Understanding the Influence of Terminal Ligands on the Electronic

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Understanding the Influence of Terminal Ligands on the Electronic Structure and Bonding Nature in [Re(µ-Q)] clusters 6

3

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2+

Walter Alfonso Rabanal-León, Juliana Andrea MurilloLopez, Dayán Páez Hernández, and Ramiro Arratia-Perez J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 27 Oct 2014 Downloaded from http://pubs.acs.org on October 27, 2014

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The Journal of Physical Chemistry

Understanding The Influence Of Terminal Ligands On The Electronic Structure And Bonding Nature In [Re6(µ3-Q8)]2+ Clusters† Walter A. Rabanal-León, Juliana A. Murillo-López, Dayán Páez-Hernández, and Ramiro Arratia-Pérez∗ Universidad Andrés Bello, Facultad de Ciencias Exactas, Ph.D. Program in Molecular Physical Chemistry, Relativistic Molecular Physics (ReMoPh) Group, Santiago 8370146, Chile. E-mail: [email protected]*

Phone: +56-2-2770-3352. Fax: +56-2-2770-3352 KEYWORDS: Rhenium hexanuclear clusters, Relativistic-DFT, ZORA, Ligand donoracceptor effects, Ligand lability.

† ∗

All the authors contribute equally to this work To whom correspondence should be addressed

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Abstract Since the synthesis of the first molecular cluster [Re6 (µ3 -Q8 )X6 ]4− and the substitutional lability of the terminal ligands prompted new developments in their chemistry, that makes these molecular clusters a reasonable point of departure for building new materials. The development of novel inorganic materials of technological interest certainly requires an understanding of the electronic structure, bonding, spectroscopy, photophysical and structural properties of these clusters. Taking into account the potential applications in material sciences, and the lack of systematization on the study of these kind of clusters, the proposal of the present work is to perform a detailed theoretical study of the [Re6 (µ3 -Q8 )X6 ]4− (Q = S2− , Se2− , Te2− ; X = F− , Cl− , Br− , I− , CN− , NC− , SCN− , NCS− , OCN− , NCO− ) clusters based on the deeply description of the electronic structure of these complexes and the bonding nature between the [Re6 (µ3 -Q8 )]2+ core and several donor/acceptor peripheral ligands. All this work was developed on the framework of the relativistic density functional theory (R-DFT), where relativistic effects were incorporated by means of a two-component Hamiltonian with the zeroth-order regular approximation (ZORA). To describe the relative stability of these complexes, we employed the global descriptors of chemical hardness (η) and softness (S) introduced by Pearson. Moreover, an analysis of bonding energetics were performed by combining a fragment approach to the molecular structure with the decomposition of the total bonding energy (EBE ), according to the Morokuma-Ziegler energy partitioning scheme. After an analysis of these results we found in all cases an extensive ionic character in the bonding between the core an each peripheral ligand. The interaction between the halide ligand and the core gives about 75% ionic character while the other ligands shows a more covalent interaction due to effective synergic mechanisms. We conclude that the most stable clusters are those which present the stronger σ-donor terminal ligands, while the cluster stability start to decrease when the π-acceptor effect will be stronger; this fact is directly related with the terminal ligand lability and with the strong electrophilic character of the [Re6 (µ3 -Q8 )]2+ core.

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Introduction Through the history, experimental chemist are always looking for the manner to manipulate the matter with the goal to produce and modify several functionalized chemical systems. This made possible the development of the organic, inorganic and supramolecular chemistry. One proof of the mentioned before, was the extensive studies of transition metal clusters which, due to their well-defined structures and unique reactivity, optical and magnetic properties, present themselves as an appealing class of structural and functional molecules used as building blocks on a wide range of areas in synthetic chemistry. 1 The first successful synthesis of the hexarhenium chacolgenide caped-clusters was reported in 1971, by Opalovskii, Fedorov and co-workers. 2,3 Twelve years later, in 1983, the 24-electron octahedral cluster core was identified on a group of chalcohalide hexarhenium compounds obtained by Leduc, Perrin and Sergent. 4 These works paved the way for the further development and study of the solution chemistry of hexanuclear rhenium chalcogenide clusters and also the base for a profitable syncretism with the solid-state chemistry. 5–7

From the perspective of creating novel materials, it must be taken into account the attractive electrochemical and photo-physical properties that are present in these kind of clusters. Firstly, a reversible one-electron oxidation event is typically observed. 6,8 Moreover, these clusters are phosphorescent, which depends on the coordination environment of the cluster, particularly of the terminal (or peripheral) ligand that is coordinated with the [Re6 (µ3 -Q8 )]2+ core. These interesting peculiarities, though not yet fully understood due largely to the complicated electronic structures of the cluster system, suggest the possibility of creating cluster-based functional materials as it is well studied experimentally by J. R. Long, P. Batail, R. Holm and Z. Zheng. 1,9–25 In addition to its optical and electrochemical properties, a feature that has attracted much attention is its promising biological activity as an efficient anticancer agent as is proposed by Ramirez-Tagle et al., 19 in which was evaluated the efficacy of the anionic hexa-iodo rhenium selenide cluster, [Re6 Se8 I6 ]3− , to selectively in3



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crease tumor cell death, leaving non-tumoral cells unaffected and also, the capabilities of this cluster to promote intracellular localization by taking advantage of its revealed luminescence.

As a counter part of the experimental results, several theoretical works have been reported by R. Arratia-Pérez and co-workers, 26–29 specially on the fields of the optical and magnetic properties for hexarhenium face-capped chalcohalide clusters. These studies were developed on the framework of approximated four-component relativistic density functional theory, in order to introduce in a proper way the intrinsic relativistic effects related to heavy atoms. In reference to the optical properties, time-dependent density functional theory calculations were carried out with the aim to simulate UV-Vis spectrum and also, to understand the role of the terminal ligands on the absorption band shifting as well as the composition of the molecular orbitals (spinors) involved on these electronic transitions.

These researchers showed that halide ligands play a fundamental role for introducing ligand charge transfer into the electronic transitions of the absorption spectra in the visible and near ultraviolet region. These transitions are halide dependent since they are red-shifted upon exchange of chlorides for bromides, or bromides for iodides, clearly implying that these bands are due to ligand-to-metal charge transfer (LMCT) transitions. Furthermore, on the study of the magnetic properties the calculations predicted isotropic g-factors for [Re6 (µ3 Q8 )X6 ]3− (Where Q = S2− , Se2− and X = Cl− , Br− , I− ) systems, 26,29 which are in good agreement with single crystal solid-state cluster EPR experiments. 8 Also, the metal and terminal ligand hyperfine tensors are anisotropic, while the hyperfine tensor arising of the capping S ligands are small and isotropic. These reversible redox couples [Re6 (µ3 -Q8 )X6 ]4− / [Re6 (µ3 -Q8 )X6 ]3− could constitute suitable nanoscale materials for applications in optical and magnetic data storage, ultrafast data communication, and solar energy conversion devices. 26,30,31

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Taking into account the potential applications in material science, and the lack of systematization on the study of these kind of clusters; it is the aim of this contribution to perform a detailed study of the relativistic electronic structure and the bonding interactions of [Re6 (µ3 -Q8 )X6 ]4− systems, using face-capped octahedral [Re6 (µ3 -Q8 )]2+ (Q = S2− , Se2− and Te2− ) clusters as fundamental building units to develop a vast diversity of molecular architectures, since the six terminal ligands are oriented in such way that each ligand is arranged perpendicularly to each other. Motivated by these, we initiated a travel on the understanding of chemical interactions in hexarhenium chalcogenide clusters, and the influence of the terminal substituents on the molecular electronic structure.

Computational Details The proposal of the present work is to perform a conscientious theoretical study of the Re6 (µ3 -Q8)X6 ]4− (Q = S2− , Se2− , Te2− ; X = F− , Cl− , Br− , I− , CN− , NC− , SCN− , NCS− , OCN− , NCO− ) clusters based on the deeply description of the electronic structure of these complexes and the bonding nature between the [Re6 (µ3 -Q8 )]2+ core and several peripheral ligands, with the aim to describe and compare the molecular properties and their relative stability. All this work were developed on the framework of the relativistic density functional theory (R-DFT) by using the Amsterdam Density Functional (ADF 2012.01) 32 code, where the scalar (SR) and spin-orbit (SO) relativistic effects were incorporated by means of a two-component Hamiltonian with the zeroth-order regular approximation (ZORA). 33,34

All the molecular structures presented above were fully optimized via the analytical energy gradient method implemented by Verluis and Ziegler, within the generalized gradient approximation (GGA) employing the non-local correction proposed by Perdew and Wang (PW91). Furthermore, uncontracted triple-ζ quality Slater-type orbitals (STO) basis set, augmented by two sets of polarization functions (TZ2P) were used for the all atoms. 35

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The complete set of geometry optimizations were done under an octahedral (Oh ) symmetry constraint, following the established by the experimental results reported by Holm and coworkers as well, and is depicted in Figure 1.

Terminal or Peripheral Ligand

Rhenium ion Re3+

Chalcogenide !3 Ligand

Figure 1: Molecular model for the [Re6 (µ3 -Q8 )X6 ]4− cluster

To describe the relative stability of these complexes, we employed the global descriptors of chemical hardness (η) and softness (S) introduced by Pearson, in connection with the study of generalized Lewis acid-base reactions. 36 On this basis, Pearson formulated his hard and soft acids and bases (HSAB) principle, in which is stipulated as hard acids preferably interact with hard bases, and soft acids with soft bases. From the DFT point of view is possible to associate the hardness with the energy “gap” between HOMO and LUMO orbitals and the softness as the reciprocal of the hardness.

In the present research, we calculated these parameters for the individual [Re6 (µ3 -Q8 )]2+ cores in the optimized geometries for each peripheral ligand. To study the stability, we searched for a path to quantify the interactions between hexarhenium chalcogenides cores and the peripheral substituents. 37 Therefore, an analysis of bonding energetics were performed 6


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by combining a fragment approach to the molecular structure of a chemical system with the decomposition of the total bonding energy (EBE ), according to Morokuma-Ziegler energy 38 partitioning scheme, as:

EBE = EP auli + EElestat + EOrb

(1)

Where EP auli , EElestat and EOrb are, the Pauli repulsion, electrostatic interaction, and orbital-mixing terms, respectively. A detailed description of the physical significance of these properties has been given by Bickelhaupt and Baerends. The electrostatic component is calculated from the superposition of the unperturbed fragment densities at the molecular geometry and corresponds to the classical electrostatic effects associated with Coulombic attraction and repulsion. The electrostatic contribution is most commonly dominated by the nucleus-electron attractions and therefore has a stabilizing influence. The Pauli component is obtained by requiring that the electronic antisymmetry conditions be satisfied and has a destabilizing character, whereas the orbital-mixing component represents a stabilizing factor originating from the relaxation of the molecular system due to the mixing of occupied and unoccupied orbitals and can involve electron pair bonding, charge-transfer or donor-acceptor interactions, and polarization.

Results and Discussion The first step on the understanding of how these different clusters could be synthesized and how we can study the relative stability among them, is through the use of the global descriptors (based on the conceptual-DFT) like hardness and softness which were previously described. To do this, we split the cluster into two fragments, the [Re6 (µ3 -Q8 )]2+ core and each [X6 ]6− set of ligands, calculating each core in the geometry of the entire cluster and thereby estimating what happens to the core in the presence of different peripheral ligands; 7



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at the end we have three data sets related to the chalcogenide present in the core, that means Q = S2− , Se2− and Te2− . In Table S1 on Supporting Information is reported the calculated and experimental geometrical parameters for the entire set of [Re6 (µ3 − S8 )X6 ]4− clusters, in order to prove the good agreement of our calculations with the experimental values reported. 13,39

The calculations done in this way allow us to obtain information related to the HOMO and LUMO energies for each [Re6 (µ3 -Q8 )]2+ core; thus applying the HSAB principle in these cases, it is easily to understand that hardest core prefers hard ligands and the softest like better the soft ligands. In general, the Re3+ ion could be considered as hard acid under HSAB theory, so it will form a more stable core with the hardest chalcogenide, that means the hardest base. Looking at the Table 1, we can observe that the average core hardness among the halogen series is higher for the sulfur core following the decreasing order S2− > Se2− > Te2− that is consistent with the bonding energy obtained for the energy decomposition analysis, and therefore the stability of each core.

Table 1: HOMO-LUMO gap (eV) and global descriptors of reactivity for each [Re6 (µ3 -Q8 )]2+ (Q = S2− , Se2− , Te2− ) core in presence of halide peripheral ligands.

[Re6 S8 ]2+

[Re6 Se8 ]2+

[Re6 Te8 ]2+

Ligand H-L gap

η

S

ω

H-L gap

η

S

ω

H-L gap

η

S

ω

F−

1.33

0.67

1.50

32.27

1.30

0.65

1.54

28.84

1.13

0.57

1.76

29.88

Cl−

1.45

0.72

1.38

28.93

1.28

0.64

1.57

29.15

1.16

0.58

1.73

29.52

Br−

1.45

0.72

1.38

28.84

1.28

0.64

1.57

29.17

1.14

0.57

1.76

29.70

I−

1.45

0.72

1.38

28.87

1.27

0.64

1.57

29.24

1.19

0.59

1.68

29.69

H-L gap: HOMO-LUMO gap = (EHOM O - ELU M O ) Hardness: η = (EHOM O - ELU M O )/2 Softness: S = 1/ η Electrophilicity: ω = µ2 /2η

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Even though there is a slightly difference on the calculated global descriptors, this is not enough significant to produce a qualitative change on the molecular properties (like bonding nature) of these systems, which is in concordance with the kinetic experimental results reported by Ibers and co-workers, which evidence that there is no preference on the substitution for Se over Te in the face-capping positions for rhenium chalcogenide clusters. That means that the stabilization of the rhenium core produced by both chalcogenides is similar. 40

On the other hand, we can generally say that the [Re6 (µ3 -Q8 )]2+ core behaves as a hard acid, so it will form more stable clusters with the hardest halogen, this behaviour is clearly exemplified in Table 2 where the stability of each core with the same chalcogenide follows the decreasing order F− > Cl− > Br− > I− . In the same way we can argue that ligand lability will increase in the opposite direction that the stability behaves, that means the iodide ligand would be the more labile and the fluoride ligand the less, but keeping in mind that all of them are labile ligands in general due to the ionic character of the bonding in all cases. These results are consistent with the work reported by Holm et.al. about thermal control of the ligand substitution in [[Re6 S8 Br6 ]4− and [Re6 S8 I6 ]4− systems. The authors conclude that [Re6 S8 Br6 ]4− cluster is less reactive due to the minor lability of the bromide with respect to the iodide ligands. 22

On Figure 2 is depicted a qualitative molecular orbital diagram relating the MOs to the core and the change due to the inclusion of the halogen ligand in a octahedral ligand field and the differences under a scalar relativistic (SR) and spin-orbit (SO) frameworks. The nature of the frontier orbitals of the core does not change considerably when the halogenligand cluster is formed, with the inclusion of the spin-orbit coupling effects appears the characteristic splitting under a octahedral symmetry being the ground state the four-fold degenerate f3/2g (γ8 ). The SO coupling slightly increase the HOMO-LUMO gap due to a greater stabilization of the f3/2g and a destabilization of the e3/2g .

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Table 2: Energy decomposition analysis for all [Re6 (µ3 -S8 )X6 ]4− complexes. All energies are in eV. Ligand (X)

EP auli

EElec

EOrb

EBE

F−

26.75

-67.24

-18.04

-58.53

Cl−

23.82

-57.01

-14.38

-47.57

Br−

22.89

-54.10

-14.02

-45.23

I−

22.59

-51.52

-13.89

-42.82

CN−

44.38

-75.23

-23.31

-54.16

NC−

34.54

-66.15

-18.54

-50.14

SCN−

13.06

-35.73

-10.09

-32.76

NCS−

33.81

-61.53

-17.66

-45.39

OCN−

19.37

-46.89

-12.17

-39.69

NCO−

34.21

-65.69

-17.27

-48.74

EP auli : Pauli repulsion energy EElestat : Electrostatic interaction energy EOrb : Orbital mixing energy EBE : Bonding Energy

One interesting case is related with the CN− and NC− peripheral ligands; on these, the energy values of the frontier orbitals are practically the same in both cases, this make the hardness and softness not good descriptors if the aim is to understand the stability of these compounds. Besides this, there is a third descriptor that allows us to understand the reasons that generate the difference in reactivity among them and this is the electrophilicity, ω, that could be interpreted as a sort of “electrophilic power ”and can be calculated as ω ≈ µ2 /2η , where µ is the electronic chemical potential and η is the hardness defined above.

In this way the core is always electrophilic, therefore this core will tend to react with the most polarizable peripheral ligand. For that reason, in the case of the CN− and NC− ligands, the most stable interaction is with the CN− due to the less electronegativity of the carbon atom. Following the same analysis for the cyanide derivatives, that means cyanate (OCN− ), 10


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Figure 2: Qualitative MOs diagram for the [Re6 (µ3 -Q8 )X6 ]4− cluster with halogen peripheral ligands. The red/blue representation is used for occupied MOs whereas green/orange was selected for unoccupied MOs. isocyanate (NCO− ) and isothiocyanate (NCS− ), it can be observed a direct relation between the cluster stability and the degree of polarizability of the ligand atom directly bonded to the [Re6 (µ3 -Q8 )]2+ core. In this sense the cluster with isocyanate ligand would be more stable than isothiocyanate, following in general the decreasing order of stability NCO− > NCS− > OCN− . The whole information related to the global descriptors for other chalcogenides is contained in the Supporting Information on Table S2, and the information of the energy decomposition analysis is collected on Table S3.

Although it might be possible to describe a relation between the global reactivity descriptors and the relative stability of the last set of ligands, there are more information related with these behavior that could be better understood in terms of the electronic structure 11



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and the possible electronic density donation or back-donation presented in this systems. In all the cases the bonding between core and peripheral ligands have an ionic character practically independent of the nature of the chalcogenide bridge ligand. The bonding energy per ligand is between 4.5 and 10.0 eV. Particularly for the halogens (σ-donor ligands) the bonding energy reduces with the weight of the ligand, of course that is directly related with the hardness of the core as was explained in the last section. Because of that the lability of the iodine is larger than the lability of the first members of the halogen series, this is in agreement with the experimental evidence about the kinetic and energetic of the substitution in these complexes. For the other ligands treated here some important regularities can be summarized.

One evidence about the preponderance of the σ-donation from the ligands to the core is the fact that in the cases in which the nitrogen atom is directly bonded to the core (NC− , NCO− and NCS− ) the orbital component of the bonding energy is almost constant. The bonding orbitals in these complexes have sigma character (a1g symmetry) with contributions from the d-orbitals of the Re atoms and symmetry adapted combinations of p-orbitals of the N atom in the ligand. Another evidence of the σ−donation is the reduction of the orbital energy contribution to the bonding energy from -21 to -12 eV when the core is bonded with C, N, and O in CN− , NC− , and OCN− ligands as can be observed on Figure 3a, Figure 3b and Figure 3c respectively. In these three molecules the orbital bonding energy decreases directly with the increment in the electronegativity of the bonded atoms and the contribution of the atomic orbitals adapted by symmetry (σ) of the ligands is also reduced. The energy decomposition analysis shows that for the CN− and NC− cases the orbitals stabilization come only from the σ-donation, the higher bonding orbital has 60% σ(CN) + 40% σ(core) for CN− and 70% σ(NC) + 30% σ(core) for NC− .

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(a)

(b)

(c)

Figure 3: σ-stabilizing orbital interaction for [Re6 (µ3 -Q8 )X6 ]4− with (a) CN− , (b) NC− and (c) OCN− ligands. The red/blue representation is used for these occupied molecular orbitals. The π-donation and/or back-donation does not occur due to the higher energy of these orbitals with respect to the high occupied orbitals of the core. The frontier molecular orbitals in these molecules are completely localized in the core and we can classify it as non-bonding core orbitals. For OCN− and SCN− besides the σ-donation appears some π back-donation with anti-bonding character in the frontier orbitals region of the molecules. Then, in these cases the nature of the frontier orbitals change with respect to the formers and introduce an amount of non-stabilizing orbital interaction. Particularly the molecule with SCN− have a slightly less orbital energy contribution to the bonding energy as a consequence of the higher contribution of the π anti-bonding to the frontier orbitals. Compiling all the information and the relative stability of each group, we constructed a general relative stability diagram as depicted on Figure 4, from this figure we can conclude that the most stable clusters are those which present the stronger σ-donor terminal ligands, while the cluster stability start to decrease when the π-acceptor effect will be stronger; this fact is directly related with the terminal ligand lability and with the strong electrophilic character of the [Re6 (µ3 -Q8 )]2+ core, as is evidenced in the recent experimental results presented by K. Brylev et al., in which use the π-acceptor benzotriazolate ion to water-solubilize the hexarhenium cluster. 41

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Acknowledgement This work has been supported by the Grants FONDECYT N◦ 1110758, Millennium RC120001 and the projects UNAB-DI-404-13/I, UNAB-DI-292-13/R, AKA-FINLAND-CONICYT CHILE 2012. J.A.M.L. acknowledges CONICYT / PCHA / Doctorado Nacional / 2013 63130287 for his Ph.D. fellowship. W.A.R.L. acknowledges CONICYT / PCHA / Doctorado Nacional / 2013 - 63130118 for his Ph.D. fellowship.

Supporting Information Available In the supporting information is reported the following information: The experimental and calculated geometrical parameters for each [Re6 (µ3 − S8 )X6 ]4− , where X = F− , Cl− , Br− , I− , CN− , NC− , SCN− , NCS− , OCN− , NCO− , for the ground state of this set of complexes under a Oh symmetry point group at spin-orbit relativistic level, the analysis of the global descriptors for each [Re6 (µ3 -Q8 )]2+ (Q = S2− , Se2− and Te2− ) core in its respective geometry for each terminal ligand, and the energy decomposition analysis (EDA) for each [Re6 (µ3 Q8 )]2+ (Q = S2− , Se2− and Te2− ) core in its respective geometry for each terminal ligand. This material is available free of charge via the Internet at http://pubs.acs.org/.

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