The detail method of sample collection was explained in our earlier study [8] . Concisely, total ten phosphate (TSP and DAP) and compost fertilizer samples were collected to observe the level of essential (Fe and Zn) and non-essential metals (Sc and Sm) from the mid-southern part of Bangladesh namely; Alfadanga and Shaltha in Faridpur, Agargaon, Mirpur-2 (Kingshook Nursery), Savar (Gerua Bazar) in Dhaka, and Mohammadpur in Magura [8] . Sample identification numbers were assigned as, C11-L, C13L, C14-L, T22-L, T32-L, T42-L, T52-L, T62-L, D24-L, and D54-L where C, T, and D means compost, TSP, and DAP, respectively. Coordination data of the sample collection points are presented in Table S1.

Sample preparation and correction of the interference were also described in the previous study [8] . In brief, collected samples were taken into an electric oven to dry about 65˚C until having constant weight. About 60 mg of dried, homogeneous, and powdered fertilizer samples were heat sealed in a small polyethylene bag. Three standard reference materials (SRMs) were used where IAEA-Soil-7 was used as a standard, and IAEA-SL-1, NIST-1633b (Coal Fly Ash) were used as the control samples. Three 0.1 mm thick Al-Au foil monitor foils were placed within the sample pile and irradiated those along with the samples to determine the neutron flux gradient. Three megawatt (MW) TRIGA Mark–II research reactor was used in this nondestructive relative standardization approach. Long irradiation of reference materials and samples in the rotary specimen rack applying 5.07 × 10¹³ ncm⁻²∙sec⁻¹ thermal neutron flux for 6 minutes at 2.4 MW was conducted. A pre-calibrated HPGe detector [CANBERRA, 25 % efficiency relative to a NaI (Tl) detector, 1.8 keV resolution at 1332.5 keV of ⁶⁰Co] connected to a digital gamma spectrometer (ORTEC, DSPEC Jr^TM) was used. The γ-rays emitted from both the samples and standards were measured at the same geometry. The dead time of the detector was kept below 15%.

Two steps of counting were performed for the long irradiation. The first counting was performed to determine Sm content in samples, standard, and controls after a decay time of 1 day, with the lifetime of 1800 - 3000 s with the acquisition software Maestro-32 (ORTEC). The second counting was conducted after 3 weeks with the lifetime of 7200 s for the determination of Fe, Sc, and Zn.

Ratio of the measured concentrations of the studied metals in control samples (NIST-1633b Coal Fly Ash and IAEA-SL-1) to their certified concentrations gave a strong quality control result for this experiment (Figure S1(a) and Figure S1(b)). Deviations were found within 5% for most of the metals in both cases except Sm in SL-1 had 12% deviation, and the deviation calculated for Zn in NIST 1633b was 28%. Overall, the QC results provided reliability of the calculated results. A three-σ criterion [8] was employed to calculate the detection limit of studied metals (Table S2).

Gaussian 09 software package [24] was used to optimize the structures of DAP and TSP and their complexes with FeSO₄, ZnO, and ZnSO₄ at gas phase. Vibrational frequencies were calculated with the density functional theory (DFT) employing (BLYP) correlation functional [25] . All calculations were conducted by SDD basis set, which can produce reliable results for the interaction between metallic compounds and phosphate fertilizers [8] [26] . After computing, several thermochemical properties such as change of electronic energies, enthalpies, Gibbs free energies, HOMO-LUMO gaps, dipole moments, hardness and softness of the fertilizers, and the fertilizer-metal complexes were investigated.

The concentrations of iron in compost, TSP, and DAP are 13,206.783 - 24,484.775 mg/kg, 2963.809 - 19,615.839 mg/kg, and 18,398.228 - 23,403.794 mg/kg, respectively (Figure 1(a)). All compost samples contain the concentra- tion of iron are (C11-L = 13,512.279 ± 457.814 mg/kg; C13L = 24,484.775 ± 740.027 mg/kg, C14-L = 13,206.783 ± 462.619 mg/kg); TSP samples (T22-L = 3806.085 ± 202.853 mg/kg, T32-L = 3435.955 ± 193.816 mg/kg, T42-L = 19615.839 ± 623.845 mg/kg, T52-L = 4147.968 ± 212.192 mg/kg, T62-L = 2963.809 ± 176.921 mg/kg); and DAP samples (D24-L = 18,398.228 ± 598.977 mg/kg, D54-L = 23,403.794 ± 695.150 mg/kg). Concentration of Fe in DAP and compost seems remarkably higher than the other studies such as Chile and Egypt (Table 1). The ranges of iron concentration in soil samples of Punjab (India) reported 2800.0 - 5700.0 mg/kg (Table S3). Therefore, the repeated use of extremely high iron-enriched fertilizers could be turned into beneficiary evil.

The concentration ranges of zinc in compost, TSP, and DAP fertilizers are 312.734 - 3359.896 mg/kg, 243.327 - 472.515 mg/kg, and 348.135 - 4426.172 mg/kg, respectively (Figure 1(d)). All compost samples (C11-L = 3359.896 ± 193.670 mg/kg, C13-L = 861.017 ± 46.716 mg/kg and C14-L = 312.734 ± 19.156 mg/kg); TSP samples (T22-L = 262.236 ± 16.421 mg/kg, T32-L = 243.327 ± 17.541 mg/kg, T42-L = 398.272 ± 26.452 mg/kg, T52-L = 357.313 ± 24.710 mg/kg, T62-L = 472.515 ± 31.520 mg/kg); and DAP samples (D24-L = 348.135 ± 23.588 mg/kg, D54-L = 4426.172 ± 259.968 mg/kg) contain Zn in extremely high concentration compared to the European and Egypt market, specially C11-L, C13-L, T52-L, and D54-L.

The average Zn concentration in the phosphate fertilizers in European market was reported 166 mg/kg [27] where average Zn content in superphosphate fertilizer of Egypt market was 107.80 mg/kg [28] and Zn content in phosphate fertilizers of Chile market was 41.3 to 600.0 mg/kg [29] . So, the concentrations of Zn in sample C11-L and D54-L were found about 20 times and 27 times higher than the European market, respectively.

Zinc is unevenly distributed in soil and its concentration ranges between 73.0 to 320.0 mg/kg in Punjab (India) [30] . Kabata-Pendias and Pendias [31] stated that calcareous soils and organic soils can contain the highest background Zn contents. Moreover, several studies of USA and European countries reported that average concentration of Zn in soil can vary between <3 and 264 mg/kg in Table S3 [31] [32] [33] [34] . Besides concentration of Zn found in agricultural soils of Japan is 2.5 to 330 mg/kg [35] . On that account, some of the fertilizer samples contain extremely high amounts of Zn.

The concentrations of scandium in compost, TSP, and DAP are 3.496 - 7.092 mg/kg, 5.735 - 11.796 mg/kg, and 6.965 - 8.423 mg/kg, respectively (Figure 1(b)). All compost samples contain the concentration of scandium are (C11-L = 3.767 ± 0.248 mg/kg, C13-L = 7.092 ± 0.461 mg/kg and C14-L = 3.496 ± 0.230 mg/kg);

TSP samples (T22-L = 5.735 ± 0.374 mg/kg, T32-L = 6.478 ± 0.422 mg/kg, T42-L = 8.432 ± 0.548 mg/kg, T52-L = 7.139 ± 0.465 mg/kg, T62-L = 11.796 ± 0.764 mg/kg); and DAP samples (D24-L = 6.965 ± 0.454 mg/kg, D54-L = 8.423 ± 0.547 mg/kg). Turra et al., 2011 reported the mean concentration of Sc in SSP fertilizers of Brazil is 24.6 mg/kg. Besides, the range of the mean concentrations of Sc in the soil reported in the studies of countries across the world is 6.1 to 18.0 mg/kg [36] [37] [38] [39] [40] (Table S3). These results showed that estimated Sm contents in the fertilizer samples are within normal limit.

Additionally, the ranges of Sm concentration in compost, TSP and DAP were measured as 2.186 - 3.879 mg/kg, 6.381 - 26.694 mg/kg, and 6.581 - 7.223 mg/kg, respectively. Average concentration of Sm in the studied fertilizer samples are less than most of the studies reported in Table 1 except Pakistan [28] [36] [41] [42] . All compost samples (C11-L = 3.161 ± 0.109 mg/kg, C13-L = 3.879 ± 0.134 mg/kg and C14-L = 2.186 ± 0.076 mg/kg); TSP samples (T22-L = 13.138 ± 0.453 mg/kg, T32-L = 13.121 ± 0.452 mg/kg, T42-L = 6.381 ± 0.220 mg/kg, T52-L = 14.703 ± 0.507 mg/kg, T62-L = 26.694 ± 0.921 mg/kg); and DAP samples (D24-L = 7.223 ± 0.249 mg/kg, D54-L = 6.581 ± 0.227 mg/kg) contain Sm within the expected limit compared to the other studies.

Equilibrium geometry and the optimized structures of TSP and its complexes TSP-FeSO₄, TSP-ZnO, and TSP-ZnSO₄ are presented in Figure 2. Chosen bond distances and angles of the complexes are summarized in Table 2 (atom numbers are indicated in the optimized structures). Few significant changes were occurred compared in the structure of TSP when it forms complex with ZnO. In ZnO-TSP, Ca(15)-O(10) elongated from 2.32 Å to 4.17 Å. To compare the structural changes in TSP-FeSO₄ and TSP-ZnSO₄, bond distances between Fe

or Zn to the oxygen of the phosphate group of TSP could follow. It was observed from the optimized structure that bond distance between Fe to oxygen of PO₄ was shorter, which is Fe(21)-O(10) 1.82 Å than Zn(21)-O(10) 1.85 Å. It could be an evidence of the strong interaction between Fe and PO₄.

Remarkable changes were seen in bond angles of TSP when formed complex with ZnO. 4 in TSP structure.

Differences of binding energy, enthalpy, and Gibbs free energy are listed in Table 3. For TSP-FeSO₄, the binding energy, enthalpy, and Gibbs free energy changes are −343.941, −346.303, and −297.207 KJ/mol. On the other hand, for TSP-ZnO, the levels are −351.292, −353.655, and −307.709 KJ/mol, for TSP-ZnSO₄ the levels are −432.682, −435.308, and −377.284 KJ/mol, respectively. Results suggested that the complexes are thermodynamically stable.

Frontier molecular orbitals (MO) i.e., highest occupied molecular orbital (HOMO), lowest unoccupied molecular orbital (LUMO), and their energy gaps are essential factors to measure the chemical reactivity, extent of affinity and kinetic stability of a complex compound [8] . Larger HOMO-LUMO gap of the complexes means high kinetic stability but low chemical reactivity. In that case, an electron requires high energy to be promoted from HOMO to a relatively high-energy level LUMO. The HOMO and LUMO energy gaps of all metal compounds, TSP, and TSP-metal complexes are summarized in Table 4 and Figure 3.

It was observed that Fe has a noticeable effect on the frontier molecular orbital energies. Compared to the TSP, the HOMO and LUMO energy gaps of the Fe-TSP and Zn-TSP complexes had significantly decreased. Among these, Fe-TSP has the least HOMO-LUMO gap. The HOMO and LUMO energy gap of the TSP, TSP-FeSO₄, TSP-ZnO, and TSP-ZnSO₄ complexes are 6.1538, 3.8203, 4.2975, 4.2431 (eV), respectively, where dipole moments of these complexes are 5.3899, 5.5839, 9.8717, 12.073 (Debye), respectively. Moreover, Fe-TSP complex structure is softer than the Zn-TSP complexes (Table 4). These results confirmed that Fe-TSP complex is more reactive and stable than Zn-TSP complexes.

Equilibrium geometry and the optimized structures of DAP and its complexes DAP-FeSO₄, DAP-ZnO, and DAP-ZnSO₄ are depicted in Figure 4. Selected bond distances and angles of the complexes are summarized in Table 5 (atom numbers are shown in the optimized structures). In the structure of DAP-ZnO, few significant changes were occurred compared to the structure of DAP. O(5)-H(7) and O(2)-H(12) bonds got elongated from 1.07 Å to 1.39 Å and 1.09 Å to 2.03 Å. Zn oxide showed strong affinity to the PO₄ of DAP since bond distance between Zn and O of the phosphate group of DAP (Zn(17)-O(3)) is only 1.85 Å. Due to the strong attraction, P(1)-O(3) bond of PO₄ of DAP-Zn had changed significantly. Besides this, the bond distance of Fe(22)-O(2) 1.95 Å in DAP-FeSO₄ is shorter than Zn(17)-O(2) 1.97 Å in DAP-ZnSO₄. This result implies that the affinity of Fe and phosphate group of the fertilizers are stronger than Zn-phosphate interaction. Therefore, P(1)-O(3) of DAP-FeSO₄ got elongated from 1.59 Å 1.66 Å (Table 5).

Moreover, remarkable changes were seen in bond angles. Specially, 4 in DAP were 103.86˚ and 118.38˚, which had changed significantly by the strong interaction of Fe and Zn compounds ( Table 5 and Figure 4). So, both Fe and Zn metals have a strong affinity to the oxygen of PO ₄ group. HOMO-LUMO gap, dipole moment change, and hardness and softness of the complexes ( Table 4) could help to understand the interactions more comprehensively.

Electronic energy, enthalpy, and Gibbs free energy of metal-fertilizer complexes are summarized in Table 3. As predicted, the difference of electronic energy, enthalpy, and Gibbs free energy of DAP-FeSO₄ are −377.809, −380.172, and −321.099 KJ/mol. On the other hand, for DAP-ZnO, the levels are −379.122, −381.485, and −342.890 KJ/mol; for DAP-ZnSO₄, the levels are −429.532, −431.950, and −367.045 KJ/mol, respectively. This suggests that the complexes are thermodynamically stable. Moreover, binding energies also recommend that the affinity of between Fe and Zn compounds toward DAP is strong. The HOMO and LUMO energies of all DAP and DAP-metal complexes are summarized in Table 4 and Figure 5. It was observed that Fe has a significant effect on the frontier molecular orbital energies. Compared to DAP, the HOMO and LUMO energy gaps of the Fe-DAP and Zn-DAP complexes are significantly decreased where the HOMO-LUMO gap of Fe-DAP was least. The HOMO and LUMO energy gap of the DAP, DAP-FeSO₄, DAP-ZnO, and

DAP-ZnSO₄ complexes are 6.7073, 4.0343, 5.4442, and 5.4440 eV, respectively. The results suggest that Fe-complex is chemically more reactive to DAP than Zn-complexes. Dipole moments of these complexes are 5.0713, 5.1759, 8.1366, and 7.3715 Debye, respectively. Trend of the dipole moment is also proving the earlier assumption. Moreover, Fe-DAP complex structure is softer than the Zn-DAP complexes (Table 4).

Therefore, quantum mechanical calculation confirmed that both Fe-DAP/TSP and Zn-DAP/TSP complexes are thermodynamically stable, which supports experimental results. It was also observed that Fe-DAP/TSP complexes are more reactive and stable than Zn-DAP/TSP complexes because Fe-DAP complex has lower HOMO-LUMO gap and Fe-PO₄ bond distance is smaller than the Zn-PO₄.