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\begin{document}

\title[Citrate-Bound Iron Oxide Clusters in Ionic Liquid Environments: Solvation, Spin-State Energetics, and Bond Dissociation]{Citrate-Bound Iron Oxide Clusters in Ionic Liquid Environments: Solvation, Spin-State Energetics, and Bond Dissociation}

%%=============================================================%%
%% GivenName    -> \fnm{Joergen W.}
%% Particle     -> \spfx{van der} -> surname prefix
%% FamilyName   -> \sur{Ploeg}
%% Suffix       -> \sfx{IV}
%% \author*[1,2]{\fnm{Joergen W.} \spfx{van der} \sur{Ploeg}
%%  \sfx{IV}}\email{iauthor@gmail.com}
%%=============================================================%%

\author*[1]{\fnm{Leonard} \sur{Komando}}\email{leonard.komando@pg.edu.pl}

\author[1]{\fnm{Maciej} \sur{Bobrowski}}\email{maciej.bobrowski@pg.edu.pl}
\equalcont{These authors contributed equally to this work.}

%\author[1,2]{\fnm{Third} \sur{Author}}\email{iiiauthor@gmail.com}
%\equalcont{These authors contributed equally to this work.}

\affil*[1]{\orgdiv{Department of Technical Physics and Applied Mathematics}, \orgname{Gda\'{n}sk University of Technology}, \orgaddress{\street{Narutowicza 11/12}, \city{Gda\'{n}sk}, \postcode{80-233}, \country{Poland}}}

%\affil[2]{\orgdiv{Department of Technical Physics and Applied Mathematics}, \orgname{Gda\'{n}sk University of Technology}, \orgaddress{\street{Narutowicza 11/12}, \city{Gda\'{n}sk}, \postcode{80-233}, \country{Poland}}}

\maketitle


\section{Contents of this Supplementary Information}

This file is intended to contain:
\begin{enumerate}
    \item Cartesian coordinates of the optimized lowest-energy structures.
    \item Additional methodological details for the relaxed Fe--O(citrate) scans.
    \item Raw scan data for each environment.
    \item Supplementary figures or tables not essential to the main text.
\end{enumerate}

\section{Cartesian Coordinates of Optimized Structures}

The Cartesian coordinates (in \AA) of all optimized structures corresponding to the lowest-energy antiferromagnetic singlet ( $S = 0$) states of \ce{Fe2O3-Citrate^{3-}} and \ce{Fe4O6-Citrate^{3-}} discussed in the manuscript are provided below. For solution-phase structures, the SMD implicit solvation model was employed with the dielectric constants specified in the main text. For each structure, the total charge, spin multiplicity, and electronic-state assignment are explicitly indicated. The reported coordinates correspond to optimized stationary points on the potential energy surface.

\subsection{\ce{Fe2O3-Citrate^{3-}} (lowest-energy antiferromagnetic singlet state, $S = 0$)}

Charge $= -3$; multiplicity $= 1$ \\
%Electronic state: broken-symmetry antiferromagnetic singlet \\
Method: UB3LYP-D3(BJ)/def2-TZVP \\


Environment: gas phase
\begin{verbatim}
26        -4.561165    0.220214    0.042652
26        -2.031182   -0.106367   -0.021241
 8        -6.252048    0.413050    0.101435
 8        -3.366648   -0.781466   -1.067317
 8        -3.092769    0.882627    1.077884
 8        -0.455323   -1.313169    0.548006
 8        -0.175323    0.358497   -0.823584
 6         0.326005   -0.658257   -0.230885
 6         1.714696   -1.151869   -0.501051
 6         2.932946   -0.382625    0.128745
 6         4.136417   -1.382556   -0.121492
 6         3.112925    0.991779   -0.520180
 6         4.283829    1.926406   -0.065715
 8         4.569501   -1.942056    0.922049
 8         4.466178   -1.595594   -1.305860
 8         5.201478    1.454117    0.635911
 8         4.184458    3.107238   -0.506069
 8         2.718236   -0.281143    1.527456
 1         3.456382   -0.840621    1.855561
 1         3.250840    0.834663   -1.593761
 1         2.187300    1.561320   -0.409491
 1         1.756488   -2.174421   -0.125484
 1         1.869414   -1.163061   -1.580471
\end{verbatim}

Environment: \ce{[BMIM][PF6]}
\begin{verbatim}
26        -4.520108    0.219189    0.142262
26        -1.994443   -0.274267   -0.092093
 8        -6.087032    0.937527    0.111501
 8        -3.439474   -0.839379   -1.064024
 8        -2.924426    0.773158    1.079875
 8        -0.353770   -1.573712    0.381260
 8        -0.065977    0.152521   -0.927612
 6         0.410923   -0.880350   -0.360905
 6         1.832861   -1.313046   -0.574040
 6         2.884747   -0.361133    0.057486
 6         4.211632   -1.180035    0.098017
 6         3.014021    0.938577   -0.729665
 6         4.001768    1.970358   -0.157236
 8         4.581322   -1.542756    1.246973
 8         4.743193   -1.475756   -0.993556
 8         5.062344    1.550065    0.366661
 8         3.681113    3.181486   -0.303162
 8         2.488236   -0.075506    1.399343
 1         3.174983   -0.543731    1.918198
 1         3.348963    0.696202   -1.742089
 1         2.034342    1.405062   -0.819352
 1         1.943740   -2.301370   -0.128668
 1         2.018961   -1.390589   -1.645796
\end{verbatim}

Environment: \ce{[MBPY][BF4]}
\begin{verbatim}
26        -4.426214    0.244112    0.008212
26        -1.891485   -0.187028    0.037788
 8        -6.106011    0.325992    0.363628
 8        -3.282237   -1.245826   -0.472260
 8        -2.877387    1.265805    0.549729
 8        -0.229902   -1.201733    0.855523
 8        -0.156412   -0.428750   -1.186806
 6         0.425927   -1.014643   -0.218613
 6         1.849376   -1.467369   -0.341589
 6         2.886842   -0.393580    0.105931
 6         4.278981   -1.108358    0.031441
 6         2.809647    0.860142   -0.768998
 6         3.645120    2.041742   -0.239656
 8         4.820565   -1.319025    1.150524
 8         4.694964   -1.466138   -1.089141
 8         3.022862    3.112719   -0.011723
 8         4.880556    1.862263   -0.095880
 8         2.643149   -0.041376    1.463704
 1         3.431893   -0.417249    1.909774
 1         3.157687    0.602806   -1.772386
 1         1.771709    1.181041   -0.846292
 1         1.987471   -2.348268    0.286817
 1         2.049497   -1.729478   -1.379006
\end{verbatim}

Environment: \ce{[EMIM][BF4]}
\begin{verbatim}
26        -4.444782    0.346862   -0.020535
26        -1.945236   -0.289095    0.035571
 8        -6.122893    0.712891   -0.088070
 8        -3.356650   -1.043600   -0.833461
 8        -2.873668    1.007661    0.923445
 8        -0.241885   -1.412807    0.730456
 8        -0.134797   -0.172019   -1.066987
 6         0.431675   -0.969323   -0.250710
 6         1.856369   -1.395481   -0.447182
 6         2.899387   -0.356266    0.054100
 6         4.274876   -1.103039    0.023121
 6         2.887382    0.911768   -0.803830
 6         3.734857    2.061038   -0.225909
 8         4.777125   -1.328831    1.157265
 8         4.714740   -1.470947   -1.085305
 8         3.131525    3.136182    0.031418
 8         4.965425    1.854024   -0.073734
 8         2.605427   -0.021376    1.408083
 1         3.368592   -0.416043    1.881204
 1         3.267446    0.656541   -1.795774
 1         1.860630    1.256055   -0.915098
 1         2.006885   -2.323193    0.105072
 1         2.030372   -1.579551   -1.506389
\end{verbatim}

Environment: EAN
\begin{verbatim}
26        -4.439821    0.351630    0.098225
26        -1.975170   -0.342829   -0.100202
 8        -6.049107    0.960305   -0.116589
 8        -3.499271   -1.083850   -0.810093
 8        -2.759317    1.062045    0.769580
 8        -0.258089   -1.464107    0.702830
 8        -0.099957   -0.270973   -1.123661
 6         0.440043   -1.041803   -0.267519
 6         1.877394   -1.446481   -0.425395
 6         2.886595   -0.411541    0.145873
 6         4.292042   -1.046803   -0.070856
 6         2.746459    0.947331   -0.529269
 6         3.764621    2.026574   -0.132815
 8         4.851083   -1.493953    0.966158
 8         4.720336   -1.125311   -1.243405
 8         4.829799    1.688309    0.439366
 8         3.452096    3.208619   -0.448628
 8         2.657414   -0.269351    1.548125
 1         3.428624   -0.723870    1.941047
 1         2.817948    0.821280   -1.612092
 1         1.749129    1.342868   -0.334164
 1         2.034289   -2.390787    0.096142
 1         2.082152   -1.583431   -1.486321
\end{verbatim}

Environment: \ce{[CH3NH3][HCOO]}
\begin{verbatim}
26        -4.490716    0.276312    0.087978
26        -2.004277   -0.334032   -0.011905
 8        -6.123088    0.836913   -0.113390
 8        -3.469585   -1.113815   -0.795335
 8        -2.868637    1.046559    0.828846
 8        -0.247822   -1.342676    0.686610
 8        -0.140752   -0.182898   -1.163533
 6         0.422022   -0.940994   -0.317215
 6         1.847874   -1.375725   -0.497744
 6         2.879944   -0.391419    0.119959
 6         4.258576   -1.095511   -0.034835
 6         2.830832    0.969584   -0.563218
 6         3.879745    2.003250   -0.129908
 8         4.746826   -1.575698    1.022919
 8         4.738465   -1.189888   -1.186578
 8         4.890499    1.628125    0.514911
 8         3.651062    3.191063   -0.492684
 8         2.598950   -0.230891    1.510226
 1         3.315079   -0.736443    1.942044
 1         2.940537    0.835812   -1.641660
 1         1.845304    1.411567   -0.408866
 1         1.974170   -2.344472   -0.013419
 1         2.053365   -1.477342   -1.562056
\end{verbatim}

Environment: Water
\begin{verbatim}
26        -4.501236    0.236949    0.075593
26        -2.004950   -0.279685   -0.086081
 8        -6.178421    0.404757    0.528429
 8        -3.473006   -1.244586   -0.638720
 8        -2.884879    1.150774    0.660704
 8        -0.259141   -1.292423    0.656061
 8        -0.158188   -0.127361   -1.192402
 6         0.409297   -0.894775   -0.350450
 6         1.829000   -1.342444   -0.541790
 6         2.872480   -0.386462    0.099666
 6         4.237257   -1.117222   -0.041549
 6         2.859234    0.980613   -0.572771
 6         3.898825    1.990775   -0.076597
 8         4.702850   -1.614385    1.020484
 8         4.734625   -1.216457   -1.187519
 8         4.934951    1.573881    0.503375
 8         3.649084    3.206297   -0.321371
 8         2.580624   -0.229207    1.488779
 1         3.272984   -0.764703    1.922851
 1         3.020429    0.854023   -1.645622
 1         1.871458    1.427807   -0.459201
 1         1.939725   -2.323313   -0.079337
 1         2.035079   -1.422522   -1.607354
\end{verbatim}


\subsection{\ce{Fe4O6-Citrate^{3-}} (lowest-energy antiferromagnetic singlet state, $S = 0$)}

Charge $= -3$; multiplicity $= 1$ \\
%Electronic state: broken-symmetry antiferromagnetic singlet \\
Method: UB3LYP-D3(BJ)/6-31+G(d) \\

Environment: EAN
\begin{verbatim}
 6         2.791645    0.368387    0.966281
 6         3.324001   -0.614247   -0.116362
 8         2.760027   -0.325931   -1.390939
 6         2.752629    1.827887    0.510747
 8         3.787502    2.503217    0.440440
26        -0.153204    1.583376   -0.245663
 8         1.575100    2.333133    0.232648
26        -0.770255   -1.112598   -0.459465
 6         1.620617   -2.388044    0.791248
 6         3.041372   -2.095082    0.316887
 8        -2.409681   -1.910038   -0.654199
26        -3.889372   -0.887877   -0.304191
 8        -3.878316    0.019451    1.318300
26        -2.784931    1.292652    0.425285
 8        -1.626692    2.681863   -0.010995
 8        -3.557332    0.693712   -1.197063
 8        -1.014082    0.241906    0.878276
 8         0.015686    0.237345   -1.542890
 8         0.691807   -2.351183   -0.129739
 8         1.392722   -2.648693    1.981489
 6         4.898281   -0.520799   -0.225707
 8         5.413032   -0.442055   -1.372156
 8         5.519811   -0.590709    0.873913
 1         1.784435    0.074870    1.277452
 1         3.449441    0.288996    1.835917
 1         1.775700   -0.230266   -1.346585
 1         3.724823   -2.351877    1.128257
 1         3.267691   -2.727513   -0.549928
\end{verbatim}

Environment: \ce{[CH3NH3][HCOO]}
\begin{verbatim}
 6         2.779022    0.355736    0.959003
 6         3.318968   -0.629887   -0.118848
 8         2.751067   -0.362114   -1.395580
 6         2.757282    1.816100    0.506343
 8         3.800130    2.480844    0.450334
26        -0.145998    1.583936   -0.254617
 8         1.588536    2.331827    0.213839
26        -0.767139   -1.112412   -0.457215
 6         1.622348   -2.398554    0.796089
 6         3.045120   -2.107611    0.324056
 8        -2.409723   -1.902591   -0.648112
26        -3.889590   -0.878272   -0.298465
 8        -3.866339    0.030062    1.324281
26        -2.779133    1.303400    0.426263
 8        -1.614613    2.686849   -0.020032
 8        -3.554650    0.703024   -1.193385
 8        -1.004975    0.247632    0.875526
 8         0.019694    0.232621   -1.548029
 8         0.693234   -2.355647   -0.124310
 8         1.393020   -2.661924    1.985702
 6         4.890105   -0.492710   -0.226058
 8         5.396120   -0.264986   -1.356103
 8         5.518810   -0.656636    0.859708
 1         1.767155    0.067796    1.259331
 1         3.425284    0.270927    1.837076
 1         1.767846   -0.255755   -1.349398
 1         3.727839   -2.357913    1.137387
 1         3.273603   -2.745458   -0.538453
\end{verbatim}

Environment: Water
\begin{verbatim}
 6         2.781421    0.355332    0.960384
 6         3.319321   -0.629961   -0.118700
 8         2.750726   -0.359197   -1.394659
 6         2.759005    1.815348    0.506964
 8         3.802156    2.480035    0.449486
26        -0.146248    1.582064   -0.250418
 8         1.590662    2.330676    0.214403
26        -0.767224   -1.112495   -0.459974
 6         1.620096   -2.396867    0.792231
 6         3.043867   -2.107995    0.322205
 8        -2.409344   -1.901569   -0.651217
26        -3.892833   -0.881038   -0.299896
 8        -3.863340    0.023984    1.325360
26        -2.781293    1.301221    0.428545
 8        -1.613483    2.685201   -0.013956
 8        -3.556003    0.703428   -1.191625
 8        -1.003009    0.243269    0.876641
 8         0.021888    0.234738   -1.548645
 8         0.693399   -2.358992   -0.130647
 8         1.387762   -2.652696    1.983027
 6         4.890442   -0.495898   -0.227426
 8         5.396242   -0.273045   -1.358754
 8         5.520375   -0.657806    0.857829
 1         1.770060    0.067536    1.262079
 1         3.428504    0.270397    1.837752
 1         1.767271   -0.252247   -1.348061
 1         3.725477   -2.359543    1.136124
 1         3.272742   -2.745314   -0.540486
\end{verbatim}


\section{Relative spin-state energies of \texorpdfstring{\ce{Fe4O6-Citrate^{3-}}}{Fe4O6-Citrate(3-)} at the 6-31+G(d) level}

\begin{table}[h]
\centering
\caption{Relative energies (kcal~mol$^{-1}$) for \ce{Fe4O6-Citrate^{3-}} at the UB3LYP-D3(BJ)/6-31+G(d) level. Values are referenced to the $S = 0$ ground state within each environment.}
\label{tab:Fe4O6_citrate_631G_RE}
\begin{tabular}{crrrr}
\toprule
$S$ & Gas & EAN & \ce{[CH3NH3][HCOO]} & Water \\
    &     & ($\varepsilon\!=\!26.3$) & ($\varepsilon\!=\!41.0$) & ($\varepsilon\!=\!78.4$) \\
\midrule
 0 &  0.00 &  0.00 &  0.00 &  0.00 \\
 1 & 11.65 & 21.37 & 10.24 & 20.71 \\
 2 & 27.31 & 38.20 & 32.34 & 37.42 \\
 3 & 49.39 & 49.74 & 50.90 & 49.09 \\
 4 & 50.45 & 48.84 & 52.26 & 63.09 \\
 5 & 34.67 & 64.13 & 70.43 & 63.63 \\
 6 & 42.22 & 39.70 & 52.17 & 60.64 \\
 7 & 36.55 & 50.07 & 57.83 & 57.04 \\
 8 & 45.17 & 33.17 & 47.83 & 47.92 \\
 9 & 21.91 & 23.74 & 23.69 & 42.11 \\
10 &  6.74 &  6.33 &  6.07 &  5.84 \\
\bottomrule
\end{tabular}
\end{table}


\section{Bond Dissociation Energy Curves}

Relaxed potential energy surface (PES) scans were performed to characterize the Fe--O(citrate) dissociation profiles in the \ce{Fe2O3-Citrate} complexes. Two scan protocols were employed (see main text), both carried out at the UB3LYP-D3(BJ)/def2-TZVP level of theory. The Fe2--O(citrate) distance was systematically varied over the range 1.6--6.0~\AA\ using a non-uniform grid to ensure adequate resolution near the equilibrium region and efficient sampling at longer separations. 

%Specifically, step sizes of 0.1~\AA\ were used between 1.6 and 2.4~\AA\ (9 points), 0.2~\AA\ between 2.4 and 4.0~\AA\ (8 points), and 0.5~\AA\ between 4.0 and 6.0~\AA\ (4 points), yielding a total of 21 scan points per curve. At each fixed Fe--O distance, all remaining geometric degrees of freedom were fully optimized, corresponding to relaxed scans along the dissociation coordinate.
Solvent effects were modeled using the SMD implicit solvation model. Four condensed-phase environments were considered: \ce{[EMIM][BF4]} ($\varepsilon = 12.8$), EAN ($\varepsilon = 26.3$), \ce{[CH3NH3][HCOO]} ($\varepsilon = 41.0$), and water ($\varepsilon = 78.4$).

\begin{table}[ht]
\centering
\caption{Definition of the Fe2--O(citrate) scan grid used in the bond dissociation energy calculations.}
\begin{tabular}{cccc}
\toprule
Range (\AA) & Step size (\AA) & Number of points & Distance values (\AA) \\
\midrule
1.6--2.4 & 0.1 & 9 & 1.6, 1.7, \ldots, 2.4 \\
2.4--4.0 & 0.2 & 8 & 2.6, 2.8, \ldots, 4.0 \\
4.0--6.0 & 0.5 & 4 & 4.5, 5.0, 5.5, 6.0 \\
\midrule
Total & -- & 21 & -- \\
\bottomrule
\end{tabular}
\end{table}


\subsection{Fe--O(citrate) Single-bond Dissociation ($S = 0$) Scan Data (Hartree)}

\begin{verbatim}
Distance (Å)      Water        [CH3NH3][HCOO]         EAN           [EMIM][BF4]
  1.6         -3512.4896684    -3512.4713371     -3512.4377879     -3512.3731608
  1.7         -3512.5203809    -3512.4903841     -3512.4678279     -3512.4027689
  1.8         -3512.5367778    -3512.4985925     -3512.4836406     -3512.4176468
  1.9         -3512.5437616    -3512.5097405     -3512.4904606     -3512.4235243
  2.0         -3512.5452496    -3512.5115024     -3512.4911005     -3512.4242307
  2.1         -3512.5435013    -3512.5099462     -3512.4888116     -3512.4221373
  2.11        -3512.5438777    -3512.5097228     -3512.4897037     -3512.4213343
  2.12        -3512.5438102    -3512.5091687     -3512.4888677     -3512.4208924
  2.13        -3512.5436015    -3512.5092182     -3512.4889238     -3512.4207772
  2.14        -3512.5432708    -3512.508683      -3512.4883744     -3512.4201984
  2.15        -3512.5430143    -3512.5084418     -3512.4882299     -3512.4209015
  2.16        -3512.5425244    -3512.5084006     -3512.4884799     -3512.419627
  2.18        -3512.5420134    -3512.5080911     -3512.487738      -3512.4186039
  2.2         -3512.5402091    -3512.507258      -3512.4852432     -3512.418176
  2.3         -3512.5378194    -3512.5034756     -3512.4833425     -3512.4140784
  2.4         -3512.5347058    -3512.5002849     -3512.4794213     -3512.4107988
  2.6         -3512.5278147    -3512.4924357     -3512.4719706     -3512.4018503
  2.8         -3512.522258     -3512.4867131     -3512.4659246     -3512.3943148
  3.0         -3512.5183206    -3512.4823982     -3512.4614084     -3512.3891254
  3.2         -3512.5151338    -3512.4796858     -3512.4581856     -3512.3840454
  3.4         -3512.5123726    -3512.4769147     -3512.455191      -3512.3811379
  3.6         -3512.5099861    -3512.4744923     -3512.4525803     -3512.378439
  3.8         -3512.5078954    -3512.4723633     -3512.4502881     -3512.3759992
  4.0         -3512.5060641    -3512.4705281     -3512.448321      -3512.375705
  4.5         -3512.5025003    -3512.4665649     -3512.4441379     -3512.3710047
  5.0         -3512.4992214    -3512.4623346     -3512.4406111     -3512.3669317
  5.5         -3512.4963977    -3512.4595546     -3512.4375309     -3512.3634511
  6.0         -3512.4939986    -3512.4571387     -3512.4348447     -3512.3605258
\end{verbatim}


\subsubsection{Double-Bond Dissociation ($S = 0$) Scan Data (Hartree)}

\begin{verbatim}
Distance (Å)      Water        [CH3NH3][HCOO]         EAN           [EMIM][BF4]
  1.6         -3512.3941504    -3512.3590567     -3512.3383766     -3512.2724675
  1.7         -3512.466434     -3512.4370112     -3512.4200337     -3512.3672232
  1.8         -3512.5218102    -3512.4857902     -3512.4648391     -3512.3974229
  1.9         -3512.5489194    -3512.5141845     -3512.4936716     -3512.4242364
  2.0         -3512.5631408    -3512.5274444     -3512.5067713     -3512.4368552
  2.1         -3512.5696315    -3512.5331251     -3512.5124029     -3512.4418815
  2.11        -3512.5699052    -3512.5333984     -3512.5125633     -3512.4418537
  2.12        -3512.570182     -3512.5337953     -3512.5129603     -3512.4422862
  2.13        -3512.5704585    -3512.5339534     -3512.5130255     -3512.4420556
  2.14        -3512.5704283    -3512.5339027     -3512.5131032     -3512.4418434
  2.15        -3512.5708531    -3512.5343735     -3512.5133755     -3512.4420973
  2.16        -3512.5708679    -3512.5343252     -3512.5133272     -3512.4420164
  2.18        -3512.5708347    -3512.5343243     -3512.5133128     -3512.4418349
  2.2         -3512.5706315    -3512.5340801     -3512.5129731     -3512.4418443
  2.3         -3512.567703     -3512.5309635     -3512.5100448     -3512.4378141
  2.4         -3512.5642438    -3512.5269688     -3512.5055968     -3512.4343009
  2.6         -3512.5550316    -3512.5176946     -3512.4952352     -3512.4209429
  2.8         -3512.5484729    -3512.5099337     -3512.4872761     -3512.4111346
  3.0         -3512.5460269    -3512.506875      -3512.4841387     -3512.4050172
  3.2         -3512.5431968    -3512.5045409     -3512.4816335     -3512.4025924
  3.4         -3512.5410433    -3512.5015102     -3512.4785728     -3512.4001437
  3.6         -3512.5390126    -3512.5005495     -3512.4771867     -3512.3981854
  3.8         -3512.5377158    -3512.4989614     -3512.4753986     -3512.3962794
  4.0         -3512.5355157    -3512.4955451     -3512.4716778     -3512.3929368
  4.5         -3512.5353321    -3512.4959276     -3512.4718848     -3512.3925882
  5.0         -3512.5345523    -3512.4940181     -3512.4701323     -3512.3897873
  5.5         -3512.5326627    -3512.4915822     -3512.4673041     -3512.3868106
  6.0         -3512.5319671    -3512.4913066     -3512.4666685     -3512.3860405
\end{verbatim}

\end{document}
