perhaps one of the most important concepts 
 in inorganic chemistry 
 is the nature of the bonding interactions between a metal center and 
 its ligands .
the covalency , or charge 
 donation from the ligands to the metal , of these bonds influences 
 the chemistry of transition metal complexes , including their reactivity , redox potentials , and magnetic 
 exchange .
ligand bonds is of fundamental importance 
 when attempting to rationalize the properties and reactivity of inorganic 
 complexes .
the influence of bonding on the metal orbitals occurs 
 through two 
 distinct mechanisms .
the first is via the direct dilution of the metal 
 d orbitals due to mixing with the ligand orbitals and is termed  symmetry 
 restricted covalency  due to its symmetry - dependent nature . 

the second , more subtle , mechanism is a distortion of the metal d 
 orbital radial wave functions due to bonding (  central field 
 covalency  ) .
accordingly , in a molecular orbital 
 ( mo ) picture , the impact of symmetry restricted covalency on the ground 
 state of an inorganic complex can be described as a linear combination 
 of metal and ligand orbitals according to eq 1 , where ( 1   ) represents the amount of 
 ligand character mixed into the metal d manifold.1 several experimental 
 techniques have been developed to assess the 
 covalency of metal 
ligand bonds , including ground state methods 
 such as analysis of hyperfine and superhyperfine couplings obtained 
 from epr and excited state techniques like visible 
 absorption and x - ray absorption spectroscopies 
 ( specifically the metal l - edge and ligand k - edge ) . as discussed in the cited references
, these methods have provided 
 significant insights into the nature of metal  ligand bonding 
 and have greatly improved our understanding of many inorganic systems .
it should be noted , however , that challenges and limitations exist 
 for all of these methods .
the extraction of covalency from epr requires 
 an epr active compound with resolvable ligand superhyperfine coupling . 

obtaining covalency information from absorption measurements depends 
 on the presence of suitable resolved spectral features and accurate 
 intensities .
additional experimental challenges are presented by the 
 ultrahigh vacuum conditions needed for transition metal l - edges and 
 the k - edges of light atom ligands ( c , n , o ) .
due in part to these 
 limitations , the extraction of reliable covalency values is often 
 quite challenging if not impossible , so additional methods for obtaining 
 this information are valuable .
the xes 
 process begins with ionization of a 1s core electron from the metal 
 using high energy incident x - rays ; the photons emitted during the 
 radiative decay of electrons from higher - lying states are then analyzed , 
 allowing xes to probe the occupied states of a metal 
 compound .
in this way , xes provides information that 
 is complementary to that obtained from xas and that is sensitive to 
 the bonding interactions of a complex .
further , as a hard x - ray technique 
 that probes core orbitals , xes is inherently element selective and 
 applicable to a wide range of sample states and environments
. the first row transition metal k xes spectrum can be 
 divided 
 into two regions : the intense k mainline ( composed of the k1,3 and k lines ) at low energy and the valence - to - core 
 region at higher energies ( figure 1 ) .
the valence - to - core 
 transitions have been shown to arise from orbitals of dominantly ligand ns and np character with a small amount 
 of metal np mixing that provides a dipole allowed 
 mechanism for the observed intensity .
as such , the valence emission 
 features are sensitive to the identity and electronic structure of 
 the bound ligands .
furthermore , the valence - to - core region can be effectively modeled 
 using a straightforward frozen - orbital one - electron scheme based on 
 density functional theory ( dft ) , as previously detailed .
the coupling of experiment to computations in 
 this manner has enabled valence - to - core xes to become a powerful probe 
 of the environment around a metal center , allowing , for example , the 
 identification of a central carbide in femoco , the detection of bridging oxos in the mn4cao5 cluster of photosystem ii , and 
 the assessment of the electronic structure of hydrogenase model compounds .
development of the k mainline , on the other 
 hand , has received 
 relatively less attention in the recent literature , especially with 
 respect to molecular systems .
assigned as metal 3p to 1s transitions , 
 the mainline has long been known to be sensitive to the spin state 
 at the metal center , with dramatic differences observed ( e.g. , decrease 
 in k intensity and decrease in the splitting between 
 the k and k1,3 ) as the nominal spin 
 at the metal is reduced . as intense , dipole - allowed transitions , the mainlines have been 
 used to assess changes in metal spin and oxidation state .
these changes can be understood 
 in a multiplet framework and are well established to be largely due 
 to modulations of the exchange integrals between the 3p hole and the 
 valence 3d electrons in the final state ; a schematic of the various states involved for a 
 3d metal is provided in figure 2(38 ) with extension to other d counts similarly 
 possible . however , to date , the analysis of k mainlines has 
 had limited application beyond their use as simple  fingerprints  
 for spin state .
we note , however , that cramer and co - workers previously invoked covalency to rationalize 
 the reduced k intensity seen for rubredoxin as compared 
 to fecl4 and similar observations were 
 made by gamblin and urch as well as glatzel 
 and bergmann .
these studies thus provided the first hints that the k mainlines 
 were not simply isolated probes of spin state , although , to our knowledge , 
 the contributions of covalency to the k mainline spectra have 
 never been systematically investigated .
pictorial depiction of 
 the transitions giving rise to the k 
 mainlines . in brief , 1s ionization from a totally symmetric s ground state ( 1s3p3d ) gives 
 rise to s and s intermediate states ( 1s3p3d ) that are split only by the small 
 1s3d exchange and , thus , are nearly degenerate .
enumerating 
 the possible final states in the absence of spin orbit coupling , one p and three p final states ( 1s3p3d ) are accessible ; the parent 3d terms 
 are shown in parentheses .
the intensity of the formally allowed transition 
 to the ( p)p state is calculated to be very 
 small and does not contribute significantly to the spectral shape . as the splitting between the k 
 mainline features is governed 
 largely by the 3p3d exchange integrals ,
they too should be 
 modulated by the metal  ligand covalency . by taking the mo description 
 of covalency expressed in eq 1 together with 
 the knowledge that the exchange integrals between the metal 3p core 
 orbitals and the ligand orbitals are expected to be much smaller than 
 the one center d3p|d3p integrals , expressions of the 
 type d3p|d3p reduce to eq 2 ,
where  clearly has a direct influence on the 
 observed splitting ( m and n are 
 rational numbers that depend on the actual orbitals involved and g1 and g3 are the 
 slater exchange integrals between the 3p and 3d electrons)2 herein , we experimentally observe significant 
 differences in the 
 k mainline spectra for a series of nominally high spin , d fe(iii ) compounds .
to explain these effects , we derive analytical 
 expressions for the k mainline splitting for d systems that define the k1,3  

these expressions nicely describe 
 the observations made between metals of different d counts and demonstrate 
 the necessity of invoking covalency to explain the trends seen between 
 the high spin ferric compounds studied .
the ligand field expressions 
 are , however , very general in nature , so we also employ computations 
 to obtain a more quantitative understanding of these spectra .
crystal field multiplet calculations are well - established as being 
 able to simulate k mainlines , so we begin by reproducing the 
 experimentally observed effects using this methodology and confirm 
 the mainline dependence on the p 
these calculations offer the ability 
 to independently tune the spin orbit coupling , ligand field , and the 
 coulomb and exchange integrals and allow us to deconvolute the effects 
 of each of these parameters .
although the ability to separately tune 
 these parameters is of much utility in isolating individual contributions , 
 the empirical nature of these modifications limits the information 
 that may be extracted .
thus , in order to obtain deeper insights , we 
 have developed a protocol for the calculation of k mainlines 
 using restricted active space configuration interaction ( ras  ci ) 
 calculations as implemented in orca .
these 
 calculations are a significant improvement over the multiplet methodology 
 as they explicitly and nonempirically include covalency , spin orbit 
 coupling , and ligand field effects . despite failing to properly include 
 dynamic correlation
, these calculations provide valuable insight into 
 the chemical factors that affect k mainlines and , together 
 with the ligand field expressions , establish a theoretical framework 
 to assess the contributions of symmetry restricted covalency to these 
 spectra .
importantly , for an initial test set of four high spin ferric 
 compounds , the general trends in the calculated spectra reproduce 
 experiment and the observed changes are shown to correlate with the 
 ligand character mixed into the metal d orbitals . this correlation 
 between the k mainline splitting and calculated metal 
ligand 
 covalency is then extended to a wider range of experimental data for 
 three additional high spin fe(iii ) compounds that were previously 
 reported , demonstrating that the splitting 
 between the k1,3 and k may be used 
 generally as a quantitative probe of metal  ligand covalency . 

the covalent modulation of the k mainline splitting is of the 
 same order of magnitude as the changes induced by a  two - electron 
 modulation of the d count ( at the atomic limit ) ; hence , these results 
 also serve as a cautionary note when employing mainlines as isolated 
  fingerprints  for spin state .
the implications of these 
 results for the broader application of k mainlines as a probe 
 of transition metal active site electronic structure are discussed .
anhydrous fef3 , fecl3 , and febr3 were obtained from aldrich and used 
 without further purification .
( et4n)[fe(sar)4 ] ( ar = 2,3,5,6-tetramethylphenyl ) was prepared by modification of 
 the method outlined in ref ( 43 ) .
namely , lithium thiolate was prepared by in situ deprotonation of the thiol with a lithium ethoxide solution , the 
 latter obtained by treatment of lithium hexamethyldisilazide with 
 excess ethanol . due to the air sensitivity or hygroscopic nature of 
 these compounds ,
samples for xes measurements were 
 prepared by grinding to a fine powder , packing into 1 mm aluminum 
 spacers without dilution , and sealing with 38 m kapton tape .
all xes spectra were collected 
 at ssrl beamline 62 ( 3 gev , 350 ma ) or chess c - line ( 5.3 gev , 
 200 ma ) . for ssrl data ,
the incident beam energy was set to 8 kev 
 using a si(111 ) liquid nitrogen cooled monochromator and was calibrated 
 using a fe foil .
focusing mirrors were used to achieve a 150  
 200 m beam at the sample , providing 10 photons / s . if necessary to prevent sample damage or detector saturation , 
 aluminum filters were inserted before the sample to attenuate the 
 incident beam .
energy resolution of the xes spectra was achieved using 
 a crystal array spectrometer employing five spherically bent ge(620 ) 
 crystals ( 100 mm diameter , 1 m radius of curvature ) aligned on intersecting 
 rowland circles , as described previously .
samples were maintained at < 20 k in an oxford cfi208 continuous 
 flow liquid helium cryostat and were positioned at 45 with respect 
 to the incident beam .
a he filled flight path was used between the 
 sample and spectrometer to reduce signal attenuation and emitted x - rays 
 were detected using an energy resolving si drift detector with a 3 
 mm vertical slit .
spectra were collected over the energy range of 
 7013 to 7123 ev with steps of 0.2 ev ( 70137079 ev ) and 0.15 
 ev ( 70797123 ev ) .
collection of data at chess was done 
 using a setup very similar to that at ssrl . in brief , the incident 
 beam was set to 9 kev using upstream multilayers ( 90 ev band - pass ) 
 and focused to a 1  3 mm spot providing 1  10 photons / s .
the sample was maintained below 30 k using a displex cryostat 
 and an array of five spherically bent ge(620 ) crystals was used for 
 energy selection .
a silicon drift detector with a 3 mm vertical slit 
 was used to detect emitted x - rays and data were collected over the 
 range of 7017 to 7121 ev with 0.36 ev steps ( 70177082 ev ) 
 and 0.24 ev ( 70827121 ev ) . for all spectra ,
the signal 
 was normalized with respect to the 
 incident flux measured in an upstream ion chamber .
the spectrometer 
 energy was calibrated using scans of fe2o3 and 
 reference energies of 7044.67 , 7060.62 , 7092.38 , and 7107.42 ev .
damage 
 scans were performed on each sample to determine acceptable exposure 
 times per spot .
if needed , data were collected from multiple spots 
 on a sample to avoid radiation damage .
all scans that showed no evidence 
 of damage were averaged using pymca and 
 the area under the spectrum from 70177120 ev was set to 1000 . 
 averaged mainline spectra were fit using blueprint xas version 1.2 .
reported values are obtained from the positions 
 of the fit components corresponding to the k and k1,3 peaks and are the average from at least 18 good fits . in 
 addition to the fits for the fef3 , fecl3 , febr3 , and ( et4n)[fe(sar)4 ] measured for 
 the present study , fits were also obtained for the previously reported 
 fe(acac)3 , ( tpfp)fecl , and fecl4 data .
representative fits and tabulated numerical data for all compounds 
 are provided in figure s1 and table s2 in the supporting information .
crystal field 
 multiplet calculations were carried out using the model implemented 
 by thole , the atomic theory developed 
 by cowan , and the crystal field interactions 
 developed by butler .
spectra were calculated 
 for 3p to 1s emission from fe d ions and 
 were energy shifted by 7055.1 ev to match experimental spectra .
except 
 when specified otherwise , lorentzian broadenings of 1.60 ev ( 70587100 
 ev ) and 5.10 ( 70207058 ev ) as well as a global gaussian broadening 
 of 1.20 ev were used to simulate lifetime and instrumental broadenings . 

ci can be broken down into two steps : an initial 
 dft calculation to generate quasi - restricted orbitals ( qros ) followed by the ras 
the initial dft calculations were performed using the bp86 functional , the zeroth - order regular approximation ( zora ) for relativistic effects following the model potential 
 implementation of van wllen , the 
 scalar - relativistically recontracted def2-tzvp basis set , and the conductor - like screening model ( cosmo ) in an infinite dielectric .
geometry optimizations 
 were performed using this same level of theory , beginning with crystal 
 structure coordinates .
qros were visualized using chimera 1.5.3 and were used to perform orbital coefficient analysis with moanalyzer ; they were also used as an input for the following 
 ras  ci and , when applicable , casscf calculations .
covalent mixings 
 and thus serve well as an input into the ras  ci calculations . 

these calculations are explained in detail in the supporting information , so only a brief description will be 
 presented here . in short , the ras  ci calculations are performed 
 to calculate the mainline transitions between the photoionized 1s3p3d intermediate state and all accessible 
 1s3p3d final states while taking 
 into account the full multiplet structure of this region .
, 
 one containing the core 1s and 3p orbitals and the other containing 
 the valence 3d orbitals .
these orbitals are frozen and then one electron 
 is removed from the core , allowing calculation of all possible septet 
 and quintet states ( which are themselves allowed to mix via spin 
transitions between the desired intermediate states and 
 final states can then be calculated , generating computed mainline 
 spectra . for sample inputs and further explanation ,
as noted in the introduction , the sensitivity of k mainlines 
 to the spin state of 3d transition metal centers is well established 
 and has been previously explained theoretically .
less explored are 
 the differences seen within a given spin / oxidation state , though these 
 are generally thought to be small , leading to the common assumption 
 that the k mainline serves as a fingerprint for spin state . however , as shown in figure 3 for a series of high - spin ferric complexes , even 
 compounds of the same oxidation state and spin state can show large 
 differences in the k mainline spectra .
namely , the energy splitting 
 between the k and k1,3 for these 
 compounds varies from 13.6 to 18.2 ev , a difference of nearly 5 ev 
 ( table 1 )
. k mainline spectra for a series 
 of ferric compounds that 
 demonstrate significant differences in mainline appearance despite 
 all compounds being high spin fe(iii ) .
previous studies and the present 
 analysis ( vide infra ) have demonstrated that k 
 mainline spectra are relatively insensitive to spin orbit , coulombic 
 repulsion , and ligand field effects ( supporting 
 information figures s2s4 ) but instead are dominated 
 by intra - atomic exchange .
this thus implies that the splitting between 
 the two dominant k mainline features must primarily correlate 
 with the number of unpaired electrons on the metal which is , in turn , 
 simply a function of the d configuration . 

however , the actual splitting requires a detailed inspection of the 
 multiplets that arise in the intermediate and final states . because 
 this is a nontrivial procedure , we provide a comprehensive collection 
 of the theoretical expressions that correlate the k mainline 
 splitting to the d configuration ( table 2 ) and detail the derivation of these equations in 
 the supporting information ( section 11 ) . 
 in the derivation
, it is assumed that in the final state only the 
 exchange couplings between the unpaired 3p electron and the unpaired 
 d electrons in their electronic 
 ground state contribute to the splitting .
this obviously 
 is a strong simplification , which , however , makes it possible to reach 
 some general conclusions . in the equations
, covalency is accounted 
 for in terms of the stevens orbital reduction factors t and e ( for the t2 g and eg orbitals , respectively ) ; these factors correspond to the quantity 
  in eq 2 . with these equations 
 in hand ,
it is illuminating to plot the values of e in terms of 4g1 + 42g3 ( a measure of p  d exchange ) for the free ion 
 case of t = e = 1 ( figure 4 ) to visualize the dependence of e on the 3d count . for d configurations where both high 
 and low spin ground states are available 

, respectively ; except 
 for the low spin ground states , these expressions are also valid for 
 tetrahedral complexes after removal of the indices  g  
 and  u  . dependence 
 of the k mainline energy splitting on the number 
 of 3d electrons is shown . when high and low spin ground states are 
 possible , these are indicated with red and blue markers , respectively .
although figure 4 nicely rationalizes  in 
 a very general way  many of the observed oxidation and spin 
 state dependencies of metal k mainlines , there are still factors 
 that will influence the  effective  values of 4g1 + 42g3 , and thus 
 possibly modulate the shapes of the mainlines , which must be assessed . 

namely , these factors include the identity of the metal , its oxidation 
 state , and the interaction of the metal with ligands . for higher metal 
 oxidation states or later transition metals , the radial wave functions 
 will be more contracted leading to higher intrinsic values of 4g1 + 42g3 .
in addition , 
 the effects of symmetry restricted and central field covalency on 
 the metal must be also considered . to estimate 
 the magnitude of the contribution that changes in effective 
 oxidation state have on the exchange energy , 4g1 + 42g3 , we performed hartree
 fock 
 and ab initio ci calculations ( details below and 
 in the computations section ) of the electronic 
 multiplets and slater  condon parameters for transition metal 
 ions in various oxidation states ( figure 5 ) . 

as expected , these values increase by , at most , 10% with increasing 
 oxidation state , reflecting a contraction of the radial wave functions 
 upon oxidation .
notably , this change  even between different 
 formal oxidation states  is less than what is observed experimentally 
 in the series of high spin ferric compounds ( 25% decrease ) .
effect 
 of varying oxidation state ( electron count ) on the effective 
 exchange energy ( 4g1 + 42g3 ) ( per spins pair ) from hartree 
fock limit calculations 
 using the computer code by r. d. cowan ( see supporting information for computational 
 results and list of values of 4g1 + 42g3 ) . as the oxidation state - dependent modification of the p 
d 
 exchange integrals does not appear sufficiently large to account for 
 the changes observed in the high spin ferric mainlines , we were left 
 with , as has been suggested previously , metal  ligand covalency 
 as the operative factor .
we thus fully explored the role of covalency 
 from both a crystal field multiplet and ras  ci perspective 
 and then use the new insights obtained to return to these ligand field 
 expressions at the end .
this analysis further develops the information 
 content of k mainlines beyond the common  fingerprint  
 interpretation . a detailed description of our calculations 
 for free atoms and ions 
 is contained in the supporting information ( section 12 ) , where we also provide a comprehensive summary of dipole 
 selection rules for all multiplets that are involved in the mainline 
 calculations for any d configuration . 

together with the extensive tabular material in section 12 of the supporting information , covalency estimates can 
 even be performed without any recourse to ab initio calculations .
simulation of 
 k mainlines has traditionally been accomplished with a crystal 
 field multiplet approach that has yielded significant insights into 
 the behavior of mainlines .
within such a quasi - atomic approach , 
 various parameters can be modified to effect spectral change : ( 1 ) 
 the 10 dq value parametrizing the ligand field splitting , ( 2 ) the 
 slater 
condon electronic repulsion parameters fdd2 and fdd4 that describe the electronic repulsion 
 within the d shell , ( 3 ) the parameters fpd2 and g1/g3 that describe the 3p/3d coulomb and exchange integrals 
 respectively , and ( 4 ) the 3p and 3d spin  orbit coupling constants .
the influence of many of these 
 parameters has been investigated previously , though in order to fully calibrate our new ras 
ci approach , 
 a systematic study of these effects for d fe(iii ) can 
 be found in the supporting information ( section 
 9 ) . as expected on the basis of the theoretical analysis in 
 table 2 and exemplified for fe below , of these parameters , only g1 and g3
have a significant influence on the calculated 
 spectral shapes ( figure 6 ) . scaling the p 
d 
 exchange integrals allows for the entire range of observed splittings 
 to be obtained , confirming previous assignments .
variation of 3p/3d or 10 dq 
 ( consistent with cramer and co - workers , supporting information figures s2 and 
 s4 ) within reasonable limits leads to essentially no discernible changes , 
 whereas modifying fpd and fdd over wide ranges 
 has only small impacts on the calculated spectra ( supporting information figure s3 ) .
calculated atomic multiplet 
 spectra on a ferric ion showing the 
 effect of reduced g1 and g3 values . to demonstrate that the experimental k1,3  

k energy splittings could be reproduced with these 
 calculations , the slater integrals were all scaled by an amount necessary 
 for the calculation to correctly match experiment ( supporting information figure s5 ) . a scalar energy shift and 
 broadening
d exchange parameters increase as expected from fef3 to fe(sar)4 ( supporting information table s1 ) and are generally in agreement 
 with the covalency values obtained from dft calculations ( table 3 ) ; by varying the values of the d  d and p  d 
 repulsion parameters we estimate the uncertainty in the gpd values to be 5% .
we note , however , 
 that equally good simulations of the experimental data could be obtained 
 with different sets of parameters and that the solution space becomes 
 even larger upon consideration of charge transfer and lower symmetry 
 systems . a less empirical methodology to investigate the effect of 
 covalency on the mainline spectra
is thus desirable . to further support 
 the assignment that the changes in the k mainlines are due 
 to differences in metal  ligand covalency , dft calculations 
 were employed . because dft generally leads to a fairly realistic description 
 of covalency ( with a slight tendency toward overestimation ) , it is 
 instructive to compare the calculated metal 
ligand covalencies 
 obtained from an analysis of the qros to the experimental energy splittings 
 for the high - spin ferric compounds ( figure 7 ) . although the covalency for these complexes is anisotropic ( e.g. , 
 different in each d orbital , table 3 ) , given 
 the experimental resolution it is appropriate to take the average covalency as a measure of the reduction of the p 
d 
 exchange ( defined by taking the average of the lwdin d populations 
 for the metal d based qros ) .
figure 7 clearly 
 demonstrates that a correlation exists between the experimentally 
 observed mainline splitting and the calculated average covalencies . 

although this correlation is satisfying and certainly captures the 
 essential physics of the problem , it can not be made any more quantitative 
 because dft is unable to explicitly calculate the multiplets that 
 account for the k mainlines .
k energy splittings 
 and the sums of the 
 qro coefficients from the metal - based d orbitals .
as 
 explained in the computations section 
 and in the supporting information , it is 
 straightforward to set up a restricted active space configuration 
 interaction protocol in which all intermediate and final states that 
 enter the mainline calculation are explicitly represented .
thus , provided 
 one uses as inputs for these calculations the dft qro orbitals that 
 show the correct covalent mixings with the ligand orbitals , one might 
 hope for a near - quantitative reproduction of the experimental spectra . as shown in figures 8 and 9 and table 4 ,
the calculated k mainline spectral shapes and energy 
 splittings correlate very well with experiment ( figures 8 and 9 ) and reproduce all of the major 
 trends .
importantly , the magnitude of the change across the series 
 of compounds is in excellent agreement with what is observed experimentally 
 ( 4.37 ev versus 4.54 ev ) .
furthermore , the calculated mainline splittings 
 correlate extremely well with the mo coefficients on the d - based orbitals 
 found in table 3 ( supporting 
 information figure s6 ) .
there is a systematic error in the 
 absolute transition energies that we attribute to the combined effects 
 of basis set incompleteness , scalar relativistic effects , and missing 
 dynamic correlation .
however , as shown by the success of related methods 
 for the calculation of x - ray absorption and emission spectra , this error is not relevant for 
 chemistry as it is highly systematic and can be eliminated through 
 calibration .
the calculated splittings are significantly larger than the 
 experimentally 
 measured ones , despite the fact that properly covalently  diluted
 
 molecular orbitals have been employed and all integrals have been 
 calculated correctly .
the reason for this behavior 
 is simply that equations of the form of eq 2 are grossly oversimplified and , possibly counter widespread belief , 
 calculating the  naked  ( unscreened ) electron  electron 
 interaction over covalently diluted mos is simply not enough to obtain 
 accurate results .
what is missing are the effects of dynamic correlation 
 which go a long way in providing a  screening  of the 
 electron  electron interaction and
this could be achieved , 
 for example , by second - order multireference perturbation theory ( raspt2 ) , 
 as in the related work by odelius et al . however
, this method is not available to us at the present stage 
 of development .
alternatively , these effects are also highly systematic 
 and hence can be accounted for , with considerable computational advantages , 
 through very modest parametrization as shown by the success of the 
 dft / cis and dft / rocis methods .
efforts along these 
 lines are underway in our research group . with 
 the results of ras 
ligand covalency , we last turn 
 to quantitatively applying this relationship to other ferric systems . 
 by applying this same methodology to three
previously reported high 
 spin fe(iii ) compounds , we see the obtained 
 relationship is generally applicable ( figure 10 ) ; this result is qualitatively the same if experimental intensity - weighted 
 average energies are used instead of fit peak positions ( supporting information figure s7 ) .
of course , 
 the covalency numbers obtained from an analysis of orbital coefficients 
 are artificial and will vary depending on the level of theory used 
 for the calculations ; hence , calibration to an  accepted  

value is necessary to establish a quantitative correlation between 
 the k mainline splitting and covalency .
as many possibilities 
 exist for reference values , all of which will give slightly different 
 correlations , we leave this exercise to the reader and simply demonstrate 
 that , according to the measure of covalency employed here , the observed 
 trend is applicable across a broad range of compounds
. correlation 
 between experimental k mainline splitting and 
 qro - derived covalency values for an expanded series of ferric compounds .
lastly , it is worthwhile to calibrate 
 the size of the effect shown 
 in figure 10 with the expected changes associated 
 with varying d count . by using the qro 
 calculated t and e values ( table 3 ) in the d ligand field expression from 
 table 2
, we can observe the effect of covalency 
 compared directly to that from d count 
 ( figure 11 ) .
the inclusion of this covalent 
 reduction reduces the splitting to what would be expected for a d ion ( for highly covalent complexes ) 
 or d ion ( for the highly ionic fluoride ) .
further , 
 for a d electron configuration , this is also complicated 
 by the fact that d and d configurations should have identical splitting 
 in the free ion limit .
these results indicate that extreme caution 
 must be exercised when attempting to relate an absolute k mainline 
 splitting to a given d configuration 
 or metal spin state .
correlations of this type will certainly be possible 
 but will only be valid over a very restricted range of possible chemical 
 variations .
effect of covalency on the k mainlines is demonstrated 
 alongside 
 the effect of d count .
the four compounds 
 from the high spin ferric series reported here are represented by 
 white circles .
in this work , we have investigated in detail 
 the multiplets that contribute to the initial , intermediate , and final 
 states of k mainline xes spectra and derived general equations 
 governing the energy splitting between the k1,3 and 
 k mainline features for any d count metal .
these equations reinforce previous work demonstrating that 
 the splitting of the mainline is primarily due to the 3p-3d exchange 
 integrals ( 4g1 + 42g3 ) , with high spin states giving rise to relatively intense 
 k features and large energy separations between the 
 two peaks .
this  free - ion  picture of the mainline shape 
 being governed by the number of unpaired electrons on the metal adequately 
 rationalized early observations and is the level of interpretation 
 that has dominated the literature ever since .
although this 
 correlation is often true , it breaks down when applied to complexes 
 that are not highly ionic .
indeed , from the data presented here  especially 
 febr3 and fe(sar)4 , vida supra  and elsewhere ( nibr2 , rubredoxin , nitrogenase 
 mofe protein ) , it is clear that in many 
 cases the mainlines deviate substantially from what would be expected 
 based upon the known nominal metal oxidation and spin states . in these 
 cases ,
applying the standard interpretation of k mainlines 
 will lead to incorrect conclusions about the metal electronic structure . from the equations in table 2 ,
we have demonstrated 
 that the value of e is dominated by the effective value of the quantity 4g1 + 42g3 , which depends upon a 
 number of factors , including the metal identity and oxidation state , 
 with higher values found for late metals and higher oxidation states . 

further , it is also modified by the stevens orbital reduction factors 
 that account for symmetry restricted metal 
ligand covalency , 
 reducing the predicted mainline splittings from what would be expected 
 for a free ion ( figure 11 ) . of these factors , 

only the covalent dilutions are subject to appreciable variation for 
 compounds with a given metal and oxidation state , implicating covalency 
 as the source of the observed modulations of the mainline splittings . using the series of high - spin ferric compounds as an example , we 
 have proposed a ras 
ci based protocol for calculating k 
 mainlines , which eliminates much of the empiricism associated with 
 the established crystal field multiplet - based approach .
these relatively 
 simple quantum chemical calculations correlate very well with the 
 experimental data and reproduce all important effects . in terms of 
 a very favorable ratio of cost to performance , we chose to take advantage 
 of the fact that density functional theory typically delivers molecular 
 orbitals that have  realistic  metal  ligand mixing 
 ratios ( e.g. , covalent dilutions ) and use these orbitals in the ras  ci 
 calculations , which properly account for all multiplet and spin  orbit 
 effects .
the missing dynamic correlation contributions in these calculations 
 lead to calculated splittings that are overestimated with respect 
 to experiment , though the correlation between theory 
 and experiment is excellent .
additionally , because the qros 
 used for these calculations have 
 reasonable covalent dilutions , they were also used to demonstrate 
 that a quantitative relationship between k mainline splitting 
 and covalency may be obtained .
doing so provides an intuitive picture 
 that nicely rationalizes the observed effects in chemically meaningful 
 terms , though it should be kept in mind that orbitals are not physical 
 observables and that one is arguing in terms of static one - electron 
 pictures that become invalid in the case of dominant multiplet effects 
 or strong electronic relaxation .
furthermore , when approaching 
 such estimates of covalency , it must 
 be clearly understood that they are based on a specific physical model 
 of the electronic structure of a given complex ( single determinant 
 mo theory , typically spin - restricted ) together with a series of approximations 
 that allow for a relationship of that electronic structure to actual 
 spectroscopic observables ( typical assumptions include frozen orbitals , 
 various one - center approximations , and the neglect of metal 
ligand 
 overlap ) . clearly , many of these assumptions are severe and it should 
 not come as a surprise when estimates obtained by different techniques 
 differ .
importantly , the compositions of individual orbitals do not 
 qualify as physical observables and hence any such procedure is not 
 physically rigorous .
it is , however , difficult to deny the usefulness of the underlying 
 intuitively appealing pictures that greatly help to rationalize trends 
 among series of related molecules .
it is useful at this point to compare the determination 
 of covalency from k mainlines to existing experimental methods 
 ( e.g. , epr superhyperfine couplings , metal l - edges , and ligand k - edges ) . 

analysis of superhyperfine couplings in epr spectra offers a measure 
 of the spin delocalized onto the ligands in the electronic ground 
 state , thus providing a way to quantify the mixing of metal and ligand 
 orbitals . because the superhyperfine couplings are dependent on the 
 identity of the ligands present , these measurements provide ligand - specific 
 covalency values .
obvious requirements include complexes that are 
 epr active and ligands with nuclear moments , restricting the range 
 of compounds for which this type of analysis may be performed .
metal l - edge and ligand k - edge xas monitor transitions from core 
 orbitals ( metal 2p or ligand 1s , respectively ) to unoccupied valence 
 orbitals with appreciable metal 3d or ligand np character . 

both of these techniques rely upon the measurement of accurate normalized 
 intensities in order to infer covalency . as the observed intensity is a product of the absorber character 
 in the acceptor mo ( i.e. ,  ) and the radial transition 
 moment dipole integral , these methods rely on the proper factorization 
 of these quantities .
hence , the abstraction of a covalency number 
 from metal or ligand xas is inherently indirect .
it is also important 
 to note that the  intrinsic  transition dipole moments 
 for a given metal or ligand are known to vary significantly with oxidation 
 state , effective charge , and nature of the donor / acceptor interaction , 
 thus introducing significant uncertainties .
it should be noted that 
 theoretical approaches can greatly aid in the determination of these 
 values .
however , this requires accurate intensities , which 
 can present a significant experimental challenge and in cases of nearby / overlapping 
 edges becomes prohibitive .
thus , though covalency measured by all 
 of these methods has provided great insights into a number of systems , 
 additional methodologies are clearly desirable .
in contrast , 
 the determination of covalencies from k mainlines 
 relies upon the covalent reduction of the 3p3d exchange integral 
 as manifested in the energy splitting between the k 
 and k1,3 features . in a simple picture
this is perhaps 
 similar to the measurement of metal l - edges in that the metal character 
 that is  lost  to the ligands is being probed ; hence , 
 k mainlines also provide a measure of the average metal  ligand 
 covalency . in contrast ,
though , the analysis of k mainlines 
 does not reference oscillator strengths , so the absolute intensities 
 of the xes features are not important and only accurate relative energies 
 are needed .
after accounting for all uncertainties in data acquisition 
 and processing , the splitting of the mainline can be determined to 
 within 0.5 ev for a typical high spin complex , which corresponds to 
 a covalency determination to within a few percent using the calibration 
 in figure 10 , a level of precision that compares 
 favorably to existing methods .
in addition to having a reasonable 
 sensitivity to covalency relative 
 to other techniques , k xes also offers numerous experimental 
 benefits .
first , it can be applied to any transition metal and is 
 not dependent on the presence of magnetic coupling between the metal 
 and ligands .
as a hard x - ray spectroscopy it can readily be applied 
 to a wide range of sample environments  including measurements 
 on dilute solutions and in extreme pressure 
 cells  that may be inaccessible 
 with other techniques .
this advantage is particularly clear in comparison 
 to first row transition metal l - edges and ligand k - edges ( of c , n , 
 o ) , which require highly damaging low energy x - rays and uhv conditions 
 that limit in situ applications .
ligand 
 covalency with promise to shed light onto many systems that would 
 otherwise be experimentally inaccessible .
lastly , as can clearly 
 be seen in figure 11 , the reduction in mainline 
 splitting due to covalency can be as 
 large as the reduction expected from a change in formal d - count .
thus , 
 any attempt to relate a given mainline splitting to a specific oxidation / spin 
 state must be undertaken with extreme caution .
cases certainly exist 
 where such an analysis is possible  comparisons between metal 
 oxides of differing oxidation states , for example  though these 
 situations are likely the exception rather than the rule .
rather than 
 reduce the utility of k mainlines , however , the theoretical 
 developments contained herein expand the information content that 
 may be extracted from k mainlines and further the ability to 
 quantitatively interpret these data .
in this work , we have demonstrated that the mainlines of metal 
 k xes spectra are a sensitive probe of the covalency of metal 
 complexes in addition to carrying spin - state information .
the effect 
 of covalency was established and explored using both crystal field 
 multiplet and straightforward ras  ci calculations .
ci 
 approach , in combination with a detailed analysis of the multiplets 
 that contribute to k mainline in general d configurations , yielded new insights into the chemical factors 
 governing mainlines .
it is now possible to obtain an experimental 
 estimate of covalency  analogous to that provided by epr , metal 
 l - edges , or ligand k - edges  from k mainlines .
finally , 
 these results indicate that caution must be used when attempting to 
 obtain spin state information from k mainlines due to the competing 
 and possibly overwhelming effect that covalency has on mainline shape 
 and energy .
 the mainline feature in metal k 
 x - ray emission spectroscopy 
 ( xes ) has long been recognized as an experimental marker for the spin 
 state of the metal center . however , even within a series of metal 
 compounds with the same nominal oxidation and spin state , significant 
 changes are observed that can not be explained on the basis of overall 
 spin . in this work , 
 the origin of these effects is explored , both 
 experimentally and theoretically , in order to develop the chemical 
 information content of k mainline xes . 
 ligand field expressions 
 are derived that describe the behavior of k mainlines for first 
 row transition metals with any dn count , 
 allowing for a detailed analysis of the factors governing mainline 
 shape . 
 further , due to limitations associated with existing computational 
 approaches , we have developed a new methodology for calculating k 
 mainlines using restricted active space configuration interaction 
 ( ras  ci ) calculations . this approach eliminates the need for 
 empirical parameters and provides a powerful tool for investigating 
 the effects that chemical environment exerts on the mainline spectra . 
 on the basis of a detailed analysis of the intermediate and final 
 states involved in these transitions , we confirm the known sensitivity 
 of k mainlines to metal spin state via the 3p3d exchange 
 coupling . 
 further , a quantitative relationship between the splitting 
 of the k mainline features and the metal  ligand covalency 
 is established . 
 thus , this study furthers the quantitative electronic 
 structural information that can be extracted from k mainline 
 spectroscopy . 
Introduction
Materials
and Methods
Computations
Results and Analysis
Discussion
Concluding Remarks