the nucleus - independent chemical shift ( nics)1 is perhaps one of the most popular criteria to determine aromaticity.2 this aromaticity index is defined as the negative of the isotropic magnetic shielding evaluated at the ring center of an ( anti)aromatic system ( nics(0)=iso ) . thus , part of its popularity is due to its ease of calculation with any standard quantum chemical program.1,2 despite the success of nics at describing aromaticity in a plethora of cyclic compounds , several aspects of nics have been subject to criticism . some authors have pointed out that the validity of nics is limited by spurious contributions from the in - plane tensor components , which are not necessarily related to aromaticity.35 to avoid these issues , some variants of nics have been proposed , such as dissected nics6 ( where the  and  components are separated ) , the nics(1)7 ( where the nics is evaluated at 1.0   above the ring center ) , and the zz component of the nics tensor ( nicszz),8 which has been proven to be particularly sensitive to -electron delocalization patterns . in several cases , nics has shown inconsistencies , but suitable conclusions have been obtained when this magnetic response has been analyzed in deeper detail.4,9 one particular example where magnetic - based descriptors of aromaticity are inconsistent is in the case of aromaticity assessment of fluorinated benzene derivatives . in 1997 , fowler et  al . compared both the total and the  current densities of benzene and hexafluorobenzene , concluding that these systems show almost a similar magnetic response and , therefore , the same aromatic character.10,11 in contrast , nics(1)zz indicates that aromaticity decreases proportionally to the number of fluorine atoms.12 the computed nicszz by wu et  al . revealed that fluorine induces only a local paratropic contribution at the hexafluorobenzene ring center , which according to the authors evaluated the changes in nicszz and nics at the ring center of benzene and hexafluorobenzene by localizing the  electrons using the block - localized wave ( blw ) function method.14 while in benzene nics(0 ) is 8.7  ppm and nics(0)blw is 1.9  ppm , the values in hexafluorobenzene are 18.0  ppm and 9.4  ppm , respectively . hence , both indexes suggest a bigger change upon blocking in benzene than in hexafluorobenzene , supporting that benzene is more aromatic than its fluorinated derivatives . the assumption in this strategy is that aromaticity is turned off after localization ( blocking ) procedure . recently , kaipio et  al.15 reopened the debate on the effect of fluorination on the aromaticity degree of arenes.12,13,15,16 current susceptibility computations indicate that the degree of aromaticity in the fluorinated benzene derivatives decreases when the number of fluorine atoms increases , contradicting previous findings based on magnetic criteria . the authors also evaluated this effect using the charge density differences between the fluorinated species and benzene , showing that the  framework is more disturbed than the  skeleton.15 here , we analyze the distance dependence of the nics values and the fluorination effect on the chemical bonding of benzene derivatives . our results support and complement the previous findings of kaipio et  al.15 in order to gain insight into the electron delocalization of the title systems , we carried out an analysis using another magnetic descriptor , the induced magnetic field ( b);17 particularly , using the z component of the induced magnetic field ( bz ) , which is equivalent to nicszz . the results are compared with the magnetically induced current densities as well as with their integrated values ( ring current strengths , rcs ) . the bz analysis shows that fluorination of benzene decreases its aromaticity in agreement with rcs values . the bonding of such systems is studied in terms of the adaptive natural density partitioning ( adndp ) analysis , which supports the inductive and resonant effects into the fluorinated benzene . the geometries were fully optimized using the pbe0 functional in conjunction with a 6 - 311++g(d , p ) basis set in gaussian09.18 the shielding tensors were computed at the same level using the giao approach , locating the ring center at the origin of the coordinate system making the z - axis identical with the highest symmetry axis . plots of b were generated using the molekel code 5.4.0.8.19 the magnetically induced current densities were obtained at the pbe0/6 - 311++g(d , p ) level using the four - component dirac coulomb hamiltonian as implemented in the dirac code.20 in dirac , the small - component basis set was generated using unrestricted kinetic balance ( ukb ) , which provides a flexible basis set for magnetic properties ( simple magnetic balance , smb).21 even though dirac is a relativistic code , the molecules studied here contain light elements of the periodic table , so that the relativistic effects are negligible . lobatto algorithm22 was used to integrate the magnetically induced current density to obtain the ring - current strengths ( rcs ) , also referred to as ring - current susceptibilities . this integration plane is a perpendicular bisector of a specific bond and starts approximately at the molecular center and extends up to 10  atomic units in all directions.21,23the magnetically induced current density plots were obtained by using the pyngl package.24 in order to gain further insight into the electron distribution , the adndp method was used.10 the full - density matrix in the basis of the natural atomic orbitals , as well as the transformation between the atomic orbital and the natural atomic orbital basis sets , were generated at the pbe0/6 - 311++g * * level using the nbo  3.0 code25 incorporated into gaussian 09 . figure  1 depicts the contour lines of the z component of the induced magnetic field ( bz ) produced by an applied external magnetic field , perpendicular to the molecular planes of benzene and hexafluorobenzene . clearly , at distances 1.0   from the ring center , the nuclear and  contributions are still present in both systems . at distances 1.0   , a well - defined shielding region ( involving the complete ring ) emerges . the continuous substitution of hydrogen by fluorine in benzene gradually decreases the size of the shielding region ( see figures  s1.1s1.2 in the supporting information ) . contour lines of the z - component of the induced magnetic field  ( bz ) , in a plane perpendicular to the molecule , for benzene ( left ) and hexafluorobenzene ( right ) . the scale is given in ppm and the spatial scale in  . when induced current densities are computed , there is a paratropic ring current at the center of the benzene ring . this phenomenon has been attributed , using a naive hydrodynamic analogy , to the superposition of diatropic currents of the  bonds.26 the magnitude of this paratropic current density diminishes after fluorination ( figure  2 ) . thus , it is clear that at the ring center , the shielding tensor should be affected by this paratropic contribution , avoiding an appropriate comparison of the magnetic descriptors among benzene and its fluorinated derivatives ( scheme 1 ) . the magnetically induced current density of benzene and hexafluorobenzene . the plots on the molecular plane and 0.52   above the molecular plane for benzene  ( left ) and perfluorbenzene  ( right ) are shown at the top and bottom of the figure , respectively . the integrated induced ring current susceptibilities , as well as different nics and bz computations , are summarized in table  1 . the rcs value for monofluorobenzene is slightly smaller and decreases as the number of fluorine atoms increases . the rcs value ( in na / t ) for benzene is 12.0 whereas for hexafluorobenzene is 9.9 . these results show the same trends as those reported by kaipo et  al.15 ( see figure  s2 in the supporting information ) , which is not surprising because the computed property is the same ; however , we calculated the rcs values with the aim of comparing them with nics and bz at the same theoretical level . notice that in this work , rcs is considered as the reference among the magnetic descriptors of aromaticity . comparison of rcs with nics(r ) and bz(r ) values calculated for benzene and fluorinated benzene derivatives . [ a ]  for system structures , see scheme 1 ; [ b ]  the negative value of both ( 1/3 ) bz(r ) and nics was used to facilitate comparison with rcs . four points at different distances with respect to the ring center were considered in order to evaluate the shielding tensor ( r=0.00 , 1.00 , 1.180 and 1.96   ) . the third and fourth points correspond to the distance where the in - plane component of nics ( 1/3(yy+xx ) ) becomes zero ( free - of - in - plane component ( fipc ) nics ) in benzene and hexafluorobenzene ( fipcmax ) , respectively . this is shown in the scatter diagrams of 1/3zz versus 1/3(yy+xx ) ( figure  3 ) , which provides information about the changes in the shielding tensor components ( anisotropy ) within the complete series of c6h6nfn molecules . this strategy was recently proposed in order to minimize the risks of reporting false ( anti)aromaticity data in inorganic heterocycles using nics.5 the shapes of all curves are in the negative region of both in - plane and out - of - plane components , which is characteristic of aromatic rings.5 plots of 1/3zz versus 1/3(yy+xx ) ( in ppm ) for the aromatic series c6h6nfn ( n=06 ) . the dots represent the distance  ( r in  ) where the in - plane component ( 1/3(yy+xx ) ) becomes zero . in figure  4 , the different magnetic criteria reported in table  1 are compared to the rcs for the series c6h6nfn . clearly , out of all the isotropic descriptors , only nics(fipcmax ) has a good linear correlation ( r=0.8512 ) with the rcs values . bz ( which is equal to nicszz ) has a good linear correlation with rcs , except for the value computed at the ring center , bz(0 ) . so , the suitable distances to compute nics or bz , as indicators of ring current intensities , are those where the nicsin - plane versus nicsout - of - plane curves show the same trend , which indicates that both magnetic criteria are mainly influenced by the same phenomena . the linear correlation of bz versus rcs suggests that bz values at distances 1.0   above the center of the molecular rings are more sensitive to both - and - ring currents . correlation between nics or the induced magnetic field and the ring current strength ( rcs ) values for the series c6h6nfn ( n=06 ) . negative values of nics are given in the y - axis to allow direct correlation as the aromaticity increases . the   electrons are localized in two sets of two - center two - electron ( 2  c2  e ) bonds ( figure  5  a ) , and the   electrons are distributed in three completely delocalized 6  c2  e bonds ( figure  5  b ) , as expected.11 in the case of hexafluorobenzene , 24  electrons are localized in twelve in - plane   lone pairs ( -lps ) . the   skeleton is comprised by six 2  c2  e cf bonds and six 2  c2  e cc bonds ( figure  6  a ) . remarkably , adndp provides two solutions to localize the   bonding in hexafluorobenzene . the first solution includes six pz - lps ( on=1.92|e| ) on the fluorine atoms and three 6  c2  e bonds ( on=2.00|e| ) distributed on the c6 fragment ( figure  6  b ) . the second solution involves six 2  c2  e cf   bonds ( on=2.00|e| ) and three 12  c2  e   bonds ( on=2.00|e| ) ( figure  6  c ) . while both solutions are viable , given that the second option completely localizes the   electrons , we consider this to be the most appropriate localization scheme . the a )  -bonding pattern and b )  -bonding pattern of benzene according to adndp . the a )  -bonding pattern and b , c )  two possible -bonding patterns of hexafluorobenzene according to adndp . the inductive effect can be clearly understood when the 2  c2  e cf bonds in hexafluorobenzene are compared with the 2  c2  e ch bonds in benzene using the same isosurface ( see figures  5  a and  6  a ) . the charge density inside the c6 ring is depleted in the case of the hexafluorobenzene . on the other hand , the resonant effect is also exhibited because the cf bonds have a -bonding character ( figure  6  c ) . a gradual substitution of h by f shows also a gradual increment of both effects ( see figure  s3.1s3.2 in the supporting information ) . therefore , the inductive and resonant effects on the fluorinated benzene are apparent from the adndp analysis . so , decreased aromaticity upon fluorination of benzene is consistent with the fact that the fluorine atoms attract electron density through cf   bonds ( inductive effect ) , deshielding the nuclear charge on carbon atoms . at the same time , the carbon atoms try to compensate this effect by withdrawing electron density from f through pz conjugation . therefore , such perturbation on the   cloud induces a loss of aromaticity , which is also supported by the analysis of the induced magnetic field ( see above ) . it has been also reported that fluorination decreases aromaticity in polycyclic aromatic hydrocarbons ( pahs).15 in contrast , the effect of fluorination on the aromaticity of a series of 1- and 2-indenones and their aza derivatives has been reported to be negligible,27 suggesting that these findings can not be extrapolated to heteroaromatic rings . a detailed analysis of the magnetic descriptors ( rcs , nics , or bz ) leads to the same conclusion , benzene is more aromatic than hexafluorobenzene . the adndp analysis supports the presence of inductive and resonant effects in the fluorinated species . the effects on the magnetic properties are rationalized as follows : the resonant effect should diminish the   electronic delocalization and , therefore , aromaticity in the fluorinated species . on the other hand , the inductive effect should decrease the charge density at the ring center and thus , decrease the magnitude of the paratropic current generated in this region . so , the evaluation of the magnetic properties at the center of the rings should strongly be influenced by this paratropic current , leading to erroneous interpretations of aromaticity . these findings could be extrapolated to any fluorinated species in the series c6h6nfn ( n=15 ) , therefore our results support the proposal of kaipio et  al.15 which states that fluorination should decrease aromaticity , due to the decrease of the   cloud on the ring . as a service to our authors and readers , this journal provides supporting information supplied by the authors . such materials are peer reviewed and may be re - organized for online delivery , but are not copy - edited or typeset . technical support issues arising from supporting information ( other than missing files ) should be addressed to the authors .
the electron delocalization of benzene ( c6h6 ) and hexafluorobenzene ( c6f6 ) was analyzed in terms of the induced magnetic field , nucleus - independent chemical shift ( nics ) , and ring current strength ( rcs ) . 
 the computed out - of - plane component of the induced magnetic field at a distance ( r ) greater than or equal to 1.0   above the ring center correlates well ( r2>0.99 ) with the rcs value . according to these criteria , 
 fluorination has two effects on the c6 skeleton ; concomitantly , the resonant effects diminish the  electron delocalization and the inductive effects decrease the charge density at the ring center and therefore reduce the magnitude of the paratropic current generated in this region . 
 the equilibrium between both effects decreases aromaticity in the fluorinated benzene derivatives . 
 these results can be extrapolated to determine the aromaticity of any derivative within the series of fluorinated benzene derivatives ( c6h(6n)fn , where n=15 ) .