time - dependent density 
 functional theory ( td - dft ) has been in the limelight 
 of quantum chemistry during the past decade . 
 indeed , paralleling the success of dft for the ground - state ( gs )
, 
 td - dft has now become the most widely applied method to explore the 
 excited - state ( es ) properties of medium and large compounds , with applications appearing in many applied fields 
 of chemical science . besides the choice of a basis set
, two approximations 
 are generally made while running td - dft calculations : the adiabatic 
 formalism is used , inducing the loss of 
 memory effects , and a specific exchange - correlation functional ( xcf ) 
 is selected to describe the nonclassical component of the electron 
though these two approximations are certainly not independent 
 of each other , it remains in practice easier to change the xcf than 
 to go beyond the adiabatic approximation , and the vast majority of 
 the benchmarks of td - dft have therefore considered this latter aspect . 

these benchmarks have been mainly focused on both vertical and 00 
 transition energies , and to a lesser extended es geometries , and have 
 much less considered the determination of other properties as illustrated 
 by ref ( 5 ) reviewing 
 td - dft benchmarks . in this framework ,
the present investigation is 
 devoted to the es dipole (  ) and traceless quadrupole ( q ) moments with a focus on medium and large -conjugated 
 molecules . to the best of our knowledge
, there are no previous 
 work devoted 
 to the benchmarking of td - dft for es quadrupole calculations , while 
 the previous investigations devoted to the assessment of xcfs in the 
 framework of calculations of the excited - state dipole moments (  ) and/or the excess dipole moment (  , the difference 
 between es and gs dipoles ) have mainly considered small compounds . 

the first comparisons probably appeared in 2002 when furche and ahlrichs 
 used experimental values to assess the performances of three generalized 
 gradient approximations ( ggas ) and two global hybrids for seven tiny 
 molecules .
for this set , they found that 
 the errors obtained with the gga ( ca .
the same year , amos , handy , and co - workers 
 compared td - dft and eom - ccsd dipole moments for numerous excited - states 
 in furan and pyrrole , in studies devoted to the assessment 
 of the hcth and b97 - 1 xcfs .
they noted that , contrary to the transition 
 energies , excited - state dipoles are strongly functional dependent , 
 and that this sensitivity is exacerbated for rydberg states .
these conclusions were refined by king in 2008 , 
 using more accurate reference values .
he 
 found that b97 - 1 provides  with average deviations 
 of ca .
0.5 d ( 1.1 d ) for a large number of ess in furan ( pyrrole ) . 
 in what is probably the largest study of  to date , 
 thiel and co - workers considered their famous set of 20 compact molecules to assess the quality of the dipole moments 
 obtained with bp86 , b3lyp , and bhhlyp using their own cas - pt2/tzvp 
 values as references .
they concluded 
 that ( i ) the dft dipole moments tend to be too small ; ( ii ) the errors 
 are smaller for the gs than the es ; ( iii ) the average deviations are 
 similar for n   * and   
  * transitions ; ( iv ) the average td - dft errors are in the 0.60.8 
 d range and only marginally depend on the functional , though these 
 average deviations are slightly smaller with bhhlyp and b3lyp than 
 with bp86 .
guido and co - workers reported the  determined 
 on five small molecules using six hybrid xcfs and also obtained excess 
 dipole values quite independent of the selected functional , with cases 
 for which  increased and decreased when increasing the 
 amount of exact exchange included in the xcf . for small charge - transfer ( ct ) molecules ,
tapavicza et al . found 
 that the cc2 and pbe0  were nicely matching experiment 
 values , whereas pbe led to too small values .
more recently , eriksen et al . compared the cam - b3lyp and eom - ccsd 
 dipoles of p - nitro - aniline in both gas and condensed 
 phases and found that this range - separated hybrid ( rsh ) xcf considerably 
 undershoots the magnitude of . a few specific investigations also appeared for larger 
 molecules . in 2009 , wong et al .
obtained the  of 
 the two lowest - lying ess in 12 oligothiophenes and found that the 
  are significantly larger with b3lyp than with a rsh , 
 but no benchmark values were provided to pinpoint the most accurate 
 functional . in 2010 , the  
 of a set of donor  acceptor benzothiazolium derivatives were 
 determined with b3lyp , cam - b3lyp , and cc2 . for the 20 dyes for which direct comparisons are possible , mean 
 absolute deviations of 5.1 and 1.7 d can be determined for b3lyp and 
 cam - b3lyp , respectively , indicating that the latter functional is 
 much more accurate for these ct molecules . in 2013 , zaleny 
 and co - workers compared the def2-qzvp gs and es dipole 
 moments computed with cc2 and seven xcfs for five photochromic molecules 
 ( four spiro derivatives and one push 
they found that none of the tested xcfs could 
 deliver accurate  in all cases , and , in contrast with 
 the previous studies , that b3lyp and pbe0 were more accurate than 
 rsh for the ct molecule .
the same year 
 peluso s group investigated the electro - optical properties 
 of a large azobenzene dye and concluded that while bmk could yield 
 a transition wavelength in very good agreement with cc2 , the  
 of the two approaches differed by more than 4 d with the sv(p ) atomic 
 basis set .
as can be seen from this literature 
 survey , more is needed to obtain a general analysis of the accuracy 
 of the td - dft . indeed , previous works were typically 
 limited to a small number of xcfs , rather compact or specific compounds , 
 and , more importantly , obtained contradictory conclusions , notably 
 regarding both the accuracy of rsh for evaluating the  
 of ct es and the amplitude of the dependency to the selected xcf . 

this has motivated the present investigation that treats a larger 
 series of  real - life  dyes and compares a large set 
 of xcfs to cc2 reference results .
all dft and td - dft calculations have been performed 
 with the gaussian09.d01 
 code , using optimal gs geometries determined 
 at the m06 - 2x/6 - 31+g(d ) level of theory .
the cartesian coordinates 
 of these structures can be found in the si of ref ( 20 ) .
dft and td - dft calculations 
 were performed using tightened dft integration grids and the aug - cc - pvtz atomic basis set .
the xcfs benchmarked here 
 are svwn5 , blyp , bp86 , olyp , m06-l , m11-l , b3lyp , pbe0 , m06 , bmk , sogga11-x , m06 - 2x , m06-hf , cam - b3lyp , m11 , and b97x - d , the six first being  pure  xcfs 
 ( free of exact exchange ) , the seven next being global hybrid xcfs 
 including a growing fraction of exact exchange , whereas the three 
 last are rsh .
note that the es dipole moments reported here correspond 
 to the total es density and do not rely on the so - called 1-particle 
 ci density .
the cc2 calculations have been performed on the 
 same geometries 
 with the turbomole program , systematically 
 using the ri scheme , and default convergence parameters 
 that were found to be sufficient for our purposes .
note that we report 
 the relaxed cc2 properties in the following and use them as reference 
 values .
as for the td - dft calculations , we selected the aug - cc - pvtz atomic basis set and did not apply the frozen - core approximation , 
 both parameters being chosen to obtain accurate reference values . 

of course , cc2 dipole moments are not error free . nevertheless , by 
 comparing the cc2/tzvp and cas - pt2/tzvp  reported by thiel , sauer , 
 and co - workers for their molecular set , a mean absolute error ( mae ) 
 as small as 0.11 d is obtained . for the 
  , the deviations between cc2 and cas - pt2 values 
 are larger due to the presence of several high - lying es suffering 
 from strong state - mixing .
nevertheless , by considering the lowest 
 es of each irreducible representation for the same set of molecules , 
 a mae of 0.43 d is obtained . in subsequent 
 works ,
thiel , sauer , and co - workers found that if a quite large atomic 
 basis set has to be selected to reach converged cc2 dipole moments , the cas - pt2 and cc2 dipole moments undergo similar 
 variations when increasing the basis set size . in short , this indicates that , despite their inherent limitations , 
 cc2/aug - cc - pvtz dipole moments can be safely used 
 to benchmark td - dft results . in the following the gs and es 
 dipole moments
are given as their 
 total values ; e.g. , for the gs , 1whereas the  
 were computed as2obviously , as 
 the total dipoles , this quantity 
 is positive irrespective of the relative amplitudes of es and gs dipoles . 
 in the tables below , to give insights into these relative magnitudes , 
 we indicate  in italics when  < 
 . for the calculations of the quadrupoles , we 
 selected only molecules with zero dipole moments and zero off - diagonal 
 quadrupoles .
we report below the traceless quadrupole , q , and more precisely , two of its independent components , qyy and qzz ; qxx being trivially obtained . in table s-1 in the supporting information , we report gs and es dipole 
 moments obtained for three molecules 
 using three different gs geometries , namely the optimal blyp/6 - 31+g(d ) , 
 b3lyp/6 - 31+g(d ) , and m06 - 2x/6 - 31+g(d ) geometries .
it turns our that 
 the  are only slightly affected by the selected 
 geometry ( variations in the 0.050.25 d range ) and that the 
 gs dipoles given by the different methods undergo similar changes 
 when modifying the structures .
for instance , the blyp , b3lyp , m06 - 2x , 
 and cc2  of 1 ( see scheme 1 ) , respectively increases by 
 + 0.23 , + 0.24 , + 0.24 and + 0.22 d when going from the m06 - 2x to the 
 blyp geometry .
the  , especially those obtained 
 at the gga level , are more sensitive to the structure .
for example , 
 the blyp es dipole of 3 decreases from 9.83 to 8.87 d 
 when going from the m06 - 2x to the blyp geometry .
in contrast , both 
 the cc2 and m06 - 2x  are less affected by the selected 
 geometry . in short ,
the conclusions obtained in this work are rather 
 independent of the selected ground - state geometry , but possibly for 
 the es dipole determined with pure xcf or , to a smaller extent , with 
 global hybrid xcfs presenting a rather limited exact exchange ratio . 

therefore , we stick to m06 - 2x/6 - 31+g(d ) geometries only in the following .
all molecules 
 treated herein are experimentally known and their 
 optical spectra have been measured ( see ref ( 20 ) for references ) . likewise , 
 the transition energies determined at various levels of theory can 
 be found elsewhere , and are therefore 
 not to be discussed in the present work .
the 15 
 medium - sized molecules included in the first part of our benchmark 
 are displayed in scheme 1 .
they were chosen to be representative of compounds of interest 
 for optical applications with both n   * 
 and    * transitions , local ( e.g. , 7 and 8) and charge - transfer excitations ( e.g. , 3 and 14 ) as well as members of the cyanine ( 1 and 11 ) and zwitterionic ( 9 ) classes 
 of dyes that are both known to be challenging for td - dft . for the 20 ess determined from this group ,
the 
  values are listed in table 1 , whereas the gs and es total dipole moments 
 values can be respectively found in tables s-2 and s-3 in the supporting information ( si ) .
first , we notice 
 that the excess dipole is often rather independent of the selected 
 xcf , except for several excited states presenting a significant ct 
 character , that is , a in 2 , a in 3 , a in 13 , a in 14 , and a 
 in 15 .
this explains why the xcf dependency was found 
 small with the set of thiel , that contains 
 ess presenting a limited ct character , but large for other sets of 
 compounds ( see introduction ) . for 9 that presents a zwitterionic nature
it is clear that no xcf delivers 
 a valuable picture for the change of dipole moments , and this is probably 
 related to the very specific electronic structure of this betaine 
 derivative . for ct states ,
a strong increase of dipole moment upon 
 excitation is , as expected , obtained and the magnitude of this increase 
 is often predicted to be much larger with pure xcfs than with both 
 global and range - separated hybrid xcfs .
this trend is related to the 
 well - known short - sightedness of pure dft functionals that allow an 
 excessive separation between the electron and the hole . however , in contrast with the transition energies , rsh do not systematically 
 outperform global hybrids for the  of ct states , for 
 example , they severely underrate the excess dipole for 3 , whereas pbe0 is close to the spot .
similarly in 14 , m06-l provides a more accurate  than cam - b3lyp , while 
 for the push  pull 10 , all xcfs undershoot the 
 cc2  by more than 1 d. 15 is another interesting 
 case , as both cc2 and rsh predict a decrease of the amplitude of the 
 dipole moment upon excitation , whereas pure xcfs foresee a large increase . 

the density difference plots corresponding to the first electronic 
 transition of 15 as given by three xcfs are displayed 
 in figure 1 .
as can 
 be seen blyp gives a strong ct between the thiophene ring and the 
 boron - containing moiety , the magnitude of this ct being attenuated 
 with b3lyp , whereas cam - b3lyp predicts a more localized   
  * valence excited - state centered around the ethynyl linker 
 and the vicinal rings .
accordingly , the ct distances , as measured 
 by le bahers metric , are 2.94 , 
 2.14 , and 0.94  with blyp , b3lyp , and cam - b3lyp , respectively , 
 paralleling the magnitude of the  for these three xcfs . 
 from these different examples
, it appears that the most accurate xcf 
 to evaluate the  of ct excited - states is strongly dependent 
 on the investigated molecule , which is in line with the previous contradictory 
 conclusions reported in the literature ( see the introduction ) .
density difference plots for the lowest dipole - allowed state of 15 as determined with three xcfs .
the blue ( red ) regions indicate 
 decrease ( increase ) of electron density upon transition . a contour 
 threshold of 8  10 au has been applied .
values in italics indicate that 
 the norm of the total es dipole is smaller than its gs counterpart .
m11-l yields excited - states 
 that 
 have a different nature for those two molecules explaining the large 
 discrepancies . average value 
 obtained from two 
 nearly degenerated excited - states ( see table s-3 in the si for details ) .
dipole moments determined from the 
 center of mass for this charged compound . with pbe0 , there is a strong mixing 
 between the n   * and   
  * like states that are nearly degenerate . in table 2
we provide 
 a statistical analysis for the data of table 1 : mean signed error ( mse ) , mean absolute 
 error ( mae ) , maximal positive and negative deviations as well as the 
 linear determination coefficient ( r ) 
 between cc2 and td - dft values .
the corresponding statistical data 
 for both  and  can be found 
 in table s-4 in the si . for the gs dipole moments ,
dft gives accurate estimates 
 with a mse in the 0.150.35 d range ( but always positive indicating 
 an overestimation by dft ) , a mae in the 0.300.50 d range ( m06-hf 
 being the only xcf to deliver an average absolute error exceeding 
 0.50 d ) , and a large determination coefficient ( r > 0.95 ) . the value of the latter tends to increase 
 with 
 the amount of exact exchange included in the xcf .
we also note that 
 the two tested meta - ggas , namely m06-l and m11-l , 
 yield more accurate  than other pure xcfs . for 
 the considered medium - sized molecules
, m06 emerges as the most accurate 
 functional for  as it delivers the smallest mae 
 ( 0.33 d ) together with a large r ( 0.99 ) , 
 though several other xcfs , e.g. , pbe0 and m06 - 2x , appear to be adequate 
 as well . for the es dipole moments ( see r.h.s . of table
s-4 in the si ) , the obtained results are both less accurate 
 and more dependent on the selected functional , and this exacerbated 
 xcf dependence of td - dft compared to dft can be ascribed to the presence 
 of ct es in the set .
the mse is positive for all pure xcf and negative 
 for all hybrid xcf , indicating that the former overestimate  ( to a larger extent than  ) , while the 
 former underestimate  , in line of conclusions 
 obtained for small molecules .
the  maes are significantly larger with the pure xcfs ( > 1 
 d , 
 m06-l and m11-l being again the most accurate of the group ) than with 
 hybrids ( < 1 d ) .
the correlation obtained with pure xcf is unsatisfying 
 for the es dipole ( r < 0.7 ) indicating 
 that their estimates are rather inconsistent , a problem that is partially 
 solved when a hybrid xcf is applied ( r > 0.8 ) , though the correlation remains worse than that for the 
 gs 
 property .
the smallest mae ( 0.71 d ) is again reached with m06 that 
 also delivers the largest r ( 0.93 ) of 
 the series . in a second group
, one finds b3lyp , pbe0 , and sogga11-x 
 that are slightly less satisfying than m06 .
for the 
 excess dipole ( table 2 ) , we notice a small mse for m11-l , due to the partial error compensation 
 between the overestimation of both  and . in contrast , hybrid xcfs that overshoot  but undershoot  , logically provide a significantly 
 too small  with the mse going from 0.45 d for 
 b3lyp to 1.15 d for b97x - d .
again , the smallest maes 
 ( ca . 1.0 d ) are reached with the global hybrid xcfs , range - separated 
 hybrids giving slightly larger deviations ( ca .
the best correlation 
 between theory and experiment is obtained with m06 - 2x ( r = 0.96 ) , and all xcfs including large shares of exact 
 exchange provide large r values , only 
 slightly smaller than the m06 - 2x value .
mse , 
 mae , max(+ ) and max( ) 
 are the mean signed error , mean absolute error , maximal positive and 
 negative deviations , respectively , whereas r is the linear determination coefficient .
the td - dft errors 
 are given with respect to cc2 , and are in d ( except for r ) .
for both 
 m11-l and pbe0 , the problematic 
 data have been removed for the statistics ( see footnotes in table 1 ) .
for the rest of this work , we have 
 therefore continued with hybrid 
 functionals only and excluded the pure xcfs that obviously deliver 
 less consistent values .
the set 
 of larger molecules represented in scheme 2 was next considered . in this
set , several 
 states with strong ct character , for example , 17 , 21 , 25 , 28 , and 30 are 
 included .
the  values are listed in table 3 together with the statistical 
 data , whereas the corresponding  and  values are given in the si . for 17 that presents a huge  at the cc2 level ( 21.8 
 d ) , both b3lyp
( 19.9 d ) and pbe0 ( 19.9 d ) provide more accurate estimates 
 than cam - b3lyp ( 16.1 d ) and b97x - d ( 14.1 d ) .
in contrast , for 30 , the b3lyp ( 10.6 d ) and pbe0 ( 9.7 d )  values 
 significantly exceed the cc2 reference ( 7.2 d ) that is reasonably 
 reproduced by cam - b3lyp ( 6.3 d ) .
this apparent lack of consistency 
 between the ct nature and the adequacy of rsh , already noted above , 
 is discussed in the following section .
values in italics indicate that 
 the norm of the total es dipole is smaller than its gs counterpart . 
 at the bottom of the table
these states were removed from the statistics . as can be seen in table s-7 in the si , for  ,
the mses are 
 positive for all xcfs except for m06-hf in this set of larger compounds . 

the  maes , in the 0.150.30 d range , are 
 obviously small for all xcfs .
very large r are also obtained irrespective of the selected functional , the poorest 
 value being 0.98 with m06-hf . for the  ,
all xcfs 
 underestimate the cc2 reference values with an error that roughly 
 increases with the amount of exact exchange included in the functional , 
 for example , the mse attains 0.25 d with pbe0 but 1.13 
 d with m06 - 2x .
1.01.5 d with most xcfs , although 
 significantly larger deviations ( > 2 d ) are reached with both m06-hf 
 and m11 .
the r values 
 are satisfying , though less impressive than for  ( see table s-7 ) . in short , the most important 
 trend obtained in section 3.1 ,
that is , 
 the overestimation of  by dft and the underestimation 
 of  by td - dft is confirmed for the compounds of scheme 2 .
nevertheless , compared 
 to those in section 3.1 , the average deviations 
 tend to be smaller for  but larger for . these changes are reflected in the statistical analysis 
 of the  given at the bottom of table 3 : the mse is positive for b3lyp and pbe0 
 but negative with all other xcfs . obviously , the maes are rather large , 
 the most accurate functional being bmk ( mae = 1.12 d ) , the least satisfying 
 being m06-hf ( mae = 2.37 d ) . in figure 2
we provide 
 the mse , mae , and r for both  and  , considering all 37 cases reported in 
 this work ( sections 3.1 and 3.2 ) , the corresponding representations for  are given in figure s-1 .
first , we note that one should expect , on average , an underestimation 
 of  and  when hybrid xcfs are used , 
 the signed errors being quite large with the three rshs and m06-hf . 
 for both  and  , the absolute deviations 
 are of the order of 1 d with b3lyp , pbe0 , m06 , bmk , sogga11-x , and 
 m06 - 2x , but are again larger with the rshs and m06-hf .
the r values are in the 0.900.95 d range 
 for  and are more dependent on the selected xcfs 
 for . indeed , if b3lyp provides the smallest mse ( top 
 of figure 2 ) , it delivers 
 the poorest r for  ( < 0.8 ) . 

in contrast m06 - 2x provides accurate trends with the largest r for  and large r for both  and . this success of m06 - 2x comes at the cost of significantly too small 
 excited - state dipole moments .
good 
 consistency with a significant but systematic deviation  actually 
 parallels its behavior for 00 energies .
mse ( top ) , mae ( center ) , and r ( bottom ) 
 obtained for the 37 es dipole moments ( left ) and excess dipole moments 
 ( right ) considered here .
see figure s-1 in the si for the corresponding graphs 
 for the gs dipole moments .
to further investigate the relationship between  and 
 the nature of the xcf in ct compounds , we have considered increasingly 
 long ,-nh2,no2-polyene chains 
 ( figure 3 ) .
the structures 
 have been optimized at the m06 - 2x/6 - 31+g(d ) level enforcing the cs geometry , whereas the electronic 
 properties have been determined with blyp , b3lyp , and cam - b3lyp using 
 the aug - cc - pvdz atomic basis set .
test calculations 
 with the corresponding triple- basis set have given very similar 
 trends .
the main results are represented in figure 3 , whereas the cartesian coordinates and the 
 corresponding transition energies and dipole moments can be found 
 in the si . when the chain length increases , 
 the transition energy to the lowest ( dipole - allowed ) excited - state 
 decreases .
as expected for such model ct systems , both blyp 
 and b3lyp deliver too small transition energies , whereas the cam - b3lyp 
 results nicely match the cc2 values .
indeed , irrespective of the chain 
 length , cam - b3lyp transition energies are the closest to the cc2 values . 

we further notice that , consistently with results obtained in the 
 previous sections , all three xcf overestimate  , with an error that is increasing with chain length for both blyp 
 and b3lyp but that is remaining rather constant with cam - b3lyp .
as 
 above , the three xcfs underestimate the cc2  for 
 rather short chains .
however , while the cam - b3lyp curve nicely follows 
 the cc2 one with a maximal  reached before 15 
 unit cells , both blyp and b3lyp show exploding  values that attain twice the reference value for the longest compound 
 investigated .
these evolutions explain the contradictory conclusions 
 obtained in the literature ( see introduction ) regarding the accuracy of rsh for determining the  
 of ct compounds . on the one hand , as cam - b3lyp provides too large 
 ( too small )  (  ) , the final 
  values are indeed significantly too small for all chain 
 lengths . on the other hand , one notices on the bottom right panel 
 of figure 3 that , depending 
 on the chain length , the most accurate xcfs can be b3lyp ( n = 9 ) , blyp ( n = 11 ) , or cam - b3lyp ( n = 15 ) , so that even xcfs providing inaccurate ct transition 
 energies can in some cases deliver rather accurate  
 due to an error compensation phenomenon .
however , it remains very 
 clear that the best trends are obtained with the rsh that provides 
 the most physically sound evolution of the excess dipole with chain 
 length .
evolution of the transition energy ( top left ) , gs total dipole 
 moment ( top right ) , es total dipole moment ( bottom left ) , and excess 
 dipole moment ( bottom right ) for increasingly long push 
all results are determined with the aug - cc - pvdz 
 basis set on the planar m06 - 2x/6 - 31+g(d ) geometries .
for this first 
 investigation of es quadrupole moments , we have selected the five 
 symmetric aromatic derivatives displayed in scheme 3 and considered the lowest dipole - allowed 
    * transitions . as for the dipole moments , 
 the gs and es values are listed in the si , whereas the excess values , q , can be found 
 in table 4 .
overall , 
 the cc2 and td - dft q are in good agreement 
 with each other , both in terms of sign and magnitude of the qyy and qzz components . for the considered set of compounds , 
 we notice a rather limited impact of the amount of exact exchange 
 included in the xcf ,
though both m06-hf ( significantly ) and m11 ( to 
 a lesser extent ) , two xcfs with very large amounts of exact echange , 
 tend to give exaggerated contrasts between the qyy and qzz components compared to cc2 .
the conclusions are similar for q. the obtained mae are of the order of 0.30.4 
 d for q and 0.20.6 
 d for q , though m06-hf ( and 
 m11 for the gs property ) deliver significantly poorer estimates .
the 
 obtained r values between td - dft and 
 cc2 are astonishingly large ( > 0.99 for all xcfs ) for q and remain rather satisfying though less impressive 
 for q. in other words , as for the dipole 
 moments , td - dft provides less accurate excited - state quadrupole moments 
 than dft does for their ground - state counterparts .
the errors that 
 can be expected from td - dft for this property are therefore ca .
0.4 
 d , though the most accurate xcf of the series for the 
 excess quadrupoles , namely cam - b3lyp , delivers tiny mse , mae , and 
 maximal deviations together with a very large r. several other xcfs , such as pbe0 and sogga11-x , also yield 
 accurate data .
interestingly , the m06 - 2x r is comparatively small , mostly due to the presence of an outlier , q3 .
we have investigated 31 ground - state dipole moments and 37 excited - state 
 dipole moments with td - dft using the large aug - cc - pvtz 
 atomic basis set and considering 16 different exchange - correlation 
 functionals .
the results have been compared to reference cc2 ( relaxed ) 
 values obtained on the same structures with the same basis set .
overall , 
 a rather small impact of the selected functional on both  and  was found , at the notable exception 
 of states presenting a charge - transfer character . on average ,
dft 
 provides too large  , whereas td - dft delivers too 
 small  , with a magnitude for the error that is 
 larger for the latter property .
consequently , the td - dft excess dipole 
 moments tend to be too small , by ca .
1.01.5 d. gga and meta - gga do not necessarily yield larger deviations than 
 hybrid xcf , but the trends obtained as measured by the correlation 
 with the cc2 values are poorer .
this conclusion also holds , to some 
 extent , for hybrid functionals with a small share of exact exchange , 
 e.g. , b3lyp .
it was known that global hybrid functionals tend to overestimate 
 the electron  hole separation in the charge - transfer state leading 
 to too small transition energies . as this exaggerated separation
can 
 compensate the generally too small  given by td - dft , 
 b3lyp or pbe0 can deliver excess dipole moments matching the cc2 data 
 even for strong ct cases , for which the transition energies obtained 
 with these functionals are obviously far from the reference values . 
 a study of increasingly long push 
pull systems indicated however 
 that the trends in  are much better reproduced by range - separated hybrids . 

overall , the xcf providing the largest correlation with cc2 for excess 
 dipoles is m06 - 2x , though this functional provides  too small by ca
cam - b3lyp is another successful 
 xcf , also giving a large r and a relatively 
 small mae .
eventually , for the five aromatic hydrocarbon derivatives 
 investigated , a generally nice agreement between the excess quadrupole 
 moments given by td - dft and cc2 is obtained , with average deviations 
 of the order of 0.4 d. .
 the accuracies of 
 the excited - state dipole and quadrupole moments 
 obtained by td - dft are assessed by considering 16 different exchange - correlation 
 functionals and more than 30 medium and large molecules . except for 
 excited - state presenting a significant charge - transfer character , 
 a relatively limited dependency on the nature of the functional is 
 found . 
 it also turns out that while dft ground - state dipole moments 
 tend to be too large , the reverse trend is obtained for their excited - state 
 counterparts , at least when hybrid functionals are used . 
 consequently , 
 the td - dft excess dipole moments are often too small , an error that 
 can be fortuitously corrected for charge - transfer transition by selecting 
 a pure or a hybrid functional containing a small share of exact exchange . 
 
 this error - cancelation phenomena explains the contradictory conclusions 
 obtained in previous investigations . 
 overall , the largest correlation 
 between cc2 and td - dft excess dipoles is obtained with m06 - 2x , but 
 at the price of a nearly systematic underestimation of this property 
 by ca . 
 1 d. for the excess quadrupole moments , the average errors 
 are of the order of 0.20.6 d for the set of small 
 aromatic systems treated . 
Introduction
Computational
Details
Results and Discussion
Conclusions