A1(a).  From slide 27 of Ref. [3]. The upper two rows gives the abbreviated figure representation of electrically neutral water molecules located on the lattice points of the structure of the extended bulk water (Cubic Ice and Water), with two physical spaces, the lattice space containing transition pathways joining two proton trap sites, and the interstitial space, shown as square spaces of edge $a_{\rm O-O }=\ \sim $3 A, but actually hexagonal tunnels in both the 3-D cubic ice and water and also the larger hexagonal tunnels in 3-D hexagonal ice and water. The two identical lower outside figures (enlarged 400%), each contains one water molecule, to show the detailed contents: (ⅰ) the positively charged oxygen core, O$^{6+}$, with only the two 1s electrons and not the two 2s and four 4p or six valence electrons (ⅱ) eight valence electrons (brown color filled circles, from the six valence electrons of the oxygen and two valence electrons, each from one of the two hydrogen atoms) and (ⅲ) four proton vacancies or four proton traps as four mid-size red circles; two are filled in blue: occupied by two protons in the four adjacent tetrahedral locations. The two proton traps or vacancies on each of the four tetrahedrally located oxygen-oxygen bonds are represented by $\mbox{O﹕}○\;\;○:\mbox{O}$. They are shown in the upper two rows and the lower mid figure (100%) as, $\mbox{O}$: ● ○﹕ $\mbox{O}$, approximately scaled with the experimental interatomic distances of $d_{\rm O-H}$ $=$ 1 A (1.001 A) and $d_{\rm O-O}$ $=$ 3 A (2.760 A), but the two small circles ●○, are not as distinct from the two larger outer circle in this $\underline {\text{our-first-iteration}}$ trial, therefore, they have been replaced as squares in all subsequent figures as $\mbox{O}$:$\square\square$:$\mbox{O}$ to meet our at one glance (A1G) criteria. In order to simplify the theoretical analysis of water A1G, the chemical letter formula of this immobile and electrically neutral water molecule is abbreviated by (H$_{2}$O)$^{0}\equiv $ V$^{0\pm }$ where the exponent 0$\pm $ indicates electrical dipole from distributed positive and negative charge densities, with net zero charge when viewed at a distance.

A1(b).  From slide 28 of Ref. [3]. The upper two rows are the same as those in the previous figure, Fig. A1(a). The lower two outside figures (enlarged 400%), each contains one water molecule, to show the detailed contents: (ⅰ) the positively charged oxygen core, O$^{6+}$, with only the two 1s electrons and not the two 2s and four 4p or six valence electrons (ⅱ) eight valence electrons (brown color filled circles, six valence electrons from the oxygen and two valence electrons from the two hydrogen atoms) and (ⅲ) four proton vacancies or four proton traps (four mid-size red circles), and on the left, three filled, occupied by three protons, while on the right, only one filled, occupied by one proton. In order to make the theoretical analysis of water tractable A1G, the chemical symbols, of this immobile and electrically neutral water molecule before trapping one more proton, is abbreviated by (H$_{2}$O)$^{0\pm }$ as explained in the previous figure, Fig. 1(a). After a proton is trapped, shown by the lower left picture, its chemical symbol is abbreviated by (H$_{3}$O)$^{1+}$$\equiv $V$^{1+}$, from the binding of p$^{+}$ to (H$_{2}$O)$^{0}$ or V$^{0}$ expressed by the equation (H$_{2}$O)$^{0 }$ $+$ p$^{+} \equiv $ V$^{0}$ $+$ p$^{+} \leftrightarrow $ (H$_{3}$O)$^{1+}\equiv $ V$^{1+}$; and as a molecular ion, it will not diffusion or drift much due to the heavy oxygen mass, but more so from not breaking the three hydrogen bonds and one oxygen lone pair bond to the four adjacent oxygen of the four water molecules, H$_{2}$O, such that the transport-transition process, from one of the three p$^{+}$ to break loose from (H$_{3}$O)$^{1+}$$\equiv $V$^{1+}$, jump over to a neighbor (H$_{2}$O)$^{0}$$\equiv $V$^{0}$ and be trapped by it to convert it to (H$_{3}$O)$^{1+}$, is preferred. During the transit between detrap and trap, the proton is also scattered by the vibrating O and H$_{2}$O, giving the phonon-scattering limited proton mobility. This transport of a proton, or positive quasi-proton, in water, is trapping limited drift-diffusion, and given the symbol p$^{+}$, to distinguish it from the ionized not-trapped hydrogen atom, represented by H$^{+}$. This local microscopic description, commonly used by molecular orbital theory, must be randomized to the whole water volume while considering statistical distribution at thermodynamic equilibrium.

A2.  from our 1991-1996 3-volume textbook, $\mathit{\boldsymbol{Fundamentals of Solid-State Electronics, Solution Manual}}$, Appendix $\textbf{TRANSISTOR RELIABILITY}$, Section 930 ACCEPTOR HYDROGENATION, Fig. 931.3 on page 146. Published by World Scientific, 1996. This figure shows a sketched electron density contour (enclosing, say 50% or $X$%, of electrical charge) employed by the conventional chemical bond model diagram of the molecular orbital theory. The contour is omitted in our chemical bond figures given in this report and in all the slides of our first presentation^[3], in order to ease the observations of the electron-pair bonds, which are further omitted in order to show the trapping transport pathways of the protons.

A3.  From slide 12 of Ref. [3], captioned by BJ. The first encounter of water physics was by the senior author (TS) 55 years ago when semiconductor technology development began. Recently, TS described to BJ his first contact to semiconductor chemistry during the selection of this figure for our first public report of our studies on water-physics^[3]. The full citation of this book is as follows: Norman Bruce Hannay (editor, Bell Telephone Laboratories), $\mathit{\boldsymbol{Semiconductors}}$, American Chemical Society (ACS) Monograph Series No. 140, Reinhold Publishing Company, New York, Chapman & Hall, Ltd, London, 767pp, 1959. This figure appeared on page 196 of Chapter 5, ${\bf{Defect\;Interactions\;in\; Semiconductors}}$, by Calvin Souther Fuller (Bell Telephone Laboratories). In 1959, TS was a senior member of technical staff at the Shockley Transistor Corporation. On a Monday morning review meeting, when this book was released by the publisher, William Shockley walked into his Monday morning staff meeting on the status of previous assignments and on new assignments, and he exclaimed in the hallway with this book in his hand, about the importance of this figure and similarity between water and the semiconductors such as silicon and germanium. Nine years earlier, in 1950, as the Director of Solid-State Electronics of the American Telephone and Telegraph Bell Telephone Laboratories, William Shockley published his monograph, ${\bf {Electrons \;and\; Holes\; in \;Semiconductors \;with \;Applications\; to \;Transistors \;Electronic}}$, and established the fundamentals of semiconductor physics by the quantum mechanics theory and also reduced the theory to the practical applications, semiconductor transistors. This Hannay's edited ACS monograph series No. 140 was written by Chemists to educate their professional colleges, chemists, about the new research area, semiconductors. The aqueous solutions were very familiar to chemists in 1959, and thus this similarity was discovered to facilitate chemists' study of semiconductor physics. Our study of water physics at Xiamen University, 55 years later, in 2014 is to try to find the well-developed semiconductor physics to explain this similarity between semiconductor and water so that chemists can make use of semiconductor physics in the applications of chemistry.

Fig. 1.  Properties of the five host particles, p$^+$, p$^−$, V$^+$, V$^0$ and V$^−$, in pure water. Parts (a) and (b) Volume or bulk concentrations and concentration ratios as a function of temperature. Parts (c) and (d) excess surface channel concentration as a function of surface potential, and parts (e) and (f) as a function of applied gate voltage at five temperatures, $T(℃) = 0$, 25, 50, 70 and 100. The input parameters are the experimental protonic density of states $V^{\rm T}=P_+=P_− =5.3796\times10^{18}$ cm$^{−3}$ and protonic-pairs' generation-recombination energy or the protonic energy gap $E_{\rm p+p−}(\text{meV}) = 643.02[1\,−\,(72.78/T^{\circ}{\rm K})+(12277/T^2)]$, the proton/proton-hole intrinsic concentration $p_{\rm i}$ (cm$^{−3}$), two trapping energies (meV), and the static dielectric constant of water, $\varepsilon_{\text{H}_2\text{O}}$/$\varepsilon_0$. At the five calculated temperatures, they are given by: $0\ ℃ = (578.3,2.487\times10^{13},128,128,87.90)$; $25\ ℃ = (575.7,7.333\times10^{13},88,88,78.36)$; $50\ ℃ = (574.6,1.7784\times10^{14},88,88,69.88)$; $70\ ℃ = (574.5,3.251\times10^{14},55,117,63.77)$; $100\ ℃ = (575.1,6.867\times10^{14},55,117,55.53)$.

Fig. 2.  Properties of the five host particles, p$^+$, p$^−$, V$^+$, V$^0$ and V$^−$, in pure water. Parts (a) and (b) Volume or bulk concentrations and concentration ratios as a function of temperature. Parts (c) and (d) excess surface channel concentration as a function of surface potential, and parts (e) and (f) as a function of applied gate voltage at five temperatures, $T(℃) = 0$, 25, 50, 70 and 100. The input parameters are the experimental protonic density of states $V^{\rm T}=N_{\text{H}_2\text{O}}=3.33429\times10^{22}$ cm$^{−3}$ and protonic-pairs' generation-recombination energy or the protonic energy gap $E_{\rm p+p−}$(meV) $= 643.02[1\,−\,(72.78/T^{\circ}{\rm K})+(12277/T^2)]$, the proton/proton-hole intrinsic concentration $p_{\rm i}$ (cm$^{−3)}$, two trapping energies (meV), and the static dielectric constant of water, $\varepsilon_{\text{H}_2\text{O}}$/$\varepsilon_0$. At the five calculated temperatures, they are given: $0\ ℃ = (578.3,2.487\times10^{13},128,128,87.90)$; $25\ ℃ = (575.7,7.333\times10^{13},88,88,78.36)$; $50 \ ℃ = (574.6,1.7784\times10^{14},88,88,69.88)$; $70\ ℃ = (574.5,3.251\times10^{14},55,117,63.77)$; $100\ ℃ = (575.1,6.867\times10^{14},55,117,55.53)$.

Fig. 3.  Properties of the five host particles, p$^+$, p$^−$, V$^+$, V$^0$ and V$^−$, and one acid impurity ion, $A^{1−} =N_{\rm HA}$, in impure acidic water. Parts (a) and (b) Volume or bulk concentrations, at two trap concentrations and 25 ℃, and at one trap concentration and two temperatures 25 ℃ and 70 ℃. Parts (c) and (d) excess surface channel concentration as a function of surface potential, and parts (e) and (f) as a function of applied gate voltage at 25 ℃ and a range of impurity concentrations, $N_{\rm HA}/N_{\text{H}_2\text{O}} = 10^{−5} \text{ to } 10^{−1}$. The input parameters are the water density $N_{\text{H}_2\text{O}}=3.3429\times10^{22}$ cm$^{−3}$, and the experimental protonic density of states $V^{\rm T}=P_+=P_− =5.3796\times10^{18}$ cm$^{−3}$ and protonic-pairs' generation-recombination energy or the protonic energy gap $E_{\rm p+p−}$(meV) $=$ $643.02[1\,−\,(72.78/T^{\circ}{\rm K})+(12277/T^2)]$, the proton/proton-hole intrinsic concentration $p_{\rm i}$ (cm$^{−3}$), two trapping energies (meV), and the static dielectric constant of water, $\varepsilon_{\text{H}_2\text{O}}$/$\varepsilon_0$. At the two calculated temperatures, they are given by: $25 \ ℃ = (575.7,7.333\times10^{13},88,88,78.36)$; $70\ ℃ = (574.5,3.251\times10^{14},55,117,63.77)$.