Electride Characteristics of M2(h5-E5)2 (M= Be, Mg; E= Sb5-)

Prasenjit Das IIT Kharagpur: Indian Institute of Technology Kharagpur Pratim Kumar Chattaraj (  [email protected] ) IIT Kharagpur

Research Article

Keywords: Electride, Binuclear Sandwich Compound, Non-nuclear attractor (NNA), localization function (ELF) basin, NLO properties

Posted Date: February 24th, 2021

DOI: https://doi.org/10.21203/rs.3.rs-232917/v1

License:   This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License

Version of Record: A version of this preprint was published at Structural Chemistry on April 23rd, 2021. See the published version at https://doi.org/10.1007/s11224-021-01783-1. 5 - Electride Characteristics of M2( -E5)2 (M= Be, Mg; E= Sb5 )

Prasenjit Das,a Pratim Kumar Chattaraja,b,*

a Department of Chemistry, Indian Institute of Technology Kharagpur, Kharagpur 721302, India b Department of Chemistry, Indian Institute of Technology Bombay, Mumbai, 400076, India *E-mail: [email protected] (PKC)

Abstract

5 Ab initio computation is performed on the binuclear sandwich complexes, M2( -Sb5)2. Eclipsed

5 - and staggered conformations are generated due to the mode of binding by Sb5 ligand with the alkaline earth metals (Be and Mg metals). The complexes are thermodynamically stable at room temperature. The electron density descriptors and the natural bond orbital (NBO) analysis

5 5 confirmed the covalent nature of the M-M bond. Both Be2( -Sb5)2 and Mg2( -Sb5)2 complexes have one non-nuclear attractor (NNA) at the center of the M-M bond which is predicted and confirmed by the electron density analysis. At the NNA the values of the Laplacian of electron density are negative and an electron localization function basin (ELF) is present at the center of the M-M bond for localized . Both the complexes show large values of nonlinear optical

5 5 properties (NLO). Both the designed binuclear sandwich complexes Be2( -Sb5)2 and Mg2( -

Sb5)2 behave as electride.

Keywords: Electride; Binuclear Sandwich Compound; Non-nuclear attractor (NNA); Electron localization function (ELF) basin; NLO properties Introduction 1

Electrides are those kinds of interesting ionic systems in which cavity trapped electrons served as

anions [1-,2,3,4]. In recent years electride properties of materials have generated great attention in experiments as well as in theoretical studies. The history of the electride systems begins with the introduction of solvated electrons in solution [5,6]. Dye et al. provided

valuable studies on electride materials [1,7,8,9,-10,11,12]. The trapped electrons in electride systems are not associated with any specific atom. These trapped electrons are confined at cavities and the interstitial position in cryptands and solid crystals, respectively [3,13]. The electron density analysis confirmed the presence of confined electrons in the cavities of solid alkali metals

+ – [14,15]. In 1983, the first stable crystalline organic electride, Cs (18-crown-6)2e was synthesized by Ellaboudy et al. [16] and in 2003, Matsuishi et al. synthesized the first stable

4+ – inorganic electride, [Ca24Al28O64] ·(4e ) [17]. In both cases, the excess electrons are confined in the void spaces. Further, six temperature and air-stable electride systems were experimentally

synthesized [18,19,20,21-,22,23,24]. In these systems, the cryptand ligands or crown ethers are complexed with alkali metals. Electride materials are very sensitive to temperature and air [25]. So, it is very challenging to synthesize and characterize air and temperature stable electride materials. The presence of cavity trapped loose electrons causes a lowering of the work function of electrides so that they can be used as an electron donor in chemical reactions. Electride materials are very interesting for their remarkable potential applications such as emitting diodes for organic light

[26], reversible hydrogen storage materials [27], catalyst for the CO2 activation [28], splitting of

N2 molecule [29,30], powerful reducing agents [31,32,33], and superconductivity [34]. The experimental identification of the position of localized trapped electrons is very difficult because of the low density of these localized electrons. So, experimentalist used indirect evidence for its experimental characterization [11,35]. Therefore, computational studies can be helpful for the

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identification of electride materials. For that purpose, people used different computational tools to characterize electride materials. Computationally, the required criteria for characterizing electride material are, (i) presence of non-nuclear attractors (NNA) of the electron density;

[1,36,37] (ii) the Laplacian of electron density ( 2 ) should be negative at the position where

NNA exists; (iii) high NLO properties; [38] (iv) existence of electron localization function (ELF) basin [14] at the NNA region. Some molecules which do not possess confined electrons in electronic structure can show one or more of the above-mentioned properties. Therefore, none of these criteria by itself can be used to characterize electride systems, unambiguously. Some previous studies reported some molecules as electride materials based on large NLOPs are not considered to be materials with electride properties on these days. By simultaneous confirmation of these four criteria, we can say that a cavity-trapped electron is present within the structure of a molecule and it constitutes a real electride material. Most recently one theoretical work has

- shown that binuclear sandwich complexes of Be and Mg atoms bonded with isoelectronic C5H5 ,

- - - N5 , P5 , As5 ligands obeyed all these above-mentioned criteria to behave as electride materials

[39]. In these sandwich complexes, the Be and Mg atoms are in +1 oxidation state.

In this article, our main objective is to introduce molecules with electride property. Here

- 5 we have taken Sb5 ligand and the complexes which are formed by the ligand are M2( -Sb5)2

(M= Be and Mg). We have used ab initio method for the study of the structure, stability, and nature of bonding in these complexes. Then the NLO properties of both these systems have been studied. Finally, the electride characteristic of these two complexes has been analyzed.

Computational Details

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We have used the MP2 method in conjunction with correlation consistent double zeta quality basis set for geometry optimization and subsequent frequency calculations [40,41]. For Be and

Mg atoms cc-pVDZ basis set and for Sb atom cc-pVDZ-PP basis set has been used along with relativistic effective core potential (RECPs) [42,43,44]. The real harmonic frequency values indicate that these are the energy minimum structures on their respective potential energy surfaces. We have used Gaussian 16 program package for all the computations [45].

We have carried out the natural bond orbital (NBO) analysis to know the charge distribution on each atom. The computation for this analysis has been performed at the MP2 method in conjunction with correlation consistent triple zeta quality basis set. For Be and Mg atoms cc- pVTZ basis set and for Sb atoms cc-pVTZ-PP basis set has been used along with relativistic effective core potential (RECPs). For this computation, we have used NBO 3.1 [46,47] as implemented in Gaussian 16.

Multiwfn program package [48] has been used for atoms-in-molecule analysis (AIM) [49] of electron density. We have used the MP2 method for this analysis and various bond critical points

(BCP) have been generated. Both AIM and ELF basin populations have been analyzed.

We have used B3LYP/cc-pVDZ/cc-pVDZ-PP method to compute the average polarizability

( ), first hyperpolarizability ( ), and second hyperpolarizability ( ), where, cc-pVDZ basis set is used for Be and Mg atoms and cc-pVDZ-PP basis set is used for Sb atoms. For this computation, the optimized structures of the complexes have been taken from the MP2 method.

The equations which are used to calculate the , and values are as follows [50],

4

1 ii 3 ix,y,z

1 1 ()2 2 () i , where iijjjijjji ix,y,z 3 jx,y,z

1 ()iijj ijij ijji 15 i,j x,y,z

RESULTS AND DISCUSSION

Geometries and Energetics

- The optimized geometries of the ligand (Sb5 ) and the complexes considered for this work are given in Figure 1. The negative charge on the ligand is delocalized through the whole cyclic ring and makes all the Sb-Sb bond lengths are equal. The ligand has D5h point group of symmetry.

The Sb-Sb bond length in the ligand is 2.724 Å. This cyclic ligand can bind the metal atoms through 1, 2, 3, 4, 5 mode of bonding, and these modes of binding are shown in Scheme 1.

For the studied complexes the 1, 2, 3, 4 modes of binding with Be and Mg metals by the ligand are unstable but the 5 mode of binding is stable. For this reason, we have taken only 5 mode of bonding throughout our manuscript. Due to this 5 mode of bonding two conformation of the complexes has been observed and that are, (i) eclipsed conformation; (ii) staggered conformation. When two cyclic rings are cis to each other eclipsed conformation has been observed with D5h point group of symmetry. But when the rings are anti to each other staggered conformation resulted and the point group for this conformation is D5d. For both the complexes, the energy difference between eclipsed and staggered conformation is almost zero. Throughout

5

the manuscript, we have considered only the staggered conformation of all the complexes. The

5 eclipsed conformation provides identical results. In Be2( -Sb5)2 complex the Be-Be bond length

5 is 2.045 Å, the Be-Sb bond length is 2.714 Å and the Sb-Sb bond length is 2.744 Å. In Mg2( -

Sb5)2 complex the Mg-Mg bond length is 2.789 Å, the Mg-Sb bond length is 3.138 Å and the Sb-

2+ Sb bond length is 2.755 Å. The M-M bond distances in the M2 molecule and the M2 has been computed and the numerical values are presented in Table S1. The Mg-Mg and Be-Be bond distances are comparable with the Mg-Mg (2.780 Å) and Be-Be (2.040 Å) single bond length as predicted by pykko [51]. There is an increase in the Sb-Sb bond lengths during complex

- formation by Sb5 ligand with the metals (Be and Mg) as compared to that in the free ligand (E).

1 2 3 4 5 - Scheme 1. The scheme for the , , , , modes of binding of the Sb5 ligand with the alkaline earth metals (Be and Mg).

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Figure 1. The optimized geometries of the ligand and the corresponding complexes. The bond lengths are in Å unit.

To know about the thermodynamic stability of the studied complexes we have taken two

5 2+ - 5 5 + - dissociation pathways, (1) M2( -E)2 = M2 + 2E ; (2) M2( -E)2 = [M2( -E)] + E . Both the pathways correspond to the breaking of the metal-ligand bonds. We have used the MP2/cc- pVDZ/cc-pVDZ-PP method for the analysis of the thermodynamic stability of the complexes.

The values of the change in Gibbs’ free energies ( G) and zero-point corrected dissociation energies (D0) for the complexes are presented in Table 1. The pathway 2 has lower numerical values of G and D0 than that of the pathway 1. Both the dissociation pathways are endergonic in

5 5 nature. Be2( -Sb5)2 complex shows higher values of D0 and G than that of the Mg2( -Sb5)2 complex. Both the complexes are thermodynamically stable due to the highly positive numerical values of D0 and G.

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Table 1. The ZPE-corrected dissociation energy (D0, kcal/mol) and Gibbs’ free energy change 5 ( G, kcal/mol) for the dissociation of M2( -Sb5)2 (M= Be, Mg) complexes.

5 2+ - 5 5 + - M2( -E)2 = M2 + 2E M2( -E)2 = [M2( -E)] + E

Complexes D0 ΔG D0 ΔG

5 Be2( -Sb5)2 529.6 514.1 156.3 150.6

5 Mg2( -Sb5)2 401.7 381.2 129.9 118.1

NATURE OF BONDING

Molecular orbitals

We have used the MP2/cc-pVDZ/cc-pVDZ-PP method for molecular orbital analysis. For both the complexes the highest occupied molecular orbital (HOMO), and the lowest unoccupied molecular orbital (LUMO) are presented in Figure 2. In both the complexes the HOMO orbital is the M-M σ-bond orbital and the LUMO orbitals are doubly degenerate. The LUMOs are distributed over the E2 fragment without any contribution from the M2 fragment. The HOMO-

5 5 LUMO energy differences are 5.69 eV and 5.89 eV for Be2( -Sb5)2 and Mg2( -Sb5)2 complex, respectively. These higher values of HOMO-LUMO energy differences of both the studied complexes indicates the stability of these complexes.

8

5 5 Figure 2. The plots of the HOMO and LUMO of Be2( -Sb5)2 and Mg2( -Sb5)2 complexes. The values in the parenthesis are the energies of the corresponding orbitals in the eV unit.

Natural bond orbital (NBO) analysis

The charge distribution over the atoms in both the complexes has been analyzed by natural bond orbital analysis. The numerical values of charges and the Wiberg bond indices (WBI) for M-M

5 bonds and M-Sb bonds are given in Table 2. In Be2( -Sb5)2 complex the natural charges on Be

5 atoms are 0.42 |e| and the WBI values for Be-Be bond is 0.639. However, in Mg2( -Sb5)2 complex the natural charges on Mg atoms are 0.71 |e| and the WBI values of the Mg-Mg bond is

0.659. So, the covalent nature of the M-M bonds is predicted from these WBI values. The M-M natural bond orbitals in both the complexes under study are presented in Figure S1 and the occupancy of these bond orbitals are given in Table 2. The atomic contribution and the orbital contribution towards the M-M bond orbitals for both the complexes are given in Table 3. From table 3, it is shown that both metals contribute equally towards the M-M bond orbitals. The M-Sb bonds are non-covalent in nature as predicted from the very low WBI values of these bonds.

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Table 2. The natural charges (q, |e|), Wiberg bond indices (WBI), occupancy of M-M bond

orbitals (NM-M, |e|), and the valence electronic configuration of M (M= Be and Mg) atoms for 5 5 Be2( -Sb5)2 and Mg2( -Sb5)2 complexes.

Complexes qM qSb WBI (M-M) WBI (M-Sb) NM-M Valence electronic configuration of M

5 1.097 0.0919 0.0919 0.2006 Be2( -Sb5)2 0.42 -0.08 0.639 0.128 1.92 2s 2px 2py 2pz

5 1.097 0.0342 0.0368 0.0582 Mg2( -Sb5)2 0.71 -0.14 0.659 0.055 1.92 3s 3px 3py 3pz

Table 3. The atomic contribution and the orbital contribution towards the M-M bond orbitals for 5 M2( -Sb)2 (M= Be and Mg) complexes. Complexes Atomic Contribution Orbital Contributions

5 Be2( -Sb5)2 Be (50%) – Be (50%) Be : 2s (90.1%) 2p (9.8%)

Be : 2s (90.1%) 2p (9.8%)

5 Mg2( -Sb5)2 Mg (50%) – Mg (50%) Mg : 3s (96.7%) 3p (2.9%)

Mg : 3s (96.7%) 3p (2.9%)

Atoms in Molecule (AIM) Analysis

The electron density descriptors of both these complexes have been computed at relevant bond

critical points (BCPs) and the numerical values are given in Table 4. We have also generated the

corresponding molecular graphs for these complexes and presented them in Figure 3. From this

analysis, it is confirmed that a non-nuclear attractor (NNA) [(3,-3) type of bond critical point] is

2 present at the middle of the M-M bond for both these complexes. The values of ρ(rc) are

negative at the NNA for both the complexes indicating the electron localization therein. We have

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5 5 found that Be2( -Sb5)2 and Mg2( -Sb5)2 complexes contain NNA-Be and NNA-Mg bond paths respectively, which are (3,-1) types of bond critical points. Again, Be-Sb and Mg-Sb bond paths

5 5 have been generated [(3,-1) type of bond critical points] for Be2( -Sb5)2 and Mg2( -Sb5)2 complexes, respectively. The contour plots of 2ρ(r) are presented in Figures 4a and 4c for

5 5 Be2( -Sb5)2 and Mg2( -Sb5)2 complexes, respectively, which indicates a portion of the electron

5 localization at the NNA region. In Be2( -Sb5)2 complex the NNA population is 1.35 |e| with

5 47% localization of electron density. However, in Mg2( -Sb5)2 complex the NNA population is

5 0.99 |e| with 42% localization of electron density. The population of NNA for Be2( -Sb5)2

5 complex is higher than that in the Mg2( -Sb5)2 complex.

We have generated the electron localization function basin (ELF) plots for both the

5 5 studied systems and presented them in Figures 4b and 4d for Be2( -Sb5)2 and Mg2( -Sb5)2 complexes, respectively. From these plots, it is shown that a basin is present at the region where

NNA exists for both the complexes. The basin population is 2.05 |e| with 60% localization of

5 5 electron density for the Be2( -Sb5)2 complex. However, for Mg2( -Sb5)2 complex, the population of the basin is 1.87 |e| with 64% localization of electron density. The ELF basin

5 5 population of the Mg2( -Sb5)2 complex is higher than that in the Be2( -Sb5)2 complex. From these results, it can be said that localization of electron density takes place at the center of the

Be-Be bond and Mg-Mg bond.

2 Table 4. Electron Density (ρ(rc)), Laplacian of Electron Density ( ρ(rc)), Kinetic Energy Density (G(rc)), Potential Energy Density (V(rc)), Total Energy Density (H(rc)), Basin Population (N(pop)), Localization Index (LI), Percentage of Localization Index (%∇ LI) at Different Critical 5 5 Points (CP) of the Be2( -Sb5)2 and Mg2( -Sb5)2 complexes at MP2/cc-pVTZ/cc-pVTZ-PP// MP2/cc-pVDZ/cc-pVDZ-PP level.

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2 Systems CP Type ρ(rc) ρ(rc) G(rc) V(rc) H(rc) N(pop) LI %LI

5 Be2( -Sb5)2 NNA (3,-3) 0.076 -0.149 0.002 -0.042 -0.040 1.35 0.63 47

NNA-Be (3,-1) 0.073 -0.051 0.029 -0.072 -0.042

Be-Sb (3,-1) 0.027 0.045 0.020 -0.028 -0.008

5 Mg2( -Sb5)2 NNA (3,-3) 0.033 -0.042 0.001 -0.012 -0.011 0.99 0.42 42

NNA-Mg (3,-1) 0.032 0.005 0.010 -0.019 -0.001

Mg-Sb (3,-1) 0.016 0.035 0.001 -0.011 -0.001

5 5 Figure 3. The plots of molecular graphs of Be2( -Sb5)2 and Mg2( -Sb5)2 complexes.

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Figure 4. The plots (a) and (c) are the Laplacian of electron density ( 2ρ(r)), blue dashed and red solid lines indicate 2ρ(r) < 0 and 2ρ(r) > 0 regions, respectively; (b) and (d) are the electron 5 5 ∇ localization function (ELF) basin of Be2( -Sb5)2 and Mg2( -Sb5)2 complexes, respectively. ∇ ∇

Nonlinear optical (NLO) property

As electride materials contain loosely bound excess electrons, they showed high values of NLO properties. For this purpose, the average polarizability ( ), first hyperpolarizability ( ), and second hyperpolarizability ( ) have been computed and the corresponding values are given in

5 Table 5. Among them Mg2( -Sb5)2 complex shows higher and values than that of the

5 Be2( -Sb5)2 complex. The values for both the complexes are zero due to symmetric geometry

[52,53]. We have compared the NLO values of our systems with some previously reported known electride materials [54,55] and presented in Table S2. Our complexes show

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comparatively higher values of than the systems under consideration. The numerical values of

of our complexes are comparatively lower than that of the systems being compared.

Table 5. Average linear polarizability ( ), first hyperpolarizability ( ), and second 5 5 hyperpolarizability ( ) of Be2( -Sb5)2 and Mg2( -Sb5)2 complexes.

5 5 NLO property Be2( -Sb5)2 Mg2( -Sb5)2

426.3 510.5

β 0.0 0.0

6.2×104 1.0×105

Electride Properties

5 5 It has been observed that both Be2( -Sb5)2 and Mg2( -Sb5)2 complexes contained an NNA at the central position of the M-M bond. An ELF basin has appeared in the position where the NNA is present and the values of 2ρ are negative therein. Both the complexes under study exhibit high values of NLO properties.∇ All the criteria for an electride material have been satisfied by

5 5 these complexes. So, Be2( -Sb5)2 and Mg2( -Sb5)2 complexes can be considered as electrides.

Summary and Conclusion

5 - The modes of binding by Sb5 ligand with the alkaline earth metals (Be and Mg metals) is more stable than the other mode of binding. The bond lengths of Be-Be and Mg-Mg bonds in

5 5 Be2( -Sb5)2 and Mg2( -Sb5)2 complexes are comparable with that in the free dimeric Be2 and

14

Mg2 molecule, respectively. Both the complexes are thermodynamically stable at room temperature as predicted from the highly positive numerical values of D0 and G for dissociation. The electron density analysis and the NBO analysis show the covalent nature of the

M-M bond and the ionic nature of the metal-ligand bonds. Again, the topological analysis of electron density shows the presence of an NNA at the central position of the M-M bond of both these complexes. An ELF basin has appeared in the position where the NNA is present and the

2 5 values of ρ are negative therein. Mg2( -Sb5)2 complex shows higher and values than

∇ 5 5 that of the Be2( -Sb5)2 complex. Our designed binuclear sandwich complexes Be2( -Sb5)2 and

5 Mg2( -Sb5)2 behave as electride.

Notes The authors declare that they have no conflict of interests regarding the publication of this article, financial, and/or otherwise.

ORCID PD: 0000-0001-7090-0272

PKC: 0000-0002-5650-7666

Supporting Information The Supporting Information is available.

Acknowledgment

PKC would like to thank DST, New Delhi, India for the J. C. Bose National Fellowship, grant number SR/S2/JCB-09/2009. PD thanks to UGC, New Delhi, India for the Research Fellowship.

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Graphical Abstract

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Figures

Figure 1

The optimized geometries of the ligand and the corresponding complexes. The bond lengths are in Å unit.

Figure 2

The plots of the HOMO and LUMO of Be2(η5-Sb5)2 and Mg2(η5-Sb5)2 complexes. The values in the parenthesis are the energies of the corresponding orbitals in the eV unit. Figure 3

The plots of molecular graphs of Be2(η5-Sb5)2 and Mg2(η5-Sb5)2 complexes. Figure 4

The plots (a) and (c) are the Laplacian of electron density (฀2ρ(r)), blue dashed and red solid lines indicate ฀2ρ(r) < 0 and ฀2ρ(r) > 0 regions, respectively; (b) and (d) are the electron localization function (ELF) basin of Be2(η5-Sb5)2 and Mg2(η5-Sb5)2 complexes, respectively.

Supplementary Files

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scheme1.jpg SupportingInformation.doc