How Strong Is the Hydrogen Bond in Hybrid Perovskites?

Hybrid organic-inorganic perovskites represent a special class of metal-organic framework where a molecular cation is encased in an anionic cage. The molecule-cage interaction influences phase stability, phase transformations, and the molecular dynamics. We examine the hydrogen bonding in four AmBX3 formate perovskites: [Am]Zn(HCOO)3, with Am+ = hydrazinium (NH2NH3+), guanidinium (C(NH2)3+), dimethylammonium (CH3)2NH2+, and azetidinium (CH2)3NH2+. We develop a scheme to quantify the strength of hydrogen bonding in these systems from first-principles, which separates the electrostatic interactions between the amine (Am+) and the BX3- cage. The hydrogen-bonding strengths of formate perovskites range from 0.36 to 1.40 eV/cation (8-32 kcalmol-1). Complementary solid-state nuclear magnetic resonance spectroscopy confirms that strong hydrogen bonding hinders cation mobility. Application of the procedure to hybrid lead halide perovskites (X = Cl, Br, I, Am+ = CH3NH3+, CH(NH2)2+) shows that these compounds have significantly weaker hydrogen-bonding energies of 0.09 to 0.27 eV/cation (2-6 kcalmol-1), correlating with lower order-disorder transition temperatures.


S2
The crystal structures were relaxed until all forces were below 0.01eV/Aǒ with an energy cutoff of 700eV using 2x2x2 k-points for the Aze + , Gua + and Hy + compounds, 2x2x1 k-points for the larger Dma + unit cell and 3x3x3 k-points for the halide perovskites, which were modeled in the 2x2x2 cubic unit cell. We use the PBEsol 3 functional, adding the D3 4 correction with BJ-damping 5 to account for dispersive interactions. The lattice vectors calculated with this approach are generally shorter than experimental values at/near RT (the temperature at which the 1 H-NMR experiments are performed), as can be seen in Table S1, Table S2, Table S3 and Table S4.   This also implies that the optimised lattice vectors will not be exactly equal in length.

Hydrogen bonding energies
To calculate the hydrogen bonding energy for a given compound all references are calculated in the same unit cell to avoid complications from the compensating background charge in the charged systems.
We tested the effect of the D3 correction by performing similar calculations with the PBEsol functional only. The results given in Table S5 show the same trends as PBEsol+D3 but the energies are slightly lower, indicating that a small amount of dispersion corrections are included in the PBEsol+D3 results.  the periodic table). The best choice should bee small enough that any steric interactions are avoided and so electronegative that the charge gets localised on the cation only. In addition the polarisability of the ion might have an effect. In Table S6 we present results of the H-bonding energy calculated with K as a reference using PBEsol+D3. It is clear that the trend is similar to the Cs calculations but the numbers are generally slightly lower. Both the Cs and K calculations were done using pseudopotentials (PPs) which include the s and p electrons of the shell below the valence shell. These electrons can then be polarised, while the frozen core can not. The standard PPs for VASP do not include alternative PPs for K and Cs. We therefore compared the effect for Na using PPs with 7 and 9 electrons respectively. We found that this lead to differences in the total H-bonding energy of 15meV, a negligible error compared to the uncertainty associated with the choice of cation. Note that using the 1 electron PP for Na involves a calculation with 0 electrons which did not give a meaningful result.

Molecular hydrogen bonding energies
To get an idea of the magnitude of the hydrogen bonding energy expected for N-H-X (X = Cl, Br, I) type hydrogen bonds (as found in the halide perovskites) we calculated the hydrogen bonding energy between CH3NH3 + and XH. These calculations were performed using GPAW 13,14 with non-periodic boundary conditions and a grid-spacing of 0.18Å. We use the PBEsol 3 functional to describe the exchange and correlation energy. Initial geometries are created with varying H-bonding lengths between the N-H of the cation and the X of HX. The HX molecule is initially aligned along the N-H direction. The (N)H-X distance is fixed during optimisation, as is the orientation of HX to avoid reorientation which might happen to maximize dipole-dipole interactions. All other coordinates are optimised until the forces are below 0.025eV/Å. The resulting energy curves, shown in Figure S1, show that the H-bonding interaction gets weaker from Cl to Br to I and the optimal H-bonding distance gets longer. Interestingly, the (N)H-X distances found in the Ma + halide perovskites fall close to the minima calculated here for all three halides.

Figure S1
Energy vs H-X distance for the hydrogen bonding between Ma + and HX (X=Cl,Br,I). The interaction energy is set to 0.0eV at a H-X distance of 4.2 Å.

Supercell convergence
In periodic DFT calculations involving charged supercells the Ewald summation results in an effective background neutralising charge, which avoids a divergent electrostatic energy. The interaction between this effective background charge and the charge of the lattice can be notoriously sensitive to the details of supercell size and shape. In our method we subtract the energies of the charged supercells before obtaining the final energy, which should make our approach significantly less sensitive to the choice of supercell than previous approaches. To demonstrate this we calculated the H-bonding energy in the 1x1x1 (4 cations) and 2x1x1(8 cations) unit cell of the Hy+ formate. The difference in H-bonding energy was below 20 meV and we conclude that interactions between the background charge and the lattice is a minor source of uncertainty.

NMR calculations:
NMR calculations were performed using the CASTEP DFT code 15 , using the gauge including projector augmented wave (GIPAW) approach 16 . The PBEsol functional was used for the exchange-correlation term 3 , and ultrasoft psuedopotentials were used 17 . Planewave basis functions with an energy cut-off of 70 Ry, and kpoint spacings of 0.03 Å -1 , were used in all CASTEP calculations. These parameters were sufficient for the convergence of NMR parameters. Initial structures were taken from calculations in VASP using the PBEsol functional, with geometries then re-optimised in CASTEP. For the geometry optimisation, the unit cell parameters were fixed, while all atomic positions were allowed to vary. NMR calculations were then performed on the optimised structures.
Calculated chemical shifts, δiso, were obtained using; δiso = -(σisoσref), where σiso is the calculated isotropic shielding, and σref is a reference value. For 1 H spectra, a σref value of 30.5 ppm was used. The calculated 1 H chemical shifts reported in the main text are the average chemical shifts for the different functional groups, see Table S8 below.

S6
NMR calculations of Am + in the gas phase were carried out using the Gaussian 09 software. 18 Geometry optimizations and NMR calculations were performed using the PBE exchange correlation functional with the 6-31G(d) basis set. To obtain δiso values a σref value of 31.8 ppm was used (determined for tetramethylsilane).

NMR shifts and hydrogen bonding
Previous work has compared calculated chemical shifts for crystals with calculated shifts for isolated molecules to give a measure of intermolecular Hbond strength. 19,20 In a similar way we calculated the chemical shifts for an isolated molecule of Am+, and then calculated the difference between this and the calculated value in the crystal (Table S7). For the N-Hs (except for NH2 in Hy+) we see differences of greater than 5 ppm between the molecule and the crystal, consistent with strong H-bonds. Similar values of ~5 ppm were obtained in ref 20 above for organic crystals. In ref 19 and 20 they also identify some C-H---O H-bonds, which give much smaller shift differences of ~ 2 ppm. Our calculated values are relatively similar between the different compounds. This is broadly in line with the findings from our approach for calculating hydrogen bond strengths, although we note that it is not possible to equate NMR shifts to bonding energies in a quantitative fashion.