Magnesium-based Oxyfluoride Superatoms: Design, Structure, and

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Magnesium-based Oxyfluoride Superatoms: Design, Structure, and Electronic Properties Celina Sikorska J. Chem. Inf. Model., Just Accepted Manuscript • DOI: 10.1021/acs.jcim.9b00083 • Publication Date (Web): 20 Mar 2019 Downloaded from http://pubs.acs.org on March 22, 2019

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Journal of Chemical Information and Modeling

Magnesium-based Oxyfluoride Superatoms: Design, Structure, and Electronic Properties

Celina Sikorska1 Laboratory of Molecular Modeling, Department of Theoretical Chemistry, Faculty of Chemistry, University of Gdansk, Wita Stwosza 63, 80-308 Gdansk, Poland

1 Corresponding

author: e-mail address: [email protected], telephone number: (+48)

58 523 5351. 1 ACS Paragon Plus Environment

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Abstract The ability of mixed ligands to form stable dinuclear and trinuclear magnesium-based superatoms has been investigated theoretically. The Mg2F5-2mOm and Mg3F7-2mOm systems (where m=1-3) were found able to form stable and strongly bound anionic clusters and those assumptions were validated by (i) the analysis of the geometrical stability, (ii) the estimated Gibbs free energies for the most probable disproportion paths these clusters might be vulnerable to (which allows examining their thermodynamic stabilities), (iii) the localization of the electron density, and (iv) the adiabatic electron affinity (AEA), vertical electron detachment energy (VDE), and adiabatic electron detachment energy (ADE) values calculated for the studied systems. It is demonstrated that the stability of the anionic daughters of these clusters increases with the number of electronegative ligands and MgnF2n+1-2mOm (n=2, 3; m=1-3) clusters are stable against electron emission. The largest electron binding energy was found for the Mg3F5O anion (VDE=6.826 eV). The strong VDE dependence on (i) the geometrical structure, (ii) the number of the central atoms, (iii) ligand type, (iv) bonding/antibonding character of the highest molecular orbital (HOMO) was also remarked and discussed.

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1. Introduction Anions retrieve an essential role in materials chemistry as oxidizing agents and building blocks of energetic materials.1,

2

Because of the ns2 np5 outer electronic

configuration, halogen atoms willingly create anions and thus are an integral unit of salts. Chlorine possesses the highest electron affinity (EA of 3.62 eV 3), of any element in the periodic table. Due to the importance of anions in the chemical industry, there has been a persistent exploration to find compounds that have extremely high EAs and can form unusual salts or ionic liquids. This exploration has led to the disclosure of a novel class of clusters named superhalogens, which have EAs higher than that of Cl and might be regarded as superatoms (as they mimic the chemistry of halogen atoms).4 The idea of superatoms was initiated by Khanna and Jena (in order to describe clusters).5,

6

Superatoms (such as

superhalogens) enlarge the conventional periodic table into a so-called three-dimensional periodic table, which may deliver building blocks for the design of new materials with eligible features.7-9 In this frame, it is important to explore novel superatoms as well as determine practicable design schemes. One class of superatoms is describing by the MXk+1 formula, where the number of electronegative monovalent (X) substituents exceeds the maximal formal valence (k) of the central metal atom (M) by one.10 In the case of divalent substituents, such as oxygen atoms, the superhalogen formula becomes MX(k+1)/2, where provided k is even. Up to now, metal oxides and halides establish two principal classes of superhalogens.4, 10-17 The inherence of metal atoms or halogen ligands, however, is not mandatory for a molecule to possess superhalogen features. Examples comprise the B(OF)4 anion (with VDE of 7.08 eV)18 which follows the MXn+1 scheme but metal and halogen atoms have been replaced with non-metal atom and fluoroxyl groups, respectively. Another significant augmentation of the superhalogen scheme is the introduction of the polynuclear (MnXn·k+1) superhalogens and 3 ACS Paragon Plus Environment


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their anionic daughters19-24, such as Xe2F13−, Rn2F13−, and Mg3F7− anions.20, 21 The discovery of novel superhalogen species together with exploring their promising features conduce to the development of new type of strong oxidizing agents. Superhalogens with strong oxidizing ability might be utilized to achieve the high oxidation states of metal atoms otherwise inaccessible in conventional chemistry. Explicitly, superhalogens were argued to be capable of effective oxidizing species with large ionization potential (IP), such as nanoparticles (e.g. fullerenes1,

21

and metal oxides25) or noble gas

atoms.26 They reveal large application potential in the formation of novel chemical species and might be applied as promising building blocks of functional materials (e.g. magnetic materials and nonlinear optical materials).23, 24 Moreover, superhalogens can be utilized in the synthesis of perovskite materials and as such they might play a role in formation of materials for optoelectronic devices and solar cells.27, 28 Recently, Jena and co-workers demonstrated that the negatively-charged counterparts of commercial electrolytes (e.g. LiClO4, LiBF4, LiAsF6, LiPF6, ) in Li-ion batteries are superhalogens.29 Since then, the idea of superhalogen has been applied to design novel electrolytes for lithium batteries.9, 30 Investigating novel superhalogens is predominantly focused on exploring greater molecular clusters which are able to create strongly bound negative ions. It seems that discovering for clusters able to bind an additional electron enormously strongly could be achieved either by inventing new polynuclear (MnXn·k+1 and MnX(n·k+1)/2 for monovalent and divalent ligands, respectively) compounds (comprising n central atoms) or by designing innovative strong electron acceptors. As to the polynuclear superhalogens, however, the earlier works are limited to non-mixed substituents19, 20, 22, 31, 32, including our contribution on the magnesium-based trinuclear superatoms,21 with only a few exceptions.33-35 It appears that there remain many problems to be subsequently explored from the theoretical point of view. To verify the limitations of mixed ligands in creating polynuclear superatoms, this 4 ACS Paragon Plus Environment

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contribution is mainly focused on the Mg2F5-2mOm (m=1, 2) and Mg3F7-2mOm (m=1-3) clusters, which meet the general formula MgnF2n+1-2mOm. The reason why we choose oxygen and fluorine as ligands is that they have high EA value (1.46 and 3.40 eV, respectively)3 and their usefulness as substituents ensuring large electron binding energy values was confirmed in the past. In particular, they has been proved to be able to form mixed mononuclear superatoms (e.g. SOxFy, PO2F2, BrOFn), which electron affinity could exceed 5 eV.33-35 To the best of our knowledge, however, there are almost any reports on superatom nature of polynuclear species with mixed ligands. Hence, in the present work, the ability of mixed ligands to form stable dinuclear and trinuclear superatoms has been investigated theoretically. In the present paper, to explore the behavior of polynuclear oxyfluoride clusters in superatom design, a series of MgnF2n+1-2mOm systems (n=2, 3; m=1-3) and their corresponding anionic daughters were theoretically constructed and examined. Also, the Gibbs free energies of the most probable disproportion reactions, that these clusters might be susceptible to, were evaluated. The obtained results indicate that the anionic clusters considered could possess considerably VDEs than EAs of halogen atoms, confirming their superatom nature. This finding delivers a novel way to design and synthesize polynuclear superatoms by surrounding central metal atoms by mixed substituents. The aim of these efforts is to deliver reliable predictions of their physical-chemical features, considering the potential utility of such molecules as oxidizing agents (electron acceptors) in diverse chemical processes as well as the role they can play in the development of materials for optoelectronic devices or solar cells. 2. Computational Details The second-order Møller−Plesset (MP2) perturbational approach together with the 6311+G(d) basis sets36, 37 was applied to obtain the equilibrium geometrical structures of both the MgnF2n+1-2mOm (n=2, 3; m=1-3) neutral clusters as well as their anionic daughters. Frequency analysis was executed (at the same MP2/6-311+G(d) level) to validate that the 5 ACS Paragon Plus Environment


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resulting geometries stand for minimal on the potential energy surface. The final energies of the species (at their equilibrium geometries obtained with the MP2/6-311+G(d) method) were calculated by applying the coupled-cluster technique with single, double, and non-iterative triple excitations (CCSD(T)) together with the 6-311+G(3df) basis sets. Thermodynamic stabilities of all studied species (in the gas phase for T=298.15 K and p=1 atm) were obtained utilizing the CCSD(T)/6-311+G(3df) electronic energies, whereas the entropies and thermal corrections were computed at the MP2/6-311+G(d) level of theory. The vertical detachment energy (VDE) values were estimated as the electronic energy differences between the neutrals and negative ions both at the optimized anion equilibrium geometries, whereas the adiabatic detachment energy (ADE) values were obtained as the electronic energy differences between the neutral and anion at each equilibrium geometry and comprising zero-point energy corrections. The ADEs were estimated (at the CCSD(T)/6311+G(3df) level of theory) by starting with the optimized anion geometry and relaxing it to its nearest equilibrium configuration after detaching an additional electron. The VDE values were estimated by performing both direct and indirect calculations. A direct scheme relays on performing the outer valence Green function OVGF method (B approximation)38-43 with the 6-311+G(3df) basis sets, whereas the latter (indirect) method relays on subtracting the negative ion energies from those of the neutral (both computed with the CCSD(T)/6311+G(3df) approach at the MP2 optimized structure of anion (Re-)), as shown in equation (1): VDE=ERe- – ERe-–

(1)

The partial atomic charges were both fitted to the electrostatic potential according to the Merz-Sigh-Kollman scheme44 and computed using Natural Population Analysis (NPA)45 method. The adiabatic electron affinity (AEA) values for the Mg2F5-2mOm (m=1, 2) and Mg3F7-2mOm (m=1-3) systems considered were obtained by utilizing the (CCSD(T))/66 ACS Paragon Plus Environment

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311+G(3df) approach. All computations were accomplished with the GAUSSIAN16 (Rev.B.01) software package.46 3. Results and Discussion The equilibrium geometries of the lowest energy MgnF2n+1-2mOm (n=2, 3; m=1–3) species (labeled 1 for each anion) together with their higher energy isomeric forms characterized by the CCSD(T)/6-311+G(3df) relative zero-point corrected energies (symbolized as ER) are provided in Figures 1–4. The corresponding harmonic vibrational frequencies (collected in Tables S2-S6 of Supporting Information) reveal that all geometries considered correspond to minima on the MP2 ground state anion potential energy surface (as all the Hessian matrix eigenvalues are positive). The large HOMO–LUMO gap (GAP) values ranging from 1.516 to 9.900 eV (see Table S1) for the MgnF2n+1-2mOm (n=2, 3; m=1–3) isomers imply that each of them might be thermodynamically stable. In the present contribution, instead of reporting the geometrical parameters exemplifying all isomers found (which are available in supporting sections 1.1-1.3) the qualitative discussion of the lowestenergy (1) geometries is yielded in the subsequent section. 3.1. Equilibrium Geometrical Structures and Relative Stabilities of the Trinuclear Mixed Mg3F7-2mOm (m=1-3) Clusters The global minimum of the Mg3F5O− anion is Cs symmetry structure (1 in Figure 1) in which three magnesium atoms lie in a triangle configuration (with valence Mg1–Mg2–Mg3 and dihedral Mg1–O–Mg3–Mg2 angles of 57.4° and 95.1°, respectively). In the 1 Mg3F5O− structure three halogen atoms (F2, F3, F4) play the same role of ring substituent that connects one given pair of magnesium atoms (via a 1.880 Å (Mg3–F3,4), 1.985 Å (Mg1,2–F2), and 2.140 Å (Mg1–F3) bonds; see Figure 1), and other two fluorine atoms (F1, F5) are terminal ligands which interact only with magnesium atom through a single 1.836 Å bonds. Finally, the oxygen atom is located on the top of the triangle and is connected to each of the three Mg 7 ACS Paragon Plus Environment


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atoms (Mg1,2–O=1.998 Å and Mg3–O=1.883 Å) and altogether forms an umbrella-like configuration. The 1 Mg3F5O− isomer resembles the structure of the triangular Mg3F7− (of C3v symmetry) anion, in which magnesium atoms lie in a triangle configuration (valence Mg1– Mg2–Mg3 and dihedral Mg1–F3–Mg3–Mg2 angles read 51.3° and 94.9°, respectively).21 Recalling that in the Mg3F7− anion (i) three terminal fluorine ligands are connected with only one magnesium ion each (via a single 1.821 Å bond), (ii) three ring F ions play the same role of bridging substituent that binds one given pair of magnesium atoms (via a 1.936 Å bond), and (iii) one halogen ion is connected with three Mg ions (via a 2.061 Å bonds), it might be assumed that Mg–F separations in the quasi-triangular 1 Mg3F5O− negative ion are of similar lengths, while the elongated distances (by 0.2 Å) are found in the Mg–F–Mg bridging parts.21 Clearly, the replacing two fluorine ligands in the Mg3F7− anion with an oxygen atom leads to the 1 Mg3F5O− anion in which the umbrella-like structure is preserved.


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Figure 1. The MP2 equilibrium geometries of the Mg3F5O anion. The bond distances (r, in Å), the OVGF/6-311+G(3df) vertical electron detachment (VDE, in eV) energies, and the relative energies (ER, in kcal/mol) calculated for Mg3F5O isomers with respect to the global minimum (1). *VDE obtained with the CCSD(T)/6-311+G(3df) approach.

In the case of a Mg3F3O2− anion, the ground state 1 Mg3F3O2− isomer (of Cs symmetry) corresponds to structure with one magnesium (Mg3) atom decorated with one fluorine (F2) ligand and two oxygen atoms localized in a triangle manner (valence O1–O2–F2 9 ACS Paragon Plus Environment


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and dihedral O1–Mg3–O2–F2 angles are equal to 45.8° and 180.0°, respectively). Such a configuration allows for forming SB connections with each of two neighboring central metal cores (Mg1, Mg2) through a Mg–F–Mg and Mg–O–Mg bridging bonds and one additional connection with neighboring metal ions through a Mg–O(Mg)–Mg bridge. The magnesium– fluorine and magnesium-oxide bond distances in the 1 Mg3F3O2− anion are within the 1.825– 2.013 and 1.866–2.004 Å range, respectively. In turn, the ground state 1 Mg3FO3− geometry (of Cs symmetry) mimics a planar system with three ring oxygen atoms (with dihedral Mg1– Mg3–Mg2–O1 angle of 0.0°) each of is involved in establishing Mg–O–Mg bridges connecting one given pair of metal atoms (via bonds in the 1.851–1.986 Å range, see Figure 3). The Mg– F distance reads 1.853 Å and Mg–O bond lengths estimated for the 1 Mg3FO3− structure span the relatively narrow 1.851–1.937 Å range. The remaining 2-15 Mg3F3O2− (Figure 2 and supporting section 1.2) and 2-9 Mg3FO3− (Figure 3 and supporting section 1.3) isomers, although geometrically stable, were found to be shifted up in energy by 11 kcal/mol or more with respect to corresponding ground states (1), thereof their synthesize is unlikely in the gas phase.


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Figure 2. The MP2 equilibrium geometries of the Mg3F3O2 anion. Bond distances (r, in Å), the OVGF/6-311+G(3df) vertical electron detachment (VDE, in eV) energies, and the relative energies (ER, in kcal/mol) calculated for Mg3F3O2 isomers with respect to the global minimum (1). *VDE obtained with the CCSD(T)/6-311+G(3df) approach.



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Figure 3. The MP2 equilibrium geometries of the Mg3FO3 anion. Bond distances (r, in Å), the OVGF/6-311+G(3df) vertical electron detachment (VDE, in eV) energies, and the relative energies (ER, in kcal/mol) calculated for Mg3FO3 isomers with respect to the global minimum (1 Mg3FO3). *VDE obtained with the CCSD(T)/6-311+G(3df) approach.

To conclude, the magnesium atoms are capable of forming stable and strongly bound trinuclear anionic clusters with mixed ligands. Obtained results (which are reported in section 3.1 and supporting sections 1.1-1.3) clearly reveal that the Mg3F7-2mOm− (m=1–3) systems (i) adopt a quasi-triangular arrangement, (ii) resemble two rhombic fragments perpendicular to 12 ACS Paragon Plus Environment

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each other, (iii) contain [𝐹 ― 𝑀𝑔 ≡ ] subunit which allows for forming triple-bridged connections between two neighboring Mg atoms, (iv) possess one rhombic part links via single-bridged connection with third Mg atom (v) include only two-fold coordinated Mg atoms. In each case, the ground state isomer (labeled 1) accepts the quasi-triangular arrangement of three metal ions. An analogous situation is observed in the non-mixed trinuclear magnesium halides (i.e., Mg3F7− and Mg3Cl7−) where three Mg atoms are linked to each other via halogen ligands, forming the triangular structures.19, 21 As far as a geometrical location of oxygen substituents in the Mg3F7-2mOm− anions is analyzed, (i) the terminal O ligands are connected with only one metal ion each, via a single bond, (ii) the ring oxygen elements play the role of bridging ligands that link one given pair of metal atoms, or (iii) the bridged O atom is connected to three Mg ions and located on the top of the ‘umbrella’ formed by all three magnesium ions present in the system. In all ground state 1 Mg3F7-2mOm− (m=1-3) structures certain oxygen atoms are linked to three metal ions, altogether establishing the quasi-triangular arrangements. 3.2. Thermodynamic Stabilities of the Trinuclear Mg3F7-2mOm (m=1-3) Clusters In order to examine the thermodynamic stability of the Mg3F7-2mOm− (m=1–3) clusters, the free enthalpies (ΔHr298), entropies (ΔSr298), and Gibbs free (ΔGr298) energies were estimated for the reactions corresponding to the most likely fragmentation channels these clusters might be susceptible to. The analysis of the vulnerability of the Mg3F7-2mOm− (m=1– 3) isomers to the MgF3−, Mg(F)O−, F− anions, MgO or MgF2 molecules detachment indicates that all these disproportion reactions are thermodynamically unfavorable (see Tables S7–S9 of the Supporting Information). Explicitly, the smallest ΔGr298 values were obtained for the MgF2 loss (i.e. Mg3F7-2mOm− Mg2F5-2mOm− + MgF2); however, all these ΔGr298 values were found to be positive (58.10–96.92 kcal/mol for the low-energy isomers (ER within 6 kcal/mol; see Table 1), which indicates the thermodynamic stability of the Mg3F7-2mOm− (m=1, 2) 13 ACS Paragon Plus Environment


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anions toward MgF2 fragment detachment. The results gathered in Tables 1 and S1–S3 clearly imply that the fragmentations leading to the Mg2F4, Mg2F5−, Mg(F)O− or MgF3− are even less likely as the obtained ΔGr298 values are of the 41.47–227.21 kcal/mol range. To conclude, each of Mg3F7-2mOm− (m=1–3) anions, once synthesized, should be stable in the gas phase as the 1–3 Mg3F5O−, 1 Mg3F3O2−, and 1 Mg3FO3− systems (the formation of higher energy 4–9 Mg3F5O−, 2–15 Mg3F3O2−, and 2–10 Mg3FO3− isomers should be considered as less probably, despite their geometrical and thermodynamic stability) and not susceptible to any disproportions. Table 1. Free enthalpies (Hr298 in kcal/mol), entropies (Sr298 in cal/(mol·K)), and Gibbs free (Gr298 in kcal/mol) energies of the fragmentation reactions (at T=298.15 K, p=1 atm) calculated at the CCSD(T)/6-311+G(3df) level for MgnF2n+1-2mOm (ER within 6 kcal/mol) anions. Species (symmetry)

1 Mg3F5O (Cs) ER=0.00 2 Mg3F5O (Cs) ER=3.08 3 Mg3F5O (Cs) ER=5.81 1 Mg3F3O2 (Cs) ER=0.00 1 Mg3FO3 (Cs) ER=0.00 1 Mg2F3O (C2v) ER=0.00 1 Mg2FO2 (C2v) ER=0.00

Fragmentation path

Hr298

Sr298

Gr298

Mg3F5O Mg2F3O + MgF2 Mg3F5O Mg2F5 + MgO Mg3F5O Mg2F4 + Mg(F)O Mg3F5O MgF3 + MgO + MgF2 Mg3F5O Mg2F3O + MgF2 Mg3F5O Mg2F5 + MgO Mg3F5O Mg2F4 + Mg(F)O Mg3F5O MgF3 + MgO + MgF2 Mg3F5O Mg2F3O + MgF2 Mg3F5O Mg2F5 + MgO Mg3F5O Mg2F4 + Mg(F)O Mg3F5O MgF3 + MgO + MgF2 Mg3F3O2 Mg2FO2 + MgF2 Mg3F3O2 Mg2F3O + MgO Mg3F3O2 MgF2 + MgO + Mg(F)O Mg3F3O2 MgF3 + 2MgO Mg3FO3 Mg2FO2 + MgO Mg3FO3 2MgO + Mg(F)O Mg3FO3 3MgO + F Mg2F3O MgF2 + Mg(F)O Mg2F3O MgF3 + MgO Mg2F3O MgO + MgF2 + F Mg2F3O MgO + Mg(F)O Mg2F3O 2MgO + F Mg2F3O 2Mg + O2 + F

74.94 114.83 119.00 192.26 71.86 111.75 115.92 189.18 69.12 109.02 113.19 186.45 107.36 121.53 225.72 238.86 129.76 248.12 352.82 104.18 117.32 208.88 118.36 223.06 250.48

39.90 45.16 41.05 74.40 39.16 44.42 40.31 73.66 36.99 42.25 38.14 71.49 35.00 35.47 69.83 69.97 43.63 70.13 95.30 34.36 34.50 59.53 34.84 60.00 76.31

63.04 101.37 106.76 170.08 60.18 98.51 103.90 167.22 58.10 96.42 101.82 165.13 96.92 110.96 204.90 218.00 116.75 227.21 324.41 93.94 107.04 191.14 107.97 205.17 227.73

3.3. Equilibrium Structures and Stabilities of the Mixed Dinuclear Anions The exploration of the potential energy surface (PES) of the negatively-charged 14 ACS Paragon Plus Environment

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Mg2F5-2mOm clusters (m=1, 2) leads to the minimum energy geometries illustrated in Figure 4. The ground state 1 Mg2F3O structure (of C2v symmetry) mimics the DB form with the metal ions connected to each other via two different ligands (F2 and O, 1 Mg2F3O in Figure 4). As expected

20, 21,

the Mg–F distances in DB connecting parts are larger (by 0.16 Å) than

the Mg–F separations in the Mg–F terminal bonds (see 1 Mg2F3O in Figure 4). The 1 Mg2F3O isomeric form is the lowest energy structure thus its presence should be anticipated in the gas phase, while the creation of the 2-5 Mg2F3O isomeric forms should be regarded as less probably (due to ER values exceeding 48 kcal/mol).

Figure 4. The MP2 equilibrium geometries of the Mg2F3O and Mg2FO2 anions. Bond distances (r, in Å), the OVGF/6-311+G(3df) vertical electron detachment (VDE, in eV) energies, and the relative energies (ER, in kcal/mol) calculated for Mg2F5-2mOm isomers with respect to the corresponding global minimum (1). *VDE obtained with the CCSD(T)/6-311+G(3df) approach.



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In the case of a Mg2FO2 system, the ground state 1 Mg2FO2 isomer (of C2v symmetry) corresponds to double-bridged structure with the Mg atoms connected with each other through two oxygen (O1, O2) atoms (with Mg1–O1,2 and Mg2–O1,2 bonds of 2.022 and 1.876 Å, respectively; see Figure 4). The SB (labeled 2, 3, 5 in Figure 4) and TB (4 in Figure 4) isomers of Mg2FO2 are considerably higher in energy (by 17 kcal/mol or more) in comparison to the ground state (1 Mg2FO2) structure, which reveals that the formation of such isomers should be considered as unlikely. According to obtained results, dinuclear mixed magnesium clusters, in contrary to non-mixed dinuclear magnesium halides, are double-bridged structures. Clearly, replacing a pair of halogen atoms in Mg2X5 (X=F, Cl)

19, 22

anions (of D3h symmetry) with an oxygen

atom leads to reducing the total number of ligands in the resulting systems. The rhombic-like geometry of the Mg2X5-2mOm allows for a more symmetrical allocation of the ligands around the central metal ions (represented by the higher-symmetry point group, C2v) with respect to triple-bridged forms (4 Mg2FO2 and 5 Mg2FO2, of Cs symmetry), which provides both higher stability and more even distribution of the additional negative charge. The importance of a ligands’ distribution in the frame of its influence on the electronic stability of resulting species is yet to be explored in section 3.9. 3.4. Thermodynamic Stabilities of the Dinuclear Mixed Anionic Clusters The thermodynamic stability of the lowest energy 1 Mg2F3O anion was verified via the computations of the disproportion energies with respect to the Mg2F3O MgF2 + Mg(F)O, Mg2F3O MgF3 + MgO, Mg2F3O MgO + MgF2 + F processes; see Table 1. The resulting 93.94, 107.04, 191.14 kcal/mol values of ΔGr298, respectively, reveal the thermodynamic stability of the 1 Mg2F3O isomer. In the case of 2–5 Mg2F3O isomeric forms, the positive ΔGr298 values estimated for the most probable fragmentation paths (see 16 ACS Paragon Plus Environment

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Table S5) confirm their thermodynamic stability, as well. Similarly, the analysis of the susceptibility of each Mg2FO2 isomer to defragmentation processes (i.e. Mg2FO2 MgO + Mg(F)O, Mg2FO2 2MgO + F, and Mg2FO2 2Mg + O2 + F) reveal that considered fragmentation paths are endothermic (ΔGr298 > 0, see Tables 1 and S10) and 1–5 Mg2FO2 systems are thermodynamically stable. Thus, both the Mg2F3O and Mg2FO2 anions are not susceptible to fragmentation, as indicated by the positive and rather large ΔGr298 values, for the disproportionation reactions examined. 3.5. Geometric Modification between the Non-charged and Negatively-charged Clusters The ground-states (1) together with the higher energy isomeric forms (ER within 20 kcal/mol) of the neutral MgnF2n+1-2mOm species are given in Figures 5-7, while their Cartesian coordinates and corresponding harmonic vibrational frequencies are depicted in Supporting Information (tables S11-S15). The ground-state geometries of the neutral and the negativelycharged Mg3F5O clusters are significantly different from each other. The non-charged 1-3 Mg3F5O systems mimic two rhombic fragments perpendicular to each other, while quasitriangular structures (4-7 Mg3F5O in Figure 5) are higher in energy (by 3.24 kcal/mol or more). In turn, the 1 Mg3F5O− negative ion prefers the triangular arrangement, while the linear configuration, that is the ground state in the non-charged Mg3F5O system, is shifted up in energy by 62.15 kcal/mol (9 Mg3F5O− in Figure 1). This switching in the order of the ground state geometries of the neutral and the anionic Mg3F5O forms indicates the significant difference between the VDE and EA values. The adiabatic electron binding energy in the Mg3F5O− anion, which is equivalent to the adiabatic electron affinity (AEA) of the Mg3F5O cluster, reads 4.459 eV. The vertical electron detachment energy for the 1 Mg3F5O− system is equal to 6.826 eV. The dissimilarity of 2.367 eV between these two energies is significant and, in fact, confirms the assumption on substantial geometric modification between the noncharged and the negatively-charged geometries of the Mg3F5O cluster. 17 ACS Paragon Plus Environment


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Figure 5. The MP2 equilibrium geometries of the Mg3F7-2mOm (m=1, 3) clusters. Bond distances (r, in Å, the relative energies (ER, in kcal/mol) estimated for the Mg3F7-2mOm isomers with respect to the corresponding global minimum (1).

The low-energy structures of Mg3FO3 clusters (1-3 Mg3FO3 in Figure 5) correspond to a triangular arrangement of central metal atoms, which reveals their similarity to 18 ACS Paragon Plus Environment

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corresponding ground state anionic daughter (1 Mg3FO3−). In the lowest-energy 1 Mg3FO3 isomer, however, one oxygen atom acts as a terminal ligand, while in the 1 Mg3FO3− anion all O atoms play the same role of bridging ligands. This distinction between lowest-energy noncharged and anionic structures results in the difference between estimated AEA (of 3.132 eV) and VDE (of 4.905 eV) values. Among trinuclear magnesium-based oxyfluoride clusters, the smallest energy difference between obtained AEA and VDE was found for Mg3F3O2 species and reads 1.662 eV. Both the 1 Mg3F3O2 and 1 Mg3F3O2− structures resemble a quasitriangular structure with a certain oxygen atom linked to three magnesium atoms, thus relatively small geometric modification upon an excess electron attachment is observed (see Figures 2 and 6).



Figure 6. The MP2 equilibrium geometries of the Mg3F3O2 clusters. Bond distances (r, in Å), the relative energies (ER, in kcal/mol) obtained for Mg3F3O2 isomers with respect to the global minimum (1).

The low-energy geometries (ER within 20 kcal/mol) of the neutral Mg2F5-2mOm species (m=1, 2) are depicted in Figure 7. The ground-state structures of the neutral and the negatively-charged Mg2F3O systems are significantly different from each other. In the 20 ACS Paragon Plus Environment

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rhombic-like 1 Mg2F3O system an oxygen atom plays a role of terminal ligand, while a rhombic-like structure with bridging oxygen atom (2 Mg2F3O in Figure 7) is slightly higher in energy (by 1.05 kcal/mol). In turn, the Mg2F3O− anion clearly prefers the bridging localization of O atom (1 Mg2F3O− in Figure 4), whereas the terminal oxygen atom localization, which is the ground state in the non-charged Mg2F3O system, is 48.07 kcal/mol higher in energy (2 Mg2F3O− in Figure 4). The non-charged Mg3FO2 system corresponds to a linear structure (1 Mg3FO2 in Figure 7), whereas 1-2 Mg3FO2 rhombic-like structures are higher in energy (ER always exceeds 14 kcal/mol). The Mg2FO2− anion, however, prefers the DB configuration (1 Mg2FO2− in Figure 4), while the linear configuration that is the ground state in the noncharged Mg3FO2 system, is shifted up in energy by 62.67 kcal/mol (5 Mg2FO2− in Figure 4). The observed switching in the order of the lowest-energy geometries of the non-charged and the anionic Mg2F5-2mOm molecular clusters results in the significant distinction between the estimated VDE and EA values. The AEAs in the Mg2F3O and Mg2FO2 read 3.917 and 2.407 eV, respectively, whereas the corresponding VDEs read 5.482 eV (1 Mg2F3O−) and 4.763 eV (1 Mg2FO2−). The considerable difference (of 1.565 eV (Mg2F3O) and 2.356 eV (Mg2FO2)) between vertical and adiabatic electron binding energies is in accordance with substantial geometric dissimilarity between the non-charged and the anionic forms of the dinuclear magnesium-based oxyfluoride clusters.



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Figure 7. The MP2 equilibrium geometries of the Mg2F5-2mOm (m=1, 2) species. Bond distances (r, in Å) and the relative energies (ER, in kcal/mol) estimated for Mg2F5-2mOm isomers with respect to the corresponding global minimum (1).

3.6. Thermodynamic Stabilities of the Non-charged Clusters The analysis of the sustainability of each magnesium oxyfluoride cluster to various fragmentations (see Tables 2 and S16 for the disproportionation reactions considered) indicates that all studied clusters are stable and not sustainable to any defragmentation. Explicitly, in the Mg3F5O and Mg2F3O case, the smallest ΔGr298 values were obtained for the Mg(F)O loss (i.e. MgnF2n-1O Mgn-1F2(n-1) + Mg(F)O); however all these ΔGr298 values were found to be positive ( 44.15-51.40 kcal/mol (Mg3F5O) 35.40-49.50 kcal/mol (Mg2F3O); see Tables 2 and S16), which confirm their thermodynamic stabilities. As far as Mg3FO3 and Mg2FO2 systems are concerned, the smallest ΔGr298 values were predicted for the MgO loss (i.e. MgnFOn Mgn-1FOn-1 + MgO); still all these ΔGr298 energies are positive and relatively large ( 91.55-100.48 kcal/mol (Mg3FO3) and 76.57-97.53 kcal/mol (Mg2FO2); see Tables 2 and S16), which reveal their thermodynamic stabilities. According to the results gathered in Tables 2 and S16, the fragmentations of the Mg3F3O2 cluster leading to the Mg2F4, Mg2F3O, or Mg(O)F are unlikely as the obtained ΔGr298 values span the 41.15–162.74 kcal/mol range. Therefore, according to the performed analysis of the sustainability of magnesium oxyfluoride 22 ACS Paragon Plus Environment

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clusters to fragmentations, the Mg3F5O, Mg3F3O2, Mg3FO3, Mg2F3O, and Mg2FO2 clusters are stable and not vulnerable to any disproportionation. Table 2. Free enthalpies (Hr298, in kcal/mol), entropies (Sr298, in cal/(mol·K)), and Gibbs free (Gr298, in kcal/mol) energies of the fragmentation reactions (at T=298.15 K, p=1 atm) estimated with the CCSD(T)/6311+G(3df) method for the MgnF2n+1-2mOm (ER within 6 kcal/mol) clusters.

Species (symmetry) 1 Mg3F5O (C2v) ER=0.00 2 Mg3F5O (Cs) ER=0.61 3 Mg3F5O (Cs) ER=2.61 4 Mg3F5O (Cs) ER=3.24 5 Mg3F5O (Cs) ER=5.37 6 Mg3F5O (C1) ER=6.11 1 Mg3F3O2 (Cs) ER=0.00 2 Mg3F3O2 (Cs) ER=4.94 1 Mg3FO3 (Cs) ER=0.00 2 Mg3FO3 (C1) ER=0.80 3 Mg3FO3 (C1) ER=1.26 1 Mg2F3O (C2v) ER=0.00 2 Mg2F3O (C2v) ER=1.05 1 Mg2FO2 (C∞v) ER=0.00

Fragmentation path

Hr298

Sr298

Gr298

Mg3F5O  Mg2F4 + Mg(F)O Mg3F5O  Mg2F3O + MgF2 Mg3F5O  MgF3 + MgO + MgF2 Mg3F5O Mg2F4 + Mg(F)O Mg3F5O Mg2F3O + MgF2 Mg3F5O MgF3 + MgO + MgF2 Mg3F5O  Mg2F4 + Mg(F)O Mg3F5O  Mg2F3O + MgF2 Mg3F5O  MgF3 + MgO + MgF2 Mg3F5O  Mg2F4 + Mg(F)O Mg3F5O  Mg2F3O + MgF2 Mg3F5O  MgF3 + MgO + MgF2 Mg3F5O  Mg2F4 + Mg(F)O Mg3F5O  Mg2F3O + MgF2 Mg3F5O  MgF3 + MgO + MgF2 Mg3F5O  Mg2F4 + Mg(F)O Mg3F5O  Mg2F3O + MgF2 Mg3F5O  MgF3 + MgO + MgF2 Mg3F3O2  Mg2FO2 + MgF2 Mg3F3O2  Mg2F3O + MgO Mg3F3O2  Mg(F)O + MgO + MgF2 Mg3F3O2  Mg2FO2 + MgF2 Mg3F3O2 Mg2F3O + MgO Mg3F3O2 Mg(F)O + MgO + MgF2 Mg3FO3  Mg2FO2 + MgO Mg3FO3  2MgO + Mg(F)O Mg3FO3  Mg2FO2 + MgO Mg3FO3  2MgO + Mg(F)O Mg3FO3  Mg2FO2 + MgO Mg3FO3  2MgO + Mg(F)O Mg2F3O  MgF2 + Mg(F)O Mg2F3O  MgO + MgF3 Mg2F3O  MgF2 + Mg(F)O Mg2F3O  MgO + MgF3 Mg3FO3  Mg2FO2 + MgO Mg3FO3  2MgO + Mg(F)O

61.75 62.44 268.92 61.14 61.83 268.31 59.14 59.83 266.31 58.51 59.20 265.68 56.38 57.07 263.55 55.64 56.33 262.81 74.27 123.21 182.65 69.33 118.27 177.70 113.10 221.47 112.29 220.66 111.83 220.21 59.43 206.48 58.38 205.44 108.37 241.67

34.71 34.62 69.75 31.60 31.51 66.64 32.08 31.99 67.12 40.20 40.11 75.24 38.42 38.33 73.46 36.63 36.54 71.67 39.17 33.47 66.78 46.34 40.64 73.95 42.30 69.91 40.49 68.10 47.71 75.31 33.31 35.13 30.71 32.54 36.38 52.37

51.40 52.12 248.12 51.72 52.44 248.44 49.57 50.29 246.30 46.52 47.24 243.25 44.92 45.64 241.65 44.72 45.44 241.44 62.59 113.23 162.74 55.52 106.16 155.66 100.48 200.62 100.22 200.36 97.61 197.75 49.50 196.01 49.23 195.74 97.53 226.05



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3.7. Factors Determining Magic Cluster Stability of the Magnesium-based Oxyfluoride Anions The electronic states in compact molecular clusters are gathered into electronic shells similarly to those in atoms resulting in the suggestion that molecular clusters might be regarded as superatoms.4, 47 Molecular clusters characterized by closed electronic shells and a large HOMO− LUMO gaps are usually chemically inert, energetically stable, and as such are denoted as “magic numbers”.47 The most stable molecular clusters (i.e., magic numbers) are created when their atomic shells are filled as the valence count access a value corresponding to a closed valence shell resembling noble gas atoms. Superatoms which need an electron to access closed electronic shells form extremely stable negative ions with filled electronic shell and a large EA. The Mg3F7-2mOm and Mg2F5-2mOm clusters might be viewed as superatoms in which the presence of an additional electron lead to acquiring filled electronic shells and a high electron binding energy. To demonstrate the magic numbers’ nature of the polynuclear magnesium oxyfluoride clusters, it needs to be recalled that the most stable oxidation state of Mg element is +2, where the valence 3s2 electrons participate toward chemical bonding. If the Mg3F7-2mOm and Mg2F52mOm

formulas are considered, an excess electron ensures an additional stabilization of the

systems as the ligand atoms require this electron for filled their electronic shell and maintaining the +2 oxidation state of the Mg atoms. In consequence, each atom in the Mg3F7− 2mOm

and Mg2F5-2mOm− systems displays electronic shell saturation (2p6 for metal and ligand

atoms), and the subsequent strong ionic bonding contributes to the enhanced stability of the magnesium oxyfluoride cluster. As it will elucidate in section 3.11, the extra electron is now distributed over substituents, thus ensuring the high VDE values of the Mg3F7-2mOm− and Mg2F5-2mOm− clusters. Since the ground state 1 Mg2F5-2mOm− and 1 Mg3F7-2mOm− anions reveal symmetry in the geometrical structure (C2v and Cs, respectively), electronic closure and high stability, each 24 ACS Paragon Plus Environment

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of them might be classified as a magic number. The enhanced stability of the magic numbers is typically accompanied by a significant energy separation between the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals (i.e. HOMO-LUMO gaps).47 The large HOMO-LUMO gap is a reliable measure of the chemical inertness of a compound. The HOMO-LUMO gaps estimated for the low-energy isomeric forms (ER within 15 kcal/mol) are in the 6.802-9.900 eV range with the largest GAPs estimated for the Mg3F5O− species; see Table 4. The large energy gaps indicate that the Mg3F5O−, Mg3F3O2−, Mg3FO3−, and Mg2F3O− anions are moderately reactive (i.e. chemically inert) and suitable to be utilized as building blocks for new functional materials design.1, 21, 25 3.8. The Performance of Theoretical Methods for Previously Described Superhalogen Anions We performed several test calculations for various well-known superhalogen anions to verify the quality of the results that might be obtained by implementing the ab initio methods. The results of these tests (for LiCl2, LiBr2, NaCl2, Na2Cl3, NaBr2, MgCl3, MgBr3, CaCl3, and CaBr3 anions) are gathered in Table 3. Explicitly, the VDE values were calculated for these anions at the CCSD(T)/6-311+G(3df) and OVGF/6-311(3df) levels at their equilibrium geometries optimized at the MP2/6-311+G(d) level (to reproduce the theory levels used in the present contribution). Next, the resulting VDE values were compared to the corresponding experimental vertical electron detachment energy (VDEexp) values found in the literature (see Table 3). As it turned out, the relative deviations (in %) estimated as VDEexp– VDEtheor divided by VDEexp (where VDEtheor stand for the VDE obtained at the CCST(T) (VDECCSD(T)) and OVGF (VDEOVGF) levels) indicate that the use of the CCSD(T)/6311+G(3df) and OVGF/6-311+G(3df) approaches leads to the errors spanning the 0.2–3.3% and 0.3–5.6% range, respectively, with the largest deviation observed for the NaBr2 anion (3.3% at the OVGF/6-311+G(3df) level of theory; see Table 3) and the NaCl2 anion (2.0%; 25 ACS Paragon Plus Environment


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Table 3) in the case of the CCSD(T)/6-311+G(3df) approach. In addition, the VDEs obtained at the OVGF level are overestimated in the studied negative ions with respect to the exact (i.e. experimental, VDEexp) values, whereas the CCSD(T)-calculated VDEs do not follow this trend as VDECCSD(T) are either underestimated (for the LiCl2, NaCl2, Na2Cl3, MgCl3, CaCl3 anions) or overestimated (for the LiBr2, NaBr2, MgBr3, CaBr3 species). Thus, the sign of a deviation (i.e. whether the obtained value is either underestimated or overestimated) cannot be predicted in the case of the CCSD(T)/6-311+G(3df) approach. Table 3. Comparison of computational and experimental VDE (in eV) values. Species

VDEOVGF DevOVGF DevREL VDECCSD(T) DevCCSD(T) DevREL

LiCl2 LiBr2 NaCl2 Na2Cl3 NaBr2 MgCl3 MgBr3 CaCl3 CaBr3

5.979 5.594 5.892 6.527 5.537 6.684 6.144 6.731 6.238

0.059 0.174 0.032 0.067 0.177 0.084 0.144 0.111 0.138

1.0 3.2 0.5 1.0 3.3 1.3 2.4 1.7 2.3

5.837 5.497 5.744 6.375 5.438 6.526 6.031 6.557 6.116

VDEexp

5.92±0.0448 5.92±0.0348 5.86±0.0648 6.46±0.0448 5.92±0.0648 6.60±0.0449 6.00±0.0449

-0.083 0.077 -0.116 -0.085 0.078 -0.074 0.031

1.4 1.4 2.0 1.3 1.5 1.1 0.5

-0.063 0.016

1.0 6.62±0.0449 0.3 6.10±0.0449

To conclude, we consider the theory levels performed in this contribution as appropriate since the anticipated errors in VDEs of the species considered should not surpass 3% (for the OVGF/6-311+G(3df) approach) and 2% (for the CCSD(T)/6-311+G(3df) technique). Moreover, the previous report on the performance of various ab initio approaches and basis sets in obtaining the vertical electron detachment energies of superhalogen anions validates the capability of the OVGF/6-311+G(3df) and CCSD(T)/6-311+G(3df) methods to reproduce the electron binding energies of such anions with decent accuracy.50 3.9. Vertical Electron Detachment Energies of the MgnF2n+1-2mOm− Clusters The vertical electron detachment energies (VDEs) for all geometrical structures of the Mg3F7-2mOm and Mg2F5-2mOm anions calculated both at the CCSD(T)/6-311+G(3df) and OVGF/6-311+G(3df) levels are provided in Supporting Information (Table S1), whereas the 26 ACS Paragon Plus Environment

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VDEs of the low-energy isomeric forms (ER within 35 kcal/mol) are also provided in Table 4. In this contribution, the VDEs estimated at the OVGF/6-311+G(3df) level are considered as the most reliable results19-21, and hence the following discussion is limited to these values. Although, it needs to be noticed that the estimated VDE values are underestimated at the CCSD(T) level (with respect to corresponding OVGF values). Table 4. The relative energy (ER, in kcal/mol), the HOMO-LUMO gap (GAP, in eV), the vertical electron detachment energy (VDE, in eV), adiabatic electron detachment energy (ADE, in eV) values calculated for the MgnF2n+1-2mOm systems (ER within 35 kcal/mol).

Species (Symmetry) 1 Mg3F5O (Cs) 2 Mg3F5O (Cs) 3 Mg3F5O (Cs) 4 Mg3F5O (C1) 5 Mg3F5O (Cs) 6 Mg3F5O (C1) 1 Mg3F3O2 (Cs) 2 Mg3F3O2 (Cs) 3 Mg3F3O2 (Cs) 4 Mg3F3O2 (Cs) 5 Mg3F3O2 (Cs) 1 Mg3FO3 (Cs) 2 Mg3FO3 (Cs) 3 Mg3FO3 (C3v) 1 Mg2F3O (C2v) 1 Mg2FO2 (C2v) 2 Mg2FO2 (Cs) 3 Mg2FO2 (Cs)

ER 0.00 3.08 5.81 12.31 14.40 26.77 0.00 13.29 20.22 22.98 33.09 0.00 11.13 11.22 0.00 0.00 17.13 22.41

GAP 9.746 9.796 9.102 9.900 8.308 9.410

VDEKT 7.659 7.371 6.464 7.403 5.715 6.647

VDECCSD(T) 5.902 5.587 5.131 6.047 4.455 5.406

VDEOVGF 6.826 6.512 6.152 7.135 5.468 6.418

8.245 8.016 8.023 8.261 7.739 6.802 7.088 7.959 8.855 6.970 5.481 2.608

5.607 5.504 5.534 5.864 5.509 4.895 4.579 5.214 5.709 4.738 2.963 1.375

4.333 4.026 4.288 4.384 4.144 3.669 3.257 3.842 4.471 3.474 1.849 3.452

5.520 5.303 5.351 5.593 5.309 4.905 4.498 4.992 5.482 4.763 * *

ADE 4.599 4.466 4.517 4.236 3.861 3.324 3.844 3.482 3.705 3.717 3.619 3.167 2.936 2.700 3.962 2.958 1.664 2.288

*The pole strength (PS) value is insufficiently large to justify the use of the OVGF technique (the PS < 0.80).

The VDE values, estimated at the OVGF/6-311+G(3df) level and gathered in Table 4, considerably exceed the EA of the chlorine atom (3.62 eV)3 affirming the superhalogen nature of the Mg3F7-2mOm and Mg3F5-2mOm anions. Explicitly, the VDE of the 1 Mg3F5O− isomer reads 6.826 eV and substantially large VDEs (5.468-6.512 eV, Table 4) were obtained for the 2, 3, 5, 6 structures, as well. In the case of the 4 Mg3F5O− isomeric form corresponding VDE is slightly larger (by 0.209 eV) with respect to the 1 Mg3F5O− ground state, which can be 27 ACS Paragon Plus Environment


associated with smaller interligand repulsion. In contrary to remaining isomeric forms (i.e., 1, 2, 3, 5, 6 in which each metal ion is surrounded by three or four ligand atoms; see Figure 1), in the 4 Mg3F5O− isomer one external Mg (Mg3) atom is two-fold coordinated, which leads to lowering the topological constrains in the 4 Mg3F5O− structure and electron binding increase. The VDE value of the lowest energy 1 Mg3FO3− reads 4.905 eV. The VDE for the 3 Mg3FO3− structure, however, was found to be slightly larger (by 0.087 eV), which might be related to the higher molecular symmetry of this isomer (C3v for the 3 Mg3FO3−) compared with the 1 Mg3FO3− (of Cs symmetry). Because of more symmetrical allocation of the electronegative ligands around the central metal atoms (represented by the higher-symmetry point group, C3v) which provides more even distribution of the additional negative charge, the electron binding energy for the 3 Mg3FO3− (VDE=4.992 eV) is larger with respect with to 1 Mg3FO3− structure (of Cs symmetry). To conclude, the VDE of the superhalogen anion strongly depends on its geometry and this conclusion is in accordance with earlier theoretical reports.18, 20, 21 3.10. Adiabatic Electron Detachment Energies of the MgnF2n+1-2mOm− Clusters To further investigate the electron binding strength issue, the relative energies were used to calculate the adiabatic detachment energy (ADE) values. The ADE is the energy difference between the neutral and the negative ion with the neutral relaxed to the nearest local minimum utilizing the anionic geometry as the starting structure. The ADE values are expected to be larger than corresponding VDEs, as the VDE is the energy difference between the neutral and negative ion both at the equilibrium geometry of the negative ion. Indeed, ADE value is always lower than the corresponding VDE value (obtained at the same CCSD(T)/6-311+G(3df) theory level, see Table 4) reflecting a large change in the geometry of MgnF2n+1-2mOm− clusters after electron detachment. Namely, the adiabatic detachment electron energies in the 1 Mg3F5O−, 1 Mg3F3O2−, 1 Mg3FO3−, 1 Mg2F3O2−, and 1 Mg2FO2− are calculated to be 4.599, 3.844, 3.167, 3.962, and 2.958 eV, respectively, whereas the corresponding VDEs read 5.902 eV (1 Mg3F5O−), 4.333 eV (1 Mg3F3O2−), 3.669 eV (1 28 ACS Paragon Plus Environment

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Mg3FO3−), 4.471 eV (1 Mg2F3O−), and 3.474 eV (1 Mg2FO2−). The considerable difference between vertical and adiabatic electron detachment energy values is in accordance with substantial geometric dissimilarity between the non-charged and the anionic forms of the magnesium-based oxyfluoride clusters. By definition, the adiabatic electron detachment energy of an anion coincides with the adiabatic electron affinity of the neutral system.51 The estimated ADEs are found to be almost equal to the electron affinities of the corresponding non-charged clusters. Explicitly, the calculated ADEs differ by only 0.140 eV (1 Mg3F5O−), 0.014 eV (1 Mg3F3O2−), 0.035 eV (1 Mg3FO3−), 0.045 eV (1 Mg2F3O2−) from the corresponding adiabatic electron affinities; see Table 4. A good agreement between ADE and AEA values both proves the accuracy of the theoretical treatment as well as lends assurance to the interpretation of the principal mechanism for stability. 3.11. HOMO Molecular Orbital Analysis To further support the discussion on the large electronic stability of the Mg3F7-2mOm− and Mg2F5-2mOm− anionic superatoms, the three-dimensional pictures of their HOMOs are provided here (see Figure 8). The HOMOs reveal the bonding character with respect to the fluorine-metal atom interaction and the anti-bonding character with respect to the oxygenmetal atom interaction. To understand the novelty of the mixed Mg3F7-2mOm− and Mg2F5− 2mOm

clusters, it needs to be recalled that for most superhalogen anions known10,

18,

the

HOMOs are disposed among the ligands with no contributions from the metal atomic orbitals (AOs) and indicates the non-bonding character with respect to the ligand-metal atom interaction. Examples include the Mg3F7− ‘non-mixed’ anion (i.e., the anion built of the same substituents) which HOMO is comprised purely of ligands’ AOs and displays a non-bonding character.21 In contrary, for the studied ‘mixed’ magnesium-based clusters the HOMO is 29 ACS Paragon Plus Environment


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comprised of both substituents’ AOs and magnesium AOs. Thus, each of these HOMOs reveals (i) a bonding character between the metal core and the smaller (more electronegative) substituent and (ii) an anti-bonding character between the central core atom and the larger (less electronegative) substituent. The observed alteration in the HOMO nature is naturally associated with the VDE decrease (by 3.653 eV (1 Mg3F5O−) with respect to this in nonmixed Mg3F7− anion). Thus, a significant VDE decrease origin from the fact that the original non-bonding HOMO in a C3v symmetry Mg3F7− anion alterations to a mixed bonding/antibonding character when one pair of the F substituents is displaced with the less electronegative oxygen atom. Still, although the studied HOMOs display the antibonding character with respect to the oxygen-metal core interaction, the strongly negative HOMO eigenvalues of −7.659 (1 Mg3F5O−), −7.371 (2 Mg3F5O−), −6.464 (3 Mg3F5O−), −5.607 (1 Mg3F3O2−), −4.895 (1 Mg3FO3−), −5.709 (1 Mg2F3O−), and −4.738 eV (1 Mg2FO2−) reveal the large electronic stabilities of studied anions and indicate that even the outermost electrons (comprising the additional electron) are anticipated to be highly bound in those negative ions.


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Figure 8. The HOMOs of the MgnF2n+1-2mOm anions (n=2, 3; m=1-3) and the corresponding orbital eigenvalue (ε, in eV) values.

3.12. The Effect of the Number of Central Metal Atoms Polynuclear superhalogens (MnXn·k+1), with the number of central metal atoms (n) higher than one, take benefit of growing the number of substituents while preserving their large stability. The electron binding energies for such molecules are anticipated to be enhanced (with respect to mononuclear superhalogens).20,

21, 24

Indeed, the computed VDE

values for the Mg3F7-2mOm− and Mg2F5-2mOm− anionic clusters display a strong dependence on 31 ACS Paragon Plus Environment


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the number of central magnesium ions. As illustrated in Figure 9, the obtained VDE values increase relatively rapid for a number of central atoms developing from 1 to 3 (for a given number of oxygen atoms). Explicitly, in the series of the mixed species containing one oxygen atom, Mg(F)O−– Mg2F3O−– Mg3F5O−, the VDE value increases sharply when going from Mg(F)O− (3.314 eV) to Mg2F3O− (5.482 eV) and constantly grows when going to Mg3F5O− (6.826 eV). Similarly, for the pair of the Mg2FO2− and Mg3F3O2− anions the electronic stability increases when going from 1 Mg2FO2− (4.763 eV) to 1 Mg3F3O2− (5.520 eV). Hence, it allows assuming that VDE values of the MgnF2n+1-2mOm− anionic clusters are strongly related to the number of central metal cores and increase with the number of metal atoms growth (for a given number of oxygen atoms).

Figure 9. The VDE dependence on the number of oxygen atoms (m) for the MgF3-2mOm−, Mg2F5− − 2mOm , and Mg3F7-2mOm (m = 0–3) anions.

3.13. The Effect of the Number of Electronegative Ligands The enormously large VDEs obtained for the polynuclear Mg3F7-2mOm− and Mg2F5− 2mOm

anions are correlated with the large electronegativity of the substituents that efficiently

supports large additional electron bonding. Moreover, the great number of electronegative ligands ensures (due to the so-called ‘collective effects’)18, 20, 21 the efficient distribution of the additional negative charge in the negative ion. Thus, the polynuclear structures with more ligands are expected to achieving larger VDEs.20, 21 Indeed, larger VDE values are estimated for larger (i.e., comprising more ligands) anions matching the Mg3F7-2mOm− and Mg2F5-2mOm− formulas. Namely, in the series of the trinuclear mixed species, Mg3FO3−–Mg3F3O2−– 32 ACS Paragon Plus Environment

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Mg3F5O− –Mg3F7−, the VDE grows significantly when going from 1 Mg3FO3− (4.905 eV) to 1 Mg3F3O2− (5.520 eV) and incessantly increases when going to 1 Mg3F5O− (6.826 eV) and 1 Mg3F7− (10.479 eV

21).

Analogously, in the series of the dinuclear Mg2FO2− –Mg2F3O−–

Mg2F5− anions the VDE considerably increases when going from 1 Mg2FO2− (4.763 eV) to 1 Mg2F3O− (5.482 eV) and further electronic stabilization is observed when going to the Mg2F5− anion (VDE=10.028 eV

21).

Clearly, replacing a pair of fluorine atoms with oxygen atom

leads to a lower number of ligands and reducing the electronic stability of the resulting system (due ‘collective effects’).18, 20 In summary, the Mg3F7-2mOm− and Mg2F5-2mOm− (m=0-3) examples indicate that replacing the fluorine ligands with oxygen substitutes leads to the superhalogen anions with smaller VDEs. The results provided indicate that decreasing the number of fluorine substituents in the system cause the VDE decrease, as both (i) the oxygen atoms are less electronegative (EA(O)=1.46 eV and EA(F)=3.40 eV)3 and (ii) introducing them is related with the total number of ligands reduction in a superhalogen anion. In consequence, electron binding energy decrease as an additional electron is delocalized over fewer and less electronegative ligands a molecule consists of. 3.14. Insights from the Analysis of the Charge Distribution The population analysis was accomplished based on the partial atomic charges (qESP) fitted with using the Merz-Singh-Kollman (MK) technique

44

and clearly reveals the

substantial charge separation (i.e. polarity) between the magnesium atoms and ligands. In particular, the estimated qESP on magnesium atoms span the 1.31-1.56 a.u. range for the most probable Mg3F7-2mOm– and Mg2F5-2mOm– isomers (n=1-3) with the highest qMgESP (i.e., 1.521.56 a.u.) for the 1 Mg3F5O– anion; see Figure 10. Thus, the enhanced electronic stabilities of the Mg3F7-2mOm− and Mg2F5-2mOm− clusters have to be correlated with the large polarity of Mg–F and Mg–O bonds with Mg+F and Mg+O charge allocation, respectively. In 33 ACS Paragon Plus Environment


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addition, the positive charge on magnesium cores allows for further stabilization of an additional electron that is distributed over ligands. The total charges on the central metal elements in the negatively-charged 1 Mg3F5O–, 1 Mg3F3O2–, 1 Mg3FO3–, 1 Mg2F3O–, and 1 Mg2FO2– are +4.60, +4.35, +4.29, +2.81, and +2.75 a.u., respectively, approving that the majority of negative charge (related to an additional electron) in the studied anions is delocalized over substituents, endorsing the superhalogen nature of Mg3F7-2mOm– and Mg2F5– 2mOm

species. In other words, the delocalization of the extra electron over electronegative

ligands assures high electron binding energy values of the Mg3F7-2mOm– and Mg2F5-2mOm– clusters (approaches 7 eV).

Figure 10. The MK partial atomic charges and NPA charge distributions (in parenthesis) in the most stable Mg3F7-2mOm– and Mg2F5-2mOm– (m=1-3) isomers (ER within 6 kcal/mol).

In order to further investigate the charge delocalization in the Mg3F7-2mOm– and Mg2F5– 2mOm

anionic clusters, the natural population analysis (NPA) at the MP2 level was

performed. According to Figure 10, where the natural charge of each atom is depicted, in the 34 ACS Paragon Plus Environment

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1 MgnF2n+1-2mOm– the charge on O and F atoms span the relatively narrow range from −1.89 to −1.83 e range and from −0.96 to −0.94 e range, respectively, whereas that on the Mg atoms are in the 1.76−1.89 e range. This implies that negative charge is mostly distributed on the ligands that is in accordance with the electronegativity of the free Mg (EA

Magnesium-based Oxyfluoride Superatoms: Design, Structure, and

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