# A 3D lead iodide hybrid based on a 2D perovskite subnetwork

M.B.H. Salah, J. Tessier, N. Mercier, M. Allain, A. Leblanc, X. Che, Claudine

Katan, Mikael Kepenekian

► To cite this version:

M.B.H. Salah, J. Tessier, N. Mercier, M. Allain, A. Leblanc, et al.. A 3D lead iodide hybrid based on a 2D perovskite subnetwork. Crystals, 2021, 11 (12), pp.1570. 10.3390/cryst11121570 . hal-03515123

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Submitted on 2 Jun 2022

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Distributed under a Creative Commons Attribution 4.0 International License
mizations, i.e., of atomic positions and cell vectors, while the centrosymmetry is preserved. The electronic structure of the relaxed geometry is described including spin-orbit coupling through the on-site approximation as proposed by Fernández-Seivane et al. [28]. To prevent conflicts between the on-site treatment and the nonlocality of C09, single point calculations were conducted with the revPBE functional on which C09 is based [29]. Core electrons are described with Troullier–Martins pseudopotentials [30], while valence wavefunctions are developed over double-ζ polarized basis set of finite-range numerical pseudoatomic orbitals [31]. In all cases, an energy cutoff of 150 Ry for real-space mesh size was used. Electronic structures were converged using k-point samplings of the Brillouin zone of 5 × 3 × 3.

### 3. Results

#### 3.1. *Crystal Structure, Thermal Stability, and Optical Properties*

A slow diffusion of ethanol into an acidic solution (HI) containing hydroxypropylamine, methylamine, and lead iodide (see Section 2) affords needle like crystals of (HPA)₆(MA)Pb₅I₁₇. Figure 1 shows a general view of the structure. The compound crystallizes in the triclinic *P*-1 space group, the independent space containing 3 HPA⁺ molecules, half MA⁺, 2 Pb²⁺ and 8 I⁻ in general positions, and 1 Pb²⁺ and 1 I⁻ located on symmetry centers. The metal iodide network consisting of connected PbI₆ octahedra has a 3D character. It can be described from a 2D perovskite subnetwork (purple octahedra, Figure 1) connected to each other by PbI₆ face-sharing octahedra (grey octahedra, Figure 1). The 2D perovskite subnetwork of corner-sharing octahedra is isolated on Figure 2a, the different views, along *a*, *b*, and *c*, highlighting the corner-sharing octahedra mode. The 2 × 2 octahedra building unit centered in the middle of the unit cell (when viewed along the *a* direction, Figures 1 and 2a) can be considered as a part of the *n* = 2 layered perovskite Pb₂I₇. The repetition of these units along *a* leads to a 1D subnetwork Pb₄I₁₈. A similar situation is found in the structure of (PA)₅Pb₅I₁₈ (PA⁺: propylammonium) compound [19]. However, while these 1D chains are connected through PbI₆ face-sharing octahedra in (PA)₅Pb₅I₁₈ leading to an overall 2D lead iodide network in this structure, these 1D chains are connected to each other through corner-sharing mode leading to a 2D step-like Pb₄I₁₇ (Pb₄I₁₆I₂/₂, two shared iodides) perovskite network extending along the *a* and *b* directions of the unit cell. As already mentioned, these 2D perovskite subnetworks are linked by Pb²⁺ cations located on symmetry centers, with corresponding octahedra sharing faces with their two neighboring octahedra, leading finally to the overall 3D Pb₅I₁₇ network.

While MA⁺ cations are located near the shared iodides connecting adjacent 2 × 2 octahedra units within the 2D perovskite subnetwork, the HPA⁺ are clearly located in channels defined by this open framework. Figure 2b shows a partial view of the structure focusing on one channel whose section is defined by 10 adjacent lead iodide octahedra, containing 6 HPA⁺ cations. We observe 3 kinds of HPA⁺ cations. They are numbered 1, 2, and 3 on Figure 2b. HPA(1) and HPA(3) at the surface of cavities clearly interact with iodides through both NH...I and OH...I interactions (see Figure 2b, such interactions with H...I distances < 3.05 Å are drawn as dashed lines). In contrast, HPA(2) cations located at the center of channels do not interact with iodides through sizeable hydrogen bonding (<3.05 Å). Meanwhile, two adjacent HPA(2) molecules mainly interact together through strong NH...O interactions (d(H...O) = 2 Å). The peculiar curled conformation of HPA⁺, related to the hydrogen bond ability of both the NH₃⁺ and the OH ends, certainly hinders formation of 2D perovskites, while favoring here a structure having a 3D metal halide network, as already observed for other intermediate size cations [23].
<figure><img src="image_2.png" /><figcaption>**Figure 1.** General view of the structure of (HPA)₆(MA)Pb₅I₁₇ showing the 3D lead iodide network resulting from 2D perovskite subnetwork (purple octahedra) linked together by PbI₆ face-sharing octahedra (grey octahedra).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Structure of (HPA)₆(MA)Pb₅I₁₇. (a) Partial view showing the 2D perovskite subnetwork along *a*, *b*, and *c* highlighting the corner-sharing connectivity; (b) partial view showing organic cations HPA⁺ and MA⁺ in channels defined by corner- and face-sharing PbI₆ octahedra, highlighting the three types of HPA⁺ cations (numbered 1, 2, and 3) and hydrogen bonding (OH...I and NH...I contacts < 3.05 Å, dashed lines).</figcaption></figure>

We further explored the stability of (HPA)₆(MA)Pb₅I₁₇ upon heating. TGA experiment shows that the compound is stable up to 200 °C and decomposes into two steps (Figure S3). Its stability in ambient air appears improved as compared to the well-known 3D MAPbI₃, since PXRD of a sample left in the air during two weeks is similar to the pristine one (Figure S4). Optical properties were investigated on (HPA)₆(MA)Pb₅I₁₇ obtained as a crystallized powder. The absorption spectrum shown in Figure 3a reveals a broad absorption band in the first part of the visible region (400–550 nm range). The corresponding Tauc plot
(Figure 3b) leads to a direct optical band gap of 2.33 eV. The (HPA)₆(MA)Pb₅I₁₇ crystallized powder also exhibits a weak broad band photoluminescence emission centered at 530 nm (Figure S5).

<figure><img src="image_4.png" /><figcaption>**Figure 3.** Absorption spectrum of a crystallized powder of (HPA)₆(MA)Pb₅I₁₇ (a) and corresponding Tauc plot (black curve) assuming a direct band gap (b), red line: fitted line giving Eg).</figcaption></figure>

## 3.2. Electronic Structure

Insights into the electronic structure of (HPA)₆(MA)Pb₅I₁₇ is provided by first-principles calculations based on density functional theory (DFT). Figure 4a shows the band structure computed at the GGA level (see Section 2 for computational details) that provides reliable description of the electronic features despite the well-known band gap underestimation. The band structure presents a direct band gap of 1.60 eV at T. We verify that the valence band maximum (VBM) is governed by I(5p) orbitals, while the conduction band minimum (CBM) is due to Pb(6p) and I(5p) orbitals (Figure S7), i.e., no cation, HPA or MA, state is found near the band edges. Interestingly, the band structure does not adopt the typical shape found for 3D, 2D, nor 1D halide perovskites. Indeed, the lower energy conduction band is flat in one direction, along *c*, and strong dispersion is observed along the two others. Such features are typically found in 2D perovskites, where flat bands correspond to the stacking direction. On the other hand, the top valence band presents sizeable dispersion only along *a*, a characteristic expected for 1D systems.

The negligible dispersion along *c*, observed both in the conduction and valence band can be assigned to the presence of the 2D perovskite subnetwork (vide supra) separated by the large cation (HPA) and the face-sharing octahedra that efficiently block the electronic coupling between layers as it has been described in previous cases [19,32]. The partial charge density plotted at the CBM (Figure 4b) adopts the form typically observed in layered perovskites with a large contribution from Pb(6p) and I(5p) orbitals along *a* and *b*, i.e., the two directions with corner-sharing octahedra. It leads to the important bandwidth following the line Z-T-R (Figure 4a). The case is different with partial charge density taken at the VBM (Figure 4c,d) that illustrates the strong interaction between iodide atoms along *a* responsible for the dispersion observed along the T-R line. As opposed to the typical shape of valence band in halide perovskites, almost no contribution arises from Pb(6s) orbitals. Instead, I(5p) orbitals directly overlap thanks to the zigzag connectivity of the octahedra in the (*a*, *c*) plane. The direct overlap between I(5p) orbitals along *a* leads to greater interaction and therefore to a higher energy of this anti-bonding combination. Since, the coupling in the *b* direction is of the classical I(5p)-Pb(6s)-I(5p) form, it lies lower in energy. As a result, the VBM is formed by couplings only along the *a* direction, giving a 1D-like character to the valence states.
<figure><img src="image_5.png" /><figcaption>**Figure 4.** (a) Computed band structure (blues lines: valence band, red lines: conduction band) of (HPA)₆(MA)Pb₅I₁₇. The system presents a direct band gap at T with E>G = 1.60 eV. (b,c) Partial charge densities computed at the conduction band minimum and the valence band maximum, respectively. (d) Same as (c) from a different viewpoint. Organic cations are not depicted for clarity (purple atoms: I, white atoms: Pb).</figcaption></figure>

Even though not quantitative, it is worth noticing that the here-computed bandgap (1.60 eV) is greater than the ones computed at the same level of theory not only for 3D halide perovskites, but also for typical 2D ones (1.1–1.3 eV). Still, it remains smaller than bandgaps of related 1D-like compounds (2.0 eV) [33]. This is indicative that the electronic dimensionality of the 3D (HPA)₆(MA)Pb₅I₁₇ structure is intermediate between 1D and 2D.

**4. Conclusions**

Using the hydroxypropylammonium (HPA⁺) intermediate size cation, a new metal halide organic–inorganic material was synthesized. The X-ray structure determination reveals a rare and unprecedented 3D inorganic network. The structure consists of a 2D perovskite subnetwork of corner-sharing PbI₆ octahedra that are in turn connected to each other by PbI₆ octahedra sharing their faces. This compound absorbs in the 400–550 nm visible range leading to an optical band gap of 2.33 eV. DFT calculations further reveal that this 3D structural network has a peculiar band structure that shows a direct band gap but reduced electronic dimensionality. On one hand, the valence band has a 1D nature and is mainly composed of p orbitals of the halide. On the other hand, the conduction band possesses a clear 2D character with contributions of p orbitals of both the metal and the halide.

**Supplementary Materials:** The following are available online at https://www.mdpi.com/article/10.3390/cryst11121570/s1, Figure S1: Calculated and experimental PXRD; Figure S2: ¹H NMR in deuterated DMSO; Figure S3: TGA; Figure S4: PXRD of aged sample; Figure S5: Photoluminescence; Figure S6: Brillouin zone for P-1 space group; Figure S7: Density of states; Table S1: Summary of crystal data and structure refinement.
**Author Contributions:** Conceptualization, N.M. and C.K.; methodology, M.K. and A.L.; investigation, M.B.H.S., J.T., X.C. and M.A.; writing, N.M., C.K. and M.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** At ISCR and MOLTECH-Anjou the work was supported by the Agence Nationale pour la Recherche (MORELESS project). This work was granted access to the HPC resources of IDRIS under the allocation 2020-A0090907682 made by GENCI.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data for this study are available from the corresponding authors upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

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