switchable molecular compounds have significant 
 potential as very 
 high - density devices in the areas of data storage systems , molecular 
 switching , and display devices . promising candidates include transition 
 metal compounds , in particular octahedral fe complexes , 
 which can exist either in a low - spin ( ls ) or a high - spin ( hs ) state , 
 depending on parameters such as temperature or pressure . light can also induce a spin - state transition 
 in many of these compounds , where the resulting 
 hs state can often be stabilized under certain conditions , typically 
 at low temperatures , thus creating a molecular switch in the on 
 position . in order to improve on the performance of these systems , it is essential to characterize the hs state thoroughly , particularly 
 in compounds where some sort of anomaly occurs ; understanding how 
 we can modify the properties and the stability of the excited hs state 
 can lead to developments toward applications at room temperature . hs switching has long been described 
 by a simple and rather complete theoretical framework , suggested by 
 a. hauser and co - workers . this theory describes the transitions 
 along a single configurational coordinate ( scc ) , typically the breathing 
 mode of the molecule ( i.e. , a symmetric stretching along the fe  ligand 
 bonds ) , which was found to be valid for all complexes with monodentate , 
 bidentate , and often even polydentate ligands . however , experiments and theory suggested that the tridentate 
 [ fe(terpy)2 ] ( terpy : 2,2:6,2-terpyridine ) 
 molecule behaves differently in several respects , the most important 
 being that the scc model for the hs  ls transition fails , and the switching mechanism involves ( at least ) two vibrational 
 modes ( configuration coordinates ) . in addition to this anomaly , the 
 nature of the hs state was unclear . due to the axial compression exerted 
 by the terpy ligands , the symmetry is lowered , and thus the octahedral t2 is split into two quintet states of different 
 symmetry with terms b2 and e. these 
 states differ in the configuration of the t2 g subshell 
 and the molecular geometry , particularly the fe n bond lengths . 
 a very recent extended x - ray absorption fine structure ( exafs ) study 
 made an attempt to determine the structure of the populated quintet 
 state , but instead of resolving the structure it could only address 
 its distortion due to limited signal - to - noise conditions . on the basis of this it was concluded that the 
 structure for the e is in somewhat better agreement with 
 the experimental data than that of the b2 , 
 although this proposed structure contradicts the energetics arising 
 from the density functional theory ( dft ) models applied by these authors , 
 which suggest b2 as the more stable quintet 
 state . in this paper , we revisit the electronic and molecular 
 structure 
 of the quintet state of [ fe(terpy)2 ] in aqueous 
 solution with advanced experimental and theoretical techniques . we 
 investigate the reasons for and the consequences of the failure of 
 the scc model ( and thus the necessity for a description with two modes ) 
 in the molecular geometry and electronic structure . by combining x - ray 
 absorption and emission spectroscopies ( xas and xes , respectively ) 
 and x - ray diffuse scattering ( xds ) in a single pump probe setup 
 at the megahertz ( mhz ) repetition rate , we acquire simultaneously time - resolved structural and electronic 
 structural data with unprecedented quality in the picosecond time 
 domain . we prepare the quintet state of [ fe(terpy)2 ] with intense , 10 ps , green ( 532 nm ) laser pulses leading 
 to metal - to - ligand charge - transfer ( mlct ) excitations that subsequently 
 relax into the hs state on a subpicosecond time scale . we exploit 
 xes and xas x - ray probes to identify the formation of the quintet 
 state and determine its lifetime ; we also employ resonant x - ray emission 
 spectroscopy ( rxes ) at the 1s  3d excitations to gain further 
 insights into the 3d states . with exafs and xds we determine the structure 
 of the molecule in the quintet state and its surrounding solvent cage . the results are compared to those obtained on photoexcited [ fe(bipy)3 ] , which has been characterized by a wide range 
 of experimental and theoretical techniques and which follows the scc model ( the formation of its photoinduced 
 quintet state was shown to be accompanied by a 0.2  elongation 
 of all fe moreover , it has served to calibrate coarsely the arsenal of different 
 x - ray tools used in this work . indeed , 
 optical tools to date suffer from the clear identification of the 
 excited state in such compounds , as this requires an unambiguous observable . the uv  vis range is quite useful in detecting ultrafast changes , 
 but the overlapping bands due to different excited states hampered 
 in most cases a clear identification of the excited - state electronic 
 and ( even more ) molecular structure . the x - ray tools employed here 
 seek to fill this knowledge gap , and exploiting laser - pump  x - ray 
 probe techniques at mhz repetition rates allows us to gain new insights 
 into both the electronic and geometric structure changes due to its 
 unprecedented signal quality , as we demonstrate in this work . the laser - pump 
 x - ray - probe experiments 
 were performed at sector 7id - d of the advanced photon source ( aps ) 
 and at beamline id26 of the european synchrotron radiation facility 
 ( esrf ) . both setups utilized amplified laser systems with adjustable 
 repetition rates in the mhz range , thus increasing the duty cycle 
 of the pump  probe studies by orders of magnitude compared to 
 others that use conventional amplified laser systems with kilohertz 
 ( khz ) rates . the experimental strategy combined different time - domain 
 x - ray tools into one single setup , which enabled simultaneous measurements 
 of x - ray diffuse scattering ( xds ) together with nonresonant x - ray 
 emission spectroscopy ( xes ) and also 
 variants of x - ray absorption spectroscopy ( xas ) : ( i ) high - energy - resolution 
 fluorescence detection ( herfd ) and ( ii ) total fluorescence 
 yield ( tfy ) xas . the former was possible owing to the implementation 
 of a secondary x - ray crystal spectrometer that energy - resolved the 
 emitted fluorescence . this spectrometer also permitted us to record 
 resonant xes ( rxes ) to better resolve the 1s pre - edge and thus exploit 
 the improved sensitivity to the 3d orbitals ( details further below ) . time - resolved xds was recorded in the forward direction up to a q - value of around 4  with a mhz - gateable , 
 single - photon - counting area detector . this strategy of combined tools 
 had been implemented and tested on the photoinduced spin transition 
 of aqueous [ fe(bipy)3 ] . the present study applied this strategy and advanced setup to obtain 
 complementary information about [ fe(terpy)2 ] , whose investigation is supported by the analysis of the [ fe(bipy)3 ] data . the experiments at 7id - d ( aps ) utilized 
 24-bunch mode ( in top - up mode with a constant 102 ma ring current ) 
 with a 6.52 mhz x - ray pulse repetition rate . x - rays were monochromatized 
 with a diamond ( 111 ) double - crystal monochromator . an amplified laser 
 system ( duetto from time - bandwidth ) generating 10 ps pulses at its 
 second harmonic , 532 nm , was used for laser excitation . it was synchronized 
 to the storage ring radio frequency system and operated at a repetition 
 rate of 3.26 mhz , half that of the x - ray rate . the time delay between 
 laser and x - ray pulses details of this time - resolved setup are 
 given in refs ( 14 ) and ( 30 ) . baez mirrors to 8  7 m , ( h  v ) on the sample , 
 and the laser beam overlapped this spot with a larger spot size ( 100 
  80 m , h  v ) . the sample consisted of a free - flowing liquid jet of 
 13 mm aqueous [ fe(terpy)2 ] solution ( total 
 volume 200 ml ) . the liquid near the nozzle output was a flat sheet , 
 with thickness 0.1 mm , which was oriented at about 45 to both 
 laser and x - ray beams . this geometry permitted simultaneous recording 
 of xds data ( collected in forward scattering direction ) and xes data 
 ( collected sideways at 90 scattering angle , along the x - ray 
 polarization vector , via the analyzer crystal ) . for these measurements 
 the incident x - ray probing energy was tuned to 8.2 kev , far above 
 the fe k edge . the xds experiments were performed with a pilatus 100 
 k detector gated and synchronized to the bunch frequency as described 
 in our previous mhz work . following masking , 
 azimuthal integration , and scaling , difference signals were constructed 
 and averaged for each time delay and then corrected for multiple - pump  pulse 
 contributions as described in ref ( 14 ) . considering the jet speed ( 6 m / s ) , the 80 m 
 spot illuminated by the laser travels only about 2 m before 
 the next laser pulse arrives 307 ns later . therefore , it is obvious 
 that the same sample volume is hit many times in such a high repetition 
 rate experiment . nevertheless , the studied [ fe(terpy)2 ] complex is very stable , and no degradation was found in 
 any of the signals with exposure . the lifetime of the excited state 
 is 2 orders of magnitude shorter than the separation between the x - ray 
 pulses ; therefore , the spectroscopic data are not affected by the 
 previous excitation pulses . on the other hand , the energy transfer 
 to the solvent leads to a temperature increase in the water , which 
 affects the x - ray scattering data . this has been circumvented by using 
 the scattering signal recorded at a t = 200 
 ps time delay as the background . the increased solvent temperature 
 due to the previous laser shots is present in this water signal , and 
 thus it serves as an appropriate reference , as explained in detail 
 in our previous work on [ fe(bipy)3 ] . the k xes , ( 1s2p ) rxes , and herfd - xas 
 data were collected using a 10 cm diameter , spherically bent ( r = 1 m ) , single - crystal ge(440 ) wafer analyzer that focused 
 fluorescence onto a mhz - gated scintillator coupled to a photomultiplier . 
 a bent si(531 ) crystal with similar dimensions was used to record 
 the k spectra ; the energy resolution was 1 ev for both setups . 
 for recording herfd - xanes ( x - ray absorption near - edge structure ) , the selected emission energy was kept constant ( at the maximum of 
 the k1 line ) , while in the case of rxes both the 
 energy of the incident beam (  ) and the fluorescence energy 
 (  ) were scanned . the recorded rxes intensity is displayed on 
 a 2d map with one axis being the incident energy and the other their 
 difference , the energy transfer (  ) . at the aps rxes data were obtained on aqueous 
 [ fe(terpy)2 ] , while at the esrf rxes data 
 were taken on aqueous [ fe(bipy)3 ] . the experiments 
 at id26 ( esrf ) utilized 16-bunch mode ( no top - up , with decaying ring 
 currents from 90 to 60 ma ) with an x - ray repetition rate of 5.68 mhz . laser excitation was made possible by moving our amplified femtosecond 
 mhz laser system ( tangerine , amplitude systmes ) from the european 
 xfel to id26 . it was synchronized to one - fourth of the 16-bunch repetition 
 rate ( 1.42 mhz ) and to the storage ring . the laser - x - ray time delay 
 was adjusted electronically similarly to what is done at aps . here we focused on recording rxes planes around the pre - edge of photoexcited 
 aqueous [ fe(bipy)3 ] ( 10 mm ) . the incident 
 radiation was monochromatized by a cryogenically cooled si(111 ) fixed - exit 
 double - crystal monochromator . in contrast to the aps measurements , 
 the x - ray ( and thus laser ) spot size on the sample was much larger 
 ( 0.6  0.1 mm , h  v ) . nevertheless the fractional excited - state population 
 was not dramatically lower than at aps due to four times larger average 
 laser power used and to the wavelength of the tangerine at its second 
 harmonic , 515 nm , which is absorbed more readily by [ fe(bipy)3 ] than 532 nm due to a larger laser cross section . x - ray emission was analyzed via four spherically bent ge(440 ) crystal 
 analyzers oriented nearly orthogonal to the x - ray beam ( and along 
 its polarization vector ) . in addition , the dispersed x - ray emission 
 was directed above the sample to an avalanche photodiode ( si with 
 effective thickness 0.1 mm and 10  10 mm surface 
 area ) . the sample consisted of the same 
 liquid sheet as described for the aps setup . in order to investigate the electronic 
 structure of the quintet states of [ fe(terpy)2 ] we carried out dft calculations using the orca2.8 program package with the gradient - corrected ( gga ) bp86 exchange - correlation functional and the hybrid b3lyp * functional in 
 combination with the tzvp basis set . this approach has been proven 
 to be rather accurate for the description of spin - state transitions 
 in several fe complexes . the geometries of the a1 , b2 , and e states were fully optimized with the bp86/tzvp 
 method and then utilized as input for the simulation of the xds data 
 and for the calculations of xanes . to verify that the optimized molecular 
 geometries corresponded to true minima on the potential energy surface they were found to be positive for the a1 and e states confirming that these geometries 
 corresponded to true minima . however , two negative and degenerate 
 frequencies were found for the b2 state . since 
 this could indicate that the obtained b2 structure 
 is a transition state , we performed single - point computations along 
 the problematic normal modes as tests . we found that the potential 
 well was rather flat around the minimum in these dimensions which 
 can lead to a numerical error , resulting in negative frequencies . 
 on the basis of this additional result , we concluded that the b2 geometry also corresponds to a true minimum . in order to be able to compare the strengths of the fe n 
 bonds in the different electronic states , the mayer bond order indices , 
 which quantify bond strengths utilizing the actual computed wave function 
 of the molecule , were calculated . the e state of 
 [ fe(terpy)2 ] with d2d symmetry is 
 susceptible to the jahn  teller ( jt ) effect . to estimate the 
 contribution of this effect , geometry optimizations were repeated 
 with the bp86/tzp method , by applying d2d and c2 point group symmetries 
 with the adf2013.01 code . ( note that in c2 symmetry the correct notation for the jt - distorted e state would be b , as seen in the correlation 
 table in the supporting information ( si ) . 
 however , in order to avoid possible confusion between b and b2 term symbols , we decided to keep 
 the e notation throughout this paper . ) potential energies 
 of excited states have been calculated using time - dependent dft ( td - dft ) 
 at the b3lyp*/tzvp level , which was found to perform well for describing 
 spin - state switching for a series of fe compounds . since the ability of dft to provide accurate 
 spin - state energetics of fe complexes is limited , the b2 and e potentials have 
 been evaluated with an ab initio multireference second - order 
 perturbation theory , the caspt2 method ( complete active space second - order perturbation theory ) . these computations were performed with the molcas7.6 program 
 package , and their detailed description is given elsewhere . the potentials were calculated along two different 
 lines , one which connects the a1 and e minima and the other the b2 and e minima . a first - principles 
 approach based on dft in the generalized gradient 
 approximation ( gga ) was adopted to model the x - ray absorption near - edge 
 spectra . the fe k - edge xanes was calculated 
 in two steps : first the charge density with a 1s core - hole on the 
 absorbing atom was computed , and then the xanes spectrum was calculated 
 for the electric dipole ( 1s  p ) transitions only , using the 
 broadening parameters given in ref ( 47 ) . these two steps were performed with the pwscf and xspectra packages , 
 respectively , of the quantum espresso suite of codes . these codes use plane - wave basis sets , pseudopotentials , 
 and periodic boundary conditions ; the [ fe(terpy)2 ] molecule was included in a cubic cell large enough to avoid 
 interactions between molecules belonging to neighboring cells . a 110 ry cutoff energy was used for the plane - wave expansion ; the 
 charge density with a core - hole on the iron atom was determined at 
 the  point ; and a 2  2  2 monkhorst pack 
 grid was chosen for the calculation of the xas spectrum of the ls 
 ground state ( 3  3  3 for the photoinduced hs state ) . spin - polarized calculations were performed in the case of the photoinduced 
 hs state ( s = 2 ) . bylander form were used , and the parameters for their generation 
 are given in ref ( 52 ) . heisenberg 
 equation and can be simulated using multiplet 
 calculations based on the ligand field multiplet ( lfm ) theory . the 1s2p rxes process for [ fe(terpy)2 ] was modeled assuming electric quadrupole transitions 
 from the initial state 1s2p3d to 
 the intermediate state 1s2p3d , 
 followed by an electric dipole emission to the final state 1s2p3d . the individual absorption and 
 emission transition matrix elements were first calculated using the 
 method developed by thole , in the framework 
 established by cowan and butler , and then combined in a postprocessing step . details about these calculations can be found in refs ( 55 ) , ( 59 ) , ( 60 ) , and ( 61 ) . the calculations were 
 performed assuming an octahedral approximation ( d4h symmetry ) , with a crystal field parameter 
 10dq = 2.0 ev for the ls state and 1.3 ev for the 
 hs state ; the transition lines were then convolved with a gaussian , 
 accounting for ( some of ) the experimental broadening ( 0.3 ev ) and 
 a lorentzian accounting for the core - hole lifetime broadening ( 1.2 
 ev for the intermediate state and 0.2 ev for the final state ) . the 
 slater integrals that describe the electronic interactions were scaled 
 down to 80% of their atomic values to account for covalency . potential 
 energy surfaces ( pess ) are the key to understanding the photophysics 
 and photochemistry of molecular systems . it has been found recently 
 that the pes of fe or ru compounds with 
 a mn6 core ( m = fe or ru ) can be described reasonably well 
 using dft and td - dft , providing a means to qualitatively examine the de - excitation mechanism . therefore , we have completed our previous calculations on [ fe(terpy)2 ] by adding 
 the potential energies for the singlet and triplet metal - to - ligand 
 charge transfer ( mlct ) states . the most relevant ones of them are 
 plotted together in figure 1 with those of 
 the lowest singlet and quintet as well as three of the triplet metal - centered 
 states , along a combined coordinate based on the r(fe  nax ) bond length and the nnn angle of the donor 
 atoms of the terpy ligands . this coordinate connects the ls and hs 
 ( e ) minima , which was found to be relevant to the description 
 of this system . the potential energy curves show 
 very similar structure and crossings to those of [ fe(bipy)3 ] . therefore , similar de - excitation 
 pathways for both complexes after the excitation into the mlct may be expected . although the metal - centered quintet ( e ) crosses the mlct band somewhat close to its minimum , 
 the coupling between these states was found negligible in a recent 
 theoretical work on [ fe(bipy)3 ] , and it was 
 suggested that the system relaxes via the metal - centered triplet states 
 before the intersystem crossing to the quintet . this theoretical expectation has been proven experimentally 
 very recently by femtosecond - resolved xes . in [ fe(terpy)2 ] de - excitation via the triplet 
 states seems highly likely given that the potential curve of the b1 state crosses the mlct band at its 
 minimum . strong coupling between them would make relaxation to this 
 metal - centered triplet state rapid . verification of this de - excitation 
 pathway in [ fe(terpy)2 ] requires more involved 
 theoretical or experimental evidence ; moreover , one should keep in 
 mind that the true triplet minima do not lie on this combined coordinate , 
 as will be obvious in the final section of this discussion . nevertheless , 
 based on the mentioned crossing and the almost identical structure 
 of potential energy curves to those of [ fe(bipy)3 ] , the system is very likely to follow a decay path that includes 
 triplets . a possible sequence is indicated by the arrows in figure 1 . from the intermediate lifetimes determined for 
 [ fe(bipy)3 ] it is understood 
 that relaxation to the quintet state takes place on the subpicosecond 
 time scale , and based on the similarities and the possibly even better 
 positioned triplet states , one can assume this is true for [ fe(terpy)2 ] as well.figure 1dft ( a1 , a2 , and e ) and td - dft ( mlct , mlct , b1 , and e ) potential 
 energy structure of [ fe(terpy)2 ] along the 
 line connecting the a1 and e minima ; 
 arrows indicate a possible chain 
 of transitions for the full photocycle . the octahedral parent term 
 symbols are also given in parentheses to aid the identification of 
 the metal - centered states . ( as the curves for the e and b2 states on this scale would almost coincide , 
 for clarity only the first one is plotted . also , in order to keep 
 the figure relatively simple , from each of the mlct , the mlct , and the metal - centered singlet states , only the lowest - lying 
 ones are plotted . note also that the arrows are only schematic representations 
 of the transitions , particularly between parallel curves , as they 
 can not represent the coupling by the other vibrational modes between 
 the connected states . ) dft ( a1 , a2 , and e ) and td - dft ( mlct , mlct , b1 , and e ) potential 
 energy structure of [ fe(terpy)2 ] along the 
 line connecting the a1 and e minima ; 
 arrows indicate a possible chain 
 of transitions for the full photocycle . the octahedral parent term 
 symbols are also given in parentheses to aid the identification of 
 the metal - centered states . ( as the curves for the e and b2 states on this scale would almost coincide , 
 for clarity only the first one is plotted . also , in order to keep 
 the figure relatively simple , from each of the mlct , the mlct , and the metal - centered singlet states , only the lowest - lying 
 ones are plotted . note also that the arrows are only schematic representations 
 of the transitions , particularly between parallel curves , as they 
 can not represent the coupling by the other vibrational modes between 
 the connected states . ) having argued that the photocycle of [ fe(terpy)2 ] in many respects resembles that of [ fe(bipy)3 ] , it is evident that experimental studies of the subpicosecond 
 processes leading to the hs ( quintet ) state can only be achieved with 
 femtosecond - resolved techniques . the lower temporal resolution synchrotron 
 studies presented here probe the system after it has already reached 
 the hs quintet state and as it decays back to the ls ground state . 
 in order to verify the formation of the hs species and quantify its 
 yield , xas and xes spectra of an aqueous solution of [ fe(terpy)2 ] the tfy - xanes spectra ( figure 2a ) show significant 
 light - induced variations , the largest ones being the intensity increase 
 of the 7125 ev b feature and the intensity decrease of the 7142 ev 
 d feature . these changes are similar to those observed for the thoroughly 
 studied [ fe(bipy)3 ] complex , thus confirming the formation 
 of the photoinduced hs state . in the xes spectra ( figure 2b , c ) , for both the k and k emission 
 lines the spectral variations associated with the formation of the 
 photoinduced hs state are evident and fully consistent with previous 
 studies . the variations of both the k and the k 
 spectra are essentially identical to those of the [ fe(bipy)3 ] complex which is expected 
 since the xes line shapes of 3d transition metal ions reflect practically 
 only the spin state . the first coordination shells of fe in both complexes 
 are distorted octahedra , and xes spectra are not sensitive to the 
 other relevant differences in symmetry . fe k - edge tfy - xanes ( a ) , 
 k ( b ) , and k ( c ) x - ray emission 
 spectra of a 13 mm aqueous solution of [ fe(terpy)2 ] , with ( red line ) and without ( blue line ) laser excitation , 
 with a time delay t = 80 ps for the laser - excited 
 data . the evolution of the intensity of the b and d features , as well 
 as the changes in the emission lines , are the signature of a change 
 from the ls to hs configuration . the photoinduced hs fraction can 
 be determined from xes by comparing the spectra to ls / hs references 
 and was found to be  = 40% . the laser on xas and xes spectra ( figure 2 , red line ) represent the laser - excited state of the [ fe(terpy)2 ] complex , which is a combination of both ls 
 and hs contributions . to infer the photoinduced hs fraction (  ) , 
 we used an approach that utilizes xes spectral differences between 
 ls and hs references , referred to as the integrated absolute difference 
 ( iad ) approach . the typical photoinduced hs fraction observed during our experiments 
 at 80 ps delay was found to be  = 40% , although at high laser 
 power 60% could also be achieved . the formation and decay of 
 the photoinduced hs state can be followed 
 by monitoring the intensity of an appropriate spectral or scattering 
 feature at different time delays ( t ) . from 
 the xanes of [ fe(terpy)2 ] the intensity of 
 the b feature at 7125 ev ( which presents the largest variation at 
 the spin - state transition ) was used for this purpose ; its time evolution 
 is displayed in figure 3 . the corresponding 
 fit of the kinetics uses a model consisting of an exponential decay 
 and a broadening by a gaussian pulse , which is described in the si . the lifetime of the photoinduced hs state 
 is hsxas = 2.61  0.01 ns . this value is fully consistent with the lifetime 
 of hsopt = 2.54  0.13 ns obtained with the optical probe for aqueous 
 [ fe(terpy)2 ] . time 
 evolution of the intensity of the 7125 ev ( b ) feature of the 
 [ fe(terpy)2 ] xanes spectrum ( figure 2a ) , reflecting a quintet lifetime of hs = 2.61  0.01 ns . having 
 verified the formation of the hs state and determined its lifetime , 
 we make an attempt at determining its structure . the theoretical molecular 
 geometry is available from dft calculations , and the ground state matches excellently the available experimental 
 data , as can be seen in table 1 . for the possible 
 quintet structures , the dft models are very similar to each other ; 
 their corresponding fe this presents a great challenge to the experimental efforts 
 that aim to determine the difference in order to identify which hs 
 state is populated . the most distinct difference between the possible 
 quintet states is the anisotropic distribution of fe n bond 
 lengths in the first coordination shell , which is present in the case 
 of the e quintet ( leading to small but appreciable differences 
 between axial and equatorial bonds ) , whereas it is lifted in the b2 state . as will be shown in the following section , 
 the very high quality of the picosecond exafs spectra presented here 
 was decisive to resolve these very small structural variations and 
 provide unambiguous assignment of the quintet structure . the 
 calculations were carried out at the dft bp86/tzvp level ( for the 
 e at the ( relaxed ) jt - distorted geometry ) . bab denotes the mayer 
 bond order index , a powerful parameter quantifying the strength of 
 chemical bonds between atoms a and b ( based on mo coefficients and 
 overlaps ) . we have measured the exafs spectra 
 of the [ fe(terpy)2 ] complex in its ground 
 ls and photoexcited hs state ( at a 
 time delay of 80 ps ) with outstanding statistical quality . the spectra 
 allowed us to verify experimentally the dft - predicted molecular geometries 
 for both spin states . moreover , the bond length accuracy of the hs 
 spectrum , unprecedented in time - resolved experiments , permitted us 
 to determine with high confidence which of the two possible quintet 
 states ( e and b2 ) is populated 
 after the light excitation . the conventional curve - fitting approach 
 of fourier - transformed exafs spectra with standard software packages has been used . a detailed description of exafs 
 data reduction procedures , fitting approach , and methods used for 
 statistical evaluation of fit errors is available in the si . the fourier - transformed ( ft ) exafs 
 spectrum of the ls ground state 
 is shown in figure 4a together with the fit 
 function . in this case we have started with the dft - optimized a1 geometry as input structure and refined it during 
 the fitting process . the inset in figure 4a 
 shows the corresponding k - weighted exafs 
 spectrum in k - space together with the fit curve . ( the spectra in this figure appear shifted , as they have not been 
 phase corrected . ) the first peak observed in the ft - exafs spectrum 
 in figure 4a corresponds to the first coordination 
 shell , which contains solely contributions from single - scattering 
 paths involving axial and equatorial n atoms ( nax and neq , respectively ) and the central fe atom . the peaks in the 
 range between 2 and 4  correspond to the second and further 
 coordination shells around the fe ion , as well as multiple 
 scattering paths from the first coordination shell . in the theoretical 
 structure of the ls singlet state , n bond lengths 
 in the first coordination shell , with the axial fe  n bonds 
 about 0.1  smaller than the equatorial ones ( cf . table 1 ) . the obtained exafs fit is in full agreement with 
 this prediction , and we can unambiguously distinguish between the 
 shorter axial fe the refined experimental bond lengths are r(fe  nax ) = 1.874  0.004  and r(fe  neq ) = 1.969  0.004  , 
 in very good agreement with the dft - calculated bond lengths listed 
 in table 1 . ( a ) exafs of [ fe(terpy)2 ] in the ground 
 state ; the fitted bond lengths are r(fe  nax ) = 1.874  0.004  and r(fe  neq ) = 1.969  0.004  . ( b ) exafs spectrum of the 
 photoexcited quintet state of [ fe(terpy)2 ] ; the fitted bond lengths are r(fe  nax ) = 2.08  0.02  and r(fe  neq ) = 2.20  0.01  . the exafs spectrum of the photoexcited [ fe(terpy)2 ] molecule measured at 80 ps time delay is presented 
 in figure 4b . the spectrum was obtained using 
 the data reduction 
 method described in the si . n bonds ( together with the expansion of outer - lying 
 coordination shells ) is clearly visible from the shift of all main 
 peaks present in the ft spectrum toward higher r - values . similarly to figure 4a , the inset shows the 
 photoexcited exafs spectrum in k - space with the corresponding 
 best - fit result . to ensure an unbiased determination of the 
 excited - state structure , 
 a range of starting parameters was used that covered the structures 
 of the two proposed quintet states ( using the corresponding theoretical 
 models ) as initial guesses . n bond lengths is preserved in the hs excited 
 state only for the e structure , whereas the structure 
 of the b2 state has fairly similar fe independent of the initial guess , 
 in all cases the fit converged to a structure with substantially distinct 
 fe  nax and fe  neq bonds lengths , 
 clearly indicating that the anisotropic bond distribution is preserved 
 in the photoexcited state and that we can distinguish between the 
 two possible excited states . furthermore , a rigorous statistical evaluation 
 of the fit results based on -analysis is discussed 
 in detail in the si and undoubtedly excludes 
 the b2 quintet state due to the lack of any 
 substantial differences between its fe n bonds within the first 
 coordination shell and supports the e quintet state as 
 the only possible structural model of the hs state . the refined fe n 
 bond lengths are r(fe  nax ) = 2.08 
  0.02  and r(fe  neq ) = 2.20  0.01  , in excellent agreement with the theoretical 
 model for the e state ( cf . table 1 ) , which allows us to unambiguously assign its structure to the dynamically 
 measured hs state . it is worth mentioning that the inclusion 
 of outer coordination 
 shells ( beyond fe n single scattering contributions in the 
 12  range in figure 4 ) was possible 
 given the superior exafs data quality obtained in the experiment for 
 both the ls ground and photoexcited hs state spectra . in both cases , 
 the statistical goodness of the fit , evaluated using the  test ( see the si for more details ) , 
 significantly improved when extending beyond the first coordination 
 shell and also by taking into account some of the multiple scattering 
 contributions from outer - lying c atoms . for both ls and hs spectra , 
 only very minor changes to the second and third coordination shells 
 of dft - optimized geometries were needed for fits to converge to minimum 
  values ( further details can be found in the si ) . the x - ray scattering 
 signal from a ( dilute ) solution usually contains only a very small 
 contribution from the solute . however , calculating the difference 
 signal s(q , t ) = s(q , t ) s(q ,  ) effectively 
 removes the otherwise dominating , but almost constant , scattering 
 signal from the solvent . this procedure thus highlights the scattering 
 signature of the structural dynamics of the solute and its environment , 
 the solvent cage , and the structural changes in the surrounding bulk 
 solvent . the analysis approach applied here is fully analogous to 
 the one presented in ref ( 14 ) , where the analogous [ fe(bipy)3 ] compound was investigated . such difference signals acquired 
 at six time delays from t = 100 ps to t = 25 ns measured on the [ fe(terpy)2 ] solution are shown in figure 5a . qualitatively , 
 the characteristic negative feature around q = 0.81.2 
  corresponds to the immediate ( on the 100 
 ps time scale ) appearance of the bond - elongated hs structure , and 
 the oscillatory feature around q = 2.2  arises from temperature ( t ) and 
 density (  ) changes in the bulk solvent , as described in detail 
 in ref ( 14 ) for the 
 [ fe(bipy)3 ] complex and in ref ( 69 ) for the ptpop complex . figure 5b shows the experimental signal s(q , t = 1 ns ) 
 as well as two simulated signals smodel =   ssolute+cage + t  st +   s , where  is the photoexcitation 
 fraction and ssolute+cage has been 
 calculated for each of the two proposed hs structures e and b2 . the t  
 st and 
   s contributions describe the changes in scattering due to bulk - solvent 
 heating and density changes , respectively , and are determined in a 
 separate experiment . figure 5c displays each of these three contributions to the model difference 
 signal at t = 1 ns , where the magnitudes of 
 the individual contributions are comparable . separate fits were carried 
 out for each time delay and for both putative hs states , yielding 
 essentially similar results . ( a ) set of difference scattering signals s(q , t ) acquired 
 for [ fe(terpy)2 ] , color - coded according to 
 time delay . the inset 
 shows the evolution of the hs fraction obtained from the magnitude 
 of the solute - related contribution to the difference scattering signal 
 as a function of time delay . ( b ) s(q , t = 1 ns ) ( black circles ) and 
 the best - fit simulated difference signal for both of the suggested 
 hs structures ( red = b2 , green = e ) . ( c ) each of the three contributions to the simulated difference 
 signal , with the two solute - related difference signals again shown 
 in red ( b2 ) and green ( e ) . bulk 
 solvent contributions are shown in light   s and dark blue t  st . the time evolution of the magnitude 
 of  , the photoexcited 
 fraction for the hs state , is shown in the inset of figure 5a . fitting  in analogy with the fit of the 
 xas signal described above , we find hsxds = 2.7  1.5 ns , which is in reasonable 
 agreement with the xas - derived value ; the larger uncertainty arises 
 from the fewer time - domain data points in the xds data set . the time 
 evolution of t and  reflects 
 the dynamics of the energy transfer to the solvent . in general , they 
 follow what was observed in the analysis of [ fe(bipy)3 ] , although the density increase 
 is somewhat smaller in magnitude in the present case ( 0.1 
 vs 0.4 kgm ) and is at the limit 
 of detection . the temperature increase is also observed to be lower 
 ( 0.3 vs 0.6 c ) , in agreement with the lower 
 concentration of excited - state solutes depositing energy to the solvent 
 through the nonradiative decay processes . finally , it is evident from 
 figure 5b that the expected difference signals 
 for the two putative structures are very similar and that they fit 
 the acquired data almost equally well . in conclusion , the xds 
 results confirm the plausibility of the 
 dft structural models , but the present data set does not allow us 
 to recognize the tiny differences of the quintet structures in the 
 variations of the solute signal . moreover , the time evolution of t and  provides invaluable insights into the 
 solvent dynamics around the excited solute . experimental and calculated 
 fe k - edge xanes spectra of ( molecular ) 
 [ fe(terpy)2 ] . with the experimental data , 
 both detection modes ( tfy : thick lines and herfd : dotted lines ) are 
 presented ; for the theoretical spectrum ( thin line ) , only the electric 
 dipole contribution is plotted . ( a ) ls ground state ; the theoretical 
 spectrum was calculated using the a1 structure . ( b ) partially excited [ fe(terpy)2 ] ( laser 
 on , t = 80 ps ) ; the theoretical spectrum was 
 constructed as a linear combination of the calculated ls ( 60% ) and 
 hs ( 40% ) spectra . ( given the similarity of the two theoretical hs 
 spectra , the reconstruction was done only for the e structure 
 for clarity . ) ( c ) photoinduced hs state of [ fe(terpy)2 ] ; the plot shows the experimental spectra reconstructed from 
 the laser on and ls measurements ( utilizing the population from xes ) 
 and the theoretical spectra calculated for both possible hs states , e ( thin line ) and b2 ( dashed line ) . k - edge 
 xanes relates to the p - projected unoccupied electronic density of 
 states of the absorbing atom . since this is largely influenced by 
 the coordination and bonding , this technique is usually rather sensitive 
 to structural changes around the absorbing atom . for the laser - induced 
 quintet state of [ fe(terpy)2 ] , the population 
 of the antibonding eg * orbitals leads to dramatic rearrangements in the molecular 
 and electronic structure which , as has been shown in figure 2a , are clearly evident in the near - edge region . 
 the structural differences between the two quintet states , however , 
 are considerably smaller , and distinguishing them with xanes is more 
 challenging . yet the electronic structure of the e and b2 states differs , and one expects that this would 
 yield differences in their xanes spectra . with the objective of obtaining 
 further insights into the nature of the quintet state while at the 
 same time assessing the capabilities of xanes to reveal electronic 
 and structural information when very small changes are involved , we 
 compare experimental xanes spectra with theoretical spectra obtained 
 from dft calculations . the experimental xanes spectra of the 
 ground and laser - excited ( t = 80 ps ) states 
 were recorded in both tfy and herfd ( taken at the maximum of the k1 peak ) modes . herfd - xanes usually leads to improvement in the energy resolution 
 when compared to the conventional detection modes . in the current experiment , although the herfd spectra appear 
 somewhat sharper and better resolved , the effect is not dramatic . this can be explained by the fact that the relatively broad energy 
 resolution of the spectrometer ( 0.8 ev ) could not improve 
 too much further on the good resolution obtained already in the tfy - xanes 
 due to the narrow energy bandwidth of the incident beam ( 0.5 
 ev ) . theoretical modeling of k - edge xanes based on the single 
 electron 
 picture has became reliable , and its combination with experiment grew 
 a powerful tool in electronic structure analysis . the theoretical spectra were obtained with such a 
 well - established , reliable approach that takes into account the 1s 
 core hole , utilizing the quantum espresso program packages . electric dipole transitions from the 1s state 
 to the unoccupied p - states were calculated , and dft ( bp86/tzvp ) optimized 
 structures for the ls and hs states were utilized . comparing first 
 the spectra of the ls ground state in figure 6a it is clear that the dft - derived spectrum agrees very well with 
 the experiment . the energy positions and the relative intensities 
 of the major spectral features , labeled b , c , and d , are well reproduced , 
 including the high - energy shoulder of peak c ( which is resolved only 
 in herfd - xanes ) . the pre - edge peak labeled a consists of mostly quadrupolar 
 transitions and so is not expected to be properly accounted for by 
 the current electric dipole calculation . comparisons to the 
 laser - excited ( t = 80 
 ps ) experimental spectra are shown in figure 6b , c , and d. in figure 6b the measured laser 
 on spectra , which contain a mixture of ls ground state and hs excited 
 state contributions , are compared with a superposition of ls and hs 
 theoretical spectra . here the proportion of hs contribution is 
 taken to be 40% based on the excitation fraction derived from the 
 xes measurement . the calculated spectrum is seen to again reproduce 
 the key spectral features , peaks b , c , and d. for a comparison that 
 is independent of the ls and hs population fractions , the differences 
 between the laser on spectra and the ls ground state spectra are shown 
 in figure 6d . here the theoretical hs ls 
 difference , which has been scaled to match the intensity of the measured 
 curves , can be seen to mimic the shape of the experimental difference 
 spectra . the agreement in both of these comparisons validates the 
 compatibility of the dft calculated hs state structure with the experimental 
 observations . to test whether xanes could distinguish between 
 the two possible 
 hs states and perhaps confirm the exafs assignment , theoretical spectra 
 for the e and b2 states were compared 
 to experimental spectra for the hs state that have been reconstructed 
 from the laser on spectra assuming a 40% hs state fraction . the calculated spectra 
 are seen to be very similar , making a definitive assignment of the 
 experimental spectra to one or the other state difficult . comparing 
 the ratio of the b and c peak intensities obtained in herfd and in 
 the calculations , one could be tempted to interpret it as supporting 
 the e model to be closer to the experiment . however , the 
 c : d peak intensity ratios might lead to the opposite conclusion , which 
 warns us that this approach might be very far - stretched , as the calculated 
 intensities are apparently not accurate enough for such conclusions 
 in the present case . the primary electronic structure differences 
 between the e and b2 quintets manifest 
 themselves in the 
 occupation of the 3d orbitals , which brings us to the discussion of 
 the variation of the experimental pre - edge region ( peaks a , a , 
 and a ) upon excitation . being sensitive to the occupation of the 
 3d orbitals , this shall provide further information on the electronic 
 structure . indeed , as is evident from figure 6 , this region shows large variations after excitation . however , in 
 conventional xanes these peaks are usually weak and overlapping , and 
 they are also partly obscured by the tail of the main k edge ; therefore , 
 they are often poorly resolved . in order to overcome these difficulties 
 and obtain better resolved spectra , we have recorded 1s2p3/2 rxes , the combination of xanes in the preedge region , and the ( 1s2p ) 
 xes around the k1 peak . exploring the pre - edge region of 1s 
 xas with rxes can reveal more details about the 3d - related part of 
 the electronic structure . we performed 1s2p rxes on light - excited 
 [ fe(terpy)2 ] at a time delay of t = 80 ps . these data are plotted in the top row of figure 7 next to the ground - state spectrum . the difference 
 between the light - excited and ground - state spectra is shown along 
 with the ( fully converted ) hs spectrum that was reconstructed from 
 the difference spectrum assuming the population obtained from xes . fe in ( close - to ) octahedral environments is expected 
 to have a single pre - edge resonance when in the ls state and three 
 resonances when in the hs state . this has been 
 confirmed in several experiments including 1s2p rxes of an fe compound at thermal spin - state switching . these resonances are clearly present in the spectra in 
 figure 7 , and the increase in resolution and 
 information content with respect to xanes is evident when these features 
 are compared to peaks a , a , and a in figure 6 . while a single - electron approach 
 usually can not give an accurate description for 1s2p rxes spectra , multiplet theory 
 can do that for both ls and 
 hs states . for octahedral complexes the 
 nature of the pre - edge transitions is electric quadrupolar due to 
 symmetry reasons . the fen6 cores in [ fe(terpy)2 ] and [ fe(bipy)3 ] are distorted 
 octahedra but at a level of distortion that makes the quadrupolar 
 description sufficient to model the spectra . the calculations assumed 
 ls and hs fe ions in octahedral crystal fields , and the 
 results reproduced the single ls and three hs resonances as can be 
 seen in figure 7 . multiplet interactions in 
 the rxes final state of the ground - state system lead to small intensity 
 peaks that appear vertically , at different energy transfer values , 
 in the plotted rxes spectra . in the measured ls spectrum the expected 
 ( vertical ) multiplet structure is weak but obviously present near 
 the single resonance at around 7113.5 ev . = 7115.5 ev incident energy ,  
 = 710.5 ev energy transfer ) which is not present in the calculation . this feature must reflect a p - type contribution as a result of orbital 
 mixing ( i.e. , covalency ) . in fact , this mixing is expected to bring 
 in a dipolar character , which is seen in the xanes - calculated dipolar 
 contribution to the pre - edges in figure 6 . 
 upon laser excitation two more peaks ( at ca . = 7116 ev ,  = 711 
 ev ) appear , while the intensity of the main peak drops . the difference 
 of these spectra together with the known hs population allows us to 
 reconstruct the 1s2p rxes spectrum of the hs state of [ fe(terpy)2 ] , which shows a striking similarity to the calculated 
 one . experimental fe 1s2p rxes spectra , from aqueous solutions of [ fe(terpy)2 ] ( top row ) and [ fe(bipy)3 ] ( bottom row ) , showing the ground state , the laser - excited state 
 at 80 ps time delay , their difference , and the reconstructed hs spectra . the theoretical spectra ( middle row ) were obtained from ligand - field 
 multiplet calculations in an approximate oh local symmetry , and there the  laser on ( partly 
 hs )  panel was constructed by the superposition of 40% hs and 
 60% ls . the spectral intensity is plotted above the plane spanned 
 by the incident energy and the difference between the incident and 
 emitted energy , the energy transfer . the energy scaling is equal for 
 both axes and identical for all the plots in order to aid the comparison . we have also studied the 1s2p 
 rxes spectra of the benchmark system 
 [ fe(bipy)3 ] which has a somewhat different 
 symmetry ( d3 ) and less geometrical constraints 
 from the ligands as they are bidentate . the measured spectra are shown 
 in the bottom row of figure 7 . despite the 
 somewhat worse energy resolution caused by a twice - larger incident 
 bandwidth , it is apparent that the spectra are very similar to those 
 of the [ fe(terpy)2 ] . the almost identical 
 difference spectra indicate that the nature of the variations in the 
 two complexes are essentially the same . the crystal field multiplet 
 calculations nicely reproduce the overall 
 spectral shapes and the difference spectra . intra - atomic electron electron 
 interactions together with a crystal - field splitting are therefore 
 the main contributions to the spectra . the calculations neglect orbital 
 mixing effects and only consider electric quadrupole transitions ; 
 as a result spectral features may be missing on the high - energy side , 
 and the spectral intensities can not be fully reproduced . the 
 chemical sensitivity of the k absorption pre - edge is very different 
 from the main edge . while the main edge spectral shape is dominated 
 by the coordination shells , the pre - edge reflects electron electron 
 interactions within the d - shell as well as crystal - field effects and 
 orbital mixing . the striking similarity of the difference spectra 
 in the two compounds shows that intra - atomic d the 1s2p rxes planes 
 thus visualize the dramatic change of the electronic levels when the 
 molecules are in their short - lived photoexcited state . however , the 
 reasonably good description by the multiplet calculations , an ionic 
 approach utilizing oh symmetry , points toward the need for more involved calculations . 
 distinguishing between e and b2 in rxes would require full multiplet calculations including dipole 
 and quadrupole transitions with molecular wave functions that describe 
 the whole complex . angular - dependent rxes could help to identify the exact 
 3d configuration in single crystals ; however , 
 this is hardly possible in solution . although the [ fe(terpy)2 ] molecule has already 
 been investigated theoretically , a few details 
 relevant to the characteristics of the quintet states have been overlooked 
 or at least not discussed in due detail . these include the relation 
 between the structural differences and the occupation of the 3d orbitals 
 in the two quintet states e and b2 , the effects of the jahn  teller ( jt ) distortion on the e , and the electronic structure origin of the two modes needed 
 to describe the spin - state transition . furthermore , the previous results 
 raise disturbing questions : is it hopeless to distinguish the electronic 
 structure differences of two possible quintets with x - ray spectroscopy ? why is the e state populated when almost all dft calculations 
 predict b2 as being more stable ? here we complement 
 the referred works by performing the necessary analysis using td - dft 
 and caspt2 and provide answers to all of the above - mentioned issues . diagram 
 of the spin - unrestricted ks molecular orbitals for the 
 quintet states of [ fe(terpy)2 ] for e , and both the highly symmetric ( d2d ) and the jahn  teller distorted ( c2 ) form is also shown . ( note that in a rigorous description 
 the latter should be denoted as b in c2 symmetry . ) the energy levels ( top ) as well as the 3d 
 representation ( bottom ) of the most relevant mos of the b2 and e states with relevant 3d character 
 are shown . in order to unveil the variations 
 in the electronic structure that 
 cause the structural and bonding differences between the e and b2 states , we compare the relevant molecular 
 orbitals ( mos ) obtained with spin - unrestricted dft . to examine this 
 in detail , in figure 8 we present the highest 
 occupied and the lowest unoccupied ( kohn  sham ) mos . ( a more 
 extended version of this mo diagram is plotted in the si . ) not surprisingly , these orbitals at the 
 homo  lumo gap have substantial fe 3d character . the most interesting 
 and relevant molecular orbitals at the gap are those with a dominant 
 contribution from the atomic fe dxy , dxz , and dyz orbitals 
 of  spin ( i.e. , spin down ) . only one spin - down electron is 
 available for these three orbitals . which of these orbitals the electron 
 occupies determines the atomic and electronic structural differences . in the simplest approximation of ligand - field theory , the fe dxy , dxz , and dyz atomic orbitals are nonbonding . however , 
 this is altered in such a covalent molecule where the atomic orbtials 
 are mixed to some extent with ligand orbitals . in the bottom of figure 8 3d representations show the actual composition 
 of these mos for the b2 state . here the 5b1 orbital is populated , which still has nonbonding dxy character ; the atomic orbital contribution ( mixing 
 coefficient ) for the fe dxy is 84.2% , 
 while those for all nitrogen orbitals are below 1% . nevertheless , 
 it is apparent that the dxz and dyz orbitals are mixed with in - phase p - type 
 orbitals from the axial nitrogens ( 58.5% fe(3d ) , 6.24% n(p ) ) . the 
 resulting 2-fold - degenerate 32e pair of mos have a ( -)bonding 
 character . however , this has no effect on the properties of the b2 state since these mos are unoccupied . in the e state ( when constraining the symmetry to d2d as in ref ( 11 ) ) , the energy order of the 5b1 and 
 32e orbitals is swapped , and the 32e orbital pair is populated by 
 a single electron . these orbitals bond to the axial nitrogens , as 
 we just discussed , which shortens the fe  nax bond 
 lengths . ( this orbital mixing and the corresponding charge transfer 
 to the ligand via the bonding is usually referred to as backbonding 
 or back - donation . ) without constraints on the symmetry , the 
 jt effect removes the 
 degeneracy of the 32e orbitals in the e state and lowers 
 the symmetry to c2 . the highest occupied 
 orbital becomes the 63b , which has the main contribution from the 
 fe dyz atomic orbital , and thus the backbonding 
 to the axial nitrogens remains effective . the enhanced axial bonding 
 is clearly reflected in the mayer bond order indices reported in table 1 and provides a natural explanation for the geometry differences 
 of the quintet states . moreover , the energies of the levels of the 
 quintet mos become strikingly similar after applying the jt distortion 
 to the e ; the frontier orbitals have almost identical 
 energies . the lumo pair 64b and 70a ( |xz,|xy ) mimics the 32e ( |xz,|xy ) pair of b2 , and the even 
 higher - energy unoccupied orbitals show high resemblance for the b2 and e ( c2 ) states ( see si ) . such similarities of 
 the electronic structure readily explain why the presented spectroscopy 
 data are so similar for the two quintet states . the question 
 remains why the e state is populated , 
 contradicting most dft results that favor the b2 state as more stable . the energy difference 
 between the quintet states is rather small , and on such a scale the 
 dft calculations show a large scatter that depends on the choice of 
 the exchange - correlation functional . therefore , 
 we have performed caspt2 calculations that provide more accurate energy 
 differences . as can be seen in figure 9(b ) , the two quintet minima are separated along 
 a line that is almost orthogonal to the line connecting the ls and 
 quintet states . the energy difference and the relative location of 
 the potential wells belonging to the e and the b2 states the energy 
 difference is 41 mev with the e state lower in energy . moreover , as the e state is expected to split due to the 
 jahn  teller effect , we can expect the energy to be even lower . ( note that the jt effect only affects the angle between the planes 
 of the two terpy ligands , which changes by 4 , while the bond 
 lengths and other angles stay practically the same . ) the combination of the energy difference from caspt2 and 
 the jt energy lowering obtained from dft suggests that the distorted e can be as much as 150 mev lower in energy than the b2 state . as the transfer to the quintet(s ) takes 
 place in the first picosecond after light excitation and the measurements 
 are performed at a delay 80 ps by which time the excess energy 
 is transferred to the solvent , we expect to find the system in the e , the more stable quintet state . yet , since geometry optimization 
 is practically impossible at the caspt2 level on a such a large system 
 with numerous electrons , one should keep in mind that this expectation 
 might be biased . finally , we address the origin of the breakdown 
 of the scc model . 
 in most octahedral fe compounds that undergo spin - state 
 transitions a single configuration coordinate is sufficient as a reaction 
 coordinate , typically the breathing mode of the molecule which is 
 proportional to the metal  ligand distance . this has been exploited 
 in a very successful quantitative approach proposed by a. hauser that 
 describes well the hs given the slower than expected relaxations ( and apparently higher 
 barrier ) found for [ fe(terpy)2 ] in different 
 matrices , it was suggested that the scc - based model is not applicable 
 to this tridentate complex , and the involvement of an extra mode , 
 probably the ligand bending measured by the nnn angle , is required , 
 which increases the barrier height . many details of this have not 
 been brought to light ; in a recent paper we found that the nnn angle 
 of the ligand and the r(fe  nax ) 
 bond lengths are promising candidates to describe the reaction coordinates . ( a ) simplified molecular - orbital diagram for the singlet 
 ground 
 state of [ fe(terpy)2 ] . ( b ) schematic representation 
 of the minima for the lowest singlet , lowest two triplet , and quintet 
 states of their potential energy surfaces , along with the filling 
 pattern of their unevenly filled t2 g or eg * spin orbitals , which are most 
 relevant to their description . on the side , surface plots present 
 the graphical representation of the two eg * antibonding orbitals of the a1 together with the structural changes when these antibonding 
 orbitals are populated . the different directions of the expansions 
 and the constraints on the ligand geometry suggest an explanation 
 for the origin of the two modes . a hollow cross indicates the position 
 reached in this configuration space when the coordinate changes at 
 populating the eg*-type orbitals are added to approximate the transition to the quintet 
 state . ( c ) caspt2 potential curves of the two possible hs ( e and b2 ) states of [ fe(terpy)2 ] along the line connecting their minima , extracted 
 from the potential energy surface of ref ( 12 ) . their spin - up eg * orbitals are both populated , and their 
 electronic structure differs only in which of the three t2g - like nonbonding orbitals are filled with a spin - down electron . starting with the description 
 of the electronic structure of the a1 ground 
 state , which has no unpaired electrons , 
 we note that the spin - resctricted ks mos have identical energies for 
  and  electrons , as is observed on the frontier orbitals 
 of this state in figure 9a . the tridentate 
 terpyridine has geometrical constraints as the n atoms of its three 
 linked pyridine rings in this planar ligand can not take up ideal octahedral 
 positions around the fe center . due to this , the energy of the molecular 
 orbitals that have a dominant contribution from the 3d orbitals will 
 have a relevant split in energy , depending on whether they are oriented 
 parallel or orthogonal to the molecular axis that goes through the 
 nitrogens of the central pyridine rings and the fe ion . this splitting is small for the dxy , dxz , and dyz nonbonding 
 or weakly backbonding orbitals but high for the dz- and dx - y - based orbitals , which originate from 
 the octahedral eg * antibonding orbitals as seen in figure 9a . in addition to the geometrical constraints , the backbonding between 
 the axial n and the fe contributes to the axial distortion of the 
 molecule as well . the stronger bonding along the axis is again clearly 
 identified in the mayer bond order indices , as seen in table 1 . to reach the quintet states , both antibonding 
 eg * orbitals 
 need to be populated 
 with a spin - up electron . however , it is revealing to examine what 
 would happen to the molecular geometry if only one of these orbitals 
 is populated . y ) mo is based on the fe dx  y atomic orbital 
 mixed with p - orbitals of the four equatorial nitrogens ; 
 therefore , populating this antibonding orbital causes an expansion 
 in the molecule in this direction , opening up the nnn angle of the 
 ligand , without affecting the axial r(fe  nax ) bond length . indeed , the transition to the a2 state is almost perfectly described by the nnn opening , 
 as can be seen in figure 9 . this suggests that 
 the opening of the nnn angle of the ligands is one of the relevant 
 modes needed for the ls the eg*|z antibonding orbital has large mixing of the fe dz with the p - orbitals of the axial n 
 atoms and smaller mixing with those of the equatorial n atoms . therefore , 
 the population of this mo leads to an increase in the lengths of the 
 fe this results in the increase of the 
 axial r(fe  nax ) bond length without 
 substantial effect on the nnn angle of the ligands because the pull 
 on the side rings at the equatorial nitrogens by the iron caused by 
 axial elongation is compensated by the simultaneous weakening of the 
 fe  neq bonds . the optimized 
 geometry of the triplet with the populated dz - based orbital , b1 , differs 
 from that of the ground state almost only in r(fe  nax ) , as shown in figure 9 . ( note that 
 the geometry optimization of the b1 could only 
 be obtained by forcing the occupation of the eg*|z mo with a symmetry constraint on the orbital populations . ) consequently , we can identify that these population changes combined 
 with the geometrical constraints of the terpy ligand explain the need 
 for the two - mode description of the switching and the breakdown of 
 the scc model in this molecule . the validity of relating the two necessary 
 configuration coordinates to electronic structure effects is further 
 supported if we add up the two vectors pointing from the singlet ground 
 state to the triplet states in this coordinate system . each of these 
 vectors represent the structural variations caused by adding one electron 
 to an eg * orbital . therefore , we can expect that their sum approximates well the real 
 quintet geometry , if the relation between structure and orbital population 
 variations is valid . the resulting position ( marked by a hollow cross 
 in figure 9 ) lies indeed fairly close to the 
 actual positions found for the quintet states with the geometry optimizations . the mismatch is comparable to the distance between the e and b2 states , which differ in the populations 
 of t2g - like orbitals . accordingly , the two modes based 
 on the opening of the nnn angle and the variation of the r(fe  nax ) bond lengths grasp rather well the main 
 structural changes , and these seem to clearly correlate with the populations 
 of the eg*-like 
 orbitals . however , remaining smaller - scale variations in the electronic 
 structure are also reflected in the molecular structure . consequently , 
 further refinement of these modes or involvement of further ones is 
 needed to obtain a complete and fully satisfactory description of 
 this system . the challengingly small 
 differences in the molecular geometry and 
 electronic structure of the b2 and e quintets were addressed utilizing a variety of time - resolved x - ray 
 techniques . the minuscule explorable differences provided a demanding 
 testing ground for the techniques , enabling assessment of their ability 
 to discern small changes that occur in short - lived transient states . the formation and decay of the high - spin state was followed with all 
 applied techniques . xanes , xes , and rxes spectra , despite their high 
 quality and clear variations , could not reveal which of the two quintets 
 is realized . xds , which captured both the light - induced conversion 
 to hs and the behavior of the solvent in the vicinity of the molecule , 
 was also unable to distinguish between the two quintets . excellent 
 quality exafs spectra were able to resolve the bond - length variations 
 accurately , leading to unambiguous identification of e 
 as the formed quintet state which is in agreement with our theoretical 
 predictions . applying theoretical calculations ( dft , td - dft , and caspt2 ) , 
 we were able to explain the electronic structure origin of the differences 
 in the properties of the two possible quintet states . we identified 
 that back - bonding in the e state is responsible for the 
 structural differences between the quintet states . we revealed why 
 the e state is the more stable one and also checked how 
 this state varies upon the jahn  teller effect . the failure 
 of spectroscopy to distinguish the quintets was readily explained 
 by the striking similarity of their molecular orbital diagrams . finally , 
 we determined why one configurational coordinate is not sufficient 
 for the description of the ls  hs transition in [ fe(terpy)2 ] . due to the anomalous behavior of [ fe(terpy)2 ] among fe complexes that undergo 
 photoinduced ls to 
 hs transitions , the identification of the quintet state produced after 
 light excitation represents a milestone . our work should inspire studies 
 of the dynamics on the way to the quintet state , during the first 
 picosecond after light excitation , using x - ray free electron lasers . this will lead to a more complete understanding of the photocycle 
 of this system , which can motivate the design of novel molecules with 
 better photoswitching performance .
theoretical 
 predictions show that depending on the populations 
 of the fe 3dxy , 3dxz , and 3dyz orbitals two possible 
 quintet states can exist for the high - spin state of the photoswitchable 
 model system [ fe(terpy)2]2 + . 
 the differences 
 in the structure and molecular properties of these 5b2 and 5e quintets are very small and pose a substantial 
 challenge for experiments to resolve them . yet for a better understanding 
 of the physics of this system , which can lead to the design of novel 
 molecules with enhanced photoswitching performance , it is vital to 
 determine which high - spin state is reached in the transitions that 
 follow the light excitation . 
 the quintet state can be prepared with 
 a short laser pulse and can be studied with cutting - edge time - resolved 
 x - ray techniques . here 
 we report on the application of an extended 
 set of x - ray spectroscopy and scattering techniques applied to investigate 
 the quintet state of [ fe(terpy)2]2 + 80 ps after 
 light excitation . 
 high - quality x - ray absorption , nonresonant emission , 
 and resonant emission spectra as well as x - ray diffuse scattering 
 data clearly reflect the formation of the high - spin state of the [ fe(terpy)2]2 + molecule ; moreover , extended x - ray absorption 
 fine structure spectroscopy resolves the fe  ligand bond - length 
 variations with unprecedented bond - length accuracy in time - resolved 
 experiments . with ab initio calculations we determine 
 why , in contrast to most related systems , one configurational mode 
 is insufficient for the description of the low - spin ( ls)high - spin 
 ( hs ) transition . 
 we identify the electronic structure origin of the 
 differences between the two possible quintet modes , and finally , we 
 unambiguously identify the formed quintet state as 5e , 
 in agreement with our theoretical expectations .