Air- and water-stable and photocatalytically active germanium-based 2D perovskites by organic spacer engineering

Summary There is increasing interest in the role of metal halide perovskites for heterogeneous catalysis. Here, we report a Ge-based 2D perovskite material that shows intrinsic water stability realized through organic cation engineering. Incorporating 4-phenylbenzilammonium (PhBz) we demonstrate, by means of extended experimental and computational results, that PhBz2GeBr4 and PhBz2GeI4 can achieve relevant air and water stability. The creation of composites embedding graphitic carbon nitride (g-C3N4) allows a proof of concept for light-induced hydrogen evolution in an aqueous environment by 2D Ge-based perovskites thanks to the effective charge transfer at the heterojunction between the two semiconductors.


Formation energies
All the calculations have been performed with the CP2K code. 1 Atom-centered Gaussian-type basis functions are used to describe the orbitals. We employ the MOLOPT 2 basis set and use a cutoff of 600 Ha for the plane waves. Core-valence interactions are described by Goedecker-Teter-Hutter pseudopotentials. 3 To calculate the formation energies from first-principles as reported in Eq. 2 of the main text, we need to build atomistic models (i) of the considered A2GeX4 perovskites: (PEA)2GeBr4, (BrPEA)2GEBr4, (BPEA)2GeI4, and (BPEA)2GeBr4, X(ii) of GeX2 (X=I, Br) and, (iii) of AX. For (PEA)2GeBr4 and (BrPEA)2GEBr4, we construct supercells starting from the experimental crystallographic structures (cf . Table S2). Then, we perform density functional theory (DFT) calculations to relax both the coordinates of the atoms and the lattice parameters.
These calculations are carried out employing the rVV10 functional, which accounts for van der Waals interactions and has been found to be suited to describe the energetics of layered and 2D materials. 4,5 In fact, the calculated lattice parameters for (PEA)2GeBr4 and (BrPEA)2GEBr4 nicely agree with those measured, with differences below 2%. To model (BPEA)2GeI4, we start from the experimental crystallographic structure of (BPEA)2PbI4 6 in which we replace Pb atoms with Ge atoms and then we fully relax both coordinates and lattice parameters. Analogously, we obtain an atomistic model of (BPEA)2PbBr4, by further replacing I with Br.
GeI2 and GeBr2 are analogously modelled constructing atomistic supercells from the experimentally available
For the s-(BPEA)I-terminated slab, the surface energy ( ) is simply given by: where slab ( ) is the total energy of the stoichiometric slab, bulk is the total energy per formula unit of the bulk material, the number of formula units in the slab supercell, and A is the surface area of the slab. For the nonstoichiometric slabs, we notice that these are generated when cleaving the surface along the plane perpendicular to apical Ge-Br bonds. Therefore, we first need to consider the cleavage energy which is defined as: where [ slab v (ns1) and slab v (ns2) are the total energies of the slabs generated upon cleavage (i.e. without relaxation), while is the number of formula units corresponding to the non-cleaved system. For each nonstoichiometric slab, the surface energy is then defined as: where slab (ns) is the total-energy of the relaxed slab. Results calculated at the rVV10 level of theory are collected in Table S3 and clearly demonstrate that the s-(BPEA)I is the most stable termination. For this reason, we employ this termination also for both (BPEA)2GeI4 and (BPEA)2GeBr4 in the calculation of the band alignment.

Band Alignment
We here employ electronic-structure calculations at the hybrid DFT level of theory, in order to align the band edges of the studied Ge-based perovskites with respect to the vacuum level. Hybrid-DFT calculations have been carried out with CP2K using the auxiliary density matrix method to speed up the calculation of exact exchange. To this end, we employ the cFIT auxiliary basis set. 10 We note that the band alignment for g-C3N4 (reported in Fig. 7 of the main text) has been carried out in a previous study. 11 Therefore, we here report on the results achieved for (BPEA)2GeI4 and (BPEA)2GeBr4. First, we reproduce the experimental band gap of the perovskites by tuning the the fraction of Fock exchange α of the PBE0 functional 12,13 . This method has been found to produce ionization potentials, electron affinities and energy levels at the semiconductor-water interface in remarkable agreement with the experiment. 14,15 In fact, mean average errors of ~0.2 eV have been estimated for these quantities in screenings performed on a large set of semiconductors. 14 The band edges are then aligned with respect to the vacuum level, by determining the electrostatic-potential line-ups across the surfaces (cf. Fig. S8). We note that the flat potential across the vacuum region ensures that no residual electrical field is present in the studied slabs (cf. Figure S7). Further, we position the standard hydrogen electrode (SHE) with respect to the vacuum level. In particular, we employ the theoretical alignment presented in Ref. 13, which has been achieved combining molecular dynamics simulation of a water-vacuum interface with a computational hydrogen electrode. 16,17 The alignment scheme presented in Fig. 7 of the main text is completed including the measured TEOA/TEOA+ redox level. 18

Solvation Gibbs free energies of A cations
We calculated the solvation Gibbs free energies ∆ solv 0 of selected A-site cations (cf. Figure S9) in aqueous environment. This quantity is defined as: where solv 0 (A + ) and vac 0 (A + ) are defined as the Gibbs free energy of the solute in aqueous solution and in vacuum. These quantities are calculated using the Gaussian09 program package. 19 In particular, we employ the B3LYP exchange-correlation functional, 20 with a 6-31++G * * basis set for C N H and the ECP lanl2dz pseudopotential for Br and I. 21,22 The implicit effect of the solvent was included performing calculations with the conductor-like polarizable continuum model (C-PCM). 23 Furthermore, to account also for the solvent explicitly, we included three water molecules for each considered cations. Calculated results are reported in Table S4.