Theoretical Study of Negatively Charged Fe––(H2O) n≤ 6 Clusters

Article pubs.acs.org/JPCA

Theoretical Study of Negatively Charged Fe−−(H2O)n ≤ 6 Clusters Miguel Castro* Departamento de Física y Química Teórica, DEPg. Facultad de Química, Universidad Nacional Autónoma de México, Del. Coyoacán, México D.F., C.P. 04510, México ABSTRACT: Interactions of a singly negatively charged iron atom with water molecules, Fe−−(H2O)n≤6, in the gas phase were studied by means of density functional theory. Allelectron calculations were performed using the B3LYP functional and the 6-311++G(2d,2p) basis set for the Fe, O, and H atoms. In the lowest total energy states of Fe−−(H2O)n, the metal−hydrogen bonding is stronger than the metal−oxygen one, producing low-symmetry structures because the water molecules are directly attached to the metal by basically one of their hydrogen atoms, whereas the other ones are involved in a network of hydrogen bonds, which together with the Feδ−−Hδ+ bonding accounts for the nascent hydration of the Fe− anion. For Fe−−(H2O)3≤n, three-, four-, five-, and six-membered rings of water molecules are bonded to the metal, which is located at the surface of the cluster in such a way as to reduce the repulsion with the oxygen atoms. Nevertheless, internal isomers appear also, lying less than 3 or 5 kcal/mol for n = 2−3 or n = 4−6. These results are in contrast with those of classical TM+−(H2O)n complexes, where the direct TM+−O bonding usually produces high symmetry structures with the metal defining the center of the complex. They show also that the Fe− anions, as the TM+ ions, have great capability for the adsorption of water molecules, forming Fe−−(H2O)n structures stabilized by Feδ−−Hδ+ and H−bond interactions.

1. INTRODUCTION The interaction of transition metal (TM) ions with water and biological molecules is an important theme of research in chemistry and biology.1−3 For instance, the functionality of biological molecules depends strongly on their three-dimensional structures, which are mainly determined through noncovalent interactions with metal ions, hydrogen-bonding interactions, and solvation. Specifically, TM+x ions, present in liquid aqueous phases, are stabilized by different kinds of hydration shells formed around the metal, with favored coordination numbers of 4 and 6 for the inner shells. They also are crucial on the catalytic properties of some enzymes, for example, nitrogenase has Fe and Mo;4,5 thus, a key point to study is on the charge that such atoms may have in this system. Recently, the development of laser vaporization techniques has permitted the study, in the gas phase, of clusters of TM+ ions with a few water molecules.6,7 Also it has been possible to study, to a lesser extent, the interactions of singly negatively charged TM− atoms with water molecules in the gas phase. For instance, the groups of Lineberger and McCoy8,9 have characterized the structural and energetic properties of the Cu− anion interacting with one water molecule; the dynamics of the neutral Cu−H2O compound, produced in situ upon electron detachment of the Cu−−H2O anion was also addressed. Weber et al.10 have studied anionic TM−H2O clusters of coinage (Cu, Ag, Au) metals by IR photodissociation spectroscopy and calculations at the coupled cluster and density-functional levels of theory. The main conclusion of these works in that the TM− ions are bound to the water molecule by a single ionic hydrogen bond, SIHB, similar to the halide−water complexes.11 A deviation from this motif was found for silver and copper.10 An important issue to address is © 2012 American Chemical Society

the role of IHB on the nascent hydration when more H2O units are attached to TM−. This is the goal of the present work. It has been also possible to study, to a lesser extent, the reactions of neutral TM atoms with H2O, being important with sources of hydrogen energy. Indeed, using matrix isolation infrared absorption methods, Kaufman et al. showed that the latter TM atoms Cr, Mn, Fe, Co, Cu, and Zn (Ni was an unexpected exception) form adducts with water; further rearrangements yield insertion compounds on photolysis.12 The Sc−Ti−V triad was also studied.13 Through matrix isolation Fourier transform infrared (FTIR) spectroscopy and density functional theory (DFT) calculations, Zhang et al. considered the reactions of neutral Fe atoms with H2O molecules.14 Employing flow tube reactors, Riley et al.15,16 have studied the interactions of neutral iron clusters, Fen, with water for n = 7−27 and 13−23, revealing a strong dependence of the reactivity on cluster size. However, the study of negatively charged iron atoms with water molecules is scarce. This can be done, for instance, by means of anion photoelectron spectroscopy methods, which have been successfully employed for the characterization of singly negatively charged iron clusters,17 Fe−n, and for the study of Fe−−benzene complexes in the gas phase.18 On the theoretical side, using DFT, Gutsev et al. have studied the reactions of neutral, singly negatively and positively charged Fen clusters with H2O.19 The purpose of this work is to study, by means of DFT based methods, the low-lying structures produced by the interactions of negatively charged iron atoms with water molecules in the Received: December 20, 2011 Revised: May 18, 2012 Published: May 18, 2012 5529

dx.doi.org/10.1021/jp212287j | J. Phys. Chem. A 2012, 116, 5529−5540

The Journal of Physical Chemistry A

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Figure 1. Low-lying states for the anion, Ia, cation, Ib, and neutral, Ic, species of Fe−H2O. Also are indicated the Fe−H and O−H bond lengths, in Å, and H−O−H angle, in degrees. The NBO charge distribution is also shown. The reported relative energies are with respect to the GS of the anion.

population analysis was done for the optimized structures;26 gross atomic charge distributions with this method were determined for a qualitative rationalization of the charge transfer effects. It should be mentioned that for the transition from the 5D (4s23d6) ground state of the iron atom to the 4s23d7 (4F) excited state we have found an excitation energy, 0.52 eV, which is in close agreement with the experimental value, 0.87 eV.27 Moreover, electron attachment to the 5D (4s23d6) GS yielding the 4s23d7 (4F) state of the Fe− ion, produces an adiabatic electron affinity (EA) of 0.65 eV, which, though overestimated, is in line with the experimental finding, 0.164 ± 0.035 eV.28 For TM atoms, Bauschlicher and Gutsev29 have found that the hybrid B3LYP approach produces EAs that are in better agreement with the experiment than the calculated values through pure DFT functionals; they even compare well with the results obtained at the CCSD(T) level. Indeed, using the B3LYP/6-311-G* method, they found 0.71 eV for the EA of Fe, which compares well with our value, after correcting for the 4s−3d mixing they obtained an estimation, 0.05 eV, nearer to the experiment. Thus, the chosen method seems to be appropriate for a reasonable description of the lowest energy states of the neutral and negatively charged iron atom, which is very important for a correct determination of the low-lying state for the singly negatively charged Fe−−(H2O)n species. We believe that the 6-311++G(2d,2p) basis set, bigger than the one employed in ref 29, is flexible enough for a reasonable description of these clusters, mainly because, as indicated by the NBO results, the extra electron is mainly located on the iron site. For this reason there were not added diffuse functions for the extra electron as was done for the study of the acetonitrile anion by Gutsev and co-workers30 or by Herbert and HeadGordon in the study of the electron detachment energies for water cluster anions.31 Even more, a C2v geometry was obtained for the water molecule, with O−H distances, H−O−H angle, and dipole moment: 0.961 Å, 105.1°, and 1.96 D, respectively, which are in good agreement with the experimental results. The distortions of H2O in the Fe−−(H2O)n clusters are referred to the isolated water molecule below. Including zero-point vibrational energy (ZPVE) for the GSs of Fe−−(H2O)n and H2O, the binding energies (Do) were determined by the difference of total energies: [Et(Fe−) + nEt(H2O)] − Et[Fe−− (H2O)n] gives the Do values for Fe−−(H2O)n. Likewise, the sequential binding energies (BE) were obtained using the formula [Et(Fe−−(H2O)n−1 + Et(H2O)] − Et[Fe+−(H2O)n]. The Do (determined without including basis set superposition errors (BSSE) which will diminish greatly the Do values) and the sequential BE will be used in this work as parameters to

gas phase. In the absence of solvent effects, as those in the liquid, we will address the nascent hydration process on the small Fe−−(H2O)n≤6 complexes emphasizing the structural, electronic, and energetic properties. The stability and growth of the hydration layers will be depicted in terms of the analysis of attractive, Feδ−−Hδ+, nonattractive, Feδ−−Oδ−, and H-bonding interactions for several isomers of each compound. The central idea is to characterize the solvation environment promoted by a negatively charged atom. It will be shown that the water molecules are attached to the metal through one of the hydrogen atoms forming weak Fe−H ionic bonds, and originating outer hydration layers for some small, n = 4, systems. Also it will be shown that for bigger clusters, planar hydration shells are observed and the metal is located at the surface, instead of the center, in such way to reduce the repulsion with the oxygen atoms. The obtained results are discussed with available experimental and theoretical data.

2. COMPUTATIONAL PROCEDURE The low-lying states for negatively charged Fe−−(H2O)n, n ≤ 6, complexes in the gas phase were determined by means of allelectron calculations performed with the B3LYP method20,21 in concert with 6-311++G(2d,2p) orbital basis sets for the Fe (15s11p6d2f)/[10s7p4d2f], O (12s6p2d)/[5s4p2d], and H (6s2p)/[4s2p] atoms.22−24 The quantum chemistry software Gaussian-03 was employed.25 First, for each Fe−−(H2O)n complex several candidates of different geometry and spin multiplicities (M = 2S + 1, S is the total spin) were tried for the structural and electronic relaxation procedure, carried out without imposing symmetry constraints. The located optimized structures were confirmed to be true local minima on the potential energy surface (PES) by estimating their normal vibrations within the harmonic approximation with the following computational protocol. Strict convergence was required for the total energy, minimized up to 10−8 au, whereas the geometries were optimized choosing a 10−5 au threshold for the rms forces. An ultrafine grid was used for these steps. These tight tolerances are needed for accurate ground state (GS) determination, because the Fe−−(H2O)n species have several isomers of different geometries and spin multiplicities within a narrow energy range. Indeed, these negatively charged species have extremely flat potential energy surfaces, complicating enormously the determination of the low-lying states. Once the GS of the “n” cluster was identified, one water moiety was added to this structure for the GS searching of the n + 1 parent. The structures contained in Figures 1−6 correspond to true minima on the PES because they have positive frequencies. A natural bond order (NBO) 5530



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analyze the evolution of the stability for the Fe−−(H2O)n clusters, when their size is increased.

Regarding the distortion of H2O in Fe−−H2O, the O−H group bonded directly to the Fe− ion has a lengthening of 0.014 Å, whereas a smaller increase, 0.003 Å, occurs in the free O−H group, and the H−O−H bond angle has a decrease of 4.4°, from the value, 105.1°, of the isolated water molecule. Thus, there is significant distortion of H2O in Fe−−H2O, which has some differences from those found in Fe+−H2O and Fe−H2O, where the H−O−H angle increases and the two O−H distances are evenly increased (Figure 1b,c). On the energetic aspect, a relatively small binding energy, Do = 8.7 kcal/mol, was obtained for Fe−−H2O, with respect to the quartet 4F state of Fe−, mainly arising between the attractions of the Hδ+ sites and Fe−. Indeed, the charge distribution for Fe−−H2O, Figure 1, shows a high negative charge on the Fe site and a highest positive charge on the H atom making the IHB. Besides, the Do for Fe−−H2O, 0.38 eV, is close to the experimental and theoretical values (at the CCSD(T) level), 0.39 eV, reported by McCoy et al.33 for Cu−−H2O, suggesting that a similar interaction, having charge−dipole and hydrogen-bonding component,33 occurs in these TM−−H2O ions. Using B3LYP/6311++G(2d,2p), we have found a Do of 41.7 kcal/mol for the Fe+−H2O cation. A significantly smaller value was obtained for the neutral Fe−H2O cluster, 6.7 kcal/mol; these estimations were done with respect to the sextet and quintet states of Fe+ and Fe. Gutsev et al.19 using the BPW91/ 6-311+G(d,p) method have determined also quintet, 5A′, and quartet, 4B2, states for Fe−H2O and Fe+−H2O, showing bent and planar structures, Fe−O bond lengths of 2.19 and 1.98 Å, respectively, and a 5A′ − 4B2 total energy separation of 148.0 kcal/mol; these results are in concordance with our findings, where those two species are separated by 149.4 kcal/mol. It should be noted that the GS of Fe−−H2O preserves the quartet state of the Fe− ion, presumably because the IHB interaction between the water molecule and the metal is weak (Do = 8.7 kcal/mol), whereas the doublet state was determined at a considerably higher energy, 47.7 kcal/mol, signifying very small contribution from this state of lower spin in the measured properties of the Fe−−H2O anion. We have found that in a sextet state for the negatively charged Fe−−H2O cluster, the metal does not form a Fe−H bond, showing instead a low-lying state where Fe− is bonded with the oxygen atom, yielding a structure similar to that of neutral Fe−H2O, Figure 1. Lying at a high energy, 16.6 kcal/mol from the M = 4 GS, small signatures are expected also from the sextet to the properties of Fe−− H2O. Fe−−(H2O)2. To the GS structure of Fe−−H2O, an extra water molecule was directly attached to the metal, forming a Fe−H contact on the opposite region of the first H2O. The addition of H2O on the H2O region of Fe−−H2O was also considered. After relaxation the obtained results are discussed below. The quartet GS of Fe−−(H2O)2 has a structure IIa with a water molecule directly attached to the Fe− anion through a IHB, with a Fe−H distance, 2.493 Å, and a Fe−Hb−O angle, 155°, which are shorter and larger than the respective values of the Fe−−H2O parent. The other molecule, being located far away from the metal, donates (D) one H-bond, whereas its other hydrogen atom points also to the metal with a Fe−H distance, 3.173 Å, that is shorter than the longer contact, 3.487 Å, of Fe−−H2O. That is, the structural parameters suggest an enhancement for the Fe−H bonding in the Fe−−(H2O)2 ion, producing a few larger O−O separation, 2.960 Å, than the, corrected by anharmonicity, experimental value,40,41 2.946 Å for

3. RESULTS AND DISCUSSION Fe−−H2O. A planar geometry in a quartet state was found for the GS of Fe−−H2O, it is of low symmetry because in principle only one of the hydrogen atoms is bonded to Fe− through a IHB with an Feδ−−Hδ+ length of 2.801 Å and a Fe− H−O angle of 144°. Though the other Fe−H contact is larger, 3.487 Å, to some degree still may have IHB interaction. This coordination, shown in Figure 1a, may impede the vibrational stretches of the O−H groups. Using the CCSD(T)//pVQZ/ MCDF method, similar results were found for Cu−−H2O by Schneider et al.;32 they show that the water molecule is bonded to Cu− through a IHB with a Cu−H distance of 2.41 Å and a Cu−H−O angle of 151° and that the longer Cu−H contact, 3.29 Å, still may present IHB character. Likewise, at the MP2 level of theory McCoy et al.33 have found also that in the global minimum of Cu−−H2O, the water molecule asymmetrically complexes with the Cu− anion, with one IHB showing a H−Cu distance of 2.328 Å, a reduced H−O−H bond angle (99°) and a larger Cu−H contact of 3.276 Å. Meanwhile, using B3LYP/ 6311++G(2d,2p) we have obtained a Cs structure for Cu−− H2O, with Cu−H distances, 2.52 and 3.38 Å, near to those obtained by Schneider et al. and McCoy et al., and with a vertical electron detachment energy (VDE), 1.66 eV, in good agreement with the experimental value,34,35 1.58 eV, and with the results, 1.65 and 1.676 eV, determined at the CCSD(T)33 and MP4SDTQ36 ab initio high levels of theory. Thus, the B3LYP/6311++G(2d,2p) method seems to be appropriate for the study of the Fe−−H2O ions. Making the difference of total energies between neutral Fe−H2O (at the same structure of the anion) and Fe−−H2O, a VDE of 1.10 eV was obtained, which is smaller than the quoted values for Cu−−H2O. The GS geometry of Fe−−H2O resembles closely the structural features of the bonding of water molecules with halide anions.11,37,38 For example, at the MP4 level Xantheas37 has determined an optimal Cs structure for Cl−−H2O, showing also one IHB with a shorter Cl−O distance, 3.103 Å, and a more open Cl−−H−O angle, 168.7°, than the Fe−O and Fe− H−O values (3.634 Å and 144°) for Fe−−H2O. A quite different geometry was found for the quartet GS of Fe+−H2O, lying at a significantly higher energy, 166.4 kcal/mol (7.2 eV) above the Fe−−H2O GS, having a C2v geometry with the oxygen atom bonded directly to Fe+ with a shorter, 2.00 Å, Fe−O bond length, showing a larger H−O−H angle, 107.5°, and with the O−H groups pointing away from the metal so that they vibrate freely (Figure 1). An intermediate structure is displayed by the quintet GS of the neutral Fe−H2O complex, located 17.0 kcal/mol (0.74 eV) above, where the oxygen atom is also attached to the metal but presents a less symmetric nonplanar structure because the hydrogen atoms are in a bent orientation. If all atomic sites are placed in a plane, as in Fe+− H2O, the H atoms show a deviation of 56° from such plane (Figure 1). The bent character is achieved to reduce the repulsion between the metal and H2O moieties. Similar results were reported by McCoy et al.33 for Cu−−H2O, Cu−H2O, and Cu+−H2O, which as the Fe0,±1−H2O species, are important for understanding the roles of copper and iron in biological systems.39 These findings show the effect of the charge (neutral, positive, and negative) on the structures of the Fe− H2O complexes, indicating an EA, 0.74 eV, which is smaller than the VDE, 1.10 eV. 5531



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Figure 2. Low-lying states (IIa, IIb, and IIc) for negatively charged Fe−−(H2O)2 complexes. Also are shown the neutral structures, IId. For each structure of lowest energy is indicated the Fe−H and O−H bond lengths, in Å, and H−O−H angle, in degrees. The NBO charge distribution is also reported. Relative energies are with respect to the GS of the anion.

mol over the GS, the internal state IIb is a transition state (TS) for the Cl−−(H2O)2 anion.37 Thus, Fe−−(H2O)2 has surface and internal stable states, differing by a small amount of energy, of about 1.0 kcal/mol, both may contribute to the observed properties of this cluster. Isomer IIc, where the H2O molecules are bonded to the metal via the oxygen atoms was found at a much higher energy, 23.4 kcal/mol above the GS, being due to the Oδ−−Feδ−−Oδ− repulsion promoted by the charge distribution and by the relatively short Fe−O distances, 2.100 Å, which are even shorter than the Fe−H separations, 2.493 and 2.666 Å, of the IIa and IIb lowest energy states. Showing also bent structure, a triplet state was found for the neutral Fe−(H2O)2 cluster, differing by 31.8 kcal/mol from the Fe−−(H2O)2 GS. Thus, a value of 1.38 eV is predicted for the EA of Fe−(H2O)2, which is smaller than the VDE, 1.52 eV, of the Fe−−(H2O)2 anion. This estimated VDE is much bigger than the experimental value for (H2O)2−, 0.045 eV,43 suggesting that in Fe−−(H2O)2 the extra electron is strongly bonded by a valence-bound state, instead of weak dipole-bound states as in the (H2O)2− ion. Furthermore, the EA/VDE for Fe−(H2O)2/Fe−−(H2O)2 are bigger than the respective values for n = 1. Neutral Fe−(H2O)2 with the ligands bonded with one of their H atoms to Fe− were found to be unstable. At higher energies, more than 20 kcal/mol, were found the doublet and sextet states for the IIa and IIb isomers, Figure 2. Small contributions are expected from these states to the measured properties of Fe−−(H2O)2. For this reason only quartet GSs will be discussed below for Fe−−(H2O)n≥3. Fe−−(H2O)3. To the internal state of Fe−−(H2O)2, M = 4 isomer IIb, forming one Fe−H contact an extra water molecule was added. The obtained triangular structure (Figure 3) after relaxation produces the GS geometry IIIa of Fe−−(H2O)3, presenting three-dimensional geometry, 3D, instead of planar, with each H2O forming one IHB and where the metal is no longer located between two waters, as in IIb, but it is moved

the water dimer, where the molecules are held together by a linear H-bond; it is also larger than the value, 2.920 Å, determined for (H2O)2 at the MP2/aug-cc-pVDZ level of theory.42 Note that in Fe−−(H2O)2 the O−H---O angle, 162°, indicates a sensible deviation of linearity for the H-bond in this cluster. Therefore, the Fe− anion perturbs considerably the structure of the water dimer. Besides, a similar cyclic structure C1 was found by Xantheas37 for the Cl−−(H2O)2 anion. The GS geometry of Fe−−(H2O)2 is of low symmetry and nonplanar because one H atom is out of the plane defined by the other atoms (Figure 2). Accepting (A) one H-bond, the water molecule directly attached to Fe− has considerable distortion, because its bend H−O−H angle is reduced by 3.3° and its O−H group bonded to Fe− has a bigger increase, 0.029 Å, in its bond length than in Fe−−H2O; smaller changes, 0.003−0.011 Å, occur in the other O−H groups. The Do for Fe−−(H2O)2, 18.4 or 9.2 kcal/mol/H2O, is slightly bigger than the Do of Fe−−H2O, being accounted for by the formation of one H-bond, which is stronger than the Fe−H one, and by the enhancement of the IHB quoted above. Indeed, the estimated sequential BE, 9.7 kcal/mol, shows significant H-bond strength on Fe−−(H2O)2. A true local minimum was found for the internal isomer IIb, where Fe− lies at the center of the cluster. This planar geometry with the water molecules bonded directly to the metal is located 1.3 kcal/mol above the GS, meaning that even at this small cluster size the H-bond, formed between the H2O units as in IIa, plays an important role in the stabilization and growth of the Fe−−(H2O)n systems. In IIb the ligands are disposed opposite to each other with one of their hydrogen atoms forming shorter Fe−H bonds, 2.666 Å, than the one of Fe−− H2O. The other hydrogen sites are in the trans position with Fe−H contacts of 3.457 Å. The water molecules are distorted too in IIb, because the bend H−O−H angles are reduced 3.7° and the H−O groups directly attached to the Fe− anion are enlarged by 0.016 Å. Xantheas has found that, lying 2.2 kcal/ 5532



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Figure 3. Structures of lowest energy for the isomers of Fe−−(H2O)3. It contains similar data as in Figures 1 and 2, as well as the acceptor (A) and donor (D) behavior of H-bonds of the H2O moieties.

molecule. Below will be shown that structure IIIa plays the role of a basic unit of growth on bigger clusters. It has been proposed on experimental grounds44,45 and on theoretical calculations42 that the water trimer has cyclic structure, with all three water molecules acting as both hydrogen bond donors and acceptors. Regarding the hydrogen atoms of the free O−H groups, two of them lie on one side of the plane of the three oxygens, the third one on the other side. Values of 2.94, 2.97, and 2.97 Å for the O−O distances and 150, 152, and 153° for the O−H---O angles were used in the fitting of the experimentally measured rotational constants of (H2O)3.45 This cyclic motif is similar to that found in the global minimum of Fe−−(H2O)3, having on average shorter O−O distances (2.953, 2.953, and 2.954 Å) and similar O−H---O angles (152°). However, the O−O lengths are larger than those

out of the plane far away from the ligands forming a surface structure with Fe−H separations of 2.80 Å, Figure 3. The other hydrogen atoms in IIIa are involved in a network of H-bonds, promoting the appearance of an equilateral triangular (H2O)3 hydration shell, where each water moiety behaves as a single donor/acceptor. Note that both oxygen and iron sites lie at the surface of the cluster. Therefore, three IHB and three H-bonds accounts for the stability of the Fe−−(H2O)3 GS, where the water units are distorted as they have reduction of 3.0° in the H−O−H angles and increases, 0.012−0.015 Å, in the O−H bond lengths. Consequently, a Do of 27.9 or 9.3 kcal/mol/H2O was determined for this trimer, which is of similar magnitude to the Do value for Fe−−(H2O)2. The sequential BE, 9.4 kcal/mol, from n = 2 to 3, shows also the stability gained by the added 5533



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Figure 4. Structures of lowest energy for Fe−−(H2O)4. The reported data are similar to those in Figure 3.

(2.798, 2.799, and 2.800 Å using MP2- and 2.807 Å using MP4aug-cc-pVDZ) found by Xantheas and Dunning.42 That is, Fe− produces a clear distortion of the cyclic structure of the water trimer. A four-membered ring isomer IIIb was also found, with one H2O not directly bonded to Fe−, but lying in the outer layer, donating one H-bond to each water molecule bonded directly to the metal. In other words, this isomer contains, instead of cyclic, a linear water trimer attached to the Fe− ion. With two IHBs and two H-bonds, IIIb is also a low-lying state, because it differs by only 0.3 kcal/mol from the IIIa GS, which, as discussed above, has a bigger total amount (six) of IHBs and H−bonds. However, note that both kinds of bonding are of larger bond strength in IIIb, as it is indicated by its shorter H---

OH distances, 2.026 Å, and the more opened H---O-H angles, 168°. An extra water molecule was added to the GS of Fe−− (H2O)2, lying oppositely to the (H2O)2 motif and forming one IHB. The resulting candidate was used to search the PES of Fe−−(H2O)3, allowing us to find out the internal state IIIc, with Fe− being indeed located near the center of the cluster, Figure 3. Presenting a Fe−H contact of 3.21 Å, two IHBs having shorter Fe−H distances, 2.52−2.69 Å, than those, 2.80 Å, of the surface IIIa state, and one H-bond, IIIc was found 2.6 kcal/mol above the GS, confirming the importance of the network of H-bonds in the stability of the GS of Fe−−(H2O)3. A qualitatively similar pyramidal geometry IIIa was obtained also by Combariza et al.,46−48 at the HF and DFT levels of 5534



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theory, and by Xantheas,37 at the MP2 level, for the GS of Cl−− (H2O)3, whereas the ring structure IIIb was determined 2.6 kcal/mol above the GS37 for such Cl−−(H2O)3 ion. However, structure IIIc of Fe−−(H2O)3 has not been previously reported for halide−water anions. Isomer IIId, with two ligands directly attached to Fe− through the oxygen sites, thus forming short Fe−O bonds, and the third one forming IHB and H-bonds, was found at a much higher energy. Lastly, the one-layer isomer IIIe showing only Fe−O bonding is also a higher energy state. Fe−−(H2O)4. Growth of the pyramidal GS structure of Fe−− (H2O)3 may be realized in at least three pathways: (1) adding an extra water molecule in the outer shell, above the triangular hydration shell (Figure 3); (2) direct attachment to the iron atom, and located on the opposite region of the (H2O)3 motif; (3) bonded to both (H2O)3 and Fe− moieties, through one IHB and one H-bond, respectively. The first path gives rise to the 3 + 1 GS isomer IVa of Fe−− (H2O)4, where the added molecule ends, behaving as DA with the water molecules of the triangular layer, rendering an increase of the size of the planar hydration layer and where the Fe− ion is located at the border of the cluster (Figure 4). Though more distorted, because the three IHBs have different Fe−H distances, it should be remarked the preservation of the Fe−(H2O)3 motif in the GS geometry of Fe−−(H2O)4. This structural feature seems to dominate the nascent hydration of singly negatively Fe−−(H2O)n charged clusters in the gas phase. Effectively, the shorter Fe−H bonds, 2.74−2.97 Å, suggest that three H2O units are in the first layer, whereas the longer one, 3.69 Å, implies that the added molecule is in the outer shell and H-bonded with the (H2O)3 motif produces a planar square (H2O)4 layer with an increased network of H−bonds. A significant increase occurs on the distances, 0.014−0.022 Å, of the O−H groups making the H-bonds; the biggest one is for the fourth water. This and the shorter H−bond lengths, 1.83− 1.96 Å, and O−H---O angles, 160−167°, imply important Hbonding in Fe−−(H2O)4. Smaller lengthening, 0.011−0.017 Å, occurs for the O−H groups directly attached to Fe−. Overall, the lengthening of the O−H bonds and the reduction of the H−O−H angles, 2.5−3.3°, reveal important distortion of the H2O units in Fe−−(H2O)4. The binding energy, 9.24 kcal/mol/ H2O, for the tetramer is of similar strength to the Do of Fe−− (H2O)3. The sequential BE, 9.10 kcal/mol, is mainly due to the contribution of the H-bonds associated with the increase of the size of the laminar hydration shell in going from Fe−−(H2O)3, having a triangular (H2O)3 shell, to Fe−−(H2O)4, with a planarsquare (H2O)4 layer. Ab initio MP2/aug-cc-pVDZ studies42 show that the water tetramer has a cyclic structure having all water molecules acting as DA; the O−O distances and O−H---O angles are 2.743 Å and 167.7°. Showing larger O−O distances (2.801, 2.863, 2.878, and 2.908 Å) and smaller O−H---O angles (160, 162, 163, and 167°), such structure appears in the GS of Fe−− (H2O)4, but with a more distorted square and a more marked departure from linearity for the H-bonds. Note that the O−O distances, both in (H2O)4 and in Fe−−(H2O)4, are shorter than those of the respective trimers, (H2O)3 and Fe−−(H2O)3. The second route of growth yields roughly a one-layer H2O− Fe−−(H2O)3 isomer, IVe, Figure 4, preserving the triangular hydration shell with its network of H-bonds. Its Fe−H distances, 2.77−2.90 Å, are similar to those of the GS of Fe−−(H2O)3, but they are longer than the Fe−H one, 2.65 Å, of the other H2O lying oppositely from the (H2O)3 motif. Note

that the H-bond lengths, 2.02−2.07 Å, are longer than those of the 3 + 1 GS, signifying an enhancement of the hydrogen binding in the IVa GS. Thus, four Fe−H attractive electrostatic interactions and three H-bonds accounts for the stability of the Fe−−(H2O)4 isomer IVe, which is near in total energy, 2.3 kcal/mol, to the GS. Third, in isomer IVc the added H2O forms only one H-bond with the (H2O)3 motif, which is preserved, because it forms three H-bonds and three IHBs, whereas the large Fe−H distance, 5.56 Å, implies the absence of IHB for the outer H2O. Showing larger H---OH distances, this 3 + 1 isomer lies 1.4 kcal/mol over the GS. It is the one that more closely resembles the 3 + 1 isomer of Cl−−(H2O)4,37 which also is near, 2.1 kcal/ mol, to the GS of the halide tetramer, and with the outer H2O bonded to both (H2O)3 and Cl−, whereas in Fe−−(H2O)4 IVc it is bonded only to (H2O)3, as it should be for a 3 + 1 isomer. Thus, small but important structural differences appear in Cl−− (H2O)4 and Fe−−(H2O)4. A pyramidal C4 structure IVh with Fe−H separations of ≈2.960 Å and a network of H-bonds with H---OH distances of 1.926 Å was identified at a higher energy, 5.0 kcal/mol above the 3 + 1 GS. The distortion, and thus the stability, of the less symmetric 3 + 1 GS may be due to Jahn−Teller effects promoted by the open-shell electronic configuration, 3d74s2, of Fe− and is due also to the preservation of the highly stable Fe−−(H2O)3 motif in the 3 + 1 GS isomer. It should be remarked also that the GS has shorter Fe−H distances and slightly shorter H---OH separations than the symmetric IVh isomer. The Jahn−Teller effects may be of lesser strength in X−−(H2O)4, as they have close shell X− anions. Effectively, at the MP2 level of theory, Xantheas37 has determined a pyramidal isomer of C4 symmetry (roughly comparable to the present structure IVh of Fe−−(H2O)4) for the GS of Cl−−(H2O)4, whereas, as quoted above, Xantheas has found that the 3 + 1 isomer (actually IVc of Fe−−(H2O)4) is located 2.1 kcal/mol above the more symmetric C4 GS isomer. It should be remarked also that the distorted 3 + 1 GS structure of Fe−−(H2O)4, containing a planar (H2O)4 layer, is quite different from the more symmetric C4 GS structure of Cl−−(H2O)4, also presenting a (H2O)4 layer. Thus, Fe−− (H2O)4 shows distorted or less symmetric low-lying states than Cl−−(H2O)4, which may be partially due to the different, openand close-shell, electronic configurations of Fe− and Cl−. The growth of the ring structure IIIb produces isomer IVb of Fe−−(H2O)4 with two waters remaining attached to Fe− and with the added moiety forming one H-bond with the central H2O moiety, which thus behaves as DD/A (Figure 4). The surface state IVb, with two IHBs and three H-bonds, differing by less than 1 kcal/mol from the GS may contribute to the observed properties of this cluster. Structure IVb, as well as IVa, of Fe−−(H2O)4 has not been before identified for Cl−− (H2O)4 ions Coordination TM+−(ligand)4 compounds in the liquid phase usually have planar square structures with the metal atom lying at the center of such complexes and bonded with the nucleophilic sites of the ligands, for example, the nitrogen and oxygen atoms of the ammonia and water molecules. With the hydrogen atoms pointing to the Fe− anion, lying at the center, a planar square geometry was chosen as a candidate for searching the PES of Fe−−(H2O)4. After some early stages of geometry optimization, the four water molecules migrate toward the same side or region, forming a linear (H2O)4 chain; they are joined by H−bonds and finally a 2 + 2 isomer 5535



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Figure 5. Lowest energy states for Fe−−(H2O)5. The reported data are similar to those in the other figures.

IVf is formed, where two ligands are directly attached to Fe−. The other two molecules are far away from the metal, each one bonded with different inner water molecules. Isomer IVf was found at 2.6 kcal/mol from the GS. Taking as candidate a pyramid with a triangular base, a similar isomer IVd was determined at 1.9 kcal/mol from the GS. The IVf and IVd structures are shown in Figure 4. Viewed as coming from the internal state IIIc of Fe−− (H2O)3, isomer IVg was obtained with the oxygen and iron sites defining a planar structure and with Fe− lying at the center of the cluster. This isomer, lying 4.1 kcal/mol above the GS, shows that clusters with Fe− located at the surface are energetically more favorable than those with a central ion and confirms that the H-bonds, overcoming the strength of the IHB, play an important role in the stability and growth of the

Fe−−(H2O)n clusters. At the MP2 level, IVg was located as a TS37 for Cl−−(H2O)4, instead of a minimum as in the iron case. The present study shows a plethora of minima states for Fe−−(H2O)4 lying within a sharp energy range. Fe−−(H2O)5. To the GS of Fe−−(H2O)4 an extra water molecule, lying oppositely to the (H2O)4 motif, was attached to the metal, producing an H2O−Fe−−(H2O)4 structure for inquiring the PES of the pentamer. During relaxation, it was found that the Fe−H bond is preserved and the added H2O is moved toward the (H2O)4 layer, from which it accepts one Hbond, yielding finally the GS isomer Va of Fe−(H2O)5. For this cluster, Fe−H contacts (two from the square layer and one from the added molecule) are much shorter than the other two and the average H-bond distance of the (H2O)4 ring, 1.896 Å, is shorter than the one of the ring (1.913 Å) for the GS of Fe− 5536



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Figure 6. (a) Lowest energy states for Fe−−(H2O)6. The reported data are similar to those in the other figures. (b) Some isomers of higher energy for Fe−−(H2O)6.

(H2O)4; the fifth H-bond is pretty short too, 1.964 Å. A similar attachment pathway to the symmetric IVh isomer yields also Va after relaxation. Therefore, aside from IHB, an enhanced network of H-bonds accounts for the stability of Fe−(H2O)5. The estimated Do, 9.2 kcal/mol/H2O, of similar strength to the Do of the tetramer, is consistent with the enforcement of the hydrogen bonding in the GS of Fe−(H2O)5. The sequential BE, 8.90 kcal/mol, indicates that the fifth moiety is slightly less bonded than the fourth one in Fe−(H2O)4, 9.10 kcal/mol, which may be traced to the increased repulsion among the more crowded molecules around the metal. Triangular (H2O)3 and planar square (H2O)4 single-rings appear for the GSs of the n = 3 and 4 clusters. Remarkably, the GS structure for n = 5 deviates visibly from the single ring motif tendency, making the four-membered ring, (H2O)4, an interesting subcluster structure at this cluster size region. Effectively, the (H2O)4 single-ring remains too in the Vc isomer, lying only 1.6 kcal/ mol above the GS, which originated through the addition of an extra H2O to the (H2O)4 layer of Fe−−(H2O)4, instead of the metal. As will be shown below, the four-membered ring appears also in the low-lying states of Fe−−(H2O)6. A distorted pentagonal pyramid structure Vb was located at less than 1 kcal/mol from the GS. It preserves the Fe−(H2O)3 building block, as revealed by the three shorter Fe−H lengths, 2.65−2.79 Å. Although the other two molecules are not allowed to form IHB, as they are far away from the metal, 4.17−4.64 Å, they present H-bonds with the (H2O)3 unit, yielding a nonplanar five-membered ring. Thus, four- and five-membered rings are formed in the low-lying states of Fe−(H2O)5 in the gas phase. They appear also in the low-lying states of Fe−− (H2O)6, where the former defines the GS; see below.

Ab initio HF/aug-cc-pVDZ studies42 indicate that the water pentamer presents cyclic structure, of pentagonal shape, with O−O separations of 2.863, 2.862, 2.863, 2.865, and 2.882 Å and O−H---O angles of 173.3, 174.8, 174.0, 175.1, and 173.0°. Showing a deviation from planarity, the cyclic (H2O)5 motif appears in isomer Vb, lying near the GS, with shorter O−O distances (2.745, 2.870, 2.745, 2.850, and 2.888 Å) and slightly smaller O−H---O angles (173.6, 171.3, 172.6, 160, and 170.3°). Performing geometry optimization with the SCF method and estimating the total energies at the MP2 level of theory, Combariza et al.46 have identified a pentagonal pyramid and a 4 + 1 (a square (H2O)4 layer and one H2O molecule attached to Cl−) isomers as the lowest energy states of Cl−−(H2O)5. Our study identifies a distorted pentagonal pyramid structure Vb as a low-lying state for Fe−−(H2O)5, whereas, as discussed above, the 4 + 1 candidate, generated by the attachment of a fourmembered ring (either symmetric or a distorted planar square geometry) and one H2O (on the opposite region of (H2O)4) to the Fe− ion, converges through relaxation into the Va GS. Thus, some isomers in Cl−−(H2O)5 are not reachable in Fe−− (H2O)5. In fact, the GS Va for Fe−−(H2O)5 does not correspond to any one of the lowest energy structures of Cl−−(H2O)5. Isomer Vd, at 2.7 kcal/mol, instead of an (H2O)4 ring, contains a linear (H2O)3 motif, which is directly attached to the Fe− ion. Another molecule increases the size of the linear chain, whereas the last one behaves as DD with the moieties at the end of the linear (H2O)3 chain, Figure 5. Thus, more compact networks of H-bond (Va, Vb, and Vc) are more stable than the more open ones. Actually, Vd was found through full optimization of a candidate linear (H2O)5 motif, joined to 5537



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Fe−, which was generated by the addition of a water molecule to isomer IVf of Fe−−(H2O)4. To isomer IVf of Fe−(H2O)4, on the opposite region of the linear (H2O)4 layer a water molecule was directly attached to the metal, lying at the center, building an H2O−Fe−(H2O)4 structure. After relaxation, this input yields a 3 + 2 isomer with the three inner ligands forming, instead of linear, a planar (H2O)3 hydration layer with relatively short Fe−H distances (2.60−2.73 Å) and short H-bonds, thus emerging a threemembered ring. The outer molecules are H-bonded to different H2O units of the ring. Then, the final result is the movement of the added H2O, from its initial position forming Fe−H bonding, toward the (H2O)4 region, producing the H2O− (H2O)3−H2O hydration environment, shown in structure Ve (Figure 5), which is located 3.1 kcal/mol above the GS. Isomer Vi has a single hydration shell; that is, all water molecules are attached directly to the metal. Forming five IHBs Vi is located at 5.3 kcal/mol from the GS. In this cluster a triangular layer is formed, showing longer Fe−H bonds, 2.77− 2.94 Å, than those, 2.67 Å, of the other two waters, which are well separated, 4.12 Å between their nearest hydrogen sites, impeding H-bond formation. Also an (H2O)3−Fe−H2O−H2O isomer Vh was identified, being nearer in energy, 3.9 kcal/mol, to the GS, than cluster Vi, reflecting the bigger stabilization gained by H-bond formation. Indeed, as discussed above for n = 2, the 1 + 1 isomer IIa is more stable than the single layer cluster IIb. Besides, the total energy difference between IIa and IIb is close to the one, 1.4 kcal/mol, between Vh and Vi. Addition of two H2O units on the same side of the (H2O)3 layer yields isomer Vf at 3.3 kcal/mol. Lastly, the growth of IVb produces the quasi-planar Vg isomer located at 3.5 kcal/mol. Fe−−(H2O)6. Growing from the n = 5 GS, as shown in Figure 6a, the GS of Fe−−(H2O)6 has a four-membered ring subcluster structure, on which the bonding of the other ligands forms a V-shaped hexagonal geometry. Note that only three water molecules present IHB through short Fe−H contacts: 2.53−2.79 Å. The outer moieties have larger Fe−H separations (3.51−4.12 Å). That is, three molecules are located in the outer layer with one of them behaving as DDA with the inner layer. As shown in the top view of VIa, one inner molecule behaves as DAA, whereas the others play an AD role in the network of Hbonds. Therefore, three IHBs and a network of seven H-bonds accounts for the stability of Fe−−(H2O)6. Its estimated Do, 53.7 or 8.9 (kcal/mol)/H2O and sequential BE, 8.1 kcal/mol, are still of substantial strength; both are less than 1 kcal/mol smaller that the respective values of the pentamer. A ring structure of chair shape has been found as the optimal geometry for the water hexamer by Xantheas and Dunning42 at the HF/aug-cc-pVDZ level, with all water molecules exhibiting a DA behavior, with shorter O−O distances (2.855 Å) than those of (H2O)5, at the same level of theory, and with O−H--O angles, 177.5°, indicating a linearity for the H-bonds. As quoted above, a chair geometry appears in the GS of Fe−− (H2O)6, with the water molecules exhibiting a more complex, DA and DAA, behavior in the network of hydrogen bonds, with larger O−O distances (2.880, 2.880, 2.944, 2.876, 2.875, and 2.944 Å) and with considerable departure of linearity for the Hbonds, because the O−H---O angles ranges from 159 to 164°. That is, Fe− perturbs strongly the chair geometry of (H2O)6. The five-membered ring plays the role of a basic unit structure for the surface isomers VIb and VIc, which are located very near in total energy, 1.2 and 1.7 kcal/mol, to the fourmembered ring GS geometry. In the first one the sixth water

molecule is attached to the distorted pentagonal hydration layer through one H-bond, whereas the other hydrogen atom points toward Fe−, though the large Fe−H distance (4.52 Å) avoids IHB formation, yielding the (H2O)5−(H2O) downward structure depicted in Figure 6a. Conversely, in VIc the sixth water is attached to the pentagon in a vertical way, producing the upward more open structure shown in Figure 6a. Thus, the more compact isomer VIb is slightly more stable. Cluster VIb was reached by the addition of one H2O to Vb, on the opposite region of the (H2O)5 layer, whereas the addition above the pentagonal layer renders VIc, after relaxation. The four-membered ring subcluster structure also appears in the VId surface isomer; the other two molecules being Hbonded on opposite sides of the (H2O)4 layer produces a less compact isomer, which with six H-bonds and three IHBs is located 3.0 kcal/mol above the GS. At relative energies of about 3 kcal/mol, initial signatures of internal clusters are revealed. This is exemplified by the VIe and VIg isomers, constituted by four-membered rings, the former having one H2O bonded to (H2O)4 and another one attached to Fe−, whereas VIg presents two molecules directly attached to the metal, producing a more visible pattern of internal cluster, Figure 6b; VIe and VIg lie at 3.5 and 4.8 kcal/mol from the GS. An octahedral structure, which usually is the GS of TM+− (H2O)6 species, via full relaxation, produces the internal structure (H2O)3−Fe−−(H2O)3 VIf, having two triangular layers attached to Fe−, with longer Fe−H bonds, 2.88 Å, than those of the GS, and with the H2O moieties in a staggered way (Figure 6b). Thus, a bigger amount of Fe−H bonds, six, and a similar amount of H−bonds, six, are formed in VIf, lying 4.2 kcal/mol above the 3 + 3 GS. Showing three IHBs and seven H−bonds, the identified GS reveals that on the studied range of cluster sizes, the former is weaker than the H-bond. Also with a structure similar to that of VIf, but with the water molecules in an eclipsed configuration, an isomer VIj was found at a much higher energy, 9.3 kcal/mol, which mainly is due to the increased repulsion between the water molecules at the top and bottom layers. Another internal structure VIh, which may be viewed as the dimer of the IIIb isomer, was determined at 5.7 kcal/mol. Lastly a nonplanar hexagonal isomer with four IHBs and six H-bonds was found at a higher energy, 6.3 kcal/mol. Performing full optimization at the SCF level, Combariza et al.46 have determined surface V-shaped hexagonal (at 5.9 kcal/ mol) and distorted hexagonal pyramid (at 3.4 kcal/mol) structures and an internal distorted octahedral one (the GS), for Cl−−(H2O)6; values in parentheses indicate the relative energies at the MP2 level. They correspond quite approximately to the VIa, VIi, and VIf isomers of Fe−−(H2O)6. Taken this into account, Fe−− and Cl−−(H2O)6 have a reverse order of low-lying states. The results reveal the type of structures and metal−ligand bonding for the Fe−−(H2O)6 clusters; three-, four-, five-, and six-membered rings of water molecules bond the metal, with a maximum of three IHBs for each ring. Surface and internal structures are originated, with the former lying at lowest total energies. The VDE for Fe−−(H2O)6, 2.41 eV, is bigger than the experimental values for (H2O)6−, 0.147 eV, measured by Bowen and co-workers;43,49 a value of 0.485 eV was reported by Ayotte et al.50 It will be interesting to determine experimentally the VDEs for Fe−−(H2O)n, to confirm or deny these findings. 5538



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4. CONCLUSIONS Singly negatively charged Fe−−(H2O)n≤6 clusters were studied at the B3LYP/6-311++G(2d,2p) level. In the determined lowlying states of Fe−−(H2O)n, some water molecules are directly attached to the metal through IHBs which, though of weak bonding strength, overcome the metal−oxygen bonding. Lowsymmetry structures are produced because only one of the hydrogen atoms, of each H2O, are involved in the Fe−H bonding, whereas the other ones form a network of H-bonds, originating the formation of surface cluster structures for the GSs of Fe−−(H2O)n≤6, which, though by a small amount of energy, less than 5 kcal/mol, are more stable than the internal isomers in the addressed size range. That is, these clusters present competition between surface and internal structures. A key question is on the size and nature, surface or internal, of the complete first solvation layer of Fe−−(H2O)n Besides, in most of the GSs of Fe−−(H2O)n≤6, the water molecules do segregate and form structures, due to hydrogen bonding, that resemble closely those of the (H2O)n≤6 clusters. However, with respect to the bare water clusters, they present significant structural changes as indicated by the longer O−O distances, fewer linear H-bonds, and the more distorted geometries of the absorbed (H2O)n≤6 clusters; they also show strong electronic changes, as revealed by the VDE of Fe−−(H2O)2 and Fe−−(H2O)6, which are considerably bigger than the experimental results for (H2O)2− and (H2O)6−. In this regard, the experimental determination of the VDE for Fe−−(H2O)n will provide valuable insight on these clusters. Another fact is that the Fe−−(H2O)n clusters have low-lying states resembling those of Cl−−(H2O)n. However, some of the identified GSs of Fe−−(H2O)n≤6 have more distorted or less symmetric geometries, mainly due to the open shell electronic structure of Fe−, as compared to the close shell ones of the halide anions. These results provide insight on the nascent hydration of a negatively charge iron atom, which is mainly determined by the attractive, Feδ−−Hδ+, nonattractive, Feδ−− Oδ−, and H-bond interactions for each Fe−−(H2O)n system.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The author deeply thanks the financial support for Project PAPIIT-IN-216811, from DGAPA-UNAM. The author expresses his strong thanks for access to the supercomputer Kan Balam at DGSCA-UNAM.

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REFERENCES

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Theoretical Study of Negatively Charged Fe––(H2O) n≤ 6 Clusters

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