The potential of imogolite nanotubes as (co-)photocatalysts: a linear-scaling density functional theory study

We report a linear-scaling density functional theory (DFT) study of the structure, wall-polarization absolute band-alignment and optical absorption of several, recently synthesized, open-ended imogolite (Imo) nanotubes (NTs), namely single-walled (SW) aluminosilicate (AlSi), SW aluminogermanate (AlGe), SW methylated aluminosilicate (AlSi-Me), and double-walled (DW) AlGe NTs. Simulations with three different semi-local and dispersion-corrected DFT-functionals reveal that the NT wall-polarization can be increased by nearly a factor of four going from SW-AlSi-Me to DW-AlGe. Absolute vacuum alignment of the NT electronic bands and comparison with those of rutile and anatase TiO2 suggest that the NTs may exhibit marked propensity to both photo-reduction and hole-scavenging. Characterization of the NTs’ band-separation and optical properties reveal the occurrence of (near-)UV inside–outside charge-transfer excitations, which may be effective for electron–hole separation and enhanced photocatalytic activity. Finally, the effects of the NTs’ wall-polarization on the absolute alignment of electron and hole acceptor states of interacting water (H2O) molecules are quantified and discussed.

[1]  Mahesh Datt Bhatt,et al.  Recent theoretical progress in the development of photoanode materials for solar water splitting photoelectrochemical cells , 2015 .

[2]  K. Yao,et al.  Nanoconfinement induced crystal orientation and large piezoelectric coefficient in vertically aligned P(VDF-TrFE) nanotube array , 2015, Scientific Reports.

[3]  A. Mostofi,et al.  Large-scale density functional theory simulation of inorganic nanotubes: a case study on Imogolite nanotubes , 2015, Materials Research Innovations.

[4]  Zhong Lin Wang,et al.  Enhanced ferroelectric-nanocrystal-based hybrid photocatalysis by ultrasonic-wave-generated piezophototronic effect. , 2015, Nano letters.

[5]  P. Launois,et al.  Hybrid, Tunable-Diameter, Metal Oxide Nanotubes for Trapping of Organic Molecules , 2015 .

[6]  S. Bu,et al.  Strain effect on the visible emission in PbTiO3 nanotubes: Template and wall-thickness dependence , 2015 .

[7]  B. Liu,et al.  Charge separation between wurtzite ZnO polar {0 0 1} surfaces and their enhanced photocatalytic activity , 2015 .

[8]  Thomas Kirchartz,et al.  Classification of solar cells according to mechanisms of charge separation and charge collection. , 2015, Physical chemistry chemical physics : PCCP.

[9]  J. Sun,et al.  Recent developments in heterogeneous photocatalytic water treatment using visible light-responsive photocatalysts: a review , 2015 .

[10]  Jie Wang,et al.  Giant electrocaloric effect in ferroelectric nanotubes near room temperature , 2015, Scientific Reports.

[11]  Damar Yoga Kusuma,et al.  Polarization Orientation, Piezoelectricity, and Energy Harvesting Performance of Ferroelectric PVDF‐TrFE Nanotubes Synthesized by Nanoconfinement , 2014 .

[12]  David Volbers,et al.  Redox shuttle mechanism enhances photocatalytic H2 generation on Ni-decorated CdS nanorods. , 2014, Nature materials.

[13]  M. Payne,et al.  Does water dope carbon nanotubes? , 2014, The Journal of chemical physics.

[14]  Chris-Kriton Skylaris,et al.  Hybrid MPI-OpenMP Parallelism in the ONETEP Linear-Scaling Electronic Structure Code: Application to the Delamination of Cellulose Nanofibrils. , 2014, Journal of chemical theory and computation.

[15]  Naresh Kumar,et al.  Structural incorporation of iron into Ge–imogolite nanotubes: a promising step for innovative nanomaterials , 2014 .

[16]  Yue Zheng,et al.  Ab initio study on mechanical-bending-induced ferroelectric phase transition in ultrathin perovskite nanobelts , 2014 .

[17]  Jennifer D. Schuttlefield,et al.  Renewable energy based catalytic CH4 conversion to fuels , 2014 .

[18]  A. Ng,et al.  Strategies for improving the efficiency of semiconductor metal oxide photocatalysis , 2014 .

[19]  G. Pacchioni,et al.  Spectroscopic properties of doped and defective semiconducting oxides from hybrid density functional calculations. , 2014, Accounts of chemical research.

[20]  P. Launois,et al.  Hexagonalization of Aluminogermanate Imogolite Nanotubes Organized into Closed-Packed Bundles , 2014 .

[21]  A. Selloni,et al.  Adsorption and reactions of O2 on anatase TiO2. , 2014, Accounts of chemical research.

[22]  Tong-Yi Zhang,et al.  Chiral selectivity of improper ferroelectricity in single-wall PbTiO 3 nanotubes , 2014 .

[23]  Yi‐Jun Xu,et al.  One-dimensional nanostructure based materials for versatile photocatalytic applications , 2014 .

[24]  M. T. García-González,et al.  Preparation and characterization of a single-walled aluminosilicate nanotube-iron oxide composite: Its applications to removal of aqueous arsenate , 2014 .

[25]  Christopher W. Jones,et al.  Direct synthesis of single-walled aminoaluminosilicate nanotubes with enhanced molecular adsorption selectivity , 2014, Nature Communications.

[26]  Juan M. Coronado,et al.  Photocatalytic materials: recent achievements and near future trends , 2014 .

[27]  A. Troisi,et al.  Understanding the Microscopic Origin of the Very High Charge Mobility in PBTTT: Tolerance of Thermal Disorder , 2014 .

[28]  Liyan Wu,et al.  Perovskite oxides for visible-light-absorbing ferroelectric and photovoltaic materials , 2013, Nature.

[29]  J. Rose,et al.  Single-step formation of micron long (OH)3Al2O3Ge(OH) imogolite-like nanotubes. , 2013, Chemical communications.

[30]  S. Dunn,et al.  Effect of Ferroelectricity on Solar-Light-Driven Photocatalytic Activity of BaTiO3—Influence on the Carrier Separation and Stern Layer Formation , 2013 .

[31]  N. Nuraje,et al.  Perovskite ferroelectric nanomaterials. , 2013, Nanoscale.

[32]  A. Walsh,et al.  Band alignment of rutile and anatase TiO₂. , 2013, Nature materials.

[33]  Ueli Heiz,et al.  Cluster size effects in the photocatalytic hydrogen evolution reaction. , 2013, Journal of the American Chemical Society.

[34]  E. Garrone,et al.  Surface properties of alumino-silicate single-walled nanotubes of the imogolite type. , 2013, Physical chemistry chemical physics : PCCP.

[35]  A. Fujishima,et al.  Visible-light-driven photodegradation of acetaldehyde gas catalyzed by aluminosilicate nanotubes and Cu(II)-grafted TiO2 composites , 2013 .

[36]  K. No,et al.  Visualization of three dimensional domain structures in ferroelectric PbTiO3 nanotubes , 2013 .

[37]  K. Maeda Z-Scheme Water Splitting Using Two Different Semiconductor Photocatalysts , 2013 .

[38]  Yuelei Zhao,et al.  Butterfly-shaped multiferroic BiFeO3@BaTiO3 core–shell nanotubes: the interesting structural, multiferroic, and optical properties , 2013, Journal of Materials Science: Materials in Electronics.

[39]  Yehea Ismail,et al.  Recent advances in the use of density functional theory to design efficient solar energy-based renewable systems , 2013 .

[40]  T J Zuehlsdorff,et al.  Linear-scaling time-dependent density-functional theory in the linear response formalism. , 2013, The Journal of chemical physics.

[41]  H. A. Duarte,et al.  Imogolite-like nanotubes: structure, stability, electronic and mechanical properties of the phosphorous and arsenic derivatives. , 2013, Physical chemistry chemical physics : PCCP.

[42]  Nicholas D M Hine,et al.  Electrostatic considerations affecting the calculated HOMO–LUMO gap in protein molecules , 2013, Journal of physics. Condensed matter : an Institute of Physics journal.

[43]  Robert A. Evarestov,et al.  BaTiO3‐based nanolayers and nanotubes: First‐principles calculations , 2013, J. Comput. Chem..

[44]  S. Bu,et al.  Effects of Wall Thickness on Morphology and Structure of Lead Titanate Nanotubes , 2013 .

[45]  A. Corma,et al.  Deep UV photocatalytic activation of ethane on silica surfaces , 2012 .

[46]  J. Feldmann,et al.  Size-selected subnanometer cluster catalysts on semiconductor nanocrystal films for atomic scale insight into photocatalysis. , 2012, Nano letters.

[47]  E. Garrone,et al.  CO2 Adsorption on Aluminosilicate Single-Walled Nanotubes of Imogolite Type , 2012 .

[48]  G. S. Martynková,et al.  Clay Minerals in Nature - Their Characterization, Modification and Application , 2012 .

[49]  Avelino Corma,et al.  185 nm photoreduction of CO2 to methane by water. Influence of the presence of a basic catalyst. , 2012, Journal of the American Chemical Society.

[50]  H. Beckham,et al.  Defect Structures in Aluminosilicate Single-Walled Nanotubes: A Solid-State Nuclear Magnetic Resonance Investigation , 2012 .

[51]  Michiel Sprik,et al.  Alignment of electronic energy levels at electrochemical interfaces. , 2012, Physical chemistry chemical physics : PCCP.

[52]  Chris-Kriton Skylaris,et al.  Pulay forces from localized orbitals optimized in situ using a psinc basis set. , 2012, The Journal of chemical physics.

[53]  H. Schwarz,et al.  Thermal hydrogen-atom transfer from methane: the role of radicals and spin states in oxo-cluster chemistry. , 2012, Angewandte Chemie.

[54]  Stefan Fischbach,et al.  Hole scavenger redox potentials determine quantum efficiency and stability of Pt-decorated CdS nanorods for photocatalytic hydrogen generation , 2012 .

[55]  H. Otsuka,et al.  Application of imogolite clay nanotubes in organic-inorganic nanohybrid materials , 2012 .

[56]  E. Garrone,et al.  Physico-Chemical Properties of Imogolite Nanotubes Functionalized on Both External and Internal Surfaces , 2012 .

[57]  L. Olivi,et al.  Physico-chemical control over the single- or double-wall structure of aluminogermanate imogolite-like nanotubes. , 2012, Journal of the American Chemical Society.

[58]  T. Kitamura,et al.  Absence of ferroelectric critical size in ultrathin PbTiO3 nanotubes: a density-functional theory study. , 2012, Physical review letters.

[59]  A. Corma,et al.  Conversion of methane into C1 oxygenates by deep-UV photolysis on solid surfaces: influence of the nature of the solid and optimization of photolysis conditions. , 2012, Chemistry.

[60]  R. Guerrero-Ferreira,et al.  Shaping single-walled metal oxide nanotubes from precursors of controlled curvature. , 2012, Nano letters.

[61]  Stefan Fischbach,et al.  Delayed photoelectron transfer in Pt-decorated CdS nanorods under hydrogen generation conditions. , 2012, Small.

[62]  Shuxin Ouyang,et al.  Nano‐photocatalytic Materials: Possibilities and Challenges , 2012, Advanced materials.

[63]  M. Alexe,et al.  One-Dimensional Ferroelectrics: Nanowires and Nanotubes , 2012 .

[64]  A. Corma,et al.  Selective, room-temperature transformation of methane to C1 oxygenates by deep UV photolysis over zeolites. , 2011, Journal of the American Chemical Society.

[65]  Nicholas D. M. Hine,et al.  Calculating optical absorption spectra for large systems using linear-scaling density functional theory , 2011, 1109.3341.

[66]  Mari-Ann Einarsrud,et al.  One‐Dimensional Nanostructures of Ferroelectric Perovskites , 2011, Advanced materials.

[67]  B. Teng,et al.  Dynamic properties of phase diagram in cylindrical ferroelectric nanotubes , 2011 .

[68]  Chris-Kriton Skylaris,et al.  Electrostatic interactions in finite systems treated with periodic boundary conditions: application to linear-scaling density functional theory. , 2011, The Journal of chemical physics.

[69]  D. Bowler,et al.  methods in electronic structure calculations , 2011, Reports on progress in physics. Physical Society.

[70]  A. Rogach,et al.  Hybrid Colloidal Heterostructures of Anisotropic Semiconductor Nanocrystals Decorated with Noble Metals: Synthesis and Function , 2011 .

[71]  M. Robinson,et al.  Accurate ionic forces and geometry optimization in linear-scaling density-functional theory with local orbitals , 2011, 1103.5869.

[72]  Christopher W. Jones,et al.  Single-Walled Aluminosilicate Nanotubes with Organic-Modified Interiors , 2011 .

[73]  H. Beckham,et al.  Formation of single-walled aluminosilicate nanotubes from molecular precursors and curved nanoscale intermediates. , 2011, Journal of the American Chemical Society.

[74]  J. Rose,et al.  Growth kinetic of single and double-walled aluminogermanate imogolite-like nanotubes: an experimental and modeling approach. , 2011, Physical chemistry chemical physics : PCCP.

[75]  M. Tagliabue,et al.  Synthesis and characterization of hybrid organic/inorganic nanotubes of the imogolite type and their behaviour towards methane adsorption. , 2011, Physical chemistry chemical physics : PCCP.

[76]  X. Gonze,et al.  Implementation of techniques for computing optical properties in 0–3 dimensions, including a real-space cutoff, in ABINIT , 2010 .

[77]  R. Orlando,et al.  Structure and energetics of imogolite: a quantum mechanical ab initio study with B3LYP hybrid functional , 2010 .

[78]  D. Kang,et al.  Facile synthesis of core–shell SnO2/V2O5 nanowires and their efficient photocatalytic property , 2010 .

[79]  Mohammad. Rasul,et al.  Heterogeneous photocatalytic degradation of phenols in wastewater: A review on current status and developments , 2010 .

[80]  Yong Zhou,et al.  High-yield synthesis of ultralong and ultrathin Zn2GeO4 nanoribbons toward improved photocatalytic reduction of CO2 into renewable hydrocarbon fuel. , 2010, Journal of the American Chemical Society.

[81]  Andrey L. Rogach,et al.  Colloidal CdS nanorods decorated with subnanometer sized Pt clusters for photocatalytic hydrogen generation , 2010 .

[82]  K. Domen,et al.  Photocatalytic Water Splitting: Recent Progress and Future Challenges , 2010 .

[83]  Christopher W. Jones,et al.  Dehydration, dehydroxylation, and rehydroxylation of single-walled aluminosilicate nanotubes. , 2010, ACS nano.

[84]  Jinlong Zhang,et al.  Recent advances in visible light-responsive titanium oxide-based photocatalysts , 2010 .

[85]  A. Manivannan,et al.  Shape-enhanced photocatalytic activity of single-crystalline anatase TiO(2) (101) nanobelts. , 2010, Journal of the American Chemical Society.

[86]  C. Saint,et al.  Recent developments in photocatalytic water treatment technology: a review. , 2010, Water research.

[87]  George Kenanakis,et al.  Light-induced photocatalytic degradation of stearic acid by c-axis oriented ZnO nanowires , 2010 .

[88]  L. Olivi,et al.  Formation and Growth Mechanisms of Imogolite-Like Aluminogermanate Nanotubes , 2010 .

[89]  Michikazu Hara,et al.  Heterogeneous photocatalytic cleavage of water , 2010 .

[90]  E. Larquet,et al.  Evidence of double-walled Al-Ge imogolite-like nanotubes. a cryo-TEM and SAXS investigation. , 2010, Journal of the American Chemical Society.

[91]  F. Alvarez-Ramírez First Principles Studies of Fe-Containing Aluminosilicate and Aluminogermanate Nanotubes. , 2009, Journal of chemical theory and computation.

[92]  J. M. Coronado,et al.  Development of alternative photocatalysts to TiO2: Challenges and opportunities , 2009 .

[93]  E. Fujita,et al.  Molecular approaches to the photocatalytic reduction of carbon dioxide for solar fuels. , 2009, Accounts of chemical research.

[94]  Yingpu Bi,et al.  In situ oxidation synthesis of Ag/AgCl core-shell nanowires and their photocatalytic properties. , 2009, Chemical communications.

[95]  M. A. Rauf,et al.  Fundamental principles and application of heterogeneous photocatalytic degradation of dyes in solution , 2009 .

[96]  Yueyuan Y. Xia,et al.  Energetic Minimum Structures of Imogolite Nanotubes: A First-Principles Prediction , 2009 .

[97]  Nicholas D. M. Hine,et al.  Linear-scaling density-functional theory with tens of thousands of atoms: Expanding the scope and scale of calculations with ONETEP , 2009, Comput. Phys. Commun..

[98]  P. Blaha,et al.  Accurate band gaps of semiconductors and insulators with a semilocal exchange-correlation potential. , 2009, Physical review letters.

[99]  Li‐Min Liu,et al.  The interaction between adsorbed OH and O2 on TiO2 surfaces , 2009 .

[100]  A. Zunger,et al.  Polaronic Hole Localization and Multiple Hole Binding of Acceptors in Oxide Wide-Gap Semiconductors , 2009, 0905.0018.

[101]  S.-W. Cheong,et al.  Switchable Ferroelectric Diode and Photovoltaic Effect in BiFeO3 , 2009, Science.

[102]  A. Troisi,et al.  Effect of the intermolecular thermal motions on the tail of the electronic density of states in polyacene crystals , 2009 .

[103]  J. Zhan,et al.  Synthesis, Optical Properties, and Photocatalytic Activity of One-Dimensional CdS@ZnS Core-Shell Nanocomposites , 2009, Nanoscale research letters.

[104]  Xianzhi Fu,et al.  Synthesis and photocatalytic activity of Zn2GeO4 nanorods for the degradation of organic pollutants in water. , 2008, ChemSusChem.

[105]  A. Fujishima,et al.  TiO2 photocatalysis and related surface phenomena , 2008 .

[106]  S. Louie,et al.  Electronic energy levels of weakly coupled nanostructures: C60-metal interfaces. , 2008, Physical review letters.

[107]  J. Woicik,et al.  Synthesis of large quantities of single-walled aluminogermanate nanotube. , 2008, Journal of the American Chemical Society.

[108]  Young Joon Hong,et al.  Photocatalysis using GaN nanowires. , 2008, ACS nano.

[109]  A. Fisher,et al.  Hydroxyl vacancies in single-walled aluminosilicate and aluminogermanate nanotubes , 2008, Journal of physics. Condensed matter : an Institute of Physics journal.

[110]  Hélio A. Duarte,et al.  Imogolite nanotubes: stability, electronic, and mechanical properties. , 2007, ACS nano.

[111]  K. Gray,et al.  The solid–solid interface: Explaining the high and unique photocatalytic reactivity of TiO2-based nanocomposite materials , 2007 .

[112]  F. Alvarez-Ramírez Ab initiosimulation of the structural and electronic properties of aluminosilicate and aluminogermanate natotubes with imogolite-like structure , 2007 .

[113]  J. Jang,et al.  Solvothermal Synthesis of CdS Nanowires for Photocatalytic Hydrogen and Electricity Production , 2007 .

[114]  Alexander L. Shluger,et al.  Trapping, self-trapping and the polaron family , 2007 .

[115]  S. Nair,et al.  Short, highly ordered, single-walled mixed-oxide nanotubes assemble from amorphous nanoparticles. , 2007, Journal of the American Chemical Society.

[116]  Georg Kresse,et al.  Erratum: “Screened hybrid density functionals applied to solids” [J. Chem. Phys. 124, 154709 (2006)] , 2006 .

[117]  Stefan Grimme,et al.  Semiempirical GGA‐type density functional constructed with a long‐range dispersion correction , 2006, J. Comput. Chem..

[118]  Arash A. Mostofi,et al.  ONETEP: linear‐scaling density‐functional theory with local orbitals and plane waves , 2006 .

[119]  S. Nair,et al.  Strain energy minimum and vibrational properties of single-walled aluminosilicate nanotubes , 2006 .

[120]  A. Nitzan Chemical Dynamics in Condensed Phases: Relaxation, Transfer, and Reactions in Condensed Molecular Systems , 2006 .

[121]  Arash A. Mostofi,et al.  Elimination of basis set superposition error in linear-scaling density-functional calculations with local orbitals optimised in situ , 2006 .

[122]  J. Paier,et al.  Screened hybrid density functionals applied to solids. , 2006, The Journal of chemical physics.

[123]  Alessandro Troisi,et al.  Charge-transport regime of crystalline organic semiconductors: diffusion limited by thermal off-diagonal electronic disorder. , 2006, Physical review letters.

[124]  Richard L. Martin,et al.  Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional. , 2005, The Journal of chemical physics.

[125]  S. Nair,et al.  Phenomenology of the growth of single-walled aluminosilicate and aluminogermanate nanotubes of precise dimensions , 2005 .

[126]  M. Payne,et al.  Using ONETEP for accurate and efficient density functional calculations , 2005 .

[127]  W. Kohn,et al.  Nearsightedness of electronic matter. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[128]  Chris-Kriton Skylaris,et al.  Introducing ONETEP: linear-scaling density functional simulations on parallel computers. , 2005, The Journal of chemical physics.

[129]  Ralf B. Wehrspohn,et al.  Nanoshell tubes of ferroelectric lead zirconate titanate and barium titanate , 2003 .

[130]  Hisayoshi Kobayashi,et al.  Photocatalytic activity for water decomposition of indates with octahedrally coordinated d10 configuration. II. Roles of geometric and electronic structures , 2003 .

[131]  Arash A. Mostofi,et al.  Nonorthogonal generalized Wannier function pseudopotential plane-wave method , 2002 .

[132]  L. Reining,et al.  Electronic excitations: density-functional versus many-body Green's-function approaches , 2002 .

[133]  Gregory S. Tschumper,et al.  Atomic and molecular electron affinities: photoelectron experiments and theoretical computations. , 2002, Chemical reviews.

[134]  A. Shluger,et al.  Thermal fluctuations, localization, and self-trapping in a polar crystal: Combined shell-model molecular dynamics and quantum chemical approach , 2001 .

[135]  J. Gustafsson The Surface Chemistry of Imogolite , 2001 .

[136]  D. Vanderbilt,et al.  Exponential decay properties of Wannier functions and related quantities. , 2001, Physical review letters.

[137]  G. Pacchioni,et al.  Theoretical description of hole localization in a quartz Al center: The importance of exact electron exchange , 2000 .

[138]  Sohrab Ismail-Beigi,et al.  LOCALITY OF THE DENSITY MATRIX IN METALS, SEMICONDUCTORS, AND INSULATORS , 1999 .

[139]  Bernd G. Pfrommer,et al.  Relaxation of Crystals with the Quasi-Newton Method , 1997 .

[140]  Burke,et al.  Generalized Gradient Approximation Made Simple. , 1996, Physical review letters.

[141]  Kohn,et al.  Density functional and density matrix method scaling linearly with the number of atoms. , 1996, Physical review letters.

[142]  Hernández,et al.  Self-consistent first-principles technique with linear scaling. , 1995, Physical review. B, Condensed matter.

[143]  A. Philipse,et al.  Synthesis of platinum nanoparticles in aqueous host dispersions of inorganic (imogolite) rods , 1994 .

[144]  T. Arias,et al.  Iterative minimization techniques for ab initio total energy calculations: molecular dynamics and co , 1992 .

[145]  Read,et al.  Calculation of optical matrix elements with nonlocal pseudopotentials. , 1991, Physical review. B, Condensed matter.

[146]  Scheffler,et al.  Analysis of separable potentials. , 1991, Physical review. B, Condensed matter.

[147]  John P. Perdew,et al.  Physical Content of the Exact Kohn-Sham Orbital Energies: Band Gaps and Derivative Discontinuities , 1983 .

[148]  M. Schlüter,et al.  Density-Functional Theory of the Energy Gap , 1983 .

[149]  G. Nenciu Existence of the exponentially localised Wannier functions , 1983 .

[150]  J. Perdew,et al.  Density-Functional Theory for Fractional Particle Number: Derivative Discontinuities of the Energy , 1982 .

[151]  M. Wilson,et al.  Detection of imogolite in soils using solid state 29Si NMR , 1982, Nature.

[152]  M. Russell,et al.  Surface Properties of Allophane, Halloysite, and Imogolite , 1982 .

[153]  S. Wada,et al.  SYNTHETIC ALLOPHANE AND IMOGOLITE , 1979 .

[154]  J. Janak,et al.  Proof that ? E /? n i =e in density-functional theory , 1978 .

[155]  V. Farmer,et al.  Imogolite, a Hydrated Aluminium Silicate of Tubular Structure , 1972 .

[156]  J. D. Cloizeaux Analytical Properties of n-Dimensional Energy Bands and Wannier Functions , 1964 .

[157]  J. D. Cloizeaux,et al.  Energy Bands and Projection Operators in a Crystal: Analytic and Asymptotic Properties , 1964 .

[158]  R. Mcweeny Some Recent Advances in Density Matrix Theory , 1960 .

[159]  Walter Kohn,et al.  Analytic Properties of Bloch Waves and Wannier Functions , 1959 .

[160]  R. S. Mulliken Electronic Population Analysis on LCAO–MO Molecular Wave Functions. I , 1955 .

[161]  G. Ciamician,et al.  THE PHOTOCHEMISTRY OF THE FUTURE. , 1912, Science.

[162]  Martin Hangaard Hansen,et al.  Towards first principles modeling of electrochemical electrode-electrolyte interfaces , 2015 .

[163]  Yaodong Yang,et al.  Silver-modified nanosized ferroelectrics as a novel photocatalyst. , 2015, Small.

[164]  Ying Yang,et al.  Photocatalytic mechanisms of modified titania under visible light , 2011 .

[165]  Anders Hagfeldt,et al.  Light-Induced Redox Reactions in Nanocrystalline Systems , 1995 .

[166]  S. Martin,et al.  Environmental Applications of Semiconductor Photocatalysis , 1995 .

[167]  A. Bard Photoelectrochemistry and heterogeneous photo-catalysis at semiconductors , 1979 .