[1] YIN X T, LV P, LI J et al. Nanostructured tungsten trioxide prepared at various growth temperatures for sensing applications[J]. Journal of Alloys and Compounds, 825, 154105(2020).

[2] NANDIYANTO A B D, OKTIANI R, RAGADHITA R et al. Amorphous content on the photocatalytic performance of micrometer-sized tungsten trioxide particles[J]. Arabian Journal of Chemistry, 13, 2912-2924(2020).

[3] HE X, WANG X Y, SUN B N et al. Synthesis of three- dimensional hierarchical furball-like tungsten trioxide microspheres for high performance supercapacitor electrodes[J]. RSC Advances, 10, 13437-13441(2020).

[4] HAI G J, HUANG J F, CAO L Y et al. Influence of oxygen deficiency on the synthesis of tungsten oxide and the photocatalytic activity for the removal of organic dye[J]. Journal of Alloys and Compounds, 690, 239-248(2017).

[5] LIU X F, ZHOU H, PEI S Z et al. Oxygen-deficient WO₃-_x nanoplate array film photoanode for efficient photoelectrocatalytic water decontamination[J]. Chemical Engineering Journal, 381, 122740(2020).

[7] QUAN H Q, GAO Y F, WANG W Z. Tungsten oxide-based visible light-driven photocatalysts: crystal and electronic structures and strategies for photocatalytic efficiency enhancement[J]. Inorganic Chemistry Frontiers, 7, 817-838(2020).

[8] PERSSON K[J]. Materials project. https://materialsproject.org/

[9] DEB S K. Opportunities and challenges in science and technology of WO₃ for electrochromic and related applications[J]. Solar Energy Materials and Solar Cells, 92, 245-258(2008).

[10] DING Y, YANG I S, LI Z Q et al. Nanoporous TiO₂ spheres with tailored textural properties: controllable synthesis, formation mechanism, and photochemical applications[J]. Progress in Materials Science, 109, 100620(2020).

[11] DONG P Y, HOU G H, XI X U et al. WO₃-based photocatalysts: morphology control, activity enhancement and multifunctional applications[J]. Environmental Science-Nano, 4, 539-557(2017).

[12] HAN L F, CHEN J L, ZHANG Y H et al. Facile synthesis of hierarchical carpet-like WO₃ microflowers for high NO₂ gas sensing performance[J]. Materials Letters, 210, 8-11(2018).

[13] LI Y S, TANG Z L, ZHANG J Y et al. Fabrication of vertical orthorhombic/hexagonal tungsten oxide phase junction with high photocatalytic performance[J]. Applied Catalysis B-Environmental, 207, 207-217(2017).

[14] HUNGE Y M, YADAV A A, MAHADIK M A et al. A highly efficient visible-light responsive sprayed WO₃/FTO photoanode for photoelectrocatalytic degradation of brilliant blue[J]. Journal of the Taiwan Institute of Chemical Engineers, 85, 273-281(2018).

[15] KARADENIZ S M, TATAR D, ERTUGRUL M et al. Structural, optical and electrochromic properties of WO₃ thin films prepared by chemical spray pyrolysis versus spin coating technique[J]. Spectroscopy and Spectral Analysis, 38, 2982-2988(2018).

[16] INAMDAR A I, CHAVAN H S, AHMED A A et al. Nanograin tungsten oxide with excess oxygen as a highly reversible anode material for high-performance Li-ion batteries[J]. Materials Letters, 215, 233-237(2018).

[17] SHENG J P, ZHANG L, DENG L et al. Fabrication of dopamine enveloped WO₃-_x quantum dots as single-NIR laser activated photonic nanodrug for synergistic photothermal/photodynamic therapy against cancer[J]. Chemical Engineering Journal, 383, 123071(2020).

[18] ZHAO L Y, XI X L, LIU Y S et al. Growth mechanism and visible-light-driven photocatalysis of organic solvent dependent WO₃ and nonstoichiometric WO₃-_x nanostructures[J]. Journal of the Taiwan Institute of Chemical Engineers, 115, 339-347(2020).

[19] ZHAO L Y, XI X L, LIU Y S et al. Facile synthesis of WO₃ micro/nanostructures by paper-assisted calcination for visible- light-driven photocatalysis[J]. Chemical Physics, 528, 110515(2020).

[20] FAN Y S, XI X L, LIU Y S et al. Growth mechanism of immobilized WO₃ nanostructures in different solvents and their visible-light photocatalytic performance[J]. Journal of Physics and Chemistry of Solids, 140, 109380(2020).

[21] MANTHIRAM K, ALIVISATOS A P. Tunable localized surface plasmon resonances in tungsten oxide nanocrystals[J]. Journal of the American Chemical Society, 134, 3995-3998(2012).

[22] KIMURA Y, IBANO K, UEHATA K et al. Improved hydrogen gas sensing performance of WO₃ films with fibrous nanostructured surface[J]. Applied Surface Science, 532, 147274(2020).

[23] LI D, HUANG W Q, XIE Z et al. Mechanism of enhanced photocatalytic activities on tungsten trioxide doped with sulfur: dopant-type effects[J]. Modern Physics Letters B, 30, 1650340(2016).

[24] QIN Y X, LIU M, YE Z H. A DFT study on WO₃ nanowires with different orientations for NO₂ sensing application[J]. Journal of Molecular Structure, 1076, 546-553(2014).

[25] CHEN Z J, CAO J X, YANG L W et al. The unique photocatalysis properties of a 2D vertical MoO₂ /WO₂ heterostructure: a first- principles study[J]. Journal of Physics D-Applied Physics, 51, 265106(2018).

[27] JIA Q Q, JI H M, BAI X. Selective sensing property of triclinic WO₃ nanosheets towards ultra-low concentration of acetone[J]. Journal of Materials Science-Materials in Electronics, 30, 7824-7833(2019).

[28] MA Y L, FENG B, LANG J Y et al. Synthesis of semimetallic tungsten trioxide for infrared light photoelectrocatalytic water splitting[J]. Journal of Physical Chemistry C, 123, 25833-25843(2019).

[30] DIRAC P A M[M]. The Principles of Quantum Mechanics, 1-22(1958).

[32] BORN M, HUANG K[M]. Dynamical Theory of Crystal Lattices, 104-113(1958).

[33] SLATER J C. Magnetic effects and the Hartree-Fock equation[J]. Physical Review, 82, 538-541(1951).

[36] KOCH W, HOLTHAUSEN M C. A chemist's guide to density functional theory[J]. Zeitschrift für Physik B Condensed Matter, 78, 317-323(2001).

[37] KOHN W, SHAM L J. Self-consistent equations including exchange and correlation effects[J]. Physical Review, 140, 1133-1138(1965).

[38] THOMAS H. The calculation of atomic fields[J]. Proceedings of the Cambridge Philosophical Society, 23, 542-548(1927).

[39] KOHN W. Nobel lecture: electronic structure of matter-wave functions and density functionals[J]. Reviews of Modern Physics, 71, 1253-1266(1999).

[40] FERMI E. Un metodo statistico per la determinazione di alcune Priorieta dell atome[J]. Rend. Accad. Naz. Lincei, 6, 602(1927).

[41] DIRAC P A M. Note on exchange phenomena in the thomas-fermi atom[J]. Proceedings of the Cambridge Philosophical Royal Society, 26, 376(1930).

[42] SLATER J C. A simplification of the hartree-fock method[J]. Self-Consistent Fields in Atoms, 81, 215-230(1975).

[43] PERDEW J P, CHEVARY J A, VOSKO S H et al. Atoms, molecules, solids, and surfaces-applications of the generalized gradient approximation for exchange and correlation[J]. Physical Review B, 46, 6671-6687(1992).

[45] VANDERBILT D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism[J]. Physical Review B, 41, 7892-7895(1990).

[46] BLÖCHL P E. Projector augmented-wave method[J]. Physical Review B Condens Matter, 50, 17953-17959(1994).

[47] HAMANN D R, SCHLÜTER M, CHIANG C. Norm-conserving pseudopotentials[J]. Physical Review Letters, 43, 1494-1497(1979).

[50] WEB V[online]. Psi-k-Ab initio(2021). http://psi-k.net/software/

[51] KAMINSKY W[online]. WinXMorph(2021). http://cad4.cpac.washington.edu/WinXMorphHome/WinXMorph.htm#opennewwindow

[52] MOMMA K[online]. Visualization for electronic and structural analysis(2021). http://www.jp-minerals.org/vesta/en/

[53] MAHAJAN S, JAGTAP S. Metal-oxide semiconductors for carbon monoxide (CO) gas sensing: a review[J]. Applied Materials Today, 18, 100483(2020).

[54] ZEB S, PENG X J, YUAN G Z et al. Controllable synthesis of ultrathin WO₃ nanotubes and nanowires with excellent gas sensing performance[J]. Sensors and Actuators B-Chemical, 305, 127435(2020).

[55] LIU D, REN X W, LI Y S et al. Nanowires-assembled WO₃ nanomesh for fast detection of ppb-level NO₂ at low temperature[J]. Journal of Advanced Ceramics, 9, 17-26(2020).

[56] OISON V, SAADI L, LAMBERT-MAURIAT C et al. Mechanism of CO and O₃ sensing on WO₃ surfaces: first principle study[J]. Sensors and Actuators B-Chemical, 160, 505-510(2011).

[57] ZHAO L H, TIAN F H, WANG X B et al. Mechanism of CO adsorption on hexagonal WO₃(001) surface for gas sensing: a DFT study[J]. Computational Materials Science, 79, 691-697(2013).

[58] JIN H, ZHOU H, ZHANG Y F. Insight into the mechanism of CO oxidation on WO₃(001) surfaces for gas sensing: a DFT study[J]. Sensors, 17, 1898(2017).

[59] TANG B L, JIANG G H, CHEN W X et al. First-principles study on hexagonal WO₃ for HCHO gas sensing application[J]. Acta Metallurgica Sinica-English Letters, 28, 772-780(2015).

[60] HAN X, YIN X H. Density functional theory study of the NO₂-sensing mechanism on a WO₃(001) surface: the role of surface oxygen vacancies in the formation of NO and NO₃[J]. Molecular Physics, 114, 3546-3555(2016).

[61] QIN Y X, LIU M, HUA D Y. First-principles study of the electronic structure and NO₂-sensing properties of Ti-doped W₁₈O₄₉ nanowire[J]. Acta Physica Sinica, 63, 207101(2014).

[62] QIN Y X, YE Z H. DFT study on interaction of NO₂ with the vacancy-defected WO₃ nanowires for gas-sensing[J]. Sensors and Actuators B-Chemical, 222, 499-507(2016).

[63] BAI S L, ZHANG K W, WANG L S et al. Synthesis mechanism and gas-sensing application of nanosheet-assembled tungsten oxide microspheres[J]. Journal of Materials Chemistry A, 2, 7927-7934(2014).

[64] YAKOVKIN I N, GUTOWSKI M. Driving force for the WO₃(001) surface relaxation[J]. Surface Science, 601, 1481-1488(2007).

[66] YANG H H, SUN H G, LI Q T et al. Structural, electronic, optical and lattice dynamic properties of the different WO₃ phases: first-principle calculation[J]. Vacuum, 164, 411-420(2019).

[68] ZHENG T T, SANG W, HE Z H et al. Conductive tungsten oxide nanosheets for highly efficient hydrogen evolution[J]. Nano Letters, 17, 7968-7973(2017).

[70] WANG F G, DI VALENTIN C, PACCHIONI G. Doping of WO₃ for photocatalytic water splitting: hints from density functional theory[J]. Journal of Physical Chemistry C, 116, 8901-8909(2012).

[71] ZHANG T, ZHU Z L, CHEN H N et al. Iron-doping-enhanced photoelectrochemical water splitting performance of nanostructured WO₃: a combined experimental and theoretical study[J]. Nanoscale, 7, 2933-2940(2015).

[72] HUANG W C, WANG J X, BIAN L et al. Oxygen vacancy induces self-doping effect and metalloid LSPR in non-stoichiometric tungsten suboxide synergistically contributing to the enhanced photoelectrocatalytic performance of WO₃-_x/TiO₂-_x heterojunction[J]. Physical Chemistry Chemical Physics, 20, 17268-17278(2018).

[73] ZHANG N, LI X Y, LIU Y F et al. Defective tungsten oxide hydrate nanosheets for boosting aerobic coupling of amines: synergistic catalysis by oxygen vacancies and bronsted acid sites[J]. Small, 13, 1701354(2017).

[74] ZHANG N, JALIL A, WU D X et al. Refining defect states in W₁₈O₄₉ by Mo doping: a strategy for tuning N₂ activation towards solar-driven nitrogen fixation[J]. Journal of the American Chemical Society, 140, 9434-9443(2018).

[75] ZHANG N, LONG R, GAO C et al. Recent progress on advanced design for photoelectrochemical reduction of CO₂ to fuels[J]. Science China-Materials, 61, 771-805(2018).

[76] LI M Q, ZHANG N, LONG R et al. PdPt alloy nanocatalysts supported on TiO₂: maneuvering metal-hydrogen interactions for light-driven and water-donating selective alkyne semihydrogenation[J]. Small, 13, 1604173(2017).

[77] WANG Z, WANG X Y, CONG S et al. Fusing electrochromic technology with other advanced technologies: a new roadmap for future development[J]. Materials Science & Engineering R-Reports, 140, 100524(2020).

[78] YAO Y J, ZHAO Q, WEI W et al. WO₃ quantum-dots electrochromism[J]. Nano Energy, 68, 104350(2020).

[79] LIN H, ZHOU F, LIU C P et al. Non-grotthuss proton diffusion mechanism in tungsten oxide dihydrate from first-principles calculations[J]. Journal of Materials Chemistry A, 2, 12280-12288(2014).

[80] HJELM A, GRANQVIST C G, WILLS J M. Electronic structure and optical properties of WO₃, LiWO₃, NaWO₃, and HWO₃[J]. Physical Review B, 54, 2436-2445(1996).

[81] WISEMAN P J, DICKENS P G. Neutron-diffraction studies of cubic tungsten bronzes[J]. Journal of Solid State Chemistry, 17, 91-100(1976).

[82] YANG S, CHA J, KIM J C et al. Monolithic interface contact engineering to boost optoelectronic performances of 2D semiconductor photovoltaic heterojunctions[J]. Nano Letters, 20, 2443-2451(2020).

[85] KOCER C P, GRIFFITH K J, GREY C P et al. Cation disorder and lithium insertion mechanism of Wadsley-Roth crystallographic shear phases from first principles[J]. Journal of the American Chemical Society, 141, 15121-15134(2019).

[86] KARIM N A, KAMARUDIN S K, SHYUAN L K et al. Study on the electronic properties and molecule adsorption of W₁₈O₄₉ nanowires as a catalyst support in the cathodes of direct methanol fuel cells[J]. Journal of Power Sources, 288, 461-472(2015).

[87] ZHANG Z F, CHEN J L, LI H B et al. Vapor-solid nanotube growth via sidewall epitaxy in an environmental transmission electron microscope[J]. Crystal Growth & Design, 17, 11-15(2017).

[88] ZHANG Z F, WANG Y, LI H B et al. Atomic-scale observation of vapor-solid nanowire growth via oscillatory mass transport[J]. ACS Nano, 10, 763-769(2016).

[89] ZHANG Z F, SHENG L P, CHEN L et al. Atomic-scale observation of pressure-dependent reduction dynamics of W₁₈O₄₉ nanowires using environmental TEM[J]. Physical Chemistry Chemical Physics, 19, 16307-16311(2017).

[90] CHEN L, LAM S, ZENG Q H et al. Effect of cation intercalation on the growth of hexagonal WO₃ nanorods[J]. Journal of Physical Chemistry C, 116, 11722-11727(2012).

[91] JIANG S, CHEKINI M, QU Z B et al. Chiral ceramic nanoparticles and peptide catalysis[J]. Journal of the American Chemical Society, 139, 13701-13712(2017).

[92] GU L J, MA C L, ZHANG X H et al. Populating surface-trapped electrons towards SERS enhancement of W₁₈O₄₉ nanowires[J]. Chemical Communications, 54, 6332-6335(2018).

[93] MEHMOOD F, PACHTER R, MURPHY N R et al. Effect of oxygen vacancies on the electronic and optical properties of tungsten oxide from first principles calculations[J]. Journal of Applied Physics, 120, 233105(2016).

[94] MIGAS D B, SHAPOSHNIKOV V L, RODIN V N et al. Tungsten oxides. I. Effects of oxygen vacancies and doping on electronic and optical properties of different phases of WO₃[J]. Journal of Applied Physics, 108, 093713(2010).

[95] SAI L W, TANG L L, HUANG X M et al. Lowest-energy structures of (WO₃)_n(2≤n≤12) clusters from first-principles global search[J]. Chemical Physics Letters, 544, 7-12(2012).

[96] HUANG X, ZHAI H J, LI J et al. On the structure and chemical bonding of tri-tungsten oxide clusters W₃O_n^- and W₃O_n (n=7-10): W₃O₈ as a potential molecular model for O-deficient defect sites in tungsten oxides[J]. Journal of Physical Chemistry A, 110, 85-92(2006).

[98] JIANG P G, XIAO Y Y, LIU W J et al. Hydrogen reduction characteristics of WO₃ based on density functional theory[J]. Results in Physics, 12, 896-902(2019).

[99] LIU W J, JIANG P G, XIAO Y Y et al. A study of the hydrogen adsorption mechanism of W₁₈O₄₉ using first-principles calculations[J]. Computational Materials Science, 154, 53-59(2018).