in 
 general , in order to understand and rationalize the physicochemical 
 properties of crystalline solids , an essential prerequisite is to 
 establish the structural properties of the material of interest . as 
 a consequence , the development of new and improved strategies for 
 determining the structural properties of crystalline materials has 
 the potential to make significant impact across the broad range of 
 fields within the physical sciences in which knowledge of crystal 
 structure is required .
although single - crystal x - ray diffraction ( xrd ) 
 is the most powerful and routine technique for determining the structural 
 properties of crystalline solids , the requirement for a single - crystal 
 specimen of appropriate size and quality imposes a limitation on the 
 scope of this technique . indeed ,
many crystalline solids exist only 
 as microcrystalline powders and are therefore not suitable for investigation 
 by single - crystal xrd . to establish the structural properties of such 
 materials ,
the most direct approach is to use powder xrd , although 
 it is important to emphasize that carrying out structure determination 
 from powder xrd data is significantly more challenging than from single - crystal 
 xrd data .
however , the opportunities in this regard have improved 
 significantly in recent years as a consequence of progress in the 
 development of new data analysis techniques ( such as the direct - space strategy for structure solution , which 
 has made a particularly significant impact in the case of structure 
 determination of organic molecular solids from powder xrd data ) . in order to allow the methodology for structure determination from 
 powder xrd data to be extended to cases of increasing structural complexity , 
 we are interested in exploring opportunities to introduce information 
 derived from other experimental and/or computational techniques within 
 the structure determination process . in this regard ,
given the complementary 
 nature of powder xrd and solid - state nuclear magnetic resonance ( nmr ) 
 spectroscopy as techniques for probing the structural properties of 
 solids , there is considerable potential to include an assessment of 
 solid - state nmr data at appropriate stages within the structure determination 
 process . in the context of structure determination of organic molecular 
 solids from powder xrd data ,
solid - state nmr has so far been used 
 only in a rather peripheral manner , by 
 providing insights on specific structural aspects that either assist 
 in setting up the correct structural model for a direct - space structure 
 solution calculation or help in validating the final structure obtained 
 from rietveld refinement ( examples of the insights obtained from nmr 
 data include the number of independent molecules in the asymmetric 
 unit , the tautomeric form of the molecule , the existence of specific 
 interactions , the existence of disorder , and the values of specific 
 interatomic distances ) .
there is considerable scope for solid - state 
 nmr and powder xrd to be used more closely in tandem , particularly 
 by developing combined approaches that exploit the enhanced information 
 content of two - dimensional solid - state nmr spectra as well as the 
 power of first - principles computational techniques , notably the gipaw 
 ( gauge including projector augmented wave ) approach , that allow solid - state nmr spectra to be predicted reliably from 
 a crystal structure .
clearly , the opportunity to carry out such calculations 
 for crystal structures generated in the context of structure determination 
 from powder xrd data , together with an assessment of the quality of 
 agreement between calculated and experimental solid - state nmr data , 
 would provide a powerful and robust assessment of the veracity and 
 quality of the crystal structure . in the present article , we 
 report a combined approach of this type and demonstrate the successful 
 application of this approach for structure determination of the 1:1 
 cocrystal containing indomethacin ( denoted ind ; scheme 1 ) and nicotinamide ( denoted nic ; scheme 1 ) . structure determination of this material , which is of relevance 
 in pharmaceutical research , was carried out directly from powder xrd data using 
 the direct - space strategy for structure solution followed by rietveld 
 refinement .
for the fully refined crystal structure , the isotropic h and c nmr chemical shifts were calculated under 
 periodic boundary conditions by the gipaw method based on density 
 functional theory ( dft ) employing a plane - wave basis set and pseudopotentials . 

the calculated chemical shifts are found to be in excellent agreement 
 with the corresponding chemical shifts measured experimentally by 
 solid - state nmr , yielding a robust confirmation 
 of the structure determined from the powder xrd data .
the powder xrd pattern of this material was recorded at 
 294 k on a bruker d8 instrument using ge - monochromated cuk1 radiation and operating in transmission mode with a foil 
 type sample holder ( data collection time ca .
nic cocrystal have been reported 
 previously , comprising two - dimensional h double quantum and n  h and h  c heteronuclear mas nmr spectra recorded 
 at h larmor frequencies of 500 and 850 mhz .
the isotropic h and c nmr chemical shifts determined in this 
 previous study were used as the experimental nmr data in the present 
 work .
nic cocrystal 
 was indexed using the ito code in the 
 program crysfire , giving the following 
 unit cell with monoclinic metric symmetry : a = 27.38 
  , b = 5.02  , c = 17.19 
  ,  = 97.4 ( v = 2343.1  ) .
given the volume of this unit cell and consideration of 
 density , the number of formula units in the unit cell was assigned 
 as z = 4 . from systematic 
 absences ,
the space group was assigned as p21/a ( corresponding to z 
 = 1 ) .
profile fitting using the le bail method , implemented in the program gsas , gave a good quality of fit ( rwp = 1.53% , rp = 1.16% ) .
the refined unit cell and profile 
 parameters obtained in the le bail fitting procedure were used in 
 the subsequent structure solution calculation .
structure solution 
 was carried out using the direct - space genetic algorithm ( ga ) technique incorporated in the program eager . in the ga structure solution calculation ,
the ind molecule was defined 
 by a total of 11 structural variables ( three positional variables , 
 three orientational variables , and five torsion - angle variables ) , 
 and the nic molecule was defined by a total of seven structural variables 
 ( three positional variables , three orientational variables , and one 
 torsion - angle variable ) . each ga structure solution calculation involved 
 the evolution of 100 generations for a population of 100 structures , 
 with 10 mating operations and 50 mutation operations carried out per 
 generation . in total , 16 independent ga calculations were carried 
 out , with the same good - quality structure solution obtained in 12 
 cases .
the best structure solution was used as the initial structural 
 model for rietveld refinement , which was carried out using the gsas 
 program .
standard restraints were applied 
 to bond lengths and bond angles , planar restraints were applied to 
 aromatic rings , and a single isotropic displacement parameter was 
 refined for each molecule , with the value for the hydrogen atoms fixed 
 at 1.2 times the value for the non - hydrogen atoms .
the known crystal structure of pure ind was included as a second 
 phase in the refinement , as an impurity amount of this phase was present 
 in the sample of the ind 
dft calculations were carried out using castep ( accelrys , 
 san diego , ca ) academic release version 
 6.0.1 , which implements dft within a generalized gradient approximation 
 and the plane - wave pseudopotential approach .
ernzerhof exchange - correlation functional with ultrasoft pseudopotentials and a basis set cutoff energy of 700 ev . the crystal structure 
 of ind 
nic determined from the powder xrd data was used as 
 the starting structure for geometry optimization , in which the positions 
 of all 56 atoms in the asymmetric unit were relaxed , the unit cell 
 was fixed , the space group symmetry ( p21/a ) was preserved , and periodic boundary conditions 
 were applied .
the nmr chemical shift calculations ( carried out 
 on the geometry optimized structure ) employed the gipaw method to determine the shielding tensor for each nucleus in the crystal 
 structure .
the calculations used a plane - wave basis set with a maximum 
 cutoff energy of 700 ev , with integrals taken over the brillouin zone 
 by using a monkhorst 
pack grid of minimum sample spacing 0.1 
  2  . to compare the results 
 directly with experimentally measured isotropic chemical shifts ,
the 
 following conversion was used : iso = ref  iso , where iso is the absolute isotropic shielding value generated from the castep 
 calculation .
the reference shieldings were established by considering 
 the mean value of the experimental isotropic chemical shifts and the 
 mean value of the calculated shieldings , giving ref values of 167.3 ppm for c and 30.9 ppm for h.
nic 
 was determined in the present work directly from powder xrd data , 
 employing the direct - space genetic algorithm technique for structure 
 solution followed by rietveld refinement .
the final rietveld refinement gave an excellent fit to 
 the powder xrd data ( rwp = 1.85% , rp = 1.37% ; figure 1 ) 
 with the following refined parameters : a = 27.3847(10 ) 
  , b = 5.01906(16 )  , c = 17.1935(6 )  ,  = 97.3103(20) ; v = 2343.96(21 )  ( space group , p21/a ; 2 range , 4 to 70 ; 3867 profile points ; 238 
 refined variables ) .
as now discussed , the crystal structure was validated 
 by assessing the level of agreement between dft - calculated solid - state h and c nmr data and the corresponding experimental 
 solid - state h and c nmr data .
nic cocrystal , showing the experimental ( red + 
 marks ) , calculated ( green solid line ) , and difference ( purple lower 
 line ) powder xrd profiles .
nic cocrystal , and red represents an impurity 
 of the pure phase of ind ) .
geometry 
 optimization of the crystal structure of ind  nic using castep 
 ( see experimental section for details ) , starting 
 from the crystal structure determined from powder xrd data , leads 
 to only very minor shifts in atomic positions [ figure 2 ; for non - hydrogen atoms , the mean atomic displacement is 
 0.077  , and the largest displacement is 0.14  ] , confirming 
 that the crystal structure determined from the powder xrd data lies 
 very close to an energy minimum for this system . as a further indication 
 of the close similarity of the dft - optimized structure and the final 
 refined structure from the powder xrd data , the fit of the optimized 
 structure to the powder xrd data was assessed by taking the optimized 
 structure as a fixed structural model in a rietveld refinement calculation 
 ( with only the nonstructural parameters refined ) .
as shown in figure 3 , this calculation reveals that the dft - optimized 
 structure gives an excellent quality of fit to the experimental powder 
 xrd data ( rwp = 1.99% , rp = 1.48% ) .
overlay ( viewed along the b - axis ) of the asymmetric unit in the crystal structure of ind 
nic 
 determined from powder xrd data ( cyan ) and the asymmetric unit in 
 the relaxed crystal structure resulting from the dft geometry optimization 
 calculation using castep ( magenta ) .
nic 
 as a fixed structural model , with only the nonstructural parameters 
 refined .
the experimental ( red + marks ) , calculated ( green solid line ) , 
 and difference ( purple lower line ) powder xrd profiles are shown . 

tick marks indicate peak positions ( black represents the ind  nic 
 cocrystal , and red represents an impurity of the pure phase of ind ) . it is well established that gipaw 
 calculations reliably reproduce experimental nmr chemical shifts for 
 cases with known crystal structures determined from single - crystal 
 xrd , with agreement typically better than 0.3 ppm for h and 3 ppm for c chemical 
 shifts .
thus , comparison of chemical shifts calculated using the gipaw method 
 for the crystal structure of ind 
nic determined here from powder 
 xrd data represents a robust and independent validation of the structure . 
 indeed , the h and c nmr chemical shifts calculated 
 for the geometry optimized structure are in excellent agreement ( see 
 figure 4 and table 1 ) with the corresponding experimental solid - state nmr data published 
 previously ( the slightly poorer agreement 
 in the h chemical shifts for the three hydrogen - bonded 
 protons is discussed below ) .
comparison of experimental and calculated ( gipaw ) 
 values of the isotropic c and h chemical 
 shifts for ind  nic .
the comparatively poorer agreement in the h chemical shifts for the three hydrogen - bonded protons is 
 discussed in the text .
iso = (iso  ref ) , with ref = 30.9 ppm for h. iso = (iso  ref ) , with ref = 167.3 ppm for c. reassignments compared 
 to those stated in table s1 of ref ( 18 ) .
the 
 h atom forming the n  ho hydrogen bond between 
 nic(1 ) and nic(3 ) [ in the structure determined from powder xrd : no , 
 2.95  ; n 
ind(1 ) [ [ in the structure determined 
 from powder xrd : no , 2.99  ; n 
in addition 
 to the good agreement between experimental and calculated chemical 
 shifts considered separately for the isotropic h and c chemical shifts ( as shown in figure 4 ) , an even more robust test is to consider the two - dimensional h and c nmr chemical shift correlations for directly 
 bonded ch , ch2 , and ch3 moieties , for which 
 excellent agreement between experimental and calculated data is again 
 achieved ( figure 5 ) .
specifically , for the 
 aromatic ch resonances , very good reproduction of the experimental 
 two - dimensional h 
c correlation spectrum 
 is obtained . in particular , the mean and highest differences between 
 experimental and calculated chemical shifts are as follows : for h , 0.4 ppm ( mean ) , 2.2 ppm ( highest ) ; 
 for c , 1.6 ppm ( mean ) , 4.3 ppm ( highest ) .
calculated ( gipaw ) h and c chemical shifts ( red crosses ) for directly 
 bonded ch , ch2 , and ch3 moieties in the ind 
considering figure 4 , the only significant 
 differences arise in the case of the h chemical shifts 
 for the oh group of ind ( exptl , 16.3 ppm ; calcd , 18.5 ppm ) and for 
 the two h environments in the nh2 group of 
 nic ( exptl , 9.0 and 7.3 ppm ; calcd , 10.5 and 8.8 ppm ) .
however , we 
 note that the difference ( 1.7 ppm ) between the experimental h chemical shifts of the two nh2 protons is exactly 
 reproduced by the calculation .
the observation that the experimental h chemical shift is ca . 2 ppm lower than the calculated value 
 in these cases is a consequence of the known temperature dependence 
 of h chemical shifts of hydrogen - bonded protons and the well - established fact that geometry optimization yields 
 a static hydrogen - bonded structure , whereas the actual structure probed 
 experimentally at ambient temperature is flexible / dynamic . as a consequence , 

geometry optimization produces a structure with stronger hydrogen 
 bonding and hence higher h chemical shifts .
we note that 
 improved agreement between the experimental and calculated h chemical shifts for these groups may be expected to result from 
 the use of molecular dynamics simulation techniques as a further assessment of the veracity of the final refined crystal 
 structure . in the crystal structure of ind 
nic 
 ( figure 6a ) , the molecules form a helical hydrogen - bonded 
 motif that follows the 21 screw axis ( parallel to the b - axis ) and is constructed from an alternating arrangement 
 of ind and nic molecules : nic(1)ind(1)nic(2)ind(2)nic(3)ind(3 ) . 

the repeat unit comprises one molecule of each type [ e.g. , nic(1)ind(1 ) 
 in the above designation ] .
thus , nic(1)ind(1 ) and nic(2)ind(2 ) are 
 related to each other by the 21 screw operation , whereas 
 nic(1)ind(1 ) and nic(3)ind(3 ) 
 are related by the unit cell translation along the b - axis . within the helical hydrogen - bonded chain , the nic(1)ind(1 ) 

interaction is an n  ho hydrogen bond ( no , 
 2.99  ; n 
h bond of nic as the donor and the o = c 
 oxygen of the carboxylic acid group of ind as the acceptor , and the 
 ind(1)nic(2 ) interaction is an o  hn hydrogen 
 bond ( on , 2.63  ; o 
h bond of the carboxylic acid 
 group of ind as the donor and the nitrogen atom in the heterocyclic 
 ring of nic as the acceptor ( all hydrogen - bond geometries quoted here 
 refer to the experimental structure determined from powder xrd data ) . 

in addition , alternate nic molecules along the helical chain [ i.e. , 
 those related by the unit cell translation along the b - axis , such as nic(1 ) and nic(3 ) ] are linked by an n 
ho , 
 170.6 ) , giving rise to a linear hydrogen - bonded motif that runs 
 parallel to the b - axis ( figure 6b ) .
( a ) crystal structure of the ind  nic cocrystal viewed along 
 the b - axis .
( b ) part of the crystal structure , viewed 
 along the c - axis , illustrating the linear hydrogen - bonded 
 chain , running parallel to the b - axis , involving 
 the amide groups of nic molecules ( black lines denote the unit cell 
 repeat along the b - axis ; the ch2co2h moieties of ind molecules are also shown , illustrating 
 the additional hydrogen bonding involving the amide group of nic ) . 
 in both panels , hydrogen bonds are indicated by green dashed lines .
nic verifies previous insights 
 deduced from a comprehensive solid - state nmr study of this material .
ho = c 
 interaction involving an aromatic c  h bond of the same molecule 
 of nic and the o = c oxygen of the same carboxylic acid group 
 of ind .
ho = c interaction ( co , 
 3.16  ; c  ho , 129.8 ) is also identified 
 in the crystal structure reported here , although , as it is geometrically 
 far from optimal , we refrain from ascribing it as a significant hydrogen 
 bond .
in conclusion , we emphasize that the approach developed 
 in the present article for using complete solid - state nmr spectral 
 data within the context of structure determination from powder xrd 
 data allows the quality of the crystal structure determined from the 
 powder xrd data to be assessed and validated both against the experimental powder xrd data ( in the rietveld refinement ) and against the experimental solid - state nmr data ( in the 
 subsequent comparison of calculated and experimental chemical shifts ) . 
 as a consequence , this approach provides a stringent and robust assessment 
 of the validity and quality of the refined crystal structure , particularly 
 when the two - dimensional correlation of h and c chemical shifts for directly bonded c 
h moieties is included in the assessment . while the 
 combined approach employed in the present work represents the first 
 example of the use of ab initio structure determination of an organic 
 molecular solid from powder xrd data followed by rigorous assessment 
 of the refined structure against complete solid - state h and c nmr spectral data
, we note that dft - calculated 
 solid - state nmr data have been used in various manifestations within 
 the process of structure determination of other types of solid materials 
 from powder xrd data .
examples include a number of strategies for 
 the structure determination of inorganic framework structures and hybrid organic  inorganic materials , as well as for elucidating specific structural details 
 ( in particular , hydrogen - bonding arrangements ) for materials of mineralogical 
 interest .
in addition , dft - based chemical shift calculations 
 have been employed successfully to augment the process of structure 
 determination of an organic polymer from wide - angle x - ray and wide - angle 
 neutron diffraction techniques .
we also 
 note that , in proof of principle investigations , comparison between gipaw calculations and experimental solid - state h nmr data has been employed within crystal structure prediction 
 studies for small organic molecules ; although demonstrated only in 
 the case of known structures ( determined previously by xrd ) , the work 
 has shown that assessment of the solid - state nmr data provides a viable 
 approach for selecting the correct structure from among those generated 
 by the crystal structure prediction algorithm . while techniques 
 for successfully determining the crystal structures of organic materials 
 directly from powder xrd data have been in use for almost 20 years
, 
 it is the much more recent advances in 
 the methodology for first - principles calculation of solid - state nmr 
 data from known crystal structures that has now created the opportunity 
 to propose and demonstrate our combined approach in which the refined 
 crystal structure is scrutinized against complete solid - state h and c nmr spectral data .
we anticipate that 
 this combined approach will be utilized extensively in the future 
 and may play an important role in enabling the application of powder 
 xrd methodology to be extended to tackle increasingly complex structural 
 problems .
 we report a strategy for structure 
 determination of organic materials in which complete solid - state nuclear 
 magnetic resonance ( nmr ) spectral data is utilized within the context 
 of structure determination from powder x - ray diffraction ( xrd ) data . 
 following determination of the crystal structure from powder xrd data , 
 first - principles density functional theory - based techniques within 
 the gipaw approach 
 are exploited to calculate the solid - state nmr 
 data for the structure , followed by careful scrutiny of the agreement 
 with experimental solid - state nmr data . 
 the successful application 
 of this approach is demonstrated by structure determination of the 
 1:1 cocrystal of indomethacin and nicotinamide . 
 the 1h 
 and 13c chemical shifts calculated for the crystal structure 
 determined from the powder xrd data are in excellent agreement with 
 those measured experimentally , notably including the two - dimensional 
 correlation of 1h and 13c chemical shifts for 
 directly bonded 13c1h moieties . 
 the 
 key feature of this combined approach is that the quality of the structure 
 determined is assessed both against experimental 
 powder xrd data and against experimental solid - state 
 nmr data , thus providing a very robust validation of the veracity 
 of the structure . 
Introduction
Experimental
Section
Results
and Discussion
Concluding
Remarks