Local structure and optical absorption of Mn2+ doped Cs2SO4 single crystals European Journal of Chemistry 16 (3) (2025) 287-291 European Journal of Chemistry ISSN 2153-2249 (Print) / ISSN 2153-2257 (Online) – Copyright © 2025 The Authors – Atlanta Publishing House LLC – Printed in the USA. This work is published and licensed by Atlanta Publishing House LLC – CC BY NC – Some Rights Reserved. https://dx.doi.org/10.5155/eurjchem.16.3.287-291.2672 European Journal of Chemistry View Journal Online View Article Online Local structure and optical absorption of Mn2+ doped Cs2SO4 single crystals Maroj Bharati 1, Vikram Singh 1 and Ram Kripal 2,* 1 Department of Physics, Faculty of Science, Nehru Gram Bharti University, Jamunipur, Prayagraj-221505, India 2 Electron Paramagnetic Resonance Laboratory, Department of Physics, Faculty of Science, University of Allahabad, Prayagraj-211002, India * Corresponding author at: Electron Paramagnetic Resonance Laboratory, Department of Physics, Faculty of Science, University of Allahabad, Prayagraj-211002, India. e-mail: ram_kripal2001@rediffmail.com (R. Kripal). 10.5155/eurjchem.16.3.287-291.2672 Received: 11 February 2025 Received in revised form: 31 May 2025 Accepted: 29 June 2025 Published online: 30 September 2025 Printed: 30 September 2025 Using perturbation theory and the superposition model, the splitting parameters for the zero field of Mn2+ doped crystals of Cs2SO4 are determined. When the local distortion is included in the computation, the estimated parameters match fairly well with the experimental ones. Theoretical evidence corroborates the experimental finding that the Mn2+ ion substitutes at the Cs+ site in Cs2SO4. The crystal's optical spectra are computed by the diagonalization of a complete Hamiltonian in the coupling scheme of the intermediate crystal-field, using the crystal field parameters obtained from the superposition model and the crystal field analysis program. The calculated and experimental band positions agree fairly well. Consequently, the results of the experiment are confirmed by theoretical analysis. Crystal fields Single crystal Zero-field splitting Superposition model Inorganic compounds Electron paramagnetic resonance Cite this: Eur. J. Chem. 2025, 16(3), 287-291 Journal website: www.eurjchem.com 1. Introduction The technique of electron paramagnetic resonance (EPR) can be used to ascertain the energies of transition metal ions' as they go through Zeeman transitions. The Mn2+ ion is the most studied transition ion, as it gives the EPR lines even at room temperature. It has a 3d5 electronic configuration and 6S5/2 ground state. Its paramagnetism can be attributed only to the electron spin because it has zero angular momentum. Small structural changes in the crystal [1-5] show sensitivity to zero- field splitting in the crystals. For use in EPR [6-9] and optical spectroscopy [10,11], the zero-field splitting (ZFS) and crystal field (CF) parameters can be modeled using the superposition model (SPM). The spin Hamiltonian (SH) is discussed together with other Hamiltonians in [12]. The parameters of the crystal field (CF) are often found using the SPM and the point-charge model [13] even if the exchange charge model (ECM) is also a useful technique for analyzing the effects of crystal fields in single crystals intoxicated with rare earth and transition ions [14]. In this study, we used SPM to calculate the ZFS parameters and the CF parameters. SPM was suggested [15] for CF based on the following assumptions: (i) An algebraic sum of the contribution of the crystal's other ions can be used to determine the paramagnetic ion's CF. (ii) All significant contributions to the conservation of free energy from each paramagnetic ion have axial symmetry with respect to their position vector when the ion is at the chosen coordinate system's origin. (iii) The CF contributions of just nearby or coordinated ions are to be taken into account. (iv) Across various host crystals, contributions to CF from a solitary ion (ligand) can be transmitted. The axial symmetry assumption, however, (ii) permits the trans- formation of one coordinate system into another; the first assumption provides support for the applicability of the superposition principle in characterizing the CF. Nonetheless, a more limited version of assumption (iii) is sometimes used, when solely the closest neighbor ions are occupied. According to the final ligand transferability assumption (iv), the only factors influencing the contributions of one ion to CF are its character and distance from the paramagnetic ion. To perform an SPM analysis on the CF, it is essential to obtain a steady polar coordinate system (RL, θL, ΦL) for each ligand or ion from the host crystal's X-ray data. When transition-metal ions are introduced, ionic size, ionic charge, and inter-ionic bonding mismatches will probably result in some degree of local distortion. To find the fitted values of the SPM power law exponents and the intrinsic parameters, a nonlinear or linear least squares fit may be performed on an adequate quantity of CF parameters. Mn2+ and Fe3+ experimental spin-Hamiltonian parameters in CaO and MgO crystals have been critically analy- ABSTRACT RESEARCH ARTICLE KEYWORDS https://dx.doi.org/10.5155/eurjchem.16.3.287-291.2672 https://www.eurjchem.com/ https://dx.doi.org/10.5155/eurjchem.16.3.287-291.2672 mailto:ram_kripal2001@rediffmail.com http://www.eurjchem.com/ https://crossmark.crossref.org/dialog/?doi=10.5155/eurjchem.16.3.287-291.2672&domain=pdf&date_stamp=2025-09-30 288 Bharati et al. / European Journal of Chemistry 16 (3) (2025) 287-291 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.287-291.2672 Figure 1. The symmetry-adopted axis system (SAAS) and the crystal structure of Cs2SO4 at room temperature. zed [16]. For the EPR data, it gives the exact values of the SPM parameters and demonstrates that the superposition principle is satisfied by the CF for 3d ions. A strict lattice relaxation model was utilized [17] to determine sets of intrinsic parameters of the SPM based on reliable ligand distances for alkali earth oxides. For Fe3+ and Mn2+ doped MgO, CaO, and SrO (R0 = 2.0 Å): __ 2b = -1552±48×10-4 cm-1 and -6440±113×10-4 cm-1, respectively, with a fixed t2 = 16 for both ions. For both Fe3+ and Mn2+, the values of __ 4b are 9.9±0.8×10-4 cm-1, with a fixed t4 of 16±4 for each ion. The fitted values for Mn2+ and Fe3+, respectively, were 17.7 and 14.4 for the separate fitting of t2. Cesium sulfate is a chemical compound that contains cesium and sulfur with formula Cs2SO4. For isopycnic centrifugation, dense aqueous solutions are made using this white, water-soluble solid. With potassium salt, it is isostructural. It is used in wastewater treatment and has high resistance to organic solvents, making it an experimental model for studying fatty acid degradation. This compound is used to study metal hydroxides and coordination geometry. Cesium sulfate is also used in biological samples such as plasma and human serum. It undergoes thermal expansion in the presence of light and emits light when heated to decomposition [18,19]. An EPR study of Mn2+ doped Cs2SO4 has been carried out in the temperature range of 77 to 293 K and spin Hamiltonian parameters of the system have been obtained [20]. According to angular variation studies, there is a complex where Mn2+ replaces a β-Cs+ ion and associates with a nearby β-Cs+ vacancy in the ab-plane along the complex's z-axis. It was discovered that the complex's z-axis and the crystal's b-axis form a 25° angle. The complex's x-axis runs along the crystal's c-axis, while its y-axis is in the same ab plane and is normal to the z-axis. In the present study, the ZFS parameters D and E are determined for the Mn2+ ion in cesium sulfate at substitutional β-Cs+ site at 293 K (room temperature, RT) using the CF parameters obtained from the SPM and perturbation equations [21]. The aim is to find the location of the Mn2+ ion and the distortion that occurs in the crystal. The results found for the Mn2+ ion at the substitutional β-Cs+ site in the cesium sulfate crystal with local distortion provide a reasonable match with the experimental values. A further objective of the study is to obtain the extent to which CF theory and SPM analysis can be applied to Mn2+ ions in cesium sulfate crystals to create an SPM parameter database. Molecular nanomagnet (MNM) design and computer modeling of their magnetic and spectroscopic characteristics will be determined by this. Single-molecule magnets (SMM) [22], single chain magnets (SCM) [23], and single ion magnets (SIM) [24] are currently included in the transition-ion-based MNM class. The above systems have drawn a great deal of attention from researchers because of the noteworthy magnetic characteristics of MNM, for instance, magnetization's macroscopic quantum tunneling, and potential applications in quantum computing and high-density information storage [22,23]. There are many synthesized SCM or SMM systems with Mn2+andCr3+ ions [25]. The parameters of the model established in this case may be used for ZFS parameter calculations for Mn2+ ions at similar sites in MNM, since model calculations for simpler crystal systems can serve as a foundation for more complex ones. The modeling utilized in this work can be extended to explore crystals of scientific and industrial interest in several other ion host systems. 2. Crystal structure The crystal structure of cesium sulfate, isomorphous to potassium, ammonium, and rubidium sulfates, has been determined by Ogg [26]. The crystal belongs to the symmetry group D2h16 and contains two reflection planes, four glide planes, twelve dyad screw axes, and sets of four centers of symmetry. The dimensions of the orthorhombic unit cell are a = 6.218, b = 10.884 and c = 8.198 Å. The structure of Cs2SO4 consists of layers of atoms parallel to the (100) planes, the spacing between which is a/2. The reflection planes are (100)1/4 and (100)-1/4, the origin of coordinates is assumed at the center of the unit cell. The unit cell contains four formula units. According to the oxygen environment, cesium atoms are classified as α- or β-type [19,26]. As a result, there are four cesium ions of α-type and four cesium ions of β-type in the unit cell. Figure 1 shows the crystal structure of cesium sulfate with the adopted symmetry axis system (SAAS). 3. Crystal field and zero field splitting parameter calculations The analysis of EPR spectra is performed with the spin Hamiltonian (Equation 1) [7,8]: Η=−+       +−+ )()1( 3 1.. 222 yxZB SSESSSDSgBµ (1) where B, µB, g, D and E are the applied magnetic field, Bohr magneton, splitting factor, second-rank axial and second rank rhombic ZFS parameters [27,28]. Crystal axes a, b and c, along with the laboratory axes (x, y, z), are shown in Figure 1. The directions of metal-ligand bonds that are mutually perpen- dicular are referred to as the local symmetry axes of the site or the symmetry-adopted axes (SAA). As demonstrated in Figure 1, the axis-x of SAAS is along the crystal axis-c, and (y, z) are perpendicular to the axis-x. When Mn2+ ions are doped into the Cs2SO4 crystal, they enter the lattice at substitutional β-Cs+ sites with some local distortion [29]. For a 3d5 ion, the spin Hamiltonian can be written as (Equations 2 and 3) [30], ΗΗΗΗ +++=Η cssso0 (2) Bharati et al. / European Journal of Chemistry 16 (3) (2025) 287-291 289 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.287-291.2672 Table 1. Atomic coordinates, bond length R (both with and without distortion), and angles θ, φ in Cs2SO4 single crystal (site I) *. Ligands x (Å) y (Å) z (Å) R (nm) (ND) R (nm) (WD) θ° (ND) θ° (WD) φo (ND) φo (WD) O1 0.250 0.417 0.067 0.13073 0.19286 87.06 88.26 90.00 91.50 O2 0.250 -0.455 0.311 0.86870 0.94870 87.95 89.95 90.00 92.00 O3 0.053 0.353 0.311 0.28706 0.46707 83.78 85.28 93.96 95.96 O4 0.553 0.147 0.189 0.30035 0.38035 86.39 94.39 84.20 90.20 O5 -0 .053 0.853 -0.311 0.67257 0.85758 92.65 94.65 92.58 92.58 O6 0.447 -0.353 0.811 0.98723 1.07223 85.28 85.28 88.85 90.85 * Substitutional: Mn (0.250, 0.308, 0.000), ND = No distortion, WD = With distortion. Table 2. The Mn2+ doped Cs2SO4 crystal's crystal field and zero field splitting parameters *. Site R0 (nm) CF parameters (cm-1) Zero-field splitting parameters B20 (cm-1) B22 (cm-1) B40 (cm-1) B42 (cm-1) B44 (cm-1) |D| (×10-4 cm-1) |E| (×10-4 cm-1) |E|/|D| Site I ND 0.200 -24985.0 -30744.3 34177.26 36217.17 50793.73 29578.1 12285.6 0.415 Site I WD 0.200 -8970.37 7147.075 2294.573 2419.935 5629.302 879.3 227.5 0.258 Exp. 879.3 13.1 0.015 * ND = No distortion 4 2 A A = 10, WD = With distortion, 4 2 A A = 10, Exp. = experimental. ( )k kq qc B C=∑Η (3) where Bkq, in Wybourne notation, are the CF parameters and C k q )( are the spherical tensor operators of Wybourne. Bkq ≠ 0 in the orthorhombic symmetry crystal field only for k = 2, 4; q = 0, 2, 4. Using SPM, the CF parameters Bkq are calculated [31]. The symmetry of the local field about Mn2+ ions in the Cs2SO4 crystal is considered orthorhombic (OR-type I) [7]. In OR-type I symmetry, the ZFS parameters D and E are established as follows (Equations 4 and 5) [31]: [ ] [ ]BBBPBBBDP G D 2 44 2 42 2 402 2 2 2220 2 20'2 2 1445 63 21 70 3 +−−         ++−−         = ςς ς (4) [ ] [ ]BBBPBBDP G E 4244402 2 2220'2 2 72103 63 212 70 6 +         +−         = ςς ς (5) In the above equations, P = 7B + 7C, G = 10B + 5C, D’ = 17B + 5C. B and C are the Racah parameters and ς are the spin-orbit coupling parameter. With the average covalency parameter N in mind, we get B = N4B0, C = N4 C0, ς = N2ς 0, where ς 0 presents free ion spin-orbit coupling parameter and B0 and C0Racah parameters for free ion [30,32]. B0 = 960 cm-1, C0 = 3325 cm-1 andς 0 = 336 cm-1for free Mn2+ ion [7]. The parameter N is evaluated from         += CB CBN 002 1 taking the Racah parameters (B = 850 cm-1, C = 2970 cm-1) obtained from optical analysis of the Mn2+ ion in zinc cesium sulfate hexahydrate, the crystal with oxygen ligands [33], as there is no optical study of Mn2+ doped Cs2SO4 reported in the literature. The CF parameters, in terms of co-ordination factor ( )φθ jjkqK , and intrinsic parameter ( )RA jk __ , using SPM are found [15,31] as in (Equation 6), ( ) ( )φθ jjkqj j kkq KRAB , __ ∑= (6) ( )RA jk __ is provided by (Equation 7) ( ) ( )RAR RRA jk j k tk __ 0 0 __ =         (7) where the ligand's distance from the dn ion is denoted by R j , ( )RAk 0 __ is the intrinsic parameter, R0 is the reference distance of the ligand from the metal ion and tk denotes power law exponent. For Mn2+doped crystals, t2 = 3 and t4 = 7 are used [31]. Different values are considered in the present calculation, as discussed later. As the coordination about the Mn2+ ion is octahedral, __ 4A is found from the relation (Equation 8) [34], ( ) DqRA 4 3 0 __ 4 = (8) From optical study [33], Dq = 790 cm-1. Therefore, ( )RA 0 __ 4 = 592.5 cm-1. For 3d5 ions the ratio __ 4 __ 2 A A falls in the range 8-12 [30,35,36]. With __ 4 __ 2 A A =10, __ 2A = 5925 cm-1. 4. Results and discussion Using SPM, parameters __ 2A and __ 4A , and the ligand arrangement about Mn2+ ion as indicated in Figure 1, the CF parameters of the Mn2+ ion at the substitutional β-Cs+ sites are calculated. Table 1 provides the atomic coordinates in the Cs2SO4 single crystal along with the bond length R (both with and without distortion) and angles θ, φ for site I. The CF parameters from Equation 6 and the ZFS parameters obtained using Equations 4 and 5 together with the reference distance R0 are depicted in Table 2. Table 2 demonstrates that R0 = 0.200 nm is somewhat less than the sum of radii of ions (0.223 nm) of Mn2+ = 0.083 nm and O2- = 0.140 nm along with no distortion yield ZFS parameters for substitutional octahedral site I to be different from the experimental values [20]. Experimental ZFS parameter values |D| and |E| (in 10-4 cm-1) for site I are 879.3, 13.1, respectively. |E|/|D| is found to be 0.015, which is quite smaller than the standard value 0.33 [28]. |D| and |E| determined theoretically without distortion are larger than the experimental values. The value of |E|/|D| is also larger than the standard value 0.33 [28]. Therefore, the local distortion is taken into account. Using the above value of R0 and local distortion, the ZFS parameter |D| for substitutional octahedral sites I is in good accord with those from the experiment [20] but |E| value is larger than the experimental one. However, this gives |E|/|D| ratio close to the standard value [28]. Thus, the theoretical |E| value seems to be more appropriate. The parameters t2 = 3 and t4 = 7 with the transformation S2 for standardization [28] have been used to obtain |E|/|D| ratio< 0.33 and calculated ZFS parameters close to experimental values. The CFA program [37] and Bkq parameters (with distortion) are used to calculate the Mn2+ doped Cs2SO4 single crystals' optical spectra. After diagonalization of the complete Hamiltonian, the positions of the energy bands of Mn2+ ions are determined. Table 3 displays the energy band positions for substitutional site I based on experimental and calculation data [33]. 290 Bharati et al. / European Journal of Chemistry 16 (3) (2025) 287-291 2025 – European Journal of Chemistry – CC BY NC – DOI: 10.5155/eurjchem.16.3.287-291.2672 Table 3. The positions of the energy bands of the single crystal of Cs2SO4 doped Mn2+, both calculated and experimental. Transition from 6A1g(S) Observed wavenumber (cm-1) Calculated wavenumber (cm-1) 4T1g(G) 18436 20310 20315 20974 20997 22543 22581 4T2g(G) 22815 22997 23021 23351 23370 23673 23688 4Eg(G) 24783 23866 23877 23929 23951 - - 4A1g(G) 24850 24863 24865 - - - - 4T2g(D 28003 26712 26757 27568 27586 27981 28004 4Eg(D) 29870 28538 28575 29754 29820 - - 4T1g(P) 32435 31232 32107 32391 32525 32580 32790 4A2g(F) - 36562 36991 - - - - 4T1g(F) 41460 40592 41107 41124 41313 41365 41510 Table 3 indicates that the calculated and experimental energy band positions agree fairly well. Therefore, the theo- retical results corroborate the experimental finding [20,33] that Mn2+ ions enter the Cs2SO4 crystal at the substitutional octahedral site. The model parameters obtained here may be utilized in ZFS parameter estimations for Mn2+ ions at comparable MNM sites. 5. Conclusions Zero field splitting parameters using perturbation theory and the superposition model for Cs2SO4 single crystals intoxicated with Mn2+ ions are estimated. The calculated ZFS parameters agree well with the experimental values. The calculated positions of the optical energy bands agree reasonably well with those obtained from the experiment. Therefore, the experimental result is supported by the theoretical analysis that Mn2+ ions occupy substitutional sites in Cs2SO4. The model parameters estimated in this study can be utilized for the calculation of the ZFS parameters for Mn2+ ions at comparable locations in molecular nanomagnets. The current modeling technique can be extended to explore crystals of numerous scientific and industrial applications. Acknowledgements We thank the Head of Physics Department of Allahabad University, Allahabad, for giving facilities of the department and Prof. Czeslaw Rudowicz of Faculty of Chemistry, Adam Mickiewicz University, Poznan, Poland, for the CFA program. Disclosure statement Conflict of interests: The authors declare that they have no conflict of interest. Ethical approval: All ethical guidelines have been adhered. Sample availability: Samples of the compounds are available from the author. CRediT authorship contribution statement Conceptualization: Ram Kripal, Vikram Singh; Methodology: Maroj Bharati, Vikram Singh; Software: Ram Kripal, Vikram Singh; Validation: Maroj Bharati, Vikram Singh; Formal Analysis: Maroj Bharati, Vikram Singh; Investigation: Maroj Bharati, Vikram Singh; Resources: Maroj Bharati, Vikram Singh; Data Curation: Maroj Bharati, Vikram Singh; Writing - Original Draft: Maroj Bharati, Vikram Singh; Writing - Review and Editing: Ram Kripal, Vikram Singh; Visualization: Vikram Singh, Ram Kripal; Funding acquisition: Vikram Singh, Maroj Bharati; Supervision: Ram Kripal; Project Administration: Ram Kripal. ORCID and Email Maroj Bharati marojbharati99@gmail.com https://orcid.org/0009-0007-8219-0993 Vikram Singh vikram.singh@ngbu.edu.in https://orcid.org/0000-0003-3813-586X Ram Kripal ram_kripal2001@rediffmail.com https://orcid.org/0000-0002-3483-8704 References [1]. Weil, J. A.; Bolton, J. R. 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Permissions for commercial use of this work beyond the scope of the License (https://www.eurjchem.com/index.php/eurjchem/terms) are administered by Atlanta Publishing House LLC (European Journal of Chemistry). http://www.physics.sk/aps/pubs/1984/%20aps_1984_34_4_195.pdf http://www.physics.sk/aps/pubs/1984/%20aps_1984_34_4_195.pdf https://www.eurjchem.com/index.php/eurjchem/terms http://creativecommons.org/licenses/by-nc/4.0 https://www.eurjchem.com/index.php/eurjchem/terms 1. Introduction 2. Crystal structure 3. Crystal field and zero field splitting parameter calculations 4. Results and discussion 5. Conclusions Acknowledgements Disclosure statement CRediT authorship contribution statement ORCID and Email References PrintField10: PrintField11: PrintField12: PrintField13: PrintField14: PrintField20: PrintField21: PrintField22: PrintField23: PrintField24: