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Molecular Origin of Properties of Organic-Inorganic Hybrid Perovskites: the Big Picture from Small Clusters Hong Fang, and Puru Jena J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.6b00435 • Publication Date (Web): 11 Apr 2016 Downloaded from http://pubs.acs.org on April 12, 2016

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The Journal of Physical Chemistry Letters

Molecular Origin of Properties of Organic-Inorganic Hybrid Perovskites: the Big Picture from Small Clusters Hong Fang, Puru Jena* Department of Physics, Virginia Commonwealth University, 701 West Grace Street, 23284, VA, United States

Abstract We show that the electronic properties, including the band gap, the gap deformation potential and the exciton binding energy, as well as the chemical stability of organic-inorganic hybrid perovskites can be traced back to their corresponding molecular motifs. This understanding allows one to quickly estimate the properties of the bulk semiconductors from their corresponding molecular building blocks. New hybrid perovskite admixtures are proposed by replacing halogens with superhalogens having compatible ionic radii. Mechanism of the boronhydride based hybrid perovskite reacting with water is investigated by using a cluster model.

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Endowed with high power-conversion efficiencies and low-cost manufacturing, organicinorganic hybrid perovskites with the general formula AMX3-xYx (A = organic cation; M = Pb, Sn, Ge; X,Y = I, Br, Cl) have emerged as the next-generation photovoltaic materials [1-14]. Their inorganic relatives CsSnX3 (X = I, Br, Cl) with Cs+ replacing the large organic cation have also attracted considerable interest due to their possible application as an excellent solar-cell absorber [15-18]. These materials show similar electronic and crystal structures, which usually makes them a ‘prototype’ in modeling the hybrid perovskites. Numerous studies on the bulk phases of these hybrid perovskites have been carried out to engineer their band gaps, understand the nature of their photoexcitation and improve their physical and chemical stability [1-14]. Most recently, based on the concept of Goldschmidt's tolerance factor, hundreds of possible hybrid perovskites composed by various organic cations A+, divalent metals M2+ and anionic X− moieties are proposed to exist [19]. Wide range of intriguing and diverse properties and functionalities are expected to emerge from these materials. However, given the large number of compositional possibilities, a fundamental understanding of the electronic structure and stability of hybrid perovskites is needed to facilitate the property prediction and design. One of the primary goals of cluster science has been to develop bulk properties from the molecular building blocks. Early works on semiconductors, such as Si, ZnS, GaAs, CdS, CdSe, W2O3, and PbS have shown continuous evolution of the structure and electronic properties of the bulk material from the molecular clusters [20-24]. Recognition of the electronic properties being modulated by the polymerization of the molecular motifs to different sizes and dimensions has led to the discovery of the quantum confinement effects and nonlinear optical properties [20]. Inspired by these early studies, we show in this work that the electronic, optical, and excitonic properties as well as the chemical stability of the hybrid perovskites stem from their respective 2


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molecular motifs. This observation allows it possible to understand and predict the properties of the bulk hybrid perovskites by using the simple molecular models. We have recently introduced the concept that the hybrid perovskites A[MX3] can be viewed as super alkali halides composed of superalkalis and superhalogens [25]. Their molecular motifs consist of the A+ cation and the [MX3]− anion bound by an ionic bond. As shown in the Supporting Table S1 [29], the organic cations A+ (as listed in Ref. 19) have lower ionization potentials (defined as the energy necessary to remove an electron from a neutral species) than lithium in the alkali group and hence can be regarded as superalkalis [26]. On the contrary, the anions [MX3]− have electron affinities (defined as the energy gained in adding an electron to a neutral species) higher than the highest value of the halogen group (chlorine) and are, therefore, named as superhalogens [27]. The nomenclature of these special ions suggests that they mimic the chemistry of the elementary halogens and alkalis, yet have distinctive properties (such as extreme size) by being atomic clusters [25].

Fig. 1 (a) Optimized molecular CH3NH3GeI3 and (b) a supercell of the experimental crystal structure of CH3NH3GeI3 from Ref. [28] using polyhedral representations of the organic cation and the [GeI3]− anion. The yellow-highlighted cation-anion couple in the supercell corresponds to the molecular motif. 3



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Table I Optimized (Calc.) average bond lengths of the isolated molecules compared to the available experimental data (Exp.) [28-29, 30-33] in the bulk crystals of the ambient phase. MA+ and FA+ denote the superalkalis [CH3NH3]+ and [HC(NH2)2]+, respectively. The bond lengths of the superalkalis in isolated molecular forms are found to be almost the same as those in the crystalline environment. The bond lengths of superhalogens coupled to different cations (given in parenthesis) show that the cations have very little influence in the geometry of the anions. For the hyperhalogens [M(BH4)3]− (M = Pb, Sn, Ge), the bond length given is that between M-B. The B-H bond length is always between 1.2 and 1.3 Å. For the hyper halogen [Ge(HCOO)3]−, the bond length is between Ge-O. Superalkali Bond (Calc.) Bond (Exp.) Superalkali Bond (Exp.) Bond (Calc.) (Å) MA+ (Å) (Å) FA+ (Å) C-N 1.49 1.49 C-N 1.31 1.31 C-H 1.09 1.09 C-H 1.09 1.09 N-H 1.04 1.04 N-H 1.01 1.02 Superhalogen Superhalogen Bond (Calc.) Bond (Exp.) Bond (Calc.) Bond (Exp.) (Å) (Å) (Å) (Å) [MX3]− [MX3]− + 2.72 (MA ) Pb-I 3.04 3.20a Sn-Br 2.89e 2.72 (Cs+) Pb-Br 2.83 2.98b Sn-Cl 2.57 2.64c Pb-Cl 2.66 2.84c Pb-(BH4) 2.77 + 2.72 (MA ) Ge-I 2.79 2.77f Sn-(BH4) 2.70(Cs+) g Ge-Br 2.55 2.53 Ge-(BH4) 2.60 Ge-Cl 2.39 2.33c Pb-(BH4) 2.77 2.99 (MA+) 3.05a Sn-I Ge-(HCOO) 1.98 2.96 (Cs+) 3.11d a Ref. [32]. b Data at 11 K from Ref. [30]. c Data of MAPbCl3, MASnCl3 and MAGeCl3 from Ref. [31] d Data of CsSnI3 from Ref. [32]. e Data of MASnBr3 from Ref. [11]. f Data of MAGeI3 from Ref. [30]. Data for CsGeI3 and FAGeI3 are 2.75 and 2.73 Å, respectively. g Data of CsGeBr3 from Ref. [33].

The optimized structures of the studied molecules are given in Figure 1 and in the Supporting Information (SI). One would imagine that the bond lengths in the isolated molecules may deviate significantly from those of the corresponding motifs in the bulk crystals, given the apparent difference between the vacuum and the crystal field. However, the calculated bond lengths of these molecules agree with the experimental data of the bulk crystals within 5% -- as shown in Table I. Such level of agreement suggests that both the superhalogens and the superalkalis (as 4


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identified above), to large extent, maintain their individual identities from isolated clusters to the composite ions in the bulk materials [25].

Fig. 2 (a) Onsets of the calculated UV-vis spectra for the admixture molecules CH3NH3PbI3−xBrx. The inset shows the first peaks of the spectra. x = 0-3 correspond to red, light red, cyan and blue, respectively. (b) The CCSD(T) (purple) and DFT-B3LYP (blue) calculated HOMO-LUMO gaps of the molecules compared to the experimental values (red) [6]. (c) The relative gap by shifting the x = 0 value at origin. The solid line shows the least-square fitting to the CCSD(T) relative gap by using Eq. (7). The calculated exciton binding energies of the molecules are shown as open stars.

For the hybrid perovskites, including CsSnI3−xBrx, CH3NH3PbI3-xBrx, CH3NH3SnI3−xBrx, CH3NH3PbI3−xClx, CH3NH3PbBr3−xClx and HC(NH2)2PbI3−xBrx, whose experimental band gaps are available, we calculated the UV-vis spectra of the their corresponding molecules, as shown in Figure 2a and Figure S2 in Supporting Information (SI). In each case, the onset of the spectrum is blue shifted with increasing x from 0 to 3. The same trend has also been observed in the available experimental spectra for the bulk materials [6, 11, 34-35]. The shift indicates that there is an increase of the optical gap upon gradual replacement of iodine by bromine or bromine by chlorine in both molecules and the bulk crystals. Such trend is connected to the increase of the 5



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fundamental gap -- either the HOMO-LUMO gap in the molecule or the band gap in the bulk material, as shown in Figure 2b and Figure S3 in SI. By comparing the dependence of the HOMO-LUMO gap and the band gap on x, it is interesting to see that the curves are almost parallel to each other. If we shift the lowest energy gap (when x = 0) in each case to the origin, as shown in Figure 2c and Figure S3 in SI , we can see that the curve of the HOMO-LUMO gap in the cluster is in good agreement with that of the bulk material (the largest deviation being about 0.2 eV). The CCSD(T) calculated HOMO-LUMO gaps and the TDDFT+B3LYP calculated optical gaps of the studied molecules are given in Table S2 in SI. Another exotic, yet fundamental property of these hybrid perovskites is that their band gap deformation potentials, ag =

∂Eg

∂ ln ( a )

(1)

are positive [15-16], i.e. the band gap Eg decreases with the lattice constant a, which is opposite to the behavior in most semiconductors [36]. To see if such property has a molecular origin, we calculated the change of HOMO-LUMO gaps of CsSnI3 and CsSnBr3 by changing the interatomic distance between Cs and Sn. The distance change is realized in three ways (one can refer to the schematic Figure S4 of SI for visualization): the first is to reduce the distance by evenly drawing the two atoms closer relative to the mid-point of the connecting line (Em); the second is to reduce the distance by only moving the cation along the line connecting Cs and Sn (Ec); and the third is to reduce the distance by only moving Sn along the line connecting Cs and Sn (Es). We choose CsSnI3 and CsSnBr3 here as prototype models of the hybrid perovskites. Note that changing the distance in the above fashion retains all the symmetry operations of the

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system as it would be the case when the material is under hydrostatic compression without any phase transition. The respective gap deformation potentials of the molecules are computed using Eq. (1) and are compared to those of the bulk crystals in Table II. The three calculated gaps against distance are given in Figure S4 of SI. Both Em and Es show positive band gap deformation potentials as does the band gap of the bulk crystal, while Ec shows negative ag. NBO analysis reveals that the HOMO orbital consists of Sn s and Br/I p states, and the LUMO orbital consists of Sn p and Br/I s states. The compositions of these states are found to be the same for the top of the valance and the bottom of the conduction bands, respectively, of the bulk crystals. Both Em and Es involve more overlapping atomic states of Sn and Br/I while Ec does not, which suggests that this is the reason for the positive ag of these materials. Indeed, according to the wavefunction analysis, when Sn is moved 0.08 Å towards the plane formed by the three Br (Figure S4), the total wave function becomes more blended: the contribution to the Sn-Br bond from Sn (s, p) increases by 0.08 %, while the contribution from Br (s, p) decreases the same amount. The larger ag of CsSnBr3 compared to CsSnI3 in the molecules as well as in the crystals should be due to the less diffusive electrons of Br compared to I, making the overlap between the atomic states more sensitive to the distance change. The calculated ag of Es is comparable to the gap deformation due to the change of lattice constant in the cubic hybrid perovskites [37-38]. The negative ag of Ec suggests that the bonding between Cs+ and the super halogen is similar to the ionic bonding in a CsCl molecule whose HOMO-LUMO gap will increase upon shortening the interatomic distance between Cs and Cl.

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Table II Calculated bandgap deformation potentials (in eV) for the Em, Ec and Es (see text for definition) of the studied molecules. These values are compared to the values of the bulk crystals obtained from the quasi-particle self-consistent GW calculations [16]. ag(Em) ag(Ec) ag(Es) ag(bulk) [15-16] CsSnI3 1.87 6.42 7.35 −0.44 10.44 8.99 CsSnBr3 2.47 −5.11

The above studies suggest that the electronic properties of the hybrid perovskites are largely decided by the bonding within the molecular motifs while the neighboring molecules should have less influence. This means that a tight-binding model [39] would be appropriate for these materials with the molecules as the basic building blocks. In such a model, the valence band of the bulk material originates from the HOMO orbital of the corresponding molecule as () = − − () ,

(2)

where EH(k) is the band energy at a wave factor k. EH is the HOMO energy of the molecule. measures the energy change under the influence of the potential ∆V from all the other molecular motifs in the crystal, = − ()|∆V| (),

(3)

where () is the orbital of the molecular motif placed at the origin. Given that ∆V should be negative, the minus sign in Eq. (3) makes positive. depends on the overlap between orbitals of the central molecular motif and the neighboring ones, = − ()|∆V( − )| ( − ), (4) where R is the lattice vector. As in Eq. (3), the minus sign here makes a positive value. () is a periodic function only related to the lattice constant and structure of the crystal. Its value is bounded by a positive upper limit FU and a negative lower limit of −FL (FL > 0). The conduction band originates from the LUMO orbital of the central molecular motif. Thus, we have an equation for the band energy EL(k), 8


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() = − − (),

(5)

where all the terms have the same meaning as in Eq. (2), except that they are all built from the LUMO orbital. Using Eq. (2) and (5), the band gap of the bulk crystal is written as, = ( − − FL ) − ( − + FU ) = HL − − ,

(6)

where HL = − is the HOMO-LUMO gap. Both = − and = FL + FU should be positive, since the unoccupied orbitals are more diffusive and will be more influenced by the potential from the other molecular motifs resulting in bigger . In the crystal structures of the hybrid perovskites, if we pair the (organic) cation and the superhalogen anion to make a lattice, it will almost look like a simple cubic structure, where FL is 0 and FU is 12. By comparing the values of HOMO-LUMO gaps of the molecules and the band gaps of the crystal in Figure 2b, the FL (FU ) values suggest that the values of ( ) and ( ) are of the order of eV, which is normally expected from a tight-binding model [39]. By decreasing the interatomic distance, the integrals in Eq. (3) and (4) will grow bigger (larger and ) and therefore will further reduce the band gap by adding to the already decreased HOMO-LUMO gap HL as shown in Table II. Referring to Eq. (6), the level of agreement between the change of the molecular gap ( HL ) with x and the crystal band gap ( ) with x, as shown in Figure 2c, suggests that the potential exerted on the central molecule from all the other molecular motifs (measured by ) and the overlap integral ( ) change little upon the change of halogens. Our calculations on the molecules do not consider the spin-orbit coupling (SOC). It has been found that, both from our calculations and others [31, 40-41], the SOC contributions to the band gap from the metal Pb, Sn and Ge are in the order of 1.0, 0.3 and 0.1 eV, respectively. For different x but the same metal, this contribution will be subtracted. The SOC contributions from the halogens will only be 9



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partially subtracted for different x. However, these values are found to be quite small (with the largest value of about 0.1 eV for iodine) [31]. Therefore, the error introduced by the lack of SOC in these molecular calculations should be small. Another limitation of the current study is that materials with metal cation mixing cannot be studied by using the molecular model, since each motif only contains a single metal cation. Equipped with the above findings, we can now start to study other molecular admixtures and ‘extrapolate’ the properties of corresponding bulk materials from these motifs. Lead-free analogues of the hybrid perovskites are desired because of environmental considerations. Therefore, we first study the systems with lead replaced by germanium. The calculated UV-vis spectra of the molecules CH3NH3GeI3−xBrx, HC(NH2)2GeI3−xBrx and CH3NH3GeBr3−xClx show the blue shift of the onsets as shown in Figure S2 of SI, suggesting that the band gap of these crystals increases as iodine is replaced by bromine or bromine is replaced by chlorine. As already shown in the above, for the hybrid perovskites, the relative HOMO-LUMO gap of the molecular motif against x (by putting the gap for x = 0 at the origin) serves as a good estimate of the relative band gap of the bulk crystal against x. We can expand the band gap of the crystal as a second-order polynomial [36], = ! + "# + $# %

(7)

with ! as the band gap for x = 0. Such an expansion has been successfully used to describe the experimental band gaps of the admixtures CH3NH3PbI3−xBrx [6]. Coefficients a and b in Eq. (7) can be obtained by polynomial fitting to the relative HOMO-LUMO gaps of the molecules against x, as shown in Figure 2c and Figure S3 of SI. With the fitted values of these two coefficients given in Table III, we can then use Eq. (7) to estimate the band gaps of the bulk

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series CH3NH3GeI3−xBrx, HC(NH2)2GeI3−xBrx and CH3NH3GeBr3−xClx for any value of x (0 < x ≤ 3). Table III Parameters of Eq. (7) for various admixtures obtained by fitting the relative HOMO-LUMO gap of the molecules against x obtained from the CCSD(T) calculations. The x = 0 value of ! is from the available experiments. The calculated energy gaps at x = 3 using the empirical relation of Eq. (7) are compared to the experimental band gaps of the crystals. MA and FA denote for CH3NH3 and HC(NH2)2, respectively.

! (eV)

a (eV)

b (eV)

0.078 1.3a CsSnI3−xBrx b 1.57 0.220 MAPbI3−xBrx c 1.3 0.326 MASnI3−xBrx 2.15c 0.057 MASnBr3−xClx 1.57b MAPbI3−xClx 0.197 b e 2.29 /2.35 0.167 MAPbBr3−xClx 1.48f FAPbI3−xBrx 0.168 1.9g 0.300 MAGeI3−xBrx 2.63 0.095 MAGeBr3−xClx 2.2g FAGeI3−xBrx 0.291 1.57b MAPbI3−x(BH4)x −0.150 f 1.48 FAPbI3−x(BH4)x 0.129 1.3c MASnI3−x(BH4)x 0.178 g 1.9 0.040 MAGeI3−x(BH4)x g 2.2 0.442 FAGeI3−x(BH4)x 1.9g 0.125 MAGeI3−x(HCOO)x g 2.2 FAGeI3−x(HCOO)x −0.103

0.027 0.025b −0.035 0.051 0.102 0.020 0.034 −0.019 0.015 −0.029 0.248 0.171 0.089 0.150 0.022 0.197 0.295

Admixture

(Calc.) (eV) 1.78 2.45 1.96 2.78 3.08 2.97/3.03 2.29 2.63 3.05 2.81 3.35 3.41 2.63 3.37 3.72 4.05 4.55

a

(Exp.) (eV) 1.8a 2.29b 2.15c 3.69d 3.1e 3.1e 2.23f 3.72h -

Eb(x=0) Eb(x=3) (meV) (meV) 3.89 8.51 6.10 22.62 3.89 11.20 14.83 35.94 6.10 50.94 18.11 44.51 5.26 18.11 10.23 28.81 28.81 49.11 15.94 36.40 6.10 70.08 5.26 75.06 3.89 28.81 10.23 71.70 15.94 105.71 10.23 148.95 15.94 240.70

Experimental value from Ref. [16]. Experimental value from Ref. [6]. For MASnI3−xBrx, the fitted bowing factor b = 0.025 eV here from the molecular HOMO-LUMO gaps is equivalent in value to 0.025×9 = 0.225 eV, agreed well to the fitted bowing factor of 0.30 eV from the experimental data of band gaps [6]. c Experimental value from Ref. [31]. d Experimental value from Ref. [42]. e Experimental value from Ref. [35]. f Experimental value from Ref. [34]. g Experimental value from Ref [28]. h Derived from the PBE value and the GW value of the material at its high-temperature cubic phase (Pm−3m) [31], by assuming that the GW correction to the band gaps obtained from PBE is the same for different phases of the material [16]. b

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There has been a recent report of successful synthesis of more than 30 new stable perovskite materials where halogen ions (Cl, Br, I) were replaced by [BH4]− superhalogen [43]. The effective ionic radius of the super ion [M(BH4)3]− is found to be very similar to that of [MBr3]− in the hybrid perovskites [25]. Based on these, we set out to study the properties of the admixtures of AMI3−x(BH4)x (A = CH3NH3, HC(NH2)2; M = Pb, Sn, Ge). There is a universal blue-shift of the onsets of the calculated UV-vis spectra upon the replacement of iodine by [BH4]−. What is interesting here is that the change of the HOMO-LUMO gap and the optical gap is small with partial replacement, however, the change jumps with full replacement in AM(BH4)3. These are shown in Figure 3 for CH3NH3PbI3−x(BH4)x and in Figure S2 of SI for the other admixtures. We expect the same behavior for the band gaps of the corresponding crystals according to our earlier discussions.

Fig. 3 (a) Onsets of the calculated UV-vis spectra for the admixture molecule CH3NH3PbI3−x(BH4)x. The inset shows the first peaks of the spectra. x = 0-3 correspond to red, light red, cyan and blue, respectively. (b) The CCSD(T) (purple) and DFT-B3LYP (blue) calculated HOMO-LUMO gaps of the molecules. (c) The relative gap by putting the x = 0 value at origin. The solid line shows the least square fitting to the CCSD(T) relative gap by using Eq. (7). The calculated exciton binding energies of the molecules are shown as open stars.

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The reason for the small change of energy gaps on partial replacement can be found using the NBO analysis of the admixtures. In the extreme cases where we have AMI3 on one end and AM(BH4)3 on the other, the HOMO and LUMO of the former are mainly from the I(5p) and M(4p~6p) electronic states, respectively, while these orbitals of the latter are from the much lessenergetic s and p states of hydrogen and boron. This explains why the difference in the gap between these two cases is as large as shown in Figure 3 (about 2 eV). However, with only partial replacement of iodine by [BH4]−, the HOMO-LUMO gap will still be decided by the I(5p) and M(4p~6p) states of the electron due to the hybridization of these more energetic and more diffusive states with the s and p states of hydrogen and boron, respectively. The same argument goes for the crystal band structures where the valence and conduction bands originating from the I(5p) and M(4p~6p) orbitals will be much wider than the bands originating from the s and p orbitals of hydrogen and boron. This is because the electronic wave functions of the former are much more diffusive, resulting in much larger overlap-integrals in Eq. (4) and wider band according to Eq. (2). The band gap will also be much smaller in such cases according to Eq. (6). Upon partial replacement of iodine by [BH4]−, however, the top of the valence band will still be determined by the I(5p) and M(4p~6p) orbitals, since these orbitals will broaden out the top of the valence band and the bottom of the conduction band (see Figure S5 of SI). Such observation suggests that, although crystals AM(BH4)3 may show large band gaps, the admixed crystals AMI3−x(BH4)x with small x should have band gaps within the visible range based on the known small band gaps (~1.5 eV) of AMI3 [6, 34]. The fitted parameters in Eq. (7) of these new admixtures together with those of the ones studied before are summarized in Table III. It is now possible to derive the band gap of the 13



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admixture material with any 0 < x ≤ 3 based on the band gap value for x = 0. The band gap calculated as such at x = 3 is given for each set of the admixtures. The predicted values agree well with the values from the available experiments, as shown in Table III. According to our prediction, band gaps of AM(BH4)3 should be similar to those of AMCl3. The TDDFT method together with the hybrid functional B3LYP is quite successful in the description of the optical excitation of finite systems of molecules and quantum dots [44-48]. The optical gap for each molecule is identified as the first electronic transition with non-zero oscillator strength, as shown by the first peak in Figure 2a and Figure S2 of SI . The exciton binding energy of the molecule is then the difference between the HOMO-LUMO gap and the optical gap [44]. The calculated exciton binding energies of the studied molecules are given in Table S2 of SI. The Wannier exciton binding energy is inversely proportional to the square of the relative dielectric constant which becomes smaller for larger band gaps [47]. The exciton binding energy of a single molecule is also related to its HOMO-LUMO gap [48]. By fitting to the data of a number of semiconductors (see Table S3 of SI) and the studied molecules in this work, we find a relation between the fundamental gap (Eg) and the exciton binding energy (Eb),

log10  Eb ( meV )  = 4.4538 − 4.9568 × exp  −0.1917 × Eg ( eV )  ,

(8)

as shown in Figure S4 of SI. Since the studied hybrid perovskites are all direct bandgap semiconductors, the semiconductors used here are of the same type. With such empirical relation, we can use the predicted band gaps of the hybrid perovskites from the molecular model (as given in Table III) to estimate the exciton binding energy of these materials, as shown in the last two columns of Table III. For example, the estimated exciton binding energy of the hybrid 14


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perovskites CH3NH3PbI3 and CH3NH3PbCl3 are 6.10 and 50.94 meV, respectively, which agree well with the measured values in these materials [49-50]. According to the estimation, most studied mixed-halide perovskites are non-excitonic, while the ones with [BH4]− should have larger binding energy. We now address the stability of the new hybrid perovskites AM(BH4)3 against moisture. It is observed in the experiments [6, 50-51] that the hybrid perovskites, especially CH3NH3PbI3, are hygroscopic and readily decompose into CH3NH2, HI and PbI2 when exposed to a trace amount of water and/or intense light. In a proposed reaction of such decomposition, the water molecule serves as a catalyst [50]. It has been shown that the degradation mechanism can be successfully modeled by using merely a single molecular motif [25]. The newly invented admixtures here with [BH4]− are also expected to be hygroscopic due to ionic nature of the bond between the superalkali and superhalogen. Calculations using the molecular model reveal that the water molecule is likely to be trapped between the organic cation and the inorganic anion of [MX3]−. The binding energy between a water molecule and the molecular CH3NH3Pb(BH4)3 is 0.59 eV which is significantly smaller (12 %) than the binding energy of 0.67 eV between a water molecule and CH3NH3PbI3 [25]. It is well known that boron hydrides are easily hydrolyzed. The reaction mechanism between water and [BH4]− is as follows [52]. The first step of the reaction will be H2O + BH4− = H3B(OH)− + H2.

(9)

The reaction is based on the fact that H is negative in BH4− and, in H2O, O is strongly negative while H is positive. Therefore, H in BH4− and H in H2O will first attract each other to form H2. Meanwhile, the positive B will attract negative O to form a complex H3BOH−. There are a few 15



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possible reaction routes afterwards between H2O and the complex H3BOH− to complete the hydrolysis process, but the first key step is to have H3BOH−. However, in the case of the hybrid perovskites, such CH3NH3[Pb(BH4)3], the reaction of the super halogen [Pb(BH4)3]− with H2O will not be the same, given the different charge states of atoms (from NBO analysis). Pb is strongly positive (+1.31e), B is strongly negative (−0.64e), and, since there are twelve H, each H will be almost neutral (−0.02e), i.e. ten times smaller than the charge on H in BH4−. Thus, the attraction between the positive H in the H2O and the H in the molecule CH3NH3[Pb(BH4)3] will be tiny and the strongly negative B in this case is unlikely to be attracted to the strongly negative O in H2O. Also, with the presence of CH3NH3+, O in H2O would rather stay with the organic cation. All these make the hydrolysis reaction in (9) difficult to happen.

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Fig. 4 Calculated reaction pathway of CH3NH3Pb(BH4)3 with a water molecule (energy difference with the transition state vs. the H-O distance). The ball-and-stick plots show the reactant, transition and product states, respectively. The corresponding data points of these states are numbered accordingly. The values in these plots show the bond length in Å.

Based on the molecular model, we have been able to identify the reaction between CH3NH3Pb(BH4)3 and the water molecule as a Grotthuss mechanism [53], where one proton of NH3 in the organic cation hops onto the water molecule and one original proton of the water molecule on the other side is transferred to [Pb(BH4)3]−. Such process, including the reactant, transition and product states, is shown schematically in Figure 4. The energy barrier between the reactant and the transition state is 0.83 eV while the barrier between the product and the transition state is negligibly small, namely, 0.04 eV. Such behavior together with the relatively

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small binding energy with water suggests that the studied admixtures with [BH4]− would be more resistant to moisture than the regular boronhydrides. We have shown that the properties of the organic-inorganic hybrid perovskites, including the fundamental gap, the gap deformation potential, the exciton binding energy, and the hygroscopicity, all originate from their corresponding molecular moieties. Therefore, it is possible to make quick estimations for the properties of new hybrid perovskites by using simple molecular models, which can serve as a preliminary screening process. Such process is useful given that there are hundreds of hybrid perovskites predicted to exist based on the Goldschmidt's tolerance factor [19] and the accurate bulk calculations based on DFT-HSE and relativistic effects, especially for those materials with heavy metals (such as lead), will be quite expensive. For example, one can easily extend the current study to new hybrid perovskites composed by superhalogens other than [BH4]−. [HCOO]− has one of the largest radii among the candidates of superhalogens [19]. According to the calculated tolerance factor, CH3NH3Ge(HCOO)3 and HC(NH2)2Ge(HCOO)3 can form the perovskite structures. By using the molecular model, we can readily predict the band gaps and the exciton binding energy for the admixtures MAGeI3−x(HCOO)x and FAGeI3−x(HCOO)x, as shown in Table III. A combination of the use of Goldschmidt's tolerance factor [19], the molecular-model method (as demonstrated here), and finally the accurate bulk calculation can be applied to identify colorful hybrid perovskites with improved stability and functionality.

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METHODS Our calculations on clusters are carried out using the GAUSSIAN03 package [54]. The hybrid density functional theory (DFT) method with Becke three parameter Lee-Yang-Parr (B3LYP) [55-56] prescription for the exchange-correlation energy is used. The fundamental gaps of the molecules are calculated using the coupled cluster method CCSD(T). The basis set used for halogen ions is 6-31+G*. For Ge, Sn and Pb, aug-cc-pVDZ basis sets with the effective core potential are used. For each admixture of AMX3−xYx (x = 0-3), the corresponding molecular motif is optimized to its ground state without any imaginary frequency. The ultra-violet-visible (UV-vis) spectrum of the molecule is then computed from 100 singlet states by using the timedependent DFT (TD-DFT) [57]. Natural bond orbital (NBO) analysis is used to obtain the atomic charge state and the bond composition of the molecule. The binding energy between two molecules is calculated using the counterpoise correction to avoid the basis set superposition error. DFT calculations for the crystalline phase are performed with the projector augmented wave (PAW) [58] and the Perdew-Burke-Ernzerhof generalized gradient approximation (PBEGGA) [59] using the VASP package [60-61]. The electronic structure calculations are performed with and without the spin-orbit coupling (SOC). The plane-wave cutoff energy is set to 600 eV. Monkhorst-Pack 6 × 6× 6 k-meshes [62] are adopted.

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ASSOCIATED CONTENT Supporting Information Calculated ionization potential and electron affinity for organic cations and inorganic anions in the hybrid perovskites, calculated UV-vis spectra for the studied molecular admixtures, calculated HOMO-LUMO gaps and the exciton binding energyies for the studied molecules, data of calculated HOMO-LUMO gaps and optical gaps, schematic plots showing the three ways to change the atomic distance, calculated gap deformation potentials, DFT-PBE calculated electronic density of states (DoS) for the crystalline admixtures MASnI2(BH4) and MAGeI2(BH4), experimental data of band gaps and exciton binding energy of direct bandgap semiconductors, and collected data of direct bandgap semiconductors and the studied molecules.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work is supported in part by the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under Award # DE-FG02-96ER45579. Resources of the National Energy Research Scientific Computing Center supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231 is acknowledged. We also thank the National Institute for Computational Sciences for letting us use their computational resources (Darter).

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