\documentclass[12pt]{article} \usepackage{makeidx} %\usepackage{epsf} \usepackage{psfig} \makeindex \begin{document} \begin{titlepage} \begin{center} \Large{ {\bf A Density Functional Study of FeO$_{2}$, FeO$_{2}^{+}$ and FeO$_{2}^{-}$ } } Alfonso T Garcia-Sosa and Miguel Castro \small{ {\em Departamento de Fisica y Quimica Teorica, Division de Estudios de Posgrado Facultad de Quimica, Universidad Nacional Autonoma de Mexico.}} \abstract{ The lowest energy structures of FeO$_{2}$ were determined by means of density functional theory techniques as implemented in the program DGauss 3.0.1. The calculations performed were of the all-electron type, using two levels of theory, namely the local spin density approximation with the use of the VWN functional, and the Generalised Gradient Approximation in the form of the Becke 1988 exchange and Perdew 1986 correlation functionals. Results were visualised by means of the program UniChem 4.0. Bond distances and angles, as well as total energies were calculated for several states of the moieties: Fe(O)$_{2}$, C$_{2v}$, Fe(O)$_{2}$, D$_{\infty\,h}$, Fe($\eta^{2}$-O$_{2}$), C$_{2v}$, Fe($\eta^{1}$-O$_{2}$), C$_{s}$, and Fe($\eta^{1}$-O$_{2}$), C$_{\infty\,v}$. Molecular orbital and harmonic vibrational analyses were carried out for these species, in addition to Mulliken population analyses. Singly positive and negative charged species were also considered and fully geometry optimized in a SCF gradient method. Accurate ionization potentials and electron affinities (both vertical and adiabatic determinations) were thus able to be computed. The results show the following for the ground state (GS) Fe(O)$_{2}$, C$_{2v}$, M= 3 : \angle OFeO= 138.1$^{o}$ (133.6$^{o}$) (Values in parenthesis are for LSDA-VWN, while the others are at the GGA-B88/P86 level). R$_{e}$ Fe-O= 1.60 \AA (1.57 \AA ), ET= -1414.2064 au (-1,410.5047 au), EA$_{h}$= 2.47 (2.60) eV, IP$_{h}$= 10.6 (10.5) eV, EA$_{v}$= 2.41 (2.20) eV, IP$_{v}$= 10.67 (10.63) eV, EA$_{exp}$= 2.349 eV (in agreement with related studies). In the GS the dioxygen molecule is found to be dissociated, compared to those states which have coordination modes where the O$_{2}$ molecule formally persists. A 3d4sp configuration for the iron atom is found to be especially relevant in Fe-O bond formation. The iron-oxygen and oxygen-oxygen bonds involved are characterized. A direct relationship is observed between these electronic and structural properties, influencing also the total energy for a given molecule. } \end{center} \end{titlepage} %****************************************************************************** \section{Introduction} Molecular oxygen is involved in several reactions both of biological and industrial importance, in which transition metals (TM), especially iron, are essential. In these, TM act as catalysts and are also involved in the activation, transport and storage of molecular species as O$_{2}$ and H$_{2}$. In particular, the understanding at a molecular level of such diverse processes as O$_{2}$ carrying in biological systems or corrosion of metals can be benefited from a deeper study of this type of metal-ligand interactions. Theoretical studies exist on iron-oxygen systems, such as laser ablated iron atoms in an o\-xy\-gen/argon at\-mos\-phe\-re \cite{laserablated+DFT}, pho\-to-oxi\-dat\-ion re\-ac\-tions of pentacarbonyl-iron \cite{fotoxpentacarbonil}, and in models of more complex systems such as iron-porphyrin and other Fe-O moieties \cite{Science}, \cite{DFTporf}. Previous work \cite{laserablated+DFT}, \cite{fotoxpentacarbonil}, \cite{semi}-\cite{Esp} on iron-oxygen systems has revealed that the assignment of a ground state (GS) for FeO$_{2}$ is strongly dependant on the level of theory used. The results presented in Table 1 illustrate the discrepancies that arise between the descriptions of this small FeO$_{2}$ system as originated from different theoretical approaches. As depicted in Table 1, it is only until recent years that the Fe-O$_{2}$ systems have been studied {\em ab-initio} by means of all-electron calculations performing both electronic and structural relaxations. Even at this high level of treatment the results show a dramatical dependence on the computational procedure employed. Semiempirical calculations offer an incorrect geometry for the calculated GS. Moving to the treatments of the all-electrons type, it is well known that the Hartree-Fock (HF) point of view alone is inadequate for an accurate description of systems containing TMs. For instance, HF does predict a correct structure, C$_{2v}$, for the FeO$_{2}$ GS \cite{FeO2HF}; however, the multiplicity observed (M=7) seems to be too high to allow the spin pairing process or chemical bond formation. When correlation effects are taken into account, such as in \cite{laserablated+DFT}, \cite{fotoxpentacarbonil}, \cite{Esp}, the description of the bonding in the GS molecule predicts more consistent results for the geometry. Nevertheless, there is some controversy on the electronic state of the GS of the FeO$_{2}$ system. Despite the available ab initio studies including correlation effects \cite{laserablated+DFT}, \cite{fotoxpentacarbonil}, \cite{Esp}, a systematic theoretical study is needed at a high level of theory which includes full structural and electronic optimization of the systems referred to and description of the bonds therein. Open shell transition metal systems present a challenge for the state-of-the-art computational methods and theories. In this regard, density functional theory (DFT), provided the use of suitable gradient corrected functionals that accurately describe the exchange-correlation interactions, has given examples \cite{DFTinChem} of being one of the most reliable tools for their study. This is seen both from a computational procedure simplicity, and a formal theory point of view. The use of a generalized gradient approximation (GGA), such as that proposed by Becke for exchange \cite{B} and Perdew for correlation \cite{P}, is appropriate for this type of TM-L systems. The present work deals with a systematic theoretical study on the FeO$_{2}$ system. Our treatment was done using DFT techniques ({\em vide infra}), and we believe that our research might help to elucidate some structural and electronic aspects of this molecule. The study involves the calculation of the structural parameters for the lowest energy states of several FeO$_{2}$ coordination modes. Furthermore, vibrational, molecular orbital, Mulliken population and charge transfer analyses were carried out on these states in order to afford insight on the nature of the chemical bond in these species. %****************************************************************************** \section{Methodology} First-principles, all-electron calculations were per\-for\-med with the co\-de DGauss 3.0.1 \cite{DGauss}, which is a {\em Linear Combination of Gaussian-type Orbitals} DFT-based method (LCGTO-DF). DZVP2 orbital basis sets were used, namely (63321/5211*/41+) for Fe and (721/51/1) for O. Additionally, TZV-A1 (10/5/5) au\-xi\-lia\-ry basis sets were used for the fitting of the density and the XC contributions to the total energy and energy gradients. The procedure involved full geo\-me\-try op\-ti\-mi\-za\-tion by a SCF e\-ner\-gy gra\-dient me\-thod of can\-di\-da\-te structures (shown in Figure 1) in different quantum states, firstly at the Local Spin-Density Approximation (LSDA) by using the Vosko, Wilk, Nusair (VWN, \cite{VWN}) functional. The convergence criteria used were tight, {\em i.e.} $\Delta$E=1x10$^{-7}$ au for the total energy, $\Delta\rho$=1x10$^{-5}$ au for the density, and $\Delta$E/$\Delta$r = 5x10$^{-5}$ au for geometry optimizations. A fine grid of 194 angular points per atom was employed for the numerical integration and second derivative evaluation. Harmonic vibrational, molecular orbital, Mulliken population and charge transfer analyses were then performed on the located lowest energy states for each coordination mode. In a second step, these structures were then fully reoptimised at the GGA level, by use of the Becke 1988 exchange \cite{B}, and Perdew 1986 correlation \cite{P} functionals. This XC scheme will be referred to as B88/P86. The same tight convergence criteria and fine numerical grid were used, and harmonic vibrational, molecular orbital, Mulliken population and charge transfer analyses performed as in the former case. The same expensive and thorough treatment was given to singly charged negative and positive states derived from the ground state. Calculations were done with a Cray YMP4/464 supercomputer. Five possible coordination modes for the dioxygen molecule with an iron atom were considered. These are shown in Figure 1. We have special attention paid to the location, in the potential energy surface of Fe-O$_{2}$, of that structure that shows a similar coordination mode and symmetry, Fe($\eta^{1}$-O$_{2}$), C$_{s}$, as that found in oxyhemoglobin. Visualizations of structures, molecular orbitals, and harmonic vibrational modes were produced in the UniChem 4.0 package \cite{unichem}. Harmonic vibrational frequencies were obtained through the square roots of the eigenvalues (divided by the reduced mass) of the second derivative matrix of the potential energy landscape (harmonic oscillator force constant matrix). %****************************************************************************** \section{Results and Discussion} The VWN and B88/P86 functionals yield the total energies for the states ordered in Table 2 with values in hartrees. Figure 2 shows the lowest energy state for each coordination mode considered at the LSDA level. Relative total energies between these states are also included, as well as structural parameters for each state. Figure 3 shows the results for the lowest energy state for each coordination mode, as well as structural parameters and relative energies calculated at the GGA level. The differences in O-O distances from the coordinated O$_{2}$ species and free O$_{2}$ are shown in Figure 2 and Figure 3. The ordering of states is essentially the same for both levels of theory. GGA produces slightly larger bond distances than LSDA. This is accounted for by the correction that the B88/P86 functional makes of the overestimation of bonding produced by the LSDA approach. Another observation is that a pattern is found between total energy and both O-O and Fe-O bond distances. The lower the total energy for a given state, the larger the O-O distance and the shorter the Fe-O one. This implies a lowering of total energy for a state with increasing dissociation of the O-O bond and increasing formation of the Fe-O bond. The bond orders calculated, presented in Table 3, show a similar picture as that observed in the structural parameters. The limit case is that of the lowest total energy structure or GS, which presents the strongest Fe-O bond order of 0.99 (1.06) at the GGA (LSDA) level of theory; and the weakest O-O bond order, of the set of states. In the GS, {\bf Ia}, there is effectively no O-O bond left, with respect to free O$_{2}$. In contrast, state {\bf IIIa} presents a lesser activation of O$_{2}$ as the difference between bond orders of the free species and the coordinated one is of a unit (there is still molecularity of dioxygen present in state {\bf IIIa}). Another proof of evidence is provided by the charge transfer in these species (see Table 4) as there exists a direct relationship between increasing Fe$\rightarrow$O charge transfer and lower total energy, at both levels of theory used, with the limit case being the GS, {\bf Ia}, with a net charge transfer of 0.831 (0.756) of a unit. Table 5 shows the progressive increase in 4p participation to the global Fe configuration in a given state with decreasing total energy for that state. The results obtained from the harmonic vibrational analyses performed on the black species in Table 2 are shown in Table 6. %----------------------------------------------------------------------------- \subsection{Ground State, {\bf Ia}} Our computed GS for Fe(O)$_{2}$, has a triangular structure of C$_{2v}$ symmetry and M=3. In this state, the binding between the O atoms is neglegible, while the bond order analysis indicates the appearance of a single bond between Fe and each O. These bonds have equilibrium bond lengths of 1.60 \AA\, and the O-Fe-O angle formed is of 138.1 $^{o}$, at the GGA level of theory. This picture is in agreement with the results obtained by Andrews {\em et al}, which have used the B3LYP hybrid functional \cite{laserablated+DFT}. They also obtain a C$_{2v}$ structure, with M=3, for the GS of FeO$_{2}$. Their results for the Fe-O bond lengths and O-Fe-O angle are very similar to our computed values. Table 7 compares structural parameters for several proposed GSs of Fe(O)$_{2}$, in a C$_{2v}$ symmetry, as reported in the literature and those obtained through the present study. Our DFT results are in disagreement with those obtained by means of Hartree-Fock calculations where the correlation effects were included through configuration interaction (CI) techniques \cite{Esp}. The CI treatment indicates that the GS of Fe-O$_{2}$ is a closed shell state, M=1, in C$_{2v}$ symmetry, with Fe-O bond lengths of 1.50 \AA\, and an O-Fe-O angle of 169.8 $^{o}$. That is, the CI GS of Fe-O$_{2}$ is closer to a linear structure than the DFT one. Looking at the bond lengths and bond angles, the CI results overestimate, with respect to DFT, the bonding in the O-Fe-O molecule. Indeed, the CI M=1 state implies a major chemical bond formation (pairing of electrons) than the DFT M=3 state. However, our calculations reveal that the singlet state is located 0.73 eV above our computed M=3 GS. It is interesting to observe that the quintet state is located only +0.30 eV above the GS, at the B88/P86 level of theory. A similar picture was obtained by Andrews {\em et al}. Their results indicate that the triplet and quintet states are almost degenerate, since the quintet is located only 0.1 eV above the triplet, using the Becke-Perdew functional \cite{laserablated+DFT}. However, the use of the hybrid B3LYP functional gives a reverse order: the quintet is the GS, with the triplet lying +0.1 eV above the quintet \cite{laserablated+DFT}. As pointed out by Andrews {\em et al}, the quintet state is not compatible with the experiment \cite{exp}, since the calculated O-Fe-O angle (of 142 $^{o}$) obtained for the triplet is more consistent with the experiment than the O-Fe-O angle for the quintuplet (equal to 118 $^{o}$). Hence, the Becke-Perdew picture, of Andrews {\em et al} and ours, indicate that the GS of O-Fe-O is more likely to be a triplet state. These studies reveal that the results obtained on systems that contain TM atoms are very sensitive to the level of theory used for XC effects. A similar conclusion has been reached before \cite{jam} in our studies of small TM clusters. In this particular O-Fe-O case, it seems that the Becke-Perdew scheme works much better than the B3LYP one. This is a surprising result, since the B3LYP functional has proven to yield results of chemical accuracy in benchmark calculations, eventhough these calculations involve systems that do not contain TM atoms. This means that more accurate functionals need to be developed for a better description of TM systems and consequently, of the XC effects which arise in them. There are experimental observations \cite{exp} that suggest a triplet GS for Fe(O)$_{2}$, instead of a singlet or a quintet. As mentioned above, Andrews {\em et al} found that the O-Fe-O angle for the GS had a defined range of values in which only the triplet species fit. Furthermore, the observed isotopic 16/18 frequency ratios for the antisymmetric and symmetric modes of the triplet state \cite{laserablated+DFT}, show an excellent agreement with the theoretical values using both Becke-Perdew and B3LYP schemes. On the other hand, their calculated values for the quintet for both functionals, were termed incompatible with the experimental ratios. Despite this, the authors point out that since both states are close in energy, more experimental studies are needed to corroborate or deny that the triplet is the true GS. In comparison, the mentioned MP2/CCSD(T) \cite{Esp} results show a poor match with the experimental picture cited above. Of all the Fe(O)$_{2}$ set of candidates, the found GS, {\bf Ia}, has the strongest Fe-O bond and the weakest (negligible) O-O bond. This state also shows the greatest Fe$\rightarrow$O charge transfer, which accounts for its high stability or lowest energy. Moreover, the Mulliken population analysis reveals that the electronic pattern of the Fe atom is of 3d4s4p type. In paricular, the GS has the most important 4p participation. In effect, state {\bf Ia} : Fe(O)$_{2}$, C$_{2v}$, M=3, has considerably lost the molecularity of O$_{2}$. This can be seen in the frontier molecular orbitals (MO) depicted in Figure 4 as well as in the vibrational modes illustrated in Figure 5 which correspond to an angular inserted dioxide species. As is observed in comparison to other states, a pattern is established between lower total energy for a given state and its increasing Fe-O bond formation and Fe$\rightarrow$O charge transfer. Alongside, this lowering of total energy is coupled to a decrease of the O-O bonding and to a greater 4p and 4s participation in the characteristic overall 3d4sp configuration for the iron atom in a given state. Mulliken population analysis on the valence MOs for the GS shows that the principal contributions to the bonds are of a 3d4sp(Fe)-2p(O) nature. For instance, the HOMO is of a bonding nature and contains 27\% of its electronic density on the 4s orbital of Fe, 15\% on orbital 3d$_{y^{2}}$, 7.6\% on orbital 3d$_{x^{2}}$, 5\% on orbital 3d$_{z^{2}}$, 5\% on orbital 3p$_{y}$, and 1.8\% on orbital 3d$_{xy}$ of the same atom. The resting 40\% of the electronic charge is shared evenly between each oxygen in orbitals 2p$_{x}$ and 2p$_{y}$. On the other hand, the LUMO is antibonding and is composed of 43.3\% of electronic density on orbital 3d$_{xz}$ of iron, and 28\% on orbital 2p$_{z}$ of each oxygen. The 3d4sp (of Fe) and 2p (of O) contributions to the bonding are noticeable in the drawings of the HOMO and LUMO, displayed in Fig. 4. The population analysis reveals that the GS has a magnetic moment located mainly on the Fe atom. This moment corresponds to the two 3d electrons that were not involved in the bond forming process. The vibrational pattern for the GS of FeO$_{2}$ is characteristic of a C$_{2v}$ structure and is illustrated in Figure 5. In a similar fashion to Table 7, Table 8 compares vibrational frequencies for several Fe(O)$_{2}$, C$_{2v}$ GSs. The present work yields harmonic vibrational analysis results in the same order of magnitude and compare well to those of Andrews {\em et al} \cite{laserablated+DFT} calculated using the B3LYP functional and those observed experimentally \cite{laserablated+DFT}; and with calculations of MP2, CCSD(T)-TZV quality \cite{Esp} cited in Table 8. The frequencies were assigned to the bands produced by FeO$_{2}$ species present in the laser ablation of iron atoms in an oxygen atmosphere. The assignment fits with a C$_{2v}$ structure where there is no longer a significant O-O bond. A series of singly, positive and negative, charged states (derived from the GS) were also searched, both with and without structural relaxation, that is, through full SCF geometry optimizations and single point SCF calculations, respectively. This made possible the determination of precise and accurate ionization potentials (IP) and electron affinities (EA), which may be connected with the corresponding experimental \cite{exp} determinations of these properties. Vertical (single point calculations, allowing no structural relaxation of the system) and horizontal (adiabatic, involving geometry optimization, {\em i.e.}, structural relaxation of the system) determinations of IPs and EAs are presented in Table 9, which has values in eV. There is a very small change in structural parameters from the neutral species to the charged ones (in the horizontal determinations). The GSs for both the negative (FeO$_{2}^{-}$) and the positive (FeO$_{2}^{+}$) species had the same geometry (inserted angular dioxide) and symmetry (C$_{2v}$) as the neutral GS. Both negative and positive GS resulted doublets, M=2, one resulting from the addition and the other from the substraction, respectively, of an electron from the neutral, M=3, GS. If we compare the calculated vertical EA, at the GGA level, of 2.410 eV with the experimental value of 2.358 eV \cite{exp}, we find a small difference of 2.2\%. This result encourages the use of a B88/P86 scheme for the study of physical and physicochemical properties of systems that require an accurate description, such as those in which TMs are present. %---------------------------------------------------------------------------- \subsection{State {\bf IIa}} As mentioned, we have also located some higher energy states of the neutral FeO$_{2}$ molecule. In what follows we will discuss shortly these findings in systems which can be of relevance in processses in which they are encountered. State {\bf IIa} has structural parameters and energy values very close to those present in the GS. Nevertheless, this linear dioxo species has peculiarities such as two degenerate negative vibrational frequencies at both levels of theory used. This indicates that such species is not at a true minimum of energy, even though it lies closely in energy (0.16 eV at the B88/P86 level) to the GS. This result confirms state {\bf Ia} as the true GS, and extends the knowledge of this system from that obtained in other studies such as \cite{fotoxpentacarbonil}, where similar structures as {\bf Ia} and {\bf IIa} were proposed as possible GSs. %---------------------------------------------------------------------------- \subsection{State {\bf IIIa}} This triangular species contains the molecular dioxygen unit, which is reflected in its calculated HOMO and LUMO orbitals (Figure 6) and its vibrational modes (Figure 7). In IIIa, the perturbation of the O-O bond, though strong, is not enough for dissociative activation as occurs in the GS. The IIIa state lies considerably higher in energy, 2.33 eV (at the B88/P86 level of theory) above the GS. Such high location is consistent with the longer Fe-O bond length and smaller Fe-O bond order as compared to those found in the GS. Eventhough both the HOMO and LUMO (shown in Fig. 6) are antibonding, they both show fragments of molecular O$_{2}$ units; $\pi^{*}_{g}$ in the former, and $\pi_{g}$ in the latter. The HOMO is composed of 30.3\% of the electronic density on the d$_{xy}$ iron orbital, in addition to 34.8\% of this density on each oxygen p$_{y}$ orbital. In contrast, the LUMO has 64.5\% of density on the 4s orbital, 27.8\% on orbital 4p$_{z}$, and 5.6\% on orbital d$_{z^{2}}$. Each oxygen atom takes 2.6\% of the total electron density of the LUMO orbital on orbitals 2p$_{z}$. Overall, these MO's show how the 3d4sp contributions of the Fe atom are involved in the bonding with the $\pi$ component of the oxygen atoms. Besides having a higher total energy than the GS, the species {\bf IIIa} has less charge transfer (which resides in back donation from iron d orbitals to oxygen molecular orbitals), and less 4p participation in the iron configuration than in state {\bf Ia}. The values framed in Figure 7 represent the mode which is possible to identify with the dioxygen molecule vibration. The frequency displacement from the value in the free O$_{2}$ molecule is presented, displaying an activation for this subunit in the molecule where the dioxygen molecule is trapped by an iron atom. This activation is evidenced in the lower frequency, larger O-O bond distance, and smaller bond order for the O-O bond in {\bf IIIa} than in the free O$_{2}$ molecule. The observed frequencies \cite{laserablated+DFT} of this Fe(O$_{2}$), C$_{2v}$, state may be assigned to our calculated values. The strongest observed band for this state, 956 cm$^{-1}$, as well as a weaker band, 548.4 cm$^{-1}$, are reasonably close to our estimations, 915.5 and 615.8 cm$^{-1}$, respectively. This agreement suggests that the triplet state is the one of lowest energy for this Fe(O$_{2}$) coordination mode. A similar assignment was done by Andrews {\em et al}, but instead of a triplet, they found that the quintet state, eventhough it is a high energy state, fits better than the triplet. Indeed, in the calculations of Andrews {\em et al}, the septet is the lowest energy state, followed by the quintet and triplet states. As pointed out by the authors \cite{laserablated+DFT}, the B3LYP scheme is biased toward high spin states. This picture exemplifies that the descriptions of TM-L systems depend sensitively on the chosen functional. Our results show the consistency of the B88/P86 XC scheme, as implemented in the DGauss program, both in the determination of the lowest energy states and in the vibrational assignments. The so called energy of dissociation is the difference in energy between the lowest energy state containing the bound molecular O$_{2}$ species and the GS where this molecularity no longer exists. For the present work, this difference occurs from state {\bf IIIa} to state {\bf Ia} and amounts to 2.27 eV (52.35 kcal/mol) at the LSDA-VWN level, or 2.33 eV (53.79 kcal/mol) at the GGA-B88/P86; which are roughly the half of that reported in the MINDO study \cite{semi}. This result suggests that the dissociation of a molecule of O$_{2}$ by a single iron atom is a less unlikely process as predicted by the MINDO study \cite{semi}. Experimentally, it has been shown that for this process to happen, a sufficiently excited iron atom has to be present to successfully react with a dioxygen molecule \cite{chemrev}. %The vibrational modes calculated for this species can be seen in Figure 7. %These vibration modes have been assigned in experimental studies as in %\cite{laserablated+DFT}. %%%AQUI VAMOs, hecahrle un ojo al pararfo antrior %---------------------------------------------------------------------------- \subsection{State {\bf IVa}} The coordination mode and symmetry of the state {\bf IVa} are very similar to those that occur in oxyhemoglobin, in which the chemical environment of the protein's active centres is provided by the heme groups, which are embedded and bonded to its globin structures. %State {\bf IVa} preserved its geometry up to the tight convergence criteria at %the LSDA level, but only up to a medium geometry convergence criteria %($\Delta$E = 5 x 10$^{-7}$ au, $\Delta\rho$= 5 x 10$^{-5}$ au) at the GGA %level. A single point B88/P86 calculation (with tight energy and density convergence criteria) reveals that {\bf IVa} has a negative vibrational frequency at {\mbox -22.8 cm$^{-1}$}, while the positive frequencies are 565.8 and 1113.4 cm$^{-1}$. This result differs from that of Andrews {\em et al}, who have found that {\bf IVa} is a true minimum since it has three positive frquencies: 134.7, 472.7, and 1159.8 cm$^{-1}$. Using a lower level of theory, as in the LSDA approach, we have also found that {\bf IVa} has three positive frequencies: 159.4, 607.3, and 1267.3 cm-1. Note that in this last case, the smallest value is very close to that of Andrews {\em et al} Then, our higher level of theory calculation indicates that {\bf IVa} is a transition state (TS). The TS nature of {\bf IVa} is reflected by the fact that a geometry optimization (at the GGA level with a tight convergence criteria) led to a structure with coordination mode and symmetry Fe($\eta^{2}$-O$_{2}$), C$_{2v}$ (by closure of the FeOO angle), which eventually fell to the lower energy {\bf IIIa} state. The vibrational analyses for {\bf IVa} produces the results depicted in Figure 9. The mode which is highlighted presents the activation of the O-O bond, which is of less extent than that present in state {\bf IIIa}. The vibrational mode possesing a negative frequency can also be seen in Figure 9. As shown above, the present work predicts an angular inserted dioxide species as the GS for the Fe(O)$_{2}$ system, 2.87 eV (at the B88/P86 level) lower than state {\bf IVa}. Specific conditions in the hemoglobin environment render a special stability to the {\bf IVa} moiety. %This behaviour, in addition to the difficulty of achieving convergence of the %calculation for this state, indicates that the state is in a very irregular %well of potential energy, and that the forces acting on the closure of the %FeOO angle are complex. %Therefore, a stabilization of this mode of coordination is hard to attain. %%This state at a medium geometry convergence criteria at the B88/P86 level %%presents a scenario similar to that in state {\bf IIIa}. %%Activation of the oxygen-oxygen bond is less in this state than in the lower %%lying state {\bf IIIa}, which can be seen in a smaller bond distance, greater %%bond order and weaker vibrational frequency for the O-O bond in {\bf IVa}. %%State {\bf IIIa} presents a case in which there is greater Fe d orbitals %%$\rightarrow$ O $\pi^{*}$ molecular orbitals charge transfer (that in turn %%debilitates the O-O bond) than in {\bf IVa}; hence, there is a greater %%activation of such bond in the former case. The HOMO for {\bf IVa} is bonding, whilst the LUMO is antibonding. In HOMO, see Fig. 8, the O$_{2}$ molecular fragment interacts through its $\pi$ antibonding orbitals with the 3d orbitals of the Fe atom. In this bonding interaction also it is recognized a considerable d$\rightarrow \pi^{*}_{g}$ charge transfer. %Once again, the molecular fragment of O$_{2}$ is visible in the %bonding behaviour of HOMO, see Figure 8, which also reveals the d$\rightarrow \pi^{*}_{g}$ %charge transfer. %----------------------------------------------------------------------------- \subsection{State {\bf Va}} This linear high multiplicity molecule owes its total spin number of six to the absence of pairing between the two free electrons on O$_{2}$ and four free electrons on iron. This mode of coordination, therefore, does not have important interactions between dioxygen and iron, and consequentially, lies high in energy with respect to states corresponding to other modes. %----------------------------------------------------------------------------- \section{Conclusions} A correct ordering by total energy of the different states and coordination modes of the FeO$_{2}$ series was constructed. The Fe(O)$_{2}$, C$_{2v}$, M=3 GS {\bf Ia} predicted by the present work is in agreement with experimental and theoretical evidence \cite{exp} \cite{laserablated+DFT}, as is another work previously published elsewhere \cite{laserablated+DFT}. Our analysis of Fe(O)$_{2}$ illustrates that a proper treatment of the XC effects is critical to the accurate description of the structural and electronic properties of transition metal systems such as Fe-O$_{2}$. There is a clear pattern found between lower energy for a given state and the increased formation of Fe-O bonds, increased activation of the oxygen-oxygen bond, increased charge transfer of an Fe$\rightarrow$O type, and electronic configurations 3d4sp with increasing participation of 4s and 4p electronic charge on iron. Charge transfer in the form of back donation from iron d orbitals to oxygen $\pi$ antibonding molecular orbitals generates the diminishing of the O-O bond. The participation of 4p orbitals in the iron configuration provides polarization for the metal atom which allows it to form strong bonds with each oxygen atom. Participation of 4s orbitals affords delocalization of electronic charge, which in turn, also favours the Fe-O bonding. The calculated GS {\bf Ia} can be seen as the last stage in a process of nearing the O$_{2}$ molecule to an iron atom. This O$_{2}$ to Fe approach may be seen to lead to lowering the total energy for the system. While the O$_{2}$ molecule transversally approaches the iron atom, lowering the total energy for a given state due to the formation of Fe-O bonds, there is a progressive breaking of the O-O bond coupled to a build up of the Fe-O bonding. This process eventually carries to the dissociative adsorption of the dioxygen molecule by a sufficiently excited Fe atom, which is the case of the most stable moiety, the GS. Indeed, the electronic pattern of the Fe atom, in the GS of FeO$_{2}$, is of 3d$^{7}$4s$^{1}$4p$^{x}$ nature, which differs from the 3d$^{6}$4s${2}$ GS configuration of the free Fe atom. Triangular structures such as {\bf IIIa} lie higher in energy than the angular inserted dioxo species such as {\bf Ia}. %The linear inserted dioxo species, however, lands on an unstable region of the %potential energy hipersurface, and hence tends to move its O-Fe-O angle back %to the angular variety of the GS. An Fe($\eta^{1}$-O$_{2}$), C$_{s}$ moiety can be present in systems such as oxyhemoglobin, probably due to the steric and electronic factors affecting the central iron atom which prevent the formation of iron-dioxo bonds (such as those present in the GS {\bf Ia}) which are lower in energy than angular Fe-(O$_{2}$) structures of the type of {\bf IVa}. Besides securing stabilization of the $\eta^{1}$-O$_{2}$, C$_{s}$ moiety, these steric and electronic factors might be responsible for the reversibility of the Fe-O union, compulsory for the dioxygen transport process, as this $\eta^{1}$-O$_{2}$, C$_{s}$ moiety is in an irregular well of potential energy. The value of 2.2\% in error between the calculated figure and the experimental one for electron affinity \cite{exp}, validates this study and affords it as a useful method to study other systems of the same kind with more metallic atoms and other substrate molecules such as H$_{2}$, N$_{2}$, NH$_{3}$, NO, etc. %---------------------------------------------------------------------------- {\bf Acknowledgements} Financial support from DGAPA-UNAM under project PAPIIT IN-101295, and supercomputing resources from DGSCA (UNAM) are greatly acknowledged. ATGS would like to thank Programa 127 "Formacion Basica en la Investigacion" for a scholarship. %----------------------------------------------------------------------------- \begin{thebibliography}{99} \bibitem{laserablated+DFT} Andrews, L. , Chertihin, G.V., Ricca, A., and Bauschlicher, C. W., Jr., {\em J. Am. Chem. Soc.}, 1996, {\bf 118}, 467-470. \bibitem{fotoxpentacarbonil} Lyne, Paul D., Mingos, D. 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