Electronic Structure, Lattice Dynamics, and Pressure-Induced Phase Transitions in Gd₂MoO₆: A Combined Theoretical and Experimental Study

Abstract

This study presents a combined theoretical and experimental investigation into the structural, electronic, and vibrational properties of Gd₂MoO₆. To gain deeper insight into its chemical composition, first-principles calculations were employed, emphasizing energy band analysis. The conduction band minimum is positioned at the high-symmetry Γ-point, while the valence band maximum appears between the Z and Γ-points. These results indicate that Gd₂MoO₆ is a semiconductor exhibiting an indirect band gap of approximately 1.92 eV. Furthermore, lattice dynamics were examined using density functional theory (DFT) to interpret the experimental Raman and infrared spectra. Hirshfeld surface and structural analyses reveal that Gd₂MoO₆ exhibits a hybrid ionic-covalent framework governed by dominant Gd–O/Gd–O and Mo–O/O–Mo bonds. Additionally, pressure-dependent Raman spectroscopy was carried out to explore structural modifications resulting from pressure variations. Based on the spectral changes, two phases’ transitions were identified at approximately 3.1–3.3 GPa and 9.5–10 GPa, potentially linked to increased disorder of octahedra induced by pressure effects. The principal component analysis and hierarchical cluster analysis identified two phase transitions at near pressure range of 3.1–3.3 GPa and 9.5–10. GPa, which are in agreement with the pressure-dependent Raman studies.

1. Introduction

Rare-earth molybdates (RE), represented by the chemical formula RE₂MoO₆ (where RE corresponds to a rare-earth ion), form a fascinating family of materials whose chemical and physical properties can be tailored through the appropriate selection of RE cations. − These compounds are widely recognized for their remarkable characteristics, including luminescence, − versatile fluorescent properties, thermal stability, , photodegradation, electrocatalytic oxygen evolution, magnetocaloric effects, − and more. ,− Their primary field of study lies on their utilization as phosphors, serving as luminescent matrices for trivalent RE ions such as Yb³⁺, Eu³⁺, Sm³⁺, Tm³⁺, Ho³⁺, Dy³⁺, Tb³⁺, and others, with their spectroscopic properties being extensively investigated owing to their potential in optics. − When doped with RE ions such as Er³⁺, Yb³⁺, or Nd³⁺, gadolinium molybdates demonstrate enhanced solid-state laser performance in the infrared and visible ranges. Specifically, Gd₂(MoO₄)₃ doped with Eu³⁺, Tb³⁺, or Dy³⁺ has been extensively studied as a potential phosphor candidate for white light-emitting diodes (LEDs) and display backlighting, due to its high quantum efficiency, thermal stability, and tunable emission spectrum. Beyond their photoluminescent properties, gadolinium (Gd)-based compounds have been widely studied in bioimaging and multiple sclerosis research, further motivating in-depth investigations into these materials. ,

Among Gd-based molybdates, Gd₂MoO₆ has attracted increasing attention due to its multifunctional properties that extend well beyond its ease of synthesis. Recent studies have demonstrated that Gd₂MoO₆ exhibits efficient down-conversion and up-conversion luminescence, making it suitable for advanced optical devices and photonic applications. Its optical response and ferroelectric-related behavior have also been investigated, highlighting its potential for device-oriented applications. Furthermore, Gd-containing oxides, including Gd₂MoO₆-based systems, have been explored for biomedical applications such as bioimaging and contrast agents, owing to the favorable magnetic and optical characteristics of Gd³⁺ ions. − In particular, Eu³⁺-activated Gd₂MoO₆ phosphors have shown intense red emission under near-ultraviolet and blue excitation, demonstrating strong potential for LEDs and solid-state lighting technologies. These results establish Gd₂MoO₆ as a versatile functional material whose optical, electronic, and magnetic properties are highly sensitive to its local structure and external perturbations.

In addition, these materials exhibit a wide range of functional properties that can be strategically modified or tuned under varying experimental conditions. Among these approaches, high-pressure techniques enable a detailed analysis of subtle changes in the crystal lattice that influence these properties, while studies at low temperatures help in understanding many physical phenomena. − These studies can provide important information on the structural aspects of compounds, which in turn provides deeper insight into the fundamental phenomena governing characteristics such as phonon anharmonicity, negative thermal expansion. , ferroelectric, structural phase transitions, , and pressure-induced amorphization. − Studies on Gd₂(MoO₄)₃ indicate that this material undergoes several structural transitions between 2 and 6 GPa, with amorphization occurring at higher pressures. These transitions are associated with the reorganization of MoO₄ tetrahedra and changes in molybdenum coordination. Due to their pressure-sensitive Raman modes, Gd₂(MoO₄)₃ materials have been explored as candidates for pressure-sensing and piezoelectric applications, where phase stability under extreme conditions is crucial. − Studies have demonstrated that external pressure induces structural transformations, influencing the vibrational properties of MoO₄ tetrahedra and making these materials promising candidates for pressure-driven phase-change applications. ,,−

Thus, the monoclinic phase of Gd₂MoO₆, belonging to the C ₂/c space group, is of particular interest due to its easy synthesis and the limited investigation of its behavior in Raman spectroscopy under high pressure. In this work, we explore the properties of Gd₂MoO₆ under high pressure using Raman spectroscopy. Initially, the electronic band structure and partial density of states (PDOS) are analyzed through first-principles calculations. Then, the nature of the observed vibrational modes is explored at the same theoretical level, allowing for the prediction of wavenumbers, mode assignments, and symmetry of each Raman-active mode. Finally, Raman spectra under high pressure are examined, unveiling changes in the band profile and indicating a potential phase transition.

2. Experimental Methodology

Polycrystalline Gd₂MoO₆ samples were synthesized by using the solid-state reaction method, which involves homogenizing precursor powders. Initially, the starting materials were manually ground for 30 min using a mortar and pestle to ensure uniform mixing. The resulting mixture was then subjected to heat treatment at 950 °C for 24 h in an ambient atmosphere using a muffle-type resistance furnace, with a controlled heating rate of 10 °C/min. The Gd₂MoO₆ sample was synthesized in a 1:1 molar ratio from gadolinium­(III) oxide (Gd₂O₃, 99.99% purity, Aldrich Chemicals Ltd.) and molybdenum trioxide (MoO₃, 99.99% purity, Aldrich Chemicals Ltd.), as represented in eq . The synthesized sample was allowed to cool to room temperature naturally, utilizing the thermal inertia of the furnace, crucible, and sample assembly.

$${\mathrm{G}\mathrm{d}}_2{\mathrm{O}}_{3(\mathrm{s})}+{\mathrm{M}\mathrm{o}\mathrm{O}}_{3(\mathrm{s})}\to {\mathrm{G}\mathrm{d}}_2{\mathrm{M}\mathrm{o}\mathrm{O}}_{6(\mathrm{S})}$$ 1

The synthesized sample was characterized by X-ray diffraction (XRD) through a powder diffraction method on a PANalytical Empyrean diffractometer. The instrument operated with Cu Kα radiation (λ = 1.5418 Å) in Bragg–Brentano geometry and featured a pyrolytic graphite monochromator at room temperature. Diffraction data were recorded over a 2θ range of 10°–80°, with a step size of 0.02° and a counting time of 2.0 s per step. The GSAS-I software was used for Rietveld refinement, utilizing crystal data from the Inorganic Crystal Structure Database (ICSD), Card No. 32173. Morphological analyses were carried by means of a high-resolution scanning electron microscopy (SEM), model Vega3 SBH from TESCAN, equipped with a Bruker Xflash 410 M energy-dispersive spectrometer (EDS). The absorption spectrum of the Gd₂MoO₆ sample was obtained by using a PerkinElmer Frontier Fourier transform infrared (FTIR) spectrophotometer. Measurements were performed in the spectral range of 4000–400 cm^–1 with a resolution of 2 cm^–1, averaging 32 scans. The analysis utilized an attenuated total reflectance (ATR) accessory with a germanium crystal. Raman measurements were performed using a Horiba T64000 spectrometer equipped with a liquid N₂-cooled CCD system. This system was integrated with the following components: (i) a 532 nm argon ion laser, (ii) an Olympus microscope lens with a focal length of 20.5 mm and a numerical aperture (NA) of 0.35 for laser focusing on the sample surface, and (iii) a spectrometer slit providing a resolution of approximately 2 cm^–1. For pressure-dependent measurements, a diamond anvil cell (DAC) was employed, utilizing a mixture of methanol–ethanol (4:1) as the pressure-transmitting medium over a range of 0.0–14.1 GPa. Pressure calibration within the sample chamber, which consists of a hole in a stainless-steel gasket positioned between two diamond anvils, was performed using the luminescence of Cr³⁺ ions in ruby.

3. Theoretical Calculations

The noncovalent interactions and voids crystal calculations were performed employing CrystalExplorer 17. For a comprehensive analysis of molecular contacts, we generated three-dimensional Hirshfeld surfaces with normalized contact distance (d _norm) mapping, derived from the external (d _e) and internal (d _i ) distances relative to van der Waals radii (r _vdW). This approach enabled both qualitative visualization and quantitative assessment of various weak interactions in the crystal structure. Furthermore, we characterized the void spaces within the primitive unit cell through procrystal electron density analysis, using an isosurface threshold of 0.02 atomic units for accurate void quantification.

The electronic and vibrational properties of Gd₂MoO₆ were investigated using Density Functional Theory (DFT) as implemented in the Cambridge Serial Total Energy Package (CASTEP). Norm-conserving pseudopotentials were employed to represent the core electrons, while the exchange–correlation effects were treated within the Generalized Gradient Approximation (GGA) using the Perdew–Burke–Ernzerhof (PBE) functional. Brillouin zone integrations were performed using a 2 × 2 × 3 Monkhorst–Pack k-point mesh. A fine energy cutoff of 820 eV was used for the plane-wave basis set, ensuring well-converged results. To account for the strong on-site Coulomb interactions of the localized d and f electrons, particularly those of Gd and Mo, the DFT + U approach was employed. , The Hubbard U parameter, which effectively corrects for these interactions, was applied to the relevant atomic orbitals. The atomic positions were optimized using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm until the following convergence criteria were met: a maximum energy change of 1.0 × 10^–6 eV/atom, a maximum force of 0.03 eV/Å, a maximum stress of 0.1 GPa, and a maximum displacement of 0.001 Å. Following structural optimization, the electronic band structure and associated properties were computed by propagating the electronic wave function along high-symmetry points in the Brillouin Zone (BZ). The chosen k-point path was Z (0.000, 0.000, 0.500); Γ (0.000, 0.000, 0.000); Y (0.000, 0.500, 0.000); A (−0.500, 0.500, 0.000); B (−0.500, 0.000, 0.000); D (−0.500, 0.000, 0.500); E (−0.500, 0.500, 0.500); and C (0.000, 0.500, 0.500). The calculations were performed on a monoclinic cell (space group C ₂/c) containing a total of 78 atoms.

The determination of vibrational frequencies involves calculating the spatial derivatives of macroscopic polarization, as detailed by Porezag and Pederson. These derivatives are numerically computed along the eigenvectors of each Raman-active phonon mode using the linear response formalism to determine the polarization for each displacement. Consequently, the Raman susceptibility tensor, which is fundamental for calculating Raman intensity, is established in eq .

$$A_{\alpha \beta }^m=\sqrt{V}\sum _{I\gamma }\frac{{\mathrm{d}\chi }_{\alpha \beta }^{(1)}}{{\mathrm{d}R}_{\mathrm{I}\gamma }}\frac{{\upsilon }_{I\gamma }^m}{\sqrt{M_{\mathrm{I}}}}$$ 2

where χ_αβ is the first order dielectric susceptibility and υ is the phonon eigenvector in the direction in which the atom I, of mass M _I at equilibrium positions R, move under excitation of a phonon mode (m), in a unit cell with volume V.

4. Results and Discussion

4.1. Crystal Structure Analysis

Figure shows the powder XRD pattern refined through the Rietveld method using GSAS I software to determine the structural parameters. The XRD pattern reveals that Gd₂MoO₆ crystals crystallize in a monoclinic symmetry with space group C ₂/c (C _2h , No. 15), containing eight molecular formula per unit cell (Z = 8). The unit cell refined parameters are a = 16.517(3) Å, b = 11.185(5) Å, c = 5.424(4) Å, with α = γ = 90.00°, β = 108.30(5) °, resulting in a V of 951.523(8) ų, values that are very close to those reported by others. , The fitting parameters, R _p = 4.48%, R _wp = 5.83%, and χ² = 1.02, indicate good agreement between the calculated and experimental XRD pattern. A schematic representation of the primitive unit cell of Gd₂MoO₆ crystals is shown in Figure , where each Gd³⁺ cation is coordinated by four oxygen eight atoms occupying octahedral sites, while the Mo⁶⁺ atoms are bonded to five oxygen atoms, forming a polyhedron.

1.

Rietveld refinement of the powder XRD data for Gd₂MoO₆; the black circles and red lines represent the experimental pattern and its refinement, respectively.

2.

A primitive unit cell of the Gd₂MoO₆ crystal in a monoclinic symmetry structure with the C ₂/c-space group view along the axis c and axis b.

4.2. Morphological Analyses

SEM-EDS measures were employed to characterize the morphology and elemental composition of the Gd₂MoO₆ compound. The SEM image revealed a nonuniform distribution of irregular format and some larger surface grains, as seen in Figure a,b. Also, it is possible to observe grain sizes between 5 and 8 μm. Additionally, the EDS spectrum shown in Figure c confirmed the presence of all expected chemical elements. The characteristic peaks of Gd, Mo, and O were also clearly identified, as shown in Figure c. The elemental compositions determined by EDS for Gd₂MoO₆, presented in Table , suggest proximity to the theoretical stoichiometry expected for the compound.

3.

SEM micrographs of Gd₂MoO₆ polycrystalline samples: (a) image acquired at a scale of 20 μm, (b) higher magnification image with a scale of 5 μm. (c) EDS spectrum showing the presence of Gd, Mo, and O elements.

1. Elemental Compositions of Gd₂MoO₆ .

element	weight %	atomic %	error (wt. %)
O	22.75	76.70	8.51
Mo	16.58	7.64	1.56
Gd	55.67	15.65	3.78
total	100	100

4.3. Structural Features and Hirshfeld Surface Analysis

The primitive unit cell of Gd₂MoO₆, presented in Figure a, exhibits a well-ordered arrangement of Gd³⁺ (gray spheres), Mo⁶⁺ (green spheres), and O^2– (red spheres) ions, forming a complex framework of polyhedral coordination environments. The Gd³⁺ cations are typically surrounded by eight neighboring atoms in a square antiprismatic geometry, while Mo⁶⁺ occupies the center of MoO₅ polyhedra, a characteristic motif in molybdates. Understanding the structure of this system in detail is critical for understanding the material stability and functional properties, as the strong ionic character of Gd–O bonds and the covalent nature of Mo–O bonds contribute to its structural and thermal resilience.

4.

(a) Gd₂MoO₆ primitive unit cell. (b) Voids within the Gd₂MoO₆ structure visualized through isosurfaces (brown) along the a–c plane. Hirshfeld surfaces plots mapped according to (c) d _norm, (d) d _e, (e) d _i , (f) shape index, and (g) curvedness.

Figure b shows the presence of voids (brown isosurfaces, 754.40 Ų) distributed along the a-c planes of the Gd₂MoO₆ primitive unit cell. These voids characterize regions of low electron density, originate from the packing inefficiencies inherent in the structure, or deliberate lattice under-coordination. Such voids act as diffusion channels for inserting external species into the structure with a free volume of 289.66 ų (30.4%). This percentage is considered high and suggests that great molecules or species with a large atomic radius can be incorporated into the lattice to optimize physicochemical properties of interest. ,

The d _norm plot (Figure c), which normalizes contact distances based on r _vdW, shows regions of strong contacts (red, predominantly around the O atoms) and weak contacts (blue). The asymmetric distribution of red spots near O atoms confirms the dominance of Gd–O/Gd–O and Mo–O/O–Mo bonds, which are primarily ionic and covalent, respectively. The presence of faint blue regions indicates areas where the packing is less dense, which correlates with the voids observed in Figure b.

The d _e map showed in Figure d reveals key intermolecular contacts through color-represented distances: red regions (≈1.2–1.5 Å) highlight close Gd–O interactions, yellow-green areas (≈1.6–2.2 Å) represent secondary Mo–O bonds, and blue zones (>2.5 Å) indicate weak Gd–Mo contacts (dispersive forces) or voids. In contrast, the d _i map (Figure e) probes internal bonding, with deep red (<1.0 Å) marking tight Gd–O coordination and orange-yellow (∼1.0–1.3 Å) reflecting covalent Mo–O bonds. The stark color contrast between Gd³⁺ (ionic, polarized electron density) and Mo⁶⁺ (covalent, localized bonds) underscores their distinct chemical roles. Furthermore, discrepancies in d _e/d _i distributions near voids further identify low-density regions, offering targets for defect engineering in crystalline materials. These maps collectively validate the ionic-covalent hybrid nature of Gd₂MoO₆, with implications for tuning properties through controlled void manipulation.

The shape index map presented in Figure f reveals critical details about the surface topology through its color gradients. Red and orange regions correspond to concave areas (donor features), typically associated with O atoms accepting metal coordination sites. In contrast, blue zones represent convex regions (acceptor features), often marking protruding metal cations such as Gd³⁺ or Mo⁶⁺. The predominance of greenish hues indicates flat, neutral surfaces characteristic of extended Mo–O–Mo bridging lattices. Complementing this, the curvedness map (Figure g) displays distinct color regions that reveal important structural features. The dominant green areas represent the MoO₅, indicating their rigid, covalent nature through moderate curvedness values (0.5–1.5 Å^–1). These regions appear as smooth surfaces, reflecting the uniform electron density distribution characteristic of strong Mo–O covalent bonds. Surrounding these green zones, blue contours mark areas of gradual electron density transition, including the interfaces between MoO₅ units and Gd coordination polyhedra as well as the boundaries of structural voids. This pattern confirms the hybrid ionic-covalent character of Gd₂MoO₆, where the MoO₅ units maintain their structural stability, while the Gd–O regions allow for greater flexibility. The blue-outlined voids, showing the lowest curvedness values (<0.3 Å^–1), identify potential sites for defect formation or ion migration pathways, which could be strategically exploited for crystal engineering. ,

Figure presents the 2D fingerprint plots of Gd₂MoO₆, which provide quantitative analyses of all intermolecular interactions. The symmetric distribution of the full fingerprint shows two prominent red spikes centered at d_i, d _e low values, corresponding to the dominant short-range Gd···O/O···Gd and Mo···O/O···Mo bonds. These features confirm the dense, well-ordered nature of the crystal structure.

5.

2D fingerprint graphs of the Gd₂MoO₆ system, displaying both overall and specific intermolecular contacts.

The decomposed 2D fingerprint plots reveal three distinct contact types: (i) Gd···O/O···Gd interactions (57.0%) dominate the fingerprint, indicating the ionic character of Gd–O bonding. The high density of these contacts indicates a tightly packed lattice with strong electrostatic cohesion, consistent with the material’s thermal stability and high melting point; (ii) Mo···O/O···Mo interactions (9.7%), which appear at shorter distances than Gd–O, highlighting the covalent nature of the MoO₅ polyhedron. The narrow distribution of these contacts demonstrates the structural rigidity and bond-length uniformity of the Mo–O polyhedra; (iii) O···O interactions (33.3%) appear at intermediate distances, indicating a bridging oxygen lattice that supports structural integrity while enabling potential ion transport. The absence of metal–metal contacts confirms that electrostatic repulsion maintains cation dispersion. This fingerprint profile validates the Gd₂MoO₆ hybrid ionic-covalent bonding lattice.

4.4. Room-Temperature Structural and Vibrational Properties

The unit cell (Gd³⁺ ions at 4e and 8f sites, Mo⁶⁺ ions at 8f sites, and O atoms at 8f sites) comprises eight formula and the factor group analysis predicts 105 optical modes (k = 0) and 3 acoustic modes for the Gd₂MoO₆ crystal cell. The distribution of the optical modes is according to the irreducible representations of the factor group C _2h = 26A_g + 28B_g + 25A_u + 26B_u, where A_u + 2B_u are acoustic modes. According to the selection rules, the A_g and B_g modes are Raman active, the A_u and B_u modes are IR active. Figure a,b shows the Raman and infrared spectra of polycrystalline Gd₂MoO₆ at room temperature, respectively. The number of vibrational modes theoretically predicted for the monoclinic phase exceed those observed experimentally, which can be attributed to the close energy proximity between some modes, the overlap of weak bands by stronger ones, and the limited resolution of the bands due to the random orientation of the crystallites within the sample. Furthermore, Table shows the observed and calculated Raman and infrared modes, together with their assignments based on DFT calculations for the monoclinic phase.

6.

(a) Experimental and calculated Raman spectra of Gd₂MoO₆ in the 45–900 cm^–1 region; (b) experimental and calculated IR spectra of Gd₂MoO₆ in the 900–100 cm^–1 region.

2. Analysis of Vibration Modes for the Gd₂MoO₆: Experimental Raman Modes (ω_R), Experimental IR Modes (ω_IR), Calculated Wavenumbers (ω_cal), Irreducible Representations (Irrep.), and their Assignments .

ωR (cm–1)	ωIR (cm–1)	ωcal (cm–1)	irrep	assignments†	ωR (cm–1)	ωIR (cm–1)	ωcal (cm–1)	irrep	assignments
		52	Bg	T y [MoO5 + GdO8]	321		300	Ag	δ [MoO5 + GdO8]
		55	Bu	T [MoO5] + T xy  [GdO8]			316	Bu	Sc [MoO5] + δ [GdO8]
76		76	Bg	T [MoO5] + T x  [GdO8]			322	Au	δ [MoO5 + GdO8]
81		86	Bg	T [MoO5 + GdO8]			330	Bg	δ [MoO5 + GdO8]
91		91	Ag	T [MoO5 + GdO8]	346		332	Ag	δ [MoO5 + GdO8]
		93	Au	T [MoO5 + GdO8]			339	Au	δ [MoO5 + GdO8]
		96	Bu	T [MoO5 + GdO8]	360		340	Bg	δ [MoO5 + GdO8]
101		98	Ag	T y [MoO5] + T [GdO8]			350	Bu	δ [MoO5] + tw [GdO8] in Gd–O–Gd bonds
		98	Bu	T [MoO5 + GdO8]			353	Au	Lib [MoO5] + δ [GdO8]
		103	Au	T [MoO5 + GdO8]			357	Bg	δ [MoO5 + GdO8]
107		108	Ag	T [MoO5 + GdO8]			358	Ag	δ [MoO5 + GdO8] + balance Gd–O
119		116	Bg	T [MoO5 + GdO8]	367		359	Bg	δ [MoO5 + GdO8] + balance Gd–O
125		118	Ag	T [MoO5 + GdO8]			360	Bu	Sc [MoO5] + δ [GdO8]
129		123	Bg	T [MoO5 + GdO8]			367	Bg	Sc [MoO5] + δ [GdO8]
		126	Au	T [MoO5 + GdO8]	383		378	Ag	δ [MoO5 + GdO8]
		131	Bu	T [MoO5 + GdO8]			386	Au	δ [MoO5 + GdO8]
		132	Ag	T [MoO5 + GdO8]			387	Bu	wag [GdO8] in Gd–O–Gd bonds
152		133	Bg	T xy [MoO5] + T x  [GdO8]	393		389	Ag	δ [MoO5 + GdO8]
		140	Bu	T [MoO5 + GdO8]	435		406	Bg	δ [MoO5 + GdO8]
167		143	Bg	T [MoO5 + GdO8]		425	407	Bu	δ [MoO5 + GdO8]
		143	Bu	T [MoO5 + GdO8]			418	Au	δ [MoO5 + GdO8]
		144	Au	T [MoO5 + GdO8]			418	Bg	δ [MoO5 + GdO8]
		147	Au	T [MoO5 + GdO8]	446		421	Ag	δ [MoO5 + GdO8]
		157	Bu	wag [GdO8] in Gd–O–Gd bonds		449	422	Bu	Lib [GdO8]
		160	Au	T [MoO5 + GdO8]			443	Bu	δ [MoO5 + GdO8]
178		162	Ag	Lib [MoO5] + δ [GdO8]			448	Ag	δ [MoO5 + GdO8]
188		167	Bg	T [MoO5 + GdO8]	479		451	Bg	δ [MoO5 + GdO8]
		167	Au	T [MoO5] + Sc [GdO8]		476	455	Au	δ [MoO5 + GdO8]
197		171	Ag	T y [MoO5 + GdO8]			499	Bu	δ [MoO5] + ρ [GdO8]
		174	Bu	T [MoO5 + GdO8]			500	Au	Sc [MoO5] + δ [GdO8]
		176	Bg	T [MoO5] + wag [GdO8]			501	Bg	δ [GdO8]
206		177	Ag	T [MoO5] + wag [GdO8]	505		505	Ag	Motion of O atoms of the Gd–O bond along the xy diagonal
		190	Bu	T [MoO5 + GdO8]		521	538	Au	strong motion of O atoms along the x-axisof the Gd–O–Gd bonds
		191	Bg	δ [MoO5 + GdO8]	522		550	Ag	Sc [GdO8], strong motion of O atoms in the Gd–O–Gd bonds
		192	Au	δ [MoO5] + wag [GdO8] in Gd–O–Gd Bonds	579		569	Bg	ν [Gd–O]
212		195	Ag	δ [MoO5] + T y  [GdO8]		556	594	Au	Sc [GdO8]
		200	Bu	Lib [MoO5] + T [GdO8]			733	Au	νas [MoO5] + wag [GdO8] in Gd–O–Gd bonds
		205	Au	δ [MoO5 + GdO8]		705	736	Bu	νas [MoO5] + wag [GdO8] in Gd–O–Gd bonds
		206	Bu	δ [MoO5 + GdO8]	706		747	Ag	νas [MoO5]
		212	Bg	δ [MoO5 + GdO8]	713		749	Bg	νas [MoO5]
231		214	Ag	Lib [MoO5] + δ [GdO8]			753	Au	νas [MoO5]
		223	Bg	δ [MoO5 + GdO8]	728		758	Bg	νas [MoO5]
		232	Au	δ [MoO5 + GdO8]		771	766	Bu	νas [MoO5]
243		246	Ag	δ [MoO5 + GdO8]	752		772	Ag	νas [MoO5]
		255	Ag	δ [MoO5 + GdO8]			783	Au	νas [MoO5]
		256	Bu	δ [MoO5 + GdO8]		786	791	Bu	νas [MoO5]
284		261	Bg	Lib [MoO5] + δ [GdO8]	773		793	Bg	νas [MoO5]
		265	Bu	δ [MoO5 + GdO8]			826	Ag	νs [MoO5]
		270	Au	Lib [MoO5] + δ [GdO8]		801	831	Bu	νs [MoO5]
		282	Bu	δ [MoO5 + GdO8]		850	839	Au	νs [MoO5]
		288	Au	δ [MoO5 + GdO8]	832		846	Bg	νs [MoO5]
		292	Ag	Sc [MoO5 + GdO8]	859		859	Ag	νs [MoO5]
312		293	Bg	Lib [MoO5] + δ [GdO8]

^aT = translational; Sc = scissoring; Tw = twisting; Lib = librational; wag = wagging; ν = stretching; ρ = rocking; δ = bending; νas = anti- symmetric stretching; νs = symmetric stretching.

4.4.1. Raman-Active Modes (A_g and B_g Representations)

To discuss the vibrational modes, we begin by examining the Raman-active modes. The Raman spectrum of the Gd₂MoO₆ crystal reveals vibrational modes associated with the A_g and B_g irreducible representations, which reflect structural deformations, polyhedral dynamics, and bonding characteristics. These modes are analyzed in three wavenumber regions for theoretical modes (in bold) with the corresponding experimental and some previously reported theoretical modes. A complete assignment is described in Table . (i) Low-wavenumber modes (50–200 cm^–1): this region is primarily characterized by translational (T, T _y , T _x , T _xy ) modes, however, the appearance of the librational and bending modes of MoO₅ and GdO₈ is also evident. At 52 cm^–1 (B_g), the vibration corresponds to a translational (T _y ) motion of MoO₅ and GdO₈, indicating rigid-body translational interactions, illustrated in Figure S1. A similar translational movement is observed at 76 cm ^–1 (B _g ), with a translational (T) motion of MoO₅ plus an additional T _x component from GdO₈ contributes to the coupling effect. The mode at 86 cm ^–1 (B _g ) and at 91 cm ^–1 (A _g ) represents other translational vibration, this time with a broader influence on the T­[MoO₅ + GdO₈] units, while the mode at 98 cm ^–1 (A _g ), where the MoO₅ and GdO₈ polyhedra exhibit T _y and T motions, respectively, reflects the lattice dynamics. At 108­(A _g ), 116 cm ^–1 (B _g ), 118 (A _g ), and 123 cm ^–1 (B _g ), 143 cm ^–1 (B _g ), and 167 cm ^–1 (B _g ), the translational modes affect both polyhedral units. The 133 cm ^–1 (B _g ) mode corresponds to T _xy translational vibrations of the [MoO₅] polyhedra coupled with T _x motions of the [GdO₈] polyedra. The mode at 162 cm ^–1 (A _g ) involves a librational motion of the MoO₅ units combined with bending (δ) vibrations of the GdO₈ polyhedra, marking the onset of mixed external and internal vibrational character. The A _g modes at 171 cm^–1 are associated with directional translational motion along the y-axis (T _y ) of the [MoO₅ + GdO₈] units, indicating anisotropic lattice dynamics governed by crystallographic orientation, while the 177 cm ^–1 (A _g ) mode is attributed to translational vibrations of the [MoO₅] units combined with wagging motions of the [GdO₈] polyhedra. Finally, the A _g mode at 195 cm ^–1 is assigned to a bending (δ) vibration of the MoO₅ polyhedra coupled with a directional translational motion along the y-axis (T _y ) of the GdO₈ units. (ii) Midwavenumber modes (200–500 cm^–1): encompassing bending (δ), librational (Lib), and scissoring (Sc) deformations, these modes predominantly influence Mo–O–Gd interactions. Bending and librational motions dominate this spectral region. The 214 cm ^–1 (A _g ) mode arises from librational vibrations of the [MoO₅] units together with bending (δ) motions of the [GdO₈] polyhedra and for the mode at 223 cm^–1 (B_g), the vibration corresponds to a bending mode (δ) of MoO₅ and GdO₈, introducing distortions in the molybdate–gadolinium oxide interactions. This bending effect of polyhedral units is reinforced by the 246 cm ^–1 (A _g ) and 255 cm ^–1 (A _g ) modes, which indicate additional structural flexibility. A librational (Lib) mode of MoO₅ appears at 261 cm ^–1 (B _g ), coupled with a bending (δ) motion of GdO₈, while at 292 cm^–1 (A_g), a scissoring (Sc) mode from [MoO₅ + GdO₈] is also present and the mode at 293 cm ^–1 (B _g ) is assigned to librational vibrations of the [MoO₅] polyhedra coupled with bending (δ) motions of the [GdO₈] units. The bending (δ) dynamic persists at 300 cm ^–1 (A _g ), 332 cm ^–1 (A _g ), 340 cm ^–1 (B _g ), 359 cm ^–1 (B _g ), 378 cm ^–1 (A _g ), 389 cm ^–1 (A _g ), 406 cm ^–1 (B _g ), 421 cm ^–1 (A _g ), and 451 cm ^–1 (B _g ), involving both polyhedral units. The mode at 359 cm ^–1 (B _g ) exhibits a significant balance contribution from Gd–O bond bending, which is also observed in the other modes listed in Table (iii) High-wavenumber Raman Modes (500–900 cm^–1): in this region, the dominant modes are Mo–O stretching (ν_s, symmetry; and ν_as, antisymmetric) vibrations, which determine the rigidity and covalent character of Mo–O bonds. The mode centered at 505 cm ^–1 (A _g ) is associated with the motion of oxygen atoms in the Gd–O bonds along the xy diagonal. The A_g mode at 550 cm ^–1 (A _g ) is assigned to scissoring (Sc) of the GdO₈ polyhedra and exhibits a strong displacement of oxygen atoms within the Gd–O–Gd bonds, confirms their structural role (illustrated in Figure S1). The B _g mode at 569 cm ^–1 corresponds to the stretching vibration (ν) of the Gd–O bond. The asymmetric stretching vibrations of the MoO₅ units appear at 747 cm ^–1 (A _g ), 749 cm ^–1 (B _g ), 758 cm ^–1 (B _g ), 772 cm ^–1 (A _g ), and 793 cm ^–1 (B _g ), while the symmetric stretching modes are located at 846 cm ^–1 (B _g ) and 859 cm ^–1 (A _g ).

4.4.2. Infrared-Active Modes (A_u and B_u representations)

The IR spectra of the Gd₂MoO₆ system exhibits vibrational modes associated with the A_u and B_u symmetrical species, which correspond to dipole-active vibrations within the structure. These modes are classified according to their spectral domains and vibrational assignments. Regarding the (i) Low-wavenumber Region (50–200 cm^–1): this region primarily consists of translational (T, T _xy , T _x , T _y ), bending and librational (Lib) motions involving the MoO₅ and GdO₈ units. At 55 cm^–1 (B_u), a translational motion (T) of MoO₅ is coupled with a T _xy mode of GdO₈, indicating a relative movement between these two polyhedral units. The 93 cm^–1 (A_u), 96 cm^–1 (B_u), 103 cm^–1 (A_u), 140 cm^–1 (B_u) and 143 cm^–1 (B_u) modes correspond to general translational (T) motions involving both MoO₅ and GdO₈, further confirming interactions between these polyhedra. The 157 cm^–1 (B_u) mode corresponds to a wagging motion (wag) of the GdO₈ unit, specifically involving Gd–O–Gd bonds. The 167 cm^–1 (A_u) mode combines a translational motion (T) of MoO₅ with a scissoring (Sc) mode of GdO₈. (ii) Midwavenumber Region (200–500 cm^–1): This region is dominated by librational (Lib), deformation (δ), and scissoring (Sc) vibrations, which involve internal distortions of MoO₅ and GdO₈. The modes at 205 cm^–1 (A_u), 206 cm^–1 (B_u), 232 cm^–1 (A_u), and 288 cm^–1 (A_u) are primarily assigned as the deformation (δ) vibrations of MoO₅ and GdO₈. The B_u mode at 316 cm^–1 is assigned to a coupled vibration involving scissoring (Sc) of the MoO₅ polyhedra and bending (δ) of the GdO₈ units, while the modes observed at 322 cm^–1 (A_u) and 339 cm^–1 (A_u) are attributed to bending vibrations of both MoO₅ and GdO₈ polyhedra, indicating collective internal deformations. The B_u mode at 350 cm^–1 corresponds to bending vibrations of the MoO₅ units coupled with twisting (tw) motions of the GdO₈ polyhedra, involving significant displacement within the Gd–O–Gd bonds. The B_u mode at 387 cm^–1 is assigned to wagging vibrations of the GdO₈ polyhedra, predominantly involving motions within the Gd–O–Gd bonding network. The modes at 407 cm ^–1 (B _u ) and 418 cm^–1 (A_u) are attributed to bending vibrations involving both MoO₅ and GdO₈ polyhedra. Finally, the B _u mode at 422 cm ^–1 corresponds to a librational motion of the GdO₈ units, while the modes at 443 cm^–1 (B_u) and 455 cm ^–1 (A _u ) are assigned to bending vibrations of both MoO₅ and GdO₈ polyhedra, reflecting complex internal lattice dynamics. (iii) High-wavenumber Region (500–850 cm^–1): this region is dominated by stretching (ν) vibrations, specifically symmetric (ν_s) and antisymmetric (ν_as) modes of MoO₅ and GdO₈. The 538 cm ^–1 (A _u ) mode is associated with a strong vibration of oxygen atoms along the x-axis of the Gd–O–Gd bonds and the A _u mode at 594 cm^–1 is attributed to scissoring of the GdO₈ units. The B _u mode at 736 cm ^–1 involves asymmetric stretching of the MoO₅ polyhedra (ν_as) coupled with wagging motions of the GdO₈ units within the Gd–O–Gd bonds. The asymmetric stretching vibrations of the MoO₅ units are further observed at 753­(A_u), 766 cm ^–1 (B _u ) and 791 cm ^–1 (B _u ). The mode centers at 831 cm ^–1 (B _u ) and 839 cm ^–1 (A _u ) (illustrated in Figure S1) correspond to the symmetric stretching (ν_s) of MoO₅, representing the fundamental stretching dynamics of the polyhedral units.

4.5. Band Structure and PDOS

Figure shows the band structure and PDOS. Figure a displays the calculated spin polarized band structure of Gd₂MoO₆ for spin up, Figure b spin down and Figure c calculated spin polarized PDOS of Gd₂MoO₆ by orbital. Analyzing the band structure is crucial for understanding the electronic properties of materials, as it provides essential insights into the energy levels and permissible electronic states within the crystal’s periodic lattice. This, in turn, sheds light on the conductivity, optical characteristics, and other key properties. Coulomb interaction with Hubbard U was incorporated with 4.38 eV for Mo 3d and 6 eV for Gd 4f orbitals according to Moore at al. The analysis reveals a band gap of 1.92 eV for the majority spin channel at the Gamma point, indicative of semiconducting behavior (Figure a). This gap is primarily attributed to the localized 4f orbitals of Gadolinium (Gd), a finding corroborated by the PDOS analysis presented in Figure c. PDOS analysis provides a detailed breakdown of the total density of states, resolving it into contributions from individual atoms and their respective orbitals. This enables a deeper understanding of the electronic structure and bonding characteristics within the material. In this context, PDOS indicates a significant contribution of the Gd 4f orbitals to the conduction band minimum states near the band gap, confirming their role in determining the observed semiconducting properties. Furthermore, the PDOS analysis reveals that the 3d orbitals of Molybdenum (Mo) atoms play a significant role in influencing the PDOS at conduction bands. This suggests that Mo 3d orbitals contribute to the overall electronic structure and may influence properties, such as conductivity or charge transport. The valence band states are dominated by the p orbitals of oxygen (O), having Mo d-orbitals and Gd f-orbitals a negligible contribution near the Fermi level. Figure shows the PDOS for spin-up and spin-down electrons selected by the atoms. The Gd atom exhibits a noticeable distortion in this distribution, as shown in Figure a, suggesting the presence of magnetic character. In contrast, Figure b,c reveals relatively symmetrical distributions for the O and Mb atoms, respectively. This asymmetry in Gd PDOS can be indicative of magnetic interactions or localized magnetic moments. The overlap of Mo-3d with the states of the O-2p states suggests hybridization (Mo–O covalent bond). Gd f-orbital peaks likely appear as sharp, localized states deeper in the conduction band, having weak contributions near the Fermi energy level.

7.

Calculated spin-polarized band structure of Gd₂MoO₆ for spin up (a) and spin down (b). (c) Calculated spin PDOS of Gd₂MoO₆ by orbital.

8.

Calculated spin PDOS of Gd₂MoO₆ o selected by atom: (a) Gd, (b) Mo, and (c) O.

4.6. Pressure Dependence on the Vibrational Modes

Pressure serves as a critical parameter for probing the vibrational and structural properties of materials, particularly tungstates and molybdates, as extensively documented in the literature. − High-pressure investigations aim to elucidate the alterations in octahedral units and the emergence of novel properties originating from such structural modifications. This way, an analysis of the Raman spectra of the Gd₂MoO₆ crystal under applied pressure, as presented in Figures and , is furnished herein. As observed, there are some modifications in the Raman spectrum of the material, including the emergence, disappearance, and abrupt shifts in wavenumbers.

9.

Pressure-dependent Raman spectra (0.01 to 14.1 GPa) of Gd₂MoO₆ crystals for the following spectral regions: (a) 75–300 cm^–1, (b) 215–380 cm^–1, (c) 330–510 cm^–1, (d) 465–660 cm^–1 and (e) 660–950 cm^–1.

10.

Wavenumber vs pressure plot (0.0 to 14.1 GPa) for the Raman modes of Gd₂MoO₆ crystals in the following spectral regions: (a) 90–270 cm^–1, (b) 220–500 cm^–1 and (c) 470–890 cm^–1.

As previously discussed, this stated material is a complex molybdate with its Raman spectra governed by the vibrational modes of the MoO₅ and GdO₈ polyhedra and the Mo–O and Gd–O bonds. Overall, the intensities of the Raman modes decrease significantly at higher pressures (Figure ). Regarding pressure dependence, the wavenumber of the Raman peaks generally increases with pressure (Figures and ). This is a common observation in high-pressure Raman spectroscopy, as the pressure compresses the bonds, leading to higher vibrational wavenumbers (blue shift). After starting running pressure, only one Raman mode, centered at 127 cm^–1, exhibits wavenumber decreases with increasing temperature (dω/dP < 0), while all the other Raman modes exhibit wavenumber increases during compression (dω/dP > 0).

Figure shows a plot of the relationship between wavenumber (cm^–1) and pressure (GPa) for the Gd₂MoO₆. The figure is divided into three panels (a–c), each representing different regions of the Raman spectra under varying pressure conditions from 0.0 to 14.1 GPa in the following spectral regions: (a) 90–270 cm^–1, (b) 220–500 cm^–1, and (c) 470–890 cm^–1. An interesting aspect observed for this material is that the pressure induces wavenumber shifts and discontinuities when the pressure increases up to 2.2 GPa, suggesting changes in the octahedral geometry and bonding environment (Figure ). Above 2.2 GPa, the Gd₂MoO₆ system exhibits a few discontinuities and abrupt shifts in the wavenumber versus the pressure profile. Notably, the disappearance of a band near 100 cm^–1 is observed, although its inherently low intensity renders the interpretation inconclusive. As such, it remains uncertain whether this mode, potentially a lattice vibration, is definitively suppressed at this specific pressure threshold. The additional spectral modifications observed at 2.2 GPa are relatively subtle; thus, they are unlikely to signify a structural phase transition. Instead, they may reflect a minor rearrangement within the crystal lattice.

However, concerning the modes emerging in the lattice mode spectral region, it is worth noting that the bands at 150 and 160 cm^–1 converge in wavenumber, a process that persists up to approximately 10 GPa. Beyond this threshold, a single band is observed, suggesting the occurrence of a structural phase transition. Additionally, above 10 GPa, the splitting of a band near 300 cm^–1 is observed with the newly emerged peak marked by an asterisk in Figure , along with a noticeable broadening of the bands in the 300–375 cm^–1 range. Furthermore, the bands between 400 and 500 cm^–1 become significantly broadened. As these features correspond to bending vibrations, the transition can be interpreted as indicative of an increase in disorder within the octahedral units.

It is noteworthy that above 5.4 GPa, certain changes are observed in the internal mode region such as the emergence of a band at 389 cm^–1 (indicated by an asterisk) and the disappearance of a band near 710 cm^–1 in the spectrum at 5.7 GPa. These alterations can be interpreted as structural accommodation under compression, although they cannot be attributed to a structural phase transition because there is no modification in the lattice mode region.

The peaks located at 98, 104, 151, and 165 cm^–1 are likely associated with lattice vibrations involving external modes of the GdO₈ and MoO₅ polyhedrons. The emergence or disappearance of peaks within this region provides strong evidence for a first order phase transition in Gd₂MoO₆, notably marked at 10 GPa by the merging of two bands. A detailed peak-by-peak analysis reveals that the material undergoes significant changes in its vibrational properties under pressure, which can be ascribed to bond compression and structural transformation. Furthermore, previous investigations on the analogous compound Gd₂(MoO₄)₃ indicate that the material undergoes several structural transitions between 2 and 6 GPa, followed by amorphization in the pressure ranges of 6 and 9 GPa. These transitions are clearly evidenced by pronounced changes of the Raman spectrum of the crystal, being associated with the continuous rearrangement and distortion of MoO₄ tetrahedra and changes in molybdenum coordination, from IV to VI. ,,

4.7. The Principal Component Analysis (PCA) and Hierarchical Cluster Analysis (HCA)

The spectral variations observed during the compression process were analyzed through PCA Figure a and HCA Figure b, as illustrated in Figure . The HCA applied to the Raman spectra collected under pressures ranging from 0 to 14 GPa (Figure b) revealed a subdivision of the data into four distinct pressure intervals: 0–1.9 GPa, 2.2–6.7 GPa, 7.1–10.0 GPa, and 10.5–14.1 GPa. This grouping reflects modifications in the Raman signal intensity, which may be associated with the appearance or suppression of specific vibrational modes. A detailed analysis of these modes is necessary to better elucidate the physical processes underlying such transformations. It is noteworthy that the smallest distance between clusters was observed between the second and third groups, indicating that in this pressure range the spectra do not undergo abrupt modifications but rather subtle variations. In contrast, the other clusters exhibited distances greater than 1, which points to more pronounced and progressive changes in the spectral profiles. This behavior highlights that only in the region where the clusters are closer together is the spectral evolution smoother, whereas in the other ranges, the transformations occur more gradually across wider pressure intervals.

11.

(a) PCA scatter plot (principal component 1 versus principal component 2) obtained from the high-pressure Raman spectra in the 75–950 cm^–1 spectral range, together with the corresponding (b) HCA dendrogram, revealing four well-defined groups associated with distinct phase transformation regimes in Gd₂MoO₆.

Based on the PCA results, the spectra were grouped into three main clusters, with the transitions between them occurring around 3.1–3.3 and 10–10.5 GPa (Figure a). These transition intervals likely indicate changes in Raman spectral intensity, which may be associated with the disappearance of certain vibrational modes or with significant modifications in these pressure regions. These findings are consistent with the clustering patterns revealed by both PCA and HCA, which delineate regions of significant spectral change. The combined use of statistical and spectroscopic analyses enables a more comprehensive investigation of the physical phenomena responsible for these patterns. Such phenomena may include phase transitions, structural rearrangements, conformational modifications, or simply fluctuations in Raman signal intensity. Integrating these complementary approaches provides deeper insight into the mechanisms underlying the clustering behavior observed in the data set. −

In the present study on Gd₂MoO₆, however, two phase transitions were identified at near pressure ranges of 3.1–3.3 GPa and 9.5–10. GPa, which agree with the PCA analysis and HCA analysis. In particular, the stretching region of the MoO₅ units displays the same number of vibrational modes throughout and evolves smoothly without any jump in wavenumber. Moreover, no evidence of amorphization was found, as all bands, particularly those corresponding to lattice modes, remain sharp and well-defined up to the highest pressure achieved in the experiment. Consequently, a clear distinction between the two compounds highlights the remarkable structural stability of Gd₂MoO₆ under compression. Naturally, further analysis using XRD data would be essential to elucidate the nature of the phase transition and characterize the high-pressure phase formed.

5. Conclusion

This study provides a comprehensive theoretical and experimental investigation of the electronic structure and vibrational properties of Gd₂MoO₆ under both ambient and high-pressure conditions. First-principles calculations reveal that Gd₂MoO₆ is a semiconductor with an indirect band gap of approximately 1.92 eV, with its conduction and valence band edges located at distinct high-symmetry points in the Brillouin zone. The vibrational properties, analyzed through DFT and high-pressure Raman spectroscopy, reveal significant pressure-induced changes. Gd₂MoO₆ shows a hybrid ionic-covalent lattice dominated by strong Gd–O and Mo–O bonds. The presence of voids and O···O contacts indicates structural flexibility and diffusion pathways, supporting its stability and potential for property tuning. The disappearance and emergence of specific Raman peaks, in particular associated with lattice mode, at a critical pressure range of 3.1–3.3 GPa and 9.5–10 GPa, indicates two structural phase transitions undergone by the material. PCA and HCA analyses identified two phase transitions in the pressure ranges of 3.1–3.3 GPa and 9.5–10.0 GPa, which are consistent with the pressure-dependent studies. These transitions suggest a reorganization of the Mo–O and Gd–O bonding environments, possibly involving changes in polyhedral connectivity. Nonetheless, future investigations incorporating XRD could provide deeper insights into the nature of this phase transition and confirm the high-pressure structural characteristics of the high-pressure phase of Gd₂MoO₆.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.5c11574.

• View of the calculated wavenumbers and related atomic displacements for some Raman and IR modes of Gd₂MoO₆ (PDF)

The Article Processing Charge for the publication of this research was funded by the Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES), Brazil (ROR identifier: 00x0ma614).

The authors declare no competing financial interest.