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[Daiki Umeyama](https://orcid.org/0000-0003-4773-4020), [Soshi Iimura](https://orcid.org/0000-0003-3270-155X)

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This document is the Accepted Manuscript version of a Published Work that appeared in final form in Journal of the American Chemical Society, copyright © 2024 American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see https://doi.org/10.1021/jacs.4c12804.[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

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[Ligand-Directed Valence Band Engineering in Pb<sup>2+</sup> Hybrid Crystals: Achieving Dispersive Bands and Shallow Valence Band Maximum](https://mdr.nims.go.jp/datasets/b08fcf8c-e0b3-4c24-9804-b2c2be9388ac)

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Microsoft Word - Main_Text_fin_clean.docxLigand-Directed Valence Band Engineering in Pb2+ Hybrid Crystals: Achieving Dispersive Bands and Shallow Valence Band Maximum Daiki Umeyama* and Soshi Iimura National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan.  ABSTRACT: While crystalline hybrid solids hold great potential as novel semiconductors, most semiconductive hybrids utilize transition metal ions, which inherently limit carrier mobility due to the small band dispersion derived from the d orbitals. The filled s orbitals of post-transition metal ions offer the potential to design dispersed valence bands, but a meth-od to translate the local structure design of these metal ions to valence band engineering is still in development. This study focuses on Pb²⁺-containing hybrid crystals, developing a simple strategy to control Pb²⁺ coordination geometry through the molecular design of azole ligands. By pre-programming the coordination number of Pb²⁺ with azolate ligands, we succeeded in obtaining an isotropic coordination environment at a higher coordination number, resulting in a dispersed valence band and shallow valence band maximum while having a wide band gap. Detailed analysis of the band structures reveals that the energy levels and symmetry of the molecular orbitals of the anions play an important role in realizing these antinomic properties. This ligand-directed approach achieves both isotropy and covalency in the coordination bond by exploiting the diversity of molecular orbitals. Our findings provide a foundation for future design strategies to optimize electronic struc-tures in hybrid materials, advancing their application in semiconductive devices. 1. INTRODUCTION The ability to control the electronic structure of solids is central to materials science because it is the primary de-terminant of charge transport properties. The control of carrier concentration and mobility is the essential factor that enables the application of semiconductors in devices.1 In particular, for sensing and photocatalysis, organic-inorganic hybrid semiconductors have great potential due to their tailorable surface area and catalytic sites based on metal selection and ligand design.2–6 The fundamental methods and knowledge for semiconducting hybrid solids have been accumulated for this realization.7 In the field of coordination polymers (CPs) and metal-organic frame-works (MOFs), reports of semiconductive CPs and MOFs have increased over the years. The majority of these mate-rials consist of transition metal (TM) ions, and electronic communication between inorganic and organic motifs is achieved by d-p or d- orbital interaction.8–10 Proper de-sign of the ligands and their combination with the right metal ions makes it possible to create carriers and control their concentration by doping.11,12 While the systematic study of TM-based CPs and MOFs advances science of semiconductive hybrid materials, the use of TM ions severely limits the ability to control the carrier mobility. This is because the contract nature of the d orbitals of TM ions intrinsically leads to small band dis-persion.13 Thus, the semiconducting properties of these hybrid materials have depended primarily on the control of the carrier concentration, leaving the control of the mo-bility behind. The tendency is more pronounced in valence bands, since conduction bands can be derived from the empty s orbitals of TM ions.14 In this context, CPs and MOFs with post-transition metal (pTM) ions with ns2np0 electronic configurations (e.g., Pb2+, Sn2+, etc.) are of par-ticular interest, which allow us to build dispersive valence bands using the antibonding interaction between filled metal orbitals and filled anion orbitals.15,16 Isotropic and spatially extended ns orbitals of these metals are expected to give more dispersive bands than TM-based materials, resulting in smaller effective mass of holes. Although not as common as structures with TM ions, many CPs and MOFs with pTM ions have also been report-ed.17 However, despite the assumed isotropy of the s orbit-als, the coordination geometry of the pTM ions is often distorted, which is a result of “stereochemically active lone pairs (LPs)”.18,19 The origin of LP formation is known to be the mixing of the metal np states to the ns state,20,21 and it is important to control the s-p hybridization of pTM ions to achieve desired properties. While factors such as the coor-dination number of pTM ions and steric hindrance of lig-ands are known to influence the LP activity in CPs and MOFs,22–24 no clear concept has been established to trans-late these findings into the engineering of the valence bands of these hybrids. This is due to the lack of a precise strategy for programming the coordination number and a deep understanding of the interactions between pTM ions and ligands. As a result, the coordination geometry of pTM ions in these hybrids is in some aspects determined by chance, making it difficult to relate the ligand design to the electronic band structures of the pTM hybrids, regardless of the preservation of the isotropy of the metal s orbital.25–28 Addressing these issues is an important challenge for the design of valence bands using occupied metal s orbitals in hybrid materials.  In this article, we focus on Pb2+ containing hybrid crys-tals and show a simple but effective strategy to actively control the coordination geometry of Pb2+, which enables the valence band engineering. Importantly, we will show that the orbital mixing in hybrid solids does not need to be considered beforehand to preserve the isotropy of the Pb-6s orbital; we only need to control the coordination num-ber of Pb2+. We demonstrate that we can pre-program the coordination number of Pb2+ by the molecular design of anionic ligands. This method causes the Pb2+ to adopt a high coordination number by ligand design, thereby pre-serving the isotropic character of the filled 6s orbital. We show that this results in a more dispersed valence band and a smaller effective mass of holes, accompanied by a shallow valence band maximum. We will clarify how these molecules interact with the Pb2+ and dominate the band dispersion on the basis of detailed analysis of the wave functions of these hybrids. Unlike the TM-based systems, where d-p interactions are dominant, importance of σ-type interactions will be highlighted. We will also show the unique advantages of hybrid materials that result from the diversity of molecular orbitals (MOs). 2. CONCEPT AND METHOD There is a useful classification of the coordination struc-ture of the Pb2+: “hemidirected” and “holodirected”. In hemidirected structures, the bonds to ligand atoms are directed throughout only part of an encompassing globe, whereas in holodirected structures, the bonds to ligand atoms are distributed throughout the entire surface of the globe.29 Hemidirected structures are associated with ste-reochemically active LPs, since the activity is obvious from the coordination geometry. A localized band structure can arise in an active LP (s-p hybridized) structure due to the mixing of the p orbitals, which induces directional orbital overlap and weakens the band dispersion compared to the omnidirectional s orbitals. The directionality of the p or-bitals allows the LP electrons to avoid interacting with other orbitals, resulting in a nonbonding character or re-duced antibonding interaction. Thus, being holodirected is a necessary (but not always sufficient) condition for sup-pressing LP activity and obtaining a dispersive valence band. One of statistical studies of Cambridge Structural Data-bese (CSD) suggests that the coordination geometry of the discrete complexes of Pb2+ is always hemidirected if the coordination number of Pb2 (nC) is 5 or less.29 In contrast, Pb2+ complexes with nC ≥ 6 are about 70% holodirected, and with increasing nC, more likely to have the holodi-rected geometry. This trend is also observed in extended Pb2+ structures (CPs and MOFs).22,24 Another comprehen-sive study of CSD combined with density functional theory (DFT) revealed that the LP activity gradually decreases (accompanied by a decreasing Pb-6p contribution to the LP) with increasing nC.30 These findings imply that we can control the LP activity of the Pb2+ (and thus the degree of valence band dispersion) in a network structure by chang-ing the nC. However, just increasing the number of the do-nor site of ligands does not necessarily give us the control over nC for dispersed bands. This is partially because some donor atoms such as the oxygen (O) of carboxylate provide an opportunistic nC. This causes the nC defined by such a ligand differ case-by-case even in a single structure.22,24,25 We hypothesized that the nC in Pb2+ containing binary hybrids could be predetermined by using molecular anions in which the number of coordination points is well defined. This assumes that all available coordination sites in the ligand molecule work as donors, which we will show to be true later. We focused on molecules containing nitrogen (N) as a donor site and decided to use azoles, which can change the number of N atoms in the five-membered ring while having an equal or similar basicity on each N atom31 (Scheme 1A). Unlike oxygen-based ligands, there is only single pair of unshared electrons on the N atom of the az-oles when written in the Lewis structures. Therefore, a single N site is not supposed to bridge metal ions. This in-dicate that each N site adds only one coordination number to a Pb2 ion, representing the well-defined character of the ligand. We used three azoles (HAz) that allow us to vary the number of N atoms, namely 1H-tetrazole (HTt), 1,2,4-triazole (HTr), and, imidazole (HIm) to complex with Pb2 ions. These aromatic amines can behave as monova-lent anions (Az) by deprotonating the hydrogen on the N atom. Since the charge balance in these binary systems requires the composition formula to be Pb(Az)2, the nC is fixed to be twice the number of N atoms in the azoles. Thus, the nC of three compounds is expected to be 8 (Az = Tt), 6 (Tr), and 4 (Im), respectively (Scheme 1B).   Scheme 1. Concept for defining the coordination number (nC) of Pb2. (A) Three Az anions used in this study to form com-plex with Pb2. (B) Stoichiometry of Pb(Az)2 requires nC to be twice the number of N atoms in the Az anions.   3. RESULTS Desired compounds were synthesized by mixing the pre-formed Az anions, deprotonated by potassium methoxide or hydroxide, with Pb2 salts under solvothermal condi-tions, yielding colorless crystals (see details in Supporting Information). Structural analysis based on single-crystal X-ray diffraction (XRD) revealed that the prepared crystals were new binary compounds with the general formula Pb(Az)2 (Figure 1A, B, C; Az = Tt, Tr, Im). Importantly, the nC in these structures found to be 8 (Az = Tt), 6 (Tr), and 4 (Im), confirming the principle of ligand-directed control of the coordination number. Note that some of the N-donors of Az ligands may remain uncoordinated in binary azolate frameworks with TM ions due to their relatively rigid co-ordination number and geometry.32,33 The fact that the ligands can define the nC of Pb(Az)2 reflects the flexibility of the coordination structure of Pb2+, as described in the literature.26,29,30 We also succeeded in preparing powder crystals of Pb(Az)2 by solvothermal synthesis, whose phase purity was confirmed by elemental analysis and powder XRD measurement (Figure S1 in SI). These are white powders whose optical absorption onsets are at 3.7 eV (Az = Tt), 4.1 eV (Tr), and 3.5 eV (Im), respectively, revealed by diffuse reflectance measurement of the powders (Figure S2 in SI).  Figure 1. Crystal structures of (A) Pb(Tt)2, (B) Pb(Tr)2, and (C) Pb(Im)2 determined by single-crystal X-ray diffraction. Green, Blue, and gray spheres represent Pb, N, C atoms, respectively. H atoms are omitted for clarity. Insets show local coordination geometry of Pb atoms. 3.1 Large nC Results in Suppressed LP Activity and Dis-persive Valence Bands in Pb(Tt)2. The coordination geometry of Pb2 in Pb(Tt)2 (nC = 8) and Pb(Tr)2 (nC = 6) is best described as a triangulated dodeca-hedron and a distorted octahedron, respectively. The co-ordination geometry of Pb2 is highly distorted in Pb(Im)2 (nC = 4) and all the coordinating N atoms are biased to one side of the coordination hemisphere. It is apparent that the Pb2 ions have active LPs in Pb(Tr)2 and Pb(Im)2, while not in Pb(Tt)2 (Figure 1, insets). Through analysis of electron density map and geometric coordinate, we will show that the LP activity is almost completely diminished in Pb(Tt)2 while Pb(Tr)2 and Pb(Im)2 have significant LP (see Discus-sion). Thus, although the design principle of the molecular anion is very simple, forcing a coordination number is a powerful method to control the activity of the LPs of Pb2+. The suppressed LP in Pb(Tt)2 suggests that s-p hybridi-zation is minimal and therefore large valence band disper-sion is expected in this compound. We used PBE hybrid functional with spin-orbit coupling (SOC) as implemented in the VASP code to calculated band structures of Pb(Az)2 (Figure 2).34–36 We notice that the dispersion of the valence band of Pb(Tt)2 is significantly larger than those of Pb(Tr)2 and Pb(Im)2, which is consistent with the expected Pb-6s character in Pb(Tt)2 near the valence band maximum (VBM). The degree of valence band dispersion is quantified by estimating the effective mass of holes(mh*) of Pb(Az)2. The calculated mh* of Pb(Tt)2 at the VBM is 1.3 (Z → P), 1.3 (Z → ), and 1.7 (Z → N). Note that Pb(Tt)2 has a relatively small and isotropic mh* for a hybrid compound. The mh* of  Pb(Tr)2 and Pb(Im)2 are heavier and more anisotropic. For example, mh* of Pb(Im)2 at VBM is 2.3 ( → B) and 17 ( → Z). 3.2 Photo Excited Carriers Are Mobile in Pb(Tt)2. The small and isotropic mh* of Pb(Tt)2 is the quality re-quired for a p-type semiconductor. As described later, the calculated energy position of the VBM of Pb(Tt)2 relative to the vacuum level is in the range where p-doping can hap-pen.37 Nonetheless, how to p-dope the crystal is a non-trivial synthetic challenge and should be the subject of an-other future study. Here, we briefly show how the transport properties of Pb(Tt)2 changes with carrier gen-eration by photoexcitation.  The conductance of the crystal was measured by attach-ing two-point silver contacts to a single crystal of Pb(Tt)2 at ambient temperature. We observed that the current was significantly increased by UVB irradiation (Figure 3). This photo response was confirmed to be reversible without pronounced hysteresis, as we observed that a dark meas-urement after an illuminated scan (and vice versa) was not affected by the previous scan (Figure S3A, 3C in SI). The I‐V relationship under irradiated condition outside the range of 1 V is non Ohmic and the current appears to saturate, which possibly occurs due to the energy transfer from ac-celerated carriers to lattice vibrations.38 Under dark condi-tions, fitting of the linear region of the I-V curve gives a conductance (G) of Gdark = 2.12(4)1014 S (Figure S3B in SI). Under the irradiation of the UVB band (4.1–5.2 eV), the conductance increased about three orders of magnitude to GUVB = 1.65(3)1011 S (Figure S3D in SI). We also observed that irradiation of a visible band (1.8–3.1 eV) had little effect on the conductivity (Figure S3E in SI). In addition, a Pb(Tt)2 crystal with vapor-deposited gold contacts exhibit-ed a similar photo response (Figure S4). These results in-dicate that the photo response originates from the bulk and that Pb(Tt)2 exhibits semiconducting properties when carriers are generated by an above-gap photoexcitation.   Figure 2. Electronic band structures of (A) Pb(Tt)2, (B) Pb(Tr)2, and (C) Pb(Im)2 (EF: Fermi energy). Orbital characters in the band structures are colored by red (Pb 6s), green (Pb 6p), and blue (N 2p).    Figure  3. Room-temperature I-V curves of a Pb(Tt)2 single crystal under dark (blue) and UVB irradiation (red).  4. DISCUSSION 4.1 Mechanism of the LP Suppression and Formation in Pb(Az)2. The crystal structures of Pb(Az)2 suggest that the coordi-nation geometry of Pb(Tr)2 and Pb(Im)2 are distorted by active LPs while Pb(Tt)2 is not. The absence of the LP activ-ity in Pb(Tt)2 suggests that the 6s character of the valence electrons of Pb2 is preserved. Conversely, the valence bands of Pb(Im)2 and Pb(Tr)2 near the band edges should contain a non-trivial amount of the 6p character. These characteristics are visualized by electron density maps and the partial density of states (PDOS) of Pb(Az)2 (Figure 4). The electron densities were mapped using the result with-out SOC for the states between 12 and 0 eV and plotted in the plane spanned by the PbLP vector and the PbN vec-tor of the shortest bond length in each crystal (see SI for the SOC exclusion). Pb(Tt)2 shows symmetric electron density around the Pb2 ions, while Pb(Im)2 and Pb(Tr)2 show asymmetric electron densities along the PbLP vec-tors as expected.   Figure  4. Partial electron densities from 12 to 0 eV and PDOS of Pb orbitals for (A) Pb(Tt)2, (B) Pb(Tr)2, and (C) Pb(Im)2. The electron densities are plotted in the plane spanned by the LP vector and the shortest PbN vector. Con-tour levels are between 0 (blue) to 0.05 a0−3 (red) (a0: Bohr radius). By analyzing the PDOS of Pb(Az)2, we can conclude that the strong anisotropy is the result of the Pb-6p orbital con-tribution to the valence band. As seen in Figure 4, the PDOS of Pb(Im)2 and Pb(Tr)2 show significant amount of Pb-6p character from 4 to 0 eV, overlapped with the PDOS of Pb 6s. The overlap indicates the hybridization of Pb 6s and 6p orbitals in this energy range. This contrasts with the domi-nance of the Pb-6s character throughout the valence band of Pb(Tt)2. There is a small amount of Pb-6p PDOS at 2 eV, which does not overlap with the PDOS of Pb-6s. Thus, the 6s-6p orbital hybridization is negligible in Pb(Tt)2, pre-serving the isotropic character of the filled Pb-6s orbital. We also quantified the magnitude of the LP activity of these compounds using the framework of bond-valence analysis of solids with active LPs.39–42 The LP vector (Φ) defined in these analyses can be used as an indicator of the strength of the LPs on Pb2. The averaged vector length ∣Φ∣ of each Pb site are ∣Φ∣ = 1.30(1)105 (Az = Im), 9.3(1)106 (Tr), and 6.371022 (Tt), respectively (Figure S6 in SI). Here we notice that the LP activity of Pb(Az)2 decreases as the nC increases, and becomes essentially zero in Pb(Tt)2. Thus, it was demonstrated that the nC is pre-programable by appropriate ligand design and that the degree of the 6s-6p mixing can be controlled by nC. Pre- served Pb 6s character resulted in dispersive valence bands in Pb(Tt)2. 4.2 VBM of Pb(Tt)2 Is Shallow Enough to Be p-Doped. In general, dispersive valence bands are indicative of strong bonding and antibonding interaction of orbitals, the latter causing the shallowing of VBM relative to the vacu-um level.43 The depth of a VBM is an important indicator of p-type doping capability, with p-doping becoming easier as a VBM becomes shallower. Using a DFT method, we esti-mated the depth of the VBMs of Pb(Az)2 by aligning the energy of these Pb 5d orbitals set at the same energy as α-PbO, whose VBM energy is experimentally known44 (see SI for the detailed procedure). The analysis suggests that the VBMs of Pb(Az)2 are at −6.1 eV (Az = Tt), −6.0 eV (Tr), and −5.5 eV (Im), respectively (Figure 5). Notably, all Pb(Az)2 compounds have shallow VBMs close to −6 eV, an empiri-cal limit considered to be p-dopable.37 The shallow VBMs of Pb(Az)2 were experimentally confirmed by photoelec-tron yield spectroscopy, which indicates that all Pb(Az)2 have the VBM levels shallower than −6 eV (Figure S5). Note that the relative order of the VBM depth of Pb(Az)2 may change due to the possible underestimation of band dispersion by the DFT method.   Figure 5. DFT-calculated band edge positions of Pb(Az)2 rela-tive to the vacuum level. Values for α-PbO (with asterisks) are experimental values from the literature.44 4.3 Dispersive Valence Band and Shallow VBM of Pb(Tt)2 Are Achieved by Large nC and Deep-Level MO with Right Symmetry. In the case of inorganic p-type semiconductors, the HOMO of the anions, the p orbitals, interacts with filled metal orbitals such as s or d. In contrast, it remains to be seen which state of the anions will produce the important interaction in our hybrid compounds due to the complexity of the MOs. The presence of Pb-6s state near the valence band top of Pb(Tt)2 indicates that the filled 6s orbital is destabilized by the antibonding interaction with a certain MO of the anion (Figure 4A). Detailed examination of the highest-energy valence band (HVB) at the  point reveals that the MO contributing to this state resembles not the anion’s HOMO, but rather the HOMO3 (Figure 6A, B). The HOMO3 is a b2 orbital as the isolated Tt anion belongs to the point group C2v. This orbital alternates in sign on the N atoms of the Tt anion and interacts out-of-phase with the neighboring Pb 6s orbitals, while the HOMO (b1) of Tt has no net interaction due to symmetry mismatch. For strong -type interaction with the Pb 6s orbital, the MOs must be a1 or b2 orbitals. Besides HOMO3, HOMO1 (a1) of the Tt anion appears to have the right symmetry to interact with the Pb 6s or-bital (Figure 6B). However, it does not contribute to the HVB due to its suboptimal topology for maximizing nodal planes with the Pb 6s orbital. This results in HOMO1 con-tributing to the fifth highest valence state at  (HVB−4), partially due to two of the four -type interactions are in-phase and bonding (Figure S7 in SI). Thus, the order of the MOs contributing to the valence bands are determined by both orbital symmetry and topology.45 This energy level inversion of the anion states is unique to hybrid com-pounds, since in inorganic compounds the filled active or-bital of the anions is always np, which has identical sym-metry regardless of the elemental species. The energy level inversion is the result of a strong covalent interaction be-tween Pb 6s and HOMO3 (Figure 6C). For Pb(Im)2, the character of the wave function near the VBM is dominated by the HOMO (b1) of the Im anion with-out contribution from the Pb 6s orbitals (Figure 6D, E). The energy level of the HOMO is so shallow that it forms a lo-calized, flat valence band as a non-bonding state, which becomes the VBM without the help of dispersion (Figure 6F). However, the state at the VBM is not a crystal orbital spread over the entire solid, and it makes little sense to discuss the physical properties of Pb(Im)2 as a semicon-ductor from its VBM level. This indicates that a shallower energy level of the anion MO is desirable to obtain a shal-low VBM, but it results in a localized state when the sym-metry of the orbitals does not match. These results suggest that the symmetry of MOs can, in some cases, influence the electronic structure of a hybrid solid more than its energy levels. The impact of MO symmetry has already been high-lighted in Pb(Tt)2, but the electronic structure of Pb(Im)2 reaffirms its importance. In the sense that the VBM is formed as non-bonding molecular state, Pb(Im)2 is an ionic crystal. Pb(Tr)2 shows an intermediate electronic structure be-tween Pb(Tt)2 and Pb(Im)2. The MO contributing to the HVB of Pb(Tr)2 at the  point is HOMO3 (a1) due to sym-metry and topology requirements, similar to the case of Pb(Tt)2 (Figure S8 in SI). However, smaller nC allows Pb 6p orbital mixing in Pb(Tr)2, which results in an asymmetric coordination geometry and reduced band dispersion.    Figure 6. Volumetric visualization for the wave function of (A) highest-energy valence band (HVB) of Pb(Tt)2, (D) HVB of Pb(Im)2, and (D’) HVB−16 of Pb(Im)2 (k = Γ). MOs of (B) isolated Tt and (E) isolated Im anions (point group C2v) calculated using Gaussian 16.46 Schematic interaction diagrams of (C) Pb(Tt)2 and (F) Pb(Im)2. The relative energy difference of MOs are highlighted by ar-rows. Note that these differences are not scaled to actual energy differences.  4.4 Comparison of Electronic Structures of Hybrid and Inorganic Semiconductors and Usefulness of the Con-cept of Controlling nC. We have started with the simple concept of controlling nC to obtain an isotropic coordination structure of Pb2+ and dispersive valence bands derived from preserved 6s char-acter. The Az anions made this possible by varying the number of N atoms in the ring. However, we explicitly state here that changing the number of N atoms also changes the pristine energy levels of the anion MOs. Since the N atoms are more electronegative than the C atoms, the energy lev-els of MOs decrease as the number of N atoms in aromatic rings increases.47,48 This results in a tendency for the MO energy levels to be lower for Im, Tr, and Tt anions, in that order (Figure S9 in SI). This effect is most apparent in the depth of the VBMs of Pb(Az)2 (Figure 5). Although it is in the p-dopable range, the VBM of Pb(Tt)2 estimated by DFT is the deepest of the three Pb(Az)2 due to the deeper MO levels of the Tt anion, despite achieving the largest disper-sion. Antibonding interaction between Pb 6s and a higher energy MO could lead to shallower VBMs, even if the dis-persion is poor (Figure 6F), which is the case for Pb(Im)2 and Pb(Tr)2. Thus, it is evident that we cannot decouple the number of the donor site of the anions from the variation of the MO energy levels inherent to the anions. Nonetheless we will show that the concept of controlling nC remains useful. Note that the dispersive valence band and shallow VBM of Pb(Tt)2 are achieved by fulfilling the following three fac-tors simultaneously: 1. The 6s character of Pb2+ is preserved by forcing large nC (isotropy). 2. There is an MO with an energy level close to Pb 6s (en-ergy matching). 3. The symmetry and topology of the MO are consistent with Pb 6s (shape matching). Condition 1 gives isotropy, while conditions 2 and 3 give covalency of the coordination bond. In the following dis-cussion, we will highlight the uniqueness of the hybrid system that achieves the coexistence of these two charac-teristics by comparing it to the electronic structure of in-organic semiconductors. In binary inorganic compounds containing Pb2, the cova-lency of coordination bonds is associated with asymmetric coordination geometry. The DFT study of -PbO and PbS indicates that the mixing of the Pb 6s and 6p orbitals oc-curs, if any, through interaction with the p orbital of the anion atoms.49 Thus, for atomic compounds, the energy level of the anion p states, which interact with metal s or-bitals, is a primary factor in determining the degree of Pb-6p mixing or LP formation. For example, LP is formed in -PbO, while it is not formed in PbS and compounds with higher period chalcogens.49 This is because the energy lev-el of the 3p orbital of S is already too high to covalently interact with the 6s orbital of Pb to gain sufficient stabiliza- tion. To compensate for the lack of stabilization energy from orbital hybridization, PbS adopts a more isotropic and dense structure, resulting in a preference for higher coordination number. The covalency of Pb-6s and O-2p in -PbO pushes up the 6s state by antibonding interaction, which makes it possi-ble for Pb-6p to mix into this state (Figure S10). In the case of hybrid system, it is remarkable that the covalency of Pb-6s and the HOMO3 in Pb(Tt)2 does not induce the Pb-6p mixing. We attribute the coexistence of the isotropy and covalency in the coordination bond to the robustness of ligand-based control of nC. Thus, the large nC make the sys-tem insensitive to the covalency or pristine energy levels of the anion MOs. Although we cannot decouple the num-ber of the donor site of the anions from the variation of the MO energy levels, the control of nC is robust enough to si-lence the latter effect. The abovementioned scheme also explains why the least covalent Pb(Im)2 exhibits the most anisotropic coordina-tion geometry. Lack of covalency results in a more iso-tropic structure in the inorganic compound, PbS. However, in the 17th valence band of Pb(Im)2, a -type antibonding interaction is found between Pb 6s/6p orbitals and the anion’s HOMO2 (Figure 6D’, E). The HOMO2 (b2) of Im is the highest-energy MO that has the right symmetry for -type interaction. The antibonding interaction is not strong enough to push the HOMO2 up close to the top of the va-lence band, since its energy level is still shallower com-pared to the MOs of the Tt anion (Figure S9 in SI). Note that the small nC of Pb(Im)2 makes it easier to introduce anisotropy in the coordination geometry for Pb 6p mixing. The mixing of the Pb-6p orbital pulls down the energy lev-el (stabilization) and reduces the band dispersion. Finally, we emphasize the benefit of achieving dispersive valence bands and shallow VBMs using second period ele-ments, because they enable the synthesis of wide gap ma-terials. For inorganic compounds, the VBM energy posi-tions are deepest for oxides and become shallower as the anion period increases as seen in sulfides and selenides. Hybrid materials can take a similar approach, as seen in semiconductors such as Pb3(C6S6).50 However, the use of higher period elements often results in smaller band gap energy. When high optical transparency or breakdown voltage is required, we need an alternative method to achieve both wide gap and dispersive bands. The second period elements alone cannot achieve this, but we showed that it is possible by being molecules. We have presented one such method in this paper, and the detailed electronic structure analysis discussed here will help to further de-velop this molecular method. 5. CONCLUSION While hybrid semiconducting materials with ns2np0 met-al ions would offer an attractive electronic structure, con-trolling their valence band dispersion and effective mass of holes are an evolving issue. We started with the simple concept of changing the number of N atoms in azoles to preprogramme the nC, and indeed succeeded in controlling the nC and coordination geometry of Pb2+ in hybrid crystals. The method thus made it possible to obtain a dispersive valence band (small mh*) with a shallow VBM and wide band gap. Furthermore, by examining the wave function of the crystal orbitals of Pb(Az)2 and the MOs of the anions, we were able to clarify the key factors for valence band dispersion and VBM shallowing in these compounds. The analysis of the electronic structure of Pb(Tt)2 reveals an energy-level inversion in which the primary interaction occurs at a much deeper level than the HOMOs of the mol-ecules. Briefly, this phenomenon stems from to the inher-ent diversity (rich symmetry and topology) of the molecu-lar anions. We emphasize that the approach of controlling the coor-dination number by molecular design was robust enough to make the system insensitive to the degree of covalency. This robustness prevents the Pb 6p orbital mixing into the VBM of Pb(Tt)2 while a right-symmetry anion MO having close energy to the Pb-6s orbital, resulting in the compati-bility of a large band dispersion, shallow VBM, and wide band gap. Such unconventionality would not be possible with simple atomic orbitals alone and represents a new frontier in materials design in organic-inorganic hybrid solids. There remains the possibility of manipulating the energy, symmetry, and topology of a particular MO by functionalizing the anions with electron withdrawing or donating groups at appropriate positions. Moreover, this molecular approach also offers the potential for engineer-ing conduction band minima, as we observe that the high electronegativity of the N atoms pulls down the unoccu-pied MOs (N-2p) energy levels lower than the Pb-6p bands in Pb(Tt)2 (Figure 2). Such approaches will be an exquisite extension of this work, and we have established an im-portant foundation for it. ASSOCIATED CONTENT  Supporting  Information. Experimental and computational details, elemental analysis, crystallographic data, PXRD, ab-sorption spectra, photoconductance, and photoelectron yield spectra. This material is available free of charge via the Inter-net at http://pubs.acs.org. The CIFs for Pb(Tt)2, Pb(Tr)2, and Pb(Im)2 has been deposited in the Cambridge Crystallographic Data Centre with CCDC numbers 2383877, 2383878, and 2383879, respectively. AUTHOR INFORMATION Corresponding Author *E-mail: umeyama.daiki@nims.go.jp Author Contributions The manuscript was written through contributions of all au-thors. Notes The authors declare no competing financial interest.  Funding Sources This work was supported by JSPS KAKENHI Grant Numbers JP24K08460 and JP21H04612. ACKNOWLEDGMENT  Part of this work was performed at the Surface and Bulk Anal-ysis Unit. The DFT calculations were performed on the Nu-merical Materials Simulator. These are shared facilities at the National Institute for Materials Science (NIMS). We thank Dr.  Junko Aimi, Dr. Kenji Sakamoto, Dr. Tetsushi Taguchi, Dr. Takeo Ohsawa, and Dr. Hiroshi Mizoguchi (NIMS) for access to equipment. ABBREVIATIONS CP, coordination polymer; MOF, metal-organic framework; TM, transition metal; pTM, post-transition metal; LP, lone pair; MO, molecular orbital; CSD, Cambridge Structural Databese; DFT, density functional theory; Az, azolate; Tt, tetrazolate; Tr, tria-zolate; Im, imidazolate; XRD, X-ray diffraction; SCO, spin-orbit coupling; VBM, valence band maximum; PDOS, partial density of states;  HVB, highest-energy valence band; nC, coordination number; mh*, effective mass of holes;  EF, Fermi energy; G, conductance; Φ, lone pair vector; a0, Bohr radius; k, wave vec-tor REFERENCES (1) Kitai, A. Semiconductor Physics. In Principles of Solar Cells, LEDs and Diodes: The role of  the PN  junction; John Wiley & Sons, Ltd, 2011; pp 1–67. (2) Aykanat, A.; Meng, Z.; Stolz, R. M.; Morrell, C. T.; Mirica, K. A. Bimetallic Two-Dimensional Metal–Organic Frameworks for the Chemiresistive Detection of Carbon Monoxide. Angew. Chem.  Int.  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