Abstract
Herein, we find the most active oxygen atom (i.e., O1) is gradually bonded with proton, and formation energy decreases until all O1 atoms are completely bonded with protons. Then, protons gradually bond with the second and third highest active oxygen atoms (i.e., O2 and O3), but the energy released by forming covalent bonds of H–O2 and H–O3 is not as high as that released by formation of H–O1 bonds. Proton involving in H–O3 covalent bond forms H-bond with O1 again (i.e., O3–H⋯O1), which makes interaction between TiO6− octahedron getting enhanced. More interesting, we find the band gap of Na3-xHxTi4O9 exhibits even-odd oscillation behavior. Such an even-odd oscillation maybe related to the activity of Ti atoms in single rutile-type octahedron. These findings demonstrate new insights for further designing and synthesizing functionalized titanate materials by engineering proton concentration and provide deep insights into understanding regulation of titanates.
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