What is the nature of bonding in [Fe(CO)3(NO)]− and [Fe(CO)4]2−?

To shed new light on the electronic structure of [Fe(CO)3(NO)]¯ complex ion, DFT-based analysis of the nature of chemical bonding has been performed. For this purpose, the extended transition state energy decomposition analysis alongside the natural orbitals for chemical valence has been used and results are compared to the nature and the strength of the interactions in isoelectronic [Fe(CO)4]2− complex ion. Based on orbital contribution to the interaction energy and charge flow between the fragments, the ground state can be best described as an open-shell singlet with zero formal oxidation state on iron and negative charge on the nitrosyl ligand. It is in agreement with the different nature of interactions when NO+ and CO ligands are bonded to Fe(−II).


Introduction
In chemical compounds, iron can be found in various oxidation states (from −II to +VI) [1]. The most common ones are +II and +III, and unusual oxidation states Fe(−II), Fe(−I) and Fe(0) have been found in organometallic compounds [1][2][3][4]. The [Fe(CO) 3 (NO)]¯ has been the subject of interest in inorganic, organic and physical chemistry, as well as in catalysis for many years [5][6][7][8][9][10]. Concerning its electronic structure, there is no general conclusion about the oxidation state of the central Fe atom and the resulting charge of the NO ligand; thus, the determination of its ground electronic state. [Fe(CO) 3 4 ] 2− with the oxidation state of the iron unambiguously accepted to be −II [11,12]. Accordingly, iron in the first complex is expected to be in -II oxidation state. On the other hand, these two species have different catalytic activities in various organic reactions pointing into a difference in their electronic structure [5,6,8,9]. The combined experimental and theoretical study proposed that the electronic structure of [Fe(CO) 3 (NO)]¯ is best described as NO − coordinated to Fe(0) [6]. More recent work gave different views on this subject more in line with the Fe(−II)-NO + bonding [7]. The vagueness of the nature of Fe-NO interaction in [Fe(CO) 3 (NO)] − is a consequence of both the diversity of the electronic structures of transition metal complexes in general [13][14][15][16] and non-innocence of the nitric oxide-type ligand [17][18][19][20][21][22][23]. Energies of iron 3d orbitals and π * orbitals of NO are of comparable energies, complicating the determination of the oxidation state of iron as well as the nature of nitric oxide-type ligand -NO + , NO radical or NO¯.

(NO)] − is isoelectronic with [Fe(CO)
In [Fe(CO) 4 ] 2− , iron is in a tetrahedral environment with formal d 10 electronic configuration. All five molecular orbitals (MOs) with dominant d-character are completely filled, giving singlet as the ground state. Excellent π * -accepting properties of the CO assist in the stability of the d 10 complex. When the isoelectronic [Fe(CO) 3 (NO)] − is considered in the same way, i.e., Fe(-II) and NO + , naturally closedshell singlet is again the ground state. In the other situation, when there is an interaction between Fe(0) and NO − , there 1 3 126 Page 2 of 8 are two unpaired electrons on the iron center (d 8 electronic configuration) and two unpaired electrons on nitrosyl anion. This leads either to the quintet or to the open-shell singlet state. Consequently, the nature of the bonding of nitrosyl ligand to the iron center must be different depending on the electronic structure. And the role of π * orbitals of the nitric oxide is different.
The problem of the description of the electronic structure in [Fe(CO) 3 (NO)] − is clearly multireference [6,7]. Closed-shell singlet state and high-spin quintet state can be adequately described by one Slater determinant, but this is not the case for the open-shell singlet state. This instantly leads to the conclusion that multideterminantal methodologies that are based on configuration interaction should be used. Unfortunately, such methods did not give equivocal findings [6,7]. Adequate treatment of the dynamical correlation is also necessary. As a single determinant method, conventional Kohn-Sham density functional theory (KS-DFT) cannot rigorously describe multideterminantal states. Noodleman's suggestion was the approach called the broken symmetry (BS), which represents multideterminantal states with only one "antiferromagnetically coupled" Slater determinant [13,[24][25][26]. Another drawback of all DFT-based methods is the dependence of the results on the choice of the density functional approximations (DFAs) employed. It is well known that the generalized gradient (GGA) functionals overestimate delocalization [27]. In contrast, hybrid functionals tend to localize electron, and the extent of the localization will be higher with a higher percentage of the exact Hartree-Fock (HF) exchange [28]. This situation occurs, e.g., in mixed-valence compounds [28], in homolytic dissociation [29,30], charge transfer [31]. One of the solutions for this kind of problem is the use of long-range separated hybrid functionals [32,33]. Alternatively, it is possible to tune the percentage of the exact exchange [28,34] or to rely on some non-conventional DFT-based methods like constrained DFT [35] or multiplet sum DFT method [36].
To shed new light on the problem of the electronic structure of [Fe(CO) 3 (NO)]¯, we performed DFT bond analysis in the framework of extended transition state energy decomposition analysis [37][38][39] with natural orbitals for chemical valence (EDA-NOCV) method [40,41] and compared it to the nature and the strength of the interactions in [Fe(CO) 4 ] 2− complex ion. EDA-based schemes have been proved to be compelling and trustworthy for understanding chemical bonding [39,[42][43][44][45]].
The nature of the metal-ligand bonding was analyzed with the extended transition state energy decomposition analysis (EDA) scheme [37][38][39]. The interaction energy, E int , between chosen fragments is decomposed into three chemically significant components: (i) the quasi-classical electrostatic interaction between the fragments (E elst ); (ii) the repulsive Pauli interaction (E Pauli ); and (iii) the orbital stabilizing contribution due to the covalency, i.e., charge transfer, and polarization (E orb ). In addition to the E int , the preparation energy E prep , the energy required to bring separated fragments from their equilibrium geometry to the geometry they adopt in complex ions, is considered. Furthermore, natural orbitals for chemical valence (NOCV) [40,41] decomposition of the electron density deformation was performed to elucidate different density transfer channels and to quantify their importance as an energy contribution to the E orb . Charge flow between the fragments was quantified with the Hirshfeld charge analysis [66]. For [Fe(CO) 4

Results and discussion
As we stated in Introduction, the determination of the spin ground state with DFT is a delicate task and strongly depends on the choice of the DFA. Therefore, we examined 12 different functionals (GGAs, meta-GGAs, hybrid functionals, as well as long-range and meta-hybrid functionals) and their performance on the spin ground state for both complexes under study (Table 1). GGA and meta-GGA functionals always give closed-shell singlet as the ground state, with triplet higher in energy. The performance of hybrid and meta-hybrid functionals depends on the percentage of the exact HF exchange. The high-spin states are more stabilized as the percentage of the exact exchange is higher. The closed-shell singlet state is still the ground state with functionals having low (TPSSh with 10%, B3LYP* with 15%) to moderate (B3LYP with 20%, M06 with 27%) amount of the HF exchange. BHandHLYP and M06-2X favor the broken symmetry solution. This is due to a large amount of the exact exchange (50% in BHandHLYP and 54% in M06-2X), leading to the artificial symmetry breaking [6,67]. The most reasonable results have been obtained with long-range separated hybrid CAMY-B3LYP: The ground state of [Fe(CO) 4 ] 2− is a closed-shell singlet with a broken symmetry singlet state approx. 70 kcal/mol higher in energy, in accordance with previous findings [11,12], while in the case of [Fe(CO) 3 (NO)]¯ closed-shell singlet and open-shell singlet are similar in energy, later being more stable for 0.8 kcal/mol. EDA analysis with CAMY-B3LYP provides insight into the nature of the Fe-CO bond ( Table 2). The attractive interactions (E elst and E orb ) are the indications of ionic vs. covalent bonding, respectively. Table 2 shows that Fe-CO bonding can be described as 50% ionic and 50% covalent in line with transfer of charge from [Fe(CO) 3 ] 2− fragment to CO. The same picture is obtained with other DFAs (Table S1 in SI).
NOCV scheme reveals three dominant electron density flow channels and clarifies the covalent character of the bonding (Fig. 1). The most important contribution is π*-back-donation from Fe d-orbitals (Fig. 1a, b). The π*-accepting properties of coordinated ligands are crucial for bonding in d 10 complexes [43]. Another important contribution is σ-donation from the lone pair of CO ligand and the charge accumulation in the bonding region (Fig. 1c). The other contributions are mainly polarization because of small Hirshfeld charge transfer, Δq, indicating the intra-fragment character of density transfers.  ) and (iii), according to our calculations, converge to the same electronic distribution. It has been previously shown [6,7], and our calculations proved, that the determination of the ground state is influenced by the chosen DFA (Table 1). High-spin states [triplet in the case (ii) and quintet in the case (iii)] are always much higher in energy. Looking only at the ground state energies will not give an unambiguous conclusion on the electronic structure. Therefore, we performed EDA analysis with a different selection of fragments, i.e., choices (i), (ii) and (iii) ( Table 3). To compare three different decisions, energy E rel is stated as the energy difference relative to the most stable relaxed fragment pairs ([Fe(CO) 3 ] − /NO).
Energy differences between three possible fragmentation choices are small and in line with DFT calculations, showing that the broken symmetry solution is more stable for approx. 0.8 kcal/mol. However, energy components are entirely different, indicating the importance of the fragment choice. Different fragment alternatives reflect the diverse nature of the interaction between fragments. The model, which is the closest to the physical reality, is the one with the lowest absolute value of E orb [68]. Orbital interaction takes into account the significance of the charge transfer between the fragments. Thus, [Fe(CO) 3 ]-NO − choice of fragments, (iii), is the most similar to the final electronic structure of the complex anion (Table 3). Moreover, in the situation (i) ΔQ is very large, showing a tendency to reduce NO + . It is noteworthy that even different DFAs, which give different ground states, in EDA analysis give the same trends (Tables  S2 and S3 in Supplementary material). NOCV analysis for the first fragmentation scheme reveals almost exclusive π*-back-donation to the NO + (Fig. 2a and  Fig. 2b). These two, most dominant electron density flows contribute more than 90% to E orb and include the transfer of 1.4 electrons, oxidize iron and suggest that iron cannot be in the −II oxidation state, supplementing previous arguments. The third density flow channel is clear σ-donation, but is of minor importance (Fig. 2c). The same analysis on the broken symmetry [Fe(CO) 3 ]-NO − also shows the importance of π bonding between the fragments (Fig. 3). Four most dominant density flow channels correspond to the α-π*-back-donation (Fig. 3a, b) and β-π*-donation (Fig. 3c, d). σ-Type interaction between the fragments (Fig. 3e) contributes around 27% to the E orb , but a minimal amount of charge is transferred between the fragments (0.09 electrons).

Conclusions
With the approach of combined energy decomposition analysis and natural orbitals for chemical valence, new insights into the electronic structure of the [Fe(CO) 3 3 (NO)] − with different DFAs at X-ray geometries (CCDC 1217933 [11], 1266312 [50]); energies are given in kcal/mol relative to the closed-shell singlet states a "Non-aufbau" occupation of KS-MOs