in monolayer - protected gold clusters ( mpcs ) with gold cores of diameter < 1.6 nm the number of au atoms is sufficiently small to make them display molecular features .
instrumental to these studies has been the possibility of preparing molecule - like gold mpcs in an atomically precise form , as assessed by mass spectrometry and single - crystal x - ray crystallography .
the structure of au25(sr)18 clusters , by far the most well known among molecular clusters , is based on a 13 gold - atom icosahedral core surrounded by 6 au2(sr)3 units , with minor differences induced by the charge state ( 1 , 0 , and + 1 ) and the ligands , even when the linear polymer ( au25)n forms .
several molecular features of au25(sr)18 clusters have been studied in detail , such as the characteristic electrochemical behavior and charge - dependent optical and nuclear magnetic resonance ( nmr ) patterns .
studies of their photophysical behavior , chirality , electron - transfer and redox - catalysis properties , have been described .
several theoretical studies have been carried out and reviewed . whereas the as prepared anionic cluster au25(sc2h4ph)18 
  is a diamagnetic species , the corresponding
the effect of the unpaired electron was detected by h and c nmr at room temperature or electron paramagnetic resonance ( epr ) at temperatures typically lower than 100 k. the jin 's group showed that the magnetic state can be switched off by reduction to diamagnetic au25(sc2h4ph)18 
 .
similarly , we demonstrated by both nmr and epr that oxidation to cation au25(sc2h4ph)18 
  generates a diamagnetic species .
dft calculations indicated that the magnetic behavior is controlled by significant splitting of the relevant orbital energy levels . 
 
the nmr spectrum of the three charge states evidenced very profound charge - induced variations in the position and shape of the peaks .
most notably , some of the ligands ' resonances undergo a significant downfield shift upon formation of paramagnet au25(sr)018 .
this was first observed by the murray 's group and then perfected by us through identification of all resonances as a function of temperature or ligand type . in this context , it is important to stress that the 18 thiolated ligands present in the 6 au2(sr)3 half - crowns ( or staples ) capping the central au13 core split into a group of 12 inner and a group of 6 outer ligands . here
, inner refers to the fact that the two terminal sr groups of (sr)au(sr)au(sr) also bind to au13 , whereas outer refers to the outmost , remaining thiolate of the half - crown .
1d and 2d nmr analysis allowed distinguishing between the two ligands ' families , also on a quantitative basis . there is a general consensus that the properties of molecular mpcs mostly depend on the number and relative position of the gold atoms . on the other hand , nmr evidence and corresponding dft calculations indicated that the singly occupied molecular orbital ( somo ) spreads onto the first groups of the thiolated ligands .
very recent studies also concluded that the ligand structure / composition can be a factor affecting the optical behavior of molecular and larger mpcs .
these results thus indicate that the highest occupied and the lowest unoccupied mos ( homos and lumos ) are not just limited to the au13 core , as often implicitly assumed , but rather involve to some extent the ligands .
another example is provided by the optical spectrum of au25 capped by thiophenolate - type ligands , which shows band shifts and a small decrease of the homo 
lumo gap compared to that of au25 capped by alkanethiolates , for which the spectrum does not depend on the ligand length : this effect shows that changing the carbon type at the  position to sulfur affects the electronic properties of the cluster . the way by which the capping ligands interact with the core , the shape and spreading of the chemically relevant orbitals , and the actual environment experienced by molecules or ions penetrating the monolayer are expected to be crucial factors also for understanding the catalytic effects of ultrasmall clusters on a truly molecular basis .
very recently , we illustrated the remarkable potentialities of pulse electron nuclear double resonance ( endor ) .
this technique is a very sensitive way of performing endor and is meant to characterize hyperfine coupling ( a ) between an unpaired electron and nuclei nearby .
this interaction consists of isotropic and anisotropic parts : the former is a through - bond contribution that depends on the number and type of bonds involved , whereas the latter depends on both through - bond and through - space ( electron - dipole / nuclear - dipole ) interactions . in the endor spectrum ,
a doublet of lines is associated with a magnetic nucleus with nuclear spin i = 1/2 .
when a < 2 , where  is the nucleus larmor frequency , the doublet is centered at  and the separation between the two lines is a. on the other hand , for a > 2 the doublet is centered at a/2 and the separation between the two lines is 2. the larmor frequency  depends only on the magnetic field b at which the endor spectrum is recorded , according to the relation  =  

i 
 b/(2 ) , where  
 i is the nucleus gyromagnetic ratio . for larger nuclear spins , such as for au
whose i = 3/2 , the quadrupolar and hyperfine interactions split the endor lines further .
the hyperfine interaction between the unpaired electron and the gold atoms could be assessed quantitatively , and the endor results could be nicely reproduced by density functional theory ( dft ) calculations , which could be particularly precise due to the very small thiolate used . here
, we describe a methodology and results that accurately enabled assessing the spin density and , therefore , the distribution of the somo in au25(sr)018 clusters .
we employed pulse endor to study the interaction of the unpaired electron with the protons of the alkanethiolate ligands , an approach that was never described before .
the resulting information was compared with that obtained by h nmr spectroscopy of how and how much the chemical shifts change when the charge state of the cluster is varied from 1 to 0 .
molecular dynamics ( md ) calculations provided useful hints in understanding differences between the endor and nmr results .
we noted that by reducing the temperature to 5 k , a pronounced increase of spin - polarization occurs .
it is thus shown that the unpaired electron can be used as a particularly sensitive probe of the main structural features of the interface between the metal core and the capping ligands , leading to establish a very precise and consistent picture of these complex systems .
the two new clusters , au25(spr)18 and au25(smepr)18 , were synthesized and oxidized along similar lines . 

h and c nmr spectroscopy measurements were carried out on 3 mm [ n - oct4n][au25(sr)18 
 ] or au25(sr)018 in benzene - d6 ( 100% , 99.96% d6 , aldrich ) .
we used a bruker avance dmx-600 mhz spectrometer equipped with a 5 mm tx-1 x , y , z - gradient powered , triple resonance inverse probe operating at 599.90 ( h nmr ) or 150.07 mhz ( c nmr ) . the temperature was controlled at 298 k with a bruker bvt-300 automatic temperature controller .
chemical shifts are in ppm units (  ) with reference to tetramethylsilane used as an internal standard for both h and c nmr .
the proton assignments were either already known or performed by 2d correlation spectroscopy ( cosy ) , total correlation spectroscopy ( tocsy ) , and nuclear overhauser enhancement spectroscopy ( noesy ) experiments .
c chemical shifts were obtained and assigned through heteronuclear multiple quantum coherence ( hmqc ) correlation experiments . for endor measurements , the samples consisted in 100 l of 0.5 mm au25(sr)018 in toluene .
each solution was introduced into the epr sample holder , a 3 ( o.d . )
 2 mm ( i.d . ) quartz tube , and degassed through freeze  pump  thaw cycles in a vacuum line and sealed at low pressure ( 5  10 torr ) .
the experiments were carried out at 5 k. h pulse endor measurements were carried out with a bruker elexsys e580 instrument equipped with a pulse endor dieletric probehead and an oxford cf935 cryostat .
we used the davies pulse sequence , with 160 ns microwave inversion pulse and 80160 ns pulse - sequence for electron - spin echo detection .
the radiofrequency pulse was 810 s long and amplified with a 150 w rf bruker amplifier .
the spectra were recorded at the top of the echo detected epr spectra ( approximately 290 mt ) , with a rf scan ranging from 1 to 20 mhz , where the proton peaks were expected .
the narrow spectral range and the long microwave pulses were chosen to spot and enhance endor lines from h with respect to au .
endor simulations were performed with a homebuilt program running on the open - source scilab-5.5.1 calculation package [ ; http://www.scilab.org ] .
the ligands were chosen to provide a progressive variation of the chain length from two to four carbon atoms , as shown in chart 1 .
the single crystal structures of the set and sbu protected clusters were available from previous work , whereas that of au25(spr)018 is described here for the first time .
the effect of branching was checked by changing a hydrogen atom with a methyl group at the  position : for this ligand , 2-methyl-1-propanethiolate , we will use the notation smepr to stress both methyl branching and that the fully extended chain length is the same as that of spr .
starting from sulfur , the carbon atoms and associated hydrogen atoms are defined as  ,  ,  , and  ; the second ch3 group of hsmepr is denoted as . monodisperse samples of the four au25(sr)18 
  clusters were prepared , and the clusters were oxidized according to a method already described .
full characterization of the purified neutral clusters was carried out by a combination of matrix - assisted laser desorption ionization time - of - flight mass spectrometry ( e.g. , fig .
s1 in esi ) , uv - vis absorption spectroscopy , differential - pulse voltammetry , and h nmr spectroscopy techniques . au25(spr)18 and au25(smepr)18 are new clusters .
1c ) in trigonal space group p3 , with three cluster molecules in the unit cell .
this mpc is highly symmetric with a 3-fold rotoinversion axis running through the central au atom . as for the other known au25(sr)18 structures ,
the 25 gold atoms can be regarded as being formed by two shells composed by an au13 icosahedral core , consisting of a central au atom with 12 au atoms directly interacting with it , and an outer shell of 12 au atoms bound to thiolate groups to form (sr)au(sr)au(sr) motifs ( fig .
it is worth noting that there is a significantly shorter auico  auico bond ( 2.7746  ) and a relatively longer auico 
concerning the orientation of the carbon chains with respect to the plane of the same half - crown , au25(spr)018 features the first case of a au25 cluster where only alternate orientations are observed . the space - filling model ( fig .
1b ) illustrates that the ligands are quite folded around the gold core , thereby forming a relatively thin monolayer , at least in the solid state .
evidence for the formation of quite thin capping monolayers was previously gathered also in solution , through electron - transfer measurements of a series of monodisperse au25(scnh2n+1)18 clusters with n varying from 2 to 18 .
of particular importance for the current investigation , from the structures of au25(set)018 , au25(spr)018 , and au25(sbu)018 we could calculate the average distances ( mediated over the six staples ) of the corresponding hydrogen atoms for both the inner and outer ligands . in this connection , it is worth noting that the average radii ( r 
 mpc ) of these three clusters nicely match those calculated from the stokes  einstein 
sutherland equation , d = k 
 b 
 t/6r 
 mpc , where d is the electrochemically determined diffusion coefficient , 
 k 
 b is the boltzmann constant , and  is the solvent viscosity : for au25(set)018 , au25(spr)018 , and au25(sbu)018 we find the couple of values 8.3 and 7.8 , 8.6 and 8.6 , 10.2 and 9.4  , respectively .
the 12 inner and the 6 outer ligands experience a different chemical environment and thus show distinct nmr spectroscopy signals .
when the cluster is in its paramagnetic state , differences are enhanced , especially for those resonances related to the proton and carbon atoms closer to the gold core .
we studied the spectra of the selected clusters in either charge state , using benzene - d 
 6 as the solvent .
2 illustrates for the case of au25(spr)18 the most salient differences in chemical shift as one goes from the paramagnetic to the diamagnetic states .
s2s4 ) and data are in esi. 
  the most significant effect of the one - electron oxidation of the native cluster is to shift downfield the nmr peaks pertaining to the protons in positions  ,  and  ( except for au25(set)18 , which has no  groups ) of the inner ligands , and in positions  and ( to a small extent )  of the outer ligands ; instead , the  protons of the outer ligands undergo an upfield shift . for the three clusters of known crystallographic structure , the chemical shift differences (  =  
 radical 
3 as a function of the average distance between the central au atom and the two or three hydrogen atoms of the specific resonance , averaged for the six half - crowns .
the positive differences roughly obey an exponential dependence on distance ( taking into account the error on the latter ) , as already commented upon for au25(sbu)18 . as to au25(smepr)18
the nmr shifts observed upon changing the charge state from 1 to 0 are related to the contact interaction of the nuclear magnetic moments with the unpaired electron , and can thus be taken as a measure of how far the spin density spreads outside the au13 core . 
  the  values can be used to estimate the isotropic hyperfine coupling constant a according to the relationship ( eqn ( 1 ) ) : 
 1 = ages(s + 1)/(3ikbt)where  is the reduced planck constant ,  
 e is the bohr magneton ,  
 i is the proton nuclear gyromagnetic ratio , and g is the isotropic g value for the unpaired electron .
the latter can be exactly calculated as g = ( g 
 xx + g 
 yy + g 
 zz)/3 , where g 
 xx 
 , g 
 yy , and g 
 zz are the main values of the g - tensor . for au25(sbu)018 , they are 1.78 , 2.40 , and 2.56 , respectively , and the same values are found for au25(set)018 : therefore , we used these values also for the other clusters . by using these values and 298 k ,
 can be expressed as 29.74 ( ppm mhz )  a ( mhz ) .
we note that eqn ( 1 ) holds true provided the pseudo - contact contribution to the chemical shifts of the ligand protons is negligible ; this is indeed supported by the remarkable agreement observed between nmr chemical shifts and dft calculations of the electron spin - density . 

table 1 shows the so - calculated a values . 
 from nmr measurements at 298 k , using eqn ( 1 ) . 
 from endor measurements at 5 k. 
 the error associated with the simulations is ca . 0.1 mhz . 

t 
 xx , t 
 yy , and t 
 zz are the main values of the anisotropic hyperfine tensor . 

endor experiments were carried out at 5 k in frozen solutions of 0.5 mm au25(sr)018 in toluene .
4 ) show a large background between 2 and 20 mhz due to an endor line of gold atoms . by focusing on the region between 8 and 16 mhz , as shown in fig . 5 for au25(sbu)018
, one can notice the presence of three symmetrical line doublets centered at the larmor frequency . at a magnetic field of 0.29 t , which is the field at which endor spectra were acquired , the larmor frequency is 12.34 mhz for the protons .
the three symmetric doublets are marked by brown ( outer ) , green ( middle ) , or black ( inner ) lines .
similar endor spectra are observed for the other clusters capped by linear - chain thiolates , but the relative intensity ratios are different . the simplest case to analyze is au25(set)018 .
the two proton types and the two ligand families generate four groups of equivalent protons : 24 ( -ch)in , 36 ( -ch)in , 12 ( -ch)out , and 18 ( -ch)out
three doublets of lines are clearly observed and positioned symmetrically around the larmor frequency , whereas a broad line is observed at ca .
the latter could be attributed to the low - frequency part of a doublet of lines pertaining to the most strongly coupled protons . however , the corresponding high - frequency component , which should occur at ca .
furthermore , in the region around 3 mhz hyperfine couplings from c nuclei could also contribute .
this makes uncertain the attribution of this feature to a proton line . for au25(set)018 , the average crystallographic distance between the alkanthiolate protons and the central gold atom increases in the order 6.27 ( -ch)in , 6.92 ( -ch)in , 7.23 ( -ch)out , and 8.26  ( -ch)out . the ( -ch)in protons are closer to the gold cluster than the other protons and , therefore , they should give rise to the most strongly coupled doublet . in the hypothesis the 3 mhz line is a proton line , this could be related to the ( -ch)in , in keeping with the aforementioned nmr results .
however , the endor lines of the ( -ch)in protons could be simply undetectable , which is indeed not unusual for strongly coupled nuclei .
the ( -ch)out protons are located at the largest distance from the center of the au core and the inner lines are thus attributed to them .
the distances characterizing the ( -ch)in and ( -ch)out proton groups are quite similar , in the solid state at least , and thus a direct assignment is difficult
. this problem can be addressed by simulation of the endor outer , middle and inner doublets .
s6 ) by using the parameters shown in table 1 , in which a ratio of 36  :  12 for the intensity of the outer and middle doublets is considered .
the position of the doublets is also in agreement with the crystallographic relative distances from the central au atom , which for this cluster are 6.92 vs. 7.23  .
this allows assigning the outer , middle and inner doublets to ( -ch)in , ( -ch)out , and ( -ch)out , respectively . regarding the ( -ch)out protons
, the simulation provides a number , 14 , that does not fully agree with that expected , 18 .
for weak couplings , however , some differences are not unusual because the endor selectivity effect reduces the endor line intensity , whereas the presence of the proton - free larmor line ( a single line associated with the solvent protons ) could contribute to the inner doublet by increasing the line intensity . depending on the prevailing effect , either a decrease or an increase in intensity may occur . for the other clusters
, we assign the ( -ch)in and ( -ch)out doublets as for au25(set)018 ; for ( -ch)in , the above considerations about the broad peak at 3 mhz are also valid .
the crystallographic distances of the ( -ch)in and ( -ch)out groups from the cluster 's center are similar , i.e. , 7.23 and 7.16  ( au25(spr)018 ) , and 7.16 and 7.28  ( au25(sbu)018 ) , respectively .
in addition to the signals already discussed , the endor spectrum of au25(spr)018 is liable to show a contribution also from the 36 ( -ch)in , whose average crystallographic distance is 8.35  , and thus shorter than that of the ( -ch)out protons , 8.64  ; a similar outcome is observed for au25(sbu)018 whose values are 8.12 and 8.20  , respectively .
however , we could still simulate the spectrum of au25(spr)018 well ( esi , fig .
s7 ) by using for the outer and middle doublets an endor intensity ratio of 24  :  12 , which corresponds to the number of equivalent ( -ch)in and ( -ch)out protons . apparently , no ( -ch)in protons need to be taken into account .
in fact , according to the nmr results , the ( -ch)in protons could have a hyperfine coupling smaller than that of the ( -ch)out protons but still detectable .
however , the room - temperature nmr data can not be directly compared with the low - temperature endor data . at room temperature ,
the random motion of the alkyl chain is fast , with the ( -ch)in atoms moving often closer to the metal core than the ( -ch)in atoms , but nmr spectroscopy only probes the average contact shift . electron - transfer and diffusion - coefficient measurements provided evidence for the ligand chains being quite mobile in solution ; for example , the d values yield r 
 mpc values smaller than the average radius of the same clusters as calculated from the crystallographic structure . at 5 k , however , whereas the ligands ' motion is very limited by the frozen glassy solution , ( -ch)in can still be present in different conformations .
it is thus conceivable that the endor doublet of the ( -ch)in protons is associated with a wide conformational distribution ( larger than that experienced by the - and , even more , the -groups ) and this would cause significant line broadening and thus spreading of the signal under the outer and middle doublets . to shed further light onto this issue , it is useful to compare the endor spectra of au25(spr)018 and au25(smepr)018 ( fig .
whereas in the latter there are 72 ( -ch)in protons that can contribute to the spectrum , the ( -ch)in and ( -ch)out protons are only 12 and 6 , respectively , i.e. , one half than those in au25(spr)018 . fig .
6 shows that in au25(smepr)018 the endor lines of the outer doublet are indeed significantly smaller than those of au25(spr)018 , and this confirms that for all clusters the outer doublet is consistently associated with the ( -ch)in protons .
this increase is attributed to a strong contribution from the ( -ch)in protons : compared to those in au25(spr)018 , in au25(smepr)018 these protons have a narrower conformational distribution due to the steric hindrance introduced by the second methyl group .
hindrance not only makes these methyl groups less mobile but also the whole monolayer stiffer and thus the mpc radius larger .
support to this view comes from the electrochemical determination of the d value in dicholoromethane ( see esi and fig .
s5 ) and , thus , r 
 mpc value of au25(smepr)018 : they are 5.16  10 cm s and 10.3  , respectively , whereas for au25(spr)018 ( which has the same fully extended length but more fluid chains in the monolayer ) they corresponding values are 6.15  10 cm s and 8.6  . the simulation of the endor spectrum of au25(smepr)018 ( esi , fig .
the number of protons required to obtain the best fit to the inner signals is indeed significantly larger than 6 , which in this specific cluster corresponds to the particularly small number of ( -ch)out protons .
we note , however , that the average crystallographic distance for the ( -ch)out protons in au25(spr)018 and au25(sbu)018 is 8.9  and thus only slightly larger than for the ( -ch)out protons .
a weak coupling is thus expected also for the ( -ch)out protons : for au25(smepr)018 these protons are particularly numerous , 36 , and this could make their contribution to the inner endor lines quite significant .
this hypothesis is reasonable but not quantifiable also because of the aforementioned problems associated with weak couplings . regarding au25(sbu)018 ( fig .
5 ) , the most evident new feature is that the outer lines are higher than the middle lines .
however , the number of protons causing an endor line is related to the area , not to the line height . the simulation ( esi , fig .
s8 ) results in a ratio of 24  :  12 between the outer and middle lines , in agreement with the attribution of the outer line to ( -ch)in and the middle line to ( -ch)out ; the outer lines are just narrower than in au25(set)018 and au25(spr)018 . as for au25(spr)018
, conformational distribution would make the contribution of the ( -ch)in protons spread in the region pertaining to the outer and middle lines . as a matter of fact
, the stokes radius of this cluster , 9.4  , is smaller than that of the stiffer au25(smepr)018 cluster . regarding the ( -ch)out protons , the best fit to the inner lines
we believe that the reason is as already described for au25(smepr)018 , i.e. , a non vanishingly small contribution from the ( -ch)out protons .
the simulations of the endor spectra provide both the isotropic and the anisotropic hyperfine values . the latter
this interaction can be described by three main values , t 
 xx , t 
 yy and t 
 zz , called hyperfine tensor main values , which are specific for each nucleus . here , the axes x , y , z represent a main reference system whose origin is at the center of the electron spin - distribution ( in our case , the gold - cluster center ) .
the values of t 
 xx , t 
 yy and t 
 zz can be obtained by averaging spatially the dipole 
dipole interaction over the spin distribution , according to the following equation ( eqn ( 2 ) ) , exemplified for x:2where  
 0 is the vacuum permeability , r is the electron - nucleus distance , g 
 e is the electron g - factor , g 
 n is the nucleus g - factor , and  
 n is the nuclear magneton .
analogous equations hold for y and z. from these equations , it results that t 
 xx + t 
 yy + t 
 zz = 0 . if the spin - distribution is axially symmetric with respect the z direction , then t 
 xx = t 
 yy and the hyperfine tensor main values are t 
 xx = t 
 yy = t and t 
 zz = 2 t .
deviation from an axially symmetric distribution leads to a hyperfine tensor whose main values are [ t 
 xx , t 
 yy , t 
 zz ] with t 
 xx  t 
 yy . 

table 1 shows that the various proton types are consistently in the form [ t , t , + 2 t ] , except for ( -ch)in in au25(set)018 in which a [ t 
 xx , t 
 yy , t 
 zz ] form is observed , with a marked difference between t 
 xx and t 
 yy . with
all cautions already discussed , if we assume that the feature at 3 mhz is due to ( -ch)in protons , its a can be estimated to be around 1520 mhz .
this would be about one order of magnitude larger than the value pertaining to the ( -ch)out protons . in this connection
, it is worth recalling that dft calculations carried out for au25(sch2ch2ph)018 showed that the spin density at ( -ch)in is one order of magnitude larger than at ( -ch)out .
if we now compare the ( -ch)in and the ( -ch)out isotropic hyperfine couplings for alkanethiolates of increasing length ( table 1 , third column ) , we note an increase in the absolute value of a , particularly in the passage from et to pr .
this suggest that the ligands are not completely indifferent to the spin distribution in au25(sr)018 , and thus to the somo structure .
another aspect regards the sign of a. according to the theory , the isotropic hyperfine coupling with a nucleus is given by ( eqn ( 3)):3where  
  is the direct spin - density and  
  is the spin - polarized density . 

 
  is mainly contributed by the unpaired electron in the somo , whereas  
  is due to spin - polarization .
the latter results from the tendency of the unpaired electron to withdraw electrons with the same spin , because of the favorable exchange interaction , and vice versa .
if g 
 n is positive , which is true for protons , then a positive a is found for a dominant direct contribution from the somo , whereas a negative value is found if spin - polarization prevails . from the simulations , we obtain the sign with respect to [ t 
 xx , t 
 yy , t 
 zz ] , i.e. , the pattern of the doublet does not change if we were to revert both the sign of a and [ t 
 xx , t 
 yy , t 
 zz ] . however , if we assume that the anisotropic interaction is mainly dipolar , then the form of the anisotropic tensor main values is [ t , t , + 2 t ] with t > 0 , and thus the sign of a is determined as shown in table 1 .
consequently , a negative value in a is an indication that a is mainly determined by spin - polarization through bonds , with a small contribution from direct spin density on the proton nuclei from the somo orbital , according to eqn ( 3 ) .
we can thus speculate that the increase of |a| as one goes from et to bu is the result of a decreasing , positive contribution to the hyperfine coupling from the direct spin - density of the somo , suggesting again that in the et cluster spin - density is more diffuse toward the ligands than in the pr or bu cases .
we can now compare these a values with those obtained from nmr measurements and the dft - calculated spin density values obtained previously . 

table 1 shows that the endor parameters differ from those obtained from the nmr signals in two ways : ( i ) in endor , the absolute values of a are significantly larger than the equivalent nmr values : 1.32.1 log units , except for ( -ch)in in au25(smepr)018 whose value is 3.0  log units ; ( ii ) some of the signs are different .
previous comparisons between the a values obtained from nmr and endor measurements carried out in solution at the same or not very different temperature provided comparable values and the same signs for many radicals .
our nmr and the endor experiments , however , refer to very different conditions . in a previous comparison of this kind ( for an iron - sulfur cluster ) ,
similar nmr and endor values were obtained , but the possibility that a strong temperature difference could lead to different results was also commented upon . additionally , we note that compared to previous investigations focusing on quite rigid radical structures and without particularly heavy atoms , here we considered entirely new systems composed of a gold nanocore and many flexible ligands . to gain insights into this aspect , we performed ab initio md calculations by using the atom centered density matrix propagation molecular dynamics model ( admp ) , as implemented in gaussian 09 .
because a converged finite - temperature sampling is exceedingly computationally costly , we resorted to use a cluster model consisting of au7(sch3)6 , which is paramagnetic in the neutral state ( fig .
the model consists of a 6 au atom ring with a central gold core atom .
we performed 2 ps md simulations at 300 and 5 k with a time step of 0.001 fs .
snapshots were collected every 1 fs , for which we evaluated the isotropic fermi constant . despite its simplicity , the model contains protons with different values of a , ranging from negative to positive values .
7 ) come from the unpaired electron in the somo , whereas protons in groups 1 have negative values due to spin - polarization . at 300 k , thermal motion tends to reduce spin - polarization on group 1 , whereas at 5 k there is a sharp distribution with a peak value ( 0.35 mhz ) more negative than the peak value at 300 k ( 0.15 mhz ) .
this is in qualitative agreement with the endor results for ( -ch)out that show an overall decrease in the absolute value of a. close inspection of the md trajectories shows that at 5 k the rotation of the methyl groups is completely frozen in the global energy minimum , whereas at 300 k free rotations cause the direct effect of the spin electron and spin - polarization to roughly average out .
the experimental and theoretical results thus point to the emergence , at very low temperature , of a pronounced increase in spin - polarization .
these results , therefore , bring some rationale to the change in sign and magnitude observed by carrying out the hyperfine - coupling constant measurements at very different temperatures .
1c ) in trigonal space group p3 , with three cluster molecules in the unit cell . this mpc is highly symmetric with a 3-fold rotoinversion axis running through the central au atom . as for the other known au25(sr)18 structures ,
the 25 gold atoms can be regarded as being formed by two shells composed by an au13 icosahedral core , consisting of a central au atom with 12 au atoms directly interacting with it , and an outer shell of 12 au atoms bound to thiolate groups to form (sr)au(sr)au(sr) motifs ( fig .
these bonds correspond to average au  au bond lengths of 2.784 , 2.927 and 3.163  , respectively .
it is worth noting that there is a significantly shorter auico  auico bond ( 2.7746  ) and a relatively longer auico 
concerning the orientation of the carbon chains with respect to the plane of the same half - crown , au25(spr)018 features the first case of a au25 cluster where only alternate orientations are observed .
1b ) illustrates that the ligands are quite folded around the gold core , thereby forming a relatively thin monolayer , at least in the solid state .
evidence for the formation of quite thin capping monolayers was previously gathered also in solution , through electron - transfer measurements of a series of monodisperse au25(scnh2n+1)18 clusters with n varying from 2 to 18 .
of particular importance for the current investigation , from the structures of au25(set)018 , au25(spr)018 , and au25(sbu)018 we could calculate the average distances ( mediated over the six staples ) of the corresponding hydrogen atoms for both the inner and outer ligands . in this connection , it is worth noting that the average radii ( r 
 mpc ) of these three clusters nicely match those calculated from the stokes  einstein 
sutherland equation , d = k 
 b 
 t/6r 
 mpc , where d is the electrochemically determined diffusion coefficient , 
 k 
 b is the boltzmann constant , and  is the solvent viscosity : for au25(set)018 , au25(spr)018 , and au25(sbu)018 we find the couple of values 8.3 and 7.8 , 8.6 and 8.6 , 10.2 and 9.4  , respectively .
the 12 inner and the 6 outer ligands experience a different chemical environment and thus show distinct nmr spectroscopy signals .
when the cluster is in its paramagnetic state , differences are enhanced , especially for those resonances related to the proton and carbon atoms closer to the gold core .
we studied the spectra of the selected clusters in either charge state , using benzene - d 
 6 as the solvent .
2 illustrates for the case of au25(spr)18 the most salient differences in chemical shift as one goes from the paramagnetic to the diamagnetic states .
s2s4 ) and data are in esi. 
  the most significant effect of the one - electron oxidation of the native cluster is to shift downfield the nmr peaks pertaining to the protons in positions  ,  and  ( except for au25(set)18 , which has no  groups ) of the inner ligands , and in positions  and ( to a small extent )  of the outer ligands ; instead , the  protons of the outer ligands undergo an upfield shift .
for the three clusters of known crystallographic structure , the chemical shift differences (  =  
 radical 
3 as a function of the average distance between the central au atom and the two or three hydrogen atoms of the specific resonance , averaged for the six half - crowns .
the positive differences roughly obey an exponential dependence on distance ( taking into account the error on the latter ) , as already commented upon for au25(sbu)18 . as to au25(smepr)18
the nmr shifts observed upon changing the charge state from 1 to 0 are related to the contact interaction of the nuclear magnetic moments with the unpaired electron , and can thus be taken as a measure of how far the spin density spreads outside the au13 core . 
 
the  values can be used to estimate the isotropic hyperfine coupling constant a according to the relationship ( eqn ( 1 ) ) : 
 1 = ages(s + 1)/(3ikbt)where  is the reduced planck constant ,  
 e is the bohr magneton ,  
 i is the proton nuclear gyromagnetic ratio , and g is the isotropic g value for the unpaired electron .
the latter can be exactly calculated as g = ( g 
 xx + g 
 yy + g 
 zz)/3 , where g 
 xx 
 , g 
 yy , and g 
 zz are the main values of the g - tensor . for au25(sbu)018 , they are 1.78 , 2.40 , and 2.56 , respectively , and the same values are found for au25(set)018 : therefore , we used these values also for the other clusters . by using these values and 298 k ,
 can be expressed as 29.74 ( ppm mhz )  a ( mhz ) .
we note that eqn ( 1 ) holds true provided the pseudo - contact contribution to the chemical shifts of the ligand protons is negligible ; this is indeed supported by the remarkable agreement observed between nmr chemical shifts and dft calculations of the electron spin - density . 

table 1 shows the so - calculated a values . 
 from nmr measurements at 298 k , using eqn ( 1 ) . 
 from endor measurements at 5 k. 

t 
 xx , t 
 yy , and t 
 zz are the main values of the anisotropic hyperfine tensor . 

endor experiments were carried out at 5 k in frozen solutions of 0.5 mm au25(sr)018 in toluene .
4 ) show a large background between 2 and 20 mhz due to an endor line of gold atoms . by focusing on the region between 8 and 16 mhz , as shown in fig . 5 for au25(sbu)018
, one can notice the presence of three symmetrical line doublets centered at the larmor frequency . at a magnetic field of 0.29 t , which is the field at which endor spectra were acquired , the larmor frequency is 12.34 mhz for the protons .
the three symmetric doublets are marked by brown ( outer ) , green ( middle ) , or black ( inner ) lines .
similar endor spectra are observed for the other clusters capped by linear - chain thiolates , but the relative intensity ratios are different .
the two proton types and the two ligand families generate four groups of equivalent protons : 24 ( -ch)in , 36 ( -ch)in , 12 ( -ch)out , and 18 ( -ch)out
three doublets of lines are clearly observed and positioned symmetrically around the larmor frequency , whereas a broad line is observed at ca . 3 mhz ( fig .
the latter could be attributed to the low - frequency part of a doublet of lines pertaining to the most strongly coupled protons . however , the corresponding high - frequency component , which should occur at ca .
furthermore , in the region around 3 mhz hyperfine couplings from c nuclei could also contribute .
for au25(set)018 , the average crystallographic distance between the alkanthiolate protons and the central gold atom increases in the order 6.27 ( -ch)in , 6.92 ( -ch)in , 7.23 ( -ch)out , and 8.26  ( -ch)out . the ( -ch)in protons are closer to the gold cluster than the other protons and , therefore , they should give rise to the most strongly coupled doublet . in the hypothesis
the 3 mhz line is a proton line , this could be related to the ( -ch)in , in keeping with the aforementioned nmr results .
however , the endor lines of the ( -ch)in protons could be simply undetectable , which is indeed not unusual for strongly coupled nuclei .
the ( -ch)out protons are located at the largest distance from the center of the au core and the inner lines are thus attributed to them .
the distances characterizing the ( -ch)in and ( -ch)out proton groups are quite similar , in the solid state at least , and thus a direct assignment is difficult . this problem can be addressed by simulation of the endor outer , middle and inner doublets .
s6 ) by using the parameters shown in table 1 , in which a ratio of 36  :  12 for the intensity of the outer and middle doublets is considered .
the position of the doublets is also in agreement with the crystallographic relative distances from the central au atom , which for this cluster are 6.92 vs. 7.23  .
this allows assigning the outer , middle and inner doublets to ( -ch)in , ( -ch)out , and ( -ch)out , respectively . regarding the ( -ch)out protons
, the simulation provides a number , 14 , that does not fully agree with that expected , 18 . for weak couplings , however , some differences are not unusual because the endor selectivity effect reduces the endor line intensity , whereas the presence of the proton - free larmor line ( a single line associated with the solvent protons ) could contribute to the inner doublet by increasing the line intensity . depending on the prevailing effect , either a decrease or an increase in intensity may occur . for the other clusters
, we assign the ( -ch)in and ( -ch)out doublets as for au25(set)018 ; for ( -ch)in , the above considerations about the broad peak at 3 mhz are also valid .
the crystallographic distances of the ( -ch)in and ( -ch)out groups from the cluster 's center are similar , i.e. , 7.23 and 7.16  ( au25(spr)018 ) , and 7.16 and 7.28  ( au25(sbu)018 ) , respectively .
in addition to the signals already discussed , the endor spectrum of au25(spr)018 is liable to show a contribution also from the 36 ( -ch)in , whose average crystallographic distance is 8.35  , and thus shorter than that of the ( -ch)out protons , 8.64  ; a similar outcome is observed for au25(sbu)018 whose values are 8.12 and 8.20  , respectively
. however , we could still simulate the spectrum of au25(spr)018 well ( esi , fig .
s7 ) by using for the outer and middle doublets an endor intensity ratio of 24  :  12 , which corresponds to the number of equivalent ( -ch)in and ( -ch)out protons . apparently , no ( -ch)in protons need to be taken into account .
in fact , according to the nmr results , the ( -ch)in protons could have a hyperfine coupling smaller than that of the ( -ch)out protons but still detectable . however , the room - temperature nmr data can not be directly compared with the low - temperature endor data . at room temperature ,
the random motion of the alkyl chain is fast , with the ( -ch)in atoms moving often closer to the metal core than the ( -ch)in atoms , but nmr spectroscopy only probes the average contact shift .
electron - transfer and diffusion - coefficient measurements provided evidence for the ligand chains being quite mobile in solution ; for example , the d values yield r 
 mpc values smaller than the average radius of the same clusters as calculated from the crystallographic structure . at 5 k , however , whereas the ligands ' motion is very limited by the frozen glassy solution , ( -ch)in can still be present in different conformations .
it is thus conceivable that the endor doublet of the ( -ch)in protons is associated with a wide conformational distribution ( larger than that experienced by the - and , even more , the -groups ) and this would cause significant line broadening and thus spreading of the signal under the outer and middle doublets . to shed further light onto this issue
, it is useful to compare the endor spectra of au25(spr)018 and au25(smepr)018 ( fig . 6 ) . whereas in the latter there are 72 ( -ch)in protons that can contribute to the spectrum , the ( -ch)in and ( -ch)out protons are only 12 and 6 , respectively , i.e. , one half than those in au25(spr)018 .
fig . 6 shows that in au25(smepr)018 the endor lines of the outer doublet are indeed significantly smaller than those of au25(spr)018 , and this confirms that for all clusters the outer doublet is consistently associated with the ( -ch)in protons .
this increase is attributed to a strong contribution from the ( -ch)in protons : compared to those in au25(spr)018 , in au25(smepr)018 these protons have a narrower conformational distribution due to the steric hindrance introduced by the second methyl group .
hindrance not only makes these methyl groups less mobile but also the whole monolayer stiffer and thus the mpc radius larger .
support to this view comes from the electrochemical determination of the d value in dicholoromethane ( see esi and fig .
s5 ) and , thus , r 
 mpc value of au25(smepr)018 : they are 5.16  10 cm s and 10.3  , respectively , whereas for au25(spr)018 ( which has the same fully extended length but more fluid chains in the monolayer ) they corresponding values are 6.15  10 cm s and 8.6  . the simulation of the endor spectrum of au25(smepr)018 ( esi , fig .
the number of protons required to obtain the best fit to the inner signals is indeed significantly larger than 6 , which in this specific cluster corresponds to the particularly small number of ( -ch)out protons .
we note , however , that the average crystallographic distance for the ( -ch)out protons in au25(spr)018 and au25(sbu)018 is 8.9  and thus only slightly larger than for the ( -ch)out protons .
a weak coupling is thus expected also for the ( -ch)out protons : for au25(smepr)018 these protons are particularly numerous , 36 , and this could make their contribution to the inner endor lines quite significant .
this hypothesis is reasonable but not quantifiable also because of the aforementioned problems associated with weak couplings . regarding au25(sbu)018 ( fig .
5 ) , the most evident new feature is that the outer lines are higher than the middle lines .
however , the number of protons causing an endor line is related to the area , not to the line height . the simulation ( esi , fig .
s8 ) results in a ratio of 24  :  12 between the outer and middle lines , in agreement with the attribution of the outer line to ( -ch)in and the middle line to ( -ch)out ; the outer lines are just narrower than in au25(set)018 and au25(spr)018 . as for au25(spr)018 ,
conformational distribution would make the contribution of the ( -ch)in protons spread in the region pertaining to the outer and middle lines . as a matter of fact
, the stokes radius of this cluster , 9.4  , is smaller than that of the stiffer au25(smepr)018 cluster . regarding the ( -ch)out protons , the best fit to the inner lines
we believe that the reason is as already described for au25(smepr)018 , i.e. , a non vanishingly small contribution from the ( -ch)out protons .
the simulations of the endor spectra provide both the isotropic and the anisotropic hyperfine values .
this interaction can be described by three main values , t 
 xx , t 
 yy and t 
 zz , called hyperfine tensor main values , which are specific for each nucleus . here ,
the axes x , y , z represent a main reference system whose origin is at the center of the electron spin - distribution ( in our case , the gold - cluster center ) . the values of t 
 xx , t 
 yy and t 
 zz can be obtained by averaging spatially the dipole 
dipole interaction over the spin distribution , according to the following equation ( eqn ( 2 ) ) , exemplified for x:2where  
 0 is the vacuum permeability , r is the electron - nucleus distance , g 
 e is the electron g - factor , g 
 n is the nucleus g - factor , and  
 n is the nuclear magneton .
analogous equations hold for y and z. from these equations , it results that t 
 xx + t 
 yy + t 
 zz = 0 . if the spin - distribution is axially symmetric with respect the z direction , then t 
 xx = t 
 yy and the hyperfine tensor main values are t 
 xx = t 
 yy = t and t 
 zz = 2 t .
deviation from an axially symmetric distribution leads to a hyperfine tensor whose main values are [ t 
 xx , t 
 yy , t 
 zz ] with t 
 xx  t 
 yy . 

table 1 shows that the various proton types are consistently in the form [ t , t , + 2 t ] , except for ( -ch)in in au25(set)018 in which a [ t 
 xx , t 
 yy , t 
 zz ] form is observed , with a marked difference between t 
 xx and t 
 yy . with all cautions
already discussed , if we assume that the feature at 3 mhz is due to ( -ch)in protons , its a can be estimated to be around 1520 mhz .
this would be about one order of magnitude larger than the value pertaining to the ( -ch)out protons . in this connection
, it is worth recalling that dft calculations carried out for au25(sch2ch2ph)018 showed that the spin density at ( -ch)in is one order of magnitude larger than at ( -ch)out . if we now compare the ( -ch)in and the ( -ch)out isotropic hyperfine couplings for alkanethiolates of increasing length ( table 1 , third column ) , we note an increase in the absolute value of a , particularly in the passage from et to pr .
this suggest that the ligands are not completely indifferent to the spin distribution in au25(sr)018 , and thus to the somo structure .
another aspect regards the sign of a. according to the theory , the isotropic hyperfine coupling with a nucleus is given by ( eqn ( 3)):3where  
  is the direct spin - density and  
  is the spin - polarized density . 

 
  is mainly contributed by the unpaired electron in the somo , whereas  
  is due to spin - polarization .
the latter results from the tendency of the unpaired electron to withdraw electrons with the same spin , because of the favorable exchange interaction , and vice versa .
if g 
 n is positive , which is true for protons , then a positive a is found for a dominant direct contribution from the somo , whereas a negative value is found if spin - polarization prevails . from the simulations , we obtain the sign with respect to [ t 
 xx , t 
 yy , t 
 zz ] , i.e. , the pattern of the doublet does not change if we were to revert both the sign of a and [ t 
 xx , t 
 yy , t 
 zz ] . however , if we assume that the anisotropic interaction is mainly dipolar , then the form of the anisotropic tensor main values is [ t , t , + 2 t ] with t > 0 , and thus the sign of a is determined as shown in table 1 . consequently , a negative value in a is an indication that a is mainly determined by spin - polarization through bonds , with a small contribution from direct spin density on the proton nuclei from the somo orbital , according to eqn ( 3 ) .
we can thus speculate that the increase of |a| as one goes from et to bu is the result of a decreasing , positive contribution to the hyperfine coupling from the direct spin - density of the somo , suggesting again that in the et cluster spin - density is more diffuse toward the ligands than in the pr or bu cases .
we can now compare these a values with those obtained from nmr measurements and the dft - calculated spin density values obtained previously . 

table 1 shows that the endor parameters differ from those obtained from the nmr signals in two ways : ( i ) in endor , the absolute values of a are significantly larger than the equivalent nmr values : 1.32.1 log units , except for ( -ch)in in au25(smepr)018 whose value is 3.0  log units ; ( ii ) some of the signs are different .
previous comparisons between the a values obtained from nmr and endor measurements carried out in solution at the same or not very different temperature provided comparable values and the same signs for many radicals .
our nmr and the endor experiments , however , refer to very different conditions . in a previous comparison of this kind ( for an iron - sulfur cluster ) ,
similar nmr and endor values were obtained , but the possibility that a strong temperature difference could lead to different results was also commented upon .
additionally , we note that compared to previous investigations focusing on quite rigid radical structures and without particularly heavy atoms , here we considered entirely new systems composed of a gold nanocore and many flexible ligands . to gain insights into this aspect , we performed ab initio md calculations by using the atom centered density matrix propagation molecular dynamics model ( admp ) , as implemented in gaussian 09 .
because a converged finite - temperature sampling is exceedingly computationally costly , we resorted to use a cluster model consisting of au7(sch3)6 , which is paramagnetic in the neutral state ( fig .
the model consists of a 6 au atom ring with a central gold core atom .
we performed 2 ps md simulations at 300 and 5 k with a time step of 0.001 fs .
snapshots were collected every 1 fs , for which we evaluated the isotropic fermi constant . despite its simplicity , the model contains protons with different values of a , ranging from negative to positive values .
7 ) come from the unpaired electron in the somo , whereas protons in groups 1 have negative values due to spin - polarization . at 300 k , thermal motion tends to reduce spin - polarization on group 1 , whereas at 5 k there is a sharp distribution with a peak value ( 0.35 mhz ) more negative than the peak value at 300 k ( 0.15 mhz ) .
this is in qualitative agreement with the endor results for ( -ch)out that show an overall decrease in the absolute value of a. close inspection of the md trajectories shows that at 5 k the rotation of the methyl groups is completely frozen in the global energy minimum , whereas at 300 k free rotations cause the direct effect of the spin electron and spin - polarization to roughly average out .
the experimental and theoretical results thus point to the emergence , at very low temperature , of a pronounced increase in spin - polarization .
these results , therefore , bring some rationale to the change in sign and magnitude observed by carrying out the hyperfine - coupling constant measurements at very different temperatures .
we used four structurally related paramagnetic au25 clusters to determine how spin density and thus orbital distribution spread onto the protecting alkanethiolate ligands .
the structures of two clusters were known , whereas that of the highly symmetric au25(spr)018 is described here for the first time .
h nmr and endor measurements proved to be very sensitive in assessing how the unpaired electron interacts with progressively more distant protons , with significant differences between the two types of ligand .
interestingly , the experimental and md results point to an increase of spin - polarization at very low temperature .
proton interaction extends to the protons at the  ,  , and  positions , with a much stronger interaction for the ligands directly connected to the au13 icosahedral core .
we thus show for the first time that orbital distribution affects atoms that can be as far as 6  from the icosahedral core . this information is deemed as essential especially for properly describing the mechanisms of the many reactions already known to be catalyzed by molecular mpcs . as a final remark
, we note that the strategy and methodologies here described are suitable to be applied to the study of other molecular clusters ( regardless of the actual metal core composition ) that already are in the form of free radicals or could generate them by electron transfer .
 
 we prepared four structurally related paramagnetic au25(sr)018 clusters . 
 1h endor and nmr signals could be successfully related to the types of ligand and the distance of protons from the central gold core . 
 it is shown that the unpaired electron can be used as a very precise probe of the structure of the interface between metal core and capping ligands . 
Introduction
Experimental
Results and discussion
X-ray crystallography
NMR spectroscopy
ENDOR
Electronnucleus interaction
Conclusions