Completing the Ba–As Compositional Space: Synthesis and Characterization of Three New Binary Zintl Arsenides, Ba 3 As 4 , Ba 5 As 4 , and Ba 16 As 11

: Three novel binary barium arsenides, Ba 3 As 4 , Ba 5 As 4 , and Ba 16 As 11 , were synthesized and their crystal and electronic structures were investigated. Structural data collected via the single-crystal X-ray diffraction method indicate that the anionic substructures of all three novel compounds are composed of structural motifs based on the homoatomic As–As contacts, with [As 2 ] 4 − dimers found in Ba 5 As 4 and Ba 16 As 11 , and an [As 4 ] 6 − tetramer found in Ba 3 As 4 . Ba 3 As 4 and Ba 5 As 4 crystallize in the orthorhombic crystal system—with the non-centrosymmetric space group Fdd2 ( a = 15.3680(20) Å, b = 18.7550(30) Å, c = 6.2816(10) Å) for the former, and the centrosymmetric space group Cmce ( a = 16.8820(30) Å, b = 8.5391(16) Å, and c = 8.6127(16) Å) for the latter—adopting Eu 3 As 4 and Eu 5 As 4 structure types, respectively. The heavily disordered Ba 16 As 11 structure was solved in the tetragonal crystal system with the space group P 42 1 m ( a = 12.8944(12) Å and c = 11.8141(17) Å). The Zintl concept can be applied to each of these materials as follows: Ba 3 As 4 = (Ba 2+ ) 3 [As 4 ] 6 − , Ba 5 As 4 = (Ba 2+ ) 5 (As 3 − ) 2 [As 2 ] 4 − , and 2 × Ba 16 As 11 = (Ba 2+ ) 32 (As 3 − ) ≈ 20 [As 2 ] 4 − ≈ 1, pointing to the charge-balanced nature of these compounds. Electronic structure calculations indicate narrow bandgap semiconducting behavior, with calculated bandgaps of 0.47 eV for Ba 3 As 4 , 0.34 eV for Ba 5 As 4 , and 0.33 eV for Ba 16 As 11 .


Introduction
Exploration into Zintl phases has been a growing field of interest in recent years, as they have shown to exhibit unique structural motifs and great potential for various applications [1,2].Zintl phases are defined as a subclass of intermetallic materials in which structures, both ionic and covalent bonding can coexist.This is because an electropositive metal (typically from group 1, 2, or the lanthanide block), when combined with an electronegative element from groups 13 to 15, can be considered as an electron donor that becomes a cation.The electrons are accepted by the other atoms in the structure, which become anions and/or use the electrons to form bonds and to satisfy their octets.In this parlance, the interactions between the cations and the anionic sublattice are viewed as electrostatic, while the rest of the chemical bonding is regarded as covalent.Thus, a charge balance in Zintl phases is an inherent feature that can be readily explained and predicted by the basic valence principles.
A large subclass of Zintl compounds contain pnictogens, i.e., elements from group 15 (Pn = P, As, Sb, Bi), and can be referred to as Zintl pnictides.By combining pnictogens with different alkali, alkaline earth, or rare earth metals, numerous Zintl pnictides with a wide array of structural motifs have been discovered and characterized [3].The electron transfer between constituting elements of different electronegativity often yields Zintl materials with narrow bandgaps and excellent electronic and transport properties, thus making them suitable candidates for thermoelectric applications [2,4,5].
Recent efforts on Zintl pnictide exploration have been primarily focused on developing novel ternary or multinary compounds [2,12], yet compositionally simpler binary phases are still occasionally discovered [13][14][15][16][17][18].Our initial experiments were focused on the development of novel thermoelectric oxyarsenides [19], which, despite being known for decades, remain relatively underexplored, with multiple predicted but yet-to-be-discovered compounds [20].Additionally, recent reports indicate their great promise for thermoelectric applications [21].While developing this project, we identified several unreported compounds within the Ba-As phase diagram.This system is somewhat underexplored compared to other compositionally similar alkaline earth metal pnictide families, primarily due to the pronounced air sensitivity of barium arsenides and the toxicity of arsenic and its compounds.In this paper, we report the synthesis and structural analysis of three novel binary Zintl arsenides: Ba 3 As 4 , Ba 5 As 4 , and Ba 16 As 11 .We also provide insights into their electronic structures and bonding, highlighting their charge-balanced nature and semiconducting behavior.

Synthesis
All starting materials [barium rods (Thermo Scientific, Waltham, MA, USA, 99%) and arsenic granules (Thermo Scientific, 99.999%)] and reaction products were stored and handled inside an argon-filled glovebox (p(O 2 ) ≤ 1 ppm).Barium was filed before use to remove oxidated coatings.Ba 3 As 4 and Ba 5 As 4 were originally discovered during metal flux reactions targeting quaternary oxypnictide phases.However, these samples were multiphase, so direct reactions were attempted.Single crystals of Ba 3 As 4 , Ba 5 As 4 , and Ba 16 As 11 were obtained via stoichiometric combinations of Ba:As (totaling about 500 mg of product per reaction), which were then placed in 3/8 ′′ OD niobium tubes and arc-welded shut under argon.These tubes were then sealed in evacuated fused silica ampoules.The temperature profile for the synthesis of Ba 5 As 4 and Ba 16 As 11 was as follows: (1) heat to 1100 • C at a rate of 100 • C/h, (2) hold at 1100 • C for 20 h, (3) then cool at a rate of 5 • C/h to 100 • C, followed by the removal of reactions from the furnace.The temperature profile for the synthesis of Ba 3 As 4 involved lower reaction temperatures, with (1) heating to 800 • C at a rate of 200 • C/h, (2) holding at 800 • C for 20 h, (3) then cooling to room temperature at a rate of 5 • C/h.Ampoules were opened in the glovebox following cooling, and crystals were removed and studied via diffraction methods.
All three phases are air-and moisture-sensitive, which prevented comprehensive studies of physical properties, although we could synthesize sizable single crystals of Ba 3 As 4 and Ba 5 As 4 by employing flux methods.
CAUTION! Arsenic and arsenic-containing compounds are highly hazardous.Proper personal protective equipment should be utilized when handling arsenic-containing compounds.Arsenic sublimes at 614 • C, which is significantly below the synthetic temperatures for these materials.As arsane gas can form from the slow hydrolysis of arsenide-bearing compounds, reactions must be performed in contained, well-ventilated areas, and crucibles and lab equipment may not be cleaned with water prior to slow oxidation.Arsenic may react with niobium at high temperatures with the formation of unadvertised side products.

Structural Characterization
Data for Ba 3 As 4 and Ba 5 As 4 were all collected at 100 K using a Bruker APEX II diffractometer (Bruker, Billerica, MA, USA) equipped with Mo Kα radiation (λ = 0.71073 Å), whereas Ba 16 As 11 data were collected with a Bruker D8 Venture Duo diffractometer using Ag radiation (λ = 0.56086 Å).Suitably sized single crystals were selected under the microscope and mounted on MiTeGen plastic loops attached to the goniometer head.Data integration and absorption correction were performed with the SAINT and SADABS program packages (version 2.03) [22,23].Crystal structures were solved by utilizing the SHELXT program, with structure refinement performed using full-matrix least squares methods on F 2 with SHELXL, using Olex2 software (version 1.5) as a graphical interface [24][25][26][27].The STRUC-TURE TIDY program was used to standardize coordinates [28].Selected details of the data collection and crystallographic parameters, such as atomic coordinates and bond distances, are provided in Tables 1, 2 and S1.

Electronic Structure Calculations
Experimentally observed unit cell parameters and atomic coordinates of ordered Ba 3 As 4 and Ba 5 As 4 compounds were used for calculations.Two unique barium positions and two unique arsenic positions were used for each experimental model (Tables S1 and S2).For Ba 16 As 11 , a disorder-free model with fully occupied non-split sites was developed for calculations with six unique barium positions and six unique arsenic positions (Table S3).Details of the electronic structure, including Total and Projected density of states (DOS) and band structure, were investigated with the TB-LMTO-ASA Program after the convergence of the total energy on the dense k-mesh, with 10 × 10 × 10 points for Ba 3 As 4 and Ba 5 As 4 and 10 × 10 × 11 points for Ba 16 As 11 in the Brillouin zone [29].Empty spheres were introduced to satisfy atomic sphere approximation (ASA) and the von Barth-Hedin exchange correlation functional was utilized [30].The Fermi level was selected as the energy reference (E F = 0 eV).A basic set included Ba [6s, 4d, 6p](4f) and As [4s, 4p](4d), with the downfolded orbitals presented in parentheses.Chemical bonding analysis was performed by calculating the energy contributions of all filled electronic states for selected atom pairs via the Crystal Orbital Hamilton Population (COHP) method [31].It should be noted that for the calculations within the TB-LMTO-ASA framework, unoptimized cells were used, which leads to some uncertainty for the bandgap size estimation.These limitations leave room for more advanced characterizations and simulations.

Synthesis
The initial discovery of the title compounds occurred during the attempted synthesis of multinary barium oxyarsenide materials-work that is still ongoing, and the results of which will be presented in a future article.While our first reactions produced novel ternary barium oxyarsenides, the title binary barium arsenides were found to be the main products.All three presented compounds were identified as black single crystals sensitive to air and moisture, that rapidly decayed when removed from the inert gas-protected environment.Such instability significantly complicated powder XRD characterization and made routine physical properties studies practically impossible.The synthetic conditions listed in the experimental section are favorable in producing noticeable amounts of the title materials, although some single crystals of Ba 3 As 4 can be obtained in the reactions with the intended introduction of oxygen.Notably, Ba 3 As 4 has been previously reported [32], although its crystal structure is not found in structural databases.
Ba 5 As 4 was found to be a major product of its intended reaction, though its phase purity could not be reasonably determined due to the air sensitivity.The Ba 3 As 4 sample contained Ba 3 As 4 as a major product, with some Ba 5 As 4 present as well.Synthetic attempts to produce Ba 3 As 4 using stoichiometric ratios of reactants at higher temperatures only yielded Ba 5 As 4 , leading us to believe that the "5-4" phase is more thermodynamically favorable at higher temperatures.Exploration into the Ba 16 As 11 phase originally began due to its exclusion from an original extensive survey into the A 16 Pn 11 phases (A = Ca, Sr, Ba; Pn = As, Sb) reported by Corbett more than two decades ago [33].While the authors failed to produce the Ba 16 As 11 phase, their suggested optimized synthetic procedures involving direct reactions in sealed metal tubes proved successful for making Ba 16 As 11 in bulk by using an elevated temperature profile of 1100 • C, as compared to prior attempts involving annealing at 850-900 • C.This previous report also indicates the need for synthesis under a dynamic vacuum to eliminate hydrogen impurities in the metals; however, this does not appear to be an issue in our reactions.This falls in line with the results of the recently reported Ba 16 Sb 11 [15].The synthesis of Ba 16 As 11 always produces a mixed product of Ba 16 As 11 and Ba 4 As 3 (or rather, As-deficient Ba 4 As 2.67 ) [34].This mixture is reasonably expected, due to the nearly identical Ba:As ratio for both compounds (Figure 1).The single crystal diffraction and electronic structure study of Ba 4 As 3 has been reported previously [34][35][36][37], but the existence of Ba 16 As 11 has never been predicted.

Crystal Structure and Bonding
The archetypes for all three reported compounds are well known and, therefore, do not require an extensive description of their crystal structures.In the following paragraphs, we will provide only a brief description focusing on the most important structural features.[35][36][37]41,42].New phases reported in this paper are highlighted in red.The formation energy for Ba 16 As 11 is not provided as it was not reported/predicted.We did not attempt to further explore periodic trends, as most of the isostructural pnictides were already reported.These materials do prove to follow known periodic trends, such as those of as phosphides (Ba 3 P 4 [43], Ba 5 P 4 [13,44]), arsenides (Sr 3 As 4 [45], Eu 5 As 4 [46], Eu 3 As 4 [47]), and antimonides (Ba 5 Sb 4 [48,49], Ba 16 Sb 11 [15]), to name a few; although, we do not exclude the possibility that the occasional discovery of some missing binary compounds within the structure types presented here is highly probable.

Crystal Structure and Bonding
The archetypes for all three reported compounds are well known and, therefore, do not require an extensive description of their crystal structures.In the following paragraphs, we will provide only a brief description focusing on the most important structural features.

Crystal Structure of Ba 3 As 4
Our structural description will begin with Ba 3 As 4 .This compositionally and structurally simple compound crystallizes in the non-centrosymmetric orthorhombic space group Fdd2 and belongs to the Sr 3 As 4 structure type [45], which is known to host multiple A 3 Pn 4 phosphides and arsenides (A = Eu, Sr, Ba; Pn = P, As) [45,47,50].Ba 3 As 4 was initially discovered by von Schnering [43] and, while this work was underway, was structurally evaluated in the dissertation of Hermann [32], but the structural entry was not (and is still not) available in the ICSD (access date 21 March 2024) [51].Our results corroborate well with the reported studies, although we observed slightly larger unit cell volumes despite lower data collection temperatures (Table 1).
According to the structural representation shown in Figure 2, one Ba 3 As 4 formula unit consists of three Ba 2+ cations and an oligomer of four As atoms joined via homoatomic covalent bonds, thus formulated as [As 4 ] 6− .There are two crystallographically independent Ba sites and two As sites occupying the 16b general position, with the exception of the special Ba2 8a site, yielding the Wyckoff sequence b 3 a and the Pearson code oF56.The structure is made up of 1/3 empty [Ba 6 ] and 2/3 arsenic-centered [AsBa 6 ] triangular prisms, sharing their rectangular faces in either parallel or perpendicular fashion to the three-fold axis of the prism (Figure 2).Our structural description will begin with Ba3As4.This compositionally and structurally simple compound crystallizes in the non-centrosymmetric orthorhombic space group Fdd2 and belongs to the Sr3As4 structure type [45], which is known to host multiple A3Pn4 phosphides and arsenides (A = Eu, Sr, Ba; Pn = P, As) [45,47,50].Ba3As4 was initially discovered by von Schnering [43] and, while this work was underway, was structurally evaluated in the dissertation of Hermann [32], but the structural entry was not (and is still not) available in the ICSD (access date 21 March 2024) [51].Our results corroborate well with the reported studies, although we observed slightly larger unit cell volumes despite lower data collection temperatures (Table 1).
According to the structural representation shown in Figure 2, one Ba3As4 formula unit consists of three Ba 2+ cations and an oligomer of four As atoms joined via homoatomic covalent bonds, thus formulated as [As4] 6− .There are two crystallographically independent Ba sites and two As sites occupying the 16b general position, with the exception of the special Ba2 8a site, yielding the Wyckoff sequence b 3 a and the Pearson code oF56.The structure is made up of 1/3 empty [Ba6] and 2/3 arsenic-centered [AsBa6] triangular prisms, sharing their rectangular faces in either parallel or perpendicular fashion to the three-fold axis of the prism (Figure 2).Each [As 4 ] 6− complex anion is nested within two pairs of mutually perpendicular [AsBa 6 ] prisms, breaking the fragment into two symmetric [As1-As2] units.The arsenic atoms in this symmetric oligomer are linked in the [As2-As1-As1-As2] fashion.This four-membered fragment is located on a 2-fold rotation axis perpendicular to the ab plane, and intersects the center of the As1-As1 bond.The refined As1-As2 and As1-As1 distances are ca.2.47 Å and 2.55 Å, respectively.Both numbers are comparable with the doubled covalent radius of As [52], as well as with the reported As-As distances in Eu 3 As 4 , Sr 3 As 4, and several other ternary Zintl arsenides [45,53].Ba-As distances are in the range of 3.27-3.50Å, being close to the sum of the covalent radii of Ba and As and to the values observed for known Zintl barium arsenides [34,[38][39][40].
3.2.2.Crystal Structure of Ba 5 As 4 Ba 5 As 4 , being more structurally complex, belongs to the Eu 5 As 4 structure type [46], crystallizing in the orthorhombic space group Cmce.This family of Zintl pnictides is less explored, with only three reported compositions: Eu 5 As 4 , Ba 5 P 4 , and Ba 5 Sb 4 [13,46,48].Akin to Ba 3 As 4 , barium-rich Ba 5 As 4 also consists of two Ba (16g and 4a) and two As (8d and 8f ) sites, yielding the Wyckoff sequence gfda and the Pearson code oC36.We could synthesize only one modification of Ba 5 As 4 , although the compositionally related Ba 5 P 4 phase is known to be dimorphic [13,44].
Ba 3 As 4 and Ba 5 As 4 structures are noticeably different.Half of the arsenic atoms in the latter dimerize, forming a homoatomic [As 2 ] 4− dumbbell with an As1-As1 distance of ca.2.55 Å (Figure 3).This is slightly longer than the doubled covalent radius of arsenic (2.38 Å) and in the compositionally similar Zintl arsenides, such as K 5 As 4 (2.45 Å) [8,52], but is comparable to the reported As-As bond length for isostructural analogs, such as Eu 5 As 4 (2.54 Å) [46].Ba5As4, being more structurally complex, belongs to the Eu5As4 structure type [46], crystallizing in the orthorhombic space group Cmce.This family of Zintl pnictides is less explored, with only three reported compositions: Eu5As4, Ba5P4, and Ba5Sb4 [13,46,48].Akin to Ba3As4, barium-rich Ba5As4 also consists of two Ba (16g and 4a) and two As (8d and 8f) sites, yielding the Wyckoff sequence gfda and the Pearson code oC36.We could synthesize only one modification of Ba5As4, although the compositionally related Ba5P4 phase is known to be dimorphic [13,44].
Ba3As4 and Ba5As4 structures are noticeably different.Half of the arsenic atoms in the latter dimerize, forming a homoatomic [As2] 4− dumbbell with an As1-As1 distance of ca.2.55 Å (Figure 3).This is slightly longer than the doubled covalent radius of arsenic (2.38 Å) and in the compositionally similar Zintl arsenides, such as K5As4 (2.45 Å) [8], [52], but is comparable to the reported As-As bond length for isostructural analogs, such as Eu5As4 (2.54 Å) [46].Each As1 atom composing the dumbbell is 6-coordinated by four Ba1 and two Ba2 atoms in a distorted trigonal prismatic fashion (Figure 3c).Alternatively, [As2] dimer can be viewed as enclosed between four adjacent [Ba2@Ba18] cubes that form the slab perpendicular to the a-axis (Figure 3a).In such an arrangement, the [As2] unit is located within a pair of edge-sharing trigonal prisms with slightly off-centered As atoms, evidenced by Each As1 atom composing the dumbbell is 6-coordinated by four Ba1 and two Ba2 atoms in a distorted trigonal prismatic fashion (Figure 3c).Alternatively, [As 2 ] dimer can be viewed as enclosed between four adjacent [Ba2@Ba1 8 ] cubes that form the slab perpendicular to the a-axis (Figure 3a).In such an arrangement, the [As 2 ] unit is located within a pair of edge-sharing trigonal prisms with slightly off-centered As atoms, evidenced by slightly elongated Ba-As contacts (Figure 3b, Table S5).This slab of face-sharing [AsBa 6 ] and [BaBa 8 ] cubes alternates with another slab of As-centered distorted [Ba 6 ] trigonal prisms centered by As2 atoms (Figure 3d).With all prisms centered by As atoms and cubes centered by Ba atoms, the structure can be viewed as an intergrowth of Mo 2 FeB 2 -and FeB-types [54,55].

Crystal Structure of Ba 16 As 11
Ba 16 As 11 is the most complex structure of the three compounds discussed in this paper (Figure 4).It crystallizes in the tetragonal space group P42 1 m and shares a structure with the Ca 16 Sb 11 archetype [33], despite being much more heavily disordered.This puts the structure more in line with our recent report on the Ba 16 Sb 11 phase, where we comprehensively discussed crystal structure, polymorphism, and details of the disorder within this family of compounds [15].
Crystals 2024, 14, x FOR PEER REVIEW 8 of 15 slightly elongated Ba-As contacts (Figure 3b, Table S5).This slab of face-sharing [AsBa6] and [BaBa8] cubes alternates with another slab of As-centered distorted [Ba6] trigonal prisms centered by As2 atoms (Figure 3d).With all prisms centered by As atoms and cubes centered by Ba atoms, the structure can be viewed as an intergrowth of Mo2FeB2and FeBtypes [54,55].

Crystal Structure of Ba16As11
Ba16As11 is the most complex structure of the three compounds discussed in this paper (Figure 4).It crystallizes in the tetragonal space group 4 2  and shares a structure with the Ca16Sb11 archetype [33], despite being much more heavily disordered.This puts the structure more in line with our recent report on the Ba16Sb11 phase, where we comprehensively discussed crystal structure, polymorphism, and details of the disorder within this family of compounds [15].The A16Pn11 (A = Ca, Sr, Ba, Eu, Yb; Pn = P, As, Sb, Bi) family of compounds comprises more than a dozen reported compositions [15,33,56], although the title Ba16As11 phase is reported in this paper for the first time.Unlike the Ba16Sb11 phase, which crystallizes in a disordered tetragonal structure of the Ca16Sb11-type and an ordered monoclinic coloring variant of the La16Rh8Sn3-type [57], we identified only the disordered tetragonal version of the Ba16As11 phase, which could be partially due to the thermodynamic stability of the compositionally similar Ba4As3 phase (Figure 1).We do not exclude the possibility that the ordered monoclinic phase exists and could be discovered in the future.
The collected single-crystal X-ray diffraction data can readily produce a structure solution in space group 4 2 , although from the subsequent refinements, we observed a severe disorder nearly identical to that in the recently reported Ba16Sb11 structure [15].In the following paragraphs, we will briefly introduce details of the crystal structure and some differences between the title compounds and previously reported structural analogs.The A 16 Pn 11 (A = Ca, Sr, Ba, Eu, Yb; Pn = P, As, Sb, Bi) family of compounds comprises more than a dozen reported compositions [15,33,56], although the title Ba 16 As 11 phase is reported in this paper for the first time.Unlike the Ba 16 Sb 11 phase, which crystallizes in a disordered tetragonal structure of the Ca 16 Sb 11 -type and an ordered monoclinic coloring variant of the La 16 Rh 8 Sn 3 -type [57], we identified only the disordered tetragonal version of the Ba 16 As 11 phase, which could be partially due to the thermodynamic stability of the compositionally similar Ba 4 As 3 phase (Figure 1).We do not exclude the possibility that the ordered monoclinic phase exists and could be discovered in the future.
The collected single-crystal X-ray diffraction data can readily produce a structure solution in space group P42 1 m, although from the subsequent refinements, we observed a severe disorder nearly identical to that in the recently reported Ba 16 Sb 11 structure [15].
In the following paragraphs, we will briefly introduce details of the crystal structure and some differences between the title compounds and previously reported structural analogs.
Similarly to the Ba 16 Sb 11 phase, the hallmark of the crystal structure of Ba 16 As 11 is best described as an arrangement of columns composed of [Ba 8 ] distorted square prisms and antiprisms that host disordered As1 and As6 atoms (Figure 4a).Each site is split into two positions, with As1A/As1B residing within the prisms and As6A/As6B occupying the antiprisms (Figure 4b).The disorder of the As1 site, although less pronounced compared to that of Sb1 in Ba 16 Sb 11 , still reveals a non-negligible occupancy of the As1B site (Wyckoff 8f ), with a site occupancy factor (SOF) of 0.034 (4).Combined with the SOF of 0.468 (7) for the As1A site (Wyckoff 4d), we yield the slightly off-stoichiometric composition of Ba 16 As 11.07 (2) , similar to the situation in the isostructural Ba 16 Sb 11.2(1) [15].For simplification, we use the simplified Ba 16 As 11 formula throughout the manuscript, although the reader should be aware that the refined composition is non-stoichiometric for both barium arsenide and antimonide.The higher multiplicity of the As1B site allows for the presence of any of two pairs of As1B-As1B homoatomic bonds that are ca.2.46 Å long.The presence of these partially occupied atomic sites is required to achieve the charge balance, as can be evidenced below.
Additional modeling was required in order to resolve the observed anomalous displacement parameter of As6, formally located in the center of the adjacent antiprism (Figure 4b).The split of the As6 site into two As6A and As6B sites (Wyckoff 4d), with SOFs of 0.543(3) and 0.466(3), respectively, is necessitated for achieving electronic stabilization through the formation of homoatomic, although slightly elongated, As6A-As6A contacts of ca.2.60 Å (Table S3).Given the partial occupancy of the As6A site, the observed [As 2 ] dimer cannot account for a full bond per unit cell.
The described disorder of several As sites results in the concomitant positional disorder of the surrounding Ba sites, and goes even further through a domino effect that causes the disorder of As5 sites and concomitant Ba sites.However, the shared face of the antiprisms that host As6 atoms is made up of non-disordered Ba2 atoms, which has previously been observed for several binary pnictides [15,33,58].The [As6Ba 8 ] antiprism -[As6Ba 8 ] antiprism -[As1Ba 8 ] prism columns are oriented along the c-axis and they are linked through the relatively short Ba2-Ba2, Ba1-Ba1, and Ba3-Ba3 contacts in the range of 3.58-3.90Å.While these values are smaller than the sum of the covalent radii of Ba, they represent an interaction between two cations, thus exceeding the doubled sum of ionic radii [59].In addition, the partial occupancy of multiple Ba sites corroborates well with the observation of such comparatively short distances [15,[38][39][40].

Structural Relationships and Charge Balance Considerations
Despite adopting different structures, the Ba 3 As 4 , Ba 5 As 4 , and Ba 16 As 11 phases share similar structural features and polyanionic arrangements.We discussed the bonding largely in the context of the framework of trigonal/square prisms/antiprisms and cubes composed of Ba and centered by As atoms.Ba-As bond distances within these polyhedra adopt a wide range of values, including 3.27-3.50Å for Ba 3 As 4 , 3.28-3.52Å for Ba 5 As 4 , and 3.20-3.64Å for Ba 16 As 11 .These values are close to the sum of the covalent radii of Ba and As, and to the values observed for known binary and ternary Zintl arsenides [34,[38][39][40]60].
As the structural complexity increases from the relatively simple Ba 3 As 4 and Ba 5 As 4 compounds to the heavily disordered Ba 16 As 11 compound, arsenic atoms become more reduced, due to the decreased number of homoatomic As-As contacts per formula unit.All As atoms in the Ba 3 As 4 phase are linked to the [As 4 ] 6− tetramer, with terminal and central As atoms being formally charged at −2 and −1, respectively.Such fully ionic approximation results in the charge-balanced composition of (Ba 2+ ) 3 [As 4 ] 6− , where Ba atoms are considered electron donors in accordance with the Zintl concept [1].A quite similar bonding situation is observed for the Ba 5 As 4 phase, where only one half of the arsenic atoms in the structure are dimerized, yielding the charge-balanced (Ba 2+ ) 5 [As 2 ] 4− (As 3− ) 2 composition, considering the fully ionic approximation.A significant increase in disorder for the Ba 16 As 11 structure results in a less straightforward Zintl count, which is in line with the previously reported Ba 16 Sb 11 phase [15].The presence of the homoatomic As1B-As1B and As6A-As6A bonds allows for careful rationalization of the structure and composition with the Zintl count, expressed as (Ba 2+ ) 16 (As 3− ) 9.87 ([As 2 ] 4− ) 0.60 (h + ) 0.01 (with h + representing an electron-hole).Apparently, the presence of extensive disorder, as well as a deviation from the ideal "16-11" composition, is required for achieving the charge-balanced composition.

Electronic Structure
Barium and arsenic have a moderate electronegativity difference (with Pauling electronegativities of 0.89 and 2.18, respectively) [61], which supports the expectation of a sizable charge transfer and, therefore, semiconducting behavior.The latter suggestion is supported by the Zintl concept rationalization of the charge balance, discussed in the previous section.The results of the electronic structure calculations, presented in Figures 5-7, corroborate well with the predicted charge-balanced nature of the title compounds and provide further insights into chemical bonding within these compounds.
presence of the homoatomic As1B-As1B and As6A-As6A bonds allows for careful rationalization of the structure and composition with the Zintl count, expressed as (Ba 2+ )16(As 3− )9.87([As2] 4− )0.60(h + )0.01 (with h + representing an electron-hole).Apparently, the presence of extensive disorder, as well as a deviation from the ideal "16-11" composition, is required for achieving the charge-balanced composition.

Electronic Structure
Barium and arsenic have a moderate electronegativity difference (with Pauling electronegativities of 0.89 and 2.18, respectively) [61], which supports the expectation of a sizable charge transfer and, therefore, semiconducting behavior.The latter suggestion is supported by the Zintl concept rationalization of the charge balance, discussed in the previous section.The results of the electronic structure calculations, presented in Figures 5-7, corroborate well with the predicted charge-balanced nature of the title compounds and provide further insights into chemical bonding within these compounds.As we mentioned in the Materials and Methods section, the disorder-free natures of Ba3As4 and Ba5As4 allowed us to study their electronic structures using the experimentally obtained cell parameters and atomic coordinates.Both compounds can be classified as narrow gap semiconductors, with a calculated direct bandgap opening of ca.0.47 eV for Ba3As4 and an indirect bandgap of 0.34 eV for Ba5As4, making them small bandgap semiconductors.The Total and Partial density of states (DOS) plots show similar patterns to other Zintl pnictides.States within the valence band in the area of −12 eV to −8 eV consist primarily of As-s states, while states above −4 eV to the valence band maxima (VBM) consist of As-p states (Figure 5), indicating poor hybridization of the As orbitals.Ba-s, Ba-p, and Ba-d states all contribute towards the same range, with Ba-d being the dominant orbital contribution.The multiple observed interactions between Ba and As within the discussed polyhedra, as well as the large coordination numbers of the Ba atoms in these compounds, support the idea that Ba-d orbitals are essential for the formation of multiple Ba-As bonds.
The study of the electronic structure of Ba16As11 is complicated by the severe disorder of multiple Ba and As sites (Figure 4b).However, we generated a simplified structural model composed of fully occupied atomic sites, which preserves the reported bonding pattern (Figure 4c), although the As6-As6 contacts of 3.15 Å are noticeably elongated.The As1 site in the simplified model is located at the origin, occupying the 2a Wyckoff site.The lower multiplicity of As1 in the simplified model, compared to the As1A and As1B sites in the refined structure (Table S3), is compensated by the SOF of 1, thus yielding the Ba16As11 stoichiometric composition, which is nearly identical to the refined one.However, the lack of As-As bonding results in an unbalanced composition, which can be described as (Ba 2+ )16(As 3− )11(h + ), considering a fully ionic approximation.It becomes evident that the top of the valence band should be shifted upwards to ca. 0.48 eV, to align with a direct bandgap opening of 0.31 eV (Figure 5c).This 0.48 eV difference corresponds to 1 electron per formula unit, indicating that the charge balance can only be achieved with the presence of the As-As pair.Besides a Fermi level shift, the Total and Partial DOS plots for Ba16As11 share similar features to those discussed for the Ba3As4 and Ba5As4 phases.As we mentioned in the Materials and Methods section, the disorder-free natures of Ba3As4 and Ba5As4 allowed us to study their electronic structures using the experimentally obtained cell parameters and atomic coordinates.Both compounds can be classified as narrow gap semiconductors, with a calculated direct bandgap opening of ca.0.47 eV for Ba3As4 and an indirect bandgap of 0.34 eV for Ba5As4, making them small bandgap semiconductors.The Total and Partial density of states (DOS) plots show similar patterns to other Zintl pnictides.States within the valence band in the area of −12 eV to −8 eV consist primarily of As-s states, while states above −4 eV to the valence band maxima (VBM) consist of As-p states (Figure 5), indicating poor hybridization of the As orbitals.Ba-s, Ba-p, and Ba-d states all contribute towards the same range, with Ba-d being the dominant orbital contribution.The multiple observed interactions between Ba and As within the discussed polyhedra, as well as the large coordination numbers of the Ba atoms in these compounds, support the idea that Ba-d orbitals are essential for the formation of multiple Ba-As bonds.
The study of the electronic structure of Ba16As11 is complicated by the severe disorder of multiple Ba and As sites (Figure 4b).However, we generated a simplified structural model composed of fully occupied atomic sites, which preserves the reported bonding pattern (Figure 4c), although the As6-As6 contacts of 3.15 Å are noticeably elongated.The As1 site in the simplified model is located at the origin, occupying the 2a Wyckoff site.The lower multiplicity of As1 in the simplified model, compared to the As1A and As1B sites in the refined structure (Table S3), is compensated by the SOF of 1, thus yielding the Ba16As11 stoichiometric composition, which is nearly identical to the refined one.However, the lack of As-As bonding results in an unbalanced composition, which can be described as (Ba 2+ )16(As 3− )11(h + ), considering a fully ionic approximation.It becomes evident that the top of the valence band should be shifted upwards to ca. 0.48 eV, to align with a direct bandgap opening of 0.31 eV (Figure 5c).This 0.48 eV difference corresponds to 1 electron per formula unit, indicating that the charge balance can only be achieved with the presence of the As-As pair.Besides a Fermi level shift, the Total and Partial DOS plots for Ba16As11 share similar features to those discussed for the Ba3As4 and Ba5As4 phases.As we mentioned in the Materials and Methods section, the disorder-free natures of Ba 3 As 4 and Ba 5 As 4 allowed us to study their electronic structures using the experimentally obtained cell parameters and atomic coordinates.Both compounds can be classified as narrow gap semiconductors, with a calculated direct bandgap opening of ca.0.47 eV for Ba 3 As 4 and an indirect bandgap of 0.34 eV for Ba 5 As 4 , making them small bandgap semiconductors.The Total and Partial density of states (DOS) plots show similar patterns to other Zintl pnictides.States within the valence band in the area of −12 eV to −8 eV consist primarily of As-s states, while states above −4 eV to the valence band maxima (VBM) consist of As-p states (Figure 5), indicating poor hybridization of the As orbitals.Ba-s, Ba-p, and Ba-d states all contribute towards the same range, with Ba-d being the dominant orbital contribution.The multiple observed interactions between Ba and As within the discussed polyhedra, as well as the large coordination numbers of the Ba atoms in these compounds, support the idea that Ba-d orbitals are essential for the formation of multiple Ba-As bonds.
The study of the electronic structure of Ba 16 As 11 is complicated by the severe disorder of multiple Ba and As sites (Figure 4b).However, we generated a simplified structural model composed of fully occupied atomic sites, which preserves the reported bonding pattern (Figure 4c), although the As6-As6 contacts of 3.15 Å are noticeably elongated.The As1 site in the simplified model is located at the origin, occupying the 2a Wyckoff site.The lower multiplicity of As1 in the simplified model, compared to the As1A and As1B sites in the refined structure (Table S3), is compensated by the SOF of 1, thus yielding the Ba 16 As 11 stoichiometric composition, which is nearly identical to the refined one.However, the lack of As-As bonding results in an unbalanced composition, which can be described as (Ba 2+ ) 16 (As 3− ) 11 (h + ), considering a fully ionic approximation.It becomes evident that the top of the valence band should be shifted upwards to ca. 0.48 eV, to align with a direct bandgap opening of 0.31 eV (Figure 5c).This 0.

Figure 1 .
Figure 1.Phase diagram with reported formation energies of selected barium arsenides[35- 37,41,42].New phases reported in this paper are highlighted in red.The formation energy for

Figure 1 .
Figure 1.Phase diagram with reported formation energies of selected barium arsenides[35][36][37]41,42].New phases reported in this paper are highlighted in red.The formation energy for Ba 16 As 11 is not provided as it was not reported/predicted.

Figure 2 .
Figure 2. (a) The Ba3As4 structure, with highlighted [As4] 6− tetramers, and the outlined unit cell; (b) the trigonal prismatic arrangement of As-centred [AsBa6] polyhedra; (c) a close-up view of the [As4] 6− Zintl anion, with reported interatomic As−As distances; (d,e) a distinct representation of the As-centered coordination polyhedra for As1 and As2.Barium atoms are shown in orange and arsenic atoms are shown in blue.Each [As4] 6− complex anion is nested within two pairs of mutually perpendicular [AsBa6] prisms, breaking the fragment into two symmetric [As1-As2] units.The arsenic atoms in this symmetric oligomer are linked in the [As2-As1-As1-As2] fashion.This fourmembered fragment is located on a 2-fold rotation axis perpendicular to the ab plane, and intersects the center of the As1-As1 bond.The refined As1-As2 and As1-As1 distances are ca.2.47 Å and 2.55 Å, respectively.Both numbers are comparable with the doubled covalent radius of As [52], as well as with the reported As-As distances in Eu3As4, Sr3As4, and several other ternary Zintl arsenides [45,53].Ba-As distances are in the range of 3.27-3.50Å, being close to the sum of the covalent radii of Ba and As and to the values observed for known Zintl barium arsenides [34,38-40].

Figure 2 .
Figure 2. (a) The Ba 3 As 4 structure, with highlighted [As 4 ] 6− tetramers, and the outlined unit cell; (b) the trigonal prismatic arrangement of As-centred [AsBa 6 ] polyhedra; (c) a close-up view of the [As 4 ] 6− Zintl anion, with reported interatomic As−As distances; (d,e) a distinct representation of the As-centered coordination polyhedra for As1 and As2.Barium atoms are shown in orange and arsenic atoms are shown in blue.

Figure 3 .
Figure 3. (a) A representation of the Ba5As4 structure, with slabs made of [BaBa8] cubes, and the outlined unit cell.As-As dimers are located between the cubes; (b,c) the trigonal prismatic arrangements of As-centered [AsBa6] polyhedra encasing the [As2] 4− anions; (d) a representation of As2centered distorted trigonal prisms of Ba atoms.The color code is the same as in Figure 1.

Figure 3 .
Figure 3. (a) A representation of the Ba 5 As 4 structure, with slabs made of [BaBa 8 ] cubes, and the outlined unit cell.As-As dimers are located between the cubes; (b,c) the trigonal prismatic arrangements of As-centered [AsBa 6 ] polyhedra encasing the [As 2 ] 4− anions; (d) a representation of As2-centered distorted trigonal prisms of Ba atoms.The color code is the same as in Figure 1.

Figure 4 .
Figure 4. (a) A view of the Ba16As11 structure along the [001] direction, with outlined barium polyhedra.The unit cell is highlighted; (b) the characteristic square prism-antiprism column, with all details of the structural disorder; (c) the simplified structural model used for electronic structure calculations.Note the noticeably elongated As6-As6 contact.The color code is the same as in Figure 1.

Figure 4 .
Figure 4. (a) A view of the Ba 16 As 11 structure along the [001] direction, with outlined barium polyhedra.The unit cell is highlighted; (b) the characteristic square prism-antiprism column, with all details of the structural disorder; (c) the simplified structural model used for electronic structure calculations.Note the noticeably elongated As6-As6 contact.The color code is the same as in Figure 1.

Figure 5 .
Figure 5. Calculated Total (DOS) and Partial (PDOS) density of states plots for (a) Ba3As4, (b) Ba5As4, and (c) Ba16As11.The Fermi level is the energy reference at 0 eV.An additional dashed line for (c) at ca. 0.48 eV indicates a 2-electron shift per unit cell, which corresponds to 1 electron per formula unit.

Figure 5 .
Figure 5. Calculated Total (DOS) and Partial (PDOS) density of states plots for (a) Ba 3 As 4 , (b) Ba 5 As 4 , and (c) Ba 16 As 11 .The Fermi level is the energy reference at 0 eV.An additional dashed line for (c) at ca. 0.48 eV indicates a 2-electron shift per unit cell, which corresponds to 1 electron per formula unit.

Figure 6 .
Figure 6.Calculated Crystal Orbital Hamilton plots (COHP) for (a) Ba3As4, (b) Ba5As4, and (c) Ba16As11.The Fermi level is the energy reference at 0 eV.An additional dashed line at ca. 0.48 eV indicates a 1-electron shift per formula unit.

Figure 7 .
Figure 7. Band structures for (a) Ba3As4, (b) Ba5As4, and (c) Ba16As11.The Fermi level is the energy reference at 0 eV.An additional dashed line at ca. 0.48 eV indicates a 1-electron shift per formula unit.

Figure 6 .
Figure 6.Calculated Crystal Orbital Hamilton plots (COHP) for (a) Ba 3 As 4 , (b) Ba 5 As 4 , and (c) Ba 16 As 11 .The Fermi level is the energy reference at 0 eV.An additional dashed line at ca. 0.48 eV indicates a 1-electron shift per formula unit.

Figure 6 .
Figure 6.Calculated Crystal Orbital Hamilton plots (COHP) for (a) Ba3As4, (b) Ba5As4, and (c) Ba16As11.The Fermi level is the energy reference at 0 eV.An additional dashed line at ca. 0.48 eV indicates a 1-electron shift per formula unit.

Figure 7 .
Figure 7. Band structures for (a) Ba3As4, (b) Ba5As4, and (c) Ba16As11.The Fermi level is the energy reference at 0 eV.An additional dashed line at ca. 0.48 eV indicates a 1-electron shift per formula unit.

Figure 7 .
Figure 7. Band structures for (a) Ba 3 As 4 , (b) Ba 5 As 4 , and (c) Ba 16 As 11 .The Fermi level is the energy reference at 0 eV.An additional dashed line at ca. 0.48 eV indicates a 1-electron shift per formula unit.
48 eV difference corresponds to 1 electron per formula unit, indicating that the charge balance can only be achieved with the presence of the As-As pair.Besides a Fermi level shift, the Total and Partial DOS plots for Ba 16 As 11 share similar features to those discussed for the Ba 3 As 4 and Ba 5 As 4 phases.Bobev acknowledges financial support from the United States Department of Energy, Office of Science, Basic Energy Sciences, under Award #DE-SC0008885.

3 As 4 Ba 5 As 4 Ba 16 As 11.07(2) b
A and B are weight coefficients.b Ba 16 As 11 notation is used throughout the manuscript.

Table 2 .
Select As-As bond lengths from Ba 3 As 4 , Ba 5 As 4 , and Ba 16 As 11 .