Quantitative Assessment of Ligand Substituent Effects on σ- and π-Contributions to Fe-N Bonds in Spin Crossover FeII Complexes.

The effect of para-substituent X on the electronic structure of sixteen tridentate 4-X-(2,6-di(pyrazol-1-yl))-pyridine (bppX ) ligands and the corresponding solution spin crossover [FeII (bppX )2 ]2+ complexes is analysed further, to supply quantitative insights into the effect of X on the σ-donor and π-acceptor character of the Fe-NA (pyridine) bonds. EDA-NOCV on the sixteen LS complexes revealed that neither ΔEorb,σ+π (R2 =0.48) nor ΔEorb,π (R2 =0.31) correlated with the experimental solution T1/2 values (which are expected to reflect the ligand field imposed on the iron centre), but that ΔEorb,σ correlates well (R2 =0.82) and implies that as X changes from EDG→EWG (Electron Donating to Withdrawing Group), the ligand becomes a better σ-donor. This counter-intuitive result was further probed by Mulliken analysis of the NA atomic orbitals: NA (px ) involved in the Fe-N σ-bond vs. the perpendicular NA (pz ) employed in the ligand aromatic π-system. As X changes EDG→EWG, the electron population on NA (pz ) decreases, making it a better π-acceptor, whilst that in NA (px ) increases, making it a better σ-bond donor; both increase ligand field, and T1/2 as observed. In 2016, Halcrow, Deeth and co-workers proposed an intuitively reasonable explanation of the effect of the para-X substituents on the T1/2 values in this family of complexes, consistent with the calculated MO energy levels, that M→L π-backdonation dominates in these M-L bonds. Here the quantitative EDA-NOCV analysis of the M-L bond contributions provides a more complete, coherent and detailed picture of the relative impact of M-L σ-versus π-bonding in determining the observed T1/2 , refining the earlier interpretation and revealing the importance of the σ-bonding. Furthermore, our results are in perfect agreement with the ΔE(HS-LS) vs. σp + (X) correlation reported in their work.

Introduction

Predictable fine tuning of the electronic structure of metal complexes is highly desirable, not least in order to optimise them for use in practical applications, such as molecular electronics, emissive devices, catalysis or photovoltaics. The choice of substituent X present in a 5‐ or 6‐membered aromatic ring is an important and frequently employed tool for fine‐tuning the electronic structure of organic and inorganic compounds.

Substituent effects are commonly parameterised using the Hammett constant (σ(X) or σ+(X)): σ(X) comes from acid/base dissociation of para/meta substituted benzoic acids, whereas σ+(X) comes from nucleophilic substitution at the carbonyl carbon in para/meta substituted benzoic acid derivatives and better reflects resonance effects.[ , ] The Hammett parameters for para‐X substituents, σp(X) and σp +(X), range from those for very Electron Donating Groups (EDG, X=NMe; σp=−0.83, σp +=−1.70) to those for very Electron Withdrawing Groups (EWG, X=NO; σp=0.78, σp +=0.79). As expected, meta‐Y substituents have far less electronic impact so have a much narrower range of σm +(Y) values, from the lowest EDG (Y=Me; σm=σm +=−0.07) to the highest EWG (Y=NO; σm=0.71, σm +=0.67).

Many studies have tried, with varying success, to rationalise how ligand substituent modifications affect key properties such as the molecular orbital (MO) energies, redox potentials as well as spin crossover (SCO) switching temperatures.[ , ] The focus herein is on SCO, which occurs when the metal ion M (usually 3d to 3d electronic configuration in octahedral geometry) can be switched between the high spin (HS) and low spin (LS) states through a trigger stimulus such as temperature, pressure, host‐guest interaction, external magnetic field or light irradiation. Systems showing thermal SCO in the solution phase are particularly suitable candidates for monitoring the X (or Y) effects on the M−L bond, as they are not complicated by the effects of crystal packing or solvatomorphs; so, providing speciation is not a problem, variations in the ligand field strength due to X (or Y) substituent, are more clearly observed in solution[ , , ] than in the solid state SCO. For thermal SCO, the switching temperature T1/2 (the temperature at which there is a 50 : 50 ratio of HS:LS) is determined in order to monitor these variations.[ , , ]

A landmark study on the effects of para‐ X (and meta‐ Y) substituents on solution SCO T1/2 values was reported by Deeth, Halcrow and co‐workers in 2016, and this was followed up with further papers by them in in 2018 and 2019. They focused on the largest known family of solution SCO active complexes, [FeII(bpp)2]2+ (where bpp=4‐X‐2,6‐di(pyrazol‐3‐Y‐1‐yl)‐pyridine; Figure 1 shows only the 16 complexes focused on herein, for which the ‘meta’ pyrazole substituent is held constant as Y=H whilst the para substituent X is varied), which had been prepared and studied by various authors across the years.[ , ] In their landmark paper they found a strong positive correlation (R2=0.92) of σp +(X) vs. T1/2 and as expected a weaker, but also negative, correlation (R2=0.61) of σm(Y) vs. T1/2. They also found, by using quantum‐chemical calculation based on Density Functional Theory (DFT), that (a) the difference between the HS and LS total energies, ΔE, correlated strongly with σp +(X) (R2=0.89) and less strongly with σm(Y) (R2=0.67); and (b) σp +(X) and σm(Y) correlated extremely well (R2=0.93–0.99) with the average energy levels, and , calculated for LS [FeII(bpp)2]2+ (R2=0.94–0.93) and LS [FeII(bpp)2]2+ (R2=0.99–0.98). They concluded that there is a “fine balance between opposing M−L σ‐ and π‐bonding effects”, and that for the present family: (a) Fe→N π‐backbonding effects must be dominating for para‐ X substituents because EDG→EWG increases the observed T1/2, the rationale being that this is expected to decrease the energy of the ligand π* MOs and therefore increase the M→L π‐backbonding, increasing the ligand field strength and T1/2, whereas (b) Fe ← N σ‐bonding effects must be dominating for the meta‐ Y substituents as EDG→EWG decreases the observed T1/2, the rationale being that this is expected to decrease the energy of the lone pairs, making them poorer M←L σ‐donors, decreasing the ligand field strength and hence also the T1/2. The quantitative EDA‐NOCV analysis carried out herein enables us to refine this interpretation, and reveals the importance of the σ‐bonding (see later).

Figure 1

Representations of (a) the members of the [FeII(bpp)2]2+ family and the Hammett constants (σp +(X)) for the para‐X substituents employed; (b) electrostatic effects on the pyridine nitrogen donor atom, N, by either (left) electron donating group (EDG) or (right) electron withdrawing group (EWG) substituent in [FeII(bpp)2]2+. Pink text for the two X for which σp + is not experimentally known but is estimated from the correlations presented herein (Table S12–S13).

The present study was motivated by the above findings and by the promise shown in our first use of EDA‐NOCV theory, which is a combination of EDA (Energy Decomposition Analysis), with the NOCV (Natural Orbitals for Chemical Valence) concept that provides quantitative and chemically intuitive analysis of bonding – to a solution SCO system, specifically a family of five [FeII( )2(NCBH3)2] complexes. The latter study first established a new and general fragmentation protocol (M+L) for computationally evaluating M−L bond strength in any kind of metal complex, diamagnetic or paramagnetic. Such corrected approach overcomes limits of partial ML fragmentations (ML ‐), proposing a common ground state (the ‘naked’ metal ion M) to treat any complex independently from the ligand coordination pocket. Then this protocol was applied to the family of five [FeII( )2(NCBH3)2] complexes, revealing a strong correlation (R2=0.99) between ΔE for the Fe−N bonds and the experimental T1/2 for solution SCO.

Another important study aimed at improved our detailed understanding of σ‐ and π‐tuning operated by para‐X‐substituents was reported by Ashley and Jakubikova in 2018. They carried out a DFT and EDA‐NOCV study on a family of LS iron(II) complexes of para‐X substituted bipyridine ligands, [Fe(bpy)3]2+, and found that the ligands show both π‐acceptor and π‐donor character, but recommend that the results should be taken with caution until they can be experimentally verified in some way. They also commented that use of substituents X should be a good way to make small adjustments of ligand field, and hence precisely tune the T1/2 in an SCO complex (without pushing the complex either LS or HS). Clearly T1/2 is an experimental outcome that can be used to validate theoretical predictions of how a change in X will tune the ligand field. Such a validation of in silico predictions, pre‐synthesis, is key as it will enable future synthetic efforts to focus on only preparing the best candidate for a desired T1/2 or indeed spin state. Given that spin state is key to properties and function, including catalytic, the importance of this is clear.

Herein, EDA‐NOCV methodology is applied for only the second time to an SCO system – in this case to the large family of sixteen para‐X substituted [FeII(bpp)2]2+ complexes (Figure 1), in order to quantify the relative importance of the σ‐ and π‐contributions to the M−L bonds as X is varied as EDG→EWG, and look for correlations between the obtained parameters and the experimentally observed T1/2 values. As this led to unexpected results, an in‐depth Mulliken charge analysis of the N‐donor atomic orbitals (AOs) population was also performed, to provide further insights and explanations.

Finally, the correlations obtained are employed (a) to test how well the known Hammett σp(X) parameters for X=SOMe and SO were reproduced, then (b) to predict approximate values for the unknown σp +(X) for these two substituents X.

Introduction to EDA‐NOCV

The EDA‐NOCV method involves a “classical” EDA, followed by a NOCV procedure. In this work, it is used to single out and quantify the various energy contributions to M−L bonding. After geometry optimisation, the compound is formally separated into two or more non‐interacting fragments, and the intrinsic, instantaneous interaction energy of the bonds formed between the fragments in the frozen (unrelaxed) geometry of the molecule is then assessed (Eq. (1)) in a stepwise fashion. The general fragmentation that we developed and validated in a previous study is employed herein (fragmentation 5 in ref; Figure S1): fragment 1 (corrected)=Fe and fragment 2= L (herein both tridentate bpp ligands).

Where: is the electrostatic interaction (usually negative/attractive), is the Pauli repulsion (repulsive/positive), is the orbital interaction (attractive/negative; see also Equation (2), below), and is the dispersion term (attractive/negative) accounting for long‐range interaction.

Subsequently, NOCV analysis decomposes (Eq. (2)) into several contributions, reflecting electron flows (i. e. deformation densities Δρ ) between (a) two MOs on different fragments to give the individual orbital contributions to the σ, π and δ bonds formed ( , i=σ, π, δ; identified by visual inspection of Δρ )[ , ] and (b) two MOs on the same fragment to give the polarization term ( ).

Information about the magnitude of the charge flow is given via the corresponding eigenvalues. Of the many contributions to , those of key importance in octahedral transition metal complexes are: six σ‐type interactions ( ) between the M AOs (d , d and s orbitals) and the MOs with the corresponding symmetry in the L fragment, plus three π‐type interactions ( ) between the remaining M AOs (d orbitals) and the L MOs of appropriate symmetry.

Note that the development and validation of this general fragmentation method (M+6 L), for dia‐ and para‐magnetic complexes and the application of it to SCO complexes for the first time in Ref. [20], and again herein, opens the door quantifying the nature of M−L bonding in more families of SCO complexes (in which the ligand field strength is very delicately poised) and we expect the resulting findings will continue to be revelatory.

Results and Discussion

DFT optimisation of [FeII(bppX)2]2+ (LS and HS)

The geometry optimisation computational protocol employed for the sixteen LS and sixteen HS [FeII(bpp)2]2+ complexes was chosen based on the functional screening we performed previously. The same computational protocol was applied to all of the candidates, in the same CPCM solvent, acetone, albeit the LS forms of the X=NMe or NH complexes were not observed experimentally. Calculating the Root‐Mean‐Square‐Deviation (RMSD) of each atomic position (Eq. S1) in the structures of these [FeII(bpp)2]2+ complexes from that of the respective LS or HS state of the X=H parent complex, [FeII(bpp)2]2+, confirmed that the variation of the para‐substituent X causes no significant deviations (RMSD <0.01 Å in all cases, Table S1). The six, out of the sixteen [FeII(bpp)2]2+ complexes, where the experimental T1/2 values were measured in nitromethane solvent (Table S1) were subjected to a geometry re‐optimisation, and then to a RMSD evaluation between the final geometries calculated in acetone vs. nitromethane. Again, the RMSD for each atomic position confirmed that, as expected, changing the dielectric constant in the CPCM model, from acetone to nitromethane, has a negligible effect on the optimised structures obtained in these two different solvents (RMSD<0.01 Å in all cases, Table S1).

EDA analysis of effects of X in [FeII(bppX)2]2+ (LS and HS)

EDA, using the previously established optimal fragmentation 5 e (M+L) (Table S2, see Computational Details section below for details), were performed on the sixteen HS and sixteen LS [FeII(bpp)2]2+ complexes (Figure 1). This quantified the overall interaction energy, ΔE, which accounts for the strength of the binding by the coordination sphere onto the iron(II) centre. The ΔE contribution for HS was half that for LS [FeII(bpp)2]2+ complexes (Table 1).

Table 1

EDA results (frag. 5 e) for the sixteen LS and HS [Fe(bpp)2]2+ complexes: all energies are reported in kcal/mol (Note: 1 eV=23 kcal/mol=8100 cm−1). Results are presented in order of increasing Hammett parameter (σp +). *Values estimated in this study.

X	T1/2	σp +	State	ΔEint	ΔEelstat	ΔEorb
NMe2	HS	−1.70	LS	−255.0	−413.8	−305.5
			HS	−120.1	−330.6	−503.9
NH2	HS	−1.30	LS	−246.7	−409.4	−309.1
			HS	−113.0	−338.2	−409.4
OH	164	−0.92	LS	−232.0	−396.2	−307.7
			HS	−98.1	−325.0	−499.5
OMe	158	−0.78	LS	−238.9	−401.2	−310.6
			HS	−104.0	−328.7	−501.6
SMe	194	−0.60	LS	−239.6	−397.1	−310.6
			HS	−104.4	−326.5	−507.0
Me	216	−0.31	LS	−235.6	−397.9	−306.7
			HS	−101.5	−314.3	−502.8
F	215	−0.31	LS	−219.5	−385.0	−296.9
			HS	−83.0	−302.9	−499.3
SH	246	−0.03	LS	−231.6	−390.7	−314.0
			HS	−98.5	−320.1	−505.6
H	248	0.00	LS	−229.1	−393.7	−296.6
			HS	−89.9	−310.7	−501.3
Cl	226	+0.11	LS	−221.7	−383.1	−311.8
			HS	−88.2	−312.4	−504.0
I	236	+0.14	LS	−224.5	−382.5	−304.1
			HS	−86.9	−300.5	−508.4
Br	234	+0.15	LS	−222.9	−383.1	−301.8
			HS	−85.5	−301.1	−505.6
CO2H	281	+0.42	LS	−223.7	−383.4	−314.2
			HS	−89.0	−313.2	−508.3
NO2	309	+0.79	LS	−205.7	−365.4	−508.7
			HS	−71.6	−296.6	−314.9
SOMe*	284	+0.25*	LS	−224.4	−368.0	−515.0
			HS	−81.0	−300.8	−305.5
SO2Me*	294	+0.54*	LS	−215.4	−359.1	−515.8
			HS	−90.1	−303.2	−314.8

T

σ

ΔE

ΔE

ΔE

NMe

NH

CO

NO

SO

This is consistent with the HS state being less enthalpically stable than the LS state; note these results are obtained at 0 K. Furthermore, as σp +(X) increases (EDG→EWG, NMe→NO), the stabilising energy ΔE drops in all cases: from about −250 to −200 kcal/mol for the LS complexes (NMe→NO) and from −120 to −70 kcal/mol (NMe→NO) for the HS complexes (Figure 2, Tables 1, 2). In the detailed analysis of the various energetic contributions to the ΔE term, the ΔE term – which accounts for the ionic bonding between the fragments – is observed to correlate well with σp +(X) for LS [FeII(bpp)2]2+ (R2=0.89, Table S3, Figure S2) and moderately well for HS [FeII(bpp)2]2+ (R2=0.73, Table S4 and Figure S3). In both cases, this behaviour can be understood as follows: as X becomes more electron poor (σp + increases) it drains more electron density away from the coordinating nitrogen (Figure 1), decreasing the favourable electrostatic interactions with the FeII ion (Tables S3‐S4).

Figure 2

Results of EDA analysis of three representative [FeII(bpp)2]2+ complexes: X=NMe (left), X=H (center) and X=NO (right), in the LS (top) vs. HS (bottom) state (using fragmentation 5 e ). For each spin state the pair of bar graphs shows the four components of ΔE (see Equation (1); only ΔE is positive) and the sum of them, ΔE (yellow).

From X=NMe to X=NO, ΔE decreases by just −60 kcal/mol (+15 %) in the LS [FeII(bpp)2]2+ and decreasing by just −35 kcal/mol (+12 %) in the HS [FeII(bpp)2]2+ complexes. In contrast, the ΔE interaction, which accounts for the covalent bonding between the fragments, remains almost constant across the whole range of σp + values: from X=NMe to X=NO, ΔE increases by just +20 kcal/mol (+3.5 %) in the LS [FeII(bpp)2]2+ and decreased by just −5 kcal/mol (−1.5 %) in the HS [FeII(bpp)2]2+ complexes. Comparing these EDA results with those for the [FeII(L)2(NCBH3)2] family ( =3‐(2‐azinyl)‐4‐tolyl‐5‐phenyl‐1,2,4‐triazole; (Table 2), few differences can be grouped up. The ΔE energies for the [FeII( )2(NCBH3)2] family are twice the size of those for the [FeII(bpp)2]2+ family, but yet, the ΔE values are almost the same (Table 2). The cause of the big difference in ΔE values is the drop in magnitude observed for the ΔE term in the [FeII(bpp)2]2+ family vs. the [FeII( )2(NCBH3)2] family.

Table 2

Range of ΔE, ΔE and ΔE values obtained from EDA analysis, in both HS and LS spin states (using fragmentation 5 e), of the sixteen [FeII(bpp)2]2+ complexes, compared with those previously obtained for five [FeII( )2(NCBH3)2] complexes: all energies are reported in kcal/mol.

	State	ΔEint	ΔEelstat	ΔEorb
[FeII(bppX )2]2+	LS	−250/−200	−415/−365 (∼45 %)	−510/−500 (∼55 %)
	HS	−120/−70	−330/−290 (∼55 %)	−315/−295 (∼45 %)
[FeII( L azine )2 (NCBH3)2] [20]	LS	−530/−500	−635/−620 (∼55 %)	−520/−500 (∼45 %)
	HS	−385/−370	−585/−570 (∼65 %)	−330/−325 (∼35 %)
bppH vs. L pyridine	LS	−53 %/−60 %	−35 %	−0.5 %
	HS	−59 %/−81 %	−40 %	−5 %

ΔE

ΔE

ΔE

[FeII(bpp)2]2+

[FeII( )2 (NCBH3)2]

bpp vs.

This is due to the fact that the two BF4 − (or two PF6 −) anions are not directly bonded at the iron(II) ion in [FeII(bpp)2]2+; whereas the two NCBH3 − anions are directly bonded to the iron(II) ion in [FeII( )2(NCBH3)2] (Table 2). Finally, it should be noted that the ratio between ionic and covalent contributions (ΔE:ΔE ratio) is important in describing the bonding between fragments. For the [Fe(bpp)2]2+ complex the ionic:covalent ratio becomes more ionic on going from LS (44 : 55) to HS (50 : 47). This is very different from the [Fe( )2(NCBH3)2] complex where the ionic bonding is already dominating in the LS state (ΔE:ΔE, 55 : 45), and this further increases in the HS state (65 : 35) (Table 2). In conclusion, EDA analysis of these families of complexes, which feature very different types of coordination environments, is shown to correctly incorporate details of the change in nature of the coordinative bond, regardless of the origin of the change.

NOCV analysis of the effects of X on Fe‐N σ‐ and π‐bonding in [Fe(bppX)2]2+ (LS and HS)

The full NOCV results obtained using the previously optimised fragmentation 5 b are reported in Tables S5–S6, with selected data shown and discussed in the following sections. From the breakdown of the ΔE term, the nine M+L bonding interactions (described by Hoffman theory ) can be identified by visual inspection and quantitatively assessed (Figure S1): six σ‐ (ΔE ), and three π‐contributions (ΔE ) to the ML interactions are sought (Figure 3 and Figure 4, Tables 3, S5–S6).

Figure 3

Example of M(d σ‐donation (left) and M(d→L π‐backdonation (right) in LS [Fe(bpp)2]2+. The direction of the charge flow is yellow→turquoise (cut‐off: ρ>0.003 e−). A complete description of each engaged bond obtained by EDA‐NOCV analysis is reported in Figures S5–S10.

Figure 4

Results of NOCV decomposition of ΔE of three representative [Fe(bpp)2]2+ complexes: X=NMe (left), X=H (center) and X=NO (right), in the LS (top) vs. HS (bottom) state (using fragmentation 5 b ). For each spin state the bar graph shows the four components of ΔEorb (see Equation (2)).

Table 3

NOCV results (frag. 5 b) for the sixteen LS and HS [FeII(bpp)2]2+ complexes: all energies are reported in kcal/mol. Results are presented in order of increasing Hammett parameter (σp +). *Hammett values estimated in this study. T1/2 values for 10 of these complexes were obtained in acetone whereas the 6 marked with † were obtained in nitromethane.

X	T1/2	σp +	State	ΔEorb,σ+π	ΔEorb,σ	ΔEorb,π
NMe2	HS	−1.70	LS	−378.5	−323.2	−52.5
			HS	−167.7	−142.1	−25.5
NH2	HS	−1.30	LS	−374.8	−324.6	−50.1
			HS	−161.9	−135.8	−26.0
OH	164	−0.92	LS	−374.6	−325.9	−48.4
			HS	−168.9	−145.6	−23.3
OMe	158	−0.78	LS	−376.1	−326.4	−49.6
			HS	−156.3	−130.9	−25.3
SMe	194	−0.60	LS	−378.5	−326.1	−52.4
			HS	−165.9	−141.7	−24.1
Me	216	−0.31	LS	−376.2	−327.7	−48.2
			HS	−170.6	−147.4	−23.1
F	215	−0.31	LS	−374.4	−326.7	−48.5
			HS	−169.2	−142.4	−26.7
SH	246	−0.03	LS	−378.6	−327.6	−51.0
			HS	−170.2	−145.9	−24.3
H	248	0.00	LS	−376.0	−328.7	−47.3
			HS	−168.9	−142.3	−26.6
Cl	226	+0.11	LS	−376.9	−327.9	−49.0
			HS	−169.1	−145.7	−23.3
I	236	+0.14	LS	−378.9	−328.5	−50.4
			HS	−169.7	−142.8	−26.8
Br	234	+0.15	LS	−377.6	−327.9	−49.6
			HS	−169.7	−142.9	−26.8
CO2H	281	+0.42	LS	−379.7	−331.1	−48.5
			HS	−171.7	−148.3	−23.3
NO2	309	+0.79	LS	−379.7	−331.8	−48.8
			HS	−171.5	−147.7	−23.7
SOMe*	284	+0.25*	LS	−375.8	−328.5	−49.7
			HS	−165.2	−142.5	−22.6
SO2Me*	294	+0.54*	LS	−378.2	−330.3	−47.8
			HS	−170.1	−147.7	−22.9

NMe

NH

CO

NO

SO

For both spin states of the sixteen complexes, the ΔE (s,p contribution remains constant as X varies (Figures S5–S10). For all sixteen LS [Fe(bpp)2]2+ complexes, the six σ‐bonds (ΔE ) account for about 85 % of the ΔE contribution to M−L bonding, leaving only 15 % of the stabilisation energy to come from the three π‐bonds. The same is observed for all sixteen HS [FeII(bpp)2]2+ complexes (ΔE :ΔE =85 : 15; Tables 3 and S5–S6). In the LS state the overall σ‐strength is mostly due to the two M→L σ‐bonds formed by the FeII(d) and FeII(d ) orbitals (ΔE<−100 kcal/mol; v i >0.90; Figure 3 (left) and Figures S5–S7).

In the sixteen HS [FeII(bpp)2]2+ complexes in which these two e anti‐bonding orbitals are half‐occupied, not empty, the ΔE stabilisation energy drops by 55 % relative to the analogous LS state complex (Tables 3 and S5–S6). In comparison, in the LS [Fe( )2(NCBH3)2] complexes the six σ‐bonds (ΔE ) account for even more, about 92 %, of the ΔE , the only exception for = were the σ‐contribution drops to 84 %; this is very likely due to a mixing between the σ‐ and π‐contribution. As well, for HS [FeII( )2(NCBH3)2] complexes, an even more inhomogeneity between ΔE and ΔE is observed (ΔE :ΔE =98 : 2).

The three π‐acceptor M→L bonds are composed by two stronger degenerate π‐bonds involving the FeII(d) and orbitals (Figures S5–S10), and a weaker π‐bond involving the FeII(d) orbital (Figures S5–S10). For LS [FeII(bpp)2]2+, these three π(M→L) interactions (slightly bonding MOs) contribute −47 kcal/mol. For HS [FeII(bpp)2]2+ these three π(M→L) bonds contribute only −25 kcal/mol due to the SCO from LS→HS reducing the population of the t‐like orbitals, i. e. π‐backdonation reduction. Overall, on LS→HS, stabilisation by ΔE, drops by about 40 % and the overall ΔE, drops by about 50 %. In comparison, for the [Fe( )2(NCBH3)2] complexes, the ΔE, term drops by about 50 %, ΔE, drops by about 90 %, and the overall ΔE, drops by about 60 %.

EDA‐NOCV analysis: Correlations with σp +(X)

For the LS [FeII(bpp)2]2+ family, when the Hammett constant σp +(X) changes from EDG (X=NMe) to EWG (X=NO), a strong correlation is observed with ΔE (R2=0.88, Figure 5a), a poor correlation is observed with ΔE (R2=0.31, Figure 5b), and a weak correlation is observed with the overall ΔE (R2=0.43, Figure 5c). No correlations are observed for the HS [Fe(bpp)2]2+ complexes: σp +(X) vs. ΔE (R2=0.30, Figure S17); ΔE, (R2=0.01, Figure S18); ΔE (R2=0.34, Figure S19). Compared to the previous studies the effects of X on π‐backdonation (ΔE ) in this LS [Fe(bpp)2]2+ family are less linear and predictable than for the σ‐donation term ΔE . ΔE shows a weak and opposite trend with the Hammett constant σp +(X).

Figure 5

Correlation of σp +(X) Hammett parameter with (a) ΔE (R2=0.91); (b) ΔE (R2=0.31) and (c) ΔE (R2=0.43) for the family of fourteen [Fe(bpp)2]2+ complexes (X=SOMe, SO are absent as σp +(X) is not available from literature).

It is important to note that this divergence is not linked with the employed level of theory, as both studies employed the same DFT theory. Herein, as X varied as EDG→EWG (−1.70→+0.79), a quantitative ΔΔE stabilisation of about 5 kcal/mol is observed, along with a much less significant ΔΔE destabilisation of about 1.5 kcal/mol (Tables 3, S5–S6). Not surprisingly, the σ‐donor properties again dominate the π‐acceptor properties, with the latter playing only a secondary role in the ligand field tuning operated by the X substituent.

EDA‐NOCV analysis: Correlations with T1/2

Herein, EDA‐NOCV analysis reveals that the observed T1/2 is also in extremely good correlation with ΔE for LS [Fe(bpp)2]2+ (Figure 6, red line, R2=0.82 and Figure S11). On the other hand, T1/2 does not correlate with ΔE (R2=0.09 Figure S12), and only very weakly correlates with ΔE (R2=0.48 Figure S13). It should be recalled (see above) that for this [FeII(bpp)2]2+ family, ΔE provides 85 % of the overall bonding stabilisation (ΔE ) so it is likely to dominate over changes in ΔE . In contrast, for the HS [Fe(bpp)2]2+ complexes none of the ΔE terms (i=σ, π, σ+π) shows a promising correlation with the T1/2 values: ΔE (R2=0.36, Figure S14), ΔE (R2=0.07, Figure S15) and ΔE (R2=0.31, Figure S16).

Figure 6

Three strong pairwise correlations (blue, red and green lines), and a cross‐correlation (black dots; grey arrow is only a guide to the eye) between the ligand donation properties ( ; calculated by EDA‐NOCV for the LS complexes using fragmentation 5 b), the Hammett constant of X (σp +), and the switching temperature (T1/2) for the twelve SCO‐active complexes for which σp +(X) is known in this family of [FeII(bpp)2]2+ complexes (X=SOMe, SO, NH, NMe are absent, as σp +(X) is not known for the first two, and the last two remain HS).

Therefore, these EDA‐NOCV results indicate that the LS state is the key spin state, as it is the one for which the electronic effect of X on the bonding properties of the [FeII(bpp)2]2+ complex can be observed, through the cross‐correlation of ΔE vs. T1/2 (Figure 6, red line, R2=0.82) and ΔE vs. σp + (Figure 6, blue line, R2=0.88) and T1/2 vs. σp + (Figure 6, green line, R2=0.92).

However, the finding herein that in LS [FeII(bpp)2]2+ only ΔE , not ΔE or ΔE , correlates with T1/2 is not consistent with either (i) the intuitive rationale of the M−L bonding provided by Deeth, Halcrow and co‐workers that M→L π‐backbonding dominates the tuning by X; or (ii) the finding observed for the [FeII( )2(NCBH3)2]2+ family of a strong correlation for ΔE vs. T1/2 (R2=0.99) and weak correlations for ΔE vs. T1/2 (R2=0.76), ΔE vs. T1/2 (R2=0.88).

For issue (i), a deeper comparison of Deeth, Halcrow and co‐workers finding vs. the present finding will be discussed shortly. For issue (ii), a deeper comparison of the EDA‐NOCV results for the [FeII(bpp)2]2+ (X substituent in dicationic complex) and [FeII( )2(NCBH3)2]2+ (CH/N replacement in neutral complex) families is too early at this stage as these are the only two SCO families studied using EDA‐NOCV to date: investigations of more such families are required and indeed warranted.

The results obtained on the SCO families under study also indicate that EDA‐NOCV analysis works much better when the number of unpaired electrons is zero (diamagnetic) i. e. for LS (better than HS). This is a consequence of using DFT as the main theoretical investigation tool in the first steps of the EDA‐NOCV analysis, along with having a d6 ion, as FeII, instead of using a (computationally prohibitively expensive) multi‐reference approach to capture and evaluate all relevant microstates. Being intrinsically a mono‐determinantal approach, DFT cannot correctly capture static correlation effects. Thus, the closed‐shell LS FeII system can be correctly described while the open shell HS FeII system is less well described and hence is less reliable. Moreover, as the LS state is the most stable species at 0 K, prediction of temperature effects for it is inherently limited. Conversely, temperature effects are important for the HS state, but cannot be explicitly considered unless more time‐consuming DFT‐based ab‐initio molecular dynamic (AIMD) calculations are used.

EDA‐NOCV analysis: Correlations with δNA

Finally, NOCV results are explored from another perspective, not yet explicitly discussed in this study. This follows from an approach first proposed by Brooker and co‐workers in 2009, then followed up in 2017, and further extended in 2021 to 5 families (42 complexes), in which the 15N NMR chemical shift (δN) of the coordinating nitrogen N of the free ligand (easy to measure or calculate) provides a quantitative report on an N‐donor ligand that has been shown to correlate well with the observed T1/2 for the corresponding complex, in families of closely related complexes, including the bpp family of interest herein.

Herein, the calculated δN of the bpp ligands is shown to correlate with one of the NOCV results, establishing a correlation between the properties of the bpp ligand before (free bpp ligand) and after coordinating the FeII ion ([FeII(bpp)2]2+ complex).

For LS [FeII(bpp)2]2+, δN shows an extremely good correlation with ΔE (R2=0.95, Figures 7a), but only a very weak correlation with ΔE (R2=0.39, Figure 7b) or ΔE (R2=0.23, Figure 7c). In contrast, for HS [FeII(bpp)2]2+, no correlations are observed for δN with any ΔE (i=σ; π; σ+π) term: ΔE (R2=0.35, Figures S20), ΔE (R2=0.04, Figures S21) and ΔE (R2=0.30, Figures S22).

Figure 7

(a) Strong correlation (R2=0.95) of ΔE with pyridine nitrogen NMR chemical shift δN in the family of sixteen LS [FeII(bpp)2]2+ complexes. (b) Weak correlation (R2=0.39) of ΔE with δN in the family of sixteen LS [FeII(bpp)2]2+ complexes. (c) Weak correlation (R2=0.23) of ΔE with δN in the family of sixteen LS [FeII(bpp)2]2+ complexes.

This is in full agreement with all of the findings discussed previously: the X substituent, the effect of which can be quantified through use of σp +(X), operates as a tuner of the coordinating nitrogen ligand field strength, by enriching or impoverishing the electron density, which in turn is reflected in the chemical shift, δN. This tweak of the nitrogen electron densities is intimately entangled with the ligand σ‐donating properties (ΔE ) of the, enthalpically most stable, LS state that, finally, leads to an increase in the experimental T1/2.

Mulliken population analysis

The EDA‐NOCV results just reported project a different interpretation of the experimental results than those proposed by Deeth, Halcrow et al. in 2016. They concluded that the dominant effect of X changing EDG→EWG was increased M→L π‐backdonation, which increased the ligand field splitting (ΔO) and the observed solution T1/2 values. In contrast, the above quantitative EDA‐NOCV analysis indicates, rather counter‐intuitively at first glance, that as X changes as EDG→EWG, the dominant effect is increased σ‐donation M←L, and hence increased ligand field splitting and observed solution T1/2 values (Figure 8).

Figure 8

(a) Simplified representation of the atomic orbitals of FeII and the coordinating N nitrogen in the Fe−N bonding for described Mulliken population analysis. (b) Representation of the N(AOs) of the pyridyl ring in the referenced [FeII(bpp)2]2+ complex (centre) and at the substituted ligands at the ending of the Hammett scale ([FeII(bpp)2]2+, σ =−1.70 (top); [FeII(bpp)2]2+, σ =+0.79 (bottom). Arrows describe directionality of the resonance effects on the N(p): toward the N for [FeII(bpp)2]2+ and away from the N for [FeII(bpp)2]2+. The effect is complementary on the N(p): enriching for N(p) in [FeII(bpp)2]2+ and impoverishing for N(p) in [FeII(bpp)2]2+.

To try to understand how X changing EDG→EWG could increase the ability of the N‐donor to act as a stronger σ‐donor to FeII, here the associated changes in the population of the key atomic orbitals (AOs) of the coordinating nitrogen, ΔN(AO), when the X substituent changes from EDG (NMe, σ +=−1.70) to EWG (NO, σ +=+0.79) are probed by looking at the Mulliken charges, N(AO), for each atomic orbital, as these provide a simple electronic population analysis. This investigation was performed on the relaxed trans‐geometry of the free ligands, optimised using the same basis set employed for the related iron(II) complexes. It is worth mentioning that the observed trends are fully consistent with those obtained for the cis‐geometry of these ligands, which is closer to the coordination geometry but is less energetically stable (Tables S7, S9). Furthermore, it is important to note that the effects of varying X, which is para to the pyridine ring N donor atom (N), are much greater on N than on the coordinating nitrogen (N) of the relatively remotely attached pyrazolyl ring, and, most importantly, the latter reveals the same trend as N does with σp +(X) (Figure S4, Tables S10–S11). Hence, as Deeth, Halcrow and co‐workers also did, it is reasonable that the following discussion focuses attention only on the effect of varying X on N.

Examining the population of the individual valence orbitals on N uncovers information otherwise lost when only the overall electron density is considered, as is case when looking at the overall atomic charge (ρ(N)) or at the 15N NMR chemical shift, δ(N (Figures S26 and S32).

Mulliken charges were therefore calculated for each valence orbital on the N‐donor atom (s, p, p, p), as the Hammett parameter of X in the ligand was changed (EDG→EWG, Figures S27–S30). The hybridised sp is also reported vs. σp +(X) (Figure S31, with the electronic population taken as the average of the s, p, p orbital population). In the defined framework, in which all of the Fe‐pyridine moiety is contained in the xy plane (Figure 8), the p ligand orbital is responsible for accepting electron density from the metal in a π‐backbonding interaction (M→L), while the p ligand orbital provides the lone‐pair that establishes the σ‐bond to the metal (M←L).

Correlations between two of the N(AOs), N(p) and N(p), and σp +(X) are seen (Figure 9a). Specifically, as the para‐substituent X changes EDG→EWG, the associated increase in the Hammett parameter, σp +(X), correlates extremely well (R2=0.91, pink line in Figure 9a) with electron depletion of the p orbital N(p) and correlates well (R2=0.79, purple line in Figure 9a) with electron accumulation in the px orbital N(p). Overall, from NMe→NO, the decrease in population of the p orbital is ΔN(p)=+0.08 e, whilst the increase in the population of the p orbital is more modest, ΔN(p)=−0.03 e.

Figure 9

(a) Reported trends for the Mulliken populations N(p) and N(p) vs. σp +(X) Hammett parameter. Very good correlation is observed for N(p) vs. σp +(X) (purple line, R2=0.79) and an extremely good correlation for N(p) vs. σp +(X) (pink line, R2=0.91). (b) Reported trends for the Mulliken populations N(p) and N(p) vs. δNA chemical shift. Extremely good correlation are observed for both N(p) vs. δNA (purple line, R2=0.93) and for N(p) vs. δNA (pink line, R2=0.99). (c) Reported trends for the Mulliken populations N(p) and N(p) vs. experimental T1/2. Very good correlation is observed for N(p) vs. T1/2 (purple line, R2=0.75) and an extremely good correlation for N(p) vs. T1/2 (pink line, R2=0.88).

Therefore, whilst electronic population in N(p) is decreased as the X substituent becomes more EWG, making it a better acceptor for M→L π backbonding, the N(p) population is increased, resulting in more available electron density in the lone‐pair, which facilitates stronger M←L σ bonding and with it an increase in T1/2 ‐ in alignment with the common interpretation from crystal field theory first principles.

For completeness, it should be noted that para‐ X substituent only has tiny effects on the N(s) (Δe −<−0.002, NMe→NO) and N(p) atomic orbitals (Δe −<−0.004, NMe→NO), which also results in a lack of correlations with σp +(X) (R2(N(s))=0.27, Figure S27 and R2(N(p))=0.02, Figure S29). Combining these to form the N(sp ) hybrid orbital, the result is a good correlation with σp +(X) (R2(N(sp ))=0.73, Figure S31).

As the N(s) and N(p) atomic orbitals look almost unaffected by the electronic nature of the X substituent, it can be assumed that the N(p) and N(p) atomic orbitals are intimately affecting each other. For EDG substituents, this behavior can be explained as arising from the enrichment of π‐density (N(p)) inducing a compensating electrostatic draining of σ‐density (N(p)), all of which directly influences the bonding properties of the coordinated N atom. The opposite trend is expected for the EWG substituents.

In previous studies it was observed that δN is intimately connected with T1/2 and hence also with σp +(X). Therefore, herein possible relationships of δN with the Mulliken population analysis results are probed (Figure 9b). Unsurprisingly, the results are in full agreement with the observations just reported for N(AOs) vs. σp +(X) trends (Figure 9a). Indeed, the correlations with N(p) and N(p) are even stronger when using δN, which has the advantages of being an easily calculated but also experimentally verifiable value for the specific ligand used, rather than using σp +(X) for the substituent used.

An excellent correlation of increasing δN with decreasing NA(p) (R2=0.99, pink line in Figures 9b, S36) and with increasing NA(p) (R2=0.93, purple line in Figures 9b, Figure S34) is observed. Again no correlation is observed for δN vs. N (s) ((R2=0.41, Figure S33) or vs. N (p ((R2=0.0002), Figure S35). When combined, a very good correlation is observed for δN with N(sp ) (R2=0.93, Figure S37). As well, very good correlations are also observed for the experimental T1/2 vs. N(p) (R2=0.88, purple line in Figures 9c and S40) and N(p) (R2=0.75, pink line in Figures 9c and S42). Experimental T1/2 was also tested vs. ρ(N) (R2=0.85, Figure S38), N(s) (R2=0.22, Figure S39), N(p) ((R2=0.03), Figure S41), and the combined N(sp ) (R2=0.74, Figure S43).

Herein, the two orbital populations N(p) and N(p) were also tested vs. the orbital energy terms ΔE , ΔE and ΔE . (Figure 10). The ΔE term correlates extremely well with both N(p) (R2=0.84, Figure 10a) and N(p) (R2=0.93, Figure 10b), revealing how the variation of occupancy in these two orthogonal orbitals contributes to the σ‐donating properties of the ligand.

Figure 10

(a) Correlation of Mulliken p‐electrons population N ) of the family of sixteen bpp ligands with the energetic term of the [FeII(bpp)2]2+ complex (R2=0.84). (b) Correlation of Mulliken p‐electrons population N ) of the family of sixteen bpp ligands with the energetic term of the [FeII(bpp)2]2+ complex (R2=0.93).

Not surprisingly, given the poor correlations of ΔE or ΔE with either the Hammett parameter σp +(X) or observed T1/2 or calculated chemical shift δN (see above), poor correlations were found for ΔE with N(p) (R2=0.49, Figure S44) or N(p) (R2=0.36, Figure S45), and for ΔE with N(p) (R2=0.29, Figure S46) or N(p) (R2=0.46, Figure S47).

For above findings to be useful, it is critical that they are not dependent on the specific method of charge analysis employed, so the same analysis was also performed using the Loewdin framework in the atomic charge assessment (Table S8, Figures S48‐S50), and this confirmed the above findings.

Comparison of these results with the literature

In their landmark 2016 paper, Halcrow, Deeth and coworkers proposed an intuitively reasonable explanation, also consistent with the calculated MO energy levels of the [FeII(bpp)2]2+ complexes, of the effect of the para‐ X substituents on the T1/2 values in this family of SCO active complexes: that M→L π‐backdonation dominates in these M−L bonds. Hence, in the quantitative EDA‐NOCV analysis of the M−L bond contributions performed herein, a correlation between ΔE and T1/2 was expected ‐ but was not observed (R2=0.09, Figure S12).

However, the proposed dominance of the M→L π‐backdonation was based on the observation of a slope difference between the correlation lines for σp +(X) vs. FeII (−0.39) and (−0.32), Error bars would have helped in analysing the significance of this small difference in slope. Indeed, a larger variance is expected for FeII E(t) than for FeII E(e), so what was claimed as a “greater effect on the averaged orbital energies than on the orbitals” could be an overstatement. Also, in ref the halogen X substituents (four dots: X=F, Cl, Br, I) had to be separately grouped from all of the other electron‐withdrawing X substituents. They behave differently to the other X groups, specifically they have a greater effect on the E(e than on the E(t. All of these effects are accurately reflected in the present EDA‐NOCV analysis, which therefore provides a coherent and detailed picture of the relative impact of M−L σ‐ versus π‐bonding in determining the observed T1/2, effectively refining the earlier interpretation by Halcrow, Deeth and co‐workers. In support of this, the perfect agreement between our results and the ΔE(HS‐LS) vs. σp +(X) reported in their work is revelatory.

Predicting σp and σp + for X=SOMe, SO2Me

In this study, several correlations have been identified whereby the electronic tuning by X modifies the electron density over the coordinating nitrogen N and, consequently, its coordinating properties in engaging in the Fe−N bond in these sixteen [FeII(bpp)2]2+ complexes. These correlations, weight averaged by the relative R2 values, can be employed to predict the Hammett constants for substituents X for which they are not known. For two out of the sixteen [FeII(bpp)2]2+ complexes, those with X=SOMe and X=SO, whilst the σp(X) parameter is known, the σp +(X) parameter is not available.[ , ]

Firstly, this approach was trialled for estimating the known σp(X) parameters, giving σp(SOMe)≈0.31 vs. the literature value of 0.49, and similarly, σp(SO)≈0.52 vs. the literature value of 0.72, with both predicted values lying about 0.2 units below the literature values. A general underestimation of the literature values is observed in all the explored correlations (Table S12).

Secondly, in the same way, the set of seven correlations, Equations S1–S7, identified in this study were used to predict the unknown values of σp +(X) for X=SOMe and X=SO (Table 4, Table S13), as ≈0.25 and ≈0.54, respectively.

Table 4

Predicted values of σ (X) for the two X substituents for which this value is not reported in literature, using the correlations identified in this study with the best correlation factor, followed by the weighted average value highlighted in yellow.

		σp +	σp +
		X=SOMe	X=SO 2 Me	R2
LS [FeII(bppX )2]2+	ΔEelstat	0.20	0.65	0.89
	ΔE orb,σ	0.01	0.50	0.88
Exp .	T 1/2	0.53	0.64	0.92
bppX	δ15NA	0.27	0.58	0.92
	ρ(NA)	0.23	0.66	0.93
	NA(px)	0.28	0.51	0.79
	NA(pz)	0.23	0.62	0.91
weight.av . (σp + )		0.25	0.54	−

σ

σ

R

LS [FeII(bpp)2]2+

ΔE

ΔE

.

T

bpp

δ

ρ(N

N

N

. (σ )

−

Finally, we note that in future studies by us and others, consideration could be given to using parameters designed for azine (and azole) derivatives, in place of the Hammett parameter which arises from consideration of benzoic acid derivatives.

Conclusion

Inspired by the 2016 landmark study by Deeth, Halcrow and co‐workers, the effect of the para‐substituent X on the electronic structure of sixteen solution SCO active [FeII(bpp)2]2+ complexes has been investigated in more depth herein, by quantifying the contributions to the M−L bonds through use of EDA‐NOCV analysis, and then, due to the unexpected findings from that study, a Mulliken charge analysis was also conducted.

Specifically, the EDA‐NOCV results unexpectedly revealed a strong correlation between the σ‐donor strength (ΔE ) of the bpp ligand in the LS [FeII(bpp)2]2+ complex and the measured T1/2 of the complex (R2=0.82), but not with ΔE or ΔE . Furthermore, ΔE also correlated strongly with the 15N NMR chemical shift δN(bpp) (R2=0.95), and with σp +(X) (R2=0.88).

These correlations, of ΔE with T1/2, σp +(X) and δN, were further probed by analysis of the Mulliken charges for the N valence orbitals. Moving from EDG to EWG para‐substituents X, the analysis of the Mulliken charges showed that the electron population in the N(p) orbital decreases (as it is delocalised in the ligand π‐system towards the X substituent), whilst the population in the nitrogen lone pair, N(p), orthogonal to N(p), increases. An enhancement of the σ‐donation (Fe←N) is therefore expected, as is enhancement of the π‐acceptor character (Fe). Both of these effects lead to an increase the ligand field and hence an increase of T1/2, as experimentally observed. The key difference from Halcrow and Deeth's intuitive finding is that the EDA‐NOCV quantitative analysis indicates that the σ‐donation Fe←N dominates, whereas they proposed that the π‐acceptor character Fe dominates. Indeed, a critical look at Halcrow and Deeth's results shows a similar dependence of both σ‐donation and π‐acceptor for [FeII(bpp)2]2+, depicting a picture not too different from ours.

It is also interesting to note that the EDA‐NOCV findings for the [FeII(bpp)2]2+ family studied herein (correlations only with ΔE , not with ΔE or ΔE ) differ from those found for the only other SCO‐active family studied to date, wherein a correlation was found only with ΔE , not ΔE or ΔE . This might indicate that EDA‐NOCV analysis may be sensitive to different coordination bond schemes (i. e. kinds of ligands), but the important point is the confirmation that excellent trends between EDA‐NOCV parameters and T1/2 values are found for the different Fe(II) families studied to date. Nevertheless, it must be borne in mind that to date these are the only two in depth studies of SCO‐active families so it is too soon to draw conclusions from this. Rather, it is clear that further such studies are warranted.

Finally, it is also important to note that while the above EDA‐NOCV analysis captures the majority of enthalpic effects, it does not account for any explicit entropic contributions. Indeed, the T1/2 values arise from a delicate balance of very subtle effects of these two contributions, that can have drastic consequences on the SCO. Hence the future development of this approach for applications in the SCO field should also involve finding ways to evaluate if, and how, entropic contributions need to be included in the EDA‐NOCV analysis when systems that are structurally very different are considered.

Computational Details

Calculations were performed using ORCA 4.1 and ADF (version 2018.106) code. The ORCA code was used to optimise the structure of sixteen of the [FeII(bpp)2]2+ complexes (in both HS and LS states); the absence of negative eigenvalues for the Hessian matrix confirmed the all computed geometries are in real minima.

Firstly, using the atomic coordinates of the sixteen LS and sixteen HS [FeII(bpp)2]2+ complexes available from the DFT study at RI‐BP86‐D3(BJ)/def2‐SVP/J+COSMO(acetone) level of theory in the paper by Deeth, Halcrow et al., a geometry re‐optimisation was performed using different RI‐BP86‐D3(BJ)/def2‐TZVPP+CPCM level of theory:[ , ] i. e. RI=resolution of identity[ , ] with a BP86 functional,[ , ] with D3 dispersion correction (including BJ damping), def2‐TZVPP basis set, and the solvent modelled by CPCM. The same was done for the trans and cis forms of the sixteen free bpp ligands.

Secondly, the optimised structures of the complexes were used for the EDA‐NOCV method that combines classical EDA with NOCV, which were performed using the ADF2019.106 program package at the BP86‐D3(BJ)/TZ2P level of theory.[ , ] It should be noted that the EDA‐NOCV is implemented with no possibility to include any solvation model. Finally, the fully optimised geometries of the ligands were used for the Mulliken and Loewdin analyses.

Conflict of interest

The authors declare no conflict of interest.

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