. introduced 
 through the active ingredient , excipients , or the atmosphere , it can 
 induce phase transitions , dissolve soluble components , and increase 
 interactions between the drug and excipients , all of which can adversely 
 affect the physical and chemical stability of the drug substance to 
 the detriment of drug product performance
. it must therefore be accounted 
 for at all stages of drug substance and product manufacturing .
not 
 surprisingly , of the many possible critical quality attributes of 
 a drug substance , hygroscopicity , a measure of the water vapor taken 
 up by a solid with the potential to effect surface and bulk properties , 
 is routinely evaluated , typically by moisture sorption analysis , at 
 the earliest stages of drug product development .
the measurement of 
 water vapor sorption isotherms must , however , be tied more directly 
 to the mechanisms by which water is taken up to truly understand the 
 impact that water sorption has on the properties of the solid . on a molecular level , water has the ability 
 to interact with a 
 substance in many ways , including ( i ) physisorption or binding to 
 the surface by hydrogen bonding , ( ii ) physical entrapment to form 
 liquid inclusions , ( iii ) absorption in localized disordered regions , 
 ( iv ) chemical addition , and ( v ) hydrate 
 formation .
hydrates often crystallize 
 because water improves crystal packing efficiency and satisfies the 
 hydrogen bonding sites of the drug better than the drug itself .
hydrates may be stoichiometric or nonstoichiometric.(3,1013 ) stoichiometric hydrates show step - shaped sorption / desorption 
 isotherms characterized by a fixed water content over a defined relative 
 humidity ( rh ) range and generally convert upon dehydration to a distinct 
 phase , crystalline or amorphous .
the waters of crystallization usually 
 play a crucial role in stabilizing the molecular network .
nonstoichiometric 
 hydrates , however , have a continuously 
 variable composition within a certain rh range that is not associated 
 with a significant change in the crystal lattice , except for possibly 
 anisotropic expansion of the network to accommodate water . dehydrating a nonstoichiometric hydrate may 
 result in an isomorphic dehydrate ( desolvate ) , a one - component phase that exhibits 
 the main structural features of its parent phase .
desolvated solvates 
 are usually metastable and easily take up the original solvent or 
 sometimes other solvents to minimize free volume ( void space ) in the 
 crystal . in some cases ,
nonstoichiometric hydrates 
 lose crystallinity and become amorphous when the very last water is forced out by extreme drying conditions . whether a crystalline hydrate is targeted as the delivery vehicle 
 for a drug in the formulated product or designed around in favor of 
 a neat form , the dehydration and rehydration processes of a hydrate 
 forming system can be complex and difficult to control .
hydrates are generally expected to be thermodynamically more stable , 
 hence less soluble and slower to dissolve than anhydrate forms above 
 the critical water activity for hydrate formation . however , as particle size / shape distribution , 
 specific surface area , and other surface properties heavily affect 
 dissolution , a hydrate may dissolve faster than an anhydrate . additionally , some hydrates are intrinsically more soluble ( less 
 stable ) in water than neat forms .
such 
 exceptions to the general solubility trend include ly334370 hcl , n-{[(5s)-3-(4-{6-[(1r,5s)-6-cyano-3-oxabicyclo[3.1.0]hex-6-yl]pyridin-3-yl}phenyl)-2-oxo-1,3-oxazolidin-5-yl]methyl}acetamide , ly156735 ( a melatonin agonist ) , and norfloxacin .
norfloxacin is considered unusual 
 because its more soluble hydrates are zwitterionic and at least one 
 of its anhydrates is charge neutral . in 
 this case , the higher solubility of the hydrate can be readily attributed 
 to the stronger hydration of the highly charged zwitterions relative 
 to the uncharged molecule in the anhydrous form .
another compound that shows water - induced proton 
 transfer to form 
 zwitterionic hydrates is the 5-ht2a and h1 inverse 
 agonist , 3-(4-dibenzo[b , f]oxepin-11-yl - piperazin-1-yl)-2,2-dimethylpropanoic 
 acid ( ly2624803 or db7 , figure 1 ) .
we previously 
 used db7 as a model compound to test the value of combining computational 
 crystal structure prediction ( csp ) methods with an industrial solid 
 form screening program . from the experimental 
 screen for solid forms , which encompassed a broad range of crystallization 
 conditions and totaled over 300 experiments
, db7 was identified in 
 nine solid forms , including three neat polymorphs ( forms i  iii ) , 
 a stoichiometric dihydrate ( hy2 ) , a nonstoichiometric hydrate ( hya ) , 
 three unstable isostructural solvates ( from methanol , ethanol , and 
 2-propanol ) , and an amorphous form . for
an amphoteric molecule with 
 measured pka values of 2.95 ( oxepine - n ) , 
 4.03 ( carboxylic acid ) , and 7.81 ( piperidine - n ) , application of the 
 pka rule of three would suggest that proton 
 transfer from the carboxylic acid to the piperidine - n is essentially 
 complete rendering db7 zwitterionic , at least in aqueous solutions 
 at moderate ph .
however , solid state n nmr spectra provided an initial indication that only hy2 
 and hya contain zwitterions ( db7 ) ; the neat forms contain 
 the neutral db7 molecule .
molecular diagrams of 
 db7 in the charge neutral anhydrous forms 
 i  iii and amorphous form and in the zwitterionic hydrates . 

the atomic numbering given on the charge neutral 
 form is also used for zwitterionic phases , which are indicated with 
 superscript  z  . in this study
, we explore through a combination of experiment 
 and 
 computation the structural and thermodynamic relationships between the hydrate / anhydrate 
 phases of db7 and their interconversion pathways as a function of 
 temperature , water activity , and ph
. a range of experimental techniques , 
 along with computed lattice energies and chemical shift prediction 
 of experimental and hypothetical structures , are used to understand 
 at an atomistic level two distinct ( de)hydration mechanisms of stoichiometric and nonstoichiometric 
 hydrates complicated by both structural disorder and proton transfer .
db7 ( form ii , purity 99.6% ) 
 was obtained 
 from lilly research laboratories .
the dihydrate ( hy2 ) was prepared 
 by dissolving amorphous db7 ( prepared by rotovapping a dichloromethane 
 solution of the compound ) in stirred water ( ph 5.9 ) at rt . within 
 15 min a thick white slurry , hy2 , had formed .
the solid product was 
 isolated by vacuum filtration and dried in a 75% rh chamber .
after 
 stirring in water at rt for 10 days hy2 transformed to the second 
 hydrate ( hya ) .
the solid product was isolated by vacuum filtration , 
 washed / transferred with water , air - dried , and equilibrated for several 
 days at 43% rh to further dry the sample .
experiments on hy2 and hya 
 were performed with samples that had been stored at 75% rh over a 
 saturated nacl solution . for solubility experiments
the hydrate samples 
 were equilibrated at 92% rh ( over a saturated kno3 solution ) , 
 for ssnmr experiments at 75 , 58 , 43 , 33 , 22 , and 11% rh and for h2o / d2o exchange ( raman ) experiments at 98 and 11% 
 rh .
the three anhydrates , forms i  iii , were prepared 
 according to ref ( 47 ) .
single crystal x - ray diffraction data were collected using a bruker 
 d8-based 3-circle geometry diffractometer equipped with 
 a cuk ( hy2 ) or mok ( hya ) radiation source and a smart 
 apex ii 6000 ccd area detector . hy2 and
hya1.95 crystals 
 were taken freshly from the mother liquor and hya1.73 after 
 storing the sample at ambient conditions ( 40% rh ) .
the structures were solved by direct methods 
 using the program package wingx ( sir2011 and shelxl2013 ) . 

the aromatic and aliphatic 
 hydrogen atoms were generated by a riding model on idealized geometries 
 with uiso(h ) = 1.2ueq(c ) for aromatic and nonterminal aliphatic hydrogens and uiso(h ) = 1.5ueq(c ) 
 for ch3 .
water hydrogen atoms and hy2 n  h were located from the difference map and refined with constrained 
 o / n  h bond distances and uiso(h ) = 1.5ueq(o)/uiso(h ) = 1.2ueq(n ) .
the hya 
 n  h proton was identified from the difference map 
 and refined isotropically .
proton disorder of the hy2 water molecules is 
 addressed in section 3.2.1 and hya water position 
 occupancies / disorder in section 3.2.2 .
the structure 
 models for both hydrates were supported with electronic structure 
 calculations ( sections 1116 of the supporting 
 information ) .
xrpd 
 patterns were obtained using an xpert pro diffractometer ( panalytical , 
 almelo , nl ) equipped with a theta / theta coupled goniometer in transmission 
 geometry , programmable xyz stage with well plate holder , cu 
k1,2 radiation source with a focusing mirror , a 0.5 divergence 
 slit and a 0.02 soller slit collimator on the incident beam 
 side , a 2 mm antiscattering slit and a 0.02 soller slit collimator 
 on the diffracted beam side , and a solid state pixcel detector .
the 
 patterns were recorded at a tube voltage of 40 kv and tube current 
 of 40 ma , applying a step size of 2 = 0.013 with 40s/80s 
 per step in the 2 range between 2 and 40. for nonambient 
 rh measurements a vgi stage ( vgi 2000 m , middlesex , u.k . ) was used .
the diffraction patterns were indexed using the first 20 peaks 
 with dicvol04 , and the space group , which was determined based on 
 a statistical assessment of systematic absences as implemented in the dash structure solution package , agreed with the single crystal data ignoring 
 temperature effects .
hastings 
 pseudo - voigt function was used for peak shape fitting . for the rietveld 

refinements the db7 molecule was refined with restraints 
 ( distances , angles , and aromatic rings flattened ) and the water molecules 
 as oxygens only .
moisture sorption 
 and desorption studies were performed with the 
 automatic multisample gravimetric moisture sorption analyzer sps23 - 10 
 ( proumid , ulm , germany ) .
the measurement cycles were started at 
 40% with an initial stepwise desorption ( decreasing humidity ) to 0% , 
 followed by a sorption cycle ( increasing humidity ) up to 95% and back 
 to 0% relative humidity ( rh ) .
the equilibrium condition for each step was set to a mass constancy 
 of 0.001% over 60 min and a maximum time limit of 48 h for each 
 step .
differential 
 scanning calorimetry ( dsc ) was conducted using a ta q1000 dsc , operated 
 with thermal advantage release 5.4.0 software ( ta instruments , usa ) 
 or a diamond dsc equipped with a controlled cooling accessory ( intracooler 
 1p ) and operated with pyris7.0 software ( perkinelmer , norwalk , ct , 
 usa ) .
a few milligrams of accurately weighed ( mettler um3 ultramicrobalance ) 
 sample was heated in perforated or sealed al - pans .
heating rates ranging 
 from 1 to 50 c min were applied with a nitrogen 
 purge .
the temperature and heat flow of the ta q1000 were calibrated 
 against indium melting .
the diamond dsc was calibrated for temperature 
 with pure benzophenone ( mp 48.0 c ) and caffeine ( mp 236.2 c ) , 
 and the energy calibration was performed with indium ( mp 156.6 c , 
 heat of fusion 28.45 j g ) .
the errors on the extrapolated 
 transition onset temperatures and enthalpy values are 95% confidence 
 intervals ( ci ) derived from at least three measurements .
isothermal 
 calorimetry was used to derive dehydration enthalpies ( see section 
 10 of the supporting information ) .
thermogravimetric analysis ( tga ) was carried out with a tga7 system 
 ( perkinelmer , usa ) using pyris 2.0 software .
two - point calibration 
 of the temperature was performed with ferromagnetic materials ( alumel 
 and ni curie - point standards , perkinelmer ) .
heating rates ranging 
 from 2 to 20 c min were applied , and dry 
 nitrogen was used as a purge gas ( sample purge , 20 ml min ; balance purge , 40 ml min ) .
raman spectra were recorded 
 with a bruker rfs 100 raman - spectrometer ( bruker analytische messtechnik 
 gmbh , germany ) , equipped with a nd : yag laser ( 1064 nm ) as the excitation 
 source and a liquid - nitrogen - cooled , high sensitivity ge - detector . 

the spectra ( 128 scans per spectrum ) were recorded in aluminum sample 
 holders with a laser power of 300 mw and a resolution of 2 cm .
temperature conditions were adjusted with a specac 
 ( grasebury specac limited , orpington , u.k . ) variable temperature cell 
 and a temperature control unit .
for investigating h2o / d2o exchange , the number 
 of scans and laser power were increased to 1064 and 400 mw , respectively . 

samples were stored and measured in hygrostats as detailed in ref ( 66 ) and section 9 of the supporting information .
principle component 
 analysis ( pca ) , a multivariate data treatment to reduce the number 
 of variables and provide a representation of the spectra in low dimensional 
 space , was used to interpret changes in the raman spectra 
 during dehydration .
max 
 normalization ( opus version 5.5 , bruker optics , ettlingen , germany ) 
 and first derivatives were calculated using simca - p ( version 11.0 , 
 umetrics ab , umea , sweden ) . the spectral region of 1800 to 30 cm was used for constructing the pca models .
infrared 
 spectroscopy was used to characterize the ionization state 
 of the crystalline and amorphous db7 forms ( see section 1 of the supporting information ) .
cross - polarization / magic 
 angle spinning nmr spectra were obtained 
 on a bruker avance iii 400 wide - bore nmr spectrometer operating at h and c frequencies of 400.131 and 100.623 mhz , 
 respectively , and using bruker 4 mm probes .
the mas rate was set to 
 10 khz  2 hz using a bruker mas - ii controller .
h 
 decoupling was achieved using the spinal64 decoupling sequence at a proton nutation frequency of 100 khz . spinning 
 sidebands
were suppressed using a five - pulse total sideband suppression 
 ( toss ) sequence .
a 3.4 ms linear rf power 
 ramp was used for cross - polarization from h to c. the acquisition time was set to 34 
 ms , and spectra were acquired over a spectral width of 30 khz with 
 a recycle delay of 7 s. the c chemical shifts were externally 
 referenced ( 0.05 ppm ) to the proton - decoupled c 
 peak of neat ( liquid ) tetramethylsilane via the high - field resonance 
 of adamantane (  = 29.5 ppm ) .
the sample temperature was regulated 
 to 25 c in order to minimize frictional heating caused by sample 
 spinning
. the crystal16 
 crystallization system ( avantium , nl ) was used to determine the kinetic 
 solubilities of forms i , ii , hya , and hy2 in an acetonitrile / water 
 ( 1:1 ) mixture .
the temperature at the point the suspension becomes 
 a clear solution upon heating or 
( at 0.1 
 c per minute , with the exception of form i where a heating rate 
 of 0.3 c per minute was used to avoid transformation to form 
 ii ) was taken as the saturation temperature of the measured 
 sample with known concentration . to make sure that solvent - mediated 
 transformations had not occurred during the measurements , excess solid 

was stirred under the same conditions , and xrpd patterns of the residual 
 solid were recorded after reaching the highest clear point temperature 
 derived from the solubility experiments .
periodic electronic structure 
 calculations were carried out with the castep plane wave code using the perdew  burke 
ernzerhof 
 ( pbe ) generalized gradient approximation ( gga ) exchange - correlation 
 density functional and ultrasoft pseudopotentials , with the addition of a semiempirical dispersion 
 correction , either the tkatchenko and scheffler ( ts ) model or grimme06 ( g06 ) . for further details
energy difference estimates between the zwitterionic 
 and neutral forms are not given because the pbe functional has been 
 shown to overstabilize the proton transfer phases of ammonia monohydrate ; this systematic error should largely cancel 
 when comparing structures with the same ionization state , as should 
 the known limitations in modeling water  water interactions .
nmr shielding calculations were performed on pbe - ts optimized 
 structural models of db7 hya using the castep nmr code 
 and on the fly pseudopotentials .
the 
 castep computed shielding constants , calc , were converted to chemical shifts , calc , according to calc = ref  calc using a reference value , ref , taken from the zero intercepts of the fits of the calculated shielding 
 vs. experimental chemical shift plot ( castep = xexp + ref ) for hya ( section 
 17 of the supporting information ) .
our 
 ability to meaningfully study the structures , stability relationships , 
 and interconversion pathways of the db7 hydrates at a 
 molecular level relied on securing highly crystalline , phase pure 
 samples of each form through exquisite control over crystallization , 
 filtration , and drying .
since both hy2 and hya are metastable with 
 respect to some or all of the neat polymorphs depending on the rh , 
 they needed to be crystallized under carefully controlled conditions , 
 then isolated and characterized before subsequent conversion to the 
 more stable neat forms . selecting for the metastable hydrates in crystallization 
 required that amorphous db7 be used as the starting material to ensure 
 that the solutions were supersaturated with respect to the hydrates 
 and free of crystalline seeds of the neat polymorphs .
even then , the 
 filtration and drying of these materials was surprisingly tricky , 
 with under or over drying leading to form conversions , amorphization , 
 particle agglomeration , and mostly brittle , chunky solids . eventually , 
 conditions were identified to selectively crystallize and recover 
 the hydrates in highly crystalline form , each with reasonably good 
 material handling properties .
the hy2 and hya materials used to fund 
 our experimental effort were generally composed of well - formed crystals 
 of similar size and shape commensurate with their high degree of crystallinity , 
 phase purity , and homogeneity ( figure 2 ) .
the molecular conformation 
 in this zwitterionic form is closely related to one of the form iii 
 conformers ( figure s2 of the supporting information ) , but with the carboxylic acid proton moved to the piperazine n3 . 

thus , the protonated piperazine is intramolecularly hydrogen bonded 
 to the carboxylate ion ( n  ho ) .
the db7 molecules form centrosymmetric 
 dimers ( figure 3a ) , which are arranged in layers 
 parallel to the bc plane .
each of the two water molecules 
 ( w1 and w2 ) forms an o  ho hydrogen bond to 
 one of the db7 carboxylate oxygens ( figure 4 ) ; the other water protons are disordered over two positions 
 each with a site occupancy of 0.5 .
w1 and w2 form infinite corrugated 
 chains , which are interlinked by the carboxylate group of db7 ( figure 4 ) , leading to zigzag sheets 
 ( figure 3b ) .
the zigzag sheets , containing 
 all of the strong hydrogen bonds , are interleaved in a zip motif along a. packing diagram of hy2 viewed along the crystallographic b axis ( a ) and c axis ( b ) .
hydrogen bonds 
 are denoted as green dotted lines and the centrosymmetric db7 dimer and zigzag sheet are highlighted .
the main difference 
 in the molecular conformation of db7 in hya and hy2 is 
 a 52 rotation of the c18c19c20o2 
 dihedral ( figure 5a ) moving the carboxylate 
 group from an intra- to intermolecular hydrogen bonding conformation . 

the conformation of db7 in hya is closely related to that 
 in anhydrate form ii ( figure s2 of the supporting 
 information ) .
owing to the shape complementarity of the db7 conformers in both hydrates , inversion related dimers similar 
 to those formed in hy2 are also seen in hya ( figures 3a and 5c ) .
however , the hya structure 
 also features intermolecularly hydrogen bonded r22(12 ) dimers involving strong n
the hya structures of the fresh and aged crystals differ in containing 
 1.95 ( hya1.95 ) and 1.73 ( hya1.73 ) mol of water 
 per mol of db7 , respectively .
the loss of 0.22 mol of 
 water on aging resulted in a volume change of 3.5% , with the c - axis change of 2.5% being the most significant . 
 three water sites ( w13 )
water site 
 w1 is disordered over two positions , which are so close in proximity 
 that only one of the two positions can be occupied at any time ( figure 6a ) .
the w1 sites refined to an occupancy of 46% 
 ( w1a ) and 52% ( w1b ) for hya1.95 , 
 and 68% ( w1a ) and 30% ( w1b ) for hya1.73 .
the site occupancy from the refinement of w2 was similar to that 
 of w1b , i.e. , 52% for hya1.95 and 30% for hya1.73 .
thus , if w2 is present , w1b is occupied , and 
 if not , w1a is likely to be occupied ( figure 6b ) .
water site w3 is also disordered over two positions , which 
 are too close to be occupied at any one time . in hya ,
one of the w3 
 water protons is located on a special position , a 2-fold axis , so 
 a maximum of 0.5 mol water per mol db7 would be present at full occupancy . 

refinement of the w3 waters revealed nearly full occupancy , 45% for 
 both hya1.95 and hya1.73 , across the symmetry 
 related sites .
as in hy2 , the hya water molecules form strong 
 hydrogen bonds to 
 db7 and one another .
w1b can form two ow1ho interactions , involving carboxylate 
 o1 and the w2 oxygen ( figure 6 ) .
w2 participates 
 in four hydrogen bonds , as a donor to the carboxylate o2 and the oxepine 
 n and an acceptor to w1b and w3 . together with the db7 carboxylate oxygens , w1b and w2 form an extended 
 ring motif ( figure 6 )
the third water molecule , 
 w3 , is hydrogen bonded to carboxylate o2 and w2 ( when present ) , linking 
 the hydrogen bonded rings along the c axis , the axis 
 most affected in length by the hya water content .
the 1d hydrogen 
 bonding network of hya is a marked contrast to the 2d sheets of water 
 and db7 molecules found in hy2 . in hya
the 1d hydrogen 
 bonded chains ( figure 5c ) are close packed 
 in the second and third dimensions through centrosymmetric db7 dimers .
( a ) overlay of db7 hy2 ( red ) and hya1.95 ( blue ) conformations ( rmsd1 = 0.38  ) .
( c ) packing diagram of hya1.95 viewed along c. centrosymmetric dimer , water position 
 w2 , and 1d building block are highlighted ; w1 and w3 are obscured 
 by the carboxylate groups in this view .
the distinct water sites are coded in different 
 colors : w1a , rose ; w1b , red ; w2 , blue ; w3 , green . 

note that only one of the two differently colored w3 orientations 
 can be occupied as the two positions are related by a 2-fold axis 
 at a proton position .
( a ) showing the time - averaged water occupancy 
 and ( b ) one of many possible instantaneous snapshots of the water 
 positions in hya in the range of occupancies seen in the two crystals .
both hydrates are zwitterionic , 
 but the n3h in each structure is close to one 
 of the carboxylate oxygen atoms . 

computationally , we can confirm the zwitterionic assignment by a method 
 used to distinguish between salts and cocrystals .
hypothetical neutral hydrates are constructed from chy2 ( section 3.4.2 ) and chya2.0 ( section 3.4.3 ) by moving 
 the acidic proton to the nearby carboxylate oxygen and adjusting the 
 bond lengths to give a cis - carboxylic acid for hya 
 and the less common trans - acid conformation for hy2 . 

full optimization of both charge neutral structures results in the 
 acidic proton moving back to reform the observed zwitterionic hydrate 
 structures , showing that both hydrates are more stable in zwitterionic 
 than neutral form with no appreciable barrier to proton migration 
 ( tables s5 and s7 of the supporting information ) .
the converse was also found : full optimization of the corresponding 
 hypothetical zwitterionic versions of forms i  iii results in 
 the proton moving to give the observed locally neutral structures .
the hydration and dehydration 
 behavior of the db7 crystal forms was investigated between 
 0% and 95% rh at 25 c ( figure 7 ) .
two 
 of the anhydrates , forms i ( figure 7a ) and 
 ii ( figure 7b ) , show almost no water 
 uptake ( form i < 0.32% and form ii < 0.04% ) up to 95% 
 rh .
in contrast , anhydrate form iii undergoes a phase transformation 
 with a mass increase corresponding to 2 mol of water per mol of db7 
 at rh values > 70% ( figure 7c ) .
the product 
 hydrate phase , confirmed to be hy2 by xrpd , shows good rh stability 
 with a marginal weight loss between 95 and 25% rh .
hysteresis was observed in the form iii / hy2 isotherm despite 
 the lengthy equilibration times ( up to 48 h ) at each rh .
the profile 
 of the moisture sorption / desorption isotherms for form iii  
 hy2 with steps accompanied by phase changes , is typical of a stoichiometric 
 hydrate .
in contrast , highly crystalline 
 hya shows the typical ( de)sorption isotherms of a nonstoichiometric 
 hydrate ( figure 7d , see also figure s3 of the supporting information ) as the mass gradually changes depending on the humidity during 
 sorption and desorption .
the lowest water content measured by tga 
 ( figure 7d ) for hya equilibrated at 0% rh corresponded 
 to 1.29 mol of water per mol of db7 .
the maximum water 
 vapor uptake into the hya structure was estimated to be approximately 
 1.85 mol of water per mol of db7 at 95% rh .
gravimetric 
 moisture sorption and desorption curves of db7 solid forms 
 at 25 c : ( a ) form i , ( b ) form ii , 
 ( c ) form iii / hy2 , and ( d ) hya .
the gray circles represent data points 
 that fulfill the preset equilibrium conditions ( see experimental section ) , whereas the crosses mark measurement 
 values that did not reach equilibrium within the allowed time limit 
 ( 48 h )
. the automated gravimetric moisture 
 sorption / desorption analysis 
 of hy2 and hya was complemented with long - term drying experiments 
 at 0% rh ( storage over p2o5 ) .
dehydration of 
 hy2 was observed immediately at this condition , and form iii was determined 
 to be a kinetic dehydration product , with further transformation to 
 the more stable forms i and ii occurring within 2 weeks .
hya 
 could be similarly dehydrated at 0% rh ; however , loss of the last 
 strongly bound 1.3 waters of crystallization from this hydrate 
 leads to a structural collapse to mainly amorphous db7 .
the amorphous 
 form has limited stability at 0% rh as there was evidence of forms 
 i and ii nucleating in small amounts during the low rh drying .
the gravimetric moisture 
 sorption / desorption studies ( figure 7 ) were 
 correlated with structural changes to hy2 
 and hya using variable - humidity xrpd at 30 c ( figures 8 and 9 ) . in agreement with 
 the results obtained in figure 7c ,
distinct 
 changes occur in the xrpd pattern of the hy2 sample at rh values < 30% 
 ( figure 7a ) .
the disappearance of high intensity 
 hy2 peaks ( e.g. , at 6.82 , 10.62 , 16.37 , 16.71 , and 17.57 2 ) 
 and appearance of form iii peaks ( e.g. , 7.33 , 12.68 , and 14.81 
 2 ) indicate a major change in the crystal structure ( figure 8c  f ) on loss of the waters of crystallization . 
 the unusual increase in volume / z upon dehydration 
 ( figure 8b ) can be attributed to the less efficient 
 packing of db7 with itself and
( a ) moisture - dependent 
 xrpd measurements showing the dehydration 
 of hy2 to form iii .
peak positions marked with * correspond to hy2 
 impurities ( dehydration not complete due to the shorter time intervals 
 of 12 h and 10% rh steps in contrast to 48 h and 5% steps 
 in figure 7c ) .
( b ) moisture - dependent changes 
 in the cell volume per asymmetric unit for the transformation hy2 
 to form iii .
( c , d ) molecular packing of db7 in hy2 and 
 ( e , f ) db7 in form iii .
disorder of the methyl group in form 
 iii is indicated with different shades of gray .
in contrast to hy2 , there is no significant change in the 
 crystal 
 lattice of hya with varying rh ( figure 9b ) 
 apart from anisotropic expansion of the network to accommodate a variable 
 amount of water .
the anisotropy of the lattice expansion was quantified 
 by indexation and rietveld refinement of the hya xrpd patterns recorded 
 at different rh values ( figure 9a ) .
using the 
 hya1.95 structure as a starting model , rietveld refinement 
 found the c axis to be affected the most by changes 
 in the water content , in agreement with the scxrd experiments , but 
 over a wider range of compositions ( table s2 of the supporting information ) .
structural refinement also revealed 
 that the water occupancy of w3 stays close to 50% ( i.e. , full ) independent 
 of the rh , suggesting that the w3 position is integral to the hya 
 structure . however , the occupancy parameters for w1 and w2 collectively 
 decreased at progressively lower rh values .
the w1w2 
 distance was also found to depend on the hydration state . at moderate 
 rhs ( 2080% )
a plateau is reached with the modeled w1w2 
 distance being too short for two distinct sites , suggesting either 
 water mobility or static disorder ( figure 9c ) .
a further distinct change in the w1w2 distance 
 is seen below 25% rh , the moisture range where in addition to continued 
 diffraction peak shifting , selected reflections , in particular ( 002 ) , 
 are broadened .
the lowest hya water content observed in the 
 rh - dependent xrpd experiments of hya was 1.32 mol of water per mol 
 of db7 ( measured with tga ) .
( b , c ) changes 
 in the hya cell volume , length of the c - axis , fractional 
 occupancies of w1 + w2 and w3 oxygens , and distance between w1 and 
 w2 oxygens on lowering the rh ( desorption ) . water position w1 was 
 modeled as one site only .
100% rh data points given in ( b ) and ( c ) 
 were derived from slurry experiments in water .
( d  f ) packing 
 diagrams of hya highlighting the water oxygen positions at different 
 hya hydration states derived from single crystal x - ray data ( d , e ) 
 and rietveld refinement of powder x - ray data ( f ) .
red lines between water 
 oxygens indicate the disordered sites for w3 and close proximity of 
 the w1 and w2 positions in ( f ) . w1a and
the moisture - dependent xrpd experiments were extended to 
 water 
 activity = 1 ( 100% rh ) by measuring 
 a thick hya slurry in water .
the powder pattern of the 100% rh hya 
 sample refined to 1.96 mol equiv of water per db7 , comparable 
 to hya1.95 observed ( by scxrd ) for a freshly crystallized 
 single crystal .
while a change in water content and unit cell volume 
 was to be expected on increasing the rh from 90 to 100% , the sharp 
 uptake of 0.10 mol water per mol db7 and unit cell volume 
 increase of 0.5% ( figure 9b ) was unexpected 
 and presumably reflects the slow hydration kinetics of hya in the 
 solid state ( table s2 of the supporting information ) .
an ordered hy2 structural model was derived from the 
 experimental crystal structure by replacing the two disordered water 
 molecules related by a 21 screw axis with one molecule 
 in each orientation ( section 12 of the supporting 
 information ) .
this lower symmetry hy2 structure ( figure s10b ) was lattice energy minimized to 
 give the computational model of the hy2 structure , denoted chy2 .
the geometry optimizations 
 of four hypothetical hydrate and framework structures derived from chy2 ( table s5 of the supporting information ) showed that proton transfer to a neutral db7 molecule occurred 
 when there was no water hydrogen bonding to the carboxylate oxygen 
 involved in the n 
although 
 the layer structure ( figure 2 ) suggests that 
 it might be possible to remove both w1 and w2 , doing this computationally 
 results in proton transfer and an unstable , low density isomorphic 
 desolvate with no strong hydrogen bonds 
 between db7 molecules .
partial removal of the w1 molecule gave hypothetical 
 zwitterionic sesquihydrate ( chy21.5(0.5w1+w2 ) ) and monohydrate ( chy21.0(w2 ) ) structures , 
 which differed in lattice energy from hy2 by 55 and 107 kj mol , respectively ( table s5 of the supporting information , averaged over the two dispersion models ) . 

estimating whether hy2 could undergo a phase transition to an isostructural 
 sesqui- or monohydrate requires comparison of the lattice energies 
 of the model hydrates with that of ice ( section 16 of the supporting information ) .
this gives an unfavorable 
 phase transition energy of more than 30 kj mol for each water removed .
thus , the computational thermodynamic estimates 
 show that a stepwise dehydration of the hy2 structure , preserving 
 the hy2 db7 framework structure ( i.e. , a structurally 
 related sesquihydrate or monohydrate as a transient , intermediate 
 hydrate along the dehydration pathway ) , is highly unlikely .
this is 
 consistent with hy2 showing a single stepwise weight loss by moisture 
 sorption analysis ( figure 7c ) and tga ( section 3.5.1 ) to water free db7 .
the two hya structures show a similar nearly full 
 occupancy of w1a + w1b ( 98% ) and w3 ( 45% ) , but 
 differ in the w2 partial occupancy ( 52% or 30% ) . to form an ordered 
 computational model of hya1.95 , the crystallographic 1.95 
 water molecules per db7 molecule had to be increased to 
 2 by modeling the 98% ( 46% w1a + 52% w1b ) , 52% 
 and 45% occupancy ratios for w1 , w2 , and w3 as 100% , 50% , and 50% , 
 respectively .
all symmetry was removed from the c2/c , z = 1 structure of hya , resulting in 
 a p1 , z = 4 cell in which 
 the four w1 sites are independently occupied and half of the w2 and 
 w3 sites are occupied ( section 13 of the supporting 
 information ) .
all possibilities leading to the described occupancy 
 ratios were used as starting structures and the lowest energy structure 
 after geometry optimization was used as chya2.0 hereafter .
similarly , for the hya1.73 structure 
 the occupancies were modeled as 100% , 25% , and 50% for w1 , w2 , and 
 w3 giving a model chya1.75(2 ) ( table s7 
 of the supporting information ) , which agreed 
 with the experimental structure .
the confirmation that the ordered 
 cell models chya2.0 and chya1.75 were reasonable representations of the disordered 
 structures is given in section 15 of the supporting 
 information .
a set of hypothetical hya framework structures 
 can be derived from the experimental structure , ranging from a hemipentahydrate 
 ( chya2.5 , 2.5 mol of water per mol db7 
 at full w1 and w2 occupancy ) to the water free framework ( table s7 
 of the supporting information ) .
the lattice 
 energy of chya2.5 was higher ( less stable ) 
 by about 2 kj mol than the sum of the lattice 
 energies of chya2.0 and 0.5 mol of ice 
 xi , implying that additional water to 
 fully occupy the w2 site would destabilize the hya structure .
computational 
 dehydration of chya2.0 to chya1.75 , chya1.5 , and chya1.25 produces a range 
 of possible structures , which are very close in energy ( table s7 of 
 the supporting information ) .
removal of 
 water from hya was calculated to be energetically quite feasible and 
 to require considerably less energy than removing comparable amounts 
 of water from hy2 ( tables s5 and s7 ) .
the calculated isomorphic hya desolvate ( chya0.0 ) also undergoes a proton transfer to the neutral molecule 
 on optimization ( table s7 of the supporting information ) .
in fact , proton transfer from db7 to db7 was observed 
 when the carboxylate of the n 
hor22(12 ) dimer ( figure 5b ) was not also acting as an acceptor for an ow  ho hydrogen bond .
thus , the hydrogen bonded water molecules 
 ( w1 , w2 , or w3 ) appear to be essential for zwitterion formation .
since chya0.0 is estimated to be over 25 kj mol less stable than form ii , an isomorphic desolvate 
 of hya containing zwitterionic or neutral db7 molecules is unlikely 
 to form .
this is consistent with a destructive dehydration mechanism 
 on loss of all waters of crystallization .
the suggestion of water mobility / disorder 
 from the diffraction experiments and static lattice energy modeling 
 led to the use of c cp / mas nmr spectroscopy to characterize hya as a function of water content . 
 except for slight peak intensity variations ,
the ssnmr spectra of 
 hya samples equilibrated between 22 and 90% rh were essentially identical 
 ( figure 10a ; figure s5 of the supporting information ) . since partial occupancy of the hya 
 water sites over this rh range
would necessarily result in a distribution 
 of hydrogen bonding arrangements ( figure 6 ) , 
 the observation of a single c resonance for each carbon 
 atom in db7 shows that the different hydrogen bonding 
 environments are effectively  averaged  as the waters 
 of crystallization move in and out of the water sites in the hya crystal 
 structure .
thus , ssnmr shows that the water of crystallization is 
 highly mobile over a wide range of moderate and high rh .
after 
 equilibrating the sample at rh  11% ( figure 10b ) , peak splitting for carbon atoms c20 , c5 , and c17 and broadening 
 of several c nmr resonances were seen across the ssnmr 
 spectrum of hya .
the additional peaks were not due to forms i  iii or hy2 ( ref ( 47 ) and figure s6 of the supporting 
 information ) phase impurities , as there is no match to their 
 chemical shifts .
instead , the emergence of low intensity peaks was 
 ascribed to restricted water mobility in the contracted hya cell , 
 which would also explain the diffraction peak broadening seen in figure 9a .
support for this interpretation of the low rh 
 ssnmr spectrum ( figure 10 ) comes from dft shielding 
 calculations on 25 variably hydrated chya structures 
 ( section 17 of the supporting information ) , which generated 80 c nmr spectra of db7 in different hya water environments .
these showed that the chemical 
 shifts of c20 , c5 , c18 , and c17 , because of their proximity to the 
 water molecules , were particularly sensitive to hydration state and 
 water positions , varying by 35 ppm ( table s11 of the supporting information ) .
since the regions in 
 the ssnmr spectrum shown computationally to be most sensitive to water 
 in the hya structure coincide with those where peak splitting is observed 
 at low rh ( figure 10 ) , we can account for the 
 peak splitting as a manifestation of reduced water mobility on the 
 ssnmr time scale .
( a , b ) representative experimental hya spectra differing 
 in water 
 content and ( c  h ) six of 80 nmr - castep computed c cp / mas nmr spectra .
( c , d ) the two db7 environments 
 observed in the ordered p1 chya2.0 model and ( e  h ) the four environments observed in 
 the ordered p1 chya1.25(13 ) model , which correspond to 0.75 w1 , 0.25 w2 , and 0.25 w3 . in contrast to hya , the ssnmr spectra of hy2 ( figure 
 s6 of the supporting information ) show 
 a distinct phase 
 change to form iii in this case between 11 and 22% rh , in good agreement 
 with the moisture sorption ( figure 7c ) and 
 xrpd data ( figure 8a , b ) . hy2 and hya were exposed to 
 deuterium oxide vapor ( 98% and 11% rh ) and characterized 
 by raman spectroscopy at different time points ( figure 11 ) to investigate water dynamics in the two hydrates .
the wavenumber 
 region 34002800 cm is composed of peaks 
 arising from (o  h ) , (n  h ) , 
 and (c  h ) stretching vibrations ; (o  d ) 
 stretching modes of d2o are seen between 2600 and 2300 
 cm .
the emergence of o  d peaks in the spectra 
 of both hydrates on exposure to deuterium oxide vapor confirms that 
 d2o displaces h2o in both crystal structures . 

thus , not only is the water of crystallization in hya mobile , but 
 water exchange is also observed for the stoichiometric hydrate , hy2 . 

water diffusion in and out of the two crystal structures is rapid 
 and quantitative , as derived from the fact that the raman spectra 
 after exposure to d2o for 72 h were indistinguishable from 
 fully deuterated hy2 and hya .
db7 also has an ammonium 
 proton that could exchange a hydrogen for a deuterium . to see whether 
 the ammonium group had undergone exchange ,
the hydrate samples that 
 had been exposed to d2o vapor were dehydrated and compared 
 to the raman spectra of the neat forms .
the comparison showed that 
 within 72 h of d2o vapor exposure the ammonium group was 
 not affected at all .
raman spectra of db7 hy2 ( a ) and hya ( b , c ) 
 as a function 
 of time of exposure to d2o vapor , 98% rh ( a , b ) 
 and 11% rh ( c ) .
d stretching vibrations 
 emerge over the course of 72 h. the tga curve 
 of hy2 ( figure 12a ) shows a one - step mass loss 
 of 8.67  0.05% , corresponding to exactly two mole equivalents 
 of water .
dehydration starts immediately under the dry conditions 
 of a nitrogen purge . on removing the 
 water of crystallization
, the clear hy2 crystals turn opaque , but 
 maintain their shape (  pseudomorphosis  ) .
slow heating dsc experiments of hy2 ( figure 12a ) using pinhole lids show four events : ( 1 ) dehydration of 
 hy2 to form iii takes place below 45 c .
( 2 ) at 95 c there 
 is an exothermic phase transformation of form iii mostly to form ii , 
 with minor amounts of form i present .
the measured enthalpy of transition 
 is in agreement with the value derived using pure form iii as a starting 
 material ( trshiii  ii = 13.3  0.2 kj mol ) .
( 3 ) upon further heating , melting of the minor 
 form i component is observed at an onset temperature of 176.0  
 0.4 c ( small peak ) .
( 4 ) at an onset temperature of 180.9  
 0.2 c , the form ii melts . by increasing the heating 
 rate used in the hy2 dsc experiments 
 to 5 c min or more ( figure 12a : 5 , 10 , and 50 c min ) ,
an additional 
 thermal event is observed above 118 c corresponding to the inhomogeneous 
 melting of form iii .
melting is followed by the recrystallization 
 of mainly form ii , then the melting of forms i and ii. 
 by embedding the hy2 crystals in high viscosity silicone oil or using 
 hermetically sealed dsc pans ( figure 12a ) , 
 the incongruent melting of hy2 ( peritectic decomposition ) is observed 
 at 89.8  1.3 c .
compared to hy2 , higher temperatures 
 are required to fully dehydrate 
 hya . by tga ,
a hya sample pre - equilibrated at 75% rh ( stored over 
 a saturated nacl solution ) showed a mass loss of 7.61  0.04% , 
 corresponding to 1.74 mol equivalents of water ( figure 12b ) . toward the end of the dehydration process a loss of birefringence 

is observed in polarized light , indicating that the strongly bound 
 water is released by a process that leads to a loss of crystallinity . 

the generation 
 of mainly amorphous db7 with form i and ii impurities was independently 
 confirmed by xrpd and raman spectroscopy .
the loss of crystallinity 
 upon dehydrating hya was also supported 
 by dsc , based on the appearance of an exothermic event immediately 
 following the dehydration endotherm . upon further heating
, the few 
 crystal nuclei produced at lower temperatures ( during dehydration ) 
 grew into a mixture of forms i and ii , evidenced by the final 
 two melting events . the lower the dehydration temperature , the less 
 form ii was observed .
dsc traces of hya collected at faster 
 heating rates ( 10 
 c min ) show an overlap of dehydration and 
 peritectic decomposition at 99 c .
the peritectic decomposition 
 of hya , measured in hermetically sealed dsc pans , is observed at 98.9 
  0.9 c .
differential scanning calorimetry ( dsc ) and thermogravimetric 
 analysis 
 ( tga ) thermograms of ( a ) hy2 and ( b ) hya .
tga curves were recorded 
 in open pans at a heating rate of 5 c min .
raman spectra were recorded for hy2 and 
 hya every 2 to 5 c 
 from 25 to 130 c , then subjected to pca to track the solid state 
 transformations ( figure 13b , c ) by comparison 
 to reference spectra of the db7 forms ( figure 13a ) .
the raman spectra recorded throughout the hy2 dehydration appear 
 as three distinct clusters , corresponding to hy2 , form iii , and form 
 ii with form i impurities ; in between the clusters ( 50 , 100 , 
 and 102 c , figure 13b ) are mixed phases . 

these results show that form iii is a distinct intermediate phase 
 along the thermally induced dehydration pathway of hy2 .
( the close 
 proximity of the dehydration product to phase pure form ii relative 
 to phase pure form i in figure 13b shows that 
 form ii is the main component , and the tightness of the final product 
 cluster shows that the form i impurities did not transform to form 
 ii . )
this dehydration pathway is in agreement with the dsc and tga 
 results in figure 12a .
the dehydration of hy2 
 does not go via an appreciably stable amorphous phase or phase pure 
 form i because the triangles representing form i and amorphous db7 
 are not located on the dehydration pathway .
the structural changes 
 accompanying the dehydration of hya to a form i and ii mixture 
 could be described with three pcs , but a continuous transformation 
 pathway is evident from two of them , figure 13c .
as the small structural variation within hya exhibiting variable 
 water content between 25 and 62 c is apparent by pc2 , pc1 shows 
 the transformation from the hya crystal lattice ( 70 c ) through 
 the amorphous state ( 82 c ) to the form i / ii mixture ( 86130 
 c ) ( figure 13c ) .
( b , c ) raman 
 principal component analysis ( pca ) plots for the first and second 
 principal component ( pc1 and pc2 ) of db7 forms occurring 
 during dehydration of hy2 ( b ) and hya ( c ) .
each triangle corresponds to a 
 raman spectrum : black , recorded during dehydration and used for constructing 
 the pca models ; gray , reference spectra for forms i and ii and 
 amorphous db7 .
numbers correspond 
 to the temperature at which each spectrum was recorded ; black ellipse 
 corresponds to the 95% hotelling t2 , and areas of distinct db7 solid forms are encircled .
the % -values on the axes indicate 
 the data variance modeled by the respective pc .
form iii was obtained for the first time following the salt disproportionation 
 of db7 phosphate at ph  6 .
only after we were unable to directly 
 crystallize form iii from solution and systematically studied the 
 dehydration mechanism of hy2 was it evident that hy2 was the kinetic 
 phosphate salt disproportionation product and necessary intermediate 
 phase for obtaining form iii .
structural analysis has shown that the 
 molecular conformation of db7 in hy2 with intramolecular 
 hydrogen bonds seems to predispose it to dehydration to form iii , 
 the only anhydrate , which also features intramolecular hydrogen bonding . to the best of our knowledge ,
following our 
 observation of batch - to - batch variability in the disorder ratio of 
 the dimethylpropionic acid side chain in form iii , we performed systematic 
 drying studies of hy2 to estimate the effects of rh and temperature 
 on the level of disorder present in the form iii dehydration product 
 and to seek conditions that would select for the ordered structures . 

the disorder ratio was quantified from the intensities of the dimethylpropionic 
 acid methyl c ssnmr peaks ( figure 14a , table s3 of the supporting information ) . unfortunately , despite the wide range of drying conditions surveyed , 
 we were not successful in preparing either an ordered form iii sample 
 or one having the minor conformation dominating .
( a ) c cp / mas 
 nmr spectra of db7 form iii produced 
 by dehydrating hy2 under a variety of conditions ( defined in the supporting information , table s3 ) .
highlighted 
 are the c18 and c21 peaks characterizing the structural disorder of 
 the dimethyl propionic acid side chain .
( b ) dsc thermograms of db7 
 form iii lots n2/0/rt/24 and n2/0/5/48 measured at 
 a heating rate of 1 c min .
lot n2/0/rt/24 was prepared by drying hy2 under n2 purge 
 at room temperature for 24 h and lot n2/0/5/48 under n2 purge at 5 c for 48 h. subsequent dsc investigations ( figure 14b ) were conducted to examine whether the disorder ratio in form iii 
 influences its solid form transformation to forms ii and/or 
 i. although the outcomes were somewhat variable , form iii samples 
 obtained by drying hy2 under a variety of conditions ( table s3 of 
 the supporting information ) ranged from 
 having only small amounts of form i to as much as 90% form i after 
 the solid state transformation .
importantly , the heat induced phase 
 transformation does not seem to be related to the disorder in form 
 iii .
form iii samples n2/0/5/48 and n2/0/rt/24 , for 
 example , show a similar level of disorder in their c 
 ssnmr spectra , but differ substantially in their thermal behavior 
 ( figure 14b ) .
thus , while the dehydration reaction 
 of hy2 always produces the two different conformations in form iii , 
 small differences in the phase purity and sample history also influence 
 the outcome of the solid form transformation to forms i and/or ii. the db7 hydrates and db7 anhydrates showed appreciable kinetic stability 
 in the solid state based on the gravimetric moisture sorption / desorption 
 analysis .
however , these forms were not sufficiently stable in suspensions 
 to obtain equilibrium solubility data of interest for quantitatively 
 establishing their thermodynamic stability relationships .
the stability 
 order of the two stable anhydrate polymorphs forms i and ii 
 and the two hydrate forms was therefore qualitatively estimated as 
 a function of temperature from kinetic solubility measurements in 
 acetonitrile / water ( 1:1 ) .
this solvent mixture was chosen because 
 the db7 and db7 solid forms were sufficiently soluble 
 to meaningfully estimate their relative solubility using the crystal16 
 parallel reactor system .
unfortunately , the fast transformation kinetics 
 of form iii to form ii in stirred solvent prevented any measurement 
 of the kinetic solubility of form iii .
the acetonitrile / water 
 solubility data for forms i and ii ( figure 15a ) agree with the monotropic relationship previously derived 
 from solubility measurements in methyl isobutyl ketone and dsc experiments , as the kinetic solubility data plotted in vant 
 hoff form showed no signs of convergence or crossover below the db7 
 melting temperature ( figure 15b ) .
hya is less 
 soluble than hy2 in acetonitrile / water ( water activity , aw , of 1:1 mixture is 0.9 at 25 c , figure 15a ) , with the vant hoff plots further suggesting 
 that hya is the thermodynamically most stable db7 hydrate 
 at this water activity below the hydrates melting points . 

the zwitterionic hydrates are much more soluble than the charge neutral 
 neat forms at all measured temperatures , but their relative solubility 
 is clearly decreasing with decreasing temperature ( figure 15b ) .
( a ) solubility ( mole fraction ) of db7 forms i , ii , 
 hy2 , and hya in acetonitrile / water ( 1:1 , aw  0.9 ) as a function of temperature and ( b ) vant 
 hoff plot of the molar solubility as a function of temperature . the critical water 
 activity defining the crossover in thermodynamic stability of the 
 db7 hydrate  db7 anhydrate pairs could not be determined 
 from the solubility measurements at a single water activity ; however , 
 these results did reveal that both forms i and ii are more stable 
 than hy2 and hya at water activities up to at least 0.9 over the investigated 
 temperature range . above aw
= 0.9 , the 
 rt thermodynamic stability order of the db7/db7 forms 
 was investigated through slurry experiments in methanol / water mixtures ( section 8 of the supporting information ) .
db7 hy2 and hya were separately added to methanol / water 
 mixtures ( aw = 0.9 , 0.95 , and 1.0 ) and 
 stirred for 21 days .
slurries in mixtures of aw = 0.9 and 0.95 resulted in form ii , while the pure 
 water slurry yielded hya . in showing that form ii is more stable 
 at aw = 0.95 and hya is more stable in 
 pure water
( aw = 1.0 , ph 5.9 ) , the critical 
 water activity at which the solubility order of form ii/hya 
 is reversed was more precisely bracketed between 0.95 and 1.0 .
the hy2 to hya transformation in water did not allow us to estimate 
 the hy2 aw dependency .
therefore , we used 
 gravimetric sorption / desorption experiments to estimate the influence 
 of moisture .
the desorption 
 curve is similar to that of phase pure hy2 ( figure 7c ) .
the water is released at rh < 25% , and the product 
 contains forms i and ii from the spiking and form iii as the 
 dehydration product . upon subsequently increasing the rh of the mixed 
 anhydrate sample , hydration of form iii to hy2 is observed as well 
 as a transformation to form ii ( figure 16 , 2 ) .
the latter , which is indicated by the decrease in mass despite 
 increasing the humidity at rh values > 85% , is consistent with the 
 greater stability ( lower solubility ) of form ii than hy2 observed 
 in 1:1 acetonitrile / water ( aw  
 0.9 ) , figure 15 .
gravimetric moisture 
 sorption and desorption curve of db7 hy2 spiked with forms 
 i and ii at 25 c . the gray circles 
 are data points that fulfill the preset equilibrium conditions ( see experimental section ) , whereas the crosses mark 
 measurement values that did not reach the equilibrium within the allowed 
 time limit ( 48 h ) .
the forms noted in parentheses were identified 
 as minor components by xrpd . to investigate the 
 influence of ph on the db7/db7 form stability , slurry 
 experiments were conducted in aqueous buffer solutions at 25 c . 

solvent mediated transformations ( smt ) starting from hy2/form iii 
 showed that hya is obtained if ph  6 and anhydrous form ii 
 if ph  5 .
in contrast , the phosphate salt of db7 was shown 
 to disproportionate in aqueous media , causing either hy2 ( ph 67.8 ) 
 or form ii ( ph 2.85 ) to nucleate .
the fact that hy2 converted to hya in the higher ph smt 
 experiments confirms that hy2 was a kinetic disproportionation product 
 at 25 c .
thus , hya is the thermodynamically most stable db7 form in water , but this stability relationship has been established 
 only at ph  5.9 ( from water slurry experiments ) .
db7 has a rich solid form landscape composed 
 of three neat polymorphs , 
 two hydrates , three solvates , and an amorphous phase . with the goal 
 of exploring the thermodynamic stability relationships between the 
 hydrates and anhydrates , as well as their interconversion pathways , 
 we have established through a combination of diverse experimental 
 techniques and computational chemistry that db7 form appearance and 
 stability depend on temperature , water activity , and ph .
form ii 
 is monotropically more stable than forms i , iii , and hy2 and usually 
 more stable than hya .
hya is the most stable db7 crystal form in saturated 
 water solutions , but only at ph  5.9 .
characterizing 
 the structure  stability relationships of 
 the db7 crystal forms was complicated not only by the difficulty in 
 isolating highly crystalline , phase pure samples of the metastable 
 forms ( section 3.1 ) , but also the slow rate 
 at which hya and hy2/form iii materials reached their equilibrium 
 moisture content .
equilibrium water contents were attainable for hya 
 using extended equilibration times at most rhs , although complete 
 rehydration to full crystallographic water occupancy was never achieved 
 even in aqueous slurries .
in contrast , the reversible dehydration 
 of hy2 to form iii mediated by water vapor was readily apparent from 
 a quick measurement of the moisture sorption  desorption isotherms 
 of either form , yet extended equilibration times did little to minimize 
 the hysteresis ( figure 7c ) caused by slow transformation 
 kinetics .
the slow interconversion of hy2 and form iii in the solid 
 state at moderate rhs frustrated attempts to establish the critical 
 water activity relating these metastable forms .
two distinctly different moisture sorption behaviors were established 
 for hy2 and hya through detailed characterization of highly crystalline , 
 phase pure samples as a function of water vapor pressure .
curiously , 
 our initial attempts to rationalize the different hygroscopicity of 
 the db7 hydrates in terms of structural features ( solvent 
 pockets , channels ) common to stoichiometric and nonstoichiometric 
 hydrates yielded anything but expected results .
figure 17 shows the void space ( default probe radius = 1.2  ) 
 created by removing the waters of crystallization from the hya1.95 , hya1.73 , hya1.32 , and hy2 structures . 

counterintuitively , the water accessible voids in nonstoichiometric 
 hya appear to be isolated from one another ( figure 17a  c ) , while water channels are clearly seen running 
 zigzag along the crystallographic b - axis in the stoichiometric 
 hydrate , hy2 ( figure 17d ) .
solvent accessible voids 
 containing waters of crystallization in 
 ( a ) hya1.95 , ( b ) hya1.73 , ( c ) hya1.32 , and ( d ) hy2 , calculated using a 1.2  probe radius .
cursory inspection of the water 
 channels in hy2 and the proximity 
 of solvent pockets in hya suggests that the direction of water ingress / egress 
 is likely to be along the b - axis in each structure . 

however , the 100 k structures individually do not reveal how either 
 hydrate framework would respond to perturbations in rh , particularly 
 at crystallization processing and storage relevant temperatures .
water 
 vapor sorption isotherms ( figure 7 ) , however , 
 show that the db7/water stoichiometry is retained across 
 a wide rh range for hy2 and that a fraction of the water in hya is 
 adventitious . yet
they reveal little as to how water is held in each 
 crystal structure or the phase transformations that accompany dehydration 
 and rehydration . indeed , only through a combination of experiment 
 and computation were we able to paint a molecular level picture of 
 two very different rh stability profiles and ( de)hydration mechanisms 
 for hy2 and hya .
nonstoichiometric hya retains between 1.29 
 and 1.95 waters of crystallization , 
 all of which reside in the same solvent pockets in the crystal structure 
 ( figure 17a  c ) and are exchangeable 
 ( figure 11b , c ) .
the conspicuous absence of 
 continuous water channels in hya suggests that for nonstoichiometric 
 hydration to occur , cooperative movement of the carboxylate and dibenzoxepine 
 groups ( figures 9d  f and 17b  c ) must temporarily open up diffusion pathways , similar 
 to that seen in -cyclodextrin ( -cd ) hydrate and ciprofloxacin .
water diffusion in and out of discrete crystallographic sites gives 
 rise to varying disorder and occupancy in the diffraction time - averaged 
 hya crystal structures , but is sufficiently rapid , at least under 
 moderate to high rh conditions , that single ,  averaged  

db7c resonances are seen in the ssnmr spectra 
 ( figure 10a ) . below 11% rh
, water mobility 
 is observably decreased with the resonances of c nuclei 
 that are in close proximity to the partially occupied water sites 
 showing splitting ( figure 10b ) .
the decrease 
 in water mobility witnessed on the ssnmr time scale at low rh is presumably 
 caused by anisotropic contraction of the hya lattice as water is continuously 
 lost from the crystal . in fact , rietveld refinement of the hya xrpd 
 patterns collected across a wide rh range confirmed that the hya lattice 
 essentially breathes to accommodate varying amounts of water with 
 smooth changes in the cell volume and shifting of the water sites / occupancies 
 ( figure 9 ) .
void space analysis of the 
 hya framework structures derived from 
 hya1.95 , hya1.73 , and hya1.32 showed 
 that as the unit cell contracts at lower hydration states ( figure 17a  c ) , the solvent accessible voids decrease 
 from 10.2% in hya1.95 to 4.2% in hya1.32 .
isostructural 
 dehydration modeling , in showing the small energy penalty that is 
 incurred to attain full water site occupancy ( hemipentahydrate stoichiometry ) 
 and the appreciably larger one for decreasing the water content below 
 1.25 mol equiv in the hya crystal structure , helped to rationalize 
 the db7/water stoichiometries that were experimentally 
 accessible . in the end ,
elevated temperatures or long - time storage 
 over p2o5 ( 0% rh ) was required to overcome the 
 activation energy for removing the final 1.3 equiv of water from the 
 contracted hya structure . however , with no clear path to an appreciably 
 stable neat polymorph , dehydration led to structural collapse as first 
 observed by dsc ( figure 12b ) , then later confirmed 
 by raman spectroscopy ( figure 13c ) . in 
 contrast to hya , hy2 retains its full complement of water over 
 a large rh range at 25 c ( figure 7c ) . 

stoichiometric hydration may not have been anticipated based on the 
 location of water molecules in open channels in the hy2 crystal structure , 
 but it was suggested by computational dehydration modeling ( section 3.4.2 ) . in revealing a significant energy penalty 
 incurred by removing water molecules from this hydrate , lattice energy 
 calculations for hy2 and hypothetical lower hydrate and framework 
 structures derived from hy2 suggested that even partial dehydration 
 to a lower isostructural hydrate would be highly unlikely .
the inability 
 to dehydrate hy2 ( without inducing a phase change ) can not be taken 
 to mean that water exchange in this channel hydrate is not possible , 
 however .
in fact , water mobility was found to be similar in hy2 and 
 hya by raman using h2o / d2o exchange ( figure 11a , for details see section 9 of the supporting information ) . that water is 
 able to rapidly enter and leave the open channels 
 in hy2 naturally raises the question : why is the stoichiometry of 
 this hydrate conserved over such a wide rh range ?
the answer lies 
 in how the hy2 crystal structure responds to the loss of water . in 
 this case , the hy2 framework , apparently incapable of making the type 
 of adjustment that hya makes to accommodate appreciably lower amounts 
 of water , experiences a significant increase in free volume on dehydration . 

the decreased packing efficiency , along with the loss of strong intermolecular 
 waterdb7 hydrogen bonds , is considerably 
 destabilizing . as a result ,
hy2 retains its full complement of water 
 under most rh conditions at ambient temperature . with even modest 
 increases in temperature ( figure 13 ) or
decreases 
 in rh ( figure 7c ) , however , hy2 gives way exclusively 
 to a neat form ( form iii ) .
the path to form iii , a neat polymorph 
 that is more efficiently packed than the isomorphic dehydrate , is 
 conceivably paved by the db7 conformations that allow 
 intramolecular hydrogen bonding seen in the parent hy2 structure to 
 be conserved ( after proton transfer ) .
some of the propionic acid side 
 chains in db7 undergo a significant conformational change 
 on loss of water from hy2 , leading to a disordered form iii structure . 

this change probably accounts for the large rh range of coexistence , 
 i.e. , hysteresis in the moisture sorption 
efficient 
 and reversible nonstoichiometric hydration may be rationalized , and 
 in favorable cases ( e.g. , cromolyn sodium , amg 222 tosylate , and pfizer s 
 glycogen phosphorylase inhibitor ) , anticipated 
 for open channel structures ; however , the hydrates of db7 highlight 
 the dangers of inferring stoichiometric vs nonstoichiometric hydration 
 from general structural features . the 
 moisture sorption properties of hya may be unconventional , but they 
 are not unprecedented .
other carefully studied systems , such as topotecan 
 hcl , paroxetine hcl form ii , gsk s apoa-1 up - regulator , ciprofloxacin , thiamine hcl , and -cd , show a similar ability to equilibrate with the humidity 
 of their surroundings despite lacking continuous channels .
however , 
 hy2 is unusual in its ability to retain stoichiometric amounts of 
 water in open water channels over such a large rh range .
clearly , 
 with neither hydrate behaving according to the conventional classifications 
 based on either structure or absorption isotherms , jumping to conclusions 
 about the hydration behavior from a few hasty experiments would have 
 been very misleading . having a molecular level understanding 
 of how water vapor is sorbed in hygroscopic materials and the risks 
 that water uptake poses to the physical and chemical stability of 
 a pharmaceutical product is invaluable ,
as some sources 
 of water uptake are more manageable than others , careful evaluation 
 of the stoichiometry , stability relationships , and transformation 
 pathways of pharmaceutical hydrates should inform the solid form screening 
 and selection process .
nonstoichiometric hydration , for example , is 
 an intrinsic and generally undesirable property of a solid form that , 
 once established , might prompt further solid form screening and ultimately 
 would have to be managed in the event that an alternate , nonhygroscopic 
 form is not found .
however , water uptake in the amorphous components 
 of poorly crystalline materials is oftentimes correctable with improvements 
 in crystallinity that are generally realized during crystallization 
 process optimization .
hygroscopicity is , of course , but one 
 of many considerations taken 
 in the selection of a crystal form for a commercial drug product . 
 perhaps more important to delivering a drug safely and efficaciously 

are the solubility and stability , both thermodynamic and kinetic , 
 of the solid - state form . as metastable forms of the 5-ht2a and h1 inverse agonist , hy2 and hya offer the advantage 
 of generally higher solubility , which might be desirable for ensuring 
 rapid oral delivery of an insomnia medication .
however , from a manufacturability 
 and control perspective , the added risk of form conversions established 
 in our assessment of the structure  stability relationships 
 would have to be carefully weighed in the selection of either of these 
 high energy forms for a commercial drug product . in this case
, the 
 difficulties we encountered with producing the db7 hydrates at small 
 scale and avoiding conversions to the more stable neat forms prompted 
 further evaluation of salt and cocrystal options to determine whether 
 these were better suited for enabling a drug product .
the computational 
 modeling of static structures derived from the 
 time and spatially averaged crystal structures supports the interpretation 
 of the experimental results and accounts for the variability in disorder 
 and water mobility shown by ssnmr and raman h2o / d2o exchange .
however , current state - of - the - art calculations still 
 struggle to obtain sufficient accuracy for the small energy differences 
 involved and can not include the important 
 effects of water activity or temperature , let alone proton - transfer 
 energies .
ideally , we would wish to simulate the nonstoichiometric 
 hya at ambient temperature to confirm how the water moves and determine 
 the correlated motions within the db7 framework ( cf .
apoa-1 up - regulator ) . nonetheless , by 
 combining such a range of experimental and appropriate computational 
 work to get a coherent molecular understanding of this complex hydrate / anhydrate 
 system , we show both the potential of computational chemistry for 
 corroborating and assisting in an experimental program , as well as 
 the need for further developments .
a polymorphic system , 3-(4-dibenzo[b , f]oxepin-11-yl - piperazin-1-yl)-2,2-dimethylpropanoic acid , has 
 two zwitterionic hydrate phases with disordered water , which differ 
 remarkably in stability and hydration / dehydration mechanisms .
the 
 full multidisciplinary investigation of the behavior of the hydrate 
 and anhydrate phases was complicated by the difficulty in isolating 
 highly crystalline , phase pure samples , the sluggish equilibration 
 of the hydrates at different rh , the metastability of the various 
 forms at different conditions , and the variable hydration state of 
 hya . however
, structural based models for both hydrates and the metastable 
 form iii rationalize this behavior .
this system exemplifies the dangers 
 in assuming behaviors based on cursory observation of stoichiometric 
 and nonstoichiometric hydration .
temperature , water activity , and 
 ph determine the stability ranges of the db7 solid forms , considerably 
 complicating the processing , storage , and handling of this  unconventional  
 pharmaceutical hydrate system .
 elucidating the crystal structures , 
 transformations , and thermodynamics 
 of the two zwitterionic hydrates ( hy2 and hya ) of 3-(4-dibenzo[b , f][1,4]oxepin-11-yl - piperazin-1-yl)-2,2-dimethylpropanoic 
 acid ( db7 ) rationalizes the complex interplay of temperature , water 
 activity , and ph on the solid form stability and transformation pathways 
 to three neutral anhydrate polymorphs ( forms i , ii , and iii ) . 
 
 hya contains 1.29 to 1.95 molecules of water per db7 zwitterion ( db7z ) . 
 removal of the essential water stabilizing hya causes it 
 to collapse to an amorphous phase , frequently concomitantly nucleating 
 the stable anhydrate forms i and ii. hy2 is a stoichiometric 
 dihydrate and the only known precursor to form iii , a high energy 
 disordered anhydrate , with the level of disorder depending on the 
 drying conditions . 
 x - ray crystallography , solid state nmr , and h / d 
 exchange experiments on highly crystalline phase pure samples obtained 
 by exquisite control over crystallization , filtration , and drying 
 conditions , along with computational modeling , provided a molecular 
 level understanding of this system . the slow rates of many transformations 
 and sensitivity of equilibria to exact conditions , arising from its 
 varying static and dynamic disorder and water mobility in different 
 phases , meant that characterizing db7 hydration in terms of simplified 
 hydrate classifications was inappropriate for developing this pharmaceutical . 
Introduction
Experimental Section
Results
Discussion
Conclusions