increased up to~15% (for 2.0–2.2 eV band gap). We analyse results of DFT(density functional theory) calculations on TiO2 nanotubesand ZnO nanowires, both pristine and doped (e.g., by AgZn,

CO, FeTi, NO and SO substitutes). To reproduce the energiesof one-electron states better, we have incorporated the Har-tree-Fock (HF) exchange into the hybrid DFT+HF Hamilto-nian. Both the atomic and electronic structure of nanomate-rials, simulated by us, are analysed to evaluate their photo-catalytic suitability, including positions of the redox poten-tial levels inside the modified band gap, the width of whichcorresponds to visible-light energies. Analysis of the densi-ties of states (DOS) for considered nanostructures clearlyshows that photocatalytic properties can be significantly al-tered by dopants. The chosen hybrid methods of first-princi-ples calculations significantly simplify selection of suitablenanomaterials possessing the required photocatalytic prop-erties under solar light irradiation.

Keywords: anatase titania nanotubes · density functional calculations · doping · water splitting · wurtzite zinc oxide nanowires

[a] Y. F. Zhukovskii, S. Piskunov, O. Lisovski, D. BocharovInstitute of Solid State PhysicsUniversity of LatviaRiga LV-1063 (Latvia)Tel. : (+371) 28824271Fax: (+371) 67132778e-mail: [email protected]

[b] O. LisovskiDepartment of Theoretical ChemistryUniversity of Duisburg-EssenEssen D-45141 (Germany)

[c] R. A. EvarestovDepartment of Quantum ChemistrySt. Petersburg State UniversitySt. Petersburg 199034 (Russian Federation)

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Yuri F. Zhukovskii is the head of the laboratoryof computer modelling of the electronic struc-ture of solids at the Institute of Solid StatePhysics (University of Latvia), Riga. He isa physicist by education, who graduated fromthe University of Latvia in 1975. In 1993, heobtained his Dr. Chem. degree from the Insti-tute of Inorganic Chemistry (Latvian Academyof Sciences) as a result of international collab-oration with the Institute of Physics (St. Pe-tersburg State University), Russia. Between1995 and 2009, he was first selected in a com-petition as a fellow at Helsinki University ofTechnology (Espoo, Finland), then gained sim-ilar status at the University of Western Ontar-io, London (ON, Canada), and at the North-western University, Evanston (IL, USA). Dr.Zhukovskii has actively participated in a number of international research collab-orations, including the EC Framework 7 Project CATHERINE, focused on nano-scale ICT devices and systems, and the Marie Curie Project CACOMEL, focusedon nanocarbon-based components and materials for high frequency electronics.Since 2016, he has been a coordinator of the ERA.Net RUS Plus Project No 237WATERSPLIT, devoted to theoretical simulations of photocatalytic abilities ofsemiconductor nanostructures, as well as the charge-transfer processes and dis-sociation of water molecules in the vicinity of doped nanoelectrodes immersedin an aqueous solution, in close collaboration with scientific groups from Ger-many (Essen) and Russia (Moscow and St. Petersburg). The main research in-terests of Dr. Zhukovskii include the physics and chemistry of crystalline solids,surface science, physics and chemistry of nanostructures, as well as computa-tional materials science and quantum chemistry.

Sergei Piskunov is a member of the laboratoryof computer modelling of the electronic struc-ture of solids at the Institute of Solid StatePhysics (University of Latvia), and graduatedfrom Riga Aviation University (Latvia) as anengineering scientist in 1998. He obtained hisPh.D. in the field of natural sciences at theUniversity of Osnabrfck (Germany) in 2003.Since 2004, he has been working at the Insti-tute of Solid State Physics of University ofLatvia. In 2006–2008, he was an Alexander vonHumboldt fellow in Duisburg-Essen University,Germany. Simultaneously, in 2005–2009, hewas involved in a fellowship at the Northwest-ern University, Evanston (IL, USA). In 2009–2012, he participated as a researcher in theproject Applications of computer science andits links to quantum physics at the Faculty of Physics and Mathematics, Univer-sity of Latvia. Dr. Piskunov has participated in a number of international re-search activities, including the EC Framework 7 Project CATHERINE and MarieCurie Project CACOMEL, both focused on nanoelectronics systems and nano-scale ICT devices. Since 2016, he has been a responsible executor of theERA.Net RUS.Plus Project No 237 WATERSPLIT. The research interests of Dr.Piskunov cover computer modelling in material science. He is also interested inapplications of quantum chemistry methods to perfect and defective crystals, aswell as 2D and 1D nanostructures.

Oleg Lisovski is a Ph.D. student at the Univer-sity of Duisburg-Essen, Germany. He beganhis education as a chemical engineer, butsoon switched this direction to theoreticalchemistry. His bachelor thesis (developed anddefended at Riga Technical University, Lativa),as well as his master’s thesis (developed anddefended at Uppsala University, Sweden),were dedicated to DFT modelling of doped ti-tania nanotubular photocatalysts. Presently,Oleg is working on his Ph.D. project, dedicat-ed to ab initio MD simulations of water neardefective metal-oxide nanotubes. Simultane-ously, he is taking part in the ERA.Net RUSPlus Project WATERSPLIT (grant No 237). Li-sovski’s main interest is renewable energy, ingeneral, and modelling of catalysts for solarwater splitting, in particular.

Dmitry Bocharov is a member of laboratory ofcomputer modelling of the electronic structureof solids at the Institute of Solid State Physics(University of Latvia). At the same time, hehas also been a docent at the Transport andTelecommunication Institute (Riga, Latvia)since 2013. He attained his M.Sc. degree ofnatural sciences in physics in 2006, and hisPh.D. degree in physics was obtained in 2012,both at the University of Latvia. In 2009–2012,he participated as a researcher in the projectApplications of computer science and its linksto quantum physics at the Faculty of Physicsand Mathematics, University of Latvia. In2014–2015, Dr. Bocharov was a fellow at thePaul Scherrer Institute (Villigen, Switzerland),participating in the SCIEX-program. Since2016, he has been taking part in the ERA.Net RUS Plus Project No 237 WATER-SPLIT. Dr. Bocharov’s research interests cover the applicability of quantumchemistry for the description of photocatalytic properties of metal oxides andprocesses in nuclear fuels (UN and UO2), and interpretation of X-ray absorptionspectroscopy (XAS), as well as experimental methods of electronic microscopy.During the last decade, he was a member of the organizing committee of theLatvian Open Physics Olympiad and the Latvian Physics Olympiad for high-school students.

Robert A. Evarestov is the head of the Depart-ment of Quantum Chemistry at St. PetersburgState University (SPbSU, Russia), from whichhe graduated as a physicist-theorist in 1960.He obtained his Ph.D. degree from SPbSU in1964, while his Habilitation degree was gainedfrom the same university in 1977. Since 1968,he has been working in the Department ofQuantum Chemistry of St. Petersburg StateUniversity (and as a Professor since 1979). In1990–1994, he was the Director of the Chemis-try Institute at SPbSU; in 1994–1998, he wasnominated as the first Vice Rector of SPbSU.Since 1999 until the present time, he has beenleading the Department of Quantum Chemis-try at SPbSU. The research interests of Prof.Evarestov cover the symmetry of crystals (themonograph Site Symmetry in Crystals, published by Springer Verlag (Germany)in 1993, 2nd Ed. in 1997). He is also interested in the application of quantumchemistry methods for the proper description of perfect and defective crystals(the monograph Quantum Chemistry of Solids, published by Springer in 2007,2nd Ed. in 2012). Now his interests are focused on both the symmetry and quan-tum chemical study of monoperiodic structures (nanotubes, nanowires). Hismonograph Theoretical Modelling of Inorganic Nanostructures: Symmetry andab initio calculations of nanolayers, nanotubes and nanowires was published bySpringer in 2015. Prof. Evarestov is a Foreign Member of Latvian Academy ofScience (since 2005), Humboldt Foundation Awardee, Germany (1998), Honora-ry Professor of SPbSU (2009), and participant of many international and Russiancollaborative projects. Since 2016, he has been a consultant of the ERA.Net RUSPlus Project No 237 WATERSPLIT.

Isr. J. Chem. 2017, 57, 461 – 476 T 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim www.ijc.wiley-vch.de 462

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it is larger than the energy required to split a water mole-cule (1.23 eV).[10,11] Bulk materials that possess band gapsin the optimal energy range, e.g., Fe2O3 (2.2 eV) andCuO (1.7 eV), unfortunately, have relatively low efficien-cies of incident photon-to-current conversion[12] or experi-ence photocorrosion.[3, 5, 13]

On the other hand, ZnO, TiO2 and SrTiO3 oxides,which stand out due to superior chemical and optical sta-bility as well as commercial availability, have broaderband gaps (3.20 eV for cubic SrTiO3,

[2] 3.20 and 3.03 eVfor anatase- and rutile-structured titania, respectively,[4,14]

vs. 3.44 eV for wurtzite-type ZnO[15]). This consequentlylimits their activity to the near-ultraviolet region of thesolar spectrum, so that only several percent of the sun-light can be harvested by such materials. Optimal widthsof the band gaps must be also combined with a properalignment of the band edges relative to both the reduc-tion (H+/H2) and oxidation (O2/H2O) potentials estimat-ed thermodynamically (@4.44 eV and @5.67 eV, respec-tively),[13] which should be positioned inside the band gap.Doping of these bulk oxides by certain substitutionalatoms should result in the appearance of additional levelsin the band gap, thus creating new optical absorptionedges and reducing the energy threshold.[8] Hence, visi-ble-light photons become capable of overcoming the gapbetween newly formed edges.[7] The efficiency of oxidedoping can be noticeably enhanced through nanoscaletransformation of their morphology.[16]

In this review, we analyse applicability of large-scalefirst-principles calculations for the description of metal-oxide 1D nanostructures doped with cations and/oranions, thus evaluating their suitability to be used forphotocatalytic water splitting. Here, we systematize ourresults obtained mainly for two classes of 1D nanostruc-tures estimated as the effective photocatalysts during thelast few years – anatase-structured titania nanotubes(NTs)[17–20] and wurtzite-structured ZnO nanowires(NWs).[21] At the same time, results of our recently per-formed ab initio simulations of strontium titanate, includ-ing both nanotubes[18] and nanowires[22] with cubic mor-phology, clearly show that their efficiency for photocata-lytic applications is markedly lower than in the case ofTiO2 and ZnO nanostructures. This is why we do not ana-lyse those results in the current review at all. Moreover,only the ground states of nanomaterials have been takeninto account in our simulations performed so far, whereasa more detailed study of their excited states, for bothpure and doped morphology, is necessary to make realprogress in this field and to better interpret the hugeamount of existing experimental data.[23]

A tight collaboration between the coauthors from bothUniversity of Latvia and St. Petersburg State University(Russia) during the last few years has been focused onthe theoretical description of inorganic 1D nanomaterials,including ab initio simulations of their morphology andelectronic structure, which has resulted in a number of

joint publications.[21,22,24–31] From 2016, this collaboration issupported by the ERA.Net RUS Plus Project No. 237WATERSPLIT.

2. Progress in Contemporary Research of DopedTiO2 Applicability for Photocatalysis

2.1 Experimental Studies

TiO2 is a well-known and inexpensive semiconductor witha number of prospective properties and numerous techno-logical applications, which are comprehensively studied inmaterials science.[32] Although the total number of bulk ti-tania polymorphs discovered so far under different condi-tions, e.g., nonequilibrium ones, is seven (each of them isconstructed using octahedrally coordinated Ti atoms),[33]

only rutile- and anatase-structured TiO2 play a substantialrole in practical applications, due to the higher energeticstability than other phases. At the same time, for theoreti-cal simulations, stable titania nanotubes are considered tobe mainly anatase-structured.[27]

Numerous experiments focused on titania doping bydifferent metal ions (e.g., Cr, Fe, Mn, Mo, Ni, V, etc.)were performed earlier.[7] In 1982, Borgarello et al. dis-covered that Cr5+-doped titania could generate hydrogenand oxygen in the process of water splitting under sun-light irradiation (corresponding wavelength interval is400–550 nm, which corresponds to values of 3.15–2.29 eVon the energy scale).[34] Cao et al. reported that Sn4+

-doped titania nanoplanes, synthesized by chemicalvapour deposition (CVD) exhibit noticeably higher pho-tocatalytic efficiency than ordinary TiO2 crystal.[35] Exper-imental studies performed on Nb-doped titania nanotubesfabricated by anodization of Ti@Nb alloys clearly exhibitenhanced photoelectrochemical splitting of H2O mole-cules, accompanied by negligible photodegradation.[36]

Klosek and Raftery demonstrated that visible-light ab-sorption in V4+-doped TiO2 is a result of the electrontransfer from the V(3d) electron-induced energy level tothe conduction band.[37] Their research became a key tomore effective ways of ethanol photooxidation under visi-ble light (another route to hydrogen generation). Fe3+

-doped titania also exhibits enhanced photocatalytic activ-ity. Moreover, electrons from Fe3+(3d) state induce addi-tional levels in the TiO2 CB.[38] Doping of titania photoca-talysts by Cr, Mg, and Fe cations can improve their effi-ciency; for example, magnesium can reduce the energybarrier for interphase transfer of electrons.[39] On theother hand, the newly induced electronic states canbehave as recombination centres, e.g., by shifting the im-purity levels to lower than the reduction SHE (standardhydrogen electrode) level.

Usually TiO2 doped by nonmetal anions exhibitsa squeeze of the band gap directly, by shifting the top ofthe VB upwards, and not an appearance of inducedlevels, like in metal-doped titania. Nevertheless, Chen


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et al. used X-ray photoelectron spectroscopy to show theappearance of extra mid-gap states in the electronic struc-ture of C-, N-, or S-doped TiO2 between the VB and theCB induced by dopants.[40] This additional density of theelectronic states explains the redshift mentioned above.Braun et al. discovered an additional eg resonance state inthe O(1s) NEXAFS (near-edge X-ray absorption finestructure) pre-edge of titania caused by N dopants.[41]

This observation was used to explain enhanced photoca-talytic activity of N-doped TiO2 under visible light. At thesame time, S dopants substituting host O or Ti atoms canimprove the photocatalytic activity of nanorods too.[42,43]

S-doped TiO2 also exhibits higher photocatalytic activitythan the N-doped system.[44] C-doped TiO2 compounds,also synthesized, exhibit a quite narrow forbidden gapand an enhanced photocatalytic activity than pure titaniawith mixed rutile and anatase domains, while dopednanotubes possess better photocatalytic activity:[45] levelsinduced in their band gap were shown to broaden the ac-tivity of doped NTs from the visible to the infraredregion. A complex study of the chemical modification oftitanium isopropoxide with different nonmetal reagentswas performed by Pillai et al. ;[46,47] it was discovered thatintroduction of N and S dopants (applying urea andsulfur acid, respectively), improved both chemical stabili-ty and photocatalytic activity of titania.

Rather limited information on the codoping of TiO2

photocatalysts is available for nonmetallic dopants so far.Yan et al.[48] reported on N- and S-codoping of TiO2 nano-tube-array films by treatment with thiourea and calcina-tion under vacuum and high temperature. Codoped NTsexhibit broadened absorption spectra, as well as enhancedphotocatalytic activity in the methylene blue degradationprocess. Alternatively, Lv et al.[49] studied N+S codopedTiO2/fly ash bead composite material and its photocata-lytic activity in the visible-light range. The materialQs abil-ity to degrade methyl orange was compared with both un-doped and P25 samples (commercially available nano-powder mixture of TiO2 anatase and rutile phases); theformer showed much higher efficiency. Li et al. suggestthat Sn-doped nanotubes (Sn/Ovac NTs) with oxygen va-cancy possess better photocatalytic performance thanpure TiO2 samples or samples without an Sn dopant or Ovacancy.[50] At the same time, Sn/Ovac NTs achieve thehighest photodegradation rate among similar samples. Be-sides doped photocatalysts, the appearance of vacanciesas point defects can result in the growth of electrical con-ductivity and changes in band-gap structures.[51]

A series of EPR and XPS studies have been performedon nitrogen-[52] and fluorine-doped,[53] as well as N+F[54]

and N+B[55] codoped titania powders synthesized via thesol-gel method in aqueous solutions of inorganic com-pounds (N-, F-, and B-containing), with subsequent calci-nation in air. In doped TiO2 powders prepared usingmethods of wet chemistry, it is necessary to take into ac-count the possible formation of both surface and bulk

dopants.[56] N, F, and B substitutes for O behave similarlyto paramagnetic (or diamagnetic) centres, which can beeffectively studied within spectral analysis of the electron-ic paramagnetic resonance.[57]

2.2 Theoretical Simulations

In spite of numerous efforts undertaken so far, compre-hensive understanding of fundamental changes in theelectronic structure of the doped semiconductors is stillnot sufficient for the rational design of their atomic com-position. It is necessary to formulate a theoretical proce-dure to predict prudently the electronic structure and thecharge redistribution in photocatalysts. A number of sim-ulations performed so far deal mainly with doped and co-doped photocatalytic bulk materials,[52–55,57–64] and theirlow-index surfaces,[65–67] as well as 0D and 1D nanostruc-tures.[68,69] There are two critical issues that are importantfor photocatalysis, but not yet well treated in convention-al density functional theory, as well as other first-princi-ples packages: 1) the lack of resources, essential for simu-lations of the strong polarization on the charged electrodesurfaces in aqueous electrolyte; and 2) the inaccuracy ofexisting DFT functionals for a proper alignment of theH+/H2 and H2O/O2 potentials with the edges of the bandgap or the induced dopant levels.[70] These great challeng-es still exist for the simulation of photocatalytic reactionkinetics driven by excess holes/electrons accumulated incatalysts.

Using the DFT method with the Perdew@Burke@Ern-zerhof functional in the framework of the generalizedgradient approximation (GGA) method, Khan et al. haveshown that simultaneous anatase-phase bulk codopingwith Mo and N atoms leads to TiO2 band-gap reductionfrom 2.12 eV to 1.50 eV, as well as enhancing visible-lightphotocatalytic activity due to the effective utilization ofelectron@hole pairs in the oxidation/reduction process.[58]

For the same anatase, spin-polarised DFT calculationspredict that 2N+W codoped TiO2 bulk can be consideredas a quite efficient visible-light photocatalyst.[59] . Houet al. modelled transition-metal ions implanted into TiO2

bulk, using the full-potential linearized augmented plane-wave (FP LAPW) method, and found that the 3d statesof V, Cr, and Fe ions play a key role for the redshift ofthe ultraviolet-visible absorption spectrum.[60] DFT+Ustudies of Nb@N@S tri-doped anatase within the GGA ap-proach and PBE exchange-correlation functional haveshown that the mixture of new N(2p) and S(3p) states onthe top of the valence band, as well as the Nb(4d) statesin the bottom of conduction band, reduce the band gapfrom 3.2 to 2.0–2.5 eV.[61] Nishikawa et al. demonstratedwithin the DV-Xa calculations that V, Cr, Mn, Fe, Co, Ni,or Rh dopants can shift the absorption of TiO2 anataseand rutile phases into the visible-light region.[62] Afterthat, they also considered the correlation between thedopantsQ radii and changes in their electronic structure,


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concluding that Ni3 + and V5+ dopants produce the bestcontribution to water splitting. Asahi et al.[63] studied theband structure of the C-, N-, F-, P-, and S-doped anatasestructure of titania bulk using the same FP LAPWmethod. The substitution of O by N, leading to mixing ofthe N(2p) and O(2p) states, produces the best conditionsfor photocatalytic applications, since such structural modi-fication results in an upward shift of the top of the VB,thus reducing the width of the band gap. Finally, Harbused screened Coulomb hybrid DFT calculations withinthe projected augmented wave (PAW) approach to calcu-late the positions of bands for Se-modified anatase bulk.[64]

Using the PAW method for DFT calculations, Nolanfound that small iron-oxide clusters can be stable at theTiO2 surface, and their presence squeezes the band gaptowards the frequency range of visible light arising fromthe presence of iron-oxide states lying above the valenceband of titania.[65] PW DFT calculations, in combinationwith ultraviolet photoelectron spectroscopy, have beenused to study the origin of the band-gap states of a rutile-structured TiO2(110) slab induced by surface @OHgroups.[66] C-, N- and S-doped (TiO2)n nanoclusters werestudied by Shevlin and Woodley using both standard andtime-dependent DFT calculations.[67] The phase structure,surface morphology, optical properties, and photocatalyticactivities of TiO2 nanoparticles monodoped and codopedby Mn and/or N were studied using DFT-GGA calcula-tions, as well as X-ray powder diffractometry, Ramanspectra, scanning electron microscopy, X-ray photoelec-tron spectroscopy, and UV-Visible diffuse reflectance.[69]

The Mn+N codoped specimen manifested a higher pho-tocatalytic activity.

Various doped materials exhibit a large mismatch be-tween the length scales over which the photon absorptionoccurs (up to micrometres). On the contrary, at relativelyshort distances, within the limit of a few tens of nanome-tres, at which electrons can be extracted, electron@holerecombination was observed.[71] A reliable approach forsolving this problem was found to be the synthesis ofnanostructured electrodes with orthogonalised directionsof photon and electron propagation, which was achievedby markedly increased surface-to-volume ratios.[16,72]

Nanotubes synthesized from the wide-gap materials ex-hibit not only large surface areas, but also high mechani-cal stability and integrity, leading to both charge transportand electron@hole separation.[73,74] TiO2 (6,6) NTs built asregularly distributed bundles consisting of rutile (110)monolayers were calculated recently using the DFTmethod.[75] The reported electronic properties of sucha structure are predicted to be close to those of TiO2

bulk. Possibilities of band-gap modification in C-dopedTiO2 NTs were estimated within the DFT-PAW ap-proach.[76] Interaction between C(2p) and O(2p) statesprovides no contribution to band-gap modification.

For the majority of DFT calculations on doped TiO2

structures mentioned above, the standard LDA or pure

GGA (mainly PBE) exchange-correlation functionalswere applied. These approaches resulted in severe under-estimation of the band gaps (except for those applied inRefs. [58,64, 65], where both GGA and Hubbard DFT+U functionals were used). Obviously, results obtained insuch calculations cannot be properly compared with ex-perimentally estimated distributions of photoinducedlevels in the band gap of doped titania. However, for sim-ulations of N- and F-doped, as well as codoped, TiO2 par-ticles (experimentally studied too, as mentioned in Sec-tion 2.1),[52–55,57] B3LYP hybrid functionals were used (to-gether with standard PBE), for adequate comparison withEPR and XPS spectra of titania powder doped with para-magnetic atoms.

Finally, very little has been reported so far on the com-puter simulations of realistic defective titania NTs: thelack of periodicity makes their theoretical study computa-tionally very time-consuming and expensive. Another ob-stacle is the fact that a consistent first-principles computa-tional methodology has been missing, until recently,[77]

which could exploit periodic roto-translational symmetryfor efficient ground-state calculations, as well as providedetailed simulations of the excited-state and charge-trans-fer processes.

3. Progress in Contemporary Researches ofDoped ZnO Applicability for Photocatalysis

3.1 Experimental Studies

Zinc oxide is one of the most attractive materials, since itis chemically stable, nontoxic, cheap, and it has botha high charge mobility and long lifetime of excited elec-trons.[15] Stable ZnO structures are mainly formed for thewurtzite phase,[31] whereas sphalerite (zinc-blende) andcubic (rock-salt) phases are usually considered metastablefor zinc oxide. Wurtzite-structured ZnO is found to be ad-vantageous over titania in terms of charge mobility;[78] onthe other hand, it is more vulnerable to photocorrosion,especially under UV irradiation (nevertheless, photocor-rosion can be inhibited, e.g., by coupling with variouscarbon structures).[79]

A number of experiments focused on applications ofzinc oxide for photocatalytic H2 generation have beenperformed so far, mainly using their doping bycarbon.[79–84] To improve the performance of ZnO@C pho-tocatalysts, it was found necessary to utilize the structuraladvantage of the carbon nanomaterials for controlling themorphology of the ZnO nanocrystals, rather than to in-troduce carbon nanomaterials merely as the precursor forthe ZnO@carbon composite.[79] Surface functional groupson the carbon nanomaterials were able to act as favoura-ble nucleation sites for ZnO nanoparticles, thus tailoringtheir microstructure and size. A method allowing suppres-sion of photocorrosion for ZnO nanoparticles by surfacehybridization with graphite-like carbon layers was devel-


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oped by L. Zhang et al.[80] The photocatalytic suitabilityof these nanoparticles was also enhanced, which can beattributed to the improved adsorption ability and crystal-linity, thus providing their high activity for significantlylonger time intervals than pure ZnO nanoparticles. In ac-cordance with the first systematic study of C-doped ZnOnanostructures as catalysts for water splitting performedby Lin et al. ,[81] they were found to be advantageous overmany other approaches for increasing solar-light utiliza-tion. Another advantage of porous carbon-doped ZnOnanoarchitectures was exemplified by their stability inphotooxidation processes, showing significantly increasedefficiency after long-term experiments, as compared withpure ZnO nanostructures. A synthesis route of C-dopedZnO through urea-assisted thermal decomposition of zincacetate, and further formation of nanorods and nano-spheres, evaluated via degradation of methylene blueunder sunlight irradiation, was recently reported by X.Zhang et al.[82] Carbon incorporation reduced the bandgap of synthesized ZnO nanostructures and improved thecharge separation efficiency, thereby enhancing sunlightphotocatalytic activity. Alshammari et al.[83] studied C-doped 2D ZnO nanoflakes with large surface areas,which could be successfully synthesized via a pyrolysisprocess using a polymer-directed agent. Carbon dopingresulted in enhanced UV and visible-light absorption,which did not affect the electron-transition characteristicsof ZnO. The direct band gap of C-doped nanoflakes wasfound to be 2.98 eV, though its light adsorption tailedbeyond the visible-light region, because of coexisting Ovacancies (VO) and C dopants, which can lead to signifi-cant charge recombination. An alternative conclusion onthe efficiency of C-doped photocatalysts was drawn byFlores et al. ,[84] who studied ZnO samples of differentmorphologies. When using C-containing reagents for thesynthesis of non-carbon-doped structures in their experi-ments, carbon could play the role of a contaminant, dete-riorating the photocatalytic efficiency in specific cases.

Alternatively, Ag-doped ZnO nanostructures were alsoinvestigated as potential photocatalysts.[85–87] M. Hsu andC. Chang studied photocatalysts fabricated of Ag-dopedZnO nanorods grown on stainless-steel wire meshes.[85] Itwas shown that silver dopants enhance absorption ofsolar light. Moreover, the hydrophilic properties of nano-rods, combined with an increased surface area and an im-proved separation of excited electrons and holes, enhancetheir overall photocatalytic activity. Thomas et al. synthe-sized Ag-doped ZnO NWs using a low-temperature elec-trochemical process,[86] and found that Ag dopants arelikely to occupy regular Zn sites. Khosravi-Gandomaniet al. studied Ag-doped ZnO nanoparticles synthesized bya sol-gel method.[87] Both pristine and Ag-doped ZnO arecrystallized in a wurtzite phase. XPS clearly shows dopantincorporation into the crystalline structure, while in UV-Vis absorption spectra, the band gaps of the considerednanostructures decrease simultaneously with the increase

of dopant concentration. Pristine and Ag-doped ZnOnanoparticles were used as source materials to grow pris-tine and Ag-doped ZnO nanowires on n-type Si sub-strates, while the Ag-doped ZnO NWs per se exhibit p-type properties.

Gallino et al. synthesized N-doped ZnO powders start-ing from commercial ZnO nano-sized particles (with<100 nm size).[88] Nitrogen impurities incorporated intopolycrystalline ZnO upon annealing in an NH3 atmos-phere demonstrate effective p-type doping. EPR experi-ments were performed when using 580 Bruker spectrome-ter (with microwave frequency 9.76 GHz) equipped witha liquid helium cryostat. All experiments were done at5 K, with a repetition rate of 1 kHz. The magnetic fieldwas measured with a Bruker NMR Gaussmeter. Wanget al. studied solution-based ZnO nanorod arrays modi-fied by controlled N doping using an advanced ion-im-plantation method.[89] They subsequently utilized NWarrays as photoanodes for photoelectrochemical watersplitting under visible-light irradiation. The gradually dis-tributed N dopants shift the optical absorption edges tothe visible-light region, which results in the efficient driv-ing of photo-induced electrons and transfer of holes.

3.2 Theoretical Simulations

Unlike experimental studies on ZnO photocatalysts, theirtheoretical simulations are rather scarce.[78,83,86,88,90,91] DFTcalculations on C-containing ZnO supercells[83] revealedthat the origin of the visible-light response of carbon-doped ZnO is related to the additional mid-gap energylevels arising due to doping, and corresponding creationof VO vacancies in the presence of carbon,[83] which areenergetically well correlated with XPS data. In pure zincoxide, O(2p) and Zn(4s) states mainly form the top of theVB and the bottom of the CB, respectively. Unlike pris-tine ZnO, the VB of C-doped ZnO is dominated by theC(2p) state, as well as hybridised O(2s) and O(2p) statesinduced by VO, while the CB mainly contains Zn(4s), par-tially accompanied by Zn(3d) states.

Pan et al.[78] explored the band structure, optical absorp-tion, and thermodynamic stability of both monodoped (Cor N anions and Cr, Sc, V, or Ti cations), as well as co-doped ZnO bulk, employing hybrid DFT calculations.The obtained results show that compensated (Ti+C) andnon-compensated (Sc+C) and (Cr+C) codoped ZnOare rather strong candidates for photoelectrochemical(PEC) hydrogen production from water, because of theirnarrowed band gap to the visible-light region, potentiallysuppressed recombination of the electron@hole pairs, suit-able band edge positions, and good thermodynamic stabil-ity for PEC water splitting.

Li et al. performed DFT calculations to study the influ-ence of Ag dopants on structural, electronic, and opticalproperties of ZnO NWs,[90] focusing on the thinnest nano-wires only. An expected finding was that Ag dopants sub-


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stitute Zn sites (but not regular oxygen or interstitialsites), regardless of defect concentration, and prefer siteson the NW edges. Simulations of optical properties showenhanced absorption in the visible-light region, whichsupports the hypothesis that ZnO NWs possess high po-tential as photocatalysts. Moreover, DFT calculations onAg-doped ZnO NWs confirm earlier experimental con-clusions on AgZn atoms in ZnO nanowires,[86] which pro-duce an impurity band, along with an absorption redshift.

The hybrid B3LYP functional was first adapted by Pac-chioni et al.[91] to compute the optical and thermodynamictransition levels between different charge states of defectimpurities (H and Zn impurities, oxygen vacancies, and Ndopants) in bulk ZnO. Nitrogen species were found to berather deep acceptors, as confirmed by a combined EPRand DFT/B3LYP study.[88] The substitutional lattice site ismore stable and better fits the experimental evidence.However, NO substitutes do not provide a viable route forp-type doping of ZnO.[91]

4. Theoretical Background

4.1 Computational Details

A series of large-scale ab initio calculations have beenperformed by us for the two classes of monoperiodicnanostructures found to be suitable for photocatalytic ap-plications. Firstly, we have studied anatase-structuredTiO2 (001) and (101) NTs, with a fixed number of atomiclayers and chiral indexes: (n,0)[17,18] vs. (@n,n),[20] respec-tively, monodoped by either C, N, S, or Fe atoms, as wellas codoped by N and S atoms, simultaneously. Alternativenanomaterials potentially suitable for photocatalysis havebeen considered to be [0001]-oriented and hollow-centredwurtzite-structured ZnO NWs monodoped by C, N, orAg atoms.[21]

To perform ab initio calculations on both types of 1Dstructures, we have applied the DFT-LCAO methodwithin the formalism of localised atomic orbitals, as im-plemented in the CRYSTAL14 code.[92] For calculationson pristine and doped TiO2 NTs, we have used theB3LYP hybrid exchange-correlation functional.[93] Forbetter reproduction of TiO2 atomic and electronic struc-ture obtained in experiments and simulations, the stan-dard B3LYP Hamiltonian has been modified by us insuch a way that the contribution of nonlocal HF exchangehas been reduced from the original 20 % to 14 %(B3LYP-mod).[17] For ZnO NWs, we have applied hybridfunctional PBE0,[94,95] without any change of the original25% contribution to the hybrid Hamiltonian from theHF exchange.[92]

To construct the basis sets (BSs) for each chemical ele-ment of considered nanostructures, we have used the for-malism of the localised Gaussian-type functions (GTFs)implemented in CRYSTAL code.[92] For TiO2 NTs (e.g.,dopants), BSs have been chosen as either the all-valence,

in the forms of 8s–411sp–1d for O, 6s–311sp–11d for C,6s–31p–1d for N, 8s–63111sp–11d for S, and 8s–6411sp–41d for Fe, or constructed using the effective core poten-tial (ECPs) implemented by Hay and Wadt[96] for the Tiatom, in the forms of 411sp–311d. For doped ZnO NWs,we have chosen the all-valence BSs 8s–64111sp–41d forZn developed by Gryaznov et al. ;[97] the same BSs, 6s–311sp–11d and 8s–63111sp–11d for C and S, respectively,have been used as for TiO2 NTs, slightly modified BS 8s–411sp–1d for oxygen,[97] as well as Hay-Wadt ECP 3111s–221p–41d for silver atoms developed by Andrae et al.[98]

To provide a balanced summation in both direct andreciprocal lattices, the reciprocal space integration overthe direct and reciprocal lattices of TiO2 nanotubes hasbeen done by sampling the Brillouin zone (BZ) of 2 X 2 ti-tania supercells with 6 X1 X1 Pack-Monkhorst k-mesh,[99]

which results in four evenly distributed k-points over thesegment of the irreducible BZ.[18] Alternatively, the recip-rocal space integration in ZnO NW calculations has beenperformed by sampling the nanowireQs BZ of 1 X1 ZnOunit cells with the 12X 1 X1 k-mesh that gives, in total,seven k-points evenly distributed along the BZ,[21] whichis a line section for 1D nanowires. CRYSTAL14 calcula-tions have been considered converged only when thetotal energy differs by less than 10@10 a.u. in two succes-sive cycles of the self-consistent field (SCF) procedure.The total geometry optimisation of TiO2 NTs and ZnONWs has been performed by keeping their bulk symmetryfixed. Within the self-consistency, the accuracies (toleran-ces) of 10@7, 10@8, 10@7, 10@7, and 10@14 have been chosenfor the calculations of the Coulomb and exchange inte-grals.[92]

4.2 Definition and Verification of Parameters

To estimate reliability of first-principles calculations onkey properties of anatase-structured TiO2 nanotubes andwurtzite-structured ZnO nanowires, results of our calcula-tions on lattice parameters of bulk titania and zinc oxidehave been verified by comparison with those measuredexperimentally (Table 1). Obviously, we can establisha good qualitative correlation between them.

To justify the correlation of the calculated band-gapedges and energy levels induced by point defects (e.g.,

Table 1. Lattice parameters of TiO2 and ZnO crystals calculated byus and measured experimentally.

method a (b) c (b) u space group

titaniaB3LYP-mod 3.80 9.65 0.21 I41/amdExperiment[a] 3.79 9.52 0.21zinc oxidePBE0 3.26 5.20 0.38 P63mcexperiment[a] 3.25 5.21 0.38

[a] Experimental values are taken from Ref. [31].


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http://www.merriam-webster.com/dictionary/studied


dopants) for TiO2 and ZnO photocatalysts with the exper-imentally determined redox potential levels,[2] we calcu-lated the one-electron energies for the stoichiometric 20-layered anatase-structured TiO2(101) and 30-layeredwurtzite-structured ZnO(0001) slabs, respectively. CRYS-TAL calculations on 2D and 1D periodic systems givequalitatively correct distributions of the discrete energiesrelative to the zero vacuum level, while direct calcula-tions of the corresponding bulk do not allow one to ach-ieve the same goal.[21] Moreover, in contrast to results ob-tained by us for thick titania slab,[18] where the differencesbetween the calculated values of energy levels and thosedetermined from experiment are practically negligible(Table 2), certain quantitative disagreement between thecorresponding values is observed for the thick ZnO slab,since the admixture of nonlocal HF exchange in thePBE0 functional has not been changed in this case fromthe standard 25% values.[92]

Defective (e.g., doped) nanostructures can be charac-terized by the presence of induced levels inside the bandgaps. The energy balance for water splitting under the in-fluence of solar light photons is found to be more compli-cated in this case. The differences between the highest oc-cupied and lowest unoccupied impurity levels inside theband gap (HOIL and LUIL, respectively) are reduced, ascompared with pristine nanostructures. At the same time,the proper disposition of these levels must be preservedrelative to the edges of the band gaps, as well as bothredox potentials (corresponding to H+/H2 and O2/H2Oelectrode processes) being separated by @1.23 eV.[13]

Thus, the conditions of nanomaterial suitability for photo-catalytic applications can be expressed by the inequali-ties:

eVB < eHOIL < eO2=H2O < eHþ=H2< eLUIL < eCB? ð1Þ

Distribution of energy levels inside the band-gap andredox potentials described by this inequality can be illus-trated by Figures 3, 5–7 in Sections 5.1, 5.2, and 6, respec-tively. Due to the dissipation of a small amount of energy

(d) during the photocatalysis, two additional requirementsmust be fulfilled as well:

eO2=H2O @ eHOIL > e ð2aÞ

eLUIL: @ eHþ=H2> e: ð2bÞ

To estimate the possibility of forming a single substitu-tional dopant in a nanotube or nanowire, we have calcu-lated the corresponding impurity defect formationenergy:

EformAdop¼ Etot

Adop=NT NWþ Etot

host @ EtotAdop@ Etot

NT NW; ð3Þ

where: EtotAdop=NT NW

is the calculated total energy of a nano-tube or nanowire containing the substitutional Adop

dopant atom; Etothost is the total energy of the host atom,

which is removed from the nanotube or nanowire; EtotAdop

isthe total energy calculated for the impurity (dopant)atom; while Etot

NT NW stands for the total energy calculatedfor the perfect nanotube or nanowire.

4.3 Atomistic Models of Doped TiO2 Nanotubes

According to our preliminary calculations, a 9-layered NTwith (36,0) chirality possesses a negative strain energy,corresponding to an energy minimum, as compared withanalogous nanotubes with other (n,0) chirality.[17,101] Sucha nanotube contains 324 atoms per NT unit cell (or 648per supercell, as given in Table 3); it is described by a di-

ameter, dNT, and the length of the NT SC is lNT (Figure 1aand Figure 1b). We consider TiO2(001) NTs containingfixed positions for dopants: substitutional CO, NO, and SO

impurities replacing the host O atoms in six possible sites(Figure 1a), while three possible substitutional sites havebeen considered for FeTi impurity atoms. Since an NTaxis-extended and roto-translated “basic” 2 X2 supercellof an arc segment possesses 12 TiO2 formula units, imple-mentation of the dopants leads to ~8% defect concentra-tion for Ti sites of TiO2(001) NT and ~4 % for their Osites (Figures 1a, 1b).

An alternative 6-layered NT with (@12,12) chirality(Figures 1c, 1d) has also been considered. The choice of

Table 2. Absolute values of levels for the CB bottom (eCB), the VBtop (eVB), and band gap (Degap), calculated for both 20-layeredrutile-type TiO2(101) and 30-layered wurtzite-type ZnO(0001) slabmodels, as well as measured experimentally.

method eCB (eV) eVB (eV) Degap (eV)

titaniaB3LYP-mod @4.3 @7.4 3.1experiment[100] @4.3 @7.3 3.0zinc oxidePBE0 @3.7 @6.9 3.2experiment[100] @4.2 @7.4 3.2

Table 3. Number of atoms per NT supercell (nNT), optimized SClength (lNT), as well as inner and outer diameters of NT (dNT_inner

and dNT_outer, respectively) as calculated for titania (001) and (101)nanotubes (Figures 1a, 1b and Figures 1c, 1d, respectively).

TiO2 NTs nNT lNT (nm) dNT_inner (nm) dNT_outer (nm)

(001) (36,0) 648 0.35 3.48 4.82(101) (@12,12) 432 0.53 3.75 4.23


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a model of a specific size is justified by the compromisebetween the minimal formation energy and a number ofatoms in the NT SC. Four possible dopant sites are shownfor nonequivalent oxygen atoms vs. two sites for Ti atoms(Figures 1c, 1d). A nanotube of such a configuration con-sists of 144 atoms per unit cell (or 432 per supercell). Inour recent paper, we considered titania (101) nanotubeswith 1 X3 and 2 X3 periodically repeated “basic” unit cellscontaining 36 and 72 atoms, respectively,[20] resulting indopant concentrations of 2.8% (12 dopant atoms pernanotube unit cell) and 1.4 % (6 dopant atoms per nano-tube unit cell), respectively.

4.4 Atomistic Models of Doped ZnO Nanowires

The regular hexagonal prismatic shape of wurtzite-typeZnO nanowires, synthesized in numerous experiments,e.g., Refs. [84,86], can only be formed if the NW axis isoriented along the [0001] crystallographic direction, beinghollow-centred.[31] Arbitrary nanowires can be stabilizedwhen they are terminated by lateral facets, which possessthe smallest surface energy among any wurtzite faces.This requirement is fulfilled for the family of six identical

1(1008 7

; (11008 7

; 10(108 7

; (10108 7

; 01(108 7

and 0(1108 7

facets of zinc oxide, since they possess the smallest sur-face energy among wurtzite faces.[102] The last edition ofCRYSTAL14 code, used for our calculations on ZnOnanowires, contains the new option NANOROD, allow-ing users to generate differently structured NWs whensetting the properly chosen Miller indices of their lateralfacets, and thus, simultaneously defining their crystallo-graphic orientations.[92]

To estimate the suitability of doped [0001]-orientedZnO NWs of different sizes for photocatalytic applica-tions, we have preliminarily considered pristine NWs ofthree different diameters (Table 4), which can be cut

from a host wurtzite-type crystal. We have performeda number of ab initio calculations on each of them, ac-companied by total geometry optimization. The initialvalues of dNW have been varied from 2.1 to 3.2 nm, whichcorrespond to a consequent extension of the hexagonalNW cross-section containing from four (4X4) to six (6X6) coordination cylinders around the NW axis. (Since thecalculated band gaps of the thinnest nanowires with 2 X2and 3 X 3 extensions considerably exceed the values ofDegap for wurtzite-structured ZnO bulk, i.e. , 3.7–4.0 eV vs.3.3–3.4 eV,[15] we have excluded estimates of their photo-catalytic suitability from further consideration).

Figure 2 shows that the structural optimization of nano-wires results in the noticeable relaxation of the outeratomic layers, while the inner atoms practically remain inthe regular cross-section sites, whereas the UC lengthalong the NW axis (lNW) is noticeably reduced with grow-ing nanowire diameter (Table 4).

We have studied whether dopants favour the inner orouter NW regular sites for substitution (Figure 2), sinceone expects the photocatalytic process to be mostly influ-enced by outer defects.[21] Further modelling is focused on

Figure 1. Schematic of a 9-layered NT with chirality indexes (36,0):(a) top view; and (b) lateral view; as well as a 6-layered TiO2(101)NT with chirality indexes (@12,12): (c) top view; and (d) lateral view.Ti atoms are shown in grey, O atoms in red, while outer substitu-tional atoms are in yellow. The “basic” UC of the nanotubes is re-peated by 18 roto-translational symmetry operators for theTiO2(001) nanotube and 6 roto-translational symmetry operatorsfor the TiO2(101) nanotube. The numbered titan and oxygen atomsof the inset show the substitutional sites for impurity defectatoms. The magnitudes of optimized SC lengths (lNT), and innerand outer diameters of nanotubes (dNT_inner and dNT_outer, respective-ly), as well as the number of atoms per supercell (nNT), are system-atized in Table 3.

Table 4. Number of atoms per unit cell of nanowire (nNW), as wellas length of optimized UC (lNW) and NW diameter (dNW), as calcu-lated for three equilibrium configurations of ZnO NWs (Figure 2images the 5W 5 NW only).

ZnONWs

nNW lNW

(nm)dNW

(nm)

4W 4 192 0.526 2.295W 5 300 0.525 2.946W 6 432 0.524 3.59


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how the electronic structure of the NWs changes alongwith the growth of the diameter dNW and defect concen-tration. We consider mainly ~3 % and ~6 % concentra-tions, the equilibrium geometry for which has been opti-mised for all doped nanowires under study.

The majority of DFT simulations performed so far toevaluate the photocatalytic suitability of concrete struc-tures correspond to vacuum conditions at T=0 K. In real-ity, a photocatalyst immersed into an aqueous solution(consisting of a disordered ensemble of water molecules,e.g., surrounding anions and cations) forms a direct con-tact with an electrolyte. Such a junction at reduction andoxidation conditions produces changes in the electro-chemical potential due to the difference between the po-tentials at the electrode/water interface.[103] The equilibri-um at the interface is achieved due to the flow of chargesfrom one side to another, which results in band bendingat the junction side. The area where the band bendingtakes place is known as the space-charge layer, which ischaracterized by the accumulation of electrons or holes atthe surface.

5. Predictions on Photocatalytic Efficiency ofDoped Titania Nanotubes

Although anatase-structured titania (001) nanolayers andnanotubes were found to be energetically less stable than

those of titania (101) (their surface energies are 0.90 J m@2

vs. 0.44 J m@2, respectively),[32] the former possess marked-ly higher chemical reactivity,[104] and mechanical plasticity(as follows from the aforementioned effect of negativestrain energy).[101] Nevertheless, this is true for chemicallyclean and structurally perfect surfaces only, because forF-terminated surfaces, the relative stability of crystallinefacets of anatase-structured titania is reversed: the (001)surface is energetically more preferable than the (101)one.[105] On the basis of theoretical predictions, uniformanatase TiO2 single crystals with a high percentage (47%)of F-doped {001} facets were synthesized (using a hydro-fluoric acid medium as a morphology-controlling agent).These data allow us to analyse the calculated propertiesof TiO2(001) NTs first.

5.1 (001)-oriented TiO2 Nanotubes

The choice of (36,0) chirality for pristine anatase-type 9-layered TiO2(001) NTs (Figures 1a, 1b) is described inSection 4.3; it corresponds to the minimum of theEstrain(dNT) curve.[92] Comparison of dopant formation en-ergies defined by Eq. (3) allows one to estimate the pref-erence of their formation in nanostructures: impurityatoms have substituted each possible irreducible host Oor Ti atom in the nanotubes with the roto-translationallyand periodically repeated UCs shown in Figure 1a. There-fore, one of the six O sites and one of the three Ti siteshave been consequently substituted by CO, NO, SO, andFeTi. According to our calculations, both C and S dopantswould prefer to be positioned at the site of the outermostoxygen, and nitrogen in proximity of the second oxygenlayer, while iron prefer sites closer to the NT inner wall(Figure 1a, Table 5). We also compare values of Eform forboth doped titania anatase bulk and (001) nanotubes.

Obviously, the lowest formation energy of anion dop-ants has been found for CO (1.16 eV). In turn, it is2.61 eV for SO-doped TiO2 nanotubes, while 3.56 eV is re-

Figure 2. (a) Cross-sectional and (b) lateral images of the dopedwurtzite-based hexagonal-shaped ZnO NW extended by 6 V 6atomic shells around the hollow-centred [0001]-oriented axis, con-taining 216 formula units (or 432 = 12 V 62 atoms) per NW unit cell.The diameter and period of a nanowire are shown by the doublearrows dNW (a) and lNW (b), respectively. An example of defect distri-bution at 3 % concentration in a wurtzite-based hexagonal-shapedZnO NW unit cell is given. Zn and O atoms are shown as small redand middle blue-grey balls, respectively. Outer (yellow) or inner(green) site alternatives are highlighted. The magnitudes of the UClengths (lNW), the diameters of the nanowires (dNW), as well as thenumber of atoms per unit cell (nNW) are systematized in Table 4.

Table 5. Defect formation energies (Eform, eV) in doped anatase-typeTiO2(001) NTs and bulk estimated using Eq (3).[a]

inset site CO NO SO FeTi

(Figure 1a) concentration of dopants

4% 8%

1 1.16[b] 3.79 2.61[b] 5.582 3.23 3.56[b] 3.6 5.423 2.99 3.95 4.34 5.37[b]

4 3.13 3.88 5.33 –5 3.31 4.08 5.65 –6 3.78 4.11 3.37 –bulk[c] 4.12 3.22 5.36 4.44

[a] Host atoms Ah substituted by impurities (h) are labelled inFigure 1. [b] The lowest formation energies for dopants are shownin bold. [c] For the bulk, concentration is one dopant per 2W 2W 2supercell.


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quired for the formation of the NO dopant vs. 5.37 eV forFeTi. The formation energy of the N+S pair has been ob-tained to be 5.64 eV, which fulfils the inequality:

2EformðSOÞ < EformðSO þNOÞ < 2EformðNOÞ, ð4Þ

thus confirming the approximate additivity of estimateddopant formation energies. When calculating the bandstructure of the doped nanotubes, only the nanotubeswith the lowest defect formation energies have beentaken into account, irrespectively of their chemical natureand number of impurity atoms.

The energy balance between the band-gap edges ofsemiconductors (e.g., mid-gap levels induced by defects)and the redox levels, as described by Eq. (1), is consid-ered as a criterion for the efficiency of photocatalyticwater splitting.[2,13,90] The total and projected DOSs com-puted for both the monodoped (CO, NO, SO, and FeTi) andcodoped (NO +SO) titania (001) nanotubes have been re-cently described by us in detail.[18] An alternative descrip-tion of the electronic structure for doped TiO2 NTs hasbeen suggested by us in the same paper, where the sche-matic representation of the band-gap edges of pristineand doped nanotubes (eCB and eVB), as well as the mid-gap states of doped TiO2 nanotubes (eHOIL and eLUIL), hasbeen given in the form of either solid or dashed horizon-tal segments (for occupied or empty levels, respectively),while both the conduction and valence bands have beenimaged as filled rectangular columns, as shown inFigure 3.[18–20] The blue and red horizontal dashed linescorrespond, in this representation, to the oxidation

(eO2=H2O) and reduction (eHþ=H2) potentials, respectively.

As the zero of the energy scale, the potential of the stan-dard hydrogen electrode (SHE) has been chosen.[2,100]

As can be observed in Figure 3, for pristine titaniananotubes, the bottom of the conduction band is ~1.0 eVabove the H+/H2 potential, whereas the top of its valenceband is ~1.2 eV below the O2/H2O potential. A carbonsubstitutional impurity in a TiO2 NT induces an unoccu-pied defect level ~0.2 eV above the oxidation potential.This leads to an unsuitable valence-band position for theoxygen evolution reaction and can cause electron@holerecombination after photoexcitation. The N-doped TiO2

NT possesses an occupied impurity state practically at thelevel of the O2/H2O potential (i.e., inequality Eq. (2b) isnot fulfilled), while the bottom of the CB relative to thepristine NT is almost unchanged. For the sulfur-doped ti-tania nanotube, we predict that the bottom of the conduc-tion band is located almost at the level of the reductionpotential (but in this case Eq. (2a) is fulfilled), while thetop of the valence band corresponds to that of the pris-tine nanotube being practically unchanged; therefore, it isa good candidate for photocatalytic applications. Theiron-doped titania NT exhibits defect-induced mid-gapstates about 0.5 eV lower than the eHþ=H2

level, which cer-tainly results in the recombination of photoexcited elec-trons and holes. At the same time, when considering thepossible configurations of the doped titania (001) nano-tube, we predict that a much more efficient nanophotoca-talyst for visible-light-driven H2O splitting could be N+Scodoped TiO2 NTs.

5.2 (101)-oriented TiO2 Nanotubes

The choice of (@12,12) chirality for pristine anatase-type6-layered (101) titania NT (Figures 1c, 1d) is also ex-plained in Section 4.3.[20] We consider four possibledopant sites for this 6-layered nanotube, to substitute thenonequivalent oxygen atoms, as shown in inset of Fig-ure 4a. The outer SO dopants are found to be the energet-ically favourable (Table 6). As it has been found, in allcases the sulfur dopant shows a trend of being displacedfrom its initial position. The direction of this displace-ment is orthogonal to the tangent line passing throughthe initial dopant position, and it is protruding out of thenanotube wall. Obviously, it is easier to follow such dis-placement from the initial S1 and S4 positions (Fig-ure 4a), which explains why formation energies of dop-ants are lower in these cases. Values of Eform for S dopantsalmost do not depend on their concentration, unlike Ndopants, for which this dependence is noticeable, exclud-ing the external N1 site. For the two sulfur dopant siteslying closer to the external S1 and S2 surface sites (Fig-ure 4a), there is a negative shift in energy for both the eCB

and eVB values. In fact, there is no difference between theCB/VB positions of the pristine nanotube and the NTscontaining S dopants at the O3 and O4 sites.

Figure 3. Energy diagram for pristine and doped anatase-struc-tured TiO2 (36,0) nanotubes with defect content of 4 % for theanion dopants and 8 % for the cation dopant. A description of thegraphical details for this diagram is given in the text above. Num-bers on the tops of the valence bands and the bottoms of the con-duction bands correspond to their edges (eVB and eCB, respectively),while those written to the left of the solid and dashed lines corre-spond to their energy levels. The zero of the energy scale corre-sponds to the standard hydrogen electrode (SHE) level.[18] Numbersin rectangles terminated by dashed vertical lines correspond towidths of band gaps.


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Doping at S1 and S4 promotes the highest photocata-lytic enhancement, reducing the gap between the eLUIL

and eHOIL states, from 4.19 eV to 3.14 eV (3.12 eV) vs.3.08 eV (3.07 eV) for 1.4 % (2.8%) defect concentrations,respectively. It means that sulfur atoms alone do not pro-vide a sufficient rise in the photocatalytic activity. S-in-duced occupied levels have been found to be lower at1.4 % concentration. Unlike S-doped nanotubes, N dop-ants do not induce any visible shift in the position of theVB top, and the CB bottom levels are almost the same asin the case of the pristine structure. N dopants, however,induce empty states inside the band gap.

The suitability of NO +SO codoped TiO2(101) nano-tubes is noticeably higher than S and N monodoped ones.Indeed, in the latter, there are only four nonequivalentdopant positions (Figure 4a). However, after one dopantis introduced, a larger number of options for differentcombinations of codopant positions appear. Due to limit-ed computational resources, we have decided to put the Sdopant in its most preferable position, S1. Therefore, inevery modelled codoped structure the S atom is fixed inposition 1, while N dopants can be inserted into different

surrounding positions. Possible dimer-type sites for S+Ncodopants are assigned by additional indexes for identifi-cation; note that not all the possibilities were implement-ed by us due to limited resources.

The energy diagram of the six studied NO +SO codopedTiO2 NTs, each with a defect concentration of 2.8%, isshown in Figure 5. Obviously, the (N3-S1)B and (N3-S1)N

configurations are identical, and one of them (the latter)is excluded from further consideration. The general ob-servation is that the photocatalytic efficiency of the simu-

lated structures may be expected. In four cases out of six,the lowest empty state eLUIL is induced slightly below theeO2=H2O level (oxygen potential), and the highest occupiedstate eHOIL is located between the empty state and the VBtop. In two cases, the distance between the empty and oc-cupied induced state is not that of (N1-S1)B or (N4-S1)B,which means that it might be relatively easy for electronsto transfer to the empty state, and consequently, to over-come the energy interval between both redox potentials(Figure 5). The general observation is that, in most cases,S and N atoms have a trend to be found closer to eachother. Based on our calculations, we predict that S or Nmonodopants introduced into the 6-layered TiO2

(@12,12) NT cannot result in a marked rise in the photo-catalytic response. On the other hand, the S+N codopingof this nanotube can result in the enhancement of photo-catalytic efficiency, at least qualitatively. Moreover, weconclude that changes in the electronic structure of TiO2

NTs, induced by codoping, depend on defect distribution,both for (001) and (101) chiralities.

Figure 4. (a) Nonequivalent positions of N or S dopants in a seg-ment of 6-layered (@12,12) TiO2(101) NT; and (b) considered sites(1.4 % defect concentration) for N dopants if the S atom is locatedin position S1. Figure 4b “FR” stands for “front”; “B” for “between”;“N” for “near”; and “UND” for “under”.

Table 6. Defect formation energies Eform (eV) in doped anatase-typeTiO2(101) NTs and bulk estimated using Eq (3).

inset site Concentration of defects

(Figure 4a) 1.4 % 2.8 %

SO NO SO NO

1 2.47[a] 3.39[a] 2.47[a] 3.39[a]

2 2.89 3.49 2.90 4.103 3.43 3.51 3.47 4.154 2.62 3.51 2.62 3.39

[a] The lowest formation energies for dopants are shown in bold.

Figure 5. Schematic of the band edges and mid-gap states of pris-tine and N + S codoped 6-layered (@12,12) TiO2(101) nanotubes(for 2.8 % defect concentration). The nomenclature of the codo-pants is described in Figure 4b. The description of the graphicaldetails and numbers is the same as that given in the caption ofFigure 3.


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6. Predictions on Photocatalytic Efficiency ofDoped Zinc Oxide Nanowires

To estimate the photocatalytic suitability of doped ZnOnanowires, we have calculated both their formation ener-gies and energy diagrams, depending on NW diameterdNW and defect concentration (Figure 2).[21] In accordancewith above analysed results of experimental and theoreti-cal studies on doped zinc oxide nanowires (Section 3), wehave considered mainly CO, NO, and AgZn dopants (modelparameters of doped ZnO NWs are considered in Section4.4).

To estimate the ability of forming a substitutionaldopant in ZnO NW, we have calculated the correspond-ing energies (Table 7) using Eq. (3). Obviously, they arelarger for inner NW defects (Figure 2), since their coordi-nation number is larger than that for outer ones. Thesmallest formation energy of doped ZnO NWs has beenfound for outer CO dopant (3.3–3.4 eV per atom, irrespec-tively of defect concentration and dNW), analogously toCO defect in TiO2 NTs.[18] Values of Eform for the outer Agand N dopants are similar for the ~6 % concentration,while for the smaller ~3 % defect density, the former aremarkedly smaller. According to our simulations of dopedtitania NTs,[18] the larger the difference between thedopant and host ionic radii, the larger the relaxationaround the defect.

The energy diagrams, analogous to those presented forTiO2 nanotubes in Figures 3 and 5, are shown for differ-ent nanowire diameters and defect concentrations in Fig-ures 6 and 7, respectively. Since comparison of the elec-tronic structure of ZnO NWs for 3 % and 6 % defect con-centrations clearly shows a higher photocatalytic efficien-cy of nanostructures with higher concentration of dopantsper NW unit cell,[21] we constructed the energy diagramdepending on the values of the NW diameter, just for thefixed 6% concentration (Figure 6).

It allows us to predict that C-doped ZnO NWs showthe most promising suitability for water splitting under

the influence of visible light in the yellow-green rangearound 2.0–2.2 eV, which can occur when the NW diame-ter grows up to 3.0–3.5 nm while the concentration is~6%. In this case, 15 % efficiency of solar-light energyconversion can be achieved.[21] This result is even morepromising than that observed by us for CO +NO codopedTiO2(001) NTs.[18] Still, the eHOIL level being equal [email protected] eV is approaching the eO2=H2O level (@1.23 eV),close to the dissipation (d) limit of Eq. (2a). However,when lowering the C content to ~3% (Figure 7), theenergy gaps for the two thickest NWs are larger, androughly equal to 2.4 eV. The benefit of the lower carbonconcentration is the lower position of eHOIL, i.e., at a saferdistance from the oxidation level, overlap with which canlead to electron@hole recombination.[2]

Silver is a promising metal for ZnO doping, as studiedearlier[85–87] and confirmed in our calculations. Although

Table 7. Eform energies (in eV) as calculated using the hybrid PBE0 functional. The defect concentration in ZnO NWs is fixed at ~3% or~6%. The “inn” stands for the inner defect configuration, while “out” for that of outer defects (Figure 2).

NW Defect and its position in nanowire

Size C Ag N

out inn out inn out inn

defect concentration ~3%4W 4 3.37 –[a] 4.41 –[a] 5.39 –[a]

5W 5 3.34 –[a] 4.40 –[a] 5.33 –[a]

6W 6 3.30 –[a] 4.37 –[a] 5.29 –[a]

defect concentration ~6%4W 4 3.33 4.01 5.74 5.04 5.33 5.495W 5 3.36 4.22 4.29 4.59 4.17 5.526W 6 3.37 4.10 4.11 4.79 4.15 5.29

[a] In the case of ~ 3% concentration of inner defects, the calculations have been found to be unstable.

Figure 6. Energy diagram for pristine and structurally modifiedZnO nanowires with ~6 % defect content, depending on dNW. Thered and blue horizontal dotted lines correspond to the redoxeO2=H2 O and eHþ=H2

eH + /H2 potentials, respectively. The zero of theenergy scale corresponds to the standard hydrogen electrode(SHE) level.[13] Solid and dashed horizontal lines describe the eHOIL

and eLUIL levels, respectively. The upper filled rectangles correspondto the conduction bands, while the lower filled rectangles standfor the valence bands. Other details of the diagram are the sameas described in the caption of Figure 3.


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the position of the eHOIL level is rather unfavourable at~6% defect concentration, it moves downwards withgrowing dNW and also with decreasing Ag content. Un-fortunately, the lowest unoccupied eLUIL levels, adjacentto both the eHOIL and eO2=H2O levels (Figure 6), might pro-mote charge recombination.

For thinner ZnO NWs with ~6 % N content, eHOIL is lo-cated above the eO2=H2O level (Figure 6), which is a majordrawback.[2] For thicker NWs, eHOIL is located below thatlevel, while the Degap is too large to ensure efficient pho-tocatalysis. A more promising result has been obtainedfor N doping at ~3 % concentration (Figure 7). Here, thewidth of Degap exceeds 2.2 eV for thicker NWs. Althoughthe eHOIL level is slightly above the oxidation level, itshifts downwards with growing NW diameter, whichallows us to make an optimistic prediction, since resultsfor larger N-doped ZnO nanowires are rather relevant toreal structures.

7. Perspectives

We have constructed atomistic models of pristine anddoped anatase-structured TiO2 nanotubes of two differentmorphologies, as well as [0001]-oriented ZnO nanowireswith varied dNT and dNW diameters and defect concentra-tion, in order to perform hybrid DFT-HF calculations andto analyse their suitability for photocatalytic applications.We have considered anionic CO, NO, SO, and NO +SO

mono- and codopants, as well as cationic AgZn and FeTi

monodopants for simulations of TiO2 nanotubes and ZnOnanowires. When performing large-scale ab initio simula-tions, we have established the highest photocatalytic effi-ciency for NO +SO codoped anatase-type TiO2 NTs, aswell as CO monodoped wurtzite-type [0001]-oriented

ZnO NWs, corresponding to an optimal 15 % solarenergy conversion efficiency.

Comparing the results obtained by us recently withthose published elsewhere, we can conclude that thehybrid DFT+HF method used by us for large-scaleLCAO calculations on doped nanostructures of metaloxides, aiming at their suitability for photocatalytic appli-cations, can be properly used for further calculations onnew nanomaterials. We have established that electronic-state levels of 1D and 2D nanomaterials can be properlycompared with redox potential levels when using DFT-LCAO CRYSTAL code, since the absolute zero vacuumlevel is reproduced correctly in these calculations.

Since structural reproducibility of experimentally syn-thesized ZnO nanowires[87,106] is noticeably higher thanthat obtained so far for TiO2 nanotubes,[103,107] we do be-lieve that the suitability of ZnO NW-based photocatalystsis more reliable for practical applications. We are plan-ning to extend the number of simulated nanostructures,both pristine and doped, for a theoretical estimate oftheir photocatalytic applicability, as well as to comparethe calculated properties with those obtained for the cor-responding newly synthesized nanomaterials.

Since our simulations in the framework of theERA.Net RUS PLUS Project 237 WATERSPLIT are notlimited by ground-state calculations, we are planning: 1)to combine them with the time-dependent first-principlescalculations (TD DFT) as considered, e.g., in Ref. [23], toachieve a proper description of nanophotocatalysts in ex-cited states (e.g., to determine the absorption spectra ofdoped nanostructures and to predict the conditions neces-sary to promote the generation of electrons and holes byphotoexcitation); as well as 2) to perform nonadiabaticmolecular dynamics simulations, combined with TD-DFTcalculations, to investigate the charge-transfer processesat the surface of doped nanostructures immersed in anaqueous solution.

Acknowledgements

This study has been supported by the EC ERA.Net RUSPlus project No 237 WATERSPLIT. R. E. appreciates theassistance of St. Petersburg State University ComputerCenter in high-performance calculations. The authors areindebted to A. V. Bandura, A. Chesnokov, E. A. Koto-min, A. Kuzmin, B. Polyakov, and E. Spohr for stimulat-ing discussions. The technical assistance of A. Chesnokovis highly appreciated as well.

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Figure 7. Energy diagram for pristine and structurally modified 5 V5 ZnO nanowires with dNW &2.9 nm for each set of concentrations.The description of the graphical details and numbers is the sameas in the captions of Figures 3 and 6.


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Received: July 26, 2016Published online: December 12, 2016


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