Revealing the Chemistry Between Band Gap and Binding Energy for Lead-/Tin-Based Trihalide Perovskite Solar Cell Semiconductors

Accepted Article

Title: Revealing the Chemistry between Bandgap and Binding Energy for Pb/Sn-based Trihalide Perovskite Solar Cell Semiconductors

Authors: Arpita Varadwaj, Pradeep R. Varadwaj, and Koichi Yamashita

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To be cited as: ChemSusChem 10.1002/cssc.201701653

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www.chemsuschem.org ChemSusChem 10.1002/cssc.201701653

Accepted Article

Revealing the Chemistry between Bandgap and Binding Energy for Pb/Sn-based Trihalide Perovskite Solar Cell Semiconductors

Arpita Varadwaj, a,b Pradeep R. Varadwaj, a,b, ∗ Koichi Yamashita a,b

aDepartment of Chemical System Engineering, School of Engineering, The University of Tokyo 7-3-1, Hongo, Bunkyo-ku, Japan 113-8656 bCREST-JST, 7 Gobancho, Chiyoda-ku, Tokyo, Japan 102-0076

A relationship between reported experimental bandgaps (solid) and presently DFT- calculated binding energies (gas) is established for the first time for each of the four ten-membered lead (and tin) trihalide perovskite solar cell semiconductor series examined in this study, including CH 3NH 3PbY 3, CsPbY 3, CH 3NH 3SnY 3 and CsSnY3, where Y = I (3 – x) Br x=1–3, I(3 – x) Cl x=1–3, Br (3-x) Cl x=1–3, and IBrCl. The relationship unequivocally provides a new dimension for the fundamental understanding of the optoelectronic features of the solid state solar cell thin films using the 0 K gas-phase energetics of their corresponding molecular building blocks.

Manuscript Accepted

∗ Corresponding Author’s E-mail Addresses: [email protected] (PRV)

Accepted Article

1. Introduction Hybrid organic-inorganic trihalide perovskite solar cell semiconductors are rising star materials for photovoltaics. 1-2 They have been demonstrated to be extraordinary for their abilities of solar power conversion efficiency (PCE) into electricity. Although perovskite compounds are known over several decades, 3a)-c) Kojima and co-workers have observed that halide perovskites

have extraordinary self-organization potential on the nanoporous TiO 2 layer of dye-sensitized cells.

They have reported a PCE of 2.2% for methylammonium lead tribromide (CH 3NH 3PbBr 3) in 2006, 3d) 3e) and of 3.8% for methylammonium lead triiodide (CH 3NH 3PbI 3/MAPbI 3) in 2009. With courageous experimental trials by diverse research groups, the first efficient solid- state perovskite cells were discovered sometime around mid-2012. Since then there has been an upsurge of scientific interest to develop and design environmentally stable and highly efficient solid state solar cells. These attempts, in fact, have led the PCE to meet at certified values of 16.2% in 2013, 20.1% in 2015 and 22.1% in 2016.4 Shin et al. have just recently reported that perovskite solar cells can display both high efficiency (21.2%) and long-term stability (1,000 hours of light

exposure) if photoelectrode materials such as Lanthanum (La)–doped BaSnO 3 (LBSO)) are introduced under very mild conditions below 200 °C.5 Hypothesis to achieve PCEs over 35% has been extensively discussed in the past two years.6 Grancini and coworkers have recently showed that stable perovskite devices can be designed by 2D/3D interface engineering that might last for a year. To this end, they have Manuscript experimentally designed a perovskite junction that comprises the 7 (HOOC(CH 2)4NH 3)2PbI 4/CH 3NH 3PbI 3 architecture. Similar other researches have indicated that large-area printed perovskite solar modules can be stable for more than 10,000 hours under continuous illumination. 8 A recent study has demonstrated that perovskite solar cells with cuprous thiocyanate (CuSCN) as hole extraction layers retain more than 95% of their initial efficiencies of over 20% under full sunlight illumination at 60 oC for more than 1000 hours, and that CuSCN is stable, efficient and cheap compared to various inorganic hole transport materials (e.g. spiro- OMeTAD). 58 Although perovskites are viable in the literature in different flavors, 11-15 an extensive class 11,13-16 of these compounds is represented by the generic formula BMY3. In BMY 3, the Y-site anion Accepted is commonly the late halogen derivative (Y = Cl, Br, I), even though non-halogenated species such – – – as HCOO , SCN , and N 3 , etc. , occupying this site is not very rare. The B-site cations are experimentally observed to be both organic and inorganic, while M is abundantly the divalent + 2+ – metal cation. Thus when B = CH 3NH 3 , M = Pb and Y = I , the resulting BMY 3 formula refers

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CH 3NH 3PbI 3. It is this system that has been extensively studied due to its high semiconducting performance for light conversion, 17 which is an organic-inorganic hybrid material. 9 When B = Cs +, M = Pb 2+ /Sn 2+ and Y = Cl –/Br –/I –, the resulting compounds are another type of perovskite 9 + + 2+ 2+ hybrids, but are purely all-inorganic. Similarly, when B = Cs /CH 3NH 3 , M = Pb /Sn and Y = – HCOO , one can come up with another type of BMY 3 perovskites that include the metal-organic perovskite frameworks. 9, 13 Recent studies show that lead-free perovskites (viz. double perovskite semiconductors) might be good for the development of high-efficiency solar cells. 18-20 Apart from the rapid progress of the field within last 7-8 years, there has been a great deal of confusion in the perovskite literature starting from the use of correct terminology.9, 10, 21 For

instance, CH 3NH 3MI3 and its sister associates have been referred in the literature to as organometallic compounds, 22-26 even though these have no such connection with organometallic chemistry. Varadwaj 9 has recently noted that these systems should not be called as organometallic because organometallic compounds are classically coordination compounds that contain at least a

carbon-metal bond, whereas CH 3NH 3MY3 (Y = Cl, Br, I) do not include any such bonding attributes. This view supported by others was immediately appeared in an editorial of ACS Energy Letters since justification of urgency in delivering this message to the community was warranted. 10a

Some recent studies have already started referring CH 3NH 3PbI 3 and its sister associates to

as "organohalide perovskites".27-30 According to Varadwaj, 9 this is also misleading because the Manuscript term "organohalide" strongly overlaps with the already established terminology called “organohalide” that readily refers to organohalide compounds that contain the carbon-halide covalent bond.30-35 This means that organochlorides, organobromides, and organoiodides, etc. , which are halogen-substituted halocarbon compounds are organohalide compounds.30-35

Iodomethane (CH 3I), CFCs (chloro-fluoro-carbonated compounds), halogen-substituted benzene derivatives (e.g., hexachlorobenzene), and others, are common examples of organohalide compounds. Similarly as the organometallic compounds (e.g., organopalladium), organohalide compounds are also classified by prefixing the organic moiety with "organo-". The primary difference between these two types of compounds is that the former are coordination compounds whereas the latter are halogen-substituted organic compounds. From these rationalizations, it is Accepted

evident that the hybrid organic-inorganic BMY 3 (B = CH 3NH 3, Y = halogen derivative) perovskite systems are neither organohalides nor organometallics, since they lack both the metal-carbon and halide-carbon coordinate and covalent topologies of chemical bonding, respectively, an important yet simplistic area of chemistry whose terminologies should be utilized with caution. This view

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might be in line with a most recent editorial of ACS Energy Letters composed by Kamat " … we often see poorly executed research that ignores the accuracy of data analysis and interpretation of ... Researchers who are new to the field should make an effort to go through the early research papers and familiarize themselves with the basic concepts of photochemistry..." 10b Another important issue of the perovskite field deals with the relationship of the polar

and/or apolar natures of the CH 3NH 3PbI 3 system with ferroelectricity and hysteresis. For instance, 36 Sharada et al. have demonstrated that tetragonal CH 3NH 3PbI 3 is nonpolar. In contrary, Rakita et al. have encouraged to treat this material as ferroelectric, 37 meaning it is polar.37-39 The latter view is in contrast with the rationalization of Yuan et al. ,47a who have asserted that “On the experimental

side, although switchable local phase contrast in PFM imaging of MAPbI 3 films was observed, which, in principle, could be explained by the MA + ordering, no reliable hysteretic piezoresponse force microscopy (PFM) loop has been observed at RT in either single crystalline or polycrystalline samples.47b To date, there is no solid experimental evidence to support the notion

of ferroelectricity in MAPbI 3 despite speculations on the polar ordering in tetragonal MAPbI 3 at RT”. Others claim that the hysteresis in the I-V characteristics of planar perovskite solar cells originates from defects at the perovskite layer interfaces, and so on. 40-50 Similarly as CH 3NH 3PbI 3, formamidinium lead triiodide perovskite (HC(NH 2)2PbI 3) 50 51 solar cell is also ferroelectric, but CsPbI 3 is not ferroelectric but hysteristic. Coequally, Manuscript CH 3NH 3PbBr 3 and HC(NH 2)2PbBr 3 are shown as ferroelectrics, but CsPbBr 3 is not; the latter is an excellent halide conductor. 52-55 The ferroelectric nature of the above materials is proposed due to the dipolar nature of the B-site organic cation.56 Since the cation experiences rotational motion

due to the increase in the temperature of the CH 3NH 3PbI 3 system, it introduces hysteresis in the material via ferroelectric polarization.40,49,57 Thus the replacement of the polar organic cations + + CH 3NH 3 (MA) and HC(NH 2)2 (formamidinium, FA) with apolar ones (i. e., those with zero dipole moments), 51-60 as well as that with larger sized cations, 61 was suggested to be ideal for testing whether the origin of the ferroelectric domain, as well as of anomalous hysteresis, is an unintended consequence of the rotational motion of the dipolar organic cation trapped inside the metal-halide inorganic cage. Toward this end, Eperson et al. ,51 Chen et al. ,59 and Kumar et al. 60 have considered the Accepted zero dipole moment inorganic cesium cation, while Haruyama et al. , 61 Hau et al. , 62 and Giorgi et 63 + al. considered the zero dipole moment organic cation called guanidinium (C(NH 2)3 , GA). The strength of the dipolar moment µ for all the notable B-site cations extensively examined so far is

in this order: μ ≫ μ > μ ≈ μCs+ ≈ 0. The trend in µ in the series is indeed consistent MA FA GA

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with the degree of charge asymmetry in the four cations (MA > FA > GA > Cs +), as well as that with their overall molecular symmetries (MA < FA < GA < Cs +). Giorgi et al. 63 have counselled theoretically that changing the nature of the organic cation from polar MA to apolar GA one can greatly reduce the abnormal hysteresis feature from perovskite-based devices. According to them,

"…in order for to have a hysteresis-free GAPbI 3 system the necessary requirement is that the organic cation has to have a zero dipole moment and a well-defined molecular size that can fit well inside the space provided by the lead iodide cavity." Interestingly, however, the prediction-based speculations of these authors do not match with a recently reported experimental finding. 51 For + instance, the replacement of MA in MAPbI 3 with the Cs cation did not lead to any such conclusion that can prove zero dipole moment cations can greatly reduce hysteresis in the material .63 This + means that the presence of the non-polar Cs cation in CsPbI 3 did not enable rationalizing what is the exact origin of ferroelectricity and hysteresis.51 It is obviously due to the fact that

CsPbI 3 perovskite solar cell devices do display significant rate-dependent current–voltage hysteresis.51,61 This result of Eperon, et al. 51 has unambiguously led the conclusion that ferroelectricity may be a dipolar dependent feature, but certainly dipole moment is not a factor controlling hysteresis. According to them, ferroelectricity is not required to explain current– voltage hysteresis in perovskite solar cells. Meloni et al. have investigated the microscopic process causing hysteresis, in particular,

to examine whether hysteresis is due to ferroelectricity or ionic polarization.57 Their results Manuscript

have concluded that the hysteresis observed in J-V curves of different MAPbY 3 perovskite solar cells is a thermally activated process. From all these discussions summarized above, it is clear that the conclusions drawn by various authors do not match one another. This is perhaps not very surprising given the research field is perhaps new, thereby needing many discussions to clear the air. Our view might be in line with Nie and teammates, 64 who have just recently speculated that the understanding of the entire

working profile of the organic cation in CH 3NH 3PbI 3 is still primitive. Yet it is anticipated that the role of the B-site cation is substantial in the photo-stability of perovskite devices, which may open roots for further future investigations.

The formula BMY3 generically represent classical perovskites that can be viewed as the Accepted + – 9, 21 combination of two monomeric fragments, B and MY3 . Thus halide perovskites resulting from the combination of organic moieties with inorganic moieties are not just driven by Coulomb type attractive electrostatic interactions. In addition to substantial contributions from electrostatics, inductive and dispersive interactions play a predominant role to enhance appreciably the

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stabilization energies for these systems. 9,21 Because these latter two interactions contribute largely -1 9 (e.g., –26.61 and –11.95 kcal mol for CH 3NH 3SnI 3, respectively ), it is customary to accept the + – fact that the intermolecular chemical bonding interactions holding the two fragments B and MY 3 + – together in the B ••• Y3M bulk/block equilibrium geometries contain appreciable amount of covalency. 9,21 + – A periodic extension of the B ••• Y3M bulk (or even a non-periodic expansion of the + – B ••• Y3M block) can lead to its supramolecular emergence in higher dimensions. For instance,

the periodic expansion of the unit cell of MAPbI 3 leads to the large-scale development of its orthorhombic, tetragonal and pseudocubic polymorphs in 3D that are stable at temperatures below 165 K, between 165 and 327 K, and above 327 K, respectively. 65-66 A computational study of Moleni et al. has suggested that when the atoms are arranged in an orthorhombic-like phase, it produces non-negligible values for all the three Pb–Y–Pb (Y = Cl, Br, I) tilting angles in the

three principal directions between 100 and 200 K for MAPbY 3 perovskites. At temperature

around 300 K, two of these three tilting angles are reduced and the structure of the MAPbY 3 system becomes tetragonal-like. Finally at 400 K, all the three tilting angles are approximately 0° and the resulting polymorph is cubic-like. 57 One of our recent investigations has indicated

that additive (cooperative) binding plays an important role during the self-assembly of the MAPbI 3 system in higher dimension. 67 It is maximized in the orthorhombic phase of the system since it Manuscript maximizes the number of short intermolecular noncovalent interactions between the host and guest species, causing the formation of the lowest energy structure. 68 Moreover, it has been realized that as dimension of the halide perovskite material increases, + – the bandgap decreases marginally. This enforces the resulting B ••• Y3M perovskites to become 69 ideal for photovoltaics. Note that bandgap (symbolically denoted by E g) is one of the most important integrated aspects of semiconductor physics.70 UV-vis and Photoluminescent spectroscopic techniques are generally yet routinely employed for the accurate determination of 71-74 Eg for solid state materials. Experimentalists often refer this property to as the onset of optical absorption. 76 It is strongly related with the so-called Shockley–Queisser limit that applies to cells with a single p-n junction architecture.76-77 It is the determinant of whether or not a given material 78

can be regarded as a metal, or an insulator, or a semiconductor. The nature of this property is Accepted controlled by many factors. For instance, it can be tuned by manipulating atomic constituents, changing the electronic structures, varying cell volume and lattice constants, and controlling the intermolecular interaction parameters, among several others.79-86 For materials with cubic

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symmetry, a linear dependence of lattice constant a on the bandgap Eg is expected since the energy associated with the latter property is inversely proportional to the square of the former. 87 The bandgap of any solid state material is theoretically determined by taking the difference between the electronic energies of the valence band maximum (VBM) and the conduction band minimum (CBM). 88 In molecular systems, the difference between the energies of the highest occupied and lowest unoccupied molecular orbitals (HOMO and LUMO, respectively) is analogous to bandgap, but it is called HOMO-LUMO fundamental gap.89-90 Although discussions

concerning the nature of the VBM and CBM for the CH3NH 3PbY 3 perovskite semiconductors is a matter of some controversy, 91 it is being increasingly recognized that the top of the VB is built by an antibonding linear combination of s states of the B-site and p-states of the Y-site, whereas the bottom of the CB is built by the π antibonding states of the corresponding species. The strong antibonding B s –Y p state may be more delocalized than the Y p alone, likely leading to a small hole effective mass, promoting large hole mobility in the perovskite solar cell. Apart from these, and from a theoretical perspective, factors that influence the determination of bandgap for solid state materials lie in the amount of Hartee-Fock (HF) exchange incorporated in density functionals, 90 the spin-orbit coupling and relativistic treatments. 92 Both favorable and contrasting views featuring whether or not one should consider these latter two attributes for the calculation of the bandgap properties of solid state materials have been discussed elsewhere. 92-93,75 In our experience,

percentages of HF and correlation exchange mixing are both vital in tuning the bandgap (or Manuscript HOMO-LUMO gap) of any crystalline material (or molecular domain). In this study, we have performed density functional theory (DFT) calculations with the standard Perdew–Burke–Ernzerhof (PBE) functional, 94 in conjunction with a moderate basis set + – [aug-cc-pVTZ(for CH 3NH 3 , Cl, Br)/aug-cc-pVTZ-PP(for PbI 3 )], to evaluate the equilibrium geometries and binding energies for ten molecular building blocks of the methylammonium lead

trihalide (CH 3NH 3PbY 3/MAPbY 3) perovskite series in the gas phase at 0 K, where Y = Br (3-x) Cl

x=1–3, I(3 – x) Cl x=1–3, I(3 – x) Br x=1–3, and IBrCl. For reasons discussed latter, similar calculations were + performed with the same level of theory [PBE/aug-cc-pVTZ(for CH 3NH 3 , Cl, Br)/aug-cc-pVTZ- – PP(for SnI 3 )] to evaluate the same properties for ten molecular blocks of tin based perovskites

called methylammonium tin trihalides (CH 3NH 3SnY 3/MASnY 3). Analogous calculations have Accepted

also performed for another two BMY 3 perovskite series. However, at this time, the B-site species is replaced by the Cs cation, whereas the M and Y site species were kept unchanged. These two

perovskite series therefore include CsPbY 3 and CsSnY 3, where Y = Br (3-x) Cl x=1–3, I(3 – x) Cl x=1–3, I (3

– x) Br x=1–3, and IBrCl. It is worth noting that the aforesaid Dunning’s type correlation-consistent

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triple-ζ basis set opted for the computation of the geometrical and energetic properties of the

CH 3NH 3PbY 3 and CH 3NH 3SnY 3 series is unavailable for the cesium atom in the EMSL basis set exchange library. 95 Instead, we have employed an all-electron DZP basis set for all atoms for the

CsPbY 3 and CsSnY 3 series. The uncorrected binding energies for all the forty perovskite blocks were corrected for basis set superposition error (BSSE) using the counterpoise procedure of Boys and Bernardi. 96 Besides, it must be kept in mind that binding energy, ∆E, is a measurable molecular and + – supramolecular property. In CH 3NH 3 ••• Y3M perovskites, it refers the strength of the Y•••H + ultra-strong hydrogen bonds ( vide infra ) that unite the two monomeric fragments CH 3NH 3 and – + – MY 3 together in complex configurations (cf. Fig. 1a). In Cs ••• Y3M perovskites, it refers the + – strength of the Y •••Cs coordinate bonds that unite the monomeric fragments Cs and MY 3 together in complex configurations. Numerous gas phase studies on hydrogen bonding,97 halogen bonding, 98-99 and coordinate bonding, 137 as well as those on noncovalent bonding interactions, estimate ∆E to quantify the interaction strength between atomic/molecular domains to understand the importance of these interactions and their cooperativeness in the emergence of two- and many- body complex systems. 100-103 A primary focus of this study is thus to connect the solid state with the gas phase molecular + – physics for the trihalide based B ••• Y3M perovskite systems. In particular, firstly, it aims to Manuscript establish whether the BSSE corrected binding energy, ∆Ecorr , calculated for each member of the

four trihalide perovskite series (CH 3NH 3PbY 3, CH 3NH 3SnY 3, CsPbY 3 and CsSnY 3) in the gas

phase has any direct connection with the bandgap E g available experimentally for the corresponding system in the solid state. If so, secondly, the next focus is to investigate whether can ∆Ecorr be utilized to predict accurately the experimentally missing bandgaps for the remaining

members of each of the four BMY3 perovskite series examined? The final aim is to show whether corr the dependence between E g and ∆E can be categorized as kind of a structure-property relationship?

Accepted

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2. Computational details

Scheme 1 illustrates the three possible orientations of the organic cation inside the lead halide 128 cuboctahedron of CH 3NH 3PbI 3, which were experimentally known. Fig. 1b illustrates the polyhedral form of the geometry depicted in Scheme 1a, showing the same orientation of the

organic cation MA inside the 2 ×2×2 supercell model geometry of CH 3NH 3PbI 3 emerged using its bulk geometry depicted in Fig. 1a. The bulk geometries for b) and c) of Scheme 1 are not shown.

Scheme 1: Illustration of the alignment of the organic cation (MA) along the a) [111], [100] and c) [110] directions in MAPbI 3 cuboctahedron. The orientation of the molecular ionic dipole of MA is displayed Manuscript for the [111] and [110] directions (red arrows), and its orientation for b) faces the viewer (not shown).

104 The Gaussian 09 software was used to optimize forty BMY 3 molecular perovskite building blocks using the PBE exchange-correlation density functional. Only the [111] orientation of the

B-site cation for the BMY 3 perovskite series is considered (Fig. 1a), which is one of the most favorable orientations of the cation in the room temperature cubic phase in the solid state.

The binding energy ∆E for each BMY 3 molecular building block is calculated using Eqn. 1,

where E T is the electronic total energy for the individual species involved. + – + – + – ∆E (B ••• Y3M) = E T (B ••• Y3M) – ET (B ) – ET (MY 3 ) ……………………………..(1) The BSSE corrected binding energy for each molecular building block is evaluated by using Eqn 2, where E(BSSE) is the BSSE energy. Accepted corr + – + – + – ∆E (B ••• Y3M) = E T (B ••• Y3M) – ET (B ) – ET (MY 3 ) + E(BSSE)…………...... ….(2) Gaussview 05 was used to visualize and analyze the geometrical and vibrational properties of 105 the BMY 3 systems.

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3. Results and discussion

(i) The CH 3NH 3PbY 3 series

An important aspect of lead/tin trihalide perovskite semiconductors lies in the nature of their bandgaps.86 For the

CH 3NH 3PbY 3 (Y = Br (3-x) Cl x=1–3, I(3–

x) Cl x=1–3, I (3–x) Br x=1–3, and IBrCl) semiconductor series, the character of the bandgap is either direct, or direct-to- indirect, or a combination of the two. If it falls into the former category, then it is excellent for direct light absorption. If it falls into the latter category, then it is good for both direct light absorption and slow electron-hole recombination (due to increasing life-time for charge carriers – Manuscript a consequence of bandgap transition), which might explain why these compounds have long diffusion lengths. 138a-b These features are necessary for an efficient extraction of charge carriers

even with modest mobility and for high 138c open circuit currents and voltages. These are essential factors for the Fig. 1: a) The unit-cell of CH 3NH 3PbI 3, illustrating the alignment of the organic cation along the [111] direction. optimization of high solar power b) The 2 ×2×2 supercell geometry of CH NH PbI , 3 3 3 conversion efficiency. 138 constructed using a). The PBE/PAW method, together Accepted with a Γ-point centered 8 ×8×8 k-point mesh for Brillouin The bandgap for the zone sampling and plane-wave energy cut-off of 520 eV, CH NH PbY series is tunable in the was used to obtain the bulk geometry a) using VASP. 110 3 3 3 1.50 – 3.10 eV range. 86,106–109 This range has been routinely determined

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experimentally with a range of very common measurement techniques by diverse research groups, which have justified urgency in publication in many high impact journals. Interestingly, the aforementioned bandgap range covers a substantial part of the visible range of the electromagnetic spectrum (1.59 (red) – 3.26 eV (violet)), and extends up to the near infrared region (0.90 – 1.58 eV). The tunability of bandgap is believed to be driven by compositional engineering of the constituent halogen derivative. For any of the four perovskite series considered in the study, this can be achieved by changing the nature of the Y-site cation from Cl through Br to I. For instance, 128 the room temperature bandgap of CH 3NH 3PbI 3 is experimentally reported to be around 1.55 eV, 86 86 whereas those of CH 3NH 3PbBr 3 and CH 3NH 3PbCl 3 are around 2.33 and 3.06 eV, respectively (Table 1). This tendency in the increase of the bandgap passing from Y = Cl through Y = Br to Y

= I for the CH 3NH 3PbY 3 series could be understood as the consequence of the shift of the energies of the valence and conduction band edges. These energies modulated by halogen replacement in

CH 3NH 3PbY 3 are substantially tuned by the degenerate p valence orbitals since 3p (Cl), or 4p (Br) or 5p (I) orbitals of the halogen derivative are involved. The attribute is reasonable since halogen

replacement in BMY 3 triggers the extent of mixing of covalent and ionic characters in various chemical bonds involved between B and M, as well as those between Y and B. This is not very Manuscript surprising since tuning the nature of the halogen derivative can tune the nature of the orbital hybridization between it and the electron density accepting orbitals of interacting species, which

is responsible for the formation and stability of the BMY 3 perovskite architecture, and the tunability of its bandgap. Moleni et al. , on the other hand, have stated that the above rationalization to explain the phenomenology of bandgap tuning in halide perovskites is inadequate since the changes in the energies of VBM and CBM cannot be fully accounted for by the energies caused by the changes of the atomic orbitals of the halide substituent. According to them, there are two such attributes. One concerns the overlap between atomic orbitals of the bivalent cation and the halide anion, and the other the electronic charge on the metal center. In particular, lower gaps are associated with Accepted higher negative antibonding overlap of the states at the VBM, and higher charge on the bivalent cation in the states at the CBM. Both VBM orbital overlap and CBM charge on the metal ion can be tuned over a wide range by changes in the chemical nature of B, M and Y, as well as by variations of the crystal structure.

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The fluorine is not included into the CH 3NH 3PbY 3 series because it is so reactive that it

does not allow the formation of any stable CH 3NH 3PbY 3 perovskite. The view is intuitive since its presence deprotonates the ammonium H atoms in MA, leading to the formation of HF species, causing its sublimation and the eventual degradation of the perovskite system. Another reason that could be attributable to this lies in its ionic size, which is so small that it is probably not adequate

for the formation of any BMY 3 perovskite stoichiometry. These explain why the crystal for

CH 3NH 3PbF 3 has not yet been experimentally reported.

For a given Y in CH 3NH 3PbY 3, there could be several geometries in the conformational + space because of the orientational degrees of freedom (disorder) of the CH 3NH 3 organic cation. In the high temperature cubic phase, three such orientations have been identified. In specific, it was showed that the cation could either be pointing at the face of the cube formed by the surrounding lead atoms ([100]), or pointing at edges ([110]), or pointing to the corners (diagonal) ([111]), Scheme 1. Leguy et al. have discussed possibilities of different bandgaps with respect to the three orientations of the dipolar B-site cation. It was 1.60 eV for [100], 1.46 eV for [110] and 1.52 eV for [111]. 128 These results suggest that the collective orientation of the dipoles in a preferential direction would result in different local bandgaps. Leguy et al. have demonstrated further that the alignment of the dipolar B-site cation is unlikely to explain the experimental Manuscript 128 variations of the measured bandgaps catalogued in literature for MAPbI 3. An underlying reason for this is that all of these techniques probe the macroscopic optical constants, which are not on the sub ∼100 nm scale, and that much of the variation in the reported experimental bandgaps result from differences in the details of the sample preparation, measurements and analysis. 128

Because of dipolar disordering, the bandgap of CH 3NH 3PbI 3 changes. This, together with the notable direct-to-indirect bandgap transition reported both experimentally and theoretically, 112 112 explains why CH 3NH 3PbI 3 could be referred as a dynamical bandgap semiconductor. In any case, our recent gas phase study on this specific system shows that there can be four potential arrangements between the organic and inorganic species in the conformational space, leading to the formation of molecular perovskite building blocks. 21 All these four blocks resemble the three Accepted orientations of the dipolar cation observed as in the crystalline phase (Scheme 1), 66,111 suggesting

that the CH 3NH 3PbI 3 system in its molecular form can be stable in the gas phase as well. The result is probably not surprising since the formation/transformation of the organic-inorganic halide

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perovskite materials is carried out through induced molecular gases, such as R-NH 2, X 2 and HX (X = halogen), among others. 150 Note that the relative energy difference between the lowest and highest energy gas-phase -1 21 conformers of CH 3NH 3PbI 3 was reported to be 1.37 eV (31.57 kcal mol ) with M06-2X/ADZP. The highest stable conformer among the four examined in that study is illustrated in Fig. 2j, with the organic cation adopts a staggered configuration similarly as observed in the solid state. 111,113- 114 The geometry of this conformer is homologous with the pseudocubic bulk geometry of the 112 CH 3NH 3PbI 3 system. Fig. 2a illustrates the periodic bulk analogue of CH 3NH 3PbI 3 in the cubic + phase, with the CH 3NH 3 organic cation aligned along the [111] direction. The properties of this and other polymorphs have been extensively studied within last 5 years to glean the details of the interplay between the organic and inorganic species, the nature of intermolecular interactions, the orientational disorder, the ferroelectricity, and the Rashba effect, among several other things. 112,127-129

Manuscript

+ – Fig. 2: Illustration of [PBE/aug-cc-pVTZ(for CH 3NH 3 , Cl, Br)/aug-cc-pVTZ-PP(for PbI 3 )] level

energy-minimized gas-phase geometries for the ten-membered CH 3NH 3PbY 3 molecular perovskite

series, where Y = I (3 – x) Br x=1–3, I (3 – x) Cl x=1–3, Br (3-x) Cl x=1–3, and IBrCl. The members include, from left, Accepted

a) MAPbCl 3, b) MAPbBrCl 2, c) MAPbBr 2Cl, d) MAPbICl 2, e) MAPbBr 3, f) MAPbIBrCl, g)

MAPbIBr2, h) MAPbI 2Cl, i) MAPbI 2Br, and j) MAPbI 3. Relative stabilities between the complex binding energies are given in eV. The dotted lines represent possible intermolecular hydrogen bonding – + contacts between the halogen in PbY 3 and the three hydrogen atoms of the –NH 3 group in CH 3NH 3 .

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Because of the reasons noted above for CH 3NH 3PbI 3, the remaining nine molecular blocks

of the ten-membered CH 3NH 3PbY 3 series adopting the same configuration were also energy- minimized with the same level of theory. This means that the orientational arrangement between the organic and inorganic species in each of these nine blocks is considered similar to that of

CH 3NH 3PbI 3 (Fig. 2j). All the optimized block geometries of the CH 3NH 3PbY 3 series are illustrated in Fig. 2. The BSSE corrected binding energies ∆Ecorr estimated for all the ten molecular blocks of

CH 3NH 3PbY 3 are listed in Table 1. These are lying between –4.61 and –5.04 eV (–106.30 and – 116.22 kcal mol -1, respectively). From the magnitudes, it can be immediately concluded that each molecular block is significantly stronger than the constituent fragments.

Table 1: Some selected physical properties of the MAPbY 3 series, where Y = Br (3-x) Cl x=1–3, I(3 – a x) Br x=1–3, I (3 – x) Cl x=1–3, and IBrCl.

corr b c d,e f System ∆E Eg (Predicted) Eg (Castelli et al. ) Eg (Expt.) MAPbI 3 –4.610 1.567 1.359 1.61 MAPbI 2Br –4.686 1.825 1.462 1.81 MAPbI 2Cl –4.757 2.064 1.624 --- MAPbIBr 2 –4.762 2.080 1.646 2.08 MAPbIBrCl –4.831 2.313 1.807 ---

MAPbBr 3 –4.837 2.332 1.964 2.33 Manuscript MAPbICl 2 –4.900 2.544 1.997 --- MAPbBr 2Cl –4.905 2.562 2.177 2.53

MAPbBrCl 2 –4.973 2.790 2.294 2.78

MAPbCl 3 –5.040 3.016 2.712 3.06 a The properties include the BSSE corrected PBE binding energies ( ∆Ecorr /eV), the linear-regression

based PBE predicted bandgaps (E g(Predicted)/eV), the bandgaps reported by of Castelli et al.

(E g(Castelli et al. )/eV) and the experimentally reported bandgaps (E g(Expt.)/eV) for the MAPbY 3 series. b See Eqn 2. c This work (see text for discussion). d 79,115 Represent periodic DFT estimated bandgaps for MAPbY 3 in the pseudocubic phase. e The GLLB-SC and G 0W0 calculated bandgaps were reported to be 3.52 and 3.59 eV for MAPbCl 3,

respectively, 2.88 and 2.83 eV for MAPbBr 3, respectively, and 2.29 and 2.27 eV for MAPbI 3, respectievly. 79 f 86 Experimental values of E g taken from ref. Accepted

corr The ∆E for CH 3NH 3PbY 3 are evidently unusually large. These are much larger than the covalent limit, –1.73 eV (–40 kcal mol -1), recommended for hydrogen bonding. 97 Because of this and because of their unified bonding characteristics, we have recently classified the Y •••H–N

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21 hydrogen bonding interactions in the BMY 3 perovskites to be ultra-strong type. Note that the

corr large ∆E values calculated for CH 3NH 3PbY 3 are not an artifact of the adopted computational

+ procedure since the [CCSD(T)/cc-pVTZ (for CH 3NH 3 , Cl, Br)/cc-pVTZ-PP (for Pb and I)] level binding energies estimated for these molecular blocks (unpublished result) differ only by 0.20 eV (~ 2-5 kcal mol -1) from the corresponding PBE estimates. And the small deviation between the ∆Ecorr values computed with these two theoretical methods is not very surprising since CCSD(T) accounts for dispersion to some greater extent. For comparison, the binding energies of similar strengths, viz. –3.01 and –4.63 eV (–69.41 -1 and –106.77 kcal mol , respectively) were previously reported for the [(NH 3)3)][Mn(HCOO) 3]

and [(CH 3)2NH 2)][Mn(HCOO) 3] perovskites, respectively. An editorial of the J. Am. Chem. Soc. has spotlighted this remarkable finding as "Small Bonds a Big Deal in Perovskite Cells ".116 Clearly,

the Y •••H–N ultra-strong hydrogen bonds found in the presently studied CH 3NH 3PbY 3 perovskites are distinguished. These noncovalent interactions and similar others in analogous systems should be considered for extensive and in-depth theoretical explorations in future studies since these attempts will not only promote the fundamental understanding of the underlying physical chemistry and chemical physics involved but also expedite the invention of new functional nanomaterials that can be prerequisite for the design of optoelectronic devices for Manuscript applications in solar energy technologies.

corr The lower and upper bounds of the ∆E listed in Table 1 are linked with the CH 3NH 3PbI 3

and CH 3NH 3PbCl 3 perovskites for the CH 3NH 3PbY 3 series, respectively. These are consistent with

the corresponding bounds of Eg experimentally reported for the same series. For instance, Table 1

lists the experimentally available Eg values for the CH 3NH 3PbY 3 series. These data show a clear

trend in the increase in the magnitude of the E g as one passes from CH 3NH 3PbI 3 to CH 3NH 3PbCl 3 in the series.

corr Fig. 3a illustrates the dependence of experimental Eg on calculated ∆E for the

corr CH 3NH 3PbY 3 series. In this analysis, we have accounted for only seven (∆E , E g) data points.

These correspond to the members MAPbI 3, MAPbI 2Br, MABIBr 2, MAPbBr 3, MAPbBr 2Cl, Accepted

MAPbBrCl 2 and MAPbCl 3. The selection is obviously due to the experimental E g data that are

known only for the above 7 members of the CH 3NH 3PbY 3 series, while those for the remaining 3 members are either unavailable or controversial. To give an example, the (periodic DFT) estimated 119 Eg for CH 3NH 3PbI 2Cl is reported to be 1.60 eV. The experimental E g for MAPbI 3‑xCl x is

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Fig. 3: Dependence a) of the experimentally reported onset of optical absorption (E g/eV) on the basis set superposition corrected binding energy ( ∆Ecorr /eV), b) of the periodic DFT bandgap reported by Castelli et al. 79,115 on the on the basis set superposition corrected binding energy ( ∆Ecorr /eV), and c) of the adjusted bandgap (eV) on the basis set superposition corrected binding energy ( ∆Ecorr /eV) for the ten-membered CH 3NH 3PbY 3 series, where Y = Br (3-x) Cl x=1–3, I(3 – x) Br x=1–3, I(3 – x) Cl x=1–3, and IBrCl .

121 reported to be close to that of tetragonal CH 3NH 3PbI 3 (Eg ∼1.50 – 1.61 eV). The close agreement

between the magnitudes of the bandgap for CH 3NH 3PbI 2Cl, CH 3NH 3PbI 3‑xCl x and CH 3NH 3PbI 3 is unclear since each should differ from one another. However, there are suggestions in the literature showing that this matching between the bandgaps of the three different systems could be

due to the miscibility of Cl in the MAPbI 3‑xCl x lattice. Others have demonstrated that the Cl content Manuscript in MAPbI 3‑xCl x is about an order of 1%, inferred by comparing the X-ray diffraction (XRD) pattern

of this species with that of the parent CH 3NH 3PbI 3 sample, as well as by examining the signatures of X-ray photoelectron spectroscopy (XPS) for both species.120,122-123 These results have led

Pellegrino et al. to conclude that the actual nature of the chlorine in the MAPbI 3‑xCl x material is controversial, 117,121 while others have noted that the reaction mechanism leading to the formation and crystallization of chlorine-containing perovskite films remain unsolved. 117-121 Yan et al. have referred the study of Mosconi, et al. 119 and then have suggested that the limited Cl content in

CH 3NH 3PbI 3−x Cl x can be speculated on the basis of the calculated sizable destabilization energy

of CH 3NH 3PbI 2Cl (0.16 eV taking CH 3NH 3PbI 3 as a reference) because of the comparatively large 121 difference in atomic radii between Cl and I. Similar other studies on CH 3NH 3PbI 3−x Cl x with Accepted some modified views can be found elsewhere. 124-126

All the experimental bandgaps reported for CH 3NH 3PbY 3, which have been used in the

regression analysis (Fig. 3a), do not correspond to the cubic phase. For instance, the Eg values for 127-129 CH 3NH 3PbI 3 are known to lie in the 1.50 – 1.69 eV range. This range covers all the three

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important temperature phases of the system. To give an example, Quarti et al. have reported

experimental Eg values of 1.65, 1.61 and 1.69 eV for the orthorhombic (4 K), tetragonal (160 K) 127 and pseudocubic (330 K) phases of CH 3NH 3PbI 3. These data show a marginal variation in the

Eg values between the three phases (all within 0.17 eV), which is unsurprising according to Leguy et al .128-129 In agreement with the view of Leguy et al. , 128 we further note that there is also a wide

variation in the experimentally determined bandgaps reported for CH 3NH 3PbBr 3. These were

originated from different research groups with different experimental settings, with the Eg values 86 131 128 132 128 86 reported to be 2.33, 2.309, 2.24 and 2.12 eV. Similarly, the Eg values of 2.97, 3.06, 91, 130 and 3.11 eV were reported for CH 3NH 3PbCl 3, and so on. Despite the wide spread variation

in the reported Eg values for most members of the CH 3NH 3PbY 3 series, it is quite natural that these each cannot fit well with the binding energies ∆Ecorr to produce a decent value for the square of

2 the adjusted regression coefficient (Adj. R ). However, the experimental Eg reported by Niemann 86 et al. for the CH 3NH 3PbY 3 series are perhaps more accurate since these were measured with the same experimental technique, in which case, a single definition might have been used for sample preparation, as well as for the measurement and determination of the bandgap values.

corr The (∆E , E g) data for the CH 3NH 3PbY 3 series illustrated in Fig. 3a were fitted to a linear Manuscript corr Eqn of the form: E g = a ×∆E + b, where a (a ≈ –3.35586) is the slope and b (b ≈ –13.89553) is the intercept. The Adj. R2 for the fit was ≈ 0.9963. The high regression coefficient suggests the

reasonable chemical accuracy of the experimental Eg data, meaning that these are physically meaningful and trustworthy. Using the relationship above, the bandgaps for the remaining three

members of the CH 3NH 3PbY 3 series have predicted, and are listed in Table 1. The above relationship clarifies the first aim of the study raised in Introduction. That is, one does indeed have

a connection between the gas-phase and solid state physics for the CH 3NH 3PbY 3 perovskites. From Fig. 3a, it is apparent that heavier the size of the halogen derivative Y, structurally

and energetically least stable would be the CH 3NH 3PbY 3 system because of the different level of orbital mixing between the interacting atoms. The stability correlates with the strength of the Accepted

bandgap for the corresponding CH 3NH 3PbY 3 series that decreases with the increasing size of the halogen derivative. Since small bandgap perovskites are accompanied with small effective masses of the charge carriers, and the latter control the photovoltaic performance of solar power conversion, this leads to a meaning that tuning the binding (energy) between the host and guest

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species can not only serve as an effective parameter for the design of the BMY 3 perovskites, but also a future artery for optimizing photovoltaic efficiencies. Interestingly, the stability preference

of CH 3NH 3PbY 3 perovskites with respect to the nature of the halogen content noted above is in 133 agreement with others. For instance, CH 3NH 3PbI 3-xBr x with Br content < 10% gives rise to better PCE, while that with > 20% Br content provides better photostability. 133 This observation is not dumbfounded because the bromine is relatively more basic than the iodine atom, in which, the former forms stronger coordination bonds with the metal ion than the latter halogen, causing the resulting perovskite material relatively more photostable. 149

Castelli et al. have performed electronic structure calculations for 240 BMY 3 + + + perovskites comprising the B-site cations as Cs , CH 3NH 3 and HC(NH 2)2 , the M-site cations as the Sn and Pb divalent ions, and the Y-site anions as the halogen derivatives mainly Cl, Br and I. 79 The bandgaps for all these perovskites were predicted to span over the 0.5 – 5.0 eV region. From the analyses of their computed data, they have noted that the trend for bandgaps for any of the ten-

membered BMY 3 perovskite series to be: BMI3 < BMI2Br < BMI2Cl < BMIBr 2 < BMIBrCl <

BMBr 3 < BMICl 2 < BMBr 2Cl < BMBrCl 2 < BMCl 3. Evidently, this trend was independent of the

nature of the B- and M-site cations in BMY3. Not only is this, but the authors have also found that

the trend is reminiscent of any of the four geometrical phases examined for the BMY 3 systems. Manuscript For instance, this trend was persistent for the two orthorhombic, one tetragonal, and one cubic 79 phases of the BMY 3 systems examined in that study. Inspection of Table 1 shows that the same unified trend as above is also reminiscent of the

corr 79 ∆E data for the CH 3NH 3PbY 3 series. This is in line with the corresponding trend observed

between the electronegativities of the Y site species in CH 3NH 3PbY 3, in which, the latter increases with the decreasing size of the halogen derivative, that is, in this order: Cl > Br > I. 79

corr Fig. 3b presents the dependence of DFT calculated Eg on ∆E for the CH 3NH 3PbY 3 series.

79,115 However, this time, the E g are taken from the study of Castelli et al., evaluated using the GPAW code.134 In doing so, firstly, the authors have employed the GLLB-SC potential of Gritsenko, van Leeuwen, van Lenthe, and Baerends (GLLB), 135 with PBEsol correlation for solids Accepted (-SC), 136 since according to their estimation this combination predict bandgaps within 0.1 eV 79 KS relative to G0W0 for this class of systems. Secondly, they have used the relationship: Eg = E gap

KS + ∆xc − ∆soc − ∆e−h to evaluate the bandgap, where ∆xc is different for each system, E gap is the

Kohn-Sham bandgap, and ∆soc and ∆e–h are ad hoc corrections accounting for spin-orbit and exciton

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effects, respectively. While several approximations were accounted for the accurate calculation of

corr the bandgaps for the 240 BMY 3 perovskite systems, the dependence between E g and ∆E in Fig.

3b is found to be poor compared to that illustrated in Fig. 3a for the CH 3NH 3PbY 3 series. This may be immediately understood from the regression coefficients (Adj. R 2) of 0.9963 and 0.9414 found for the fits illustrated in Figs. 3a and 3b, respectively. The poorness of the fit in Fig. 3b is apparently due to periodic DFT data since these are certainly not produced within 0.1 eV of the experimentally determined values.

corr Fig. 3c is illustrates the dependence of adjusted Eg against ∆E . The linear relationship

corr corr that best describes the ( ∆E , E g) data is represented by: Eg = –3.36857 ×∆E – 13.96099, where Adj. R 2 ≈ 1.

(ii) The CsPbY 3 series

The CsPbY 3 series comprises another potential lead containing all-inorganic halide perovskite compounds. The members of this series have also been exploited for solar energy applications. Even though these are somehow toxic due to the presence of lead, they exhibit attractive optoelectronic properties. Experimental bandgaps are known only for a few members of the series Manuscript (Table 2). Since these have been examined and reported by diverse research groups, there are

variations between the E g values reported for some known members of the series.

corr Fig. 4a presents the dependence of E g on ∆E for the CsPbY 3 series. Only five members

of the series are included for the fitting analysis. These are CsPbI 3 (1.73 eV), CsPbI 2Br (1.90 eV),

CsPbIBr 2 (2.05 eV), CsPbBr 3 (2.31 eV) and CsPbCl 3 (2.86 eV), with the parentheses values

represent the experimental bandgaps (Table 2). Similarly as observed for the CH 3NH 3PbY 3 series

corr (Fig. 3a), a linear relationship between Eg and ∆E is also revealed for the CsPbY 3 series. The Adj. R 2 for the fit is ≈ 0.9811, which is also reasonably good. The relationship that describes the

corr (∆E , Eg) data in the fit can be represented by the mathematical equation given by: Eg = –

3.38377 ×∆Ecorr – 11.1025. Accepted

79,115 corr Fig. 4b illustrates the dependence of periodic DFT Eg values of Castelli et al. on ∆E

for the CsPbY 3 series. Interestingly, however, this time, we did not notice any such obvious linear

corr dependence between E g and ∆E for the series. As already indicated above, the discrepancy is

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Table 2: Some selected physical properties of the CsPbY 3 series, where Y = Br (3-x) Cl a x=1–3, I(3 – x) Br x=1–3, I(3 – x) Cl x=1–3, and IBrCl .

corr b c d System ∆E Eg (Predicted) Eg (Castelli et al. ) Eg (Expt.) e,i CsPbI 3 –3.777 1.691 1.624 1.73 f CsPbI 2Br –3.841 1.902 1.466 1.90 CsPbI 2Cl –3.895 2.081 1.306 -- g CsPbIBr 2 –3.907 2.120 2.077 2.05 CsPbIBrCl –3.959 2.293 1.978 -- e j CsPbBr 3 –3.975 2.346 1.639 2.31 (2.24) CsPbICl 2 –4.007 2.451 2.207 -- CsPbBr 2Cl –4.024 2.510 1.709 -- CsPbBrCl 2 –4.072 2.666 1.797 -- h k CsPbCl 3 –4.112 2.799 2.265 2.86 (3.0) a The properties include the BSSE corrected PBEPBE binding energies ( ∆Ecorr /eV), the linear-regression

based PBE predicted bandgaps (E g(Predicted)/eV), the bandgaps reported by of Castelli et al.

(E g(Castelli et al. )/eV) and the experimentally reported bandgaps (E g(Expt.)/eV) for the CsPbY 3 series. b See Eqn 2. c This work (see text for discussion). d 79,115 Values represent the data of the CsPbY 3 series in the pseudocubic phase, Refs. e Ref. 82 f Ref. 83 g Ref. 84 h 85,139b i 146 j 85 k 139a Ref. . Ref. . Ref. . Ref. Manuscript

Fig. 4: Dependence a) of the experimentally reported onset of optical absorption (E g/eV) on the basis set Accepted superposition corrected binding energy ( ∆Ecorr /eV), b) of the periodic DFT bandgap of Castelli et al. 79,115 on the on the basis set superposition corrected binding energy ( ∆Ecorr /eV), and c) of the adjusted bandgap corr (eV) on the basis set superposition corrected binding energy ( ∆E /eV) for the ten-membered CsPbY 3 series, where Y = Br (3-x) Cl x=1–3, I(3 – x) Br x=1–3, I(3 – x) Cl x=1–3, and IBrCl .

apparently due to the scattering nature of the inaccurate Eg data evaluated with periodic DFT

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calculations. This can be inferred from Table 2, which compares the bandgap values obtained using

different procedures. We comment further that the Eg values listed in the Computational Materials 115 79 Repository for the CsPbY 3 series, which have been used by the Castelli et al. in Ref. , do fail to reproduce the expected trend they have claimed in their study for the same series. For instance,

our analysis of their Eg data did not gave this following trend for the CsPbY 3 series as observed

corr for the ∆E series: CsPbI3 < CsPbI2Br < CsPbI2Cl < CsPbIBr 2 < CsPbIBrCl < CsPbBr 3 <

CsPbICl 2 < CsPbBr 2Cl < CsPbBrCl 2 < CsPbCl 3. Rather, their E g data show this trend: CsPbI 3 <

CsPbI 2Br < CsPbI 2Cl < CsPbBr 3 < CsPbBr 2Cl < CsPbBrCl 2 < CsPbIBrCl < CsPbIBr 2 <

CsPbICl 2 < CsPbCl 3. The italic fonts show the disorder, thereby questioning on the accuracy of the theoretical methods that are currently in use for the prediction of the bandgaps for solid state systems. It is not very surprising to see the bandgap data for perovskites with such an inaccuracy since these are by far more common in the chemistry literature. This can be readily understood from a recent study of Qurati et al. 127 For instance, in this study, the authors have experimentally measured the bandgaps of 1.65 (4.2 K), 1.61 (160 K) and 1.69 eV (330 K) for the orthorhombic,

tetragonal and pseudocubic phases of CH 3NH 3PbI 3, respectively. Their high level SOC-GW (Spin- Orbit Coupling incorporated GW) calculations gave bandgaps of 1.81, 1.67, and 1.16/1.28 eV for Manuscript the polymorphs of the corresponding phases of the same CH 3NH 3PbI 3 system, respectively. From these results, it is obvious that while the largest bandgap of 1.69 eV is experimentally determined

for the pseudocubic polymorph of CH 3NH 3PbI 3 in the cubic phase, the high level SOC-GW calculation has predicted this polymorph to have the lowest bandgap of 1.16/1.28 eV compared to the polymorphs of the other two phases, thus leading to the controversy. In fact, there is no such qualitative/quantitative matching between the trends in the bandgap values for the three

polymorphs corresponding to the three phases of the CH 3NH 3PbI 3 system as determined experimentally and theoretically. These suggest that SOC-GW results are neither quantitatively accurate, nor reproduce any such physically meaningful trend between the bandgaps of the three polymorphs as inferred from the experimentally measured values. This view might be in line with Accepted Zhu et al.,75 who have demonstrated that the generalized gradient approximation (GGA) method usually underestimates the bandgap. Inclusion of the effect of SOC further decreases the bandgap upto 1.0 eV, meaning its effect significantly underestimates the bandgap for most of the perovskite materials contianing heavy atoms (Pb and I etc. ). This specific feature has led Zhu et al. 75 to

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conclude that the GGA method can be resonable for the estimation of bandgaps for the

CH 3NH 3MI 3 (M = Pb, Bi) perovskites without SOC. While this might be the case, we comment that the SOC indeed largely underestimates the bandgap for these perovskite materials (occasionally even in a spurious manner). However, its inclusion is probably useful to understand the Rashba splitting (a consequence of relativistic effect) associated with the VBM and CBM, and the way the bands split and switch the character of the bandgap from direct-to-indirect or vice- versa for the heavy ion containing perovskites.112

corr Fig. 4c illustrates the dependence of adjusted Eg on ∆E for the CsPbY 3 series, with Adj.

2 R ≈ 1. This, together with the result presented in Fig. 3c for the CH 3NH 3PbY 3 series, demonstrates that the adopted modellization is reasonable to examine the accuracy and reliability of the bandgap physics of hybrid organic-inorganic (and all-inorganic) halide perovskites. This result also suggests the fact that the zero Kelvin calculations are always fascinating, and have positive impact on the fundamental understanding of the physical chemistry of any chemical system under investigation. The view is true not only for the four perovskite series examined in this study, but

also for any other BMY 3 halide perovskite series regardless of the varied nature of the B- and M- site cations.

Manuscript

(iii) The CH 3NH3SnY 3 and CsSnY 3 series

In order to confirm whether or not the physical chemistry established in Figs. 3a and 4a, as

well as that in Figs. 3c and 4c, for the MAPbY 3 and CsPbY 3 series, respectively, is genuine and

meaningful, we have continued performing similar analyses for another two BMY 3 perovskite + + series. In these two series, the B-site species are same as Cs and CH 3NH 3 , the Y site species are

Br (3-x) Cl x=1–3, I(3 – x) Br x=1–3, I (3 – x) Cl x=1–3, and IBrCl, but the M-site species is replaced by tin (Sn).

Thus, both the CH 3NH 3SnY 3 and CsSnY 3 series include the same number of molecular building

blocks similarly as discussed above for the CH 3NH 3PbY 3 and CsPbY 3 series. This means that the

block geometries for the members of the CH 3NH 3SnY 3 series are topologically analogous with Accepted

those illustrated in Fig. 2 for the CH 3NH 3PbY 3 series. The above two Sn containing series are potential lead-free organic-inorganic and all-inorganic hybrid perovskites for solar energy applications, respectively. These are nontoxic, and environmentally friendly. They also display attractive optoelectronic properties, with bandgaps (cf. Tables 3 and 4) comparable with those of

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the corresponding CH 3NH 3PbY 3 and CsPbY 3 series, respectively (cf. Tables 1 and 2). While the large-scale synthesis of tin based solar cell perovskites has not been successful till date due to their low stabilities, many recent researches are involved in the exploration of the compositional engineering of these materials to modify them, as well as their electronic and optical properties so as to enforce them to stand fit for applications in photovoltaics.

corr Nevertheless, the calculated ∆E for the CH 3NH 3SnY 3 and CsSnY 3 series are summarized in Tables 3 and 4, respectively. A comparison of these with those summarized in

Tables 1 and 2 for the corresponding lead containing perovskite series, CH 3NH 3PbY 3 and CsPbY 3, respectively, reveals the fact that the Sn 2+ perovskites are energetically less stable than the corresponding Pb 2+ analogues; this is true regardless of the nature of the Y-site anions involved.

Table 3: Some selected physical properties of the CH 3NH 3SnY 3 series, where Y = Br (3- a x) Cl x=1–3, I(3 – x) Br x=1–3, I(3 – x) Cl x=1–3, and IBrCl.

corr b c d,e System ∆E Eg (Predicted.) Eg (Castelli et al. ) Eg (Expt.) f MASnI 3 –4.545 1.295 0.438 1.30 f MASnI 2Br –4.610 1.564 0.555 1.56 MASnI 2Cl –4.665 1.791 0.778 --- f MASnIBr 2 –4.675 1.832 0.710 1.75

MASnIBrCl –4.731 2.060 1.421 --- Manuscript f, g MASnBr 3 –4.742 2.106 1.100 2.15 MASnICl 2 –4.786 2.289 1.544 --- MASnBr 2Cl –4.798 2.336 1.695 --- MASnBrCl 2 –4.855 2.570 1.914 --- g MASnCl 3 –4.912 2.806 2.226 3.69 a The properties include the BSSE corrected PBE binding energies ( ∆Ecorr /eV), the linear-regression

based PBE predicted bandgaps (E g(Predicted)/eV), the bandgaps reported by of Castelli et al.

(E g(Castelli et al. )/eV) and the experimentally reported bandgaps (E g(Expt.)/eV) for the CH 3NH 3SnY 3 series. b See Eqn 2. c This work (see text for discussion). d Values represent the pseudocubic phase, Refs. 79,115 e The GLLB-SC and G 0W0 calculated bandgaps were ca. 2.27 and 2.30 eV for MASnCl 3, respectively, 79 1.25 and 1.29 eV for MASnBr 3, respectively, and 0.70 and 0.89 eV for MASnI 3, respectively. f Ref. 140 Accepted g Ref.141

corr Examination of the ∆E values of Table 3 suggests that the heaviest member CH 3NH 3SnI 3

corr -1 of the CH 3NH 3SnY 3 series is least stable and having an ∆E of –4.545 eV (–104.82 kcal mol ).

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In contrary, the most stable (and lightest) member of the same series is CH 3NH 3SnCl 3, with an

corr -1 corr ∆E of –4.912 eV (–113.27 kcal mol ). For the CsSnY3 series, the calculated ∆E are lying between –3.713 and –4.036 eV (–87.40 and –94.15 kcal mol -1, respectively) (Table 4). This

corr indicates that the smallest and largest values of ∆E are also associated with the heaviest (CsSnI 3)

corr and lightest (CsSnCl 3) members of the series, respectively. The stability preference (∆E ) for

each of these two series follows this order: BSnI3 < BSnI2Br < BSnI2Cl < BSnIBr 2 < BSnIBrCl <

BSnBr 3 < BSnICl 2 < BSnBr 2Cl < BSnBrCl 2 < BSnCl 3 (B = CH 3NH 3, Cs). Encouragingly, this preference in the complex stabilities is consistent with that found for each of the Pb-based

perovskite series, CH 3NH 3PbY 3 and CsPbY 3, discussed above.

Table 4: Some selected physical properties of the CsSnY 3 series, where Y = Br (3-x) Cl a x=1–3, I(3 – x) Br x=1–3, I (3 – x) Cl x=1–3, and IBrCl .

corr b c d e,f System ∆E Eg (Predicted.) Eg (Castelli et al. ) Eg (Expt.) g,h e CsSnI 3 –3.713 1.255 0.230 1.27 (1.31) e CsSnI 2Br –3.790 1.446 0.359 1.44 CsSnI 2Cl –3.842 1.576 0.366 --- e CsSnIBr 2 –3.866 1.634 0.441 1.63 CsSnIBrCl –3.914 1.754 0.824 --- e CsSnBr 3 –3.942 1.823 0.515 1.80 Manuscript CsSnICl 2 –3.963 1.873 1.168 --- e CsSnBr 2Cl –3.988 1.935 0.552 1.90 e CsSnBrCl 2 –4.036 2.055 0.590 2.10 e CsSnCl 3 –4.083 2.171 0.969 2.80 a The properties include the BSSE corrected PBEPBE binding energies ( ∆Ecorr /eV), a linear-regression

based PBE predicted bandgap (E g(Predicted)/eV), the bandgap reported by of Castelli et al. (E g(Castelli

et al. )/eV) and the experimentally reported bandgap (E g(Expt.)/eV) for the CsSnY 3 series, . b See Eqn 2. c This work (see text for discussion). d Values represent the cubic phase, Refs. 79,115 e Ref. 142 f Sabba et al. have reported the onset of optical bandgap edge transitions at 1.27, 1.37, 1.65 and 1.75 143 eV for eV CsSnI 3, CsSnI 2Br, CsSnIBr 2 and CsSnBr 3 respectively. g Varied values of bandgaps reported by others can be found in Refs. 145-146 h Refs. 148 Accepted

corr The dependence of experimental Eg on calculated ∆E for the CH 3NH 3SnY 3 series is

shown in Fig. 5a, whereas that for the CsSnY 3 series is depicted in Fig. 6a. For the former series,

Accepted Article

Fig. 5: Dependence a) of the experimentally reported onset of optical absorption (E g/eV) on the basis set superposition corrected binding energy ( ∆Ecorr /eV), b) of the periodic DFT bandgap of Castelli et al. 79,115 on the on the basis set superposition corrected binding energy ( ∆Ecorr /eV), and c) of the adjusted bandgap (eV) on the basis set superposition corrected binding energy ( ∆Ecorr /eV) for the ten-membered CH 3NH 3SnY3 series, where Y = Br (3-x) Cl x=1–3, I(3 – x) Br x=1–3, I(3 – x) Cl x=1–3, and IBrCl .

a data set comprising four experimental Eg values was used for regression analysis since Eg for the

remaining five members are unavailable (Table 3). The Eg value of 3.69 eV is feasible for another

member of this series, CH 3NH 3SnCl 3, but this value is unusually large as it corresponds to the 141 monoclinic polymorph of the system. Similarly, for the CsSnY 3 series, a data set comprising

six experimental E g values was used. The choice is also reasonable since Eg for the remaining three Manuscript members of the series are missing in the literature, and that the Eg available for the remaining

member (CsSnCl 3) of this series is seemingly inaccurate. This can be inferred from the Eg data summarized in Table 4. For instance, from a close inspection of Table 4, it is quite apparent that

the tuning of Y with the decreasing size of the halogen derivative increases the value of E g by 0.1

– 0.2 eV in each successive step starting from the E g of 1.27 eV reported for CsSnI 3. However,

there is an abrupt increase in the Eg value of CsSnCl 3 (2.80 eV) by 0.7 eV when passing from value

reported for its nearest neighbor CsSnBrCl 2 (2.10 eV). This abrupt change questions on the

reliability of the value of experimental Eg reported for CsSnCl 3. Similarly, Ananthajothi et al. have

reported an experimental Eg of 2.60 eV for the orthorhombic phase of CsSnCl 3 using UV-visible and photoluminescence measurements. 144 Again, this is smaller than the value mentioned above Accepted 142 for CsSnCl 3 as reported by Peedikakkandy et al. Even so, this latter number is still very large compared to what can be expected. This argument is valid since there is a systematic difference of

0.2 – 0.3 eV between the E g values of the members of the CH 3NH 3PbY 3 series as one passes from

CH 3NH 3PbI 3 to CH 3NH 3PbI 2Br to the next member and so on (Table 1). (The same argument is

Accepted Article

applicable to the CsPbY 3 series as well (Table 2)) Moreover, from Tables 3 and 4, it can be

concluded that E g for a given member of the CH 3NH 3PbY 3 perovskite series is larger than that of

the corresponding member of the CH 3NH 3SnY 3 perovskite series (see Tables: 1 vs. 3). This is the general trend between the bandgap values of Pb and Sn based halide perovskites, which is true

regardless of the nature of the B-site cation. However, the CH 3NH 3PbCl 3 and CH 3NH 3SnCl 3 pair

is exceptional, and in this case, the E g for the latter system is substantially larger than that of the former (values: 3.06 vs. 3.69 eV). The difference is not unusual since these values corresponding to these compounds have adopted to two significantly different geometrical polymorphs (the

former cubic and the latter monoclinic). Notwithstanding, the inclusion of the E g value of 2.60 eV 2 (for orthorhombic CsSnCl 3) into the data set of CsSnY 3 has resulted the Adj. R for the fit worse

since this E g value contains either large experimental error or the sample prepared with large impurities that has affected the exact location of the peak in the measured optical spectra.

corr Nevetheless, for both the CH 3NH 3SnY 3 and CsSnY 3 series, the dependence between E g and ∆E has appeared to be linear. The Adj. R 2 for the two fits are found to be 0.9676 and 0.9891,

Manuscript

Fig. 6: Dependence a) of the experimentally reported onset of optical absorption (E g/eV) on the basis set superposition corrected binding energy ( ∆Ecorr /eV), b) of the periodic DFT bandgap of Castelli et al. 79,115 on the on the basis set superposition corrected binding energy ( ∆Ecorr /eV), and c) of the adjusted bandgap corr (eV) on the basis set superposition corrected binding energy ( ∆E /eV) for the ten-membered CsSnY3 series, where Y = Br (3-x) Cl x=1–3, I(3 – x) Br x=1–3, I(3 – x) Cl x=1–3, and IBrCl . The experimental Eg value used in a) for CsSnCl 3 is used as an outlier.

respectively. Accepted

79,115 corr The dependence of periodic DFT Eg values of Castelli et al. on calculated ∆E for

the CH 3NH 3SnY 3 and CsSnY 3 series is illustrated in Figs. 5b and 6b, respectively. While the linear

corr 2 regression analysis between E g and ∆E has resulted an Adj. R value of 0.9381 for the former

Accepted Article

series, there was no such reasonable regression coefficient obtained for the latter series. This is

undeniably due to the Eg values reported with periodic DFT for the latter series that did not fit with

corr 79,115 the ∆E data. These Eg values are not very meaningful either quantitatively or qualitatively since they do not follow any such physically acceptable order, similarly as noted above for the 79, 115 CsPbY3 series (vide supra ). Moreover, Castelli et al. ’s data gave the following ordering for

the bandgaps for the CsSnY 3 series: CsSnI 3 (0.230) < CsSnI 2Br (0.359) < CsSnI 2Cl (0.366) <

CsSnIBr 2 (0.441) < CsSnBr 3 (0.515) < CsSnBr 2Cl (0.552) < CsSnBrCl 2 (0.590) < CsSnCl 3 (0.969)

< CsSnIBrCl (0.824) < CsSnICl 2 (1.168). In this ordering, the positions of most of the members

of the series are altered compared to that found for the other two series (CH 3NH 3SnY 3 and CsPbY 3, see above). And there is no such obvious connection between electronegativity and bandgap is observed for the series. 115 Similarly, the Eg data of Castelli et al. gave the following order for the CH 3NH 3SnY 3

series: MASnI 3 (0.438) < MASnI 2Br (0.555) < MASnI 2Cl (0.777) < MASnIBr 2 (0.710) <

MASnIBrCl (1.421) < MASnBr 3 (1.100) < MASnICl 2 (1.544) < MASnBr 2Cl (1.695) < MASnBrCl 2

(1.914) < MASnCl 3 (2.226), where parentheses values represent E g in eV. Clearly, this ordering is not consistent with that found for the ∆Ecorr values for the same series (cf. Table 3). Because of

2 this, the Adj. R for the CH 3NH 3SnY 3 series is found to be poor. Manuscript corr The relationships between adjusted E g and ∆E for the CH 3NH 3SnY 3 and CsSnY 3 series are illustrated in Figs. 5c and 6c, respectively.

4. Conclusions This study has presented the PBE level binding energies for forty trihalide perovskite

molecular building blocks. These have included the four series CH 3NH 3PbY 3, CsPbY 3,

CH 3NH 3SnY 3 and CsSnY 3; each comprising ten members. The binding energy for each member

of the CH 3NH 3MY 3 (M = Pb, Sn) series is evaluated to be much larger than the covalent limit (– 40 kcal mol -1). Unambiguously, this suggests that the Y•••H–N intermolecular hydrogen bonding

interactions in CH 3NH 3PbY 3 and CH 3NH 3SnY 3 comprise appreciable amount of covalency with

predominant Coulombic interactions. A similar conclusion can be drawn for the Y•••Cs dative Accepted

coordinate bonding interactions evolved for the CsPbY 3 and CsSnY 3 series. corr For any of the four BMY 3 perovskite series examined, the trend in the ∆E values

between the ten members is revealed to follow this order: BMI3 < BMI2Br < BMI2Cl < BMIBr 2 <

BMIBrCl < BMBr 3 < BMICl 2 < BMBr 2Cl < BMBrCl 2 < BMCl 3. The ordering is thereby likely

Accepted Article

for any BMY 3 halide perovskite series regardless of the nature of the B- and M-site cations. We have shown that the above-mentioned ordering is reminiscent when basis sets of different varieties

could be employed, meaning that this trend is an inherent characteristic of for any BMY 3 halide perovskite series. Encouragingly, this result by some means supports the speculations of Fang and coworkers. 93 That is, it is possible to image big pictures of the halide perovskite solar cells from the fundamental understanding of the physical chemistry and chemical physics of their molecular building blocks.

The trendy result presented above for each BMY 3 perovskite series was recently proposed by Castelli et al. 79 for bandgaps. According to them, the trend is true for each of the four perovskite series examined in this study, as well as for a few other series containing formamidinium as the B-site cation; all predicted using periodic DFT calculations at some levels of sophistication. When we have carried out a detailed analysis on their bandgap data for each of the four series examined in this study for the pseudocubic phase (which are catalogued in the Computational Materials Repository Database 115 ) we have found that the above trend Castelli et al. 79 proposed for the

bandgaps is reflected only for the CH 3NH 3PbY 3 series. However, their bandgap data did not enable

us to extract the aforementioned trend as they have claimed for the other three series, CsPbY 3,

CH 3NH 3SnY 3 and CsSnY 3. This result unequivocally substantiates that the accuracy of the bandgap data of Castelli et al. is perhaps no good, and for some cases, the data are meaningless (e.g. for the two Cs containing perovskite series).

The study has not intended to provide any criticism toward the results reported previously Manuscript using periodic DFT calculations. It has only attempted to provide justification on the inability of such computationally expensive methods to reproduce experimental data both quantitatively and qualitatively. This view might be in agreement with a rationalization of Giorgi et al. , 147 who have showed that hybrid methods applied on top of the spin–orbit calculated structures are not able to open the bandgap sufficiently to reproduce the experimental value, revealing the need of further and more computationally demanding procedures to get improved agreement. corr The dependence of experimental E g on calculated ∆E revealed in this study is a structure- property relationship. This is because the latter property refers to the energy of the dominant

geometrical motifs in the studied BMY 3 perovskites (viz. the Y•••H–N intermolecular hydrogen

bonding interactions in CH 3NH 3PbY 3 and CH 3NH 3SnY 3, and the Y •••Cs dative coordinate

bonding interactions in CsPbY 3 and CsSnY 3), which are undoubtedly responsible for unitizing the Accepted + – two monomeric fragments B and MY3 together in complex configurations. The intermolecular/coordinate interactions with varied nature of their strengths are responsible to + – provide definite geometrical stabilities and shapes to the overall B MY 3 perovskite structures, resulting in the evolution of various types of polymorphs with respect to the change of temperature. corr In any case, the chemistry established in this study between Eg and ∆E does not only provide an

Accepted Article

additional dimension to the fundamental understanding of the optoelectronic chemistry of the

BMY3 perovskite solar cell materials, but also assist predicting the bandgap of the missing ones that are yet to be experimentally determined. Since the nature (viz. magnitude) of the bandgap controls the size (heavy/light) of the effective masses responsible for transport of charge carriers, and since these two properties are controlled by the extent of hydrogen/coordinate bonding 151 4– between the host and guest species, with the latter controls the extent of tilting of the MY 6 151 octahedra in BMY 3 perovskites in the orthorhombic phase, it could be said with some confidence that ∆Ecorr can be used as an additional measurable intermolecular parameter to stimulate the design of any stable and high performance perovskite material and its properties for efficient photovoltaic applications.

Acknowledgments The authors gratefully acknowledge Institute of Molecular Sciences (IMS), Okazaki, Japan for the supercomputing facilities, and CREST for generous funding (Grant No: JPMJCR12C4). This research was also supported by MEXT as "Priority Issue on Post-Kcomputer” (for development of new fundamental technologies for high-efficiency energy creation, conversion/storage and use).

Conflict of interest The authors declare no conflict of interest.

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