Quantitative and Chemically Intuitive Evaluation of the Nature of M−L Bonds in Paramagnetic Compounds: Application of EDA‐NOCV Theory to Spin Crossover Complexes

Abstract To improve understanding of M−L bonds in 3d transition metal complexes, analysis by energy decomposition analysis and natural orbital for chemical valence model (EDA‐NOCV) is desirable as it provides a full, quantitative and chemically intuitive ab initio description of the M−L interactions. In this study, a generally applicable fragmentation and computational protocol was established and validated by using octahedral spin crossover (SCO) complexes, as the transition temperature (T 1/2) is sensitive to subtle changes in M−L bonding. Specifically, EDA‐NOCV analysis of Fe−N bonds in five [FeII(L azine)2(NCBH3)2], in both low‐spin (LS) and paramagnetic high‐spin (HS) states led to: 1) development of a general, widely applicable, corrected M+L6 fragmentation, tested against a family of five LS [FeII(L azine)3](BF4)2 complexes; this confirmed that three L azine are stronger ligands (ΔE orb,σ+π=−370 kcal mol−1) than 2  L azine +2 NCBH3 (=−335 kcal mol−1), as observed. 2) Analysis of Fe−L bonding on LS→HS, reveals more ionic (ΔE elstat) and less covalent (ΔE orb) character (ΔE elstat:ΔE orb 55:45 LS→64:36 HS), mostly due to a big drop in σ (ΔE orb,σ ↓50 %; −310→−145 kcal mol−1), and a drop in π contributions (ΔE orb,π ↓90 %; −30→−3 kcal mol−1). 3) Strong correlation of observed T 1/2 and ΔE orb,σ+π, for both LS and HS families (R 2=0.99 LS, R 2=0.95 HS), but no correlation of T 1/2 and ΔΔE orb,σ+π(LS‐HS) (R 2=0.11). Overall, this study has established and validated an EDA‐NOCV protocol for M−L bonding analysis of any diamagnetic or paramagnetic, homoleptic or heteroleptic, octahedral transition metal complex. This new and widely applicable EDA‐NOCV protocol holds great promise as a predictive tool.


Introduction
The functiono fm etalloenzymes, [1] catalysts [2] and materials [3] is often utterly dependent on the finely tuned properties of a first-row transition metal ion(s), M, at the active site. Finetuning the MÀL interactions [4] -and hence the ligand field imposed on M-in ap redictable manner [5] is generallyd one by a series of small modifications to ap articularl igand skeleton, such as varying as ubstituent or exchanging aC Hf or an N atom in ah eterocycle,w ithin af amily of relatedc omplexes. [5b,k, 6] We have trialled an ew in silico approach to improving our detailed understandingo fMÀL interactions in any octahe-dral complex, [7] in particular aiming to address this in paramagnetic 3d complexes.
Bold formatting is used to highlight the fragmentation schemeu sed for the MÀL complex.I talics are used for low spin (LS)a nd high spin (HS)s tate abbreviations.B old and italic formatting is used for the organicl igand family, L azine ,u sed in the complexes investigated in this study.
Specifically,energy decomposition analysis(EDA) and natural orbitalfor chemical valence theory (NOCV) [8] were used in combination [9] in order to provide af ull, quantitative and chemically intuitive ab initio description of the MÀL interactions during bond formation:t he various contributions to the total interac-tion energy (DE int )a re assessedb yt he use of EDA, and then a breakdown of the orbital contribution (DE orb )t oq uantitatively assess the MÀL bond character is achieved by the use of the NOCV scheme.
Whilst EDA-NOCVm ethodology has been extensively used to study diamagnetics ystems, [10] it has rarely been applied to paramagnetic transition metal complexes, [11] lanthanide/actinide complexes, [12] or indeed to other open-shell radicals ystems; [13] the somewhat related ALMO-EDA has been used to investigatep ressure-induced SCO. [14] Nevertheless there were no systematic studies that could provide guidance with respect to ag eneral fragmentation scheme (i.e., M n + + + L 6 vs. ML 5 n + + + L for ag eneral ML 6 complex) suitable for EDA-based bonding analyses and direct comparison of any metal complex-so we rigorously,a nd successfully,address this issue herein.
Our first, and key,s tep was therefore to establish as uitable, generally applicable fragmentationa nd computational protocol for the EDA-NOCV analysis of any diamagnetic or paramagnetic, homoleptic or heteroleptic, octahedral complex. To do this, at est system that enables validation of the outcomes must be chosen.
Spin crossover (SCO)-active complexes [15] provide av ery sensitive experimental probe of subtle changes in MÀL bonds as L is modified, as the transition temperature (T 1/2 )a tw hich the complexs witches betweent he low-spin( LS) and high-spin (HS) states in solution is sensitivet ot hese changes. [5b,d,k, 6c] Hence, af amily of five [Fe II (L azine ) 2 (NCBH 3 ) 2 ]c omplexes that vary in the choice of the azine ring (Figure 1), for which al inear correlationo ft he T 1/2 with the 15 NNMR chemical shift of the coordinating azine nitrogen atom in the respective ligand, [5k] was chosen as the test system to trial this new approacht oi mprovingo ur detailedu nderstandingo fMÀL interactions in octahedral complexes. [7] Application of the resulting new protocol to this family of SCO-active complexes then enabled us to evaluatet he changes in the bondingp roperties across the family,o btained by EDA-NOCV calculations, [9] such as the s-donora nd p-acceptor character of the respective ligands, against the trend in the observed T 1/2 values of the complexes. Doing this enabled us to determinew hether or not the theoretical findings are consistentw ith experiment, and hence provide quantitative and chemically intuitive insights into the nature of the MÀL bonds under consideration.
Finally,t he optimized EDA-NOCV protocol developed for the SCO-active [Fe II (L azine ) 2 (NCBH 3 ) 2 ]c omplexes was then used for the closely related [Fe II (L azine ) 3 ](BF 4 ) 2 family of LS complexes, [16] where our calculations showed that three L azine ligands produce as tronger octahedrall igand field than ac ombinationo f 2 L azine + 2NCBH 3 ,which is in line with experimental findings.
Overall, this study has established and validated ag enerally applicable fragmentation and computational protocol for EDA-NOCV MÀL bondinga nalysis of any diamagnetico rp aramagnetic, homoleptic or heteroleptic, octahedralt ransition metal complex.

Computational Details
Geometry optimization:A safirst step, accurate structures for these five [Fe II (L azine ) 2 (NCBH 3 ) 2 ]c omplexes in both the LS and HS states are required, so density functional theory structure optimizations of the complexes were performed with the ORCA 4.1 software package. [17] After testing several computational features (details in Section S1.1, Ta bles S1-S3 and Figures S2-S9 in the Supporting Information), the level of theory with the best overall performance was identified to be RI-BP86-D3(BJ)/def2-TZVPP + CPCM(CHCl 3 ). [18] That is, usage of the BP86 functional [18e,f] together with the resolution of identity (RI) approximation, [18h,i] Grimme's D3 dispersion correction (including BJ damping), [18a,b] ad ef2-TZVPP basis set [18c] and implicit CPCM-solvent model. [18g] Using this protocol all of the calculated structures, for both the LS and HS complexes, are in good agreement with the available experimental Xray crystallographic data for the LS and HS states of the [Fe II (L pyridine ) 2 (NCBH 3 ) 2 ]c omplex [19] (Table S3). The [Fe II (L azine ) 3 ](BF 4 ) 2 complexes had been previously optimized by using the same protocol. [16] These sets of optimized structures were then used in single-point calculations for the subsequent EDA-NOCV analyses performed using the ADF program package (version 2018.106;  [16] please note that the ADF version used does not allow the inclusion of solvent effects when performing EDA-NOCV) at the BP86-D3(BJ)/ TZ2P level of theory. [20] Introduction to EDA-NOCV:T he EDA-NOCV [9] method combines the classical EDA (Energy Decomposition Analysis), developed by Ziegler and Rauk,[4b,21] with the natural orbitals for chemical valence (NOCV) extension, developed by Mitoraj and Michalak. [8] As implemented in the 2009 release of the ADF program package, [20b] it can be employed to quantify the bonding interactions in the complexes between the metal M and the surrounding ligands L in a chemically intuitive manner.T od os o, EDA-NOCV [9] requires the complex to be split into two (or more) fragments, and the intrinsic, instantaneous interaction (relative stabilisation) energy DE int of the MÀL bonds formed between the two (or more) fragments in the frozen (unrelaxed) geometry of the molecule is then assessed. [22] This total interaction energy, DE int ,iscomprised of four main contributions [Eq. (1)]: The electrostatic interaction (DE elstat )i su sually attractive (negative). It is computed quasi-classically as the interaction between the unperturbed charge distributions of the atoms of the fragments. The Pauli repulsion (DE Pauli )c omes from the energy increase arising from the required transformation from the superposition of the unperturbed electron densities of the isolated fragments to the proper,a ntisymmetrized and normalized wavefunction in the resulting bond, so is the only positive term in Equation (1). The orbital interaction term [DE orb ;s ee also Eq. (2), below] is negative and accounts for the electron density distortion associated with the electron flow between 1) two different fragments to give the individual orbital contributions to the s, p and d bonds formed (DE orb,i , i = s, p, d)and 2) two regions of the same fragment to give the polarization term (DE orb,pol ). The dispersion term (DE disp )i sa ne xtra contribution obtained from the explicit calculation of dispersive interactions, [18a,b] and is usually rather small and negative.
Comparison of DE elstat and DE orb can be used [23] as ap robe for determining the ratio between electrostatic (ionic) and covalent contributions to bonding between fragments.
Additionally,E DA-NOCV is ac harge decomposition method, since the DE orb contribution to DE int is commonly further split up into five subcontributions [Eq. (2)]: and the charge flow associated with interactions between fragments (DE orb,i ; s, p and d bond formation) and within fragments (DE orb,pol ), into these different components can be separated via deformation densities D1 i .T he NOCV Scheme provides pairwise energy contributions to DE orb,i [9a, 24] for each pair of interacting orbitals. By visual inspection of the deformation densities D1 i it is possible to identify the various interaction types leading to bond formation (s, p and d)a nd hence their contributions (DE orb,s , DE orb,p and DE orb,d )t ot he total orbital interaction DE orb .A dditionally,i nformation about the magnitude of the charge flow is given by the corresponding eigenvalues. [9] Of the terms that contribute to the overall DE orb term, herein particular attention is focussed on the nine terms identified by using Hoffmann's theory as these are of key importance for describing bonding in transition metal complexes: [25] at otal of six s-type interactions (DE orb,s )b etween the M AOs (d x 2 Ày 2 ,d z 2 ,p x ,p y ,p z and s orbitals) and the MOs with the corresponding symmetry in the L 6 fragment, plus three p-type interactions (DE orb,p )b etween the re-maining MA Os (d xy ,d xz ,d yz orbitals) and the L 6 MOs of appropriate symmetry. Development of ac omputational protocol for ap hysically meaningful and chemically intuitive fragmentation scheme for any octahedral transition metal complex:I nterpretation of EDA-NOCV results is known to be highly dependent on the choice of fragmentation of the molecule. [4b, 26] Moreover,c omplexes involving 3d metal ions pose as pecial challenge as it is desirable to reflect physically meaningful orbital occupations and energies in both possible situations:t he bound complex and the isolated fragments. In the latter case, oftentimes the best representation would be achieved with fractionally occupying the energetically lowerlying 3d orbitals of the metal, [27] while in the former the occupation of the appropriate antibonding molecular orbitals with dc haracter at the metal centre is mandatory.T ofind abalance between meaningful reference states, chemically intuitive orbital occupations and computational feasibility,aseries of systematic EDA-NOCV calculations with various fragmentation schemes and additional computational protocols has been performed which is detailed in the following. The result of this rigorous study is ar obust fragmentation protocol that will enable the application of EDA-NOCV analysis to any monometallic octahedral complex, regardless of whether homo-or heteroleptic and dia-or paramagnetic.
The family of five SCO-active [Fe II (L azine ) 2 (NCBH 3 ) 2 ]c omplexes comprise one metal ion (Fe 2 + ), two constant axial anionic co-ligands (NCBH 3 À )a nd two varying equatorial neutral bidentate L azine ligands. In the first step, af ull test of five possible fragmentations that the LS [Fe II (L azine ) 2 (NCBH 3 ) 2 ]c omplexes could be broken into (1-5,F igure 2) was carried out, as these being diamagnetic led to easier wavefunction convergence and clearer visual analysis of the NOCV results than for the analogous paramagnetic high-spin state complexes. To our knowledge, as ystematic study of fragmentation schemes, at the level presented here, is an ovelty in the EDA- NOCV-based bonding analysis of transition metal complexes with d orbital configurations other than d 0 and d 10 . [13b,c] Fragmentations 1 and 2 ( Figure 2) represent the most commonly used fragmentation types in the EDA-NOCV literature when diamagnetic transition metal ions (LS d 6 or d 10 )a re present, removal of as ingle ligand. [26a, 28] Here either L = [NCBH 3 ] À (fragmentation 1) or [L azine ]( fragmentation 2)i sr emoved, so these provide detailed information on as ingle type of FeÀL interaction. However,t he presence of another ligand of the same type in the other,i ron-containing, fragment makes these two fragmentation choices less than ideal here. Hence fragmentations 3 and 4 (Figure 2), in which a pair of identical ligands are removed, either both [2 NCBH 3 À À ] (fragmentation 3)o rb oth [2 L azine ]( fragmentation 4)l igands, should provide ac leaner analysis of the details of the different types of FeÀL bonds. These fragmentation schemes are described in detail in Sections S3.1-S3.4. However,a ll four of these fragmentations, 1-4,w ould only really be useful for examining trends within af amily of very closely analogous complexes-confidently comparing very different coordination environments around M will be rather difficult, as the fragmentation is not general enough for that:T he remaining metal-bound ligands will surely affect the electronic environment of the metal ion so will subsequently influence the MÀL bonding character.
In light of this, fragmentation 5 (Figure 2), in which all of the ligands are removed from the metal centre, is the most unbiased of all of these fragmentation options, and opens up the general application of the EDA-NOCV analysis to any family of monometallic complexes. Whilst the Fe do rbital energies in fragmentations 1-4 are comparable to the frontier orbital energies of the ligands, as expected within Hoffman's MO diagram ( Figure S1), this is not the case in fragmentation 5.D ue to the absence of partial ligand fields, which are induced by lone-pair containing ligands surrounding the metal ion containing fragment in the other fragmentation schemes (1-4), the attractive potential of the Fe 2 + centre is not "buffered" by electron density in the vicinity anymore and is therefore fully experienced by the de lectrons.
So, although using Fe 2 + instead of Fe 0 as af ragment appears intuitive and convenient at first, the resulting Fe 2 + da tomic energies for fragmentation 5a (no corrections, Section S2.9 and Ta ble S4), are very low in energy (ca. À26.0 eV,s ee Ta bles 1a nd S4), compared to the energies of the frontier orbitals of the ligands (between À4.0 and + 4.0 eV,see Ta ble S5).
This strongly challenges the physical justification for this description of MÀL bonding interactions because of the poor match in energies between interacting frontier orbitals. To overcome this dilemma, the free ion M n + + of 5a was surrounded by varying amounts of negative charges in order to emulate the electron density of the ligand lone-pairs (fragmentations 5b-5d). As lightly different approach was taken with scheme 5e:H ere the electron density of the isolated Fe 2 + AOs was mapped onto the neutral Fe 0 AOs. These approaches, 5a-5e,a re described in detail in Section S2.9, but are summarized as follows: Fragmentation 5a:Fe 2 + Fragmentation 5b:Fe 2 + + 6 À0.425e Fragmentation 5c:F e 2 + + 6 À1.0e Fragmentation 5d:Fe 2 + + 6 À2.0e Fragmentation 5e:F e 2 + density mapped onto Fe 0 (AOs) All treatments (5b-5 e)e ffectivelyr escaled the Fe 2 + do rbitals towards more positive energy levels (Tables 1a nd S4). We found that through the computational protocols 5b and 5e the Fe 2 + orbital energies were brought closest to the energy levels of Fe 0 in spherical symmetry,a nd hence also to the ligand frontier orbital energies, which in turn yields am ore chemically intuitive MO diagram for fragmentation into the isolated metal ion and the surrounding ligands with much better matching orbital energies. Fragmentations 5b and 5e were found to have different advantages and disadvantages (vide infra;a nd see Sections S2.9 and S3.5 for more details) so both were applied for in depth analysis of the complexes depending on the quantity in question. Specifically, 5b allowed for identification of chemically intuitive bonding interactions by NOCV analysis but underestimated the Pauli repulsion (DE Pauli )i nt he EDA, whereas for 5e it is the other way around. Hence, we have employed fragmentation 5e to obtain information about the contributions to the intrinsic bond energy (DE elstat , DE Pauli , DE orb , DE disp )a nd-in separate calculations-fragmentation 5b to gain deeper insight into the orbital interactions and the relative contributions within by NOCV decomposition analysis.
As the purpose of this work is to provide ar obust computational protocol to enable the application of EDA-NOCV analysis to any monometallic complex, regardless of spin state or the exact nature of the coordination pocket provided by the coordinating ligands, a detailed description of the results of applying these two general fragmentations, 5b/5 e (i.e.,c orrected M n + + + L 6 ), in the EDA-NOCV analysis of three families of complexes follows.

Results and Discussion
As noted above, DE elstat and DE orb [Eq. (1)] are the EDA quantities that give indications of the ionic and covalentc haracter of the chemical bondsf ormed betweent he two fragments (5e; M n + + + L 6 ).
The term (fragmentation 5b; M n + + + L 6 )t hat is expected to be most sensitivet ot he differences in the MÀL azine bonds (due to the 5d ifferenta zines), and hence reflects the changes in the SCO properties,i sDE orb [Eq. (1)],i np articulart he s and p contributions that involve the metal ion [Eq. (2); DE orb,s and DE orb,p ]. Visual representations of all the s and p contributions to the MÀL bonding are provided by the NOCV deformation densities D1 (i) for each of the fragmentations employed. It should be noted that the general appearance is the same for the other four complexes in the respective family (treated with the same fragmentation), regardless of the different L azine ligands.
Furthermore, NOCV analysisu sing fragmentation 5b reveals the ratio of s and p contributions to DE orb is about 90:10 (DE orb,s :DE orb,p ;F igure 5, Ta ble S21).
Focusing first on the M ! L s interactions, those involving the Fe 2 + pa nd so rbitals provideaconstant stabilization energy across the entire family (TableS21 and Figure S27). Hence, as expected, the variation in DE orb,s as the L azine changes from L 4pyrimidine to L pyrazine is duet oc hanges in the s interactions formed by the Fe 2 + d z 2 and d x 2 Ày 2 orbitals (D1 1 and D1 2 ,F igures 3a nd S27). Unsurprisingly,t hese DE orb,s values do not fit the experimentalo bservations (order of T 1/2 values). The L pyridazine complex shows significantly smaller d z 2 (À102 kcal mol À1 )a nd d x 2 Ày 2 (À110kcal mol À1 )o rbital interactions than are seen in the other complexes (À113t oÀ114, and À116t o À119kcal mol À1 ,r espectively;FigureS27, Ta ble S21).
Focusing next on the analysiso ft he three M!L p-backdonation contributions, DE orb,p ,r eveals: D1 3 is mainly associated with the interaction of M with the diazine ring in the yz plane (DE orb,3 about À1t oÀ30 kcal mol À1 across the family); while D1 4 is mainly associated with the interaction of M with the triazole ring in the xz plane (DE orb,4 constant at À11 kcal mol À1 across the family). D1 5 lies in the L azine plane (xy)s ob oth the diazine ring and the triazole ring of each L azine ligand participates in this bond (DE orb,5 constant at À15 kcal mol À1 across the family;F igure S27, Ta bleS21). As for the DE orb,s values, the DE orb,p values do not parallel the order of T 1/2 values:a gain the L pyridazine complex is the outlier, with as ignificantly bigger DE orb,3 (À30 kcal mol À1 )t han the rest (À1t oÀ4kcal mol À1 ).

HS [Fe II (L azine ) 2 (NCBH 3 ) 2 ]
Movingt ot he HS familyo f[ Fe(L azine ) 2 (NCBH 3 ) 2 ]c omplexes (again using fragmentations 5b and 5e,S ections S2.9 and S3.6), unsurprisingly,t he change in Fe II spin state dramatically affects the MÀL interactions. The EDA (fragmentation 5e) shows that on going from LS to HS the DE int stabilization for the [Fe(L azine ) 2 (NCBH 3 ) 2 ]f amily (Table S22) decreases by ca. 25 %, from about À500 to À370 kcal mol À1 .T he exact valuesd epend on the L azine present;t hose for L pyridine are shown in Figure 4.   This is consistentw ith the HS state being less stable enthalpically than the LS state, as expected as the HS state only becomes more stable than the LS state at higher temperatures when the entropicc ontributions become large enough to outweigh the enthalpic term. The three main contributions to DE int [DE orb , DE Pauli and DE elstat ;E q. (1), Figure 4, Table S22] are also reduced in magnitude when changing from LS to HS. Of them, the largestr eduction is observed for DE orb (from about À500 to about À330 kcal mol À1 ). In addition, the DE orb :DE elstat ratio goes from 44:55 for LS to 35:63 forH S, values consistent with the HS state being less covalent and more ionic than the LS state. This quantitative analysisc onfirms the significant change in the nature of the MÀL interactions that is anticipated on change of spin state. More details of the changes in MÀ L bondingo nc hangings pins tate are revealed by comparison of the results of the NOCV analysis( fragmentation 5b)f or both spin states (Figures 5, 6and S28, Table S22).
The DE orb,s + p forL S[ Fe(L azine ) 2 (NCBH 3 ) 2 ]l ies between À330 and À350 kcal mol À1 and almostt wo-thirds of this orbital interaction is provided by DE orb,s ,i np articular by the formationo f MÀL s bonds involvingt he M d z 2 and d x 2 Ày 2 (unoccupied) orbitals (DE orb,s > 100 kcal mol À1 each). In contrast, in HS [Fe(-L azine ) 2 (NCBH 3 ) 2 ]t hese two orbitals are now half-occupied so MÀL antibonding interactions are also present, dropping the DE orb,s stabilization energy values to less than À35 kcal mol À1 each;c onsequently,t he total DE orb,s + p stabilization energy drops to between À145 and À160 kcal mol À1 in the HS state ( Figure 6). As for the LS analogues, ac onstant contribution to DE orb,s ,a lmost unaffected by the spin state, is observed for the contributions where sa nd po fF e 2 + are involved, that is, DE orb,s (s,p x ,p y ,p z )( Figure S28, Ta ble S22).
Whilstt he p contributions (DE orb,p )t oDE orb,s + p are small in both spin states ( Figure 5; LS À27 kcal mol À1 vs. HS À3kcal mol À1 ), those involving the t 2g orbitals donating electron density backt ot he ligandss how al arge reduction in magnitude of stabilization on going from LS to HS (FigureS28, j v 24 j a )d ue to the lower number of electrons presenti nt hem.
In contrast, the fragment polarization contributions( DE orb,pol ) provide greater stabilization in the HS state, by about À30 kcal mol À1 (Figure 5), regardless of L azine .
In an utshell, as expected by the occupationo fa ntibonding orbitals, spin state switching from LS to HS (Figures 4, 5a nd 6) greatly reduces the orbitalc ontributions( DE orb )b etween M and L 6 ,b yc a5 0%,w hile the electrostatic interactions (DE elstat ) only drop by = 10 %, reflecting the reduction in the hardness of the metal ion as the radius increases (from 0.75 LS to 0.95 HS). [29] This is consistentw ith the classical view,t hat on switchingf rom LS to HS the MÀL bond becomes more ionic and less covalent, with longera nd weaker bonds due to decreasesinb oth the s and p interactions.
Correlation of EDA-NOCV parameterswith T 1/2 Given the above,t he DE orb,s + p values obtained from the EDA-NOCV analysis were expectedt oc orrelate with the ligand field strength of the bonds formed between the fragments M n + + and L 6 .T his is au seful test of whether or not this approach can provide au seful, general, quantitative and predictivet ool for predicting T1 = 2 for an SCO system.
Av ery good correlation (R 2 = 0.95) between the EDA-NOCV calculated DE orb,s + p and the experimentally observed T 1/2 is observed, regardless of whether the family of LS and HS state complexes is examined (Figure 6a nd S29). This indicates that the new computational protocoli sp leasingly sensitive, which is quite remarkable given that computed EDA-NOCV DE orb,s + p valuesf or L 4pyrimidine , L 2pyrimidine , L pyridine in particularlie within fractions of kcal mol À1 of each other.N oc orrelation between T 1/2 and the small differenceb etween the DE orb,s + p values for the LS and HS states (D LS-HS DE orb,s + p )i so bserved (R 2 = 0. 12,Figure S29). Rather,t he single spin state trend (LS is the easier of the two to calculate) should be used, as it appears to be a good predictivet ool. In summary,i ti se vident from these results that the change of L azine induces different alterations in the s and p interactions, which only correlate (extremely well) with the T 1/2 values when the synergy of the two contributions (DE orb,s + p )i sc onsidered ( Figure 6). The results also confirm the expected extreme difficulty in foreseeing the effect of al igand on the T 1/2 of ac omplex on the basis of simple consideration of s or p contributions.  (Table S23). This is not surprising as in the present case none of the ligands are charged, whereas in the [Fe(L azine ) 2 (NCBH 3 ) 2 ]c omplexes two anionsa re involved. This results, when going from [Fe(L azine ) 2 (NCBH 3 ) 2 ]t o[ Fe(L azine ) 3 ] 2 + (Table S23), in al arge decrease in DE elstat stabilization( ca. À620 to À400 kcal mol À1 )a nd as lighti ncreasei nDE orb stabilization (= À15 to À20 kcal mol À1 ). The same magnitude of increase in stability observed for the DE orb term is observed as an increasei nDE Pauli stabilization (=+15 to + 20 kcal mol À1 ). This is consistentw ith the general trend that theset wo terms, DE orb and DE Pauli ,a re intimately connected in describing the covalent bonding between fragments (TableS23). The NOCV analysisr eveals that on step-ping across the five L azine ligand from L 4pyrimidine (weakest field strength,l east negative DE orb,s + p ) to L pyridazine (strongest field strength,m ost negative DE orb,s + p )t hat:1 )the s bonds (DE orb,s ) involving the d z 2 and d x 2 Ày 2 orbitals strengthen by about À5t o À10 kcal mol À1 per bond per step and 2) the p backbonds (DE orb,p )i nvolving the d xy ,d zx ,d zy orbitals strengthen by about À5t oÀ15 kcal mol À1 per bond per step (Figures 7a nd S30, Ta ble S23).
On the other hand, as before,t he bonds involving s, p x ,p y and p z orbitals show marginal differences ( Figure S23, Ta ble S30).
Analysis of the s and p contributionss hows that the s interaction is almost eight times larger than the p interaction regardless of L azine .The s strength (DE orb,s )oft he L azine ligands follows the order: L pyridazine > L 4pyrimidine > L 2pyrimidine > L pyrazine > L pyridine . Interestingly the order of the p strength( DE orb,p )o ft he L azine ligands differs (and the values are far from showingamonotonic trend): L pyridine > L pyrazine > L pyridazine > L 2pyrimidine > L 4pyrimidine .

Conclusions
In this study,w ea imed to providen ew insights into the details of the nature of MÀL bonds.T od os o, EDA-NOCVw as employed as it provides results that are both quantitativea nd chemically intuitive. This makes it av ery powerful tool for both theoreticians and inorganic chemists. Hence, it wass urprising to find that, prior to this study,t he choice of fragmentation issue in EDA-NOCV had not been rigorously developed to provide ag eneral, widely applicable and consistent scheme for use in any 3d complex, regardless of whether the coordination was homoleptic or heteroleptic,o rt he complex was paramagnetic or diamagnetic.
Therefore, the first step was to consider ar ange of possible fragmentations of the complexes, starting from the usual literature fragmentation used (loss of one ligand). That, and the related fragmentations (loss of pairs of ligands) were found to be unsatisfactory,a nd also lacked generality,t hat is,t he potential to be used for any complex regardlesso fl igand type or charge.H ence ap rotocol that enables robusta nd general EDA-NOCV analysiso fa ny octahedral coordination complex, fragmentation into M n + + + + L 6 ,w as developed. By keeping one fragment as ac onstantp ure (unperturbed by the any ligand) metal ion M n + + ,a ny and all changes to the other," all ligand", fragment can then be analysed in depth and compared.
Af amily of SCO-active Fe II complexes,[ Fe(L azine ) 2 (NCBH 3 ) 2 ], was chosen as the test system for this study,a st he experimentally observeds olution switchingt emperatures (T 1/2 )p rovided the order of L azine ligand field strengths. Also, the chance to work on both spin states, diamagneticL Sa nd paramagnetic HS, enabled us to significantly increaset he small handful of reports of EDA-NOCV analysiso fp aramagnetic transition metal complexes [11] and, above all, to critically tackle this class of system in depth for the first time. Moreover,t his work is also the first to focus on EDA-NOCV analysiso ft he complex electronic structures of SCO-active systems, enabling in depth analysis and comparison of the MÀL bonding in both of the thermodynamically accessible spin states, diamagneticL Sa nd par-amagneticH S.
Regardless of whethert he LS or HS family of [Fe(L azine ) 2 (NCBH 3 ) 2 ]c omplexesw as examined by EDA-NOCV, the analysisi dentified ag ood correlation (R 2 :L S0 .99;H S0 .95) between decreasing T 1/2 and increasingl igand field strength as quantified by the DE orb,s + p term. In addition, comparison of the results for [Fe(L azine ) 2 (NCBH 3 ) 2 ]w ith those subsequently ob-tained on the LS [Fe(L azine ) 3 ](BF 4 ) 2 complexes revealed that only the corrected M n + + + + L 6 fragmentation provides ag eneral protocol suitable for comparing different types of complexes. It should be noted that the above analysisn eglects any entropic contributions, which are known to be key in SCO, so the next big step in the development of this approach for applications in the SCO field will be understandingh ow the inclusion of computed entropic contributions can be included so that the unbiased determination of the T 1/2 values on the basis of the EDA values will be possible.
In conclusion, the EDA-NOCV protocold eveloped and validated herein employsanew and general fragmentation type (M n + + + + L 6 )t hat provides ac lear,q uantitative and chemically intuitive description of the MÀL bonds in these paramagnetic and diamagnetict ransition metal complexes. This new protocol should be widely applicable, ap oint we are currently testing further (with more families of SCO and/orr edox-active3 d coordination complexes)i no rder to prove that it is general, thereby unlocking the great promise it holds as ap redictive tool.