Electronic Structure of Bi-Activated Luminescent Compounds and Pure Bismuth Photocatalytic Compounds

A straightforward method to determine vacuum referred binding energies is X-ray or ultraviolet photo-electron spectroscopy (XPS or UPS). Electrons are ejected from occupied states in the sample and their kinetic energy is measured in the vacuum. The methods works well for conducting materials like metals and semi-conductors. However, such method applied to wide bandgap insulators faces problems with sample charging. Contact potentials can also introduce systematic errors. To deal with systematic errors, usually an internal reference is used like the binding at the top of the valence band or the Fermi level in metals. We will use information from photoelectron spectroscopy for a couple of pure Bi-compounds. Unfortunately, the method is not sensitive enough to probe electron binding energies in dopant states when concentrations are in the 1 mole% region.

Flatband potentials are measured by the onset potential for generating photocurrents in semi-conductors. Figure 1a shows CB-bending at the photo-anode water interface. By applying a bias the bending can be reduced to zero (flatband) which then provides information on the energy at the conduction band bottom. For example in Ref. 21 the flatband potential of BiVO₄ was determined as −0.58 eV vs the Ag/AgCl redox potential at pH = 6.6. This potential can then be converted to a VRBE at the CB-bottom of −4.49 eV. Subtracting the bandgap energy as determined from a Tauc plot then provides the VB-top at −7.0 eV.

An empirical method frequently encountered in the field of photocatalytic materials is based on the concept of absolute electronegativity of semiconductors. Pearson's ²² or Mulliken's absolute electronegativity of an atom is defined as the arithmatic average of electron affinity and first ionisation potential of that atom. The absolute electronegativity of a semiconductor is then defined as the geometric mean value for the compound, and it defines the mid bandgap VRBE. Meng et al. ²³ used that method to determine the VRBE at the CB-bottom and VB-top of bismuth photocatalytic semiconductors. The method is however rather inaccurate. In this work we will see that for pure Bi-compounds it systematically predicts too low VRBEs at the band edges.

Ab-initio and first principle calculations can provide detailed insight in the electronic bandstructure, the wavefunctions of initial and final states in luminescence transitions, and lattice relaxation phenomena. However, calculations still face severe problems when dealing with unoccupied states like that of the conduction band. Bandgaps tend to be largely (30%) under-estimated, and special methods are needed to repair that. At this stage we rate the accuracy of computational methods to establish VRBE energies too poor to be useful for our purpose. What remains as most reliable are the results from the measurement of flatband potentials in electrochemistry and the chemical shift method from lanthanide spectroscopy.

A lanthanide VRBE scheme as in Fig. 2 shows the binding energies in the divalent and trivalent lanthanide 4fⁿ states and the lowest energy 4f^n-1 5d excited states together with that at the band edges. With the development of the chemical shift model in 2012 ¹⁶ and its further refinement in 2020 ^24,25 we are able to construct such schemes routinely with sufficient accuracy to explain and predict many lanthanide luminescence phenomena.

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The main physics behind the chemical shift model is a screening of the positive charge of the lanthanide by the surrounding chemical environment. An Ln²⁺ will be effectively screened by −2e of negative charge and an Ln³⁺ by −3e of negative charge. Screening is most optimal in a metal environment where the free conduction band electrons can approach the lanthanide most closely. Screening is least optimal in a fluoride compound where electrons are strongly bonded in the 2p⁶ fluorine orbitals. In between, screening scales with how strong electrons are bonded in the anion which in turn follows the familiar nephelauxetic sequences, i.e., $F\lt O\lt {Cl}\lt {Br}\lt N\lt I\lt S\lt {Se}$ and within the oxides ${{SO}}_{4}^{2-}\lt {{CO}}_{3}^{2-}\lt {{PO}}_{4}^{3-}\lt {H}_{2}O\lt {{BO}}_{3}^{3-}\lt {{SiO}}_{4}^{4-}\lt$ aluminates < ${{RE}}_{2}{O}_{3}$. ²⁰ The Coulomb repulsion between the negative screening charge with an electron in the lanthanide causes a reduction in that electron binding energy. This reduction is called the chemical shift and is by definition zero for the electrons in the free and unscreened lanthanide ions. Equation 1 is the expression from the chemical shift model for the VRBE in the Eu²⁺ ground state where the second term on the right hand side represents the chemical shift. ^24,25 The value of −24.92 eV is the binding in the 4f⁷ ground state of Eu²⁺ as free ion and is equivalent to the negative of the 3th ionisation potential of Eu.

$$\begin{eqnarray}&&\begin{array}{l}{E}_{4f}(7,2+,\ A)=-24.92\\ \quad +\,\displaystyle \frac{18.05-U(6,A)}{0.777-0.0353U(6,A)}\end{array}\end{eqnarray} \tag{ 1 }$$

Over the years YPO₄ has served as a model compound to develop, to test, and to refine the chemical shift model, and a diversity of techniques has been applied to obtain data on energy level locations. Figure 2 shows the lanthanide VRBE diagram for YPO₄. It was obtained with the refined chemical shift model and the diagram can also be found in Ref. 25. The main parameter is the Coulomb repulsion energy $U(6,A)$ defined as the electron binding energy difference between the Eu²⁺ and Eu³⁺ ground states in chemical environment A. Its value can be deduced from a so-called host referred binding energy (HRBE) diagram derived from lanthanide spectroscopic data. It can also be deduced from the observed centroid shift ${\epsilon }_{c}(A)$ of the Ce³⁺ 5d-levels in the compound. ²⁶ Equation 1 connects the value for $U(6,A)$ with the VRBE ${E}_{4f}(7,2+,A)$ in the 4f⁷ ground state of Eu²⁺ in chemical envrionment A. $U(6,{free})$ is 18.05 eV for free europium ions and varies from 7.6 eV in highly ionic fluoride compounds (strong anion electron bonding) down to ≈6.0 eV in highly polarizable sulfide and selenide compounds (weak anion electron bonding). The smallest value of about 5.7 eV applies for Eu metal with free conduction band electrons. For YPO₄ in Fig. 2 a value of 7.09 eV applies.

In the refined chemical shift model of 2020, the nephelauxetic effect on the binding energy in the lanthanide 4fⁿ ground state was included. It turns out that the binding energy for $n\geqslant 8$ may increase (becomes more negative) several 0.1 eV due to the nephelauxetic effect; the effect for $n\leqslant 7$ is quite insignificant. The schemes and VRBE data presented in this work were all obtained with the refined chemical shift model.

Bi³⁺ is the preferred valence and has been studied as luminescent center in many types of inorganic compounds. Plenty of information is available on the intrinsic transitions between the ¹ S₀ ground state and excited states, known as the A, B, and C-band transitions, see Fig. 3 (a). In addition to these intrinsic transitions, also bands attributed to a transition from Bi³⁺ to the CB is regularly observed which is known as the D-band. With knowledge on the VRBE at the CB-bottom and the D-band energy one may derive the VRBE in the Bi³⁺ ground state. This method was first employed by Awater and Dorenbos. ^28–30 Regarding Bi³⁺ we can limit here with reviewing and updating the results of that earlier work.

We will start with our model compound YPO₄. Blasse et al. ² already reported in 1968 a broad 3.7 eV emission band with excitation around 5.4 eV. The excitation band was assigned to the Bi³⁺ A-band in Ref. 31. In 2013 Boutinaud et al. ³² suggested that the 3.7 eV emission might origin from a metal to metal charge transfer (MMCT). One year later, Cavalli et al. ³³ extended the studies into the vacuum ultraviolet and reported a broad band between 150 nm and 190 nm that was attributed to the C-band excitation. Again one year later Srivastava et al. ³⁴ assigned the 3.7 eV emission to pairs of Bi³⁺ in YPO₄. Awater and Dorenbos ³⁰ resolved the band between 150 nm and 190 nm into a relatively narrow C-band excitation at 7.9 eV with a broader lower energy band around 7.29 eV which was attributed to the D-band or Bi³⁺ $\to$ CB transition. This D-band can now be used to located the ¹ S₀ ground state of Bi³⁺ below the CB. In Fig. 4 we assumed like in Ref. 35 that the VRBE of the electron after D-band excitation falls in between the genuine CB-bottom and E_X . The VRBE in the Bi³⁺ ground state, or equivalently the (Bi³⁺/Bi⁴⁺) charge transition level, is then at −8.2 V.

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Upon X-ray irradiation of YPO₄:Bi³⁺, a new type of emission appears around 1.85 eV (670 nm) that was attributed to Bi²⁺ emission. ³⁰ The emission shows a quenching temperature of T₅₀ = 380 K which translates to a quenching energy barrier of about 0.6 eV. Putting things together the Bi²⁺ ground state or (Bi²⁺/Bi³⁺) charge transition level is then estimated at VRBE of −3.5 eV. Note that in Fig. 4 the (Bi²⁺/Bi³⁺) charge transition level falls below the VRBE in the ³ P₁ excited state of Bi³⁺. Upon A-band excitation of Bi³⁺, spontaneous electron transfer to a neigboring Bi³⁺ to form a Bi⁴⁺-Bi²⁺ pair is then energetically possible. It is now well accepted that the 3.7 eV emission reported already in Ref. 2 originates from Bi-pair emission as suggested in Ref. 34. With the derived charge transition level energies, it becomes clear that Bi³⁺ forms a 1.57 eV deep trapping center for a hole from the VB and it also forms a ≈2.9 eV deep trapping center for an electron from the CB. The electron and hole trapping properties of Bi³⁺ together with that of trivalent lanthanides in YPO₄, LaPO₄, LuPO₄ and their solid solutions were studied in Ref. 5 by means of thermo-luminescence and spectroscopic techniques. The results are consistent with the VRBE scheme of Fig. 4. Recently Liu et al. ³⁶ conducted an experimental and theoretical study on charge carrier storage properties of Bi³⁺ in YPO₄. Density Functional Theory (DFT) confirms the location of the charge transition levels above the VB and below the CB. Their calculation also suggest that it is better to speak of a (Bi³⁺-Bi³⁺)* excited pair state than in terms of a Bi⁴⁺-Bi²⁺ state. That suggestion was followed in Fig. 4.

Figure 5 shows a stacked VRBE diagram with a compilation of Bi³⁺ VRBE data in inorganic compounds. Here compounds were selected where data are reasonably reliable and where one may illustrate the trends in level location with type of compound. A quite similar diagram with more compounds can be found in Awater et al. ^28,29 In each case the VRBE at the VB-top and CB-bottom is based on lanthanide spectroscopy data combined with the Refined Chemical Shift model. Compounds are in sequence of decreasing value for $U(6,A)$.

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Clear trends are observed in Fig. 5. In sequence of decreasing U-value, the polarizability of the anion ligands and its screening potential of the positive Bi³⁺ cation increases. The chemical shift increases and the VRBE in the Bi^{3+ 1} S₀ ground state becomes less negative from values around −11 to −10 eV for U = 7.3–7.4 eV in fluoride compounds to values increasing from −8 eV to −7 eV in oxide compounds with $U=7.1\to 6.4\,\mathrm{eV}$ until finally around −5 eV for CaSe with U = 6.22 eV. The VRBE in the ³ P₁ excited Bi³⁺ state changes then from −5 to −2.5 eV. The excited state VRBE increases therefore less strongly than the ground state VRBE, and as a consequence the energy of the A-band absorption and emission decreases with decreasing U-value.

Figure 6 compiles data on the A-band absorption energy against the U-value assigned to the compound. A clear trend is revealed that confirms a long known observation that the A-band energy lowers with increasing nephelauxetic effect. ^1,2 In other words it scales with how strong electrons are bonded in the anions and therefore with the $U(6,A)$ value of the chemical shift model. Data on Bi³⁺ in GdOCl, LaOBr, YOCl, and LaOCl are outlyers in Fig. 6 which may suggest that either improper assignments have been made or that specific compound properties are at play; this needs further analysis.

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Bi³⁺ is the preferred valence in inorganic compounds but also Bi²⁺ can be stable although information is much less abundant. The Bi²⁺ emission is usually found in the 550–720 nm spectral region. ^37–39 Interest in Bi²⁺ has increased because of potential phosphor application in white-LEDs, and there is also active research in afterglow and storage phosphor applications where Bi³⁺ may act as a stable electron trapping and/or hole trapping center ^5,17,40,41 as illustrated in Fig. 1b.

Various methods to determine or estimate the VRBE in the ${}^{2}{P}_{1/2}$ ground state and emitting ${}^{2}{P}_{3/2}(1)$ excited state of Bi²⁺ were used in Ref. 29. For a couple of compounds one can use information on energy of electron transfer from Bi²⁺ to the CB-bottom or from the VB-top to Bi³⁺. However, very little information appears available. The presence of Bi²⁺ emission and the quenching temperature of that emission also provides information on excited state level location with respect to the CB-bottom. Information on the VRBE in Bi²⁺ levels has been compiled in the stacked diagram of Fig. 7.

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For the compounds 1 until 14, Bi²⁺ emission and its excitation spectra have been reported. ²⁹ The approximate VRBE energies in the ${}^{2}{P}_{3/2}(1)$ excited state were deduced from the thermal quenching temperature T₅₀ or the onset of thermal quenching T_k of the Bi²⁺ emission. We regard the thermal ionization to the conduction band as the quenching mechanism, and with a typical lifetime of 10–20 μs ^39,42–44 roughly 600 K eV⁻¹ change in T₅₀ is assumed. The relatively low quenching temperature of T₅₀ = 250 K in SrB₆O₁₀ then translates to a ${}^{2}{P}_{3/2}(1)$ location less than 0.5 eV below the CB-bottom. T₅₀ values are also known for CaSO₄, Sr₂P₂O₇, Ba₃(PO₄)₂, and YPO₄ (see Fig. 4). In each case, a VRBE in the Bi²⁺ ground state is found around −3.6 eV, and similar values for compounds where only a lower limit for T_k is available was assumed.

The data on YPO₄ (compound 14) are the same as in Fig. 2 and Fig. 4. The last three compounds NaYGeO₄, MgGeO₃ and Y₃Al₅O₁₂ in Fig. 7 have relatively low VRBE at the CB-bottom, i.e. <−2 eV, and no Bi²⁺ emission is observed. Evidently the ${}^{2}{P}_{3/2}(1)$ excited state is located inside the CB. For these compounds Bi²⁺ VRBE values can be estimated from thermoluminescence data on Bi³⁺ (co)-doped compounds. Bi³⁺ acting as an electron trapping center was studied in NaYGeO₄ by Lyu et al., ¹⁷ in MgGeO₃ by Katayama et al., ⁴¹ and in Y₃Al₅O₁₂ by Katayama et al. ⁴⁰ For example in Bi³⁺ doped NaYGeO₄ a glow peak at ≈290 K has been assigned to electron release from Bi^{2+ 17} and this translates to a Bi²⁺ g.s. location about 0.6 eV below the CB-bottom as in Fig. 7. The glow peak appears at 320 K in MgGeO₃ and at 375 K in Y₃Al₅O₁₂. Dashed arrows (1), (2), (3) are observed charge transfer bands. Arrow 1) of length 5.34 eV was assigned to the Bi³⁺ $\to$ CB transition and provides the Bi³⁺ VRBE. ¹⁷ The charge transfer band at 4.86 eV (arrow 2) in MgGeO₃ from Ref. 41 was assigned to the Bi³⁺ $\to$ CB transition. However, one may not fully exclude that it is the VB $\to$ Bi³⁺ CT, and both options are illustrated in Fig. 7. Similar applies to the 5.93 eV (arrow 3) CT-band in Y₃Al₅O₁₂ from Ref. 45 that was assigned to the Bi³⁺ $\to$ CB transition in Ref. 28. The other option is also shown in Fig. 7. This ilustrates that depending on level locations in the bandgap a proper assignment of broad CT-bands becomes difficult or ambiguous.

Thermoluminescence can also be used to determine the VRBE in the Bi³⁺ ground state. In Eu³⁺ and Bi³⁺ co-doped YPO₄, Eu³⁺ appears to be a deeper electron trap than the hole trap depth of Bi³⁺. During TL-readout the hole is released from Bi⁴⁺ to recombine with the electron trapped on Eu²⁺ to generate Eu³⁺ emission apearing as a TL-glow peak around T_m  = 500 K. ⁵ With such information we can then estimate that the VRBE in the Bi³⁺ ground state must be at least 1 eV above the VB-top which is then consistent with Fig. 4.

Figure 7 shows that the VRBE in the Bi²⁺ ground state is fairly constant with values (tentatively) slighty below 4 eV in fluoride compounds to values around −3.6 eV in more polarizable oxide compounds. Comparing Fig. 5 with Fig. 7 one may notice that, at a given U-value, the VRBE in the Bi²⁺ ground state tends to fall below the VRBE in the Bi³⁺ excited state. This was clearly illustrated for Bi²⁺ and Bi³⁺ in YPO₄ in Fig. 4. This confirms again that when two Bi³⁺ dopants are close together and one of them is brought to the excited state, a lower energy (Bi³⁺-Bi³⁺)* excited pair state may form. The electron back transfer may then generate so called Bi-pair emission or, in case the back transfer is radiationless, form a concentration quenching route for ordinary Bi³⁺ A-band emission as suggested in Awater et al. ²⁹

Fluorides. The VRBE of −9.6 eV at the VB-top of BiF₃ is from X-ray photoelectron spectroscopy (XPS). ⁴⁷ Information on ${E}_{{fa}}\approx 4.0\,\mathrm{eV}$ and ${E}^{{ex}}=4.65\,\mathrm{eV}$ from Refs. 48, 49 was used to estimate the flatband potential and E_C . Figure 8 shows for BiF₃ the ⁵ D₄ excited state of Tb³⁺ at −5.77 eV. The emission from this state has a reported quenching temperature of T₅₀ ≈ 300 K. ⁴⁹ In Ref. 18 such quenching temperature was related to an energy difference with ${E}_{C}\approx E{(}^{5}{D}_{4})+0.4+{T}_{50}/475$. We thus estimate ${E}_{C}\approx -4.7\,\mathrm{eV}$ which is fully consistent. For NaBiF₄, with ⁵ D₄ level at −5.66 eV and luminescence quenching temperature T₅₀ = 450 K from Ref. 49 one obtains ${E}_{C}\approx -4.3\,\mathrm{eV}$. Further, with ${E}^{{ex}}=5.0\,\mathrm{eV}$ and E_fa  = 4.5 eV, ^49,50 the VRBE at the VB-top at −9.5 eV and the flatband potential at −5 eV is derived.

Oxides. For the monoclinic phase of BiPO₄, a flatband potential of −4.1 eV is from Refs. 51, 52 and with ${E}_{{fa}}\approx 4.2\,\mathrm{eV}$ and ${E}^{{ex}}=4.8\,\mathrm{eV}$, ^52,53 E_V and E_C were obtained. The VRBEs in the host bands of Bi₄Ge₃O₁₂ are an educated guess where we assumed a flatband potential of −4 eV which is typical for other Bi-compounds in Fig. 8. Subtracting E_fa  = 4.16 eV from Ref. 54 assigned to the indirect bandgap provides E_V  = −8.16 eV. The optically determined ${E}^{{ex}}({LT})\approx 4.7\,\mathrm{eV}$ then provides E_C . ^55,56

Transition metal compounds. For Bi₂WO₆, the flatband potential of −4.48 eV and E_fa  = 2.9 eV were used. ⁵⁷ Reports on the maximum of the absorbance vary from 3.7 eV in Refs. 58, 59 to 4.1 eV in Refs. 57, 60, 61 which gives uncertainty in E^ex and where to locate E_C ; a value of 3.9 ± 0.2 eV was used. For the triclinic β-BiTaO₄ phase we used the flatband potential of −4.22 eV and E_fa  = 3.18 eV from Ref. 62 to derive E_V , and with ${E}^{{ex}}=3.9\,\mathrm{eV}$ to derive E_C . ^63–65 For the α-BiNbO₄ phase we used a flatband potential of ≈−4.4 eV and E_fa  = 2.6 eV to obtain E_V . ⁶⁶ With ${E}^{{ex}}=4.0\,\mathrm{eV}$, E_C is found. ^63,67 For monoclinic phase BiVO₄ we used the flatband potential of −4.49 eV and E_fa  = 2.51 eV from Ref. 21 to determine E_V and ${E}^{{ex}}=2.75\,\mathrm{eV}$ from Refs. 68, 69 to determine E_C .

Halo-oxides. For the halo-oxide family information on electrochemical flatband determination was not found, and other methods were followed to deduce them. For BiOF with $U=6.8\,\mathrm{eV}$, the (Eu²⁺/Eu³⁺) charge transition level is at −3.97 eV. The $\mathrm{VB}\to {\mathrm{Eu}}^{3+}$ charge transfer band is at 4.49 eV, ⁷⁰ and then E_V  = −8.46 eV. The host absorption maximum is seen at 4.88 eV in Ref. 71 and at 4.63 eV in Ref. 72 yielding E_X  ≈ −3.8 eV. In Ref. 73 a VB-top at −8.39 eV was suggested to explain the mechanism of photocatalytic activity. With computational methods the VB-top is found at −8.2 eV. ⁷⁴ Considering systematic errors of several 0.1 eV in each method used, the VRBE at the VB-top appears consistent. To estimate the flatband potential, E_fa needs to be added to E_V  = −8.46 eV. Experimental values of 3.6 eV and 4.2 eV have been reported. ^72,73,76 A computed value of 4.2 eV is reported in Ganose et al. ⁷⁴ We estimate a flatband potential somewhere around −4.5 ± 0.3 eV.

For BiOCl, E_fa  = 3.5 eV and ${E}^{{ex}}=4.0\,\mathrm{eV}$ are reported. ^75–77 Information on flatband potential studies was not found and the VRBE was derived from lanthanide spectroscopy instead. The (Eu²⁺/Eu³⁺) charge transition level when $U=6.7\,\mathrm{eV}$ is at −3.92 eV, and with a $\mathrm{VB}\to {\mathrm{Eu}}^{3+}$ CT band reported near 3.55 eV ^75,78,79 the VB-top is reached at −7.47 eV. Adding E_fa , a flatband potential around −3.97 eV is expected.

For BiOBr, experimental information on lanthanide spectroscopy and flatband studies are not available. From the absolute semiconductor electronegativity, the mid bandgap VRBE is calculated at −6.1 eV. ^23,80 With ${E}^{{ex}}=3.5\,\mathrm{eV}$ and ${E}^{{fa}}\approx 2.8\,\mathrm{eV}$, ^79–82 the VB-top would be at −7.5 eV, the flatband at −4.7 eV, and E_C at −3.9 eV. However, as will be shown later absolute semiconductor electronegativity systematically provides too low values for the band positions in pure Bi-compounds. We tentatively assumed 0.3 eV higher values which locates the flatband at −4.4 eV.

For BiOI, we followed the same method as for BiOBr. The concept of absolute semiconductor electronegativity used in Refs. 23, 83 yields the mid bandgap VRBE at −5.94 eV. With ${E}^{{ex}}=2.6\,\mathrm{eV}$ from Refs. 80, 84, 85 and E_fa  = 1.94 eV from Refs. 80, 83, 84, one obtains E_V  = −6.85 eV, a flatband at −4.9 eV, and E_C at −4 eV. These values are quite similar to that of computational studies in Ganose et al. ⁷⁴ providing E_V  = −7 eV and a flatband at −5 eV. Yet, because of the systematic error, we will place the band edges at 0.25 eV higher energy bringing the flatband at −4.65 eV.

BiI₃ , Bi₂ O₃ and Bi₂ S₃ . For BiI₃, a workfunction of 5.8 eV as obtained from photoelectric effect measurements suggest E_V  = −5.8 eV. ⁸⁶ UPS studies indicate E_V between −6 and −6.3 eV. ¹³ A strong exciton peak at ${E}^{{ex}}=2.0\mbox{--}2.1\,\mathrm{eV}$ is reported in Refs. 87– 89 with direct bandgap of 1.96 eV and indirect bandgap of 1.67 eV. ⁸⁸ Altogether we used ${E}_{V}\approx -6.2\,\mathrm{eV}$, a flatband near −4.3 eV and E_C near −4.1 eV in Fig. 8 as compromise between the different sets of data.

Bi₂O₃ is well-studied for photo-catalytic purposes ^90–92 with a measured flatband potential of −4.37 eV. ⁹⁰ With ${E}^{{ex}}=3.1\,\mathrm{eV}$ and E_fa  = 2.8 eV, ${E}_{V}\approx -7.2\,\mathrm{eV}$ is obtained. ^90,92–94 We can also exploit data on Pr³⁺ in Bi₂O₃. Pr³⁺ creates a broad unresolved diffuse reflectance band extending from 425 nm (2.9 eV) to 525 nm (2.4 eV) ⁹⁴ that we here attribute to the Pr${}^{3+}\to \mathrm{CB}$ intervalence charge transfer (IVCT) band. With the (${\Pr }^{3+}/{\Pr }^{4+}$) charge transition level at −6.88 eV for $U(6,A)$ = 6.55 eV this is fully consistent with the VRBE data in Fig. 8.

Bi₂S₃ has a measured flatband potential of −4.26 eV. ⁹⁰ With ${E}^{{ex}}=2.4\,\mathrm{eV}$ and E_fa  = 1.6 eV, ^95,95–97 E_V  = −5.86 eV and E_C  = −3.4 eV are obtained.

A first inspection of Fig. 8 shows that the flatband potentials are fairly constant and usually fall between −4 and −4.5 eV. For the two fluoride compounds they are 1 eV lower. For each compound in Fig. 8, the VRBE at mid bandgap was also calculated from the absolute semiconductor electronegativity, see also, ²³ and the values are connected by the dashed line. In all cases it runs significantly below the mid bandgap energy as derived experimentally. Clearly there appears to be a systematic difference which raises doubts on the validity of the frequent use of absolute semiconductor electronegativity in the field of photocatalytic compounds. For compounds where information on lanthanide spectroscopy combined with the chemical shift model has been used, results are consistent with experimental flatband determinations.

Bi³⁺ has similar ionic radius and charge as La³⁺ and also the crystal structure of a pure Bi-compound is usually similar to that of the equivalent La-compound. It is then of interest to compare the VRBE in the pure Bi-compounds of Fig. 8 with that of La-compounds as shown in 9. Since there is no equivalent La-compound for Bi₄Ge₃O₁₂ we used information on LaAlGe₂O₇ instead. Lanthanide spectroscopy on La₂WO₆ appears too scarce, and instead we used Y₂WO₆ as equivalent compound for Bi₂WO₆ in Fig. 9. The standard method of the (refined) chemical shift model was used to construct the lanthanide VRBE diagrams. The two fluorides are  11 eV wide bandgap compounds. The VB-top in the oxide and halo-oxide compounds are found in the −8 eV to −9 eV region, and that of LaI₃ and La₂S₃ at 3 eV higher energy. Note the relatively low lying CB-bottom in the four transition metal based compounds which is dominated by the VRBE in the 5d (W⁵⁺ and Ta⁴⁺), 4d (Nb⁴⁺), and 3d (V⁴⁺) orbitals. ⁹⁸ Germanium based compounds, as in LaAlGe₂O₇ also tend to have low lying CB-bottom.

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For several of the La-compounds and for Y₂WO₆, spectroscopic data on Bi³⁺ is available enabling to determine or estimate the VRBE in the Bi³⁺ and Bi²⁺ impurity ground states. Bi data for LaPO₄ can be found in Ref. 5 for Y₂WO₆ in Refs. 2, 28, 99, for LaNbO₄ in Refs. 28, 100, for LaVO₄ in Refs. 28, 101. For LaOBr we interpreted a broad 4.26 eV excitation band for Bi emission ¹⁰² as the VB $\to$ Bi³⁺ CT-band. Similar was done for the 4.48 eV excitation band in Bi³⁺ doped LaOCl in Ref. 103 and for the 5.0 eV band in La₂O₃ from Refs. 104, 105. The interpretation of the broad bands in these latter three compounds remains speculative. The alternative interpretation of a Bi³⁺ $\to$ CB or a broad band (Bi³⁺-Bi³⁺) pair excitation cannot be excluded at this stage.

In Fig. 9 the VRBE of the CB-bottom, flatband potential, and VB-top of the corresponding pure Bi-compounds of Fig. 8 are connected by curves a), b), and c), respectively. Curve c) tends to follow the same patterns as the VRBE at the VB-top of the La-compounds whereas the flatband potential is fairly constant around −4 eV without a correlation with the CB-bottom of the La-compounds.