Strong Effect of Anionic Boron-Induced Bonding in LiBSi2 - Inorganic

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Strong Effect of Anionic Boron-Induced Bonding in LiBSi2 Aleksandr Pishtshev* Institute of Physics, University of Tartu, 50411 Tartu, Estonia

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S Supporting Information *

ABSTRACT: Results of periodic DFT simulations have been used to gain a new view of the crystal chemistry of LiBSi2 in terms of computational modeling of the LiB + 2Si → LiBSi2 synthesis reaction. It was shown that both the strong alkali-metal−[BSi2]− interaction and the rich behavior of B−Si couplings are the main distinctive features of the chemical bonding picture in LiBSi2. In particular, an interplay between charge transfer from easily ionizable lithium linear chains to the boron atoms and strong covalent connectivities in the tetrahedral B−Si framework is of great importance for the bonding architecture in LiBSi2. The activation of positively ionized silicon species Si+ and the formation of electron-rich B3− anions in the [BSi2]− group were found to play a key role in providing the stability of boron−silicon polar covalent bonds. It was suggested that the Si+−B3−−Si+ bonding pattern featuring the high anionic state of the boron atom can be identified as a boryl anion.

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INTRODUCTION A functional role of Si−Li and B−Si linkages in molecular systems is well-known for a number of organometallic compounds (e.g. refs 1 and 2). Recent synthesis of a novel composite with a zeolitic framework, LiBSi2, opened a route to an innovative class of inorganic compounds, structural details of which involve a unique topology of B−Si orderings.3 The main purpose of this work is to describe the crystal design of the bulk LiBSi2 and the ways in which bonding interactions are arranged in its structure. Since Si−B chemistry may exhibit in the solid state a wide variety of possible configurations and connections,2 we start with a description of the key physicochemical factors governing the synthesis3 LiB + 2Si → LiBSi2. We assume that at the level of interatomic distances the two most essential factors in the formation of LiBSi2 are as follows: (i) a high pressure that should be forceful enough to dissolve silicon atoms in a molten phase of LiB and (ii) a heat treatment of the three-component melt, which should regulate both the degree of decomposition of LiB and the subsequent activation processes related to the diffusion of silicon. The last factor is especially significant, because it is attributed to a function of actual electronic shells of building blocks to control in a reaction medium the diffusion rates in terms of degree of bonding.4 In particular, in a melt crystallization process, this factor affords the structural-charge balance between the chemical stabilization of Si atoms and the host Li−B environment. Correspondingly, our goal is to perform an analysis of the main bonding patterns associated with different lattice configurations that are formed when a host matrix of the molten LiB is filled in silicon. Such analysis being considered in terms of the main building blocks could reveal the channels for distribution of strong covalency in the tetrahedral B−Si framework. The other essential aspect of the © 2017 American Chemical Society

relationship between the structure and reactivity is information on the way in which the functionality of lithium linear chains ranges among a Li−B electron transfer, stabilization of the Li− BSi2 lattice connections, and activation of the covalent interactions in Si−B−Si structural blocks.

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METHODOLOGY

Materials. According to ref 3, LiBSi2 belongs to a particular group of crystalline systems displaying various topologies within open zeolitic-type frameworks; it crystallizes with a tetragonal symmetry of the space group P42/nmc in the structure indexed with the lattice parameters a = 6.832 Å and c = 8.839 Å and containing eight formula units per the unit cell. A crystal-chemical background of the material has been characterized as unique because it is associated with the specific orderings of boron and silicon atoms in the tetrahedral B−Si framework.3 Methods and Computational Details. Using the Vienna ab initio simulation package5 (VASP) with the potential projector augmented-wave method6,7 (PAW), we performed a series of periodic pseudopotential DFT calculations with the Perdew−Burke−Ernzerhof (PBE) GGA exchange-correlation functional.8 Our main task was to examine the electronic behavior of the cationic and anionic components of LiBSi2, focusing on structural stability, chemical bonds, and valence states. The calculations have been made for the plane-wave basis sets of the PAW−PBE pseudopotentials corresponding to 1s22s1, 2s22p1, and 2s22p63s23p2 valence electron configurations for Li, B, and Si elements, respectively; energy cutoffs of 700 eV and above were used. Brillouin zone integrations were performed by utilizing the tetrahedron method with Blöch corrections.6 Three different descriptors have been employed as postprocessing classification methods. First, a grid-based Bader analysis algorithm9 implementing the AIM approach10 has been applied to analyze the Received: July 20, 2017 Published: August 22, 2017 10815

DOI: 10.1021/acs.inorgchem.7b01837 Inorg. Chem. 2017, 56, 10815−10823

Article

Inorganic Chemistry

Figure 1. Theoretical modeling of the LiBSi2 synthesis in terms of the macroscopic P2 → P42/nmc transformation: (A) scheme of the starting configuration, the P63/mmc-LiB host matrix surrounded by silicons; (B) model packing motif reflecting the preliminary distribution of the guest silicons and corresponding to the P2 space group (its crystallographic data are given in section 1 of the Supporting Information); (C) Native structure of LiBSi2. All of the structures are drawn along the a axis.

symmetry reduction P63/mmc → P42/nmc (caused by packing of Si atoms) may proceed in a more complex fashion because the crystal structures of LiB and LiBSi2 pertain to different lattices. Correspondingly, to compose a reconstruction route along which we can model the synthesis reaction, one should transform the preliminary atomic configuration of the ternary chemical composition to a trial lattice template of a lower symmetry. That is, we assigned the P2 space group as a lowsymmetry turning point in the relevant chain of group− subgroup relations (Scheme 1) that links reduction to partial

calculated charge-density distributions. Second, a topology analysis of the valence charge densities was performed in terms of the electron localization function11 (ELF). Third, to characterize the contribution of many-body polarization effects, the polar character of chemical bonds was described in terms of the Born dynamic charges.12 For group-theoretical considerations and evaluation of crystallographic sites, we employed the program SUBGROUPGRAPH13 hosted by the Bilbao Crystallographic Server14,15 and the program FINDSYM16 of the ISOTROPY software suite.17 The structural and ELF visualizations were carried out by using the VESTA program.18

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RESULTS AND DISCUSSION In Figures 1−5, and in Tables 1−5, we characterized the bonding situation in LiBSi2 and related systems in terms of interaction geometries, valence electron transfer, and topologies of the spatial electronic charge distribution. Graphical reproduction of the LiBSi2 assembly and details of the electronic structures and equilibrium geometries are given in the Supporting Information. For a better understanding, calculations of the LiB system were taken as a reference point for interpretation of the Li−B bonding interactions and analysis of silicon-induced changes in LiBSi2. Modeling of Structural Chemistry. From a crystal chemistry point of view, a change in chemical composition may lead to a transformation of the original crystal structure. The corresponding modification may cause a reduction of the lattice space symmetry which is regulated by accommodation of the guest (inserted) atoms in the base material. In this regard, to clarify the way in which the formation and stabilization of chemical bonds may proceed, we performed a theoretical assembly of LiBSi2 by modeling the synthesis LiB + 2Si → LiBSi2 in terms of a sequence of intermediate structural geometries and packing configurations. A pictorial overview showing how silicons are distributed in the LiB lattice is outlined in Figure 1 (sections 1 and 2 of the Supporting Information specify these distributions in more detail). The following points were taken into account in computational modeling. First, we suggested that the P63/mmc architecture19 of LiB can be chosen as the symmetry-adapted basis and, therefore, can be taken as a starting point for simulations. Under this assumption, the imposed constraints of the corresponding point symmetry select the active space where the guest silicons could be initially positioned. In order to satisfy the stoichiometry of LiBSi2, among available vacant sites of the LiB lattice we decided on the 4e Wyckoff crystallographic positions for filling by silicons. Further, we note that the

Scheme 1. Two Group−Subgroup Sequences in Terms of the Bärnighausen Tree20 for a Model of LiBSi2 Assembly

recovery of the symmetry between two systems characterized by the P63/mmc and P42/nmc space groups. In other words, this step turns our initial construction into the target model template shown in Figure 1B. Note that, although the template describes a trial crystalline superstructure of low symmetry, according to Scheme 1 it presents a large freedom for the crystal assembly through retrieval of an optimal set of the most favorable packing configurations. Finally, since the synthesis routes of LiBSi2 are rendered in terms of the LiB and Si building blocks (Figure 1), our final task was to explore how B−Si coordinations are established and evolve when chemical interactions are looking for new atomic equilibrium positions to provide the balance of forces. Accordingly, on the basis of the hierarchical sequence of intermediate configurations (transition structures) we built up a trajectory in the energy space. With respect to internal geometries, this trajectory corresponds to a certain iterative process characterized by two routing factors: a stepwise decrease in the total energy and a progressive reduction of the space symmetry P2 → P42/nmc as imaged in section 2 of the Supporting Information in terms of a number of representative points. Figure 1B,C demonstrates initial and final lattice configurations of the P2 and P42/nmc structures, respectively. Charge Partitioning, Electron Counting, and Genesis of Chemical Interactions. Quantitative changes in chemical bonding upon silicon incorporation can be characterized in terms of the Bader effective charges (QB): they are presented in 10816


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more electropositive lithium to boron indicates that predominantly ionic interactions are distributed across the Li−B bonds. Further, simulations carried out over the P2 → P42/nmc pathway showed that by testing different configurations the system provides the inserted Si atoms with the special coordination ability to selectively break the original B−B covalent connections. This implies that, in order to achieve a better stability, silicon atoms trigger the formation of B−Si covalent linkages that readily transform the linear B−B bonds into new Si−B−Si building units. Thus, from our analysis it follows that the electronic behavior of silicons in the neutral LiB matrix is governed by a oneelectron loss on a lithium atom, which in turn creates a proper oxidative activity for the boron−silicon bond formation. In the context of electron counting we can say that by accommodation of the donated electron (B + e− = B−) boron acquires the valence-shell configuration [He]2s22p1 → [He]2s22p2, which is isoelectronic with the carbon atom. Accordingly, the B−−B− and B−−Si connections represent the isoelectronic counterparts of C−C and C−Si bonds, respectively. From this analogy it becomes apparent how the appropriate number of shared electrons needed for covalency enhancement may be provided and also how boron begins to promote strong covalent bindings within the boron−boron (in LiB) or boron−silicon (in LiBSi2) linkages. Because Li is the most electropositive element, under the condition that compensation of the positive charge on cations is provided by the [BSi2]− anionic framework one can assign the distribution of valence electrons (formal charges) as Li+(BSi2)−. Another structural aspect of silicon-induced changes in the charge partitioning can be characterized in terms of a classical Zintl phase. In LiBSi2, it is represented by two interpenetrating sublatticesone (ionic) is composed of linear chains of fully oxidized Li+ cations, and the other (polar covalent) is made of anionic [BSi2]− units. Hence, a correlation between structure and properties in LiBSi2 can be quantitatively seen in the context of an isoelectronic model. Noting that the [BSi2]− anion represents an isoelectronic analogue of carbon, we may relate the stability of a covalent structure of [BSi2]− to that displayed by one of the typical carbon allotropes (due to sp3 hybridization). For instance, by using the isoelectronic analogy25 one may explain why the formation mechanism of BSi2− is attributed to special conditions of synthesis such as high pressure and temperature. Moreover, in complete analogy

Table 1 versus data related to LiB. For a further analysis, it is useful to note that comparative investigation of the valence Table 1. Comparison of Bader Effective Charges QB(M) (in Units of |e|) Calculated for LiBSi2 and LiBa LiBSi2 LiB a

Li

Si(I)

Si(II)

B

+0.86 +0.84

+0.55

+0.60

−2.01 −0.84

The overall effective charge of the [BSi2]− anion is −0.86 |e|.

charge partitioning schemes can indicate how the different lattice sites being divided structurally may also differe in the bonding nature.21 In particular, an examination of ELF visualizations of Figure 2 shows the following features: (i) a global separation into electron-rich and electron-deficient spatial regions in electron density distributions, (ii) a tendency of lithium atoms to be easily oxidized to the stable Li+ cations bearing a high (positive) charge density, which is a well-known characteristic feature in the chemistry of lithium,22,23 and (iii) e−

reduction of boron caused by the Li → B charge transfer. Next, we note that modeling the synthesis of LiBSi2 in terms of intermediate geometries allowed us to simulate the energetics of transformations via a sequence of redistributions of atomic coordinates; each member of the sequence gradually lowers the total energy down relative to the previous member (as pictorially demonstrated in section 2 of the Supporting Information). As explained in ref 24 for molecular systems, such significant movements of atoms, which are looking for new equilibrium positions, are governed by the necessity to secure conditions that could provide maximum bonding in the course of the chemical reaction. By analogy with the requirement24 of holding the overall bonding character of the electron subsystem with respect to transition configurations of a molecular structure, one can suggest that the crystallization of LiBSi2 should keep the ionic character of the Li−B connections unchanged, thereby preventing the direct coordination of the Si atoms to Li. This assumption is well supported by the form of the traditional ionic image the ELF distribution pattern has for the Li+ cation in Figure 2a; it is characterized by the outer boundary partitioning related to the closed 1s and empty 2s lithium shells as well as by characteristic regions of charge depletion around the Li−B connections. Moreover, the significant charge transfer of about 0.86 e (Table 1) from the

Figure 2. Valence ELF representations of (a) LiBSi2 projected onto the (2,0,0) plane, (b) LiBSi2 projected onto the (0.0,1.1,0.6) plane, and (c) P63/ mmc-LiB projected onto the (1,1,0) plane. The numerical values of ELF normalized between 0 and 1 are illustrated by the color scale, which indicates the dark blue isosurface as the highest charge density (electron-rich) region followed by light blue, green, yellow, and orange, with red as the lightest charge density (electron-deficient) region. The presence of the ELF peaks, which are located in the central regions of the B−Si connections, shows the predominantly covalent character of these bonds. 10817


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Inorganic Chemistry with the unique stability of diamond, which is caused by the absence of inner p electrons,26 one may also expect that just boron plays the major role in providing structural stability in the assembly of the [BSi2]− three-dimensional framework. Mechanism of B−Si Bond Activation. On the basis of the results of Table 1 and Figure 2 one can characterize the [BSi2]− anion as an electron-withdrawing group which is formed by a bridging boron with a formal charge of −3 e and two attached silicon ions with positive charges of +1 e each. A detailed inspection of silicon-induced changes allows us to distinguish two sequential events associated with the two-step mechanism of the LiB + 2Si → LiBSi2 synthesis. The first event reflects the stage of prearrangement and gathering of intermediates. It corresponds to an efficient breaking of B−B bonds in the LiB melt and provides a set of structural fragments that may further be reassembled under the reaction conditions. As the Li−B bond may exert significant reactivity due to its highly ionic character, one can suggest that, in a fashion similar to that which happens during heterolytic bond cleavage in a neutral molecule, this bond undergoes dissociation into two reactive intermediatesthe Li+ cations and B− anions, respectively. The key point here is that the extra electron donated by lithium stays with the more electronegative boron and keeps the boron atom in the anionic state (B−). Another important point is the carbon-like electron configuration of B−, which, similarly to the carbon behavior in a typical C−Si bond,27 polarizes the B−−Si connections. This facilitates a prebonding activation process in the following direction: once two Si atoms were embedded into the LiB melt, dynamics of their coordination at the boron

Figure 3. Valence ELF isosurfaces evaluated at ELF = 0.822 for LiBSi2. The color codes of atoms are the same as in Figure 1. Electron density localization domains within the [BSi4]+ tetrahedra represent six regions of shared electron pairs associated with four covalent bonds at the central boron and two covalent bonds connecting the neighboring silicons.

structural stability by involving a considerable amount of covalency (Figure 3). In order to test the stability of the way along which lithium donates the valence electron into the B−Si bonding effect, a e−

center is determined by the single ionization Si ⎯⎯⎯→ Si+. Silicon oxidations begin immediately after the Li−B bond is cleaved into the charged fragments, Li+ and B−, and stop by the formation of new silicon valence basins suited for the accommodation of electron pairs. The positive charge of silicons makes them a primary target for the chemically active anionic boron atoms, so that the first event is completed by the further reduction of the boron anion to the highest anionic

possible change of the Li → B charge-transfer channel was considered in two limiting cases. The first is a small delithiation, which was modeled by incorporation of a single neutral Li vacancy into the lithium sublattice of LiBSi2. Numerical simulations of a 2 × 2 × 1 supercell, which corresponds to a chemical composition of Li0.96875BSi2, were performed to evaluate variations caused by the vacancy. Analysis of the electron density redistribution did not reveal a significant effect of the weak lithium deficiency. In particular, the small degree of delithiation in LiBSi2 has no effect on the total covalency strength or on the performance of covalency channels in the local area around the cationic defect. The other case represents a hypothetical limit of the LiBSi2

state B− ⎯⎯⎯⎯→ B3 −, for which two approaching silicons serve together as an electron pair donor. The second event relates to an addition of two silicons to the active boron anion. It begins when the electron-rich boron B3− and two silicon targets Si+ are entering into two-side contact (just as in a [BSi2]− molecular cluster28,29) and results in the Si(I)−B−Si(II) structural motif which features two separate (left and right) bonding domains. Formation of new B−Si tetrahedral bonds proceeds via delocalization of two electrons supplied from the ionic form of B3− into the proper shared areas common with the neighboring ionized silicons, thereby making them strongly covalently attached (Figure 3). The bonding-activation process prepares the preferential binding sites for the participating atoms and yields the [BSi2]− polyatomic anion of a well-structured triangle configuration with the central (bridging) boron atom; it further combines with the Li+ cation to provide both the charge compensation and lattice stabilization. In this context, the network of ordered six- and seven-membered rings of the B and Si atoms presented in the structure of LiBSi23 may be considered as a cooperative accommodation of the [BSi2]− building units. The explanation is that, with respect to bonding preferences, these units act like carbon: i.e., it may be beneficial to perform an assembly of three-dimensional packings in order to provide a greater

composition (LiBSi 2 ⎯⎯→ BSi 2 ), which has been previously suggested30 to predict the bulk BSi2 on the basis of the LiBSi2 reduced lattice geometry under the terms of the original spacesymmetry preservation. The results of computational simulations allowed the authors to claim30 that the P42/nmc structure of BSi2 is stable in dynamic and mechanical senses. However, one doubt arises with regard to the mechanistic character of this transformation: since a complete elimination of the cationic (lithium) sublattice will have an immediate effect on the stability of the total valence charge density, it is unclear how much electronic control the system could afford freely to redistribute the charge while keeping both the unit cell shape and the corresponding point symmetry of internal atomic positions. Simple electron-counting considerations indicate that the lithium removal does form finite electronic band occupations, which strongly suggests the appearance of generic metallic properties. In light of this, of special importance will be effects such as the interplay between the internal electric field and delocalized free carriers and effective charge screening. Hence, to provide the proper charge redistribution and, therefore, the net compensation of the “biased” spatial charge in the former anionic sublattice, the BSi2 system should adopt a new, distorted crystalline arrangement. In other words, it would be favorable to the original symmetry to be reduced in order to receive increased possibilities to account for the modified

−e −

−Li

+2e−

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composition of LiB0.875Cl0.125Si1.75. The solid solution is characterized by a single replacement of one BSi2 group in the 32-atom unit cell of LiBSi2 by a chlorine atom. The structural geometry of such a quaternary system is shown in Figure 4. We also verified that at the stoichiometry ratio of the

charge and force balances in terms of symmetry lowering. Obviously, this reasoning opposes the assumption30 of a tetragonal structure of BSi2 similar to that of LiBSi2. To clarify the underlying mechanism of lattice instability more rigorously, we performed accurate calculations of lattice dynamics of the bulk BSi2 in harmonic approximation by using a numeric algorithm of finite central differences (as implemented in VASP) with a step-size value of 0.018 Å. Unlike the prediction of structural stability,30 our result of stability testing exhibited that the P42/nmc equilibrium phase of BSi2 is definitely unstable; the vibrational spectrum of the tetragonal system under consideration contains two imaginary modes corresponding to A2u and B2u optical vibrations. Generally, this result is principally important because it confirms the central stabilizing role lithium plays in the P42/nmc equilibrium structure of LiBSi2. Features of Site-Specific Bonding in [BSi2]−. With respect to the high anionic state of the boron atom in LiBSi2 we can reveal three characteristic features of spatial nonuniformity of valence electron density. First, we refer to the bond-length patterns reported for LiBSi2:3 the B−Si(I) and B−Si(II) distances of 2.076 and 2.052 Å, respectively, are significantly longer than those evaluated as the sum of covalent radii of each atom (1.95 Å) or than that (1.87 Å) predicted for the [BSi2]− molecular cluster at the DFT-B3LYP/6-311+G(d) level.28 By using the C → B− isoelectronic analogy, one can compare the B−Si elongated lengths with the regular geometry of the wurtzite SiC.31 The latter demonstrates a mean value of 1.89 Å for the ordinary C−Si bond length and the typical Si−C−Si tetrahedral bond angle of 109.56°. Similar variation takes place also for the Si(I)−Si(II) distance in LiBSi2, whose length of 2.436 Å exceeds both the double covalent radius of 2.22 Å and the estimate of 2.32 Å for the molecular system.28 Within a simplified bonding picture, the lengthening can be attributed to the shared electron pairs surrounding the central boron from both sides. That is, the nucleophilic boron carrying a high negative charge favors an additional repulsion, while the neighboring silicon atom carrying a positive charge may cause an additional attraction of these electron pairs. Second, the treatment of silicon distribution effects in terms of energetics of the P2 →P42/nmc transformation showed that

Figure 4. Structural illustration of the chlorinated phase of LiBSi2 corresponding to the composition of LiB0.875Cl0.125Si1.75. The color codes of the Li, B, and Si atoms are the same as in Figure 1, and the Cl atom is marked by a harlequin color. A characteristic pattern of the geometry is that Cl is coordinated to the lithium atoms. On the lefthand side the total charge partitioning scheme of the ClLi4 tetrahedron is displayed in terms of valence ELF isosurface (at ELF = 0.822).

chlorine content, 1/8, the substituted system remains dynamically and mechanically stable. As one can see from Table 2, the effect of chlorine substitution profoundly alters the Table 2. Bader Effective Charges Calculated for the Chemical Composition of LiB0.875Cl0.125Si1.75 (in Units of |e|)a Li

Si

B

Cl

Qlow B (M) Qupp B (M)

+0.65 +0.12

+0.17 +0.525

−0.94 −1.08

−0.53 −0.53

Qavg B (M)

+0.325

+0.37

−1.04

−0.53

a

Abbreviations are the same as in Table 1. Values are presented with upp the following charge scheme: Qlow B (M), lowest level; QB (M), highest (M), averaged over the unit cell. level; Qavg B

e−

the Li → B charge transfer is not yet sufficient to allow the HOMO−LUMO energy difference. That is, the formation of the insulating state of LiBSi2 should result from the stronger bonding process across the B−Si and Si−Si adjacent connections in comparison with the effect of the direct (nonpolar) covalent boron linkage in LiB. With respect to Li+(BSi2)− and Si+B3−Si+ formal charge partitions, one can note that the opening of a band gap indicates that valence electrons in the [BSi2 ] − group possess the Lewis octet stable configuration, as opposed to monovalent lithium borides exhibiting a metal state. This is a key motif of the bonding picture in which the boron center in [BSi2]− is of high functional importance for the design of LiBSi2 as a bulk semiconductor. The important aspect here is that destabilization of the Li−B charge transfer channel not only may cause a narrowing or even collapsing of the band gap in the electron spectrum but also may soften the nucleophilic behavior of the boron centers. To simulate the chemistry of the insulating behavior in LiBSi2, we performed the DFT-based computational analysis of the ground state of the hypothetical system with a chemical

bonding situation. In particular, the lack of one BSi2 group leads to a suppression of the anionic state of boron atom. Moreover, e−

the Li → B charge transfer channel becomes significantly weakened and less able to hold lithium in the pure ionic state. From the PBE-GGA electron structure calculations we revealed that the reorganization of the valence electron density caused by chlorination leads to collapsing of the Kohn−Sham (KS) band gap. Such a crucial change in the electronic behavior from insulating to metallic is associated with the spatial delocalization of the charge density around the Cl atom in the ClLi4 group (as indicated in Figure 4). This implies at the level of chemical ordering that partial chlorination of LiBSi2 readily breaks the long-range ordered (periodic) pattern of the BSi2 groups within the crystal lattice of LiB0.875Cl0.125Si1.75. In other words, the result that the ground state is largely affected by chlorine substitution means that the high anionic state of the boron atom (i.e., corresponding to strong localization of the valence electrons) in LiBSi2 is a site-specific charge effect. The effect is 10819


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how the nucleophilicity effect appears in LiBSi2 is somewhat conceptually similar to that of how a carbene complex turns out to be nucleophilic at the carbenic center atom.36 In the present work, by exploring the bonding functionality of boron we showed that its nucleophilic state is activated by electrondonating lithium to which the [BSi2]− group becomes ionically bonded; the group is finally stabilized by two adjacent silicons that serve as additional electron donors to ”vacant” p orbitals of the B− initial binding state. From this picture one can reveal that the [BSi2]− group in the periodic lattice of LiBSi2 shares (when linked to lithium) properties similar to those of a boryl anion of the lithioboranes37 R2BLi (R = H, CH3, NH2, OH, F). Moreover, the high anionic state of boron can be examined in the following two comparisons. First, note that conceptually a canonical boryl anion (e.g., refs 38−40 and references therein) represents a negatively charged boron radical (in most cases, of the organic origin) of the form [R2B]− characterized by a threecoordinate nucleophilic boron center.37,39,41 Second, a striking resemblance to the reference boryl anion40 can be seen from comparative bonding analysis of the boron centerit is connected with an anionic charge, which is formally presented by six valence electrons at the boron site. Such accommodation of the valence electrons provides a way of stabilization of the boron anionic state via completing an octet of the covalent Lewis structure. In the [BSi2]− group, the stabilizing effect is achieved by combination of two processes: (i) sharing of an electron pair with each of two adjacent silicon atoms and (ii) delocalization of the lone-pair electrons toward upper and lower silicons to form a covalently bonded [BSi4]+ tetrahedron. Nucleophilic Boron in MBSi2 (M = Na, K) Compounds. In this section, we investigate whether the mechanism of lithium−boryl cooperativity may be extended to the other alkaline elements. To examine the effect of isoelectronic substitution on stabilization of the negative charge on the boron center in the [BSi2]− group, we considered two completely substituted modifications of LiBSi2, one by replacing an Li atom with Na and the other with K, respectively. The only constraint we stipulated is that the change of the electropositive cation in M position retains the tetragonal symmetry of the LiBSi2 lattice.30 In Tables 4 and 5 and Table S1 of the Supporting Information (section 4), we summarized the ground state properties of both hypothetical crystal systems, NaBSi2 and KBSi2. The dynamic stability of their tetragonal geometries is provided by the total positivity of

cooperative in the sense that it is governed by the joint coordination of the Li+ and BSi2− sublattices to yield the global structural stability and bulk dielectric behavior of the material. The interplay of the dynamic hybridization and strong electron localization represents the third feature of bonding in LiBSi2. This feature is determined by a certain readiness of the electron shells to be distorted via local redistributions of the electronic charge density induced by the vibrating lattice. In the context of chemical bonding in a periodic medium, such particular distortions of the valence electronic states have a polarization character. That is, through a π-bonding channel they give rise to the purely dynamic part of the charge transfer which is caused by interactions of valence electrons with the IR (dipole-active) lattice optical vibrations of the proper symmetry.12,32,33 Since a set of optical vibrational modes of LiBSi2 in a Γ point holds a sufficiently large amount of 20 IR vibrations,34 it is reasonable to examine the way in which the charge transfer channels associated with donations of an electron from lithium and silicon atoms to boron may be noticeably affected by the interaction with the relevant IR modes. For both channels, the most indicative factor that directly evaluates the dynamic contributions is a matrix of the Born effective charges12 Ẑ̂ *. By testing of the in-plane and outof-plane charge rearrangements this factor estimates to what degree the dynamic distortions of the many-body nature contribute to the formal (nominal) ionic values (e.g., refs 33 and 35). In Table 3, the Born effective charges calculated for Table 3. Principal Values of the Matrix Zij* of the Born Effective Charges in LiBSi2 along with Their Averages over Crystal Axes Z̅ *(M) = (1/3)(Z*xx(M) + Z*yy(M) + Z*zz(M)) (in Units of |e|) Z*ii Z̅ *(M)

Li

Si(I)

Si(II)

B

(+1.62; +1.07; +1.48) +1.40

(+1.17; −0.07; +0.40) +0.5

(+0.26; +0.11; +0.58) +0.31

(−2.09; −2.09; −2.48) −2.21

lithium, boron, and silicon are given in terms of principal values. It is seen that, in full accordance with the model of formal charge partitioning, the most positive and negative local charges are characteristically concentrated on lithium and boron, respectively. This not only strongly supports the greatly ionic character of Li−B bonding in LiBSi2 but also reveals that the electron distribution established along the Li−B chargetransfer direction acquires a noticeable polarization contribution. Moreover, both the highly positively polarized lithium and the negative value of the Born effective charge on boron point to a further consolidation of the anionic state of boron caused by the cooperativity effect of dynamic electronic polarization. One can also emphasize the polar difference of the dynamic charges on inequivalent Si(I) and Si(II) sites. It corresponds to the situation when the vibrational shifts of the electron density are markedly varied between the neighboring silicon sites. This fact confirms our suggestion that the overall electron density distribution is greatly polarized along the B−Si connections and indicates that the degree of this polarization is governed by the “electrostatic” boron−lithium coordination. LiBSi2 as a Boryllithium Compound. In the context of crystal chemistry, the most significant feature of the bonding geometry in LiBSi2 is associated with the trivalent nucleophilic state of boron (B3−) of the [BSi2]− group. Since a B− ion is isoelectronic with a carbon atom, the elegant explanation of

Table 4. Simulated Bond Lengths (in Å) and Angles (in deg) for ABSi2 (A = Li, Na, K)a A−B

B−Si(I)

B−Si(II)

∠Si(I)−B−Si(II)

LiBSi2 exptl3

2.335 2.335 (2.30)

2.067 2.076 (1.95)

2.047 2.052

112.0

NaBSi2 theor30

2.555 2.556 (2.65)

2.133 2.129

2.072 2.070

114.4

KBSi2 theor30

3.208 3.245 (3.05)

2.095 2.091

2.018 2.013

120.7

a

For comparison, the alkali−boron equilibrium distances were also estimated in terms of of Slater atomic radii43 (shown in parentheses). 10820


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Inorganic Chemistry Table 5. Bader Effective Charges (In Units of |e|) Calculated for MBSi2 (M = Na, K) NaBSi2 KBSi2

M

Si(I)

Si(II)

B

+0.79 +0.73

+0.18 +0.40

+0.46 +0.67

−1.43 −1.80

and, therefore, becomes more important. In particular, PBEGGA calculations showed that the KS band gap goes down to 0.77 eV for NaBSi2 and collapses to 0 for KBSi2 (in comparison with an estimate of 1.11 eV for LiBSi2). (iii) As the original crystal symmetry is preserved, reaccommodation of the [BSi4]+ tetrahedra in the substituted system gives rise to a large enlargement of the unit cell volume. (iv) This volume increase strongly softens the structural stability by lowering the main elastic and vibrational characteristics.

zone-centered vibrational modes; validation of inequalities42 for the elastic constants guarantees the mechanical (elastic or macroscopic) stability. Note that with respect to the thermal stability both systems turn out to be metastable because estimates of a heat of formation according to the standard decomposition pathway gave positive values, +6.2 and +10.4 kJ/mol, for NaBSi2 and KBSi2, respectively. In contrast, the bulk LiBSi2 is a thermodynamically stable material: the estimate of the enthalpy difference between LiBSi2 and its constituent elements yields a negative value, −14.8 kJ/mol. A comparison of the bonding geometries of Table 4 shows that the alkali-metal−boron separation in the MBSi2 (M = Na, K) systems exhibits a strong growth, which is characterized by the distances 2.555 and 3.208 Å for the Na−B and K−B connections, respectively. On the other hand, as seen from Table 5 and Figure 5, this elongation does not have a considerable effect on the donor character of the M−B charge transfer channel. Furthermore, the bond lengths estimated via the corresponding sums of empirical Slater atomic radii are quite similar or close to those obtained from the theoretical calculations. This indicates that a possible change of bonding connections in both systems (relative to LiBSi2) may be considered in terms of coordination geometry features of the relevant functional groups. In particular, from Table 4 we observe the situation when the [BSi4]+ structural group differs in the degree of tetrahedral incongruence within the range of ABSi2 (A = Li, Na, K). That is, the replacement of lithium by the other alkaline substituent leads to a significant widening of the Si(I)−B−Si(II) bond angle at the central boron of [BSi2]− from 112.0° in LiBSi2 to 120.7° in KBSi2. In comparison with LiBSi2 (Table 1), such substitution modifies donation of the silicon atoms to boron in order to take account of the change in cation, but it has no strong impact on the nucleophilic behavior. Summarizing, one can suggest the following features of the substitution effect. (i) The central boron in both substituted systems behaves nearly similarly to LiBSi2, but being directly connected to sodium or potassium it exhibits a weaker nucleophilic performance. (ii) Upon cation replacement in M+[BSi2]− the partial delocalization of valence charge density affects the charge transfer along the metal−boron connection

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CONCLUSION

In this work, we provided insight into the bonding properties of the bulk LiBSi2, and the mechanisms, according to which the boron−silicon coupling mediates an assembly of the periodic crystal system. We found that the bonding architecture of LiBSi2 is characterized by a high anionic state of the boron e−

atom, which is activated by the Li → B charge transfer during the insertion reaction LiB + 2Si → LiBSi2. We suggested that the underlying mechanism of this reaction can be decomposed into two main stages: thermal initiation followed by the B−B bond cleavage and Si insertions via their attachments at the adjacent sides of the boron atoms. On the basis of periodic DFT calculations we showed that B and Si atoms make a concerted effort to provide effective stabilization of silicon positions within the boron environment. The stabilization proceeds toward the enhancement of boron reduction, supported by silicons, and results in the development of the highly anionic state at the boron site (B3−), which in turn corresponds to the formation of a boryl anion. By considering the range of ABSi2 (A = Li, Na, K) crystalline systems along with BSi2, we studied the way in which the Si incorporation into LiB changes the charge and electronic states of interacting atoms, discovered the central role of lithium in providing the lattice stability, and recognized how important is the functional role of B3− as a strong covalent linker in the creation of B−Si interlocking bonds and Si−B−Si linkages.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.inorgchem.7b01837. Results of computational design, details of the electronic structures of LiBSi2 and LiB, and equilibrium geometries of ABSi2 (A = Li, Na, K) systems (PDF)

Figure 5. Evolution of the valence charge redistribution caused by the cation replacement effect. Projections of the ELF representations for NaBSi2 and KBSi2 are given in terms of crystallographic planes. The color codes are the same as in Figure 2. 10821


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Inorganic Chemistry

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AUTHOR INFORMATION

Corresponding Author

*E-mail for A.P.: [email protected]. ORCID

Aleksandr Pishtshev: 0000-0002-6732-1453 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by institutional research funding IUT2-27 of the Estonian Ministry of Education and Research. The author thanks Dr. M. Klopov for help in the preparation of Figures 2 and 5.

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REFERENCES

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Strong Effect of Anionic Boron-Induced Bonding in LiBSi2 - Inorganic

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