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Article

Diversity of Molecular–Network Conformations in the Over-Stoichiometric Arsenoselenides Covering a Full Thioarsenides Row As4Sen (0 ≤ n ≤ 6)

by
Oleh Shpotyuk
1,2,3,*,
Malgorzata Hyla
1,
Zdenka Lukáčová Bujňáková
4,
Yaroslav Shpotyuk
5,6 and
Vitaliy Boyko
2
1
Institute of Physics, Jan Dlugosz University in Częstochowa, 13/15, al. Armii Krajowej, 42-200 Częstochowa, Poland
2
O.G. Vlokh Institute of Physical Optics, Ivan Franko National University of Lviv, 23, Dragomanov Str., 79005 Lviv, Ukraine
3
Scientific Research Company “Electron-Carat”, 202, Stryjska Str., 79031 Lviv, Ukraine
4
Institute of Geotechnics of Slovak Academy of Sciences, 45, Watsonova Str., 04001 Košice, Slovakia
5
Department of Sensor and Semiconductor Electronics, Ivan Franko National University of Lviv, 107, Tarnavskoho Str., 79017 Lviv, Ukraine
6
Institute of Physics, University of Rzeszow, 1, Pigonia Str., 35-959 Rzeszow, Poland
*
Author to whom correspondence should be addressed.
Molecules 2025, 30(9), 1963; https://doi.org/10.3390/molecules30091963
Submission received: 7 April 2025 / Revised: 24 April 2025 / Accepted: 25 April 2025 / Published: 29 April 2025
(This article belongs to the Special Issue Exclusive Feature Papers in Physical Chemistry, 3nd Edition)
Browse Figures
Versions Notes

Abstract

:
Molecular network conformations in the over-stoichiometric arsenoselenides of canonical AsxSe100−x system (40 ≤ x ≤ 100) covering a full row of thioarsenide-type As4Sen entities (0 ≤ n ≤ 6) are analyzed with ab initio quantum-chemical modeling employing cluster-simulation code CINCA. Native (melt-quenching-derived) and nanostructurization-driven (activated by nanomilling) polymorphic and polyamorphic transitions initiated by decomposition of the thioarsenide-type As4Sen cage molecules and incorporation of their remnants into a newly polymerized arsenoselenide network are identified on the developed map of molecular network clustering in a binary As-Se system. Within this map, compositional counter lines corresponding to preferential molecular or network-forming tendencies in the examined arsenoselenides are determined, explaining that network-crystalline conformations prevail in the boundary compositions corresponding to n = 6 and n = 0, while molecular-crystalline ones dominate inside the rows corresponding to n = 4 and n = 3. A set of primary and secondary equilibrium lines is introduced in the developed clustering map to account for inter-phase equilibria between the most favorable (regular) and competitive (irregular) thioarsenide phases. Straightforward interpretation of decomposition reactions accompanying induced crystallization and amorphization (reamorphization) in the arsenoselenides is achieved, employing disproportionality analysis of thioarsenide-type molecular network conformations within the reconstructed clustering map. The preference of network clustering at the boundaries of the As4Sen row (at n = 6 and n = 0) disturbs inter-phase equilibria inside this row, leading to unexpected anomalies, such as absence of stable tetra-arsenic triselenide As4Se5 molecular-crystalline species; polyamorphism in mechanoactivated As4Sen alloys (2 ≤ n ≤ 6); breakdown in the glass-forming ability of melt-quenching-derived arsenoselenides in the vicinity of tetra-arsenic biselenide As4Se2 composition; plastically and normally crystalline polymorphism in tetra-arsenic triselenide As4Se3-based thioarsenides, and so on.

Graphical Abstract

1. Introduction

Arsenic selenide alloys AsxSe100−x (also referred to as arsenoselenides) are an important class of substances that can be easily stabilized in a vitreous state starting from high-entropy melt by, respectively, rapid quenching within the broad compositional domain around stoichiometric arsenic triselenide As2Se3 (corresponding to x = 40), and stretching downwards to glassy Se (x = 0) and upwards to over-stoichiometric As-bearing species in a glassy state with up to ~70–75 at. % of arsenic (40 ≤ x < 70–75), or a glassy-crystalline state beyond this composition (x ≤ 100) [1,2,3,4,5]. Because of the full saturation of covalent chemical bonding in such binary chalcogenide systems, where elemental As and Se constituents are respectively two- and three-fold coordinated [1], their compositions are often defined by mean coordination number (MCN), that is, the average number of covalent chemical bonds per atom (MCN = 2 + 0.01x) [1,2].
Under-stoichiometric Se-bearing AsxSe100-x alloys (0 ≤ x ≤ 40, 2.00 < MCN < 2.40) exhibit glassy conformations possessing layered- or chain-type network structures [3,4] insensitive to post-technological modification [6,7]. In contrast, over-stoichiometric As-bearing AsxSe100−x compounds (40 ≤ x ≤ 100 or 2.40 ≤ MCN ≤ 3.00) attract significant attention in the contemporary glass manufacturers’ community in view of their post-technological modification possibilities, revealed by the diversity of structural conformations that can be derived from thioarsenide-type As4Sen entities (0 ≤ n ≤ 6) [6,7,8,9,10,11]. Herein, we employ the thioarsenide nomenclature considering the As4Xn molecules as derivatives from As4 tetrahedra (n = 0) modified by insertion of the n-th chalcogen atom X into one of six intramolecular (As-As) bonds, which was initially introduced for analysis of molecular packing and electron density distribution in an analogous As-S system [12,13,14,15].
Within a full row of such introduced thioarsenide-type As4Sen molecular entities from As (tetra-arsenic As4, n = 0) to tetra-arsenic hexaselenide As4Se6 (n = 6), we fit in over-stoichiometric As-bearing AsxSe100-x species deviated from ‘pure’ As (corresponding to x = 100, MCN = 3.00) to arsenic triselenide As2Se3 (corresponding to x = 40, MCN = 2.40) equivalent to As4Se6. With respect to the equilibrium phase diagram of a binary As-Se system [16,17], there are two intrinsic molecular-crystalline species within this compositional domain, these being monoclinic tetra-arsenic tetraselenide, As4Se4 (equivalent to arsenic monoselenide, AsSe [18,19,20]), and orthorhombic tetra-arsenic triselenide, As4Se3 [21]. However, the boundary species within the As4Sen thioarsenides row (n = 6 and n = 0) are composed by network-crystalline structures typical for 2D-layered arrangements of corner-shared AsSe3/2 pyramids in monoclinic As2Se3 [18,22] or honeycomb arrangements of chair-configurated As4 rings in both rhombohedral (grey or metallic α-As) and orthorhombic (black or semiconducting β-As) allotropes [23,24,25,26]. The crystalline conformation composed of individual tetrahedral As4 molecules characteristic of yellow or insulator γ-As is very unfavourable, existing only in a gaseous state [25,26].
It is worth noting that similar molecular-crystalline allotropes are possible in tetra-arsenic triselenide thioarsenides due to phase equilibria in the vicinity of the As4Se3 composition [16,17]. Thus, with respect to Blachnik and Wickel [27], the monoclinic α-As4Se3 existing at ambient temperature transforms under heating above 412 K into high-temperature orthorhombic α’-As4Se3 modification, and under heating above 447 K, the latter transforms in plastically crystalline β-As4Se3 and an amorphous substance of unknown composition, while only orthorhombic α’-As4Se3 phase could be stabilized in metastable form by conventional melt quenching. That is why polymorphic inter-crystalline transitions are expected in molecular As4Se3 [9], in addition to polyamorphic transitions in AsxSe100−x alloys within a whole glass-forming region (40 ≤ x < 70–75, 2.40 ≤ MCN < 2.70–2.75) [8,10,11].
As was suggested recently by Shpotyuk and co-workers [8,9,10,11], similar decomposition reactions are also expected in other As4Sen thioarsenides, resulting in a rich variety of molecular-to-network transitions. Specifically, polyamophic transitions are expected in over-stoichiometric arsenoselenides between some network species (network-forming clusters, NFC) derived from thioarsenide-type molecules (referred to as molecular-forming clusters, MFC), these transformations being activated by high-energy mechanical milling (nanomilling) [8,9,10,11]. This specificity determines the governing tendency of molecular-to-network transitions in thioarsenide-type arsenoselenides.
The objective of this research is comprehensive analysis to systemize a full row of thioarsenide-type As4Sen molecular and network entities in over-stoichiometric arseno-selenides AsxSe100−x (40 ≤ x ≤ 100; 2.40 ≤ MCN ≤ 3.00). The generalized approach, which allows mapping of thioarsenide-type As4Sen MFC and NFC, will be developed, employing ab initio quantum-chemical modeling with cluster-simulation code CINCA (cation-interlinked network cluster approach) [28,29]. This research is grounded in molecular network disproportionality analysis of As4Sen thioarsenides (n = 0, 1, 2 [10], n = 3 [9], n = 4 [8], and n = 5, 6 [11]). Most plausible scenarios of nanostructurization-driven polymorphic and polyamorphic transitions are justified for over-stoichiometric arsenoselenides, covering a full row of As4Sen molecules and their network derivatives (0 ≤ n ≤ 6).

2. Results and Discussion

2.1. Mapping of Molecular- and Network-Type Clusters in AsxSe100−x Arsenoselenides (20 < x ≤ 100)

Let us examine a full row of thioarsenide-type As4Sen MFC (0 ≤ n ≤ 6) and their derivatives (NFC) within over-stoichiometric As-bearing arsenoselenides AsxSe100−x (40 ≤ x ≤ 100; 2.40 ≤ MCN ≤ 3.00). In fact, the As4Sen MFC are derivatives from the tetrahedral As4 cage molecule stabilized by insertion of the n-th Se atom instead of one of six As-As bonds [12,13,14,15], while the As4Sen NFC can be derived from the respective MFC by breaking in available Se atom positions followed by insertion of the remainder in a newly polymerized network. Therefore, in the atomic clusters nomenclature [28,29], the NFC formed by N breaks in Se atom positions are denoted by the number of these breaks following the thioarsenide formula xN-As4Sen, while the iso-compositional parent MFC stabilized without breaking is labeled as x0-As4Sen. In reality, we deal with iso-compositional MFC and NFC obtained by H atom termination in the broken Se atom positions of thioarsenide-type As4Sen molecule (MFC) due to Se-H bonds (if a few configurations are possible, these clusters differ by an additional digit at the second place). For comparison, the forming energies of As4Sen MFC and NFC Ef = (EfΣ)av are averaged for all (4 + n) atoms and simplified with respect to the forming energy of a trigonal AsSe3/2 pyramid (−72.309 kcal/mol) [29].
Compositional landscape mapping of all possible MFC and NFC in AsxSe100-x in a broad compositional domain around the As2Se3 stoichiometry (20 < x ≤ 100, 2.2 < MCN ≤ 3.0) covering a full row of thioarsenide-type As4Sen entities (0 ≤ n ≤ 6) is reproduced in Figure 1, while a partial fragment of this map showing fine details of molecular network clustering within a range of glass-forming As4Sen thioarsenides (2 ≤ n ≤ 6) is reproduced in Figure 2. The calculated Ef energies for iso-compositional MFC and NFC are gathered in Table 1.
In a group of under-stoichiometric Se-bearing AsxSe100−x alloys deviated from chemical As2Se3 stoichiometry (x = 40, MCN = 2.40) towards more Se-rich specimens (20 < x ≤ 40), we deal with two-cation As2Sem NFC representing themselves as AsSe3/2 pyramidal units cross-linked by Se chains. Homogeneous linking with an equal number of Se half-atoms in all chains (Δl) corresponds to the canonical ‘chain-crossing’ model [2,3,4,5] (in the case of equivalent chains, Δl = 0 [29]). The diversity of As2Sem NFC is defined by Δl parameters for each composition. Thus, going from stoichiometric As2Se3net to Se-rich NFC through points corresponding to the most favorable entities (see Figure 1), we obtain a set of cut-section lines governing local (between neighboring NFC) and global (between terminated counterparts) decomposition reactions in under-stoichiometric arsenoselenides AsxSe100−x (x ≤ 40). It is worth noting that on the molecular network clustering map reproduced in Figure 1, we also denote the forming energy of a quasi-tetrahedral Se = AsSe3/2 unit based on double As = Se covalent bond [29], which seems to be far from the set of the lines ascribed to the As2Sem NFC based on single As-Se bonds. This finding contradicts speculations that this optimally constrained quasi-tetrahedral unit can be considered as the principal glass-forming building block in the As2Se5 compound.
In a group of tetra-arsenic hexaselenide thioarsenide-type As4Sen entities (n = 6) corresponding to chemical stoichiometry in the AsxSe100−x system (that is, As2Se3 compositionally equivalent to As4Se6), the parent x0-As4Se6 MFC composed of four corner-sharing AsSe3/2 units in an optimally constrained topology (with the number of constraints per atom nc = 3.00 strictly corresponding to space dimensionality, 3D) has very unfavorable cluster-forming energy of Ef = −0.67 kcal/mol (see Table 1, Figure 1, Figure 2 and Figure 3a). The best energy, Ef = 0.31 kcal/mol (with respect to the energy of a single AsSe3/2 pyramid [29]) is achieved for the NFC derived from this parent x0-As4Se6 MFC by breaking in four of six Se atom positions, labelled as x4-As4Se6 NFC (see Figure 4). This NFC can be imagined as two corner-sharing AsSe3/2 pyramidal units forming the topologically optimal layer-type network with nc = 3.00 [11]. The calculated geometrical parameters of this x4-As4Se6 NFC, also labelled as As2Se3net and denoted by an open circle in the compositional molecular network map (see Figure 1 and Figure 2), are found to be in very good agreement with those characteristic of the known crystalline counterpart, which is monoclinic As2Se3 [21,22].
Among tetra-arsenic pentaselenide As4Sen entities (n = 5, MCN = 2.44), the parent x0-As4Se5 cage MFC composed of four small rings (2 pentagons, 2 hexagons) built of ten heteronuclear (As-Se) bonds and one homonuclear (As-As) bond in under-constrained topology (nc = 2.89) possesses gradually improved Ef = 0.32 kcal/mol (see Figure 3b) [11]. The iso-compositional NFC stabilized as derivatives from this x0-As4Se5 MFC by breaking in Se atom positions (x4-As4Se5; x3-1-As4Se5; x3-2-As4Se5; x5-As4Se5) become competitive by their Ef energies to parent x0-As4Se5 MFC (see Table 1, Figure 1 and Figure 2), preventing thioarsenide-type As4Se5 alloy from spontaneous crystallization [11].
In a group of tetra-arsenic tetraselenide As4Sen entities (n = 4) with MCN = 2.50, the parent x0-As4Se4 MFC of D2d symmetry (proper to As4S4 realgar [12,15]) is composed of eight small rings, resulting in nc = 2.875 and the best Ef energy among thioarsenide-type molecules, Ef = 0.40 kcal/mol (see Table 1, Figure 1, Figure 2 and Figure 3c) [8]. This MFC is the main block of the molecular-crystalline counterpart (monoclinic As4Se4) [18,19,20]. The most plausible NFC of this type is the optimally constrained cluster (nc = 3.00) stabilized by breaking in one of four equivalent Se atom positions (x1-As4Se4), which has three small rings, and over-constrained clusters with nc = 3.25, such as x3-As4Se4 and x4-As4Se4 (see Table 1, Figure 1 and Figure 2). The former, with Ef = 0.25 kcal/mol, seems competitive with x0-As4Se4 MFC, contributing to the optimal glass-forming ability of As4Se4 alloy [8,30]). The nanomilling-driven decrease in molecularity due to molecular-to-network transition essentially modifies the arrangement of diffuse peak-halos in the XRPD pattern of this alloy [7,8].
We do not exclude among As4Se4-based thioarsenides the possibility for pararealgar-type x0-pr-As4Se4 MFC and respective NFC [30]. By analogy with the pararealgar As4S4 molecule of Cs symmetry [12,15], the x0-pr-As4Se4 MFC (see Figure 3d) is composed of two homonuclear (As-As) bonds in neighboring geometry forming four small rings (1 hexagon, 2 pentagons, 1 tetragon), resulting in more under-constrained topology (nc = 2.75) as compared with realgar-type x0-As4Se4 MFC (Figure 3c). Despite the Ef energy of x0-pr-As4Se4 MFC being competitive (0.30 kcal/mol), it has been still worse than this energy in x0-As4Se4 MFC, meaning an absence of pararealgar-type polymorph in the As-Se system. Nevertheless, this analysis does not disfavor x0-pr-As4Se4 MFC and its network derivatives, which could be stabilized in disordered materials such as glasses in non-equilibrium conditions of melt quenching [8,30]. With respect to modeling [30], the most favorable (apart from x0-pr-As4Se4 MFC) are optimally and over-constrained NFC, marked on the map of Figure 1 as x1-1-pr-As4Se4 (nc = 3.0), x4-pr-As4Se4 (nc = 3.25), and x3-3-pr-As4Se4 (nc = 3.25).
There are three molecular-type conformations differing by their arrangement of four As atoms forming three homonuclear (As-As) bonds among tetra-arsenic triselenide As4Sen entities (n = 3) with MCN = 2.57, these being triangular-pyramidal conformation I due to basal (As3) = (As-As-As) triangular neighboring with AsSe3/2 pyramid (see Figure 3e); open chain-like (As4) = (As-As-As-As) conformation II due to three homonuclear (As-As) bonds in zig-zag sequence (Figure 3f); and star-like (As3)As conformation III due to three homonuclear (As-As) bonds having a common origin on the fourth As atom (Figure 3g) [9,15]. In view of the calculated cluster-forming energies [9], the I-As4Se3 conformation, which is isostructural with the cage molecule in α-/β-modifications of dimorphite As4S3 [12,31,32,33], is the most favorable, approaching Ef = 0.33 kcal/mol (see Table 1), which is less than in realgar-type x0-As4Se4 MFC, but more than in pararealgar-type x0-pr-As4Se4 MFC. The optimized configuration of this x0-I-As4Se3 MFC (see Figure 3e) [9] is composed of four small rings (3 pentagons, 1 triangle) by all seven atoms positioned at the surface of the same sphere in the under-constrained topology of the C3v symmetry (nc = 2.71), resulting in a 0D structure with evident features of plastically crystalline phase (low calorimetric heat-transfer and strong thermal expansion responses) [27,34]. Other MFC iso-compositional to tetra-arsenic triselenide As4Se3 (such as x0-II-As4Se3 and x0-III-As4Se3) are unfavorable as compared with this x0-I-As4Se3 MFC (shown in Figure 3e), but they cannot be excluded from comprehensive consideration in view of their network derivatives, such as optimally constrained x1-1-II-As4Se3 NFC (nc = 3.00), and over-constrained x3-II-As4Se3 and x3-III-As4Se3 NFC (both with nc = 3.43, see Table 1).
The equilibrium between molecular and network-forming clustering is drastically disturbed in the transition to tetra-arsenic biselenide As4Sen entities (n = 2) with MCN = 2.67, that is, at the border of the glass-forming region in the binary As-Se system [16,17]. Both parent MFC of this type (the x0-I-As4Se2 with nc = 2.50 composed by (As-As) bond attached to As3 triangle, and x0-II-As4Se2 with nc = 2.67 composed by four (As-As) bonds in zig-zag configuration) are unfavorable (see Table 1, and Figure 3h,i) [10]. The same is true of NFC derived from these MFC by breaking in one of two available Se atom positions. Conversely, the over-constrained x2-II-As4Se2 NFC derived by double x2-breaking (with tetragon-like As4 arrangement of four homonuclear As-As bonds) possesses Ef = −0.72 kcal/mol. This NFC facilitates decomposition of the x0-I-As4Se3 MFC into realgar-type x0-As4Se4 MFC accompanied by the extraction of amorphous phase compositionally very close to As4Se2 [10].
In a group of tetra-arsenic monoselenide thioarsenide-type As4Sen entities (n = 1) corresponding to MCN = 2.80, only two clusters are possible, with both x0-As4Se MFC (depicted in Figure 3j) and x1-As4Se NFC being under-constrained [10]. These clusters cannot be stabilized in realistic arsenoselenide conformations because of very unfavourable Ef energies (see Table 1).
In a group of As4-type clusters restricting row of thioarsenide-type As4Sen entities at n = 0 corresponding to x = 100 and MCN = 3.0 in the AsxSe100-x system, the molecular network balance is defined by two principal clusters characteristic of As polymorphs, these being the x0-As4 = As4mol MFC in the form of a regular pyramid-shaped As4 tetrahedron (as shown in Figure 3k), and As6(2/3) = As4net NFC in the form of a flattened pyramid-shaped unit derived from As4mol by breaking in one of three As-As bonds at each As atom within a two-dimensional double-layered network of chair-configurated 6-fold rings (see Figure 5) [10]. Within the arrangement of the three nearest neighbours, these clusters are differentiated by the calculated Ef forming energies, as shown in Table 1. The origin of network-type orthorhombic and rhombohedral As allotropes can be reasonably explained by distortion pathways beyond the three nearest neighbours [23,24,25,26], but this specificity cannot be accounted for in the current CINCA modelling. The under-constrained configuration of tetrahedral As4mol MFC (having nc = 2.25 in view of four small rings involved, 4 triangles) appears to be very unfavourable, resulting in the Ef forming energy approaching only −4.31 kcal/mol, thus confirming the γ-As phase stabilization exceptionally in a gaseous state [25,26]. In contrast, the over-constrained configuration of As4net NFC (having nc = 4.5 in view of only one small ring involved, 1 hexagon) composing a double-layer honeycomb structure of chair-configurated As6(2/3) rings typical for rhombohedral (grey or metallic α-As) and orthorhombic (black or semiconducting β-As) allotropes [23,24,25,26] are more promising in crystallization processes, resulting in Ef~ −2.46 kcal/mol (see Table 1). This explains the appearance of rhombohedral α-As phase as the most stable allotropic modification under nanostructurization-driven transformations in melt-quenched As-Se alloys [10].
Within the compositional map of molecular network clustering in the AsxSe100-x alloys covering a full row of thioarsenide-type As4Sen entities (0 ≤ n ≤ 6) reproduced in Figure 1, we can distinguish between a molecular-forming counter line connecting the settle-points of the most favorable MFC (shown as dotted red-colored line) and a network-forming counter line connecting the settle-points of the most favorable NFC (depicted as dotted blue-colored line in Figure 1). By comparing these compositional counter lines, it can be seen that the network-crystalline conformations prevail at the boundary of the As4Sen row for n = 6 (As4Se6) and n = 0 (As4), and exceptionally for n = 2 (As4Se2), while thioarsenides inside this row for n = 5 (As4Se5), n = 4 (As4Se4), and n = 3 (As4Se3) are dominated by a molecular-forming trend. It is worth noting that both MFC and NFC with n = 1 (As4Se) are very unfavorable with respect to other thioarsenides.
In full harmony with these findings, the boundary thioarsenides labeled in Figure 1 by open red circles possess the network-crystalline conformations at n = 6 (due to x4-As4Se6 = As2Se3net NFC, the basic structural motives of monoclinic As2Se3 [21,22]) and n = 0 (due to x0-As6(2/3) = As4net NFC, the basic structural motives of network As polymorphs, the rhombohedral α-As or orthorhombic β-As [23,24,25,26]), and molecular-crystalline conformations at n = 4 (due to x0-As4Se4 MFC, the basic motives of monoclinic As4Se4 [18,19,20]) and n = 3 (due to x0-I-As4Se3 MFC, the basic structural motives of As4Se3 allotropes [27]). Thus, the boundary crystalline entities terminating the thioarsenides As4Sen row at n = 6 and n = 0 possess the better network-forming ability, while a molecular-crystalline tendency prevails inside this thioarsenides row at n = 4 and n = 3.

2.2. Inter-Phase Equilibria in Over-Stoichiometric Arsenoselenides AsxSe100−x (40 ≤ x ≤ 100) Governed by Molecular Network Clustering

The coexistence of several stable crystalline phases in the AsxSe100-x alloys (40 ≤ x ≤ 100), covering a full row of As4Sen thioarsenides (0 ≤ n ≤ 6)—two of which are of network-type, terminating this row by boundary entities with n = 6 (As2Se3net equivalent to As4Se6) and n = 0 (As4net); and two others of which are molecular-type, forming an intrinsic part of this row at n = 4 (As4Se4mol) and n = 3 (As4Se3mol)—is defined by primary full equilibrium line 1 connecting the respective settle-points corresponding to the forming energies (Ef) of these most favorable (regular) crystalline entities [As2Se3net–As4Se4mol–As4Se3mol–As4net]. In reality, equilibrium line 1 is composed of three cut-sections, these being (i) left-terminated network–molecular [As2Se3net–As4Se4mol], (ii) intrinsic molecular–molecular (As4Se4mol–As4Se3mol), and (iii) right-terminated molecular–network [As4Se3mol–As4net].
Because of the sharp drop in the Ef energy for As4net NFC (see Table 1), a few cut-section lines corresponding to partial inter-crystalline equilibria can be derived from this primary equilibrium line 1, such as primary partial equilibrium line 3 for regular boundary–boundary thioarsenide entities [As2Se3net–As4net], and lines 3.1 and 3.2 for regular intrinsic-boundary entities [As4Se4mol–As4net] and [As4Se3mol–As4net], respectively. The cross-point of any of these primary (full or partial) equilibrium lines with respective thioarsenide compositional line (defined by n parameter or MCN value) corresponds to a simple mixture of these boundary regular phases, the amounts of which are inversely proportional to the distances to the boundary points.
Thus, the thioarsenide-type entities (NFC and MFC) positioned at the molecular network clustering map below the primary full equilibrium line 1 [As2Se3net−As4Se4mol−As4Se3mol−As4net] represent amorphous substances that can be stabilized by decomposition on the regular phases positioned most closely along this line. Respectively, the primary partial equilibrium lines 3, 3.1, and 3.2 define amorphous substances, which can be stabilized by decomposition on a mixture of respective boundary thioarsenide-type phases.
In a similar manner, a set of secondary equilibrium lines can be introduced for thioarsenide-type entities that are competitive to most favorable (regular) ones. The first of such irregular entities corresponds to the As4mol MFC, which possesses a smaller Ef energy than iso-compositional As4net NFC (see Table 1). Therefore, the secondary equilibrium line 4 [As2Se3net−As4mol] connecting the settle-points of regular network-type As2Se3net and irregular molecular-type As4mol entities can be introduced to define a mixture of both components. By analogy, the secondary partial equilibrium line 4.1 for a mixture of regular As4Se4mol and irregular As4mol entities and secondary partial equilibrium line 4.2 for a mixture of regular As4Se3mol and irregular As4mol entities can be reconstructed on the clustering map (Figure 1). The cross-point of any of these secondary equilibrium lines with the respective thioarsenide composition (defined by the n parameter) corresponds to a mixture of both boundary phases.
The absence of regular crystalline structures corresponding to the x0-As4Se6 MFC (labeled as As4Se6mol in Figure 1) does not mean an absence of these thioarsenide-type structural entities in amorphous arsenoselenides derived in more non-equilibrium technological conditions or under nanostructurization influence [11]. That is why the secondary equilibrium line 2 [As4Se6mol−As4mol] connecting the settle-points of both irregular molecular boundary entities terminating the thioarsenides As4Sen row at n = 6 and 0 can be introduced. This equilibrium line 2 (As4Se6mol−As4mol) defines a mixture of both irregular molecular thioarsenide-type phases, which can be extracted in arsenoselenide compounds in amounts inversely proportional to the distances to the respective boundary points.

2.3. Disproportionality Analysis of Native and Mechanoactivated Molecular Network Conformations in Over-Stoichiometric AsxSe100−x Arsenoselenides (40 ≤ x ≤ 100)

Crystallization processes in amorphous alloys can be essentially complicated by the accompanying decomposition reactions [35,36,37,38]. Thus, crystallization without compositional changes (also known as polymorphous crystallization [36]) occurs if the free energy of supersaturated crystalline alloy is lower than that of amorphous alloy [36]. The primary crystallization in one of the stable boundary phases occurs if the concentration of amorphous substance shifts until the stable phase stops crystallizing by reaching the metastable equilibrium. At last, if simultaneous decomposition of amorphous alloy into two stable phases occurs with the greatest driving force, then eutectoid crystallization can be realized by discontinuous reaction in a whole range of compositions.
Similar processes are expected in amorphous chalcogenide alloys prepared by conventional melt quenching [5], in part, the thioarsenide-type As4Sen alloys. Thus, more than four decades ago, Blachnik and Wickel [27] recognized the thermal behaviour of A4B3 cage-like molecules (A = P, As; B = S, Se) in plastically and normally crystalline modifications of these A4B3 polymorphs. In their suggestion [27], these chalcogenide alloys decompose peritectoidally into A4B4 molecules and unidentified amorphous substance.
In molecular network alloys like binary arsenoselenides, inter-phase equilibria lead towards polymorphic and polyamorphic transitions in the vicinity of some thioarsenide-type As4Sen compositions, especially under mechanoactivated nanostructurization [8,9,10,11].
Disproportionality analysis employing the map of molecular network atomic clustering in the As-Se system (Figure 1) serves as a key to understanding the essence of such processes. Within this map, each NFC contributing to amorphization can be presented by the settle-point below the network-forming counter line (bold blue dotted line in Figure 1). The polymorphous crystallization with negative energetic barrier can be realized in this alloy as a spontaneous transition into a crystalline state along a vertical compositional line. In boundary arsenoselenides terminating the row of thioarsenides As4Sen (for n = 6 and n = 0), crystallization prevails by transition into the most favorable state of x4-As4Se6 = As2Se3net and As4net NFC, having the best cluster-forming energies Ef as compared with iso-compositional x0-As4Se6 = As4Se6mol and x0-As4 = As4mol MFC. In arsenoselenides inside the As4Sen row (for n = 4 and n = 3), polymorphous crystallization prevails by transition into most the favorable state of x0-As4Se4 = As4Se4mol and x0-As4Se3 = As4Se4mol MFC, having the best Ef energy as compared with iso-compositional x1-As4Se4 and x1-1-II-As4Se3 NFC.
It is worth noting that if the NFC settle-point is located below one of the equilibrium lines defined by some boundary arsenoselenide compounds, these NFC are metastable undergoing spontaneous decomposition into a mixture of these boundary compounds. Decomposition in As6(2/3) = As4net NFC contributes to primary crystallization of regular As phase (the rhombohedral α-As [23,24]), while x0-As4 = As4mol MFC contribute to the irregular amorphous phase of this alloy. Thus, with respect to the clustering map (see Figure 1), the As4Sen conformations based on NFC with Ef energies above the secondary equilibrium line 4 (As2Se3net−As4mol) connecting the settle-points corresponding to the most favorable x4-As4Se6 = As2Se3net NFC and competitive x0-As4Se4 = As4Se4mol MFC serve as principal building blocks for amorphous arsenoselenides, which can be fabricated by conventional melt quenching.
Let us analyze the expected amorphization/reamorphization scenarios in these alloys, covering a full row of thioarsenide-type As4Sen entities (0 ≤ n ≤ 6).
In the point of stoichiometry (MCN = 2.40), the most favorable x4-As4Se6 = As2Se3net NFC composed of two corner-sharing AsSe3/2 pyramids in optimally constrained geometry (nc = 3.00) are preferred over parent x0-As4Se6 = As4Se6mol MFC (see Table 1), determining the network nature of both crystalline and amorphous thioarsenide-type polymorphs [6,7,11].
With the transition to As4Se5 thioarsenides, polymorphous crystallization into one stable phase is suppressed by competitive amorphization due to the x4-As4Se5 NFC with Ef energy above the secondary equilibrium line 4 [As2Se3net−As4mol] (see Figure 1). At this point (MCN = 2.44), decomposition into the nearest regular phases (based on As2Se3net NFC and As4Se4mol MFC) results in their mixture with Ef = 0.346 kcal/mol, which is 0.026 kcal/mol better than in the x0-As4Se5 MFC [11]. This means that just-formed x0-As4Se5 MFC will be spontaneously decomposed on these boundary entities without stabilization of the crystalline phase.
At the point of the As4Se4-type thioarsenides (MCN = 2.50), the known molecular-crystalline counterpart (which is monoclinic As4Se4 [18,19,20]) is preferred due to the x0-As4Se4 = As4Se4mol MFC of the best cluster-forming energy among all thioarsenide-type entities (Ef = 0.40 kcal/mol, see Table 1) [8]. The competitive NFC of this type (x1-As4Se4, x4-As4Se4, x3-As4Se4, x4-pr-As4Se4, x1-1-pr-As4Se4, x2-1-As4Se4, x3-3-pr-As4Se4) are tightly and uniformly grouped on the clustering map above the secondary equilibrium line 4 [As2Se3net−As4mol], approaching the settle-point of As4Se4mol MFC but not overcoming it (Figure 1). This speaks in a favor of high crystallization ability of this arsenoselenide alloy. Moreover, because of the NFC positioned on the clustering map above the secondary equilibrium line 4 [As2Se3net−As4mol] and primary partial equilibrium line 3 [As2Se3net−As4net], nanomilling-driven amorphization and re-amorphization processes in this alloy can also be facilitated, resulting in stabilization of both molecular- and network-type As polymorphs based on As4mol MFC and As4net NFC.
In As4Se3-type thioarsenides (MCN = 2.57), molecular network disproportionality is highly disturbed. Polymorphous crystallization of this alloy into orthorhombic α’-As4Se3 phase dominates because of the preference of dimorphite-type x0-I-As4Se3-As4Se3mol MFC, possessing very promising Ef energy, approaching 0.33 kcal/mol (see Table 1) [9]. The NFC contributing to the amorphization of this alloy are located in the narrow interval above the secondary equilibrium line 4 [As2Se3net−As4mol] and below the primary partial equilibrium line 3 [As2Se3net−As4net] (see Figure 1). There are no As4Se3-type NFC closely approaching the x0-I-As4Se3-As4Se3mol MFC. This means that direct crystallization of this alloy from the NFC state is rather impossible, in view of the competitive decomposition of these entities within the nearest equilibrium lines. Spontaneous decomposition of these NFC prevails along the primary partial equilibrium line 3 [As2Se3net−As4net] and secondary partial equilibrium line 4.1 [As4Se4mol−As4mol], resulting in both As polymorphs based on As4mol MFC and As4net NFC, whereas induced decomposition along secondary equilibrium line 4 [As2Se3net−As4mol] results in amorphous As based on As4mol MFC.
As follows from the clustering map (Figure 1), the x2-II-As4Se2 NFC (which can be derived from the As4Se2-II molecule by double breaking in all available Se atom positions) is the last suitable candidate introducing network polyamorphism in this thioarsenide alloy [10]. Both parent MFC related to As4Se2 stoichiometry (x0-I-As4Se2 and x0-II-As4Se2) are very unfavorable, but the x2-II-As4Se2 NFC is prone to spontaneous decomposition along the secondary partial equilibrium line 4.2, and primary partial equilibrium line 3.1 and 3.2, resulting in regular thioarsenide-type phases (based on the most favorable As4Se4mol and As4Se3mol MFC and As4net NFC). However, complete eutectoid crystallization of this alloy is rather prohibited by the positive barrier of competitive induced decomposition along the primary partial equilibrium line 3 [As2Se3net−As4net]. The former spontaneous decomposition processes explain the location of the glass-forming border in the As-Se system near the As4Se2 composition, while the latter over-barrier decomposition processes are responsible for the nanostructurization-driven re-amorphization in this alloy [10].
With further increase in As content towards tetra-arsenic monoselenide As4Se stoichiometry (MCN = 2.80), a complete breakdown in forming ability occurs for iso-compositional MFC and NFC, presumably because of unrealistic steric constraints limiting the stabilization of As4Se entities [10]. Only products of eutectoid decomposition on the most favorable thioarsenide-type entities (mainly As4Se3mol and As4net) can be stabilized in this alloy.
Disproportionality analysis of thioarsenide-type As4Sen conformations is reasonably completed in the As polymorphs [23,24,25,26] by preference of the As6(2/3) = As4net NFC in a form of chair-configurated 6-fold rings over the x0-As4 = As4mol MFC in a form of pyramid-shaped As4 tetrahedra. From most principal viewpoints, the diversity of decomposition reactions in over-stoichiometric arsenoselenides covering a full row of As4Sen entities (0 ≤ n ≤ 6) is governed by this anomaly in their boundary conformations.

3. Methods

3.1. Cluster Modeling of Molecular Conformations in Covalent-Bonded Substances

The optimized conformations of thioarsenide-type As4Sen molecular entities (MFC and NFC) were reconstructed employing ab initio quantum-chemical modeling with cluster-simulation code CINCA (cation-interlinked network cluster approach) [28,29]. The HyperChem Release 7.5 program package based on the restricted Hartree–Fock self-consistent field method with split-valence double-zeta basis set and single polarization function 6-311G* [39,40,41] was used. The geometrical optimization and single-point energy calculations were performed by the Fletcher–Reeves conjugate gradient method until a root-mean-square gradient of 0.1 kcal/(Å·mol) was reached. For comparison within the As-Se family, the final average cluster-forming energies were averaged for all constituent atoms in the molecule Ef = (EfΣ)av and recalculated with respect to the forming energy of a single trigonal AsSe3/2 pyramid (Ef = −72.309 kcal/mol [29]).
The CINCA modeling [28,29] allows simulation of molecular-type conformations in solid systems possessing full saturation of covalent bonding like the AsxSe100-x alloys characterized by different numbers of covalent chemical bonds per atom (MCN). To compare the clusters, accounting for small rings characteristic of molecular thioarsenide-type structures, the average number of the Lagrangian constraints (nc) associated with stretching and bending forces ascribed to intra-molecular bonds within the cluster was recalculated using the Phillips–Thorpe constraint-counting algorithm [42,43,44].

3.2. Disproportionality Analysis of Molecular Network Conformations in Chalcogenide Alloys

Disproportionality analysis of molecular network conformations foresees energetic differentiation between all possible thioarsenide-type As4Sen molecules (nominated as parent MFC) and molecular prototypes of iso-compositional NFC derived from these MFC by all possible breaks on separate homonuclear (Se1/2…Se1/2) fragments in available Se atom positions [28,29]. The self-consistent molecular configurations of the NFC were reconstructed by saturating the Se dangling bonds with the hydrogen (H) atoms, with low bonding energy in the covalent structures (∼3 kcal/mol [41,45,46]). This termination procedure is also quite reasonable since the electronegativity of terminated H atoms (2.20) is close to those of other atoms in As-Se conformations, being intermediate between the electronegativities of the As and Se atoms (respectively approaching 2.18 and 2.55 [47]). Therefore, there are no strong disturbances in electron density distribution within the NFC in chalcogenide compounds due to terminated H atoms, transforming these network entities (NFC) into self-consistent molecular prototypes.

4. Conclusions

Molecular network conformations in over-stoichiometric As-bearing arsenoselenides AsxSe100−x (40 ≤ x ≤ 100) covering a full row of thioarsenide-type As4Sen entities (0 ≤ n ≤ 6) are comprehensively and systematically analyzed by ab initio quantum-chemical modeling employing the cluster-simulation code CINCA (cation-interlinked network cluster approach). Native (melt-quenching-derived) and nanostructurization-driven (activated by high-energy milling) polymorphic and polyamorphic transformations initiated by the decomposition of thioarsenide-type As4Sen cage-like molecules and incorporation of their remnants into a newly polymerized arsenoselenide network are identified on the map of molecular network clustering in an As-Se sysyem. Within this map reconstructed for over-stoichiometric arsenoselenides within a full row of thioarsenide-type As4Sen entities (0 ≤ n ≤ 6), the compositional counter lines corresponding to preferential molecular- or network-forming tendencies in a system are determined, showing that network-crystalline conformations prevail in the boundary As4Sen compositions (n = 6 and 0), while molecular-crystalline conformations dominate inside the As4Sen row (n = 4 and 3). A set of primary and secondary equilibrium lines is introduced in the clustering map to account for inter-phase equilibria between the most favorable (regular) and competitive (irregular) thioarsenide phases. Straightforward interpretation of decomposition reactions accompanying induced crystallization and amorphization (reamorphization) processes in the arsenoselenides is achieved employing disproportionality analysis of thioarsenide-type molecular network conformations within the developed clustering map. Bifurcation of molecular network clustering at the boundaries of the thioarsenides As4Sen row is shown to disturb the inter-phase equilibria inside this row, leading to many unexpected consequences, such as the absence of stable tetra-arsenic pentaselenide (As4Se5) molecular-crystalline species; polyamorphism in mechanoactivated thioarsenide-type As4Sen alloys; breakdown in the glass-forming ability of melt-quenching-derived arsenoselenides in the vicinity of tetra-arsenic biselenide (As4Se2) composition; plastically and normally crystalline polymorphism in tetra-arsenic triselenide (As4Se3) thioarsenides, and so on.

Author Contributions

Conceptualization, O.S.; methodology, Y.S. and Z.L.B.; formal analysis, O.S., M.H., Y.S., Z.L.B. and V.B.; investigation, O.S., M.H., Y.S., Z.L.B. and V.B.; data curation, M.H., Y.S., Z.L.B. and V.B.; writing—original draft preparation, O.S.; writing—review and editing, Y.S. All authors have read and agreed to the published version of the manuscript.

Funding

This research is supported by the Slovak Research and Development Agency under contract APVV-18-0357 and Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic under contract 2/0112/22 (ZLB). Part of the research was performed within the common Polish–Slovak research cooperation program for the years 2024–2025 co-financed by the Polish National Agency for Academic Exchange (agreement BPN/BSK/2023/1/00001/U/00001) and Slovak Research and Development Agency (project SK-PL-23-0002).

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.

Acknowledgments

YS is grateful to SAIA for support within the National Scholarship Program of the Slovak Republic.

Conflicts of Interest

O.S. was employed by the Scientific Research Company “Electron-Carat”. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Molecules 30 01963 g001
Figure 1. Compositional map of molecular network clustering in AsxSe100−x alloys (20 < x ≤ 100, 2.2 < MCN ≤ 3.0) covering full row of thioarsenide-type As4Sen entities (0 ≤ n ≤ 6). The MFC are denoted by full red-colored rhombs, with ‘x0′ notation showing the absence of breaking in Se atom positions. Tho MFC that have crystalline counterparts are marked by open red circles. In the cases of a few MFC, they are additionally distinguished by -I, -II, or -III digits, while pararealgar-related As4Se4 MFC are labeled as ‘pr’. The NFC derived from As4Sen MFC by N-fold breaking in Se atom positions are denoted by full black circles, with the right notation showing the number of breaks (xN). The NFC undergoing separation on a few parts are denoted by open black squares with the same indication of breaking. The dotted red-colored counter line connecting the settle-points of the most favorable thioarsenide-type MFC corresponds to the preference of the molecular-forming tendency in a system, while the network-forming tendency prevails along dotted blue-colored counter line connecting the settle-points of the most favorable NFC. The equilibrium lines numbered as 1, 2, 3, 3.1, 3.2, 4, 4.1, and 4.2 correspond to primary and secondary inter-crystalline phase equilibria in the binary As-Se system.
Figure 1. Compositional map of molecular network clustering in AsxSe100−x alloys (20 < x ≤ 100, 2.2 < MCN ≤ 3.0) covering full row of thioarsenide-type As4Sen entities (0 ≤ n ≤ 6). The MFC are denoted by full red-colored rhombs, with ‘x0′ notation showing the absence of breaking in Se atom positions. Tho MFC that have crystalline counterparts are marked by open red circles. In the cases of a few MFC, they are additionally distinguished by -I, -II, or -III digits, while pararealgar-related As4Se4 MFC are labeled as ‘pr’. The NFC derived from As4Sen MFC by N-fold breaking in Se atom positions are denoted by full black circles, with the right notation showing the number of breaks (xN). The NFC undergoing separation on a few parts are denoted by open black squares with the same indication of breaking. The dotted red-colored counter line connecting the settle-points of the most favorable thioarsenide-type MFC corresponds to the preference of the molecular-forming tendency in a system, while the network-forming tendency prevails along dotted blue-colored counter line connecting the settle-points of the most favorable NFC. The equilibrium lines numbered as 1, 2, 3, 3.1, 3.2, 4, 4.1, and 4.2 correspond to primary and secondary inter-crystalline phase equilibria in the binary As-Se system.
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Figure 2. Fragment of compositional map of molecular network clustering in over-stoichiometric arsenoselenides reproduced within a range of glass-forming As4Sen thioarsenides (2 ≤ n ≤ 6).
Figure 2. Fragment of compositional map of molecular network clustering in over-stoichiometric arsenoselenides reproduced within a range of glass-forming As4Sen thioarsenides (2 ≤ n ≤ 6).
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Figure 3. Ball-and-stick presentation of optimized configurations of thioarsenide-type As4Sen MFC: (a) tetra-arsenic heksaselenide x0-As4Se6, (b) tetra-arsenic pentaselenide x0-As4Se5, (c) tetra-arsenic tetraselenide of realgar modification x0-As4Se4, (d) tetra-arsenic tetraselenide of pararealgar modification x0-pr-As4Se4, (e) tetra-arsenic triselenide in dimorphite-type triangular-pyramidal (As3)-As configuration x0-I-As4Se3, (f) tetra-arsenic triselenide in chain-like (As4) configuration x0-II-As4Se3, (g) tetra-arsenic triselenide in star-like (As-As3) configuration x0-III-As4Se3, (h) tetra-arsenic biselenide in combined triangular-star (As3)As configuration x0-I-As4Se2, (i) tetra-arsenic biselenide in chain-like (As4) configuration x0-II-As4Se2, (j) tetra-arsenic monoselenide x0-As4Se, (k) tetra-arsenic in tetragon-like configuration x0-As4. The Se and As atoms are blue- and red-colored, the bonds between atoms are denoted by respectively colored sticks, and the cluster-forming energies Ef are given in respect to the energy of AsSe3/2 unit (Ef(AsSe3/2) = −72.309 kcal/mol [29]).
Figure 3. Ball-and-stick presentation of optimized configurations of thioarsenide-type As4Sen MFC: (a) tetra-arsenic heksaselenide x0-As4Se6, (b) tetra-arsenic pentaselenide x0-As4Se5, (c) tetra-arsenic tetraselenide of realgar modification x0-As4Se4, (d) tetra-arsenic tetraselenide of pararealgar modification x0-pr-As4Se4, (e) tetra-arsenic triselenide in dimorphite-type triangular-pyramidal (As3)-As configuration x0-I-As4Se3, (f) tetra-arsenic triselenide in chain-like (As4) configuration x0-II-As4Se3, (g) tetra-arsenic triselenide in star-like (As-As3) configuration x0-III-As4Se3, (h) tetra-arsenic biselenide in combined triangular-star (As3)As configuration x0-I-As4Se2, (i) tetra-arsenic biselenide in chain-like (As4) configuration x0-II-As4Se2, (j) tetra-arsenic monoselenide x0-As4Se, (k) tetra-arsenic in tetragon-like configuration x0-As4. The Se and As atoms are blue- and red-colored, the bonds between atoms are denoted by respectively colored sticks, and the cluster-forming energies Ef are given in respect to the energy of AsSe3/2 unit (Ef(AsSe3/2) = −72.309 kcal/mol [29]).
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Molecules 30 01963 g004
Figure 4. Ball-and-stick presentation of H-atom-saturated As2Se5H4 molecular prototype of the x4-As4Se6 = As2Se3net NFC (on the right) derived from parent thioarsenide-type x0-As4Se6 = As4Se6mol MFC (on the left) by breaking in four equivalent Se atom positions. The terminated H atoms are grey-colored; Se and As atoms are blue- and red-colored, respectively; and the bonds between atoms are denoted by respectively colored sticks.
Figure 4. Ball-and-stick presentation of H-atom-saturated As2Se5H4 molecular prototype of the x4-As4Se6 = As2Se3net NFC (on the right) derived from parent thioarsenide-type x0-As4Se6 = As4Se6mol MFC (on the left) by breaking in four equivalent Se atom positions. The terminated H atoms are grey-colored; Se and As atoms are blue- and red-colored, respectively; and the bonds between atoms are denoted by respectively colored sticks.
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Molecules 30 01963 g005
Figure 5. Ball-and-stick presentation of H-atom-saturated As6H6 molecular prototype of the As6(2/3) = As4net NFC in the form of a flattened pyramid-shaped unit (on the right) derived by distortion from parent x0-As4 = As4mol tetrahedral-like MFC by breaking in one of three (As-As) bonds at each As atom. The terminated H atoms are grey-colored, As atoms are blue-colored, and chemical bonds between atoms are denoted by respectively colored sticks.
Figure 5. Ball-and-stick presentation of H-atom-saturated As6H6 molecular prototype of the As6(2/3) = As4net NFC in the form of a flattened pyramid-shaped unit (on the right) derived by distortion from parent x0-As4 = As4mol tetrahedral-like MFC by breaking in one of three (As-As) bonds at each As atom. The terminated H atoms are grey-colored, As atoms are blue-colored, and chemical bonds between atoms are denoted by respectively colored sticks.
Molecules 30 01963 g005
Table 1. Parameterization of thioarsenide-type As4Sen MFC and their network derivatives (NFC) in over-stoichiometric arsenoselenides AsxSe100−x (the cluster-forming energies (EfΣ)av are defined with respect to the energy of a single AsSe3/2 pyramid, Ef(AsSe3/2) = −72.309 kcal/mol [29]).
Table 1. Parameterization of thioarsenide-type As4Sen MFC and their network derivatives (NFC) in over-stoichiometric arsenoselenides AsxSe100−x (the cluster-forming energies (EfΣ)av are defined with respect to the energy of a single AsSe3/2 pyramid, Ef(AsSe3/2) = −72.309 kcal/mol [29]).
MCN;
n		Thioarsenide-Type As4Sen MFCThioarsenide-Type As4Sen NFC
MFC Nomenclature; nc; Small RingsEf,
kcal·mol−1		NFC Nomenclature;
nc; Separate Units, and/or Small Rings 		Ef,
kcal·mol−1
2.40;
n = 6		x0-As4Se6 = As4Se6mol;
nc = 3.00; 4 hexagons		−0.67 x4-As4Se6 = As2Se3net;
nc = 3.00; 2 separate units, no small rings		0.31
2.44;
n = 5		x0-As4Se5; nc = 2.89;
2 hexagons,
2 pentagons		0.32x1-1-As4Se5; nc = 2.89; 2 pentagons−1.01
x1-2-As4Se5; nc = 3.00; 1 pentagon, 1 hexagon−0.37
x2-1-As4Se5; nc = 3.00; 1 pentagon−6.07
x2-2-As4Se5; nc = 3.11; no small rings−8.02
x2-3-As4Se5; nc = 3.11; 1 hexagon−0.60
x3-1-As4Se5; nc = 3.11; no small rings0.16
x3-2-As4Se5; nc = 3.00; 2 separate units, 1 pentagon0.05
x4-As4Se5; nc = 3.11; 2 separate units, no small rings0.22
x5-As4Se5; nc = 3.11; 3 separate units, no small rings0.05
2.50;
n = 4		x0-As4Se4; nc = 2.875;
4 pentagons,
4 hexagons 		0.40x1-As4Se4; nc = 3.00; 2 pentagons, 1 hexagon0.25
x2-1-As4Se4; nc = 3.125; 1 pentagon−0.42
x2-2-As4Se4; nc = 3.25; 1 hexagon−9.64
x3-As4Se4; nc = 3.25; no small rings0.05
x4-As4Se4; nc = 3.25; 2 separate units, no rings0.11
x0-pr-As4Se4; nc = 2.75;
1 hexagon,
2 pentagons,
1 tetragon		0.30 x1-1-pr-As4Se4; nc = 3.00; 2 pentagons−0.25
x1-2-pr-As4Se4; nc = 2.875; 1 pentagon, 1 tetragon−1.39
x1-3-pr-As4Se4; nc = 3.00; 1 hexagon, 1 tetragon−1.55
x2-1-pr-As4Se4; nc = 3.00; 1 tetragon−4.93
x2-2-pr-As4Se4; nc = 3.125; 1 pentagon−7.36
x2-3-pr-As4Se4; nc = 3.00; 1 tetragon−9.78
x2-4-pr-As4Se4; nc = 3.25; 1 hexagon−5.66
x3-1-pr-As4Se4; nc = 3.00; 2 separate units, 1 tetragon−0.85
x3-2-pr-As4Se4; nc = 3.25; no small rings−2.81
x3-3-pr-As4Se4; nc = 3.25; no small rings−0.47
x4-pr-As4Se4; nc = 3.25; 2 separate units, no rings−0.03
2.57;
n = 3		x0-I-As4Se3; nc = 2.71;
3 pentagons,
1 triangle 		0.33x1-I-As4Se3; nc = 2.86; 1 pentagon + 1 triangle−1.90
x2-I-As4Se3; nc = 3.00; 1 triangle−9.13
x3-I-As4Se3; nc = 3.00; 2 separate units, 1 triangle−1.47
x0-II-As4Se3; nc = 2.71;
2 pentagons,
2 tetragons		−0.94x1-1-II-As4Se3; nc = 3.00; 1 tetragon, 1 pentagon−0.60
x1-2-II-As4Se3; nc = 2.86; 2 tetragons−2.36
x2-1-II-As4Se3; nc = 3.29; 1 pentagon−8.76
x2-2-II-As4Se3; nc = 3.14; 1 tetragon−5.80
x3-II-As4Se3; nc = 3.43; no small rings−0.60
x0-III-As4Se3; nc = 2.57;
1 hexagon,
3 tetragons 		−2.44x1-III-As4Se3; nc = 2.86; 2 tetragons−3.22
x2-III-As4Se3; nc = 3.14; 1 tetragon−1.29
x3-III-As4Se3; nc = 3.43; no small rings−0.88
2.67;
n = 2		x0-I-As4Se2; nc = 2.50;
1 pentagon, 2 tetragons, 1 triangle		−3.59x1-I-As4Se2; nc = 2.83; 1 tetragon, 1 triangle −3.27
x2-I-As4Se2; nc = 3.17; 1 triangle−4.42
x0-II-As4Se2; nc = 2.67;
5 tetragons		−4.42x1-II-As4Se2; nc = 3.00; 3 tetragons−3.46
x2-II-As4Se2; nc = 3.33; 1 tetragon−0.72
2.80;
n = 1		x0-As4Se; nc = 2.40; 2 tetragons, 2 triangles−5.20x1-As4Se; nc = 2.80;
2 triangles, 1 tetragon 		−8.30
3.00;
n = 0		x0-As4 = As4mol; nc = 2.25; 4 triangels−4.31As4net; nc = 4.50;
1 hexagon 		−2.46
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Shpotyuk, O.; Hyla, M.; Lukáčová Bujňáková, Z.; Shpotyuk, Y.; Boyko, V. Diversity of Molecular–Network Conformations in the Over-Stoichiometric Arsenoselenides Covering a Full Thioarsenides Row As4Sen (0 ≤ n ≤ 6). Molecules 2025, 30, 1963. https://doi.org/10.3390/molecules30091963

AMA Style

Shpotyuk O, Hyla M, Lukáčová Bujňáková Z, Shpotyuk Y, Boyko V. Diversity of Molecular–Network Conformations in the Over-Stoichiometric Arsenoselenides Covering a Full Thioarsenides Row As4Sen (0 ≤ n ≤ 6). Molecules. 2025; 30(9):1963. https://doi.org/10.3390/molecules30091963

Chicago/Turabian Style

Shpotyuk, Oleh, Malgorzata Hyla, Zdenka Lukáčová Bujňáková, Yaroslav Shpotyuk, and Vitaliy Boyko. 2025. "Diversity of Molecular–Network Conformations in the Over-Stoichiometric Arsenoselenides Covering a Full Thioarsenides Row As4Sen (0 ≤ n ≤ 6)" Molecules 30, no. 9: 1963. https://doi.org/10.3390/molecules30091963

APA Style

Shpotyuk, O., Hyla, M., Lukáčová Bujňáková, Z., Shpotyuk, Y., & Boyko, V. (2025). Diversity of Molecular–Network Conformations in the Over-Stoichiometric Arsenoselenides Covering a Full Thioarsenides Row As4Sen (0 ≤ n ≤ 6). Molecules, 30(9), 1963. https://doi.org/10.3390/molecules30091963

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