cryptophane - a 
 was the first cryptophane synthesized by collet et 
 al . in 1981 .
it is composed of two equivalent 
 cyclotribenzylene ( ctb ) caps bound together by three ethylene - dioxy 
 linkers . on each phenyl ring
a 
 has been the subject of many interesting studies in the field of host 
it has a hydrophobic three - dimensional cavity capable of 
 binding small organic molecules such as chloromethanes as well as xenon atoms .
the previously investigated chloromethane complexes of cryptophane - c 
 revealed a surprisingly high affinity constant for dichloromethane 
 and relatively low affinity constant for chloroform .
this has brought up the question of what structural properties 
 have the largest effect on the complexation .
cryptophane - a and -c 
 are both anti - isomers , but the latter has nonequivalent 
 caps with only one of the caps carrying the methoxy substituents on 
 the phenyl groups ( see molecules 1 and 2 in scheme 1 ) . apart from this , the two molecules 1 and 2 are identical . 

they 
 also have the same cavity volumes . as will be discussed in the present 
 work ,
cryptophane - a in solution is in exchange between its conformers 
 similarly to cryptophane - c .
the encapsulation of a chloromethane guest 
 changes the probability distribution of the conformers as it has been 
 seen before .
nuclear magnetic resonance ( nmr ) 
 is a perfect tool for characterizing the encapsulation process but 
 also for following the guest - induced changes in the host .
these chemical 
 events can be explained , for instance , by means of nmr spin  echo 
 experiments . in this work ,
translational diffusion was investigated 
 in order to reveal the eventual presence of another guest , water , 
 inside the host cavity .
meiboom  gill 
 ( cpmg ) relaxation dispersion methodology was dedicated 
 to shed light on the host conformational exchange .
obviously , upon 
 encapsulation , both h and c spectra displayed 
 changes of the peak positions .
it is not only the peak position that 
 is very informative but also the intensity and broadening of the guest h signal in the free and bound position , in particular if 
 the host and the guest are present in close to the 1:1 molar ratio . 

this concentration ratio also allows a better estimation of the affinity 
 constant from the h spectrum .
the comparison of the data 
 to cryptophane - c is not sufficient to draw the final conclusion concerning 
 the relation between the structure of the caps and the affinity . to 
 complete the analysis ,
another cryptophane - a derivative was chosen 
 in which the methoxy groups attached to the ctb rings were replaced 
 by butoxy groups , resulting in a third cryptophane with the same cavity 
 volume ( see molecule 3 in scheme 1 ) .
the trans - conformers of cryptophane - a are shown in figure 1 , and its analogue with butoxy groups replacing 
 the methoxy substituents , denoted cryptophane - but , is shown in figure 2 .
( a ) the t1t1t1 conformer of cryptophane - a 
 with the 
 atom numbering .
cryptophane - a and cryptophane - but 
 were synthesized by brotin et al.c labeled chloroform and the deuterated solvent , 1,1,2,2-tetrachloroethane - d2 , were obtained from cambridge isotope laboratory . 

the raw solid cryptophanes 
 contained chcl3 , ch2cl2 , and ethanol 
 coming from the recrystallization .
a 30 mm solution of cryptophane - a 
 was prepared without any purification ( sample 1 ) .
another solution , 
 sample 2 , with 10 mm cryptophane - a containing 60 mm added nonlabeled 
 chloroform was prepared with no purification . for quantitative analysis , 

the material was dipped into nonlabeled chloroform or dichloromethane 
 and the solvent was then let to evaporate .
the following solutions in 1,1,2,2-tetrachloroethane - d2 were prepared:(3)12 mm cryptophane - a and 13 mm ch2cl2(4)11 mm cryptophane - but and 13 mm ch2cl2(5)10 mm cryptophane - a and 
 11 mm chcl3(6)11 mm cryptophane - but and 12 mm chcl3(7)20 mm cryptophane - a and 15 mm ch2cl2(8)10 mm cryptophane - a and 62 mm chcl3(9)10 mm cryptophane - but 
 and 90 mm chcl3(10)10 mm cryptophane - but and 25 mm chcl3(11)10 mm cryptophane - but , 
 9 mm chcl3 , and 6.5 mm ch2cl2(12)30 mm cryptophane - a and 
 150 mm chcl3 12 mm cryptophane - a and 13 mm ch2cl2 11 mm cryptophane - but and 13 mm ch2cl2 10 mm cryptophane - a and 
 11 mm chcl3 11 mm cryptophane - but and 12 mm chcl3 20 mm cryptophane - a and 15 mm ch2cl2 10 mm cryptophane - a and 62 mm chcl3 10 mm cryptophane - but 
 and 90 mm chcl3 10 mm cryptophane - but and 25 mm chcl3 10 mm cryptophane - but , 
 9 mm chcl3 , and 6.5 mm ch2cl2 30 mm cryptophane - a and 
 150 mm chcl3 the solubility 
 of cryptophane - a in tetrachloroethane is much higher 
 than that of cryptophane - c and cryptophane - but .
h and c experiments 
 were performed with bruker avance spectrometers operating at 9.4 , 
 14.1 , and 16.5 t using 5 mm ( bbi and bbo at 9.4 t , txi and bbo at 
 14.1 t , and cryo - txi at 16.5 t ) probe heads . at 9.4 t
, the temperature 
 calibration was done using a standard methanol calibration sample , 
 while a resistance detector made of copper wire dipped into silicon 
 oil contained in a 5 mm nmr tube was used at the two higher fields . 

the accuracy of the temperature determination is estimated at 1 
 k. all the experiments measuring build - up or decay were repeated at 
 least twice .
the peak assignment was based on dqf - cosy , ( 2d ) noesy , 
 ( 2d ) roesy , as well as h  c edited 
 hsqc experiments .
the exsy measurements were performed at 250 
 k and 16.5 t using the implementation as the dpfgsenoe sequence with 
 two selectively refocusing shaped pulses and one hard  pulse 
 in the middle of the mixing time interval .
the semi - selective inversion pulses were implemented as gaussian 
 g3 cascades with a duration of 1820 
 ms .
experiments were performed 
 with 64 accumulated signal transients , using a relaxation delay of 
 3540 s. only the doublets of the c - labeled chloroform 
 were evaluated . the purpose of the label is to enhance the proton 
 spin  lattice relaxation .
the evaluation of the exchange rate 
 of the forward ( complexation ) reaction was based on the approach proposed 
 originally by macura et al . and described 
 by hu and krishnamurthy .
the exchange 
 rate of the backward ( decomplexation ) reaction was based on the principle 
 of detailed balance , in order to avoid the error coming from small 
 intensities at very short mixing times in the initial rate regime .
c spectra were recorded with 
 waltz16 proton decoupling 
 at 9.4 t , while waltz65 was used at 14.1 and 16.5 t. the decoupling 
 power corresponded , on average , to the nutation frequency of 2.8 khz . 

lattice relaxation times of the guest ( chcl3 ) were measured by the inversion  recovery 
 method using 1619 recovery delays ranging from 0.5 ms to 30 
 s with a relaxation delay of 35 s. the heteronuclear overhauser enhancement 
 was measured with the dynamic noe sequence .
the noe build - up period was set to 5t1 and the relaxation delay to 10t1 . in 
 the spectrum with no noe enhancement ,
the 2d noesy and roesy at 9.4 and 14.1 t were recorded 
 at 235 , 
 240 , 255 , and 258 k. the detection method used was states -tppi .
the 
 mixing times were 0.020.24 s for the noesy and 0.040.2 
 s for the roesy .
the spin lock power was set to 3 khz . in the direct 
 dimension ,
8 scans were used with 16 dummy scans , with a relaxation 
 delay of 57 s. the size of the direct fid was 4096 data points , 
 giving an approximately 0.6 s acquisition time in the t2 domain .
512 and 768 data points were used in the indirect 
 ( t1 ) dimension , which were zero filed 
 to 4096 points .
the noesy pulse sequence contained 
 a hard -pulse in the middle of the mixing time and two z gradients with a power of 40% and 40% of the maximum 
 value .
the h diffusion 
 experiments were performed at 258 and 
 268 k using a pulse - gradient stimulated echo ( pgste ) sequence with 
 a longitudinal eddy - current delay ( led ) and bipolar gradient pulses . 

the calibration of the gradients 
 was accomplished by measuring the diffusion coefficient of a well - known 
 sample at 298 k. in our case , the bruker 
 standard 
sample which is composed of 1% 
 h2o in d2o with 0.1 g / l gdcl3 was 
 used . during the diffusion experiments ,
the gradient strength was 
 linearly incremented in 32 steps from 2 to 95% of its maximum value ; 
 the diffusion time  and the gradient pulse duration  
 were kept constant .
the c cpmg measurements were 
 performed at two static 
 magnetic fields ( b0 = 14.1 and 16.5 t ) 
 and two temperatures ( t = 298 and 310 k ) .
the carbons 
 1 and 2 corresponding to the cryptophane - a linkers 
 and the aromatic carbon 6 ( see figure 1 ) were 
 considered .
gill 
 ( cpmg ) sequence with proton decoupling during acquisition and a proton 
 180 pulse at every second echo in the c cpmg pulse 
 train to avoid the csa - dd cross - correlation effects . for each r2 measurement ,
the 
 delay between the 180 pulses in the cpmg pulse train , cpmg , was kept constant while the number of 180 pulses 
 was increased .
every experiment was recorded with 1024 scans and 16 
 dummy scans with a relaxation delay of 2 s. the c cpmg 
 relaxation dispersions were established for cpmg ( = 1/(2cpmg ) ) values ranging from 166.7 to 2500 
 hz .
all calculations were 
 performed in a similar way as reported for cryptophane d and c. the gaussian 09 package was used .
geometries 
 were optimized at the level of the dft - b3lyp functional with the basis 
 set 6 - 31g(d ) . each optimized structure
was then taken and a single 
 point energy calculation was done , together with the calculation of 
 the c chemical shift using the giao method , with the larger basis set 6 - 311+g(2d , p ) .
the 
 calculated chemical shifts reported are referenced to the calculated 
 chemical shift of tms at the same level of theory .
all the calculations 
 were performed using the conductor polarizable continuum model ( cpcm ) with the parameters appropriate for dichloroethane solvent .
two 
 sets of calculations were made : one for the empty host and one with 
 a chloroform molecule inside the cavity . the van der waals interaction 

was taken into consideration in all structures optimized with the 
 b3lyp functional by adding , after the geometry optimization , the empirical 
 term to the dft energies .
following 
 our earlier work , the complex formation 
 in the host  guest ( h  g ) systems is described in terms 
 of the reaction1 nmr methods 
 allow investigation of 
 the reaction kinetics at equilibrium , when the concentrations of various 
 species are constant in time .
the forward and backward processes are 
 individually described by the rate expressions:23 the 
 ( pseudo ) first - order rate constants , kfb ( free - to - bound ) and kbf ( bound - to - free ) , 
 are defined according to4 the equilibrium constant for the complex 
 formation ( the affinity 
 constant ) is given by5 equation 5 can 
 be reformulated in terms of 
 the principle of detailed balance:6 equations 16 form the basis of 
 the discussion of the kinetics and thermodynamics 
 of our systems . the solutions with 
 approximately 1:1 
 host : guest ratios ( samples 36 ) are very informative compared 
 to the solutions with high guest excess ( samples 810 and 12 ) . 
 in the case of samples 36 , the intensity and
the integral 
 of the bound guest peak are higher than those for the free guest . 

this implies a relatively high affinity to the host . in order to extract 
 more information on kinetics ,
namely , the exchange rates , it is possible 
 to perform line - shape fitting on the spectra in which 
 the exchange caused line - broadening is higher than 1/t2 * , i.e. , the combined effect of the natural line width 
 in the absence of exchange and magnetic field inhomogeneity .
this 
 is not a problem in the case of the dichloromethane guest , since , 
 even at the lowest temperature ( 235 k ) , the exchange - caused line - broadening 
 is large ( see figure 3 ) .
the proton spectrum of ch2cl2@cryptophane - a 
 in 1,1,2,2-c2d2cl4 ( sample 3 ) at 
 14.1 t and 235 k. the exchange 
 rates in the case 
 of chcl3 at 235 , 245 , and 255 k ( bold font ) were determined 
 by exsy experiments , in other cases by line - shape fitting ( samples 
 3 and 5 ) .
the equilibrium constant ( k ) was calculated 
 from the concentrations of the species . in the case of chcl3@cryptophane - a at low 
 temperatures , 
 the exchange of the guest is not fast enough for line - shape fitting . 

the rate constants kfb reported in table 1 at 235 , 245 , and 255 k were obtained from the exsy 
 experiments , while kbf were calculated from the principle of detailed balance . 

the rates and populations for chcl3@cryptophane - a at higher 
 temperatures are based on the line - shape fitting .
this can be explained by the size difference between the two guests 
 ( indeed , the van der waals volumes of dichloromethane and chloroform 
 are , respectively , equal to 55 and 72  ) . for both guests ,
the only difference between the 
 two hosts is that cryptophane - c has nonequivalent caps , since the 
 methoxy groups are missing from one of them .
a hypothesis formulated 
 in our recent cryptophane - c study is that 
 the methoxy groups block the entrance and exit of the cavity . in the 
 case of cryptophane - a , the methoxy groups from the caps ( see figure 1 ) present an even more severe hindrance for the 
 guest .
thus , the corresponding exchange processes are expected to 
 be slower for cryptophane - a , in agreement with the present observations . in the case of both guests ,
this means 
 that the affinity of cryptophane - a is very high both to chloroform 
 and to dichloromethane . knowing the total concentrations of the compounds
, 
 one can calculate the concentration of the species ( [ h ] , [ g ] , [ hg ] , 
 see the supporting information ) and calculate 
 the equilibrium constant at every temperature . from table 1 ,
the affinity constant is higher for chloroform 
 than for dichloromethane at 235 k. this is interesting , since chloroform 
 is the bigger guest , which might be expected to fit worse inside the 
 host cavity .
it is also noteworthy that the equilibrium constant determined 
 here for the dichloromethane guest is much higher than it was reported 
 in earlier work from our laboratories , where a large excess of dichloromethane compared to the cryptophanes 
 led to a large uncertainty in the free host concentration .
the data analysis of the solutions 
 containing cryptophane - but and dichloromethane is difficult because 
 the exchange at low temperatures is rather slow and only the integrals 
 can be used for estimating the approximate concentration of the species 
 present .
an example of the h spectrum of sample 4 at 245 
 k is shown in figure 4 .
the proton spectrum of 
 ch2cl2@cryptophane - but 
 in 1,1,2,2-c2d2cl4 ( sample 4 ) at 
 14.1 t and 245 k. nevertheless , it is possible 
 to calculate the populations of the 
 free site pf and of the bound site pb ( where pb = 1 
  pf ) at this temperature range 
 ( see table 2 ) . at higher temperatures ,
overlap 
 occurs between the bound guest and the signals from the butoxy groups . for chcl3@cryptophane - but
, it was possible 
 to measure 
 signal integrals at the low temperatures ( 235 and 245 k ) and to perform 
 the line shape analysis between 255 and 305 k. comparing the values 
 of the bound site population pb in tables 1 and 2 , one can notice that 
 the bound site population is the highest out of the four complexes 
 in the case of ch2cl2@cryptophane - but .
the equilibrium constant values for both complexes are very high , 
 falling actually in the range where nmr is not the most suitable technique . 

the values reported here for the dichloromethane complex carry a big 
 error , since the concentration of the host is very low ( see the supporting information ) and the baseline and 
 integration error sum up . nevertheless , it is still possible to draw 
 the conclusion that the equilibrium constant is very high .
surprisingly , 
 the exchange is faster in the case of chcl3@cryptophane - but 
 than chcl3@cryptophane - a , while the affinity constants 
 are similar .
a possible explanation of this observation ( as suggested 
 by one of the reviewers ) is that the bulky butoxy groups can not organize 
 in the closed conformation ( see below ) . summarizing the exchange rates 
 between free and complexed sites
, one can state that the chcl3 guest is typically in slow exchange , while ch2cl2 exchanges faster on the chemical shift time scale . 
 using the arrhenius and vant hoff equations , it is possible 
 to estimate the activation energy and the reaction enthalpy of the 
 complexation reactions ( see the supporting information ) .
the activation energy 
 obtained for the ch2cl2@cryptophane - a system 
 agrees with previous studies .
the activation 
 energies for the chcl3@cryptophane - a 
 are the highest , which agrees well with structure and size considerations 
 such as the previously mentioned blocking effect of the methoxy groups 
 connected to the ctb rings . the lower activation energy of chcl3@cryptophane - but indicates also that the butoxy groups play 
 a role in the complexation dynamics , but it is not as obvious as in 
 the case of cryptophane - a . looking at these results , it is worthwhile 
 to not forget to take 
 account of experimental errors coming from the sample preparation , 
 the integration , and the line - shape fitting .
the estimated error of 
 total concentrations is 20% ( based on repeated sample preparations ) 
 and is obviously propagated to the association constant k and the exchange rate constant k1 ( the 
 other parameters , determined by integration or by line - shape fitting , 
 carry a lower error which can be estimated around 5% ) .
the samples 
 containing close to 1:1 molar ratio of the host and the guest also 
 suffer from the low intensity of the peak of the free site .
this is , 
 on the other hand , the consequence of the high affinity constant which 
 was  hidden  in earlier work by the high excess of the 
 guest . in order to probe the mobility of the guest 
 within the cryptophane cavity , relaxation of chloroform , both in the 
 free and the bound state ,
the longitudinal relaxation 
 rate r1 ( inverse of the longitudinal relaxation 
 time t1 ) and the heteronuclear noe were 
 measured for the c of the guest , in analogy with earlier 
 work from our laboratories .
one can see that , when chloroform is free in the 
 solution , extreme narrowing conditions are achieved ; indeed , the c spin - relaxation rate r1 is 
 independent of the magnetic field and a full noe is retrieved .
concerning 
 the bound chloroform , the reported values show a field dependence 
 of the longitudinal relaxation rate r1 as well as a noe enhancement less than full . in order to explain 
 these results , the motion of chcl3 encapsulated in the 
 cryptophane -
for the global correlation time , 
 the value of 2.7 ns , estimated from the plot of r versus the temperature established earlier , was used .
the resulting square of the generalized order 
 parameter , s , is also shown in the table . 
 it can be seen that the lipari 
szabo order parameter for the 
 guest within the cryptophane cavities agrees quite well with the corresponding 
 quantities from the solid state .
the s value found is high , indicating 
 that the motion of the chcl3 molecule is restricted inside 
 the host cavity . as there 
 is no doubt concerning the encapsulation of dichloromethane or chloroform 
 within cryptophane
, one can wonder if other species present in our 
 solutions can enter the host cavity .
the question can especially arise 
 for water ( all the samples contain a small amount of water coming 
 from the walls of the glass materials ) , as its molecular size is smaller 
 than the one of dichloromethane or chloroform . to bring out the possible 
 encapsulation of water ,
h diffusion experiments were performed on sample 7 and were compared 
 to the results obtained on a sample containing dichloromethane in 
 the same solvent but without cryptophane .
self - diffusion coefficients 
 for cryptophane - a , dichloromethane , and water are given in table 5 for the two samples investigated and for the two 
 temperatures considered ( 258 and 268 k ) .
first , 
 one can observe that the diffusion coefficient of each species 
 varies as expected with the temperature .
the self - diffusion coefficient 
 of ch2cl2 in the sample containing the host 
 ( sample 7 ) is much lower than the one in the sample without cryptophane - a 
 ( roughly 4 times smaller at 258 k and 3 times smaller at 268 k ) , indicating 
 changes in the translational motions of ch2cl2 .
moreover , its diffusion coefficient at 258 k is close to the value 
 found for cryptophane , which definitely proves that dichloromethane 
 and cryptophane diffuse as one entity at this temperature . 
 at 268 k ,
d is roughly 2 times larger than d. this larger diffusion coefficient can be explained by the fact 
 that d can 
 be seen as an apparent diffusion coefficient to which the diffusion 
 of both bound and free molecules contributes . indeed , as the exchange 
 is getting faster and the association constant decreases with the 
 temperature , the contribution coming from the free dichloromethane 
 is more important , leading d to increase .
looking now at the self - diffusion 
 coefficients of water , d , in the samples with and without 
 cryptophane , it is interesting to notice that they do not evolve in 
 the same way as for dichloromethane .
even if they slightly 
 decrease , they are still 10 times larger than the diffusion coefficients 
 of cryptophane .
consequently , water may be interacting with the cryptophane 
 but does not enter the cavity in solution , thus proving the hydrophobicity 
 of the host cavity .
this observation 
 differs from the conclusions obtained in the solid state by taratula 
 et al . , which were however obtained in 
 the absence of other suitable guests . in our earlier 
 studies
, it was shown that the complexation of chloromethane changes 
 the probability distribution of the host conformers
. this has an effect on the chemical shifts in both the h and c spectra because they are the weighted averages 
 of the chemical shifts of all the conformers in fast exchange in solution . 

the exchange between the host conformers is always fast in the investigated 
 temperature range , as opposed to the guest exchange ( discussed above ) 
 which can be both fast and slow in this range . in the case of 
 cryptophane - a and cryptophane - but , the equilibrium constant for both 
 guests , chloroform and dichloromethane , is higher than in the case 
 of previously investigated compounds .
this means that , at low temperatures , 
 when the equilibrium is shifted toward complex formation , even at 
 low concentration of the guest ( 1:1 host : guest ratio ) the complexed 
 forms dominate the spectra . in order to investigate the influence 
 of complexation on the conformational distribution
, it is an advantage 
 to look at spectra with low guest concentrations , at least lower than 
 the total concentration of the host .
one way to create these conditions 
 is to work on samples containing more than one guest . for cryptophane - a , 

the h and c spectra of sample 1 ( cryptophane - a 
 containing solvents of purification ) at 240 k are shown in figures 5 and 6 . the h spectrum 
 of the solution containing 30 mm cryptophane - a , 
 8 mm chcl3 , 7 mm ch2cl2 , and 10 mm 
 ch3ch2oh in 1,1,2,2-c2d2cl4 ( sample 1 ) . the spectrum was recorded at 14.1 t and 
 240 k. the capital letter a denotes the chcl3@cryptophane - a , 
 b the ch2cl2 complex , and c the ch3ch2oh complex .
the c spectrum of the solution containing 30 mm cryptophane - a , 
 8 mm chcl3 , 7 mm ch2cl2 , and 10 mm 
 ch3ch2oh in 1,1,2,2-c2d2cl4 ( sample 1 ) .
the spectrum was recorded at 14.1 t and 
 240 k. the capital letter a denotes the chcl3@cryptophane - a , 
 b the ch2cl2 complex , and c the ch3ch2oh complex .
nevertheless , one can see three sets of signals for the three 
 complexed forms of the host .
the chloroform complex is labeled with 
 the capital latter a , the dichloromethane complex with b , and ethanol 
 with c. both spectra are very informative . at this temperature ,
the 
 free peaks of the guest are too small to allow reliable integration 
 or not even observable .
this is not a surprise for chloromethanes , knowing the high affinity 
 of the host to these guests .
. it can be further 
 seen in figure 5 that the chloroform complex 
 has only one peak for the linker protons ( figure 5 , peak ( a)1,2 ) , in contrast to the other guests 
 which have two peaks for the linker protons ( figure 5 , peaks ( b , c)1,2 ) .
the two proton 
 peaks in the case of other guests are dipolarly coupled to each other 
 ( cross - relaxed by each other ) , according to noesy and roesy spectra 
 ( see below ) .
it can 
 be seen that the difference between protons 3 and 6 is the biggest 
 in the case of the chloroform complex and the smallest in the case 
 of the ethanol complex . in figure 6 , 
 the c spectrum 
 of the same sample is shown .
it is also possible to see here three 
 separate sets of peaks for the three complexes ( figure 6 , peak sets a , b , c ) .
the spectrum shown here is a proton - decoupled c spectrum which is easy to interpret ; every peak represents 
 a chemically and magnetically nonequivalent site in the molecule in 
 question .
the peak of the 
 methoxy group is shifted upfield going from ethanol to chloroform 
 guest ( figure 6 , peaks ( a)m , ( b)m , and ( c)m ) . 
 the opposite behavior is true for the linker carbons .
the signals 
 belonging to the linkers are shifted downfield , and the chloroform 
 complex has the highest chemical shift value . as in the case of the 
 proton spectrum , the difference between the signals of the aromatic 
 carbons is the highest in the case of the chloroform complex and the 
 lowest in the case of the ethanol complex . if a high excess of chloroform 
 ( host : chloroform = 1:6 , sample 2 ) is added to the same solution , it 
 will  push  the other guests out of the cavity and the 
 free guest peaks are observable again ( see the supporting information ) . figures 7 and 8 show the h and c spectrum 
 of solution number 11 for the cryptophane - but complexes . the h spectrum of the solution containing 10 mm cryptophane - a , 
 9 mm chcl3 , and 6.5 mm ch2cl2 in 
 1,1,2,2-c2d2cl4 ( sample 11 ) .
the 
 spectrum was recorded at 16.5 t and 250 k. the capital letter a denotes 
 the chcl3 and b the ch2cl2 complex .
the c spectrum of the solution 
 containing 10 mm cryptophane - a , 
 9 mm chcl3 , and 6.5 mm ch2cl2 in 
 1,1,2,2-c2d2cl4 ( sample 11 ) .
the 
 spectrum was recorded at 16.5 t and 250 k. the capital letter a denotes 
 the chcl3 and b the ch2cl2 complex . in this case , the sample does 
 not contain any ethanol but only 
 dichloromethane and chloroform in close to equimolar amount . both 
 spectra show exactly the same behavior concerning the chemical shift 
 changes as in the previous case . by calculating the chemical shift 
 differences of the aromatic carbon signals 3 and 6 (  = 3  6 ) , together with the full width 
 at half - height ( fwhh ) of carbons 1 , 3 , and 6 for the two hosts 
 ( see the supporting information ) , it can 
 be seen that the signals at low temperatures are broadened by both 
 conformational exchange of the hosts and the exchange of the guest . 
 by increasing the temperature
this is due to the increasing amount of noncomplexed 
 host , characterized by smaller -values . at temperatures higher 
 than 275 k ,
the peaks start to broaden again and , in the case of chloroform 
 complexes , the peaks broaden into the baseline and further analysis 
 is very difficult .
the spectra displayed in figures 7 and 8 ( sample 11 ) were recorded 
 at 250 k. in the h spectrum ( figure 7 ) , it can be seen 
 that the position of the bound ch2cl2 peak is 
 very close to signal number 4 and other impurities , making , 
 unfortunately , the integration difficult .
nevertheless , one can try 
 to fit a lorentzian to the peaks and extract information on the concentration 
 ratio between bound and free ch2cl2 , because 
 in this case not only the quantitative information is useful .
the 
 quantitative information can be used to get a better picture of the 
 affinity of the host .
one can see that the ratio [ hg]/[g ] = kfb / kbf is much lower than that in table 2 .
this is the effect of having two guests present 
 at the same 
 time .
the data in table 6 indicate that the 
 affinities of cryptophane - but to both chloromethanes are rather similar . the experimental information provided by the simple spectra is 
 not sufficient to draw a definite conclusion on the type of conformers 
 preferred by the different guests .
in order to give a more detailed 
 answer , one needs to look at the structure and symmetry properties 
 of the conformers . in the case of cryptophane - a , the quantum chemical 
 optimization was done previously by brotin et al .
the present study complements that work by reporting also 
 the chemical shifts of the c sites in the conformers . 

moreover , an attempt to correct the calculated energies with the van 
 der waals contribution is performed here . 
 as it was described in detail earlier
the all - trans conformers for cryptophane - a and cryptophane - but are shown in figures 1 and 2 , respectively .
there 
 are two types of trans conformers ( both characterized 
 by the -o-1-2-o- dihedral angle close to 180 ) 
 which differ in the relative orientation of the bond connecting carbons 
 1 and 2 with respect to the methoxy or butoxy groups 
 on the ctb rings .
this means that there is no chemical shift difference between carbon 
 number 1 and 2these nuclei become symmetry - equivalent . 

a complication occurs when chcl3 enters the cavity : since 
 it belongs to the c3v symmetry group , it reduces the symmetry of the complex to c3 .
there are two basic types 
 of gauche conformers , denoted g+ and g , with the only 
 difference in the sign of the -o-1-2-o- dihedral angle 
 ( + 60 , 60 ) .
this 
 means that the equivalence of the linker carbons no longer holds : 
 they have different chemical shifts .
additionally , there are also 
 two types of g+ and g conformers , which are denoted g+,g+b , g , and g  b . 

the difference between the conformers with and without subscript  b  
 is the orientation of the linker 12 bond with 
 respect to the methoxy groups and , more importantly , to the other 
 linkers .
the three linkers can take different conformations independently 
 of each other , which results in a large number of possible species . 

g conformer , 
 and the green framework depicts the g  bg  g. the g 
g conformer is 
 the molecule with black colored carbons , while the green molecule 
 is the g 
bg  g. because of the 
 equivalence of the caps , if one exchanges all the linkers from g,+ to g,+b , one gets back the original conformer ; this means that the all - gauche conformers are pairwise equivalent ( e.g. , g  bg  bg  b = g  g  g )
. the gauche conformers have one very important 
 and useful property in common : the linker carbons are nonequivalent 
 and their chemical shifts are different .
b denotes 
 a conformer optimized with a methoxy dihedral of around 110. 
 the calculated shifts for the individual carbons differ by a few tenths 
 of a ppm . here
, the average values are given . as it can be seen in the table , when the gauche conformer changes to gauche b , the chemical shifts 
 of the corresponding carbons 1 and 2 exchange places . 

this would not cause any complication , if the exchange of the linkers 
 was synchronized , meaning that they only change simultaneously .
this 
 is not the case and the dynamics of the linkers can average the chemical 
 shift to only one single peak , even if the symmetry of the conformers 
 is only c3 .
the chemical shifts and homonuclear j - couplings between the linker protons ( there are four of them in 
 each linker , with in principle different shifts and coupling , but 
 they show up as two multiplets ; see , e.g. , figure 5 ) are not averaged out for the dichloromethane ( and ethanol ) 
 complex .
the observed chemical shifts for the proton - carrying 
 aromatic carbons 
 also display conformation dependences .
the situation of the chemical 
 shifts of carbons 3 and 6 is more complicated , because of the close 
 vicinity of the methoxy groups to number 6 .
the one with lower energy corresponds to the methoxy 
 groups in the plane of the aromatic rings , with the dihedral angle 
 ( 6 - 1-o - m ) around zero .
when the same dihedral is around 110 , 
 the methoxy group points out of the plane of the aromatic ring .
the 
 energy difference between these two methoxy group conformers is only 
 about 6 kj / mol , more or less independent of the linker conformation . 

the dynamic behavior of the methoxy groups plays an important role 
 both in the kinetics of the complexation ( as discussed in the case 
 of cryptophane - c ) and in the chemical shift of the carbon 
 number 6 .
the calculated chemical shifts and the difference between 
 them are shown in table 7 .
there are 
 two important conclusions that can be drawn looking at 
 table 7 .
the first is that the chemical shift 
 difference between carbons 3 and 6 decreases going from the all - trans conformers to the all - gauche conformers . 

the second conclusion is that the orientation of the methoxy groups 
 affects this difference dramatically .
namely , in the case of trans and gauche conformers , 
 the order of the peaks ( the sign of the -value ) is reversed . 
 in the case of gauche+ ,
, 
 it is known that the order of the peaks 3 and 6 in the carbon spectrum 
 is never exchanged .
the explanation of this observation is that it 
 almost never happens that all six of the methoxy groups are oriented 
 with a dihedral angle of 110. this , in turn , has an 
 effect on the kinetics of the complex formation , since the reaction 
 can only occur when two methoxy groups on the opposite sides of a 
  cavity window  point out of the aromatic plane .
this 
 is shown in figure 10 , where the conformer g  g  g is displayed in the van der 
 waals representation when two methoxy groups on the opposite sides 
 have a dihedral angle of zero ( figure 10a ) 
 and 110 ( figure 10b ) .
( a ) the molecule 
 with the 6 - 1-o - m dihedral angle close to zero , blocking the exit . 

( b ) the molecule with the 6 - 1-o - m dihedral angle close to 110 , 
 out of the way .
it can be seen that 
 it is not possible for chcl3 to 
 exit when the methoxy groups block the way . as anticipated above , 

this increased steric hindrance can be seen as the origin of the slower 
 dynamics of both guests@cryptophane - a compared to cryptophane - c .
cryptophane - but is a larger molecule , and the dft calculations 
 are time - consuming . due to this ,
the chemical shifts of only three 
 noncomplexed ( g+g+g+ , t1t1t1 , t2t2t2 ) and two chloroform - complexed ( g+g+g+ , t1t1t1 ) conformers were calculated ( see the supporting information ) .
the shift difference between the 
 proton - carrying aromatic carbons is highest in the case of the trans conformer and lowest in the case of the gauche conformer .
the chemical 
 shifts of the linker carbons are moved downfield ( to higher shift 
 values ) , if the trans character of the complex increases , 
 and the shift difference ,  , between the aromatic carbons also 
 increases .
however , with this information at hand , it is still not 
 possible to decide which trans conformer is preferred 
 by the complex .
the only conclusion possible to draw is that the trans character increases in the case of binding of both 
 chloromethane guests .
one possible help to decide which trans conformer 
 is preferred by the complex can be provided by the dft - calculated 
 energies of the different complexes .
the problem with the energies 
 is that they are basis - set - dependent and that the contribution coming 
 from the dispersion correction is an empirical estimate .
first , there are two energy values coming from the small and large 
 basis set and containing only the zero point correction and the thermal 
 contribution ; in addition , there are the energies containing the dispersion 
 contribution . from the relative energies of the noncomplexed cryptophane - a 
 conformers with respect to the lowest values within the respective 
 approximation level ( see the supporting information ) , it can be seen that there are big differences between different 
 calculations . in the case of no dispersion correction ,
the minimum 
 occurs at the t1t1t1 conformation with both basis 
 sets and the dispersion - corrected energies have their minimum at the g
, one can calculate the probability distribution 
 of the conformers and weight the calculated chemical shifts with it . 

the calculated weighted average -values for the small 
 and large basis set are 11.6 and 10.6 ppm , respectively , which does 
 not match with the measured values . calculating the weighted chemical 
 shifts in the same way , but using the dispersion - corrected energy 
 data , one obtains 6.7 and 6.5 ppm .
one has to keep in mind that in reality 
 there was never any noncomplexed cryptophane - a in the solutions studied . 

the situation is more complicated in the case of chcl3@cryptophane - a and chcl3@cryptophane - but complexes .
first , 
 as it was mentioned before , all the gauche conformers 
 have at most c3 symmetry .
this also means 
 that there is a difference in energy , dependent on the orientation 
 of the chloroform molecule within the cavity .
the two possible orientations of chcl3 inside the cavity 
 of the g  g  g conformer of 
 cryptophane - a .
it is also possible 
 to change the linkers to gauche+b conformation 
 and let the orientation of chloroform 
 to remain unchanged .
this complication arises only because the chloroform 
 molecules can not turn around in the cavity ( see relaxation data above ) . from the energies of the chloroform - complexed cryptophane - a (
see 
 the supporting information ) , it can be 
 seen that , without the dispersion correction , a minimum occurs at 
 the t2t2t2 with the small basis set and at the g  bt1t1 conformer with the large basis set . for the 
 dispersion - corrected data ,
looking at the probability - weighted sum 
 of the chemical shift differences between the proton - carrying aromatic 
 carbons 3 and 6 , one obtains similar values as before : 11.3 and 10.5 
 ppm without the dispersion correction and 10.5 and 8.6 ppm with the 
 dispersion correction .
it is thus confirmed again that the complexation 
 of chloroform will increase this difference , but still it is not possible 
 to select the preferred conformers .
so far , the 
 only conclusion that can be drawn is that some guests prefer different 
 conformations of the host .
thus , guests can either fit into major 
 or minor states of the host .
the main concern is that , due to a fast 
 conformational exchange of the host ( see above ) , minor states are 
 not observable on the recorded spectra .
only a set of peaks corresponding 
 to an average of these major and minor states is detectable . in order 
 to get more information on this conformational or chemical exchange , 
 the c cpmg relaxation methodology , which 
 allows one to characterize physicochemical parameters of systems under 
 conformational exchange , was applied on sample 12 .
as observed in 
 figures 12 and 13 , the 
 transverse relaxation rate r2 of the linkers 
 ( singlet peak for carbons 1 and 2 , as seen in figure 6 ) and of the aromatic carbon 6 varies as expected 
 with the repetition rate cpmg ( = 1/(2cpmg ) ) , indicating the presence of dynamical processes occurring 
 in the micro- to millisecond range .
c relaxation dispersion 
 curves obtained for the cryptophane - a 
 linkers ( triangles ) and the aromatic carbon 6 ( lozenges ) at 298 k 
 ( sample 12 ) .
filled symbols , transverse relaxation rates r2 obtained at 14.1 t ; empty symbols , transverse relaxation 
 rates r2 obtained at 16.5 t. c relaxation dispersion curves obtained for 
 the cryptophane - a 
 linkers ( triangles ) and the aromatic carbon 6 ( lozenges ) at 310 k 
 ( sample 12 ) . filled symbols , transverse relaxation rates r2 obtained at 14.1 t ; empty symbols , transverse relaxation 
 rates r2 obtained at 16.5 t.
the two - field dispersion data obtained at 14.1 
 and 16.5 t for both 
 linker and aromatic carbons were fitted according to the luz 
meiboom 
 equation for a two - site fast exchange:7where r20 is the transverse relaxation 
 rate in the absence of exchange , pmajor is the relative population of the major state in exchange ,  
 corresponds to the resonance frequency difference between the spins 
 in the major and minor states , and texch is the exchange time between the two states .
of course , the assumption 
 of a two - site exchange is probably an oversimplification , but this 
 model , which is usually the first employed for analyzing experimental 
 data , is adequate for having an estimation 
 of the parameters of interest . in order to get accurate parameters ,
the two - field dispersion curves were fitted 
 simultaneously for each 
 case ( linker and aromatic carbons ) by using a nonlinear least - squares 
 fitting procedure .
the thermodynamic parameter pminor ( = 1  pmajor ) , the 
 structural parameter  , the kinetic parameter texch , and the relaxation rate in the absence 
 of exchange r20 deduced from the fitting of the c transverse dispersion curves are listed in table 8 for the two fields and the two temperatures investigated . at 16.5 t ,
 
 corresponds 
 to ( 16.5/14.1 ) times the value obtained at 14.1 t. errors are deduced 
 from monte carlo iterations . considering the calculated errors , the results obtained for the 
 linker and the aromatic carbons are quite similar as expected , showing 
 the reliability of the method . in both cases , the population of the 
 minor state is not affected by the temperature .
the value found for pminor is around 0.05 , indicating the presence 
 of a low - populated state .
the exchange time texch is in the millisecond range , and the exchange rate , defined 
 as ( 1/texch ) , is increasing with temperature , 
 agreeing with the arrhenius equation .
concerning the exchange - free 
 relaxation rate r20 , it varies only little with the changes of 
 temperature and field , with the transverse relaxation of the aromatic 
 carbon being slightly faster . according to the  values 
 found for the linker and the aromatic carbons , the cryptophane - a minor 
 state ( if it would be visible on the spectrum ) should appear a few 
 thousand hertz away ( roughly 67 ppm at 298 k and 810 
 ppm at 310 k ) from the peaks corresponding to the major state . by 
 comparing these results to those obtained by quantum chemical calculations 
 ( see table 7 ) , one can see that the  
 values are consistent with the calculated chemical shifts when going 
 from the trans conformers ( which should correspond 
 to the major state ) to the gauche conformers ( which 
 could be attributed to the minor state ) .
the analysis of the c 
 relaxation dispersion curves revealed that a fast conformational exchange 
 is occurring in the complexed cryptophane - a system . to complete this 
 study and to give a possible solution of the above - mentioned conformational 
 problem , it is relevant to measure the cross - relaxation rates between 
 the linker protons and the aromatic proton number 3 .
after this , one 
 can make comparisons with the distances from the dft - optimized conformer 
 structures : the cross - relaxation rates are proportional to the inverse 
 sixth power of the corresponding proton 
one 
 can see that a high cross - relaxation rate is expected in the 
 case of the gauche conformers , since the distances 
 are the shortest there .
it is interesting to notice that , in the case of dichloromethane 
 complexes , there are no big differences between the two peaks in the 
 spectrum .
however , there is a big difference between the ch2cl2 and chcl3 complexes in cryptophane - a .
the 
 cross - relaxation rate decreases by half in the case of the chloroform 
 guest .
this suggests that 
 the conformational changes are much smaller in the case of the latter 
 host .
this is also indicated in the spectra : there are always two 
 peaks in the proton spectra of cryptophane - but , and the chemical shift 
 difference between carbons 3 and 6 is also smaller .
looking at the 
 cross - relaxation data at 258 k ( the same temperature as used in cryptophane - c 
 measurements ) , it can be noted that the 
 cross - relaxation rates in ch2cl2@cryptophane - c 
 are by a factor of 4 smaller .
the small cross - relaxation rate of chcl3 means 
 that probably the t1t1t1 conformer is preferred 
 over the t2t2t2 .
the high cross - relaxation rates of 
 the chcl3 guest with both hosts ( cryptophane - a , cryptophane - but ) 
 are very surprising and shed light on the possible problems with dft 
 calculations , namely , that the optimized structures are static and 
 the systems are not . consistently with the carbon-13 relaxation data , 
 chloroform can be thought of as moving in a cone inside the cavity . 

it is impossible that one measures such a high cross - relaxation 
 rate at this distance . in reality
this also means that the position of chloroform predicted by dft is 
 not fully correct .
this can , in turn , perhaps be traced back to the 
 lack of van der waals contribution during the geometry optimization 
 procedures .
the investigation of 
 chloromethanes@cryptophane with the help of 
 different nmr methodologies sheds light on the complexation process . 
 besides the fact that the chloromethane and the cryptophane diffuse 
 as a single entity , it was also proven that a conformational variability / selection 
 of encapsulation of chloromethane guests into the host cavity is also 
 occurring
this phenomenon , already observed on variable temperature 
 spectra , was studied further by dft calculations and cpmg relaxation 
 dispersion .
these techniques gave structural information about the 
 host but also allowed the determination of both kinetic and thermodynamic 
 properties related to the conformational changes of the host .
nevertheless , 
 the results obtained in this study for the solution state differ from 
 the previously proposed induced fit model by taratula et al . in the 
 solid state .
both the conformations of the methoxy 
 groups and of the linkers play an important role in the case of cryptophane - a 
 guest encapsulation , as in the case of cryptophane - c .
this model was 
 supported by the dynamical measurements of guest exchange and the 
 activation energies .
moreover , the conformational changes of the host 
 are different from those experienced in cryptophane - c . here
, the trans character plays an important role in the case of cryptophane - a , 
 which can be caused by the methoxy groups being too close to each 
 other when lying in the plane of the aromatic rings , which is their 
 most stable position . in the case of cryptophane - but , the gauche character of the linkers
is more pronounced and , 
 as shown in the proton and carbon spectra , there is less change experienced 
 by the host upon complex formation . both hosts have a surprisingly 
 high affinity constant to chcl3 , compared to other cryptophane 
 hosts .
this can be explained by the volume differences of the conformers . 
 in the case of cryptophane - c ,
the gauche conformers 
 were more populated , while the trans conformers are 
 more important in the case of cryptophane - a .
however , 
 it should be noted that the explanation of the thermodynamic stability 
 by the cavity size does not work in the case of cryptophane - but .
it 
 does explain the difference between dichloromethane complexes but 
 not that between the chloroform encapsulation in various hosts .
the 
 stabilities of the chloroform complexes are very similar which is , 
 at the present stage of the research , surprising and requires more 
 investigation .
 host  guest 
 complexes between cryptophane - a as host and dichloromethane 
 and chloroform as guests are investigated using 1h and 13c nmr spectroscopy . 
 moreover , a related cryptophane , with 
 the methoxy groups replaced by butoxy units ( cryptophane - but ) , and 
 its complexes with the same guests were also studied . 
 variable temperature 
 spectra showed effects of chemical exchange between the free and bound 
 guests , as well as of conformational exchange of the host . 
 the guest 
 exchange was studied quantitatively by exchange spectroscopy or line 
 shape analysis . 
 extraction of kinetic and thermodynamic parameters 
 led to the characterization of the affinity between guests and hosts . 
 on the other hand , 
 the host exchange was investigated by means of 13c carr  purcell  meiboom  
 gill ( cpmg ) relaxation 
 dispersion which aims at the determination of the transverse relaxation 
 rate r2 , the inverse of the transverse 
 relaxation time t2 , as a function of the 
 repetition of the  pulses in a cpmg train . 
 the variation of 
 the measured transverse relaxation rate with the repetition rate cpmg indicated conformational exchange occurring on the microsecond  
 millisecond 
 time scale . 
 structural information was obtained through measurements 
 of cross - relaxation rates , both within the host and between the host 
 and the guest protons . 
 the nmr results were supported by dft calculations . 
Introduction
Experimental Section
Results
Conclusions