Recent advances in in silico design and characterization of superalkali-based materials and their potential applications: A review

In the advancement of novel materials, chemistry plays a vital role in developing the realm where we survive. Superalkalis are a group of clusters/molecules having lower ionization potentials (IPs) than that of the cesium atom (3.89 eV) and thus, show excellent reducing properties. However, the chemical industry and material science both heavily rely on such reducing substances; an in silico approach-based design and characterization of superalkalis have been the focus of ongoing studies in this area along with their potential applications. However, although superalkalis have been substantially sophisticated materials over the past couple of decades, there is still room for enumeration of the recent progress going on in various interesting species using computational experiments. In this review, the recent developments in designing/modeling and characterization (theoretically) of a variety of superalkali-based materials have been summarized along with their potential applications. Theoretically acquired properties of some novel superalkali cations (Li3 +) and C6Li6 species, etc. for capturing and storing CO2/N2 molecules have been unveiled in this report. Additionally, this report unravels the first-order polarizability-based nonlinear optical (NLO) response features of numerous computationally designed novel superalkali-based materials, for instance, fullerene-like mixed-superalkali-doped B12N12 and B12P12 nanoclusters with good UV transparency and mixed-valent superalkali-based CaN3Ca (a high-sensitivity alkali-earth-based aromatic multi-state NLO molecular switch, and lead-founded halide perovskites designed by incorporating superalkalis, supersalts, and so on) which can indeed be used as a new kind of electronic nanodevice used in designing hi-tech NLO materials. Understanding the mere interactions of alkalides in the gas and liquid phases and the potential to influence how such systems can be extended and applied in the future are also highlighted in this survey. In addition to offering an overview of this research area, it is expected that this review will also provide new insights into the possibility of expanding both the experimental synthesis and the practical use of superalkalis and their related species. Superalkalis present the intriguing possibility of acting as cutting-edge construction blocks of nanomaterials with highly modifiable features that may be utilized for a wide-ranging prospective application.

In the advancement of novel materials, chemistry plays a vital role in developing the realm where we survive. Superalkalis are a group of clusters/molecules having lower ionization potentials (IPs) than that of the cesium atom (3.89 eV) and thus, show excellent reducing properties. However, the chemical industry and material science both heavily rely on such reducing substances; an in silico approach-based design and characterization of superalkalis have been the focus of ongoing studies in this area along with their potential applications. However, although superalkalis have been substantially sophisticated materials over the past couple of decades, there is still room for enumeration of the recent progress going on in various interesting species using computational experiments. In this review, the recent developments in designing/modeling and characterization (theoretically) of a variety of superalkali-based materials have been summarized along with their potential applications. Theoretically acquired properties of some novel superalkali cations (Li 3 + ) and C 6 Li 6 species, etc. for capturing and storing CO 2 /N 2 molecules have been unveiled in this report. Additionally, this report unravels the first-order polarizability-based nonlinear optical (NLO) response features of numerous computationally designed novel superalkali-based materials, for instance, fullerene-like mixed-superalkali-doped B 12 N 12 and B 12 P 12 nanoclusters with good UV transparency and mixed-valent superalkali-based CaN 3 Ca (a high-sensitivity alkali-earth-based aromatic multi-state NLO molecular switch, and leadfounded halide perovskites designed by incorporating superalkalis, supersalts, and so on) which can indeed be used as a new kind of electronic nanodevice used in designing hi-tech NLO materials. Understanding the mere interactions of alkalides in the gas and liquid phases and the potential to influence how such systems can be extended and applied in the future are also highlighted in this survey. In addition to offering an overview of this research area, it is expected that this review will also provide new insights into the possibility of expanding both the experimental synthesis and the practical use of superalkalis and their related species. Superalkalis present the intriguing possibility of acting as cutting-edge construction blocks of Introduction Superalkalis are one distinct class of superatoms that consist of characteristics similar to those of alkali metals but have a substantially lower ionization potential (IP) than them (Wang et al., 1999). As a result, due to their low IPs, superalkalis quickly lose their valence electrons (Gutsev and Boldyrev, 1982;Jena, 1995, Khanna andJena, 2011). Gutsev and Boldyrev were the first to make use of the term "superalkali" in 1982 to refer to the distinct electronic structures of numerous radical forms of lithium and sodium-related species (Gutsev and Boldyrev, 1981). Recent research has proven that superalkalis are the superior supplier of extra electrons for creating novel materials with high initial hyperpolarizabilities than other materials that drop electrons rapidly from their outermost shell (Wang et al., 2012;Sun et al., 2014b, Sun et al., 2014a, Sun et al., 2016a. These species can give one electron to other molecules and survive as cations due to their IPs being lower than those of the alkali metal atoms (5.39-3.89 eV) in the periodic table of all elements (Lias et al., 1988) which means that they are more reactive even though they do not always resemble other elements . Researchers are constantly executing appropriate research work on the designing and characterization (experimentally or theoretically) of the superalkalis along with their potential applications. Nowadays, scientists have put significant effort into creating and describing diverse comical superalkali-based species.
The standard formula for superalkalis is M k+1 L, where k is 1 for L (F, Cl, Br, and I) and 2 for L (O) atoms; Li n X (Velickovic et al., 2006;Velickovic et al., 2007;Velickovic et al., 2012) extended to K 2 X (X = F, Cl, Br, and I) (Velickovic et al., 2011) and Li 3 O (Zintl and Morawietz, 1938;Kudo et al., 1978;Wu et al., 1979) are two instances that come up frequently in this series. Li 2 F has been the subject of extensive theoretical (Gutsev and Boldyrev, 1982;Honea et al., 1989, Honea et al., 1993Rehm et al., 1992;Koput, 2008;Wright et al., 2009) and experimental (Yokoyama et al., 2000;Neskovic et al., 2003;Fernandez-Lima et al., 2009) research. Well-known superalkalis, M 3 O (M = Li, Na, and K), have a greater propensity than their equivalent alkali atoms to lose an outer electron (Gutsev and Boldyrev, 1987;Rehm et al., 1992). Comprehensive experiments on the superalkalis having one nonmetal acting as the central atom (B, N, and O) connected by the alkali metal atoms can be seen in the literature, for instance, OM 3 (M = Li, Na, and K) (Wang et al., 2011;Zein and Ortiz, 2011), NLi 4 (Rehm et al., 1992), CLi 5 , SiLi n (n = 1-5), CLi 6 (Schleyer et al., 1983;Otten and Meloni, 2018), and BLi 6 . Next, a comprehensive work based on the in silico approach for binuclear superalkali cations having the formula M 2 Li 2k+1 (M = F, O, N, C, and B for k = 1, 2, 3, 4, and 5, correspondingly) was reported by Tong et al. (2009). Furthermore, using the ab initio-based inspections, a series of binuclear superalkali cations M 2 Li 2k+1 + (F 2 Li 3 + , O 2 Li 5 + , N 2 Li 7 + , and C 2 Li 9 + ) was proposed by the same group (Tong et al., 2011). Then, focusing on the expansion from mono to binuclear superalkali cations, attempts have been made by Tong et al. (2012) in describing polynuclear superalkali cations YLi 3 + (Y = CO 3 , SO 3 , SO 4 , O 4 , and O 5 ) (Tong et al., 2013). The aforementioned remarkable cations/compounds offer a great deal of potential for use in the production of novel chargetransfer (CT) salts and cluster-assembled nanomaterials with customized characteristics, the reduction of carbon dioxide (CO 2 ), and activation of very stable nitrogen molecules (N 2 ), nitrogen oxides (NO), or as hydrogen (energy) storage materials as well as noble-gas trapping agents, ferroelectrics, catalysts, and nonlinear optical (NLO) response, among other things (Zhang et al., 2021b;Zhang et al., 2021a). These molecular species have the capability to reduce substances and can be employed to produce various cutting-edge building blocks of nanoscale materials having highly tunable features, particularly the CT salts. The superalkali cations can produce the CT salts such as a crystal salt Li 3 O + NO 2 − consisting of a single singly charged superalkali cation (Li 3 O + ) (introduced by Zintl and Morawietz, 1938) that alkali elements cannot because of the unfavorable energetics, the metal atom's relatively high IP, or steric hindrance (Li et al., 2008;Tong et al., 2009). Subsequently, the real nature of sodium nitrate (NaNO 3 ) was revealed to be sodium oxide nitrite, Na 3 O + (NO 2 ) − (Jansen, 1977). They can be utilized to create uncommon CT salts whose counterparts have a low electron affinity (EA). In silico design and characterization of superalkalis based on Zintl ions and the superatom compounds with an NLO response have been reported by some research groups along with Zintl clusters as a new class of superhalogens which can be seen in the literature (Reddy et al., 2018b, Reddy et al., 2018aSun et al., 2018;Sinha et al., 2022). Design, synthesis, and potential applications of new materials consisting of large second-order NLO responses (involving optical data storage, optical computing, telecommunications, optical information processing, etc.) have gained increasing attention (Chemla and Zyss, 1987;Prasad and Williams, 1991;Bredas et al., 1994;Geskin et al., 2003). Several reports on organic Frontiers in Chemistry frontiersin.org 02 molecules consisting of donor-acceptor-(D-A) or donor-πconjugated bridge-acceptor (D-π-A) skeletons can be seen in the literature which demonstrate considerably large first hyperpolarizabilities and show high photovoltaic performance in developing new non-fullerene small-molecule acceptors (Marder, 2006;Wei et al., 2022). Such frameworks found with larger CT in the systems can establish substantial differences between the dipole moments of the ground state and the excited state as well as low-energy CT transitions (Xu et al., 2007). For example, a sequence of formal D-A chromophores is expected to show a significant NLO response and high stability when M 3 O (electron donor) interacts with its counterpart, BC 59 (electron acceptor), and creates the CT dyads as M 3 O-BC 59 (Tu et al., 2014).
Moreover, superalkali cations may interact with superhalogen anions, just like alkali metal cations, and this interaction is predicted to be stronger than the former due to the even lower IPs of the superalkalis. The ability of the superalkali clusters to replicate the chemical behavior of alkali metals makes them potentially useful as building blocks in the construction of innovative nanostructured materials, which is one of their most intriguing discoveries. In some situations, they can combine to form assemblies or super-atom compounds while retaining their identity, much like regular atoms, and thus can demonstrate unique chemical or tunable electronic characteristics. Examples include BF 4 -M (M = Li, FLi 2 , OLi 3 , and NLi 4 ) (Yang et al., 2012), BLi 6 -X (X = F, LiF 2 , BeF 3 , and BF 4 ) (Li et al., 2008), Na 2 XY (X = SCN, OCN, and CN; Y = MgCl 3 , Cl, and NO 2 ) (Anusiewicz, 2010), and Al 13 (K 3 O) as well as Al 13 (Na 3 O) (Reber et al., 2007). As a result, it makes sense to study the characterization and prediction of the superalkalibased clusters. Recent investigations have attempted to suggest various unique superalkali species (Sun et al., 2016bTkachenko et al., 2019;Ye et al., 2022;Sun et al., 2022), including organic heterocyclic superalkalis [C 3 N 2 (CH 3 ) 5 acquired from a familiar aromatic heterocycle, pyrrole] , organo-Zintl superalkalis (P7R4)   (Hou et al., 2013), and aromatic superalkali species [MLi n+1 + aromatic superatom cations and Au 3 core connected with pyridine (Py) and imidazole (IMD) ligands] (Sun et al., 2013;Parida et al., 2018) (33a, 33b).
As was earlier mentioned, the superalkali clusters are a common type of super-atoms that can function as alkali metal atoms, so they can construct an extended nanostructure when put together (Reber et al., 2007;Reber and Khanna, 2017). Additionally, it has been suggested that superalkali cations could act as hydrogen storage materials (Barbatti et al., 2002;Giri et al., 2011;Pan et al., 2012) and noble gas-trapping agents (Chakraborty et al., 2010;Pan et al., 2013a;Pan et al., 2013b). For instance, Giri et al. (2011) (Pan et al., 2013a) and up to 12 Xe atoms (Pan et al., 2013b). The trinuclear Au 3 (IMD) 3 [IMD = imidazole] combination turns aromatic, according to a recent work on the construction of a novel family of organometallic superalkali compounds (Gutsev and Boldyrev, 1982;Gutsev and Boldyrev, 1985;Parida et al., 2018;Tkachenko et al., 2019). Examining large systems such as fullerenes, the prediction of superalkali@C60 endofullerenes, their enhanced stability, and interesting properties have been reported comprehensively by Misra et al. in 2016 along with an understanding of the nanoconfinement effect on halogen bonding in (CH 3 Br···NH 3 )@C 60 (Srivastava et al., 2016b;Srivastava et al., 2016a).
Even though superalkalis have advanced significantly over the past several decades, an overview of the recent advances in a variety of remarkable species appears to be missing in the literature Pal et al., 2021). The most advanced developments in recent years, design/ modeling, characterization in the framework of in silico approaches, and first-time use of superalkali-based novel materials are outlined in this review along with their potential applications. We attempted to share the predictions for their future growth in the hopes of pointing designers in the right direction as they continue to create and use such special species. We believe that this report can open new directions in the organized interpretation of the superalkali-based materials.

Results and discussion
In this section, the authors have attempted to provide snippets on the structure, stability, and electronic features of various superalkali-based species such as NM 4 (M = Li, Na, and K) superalkalis; ab initio exploration of the polynuclear K-and Na-based superalkali hydroxides as superbases; theoretical studies on the hydration effect on the superalkali cations, Li 3 + ; and the role of the size and composition on the design of superalkalis. Moreover, in terms of the applications of a range of superalkali-based materials (i.e., high-performance NLO material/molecular switch), design and characterization (theoretically) of a novel series of D-A frameworks through superalkali-superhalogen assemblage, superalkalis doped with B 12 N 12 nanocages, boron phosphide nanocages doped with superalkalis as novel electrides, and innovative inorganic aromatic mixed-valent superalkali electride, CaN 3 Ca, have been highlighted in this report. This report unravels a brief overview of the capturing of nitrogen by unveiling the potential of superalkali cation Li 3 + and the reduction/activation of carbon dioxide with a superalkali. A short description of the modeling of aromatic organometallic superalkali complexes and superalkali ligands as the building blocks for aromatic Frontiers in Chemistry frontiersin.org 03 trinuclear Cu(I)-NHC complexes, the nature of the aluminum trimer combined with different superatom clusters, superalkali-alkalide interactions, ion pairing in low-polarity solvents, and lead-based halide perovskites associated with superalkali species have been reported.

Structural and electronic features of superalkali-based species
Superalkalis are known as super-atoms which can imitate the chemistry of atoms and can be used in the synthesis of novel materials with diverse interesting features. Using high theoreticallevel Gaussian 3 (G3) calculations, Zhang and Chen proposed models of a small series of superalkali NM 4 (where M = Li, Na, and K) (see Figure 1A) clusters consisting of homo-and hetero-alkalis, and studied their stability and electronic structures . The calculated vertical IPs (3.22-3.74 eV) have been found to be smaller than that of the Cs atom having an IP value of 3.89 eV, and binding energies (BEs) and positive energies of the dissociation channel such as (NM 3 + M') confirmed the stabilities (thermodynamically) of all probed species where NLi 4 was found to be the most stable among all the homo-and hetero-superalkalis. The order of the calculated BEs for the NM 4 clusters was found to be NLi 4 (−9.25 eV) > NNa 4 (−5.88 eV) > NK 4 (−1.92 eV), separately, where the size of the alkaline atoms has a substantial impact on the overall stability of the clusters when such atoms are combined, followed by ionic bond formation. Encouraged by the reports highlighted in this study, novel materials can be constructed by the previously designed and characterized (theoretically) species having high stability along with tetrahedral geometry. It is important to note that the structures of the NM 4 species with homogeneous alkali atoms (like NLi 4 , NNa 4 , and NK 4 ) have Jahn-Teller distortion-resistant T d symmetry, while the clusters constructed from the heterogeneous alkali atoms have C 3v symmetry. Furthermore, the Frontier molecular orbital (FMO) approach appeared to show that the highest occupied molecular orbitals (HOMOs) of all such species are mainly spread over the complete clusters shown to diminish the repulsion among the electrons repelling each other. Their ab initio modeling approaches (MP2/MP4) described the highly symmetric structural parameters and the low IP values of the NM 4 clusters from the electronic origin point of view. It is to be noted that although significant signs of progress have been made in designing, synthesis, and characterization of superhalogens, there is still room for related studies on superalkalis. With the combination of superalkalis having low IPs and superhalogens having high EA, super-ions may be used as construction blocks of a novel series of supersalts having uses in multiferroic materials, metal-ion batteries, solar cells, and so on. Jena et al. thoroughly described the role of size and composition in the design of supersalts consisting of two dissimilar classes of clusters belonging to the closo-borane family, Li m B n X n (m = 1-3; n = 6, 12; X = H, F, and CN) and Zintl ion family, Li m Be@Ge 9 , in the framework of the density functional theory (DFT) with hybrid exchange-correlation functional (ωB97xd) as well as Gaussian basis sets [6-311+G (d, p)] (Banjade et al., 2021). In this work, the stabilities of such a composition of clusters were regulated by the Wade-Mingos polyhedral skeleton electron pair theory (i.e., shell closure rule), and additionally, the jellium shell closure rule was deployed to understand the stability of the Be@Ge 9 cluster. The analyzed IP values were well-connected to the EAs of the X ligands (the higher the EA, the larger the IP). They found that like the lowest IP value (2.84 eV) for Li 3 B 6 H 6 among Li 3 B n X n clusters, both the closo-borane family and Zintl ion-related clusters followed the same IP patterns; however, conversely and beyond the hope, the IP values were not reduced (n = 6-12) with enhancing the cluster volume followed by being weakly bounded. It should be noted that EAs of the B n X n enhanced proceeding from n = 6 to n = 12, since the association of the Li atoms with the B 12 X 12 cluster is stronger than that with the B 6 X 6 cluster. Likewise, as the substitution of the X travels from the H atom to the F atom to the CN group in the Li 3 B 12 X 12 clusters (X = H, F, and CN), the IP values are enhanced. The charge density difference (CDD) plots were visualized for all six species (three closo-borane and three Zyntl ion families). For example, in the case of Li 3 B 6 H 6 , the CDD showed that the electrons have been amassed in the area sandwiched between the three successive Li-B bonds and uniform diffusion of the electron near the Li-B bonding region (see Figure 1B), whereas a much larger charge accumulation between the Li and F atoms can be seen for the Li 3 B 6 F 6 cluster. These findings were consistent with the structural features. Furthermore, electron accumulation along the Li-C bonds for the Li 3 B 12 X 12 clusters demonstrated that the Li atoms were bonded to mostly the X atoms (see Figure 1C) which agreed with their geometries. Very importantly, however, there was an increment in the cluster volume and the F atom, as well as the CN group consisting of more electronegativity than the H atom, and stronger interactions between the cluster and the Li atoms have been observed. The IPs of the Zintl-ion family clusters were found to be higher than those in the closo-borane-family clusters since these behave like superalkalis. Very interestingly, it is noteworthy to mention that despite having the same electron count in both the Li 5 Ge 9 and Li 3 Be@Ge 9 clusters, the IP of the former is found to be smaller than that of the latter, implying that, indeed, composition matters therein.
Using the ab initio modeling approach, Li et al. reported an extensive study on the influence of hydration on the structure, stability (through energy decomposition analyses), and electronic features of the superalkali cation Li 3 + in the framework of the MP2/6-311++(d, p) level of theory (Hou et al., 2018). Assuming all possible arrangements of H 2 O molecules around the Li 3 + cation, a series of Li 3 + (H 2 O) n (n = 1-5) structures (see Figure 1D) have been obtained where the Li 3 + cation is observed to have a maximum of four coordination numbers.
Interacting with five molecules of water, the CT of the Li 3 + cation appeared to be critically irregular which was shown by natural population analysis (NPA), and as a result, the Li 3 + cation lacks the ring conjugation and comes apart into the isomer of Li ) at 298.15 K, the lowest-energy isomers of Li 3 + (H 2 O) n (n = 1-5) are not appropriate for detaching spontaneously. It is important to mention that a coordination number of 12 has been vaticinated for the Li 3 + cation associated with hydrogen clusters. The outcomes of the in silico approach revealed that structural and electronic integrity was maintained by the Li 3 + cation followed by low-lying isomers of the Li 3 + (H 2 O) 1-4 complexes, while in the lowest-energy structure of Li 3 + (H 2 O) 5 , it destroyed and left its superalkali individuality. Based on such findings, like Li + in water clusters, the superalkali Li 3 + cation contributes to the same maximum coordination number. Like the case of the lithium-ion hydrates, the localized molecular orbital energy decomposition approach showed that the electrostatic interactions play a prime role in the binding of the water molecules with the Li 3 + cation. A sharp increase in the contribution of the exchange-repulsion energy can be seen when the number of water ligands arrives at five and even this exchange-repulsion energy surpasses that of the electrostatic term.
Very recently, computational designing and characterization of Na-and K-based superalkali hydroxides acting as superbases have been reported by S. K. Pandey for the first time (Pandey, 2021b). A new kind of hydroxide of the superalkalis (XM n+1 OH) [where the fragment XM n+1 refers to the superalkali moieties, X (F, O, and N), and n ≥ 1] has been modeled, and inclusive computational experiments on such fascinating species have been performed using the framework of the ab initio method (see Figure 1E). To inspect the relative basic nature of such polynuclear superalkali hydroxides (SAHs) against the representative alkali metal hydroxide (KOH, NaOH, and LiOH) along with the Li-related SAHs, the ab initio findings demonstrated that both the Na-and K-based SAHs are stronger bases than the LiOH and Li-related SAHs which is due to the larger gas-phase proton affinity (PA) and gas-phase basicity To probe the structure, stability (bonding features), and electronic properties of the SAHs, the popular noncovalent interaction (NCI)-plot and quantum theory of atoms in molecules (QTAIM) tools were used for a variety of chemical to biochemical species to materials along with exploration of the computational studies on the HAP biomaterials including the first-principle DFT, ab initio modeling, and molecular dynamics simulations (Awasthi et al., 2021a;Awasthi et al., 2021b;Pandey, 2021a;Pandey and Arunan, 2021). In this report, new insights into the basicity features were facilitated by an ab initio modeling approach. Design, fabrication, and synthesis of the theoretically explored SAHs may lead to providing an alternative pathway for the experimentally availing applications.
High-performance NLO response material/molecular switch Very recently, Bano et al. presented theoretical work where they showed that the mixed superalkalis (Li 2 NaO, Li 2 KO, Na 2 LiO, Na 2 KO, K 2 LiO, K 2 NaO, and LiNaKO) could be a better alternative than the pure superalkalis for B 12 N 12 nanocages in designing hi-tech NLO materials (Bano et al., 2022). The optimized structures of the mixed-superalkalidoped B 12 N 12 complexes can be seen in Figure 2A. Throughout the computational experiments, the structure, stability, electronic, and NLO response features of superalkali cluster-mixed B 12 N 12 nanocages were examined. They have chosen a total of seven (A-G) thermodynamically stable designed complexes consisting of very high interaction energies ranging from −98.02 kcal/mol to −123.13 kcal/mol, which were compared with the previously reported Li 3 O@ B 12 N 12 having an interaction energy (E int ) as −92.71 kcal/mol along with the narrow variation of the HOMO-LUMO energy gaps (from 3.36 eV to 4.27 eV) compared against the pristine B 12 N 12 (11.13 eV) species. This group confirmed the CT phenomenon occurring in such probed complexes which were acquired from the NPA technique, non-bonding interactions between the doped superalkalis and nanocages followed by the QTAIM, as well as NCI-plot tools. The maximum absorbance was found in the near-infrared (IR) region ranging from 1,076-1,486 nm which appeared to be transparent in the ultraviolet (UV) region. The computed first hyperpolarizability (β tot ) of complex C was analyzed as 1.7 × 10 4 au which was much greater than that of the pure Li 3 O superalkali-doped B 12 N 12 complex (3.7 × 10 4 au) perceived from the same theoretical level of approach (by Sun et al. in 2016). As in nanoelectronics, designing and synthesizing stable and high-performance NLO Frontiers in Chemistry frontiersin.org 06 materials is the foremost precedence for the scientists and researchers; an increased NLO response was detected in this work by a large second hyperpolarizability. To gain more insights into such complexes, they also computed hyper-Rayleigh scattering (6.71 × 10 10 au), second harmonic generation (1.17 × 10 10 au), and electro-optical Pockels (3.29 × 10 10 au) effect along with the maximum obtained values of the electric field-induced second harmonic generation (3.46 × 10 10 au) and electro-optic-dc-Kerr effect (3.96 × 10 11 au) at 1,064 nm wavelength. At the same wavelength for all A-G complexes, significant increments in quadratic nonlinear refractive index (n 2 ) values were seen along with the largest value of 3.35 × 10 -8 cm 2 ·W −1 . The theoretical findings based on the ωB97XD/6-31G (d, p) level of approach indicated that such mixed superalkali-doped nanoclusters could have broad applications in designing, fabrication, and characterization of hi-tech optoelectronics (i.e., high-performance NLO materials).
However, various procedures can be seen in the literature in designing high-performance NLO materials; the NLO response of three series (a total of 10 isomers, I-X) of theoretically designed compounds Li 2 F@B 12 P 12 , Li 3 O@B 12 P 12 , and Li 4 N@ B 12 P 12 having three (I-III), four (IV-VII), and three (VIII-X) isomers, correspondingly, was inspected thoroughly using the DFT approach (see Figure 2B) (Ullah et al., 2019). This research work explored the effects of superalkali (Li 2 F, Li 3 O, and Li 4 N) when these were doped on the B 12 P 12 nanocage. The computational outcomes showed that most of the complexes [all isomers of the Li 2 F@B 12 P 12 and Li 3 O@B 12 P 12 model compounds (I-III and IV-VII) along with one isomer of the Li 4 N@B 12 P 12 complex (IX)] possessed excess electrons, whereas only two isomers of the Li 4 N@B 12 P 12 (VIII and X) compound were found to be inorganic electrides. It was computationally inspected that the superalkalis were chemisorbed on the boron phosphide nanocage and all such formed nanocage complexes were found to be quite stable which was confirmed by their calculated BEs. There was substantial enrichment in the first hyperpolarizability values of the system when doping a B 12 P 12 nanocage with the superalkali. Isomer III of the Li 2 F@B 12 P 12 system showed the largest first hyperpolarizability (3.48 ×10 5 au) and lowest the HOMO-LUMO gap (1.46 eV) among the three isomers (I-III) along with good transparency in the UV region, showing that the superalkali Li 2 F provided better hyperpolarizability increment than the Li 3 O and Li 4 N superalkalis when associated with the B 12 P 12 nanocage. In addition, the influences of several superalkalis and various doping locations on the NLO response were comprehensively examined for all three variants of model systems in the framework of the quantum chemical calculations using the DFT approach. This work will promote prospective uses of the C 60 -like B 12 P 12 -based nanostructures doped with the superalkali and novel electronic nanodevices, and hi-tech NLO materials consisting of good UV transparency could be designed by the employment of new excess electron systems and electrides (VIII and X).
As several research groups have focused on designing novel superatoms with high NLO responses, A. Omidvar reported a range of representative D-A model skeleton species having elevated NLO responses through bonding the superalkali-like M 3 O (K 3 O, Na 3 O, Li 3 O, Li 2 KO, Li 2 NaO, Na 2 KO, Na 2 LiO, K 2 LiO, K 2 NaO, and LiNaKO) blended with the superhalogens (Al 13 cluster) (see Figure 3A) (Omidvar, 2018). These superalkalis consist of a low IP to the superhalogen Al 13 having a larger EA. Additionally, the electric field gradient tensors of the 17 O nuclei and the natural bond orbital (NBO) analysis-based charges of the M 3 O superalkalis were also computed. In this study, he represented the theoretical signatures for the feasibility of employing the super-atoms Al 13 and M 3 O as construction blocks to construct nanomaterials with strong NLO responses. He observed that the IP and 17 O nuclear quadrupole resonance parameters of the M 3 O superalkalis have been efficiently affected by the M ligands. The electron transfer phenomenon in such types of super-atoms in the bonding superalkalis is responsible for the competent narrow HOMO-LUMO gap as well as increasing the first hyperpolarizability remarkably in the pristine Al 13 cluster. Significant CT takes place from the M 3 O component to the Al 13 assembly. It was observed that the data based on the η Q parameters of the 17 O nuclei significantly increase when the pure ligands were substituted with the doped ligands in the M 3 O superalkali species. The Q value (an asymmetry parameter) provides evidence of the chemical bonds taking part therein. Importantly, according to the findings of this investigation, the electropositivity of the alkali ligands was shown to play an important role in the determination of the IPs of the superalkalis. Moreover, a comprehensive exploration of the NLO response of the super-atoms M 3 O-Al 13 can be seen that is altered by the oriented external electric fields. When the imposed oriented external electric field is enhanced along the CT direction (M 3 O → Al 13 ) ranging from zero to a critical external electric field, a gradual increment in the first hyperpolarizability can be seen for the superatom compounds which appears to be used as an effective approach based on the theoretical findings.
Using quantum mechanical approaches, a total of three configurations [two C 3v point groups (1 and 3) and one D 3h point group (2)] of trigonal bipyramidal (TBP) CaN 3 Ca structures were chosen as models, and the role of the NLO response was analyzed by aiming at pioneering hi-tech singlepole double-throw (SPDT) NLO molecular switches (Wang et al., 2020). One marginally longer and one shorter vertical Ca-N 3 3− length was found in the case of both C 3v configurations (1 and 3), whereas there were two identical bond lengths of Ca-N 3 3− in configuration 2. The ab initio (MP2/6-311+G (3df) methodbased equilibrium structures of the chosen CaN 3 Ca species can be seen in Figure 3B where the Ca atoms are located over and Frontiers in Chemistry frontiersin.org 07 under the usual triangular N 3 ring. It should be noted that energy configurations 1 and 3 are 3.99 kcal/mol smaller than that of configuration 2 at the CCSD(T)/6-311+G (3df) level of theory which illustrates that the former two configurations (1 and 3) have a larger thermal stability than configuration 2. Moreover, in the case of the configuration 2, the excess electrons equally occupied the two hemispherical orbital lobes (HOMOs) positioned over the two extremes of the CaN 3 Ca molecule, while in the case of the other two configurations (1 and 3), the excess electrons mainly occupied one hemispherical orbital lobe (HOMO) (located on the left side for 1 and right side for 2) of the CaN 3 Ca species. Importantly, Figure 3B also confirms that a uniform external electric field (EEF) triggered a reversible configuration conversion between 1 (L1 > L2) and 3 (L1 < L2). Hence, by deploying an appropriate external homogeneous electric field, interconversion between 1, 2, and 3 can be realized easily. All these species belonged to the novel alkaline-earth-based aromatic mixed-valent superalkalis along with acting as fascinating electrides. Very importantly, the electronic structure of the salt-like species containing configuration 2 showed a delocalized structure in the form of e 0.5− ···Ca 2+ N 3 3− Ca 2+ ···e 0.5− demonstrating class III-type mixedvalent superalkali electrides, whereas the other two configurations 1 and 3 were confirmed as the rare inorganic Robin-Day class II-type structure consisting of localized redox centers. Moreover, comparison outcomes of remarkable static and dynamic first hyperpolarizabilities of all three configurations have been reported since all three were excellent candidates for SPDT NLO molecular switches.
Finally, using the ab initio modeling approach, Zhang et al. showed that the phenalenyl radical and M 3 ring (M 3 -PHY, M = Li, Na, and K) stacked with parallel and vertical geometries are potential applicants for molecular switches which can exist in both superalkali electrides and superalkalides (Yi et al., 2022). A range of similar kinds of interesting research studies can be seen in the aforementioned literature. In this work, they have shown that M δ− -M 2 (1−δ)+ -PHYacts as a superalkalide, whereas the e − ···M 3 + -PHY acts as a superalkali electride where the former may isomerize to the latter using suitable long-wavelength irradiation and the latter may isomerize to the former with appropriate shortwavelength irradiation. In this report, the researchers have combined both electride and alkalide characteristics in one molecular switch and concluded that both forms demonstrated an excellent functioning NLO response.

Capturing carbon dioxide/nitrogen/ hydrogen
Reduction (via electron transfer i.e. CT phenomenon) of carbon dioxide (CO 2 ) by the capability of the superalkali Li 3 F 2 has been shown by Park and Meloni (2017). The equilibrium structure of neutral planar and non-planar clusters trapping the CO 2 and N 2 molecules can be seen in Figure 4A. To attain trustworthy outcomes on the structural and energetics/stability of the species, a composite CBS-QB3 model was deployed. The association of CO 2 with the Li 3 F 2 superalkali was examined by scanning the potential energy surface (PES) which led to the formation of their transition states (TSs) and minima. Structural alterations were exposed in the terms of spin density and charge flow. The large BE (ionic interactions between the Li 3 F 2 and CO 2 having the largest BE (163 kJ/mol) among the three optimized structural isomers), CT phenomenon, and the HOMO-LUMO gap explained the energetics and stability of the Li 3 F 2 /CO 2associated species. It is worth mentioning that the largest determined BE (163 kJ/mol) was found to be significantly larger than that of the superhalogen cluster Sb 3 F 16 /CO 2 reported by Czapla and Skurski (2017). The choice of the Frontiers in Chemistry frontiersin.org 08 Li 3 F 2 toward the CO 2 has been taken using the same level of approach by which computational experiments on the association of the most copious atmospheric N 2 gaseous molecule have been conducted (a very small chemical affinity of the Li 3 F 2 for N 2 ). In the case of the N 2 association with the superalkali Li 3 F 2 , the calculated BE value was only 51 kJ/mol, which reveals that the capability of the superalkali Li 3 F 2 for CO 2 reduction has high selectivity over the N 2 molecule. CO 2 is actively reduced by the superalkali Li 3 F 2 followed by transferring an electron as well as geometric change which brings up the CO 2 molecule in a bent shape, and it can be probably used in transforming CO 2 into fuel.
With the deployment of the MP2/6-311+G(d) level of approach, an investigation was conducted by Yu et al. (2020) to obtain new insights into the capability of the superalkali cation Li 3 + for capturing N 2 gas as well as its behavior in gaseous nitrogen. To reduce inter-ligand Coulombic repulsion, the N 2 molecules (i.e., a maximum coordination number of 12 was envisaged for the trinuclear Li 3 + because every vertex Li can capture four N 2 molecules) approached to attach at various apexes of the trinuclear Li 3 + core of the Li 3 + (N 2 ) n (n = 1-7) complexes which were confirmed by the structure, stability, and electronic feature analyses. It is worth to mention that only in the case of the lowest-lying series of the Li 3 + (N 2 ) n complexes (where the number "n" ranges from 1 to 4) complexes, the trinuclear Li 3 + core retains its superatom dignity using the NPA and FMO approaches. Importantly, the interaction between the Li 3 + with N 2 [for example, it reached up to −24.5 kcal/mol for the Li 3 + (N 2 ) 4 complex] is stronger than that with H 2 but weaker than that with H 2 O molecules. The difference in the Gibbs free energies for the same series of model complexes (through possible fragmentation channels) specified the thermodynamic stability of the Li 3 + in the (N 2 ) n clusters. As electrostatic interaction plays a dominant role over the polarization component in the case of the Li 3 + (H 2 O) n complexes, a different case was found in the construction of the Li 3 + (N 2 ) n complex having a non-covalent nature where the electrostatic and polarization components contributed almost equally. Furthermore, they concluded that the superalkali trinuclear Li 3 + cation is a much better candidate than its other heavy alkali metal cations (Na 3 + and K 3 + ) in terms of capturing N 2 molecules which is due to a larger BE and favorable structural features for the Li 3 + (N 2 ) n complexes as compared to the N 2 associated with the Na + and K + cations. Moreover, by resemblance, the Li 3 + superalkali cation (along with retaining its identity) has been predicted to have 12 maximum coordination numbers in the nitrogen clusters whose structure (see Figure 4Ba) was assured by the ab initio molecular modeling approach with the deployment of the MP2/6-311+G(d) level of theory and the local minima was confirmed by the frequency calculations. Analogous to the isolated Li 3 + alkali metal cation, a delocalized s-type bonding HOMO was detected in the case of Li 3 + (N 2 ) 12 which can be seen in Figure 4Bb. The computed NMR Frontiers in Chemistry frontiersin.org 09 parameters (chemical shifts ranging from −95.5 to −94.1 ppm and −66.8 to −64.0 ppm for the 15 N1 and 15 N1′ nuclei, correspondingly) can indeed provide significant information for the experimental classification of the complexes. Of course, this work provided an in-depth understanding of the mechanism of binding interactions in the Li 3 + (N 2 ) n complexes and explored the superalkali-based nitrogen-gas-trapping agents by spurring more computational and experimental attempts.
As CO 2 , with the property of trapping greenhouse gases, has a crucial role in the global carbon balance purpose along with its conversion into fuel, a very recent in silico-based report by H. Srivastava and A. K. Srivastava on the activation of CO 2 by various types of superalkalis can be seen in the literature where they showed comprehensive and interesting theoretical outcomes (see Figure 4C) . Some studies on the superbases which were designed with the help of superalkalis can be seen in the literature Misra, 2015, Srivastava andMisra, 2016). Because of the superalkalis, for example, typical superalkalis (FLi 2 , OLi 3 , and NLi 4 ), special superalkalis [Al 3 , Mn(B 3 N 3 H 6 ) 2 , B 9 C 3 H 12 , and C 5 NH 6 ], binuclear superalkalis (Li 3 F 2 ), non-metallic superalkalis (O 2 H 5 and N 2 H 7 ), and polynuclear superalkalis (Al 12 P, N 4 Mg 6 M) having lower IP than those of the alkali atoms and can easily transfer an electron (due to its hypervalent nature) to the CO 2 molecule, these species possess strong reducing power and play an imperative role in altering the geometry of CO 2 (bent shape) from its linear structure by donating an electron to it, which have been reported based on the quantum chemical methods. Examining different theorybased reports, it was observed that the extent of the CT (electron transfer) is mainly dependent on the size, geometrical, and electronic features as well as the (IPs) of the superalkali species. In silico-based investigations and discussions on the activation of CO 2 by a small Li 3 F 2 cluster inside the Buckminsterfullerene can also be seen in the literature. It was also found that the CO 2 molecule is not only activated by the C 6 Li 6 molecule but also a total of six CO 2 molecules can be trapped by the same species. From this report, Srivastava et al. came up with concluding remarks that the reported theoretical findings imply that superalkalis could be utilized as an economical catalyst for the activation of a CO 2 molecule, and since the fuel can be formed by the activated CO 2 ion like methanol (CH 3 OH) followed by the hydrogenation reaction. Moreover,  have reported various computational experiments using the DFT as well as ab initio modeling approaches on the superalkali cations (X = F, O, and N) with methyl ligands, superalkali behavior of ammonium and hydronium cations, and many more studies (Srivastava, 2019b). Moreover, introducing the superalkalis, an ab initio study on singleand double-electron reductions of CO 2 was reported in 2018 (Srivastava, 2018).

Complex formations and interactions involved therein
To begin with the idea of superalkalis, complexes are superalkalis with a lower IP than the corresponding alkali and alkaline earth metals; Parida et al. reported work on the computational designing of aromatic organometallic superalkali complexes using the first principle calculations (see Figure 5A) (Parida et al., 2018). A trigonal all-metal core coupled with imidazole (IMD) and pyridine (Py) has been proposed which facilitate the probable existence of a superalkali complex. Low IEs (as compared to the Cesium atom) were found for the organometallic complexes, Au 3 (IMD) 3 and Au 3 (Py) 3 , which imitated the general features of a superalkali very well. All the superalkali clusters revealed sp 2 hybridization, and therefore, a planar geometry all along with the Au 3 + ring showed a "doubly aromatic" character. The HOMO-LUMO gap value of the Au 3 (Py) + species (4.11 eV) was found to be greater than that of the Au 3 (IMD) + (3.84 eV). As some of the organometallic complexes were capable of showing good NLO features using the static first-order hyper-polarizability calculations, it also appeared that the characteristics of such Au-based complexes are like the features of a superalkali. Such outcomes concluded that various coinage metal-based superalkali complexes having broad applications can be synthesized in the laboratory. Combinations of aluminum trimer and two distinct forms of the representative superatom clusters [(super) alkalis: M = F, FLi 2 , OLi 3 , and NLi 4 ; and (super) halogens: X = LiF 2 , BeF 3 , and BF 4 )] were chosen, and the diverse structural, stability (interactions involved in the Al 3 -M and Al 3 -X superatom compounds), and electronic features were theoretically explored by Yang et al. (2018) at the MP2/6-311+(3df) level of theory. The Al 3 -M and Al 3 -X compounds (see Figure 5B) showed different structures where point-to-side interactions were seen between the Al 3 and X components of the Al 3 -X compound, providing the most favorable bonding pattern while the least preferable was face-to-face. In the case of Al 3 -M systems, Al 3 favored interacting with the FLi 2 and Li (super) alkalis via its ring plane, whereas it favored binding with NLi 4 and OLi 3 superalkalis over the Al-Al edge. Interestingly, the Al 3 moiety of the Al 3 -X species acts as the cation (electron donor), whereas it acts as an anion (electron acceptor) in the Al 3 -M compound assured by the NPA approach. Enhanced CT was detected between the Al 3 component and the super-atoms (M and X) in both polar and nonpolar solvents. The HOMO-LUMO gap values, BEs, and bond energies were calculated to be large which confirmed the stability of such blended species (Al 3 -M and Al 3 -X compounds) supported by strong interactions taking part between the Al 3 and super-atoms (M/X). Importantly, the solvent effect has an important role in the case of the Al 3 -M (especially, the Al 3 -NLi 4 ) compounds where it was found that such species were better stabilized in the presence of the solvent molecules, whereas the outcomes were not significant for the Frontiers in Chemistry frontiersin.org stability of the Al 3 -X compounds. Moreover, the Al 3 + ring exhibited different aromatic characters (σ and π aromaticity) when associated with diverse superhalogen anions either in the gas or in liquid phases.
As it has been conventionally considered that the anionic alkali metals in the solution possess a gas-like and unperturbed nature recently, Barrett et al. reported experimental and theoretical findings on superalkali-akalide interaction-related studies which assisted ion pairing in alkalide solutions in solvents having low polarity (Riedel et al., 2021). The experimental evidence (based on coherent neutron scattering, dielectric spectroscopy, and concentration-dependent macroscopic ionic conductivity) of the observation and influence of ion pairing of alkalides in the solution agreed with each other. Furthermore, to understand the structural, stability, and electronic features, the DFT studies for a range of possible superalkali-alkalide complexes chosen as models were carried out in the framework of ab initio simulations, including the superalkalis and superalkali dimers where such species were revealed to play the dominant role in the solution. The visualized singly occupied molecular orbital (SOMO)/HOMO 3D isosurface maps of the superalkali K-15-crown-5 2 model (a), superalkali−alkalide (K-15-crown-5 2 ) δ+ (Na) δ− associated with the alkalide in the axial (c), and equatorial (d) sites concerning the sandwich complex are exemplified in the form of a cartoon (b) as shown in Figure 5C. The conformational flexibility of the alkalide systems measured by the temperaturedependent alkali metal NMR spectra appeared to show both reversible perturbation and thermally triggered demonstrating a complex replacement mechanism for the ion-paired moieties. The outcomes of their research work facilitated a picture of alkalide moieties acting as a gas-like ion in the solution and attached a great significance to the interactions of the alkalide with its complex counteraction (superalkali) which could be chemically regulated and established by contemplating the interactions between the superalkali and alkalides. Recently (in 2021), to synthesize aromatic trinuclear Cu(I)-NHC complexes constructed from superalkali ligands as a building block, a variety of NHC (N-heterocyclic carbene) ligands based on imidazole and benz-imidazole have been computationally designed by Giri et al. Six different ligands were chosen based on the pyridazine, pyrimidine, and pyrazine acting as the skeletons (Parida et al., 2019). According to the outcomes of the calculated vertical electron affinity, all of the ligands chosen in this work seem to be of the superalkali kind of molecule which has excellent NLO properties. The Cu(I)@NHC complexes were formed by the NHC ligands consisting of trinuclear Cu 3 as the central moiety. From the contribution of canonical molecular orbitals toward the computed nucleus independent chemical shift (NICS) values, the trinuclear Cu 3 ring appeared to show high σand low πaromaticity. Depending on the various ligand environments, the aromatic features were altered along with other reactivity parameters such as electrophilicity and hardness. According to their theoretical findings, a more reactive and less aromatic complex can be produced by the pyrazine-based NHC ligand as opposed to pyridazine and pyrimidine-based NHCs. Like the BH 3 molecule, the inspected super-atomic clusters exhibit sp 2 hybridization based on the natural localized molecular orbitals (LMOs). Very interestingly, the UV-Vis spectrum calculations using the first principle study in the acetonitrile solvent showed a blue shift. It is believed that such modeled and theoretically explored complexes can be simply synthesized and utilized as catalysts in advanced synthetic chemistry.
The influence of variations in the ionicity of CT and bonding mechanism on the geometrical and electronic features of novel lead-based halide perovskites formed by introducing the superalkali species was reported by Paduani and Rappe in 2017 with the employment of the scalar relativistic DFT approach (Paduani and Rappe, 2017). In this work, the authors used two superalkalis such as Li 3 O [see Figure 5Da] and Li 3 S [see Figure 5Db] which were replaced by the Cs atoms in the CsPbI 3 having a cubic structure which were detected to be slightly tetragonally distorted, and the band gap values of both superalkali-based species were much lower than that of the cubic CsPbI 3 . The in silico-based outcomes facilitated encouraging performance which can have applications in optoelectronics, for instance, as long-wave infrared (IR) sensors and thermoelectrics. They found that the incorporation of suitable superalkali species at the cationic A-positions in the ABX 3 -type (CsPbI 3 ) structure can have the capability to tune the band gap of such species. Smaller band gaps (mainly occurring from the effective hybridization between the Pb and Li s-states at the top of the valence band) for the minimum-energy (i.e., equilibrium) crystal structures of both the [Li 3 S]PbI 3 and [Li 3 O]PbI 3 compounds were analyzed as 0.41 eV (indirect) and 0.36 eV (direct), correspondingly, where the latter is slightly larger than the former. The [Li 3 O]PbI 3 compound was hoped to be more resistant to water exposure which was confirmed by the cluster calculations. In comparison to the CsPbI3 species, harsh alterations can be seen in the shape of both valance and conduction bands when the chemical environment was changed in the case of the Pb-halide perovskite structure. Because of the construction of the delocalized energy states, additional electronic states near the Fermi level were formed by introducing the superalkali cations. Such studies have the capability to crease the excitation diffusion length at a longer wavelength and promote hole mobility. Berry-phase simulations demonstrate considerable spontaneous polarization in both novel materials [Li 3 O]PbI 3 and [Li 3 S]PbI 3 having noncentrosymmetric structures (lacking inversion symmetry) and thus, allow this material to be used in communications, ferroelectrics, and remote sensing in a prolonged spectrum region.
Taking a quick glimpse at a different type of superalkali cation, a series of interesting computational experiments on the structural, stability/energetics, and electronic feature analyses of some new series of interesting non-metallic superalkali cations such as chain-shaped F n H n+1 + species, O x H 2x+1 + clusters, and N n H 3n+1 + species were reported by Srivastava (2019a), Srivastava (2019d), and Srivastava (2019c).

Concluding remarks and future perspectives
The recent advances in the theoretical development, characterization, and first-time use of superalkalis are outlined in this review. In this report, we have made an effort to provide a general overview of modeling/design and characterization (theoretically) of superalkalis and their applications including sharing predictions for their future growth in the hopes of pointing designers in the right direction as they continue to create and use these special species. Efforts have been made to unveil the potential of some novel superalkali cations (Li 3 + ) and C 6 Li 6 type species for capturing and storing CO 2 /N 2 molecules. The first-order hyperpolarizability-based NLO response properties of many new computationally designed superalkali-based materials (for example, fullerenes such as mixed-superalkalidoped B 12 N 12 and B 12 P 12 nanoclusters having good UV transparency and novel inorganic aromatic mixed-valent superalkali CaN 3 Ca as an alkali-earth-based high sensitivity multi-state NLO molecular switch, and novel lead-based halide perovskites formed by introducing the superalkali species) which can, indeed, be used as a new kind of electronic nanodevice for designing hi-tech NLO materials have been unraveled in this review. Understanding the mere interactions of alkalides in a solution, as well as in the gas phase where the potential to influence how such systems can be extended and applied in the future, is also highlighted in this survey. Understanding earned from this report will, indeed, assist in the discovery of novel superalkalis and will enrich the library's arsenal of supersalts.
Frontiers in Chemistry frontiersin.org Although, based on this review, we can predict the forthcoming directions at the industrial level, there are still tasks to better understand the fascinating features of superalkalis and their characteristics to be measured precisely in the fields of inorganic, organic, and material chemistry. We are hopeful that further experiments, as well as theoretical investigations, will be capable of developing the present strategies and contributing to our future sights in better understanding the attentiongrabbing features of a variety of already synthesized and designed/modeled novel superalkalis or related species. Moreover, the reported model complexes (as building new materials) in this report will be advantageous, and these may pave alternative pathways for experimentally rewarding applications and can have potential uses in advanced synthetic chemistry as catalysts.

Author contributions
SP contributed mainly to this report (selection of the topic, its conception, and design). Material preparation, data collection, and figure implementation were mainly performed by SP. All version of the drafts of the manuscript were written and edited by SP, and all other co-authors commented on all drafts of the manuscript. All the authors read and approved the final manuscript.