The obtained structural properties in real and reciprocal space are given in Figure 3. The total pair correlation function g(r) is represented in panel a. When compared to available experimental data (Xin et al., 2008; Fabian et al., 2010), one acknowledges an excellent agreement for all typical features: position, width and intensity of the principal peak at r = 2.44 Å defining the first correlation or bond distance dominated by As-Se correlations (experimentally 2.39–2.41 Å Renninger and Averbach, 1975; Mastelaro et al., 1992; Xin et al., 2008), and the secondary peak at r = 3.71 Å (experimentally 3.62–3.68 Å from various probes Renninger and Averbach, 1975; Xin et al., 2008), a slight overestimation of the bond distances being acknowledged when compared to experimental findings. The origin of the principal peak is essentially due to As-Se correlations with a moderate contributions from As-As and Se-Se bonds which is an indication of broken chemical order that has been also evidenced in another stoichiometric chalcogenide (Petri et al., 2000). The partial correlations (As-As, As-Se, Se-Se) are, indeed, also represented and two small contributions at 2.55 and 2.37 Å signal the presence of homopolar As-As and Se-Se bonds, respectively (blue curves in Figure 3A).

In Figure 3B the total structure factor S_T(k) is represented and compared to corresponding experimental data (Xin et al., 2008; Fabian et al., 2010). The agreement between experiments and simulation is found to be excellent for all momentum transfers k, and the two principal peaks at k_PP1=2.2 Å⁻¹ and k_PP2=3.7 Å⁻¹ are very well reproduced, as are also the peaks obtained at higher k (k > 6 Å⁻¹). Note that the first sharp diffraction peak (FSDP), while rather small in experiments (Xin et al., 2008), reduces in the simulations to a simple shoulder on the low wavevector side of the principal peak at 2.1 Å⁻¹. In contrast to similar chalcogenides (GeSe₂), we are not aware of a full resolution of partial structure factors from isotopic substituted neutron diffraction. However, it has been pointed out (Bauchy et al., 2014) that the partial resolution from anomalous X-ray scattering (Hosokawa et al., 2001, 2006) can be also very well reproduced. Such experiments reveal, furthermore, that only an As-related partial displays a FSDP at k≃1.2 Å⁻¹, which is an indication that correlations in medium range order (i.e., at low k) mainly arise from As atoms. Many other physical and chemical properties can be inferred from the simulated structure and the dynamics (Bauchy et al., 2013, 2014; Micoulaut and Bauchy, 2013).

Following a strategy developed for Ge-Se glasses (Micoulaut et al., 2013), the infrared (IR) absorption spectrum can be determined from dipole-dipole correlations. During the DFT calculation, the total dipole moment M(t) is directly calculated (Silvestrelli et al., 1997) and contributes via the Fourier transform of the dipole-dipole autocorrelation function to the IR absorption spectrum using the maximum entropy inversion method (Silver et al., 1990):

where V is the volume, β=1/k_BT, and n(ω) the refractive index. Figure 4 shows the computed IR spectra α(ω)n(ω) for different temperatures. As in previous investigations of chalcogenides (Micoulaut et al., 2013), the main features are qualitatively reproduced from the simulation such as the main peak at 150-200 cm⁻¹ and the broad band between 50 and 130 cm⁻¹, these two features being detected experimentally (Lucovsky et al., 1975), as well as the shoulder peak at 250 cm⁻¹. It should be noted that the reproduction of IR properties have been found to be highly sensitive to the method employed and a previous methodological study for Ge-Se glasses has shown that a direct calculation inspired by linear response theory and the time dependence of the dipolar momentum M(t) was much more accurate than an alternative method (Giacomazzi et al., 2007, 2011). The latter builds on the response to a finite electrical field in conjunction with the computation of coupling tensors (dynamical Born charge Resta, 1994) based on the first derivative of the atomic forces with respect to the electrical field.

With increasing temperature, the entire spectra shifts to lower frequencies, which is consistent with an overall temperature induced softening of the vibrational motion, the main peak shifting from ≃ 180 cm⁻¹ at room temperature to about 160 cm⁻¹ at 800 K. One furthermore notes the vanishing of the low-frequency bands at 50–130 cm⁻¹ (barely detectable at 600 K) and the emergence of a shoulder peak at ≃ 300–360 cm⁻¹ which is visible at 300 K, albeit minuscule (arrows). The detail of the typical mode vibrations can be analyzed to further decode the IR spectra, in relationship with structural features.

The IR spectrum can be analyzed from a vibrational cluster analysis (Table 1) on typical As-centered species. DFT based calculations of the clusters (some of them represented in Figure 1) provide a complementary indication and an assignment of the typical bands observed in Figure 4. In the present case, three typical clusters have been considered: the PYR unit which is the dominant motif of the network structure, the QT containing the double As=Se bond, and a pure tetrahedral AsSe_4/2 (TETRA) which has been suggested to be part of the structure in combination with the presence of As-As homopolar bonds (Hosokawa et al., 2013). It is seen that the PYR unit gives essentially rise to bands found in the 70–120 cm⁻¹ region, and are associated with bending/stretching and/or deformation modes of the local geometry, the modes at the largest frequencies (250 cm⁻¹) giving rise to umbrella flip modes, while smaller modes are found to be linked with breathing modes.

Interestingly, the analysis of the other clusters (TETRA, QT) indicate additional contributions at higher frequencies (180–260 cm⁻¹), consistently with the emergence of additional bands in this frequency range with increasing temperature as discussed below. The addition of an extra coordination sphere of Se atoms to As-centered unit brings the calculated frequencies somewhat closer to the experimental values found for the main peak (modes detected in the 180–220 cm⁻¹ range), although it cannot be eluded that these modes might also be the result of vibrational motions arising from linkages of elementary PYR units (Lucovsky et al., 1975). Most importantly is the fact that both QT and TETRA have an additional frequency found at ≃365 cm⁻¹ which is associated, in the case of the QT, with the vibrational motion of a double As=Se bond, as independently suggested by a Raman mode calculation (Jackson et al., 1999; Ravindren, 2014). This typical frequency is not found from the vibrational analysis of a PYR cluster (Table 1), and appears therefore to be specific of the tetrahedral defect coordination.

The calculated Raman active modes reveal, indeed, dominant vibrations at 235 cm⁻¹ and 260 cm⁻¹ are due to As-Se asymetric (in phase bond stretching) and symmetric stretching, respectively, as found experimentally (Chen et al., 2010), the only mode standing apart from the others with no possible overlap corresponding to a vibration of the Se=As double bond, expected experimentally to be near 360 cm⁻¹. It should be stressed that similar solitary modes have been determined in corresponding P-Se, P-S (Georgiev et al., 2001; Boolchand et al., 2009) and As-S glasses (Chen et al., 2008; Chakravarty et al., 2019) where the presence of P=Se and As=S double bonds could be determined independently, including from NMR (Tullius et al., 1990; Georgiev et al., 2001).

Experimentally, it has been found that the principal modes of the Raman spectrum of As₂Se₃ are spread out contiguously between 190 cm⁻¹ and 300 cm⁻¹ but with signatures of QT units found at larger frequencies (Chen et al., 2010; Ravindren, 2014) and these typical modes associated with the As=Se double bond do exist besides the main bands and have been identified at 355 cm⁻¹ and 475 cm⁻¹. In contrast to the most recent work on As-Se (Chen et al., 2010; Ravindren, 2014), previous experimental studies on Raman (Kostadinova, 2009) or IR (Lucovsky et al., 1975) have not focused (ω <330 cm⁻¹) on this high frequency domain and it would certainly be interesting to probe, at least for the IR absorption, how the present numerical results can be compared.

An inspection of the fraction of r-fold species (Figure 5) that is calculated from the network structure indicates that the 600 K and 800 K liquids can contain a large fraction of As^IV (i.e., a 4-fold As, Micoulaut and Bauchy, 2013). The structure of the liquids is, thus, at variance with the amorphous structure which is found to be mostly populated by 3-fold PYR units with minority species (≃10 %) made of As^IV that can be determined from different methods (Bauchy et al., 2014). However, as the temperature is increased across the glass transition region, the fraction of such species grows in an important fashion, leading to a fraction of about ≃40% at 1200 K, and representing the dominant motif in the stable liquid. One can thus conclude that the abrupt decrease of 4-fold coordinated As is an important structural feature driving the onset of the glass transition in As₂Se₃. These findings actually contrast those found for Ge-Se liquids where the dominant tetrahedral order prevails over extended ranges in temperature (Massobrio et al., 2001; Salmon, 2007).

In order to probe the stability of such tetrahedral motifs, we have calculated their population in the supercooled liquids as well as in the 300 K glass under special numerical preparation condition (see below).

In Figure 6A we represent the statistics of As^IV in the two target liquids at 600 K and 800 K over the picosecond time domain which corresponds to multiple bond lifetimes. Evolution with time evolves for e.g., the lowest temperature (600 K) around 8 ± 2.5 % with a bond lifetime that we have calculated to be of about 0.82 ps. The situation is somewhat different for the amorphous system. For the latter, the starting configuration at 300 K has been chosen to be a 1,000 K atomic system containing about 40% As^IV and hyperquenched (Figure 5), a Nosé-Hoover thermostat being applied with a frequency of 800 cm⁻¹ (corresponding to a relaxation time for the thermostat of 41.69 fs). A subsequent relaxation led to a modification of the structure, and the inspection of Figure 6B suggests a rapid evolution of a starting “liquid-like” network with numerous miscoordinated defects containing QT into a structure with the predominant PYR local structure, the evolution being merely fulfilled within the picosecond timescale. For the particular As^IV defect, the decrease is linked with a global decrease of As^IV having one or two homopolar As-As bonds whose initial probability is in a ratio of nearly 1:1. The trend in all defect coordinated species is found to parallel the energy of the system (not shown) which decreases with the same trend within the first picosecond.

As a result, such defects represent minority species of the As₂Se₃ glass but these give rise, as evidenced from Figure 4 and Table 1, to specific spectroscopic signatures in the high frequency domain of both IR and Raman spectra, as also detected in other Group V chalcogenides (Georgiev et al., 2001; Chen et al., 2008; Boolchand et al., 2009; Chakravarty et al., 2019).

The 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.