Stability of one- and two-layers [TM(Benzene)m]±1, m ≤ 3; TM = Fe, Co, and Ni, complexes

Journal of Molecular Structure 1125 (2016) 47e62

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Stability of one- and two-layers [TM(Benzene)m]±1, m
3; TM ¼ Fe, Co, and Ni, complexes Raúl Flores, Miguel Castro* n, M rica, DEPg, Facultad de Química, Universidad Nacional Auto noma de M Departamento de Física y Química Teo exico, Del. Coyoaca exico D.F., C.P. 04510, Mexico

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 February 2016 Received in revised form 6 June 2016 Accepted 20 June 2016 Available online 22 June 2016

The structural and energetic properties for neutral and charged complexes of transition metal atoms and benzene molecules, TM(C6H6)m
3, TM ¼ Fe, Co, Ni, were studied using density functional theory. Including dispersion corrections all-electron calculations were done with the BPW91eD2 and M11L functionals. Basis sets of 6e311þþG(2d,2p) and Def2TZVP quality were employed. Binding energies, D0, ionization energies, IE, and electron affinities, EA, were determined for the located ground states. Structural and electronic parameters accounting for the stability of TM(C6H6)m were also addressed. Metal-carbon (h2eh6) coordination occur in the neutral and positively charged TM(C6H6)1,2 species. But in the CoeC6H6 and NieC6H6 ions the metal atom seats on two hydrogen atoms, h2H, of the benzene ring, with the peculiarity that the ground state geometries are planar. In the neutral and charged TM(C6H6)3, TM ¼ Fe, Co and Ni species a benzene molecule lies in the external region and by means of CHep and p ep stacking interactions it is bonded to the ligands lying in the first coordination layer. Although weak, some external molecules present direct interactions with the metal atom. The D0 for the molecules in the outer region is much smaller than the one for the ligands in the first layer. Therefore, solvent behavior is exhibited by the studied neutral and charged [TM(C6H6)3]±1 complexes. Experiment and theory agree that: D0(Feþ(C6H6)2) > D0(Coþ(C6H6)2) > D0(NiþC6H6)2) and D0(NiC6H6) > D0(CoC6H6). Reasonable accuracy was found for the D0 of each complex; other tendencies are not fully reproduced at these levels of theory. The small D0’s of CoC6H6 and NiC6H6 and those of the anions, complicate their determination. In general, the EA increases from m ¼ 1 to 2 and from 2 to 3. The IE decreases from m ¼ 1 to 3, being due to delocalization trough the CdeeHdþ/p network of bonds. © 2016 Elsevier B.V. All rights reserved.

Keywords: DFT Metal-benzene systems Solvent effects in mixed complexes CHep and pep interactions

1. Introduction Recently developed experimental methods make feasible the synthesis as well as the characterization, in the gas phase, of mixed complexes containing transition metal (TM) atoms and different kinds of molecules [1e7]. These studies are important as they provide insight on the fundamental metaleligand interactions, in the absence of solvent effects, mainly accounting for the structural, electronic, and energetic properties of such compounds. For example, for TMn-benzenem systems, Kaya and coworkers have found that early TMs have a tendency to form multiple decker sandwich (MDS) structures with alternating layers of ligands and metal, whereas later TM atoms prefer to form riceeball (RB) motifs

* Corresponding author. E-mail address: [email protected] (M. Castro). http://dx.doi.org/10.1016/j.molstruc.2016.06.052 0022-2860/© 2016 Elsevier B.V. All rights reserved.

where the TM cluster is fully covered with benzene molecules [1]. In a recent work, Duncan and co-workers have found that larger Niþ(C6H6)m (m  3) complexes present external benzene molecules that are weakly bonded, acting essentially as solvent moieties [8]. This solvent behavior was addressed also by theoretical methods [9]. It was shown that there are many Niþ(C6H6)m3 motifs, lying near in energy. Two kind of isomers where found for these complexes. In the first type, there are three benzene molecules interacting directly with the nickel atom (one layer structure). In the second isomers, two benzene molecules are bonded directly with the metal atom; and the third molecule is absorbed on Niþ(C6H6)2 by CHep or pp interactions (two layer structure) [9]. Infrared spectra (IR) for these complexes was obtained by Density Functional Theory (DFT) including dispersion corrections [10]; it was found that the theoretical results matches with the experiment [9]. Aside from Niþ(C6H6)2, Feþ(C6H6)2 and Coþ(C6H6)2 show also high intensity in the mass spectra of the (n, m) species [1], implying high

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R. Flores, M. Castro / Journal of Molecular Structure 1125 (2016) 47e62

stability, which can be due by their prototypical sandwich geometry. An interesting point is the feasibility for the attachment of another benzene molecule to TM(C6H6)2 TM ¼ Fe, Co, and Ni and to study the stability of the one- and two-layer (1,3) isomers along this triad. The question is whether neutral, positively (þ1) and negatively (1) charged iron, cobalt, and nickel tri-benzene species may have similar structures. The behavior of the energetic properties: ionization energies (IE), electron affinities (EA) and binding energies (D0) as m increases in each TM(C6H6)m
3 complex is other important point that will be studied. Solvent effects in TM(C6H6)m needs the study of benzene-benzene interactions, which are of fundamental importance as they are the prototypical non-covalent interactions of aromatic p-systems. Treatment of pp stacking interactions poses a challenge for the theoretical tools, originating from the weak forces yielding flat potential energy surfaces (PES). Even the small binding energies of pp systems, which are typically less than 3.0 kcal/mol, play a crucial role in determining protein and DNA stability [11e13]. They are important also in the design of devices with required electronic or energetic properties [14,15]. Besides, there are metals weakly interacting with aromatic entities in some enzymes [16,17]. It is known that there is a dependency between catalytic properties of metalloenzymes and the metal. A metal replacement may change the enzyme functionality [18]. It is interesting to determine the role of the weak metalearomatic interactions in such catalytic behavior. The purpose of this work is to study, using DFT, the structural and electronic properties for the ground states (GS) of neutral and charged (1, þ1) TM(C6H6)m m
3 (TM ¼ Fe, Co, and Ni) compounds. The behavior of the solvent molecules will be compared along such iron, cobalt, and nickel complexes. From m ¼ 2 to 3, Fe(C6H6)3, Co(C6H6)3 and Ni(C6H6)3 have several possibilities of growing. Structural stability will be studied through a vibrational analysis, done under the harmonic approximation. A comparative study of IE, EA, and D0 will be done. 2. Methodology Low-lying states of Fe(C6H6)m
3, Co(C6H6)m
3 and Ni(C6H6)m
were studied by means of all-electron calculations, performed with the BPW91 [19,20] and the meta-GGA M11L methods [21]. Longerange correlation accounting for van-der-Waals forces was included through the semi-empirical D2 dispersionecorrection, as developed for BPW91; this method will be labeled as BPW91-D2 [10]. The 6-311þþG(2d,2p) and Def2TZVP basis sets, developed by Pople and Ahlrichs groups, were used [22]. Calculations were done using the quantum chemistry software Gaussian 09, version D.01 [23]. The evolution of the geometry during the optimization procedure and the molecular orbitals (MO) of the neutral species were analyzed with the Gauss View package. Employing an ultrafine grid, strict convergence was required for the total energy, minimized to 108 a.u. The geometries were optimized with a 105 a. u. threshold for the RMS forces. Tight tolerances are needed, because it was found that neutral and charged [TM(C6H6)m
3]±1 complexes present several isomers within a narrow energy range. The optimized structures were confirmed to be true local minima by estimating the normal vibrations within the harmonic approximation. Natural bond order (NBO) population analysis was obtained for the lowlying states; gross atomic NBO charge distributions were used for a qualitative understanding of the charge transfer effects [24]. Different multiplicities (M ¼ 2S þ 1, S is the total spin) were tried for geometry optimization, carried out without imposing symmetry constraints. As seen in Table 1, small spin contamination, less than 10%, was found for the low-lying states. Distortions of the benzene rings in the TM(C6H6)m
3 complexes are referred to the CeC and CeH bond lengths, determined for the free benzene

3

molecule. Including zero-point vibrational energy (ZPVE) for the total energies (E) of the GS of the metalebenzene species and benzene, the binding energy (D0) for the added molecule was determined through the difference of total energies. For instance, the equation [E(TM(C6H6)m-1) þ E(C6H6)] e E[TM(C6H6)m] yields D0 for the added C6H6 unit to TM(C6H6)m-1. Adiabatic EA’s were obtained by the difference of total energies of the neutral and anion GS’s. Likewise, IE were estimated also by the difference of total energies of neutral and cation GS’s. It should be noted that BPW91 has been validated to describe the metalemetal interaction in TMn systems [25], which is important for a proper study of TM atoms or TM clusters interacting with benzene molecules [26,27]. Moreover, tilted-T shape (tT) and parallel displaced (PD) structures of the benzene dimer have been addressed previously by means of BPW91-D2. It was found that, compared to high level ab-initio wave function-based methods and with the experiment, the BPW91-D2 level of theory provides reasonable description of the structural and energetic details of the benzene dimer [9]. Also BPW91-D2 has predicted reasonably well the IR spectra of Niþ(C6H6)m in the gas phase [9]. However, there is a reason to use another functional. BPW91-D2 exhibits strong deviations from the experimental values of D0, EA, and IE. The M11L meta-GGA method, may be appropriate for an accurate study of TM(C6H6)m
3 systems because it includes also long range dispersion interactions. Thus, both DFT methods will be used to study Fe(C6H6)1,2, Co(C6H6)1,2 and Ni(C6H6)1,2; the obtained results of D0, EA, and IE will be compared with the available experimental data for these complexes. This comparison will provide confidence on the chosen theoretical methods for exploring the structural and energetic properties of Fe(C6H6)3, Co(C6H6)3 and Ni(C6H6)3 where the experimental data is scarce. It was found that M11L/Def2TZVP produces D0s which are near to the experimental results. But, aside from this D0 accuracy, it does not reproduce the observed D0 tendencies for the Fe(C6H6)1,2, Co(C6H6)1,2 and Ni(C6H6)1,2 triad of neutral and charged complexes. BPW91-D2/6-311þþG(2d,2p) produces D0’s which follow such trends, despite of presenting larger deviations from the experiment. The M11L/Def2TZVP and BPW91-D2/6-311þþG(2d,2p) D0s are shown in Table 1. These results are the ones that will be mainly discussed in this work. In Table SI-1, in the supporting information, are reported all the computed D0’s, using the two functionals and two basis sets. For the benzene dimmer M11L/Def2TZVP and BPW91/6-311þþG(2d,2p) renders accurate D0 results, 0.059 and 0.065 eV, which are in accord with a recent experimental determination, 0.067 ± 0.01 eV [28]. 3. Results and discussion 3.1. Structural properties for the GS’s of Fe(C6H6)1,2, Co(C6H6)1,2 and Ni(C6H6)1,2 The M11L GS structures of [TMC6H6]±0,þ1,1, TM ¼ Fe, Co, and Ni, are reported in Fig. 1. Bonding of the benzene molecule with a single TM atom may produce six metalecarbon bonds. In fact, h6ecoordination is formed in FeC6H6 and NiC6H6, where such bonding is symmetrical since for each neutral complex the TMeC distances are equal, producing 3A1 and 1A1 electronic states, respectively. However, low h2ebonding arises in the 4A00 GS of CoC6H6, which is in line with the smaller binding energy of this complex; see Table 1. The metaleligand bonding is due to covalent bond formation principally arising from the 3deelectrons of the TM atoms and the peclouds of the benzene molecules. As seen in Fig. 2, the HOMO, HOMOe1, HOMOe3 and HOMOe4 levels of FeC6H6 show Fe(3d)-benzene (p) bond formation. Except that HOMO is nonbonding; a similar scheme appears in NiC6H6. Antibonding

R. Flores, M. Castro / Journal of Molecular Structure 1125 (2016) 47e62

49

Table 1 Binding energies, D0 in eV, of TM(C6H6)1,2 (TM ¼ Fe, Co, Ni) complexes. Also are indicated the electronic states, and the 〈S2〉 values. State

S2

BPW91-D2/6-311þþG(2d,2p)

M11L/Def2TZVP

Theorya,d,e

Experiment

Fe(C6H6) Feþ(C6H6) Fe(C6H6)

3

A1 2 B 4 A

2.076 0.762 3.893

1.63 3.00 (M ¼ 4) 1.70

1.42 2.39 0.76

1.71a 3.28a, 2.22d, 2.46d

>0.7a 2.15 ± 0.10b, 2.38 ± 0.22f

Co(C6H6) Coþ(C6H6) Co(C6H6)

4 00

A A1 3 A1

3.756 2.018 2.007

1.49(M ¼ 2) 3.56 0.86(0.28)

0.23 2.03 0.26

1.83a 3.91a, 2.71d

0.34a 2.65 ± 0.11b e

Ni(C6H6) Niþ(C6H6) Ni(C6H6)

1

A1 B2 2 A1

e 0.762 0.758

1.62 3.32 0.29

0.94 2.52 0.20

1.70a, 1.22e 3.26a, 2.57d, 2.57e

0.87e1.30a 2.52 ± 0.11b e

3

A1g B1g 2 0 A

2.097 0.769 0.812

1.43 2.79 1.63

0.93 2.46 1.23

1.71a 3.28a

2 0

A A1g 1 0 A

0.790 2.025 e

1.68 2.21 2.16

1.49 1.63 1.81

0.42a 1.97a

1.71a 1.73 ± 0.11b e

1 0

2

A Bg 2 Au

e 0.766 0.759

1.56 2.00 1.36

1.12 1.42 0.76

0.02a, 1.40e 1.46a, 1.91e

e 1.52 ± 0.12b e

e

e

0.065

0.059

3

2

Fe(C6H6)2 Feþ(C6H6)2 Fe(C6H6)2

2

Co(C6H6)2 Coþ(C6H6)2 Co(C6H6)2

3

Ni(C6H6)2 Niþ(C6H6)2 Ni(C6H6)2 (C6H6)2 a b c d e f

Reference Reference Reference Reference Reference Reference

1.94 ± 0.17b

0.067 ± 0.01c

[31]. [7]. [28]. [32]. [33]. [35].

(FeC6H6 and NiC6H6) and weak-bonding (CoC6H6) character was found for the LUMO’s. Note the weak bond signatures of HOMO[ and HOMO-1Y in CoC6H6; being in line with its smaller D0. Electronic configurations for the [TMC6H6]±0,þ1,1, TM ¼ Fe, Co, Ni GS’s are shown in Table SI e 2. Maximum h6 coordination takes place in FeþC6H6, CoþC6H6 and þ Ni C6H6, with the peculiarity that the TMeC bond lengths increase along this triad of half sandwich structures; Fig. 1. Electron deletion from the HOMO[ of FeC6H6 produces a state of lower symmetry, 2B, for the FeþC6H6 cation. Specifically, boding with the Feþ ion produces visible distortion of the benzene molecule. For example, in FeþC6H6 two FeeC distances, 2.007 Å, are shorter than the other four, 2.072 Å, invoking the shape of a boat for the benzene ring. The 2 B2 state of NiþC6H6 shows two different NieC bond lengths also. These forms will be labeled as boat shape. While in the 3A1 GS of CoþC6H6 the benzene ring is planar. The boat shape has a main consequence in the IR spectrum. There will be two groups of frequencies in the CeH stretching region, one corresponds to the vibrations of the carbon atoms closest to the metal and the other frequency belongs to the other carbon atoms. This has been verified before for the NiþC6H6 ion [9]. It is expected a single (frequency) peak in the experimental IR spectra for the (h6) complexes, where the benzene ring preserves its planar geometry. As will be discussed in a further section, the estimated IR spectra for the boat structures of FeþC6H6 and NiþC6H6 show doublets in the CeH stretching region. Such doublet is less clear in other complexes where the benzene ring is planar. Electron attachment at the LUMO[ level of FeC6H6 lowers the symmetry (C2) of FeC6H6-, since a 4A state was obtained for this anion, which preserves a tri-dimensional h6 geometry (3D). Unexpectedly, M11L produces planar structures for the 3A1 and 2A1 GS’s of CoC6H6- and NiC6H6-, where the metal is not bonded to the carbon atoms; instead, hydrogenemetal non-covalent bonds are

formed; this may be due to the strong repulsion between the Co/ Ni ions with the p-electrons; Fig. 1f and i. Thus, quite different IR spectra are expected to be observed in these h2 Co/H/Ni/H species. The 3D isomers of these anions were found at higher energies, at 13.1 and 3.6 kcal/mol, respectively. Contrarily, BPW91eD2 gives 3D (h6) GS’s for CoC6H6- and NiC6H6-, locating the 2D isomers at higher energies; Figs. SI-1a and b. These results may signify an overestimation of the metal-ligand bonding by BPW91-D2, even if dispersion correction is included. Another marked structural difference occurs in CoC6H6; here BPW91 gives h6 bonding and, as shown above, M11L yields h2. Triplet and quartet spin states were found for FeC6H6 and CoC6H6, respectively; while a singlet occurs in NiC6H6. The spin contamination must be negligible in calculations where spin multiplicity is utilized [29]. Our results, shown in Table 1, reveal that the errors for 〈S2〉 are less than ten per cent. In Fig. SIe2 are shown the spin density (SD) contour-plots for the neutral and charged monobenzene complexes. In the formers, the spin is mainly located on the Fe (SD ¼ 2.13) and Co (SD ¼ 2.99) atoms. A similar behavior was observed in the other TMC6H6 species. The SD’s on the Fe and Co atoms implies opposite SD’s (0.08Y and 0.10Y) on the benzene molecules. A more plenty antiferromagnetic behavior was found on FeC6H6-, where Fe and benzene have SD’s of 3.65[ and 0.65Y, respectively; being consistent with the electron population, 0.63e, on the benzene ring. Both, transferences of charge and of spin density are carried out in this negatively charged complex. Thus, complicated magnetic patterns start to appear on these small TM-benzene complexes. Electron ionization decreases the multiplicity for FeþC6H6 (M ¼ 2) and CoþC6H6 (M ¼ 3); whereas electron addition increases the M value for FeC6H6- (M ¼ 4) and decreases the one for CoC6H6- (M ¼ 3). As expected, doublet states were identified for the cation and anion of the nickel benzene complexes. This M11L spin-state assignment is in accord with that obtained by

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Fig. 1. M11L ground states of neutral and charged FeC6H6, CoC6H6 and NiC6H6 complexes. Some distances, in Å, NBO charges in electrons (e) for the metal and ligands, and the coordination (h) are shown.

means of BPW91-D2; differences were found in FeþC6H6 and CoC6H6, where M11L indicates doublet and quartet, whereas BPW91-D2 assigns quartet and doublet GSs, respectively. See Fig. 1 and SI-1a. Experimental determination of the EA, IR spectra, and magnetic moments will provide valuable information for the appropriate assignment of the GS geometry for these monobenzene metal complexes. Sandwich structures were found for the Fe(C6H6)2, Co(C6H6)2 and Ni(C6H6)2 adducts, the first one posses a high symmetry GS, 3 A1g, and the other two show states, 2A1 and 1A0 , of lower symmetry. Indeed, Fe(C6H6)2 has h6eh6 bonding; whereas distorted sandwich shapes appear in Co(C6H6)2 and Ni(C6H6)2 as they have h6eh2 bonds, which is due to the increased metal-ligand repulsion, produced by the increased number of electrons in Co and Ni and by addition of two benzene molecules; Fig. 3. In these neutral and charged complexes, the benzene ligands are attached on the metal sites in some way to minimize the repulsion and to form a maximum number of metalecarbon bonds. For example, electron addition to the LUMO[ level, shown in Fig. 4, of Fe(C6H6)2 reduces the bonding, to h6eh2, of the Fe(C6H6) 2 anion, yielding an state (2A) of lower symmetry. Although with the same h6eh2 coordination as the neutral, a more open structure is produced in the 1A state of the Co(C6H6) 2 ion. Likewise, electron attachment to Ni(C6H6)2 reduces the bonding, from h6eh2 to h2eh2, of Ni(C6H6) 2; however, a more symmetric state, 2Au, was found for this anion. The h6eh2 or h2eh2 structures of these anions, indicate that repulsion is minimized by putting the benzene p-clouds far away from each other and by increasing the separation between the h2-benzene

ligand and the (rich in electrons) TM atoms. As expected, positively charged species have maximum bonding. In fact, h6eh6 patterns were found on Feþ(C6H6)2 and Coþ(C6H6)2 with the feature that in the former the benzene units have boat shapes and planar forms in the latter. Thus, states of high symmetry, 2B1g and 3A1g, are assigned to these cations. Electron deletion from Ni(C6H6)2 produces a notorious change in the bonding, from h6eh2 to h3eh3, of Niþ(C6H6)2. The more symmetric h3eh3 coordination yields a more symmetric state, 2Bg, for this ion. As seen in Fig. 3, coordination in the di-benzene complexes of nickel tends to be lower than those of iron and cobalt. This may due that the 3d orbitals in nickel are almost full; the nickel atom needs less amount of electrons to fill its valence layer, thus few number of bonds are formed. Below will be discussed the relation between coordination and metaleligand binding energies. Referred to the mono-benzene complexes, Fe(C6H6)2 and Ni(C6H6)2 preserve their spin state, triplet and singlet, respectively. Spin quenching, from quartet to doublet, was obtained for  Co(C6H6)2. Spin reductions occur also on Fe(C6H6) 2 and Co(C6H6)2 , from M ¼ 4 and 3 to 2 and 1, respectively; while a doublet was found for the Ni(C6H6) 2 anion. As seen in Fig. SI-3, the spin densities are mainly located on the TM atoms. The exception is just 2 2 Ni(C6H6) coordination, where the spin is 2 , presenting h eh entirely moved from the metal towards the benzene rings. Note also that, as FeC6H 6 , an small anti-ferromagnetic coupling takes place also in the Fe(C6H6) 2 anion. That is, complicated spin distributions are presented by the negatively charged iron and cobalt dibenzene complexes. Further, doublet, triplet, and doublet were

R. Flores, M. Castro / Journal of Molecular Structure 1125 (2016) 47e62

Fig. 2. Frontier HOMO and LUMO molecular orbitals of FeC6H6, CoC6H6 and NiC6H6. Orbital energies appear in eV.

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Fig. 3. M11L/Def2TZVP low-lying states of neutral and charged Fe(C6H6)2, Co(C6H6)2 and Ni(C6H6)2 adducts. Some distances, in Å, NBO charges in electrons (e) for the metal and ligands, and the coordination (h) are indicated.

found for the Feþ(C6H6)2, Coþ(C6H6)2 and Niþ(C6H6)2 ions, with the peculiarity that the SD’s, though mainly located on the TM atoms, present some signatures on the two benzene rings, which is more clearly seen on the Coþ(C6H6)2 cation. The M11L spin-state location for these TM(C6H6)2 complexes is similar to that found using BPW91-D2; see Fig. SI-4. Key values of the NBO atomic charges of TM(C6H6)1,2 species are shown in Figs. 1 and 3. Electron detachment is principally done from the metal atoms in TM(C6H6)1, as seen in Fig. 1a, d, and g large amounts of positive charge resides on the Fe, Co, and Ni sites of the respective cations. As shown in Fig. 3a, d and g, this behavior is different on TM(C6H6)þ 2 ; in these ions the Ni site has large positive charge (þ0.60e), it decreases in Co (þ0.24e) and it is negative on the Fe (0.21e) site. In the TMC6H6 anions, the added electron is

mainly stabilized on the metal sites; Fig. 1c, f, and i. A different charge distribution was found in the TM(C6H6)2 anions, where the extra electron is mainly stabilized in the less coordinated benzene rings; for instance, large negative charges of 0.58, 0.56, and 0.62e were found for the h2 bonded benzene molecules in Fe(C6H6)2, Co(C6H6)2 and Ni(C6H6)2; Fig. 3c, f, and i. In the neutral TMC6H6 complexes, some small metal-to-benzene transferences of electrons are done; whereas an uneven charge distribution was found in TM(C6H6)2. For example, as seen Fig. 3, in Co(C6H6)2 and Ni(C6H6)2, small positive charges (þ0.16 and þ 0.15e) remains on the Co and Ni sites and charge neutrality is mainly completed by the h2 benzene molecules, as they have negative charges of 0.19 and 0.20e, respectively; very small positive charges appear on the h6 ligands. In Fe(C6H6)2 the Fe site is

R. Flores, M. Castro / Journal of Molecular Structure 1125 (2016) 47e62

Fig. 4. Frontier HOMO and LUMO molecular orbitals of Fe(C6H6)2, Co(C6H6)2 and Ni(C6H6)2. Orbital energies appear in eV.

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negatively charged (0.14e) and the two ligands are equally charged (þ0.07e). The benzene molecule has a negative EA, thus it was expected that it would transfer negative charge to the metal atoms. But, as discussed above, the NBO analysis for the neutral clusters reveal that some benzene moieties have the capacity to partially absorb electrons from the metal atoms. 3.2. Binding energies of the TM(C6H6)1,2 TM ¼ Fe, Co, and Ni, species Attempts to obtain the D0, EA, and IE of TM(C6H6)1 and TM(C6H6)2, TM ¼ Fe, Co, and Ni have been done by several groups [1,7,30,31]. It was recognized that an accurate determination of such properties poses a challenge for the experimental and theoretical methods; despite their relatively small size. In a first step we will compare our findings with reported experimental and theoretical results. This will allow to know if the chosen methods are suitable for an accurate study of such complexes. Table 1 contains the estimated D0s for the mono and di-benzene species and for the (benzene)2 dimer. Pople, 6-311þþG(2d,2p), and Ahlrichs, Def2TZVP, basis sets were used for the chosen functionals. It was found that BPW91eD2, either with 6e311þþG(2d,2p) or Def2TZVP basis sets, yields considerable overestimation for D0, either for neutral and charged complexes; Table SI-1. Whereas M11L coupled to the Def2TZVP basis sets, produces D0’s that in some cases are very near to the experimental results. Both BPW91eD2 and M11L methods as well as the experimental results indicate that the D0’s for FeC6H6 and NiC6H6 are clearly bigger than that of CoC6H6. Remarkably, M11L/Def2TZVP gives a D0(0.23 eV) which is near to the proposed experimental value (0.34 eV) by Jena et al. [31]; Table 1. The small binding energy of CoC6H6, complicating its experimental and theoretical determinations, is consistent with its low h2 coordination, as referred to the h6 patterns of FeC6H6 and NiC6H6; Fig. 1. Note that the experimental D0 values shown in Table 1 for the neutral TM(C6H6)1,2 species [31], takes as input the measured D0’s for the TM(C6H6)þ1 1,2 ions by Armentrout et al. [7] and corrections were done for the experimental IEs of the involved neutral complexes, see Reference 31 for more details. Also the M11L D0 values for NiC6H6 are nearer to the experiment than the BPW91-D2 ones; Table SI-1. Specifically, with both basis sets M11L yields a D0 for NiC6H6 that falls in the experimental range. Note that for CoC6H6 and NiC6H6, small D0 improvements, 0.10 and 0.04 eV, were obtained from M11L/6-311þþG(2d,2p) to M11L/Def2TZVP. This is supported on the fact that Def2TZVP is near to the basis set limit for any functional [22]. Small changes appear also for the other species; Table SI-1. The estimated D0 for Co(C6H6)2 is bigger than those of Fe(C6H6)2 and Ni(C6H6)2; which is the opposite behavior as that for the monobenzene species. Roughly, this may be partially accounted by the more open structure of Co(C6H6)2, minimizing the repulsion effects, and by its charge distribution, promoting the attraction between Coþ0.16 and benzene B0.20. Similar structural and electronic features appear on Ni(C6H6)2, but from Co to Ni the added electron increases the repulsion. Large repulsion between the p- and 3delectrons may appear also on the compact geometry of Fe(C6H6)2, that could not be entirely suppressed by the charge distribution on the Fe0.14 and benzeneþ0.07 moieties. See Fig. 3. Note that only the D0 of Co(C6H6)2 is known, which is underestimated by both BPW91-D2 and M11L methods. In general, from the mono-to the di-benzene complexes an enhancement of the binding energy is observed. For example, M11L/Def2TZVP shows that the D0 of CoC6H6 is quite small, 0.23 eV, whereas the D0 of Co(C6H6)2, 1.49 eV, is bigger by a factor of 6.50. This is in accord with the experiment [31], yielding an increase factor of 5.0. BPW91-D2 yields smaller

factors, z 1.20, for the D0 of the Co(C6H6)2 adduct. Likewise, referred to those of the one-benzene clusters, M11L/Def2TZVP gives a D0 increase of 1.19 for Ni(C6H6)2 and a decrease, 0.65, for Fe(C6H6)2. BPW91-D2 does not renders an increase for the D0 of the nickel and iron di-benzene complexes; see Table 1. Comparisons of the D0 results for the positively charged species with the experimental results, determined by Armentrout et al. [7] produces similar tendencies as those quoted above for the neutrals. That is, each M11L D0 value for FeþC6H6, CoþC6H6 and NiþC6H6 is in near agreement with the experiment, notably the last two. While BPW91-D2 overestimates somehow this property; see Table 1. Despite such accuracy, M11L does not mimic the D0(CoþC6H6) > D0(NiþC6H6) > D0(FeþC6H6) experimental order [7]. Though its D0’s overestimations, BPW91-D2 reproduce such trend [7]; Table 1. However, on the di-benzene cations, both levels of theory are in concordance with the experimental order: D0(Feþ(C6H6)2) > D0(Coþ(C6H6)2) > D0(Niþ(C6H6)2), where M11L yields also more accuracy. Note the h6eh6 geometry of Feþ(C6H6)2 with shorter FeeC bonds and where the charge distribution renders attraction between iron and benzene rings. Larger CoeC distances occur in Coþ(C6H6)2; while Niþ(C6H6)2 has low bonding; Fig. 3. These features may account for the D0 order of these cations. From TMþC6H6 to TMþ(C6H6)2, TM ¼ Fe, Co, and Ni the experimental D0’s determined by Armentrout et al. [7] show D0(TMþC6H6)/D0(TMþ(C6H6)2) factors of 0.90, 0.65, and 0.60, respectively. Showing factors of 1.03, 0.80, and 0.56 for such changes, M11L partially reproduces such tendency. Whereas BPW91eD2, yielding factors of 0.93, 0.62, and 0.60, is in concordance with the experiment. From FeþC6H6 to Feþ(C6H6)2 the D0 reduction is small; while larger decreases occur for Co and Ni. The D0(TMþC6H6) > D0(TMþ(C6H6)2) behavior is opposite to the one found for the neutral species, quoted above. Roughly it means that the positive charge, mainly lying on the metal atom in TMþC6H6, has a bigger ability for the electrostatic attraction of the p-electrons from the benzene ring, Fig. 1. Indeed, FeþC6H6, CoþC6H6, and NiþC6H6 have h6 bonding and high positive charges on the metal atom. In the TMþ(C6H6)2 adducts the charge distributions and the coordination patterns are more intricate. From NiþC6H6 to Niþ(C6H6)2 the huge D0 reduction may be accounted the by low coordination, h3, of the added molecule and by the reduction of the positive charge on the Ni site, from þ0.86 to þ0.60 e. Likewise, from CoþC6H6 to Coþ(C6H6)2 the h6 bonding is preserved but the positive charge on the cobalt atom is considerably reduced, from þ0.86 to þ0.24e and the CoeC distances are clearly larger. In Feþ(C6H6)2, with a small D0 reduction, keeps the h6 bond and the Fe site has small negative charge. As will be shown bellow, the HOMO levels of Co(C6H6)2 and Ni(C6H6)2 have bonding character. That is, electron deletion from these orbitals will decrease the binding energy for the respective ions. This is consistent with the observed huge D0 reduction for Coþ(C6H6)2 and Niþ(C6H6)2. Since the HOMO[ of Fe(C6H6)2 is non-bonding, electron deletion produces an small D0 change for Feþ(C6H6)2, as it was found experimentally. The DFT results shows the D0 (FeC6H6-) > D0 (CoC6H6-) > D0 (NiC6H6-) order, which is in line with the increased repulsion, since number of electrons increases, along the Fe, Co, Ni triad; Table 1. Roughly, the D0’s for these anions are smaller than those of their respective neutral and cations. A different order was found for the di-benzene anions: D0 (Co(C6H6)2-) > D0 (Fe(C6H6)2-) > D0 (Ni(C6H6)2-). Remarkably, M11L shows that the D0 of Co(C6H6)2 is larger than those of Co(C6H6)2 and Coþ(C6H6)2, whereas the BPW91-D2 results indicates that the D0 of Co(C6H6)2 and Coþ(C6H6)2 are comparable. Thus, the Co(C6H6)2 adduct posses marked ability for the absorption and stability of an extra electron. Two electronic details: a closeeshell system and the 18e rule accounts for the stability of this complex. This is in line also with its

R. Flores, M. Castro / Journal of Molecular Structure 1125 (2016) 47e62

EA, discussed in section 3.4. Differently, the D0 of Fe(C6H6)2 is bigger than that of Fe(C6H6)2 but smaller than the D0 of the cation. While the D0 of Ni(C6H6)2 is clearly smaller than those of the neutral, Ni(C6H6)2, and cation, Niþ(C6H6)2, at both levels of theory; Table 1. 3.3. Ionization energies of the TM(C6H6)1,2 TM ¼ Fe, Co, and Ni, complexes The M11L/Def2TZVP and BPW91-D2/6-311þþG(2d,2p) levels of theory produce adiabatic IEs, for the TM(C6H6)1,2 species, which are in good concordance with the experimental values [1,33]. The experimental results suggest the Fe(C6H6) > Ni(C6H6) > Co(C6H6) order for the ionization energy, which is fulfilled by the M11L results shown in Table 2. Whereas BPW91-D2 yields a biggest IE for NiC6H6 (6.51 eV), followed by FeC6H6 (6.46 eV) and CoC6H6 (5.80 eV). As seen in Fig. 1, electron deletion from the TMC6H6 species produces significant structural relaxation for the TMþC6H6 ions. For example, from FeC6H6 to FeþC6H6 the h6 bonding is preserved with the peculiarity that this ion has shortest FeeC distances (2.007 Å), as referred to those of CoþC6H6 (2.094 Å) and NiþC6H6 (2.097 Å). Thus, the structure of FeþC6H6 implies huge stability, being consistent with the highest IE of FeC6H6. From CoC6H6 to CoþC6H6, the strong change in the metaleligand bonding, moved from h2 to h6, producing high stability for the cation, partially accounts for the relatively high IE of this complex. Both, NiC6H6 and NiþC6H6 show h6 pattern, the stronger metaleligand bonding in the ion is reflected in the deviation from planarity of the benzene ring, note that in the cation the positive charge on the Ni site is bigger than that in the neutral. Thus, the high stability of the ion adds to the high IE of NiC6H6. The experiment yields the Fe(C6H6)2 < Co(C6H6)2 < Ni(C6H6)2 order for the IE of the dibenzene species, which is different from that of the one-benzene clusters, as Ni and Fe are in different places. Both levels of theory, M11L and BPW91eD2, are in agreement with this observed order, which is similar to the one of the isolated Fe < Co < Ni atoms, where the increase of the positive (Z) charge along the triad governs such order. The HOMO[ of Fe(C6H6)2, shown in Fig. 4, is non-bonding, and with small 3d signatures on the iron atom, meaning a low ionization energy from such orbital. Likewise, the HOMOY of Co(C6H6)2, from which the electron is deleted, shows some delocalization but its bigger signatures on the metal suggest a larger IE than in the iron complex. Note that Ni(C6H6)2 is a close shell system, M ¼ 1, where the HOMO level, presenting also signatures on the Ni atom, has a deeper orbital energy (4.13 eV) than those of the Co (3.90 eV) and Fe (3.25 eV) di-benzene species. These electronic and energetic features may account for the larger IE of the Ni(C6H6)2 compound. Besides, in the Niþ(C6H6)2 adduct appears: a)

55

h3eh3 bonding, b) short NieC distances (2.040e2.198 Å), c) a bigger positive charge (þ0.59 e) on the nickel atom than that (þ0.15 e) of the neutral; and c) the orientation of the benzene rings diminishes the repulsion; Fig. 3. These structural and electronic features contribute to the stability of Niþ(C6H6)2 as it is shown by its larger IE. From Co(C6H6)2 to Coþ(C6H6)2 the coordination is increased since it is moved from h6eh3 to h6eh6, signifying an enhanced stability, which is reflected in the relatively high IE for the Co(C6H6)2 adduct. An smaller difference of total energies was found between Fe(C6H6)2 and Feþ(C6H6)2 since both have h6eh6 bonding with similar FeeC distances. The fact that in Feþ(C6H6)2 appear a negative charge on the Fe site adds also to the smaller IE of Fe(C6H6)2, compared to those of Co(C6H6)2 and Ni(C6H6)2. Overall, experiment and theory reveal that the addition of one benzene molecule to TMþC6H6 (TM ¼ Fe, Co, Ni), produce considerable structural and electronic relaxation on the TMþ(C6H6)2 adducts. 3.4. Electron affinities of the TM(C6H6)1,2 TM ¼ Fe, Co, and Ni, compounds It is interesting to search if the TM(C6H6)1 and TM(C6H6)2 systems, rich in 3d- and p-electrons, are able to absorb and to stabilize an extra added electron, despite the expected increased repulsion. Indeed, results for the EA of the TM(C6H6)1,2 complexes is scarce, which may be due to the low values of this property, as it is indicated by the reported experimental and theoretical values, see Table 3. From FeC6H6- to FeC6H6- the attached electron is principally stabilized on the benzene ring (0.62 e) and with larger FeeC distances, the h6 coordination was preserved. The estimated (M11L) EA is low; whereas BPW91eD2 yields an EA, 0.47 eV, matching the experiment, 0.46 ± 0.10 eV [36]; Table 3. Note the non-bonding character of the LUMO[ level of FeC6H6, where the electron is added; Fig. 2. In CoC6H6 and NiC6H6, having h2 (CoeC) and h6 (NieC) bonding, respectively, electron attachment produces strong relaxation because the three-dimensional (3D) structures are moved into 2D ones, where the metal atoms are absorbed on two hydrogen sites. The interaction of two CdeHdþ dipoles with the Co or Ni anions may stabilize such 2D structures. Effectively, in  CoC6H 6 and NiC6H6 , the added electron mainly resides on the metal atoms; see Fig. 1. A quite low value (0.27 eV) was found for the EA of CoC6H6 at the BPW91-D2 level of theory, but M11L yields a much bigger EA (1.04 eV). The M11L EA of NiC6H6 is also a positive value (0.31 eV). That is, the M11 level of theory predicts that one electron attachment on CoC6H6 and NiC6H6 is feasible. The added electron is stabilized by the Cod/Hdþ and Nid/Hdþ interactions. The EAs, 0.31 and 1.04 eV, could be measured experimentally. BPW91/6-311þþG(2d,2p) shows h6 and h2 NieC coordination for NiC6H6 and NiC6H6-, respectively; the total energy difference

Table 2 Ionization energies of TM(C6H6)1,2, (TM ¼ Fe, Co, Ni) complexes, in eV. BPW91-D2/6-311þþG(2d,2p)

M11L/Def2TZVP

Fe(C6H6) Co(C6H6) Ni(C6H6)

6.46 5.80 6.46

6.34 5.37 5.76

Fe(C6H6)2 Co(C6H6)2 Ni(C6H6)2

5.10 5.27 6.02

4.82 5.00 5.46

Fe(C6H6)3 Co(C6H6)3 Ni(C6H6)3

4.88 5.15 5.94

4.65 4.89 5.34

a b

Reference [33]. Reference [1].

Theorya

Experimentb

6.17

>6.42 5.55 ± 0.04 5.99e6.42

5.68

5.18 ± 0.05 5.53 ± 0.03 5.86 ± 0.03

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R. Flores, M. Castro / Journal of Molecular Structure 1125 (2016) 47e62

Table 3 Electron affinities of TM(C6H6)1,2,3 (TM ¼ Fe, Co, Ni) complexes, in eV. BPW91-D2/6-311þþG(2d,2p) Fe(C6H6) Co(C6H6) Ni(C6H6)

M11L/Def2TZVP

0.47 0.27 0.15

0.13 1.04 0.31

Fe(C6H6)2 Co(C6H6)2 Ni(C6H6)2

0.67 0.75 - 0.05

0.42 0.35 0.06

Fe(C6H6)3 Co(C6H6)3 Ni(C6H6)3

0.84 0.91 0.47

0.58 0.45 0.29

a b c

Theorya

Experiment

0.35

0.46 ± 0.10c e e

0.39

0.78 ± 0.10c 0.50 ± 0.10b e

Reference [34]. Reference [30]. Reference [36].

between these neutral and charged species gives a small EA, of 0.15 eV. Without dispersion correction and different basis sets, BPW91 gives an EA of 0.35 eV for NiC6H6 [34]. The very low EA of these complexes complicate their experimental and theoretical determination. The experimental measurements of the EA, which is a complicated task since such property may have very low values, will confirm or deny the planar structure of CoC6H6- and NiC6H6-. Both levels of theory assign a negative EA (0.05 and 0.06 eV) to Ni(C6H6)2, which is in accord with a reported value, 0.39 eV, by Rao and Jena [34]; employing the BPW91/6-311þþG(d,p) method. The obtained geometry by these authors for the sandwich Ni(C6H6)2 complex, having h6eh2 coordination, see Fig. 1 of Reference 34, is similar to the one found in the present work, Fig. 2h. These EA results are consistent with the fact that it is not possible to observe Ni(C6H6) 2 in the mass spectra of nickelebenzene cluster anions [37]. The strong repulsion may avoid the formation of such ion. Note also the nonbonding nature of the LUMO of Ni(C6H6)2, where the electron is added, Fig. 4. Bowen et al. have observed the Co(C6H6) 2 ion, the experiment yields an EA of 0.50 ± 0.10 eV [30]. The theoretical results show that electron addition kept the h6eh2 coordination in the Co(C6H6) 2 ion, which having shorter CoeC distances than those of the neutral parent, Fig. 2d, satisfies the 18 e rule. Moreover, the LUMO[ of Co(C6H6)2, where the electron is added, is of bonding character, see Fig. 4 These structural and electronic features account for the observed stability of the dibenzene cobalt anion. Indeed, M11L indicates an EA of 0.35 eV for Co(C6H6)2, differing by 0.15 eV from the experiment. An overestimation of 0.25 eV was found for this property at the BPW91-D2 level of theory. Thus, referred to the experiment, M11L has a better performance for the EA of Co(C6H6)2. However, for Fe(C6H6)2 BPW91-D2 produces and EA, 0.67 eV, which in better agreement with the experiment, 0.78 ± 0.10 eV [36] that the M11L value, 0.42 eV; see Table 3. Note that electron addition to Fe(C6H6)2 produces large structural relaxation as the h6eh6 bonding turns into h6eh2 in Fe(C6H6) 2 . Thus, the relatively good agreement between theory and experiment provides confidence in the identified lowest energy state of Fe(C6H6)2. M11L shows a decrease of the EA from the Fe to Co to Ni di-benzene species; which is in line with the increased number of electrons along triad, producing an increased repulsion. Except for a maximum in Co(C6H6)2, BPW91-D2 shows a similar behavior. 3.5. Structural properties of TM(C6H6)3, TM ¼ Fe, Co, and Ni Addition of one benzene molecule to the neutral low-lying states of TM(C6H6)2 (TM ¼ Fe, Co, and Ni) produce the M11L GS structures for the corresponding TM(C6H6)3 systems shown in

Fig. 5. Some isomers lying near in total energy to the GS are reported also for each tri-benzene metal system. Several absorption modes, of different multiplicities, were inspected for each m ¼ 2 to 3 growing case. 1) The added molecule was approached in a perpendicular manner to one benzene ring of TM(C6H6)2. 2) The external ring approaches in a parallel way to an internal ligand. These modes, involving the interaction of two benzene rings, mimics the tilted T-shape and PD structures of the benzene dimmer. 3) The benzene molecule was placed initially on a lateral side of the TM(C6H6)2 sandwich motifs, bridging the two internal rings. These candidates may produce, through relaxation, twoelayer isomers. 4) Also were tried one-layer inputs, where the three benzene units are directly attached to the metal. The low-lying states obtained are discussed below. A two-layer distorted structure Fe-IIIa, shown in Fig. 5a, was found as the GS for Fe(C6H6)3. In this structure, the h6eh6 bonding in the Fe(C6H6)2 subcluster is preserved, whereas the third benzene molecule, lying in the external region, is absorbed by means of CeH/p interactions on the B ligand. The distance between the centers of the B and C rings (4.98 Å) is similar to that of the titled Tshape (4.96 Å) benzene dimmer. Thus, vdW forces account for the binding of the outer moiety in Fe(C6H6)3. Note the attractive interaction of the Hdbþ atom (having partial positive charge) of B  with the nearest carbon atoms (Cdext , having partial negative charges) of the benzene external C molecule (Fig. 5a). The estimated D0, 0.12 eV, for the C molecule is considerably smaller than  the D0 for Fe(C6H6)2. The Hb atom forms three Hdbþ/Cdext contacts, which have distances (2.97e3.05 Å) similar to those (2.96e3.04 Å) of the tT-shape isomer of Bz2; they are marked by dashed lines in the GS of Fe(C6H6)3. In the structure Fe-IIIa, the distances between the iron atom and the carbon sites of the A and B rings, are approximately the same than those for the GS of the di-benzene sandwich Fe(C6H6)2 complex, Fig. 3b. Thus, slight structural changes are produced on the Fe(C6H6)2 core by the C unit, which is line with its small binding energy. Another isomer Fe-IIIb, where the C molecule is adsorbed in a PD way on the A ring was found negligible near in energy to the Fe-IIIa GS. Similarly, the Fe-IIIc motif, where the external C molecule bridges the two internal A and B ligands, was found also near in energy to the GS. The isomer where the C ligand seats in a tT-shape way on B was found at 1.2 kcal/mol from the GS. These results seems to indicate that the external C molecule has some mobility around the m ¼ 2 core. At the M11L level of theory, the one layer structure was located at 10.3 kcal/mol from the IIIa GS. BPW91-D2 yields also a two-layer structure, Fe-IIIa-D2 in Fig. SI-5a, for the GS of Fe(C6H6)3. Note that Fe-IIIa-D2 GS structure is more symmetrical than the one obtained, Fe-IIIa GS, using M11L. However, the BPW91-D2 estimated

R. Flores, M. Castro / Journal of Molecular Structure 1125 (2016) 47e62

57

Fig. 5. Identified M11L low-lying states of Fe(C6H6)3, Co(C6H6)3 and Ni(C6H6)3. Some distances, in Å, NBO charges in electrons (e) for the metal and ligands, and the coordination (h) are indicated.

Table 4 Binding energies, D0, for the TM(C6H6)3, TM ¼ Fe, Co, and Ni ground states. Also are indicated the multiplicities, M, and the 〈S2〉 values. M

〈S2〉

M11L/Def2TZVP (eV)

BPW91-D2 /6-311þþG(2d,2p) (eV)

Fe(C6H6)3 Feþ(C6H6)3 Fe(C6H6)3

3 2 2

2.097 0.768 0.809

0.12 0.29 0.27

0.10 0.32 0.27

Co(C6H6)3 Coþ(C6H6)3 Co(C6H6)3

2 3 1

0.789 2.025 e

0.16 0.26 0.25

0.17 0.29 0.33

Ni(C6H6)3 Niþ(C6H6)3 Ni(C6H6)3

1 2 2

e 0.766 0.757

0.13 0.24 0.48

0.31a (0.14)b 0.39a (0.30)b 0.83a

a b

One-layer isomers. Two-layer isomers.

D0 value 0.10 eV (2.3 kcal/mol) for the adsorption of C is near to the M11L D0 (0.12 eV); Table 4. Several BPW91-D2 isomers of Fe(C6H6)3 are shown in Fig. SI-5. The BPW91-D2 method locates the one-layer motif of Fe(C6H6)3 nearer in energy, þ3.4 kcal/mol, to the two-layer GS, than M11L. Both BPW91-D2 and M11L one-layer geometries are similar. A two-layer structure, Co-IIIa shown in Fig. 5e, was determined also for the GS of Co(C6H6)3. As in Co(C6H6)2, Fig. 3e, with similar

CoeC distances the h6eh2 coordination is kept in Co-IIIa; where the external molecule is more favorably absorbed on the h6 ligand through the interaction of the CdeHdaþ dipole with the p-electrons  of C. In Co-IIIa, three CdeHdaþ/Cdext contacts are formed, they have shorter distances, 2.853e3.010 Å, that those of Fe-IIIa. The attraction of Codþ and one of the carbon atoms of C, separated by 3.75 Å, adds also to the binding of C. A D0 of 0.16 eV was obtained for the GS of Co(C6H6)3, this value is bigger than those of the iron and nickel

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tri-benzene complexes. The isomer Co-IIIb, where the C molecule is attached, in a parallel fashion, on the h6 coordinated A ligand was located near in energy, þ1.8 kcal/mol, from the GS. A titled T-shape adsorption of C on the h6 ligand produces the Co-IIIc isomer, which lies at higher energy (2.5 kcal/mol) from the Co-IIIa GS. The BPW91D2 approach yields also a two-layer motif with M ¼ 2, as M11L, for the GS of Co(C6H6)3. In the Co-IIIa-D2 structure, Fig. SI-6a, the external C molecule is attached, on the h6 bonded A ring, through  six CdeHdaþ/Cdext contacts, instead of three as in Co-IIIa. Nevertheless, such larger amount of contacts produces a slightly larger BPW91-D2 D0 value (0.17 eV) for the adsorption of C. Some BPW91D2 Co(C6H6)3 isomers, lying near in energy to the Co-IIIa-D2 GS are shown in Fig. SI-6. Three two-layer motifs lying in a sharp energy range, shown in Fig. 5, emerged for Ni(C6H6)3. Forming three and two  CdeHdþ/Cdext contacts with A and B, respectively, the external C molecule bridges the internal benzene molecules in the labeled GS structure Ni-IIIa. These dipoleep interactions produce a small binding energy, of 0.13 eV, for the adsorbed moiety. The isomer NiIIIb where the outer C molecule is attached on the Ni(C6H6)2 core by means of pep stacking interactions is degenerated with Ni-IIIa. The tilted T-shape isomer Ni-IIIc lies also negligible near in total energy. This M11L results, differ somehow from those obtained using BPW91-D2 because at this level of theory a one-layer structure, NiIIIa-D2 shown in Fig. SI-7, was determined as the GS; whereas two two-layer isomers are located relatively near in energy, about 4 kcal/mol, to the GS. Consistently with the direct bonding of the C molecule with the nickel atom, a bigger D0, 7.1 kcal/mol, was obtained. Several BPW91-D2 isomers of Ni(C6H6)3 lying within less than 6 kcal/mol are shown in Fig. SI-7. 3.6. Low-lying states of Feþ(C6H6)3, Coþ(C6H6)3, and Niþ(C6H6)3 Electron detachment from Fe-IIIa produces a two-layer GS, Feþ IIIaþ in Fig. 6a, for Fe(C6H6)þ 3 . In the Fe-IIIa structure the C molecule, bridging the A and B ligands, is more strongly bonded on the Fe(C6H6)þ 2 subcluster since the D0, 6.6 kcal/mol, is bigger than that of the neutral parent. This D0 result is clearly smaller than that of þ the Fe(C6H6)þ 2 GS, confirming the solvent behavior in Fe(C6H6)3 . In þ the Fe-IIIa GS, the huge positive charge (þ0.60 e) on the A and B units enhances the CeHb, CeHb and CeHa dipole moments, yielding bigger attractive interactions with the peelectrons of the C moiety. For example, the C0.16eHþ0.27 group, forming four contacts b with C, has larger bond length (1.090 Å) and charge polarization than the C0.15eHþ0.25 groups, with distances of 1.088 Å, not b forming contacts. The parallel two-layer Fe-IIIbþ isomer was located very near in energy, at 2.2 kcal/mol, to the GS. Whereas the one-layer structure Fe-IIIcþ, shown in Fig. 6, was determined at about 15.2 kcal/mol. From Fe-IIIa to Fe-IIIaþ the IE (4.65 eV) of Fe(C6H6)3 is smaller than those of Fe(C6H6)2 and FeC6H6, indicating that the IE decreases as the number of benzene molecules in the complex increases, Table 2. The BPW91-D2 method finds also the bridge (Fe-IIIaþ-D2) and parallel (Fe-IIIbþ-D2) isomers, shown in Fig. SI-8, as the low-lying states of Fe(C6H6)þ 3 . At this level of theory these isomers have an energy gap of 1.7 kcal/mol. The one-layer isomer was determined at a higher energy, 15.9 kcal/mol. Thus, the BPW91-D2 order for the Fe(C6H6)þ 3 states is similar to the one obtained by means of M11L. However, the Fe-IIIaþ-D2 GS structure is more symmetrical and shorter CeH/C contacts are formed. These features may account for the bigger D0, 0.32 eV, obtained with BPW91-D2; see Table 4. The BPW91-D2 IE (4.88 eV) of Fe(C6H6)3 is in accord with the M11L value, Table 2. 6 In the Co(C6H6)þ 3 GS, shown in Fig. 6d, two benzene rings are h coordinated and the third one is attached on the B ring by means of

six CeHb/C contacts, which contributes to a D0 of 0.26 eV. The B and C pair in Co-IIIaþ closely resemble the tilted T-shape motif of the isolated benzene dimmer. Referred to D0 of Bz2 (0.059 eV), the larger D0 in Co-IIIaþ is due to the induced polarization on the CeHb group of B. Another h2eh2 (Co-IIIbþ) and parallel h6eh6 (Co-IIIcþ) two-layer isomers are near in energy, at 0.8 and 1.5 kcal/mol, respectively. The one-layer motif lies at a higher energy, 8.7 kcal/ þ mol. In the BPW91-D2 GS of Co(C6H6)þ 3 , Co-IIIa -D2 in Fig. SI-9, the external C molecule is also mainly attached on one of the h6 rings through six CeHa/C contacts, other link is formed with B, yielding a few bigger D0, 0.29 eV, than M11L. Except by the fact that the M11L Co-IIIbþ motif was not found using BPW91-D2, these methods produce a similar order for the isomers of Co(C6H6)þ 3 . That is, these levels of theory agree that two-layer structures appear as the low-lying, in triplet (M ¼ 3) spin-states, of the tri-benzenecobalt cation. See Fig. 6d and SIe9. They also agree in that the IE of Co(C6H6)3 is smaller than those of the mono- and di-benzenecobalt complexes; see Table 2. In the GS of Ni(C6H6)þ 3 the external C molecule, forming two CeHa,b/C links with each one, bridges the internal A and B rings, producing a more symmetrical structure than the GS of Ni(C6H6)3. Indeed, in the Ni-IIIaþ GS, Fig. 6g, appears an h3eh3 coordination in the Ni(C6H6)þ 2 subcluster, whereas in the neutral Ni(C6H6)3 GS, the A and B units are unevenly h6eh2 bonded with the metal. Note also the more distorted geometry of the Ni(C6H6)þ 2 GS. However, at the M11L level of theory, the D0 of Ni(C6H6)þ 3 , 0.24 eV, is smaller than þ those of Fe(C6H6)þ 3 and Co(C6H6)3 . Contrarily, the IE (5.34) of Ni(C6H6)3, is larger than those of Fe(C6H6)3 and Co(C6H6)3; see Table 4. Therefore, the IE(Fe(C6H6)3) < IE(Co(C6H6)3) < IE(Ni(C6H6)3) and D0(Feþ(C6H6)3)>D0(Coþ(C6H6)3)> D0(Niþ(C6H6)3) orders are similar to those of the TM(C6H6)2, TM ¼ Fe, Co and Ni, complexes, which is accounted by the small perturbation that the third added benzene molecule produces on these m ¼ 2 sub-clusters. Electron deletion from the neutral Ni-IIId one-layer structure produces, through relaxation, the Ni-IIIbþ structure, shown in Fig. 6h, where the C moiety is absorbed on B by means of dipoleep interactions. In this isomers appear electrostatic attraction between C and the metal atom, which is promoted by the relatively short separations (2.793e2.831 Å) of two carbon atoms (which have partial negative charges) from the nickel site (which has a large positive charge). That is, though there are not formed covalent bonds between the nickel atom and C, Ni-IIIbþ may be considered as a one-layer isomer. More appropriately, in Ni-IIIbþ the C moiety is in the border of the first and second coordination layer. This isomer is very near in energy to the Ni-IIIaþ two-layer GS. The parallel Ni-IIIcþ motif is near also. BPW91-D2 indicates a one-layer isomer for the GS of Ni(C6H6)þ 3, see Fig. 4a of reference 9, whereas bridge and parallel two-layer isomers are near in energy, 2.0 and 3.0 kcal/mol, to the GS [9]. For the one-layer GS BPW91-D2 yields a D0 of 0.39 eV, and for the two-layer isomer the D0 is of 0.30. Both M11L and BPW91-D2 D0 estimations for the two-layer isomers of Ni(C6H6)þ 3 (0.24 and 0.30 eV) are consistent with the experimental upper limit D0 (Ni(C6H6)þ 3 ) < (0.39 eV) [8]. Note that the BPW91-D2 D0 for the onelayer GS is close also to this limit. 3.7. Lowest energy states of [Fe(C6H6)3], [Co(C6H6)3], and [Ni(C6H6)3] Several two-layer states lying in a sharp energy range, < 1 kcal/ mol, were found for Fe(C6H6) 3 . They are reported in Fig. 7. In FeIIIa, labeled as the GS, the external molecule C is absorbed on B by means of dipoleep interactions furnished between one CeH group of C and the peelectrons of B. The average, 2.787 Å, of the C-Hc/C links in Fe-IIIa is shorter than that, 2.974 Å, of neutral Fe-IIIa,

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Fig. 6. Located M11L/Def2TZVP lowest energy states of Feþ(C6H6)3, Coþ(C6H6)3 and Niþ(C6H6)3. Some distances, in Å, NBO charges in electrons (e), for the metal and ligands, and the coordination (h) are indicated.

signifying stronger attractive interaction, despite of the expected increase of repulsion in the anion. Indeed, a larger D0 (0.27 eV) was found for Fe(C6H6) 3 , as referred to that of the neutral, see Table 4. Note that the negative charge is mainly accumulated (- 0.60 e) on the benzene B molecule on which it is seated the external molecule C through its CdeHdcþ dipole. Therefore, this charge distribution makes favorable the enhancement of the binding energy in the tilted T-shape isomer of the Fe(C6H6) 3 anion. Other two bridge isomers, FeIIIb and FeIIIc, were identified also as low-lying states, see Fig. 7. Presenting also a doublet spin-state, the one-layer structure emerges at a higher energy (11.6 kcal/mol). The difference of the total energies between the Fe-IIIa and Fe-IIIa lowest energy states, indicates an EA of 0.58 eV for the Fe(C6H6)3 cluster. This M11L estimation is even larger than the EA for the sandwich di-benzene Fe(C6H6)2 complex, which reveals the capability of Fe(C6H6)3 for the absorption and further stabilization of an extra added electron. The stabilization is done through the network of metal-carbon and dipoleep bonding interactions. The BPW91-D2 method indicates also a titled T-shape for the GS structure of Fe(C6H6) 3 , shown in Fig. SI-10a. The D0 value, 0.27 eV,

and the EA, 0.84 eV, are similar to the M11L estimations. These results confirm the increase of these properties produced by the added electron to the neutral. However, at the BPW91-D2 level of theory, another two layer isomers and the one layer structure are extremely near in energy to the Fe-IIIa-D2 isomer. Both, M11L and BPW91-D2 approaches reveal that the D0 of Fe(C6H6) 3 is smaller than the D0 of the Fe(C6H6)þ 3 cation. The M11L lowest energy states of Co(C6H6) 3 are contained also in a very small energy range. These structures, shown in Fig. 7def, have similar structural patterns as those of Fe(C6H6) 3 . Indeed, in the titled T-shape Co-IIIa isomer the C molecule is bonded on the B ring by means of dipole-p interactions, producing a D0 (0.25 eV), being also bigger that of the neutral Co-IIIa GS (0.16 eV). It is also slightly smaller than the D0 for the GS of the Co(C6H6)þ 3 ion, see Table 4. The difference of the total energies between the Co-IIIa and Co-IIIa lowest energy states, produces an EA of 0.45 eV for the Co(C6H6)3 cluster, which is clearly larger than the EA of Co(C6H6)2, 0.35 eV. It is quoted that the M11L one-layer Co(C6H6) 3 structure emerges at a higher energy, 5.1 kcal/mol. BPW91-D2 locates a one-layer isomer, Co-IIIa-D2 in Fig. SIe11,

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Fig. 7. Determined M11L/Def2TZVP isomers of Fe(C6H6)3, Co(C6H6)3 and Ni(C6H6)3. Some distances, in Å, NBO charges in electrons (e), for the metal and ligands, and the coordination (h) are indicated.

for the GS of Co(C6H6) 3 ; whereas a tilted T-shape structure, CoIIIdeD2, was found near in energy, 1.6 kcal/mol from the GS. This order of states differs somehow from the one found with M11L, where a tT-shape motif defines the GS and the one layer isomer is located at higher energy. However, a two-layer isomer Co-IIIb-D2, is degenerate with Co-IIIa-D2 and another two-layer bridge structure, Co-IIIc-D2, appears also close. Thus, the description of the low-lying states of the Co(C6H6) 3 anion are quite sensitive to the used level of theory, since several one- and two-layer isomers are contained within a small energy range. The BPW91-D2 D0 for the Co-IIIa-D2 isomer, 0.33 eV, is bigger than those of the Co(C6H6)þ 3 and Co(C6H6)3 GS’s, see Table 4. Note that the two-layer Co-IIIb-D2 isomer has a similar D0 value. Subtracting the total energy of the one-layer Co-IIIe-D2 neutral motif, Fig. SI-6e, from

that of the Co-IIIa-D2 GS yields an EA, 0.91 eV, which confirms the particular stability of Co(C6H6) 3 , as this value is bigger than those of the iron and nickel tri-benzene species (using BPW91-D2); see Table 3. A one layer isomer, shown in Fig. 7g, defines the GS of Ni(C6H6) 3, where the benzene rings are h2 coordinated with the metal. Additionally, A is attached on B by means of dipoleep interactions. Note also the A-C pep stacking and the attraction between Nidþ and the Ad, Bd, and Cd molecules. These features may account for the D0 (0.48 eV) of Ni(C6H6) 3 , which is considerably larger than  those of Fe(C6H6) 3 and Co(C6H6)3 and than those of the neutral and cation tri-benzene systems, Table 4. However, the EA (0.29 eV) of  Ni(C6H6)3 is smaller than those of Fe(C6H6) 3 and Co(C6H6)3 , Table 3, which may be related to the low ability of the nickel atom in this

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complex, having more electrons than the iron and cobalt atoms, to contribute to the stabilization of the negative charge. Indeed, in NiIIIa the extra electron is mainly stabilized on the benzene rings;  whereas in Fe(C6H6) 3 and Co(C6H6)3 the electron is delocalized through the (A and B) benzene and metal moieties, see Fig. 7a, d, and g. The two-layer isomers start to appear at higher energies, at 4.5 kcal/mol, signifying that the one-layer isomer Ni-IIIa may principally occur in the synthesis of the Ni(C6H6) 3 anion in the gas phase. The BPW91-D2 results for the Ni(C6H6) 3 anion are in near agreement with the M11L findings. a) A one-layer isomer is the lowest energy state, since the two-layer structures appear at clearly higher energies, see Fig. SI-10. b) The D0 of this anion is larger than  those of Fe(C6H6) 3 and Co(C6H6)3 . In fact, these methods show the   Fe(C6H6) < Co (C H ) < Ni(C H 3 6 6 3 6 6)3 tendency for D0; see Table 4c) The EA of the Ni(C6H6)3 complex is much smaller than those of Fe(C6H6)3 and Co(C6H6)3; Table 3. Thus, M11L and BPW91-D2 assign a one-layer isomer for the (doublet) GS of Ni(C6H6) 3. IVc Vibrational Analysis of Fe(C6H6)m, Co(C6H6)m, and Ni(C6H6)m, m
3, and Density of States for some complexes. For the ground states of the neutral and charged Fe(C6H6)m, Co(C6H6)m, and Ni(C6H6)m, m
3, species, the infrared (IR) spectra was determined under the harmonic approximation. The CeH stretching and finger print regions were analyzed. The former, discussed firstly, is important because the metalebenzene bond formation produce some direct effects on the CeH stretching frequencies. That is, the IR spectrum in this high frequency region provides valuable information on the geometry of the complex, indicating for instance the deviations from planarity of the bonded benzene molecules. The IR spectrum of neutral FeC6H6, CoC6H6 and NiC6H6 present a single resonance band in the CeH stretching region, implying small deviations of planarity for the benzene rings; see Fig. SIe13A. Effectively, FeC6H6 and NiC6H6 present h6 coordination; whereas CoC6H6 shows weak h2 bonding. On the other hand, the IR spectra for the boat structures of FeþC6H6 and NiþC6H6 show doublets in the CeH stretching region, 3162e3169 cm1 and 3167e3162 cm1, respectively; see Fig. 13B. Likewise, the single peak in FeC6H6- is consistent with the h6 bonding of this anion. Whereas the h2 Co/H and Ni/H interactions in the CoC6H6- and NiC6H6- anions is reflected in their more complicated IR spectra in the CeH stretching region; see Figu 13C. The single CeH resonance band for Fe(C6H6)2 reflects its symmetrical h6eh6 coordination. The more involved spectra of Co(C6H6)2 and Ni(C6H6)2 account for their h6eh2 patterns: the strong peaks, at 3143e3157 cm1 for the former and 3142e3157 cm1 for the later, belongs to the h2 molecule and those at 3154 cm1 for Co(C6H6)2 and 3151 cm1 for Ni(C6H6)2, are for the h6 rings, see Fig. SIe14A. Likewise, four CeH bands appear for Feþ(C6H6)2, reflecting the boat shapes of the A and B rings, whereas one strong band emerges for Coþ(C6H6)2 indicating minor dispersion of the CeH distances. The h3eh3 bonding of Niþ(C6H6)2 originates the formation of several CeH bands; (Figs. SIe14B-b and 14A-c). A close relation between structure and IR spectrum is revealed by these results. Remarkably, the IR spectrum of the Fe(C6H6)2, Co(C6H6)2 and Ni(C6H6)2 anions presents an involved structure of CeH stretching bands. It will be interesting to know the experimental IR spectra in this region to confirm or deny these results. See Fig. 14C. The predicted IR spectra of the neutral and charged Fe(C6H6)3, Co(C6H6)3 and Ni(C6H6)3 species is reported in Figs. SIe15A, B, and C. They provide valuable information on the growing of these systems as more benzene units are added. The rich structure shown by the IR spectra of the Fe±1(C6H6)3, Co±1(C6H6)3 and Ni±1(C6H6)3 cations and anions is remarkable. It is expected that these results will motivate the experimental IR spectra study of these systems in

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the CeH stretching region. Three main features arise from the IR spectra in the finger print region of the studied complexes. a) They show vibrational resonances near those of the isolated benzene molecule. For example, the out of plane CeH bend is preserved is most of the neutral and charged species; Figs. SIe16A e 18A. b) Some forbidden IR vibrations of the benzene molecule, with null dipole moment, becomes IR active in the reduced symmetry of the complexes, which have dipole moments. This is clearly observed in the rich IR spectra of the Fe(C6H6)2,3, Co(C6H6)2,3 and Ni(C6H6)2,3 anions, Figs. SIe17C and 18C. c) Some IR-active modes in bare benzene become forbidden in the neutral and charged compounds. Indeed, the in plane CeH bend distortion is negligible in most of the neutral and charged Fe(C6H6)m Co(C6H6)m and Ni(C6H6)m, m
3, species. We have found that the calculated density of states (DOS) for the GS of a given anion [38,39] is in good agreement with the experimental photoelectron spectrum (PES), aiding to the GS assignment. However, the experimental PES study of the systems addressed in the present work is scarce, only there are reported data for Fe(C6H6), Fe(C6H6)2 and Co(C6H6)2 by the group of Bowen [36,30]. Thus, we proceed to the comparison of the calculated DOS and the PES for these systems. The DOS spectra are constructed using Gaussians for the orbital energies; it was chosen a width of 200 meV. Besides, the Fermi level of the DOS is aligned with the EA values determined experimentally [36,30]. The M11L estimated DOS for the Fe(C6H6) anion presents four a, b, c, and d main peaks, see Fig. SIe19. Although with a different intensity the peak “a” was found at about the same energy (0.60 eV) as the strongest band in the experimental PES [36]. The other b, c, and d peaks, as well as their separations, roughly mimics the observed peaks at about 1.08, 1.30 and 2.15 eV in the experiment [36]. Remarkably, the whole contour of the M11L DOS for Fe(C6H6)2 closely mimics the measured PES [36]. For instance, the DOS shows a, b, c, d, and e peaks, see Fig. SI-20, that nearly reproduces the observed signatures at about 1.0, 1.3, 1.6, 2.0, and 2.3 eV of the PES [36]. The broad form of the PES of Fe(C6H6)2 may reflect the distorted geometry of this anion, where the extra electron produces an uneven h6eh2 bonding of the benzene molecules, as referred to the h6eh6 bonds of neutral Fe(C6H6)2. The agreement between theory (DOS) and experiment (PES) provides confidence in that the calculated structure for Fe(C6H6) and Fe(C6H6)2 may correspond to the true GS’s of these anions. That is, such concordance support the assignment of a quartet (M ¼ 4), with h6 bonding, for the GS of Fe(C6H6) and a low spin state, a doublet (M ¼ 2), with h6eh2 coordination, for the GS of Fe(C6H6)2. The M11L DOS for Co(C6H6)2 shows three a (0.7 eV), b (1.0 eV) and c (at 2.0 eV) peaks, see Fig. SI-21, that roughly accounts for two signatures, at 0.70 and 2.20 eV, of the experimental PES; but fails in the description of the middle broad band centered at 1.45 eV. In this case, the BPW91eD2 level of theory produced a DOS containing three main features located at 0.70, 1.36, and 2.14 eV, that more closely reproduces the experimental PES [30]. The BPW91eD2 DOS is shown in Fig. SI-24. Note that M11L and BPW91-D2 assigns an h6eh2 coordination to the GS of Co(C6H6)2, but differs in the details of the orientation of the h2eB benzene molecule; see Fig. 3 and SIe4. Thus, the singlet (M ¼ 1) h6eh2 BPW91-D2 structure of Co(C6H6)2 is a more firm candidate for the GS of this anion. Regarding an accurate description, these results reveal that these metal-benzene systems pose a challenge for the state of the art of the quantum computational tools. 4. Conclusions Structural and energetic properties accounting for the stability of TM(C6H6)m
3, TM ¼ Fe, Co, Ni, clusters were studied using M11L

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R. Flores, M. Castro / Journal of Molecular Structure 1125 (2016) 47e62

and BPW91-D2 DF methods, which include dispersion corrections. Half sandwich h6 motifs occur in most of the studied neutral and charged TM(C6H6)1 species. However, a low h2 coordination was revealed for Co(C6H6)1 by the M11L approach. This is consistent with the small M11L D0 (0.23 eV) of this cluster, which is near to an experimental value (0.34 eV). Also, instead of h6 metalecarbon bonding as in FeeC6H6, M11L shows that in CoeC6H6 and NieC6H6 the metal atom seats on two hydrogen sites, h2H, of the benzene ring, producing planar GS geometries. In the studied neutral and charged TM(C6H6)1,2 species, the benzene molecules are absorbed on the metal in some way to minimize the repulsion and to form a maximum number of metalecarbon bonds. The cations reach maximum coordination, h6 or h6eh6 for Feþ(C6H6)1,2, Coþ(C6H6)1,2 and Niþ(C6H6)1,2, excepting Niþ(C6H6)2, which has h3eh3. Lower coordination schemes, due to the increase of repulsion, was reached in the anions: h6eh2 for Fe(C6H6)2 and Co(C6H6)2 and h2eh2 or h3eh2 for Ni(C6H6)2. Low coordination in the Ni(C6H6)2 species may reflect the increase of electrons from Fe to Co to Ni; despite of this, experiment and theory agree in that the D0 of NiC6H6 is larger than that of CoC6H6; they also agree in the D0s enhancements in going from the mono-to the di-benzene neutral complexes. The M11L D0 of FeC6H6, CoC6H6, and NiC6H6 are nearer to the experiment than the BPW91-D2 ones. Also M11L shows a better performance for the D0s of FeþC6H6, CoþC6H6, and NiþC6H6, though it does not reproduce the D0(CoþC6H6) > D0(NiþC6H6) > D0(FeþC6H6) experimental order. However, the BPW91-D2 D0s, which are more deviated from the experimental values, are in accord with such trend. Both methods reproduce the experimental order: D0(Feþ(C6H6)2) > D0(Coþ(C6H6)2) > D0(Niþ(C6H6)2). From TMþC6H6 to TMþ(C6H6)2, TM ¼ Fe, Co, and Ni, the experimental results shows D0s reductions, M11L partially reproduces this tendency; whereas BPW91-D2 is in concordance with this behavior. The D0(TMþC6H6) > D0(TMþ(C6H6)2) behavior is opposite to the one found for the neutral species, meaning that the positive charge, mainly lying on the metal atom in TMþC6H6, has a bigger ability for the attraction of the p-electrons; their charge distribution, Fig. 1, is consistent with this observation. Coordination and charge distribution, accounting for the D0 reduction of TMþ(C6H6)2 were discussed. The Co(C6H6)2 ion has clear ability for to stabilize the added electron, as it is shown by its large D0. Overall, the D0 of the anions are smaller than those of the cations and comparable those of the neutrals. Low values were obtained for the EAs of the studied TM(C6H6)1,2 species, complicates the theoretical and experimental determination. The estimated EA for Co(C6H6)2 is in accord with the experiment. The stability of Co(C6H6)2 is accounted in terms of the h6eh2 coordination, satisfying the 18e rule. In general, the calculated EAs increases from m ¼ 1 to 2, and they tend to increase from m ¼ 2 to 3. Due to electron delocalization trough the CdeeHdþ/p network of bonds, the IEs decreases from m ¼ 1 to 3. This network contributes also to the stabilization of the added electron in the TM(C6H6)3 anions. The coordination schemes of the bare m ¼ 2 clusters are roughly kept in the m ¼ 3 complexes. This is a consequence from the low D0 of the added benzene molecule; being considerably smaller than the D0s of the m ¼ 2 parents, confirms the solvent behavior in the studied TM(C6H6)3 systems. Effectively, two-layer isomers define the GSs of the studied neutral and charged tri-benzene clusters. However, two-layer isomers were found near in energy to the onelayer GSs. BPW91-D2 locates these isomers within a sharper energy gap, marking the sensitive of these systems to the used level of theory. For some systems one-layer structures define the GSs. For instance, for the Ni(C6H6)3 anion, a one-layer isomer is the GS, whereas the two-layer structures appear within a range of less than

5 kcal/mol. The solvent behavior is mainly accomplished by means of weak dipoleep interactions, carried out between the CdeHdþ groups and the p-electrons. The D0 and EA of TM(C6H6)3, TM ¼ Fe, Co, Ni, show the ability of these clusters for the absorption of an extra electron. Acknowledgements Financial support from DGAPA UNAM, project PAPIIT-IN-212315, is greatly thanked. We also strongly appreciate the Grant CB-201217855 from CONACyT. R. Flores acknowledges a fellowship from CONACyT, Mexico. Access to the supercomputer Miztli at DGSCAUNAM is deeply thanked. Valuable discussions on metal-ligand systems with Dr. Jorge Soto are greatly appreciated. Appendix A. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.molstruc.2016.06.052. References [1] T. Kurikawa, H. Takeda, M. Hirano, K. Judai, T. Arita, S. Nagao, A. Nakajima, K. Kaya, Organometallics 18 (1999) 1430. [2] A. Nakajima, K. Kaya, J. Phys. Chem. A 104 (2000) 176e191. [3] T.D. Jaeger, D.V. Heijnsbergen, S.J. Klippenstein, G. von Helden, G. Meijer, M.A. Duncan, J. Am. Chem. Soc. 126 (2004) 10981e10991. [4] K. Eller, H. Schwarz, Chem. Rev. 91 (1991) 1121e1177. [5] D. Caraiman, D.K. Bohme, J. Phys. Chem. A 106 (2002) 9705e9717. [6] F. Mayer, F.A. Khan, P.B. Armentrout, J. Am. Chem. Soc. 117 (1995) 9740e9748. [7] P.B. Armentrout, Int. J. Mass. Spectrom. 227 (2003) 289e302. [8] T.D. Jaeger, M.A. Duncan, J. Phys. Chem. A 109 (2005) 3311e3317. [9] M. Castro, R. Flores, M.A. Duncan, J. Phys. Chem. A 117 (2013) 12546e12559. [10] S. Grimme, J. Comput. Chem. 27 (2006) 1787e1799. [11] V.R. Cooper, T. Thonhauser, A. Puzder, E. Shroder, B.I. Lundqvist, D.C. Langreth, J. Am. Chem. Soc. 130 (2008) 1304e1308. [12] L.R. Rutledge, L.S. Campbell-Verduyn, S.D. Wetmore, Chem. Phys. Lett. 444 (2007) 167e175. [13] S.K. Burley, A.G. Petsko, Science 229 (1985) 23e28. [14] R.J. Lane, C.G. Saunders, Cryst. Eng. Comm. 15 (2013) 1293e1295. [15] B. Ferguson, C. Glidewell, E.S. Lavender, Acta. Cryst. B55 (1999) 591e600. [16] A. Addlagatta, C. Kishor, T. Arya, J. Med. Chem. 56 (2013) 5295e5305. [17] F. Liu, I. Rehmani, S. Esaka, L. Chen, V. Serrano, A.B. Liu, Proc. Natl. Acad. Sci. U. S. A. 110 (2013) 9722e9727. [18] C.E. Valdez, Q.A. Smith, M.R. Nechay, A.N. Alexandrova, Acc. Chem. Res. 47 (2014) 3110e3117. [19] A.D. Becke, Phys. Rev. A 38 (1988) 3098e3100. [20] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244e13249. [21] R. Peverati, D.G. Truhlar, J. Phys. Chem. Lett. 3 (2012) 117e124. [22] F. Weigend, R. Ahlrichs, Phys. Chem. Chem. Phys. 7 (2005) 3297e3305. [23] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G.A. Petersson, et al., Gaussian 09 Revision D.01, Gaussian Inc., Wallingford CT, 2010. [24] A.E. Reed, L.A. Curtiss, F. Weinhold, Chem. Rev. 88 (1988) 899e926. [25] G.L. Gutsev, C.W.J. Bauschlicher, J. Phys. Chem. A 107 (2003) 7013e7023. [26] R. Pandey, B.K. Rao, P. Jena, Chem. Phys. Lett. 321 (2000) 142e150. [27] I. Valencia, M. Castro, Chem. Phys. Lett. 12 (2010) 7545e7554. [28] T. Limori, Y. Aoki, Y. Ohshima, J. Chem. Phys. 117 (2002) 3675e3686. [29] D.C. Young, Computational Chemistry, John Wiley & Sons, Inc, 2001, p. 228. [30] M. Gerhards, O.C. Thomas, J.M. Nilles, W.J. Zheng, K.H. Bowen Jr., J. Chem. Phys. 116 (2002) 10247e10252. [31] R. Pandey, B.K. Rao, P. Jena, M.J. Alvarez-Blanco, J. Am. Chem. Soc. 123 (2001) 3799e3808. [32] C.W.J. Bauschlicher, H. Partridge, S.R. Langhoff, J. Phys. Chem. 96 (1992) 3273e3278. [33] B.K. Rao, P. Jena, J. Chem. Phys. 116 (2002) 1343e1349. [34] B.K. Rao, P. Jena, J. Chem. Phys. 117 (2002) 5234e5239. [35] R.L. Hettich, T.C. Jackson, E.M. Stanko, B.S. Freiser, J. Am. Chem. Soc. 108 (1986) 5086e5093. [36] W. Zheng, N.S. Eustis, X. Li, J.M. Nilles, O.C. Thomas, K.H. Bowen, A.K. Kandalam, Chem. Phys. Lett. 462 (2008) 35e39. [37] W. Zheng, J.M. Nilles, O.C. Thomas, K.H. Bowen Jr., J. Chem. Phys. 122 (2005) 044306. [38] M. Castro, S.-R. Liu, H.-J. Zhai, L.-S. Wang, J. Chem. Phys. 118 (2003) 2116e2123. [39] R. Flores, H.F. Cortes, M. Castro, J. Mol. Struct. 1103 (2016) 295e310.