Molecular dynamic simulations uncover the various aspects that affect the adsorption process, such as the electrostatic interaction, binding energy, Gibbs free energy, adsorption energy and loading value. All these factors were illustrated in Figure 1. The binding energy affects the molecules’ structural stability ^[1][15], whereby the negative value of the binding energy shows that the structure is stable. Zhang et al. (2018) ^[2][16] studied the interaction at the molecular level to understand the mechanism of graphene oxide for the adsorption process of aromatic compounds. The π-π interaction was defined for geometrically optimized molecular structures and adsorption energies were calculated. The higher the adsorption energy, the more the adsorption capacity and hence the better the adsorbent. A simulation study discussing Gibbs free energy was also conducted to help in understanding the adsorption process by indicating the thermodynamic feasible interaction of the adsorbent with sorbate ^[3][17]. The negative value of Gibbs free energy indicated the spontaneous reaction, which demonstrated feasibility for the adsorbent to sorb pollutant.

The equations used to calculate the adsorption energy and interaction energy are provided in Equations (1) and (2), respectively:

In Equation (1), E₁ represents the energy of a complex comprising the adsorbent + contaminant while E₂ and E₃ correspond to the energy of the isolated adsorbent and contaminant, respectively:

For Equation (2), V_ij depicts the interaction energy while V_LJ represents the energy that was dependent upon the distance between atoms and V_C, the energy obtained by the electrostatic conversion factor.

Different types of simulation software, such as Gromacs 5.0.2 software ^[4][22], HyperChem 8 software ^[3][17], Materials Studio (MS) software ^{[3][4][5][6][7][8][9][10][11][12]}[5,13,17,18,19,20,21,22,23,24], Gaussian 09 software ^[13][14][25,26], Tera-Chem software ^[15][27] and LAMMPS software ^[12][24] were used for the molecular dynamics simulation (MDS) study. Most studies were based on the Monte Carlo simulation approach ^[9][16][20,28] and density functional theory (DFT) ^[9][17][20,29]. The Monte Carlo Simulation (MCS) approach was a collection of different methods including configurational bias simulation in which the adsorption of sorbate molecules was observed when the sorbate molecule fitted the pores of the framework without steric overlap ^[18][30]. Particularly, the Metropolis Monte Carlo was used during MCS in which the adsorption of sorbate molecules was observed by their positions and orientations while the sorbent was treated as a rigid body ^[19][31]. The Grand Monte Carlo Simulation (GMCS) approach was used to prognosticate the adsorption of pollutants on the adsorbent. A grand canonical simulation approach allows the number of molecules or particles to change, providing a convenient way to perform simulation calculations where the system is altered by external conditions ^[20][32]. By performing these calculations, adsorption isotherms were obtained and the shape of the isotherms indicated the adsorbent’s behavior for the pollutant ^[20][32].

On the other hand, the DFT calculations stated that all ground-state properties were a function of the charge density, ρ, and the total energy, E_t (kcal/mol) ^[21][33]. Different modules could be employed using DFT, in which molecular structures were optimized and adsorption energy calculations were performed to estimate adsorption during the process. For this purpose, the geometry optimization of molecular structures was initially performed to obtain the most stable structure, followed by the application of the electronic distribution density method to manipulate the charge transfer and then a molecular dynamic simulation to analyze the thermal stability that assisted in calculating the energy values for adsorption capacity estimation ^[22][34]. The molecular simulation showed great potential to predetermine the adsorption capacity of the adsorbent before proceeding with the actual process, which was costly and time-consuming to be realized from experimental interrogation ^[23][35]. Moreover, the molecular dynamic simulation provided a platform where the adsorption phenomenon was studied microscopically within a sufficient time period, economical means, and space. To date, molecular simulation is regarded as a successful research tool to explicate the adsorption process ^[6][20][13,32].

Carbon-based adsorbents are widely used in water and wastewater treatment as they are abundant and have good efficiency to adsorb pollutants from water ^[21][22][33,34]. Moreover, carbon-based compounds have great thermal stability and a good adsorption capacity ^[24][8].

It was observed that the adsorption capacity could be estimated, and the adsorption process was understood using the molecular interaction energy. With simulation calculations, the interaction energy for methylene blue adsorption on the Bituminous Coal surface was calculated to be −122.28 kJ/mol ^[25][36], suggesting a spontaneous interaction of MB with the carbon-based adsorbent. In addition, the molecular simulation illustrated that the MB molecules’ attraction with the water molecules was due to hydrogen bonding and the negative value of ΔG⁰ was in agreement with the spontaneous adsorption simulation results. The adsorption process was discovered to be affected by the electrostatic field, the pore size of the adsorbent and ultrasound waves. In a simulation study for phenol adsorption ^[4][22], it was observed that the increase in the electrostatic field enhanced the interaction energy to promote adsorption, i.e., the Van der Waals energy of C-P was −1571.21 kJ/mol under zero electrostatic field. It was seen that when there was no electrostatic field (on the left side), the Van der Waal energy was around −1500 kJ/mol, and when a 3 V/nm electrostatic field was applied, it was increased to around −1700 kJ/mol. The graphs show that when the electrostatic field strengths were increased to 1 V/nm, 2 V/nm, 3 V/nm, 4 V/nm and 5 V/nm, the values of the Van der Waals energy (VLJ) were improved (which enhanced the adsorption capacity) by −1701.38 ± 11 kJ/mol, −1768.63 ± 11 kJ/mol, −1785.83 ± 11 kJ/mol, −1798.96 ± 11 kJ/mol and −1803.04 ± 11 kJ/mol, respectively. The effect of the pore size and adsorbent concentration on the adsorption process were understood using a simulation study for phenol removal via activated carbon by Galdino et al. (2021) ^[26][37], where different carbon with varying pore sizes (e.g., 8.9, 18.5 and 27.9 Å) were simulated to observe the isotherms. It was reported that at a low concentration, a pore size of 8.9 Å was the most efficient in removing diluted phenol in water. Moreover, a smaller pore size enhanced filling, resulting in efficient adsorption ^[26][37]. Thermodynamic parameters also played a significant role in adsorption capacity, which could be influenced by the electrostatic field and ultrasound waves as they would promote a molecular interaction that enhanced the sorption ability.

Oxides and hydroxides are classified as good adsorbents because of their excellent adsorption capacity. Compounds such as graphene oxide and its derivatives are primarily used for wastewater treatment ^[8][19], while double-layered hydroxides have various remarkable applications in the field of wastewater treatment due to their excellent adsorption ability ^[25][27][36,39]. Graphene oxide and its derivatives have recently caught much attention due to their unique physicochemical properties ^[2][16]. Graphene oxide has been declared as the most promising nano-adsorbent for water treatment so far ^[16][28], which is used mostly for organics removal from wastewater ^[2][28][16,40] Double-layered hydroxides have attracted significant attention in recent years ^[29][41] and have been recognized as good adsorbents because of their high surface area and ion exchangeability ^[25][27][36,39]. A combination of double-layered hydroxide and graphene oxide was also introduced for wastewater treatment, which demonstrated a remarkably excellent adsorption capacity for the removal of dye pollution from wastewater ^[30][42]. Another attractive class of oxides and hydroxides is functionalized mesoporous silica, considered one of the best adsorbents due to its high adsorption performance and well-organized pore system ^[3][7][17,18].

It was found that the Gibbs free energy, binding energy and adsorption energy helped in determining the adsorption capacity of the adsorbent. Delgadillo-Velasco et al. (2018) ^[3][17] studied the adsorption of phosphates on various adsorbents including classes of oxides and hydroxides, which were proven to be the best adsorbent for phosphate removal from water with a maximum adsorption capacity of 193.75 mg/g at pH 7 in comparison to natural zeolite and silica with adsorption values of only 2.92 and 4.17 mg/g, respectively. Moreover, the Gibbs free energy of −21.38 kcal/mol revealed that it was possible to recover the phosphates and reuse them later. AThis simulation study could help in future research to understand the recovery of metal elements after the adsorption process. The class of oxides and hydroxides achieved the maximum value of −21.38 kcal/mol.

Meng et al. (2018) ^[9][20] studied the binding energy and interaction of adsorbents for the removal of methyl orange and Cr anionic contaminants from mixed wastewater by Zn-Al layered double hydroxides. They found that the negative charge part of the contaminant was very close to the LDH layers and reaffirmed the interaction between OH and LDH. Moreover, the binding energy between the ZnAl-LDH layer and MO was more than the binding energy between the ZnAl-LDH layer and Cr, e.g., 4.56 eV versus 3.73 eV. So, methyl orange had a stronger affinity than Cr for ZnAl-LDH layers. Cao et al. (2021) ^[31][43] and Pelalak et al. (2021) ^[13][25] determined adsorption energies for the estimation of the adsorption capacity in the removal of dyes (TAF/MPS-water-RB and TAF/MPS-water-NR) using amino-functionalized silica, which was simulated to be −211.8159 and −4.8448 kcal/mol, respectively ^[31][43]. So, for the removal of cationic dyes, TAF/MPS (3-Trimethoxysilylpropyl) with a diethylenetriamine linker was proven to be an efficient adsorbent. The latter also studied functionalized meso-silica for the adsorption of different pollutants in wastewater, and calculated the adsorption energy with a simulation study, which was obtained at −113.92, −247.00 and −166.01 kcal/mol for MPS-linker-water-NR, MPS-linker-water-CV and MPS-linker-water-OII, respectively. The adsorption energy of MPS-linker-water-NR was less negative than that of MPS-linker-water-CV and MPS-linker-water-OII.

A molecular simulation helped determine the adsorption sites and indicated how adsorption increased with the introduction of other compounds and elements, i.e., the introduction of the GO layers into the LDH structure. The interaction energy represented the stability of the sorption system, with the more negative value having more stability. Chang et al. (2019) ^[8][19] systematically calculated adsorption energies to investigate the interaction of dye molecules with graphene oxide (GO) in a study of organic pollutants removal by a magnetic CoFe₂O₄/graphene oxide adsorbent. The negative interaction energy between the dye and the GO model suggested greater stability of the adsorption system, in which the calculated adsorption order of GO with the three dyes was MB > RhB > MO at −1.523, −1.505, and −0.209, respectively. Dhar ^[30][42] also studied the interaction of methylene blue (MB) with graphene oxide (GO) layers and observed a significant attraction between the MB molecules and GO layers of the composite. Dhar found three major interactions in the simulation environment, in which the hydrogen bonding interaction, pi donor interaction and non-bonding interaction in between oxygen and sulfur were clearly observed. The values of these interacting distances were 2.49–3.04 Å for the nonclassical hydrogen bonds between hydrogen and oxygen C−H···O, 2.45–3.00 Å for the pi-donor interaction H−O and 3.29 Å for the non-bonding interaction between sulfur···oxygen.

Zeolite compounds are regarded as a unique and distinct class of adsorbents due to their ion exchangeability and well-defined structures ^[28][32][33][3,40,44]. These compounds are mostly used for environmental applications and also in the field of wastewater treatment because of their low cost and high surface area.

The simulation study for different zeolites revealed that the adsorbent’s structure and surface-to-volume ratio played a significant role in the adsorption process. Bedneezad et al. (2019) ^[32][3] studied the adsorption of methylene blue dye on natural clinoptilolite and clinoptilolite modified by iron oxide nanoparticles and concluded that effective adsorption happened as a result of the high surface-to-volume ratio of the modified adsorbent as well as the density of the functional groups. In a simulation study for the adsorption of Cu²⁺, Cd²⁺ and Pb²⁺ ions on different sodium-based zeolites ^[12][24], it was found that different zeolites have varying tendencies to adsorb them. The LTA/Na zeolite showed the highest adsorbed ions of 69% while the FAU structure showed the lowest with 46% for cadmium adsorption. For Pb²⁺, LTA also had maximum adsorbed ions of 53%. On the other hand, for the Cd ion adsorption, the EDI zeolite showed a good percentage with 61%. Different zeolites had different tendencies to attract different ions or pollutants; similarly, different zeolites were elucidated to have different adsorption performances at varying temperatures. Mohammed et al. (2019) [5] performed a simulation study for a faujasite-type Y zeolite at three different temperatures of 293, 303 and 313 K. It was found that the phenol adsorption decreased (84, 82 and 80 mg/g, respectively) with greater temperature due to increased entropy.

The size of the adsorbent also played a significant role in the adsorption process. Dryaz et al. (2021) ^[17][29] demonstrated in their study that the adsorption energy was affected by the size of the adsorbent. It was observed that for red dye adsorption on zeolite clinoptilolite, the size of the adsorbent simulation cell affected the adsorption energy value, in which an increase in the size of the box decreased the value. The adsorption energy values were obtained at −42.22350801, −40.83882700 and −38.15356471 kcal/mol, respectively. Another factor that affected the adsorption process was the electrostatic interaction, which helped to promote the adsorption phenomenon. Capa-Cabos et al. (2021) ^[34][46] studied this for the adsorption of phosphate pollutant on a faujasites zeolite. They found that the electrostatic interaction of the ions and oxygen atom from the zeolite promoted adsorption via the change in hydrogen atoms arrangement. In the heavy metal sorption by zeolites, the sorption isotherms were studied ^[35][14], and the loading per cell indicated the adsorption capacity. The loading value of the lead ions on zeolite was determined and a maximum loading value of 728 was obtained for the CLO zeolite framework while MWF showed maximum loading for the Cadmium ion with a loading value of 450. Hence, every zeolite had a different tendency to sorb various contaminants.

A new class of hybrid material used for different applications of separation and purification is the metal–organic framework ^[10][36][37][21,45,47]. Their exceptional good qualities, which include low density and big pore size, have attracted a notable amount of attention among various classes of adsorbents ^[38][48].

In the view of research related to the simulation study of wastewater treatment using the metal–organic framework (MOF), it was found that different MOF exhibited different binding properties for the same pollutant. In the simulation study of androgens and progestogens removal from water, four other MOFs, i.e., MIL-101(Cr), MIL-100(Fe), MIL-53(Al) and UiO-66(Zr) were studied ^[38][48]. The binding energies were calculated for these adsorbents, and it was found that UiO-66(Zr) had the highest adsorption capacity with a binding energy of −7.96 kcal/mol. The surface of the adsorbent played a significant role in the adsorption process. In the simulation study for the adsorption of endocrine-disrupting compounds and the pharmaceuticals/personal care products study conducted by Li et al. (2021) ^[39][53], they revealed that the adsorption energies of the DBP/MONTs (hkl) interfaces were dependent upon the surface. The values obtained for the (0 0 e1), (1 0 0), (1 1 1) and (2 1 0) surfaces were reported to be 2.60 × 10⁵, −3.62 × 10⁴, 4.88 × 10⁴ and 2.89 × 10⁵ kcal/mol, respectively.

In a study on the capture of pesticides from wastewater using the Zeolitic imidazolate framework ^[7][18], the loading value of prothiofos and ethion obtained for the ZIF-8 unit cell with a size of 2 × 2 × 2 was 14 and 11 molecules, while for ZIF-67, there were 10 and 9 molecules, respectively. So, the adsorption capacities of prothiofos onto ZIF-8 and ZIF-67 were 366.7 and 261.1 mg/g, respectively. ZIF-8 proved to be a better adsorbent for prothiofos contaminants and also for ethions with an adsorption capacity of 279.3 mg/g. Firouzjaei et al. (2020) ^[40][50] and Abdelhameed et al. (2021) ^[41][51] observed adsorption energies to estimate its capacity for contaminant removal. Firouzjaei et al. (2020) ^[40][50] studied the graphene oxide-copper-metal organic framework nanocomposite for dye removal, and obtained an adsorption energy of −323 and −119 kcal/mol for GO-Cu-MOF and Cu-MOF, respectively. GO-Cu-MOF served as a better adsorbent than Cu-MOF for dye removal from water. Abdelhameed et al. (2021) ^[41][51] studied amino-functionalized Al-MIL-53 for the adsorption of a dimethoate pesticide, in which the adsorption energies were calculated for two surfaces of Al-MOF. In their study, it was found that the MOFs (001) surface had greater adsorption energy than the MOFs (100) surfaces. The maximum adsorption energy was obtained using Al-BDC-NH₂ at −31.4 and −46.1 kcal/mol for surfaces 001 and 100, respectively. The adsorption energies were increased with BDC-NH₂ contents as HBs formed between MOF-amine groups with the dimethoate molecules.

Among all adsorbents, clay is the most commonly used and inexpensive adsorbent. It is naturally available and widely used in water and wastewater treatment fields ^[39][42][43][52,53,54].

The molecular dynamics simulation for clay as an adsorbent uncovered the various factors that affected the adsorption phenomenon. Bergaoui et al. (2018) ^[44][55] studied the adsorption mechanism of methylene blue onto organo-bentonite and found that the adsorption of MB occurs on the bentonite as well as on the rarasaponin parts. No hydrogen bonding was observed. Van der Waals forces were repulsive for rarasaponin/MB with a strong electrostatic interaction with and attraction for bentonite/MB with zero electrostatic forces, in which Bentonite was calculated to be 12,750.27 kcal/mol while rarasaponin was 138.586 kcal/mol. Ouachtak et al. (2020) ^[45][59] calculated the adsorption energy for the sorption of Rhodamine B dye on the magnetic montmorillonite composite γ-Fe₂O₃@Mt. Their results showed that the adsorption energy of a single RhB molecule adsorbed on the maghemite (311) nanosurface, was the lowest among the five studied surfaces with a value of −1259.9 kcal·mol⁻¹, indicating that it was most preferred for RhB removal. According to Hounfodji et al. (2020) ^[46][58], clay was a cheap and good quality adsorbent with a regeneration ability for pharmaceutical wastewater treatment in comparison to carbon-based compounds, i.e., activated carbon, which had a low regeneration ability with expensive preparation methods. In the research study for molecular insights on the adsorption of some pharmaceutical residues, it was found that paracetamol was strongly adsorbed on kaolinite with an adsorption energy of −159.4 kJ/mol.

No doubt, many improvements have been observed in the adsorption process with the modification and studying of adsorbents, but the diversity and operating range of studies are still limited. The study of adsorbents is highly attractive for future considerations due to their advantages of being portable and easy to maintain. There are very few simulation studies discussing adsorbent regeneration and reuse. Most of the spent adsorbents can be potentially recovered, regenerated, and further managed through reuse or safe disposal. But it may not be something potentially plausible to be conducted using molecular simulation at the moment due to challenges such as technical barriers in molecular modeling, including adsorbent aging, the plant operational environment, etc. ^[23][35]. In addition, this can be attributed to a limitation of the molecular simulation approach to model equilibrated chemical reactions and differences in the time scale between the simulation window and the actual regeneration process for properly sampling and equilibrating these systems. There are some simulation studies discussing adsorbent recovery using thermodynamic properties. Delgadillo-Velasco (2018) ^[3][17] stated in their study that for phosphates removal from water using molecular simulation studies, iron(III) hydroxide allowed the formation of the complex ≡FePO₄H₂, with a Gibbs free energy of −21.38 kcal/mol, and could again become FeOOH, which showed that it was possible to recover the phosphates and reuse them later. The separation of contaminants from the adsorbent would provide adsorbents for reuse.

In addition, there are still limited studies regarding the screening of adsorbents using molecular simulations for different contaminants such as heavy metal elements (i.e., mercury, arsenic, etc.) removal to represent varying water resources. Therefore, more future works are necessary to predict the performance of the adsorption process for contaminant removal from water and to investigate it under a broad range of operating conditions. It will help better understand the adsorption mechanism on various adsorbents using a feasible and low-cost research approach to help select the best material for a specific application. Over and above, molecular simulations can also serve in exploring new adsorbents in the field of water and wastewater treatment.