## 1 Introduction and State of the Research  
Conventional wastewater treatment plants are not designed to efficiently remove environmentally harmful pharmaceuticals and personal care products (PPCPs) [1], one of the largest groups of emerging contaminants. With their global consumption, human's low metabolic capability, and their improper disposal [2], PPCPS (such as antibiotics, preservatives, insect-repellents, sunscreens, and non-steroidal anti-inflammatory drugs (NSAIDs) such as ibuprofen, which is the largest group of over-the-counter drugs) can penetrate the environment in many ways, such as hospital discharge, domestic wastewater, unsuitable manufacturer disposal, etc. [2]. These compounds are persistent in the environment, harmful to organisms and humans alike, and, in the case of antibiotics, might lead to the development of antimicrobial resistance. The valuable ability of low-cost natural zeolite, clinoptiolite, to be used in ion exchange or molecular sieving, for example, due to its movable extra-framework cations, can make it a suitable candidate for environmental purification such as wastewater treatment; in addition, due to its biocompatibility, it can be utilized for drug delivery applications [3, 4, 5, 6, 7, 8]. Clinoptilolites are abundant worldwide and isomorphous with heulandites but have a higher Si/Al ratio of \(\geq\)4 [9]. The Si and Al distributions within the framework strongly affect the extra-framework cations behavior. The conventional unit cell of clinoptilolite consists of 108 framework atoms and extra-framework content (M\({}_{x}\)D\({}_{y}\)) which balances the negative framework charge induced by the substitution of Si with Al as represented by the general formula M\({}_{x}\)D\({}_{y}\)[Al\({}_{x+2y}\)Si\({}_{n(x+2y)}\) O\({}_{2n}\)]\(\cdot\)mH\({}_{2}\)O, where n = 36 and x + 2y \(\leq\) 7. M and D represent the monovalent and divalent cations, respectively, and m represents the number of water molecules in clinoptilolites. The extra-framework cations encountered most frequently in clinoptilolites are Na\({}^{+}\), K\({}^{+}\), Ca\({}^{2+}\), Mg\({}^{2+}\), Sr\({}^{2+}\), and Ba\({}^{2+}\), which can be used in multiple industrial applications. H\({}_{2}\)O molecules play an important role since they establish incomplete hydration spheres by exposing their negative dipoles to the positive portion of the channel cations. The large unit cell in clinoptilolites, as well as the extra-framework cations that are movable and not confined and the complexity of the interaction between the framework, the extra-framework atoms, and water molecules, render the application of electronic structure calculations such as DFT a challenging task [10]. Although various computational methods for investigating different zeolites and their applications have been discussed, they are not often employed for clinoptilolites, with only a few exceptions that are discussed in the following. [PERSON] et al. [11] used interatomic potentials with energy-minimization procedures and Monte Carlo (MC) to study the distribution of Al in Na- and Ca-dominated dehydrated clinoptilolites. [PERSON] et al. [12] modeled two different Ca-rich natural hydrated zeolites, Goosecreekite and Gismondine, using force-field simulations after they successfully studied their aluminum distribution in dehydrated clinoptilolites; however, they found that their cationic distributions and the experimental counterpart obtained using the same potentials are somewhat different. Moreover, [PERSON] et al. [13] explored the ordering of Al atoms in heulandite-structured materials using periodic lattice simulation techniques; they also demonstrated the failure of standard MC techniques. In a follow-up work, they employed the same techniques to explore the distribution of Al in calcium heulandite lattice [14]. [PERSON] et al. investigated the distribution of cations with the ONIOM two-layer model (DFT/MM) and periodic DFT [10]. Anhydrorous and hydrated clinoptilolites were investigated by [PERSON] et al.