perovskites 
 display a wide range of properties due to their ability 
 to accommodate varying cations , substitutions , nonstoichiometry , and 
 structural defects .
they are consequently used in a widespread variety 
 of applications . of specific interest to this work is their application , 
 when hydrated , as proton conductors at intermediate to high temperatures 
 ( above ca .
. led to the discovery that perovskites such 
 as layo3 , srzro3 , srceo3 , baceo3 , ktao3 , sr2ganbo6 and 
 ba3canb2o9 have high proton conductivities under humid conditions .
all of these 
 materials require cation substitution in order to create oxygen vacancies 
 and , upon hydration , the hydroxyl defects responsible for their proton 
 conductivities .
in contrast , ba2in2o5 is an inherently oxygen deficient perovskite , and hence cation substitution 
 is not required to allow water uptake .
compensation of the ba and in cation 
 charges in ba2in2o5 requires the 
 removal of one - sixth of the o atoms in the perovskite structure , yielding 
 a high intrinsic concentration of o vacancies along with both tetrahedrally 
 and octahedrally coordinated in ions .
the vacancies order 
 at room temperature into an orthorhombic structure , resulting in three 
 crystallographically distinct o sites ( figure 1a ) .
the labeling used here has o1 sites at the equatorial positions 
 of in octahedra , o2 sites bridging in octahedra and tetrahedra and 
 o3 sites within the in tetrahedral layer .
we use this labeling scheme 
 for both the dry and hydrated structures in contrast to some earlier 
 work .
the structure type is named brownmillerite 
 after the original ca2fealo5 mineral which has 
 a similar arrangement of o vacancies .
an understanding of the water uptake and protonic conduction processes 
 in this system is of particular interest as the extremely large number 
 of vacancies in the brownmillerite structure facilitates a level of 
 hydration rarely possible in related materials . a tga study of ba2in2o5 under 
 wet air by jayaraman et al
. found a maximum 
 weight gain at around 200 c , indicating the formation of the 
 ba2in2o4(oh)2 phase .
further 
 heating results in weight reduction due to h2o loss , and 
 a neutron powder diffraction study under controlled humid air by yildirim 
 et al . showed that only ba2in2o5 is present above 350 c .
0.5 mol of h2o 
 per formula unit ) with a slight deviation from the brownmillerite 
 structure with the ima2 space group .
complete hydration 
 of ba2in2o5 results in a tetragonal 
 structure with space group p4/mbm where the intrinsic o vacancies of ba2in2o5 in the o3 layer are fully occupied by the water o atoms , 
 yielding the composition ba2in2o5.h2o ( or ba2in2o4(oh)2 ) .
the 2c positions 
 ( in the o3 plane ) are fully occupied by one of the water protons ( h2 ) 
 while the second proton ( h1 ) partially occupies ( 12.5% ) the 16l positions ( in the o2 plane ) according to the combined 
 x - ray and neutron diffraction analyses of jayaraman et al . ( figure 1b ) . this model 
 should be contrasted with that proposed in the earlier studies of 
 zhang and smyth where the water was believed 
 to react with ( o1 ) vacancies in the perovskite slabs , the vacancies 
 resulting from p - doping and/or frenkel defects created by occupancy 
 of vacant o3 sites .
( a ) room temperature crystal structure of the brownmillerite 
 ba2in2o5 structure in space group ibm2 with an octtetocttet 
 staggered o vacancy pattern .
( reproduced from reference ( 24 ) by permission of the pccp 
 owner societies . ) ( b ) room temperature crystal structure of tetragonal 
 ba2in2o4(oh)2 in space 
 group p4/mbm , showing the partially occupied h1 and fully occupied h2 
 positions .
schematic representations of the o3 layer of ( c ) ba2in2o5 and ( d ) ba2in2o4(oh)2 .
the interlayer ba atoms in b , c , and 
 d have been omitted for clarity .
early force field calculations 
 of the energetics of defect formation 
 by fisher and islam questioned the role 
 of the o1 vacancies proposed in the zhang and smyth model and confirmed that the water oxygen atoms occupy 
 the vacant o3 sites .
they suggested , however , that the lowest energy 
 site for the protons were the o1 sites .
a subsequent dft based , explicit 
 full optimization of a large number of possible proton arrangements 
 of the hydrated material ba2in2o4(oh)2 ( two formula units , i.e. , 24 ions per unit cell ) 
 by martinez et al . identified a set of 
 low energy structures with two protons ( h2 ) in the o3 layer occupying 
 half of the 4h ( x , x + 0.5 , 0.5 ) positions , and two other protons ( h1 ) in one of the 
 two o2 layers occupying one-16th of the 32y positions . 

the 32y positions are defined by martinez et al . and are derived from the 4e positions of the o2 site in the p4/mbm space group by the eight displacements ( 0.4  , 0.4 
  , 0.4  ) .
note that this 32y position 
 is not found in the international tables for crystallography for the p4/mbm space group ( no . 127 ) but it is nevertheless useful for visualization 
 of the proton positions .
zhang and smyth reported protonic 
 conductivity of ba2in2o4(oh)2 under humid air , where three regions of protonic conduction 
 were observed corresponding broadly to temperatures below 400 c , 
 between 400 and 925 c , and above 925 c .
these authors 
 proposed both grotthuss ( h - hopping ) and vehicle ( oh - hopping ) mechanisms 
 as being involved in protonic conductivity : the grotthuss mechanism 
 dominating at low temperature ; the vehicle mechanism or a combination 
 of vehicle and grotthuss mechanisms dominating at elevated temperatures .
a study of ba2in2o4(oh)2 and of its ti - doped derivatives using h and h solid 
 state nmr experiments under magic 
 angle spinning ( mas ) identified three distinct proton sites ( giving 
 rise to a higher frequency split resonance and a lower frequency broad 
 resonance ) , while only two proton sites are anticipated based upon 
 the tetragonal crystal structure obtained by jayaraman et al .
( figure 1b ) . the increased 
 splitting of proton sublattices in the nmr data
as compared with the 
 number of crystallographic sites found by neutron diffraction was 
 interpreted as a result of a further ordering of proton sites with 
 respect to the average structure .
the authors postulated that this 
 arises from the actual unit cell being larger than the average unit 
 cell of the p4/mbm space group used 
 in the refinement of the diffraction data ( a larger cell having been 
 observed in their electron diffraction studies ) , nmr being sensitive 
 enough to distinguish between variations of different ordering schemes 
 for at least one of the two environments .
our previous paper 
 on ba2in2o5 focused on the dry material 
 and used dft methods to rationalize 
 the o spectra seen in this system .
the current work examines hydrated ba2in2o5 [ i.e. , ba2in2o4(oh)2 ] using both current solid state o and h nmr spectroscopy techniques and dft calculations .
the dft 
 energetics and gipaw calculations are first presented to describe 
 the various configurations investigated in this work .
we reproduce 
 the general results of the dft study by martinez et al . , although differences in the ground state structure 
 and the energies of the other low energy structures are observed . 

first - principles periodic dft nmr calculations within the gauge - including 
 projector augmented wave ( gipaw ) approach are then performed to help interpret the nmr spectra .
high magnetic 
 field strengths are used to obtain nmr spectra of the hydrated material . 

the individual o and h nmr shifts 
 are assigned to specific oxygen and proton environments , the dft results 
 allowing us to assign the three h nmr signals seen at 
 room temperature to specific local environments .
we show that multiple 
 low energy structural configurations are responsible for the experimental h nmr spectra .
the o nmr spectra well reproduced 
 with these multiple configurations , allowing us to assign the proton 
 donor and acceptor oxygens .
ba2in2o4(oh)2 was prepared by slow cooling of ba2in2o5 ( dried at 400 c under a 
 flow of dry n2 for 12
h ) from 350 c to room temperature 
 ( at a rate of 0.1 c.min ) under a flow of 
 wet n2 gas .
the water vapor pressure corresponds to 2030 
 mbar ph2o ( 2.3% ( w / v ) h2o ) 
 and was controlled by bubbling n2 through water at room 
 temperature.o enriched 
 ba2in2o4(oh)2 was synthesized 
 by heating previously synthesized ba2in2o4(oh)2 in a 50% o enriched o2 gas ( isotec , used as received ) atmosphere with 2.3% ( w / v ) 
 h2o ( nonenriched ) in a closed quartz tube , at 1000 c 
 for 24 h. during o enrichment with the closed quartz 
 tube , the initial air inside the tube was removed by vacuum while 
 concurrently freezing the h2o inside the tube with liquid 
 n2 .
powder x - ray diffraction patterns were obtained 
 on either a panalytical empyrean or bruker d8-focus x - ray diffractometer 
 using cu k radiation (  = 1.5418  ; figure s1 in 
 the supporting information ) .
thermogravimetric 
 analyses ( tga ) were performed on a mettler toledo tga / sdta851 thermobalance 
 using an alumina crucible ( supporting information figure s2 ) .
all measurements were performed under flowing dry nitrogen , 
 in a temperature range of 30800 c and at a heating rate 
 of 10 cmin .
tga showed that both ba2in2o4(oh)2 and o enriched ba2in2o4(oh)2 contain 1 mol of water per formula unit , as anticipated .
solid 
 state o mas nmr experiments on ba2in2o4(oh)2 were performed on 9.4 t bruker avance 
 400 mhz and 16.4 t bruker avance iii 700 mhz spectrometers using bruker 
 2.5 mm hx probe and bruker 3.2 mm hxy ( in double resonance mode ) probe , 
 respectively .
unless otherwise stated , spectra were recorded using 
 a solid /2 pulse length of 1 s , corresponding 
 to a radio frequency ( rf ) field amplitude of 83 khz , and a 
 mas frequency of 30 khz at 9.4 t , and a solid /2 pulse 
 length of 1.7 s , corresponding to a rf field amplitude 
 of 50 khz , and a mas frequency of 20 khz at 16.4 t. the o 3qmas experiment was performed at 9.4 t with 128 t1 increments of 1320 scans each .
hard and soft 
 pulses are performed at rf fields of 150 and 10 khz , respectively . 

the h  o cross - polarization ( cp ) and 
 heteronuclear correlation ( hetcor ) spectra were obtained at 16.4 
 t with a o rf field amplitude of 50 khz , while 
 the h rf field amplitude was ramped to obtain maximum 
 signal at 83 khz .
small phase incremental alternation with 
 64 steps ( spinal64)h heteronuclear 
 decoupling was applied during the acquisition .
all o nmr data were collected on a freshly o enriched ba2in2o4(oh)2 sample packed 
 in a zro2 rotor .
a recycle delay of 10 s was used for all 
 experiments , with 20480 scans for o hahn - echo experiments 
 and 48 t1 increments of 256 scans for 
 the hetcor spectra .
h mas nmr experiments were performed 
 on a 16.4 t bruker avance iii 700 mhz spectrometer equipped with a 
 bruker 4 mm hxy probe ( in double resonance mode ) .
one dimensional 
 ( 1d ) spectra were recorded under mas using a rotor - synchronized spin 
 echo sequence to suppress the proton background of the probe .
all h spectra were recorded at a 
 rf field amplitude of 100 khz and a mas frequency of 12.5 khz with 
 recycle delays ranging from 4 to 60 s depending on the t1 relaxation times .
temperature calibration was performed 
 using the pb resonance of pb(no3)2 as a chemical shift thermometer .
the sample 
 temperatures quoted subsequently have all been corrected and have 
 an accuracy of 10 c .
additional fast mas h 
 nmr experiments were recorded on the same spectrometer with a bruker 
 1.3 mm hx probe spinning at 60 khz , using a rotor - synchronized spin 
 echo sequence , an rf field amplitude of 115 khz , and recycle delay 
 of 8 s. o and h chemical shifts were 
 externally 
 referenced to water at 0.0 and 4.8 ppm , respectively , at 20 c . 

nmr data were processed using topspin 3.0 and matnmr , the latter running within 
 the matlab package .
the 
 first - principles solid state electronic structure calculations used 
 here are similar to those reported in our previous work on ba2in2o5 and in related studies and were all performed within the castep code .
structural models of ba2in2o4(oh)2 were derived , as described later , from the 
 experimental neutron diffraction model by jayaraman et al .
full structural optimizations ( both cell and 
 atomic positions ) of ba2in2o4(oh)2 ( two formula units ) were performed in the absence of any 
 symmetry operators ( i.e. , in space group p1 ) , using 
 a plane wave kinetic energy cutoff of 40 ry and a linear spacing of 
 0.04  or smaller for the reciprocal space 
 sampling mesh , yielding monkhorst 
full details of all of these structures 
 are presented in the supporting information ( si ) .
convergence 
 of total energy with respect to numerical parameters was estimated 
 at 0.2 kjmol per atom or better .
structural 
 optimizations ( both cell parameters and atomic positions ) pursued 
 until the energy difference , maximum atomic force , maximum atomic 
 displacement , and maximum stress tensor component fell below tolerances 
 of 1  10 ev , 1  10 ev , 1  10  , and 5  10 gpa , respectively .
the 
 effect of decreasing these listed tolerances by a further order of 
 magnitude was investigated , yielding only minimal changes in geometry 
 and computed nmr parameters . to facilitate our exploration of the 
 complex energy landscape ,
however , given the relatively similar 
 bonding sites being considered for the h , we assume that these contributions 
 will largely cancel when comparing the relative energies .
previous 
 work on a series of iron- and aluminum - oxyhydroxides calculated a 
 less than 1.5 kj/(mol of h ) variation in vibrational free energies 
 at room ( 25 c ) and synthesis ( 350 c ) temperatures for 
 h across three compounds with both fe and al cations .
this error is as small or smaller than that found later between 
 different dft approaches , justifying exclusion of these contributions .
the hydration enthalpy of formation for the ground state configuration 
 was calculated for the theoretical reaction of ba2in2o5 ( staggered configuration ) with one isolated water molecule h2o ( calculated 
 in a large unit cell with volume of 332  ) .
dft total 
 energies of geometry - optimized structures were used in this calculation . 

the experimental enthalpy of hydration is reported to be 0.65 
  0.08 ev ( 63 kjmol ) with the zhang  smyth model and 0.76 ev ( 74 
 kjmol ) ( trapped ) and 0.3 ev ( 29 
 kjmol ) ( untrapped ) with the trapping model 
 by schober and friedrich at temperatures 
 of 6231073 k. boltzmann distribution weights at 350 
 c were calculated according 
 to weighti = ( exp(ei / rt))/(i exp(ei / rt ) ) where ei is the relative energy of a configuration 
 from the ground state configuration , per mole of hydrogen .
fully periodic 
 calculations of nmr parameters within the gauge - including projector 
 augmented wave ( gipaw ) approach have been performed 
 using the castep code , including determination of electric field gradient 
 tensors and associated quadrupolar interaction parameters for o sites .
the nmr parameters 
 are obtained from single point calculations within the optimized geometry , 
 differing only from the prior optimization runs in that a larger basis 
 set cutoff of 60 ry was applied .
the isotropic shielding was obtained 
 as iso = ( xx + 
 yy + zz)/3 , where xx , yy , and zz are the principal components of the shielding tensor , ordered such 
 that |zz 
the chemical shift iso is 
 then derived from the computed site shielding iso by application of a shielding reference ref with 
 the expression iso = ref + miso .
both ref and the 
 scaling factor m for o are taken unmodified 
 from previous work by the current authors which obtained ref = 223.70  3.03 ppm and m = 0.888 
  0.014 with a mean absolute error ( mae ) in computed shifts relative 
 to experiment of 12.1 ppm across a range of phases
. meanwhile , ref and m for h are determined from a fit of the results of nmr 
 castep calculations on mg(oh)2 ( iso = 
 30.89 ppm ; iso = 0.5 ppm ) in combination with 55 different proton sites in four separate organic 
 molecules as computed recently by yates et al .
, yielding ref = 
 28.45  0.51 ppm and m = 0.930  
 0.020 with a mae ( defined similarly to those given earlier ) of 0.29 
 ppm ( si figure s3 ) .
we note that all but 
 one of the proton sites used in deriving the shielding reference arise 
 within organic molecules , and thus we might expect some discrepancy 
 between experimental and calculated h chemical shifts 
 in ba2in2o4(oh)2 as discussed 
 later .
chemical shift anisotropies and asymmetries are also computed , 
 defined as aniso = zz  ( 1/2)(xx  
 yy ) and cs = 
 ( yy  xx)/(zz  
 iso ) , respectively . the quadrupole coupling constant 
 for o
is obtained as cq = eqvzz / h and 
 the asymmetry as q = ( vxx  vyy)/vzz , where an 
 ordering |vzz|  
 |vyy|  |vxx| of the principal components 
 of the traceless electric field gradient tensor is assumed .
the experimental 
 value q = 0.02558 barns has been used for 
 the o nuclear electric quadrupole moment . unless otherwise specified , all of the 
 corresponding simulated o nmr spectra were obtained by 
 simulation of each individual o site using simpson and summation of these spectra , resulting in the final 
 spectra .
the structural optimization 
 of ba2in2o4(oh)2 was performed 
 with the same approach as that 
 used for ba2in2o5 in our previous 
 work taking the p4/mbm structure ( figure 1b ) of jayaraman 
 et al . as the starting point .
the cell 
 lengths of the p4/mbm cell are given 
 by 2ap  2ap  2ap ( where ap is the notional perovskite unit cell length ) .
all structures feature 
 full occupancy of the o3 layer proton positions ( 2c site ) but have various proton configurations in the o2 ( 16l site with fractional occupancy of one - eigth ; 14 arrangements ) 
 and o1 ( two arrangements ) layers , o1 occupancy not being observed 
 by jayaraman et al . but identified theoretically 
 by fisher and islam .
this results in 
 configurations that are similar to those found in the study by martinez 
 et al .
the configurations are then ranked 
 in terms of the calculated total energies ( figures 2 and 3 and table 1 ) . as was also shown by martinez et al .
, all configurations undergo significant relaxations from the average 
 positions suggested by jayaraman et al . the o2 layer protons ( h1 ) move off the 16l positions 
 [ with fractional coordinates ( x , y , 0.25 ) ] suggested by neutron diffraction into the  32y  positions ( with values 
 close to x  0.07 , y  
 0.07 , 0.25  0.04 , e.g. , with x = 0.10 , y = 0.13 ) retaining the nomenclature previously used by 
 martinez et al .
the computationally relaxed 
 ground state forms alternating layers of o2o3o2o1 
 oxygens , partially occupied , fully occupied , nonoccupied , and nonoccupied 
 by protons , respectively ( figure 2b ) .
thus , 
 the o3 layer o vacancies of ba2in2o5 are fully occupied by a hydroxyl group ( figures 1c and 2d ) , while the second water proton 
 occupies one of the two nearby o2 layers .
however , only one of the 
 o2 layers is protonated , while the other remains empty ( figure 2b ) .
o2in , 
 and thus o3 oxygen atoms are in a significantly different electronic 
 environment ( table 1 )
o2in is substantial which may have 
 implications for the o nmr spectra of this phase ( table 1 ) .
the optimized structures also indicate that hydrogen 
 bonding constitutes the main interaction driving the formation of 
 a range of distinct chemical environments for both protons and oxygen 
 ions .
( a ) room temperature crystal structure of tetragonal ba2in2o4(oh)2 in space group p4/mbm showing 
 full occupancy of the protons in the o3 layer ( 2c site ) and partial occupancy in the o2 layer ( 16l site ) ( denoted , as in figure 1b , by partially 
 filled white balls ) .
( b ) schematic representation of the 14 proton h1 configurations 
 considered , differing in terms of the arrangement of protons in the 
 o2 layers ( 16l site ) .
eight configurations ( a  h ) 
 correspond to two - layer hydroxyl ( tlh ) forms ; four configurations 
 ( i  l ) , to one - layer hydroxyl ( olh ) forms ; and two configurations 
 ( m  n ) , to one - layer water ( olw ) forms .
protons were placed 
 initially in the 16l positions with fractional occupancy 
 of one - eighth determined by neutron diffraction , and subsequently moved to the 32y positions 
 on geometry optimization as in the previous study of martinez et al . the calculated energy per formula unit ( containing 
 two h atoms ) of each configuration , relative to the ground state structure 
 i , is also shown on the right - hand side of each configuration .
a hydration 
 enthalpy ( hh ) of 79.3 kjmol to form the ground state configuration i from dry 
 ba2in2o5 and a single molecule of 
 h2o was calculated .
the hydration enthalpies of other configurations 
 can be achieved by adding the relative energies to 79.3 kjmol .
dft optimized geometries 
 of ( a ) configuration i ( ground state ) , 
 ( b ) configuration l , ( c ) configuration j , and ( d ) configuration k 
 showing the o3 and o2 ( z  0.25 and 0.75 ) 
 layer protons .
the configurations were grouped 
 into three different types . in 
 the two - formula - units cell of ba4in4o8(oh)4 ,
two out of four protons are always in the o3 layer 
 ( h2 ) and the other two are each either in a different o2 layer ( h1 ) 
 [ two - layer hydroxyl ( tlh ) , configurations a 
h ] , in the same 
 o2 layer ( h1 ) [ one - layer hydroxyl ( olh ) , configurations i 
l ] , 
 or present as one water molecule ( two protons attached to one oxygen ) 
 per layer [ one - layer water ( olw ) , configurations m and n ] ( figure 2 ) .
olh configuration i represents the ground state 
 structure ( with hydration enthalpy , hh = 79.3 kjmol ) in which 
 the protons in the o2 layer ( h1 ) point toward two different o3 acceptors . 

configurations in which the protons are located within one o2 layer 
 ( h1 ) ( olh , eref = 08.8 kjmol ) are systematically lower in energy than the olw 
 ( eref 17.8 and 35.8 kjmol ) and tlh ( eref = 10.248.8 kjmol ) arrangements . here
all energies are given as eref to denote their being referenced to the 
 energy of the ground state structure i. all of the olw configurations 
 considered are unstable , configuration m relaxing to a mixed o1 and 
 o2 layer protonation and configuration n to an olh configuration . 

structures where a proton is located in the o1 plane are noticeably 
 higher in energy . for example , two configurations were also considered 
 where the o3 layer is fully protonated and one o2 site and one o1 
 site are also protonated , the two structures differing in the relative 
 orientations of the o1 and o2/o3 protons
. both of these structures 
 are much higher in energy , occurring at 34.6 and 48.3 kjmol above the ground state structure .
the protons in 
 both of these structures are located within the plane of the o1/in 
 layers , in contrast with the structures proposed by fisher and islam in which the o1h bonds were oriented 
 perpendicular to the plane .
note that the previous study of 
 martinez suggested the present 
 configuration l as the ground state structure ( first low energy state ) , 
 in which the o2 layer protons point toward the o1 oxygen site ( figures 2b and 3 ) ; a structure close 
 to configuration i represented their first excited state .
studies disagree on the energy ordering 
 of structures at the 6 kjmol ( or 
 just 3 kj/(mol of h ) ) level suggests that the dft approach 
 used can not be regarded as yielding energies any more accurately than 
 to within a few kj/(mol of h ) .
thus , it is clear that we should consider 
 more than just the ground state structure when analyzing our nmr data . 

bielecki et al . , in an inelastic neutron 
 scattering ( ins ) study of hydrogen bonding in this material , suggested 
 that the second lowest energy structure of martinez et al . should not exist due to its strong hydrogen 
 bonds , which would result in higher frequency o 
however , our related structure ( ground 
 state structure i ) has a longer hydrogen bond distance ( 1.819  ; 
 see table 1 ) than that obtained by martinez 
 et al .
( 1.7  ) . hence , structure 
 i is likely consistent with the lower frequency o 
h wag modes 
 observed experimentally and can not be ruled out on the basis of the 
 ins data .
the thermal energy kbtna ( or rt ) at a typical hydration 
 synthesis 
 temperature ( 350 c ) is 5 kj .
assuming fast cooling ( equilibrium 
 of atomic motion is not reached in the given time frame and temperature ) , 
 this suggests that configurations with up to 5 kj/(mol of 
 h ) may be present at significant concentrations at room temperature . 

a previous thermogravimetric 
 study of hydrated ba2in2o5 by schober 
 and friedrich suggests an activation 
 energy of 0.3 ev ( 30 kjmol ) for 
 trapping effects in the hydration , as well as a hydrogen diffusion 
 enthalpy ( h * ) of 0.34 ev with diffusion coefficient 
 prefactor ( d0 ) of 0.34  10 cm / s .
these values all suggest that at least some h 
 can readily diffuse at room temperature ( as will be explored later 
 by h nmr spectroscopy ) . however , we propose that either 
 some of the h ions are significantly less mobile or that 
 the cooperative motion of the h needed to reorder is inhibited , despite 
 the good mobility of individual h ions .
we therefore consider 
 gipaw calculations on the first four lowest energy structures i , j , 
 k , and l , all of which are of olh - type and have relative energies 
 in the range of 08.8 kjmol ( or 04.4 
 kj/(mol of h ) ) , consistent with the possibility of thermal excitations 
 being trapped in the system and the uncertainty in dft energies and 
 neglected vibrational energies mentioned earlier .
we also limit ourselves 
 to these four structures as they are clearly distinct in character 
 from the next highest energy structures c , a , and b [ at 10.2 , 12.5 , 
 and 13.0 kjmol , respectively ( or 6 
 kj/(mol of h ) ) ] , which all have protons in both o2 layers ( z = 0.25 and 0.75 ) .
means and standard deviations ( in 
 parentheses ) of the values are shown . for values marked with an asterisk 
 ( * ) ,
structure 
 are switched in order to match this work and the previous publication 
 on the ba2in2o5 phase .
assuming 
 all of the structures occur with a boltzmann distribution 
 established at 350 c , the relative amounts of each configuration 
 are given by the boltzmann weights 0.25 , 0.11 , 0.11 , and 0.15 for 
 i , j , k , and l , respectively , and 0.09 , 0.08 , 0.07 , 0.06 , and 0.05 
 for the configurations c , a , b , d , and n , respectively ; the remaining 
 seven configurations have weights of less than 0.01 contributing total 
 weights of approximately 0.02 .
the x - ray 
 powder diffraction pattern of ba2in2o4(oh)2 samples and the o enriched counterpart 
 prepared in this study are consistent with previous reports ( figure s1 in the supporting information ) and indicate that the structure has tetragonal p4/mbm symmetry .
the 1d o mas nmr spectrum of o enriched 
 ba2in2o4(oh)2 obtained 
 at 9.4 t under conditions where the line shape distortion is minimal 
 ( i.e. , with short pulse length ) shows 
 a complicated pattern characteristic of multiple overlapping o resonances ( figure 4 ) .
four sites 
 could be resolved in the o 3qmas experiment ( figure 5 ) , which could be satisfactorily fit with the nmr 
 parameters given in table 2 .
fitting of the 
 1d o mas nmr spectra with these parameters yields an 
 intensity ratio of 4:1:6:4 for the resonances with chemical shifts 
 of 188 , 173 , 152 , and 97 ppm , respectively ( figure 4 ) .
in addition to these resonances there is a fifth peak at 
 220 ppm which nutates at the same frequency as water ( i.e. , it must 
 be associated with a very small or zero quadrupolar coupling ) and 
 is tentatively attributed to either a possible h2o molecule 
 on the surface of the material as also discussed in our previous paper , or to an impurity phase .
the o 
 signals in the 3qmas show a broadening along the + 1 direction ( positive 
 slope diagonal ) , which is attributed to a distribution of chemical 
 shifts arising from a distribution of different local environments .
an asterisk denotes 
 the most plausible 
 o and h environments from four hydrated models .
standard deviations 
 are also given in parentheses ; deviations of quadrupolar parameters cq and q are less than 0.01 
 and are therefore omitted .
obtained from the averaged dft calculated 
 nmr parameters of the four low energy structures i , j , k , and l. the 
 calculated values of 1 are obtained with 1 = ( 27iso  102)/17 with 2 = iso 
( 3/500)((cq2(1 + q2/3))/02 ) for o ( i = 5/2 ) ( see ref ( 58 ) ) , the errors arising from 
 the range of iso values .
iso was determined from the center of gravity of 
 each peak in f2 ( 2 ) and f1 ( 1 ) as iso = ( 10/27)2 + ( 17/27)1 and cq from the fit of the 2 cross - sections through the 
 ridge line shapes .
o mas nmr 
 spectra of o enriched ba2in2o4(oh)2 obtained at 9.4 
 and 16.4 t. experimental spectra are shown with full lines and total 
 best - fit simulations in black dashed lines .
the individual site components 
 are shown as dashed lines in red ( site a , o1 ) , blue ( site b , acceptor 
 o1 ) , orange ( site c , combination of acceptor o2 and acceptor o3 ) , 
 pink ( site d , donor o2 and donor o3 ) , and green ( small quadrupole 
 coupling impurity site ) ( see table 2 ) .
assignments 
 of the o sites are made by comparison with parameters derived from 
 dft gipaw calculations ( see figure 6 ) .
two - dimensional o 3qmas spectrum 
 of o 
 enriched ba2in2o4(oh)2 obtained at 9.4 t. right : experimental cross - sections ( full lines ) 
 obtained at 1 = 140 ( pink ) , 174 ( orange ) , 192 ( blue ) , 
 and 207 ppm ( red ) along with best - fit simulations ( dashed lines ) using 
 the parameters given in table 2 .
the weaker 
 high frequency component in the 1 = 140 ( pink ) slice 
 results from an overlap with the more intense resonances with larger 
 1 values ( as explained in the main text ) and has 
 thus not been included in the line - shape simulation .
the o isotropic chemical shifts , iso , obtained by gipaw calculations of the lower energy i , 
 j , k , and 
 l structures of ba2in2o4(oh)2 are also given in table 2 and are 
 found to span a wide range of values for each o sublattice o1 , o2 , 
 and o3 ( figure 6 ) .
nevertheless , we may divide the sites into three general types 
 of oxygen atoms , namely , bare oxygens ( o ) , oxygens directly bonded 
 to a proton ( h - donor o ) , and oxygen ions that are hydrogen bonded 
 to a proton ( h - acceptor o ) .
( a ) simulation of the gipaw calculated o nmr spectra 
 of the 12 sublattice o sites occurring in the lowest energy optimized 
 structure i of ba2in2o4(oh)2 .
all of the spectra were simulated at 9.4 t. ( b ) comparison of the 
 experimental o nmr spectra of o enriched 
 ba2in2o4(oh)2 ( black lines ) 
 and the sum of the simulation of the gipaw calculated o nmr spectra ( dashed red lines ) of all o sites of the four lower 
 energy structures ba2in2o4(oh)2 ( i , j , k and l , combined with relative weights of 0.25 , 0.11 , 
 0.11 and 0.15 ) at 9.4 and 16.4 t. more specifically , we note that o1 , h - acceptor o1 , o2 , h - donor 
 o2 , h - donor o3 , and h - acceptor o3 local environments occur in all 
 of the low energy structures i , j , k , and l ( see table 2 ) .
a range of cq are also observed , 
 where cq for the h - acceptor o sites ranges 
 from 3.8 to 4.5 mhz , the h - donor o sites from 5.3 to 6.9 mhz , and 
 the bare o sites from 4.9 to 5.5 mhz .
two distinct ranges for the 
 quadrupolar asymmetry parameter q are obtained : 
 those for bare o sites are approximately 0.1 , while those for h - donor 
 and -acceptor o sites are approximately 0.7 . taking the ground state 
 structure i as an example , the o1 ( sites 14 in figure 6a , iso = 170.4 ppm ) , o2 ( sites 
 5 and 8 in figure 6a , iso = 159.6 ppm ) , and h - acceptor o3 ( sites 9 and 12 in figure 6a , iso = 156.4 ppm ) all contribute 
 to the high frequency resonances in the experimental spectrum ( mean , 
 164 ppm ) , while the h - donor o2 ( sites 6 and 7 in figure 6a , iso = 114.4 ppm ) and h - donor o3 ( sites 
 10 and 11 in figure 6a , iso = 94.5 ppm ) contribute to the lower frequency resonances ( mean , 
 104 ppm ) ( see table 2 ) .
o double resonance experiments 
 probe the h  o heteronuclear dipolar 
 coupling ( and hence the h  o heteronuclear 
 distance ) and were therefore carried out to investigate the spatial 
 proximities between the o sites and protons .
the o cross - polarization ( cp ) spectrum of o enriched 
 ba2in2o4(oh)2 recorded 
 with a very short contact time ( cp = 40 s ) 
 is given in si figure s4b and reveals a 
 single resonance corresponding to the low frequency signal at iso = 97 ppm , confirming its assignment to h - donor oxygens . 

additionally , a two - dimensional h  o heteronuclear correlation ( hetcor ) spectrum , also recorded with 
 cp = 40 s , shows that this 97 ppm resonance 
 correlates with all of the h signals ( see si figure s4a and section 3.2.3 ) .
the o cp spectrum obtained with a longer contact 
 time of 2.5 ms ( si figure s4b ) still does 
 not contain the signals observed at high frequencies ( iso = 188 and 173 ppm ) in the o mas spectrum ( figure 4 ) , indicating that the o sites that give rise to 
 these resonances are not in close proximity to the protons ( or that 
 the associated protons are too mobile ) .
instead a weak resonance at 
 iso = 152 ppm is observed which is tentatively assigned 
 to an h - acceptor oxygen .
the o cp kinetics curve ( si figure s5 ) shows the slower cp dynamics associated 
 with the 152 ppm compared to the 97 ppm resonance , consistent with 
 our assignment of the 152 ppm resonance to a h - acceptor o site .
assuming that all of the low energy configurations , i , j , k , and 
 l contribute to the spectrum with weights from the bolztmann distribution 
 at 350 c ( given by 0.25 , 0.11 , 0.11 , and 0.15 , respectively ) , 
 we combined all of the oxygen resonances obtained from the gipaw calculations 
 to yield the simulated spectra shown in figure 6b . a peak intensity ratio of 4.3:1:6.3:4.3 ( from high to low frequency ) 
 is derived , which is remarkably close to the experimentally derived 
 4:1:6:4 ratio . on the basis of this reasonable agreement , the experimentally 
 observed high frequency resonance at iso = 188 

ppm is , therefore , assigned to the bare o1 sites ; the other high frequency 
 weaker resonance at 173 ppm , to the acceptor o1 sites ; the next resonance 
 at iso = 152 ppm , to the bare o2 sites and 
 h - acceptor o3 sites ; and finally the lowest frequency resonance at 
 iso = 97 ppm , to the h - donor o2 and h - donor 
 o3 sites , in agreement with the o cp experiments , all 
 of these sites corresponding to the 48 o sites in the four ba4in4o8(oh)4 configurations , 
 i , j , k , and l ( figure 3 and table 2 ) . in summary
, the present first - principles calculations 
 permit the assignment of the o mas nmr spectrum of ba2in2o5(oh)2 , yielding chemical 
 shifts and quadrupolar parameters in reasonable agreement with the 
 experimental trends , albeit with some minor differences in the chemical 
 shifts , quadrupolar parameters , and relative resonance intensities . 

a likely source of error in the intensities is the assumption that 
 only structures i , j , k , and l contribute to the experimental spectra 
 in proportions governed by their relative energies and the synthesis 
 temperature .
however , the assignment of the  high  and 
  low  shift peaks in the o mas nmr experimental 
 spectra is consistent ; i.e. , we expect nondonor oxygen resonances 
 to occur in the high frequency region and a donor oxygen to occur 
 in the low frequency region .
overall , while relative intensities of 
 the experimental peaks may vary , their assignment to these chemical 
 environments is sound .
the 
 room temperature h mas nmr spectrum of ba2in2o4(oh)2 obtained at 16.4 t clearly shows 
 three distinct proton sites at shifts of 7.3 , 3.3 , and 1.7 ppm in 
 a 2:1:1 intensity ratio ( figure 7 ) .
h / h nmr resonances in approximately the same chemical 
 shift range were observed by jayaraman et al . in their study of this material ; however , these authors observed 
 a splitting of the higher frequency resonance ( of approximately 12 
 ppm ) , a broader resonance being observed at lower frequencies ( at 
 approximately 2.5 ppm ) and the high ( split ) and low frequency resonances 
 occurring with intensity ratios of 1:1 .
the three resonances observed in our study are fairly 
 broad , and we assign this to inhomogeneous broadening ( i.e. , a chemical 
 shift distribution ) rather than to the effects of strong homogeneous 
 dipolar interactions between protons , as similar h line 
 widths were obtained in spectra acquired under fast mas conditions 
 ( si figure s6 ) .
h nmr spectrum of ba2in2o4(oh)2 : ( a ) experimental data , ( b ) simulation of 
 combined gipaw calculated parameters of structures i and l , ( c ) all 
 structures with eref < 20 kjmol , and ( d ) structures i , j , k , and l. the blue dashed 
 line with double arrows indicates the 26 ppm region corresponding 
 to the h1 protons in the o2 plane , and the red dashed line with double 
 arrows indicates the 711 ppm region corresponding to the h2 
 protons in the o3 plane .
simulations are carried with a 0.8 ppm lorentzian 
 line broadening summing the spectra using the respective 350 c 
 boltzmann weights for structures i and l in b ; i , j , k , l , c , a , b , 
 d , and n in c ; and i , j , k and l in d. in order to assign all three resonances observed in the experimental h mas nmr spectrum of ba2in2o4(oh)2 , we computed the h site shielding tensors 
 in the proton arrangements discussed earlier ( table 2 and figure 7 and si figure s7 ) . a simulation of the h spectrum 
 using the calculated nmr parameters ( si figure s7 ) of the lowest energy structure i contains three peaks 
 with a 1:1:2 ratio ( 9 , 8 , and 5 ppm ) , providing 
 a poor match with the experimental spectrum ( figure 7a ) .
thus , in order to generate a spectrum that is closer to 
 the experimental one , other low energy structures were also considered . 

inclusion of the first high energy configuration ( l ; with boltzmann 
 weights of 0.25 and 0.11 for i and l ) improves the fit to the spectrum 
 in the low part per million region but worsens it in the higher frequency 
 region ( figure 7b ) .
when all of the low energy 
 configurations , with respective weights , are considered ( eref < 20 kjmol ) , we do not 
 observe a narrow peak at the high shift region in the spectrum ( figure 7c ) . concentrating on nmr parameters obtained in 
 the four most stable configurations ( structures i , j , k , and l ) , the 
 calculations yield o3 layer proton resonances at iso of 7.89.3 ppm ( due to configuration i ) , 8.69.1 ( configuration 

j ) , 9.7 ( configuration k ) , and 9.19.9 ppm ( configuration l ) 
 ( figure 7d ; spectrum shown with 350 c 
 boltzmann weights ) . in some proportion , all of these o3 layer h signals are likely to contribute to the broad signal ( 1/2 = 800 hz ( 1.5 ppm on 16.4 t magnet ) ) observed experimentally 
 at approximately 7.3 ppm for ba2in2o4(oh)2 ( figure 7a ) .
two distinct 
 sets of shifts are observed , at 5.2  0.2 ppm from the o2 layer 
 protons ( h1 ) in structures i and k and at 3.9  0.2 ppm arising 
 from structures j and
l ( figure 7 , table 2 ) , which are reasonably close to the two experimental 
 resonances observed at 3.3 and 1.7 ppm . of note ,
the spectrum 
 simulated with structure i resembles that 
 obtained by jayaraman et al .
, predicting 
 the small splitting at higher frequency and the absence of a splitting 
 at lower frequency .
this may suggest that the sample prepared by these 
 authors is more ordered than ours ( i.e. , contains fewer proton configurations ) , 
 with a structure that is closer to that of the thermodynamic ground 
 state .
the apparent offset in iso between 
 the calculated 
 and experimental values for all of the structures and sites is relatively 
 constant at approximately 2 ppm , a value larger than the h calculated standard deviation of 0.29 ppm ( see computational methods and si figure 
 s3 ) and may be due to a systematic error in the h shielding 
 reference , arising out of the use of primarily organic phases in deriving 
 ref .
more work is required to obtain a reliable 
 set of reference parameters for protons in inorganic materials , preferably 
 considering hydrated oxides and simple hydrous phases .
in addition , 
 proton motion and , likely , systematic deviation in calculated to experimental 
 lattice constants may also play a role in the h chemical 
 shift . the fact that the protons are involved in chains of hydrogen 
 bonding in the ba2in2o4(oh)2 system means that the h chemical shift will be very 
 sensitive to lattice dilation / contraction .
nonetheless , the relative 
 chemical shifts and relative intensities of the calculated resonances 
 are in good agreement with experiment . of note ,
the results show that 
 configurations in which the o2 protons are involved in hydrogen bonds 
 with both the o3 and o1 sublattices must be included 
 in order to account for the split h1 ( o2 ) resonance observed in our 
 sample .
it is evident from the ho ( hydrogen 
 bond ) distances 
 in table 1 and the h chemical shifts 
 in table 2 that longer hydrogen bonds result 
 in a lower h chemical shift .
a study by yesinowski et 
 al . on a series of hydrated silicates 
 yielded an inverse correlation between donor o to acceptor o distance 
 and h chemical shift characterized by the following equation.1applying this equation to the o  o distances 
 from the i , j , k , and l structures , we calculate h shifts 
 of 7.4 and 9.7 ppm for o2 and o3 layer protons , respectively .
slightly 
 better fits to experiment were obtained by using the empirical equations 
 derived by xue and kanzaki for a wider range of hydrous silicates 
 and related inorganic materials ( yielding 5.5 and 8.0 ppm for the 
 o2 and o3 layer protons ) .
these simple 
 calculations provide trends and allow us to distinguish the o3 and 
 o2 layer protons from each other , but do not provide the ability to 
 further separate the two types of o2 layer protons .
the predicted 
 shifts are noticeably larger than those observed experimentally , particularly 
 for the o2 coordinated protons , most likely due the very different 
 systems studied here than used to derive the empirical correlations .
variable temperature h solid state mas nmr experiments 
 up to 195 c show that all of the protons in ba2in2o4(oh)2 are mobile on the nmr time scale , 
 the resonances first broadening and then completely coalescing at 
 around 150 c , yielding a single site with an isotropic chemical 
 shift of 4.4 ppm . such a coalescence process occurs when the proton - hopping 
 frequency k equals /2 
 ( where  is the frequency separation between the peaks ) 
 indicating that the hopping rate between the two o2 environments ( 1.7 
 and 3.3 ppm ) must be greater than k  2.2 
 khz , while that between the o1 and o2 sites is 7 khz ( where 
 shifts of 7.3 and 2.5 ppm are used in this calculation , 2.5 ppm being 
 the predicted shift following coalescence of the 1.7 and 3.3 ppm resonances ) . 
 as the temperature is increased further , the peak height of the new 
 resonance increases as the line width narrows , due to an increase 
 in proton motion . a weak resonance at 1.7 ppm persists even at 195 
 c , this being assigned to both structures l ( containing o2h2 
 protons pointing to the o1 ( bare ) oxygens ) and j ( containing o2h2 
 protons alternatively pointing to both o1 and o3 sites j ) .
we suggest 
 the o2h1o1 protons are more strongly trapped , 
 while the o2h1o3 protons undergo more rapid 
 exchange with the o3h ( h2 ) protons .
two dimensional 
 exchange nmr experiments were performed to explore 
 motion on a longer time scale ( figure 9 ) .
both 
 chemical exchange and magnetization exchange ( due to spin - diffusion ) 
 will result in cross - peaks situated off the h vs h diagonal . at 42 c , cross - peaks are observed between 
 the two distinct protons assigned to the o2 layer ( h1 ; sites at 1.7 
 and 3.3 ppm ) at a mixing time of 1 ms , indicating that these sites 
 occur within a single particle .
the cross - peaks are most likely generated 
 from a combination of slow motion and spin diffusion .
longer mixing 
 times reveal cross - peaks between all of the resonances , most likely 
 as a result of spin diffusion .
the observation of h1h1 and 
 h1h2 cross - peaks at short mixing times ( 0.1 and 1 ms , respectively ) 
 at 80 c is ascribed to the onset of motion , since the spin diffusion 
 rates are unlikely to increase with temperature . at a temperature 
 of 150 c ,
all protons exchange rapidly at a rate in excess of 
 10 khz , in agreement with the variable temperature h spectra 
 ( figure 8) .
variable temperature h mas nmr spectra of 
 ba2in2o4(oh)2 obtained 
 at a mas rate 
 of 20 khz and at 16.4 t. ( a ) full spectral width showing the isotropic 
 region and the spinning sideband manifold marked with asterisks .
( b ) 
 magnified view highlighting the coalescence of the 1.7 and 3.3 ppm 
 resonances and coalescence of all the resonances above 150 c .
the relatively rapid exchange 
 between different proton sites at 
 room temperature may seem inconsistent with the presence of multiple 
 proton environments associated with excited states .
however , the existence 
 of some mobile protons does not necessarily imply that all of the 
 protons can reorder into the unique ground state .
local orderings , 
 even ones that allow significant h transport , could still be effectively 
 locked in place as a cooperative ordering transition to the ground 
 state could be inhibited , or some of the h could be immobile .
the 
 2d spectra indicate that some of the proton configurations are present within the same particle .
we indicated earlier that , within 
 the errors of the dft , no unique ground state structure emerges ( ours 
 differing from that of martinez et al . ) .
thus , it is likely that the lower energy structures reflect the 
 different possible h - bonding configurations within one particle and 
 that the four lowest structures identified in this study represent 
 the more probable configurations . a future study treating the h ordering 
 with a more complete thermodynamics and kinetic model would be valuable , 
 but this is beyond the scope of this current work .
variable temperature 
 two - dimensional h chemical exchange 
 experiments as a function of mixing time , obtained at a mas rate of 
 20 khz and at 16.4 t. only the isotropic region is shown .
single pulse 
 1d h spectra ( from figure 8) are 
 shown above the 2d plots .
in summary , 
 we have performed a comprehensive structural analysis 
 of the hydrated form of brownmillerite , ba2in2o4(oh)2 , using multinuclear solid state nmr 
 spectroscopy in combination with solid state dft calculations .
we 
 reproduce the structural analysis of a large number of possible proton 
 positions of martinez et al .
three different proton sites were observed by h mas nmr 
 spectroscopy , which were found to exchange at 150 c on the nmr 
 time scale with hopping rates in excess of 10 khz .
assignment of these 
 resonances make use of extensive total energy dft calculations of 
 a wide range of proton configurations , which yielded four chemically 
 similar low energy configurations , the simulated h gipaw 
 nmr spectra of which are in relatively good agreement with the experimental 
 data .
the three resonances can be assigned as follows : the high frequency 
 shift corresponds to o3 layer protons ( h2 ) , while the two lower frequency 
 shifts arise due to two types of configurations of o2 layer protons 
 ( h1 ) with shorter and longer ho ( hydrogen bond ) 
 distances and a difference in o  ho angles . 

distinct o2 layer proton ( h1 ) configurations are observed in four 
 low energy structures that perhaps coexist at room temperature .
the o nmr spectrum of ba2in2o4(oh)2 is dominated by four o sites , which can be rationalized 
 by the dft gipaw calculations , which reveal that h - donor oxygens appear 
 at lower shift while the nonhydroxyl oxygens and h - acceptor o are 
 visible at higher shifts .
we suggest that all the lower energy proton 
 sites should be considered in any proposed proton conduction mechanism 
 within the ba2in2o4(oh)2 phase .
the joint experimental and theoretical approach presented 
 in this 
 work can be readily applied to investigate h - bonding and local structure 
 in other hydrated perovskites .
the current work suggests that multiple 
 h - bonding motifs are likely present in related structures , the relative 
 energies of these strongly affecting proton trapping and conductivity .
 a structural characterization 
 of the hydrated form of the brownmillerite - type 
 phase ba2in2o5 , ba2in2o4(oh)2 , is reported using experimental 
 multinuclear nmr spectroscopy and density functional theory ( dft ) 
 energy and gipaw nmr calculations . 
 when the oxygen ions from h2o fill the inherent o vacancies of the brownmillerite structure , 
 one of the water protons remains in the same layer ( o3 ) while the 
 second proton is located in the neighboring layer ( o2 ) in sites with 
 partial occupancies , as previously demonstrated by jayaraman et al . 
 
 ( solid state ionics2004 , 170 , 2532 ) using x - ray and neutron studies 
 . calculations 
 of possible proton arrangements within the partially occupied layer 
 of ba2in2o4(oh)2 yield 
 a set of low energy structures ; gipaw nmr calculations on these configurations 
 yield 1h and 17o chemical shifts and peak intensity 
 ratios , which are then used to help assign the experimental mas nmr 
 spectra . 
 three distinct 1h resonances in a 2:1:1 ratio 
 are obtained experimentally , the most intense resonance being assigned 
 to the proton in the o3 layer . 
 the two weaker signals are due to o2 
 layer protons , one set hydrogen bonding to the o3 layer and the other 
 hydrogen bonding alternately toward the o3 and o1 layers . 
 1h magnetization exchange experiments reveal that all three resonances 
 originate from protons in the same crystallographic phase , the protons 
 exchanging with each other above approximately 150 c . 
 three 
 distinct types of oxygen atoms are evident from the dft gipaw calculations 
 bare oxygens ( o ) , oxygens directly bonded to a proton ( h - donor o ) , 
 and oxygen ions that are hydrogen bonded to a proton ( h - acceptor o ) . 
 
 the 17o calculated shifts and quadrupolar parameters are 
 used to assign the experimental spectra , the assignments being confirmed 
 by 1h17o double resonance experiments . 
Introduction
Materials and Methods
Results and Discussion
Conclusions