Introduction

Resistance to herbicides by weeds has resulted in an increase in the concentration used of these pesticides [1]. The world estimate of losses in agricultural production by weeds is 34% higher than the estimated losses with animal pests and pathogens (18 and 16%) [2], making the use of pesticides necessary from an economic and agricultural point of view.

In order to reduce the environmental impacts of agricultural activities, environmental legislation for the use of pesticides and herbicides is becoming increasingly stringent [3,4,5]. The excessive use of herbicides has been related to the contamination of water bodies and soils, promoting an accumulation of these persistent contaminants, result of its high stability in the environment [6, 7].

An herbicide that has been extensively used since 1974 is glyphosate (N-(phosphfometila) glycine — C3H8NO5P) (Fig. 1), which is an organophosphate with a broadly effective spectrum, non-selective, and being one of the most used herbicides in the world [6,7,8]. The solubility of glyphosate in water is 12 g L−1 [9] which justifies, together with its extensive use, its frequent detection in aquatic environments, especially groundwater from soils with shallow water table and/or low in oxides [6].

Fig. 1
figure 1

Structural representation of the glyphosate molecule

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Glyphosate can cause numerous environmental problems because it blocks an enzymatic pathway that exists only in plants and bacteria and has a toxic effect on animals [8, 10]. In this context, ways to remove this pollutant, mainly from water bodies, are of paramount importance for the protection of ecosystems and maintenance of biodiversity, requiring efficient methods with technological and economic feasibility of application [11]. Among the most used removal methods are adsorptive processes, which give good quality to the treated effluent, operational flexibility, possibility of adsorbent regeneration, and effective and economical method [12].

Activated charcoal, as adsorbent, is still widely used, removing dyes [13], metals [14, 15], and radionuclides [16], among other pollutants; however, it is a high-value alternative [8]. Thus, the search for low-cost adsorbents [11], such as agricultural waste [17, 18] and industrial by-products [19], and natural substances such as minerals [20, 21] and biopolymers [22, 23] have increased.

In the biopolymers class, cellulose stands out because it is abundant [24], presents good potential as adsorbent material, and is a non-toxic, hydrophilic, biodegradable, and chemically modifiable material [25,26,27]. Its application extends to some derivatives such as cellulose acetate, diethylaminoetil cellulose, cellulose xanthate, methylcellulose, and nitrocellulose among others that have applications in several areas besides adsorption [28,29,30,31,32,33,34,35,36].

Cellulose, together with some derivatives such as cellulose acetate, carboxymethylcellulose, and cellulose xanthate, were theoretically studied by Reis et al. [22, 37] using calculations based on the density functional theory (DFT). The biopolymers proved to be excellent adsorptive matrices for Cd2+, Cu2+, and Cr3+ metals, providing promising prospects for the application of cellulose and its derivatives.

In this context, in view of the gradual increase in glyphosate concentrations in the environment and the excellent adsorptive capacity of cellulose and derivatives, the present work aims to evaluate from theoretical calculations the interaction of glyphosate with cellulose and its diethylaminoethyl cellulose derivative in order to verify the potential for contaminant removal. It is worth mentioning that the need for efficient adsorptive materials for removing contaminants is urgent and many possibilities need to be evaluated, which makes theoretical studies the best alternatives for directing experimental research, optimizing study time, and contributing with relevant structural information on biopolymers and glyphosate.

Computational methods

The studies of adsorptive processes were carried out using the DFT [38,39,40,41] with the hybrid functional wB97XD [42] and basis set 6–31 + G(d,p) [43,44,45]. The structures of the adsorption matrices of cellulose (CE) and diethylaminoetil cellulose (DEAEC) and the glyphosate adsorbate (GLY) were optimized to the minimum of energy. To confirm that optimized structures were at their minimum energy, frequency calculations were used and no imaginary frequency was found. No dispersion model was included, because the functional wB97XD has empirical corrections of atom–atom dispersion (EDFT-D = EKS-DFT − Edisp.) [42, 46,47,48]. The effect of water as solvent was considered in the optimization and in all calculations using the continuous solvent model SMD [49]. The basis set superposition error (BSSE) was not used because in previous work, it was evaluated that the effect of the solvent significantly modifies the results of the interaction process [50] and the BSSE is evaluated for gas phase.

The energies of the molecular orbitals HOMO (highest occupied molecular orbital) and LUMO (lowest unoccupied molecular orbital) were used to obtain chemical hardness (η) and chemical softness (S). By DFT, chemical hardness can be calculated by Eq. 1 [51]:

$$\eta =\frac{1}{2}({E}_{\mathrm{LUMO}}-{E}_{\mathrm{HOMO}})$$
(1)

where ELUMO − EHOMO are the energies of the LUMO and HOMO, respectively. Equation 1 can be used taking into account Koopmans’ theorem [52].

Chemical softness is the inverse of hardness and was determined by Eq. 2:

$$S= \frac{1}{\eta }$$
(2)

Frontier molecular orbitals (FMOs) and molecular electrostatic maps (MEPs) were generated with isovalue 0.02 and density 0.001 au, respectively.

The binding energy (EBind) of the interaction process was quantified by Eq. 3:

$${E}_{\mathrm{bind}}= {E}_{\mathrm{complex}}- [{E}_{\mathrm{adsorbent}}+{E}_{\mathrm{adsorbate}}]$$
(3)

where Ecomplex corresponds to the energy of the complex (adsorbent + adsorbate) and Eadsorbent and Eadsorbate are the electronic energies of the adsorbent (adsorptive matrix) and adsorbate (glyphosate), respectively. In the electronic energy was added the zero point energy (ZPE). The Gibbs energy (ΔG) and enthalpy (ΔH) were also determined by the difference of the energies (Gibbs and enthalpy) of complex subtracted from the isolated values of the molecules, Eqs. 4 and 5:

$$\Delta G= {G}_{\mathrm{complex}}- [{G}_{\mathrm{adsorbent}}+{E}_{\mathrm{adsorbate}}]$$
(4)
$$\Delta H= {H}_{\mathrm{complex}}- [{H}_{\mathrm{adsorbent}}+{H}_{\mathrm{adsorbate}}]$$
(5)

All calculations were performed using the Gaussian 09 program [53] and some structures were drawn with the Gauss View program [54].

To characterize the interactions between glyphosate and biopolymers, as well as the nature of the interaction, QTAIM analyses [55,56,57,58,59] were performed. The parameters considered in the analyzes were electronic density (ρ(r)), laplacian of electronic density (∇2ρ(r)), potential energy density (V(r)), kinetic energy density (G(r)), and energy density at the bond critical point (BCP) (H(r)), used for all complexes. The laplacian of electronic density allows analyzing the nature of the bond/interaction. ∇2ρ(r) < 0 refers to a covalent bond, while ∇2ρ(r) > 0 indicates noncovalent bond. A joint analysis with the energy density in BCP (H(r) = G(r) + V(r)) allows a more detailed description, in which ∇2ρ(r) > 0 and H(r) > 0 indicates that the bond, or interaction, will be electrostatic, while ∇2ρ(r) > 0 and H(r) < 0 indicate that the interaction is partially covalent. All QTAIM analyses were performed using the AIMALL package [60].

Results and discussion

Structures before complexation

The biopolymers CE and DEAEC were studied using three monomeric units of each and the cut ends were completed with hydrogen atoms. This methodology was previously used by the research group [22, 23, 37] in order to achieve a lower computational cost and reduce as much as possible the loss of the original properties of CE and DEAEC. In addition to the CE, the study of the DEAEC was motivated by studies in the literature, which suggest that modified cellulose, that is, with different functional groups inserted in its structure, lead to a higher adsorption potential.

To reproduce the possibilities of adsorption of the experimental data, two oxygen were deprotonated from CE and DEAEC. In this context, the DEAEC and CE present regions with negative charges and the DEAEC presents electropositive regions, which allow evaluating the adsorption potential of biopolymers under these conditions [50, 61,62,63]. Only the adsorptive matrices were modified and the adsorbate (glyphosate) was kept in its neutral form.

Initially, an analysis of possible sites of interaction was performed and the analysis of molecular electrostatic potential (MEP), FMOs, and reactivity indices (RI) was used.

The molecular structures MEPs and FMOs for CE and DEAEC biopolymers are represented in Fig. 2. For MEPs, colors in blue tones indicate partially positive regions while red/orange colors are partially negative regions. MEP values are also represented in kcal mol−1 (Fig. 2). Thus, it is found that for CE, the MEP shows that the regions with the highest negative partial charges are concentrated in the region of (–O−) with values of ≅  − 225.90 kcal mol−1 and − 213.35 kcal mol−1. The DEAEC presents higher negative partial charges in the anionic oxygen groups (–O−) (≅ − 163.15 kcal mol−1); on the other side of the DEAEC structure, it is possible to observe a positive partial charge region located in the protonated amine group (–NH+(CH2CH3)2), ≅ 89.98 kcal mol−1.

Fig. 2
figure 2

Structural formula, molecular electrostatic potential and frontier molecular orbitals (HOMO and LUMO) for a cellulose and b diethylaminoethyl cellulose. Values of MEPs in kcal mol−1

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Analyzing the FMOs (Fig. 2), the HOMO and LUMO of the CE and DEAEC matrices can be observed. For CE, a LUMO with probability density is observed in groups –OH, while the HOMO have π orbitals in the anionic oxygen group –O−.

The DEAEC biopolymer has a high probability density in the group –NH+(CH2CH3)2 for LUMO and, at the left end, regions with some probability density for the HOMO.

Figure 3 shows the MEP and the FMOs for adsorbate. It can be observed that GLY presents a LUMO orbital with a high probability density (Fig. 3a), which indicates that an interaction may occur between LUMO (adsorbate) and HOMO orbitals of the adsorbent. On the other hand, the HOMO shows possibilities of interaction with –O− group, nitrogen and hydrogen along the molecule chain.

Fig. 3
figure 3

Representation of the frontier molecular orbitals LUMO and HOMO in (a) and in (b) molecular electrostatic potential of glyphosate. Values of the MEP in kcal mol−1

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Analyzing the MEP for the GLY (Fig. 3b), one can observe predominantly green and blue regions, that is, GLY has positive partial charges in most of its structure (values of MEPs ≅ 25.10 kcal mol−1, 59.55 kcal mol−1, and 31.38 kcal mol−1). A reddish region can be observed in the oxygen atom of the phosphate group (–PO(OH)2), ≅  − 45.81 kcal mol−1, indicating that the molecule has a significant negative partial charge in this structural part.

From the energy of the HOMO and LUMO orbitals, the reactivity indices hardness (η) and softness (S) were determined (Table 1) and follows Pearson’s acid–base theory [64, 65].

Table 1 Values of HOMO, LUMO, hardness (η), and softness (S) for the matrices (adsorbents) and the contaminant (adsorbate). Data in kcal mol−1
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The results of Table 1 show that the chemical softness and hardness are similar and it is possible to suggest that the interaction of GLY with both CE and DEAEC will be effective due to the proximity of the reactivity indices as expressed by Pearson’s concept [64, 65].

Analyzing in a general way the results of the FMO, MEP, and RI, it is possible to infer the importance of the quantum descriptors for the adsorption process because they allow to predict the interaction site, if the matrices will interact properly with the contaminate, reducing computational time, and are able to assist in the experimental part as described in several works [21, 66].

Complex structures

The post-complexation analyses were performed using the results obtained from the analyses of FMOs, MEPs, and reactivity index. The sites chosen to adsorb GLY in biopolymers were terminal groups –O− and –OH for CE and for DEAEC in the –O− and –NH+(CH2CH3)2 groups. The study was carried out using optimized structures. Figures 4 and 5 show the interaction sites analyzed.

Fig. 4
figure 4

Spatial arrangement and interaction positions for GLY and CE. In a configuration 01 (CE-GLY1) and in b configuration 02 (CE-GLY2)

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Fig. 5
figure 5

Spatial arrangement and interaction positions for GLY and DEAEC. In a configuration 01 (DEAEC-GLY1) and b configuration 02 (DEAEC-GLY2)

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The vibrational frequencies and the interaction bond lengths of the complexes formed were determined and are represented in Table 2. The bond distances determined ranged from 1.68 to 3.11 Å, indicating that the interaction actually occurs due to the proximity of the molecules. It is important to emphasize that the interactions are formed predominantly by hydrogen bonds (Figs. 4 and 5) and that the interactions of GLY with CE were those with lower bond lengths when compared to interactions in DEAEC.

Table 2 Calculated interaction distances (in Å) and vibrational frequencies (in cm−1) of GLY, CE, DEAEC, and complexes formed
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Experimental infrared (IR) data for glyphosate [68,69,70,71,72] show that the vibrational band between 1600 and 1800 cm−1 is attributed to the –CO2 group (C = O). The PO3H2 group showed stretching bands at 911–1223 cm−1 attributed to P-OH and bands in the region of 1090–1094 cm−1 and 1268–1271 cm−1 corresponding to P-O− and P = O, respectively. Angular deformations in the region of 830 cm−1 (P–O–H) and between 1483 and 1563 cm−1 correspond to C–N–H. According to the literature, these are characteristic bands for glyphosate at pH = 7 [67,68,69,70,71]. The theoretical results for glyphosate are close or within the experimental ranges (Table 2) proving that the calculations adequately describe the GLY molecule. The experimental IV for CE and DEAEC were not reported in the present work because only three monomeric units of each polymer were considered theoretically and the results may not be as suitable as for GLY.

Simulated IR after complexation showed that there is a change in vibrational bands for GLY and for the matrices (Table 2) and can be evidenced in experimental measurements proving the interaction.

Adsorption processes involve the interaction of atoms, ions, or molecules with a surface and this interaction is due to energies derived from the electronic stability of each chemical species involved in the adsorption process. In this sense, the binding energy (EBind), Gibbs energy (ΔG), and enthalpy (ΔH) involved in the interactions were calculated and are represented in Table 3. The energies were obtained in order to observe the magnitude of the interactions of the complexes formed and the spontaneity related to each interaction.

Table 3 The binding energy (EBind) at 0 K, enthalpy (ΔH), and Gibbs energy (ΔG) at 298 K for the complexes studied. Values in kcal mol−1
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From the results shown in Table 3, it can be noted that for EBind in general, the CE and DEAEC are good adsorption matrices for removing the GLY contaminant. The interaction of GLY with the biopolymers CE and DEAEC in configuration 01 were those that presented values EBind most significant for the adsorption process, which indicates that the interaction sites of Figs. 4a and 5a are the ones that best interact with the GLY molecule sites. The bond lengths for the complexes in configuration 01 were also the smallest as noted in Table 2.

The negative values ΔH prove that all processes are exothermic. The CE-GLY1 interaction showed value of ΔG < 0 indicating that this interaction is spontaneous (ΔG =  − 27.30 kcal mol−1). It is noteworthy that the effect of the solvent significantly alters the Gibbs energy values of the adsorption process as highlighted by Costa et al. [50].

In order to characterize the nature of the interactions for the complexes formed, the topological analysis QTAIM was performed and the results are shown in Table 4. Table 4 presents all topological parameters obtained from Quantum Theory of Atoms in Molecules by Bader et al. [56,57,58] for the interactions found (Figs. 4 and 5).

Table 4 Topological parameters calculated in the BCPs of the interactions. Values in atomic units (au)
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From the topological parameters, there are the following considerations: the electronic density can give indications of the strength of the interaction indirectly, because a higher value of electronic density is related to a greater bond force in the interaction BCP [71]. The CE-GLY1 complex has two strongest interactions a and c with values of ρ(r) = 0.046006 u.a. and ρ(r) = 0.038594 u.a. and the CE-GLY2 has only one strongest interaction f with value of ρ(r) = 0.049337 u.a. DEAEC-GLY1 has one strong interaction h (ρ(r) = 0.034768 u.a) and for DEAEC-GLY2, the interaction k is the most significant (ρ(r) = 0.014307 u.a.). The ρ(r) values reflect the proximity of the contaminate with the matrices as described by the bond lengths of the interactions (Table 2).

The laplacians of electronic density are positive, indicating non-covalent interaction. The interactions a, f, and i are partially covalent according to the values of ∇2ρ(r) and H(r). All other interactions found are electrostatic interactions, which adequately reflect the energy values found.

The interaction energies in the BCPs can also be estimated by the relation Eint = V(r)/2 [62, 72]. From the results (Table 4), it is possible to infer that the most effective interactions are a and c for CE-GLY1; f for CE-GLY2. For DEAEC-GLY1 is the interactions h and DEAEC-GLY2 is the interaction k. Eint values reflect the trend found for EBind and the bond lengths of the interactions.

Conclusion

The study presented the results obtained from the interactions of the cellulose and diethylaminoethyl cellulose matrices with the herbicide glyphosate, in order to verify the potential for removal of the contaminant. The analysis of MEPs, FMOs, and reactivity indices allowed to infer the probable sites of interaction of the matrices with the herbicide that were in the groups –O− and –OH of cellulose and in the groups –O− and –NH+(CH2CH3)2 of DEAEC. The QTAIM analysis corroborated with the results obtained for binding energy. Thus, the use of cellulose and diethylaminoethyl cellulose biopolymers as adsorption matrices for the removal of the glyphosate herbicide from water bodies is feasible from a theoretical point of view, presenting good results that, theoretically, enable its use as an adsorbent material for removing the herbicide.