boronic acids and boronic esters(1 ) are particularly important classes of compounds that have a wide range of uses and applications .
for example , they are used in catalytic additions to ketones,(2 ) asymmetric conjugate additions,(3 ) enzyme inhibition , potent and selective serine protease inhibition , suzuki coupling reactions in organic synthesis , materials synthesis , and neutron capture therapy treatments for cancer patients .
given the broad utility of boronic acids and esters , an understanding of the structural and electronic properties of these compounds is important .
boron has two quadrupolar nmr - active isotopes , b ( i = 3 ; n.a .
= 19.9% ;   10.744% ) and b ( i = 3/2 ; n.a .
= 80.1% ;   32.084%).(24 ) both of these nuclides have small to moderate nuclear electric quadrupole moments , q ( q(b ) = 84.59 mb ; q(b ) = 40.59 mb).(25 ) the b nucleus is more receptive to nmr studies due to its higher natural abundance , smaller quadrupole moment , and availability of a central transition ( ct ) ( i.e. , mi = + 1/2  1/2 ) .
when nmr experiments are conducted on solutions , rapid tumbling of the solute molecules leads to an averaging of molecular orientations . in many cases ,
this leads to sharp peaks , and isotropic chemical shift data may be obtained since the motion of the solute molecules is isotropic over the time scale of the nmr experiment .
it is well - known that such nmr experiments can be applied to help elucidate and assign the structure of the compound being studied , provide data about the chemical environment of the nucleus being studied , provide information about dynamics such as reaction rates , or simply monitor a reaction in progress from initiation to completion .
comprehensive b nmr studies have been conducted on boron compounds in solution and many isotropic chemical shifts ( iso ) have been recorded .
the known boron chemical shift range for tricoordinate and tetracoordinate species covers approximately 210 ppm , with tetracoordinate species falling between iso = 20 and 120 ppm and tricoordinate species falling between iso = 90 and 20 ppm with respect to f3bo(c2h5)2 at 0 ppm .
boronic acids and esters have chemical shifts in solution ranging from about 18 to 31 ppm.(26 ) the chemical shifts for b have been shown to correlate with the ligand  electron - donating ability.(26 ) thus , the interpretation of b chemical shifts may provide insight into  bonding . for tricoordinate boron compounds of the series br3 , bxr2 , bx2r , and bx3 ( x = electron - withdrawing ligand ; r = alkyl group ) ,
as one progresses from br3 to bx3 , the b isotropic chemical shifts decrease systematically , which has been interpreted as being associated with increased -electron backbonding from x to b.(26 ) in addition , a sterically congested environment tends to cause decreased -bonding ; hence , a positive shift may be observed with increasing steric bulk about the boron.(26 ) in powdered samples , the lack of rapid molecular tumbling corresponds to a static distribution of crystallite , and hence molecular , orientations .
this leads to broadening of the nmr line shape . for b , solid - state nmr ( ssnmr ) spectra can provide information about both the quadrupolar interaction between the nucleus and the electric field gradient ( efg ) , as well as chemical shift anisotropy ( csa ) ,
an advantage of ssnmr experiments using quadrupolar nuclei is that additional parameters that reflect the orientation - dependence of the nmr interactions are available to describe the local geometry and bonding environment .
we report the experimental characterization and interpretation of boron chemical shift ( cs ) and efg tensors in a series of solid boronic acids and esters ( figure 1 ) .
boron-11 ssnmr experiments were performed under stationary and magic - angle spinning ( mas ) conditions at magnetic field strengths ( b0 ) of 9.40 and 21.1 t. at 21.1 t , the influence of the cs tensor on the observed ssnmr line shapes becomes extremely important as its line shape contribution ( in hz ) is proportional to b0 .
in addition to improving sensitivity , ultrahigh - field ( > 18.8 t ) nmr spectrometers should therefore provide more precise measurements of the influence of the cs tensor on ssnmr spectra . in the case of quadrupolar nuclei , such as b ,
a high magnetic field usually produces narrower ct line shapes since the central transition signal broadening associated with the second - order quadrupolar coupling scales inversely with magnetic field .
structures of the boronic acids ( 15 ) and boronic esters ( 610 ) used in this study .
we also report on molecular orbital ( mo ) analyses performed to provide insight into the relationship between the molecular and electronic structure around the boron nucleus and the b nmr parameters .
csa is often rationalized by considering contributions to the paramagnetic shielding term , as outlined in ramsey s theory of nuclear magnetic shielding .
this theory posits that the nuclear magnetic shielding tensor can be broken down into two terms , a diamagnetic term ( dia ) and a paramagnetic term ( para ) .
the theory may be applied in explaining the effects of orbital - mixing - induced paramagnetic shielding on csa .
interpretation of experimental data alongside quantum chemical calculations has the potential to provide important information relating nmr parameters and molecular and electronic environments about the boron nucleus .
the b ssnmr spectra presented here are affected by nuclear magnetic shielding (  ) and the quadrupolar interaction between q and the efg at the nucleus .
the hamiltonian operator for b in a magnetic field may be expressed as : 

 where the first term represents the zeeman interaction , the second represents the quadrupolar interaction , and the third represents the magnetic shielding interaction .
magnetic shielding may be generally represented by a second - rank tensor , . diagonalization of the symmetric portion of  yields the orientation of its principal axis system ( pas ) relative to an external axis system . in its pas , the three principal components ( i.e. , the diagonal matrix elements ) of the symmetric  are ordered as follows : 11  22  33 .
the experimentally observed iso may be defined in terms of magnetic shielding if a suitable shielding reference exists : 

 where ii = 11 , 22 , 33 , iso .
the three principal components of the cs tensor are ordered as follows : 11  22  33 . for both the  and cs tensors ,
, the maryland convention will be used for reporting the  and cs tensor parameters.(31 ) the span (  ) is defined as:(31 ) the skew (  ) is defined as:(31 ) as with the shielding and shift tensors , the efg tensor may be diagonalized to provide the principal elements of the tensor and the orientation of the pas .
the principal components of the efg tensor are defined as follows : |v33|  |v22|  |v11| . the quadrupolar coupling constant ( cq )
may be expressed as : 

 where e is the fundamental charge and h is planck s constant .
the asymmetry parameter of the efg tensor is defined as : 
  it is useful to discuss the breadth of the ct powder pattern due to second - order quadrupolar interactions , for a stationary sample , ignoring csa for the moment:(32 ) 
 the breadth of the ct ( ct ) is inversely proportional to the larmor frequency ( l ) of the nucleus being studied . since l is directly proportional to b0 , this implies that ct is inversely proportional to b0 .
the use of a larger b0 therefore results in a decrease in second - order quadrupolar broadening of the central transition in frequency units . boron-11
the paramagnetic shielding term may be defined as : 

 where the terms in the numerator represent the degree of orbital mixing between the occupied and virtual orbitals contributing to a particular shielding component (  and  are permuted over x , y , z ) , and the term in the denominator represents the energy gap between the two wave functions involved in the mixing .
the five boronic acids [ 2-(tert - butyldimethylsilyloxy)naphthalene-6-boronic acid ( 1 ) , 2,6-dibromophenylboronic acid ( 2 ) , 2-chloropyridine-3-boronic acid ( 3 ) , 2-(hydroxymethyl)phenylboronic acid cyclic monoester ( 4 ) , and 2-acetyl-3-thiopheneboronic acid ( 5 ) ] , and five boronic esters [ 4-fluorophenylboronic acid neopentylglycol ester ( 6 ) , 4-nitrophenylboronic acid pinacol ester ( 7 ) , 1h - indazole-5-boronic acid pinacol ester ( 8) , 4-(2-propynylcarbamoyl)phenylboronic acid pinacol ester ( 9 ) , and 2,4,6-trimethoxyphenylboronic acid neopentyl glycol ester ( 10 ) ] in this study ( figure 1 ) were purchased from aldrich and were used without further purification .
samples were powdered and packed in a glovebox under an inert atmosphere of nitrogen into 4 mm o.d .
zro2 rotors , and nmr experiments were conducted using a bruker avanceiii nmr spectrometer ( b0 = 9.40 t , l(b ) = 128.38 mhz ) .
a bruker 4.0 mm hxy triple - resonance mas probe tuned to b on the x channel was used .
solid nabh4 has a chemical shift of 42.06 ppm relative to the primary standard , liquid f3bo(c2h5)2 ( where (b ) = 0.00 ppm).(33 ) for both mas and stationary samples , the hahn echo ( /2  1   
typical /2 pulse lengths for solid nabh4 were 3.0 s . for the 10 samples under study , the
pulse was used ( e.g. , 3.0 s/(i + 1/2 ) = 1.5 s , where i = 3/2 for b ) .
signal averaging was carried out over a period of 4 min to 4 h for both static and mas samples .
qcpmg experiments ( /2  1    2  acq( )  [ 3    4  acq(2)]n)(36 ) were also performed , where the number of full echoes acquired ( n ) depended on the transverse ( spinspin ) relaxation time constant t2 . in most cases , 96 full echoes were acquired . the value of 2 was varied from 450950 s , depending on the desired spikelet separation in the frequency domain , cpmg .
modified qcpmg experiments were conducted , where the  pulse in the echo train was replaced with a /2 pulse.(37 ) double - frequency sweep ( dfs ) shaped pulses were also used in conjunction with hahn echo and qcpmg experiments to enhance the ct signal intensity .
the probes used at both fields exhibit a small , but manageable background b signal in the acquired spectra , as a result of boron nitride in the stators .
the hahn echo pulse sequence was generally found to be effective at suppressing the background signal .
samples were powdered and packed in a glovebox under a dry argon atmosphere into 2.5 mm o.d .
zro2 rotors , and nmr experiments were conducted using a bruker avanceii nmr spectrometer ( b0 = 21.1 t , l(b ) = 288.80 mhz ) .
spectra were acquired using topspin 1.3 software at the national ultrahigh - field nmr facility for solids in ottawa ( www.nmr900.ca ) .
a bruker 2.5 mm hx mas vt probe tuned to b on the x channel was used .
the referencing , calibration , and setup procedures were identical , and the pulse sequences , pulse widths , pulse delays , and experiment times were similar to those used at 9.40 t. the mas speed was 30 khz .
all mas samples were cooled to room temperature using a vt unit to prevent sample decomposition caused by heat production at fast spinning speeds .
fids were left - shifted to the echo maxima when necessary , apodized using a gaussian function of 525 hz for mas samples and 20200 hz for stationary samples , then fourier transformed .
stack plots were produced with dmfit.(40 ) spectral simulations were performed using the wsolids1 program(41 ) which incorporates the space - tiling algorithm of alderman et al.(42 ) the error associated with spectral parameters was determined heuristically by analyzing the spectra ( mas and static echo , but not qcpmg ) obtained at both magnetic fields . in simulations , each nmr parameter was varied individually from the optimum value until a noticeable discrepancy with the experimental spectrum was observed .
of the compounds studied , an x - ray crystal structure is available for compound 4(43 ) only ; this structure indicates a single crystallographically unique boron site .
nmr spectra acquired presently strongly suggest that there is a single unique boron site for all other compounds studied as well .
as such , all spectra were simulated using a single boron site for each compound . in some cases , boric acid or other decomposition products were included in simulations as an additional boron site . a model for each compound
these structures were then subjected to geometry optimization using the b3lyp hybrid dft functional ( b3lyp)(44 ) and the 6 - 311+g * basis set for all atoms , while keeping the coordinates of the carbon and hydrogen atoms in the aromatic ring system frozen so as to not perturb the planarity of the aromatic system and to assist in convergence . on the resulting optimized structure , b3lyp
was then used to perform an unrestrained second geometry optimization using the 6 - 311+g * basis set .
dihedral angles ( ccbo ) of interest were altered simply by defining a new ccbo in gaussview for the optimized structure .
although the crystal structure for phenylboronic acid has been reported,(45 ) geometry optimizations were performed in order to systematically vary ccbo .
these computations were performed to isolate the impact of varying ccbo on the boron magnetic shielding tensor .
efg and  tensors were calculated using gaussian 03(46 ) running on an in - house 304 cpu system , and the amsterdam density functional package(47 ) ( adf ) running on the high performance computing virtual laboratory ( www.hpcvl.org ) cluster .
dft calculations employing b3lyp(44 ) used the 6 - 311+g * basis set on all atoms .
restricted hartreefock ( rhf ) calculations were also carried out using the same basis set .
finally , magnetic shielding , efg , and mo analysis calculations using adf and employing the gga - revpbe dft method ( gga - revpbe ) were carried out using the tzp basis set on all atoms .
boron-11 quadrupolar coupling constants were calculated from the largest principal component of the efg tensor , v33 , using eq 5 .
calculated nmr parameters were parsed using efgshield.(48 ) the factor 9.7177  10 v m per atomic unit is used to convert v33 from atomic units to v m.(49 )
shown in table 1 are the boron efg and cs tensor values obtained via analytical simulations of the b nmr spectra of boronic acids and esters 110 . by simultaneously fitting data at both 9.40 and 21.1 t , the cq , q , and iso values were determined from mas nmr spectra .
subsequently , stationary spectra were analyzed to determine the  ,  , and euler angles relating the two tensor pass ( see figures 29 , s3 and s4 ) .
experimental cq , q , iso ,  ,  , and euler angles for each boronic acid and ester compound studied .
boric acid is included as the impurity present at 19.6 ppm in compounds 2 and 3 .
the nmr parameters were included in the simulations of compounds 2 and 3 using 4 and 10% intensity relative to the main signal , respectively . a small range in cq(b )
is observed ( i.e. , from 2.66 mhz for compound 9 to 3.29 mhz for compound 1 ) . in general , the cq(b ) values for the boronic acids tend to be slightly larger than for the esters ; however , there is clearly overlap in the ranges for each class of compound ( see figure s2 ) .
there is very little variation in the measured iso(b ) , which ranges from 26.0 ppm ( compound 5 ) to 31.0 ppm ( compound 4 ) , that is , only about 5% of the total known range for tricoordinate boron .
because this range is so small , it is difficult to conclusively relate iso(b ) to any single structural or electronic feature , although there is a good correlation between the experimental isotropic chemical shift values and the calculated isotropic magnetic shielding values ( vide infra ) . in general , the directions of the eigenvectors corresponding to v33 and 33 are coincident within experimental error , as quantified by the euler angle . overall , we find that the span is the most sensitive nmr parameter to changes in the molecular and electronic structure from compound to compound , ranging from 10 ppm ( compound 9 ) to 40 ppm ( compound 2 ) ; that is , the variation in  ( 30 ppm ) represents 75% of the maximum span value ( 40 ppm ) observed .
because the span has the largest relative variation among the nmr parameters , it is our primary focus and its relationship with the local boron electronic and molecular structure is discussed in a subsequent section . shown in figure 2 are b ssnmr spectra of boronic ester 8 obtained at 9.40 and 21.1 t. as a representative example , we discuss in some detail these spectra and the extracted parameters .
the cq(b ) value obtained for 8 is 2.76    0.20 mhz and q = 0.59    0.10 .
csa is present and broadening is therefore observed in the spectrum due to both the quadrupolar interaction as well as csa (  = 14    2 ppm ) .
the isotropic chemical shift of 30.3    1.0 ppm falls within the expected range for a boronic ester.(26 ) for the data obtained at both magnetic fields , simulated spectra fit very well with the experimental data ; hence , there are small experimental error values associated with the reported data ( table 1 ) .
the b nmr spectra of both mas and stationary samples are less broad at 21.1 t. this narrowing is seen for all samples in the present work , as the broadening of the ct due to the second - order quadrupolar interaction decreases with increasing b0 and is always the case when broadening in the spectrum is dominated by the second - order quadrupolar interaction .
qcpmg spectra were also obtained and each corresponding manifold of spikelets mimics the line shape of the stationary spectra .
experimental spectra of a powdered sample undergoing mas are shown in ( a ) b at 9.40 t and ( c ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( b ) and ( d ) ) using the parameters given in table 1 .
experimental spectra of stationary powdered samples are shown in ( e ) b at 9.40 t and ( g ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( f ) and ( h ) ) using the parameters given in table 1 .
experimental qcpmg spectra of stationary powdered samples are shown in ( i ) b at 9.40 t and ( j ) b at 21.1 t. depicted in figures 39 are the b ssnmr spectra of compounds 14 , 7 , 9 , and 10 , respectively . upon examination of the spectra
it is seen that the b line shapes associated with the boronic acids tend to be broader than the spectra of boronic esters .
this observation is associated with the fact that the boronic acids tend to have larger cq(b ) and  values . in table 1 ,
nmr parameters are also listed for boric acid , a known decomposition product of boronic acids.(1 ) this decomposition product is clearly identified in compounds 2 and 3 ( figures 4 and 5 ) as purchased and is responsible for the peak with iso = 19.6 ppm .
in addition , spectra for compounds 1 , 2 , and 4 ( figures 3 , 4 , and 6 ) contain broad , low intensity features buried underneath the main signal .
we speculate that these peaks are likely due to small amounts of an unknown impurity , decomposition product present in the sample , or possibly the result of less effective suppression of the signal due to boron nitride inside the stator .
experimental spectra of a powdered sample undergoing mas are shown in ( a ) b at 9.40 t and ( c ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( b ) and ( d ) ) using the parameters given in table 1 .
experimental spectra of stationary powdered samples are shown in ( e ) b at 9.40 t and ( g ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( f ) and ( h ) ) using the parameters given in table 1 .
experimental qcpmg spectrum of a stationary powdered sample is shown in ( i ) b at 9.40 t. solid - state boron-11 nmr spectroscopy of 2 .
experimental spectra of a powdered sample undergoing mas are shown in ( a ) b at 9.40 t and ( c ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( b ) and ( d ) ) using the parameters given in table 1 .
experimental spectra of stationary powdered samples are shown in ( e ) b at 9.40 t and ( g ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( f ) and ( h ) ) using the parameters given in table 1 .
the small peaks in spectra ( ad ) seen at 1 and 19 ppm are due to boric acid , and its spectral parameters may be found in table 1 .
experimental spectra of a powdered sample undergoing mas are shown in ( a ) b at 9.40 t and ( c ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( b ) and ( d ) ) using the parameters given in table 1 .
experimental spectra of stationary powdered samples are shown in ( e ) b at 9.40 t and ( g ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( f ) and ( h ) ) using the parameters given in table 1 .
experimental qcpmg spectrum of a stationary powdered sample is shown in ( i ) b at 9.40 t. the small peaks in spectra ( ad ) seen at 1 and 19 ppm are due to boric acid , and its spectral parameters may be found in table 1 .
experimental spectra of a powdered sample undergoing mas are shown in ( a ) b at 9.40 t and ( c ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( b ) and ( d ) ) using the parameters given in table 1 .
experimental spectra of stationary powdered samples are shown in ( e ) b at 9.40 t and ( g ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( f ) and ( h ) ) using the parameters given in table 1 .
experimental spectra of a powdered sample undergoing mas are shown in ( a ) b at 9.40 t and ( c ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( b ) and ( d ) ) using the parameters given in table 1 .
experimental spectra of stationary powdered samples are shown in ( e ) b at 9.40 t and ( g ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( f ) and ( h ) ) using the parameters given in table 1 .
experimental qcpmg spectrum of a stationary powdered sample is shown in ( j ) b at 21.1 t. solid - state boron-11 nmr spectroscopy of 9 .
experimental spectra of a powdered sample undergoing mas are shown in ( a ) b at 9.40 t and ( c ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( b ) and ( d ) ) using the parameters given in table 1 .
experimental spectra of stationary powdered samples are shown in ( e ) b at 9.40 t and ( g ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( f ) and ( h ) ) using the parameters given in table 1 . experimental qcpmg spectrum of a stationary powdered sample
is shown in ( i ) b at 9.40 t. solid - state boron-11 nmr spectroscopy of 10 .
experimental spectra of a powdered sample undergoing mas are shown in ( a ) b at 9.40 t and ( c ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( b ) and ( d ) ) using the parameters given in table 1 .
experimental spectra of stationary powdered samples are shown in ( e ) b at 9.40 t and ( g ) b at 21.1 t. best - fit spectra were simulated using wsolids ( traces ( f ) and ( h ) ) using the parameters given in table 1 .
experimental qcpmg spectrum of a stationary powdered sample is shown in ( i ) b at 9.40 t. figures s10s18 ( supporting information ) illustrate the b0 dependencies of the second - order quadrupolar interaction and csa observed in the magnetic resonance line shape for several of the boronic acids and esters . shown in these figures
are the stationary spectra for each compound , the corresponding best - fit analytical simulation , and a simulation where the csa is ignored ( i.e. ,  = 0 ppm ) . comparing the traces where csa is included to those where
it is not for the data acquired at 9.40 t , one clearly sees that the difference between the two traces is minimal . at 21.1 t
figure 10 is a graphical representation of the measured  values for different trigonal planar boron bonding environments.(50 ) as the central boron atom is bound to more oxygen atoms and fewer carbon atoms , the experimental  values decrease dramatically .
the oxygen atoms can donate electron density through lone pairs of electrons into the vacant p - orbital of the boron .
as described in more detail later , the contributions to the paramagnetic portion of the total  in the boron trigonal plane are reduced upon increasing oxygen coordination , which can explain the observed decrease in the measured .(50 ) the boronic acids and esters have  values in the small / intermediate range relative to borates on the low end and boranes on the high end .
even though the spans being examined are small , they are the most characteristic nmr parameters for each compound and can successfully be related to the immediate bonding environment ( figure 10 ) .
graphical representation of experimental  values for the compounds being studied ( table 1 ) and different borate and borane compounds.(50 ) data points indicate average values for a range of compounds ( boronic acids and esters ) or single experimental measurements ( borate and borane ) .
the vertical bars for the boronic acid and ester data show the range of  for each class of compound . in the case of borane and borate ,
the vertical bars represent the experimental measurement error for one compound ( trimesitylborane and triphenylborate).(50 ) as the central boron atom is bound to more oxygen atoms and fewer carbon atoms , the experimental  values decrease dramatically .
we briefly digress here to assess the effectiveness of modified - qcpmg(37 ) and dfs - modified - qcpmg signal enhancement techniques for boronic acids and esters .
modified - qcpmg is similar to the conventional qcpmg pulse sequence , except that the  pulses in the qcpmg echo train are replaced with /2 pulses.(37 ) the sequence suppresses homonuclear dipolar coupling ; hence , a longer effective t2 is observed , allowing more echoes to be acquired in the time - domain and resulting in sharper spikelets in the frequency - domain .
we postulate that this sequence could be beneficial due to the large magnetogyric ratio and natural abundance of b. presently , the modified - qcpmg pulse sequence results in signal enhancement factors ranging from 1.04 in compound 9 to 1.42 in compound 5 , relative to the standard qcpmg pulse sequence .
similarly , the dfs modified - qcpmg pulse sequence provides signal enhancement factors ranging from 1.80 in compound 8 to a high of 2.95 in compound 5 , relative to the standard qcpmg pulse sequence .
as an example , shown in figure 11 are qcpmg , modified - qcpmg , and dfs modified - qcpmg nmr spectra for a representative boronic ester ( 9 ) , where signal enhancement factors of 1.04 and 2.16 are achieved .
figure 11 also presents analogous data for a representative boronic acid ( 3 ) , where signal enhancement factors of 1.35 and 2.71 are obtained .
further examples of signal enhancement for additional boronic acids and esters may be found in the supporting information ( figures s5 to s9 ) .
although we were able to acquire high - quality b ssnmr spectra without the use of these signal enhancement techniques in the present study , it is worth noting that they were successful and that they might be useful for b ssnmr in more dilute systems .
one specific example could involve achieving signal enhancement of the b ct of boronic acids present in dilute quantities in systems such as modified protease inhibitors.(10 ) solid - state boron nmr spectroscopy of 9 ( left ) and 3 ( right ) .
experimental b spectra of stationary powdered samples at 9.40 t are shown in ( a ) and ( d ) using the qcpmg pulse sequence ; ( b ) and ( e ) using the modified - qcpmg pulse sequence with a signal enhancement factor of 1.04 and 1.35 , respectively ; and ( c ) and ( f ) using the dfs modified - qcpmg pulse sequence with a signal enhancement factor of 2.16 and 2.71 respectively , relative to qcpmg .
are the boron efg and  tensor results calculated using b3lyp , rhf , and gga - revpbe methods for compounds 110 ( see also tables s1 to s3 ) .
the gga - revpbe calculated isotropic magnetic shielding constants are plotted against the experimental values of iso in figure 12 .
a good correlation exists between the experimental and calculated data , as quantified by a correlation coefficient of r = 0.9000 ( excluding an outlier for boronic acid 2 ) .
the experimental spans are also best reproduced by the gga - revpbe calculations , as quantified by a correlation coefficient of r = 0.9818 , once one outlier is excluded ( figure 12 ) .
the outlier , corresponding to boronic acid 1 , may be tentatively rationalized by considering the relatively large experimental error associated with this particular measurement .
correlation between the calculated ( adf / gga - revpbe ) and experimental span values ( a ) and calculated total isotropic shielding and experimental isotropic chemical shift values ( b ) measured in the solid state for each boronic acid and ester studied .
 data ( ( a ) , diamonds ) are described by a r value of 0.9818 and a trendline given by y = 1.0536x + 0.482 .
one data point for boronic acid 1 ( ( a ) , square ) is not taken into account and is plotted separately .
data in part ( b ) ( diamonds ) have a r value of 0.9000 with a trendline given by y = 1.0117x + 99.8 .
one stray data point for boronic acid 2 ( ( b ) , square ) is not taken into account and is plotted separately .
corresponds to boronic acid dimer . calculated values for boronic acid dimers which take into account hydrogen bonding interactions
hybrid dft calculations were performed using the b3lyp functional and the 6 - 311+g * basis set on all elements .
rhf calculations were performed using the 6 - 311+g * basis set on all elements .
adf calculations were performed using the gga - revpbe functional and tzp basis set on all atoms .
boric acid is included as the impurity present at 19.6 ppm in compounds 2 and 3 .
the gga - revpbe - calculated values can be used to discuss the impact of hydrogen bonding , electronic substituents , and ccbo on the span .
the two hydroxy groups present in boronic acids are capable of engaging in intermolecular hydrogen bonding .
therefore , if hydrogen bonding interactions are present , the boronic acids being considered usually exist as dimers .
only one crystal structure exists for the compounds being studied , that of compound 4 , which is a dimer.(43 ) boronic acids may also exist as oligomers in the solid state , as discussed , for example , by maly et al .
we performed calculations on both boronic acid monomers and dimers to assess the impact of hydrogen bonding on the b nmr interaction tensors .
we find that cq(b ) generally decreases slightly in the dimers , relative to the monomers .
there is no consistent trend in the change of  as a result of hydrogen bonding in the dimers .
we attribute this observation to the fact that the value of ccbo ( as shown in figure 13 ) of the optimized structures changes differentially from compound to compound as a result of dimerization , in addition to the simple fact that the hydroxy groups are hydrogen bonded .
correlation between the calculated  values and ccbo for monomeric and dimeric forms of phenylboronic acid . shown
are results for ( diamonds ) gaussian ( b3lyp ) monomer , ( squares ) gaussian ( b3lyp ) dimer , ( triangles ) adf ( gga - revpbe ) monomer , and ( circles ) adf ( gga - revpbe ) dimer . shown in red
therefore , we next studied the impact of varying ccbo upon calculated  values . shown in table 2 are the gga - revpbe optimized dihedral angles for each boronic acid and ester ( see also figure 13 ) , where the two carbon atoms are located in the aromatic ring , and the boron and oxygen atoms are part of the boronic acid or ester functionality . as noted earlier , ccbo is altered primarily by sterics , and depends on the bulkiness of nearby substituents on the aromatic ring .
for example , for every boronic acid and ester possessing bulky substituents on the aromatic ring , particularly in the ortho position , the value of ccbo is always much greater relative to when there is a less bulky substituent .
as this angle is systematically varied , the orientations of mos centered on boron , relative to the aromatic ring , change accordingly .
an examination of the correlation between experimental and calculated spans ( figure 12 ) suggested a potential relationship between ccbo and both the experimental and calculated  values .
previous work by zhang et al . reported a dependence of the computed energy of boronic acids on this dihedral angle.(54 ) a plot of the value of  as a function of the calculated value of ccbo for each compound reveals no clear and direct correlation , which is not surprising , as there are several variables changing simultaneously .
for example , boronic acids have hydrogen bonding interactions taking place whereas the esters do not ; the aromatic substituents are different on the various compounds , and the dihedral angle changes primarily due to sterics . to determine
if there is an underlying fundamental correlation between span and ccbo , phenylboronic acid was chosen as a model system .
the value of ccbo was then systematically altered from 0 to 90 in 10 steps .
for each ccbo , spans were calculated using both b3lyp and gga - revpbe density functional methods .
two important conclusions may be drawn : ( i ) for all four data sets , there is a distinct positive correlation between  and ccbo ; ( ii ) in all cases , the  values are smaller for the phenylboronic acid monomer than for the dimer .
it is clear that calculations predict that the presence of the hydrogen bonding interaction results in an increased span .
the calculated variation of the span results from small changes ( on the order of 15 ppm ) in the values of the principal components of the magnetic shielding tensor as a result of hydrogen bonding . in no case
do the calculations imply that the span varies because of the unilateral change of a single component ( see table s6 ) .
it is the combination of these small changes , specifically in 11 and 33 , rather than a significant change in a single principal component , which leads to variation in the  values .
the 33 values become slightly larger , and the 11 values become smaller , resulting in an increased span overall .
gga - revpbe calculations for the phenylboronic acid monomer were used to compile shielding tensor magnitude and orientation information at each ccbo . not surprisingly , the eigenvector corresponding to 33 remains nearly perpendicular to the boron bonding plane . for phenylboronic acid , 33
is calculated to intersect the boron bonding plane at an angle ranging from 76 to 90 , depending on the value of ccbo .
in addition , for boronic acids and esters 110 , 33 remains perpendicular ( within 18 ) to the boron bonding plane .
( compound 4 is an exception to this rule with 22 being perpendicular , although compound 4 is also unique in the sense that it is a boronic acid monoester ) . to relate
the mos to the observed and calculated  values , the individual mo contributions to total shielding must first be examined .
as previously mentioned , magnetic shielding may be partitioned into dia and para components . as conventionally partitioned , the paramagnetic shielding term is often the dominant term that contributes to shielding tensor anisotropy .
if virtual rotation of this orbital by 90 produces a favorable overlap with a virtual p orbital of the boron atom , the situation results in paramagnetic contributions to the component along the axis of virtual rotation.(50 ) consider the action of the angular momentum operator ( eq 8) on a given mo wave function that can account for contributions to paramagnetic shielding due to orbital overlap between occupied and virtual states .
the action that this angular momentum operator has on a p - character orbital , which is the case for the boron compounds being examined , can be visualized as a 90 rotation of the occupied orbital .
if para is the dominant contributor to shielding anisotropy , we anticipate that there should be a relationship between the observed  and the mos involved in mixing . to assist in visualization of this concept , consider the pair of mos which give the greatest contributions to para for compound 6 ( figure 14 ) .
occupied orbital 33 ( homo-7 ) and virtual orbital 65 ( lumo+24 ) for compound 6 .
these are the two orbitals involved in mixing which yield the largest contribution to total isotropic para .
note the orbital overlap between a 90 virtual rotation of occupied orbital 33 out of the plane of the page and virtual orbital 65 .
interestingly , however , when considering compounds 110 , there is no clear correlation between span and orbital energy gap between the occupied and virtual states that give the largest contribution to the total isotropic para .
there is also no obvious correlation between the span and total isotropic para . from compound to compound , different effects need to be considered , including : hydrogen bonding , ccbo , and varying electronics of the different substituents on the aromatic ring .
it is likely a composite of these different effects that clouds the relationship between  and orbital energy gap or total isotropic para .
when considering our model phenylboronic acid monomer system , there is a clear correlation between  and total isotropic para .
in addition , when the same pair of occupied and virtual mos are considered from compound to compound , as the orbital energy gap decreases , the span values increase , which is the expected correlation when the span is dominated by para . both the paramagnetic shielding tensor components as well as the total magnetic shielding components
as ccbo increases from 0 to 90 , the separation between 11 and 33 increases , which equates to an increasing span ( eq 3 ) . in the plot
where the contributions to paramagnetic shielding are plotted against ccbo , the paramagnetic contribution to 11 becomes increasingly negative with increasing dihedral while the paramagnetic contribution to 33 also decreases slightly . as a consequence of the paramagnetic contribution to 11 becoming increasingly negative , the total isotropic para will become more negative and the span will increase .
however , a plot of total magnetic shielding against ccbo reveals that 11 shifts in the negative direction , while 33 becomes more positive as ccbo increases .
consequently , we conclude that diamagnetic shielding contributions play a non - negligible role in determining the span values observed .
numerical values are tabulated in the supporting information ( see tables s4 and s5 ) .
plot of the adf / gga - revpbe calculated total magnetic shielding tensor components ( bottom ) and total isotropic para tensor components ( top ) versus ccbo for phenylboronic acid .
the three data sets on each plot represent 11 ( diamonds ) , 22 ( squares ) , and 33 ( triangles ) . due to the demonstrated importance of diamagnetic
shielding , a brief study was conducted to determine the effects of strong and mild electron - donating and withdrawing groups on the boron shielding tensor .
phenylboronic acid was used as a control molecule , and a steric group ( bromine ) , a mild electron - donating group ( carboxylic acid ester ) , a strong electron - donating group ( amine ) , a mild electron - withdrawing group ( carboxyl ) , and a strong electron - withdrawing group ( nitro ) were each substituted in the ortho , meta , and para positions of the aromatic ring .
while changes in the isotropic shielding constant are small for all substituents , we find that the presence of electron - withdrawing groups correlates with increases in the calculated  values ( up to 13.5 ppm ) , whereas electron - donating groups have less of an effect on the calculated  values .
for both shifts in 11 in the negative direction which increase  , and shifts in 11 in the positive direction which decrease  , in general , it was 11 that had the largest change in magnitude as a result of substitution .
these results are logical since tricoordinate boron compounds that feature boron atoms bound to multiple oxygen atoms have smaller observed  values due to the lone pairs on the oxygen donating electron density to a virtual mo centered on the boron atom.(50 )
in this study , b cs and efg tensor information was successfully extracted from the b ssnmr spectra acquired for 10 boronic acids and esters .
signal enhancement techniques were successfully applied and enhancement factors of up to 1.42 were achieved for modified - qcpmg , whereas factors of 1.802.95 were achieved for dfs modified - qcpmg , relative to the qcpmg sequence alone .
the cq and  values were found to be larger , on average , for boronic acids than for esters .
for the five boronic acids , the span has an average value of 30.8 ppm , while for the five boronic esters , the average value is 17.8 ppm . in the case of b
quadrupolar coupling constants , the average value is 3.0 mhz for the boronic acids and 2.8 mhz for the boronic esters .
the ranges associated with cq and iso are small relative to their absolute magnitudes from compound to compound .
however , the cs tensor span exhibits a significant relative range ( 75% ) and is the nmr parameter most characteristic of the molecular and electronic structure for the compounds studied .
it has been advantageous to acquire data at high magnetic field strength as the effects of csa could be more precisely quantified .
good correlation between experimental and gga - revpbe calculated spans as well as between the calculated isotropic shielding and experimental chemical shift values was observed .
the span was shown to be positively correlated with ccbo in a model boronic acid over the range of 090 degrees .
this is true regardless of whether hydrogen bonding is taking place , although  does not increase as steeply with ccbo when hydrogen bonding is occurring .
the hydrogen bonding interaction is correlated with a decrease in the total paramagnetic contribution to the isotropic magnetic shielding and a decrease in the span .
contrary to the situation typically seen for larger spans , the diamagnetic part of the shielding tensor was shown to play a key role in explaining the observed trends in csa . finally , the presence of an electron - withdrawing group substituted on a model boronic acid resulted in an increase in the calculated . we have shown that the boron chemical shift tensor in boronic acids , and particularly the span of the cs tensor , is governed by a delicate interplay of several competing factors , including hydrogen bonding , dihedral angle , and the various electron - donating or withdrawing substituents bound to the aromatic ring .
we speculate , therefore , that future b ssnmr experiments performed on similar materials will be most beneficial in comparative studies , where specific individual changes in structure may be probed and characterized .
 the results of a solid - state 11b nmr study of a series of 10 boronic acids and boronic esters with aromatic substituents are reported . 
 boron-11 electric field gradient ( efg ) and chemical shift ( cs ) tensors obtained from analyses of spectra acquired in magnetic fields of 9.4 and 21.1 t are demonstrated to be useful for gaining insight into the molecular and electronic structure about the boron nucleus . 
 data collected at 21.1 t clearly show the effects of chemical shift anisotropy ( csa ) , with tensor spans (  ) on the order of 1040 ppm . 
 signal enhancements of up to 2.95 were achieved with a dfs - modified qcpmg pulse sequence . to understand the relationship between the measured tensors and the local structure better , calculations of the 11b efg and magnetic shielding tensors for these compounds were conducted . 
 the best agreement was found between experimental results and those obtained from gga revpbe dft calculations . 
 a positive correlation was found between  and the dihedral angle ( ccbo ) , which describes the orientation of the boronic acid / ester functional group relative to an aromatic system bound to boron . 
 the small boron csa is discussed in terms of paramagnetic shielding contributions as well as diamagnetic shielding contributions . 
 although there is a region of overlap , both  and the 11b quadrupolar coupling constants tend to be larger for boronic acids than for the esters . 
 we conclude that the span is generally the most characteristic boron nmr parameter of the molecular and electronic environment for boronic acids and esters , and show that the values result from a delicate interplay of several competing factors , including hydrogen bonding , the value of ccbo , and the electron - donating or withdrawing substituents bound to the aromatic ring . 
Introduction
Conventions and Background
Experimental and Computational Details
Results and Discussion
Conclusions