Optimizing Irrigation and Fertilization Contributes to Mitigating Nutrients Leaching While Improving Crop Yield: Insights From a Field Experiment and Density Functional Theory Calculation

Abstract

Nitrogen (N) and phosphorus (P) losses from farmland pose a significant threat to non-point source pollution in plateau lakes. Reducing nutrient loss from cropland is essential for the sustainable agricultural and ecological development of plateau lakes. The study aimed to investigate the effects of optimizing irrigation and fertilization on N and P losses based on field experiments and density functional theory calculation. The findings showed that ditch irrigation contributes to N and P leaching through their interactions with water and colloids, while drip irrigation reduces the transfer capacity for N and P by decreasing the intensity and volume of leachates. Additionally, changing from conventional fertilization to multiple fertilization based on the nutrient needs of corn significantly improved fertilizer efficiency, resulting in reductions in N and P losses of 25.2–72.4% and 24.2–67.6%, respectively. Additionally, the optimization of irrigation and fertilization led to an 11.3% improvement in crop yield. These results contribute to a better understanding of the mechanisms through which agricultural practices affect nutrient losses and have significant implications for optimizing farmland management in the Erhai Lake basin. Importantly, this research is of great significance in mitigating the threat of agricultural non-point source pollution in ecologically fragile plateau lakes.

Keywords

Nitrogen and phosphorus leaching - Erhai Lake - Irrigation and fertilization - DFT calculation

Significance

Nutrient loss from arable land, especially in the fragile ecological zone of plateau lakes, resulting in agricultural surface pollution has become a serious threat to the ecological environment and sustainable human development. Therefore, elucidating the mechanism of nutrient loss from arable land in plateau lakes and formulating preventive and control measures are particularly important for reducing agricultural surface pollution and promoting the sustainable development of agriculture in plateau lakes and their ecological security.

Highlights

• Optimizing irrigation and fertilization reduced N and P losses of 72.4 and 67.6%, respectively.

• Drip irrigation reduces N and P losses by decreasing the intensity of interflow.

• Periodical fertilization contributes to improving its efficiency and crop yield.

• Interactions of colloids and H₂O with nutrients contribute to their leaching.

1

Introduction

Nitrogen (N) and phosphorus (P) leaching from croplands has received considerable attention for its potential impact on ecosystem balance and sustainability, especially in ecologically sensitive and fragile plateau lakes such as Erhai Lake [1], [2]. Encouragingly, previous studies have shown that changing the fertilization and irrigation management of cropland in the Erhai Lake basin may be an effective approach to mitigating its agricultural non-point source pollution [3], [4]. However, the differences in optimizing fertilization and irrigation management measures lead to uncertainty about their effectiveness in reducing nutrient leaching from cropland [3], [4]. Additionally, the strong interactions between soil leachate and shallow groundwater in the Erhai Lake basin may significantly affect the effectiveness of cropland optimization measures [5], [6]. Therefore, continuous optimization of irrigation and fertilizer management in the Erhai Lake basin is crucial to mitigating the risk of nutrient losses from croplands contributing to non-point source pollution in plateau lakes with low ecological sensitivity. Additionally, understanding the soil–water interaction during nutrient migration is essential for refining agricultural water and fertilizer management practices.

Improving the efficiency of water and fertilizer use can lead to a significant improvement in their use, while reducing losses through leaching and ultimately increasing crop yield. Previous studies have shown that drip irrigation can not only significantly reduce irrigation water use but also increase yield while reducing nitrogen and phosphorus leaching [7], [8]. In Addition, previous reports have shown that precise optimization of fertilization and topdressing according to crop growth cycles can significantly reduce N leaching and improve the efficiency of fertilizer to increase crop yield [9], [10]. However, the spatial variability in soil properties and climatic conditions leads to uncertainty in the effectiveness of agricultural management practices. Therefore, it is essential to conduct field experiments in the Erhai Lake basin to investigate whether optimized irrigation and precision fertilization can be effective measures to mitigate nutrient loss in croplands and reduce agricultural non-point source pollution in Erhai Lake. Additionally, improving the mechanism by which water transport in irrigation affects nutrient migration will further help us to optimize farmland management measures.

Density functional theory (DFT) calculations have been extensively used to investigate the interactions and adsorption behaviors of soil substances using various exchange-correlation functions, including the generalized gradient approximation (GGA) functional [11]. Previous reports have shown that DFT can clearly demonstrate the interaction mechanism between soil and nutrients, as well as the electron transfer, chelation, and complexation mechanisms of soil amendments on soil material transport [12], [13], [14]. Therefore, the application of DFT calculations is poised to enhance our understanding of the soil–water interactions during irrigation and their impact on the leaching and loss of dissolved nutrients. More importantly, it will enable us to continually optimize cropland management measures on this basis to reduce nutrient leaching from cropland.

This work seeks to examine the effects of alterations in irrigation on the leaching characteristics of N and P through field experiments on the eastern shore of the Erhai Lake basin. Furthermore, DFT calculations are utilized to elucidate the interactions between soil and water migration, as well as their influence on the movement of dissolved N and P within water. These findings contribute to a better understanding of the impact of irrigation water on the leaching losses of soil N and P and aid in optimizing irrigation and fertilization management practices in the Erhai Lake basins. Importantly, this research holds significant implications for mitigating the potential threat of agricultural non-point source pollution to the ecologically sensitive plateau lakes.

2

Results and Discussion

2.1

Optimization of Irrigation and Fertilization Contributes to the Reduction of Nutrient Losses from Cropland

Optimization of irrigation and fertilization practices significantly reduces nutrient concentrations in soil leachate ([Figs. 1], [S1], and [S2]). Total N (TN) concentrations decreased significantly with increasing soil depth. TN concentrations in W₂ are significantly lower than in W₁, and they decrease with increasing fertilization frequency (T₂–T₄, [Fig. 1a]). It is worth noting that the TN concentration (67.74 mg L⁻¹) in W₂T₄ in the 20-cm soil layer is 206.72 mg L⁻¹ lower than that in the control (CK) (274.46 mg L⁻¹). Changes in TDN (total dissolvable nitrogen, accounting for over 90% of TN) with changing irrigation and fertilization practices are similar to those in TN ([Fig. 1b]). TDN concentration in W₂T₄ (64.34 mg L⁻¹) in the 20 cm soil layer is 195.29 mg L⁻¹ lower than in CK (259.63 mg L⁻¹). Correspondingly, changes in nitrate nitrogen (NO₃ ⁻–N), nitrite nitrogen (NO₂ ⁻–N), and ammonium nitrogen (NH₄ ⁺–N) are similar to those in TN and TDN ([Figs. 1c] and [S1d],[e]).

Figure 1 Concentrations of (a) TN, (b) TDN, and (c) NO₃ ⁻-N in leachates at varying depths (0–20, 20–40, and 40–60 cm) within fields. The letters “a”, “b”, and “c” denote significant differences in concentration at different depths. The symbols “**” and “***” indicate significant differences at levels of “p < 0.01” and “p < 0.001” between CK and the experimental treatments, respectively. These findings are derived from the eighth leachate sample collected in the fields, with a sampling interval of 15 days.

Total P (TP) concentration decreases with increasing soil depth and reaches 0.91 mg L⁻¹ in CK in the 20-cm soil layer, which is three times greater than in W₂T₄ ([Fig. 2a]). TDP concentrations decrease significantly with increasing fertilization frequency and decreasing irrigation. The concentration of TDP in W₂T₄ (0.21 mg L⁻¹) in the 20-cm soil layer is 0.52 mg L⁻¹ lower than that of CK (0.73 mg L⁻¹, [Fig. 2b]). PO₄ ³⁻–P concentration in leachates in the 20-cm soil layer showed a similar distribution with TDP and TP ([Fig. 2c]), but there is a higher concentration of PO₄ ³⁻–P in the 60-cm soil layer than the one in the 40-cm soil layer in CK and W₁. The soil in cropland in the Erhai Lake basin has a texture of sandy silt, with a high soil porosity [15], [16]. Implementation of farmland management techniques such as returning straw to the field and applying organic fertilizers can lead to a notable increase in soil organic matter (SOM), subsequently enhancing soil porosity and reducing soil bulk density ([Table S1]) [17], [18]. Although high-porosity soils promote gas exchange and nutrient cycling to enhance crop uptake of soil nitrogen and phosphorus [19], [20], they also promote water loss during furrow and flood irrigation [21], [22]. In addition, shallow groundwater in the Erhai basin is capable of frequent material exchange with soil leachate ([Fig. S6]) [15], [23], which further leads to nutrient leaching from deeper soils [23], [24]. On the contrary, the reduction of 12.66% to 23.92% in leachate in drip irrigation indicates its ability to weaken the intensity of soil leaching ([Table S12]).

Figure 2 Concentrations of (a) TP, (b) TDP, and (c) PO₄ ³⁻–P in leachates at varying depths (0–20, 20–40, and 40–60 cm) within fields. The letters “a”, “b”, and “c” denote significant differences in concentration at different depths. The symbols “**” and “***” indicate significant differences at levels of “p < 0.01” and “p < 0.001” between CK and the experimental treatments, respectively. The mark of “ns” means there is no significant difference between CK and the experimental treatments. These findings are derived from the eighth leachate sample collected in the fields, with a sampling interval of 15 days.

Dissolved organic carbon (DOC) concentrations at different soil depths after optimization of irrigation and fertilization showed significant differences compared to CK ([Figs. 3] and [S4]). There was a noticeable decrease in DOC concentration with increasing soil depth. Furthermore, the leachate at a 20 cm soil depth showed a decrease in DOC concentration with increasing fertilization frequency at the same irrigation ([Fig. 3a]). The DOC concentration in the 20-cm leachate in the W₂T₄ (1.40 mg L⁻¹) field was only 46.5% of that in CK (3.01 mg L⁻¹). Colloids can hold soluble nitrogen and phosphorus hostage by electrostatic adsorption and ion exchange of surface charges to influence the transport of soluble nutrients [25], [26]. In contrast, drip irrigation avoids colloid migration during diffuse irrigation to reduce soil nutrient leaching [27], [28].

Figure 3 Concentrations of (a) DOC and (b) colloid in leachates at varying depths (0–20, 20–40, and 40–60 cm) within fields. The letters “a”, “b”, and “c” denote significant differences in concentration at different depths. The symbols “**” and “***” indicate significant differences at levels of “p < 0.01” and “p < 0.001” between CK and the experimental treatments, respectively. These findings are derived from the eighth leachate sample collected in the fields, with a sampling interval of 15 days.

To further investigate the effects of alterations in irrigation and fertilization on the loss of nutrients from croplands, we calculated the total loss of N, P, and DOC in leachates collected using ceramic suction cups ([Fig. 4]). TN losses in W₂T₄ (800.43 mg) have a reduction of 72.4% compared to CK (2904.58 mg, [Fig. 4a]). Furthermore, the cumulative total dissolvable nitrogen (TDN) and NO₃ ⁻–N losses in W₂T₄ were 764.02 and 677.00 mg, accounting for 72.2 and 69.9% of CK, respectively. The TP losses after optimization of irrigation and fertilization are ranging from 24.2 to 67.6% of CK (11.16 mg) ([Fig. 4b]). The reductions of TDP losses in treatments ranged from 29.2 to 66.5% of CK. Notably, irrigation W₁ exhibited a comparable reduction in PO₄ ³⁻–P loss, ranging from 76.7 to 77.8% compared to CK. The reduction in DOC loss decreases with increasing fertilization frequency and decreasing irrigation ([Fig. 4c]). There was a reduction of 72.6% of DOC loss in W₂T₄ (67.73 mg) compared to CK (247.24 mg).

Figure 4 Accumulated losses of (a) N, (b) P, and (c) DOC and colloid of leachates in fields. The symbol of “***” indicates the significant differences at levels “p < 0.001” between CK and the experimental treatments.

DFT calculations were employed to explore the mechanisms by which irrigation affects nutrient loss. Adsorption energy can serve as a direct indicator of the strength of interactions between substances, as determined through the computation of molecular models ([Fig. 5]). The optimized structure of SiO₂–H₂O–NH₄ ⁺ ([Fig. 5a]) exhibits a higher concentration of NH₄ ⁺ ions compared to the optimized structure of SiO₂–H₂O–PO₄ ³⁻ ([Fig. 5b]), but a lower concentration compared to the optimized structure of SiO₂–H₂O–NO₃ ⁻ ([Fig. 5c]). The adsorption energy between SiO₂ and NO₃ ⁻ (−25.06 eV) is 12.83 eV higher than that between SiO₂ and NH₄ ⁺ (−12.23 eV), but notably lower than that between SiO₂ and PO₄ ³⁻ (−44.07 eV, [Fig. 5d]). The adsorption energies of H₂O adsorbed on SiO₂ surpass those of solutes adsorbed on SiO₂ (i.e., NH₄ ⁺, NO₃ ⁻, and PO₄ ³⁻). According to DFT calculation, the adsorption energies of colloids with NO₃ ⁻, NH₄ ⁺, and PO₄ ³⁻ are −34.31, −37.64, and −219.21 eV, respectively, which are 2.8, 1.3, and 5.0 times greater than the adsorption energies of soil and NO₃ ⁻, NH₄ ⁺, and PO₄ ³⁻ ([Table S13]). This is attributed to the strong interaction between colloids and dissolved N and P through mechanisms such as hydrogen bonding, ion exchange, and electrostatic adsorption [25], [26]. Additionally, H₂O molecules enhance their interaction with solutes through electrostatic interactions and electron transfer, thereby increasing their ability to hold nutrient ions adsorbed on the SiO₂ surface. In contrast, drip irrigation contributes to the reduction of soil–water content and leaching intensity to mitigate the downward force relay of H₂O on solutes during downward solute migration and subsequently avoids soil nutrient leaching [29], [30].

Figure 5 Molecular models of (a) crystal face (011) of SiO₂ and H₂O–NO₃ ⁻ solution, (b) crystal face (011) of SiO₂ and H₂O–NH₄ ⁺ solution, and (c) crystal face (011) of SiO₂ and H₂O–PO₄ ³⁻ solution. (d) Adsorption energy of H₂O adsorbed by SiO₂ and solutes adsorbed by SiO₂, respectively. The solutes include NO₃ ⁻, NH₄ ⁺, and PO₄ ³⁻.

EDDs of the molecular models were used to further investigate the influence of irrigation water on the movement of nutrients (i.e., NH₄ ⁺, NO₃ ⁻, and PO₄ ³⁻, [Fig. 6]). The blue region indicates a decrease in electrons, while the red region indicates an increase in electrons. The prominent red region around O in NO₃ ⁻ and the blue region around H in H₂O indicate electronic migration from H to O ([Fig. 6a]). In the NH₄ ⁺ solution, there is a red region around N and a blue region around H, indicating electron transfer from N in NH₄ ⁺ to H in H₂O ([Fig. 6b]). Similarly, there is electron transfer from H in H₂O to O in PO₄ ³⁻ ([Fig. 6c]). Furthermore, the adsorption energy between H₂O and NH₄ ⁺ (−4.91 eV) is comparable to that between H₂O and NO₃ ⁻ (−4.97 eV), but significantly lower than that of PO₄ ³⁻ (−15.70 eV, [Fig. S5]).

Figure 6 Patterns of EDDs in the solutions of (a) H₂O and NO₃ ⁻, (b) H₂O and NH₄ ⁺, and (c) H₂O and PO₄ ³⁻.

2.2

Changes in Crop Yield Following the Optimization of Irrigation and Fertilization

To investigate the effects of alterations in irrigation and fertilization on crop growth, we conducted measurements on crop height and 100-grain weight ([Fig. 7]). The results indicate a clear decrease in crop height as the volume of drip irrigation is reduced and fertilization frequency is increased ([Fig. 7a]). The tallest crop was observed in W₁T₂, reaching a height of 172.15 cm, which is 4.8 cm taller than CK. Conversely, the shortest crop height was recorded in W₂T₄ (159.32 cm), which is 8.0 cm shorter than the control group. The highest 100-grain weight was observed in the W₂T₄ treatment group (34.94 g), closely followed by the 100-grain weight of W₁T₄ (33.98 g, [Fig. 7b]), they are 11.3 and 8.2% heavier than those of the control group, respectively. Notably, the 100-grain weight generally increases with a higher fertilization frequency. Drip irrigation, in comparison to ditch irrigation, can reduce the speed and extent of nutrient transport during the irrigation process, resulting in a greater retention of soil nutrients in the surface soil [31], [32]. The hydrophilic and fertilizer-orientated nature of the plant root system promotes its lateral development during drip irrigation to enhance nutrient uptake, and the high-velocity flow of water in furrow irrigation disrupts the soil structure, leading to stripping and loss of topsoil to reduce soil fertility and crop growth [33], [34], [35]. However, it is difficult for the crop’s laterally growing root system to effectively utilize the nutrients in the deep soil to meet the growth and development of maize at the elongation stage, which subsequently limits the height of the maize plant ([Fig. S6]) [36], [37]. Reducing irrigation intensity contributes to avoiding leaching of the soil by the leaching solution to enhance the retention of N-containing ions in the soil [38], [39]. It will help to stimulate soil nutrient cycling and crop root development to increase crop yields [40], [41]. There are significant differences in the soil nutrient requirements of maize at different periods [42], [43], and multiple fertilizer applications can avoid the problems of the uncoordinated release of fertilizer with the growth period and excess nutrients in a single application [42], [43]. At the same time, proper application of fertilizer can effectively stimulate soil microbial activity to improve nutrient uptake by the crop [40], [41], [44].

Figure 7 (a) Crop height and (b) 100-grain fresh weight in different experiment plots. The letters “a”, “ab”, and “b” indicate the significant differences between CK and the experimental treatments.

3

Conclusions

A field experiment to optimize irrigation and fertilization was conducted to study their effects on N and P losses in farmland, and DFT calculation was employed to reveal the effects of irrigation-induced interflow on N and P losses. Optimized irrigation and fertilization have a significant impact on nutrient retention and crop productivity in the agricultural areas of the Erhai Lake basin. Quantitative drip irrigation (84 m³ ha⁻¹ per 6 days) and staged fertilizer application (elongation and 11-leaf stage) were effective in reducing N and P losses by 25.2–72.4% and 24.2–67.6%, respectively, while increasing yields by 11.3%. Furthermore, the DFT calculation clearly showed that the switching from ditch irrigation to drip irrigation significantly reduced the movement of nitrogen and phosphorus nutrients carried by irrigation water, thereby increasing the soil’s nutrient retention capacity. These findings may further expand the current understanding of the effects of irrigation on nutrient movement and have significant implications for refining agricultural management practices in the Erhai Lake basin and increasing crop yield. Importantly, these measures are critical to mitigating nutrient loss from farmland at its source and addressing the threat of non-point source pollution from agriculture in plateau lakes.

4

Materials and Methods

4.1

Site Description and Experimental Design

The field experiment was conducted from May 2023 to July 2023 in an agricultural area in the Erhai Basin of Yunnan Province in southwestern China, which has a meso-subtropical southwestern monsoon climate. The area experiences an average annual temperature of 15.5°C, with an average maximum temperature of 22.2°C and an average minimum temperature of 10.2°C. The annual rainfall ranges from 1000 to 1100 mm, with 95% of the rainfall occurring during the rainy season from May to October. The topsoil typically exhibits higher nutrient concentrations compared to the subsoil, as indicated in [Table S1] detailing the soil properties. The soil in field plots has a texture of sandy silt, with a bulk density of 1.09, 1.23, and 1.34 g kg⁻¹ at depths of 0–20, 20–40, and 40–60 cm, respectively.

The amount of fertilizer applied during the maize season was 150 kg N ha⁻¹, 90 kg ha⁻¹ for P₂O₅, and 36 kg ha⁻¹ for K₂O. The application rates for the basic fertilizers N, P₂O₅, and K₂O were 6, 6, and 8 kg ha⁻¹, respectively. The timing and quantity of topdressing were adjusted according to corn growth cycle while maintaining a constant total fertilizer rate. This included CK (T₁, topdressing at the 11-leaf stage), T₂ (topdressings at the elongation and 11-leaf stages, respectively), T₃ (topdressings at the elongation, 11-leaf, and heading stages), and T₄ (topdressings at the elongation, 11-leaf, heading, and maturity stages). The topdressing method used a pressure differential fertilizer tank for integrated fertilization of water and fertilizer. The irrigation treatments consisted of CK (furrow irrigation every 6 days), W₁ (drip irrigation every 6 days at 105 m³ ha⁻¹), and W₂ (drip irrigation every 6 days with 84 m³ ha⁻¹). Consequently, the experimental treatments included CK, W₁T₂, W₁T₃, W₁T₄, W₂T₂, W₂T₃, and W₂T₄, with three parallel plots (each with an area of 25 m² per plot) for each treatment. Other field management measures were carried out according to local conventional management practices.

4.2

Sampling and Test

A soil profile was excavated in the experimental area to investigate the physicochemical properties of the soil at different depths, as detailed in [Table S1]. After collection, samples from different soil layers were immediately sealed in plastic bags and stored at 4°C until extraction of ammonium and nitrate. Nitrogen and phosphorus concentrations in the soil samples were determined using an Auto Analyzer-AA3 (SEAL, Germany). Additionally, periodic soil samples were taken from the different depths of the profile for soil bulk density measurements [6].

Leachate from different soil layers (0–20, 20–40, and 40–60 cm) within each experimental plot was collected using ceramic suction cups [45], [46]. The leachate in the ceramic suction cup was monitored and measured every 15 days. The leachates were then stored at 4°C and analyzed within 48 h. An alkaline potassium persulfate solution was used to digest the leachate, followed by filtration of samples through a 0.45-μm membrane for the analysis of total N (TN) using an Auto Analyzer-AA3 (SEAL, Germany) [6]. Similarly, concentrations of other nutrients, including total P (TP), total dissolvable phosphorus (TDP), PO₄ ³⁻–P, NO₃ ⁻–N, NH₄ ⁺–N, and DOC, were determined using an Auto Analyzer-AA3 (SEAL, Germany) after the pretreatment of the leachates [47], [48]. Additionally, five maize plants were randomly selected from each experimental plot, and their plant height and 100-grain weight were measured to assess the effects of the different treatments on maize growth and yield.

4.3

Data Analysis

The hydraulic conductivity of soil refers to the volume of water that will move through a given area over a given time period and under a specific water potential gradient when the soil is fully saturated with water [49]. This property is influenced by soil texture, bulk density, and the distribution of pores within the soil. The spatial distribution of soil texture, bulk density, pore distribution, and organic matter content plays an important role in determining the spatial variability of saturated hydraulic conductivity (K_s ) [50]. The formula for calculating hydraulic conductivity is as follows:

K s = 10 QL ΔhAt

where Q is the stable infiltration volume (cm³), and L is the length of the cutting ring (cm). The letters h, A, and t indicate the height of the water head (cm), the cross-sectional area of the cutting ring (cm²), and the time interval, respectively. Furthermore, due to the predetermined suction range of the ceramic suction cup within the soil layer, it is possible to calculate the reduction rate (R_t ) of nutrient losses per hectare (ha) in the experimental treatments compared to the control group (CK):

R t = 1000 h V c V ck C ck − 1000 h V c V t C t 1000 h V c V ck C ck

where V_c is the suction range of the ceramic suction cup. V_ck and C_ck are the leachate volume and its nutrient concentration in the ceramic suction cup in CK, respectively. V_t and C_t mark the leachate volume and its nutrient concentration in the ceramic suction cup in treatments, respectively. The h means the soil depth. Therefore, the above equation can be simplified as follows:

R t = T ck − T t T ck

where T_ck and T_t indicate the accumulated N and P losses from leachates in CK and treatments.

Analysis of variance (ANOVA) was used to illustrate the notable differences between treatments using SPSS software (version 27.0, Inc., USA). In addition, Origin software (version 2018, USA) was utilized to compute the mean and standard deviation ([Tables S2–S11]) and to generate graphical representations.

4.4

DFT Computation

A study conducted by Song et al. suggests that the primary constituent of soil in the Erhai Lake basin is alpha quartz (α-SiO₂) with a dominant crystal face (011), as determined by X-ray diffraction (XRD) analysis [51]. Consequently, we constructed molecular models of soil based on SiO₂ with a crystal face (011) and studied the soil–water interactions and their effects on the levels of dissolved N and P. To investigate the variances in the adsorption of H₂O and solutes by soil, we used molecular dynamics calculations using the GGA and the all-electron double-numeric plus polarization (DNP) functional [52]. The adsorption capacity between soil and water, as well as nutrient solutes, was evaluated using calculated adsorption energy (ΔE _ads).

∆ E ads = E ab − E a + E b

where E_sw is the total energy of the molecular models for the mixed system of SiO₂–H₂O and H₂O-solutes, the E_a and E_b indicate the total energy of the independent molecular models for SiO₂, H₂O, and solutes, respectively. The electronic transfer between H₂O and nutrient solutes, such as NO₃ ⁻ and PO₄ ³⁻, was investigated using the electron density difference (EDD) method, with a self-consistent field (SCF) tolerance level set at 1 × 10⁻⁶ eV atom⁻¹.

Author’s Contributions

D.H.: Conceptualization, calculation, formal analysis, and draft. Y.W.: Conceptualization, calculation, formal analysis, and draft. Y.Z.: Calculation and formal analysis. W.T.: Idea, conceptualization, formal analysis, and writing—review and editing. B.Z.: Idea, conceptualization, formal analysis, and, writing—review and editing.

Conflict of Interest

The authors declare that they have no conflict of interest.

Acknowledgments

The authors thank the Key Project of the National Natural Science Foundation of China and the National Key Research Plan of China for providing the funding support for this project.

Data Availability

The datasets used or analyzed during the current study are available from the corresponding author upon reasonable request.

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Publication History

Received: 28 June 2024

Accepted after revision: 04 September 2024

Article published online:
20 December 2024