When studying condensed matter theoretically, especially soft condensed matter, noncovalent bonding often plays a very important or even crucial role. Hydrogen bonding is a typical and extremely important non-covalent bonding interaction^[1]. In 1981, Nishizawa et al. Observed the interaction between potassium ion and non-polar aromatic ring structure through experiments, and the binding energy was about -19 kcal/mol^[2]. Later, it was understood that this noncovalent bonding interaction widely exists between ions and π-electron-containing structures, which is called ion-π interaction (Fig. 1)^[3]. Ion-π interaction can be divided into cation-π interaction and anion-π interaction according to the form of interaction.

In aqueous solution, ions usually exist in the state of hydrated ions, and the hydration of ions will significantly weaken the interaction between other aromatic ring structures. Taking a specific aromatic ring structure such as a benzene molecule containing only a single six-membered ring as an example, the results of first-principles calculations show that the K⁺-π between the K⁺ and the benzene molecule decreases from − 16.2 kcal/mol to − 6.5 kcal/mol when the number of water molecules around the K⁺ ion increases from 0 to 18^[4]. Therefore, the ion-π interaction in aqueous solution is much weaker than that in vacuum. Correspondingly, the single adsorption time (dwell time) of Na⁺, Li⁺ plasma on benzene molecules is very short, often less than 1 ns. Obviously, in aqueous solutions containing a large number of ions, the hydrated ion-π interaction cannot only consider the adsorption stability of a single ion. The importance of this role must be based on the idea of statistical physics, considering a large number of hydrated ions and their cumulative effects on the time scale. In other words, the effect of hydrated ion-π interaction on the macroscopic scale must be closely related to the ion concentration of the solution. Still taking benzene molecule as an example, although the residence time of an ion on a single benzene molecule is very short, when the ion leaves, after a period of time, other ions will be adsorbed on the benzene molecule. When the ions in the solution reach a certain concentration, this continuous adsorption-desorption dynamic process leads to a considerable proportion of the time that there is ion adsorption on the surface, and the probability of a hydrated ion adsorbed on the benzene molecule (considering the long-term average results) is determined by the strength of the hydrated ion-π interaction, the ion concentration, and the temperature. The numerical simulation shows that in NaCl solution, which is equivalent to the salt concentration in blood, the average residence time of a single Na⁺ ion on the surface of benzene molecule is only 0. 2 ns, but the total residence time of the ion on the surface of benzene molecule is 3. 8 ns, which is close to 40% of the total simulation time^[5]. Therefore, in many practical processes, the hydrated ion-π interaction often plays a very important or even key role^{[6⇓⇓⇓⇓⇓~12]}. It is worth noting that on the surface rich in aromatic ring structures, especially on the surface with multiple aromatic rings, such as graphite and graphene, the multiple aromatic ring structures will greatly enhance the hydrated ion-π interaction, which leads to a large enrichment of ions on the solid surface^[6,13,14]. When the concentration of ions in solution is high enough, a large number of ions adsorbed on the surface will spontaneously form an ordered structure under the action of electrostatic interaction between ions and thermal disturbance at room temperature. However, the difference between the interaction of π electrons and anions and cations controls the number ratio of these adsorbed anions and cations, which is different from that in conventional three-dimensional crystals, resulting in two-dimensional crystals with abnormal stoichiometric ratios, such as disodium chloride (Na₂Cl,Na,Cl element ratio 2 ∶ 1), trisodium chloride (Na₃Cl,Na∶Cl 3 ∶ 1) and calcium chloride (CaCl, Ca ∶ Cl = 1 ∶ 1)^[9,11].

Low-dimensional magnetic materials have been studied extensively and deeply at home and abroad because of their great advantages in miniaturization and high integration. At present, the low-dimensional ferromagnetic materials that have been experimentally synthesized include two-dimensional ferromagnetic materials such as FGT materials, CrI₃, CrBr₃, and one-dimensional magnetic materials such as composite structures composed of carbon nanotubes loaded with magnetic substances^{[15][16][17][18]}. Although these low-dimensional magnetic materials have shown great potential for application, there are still some problems such as low Curie temperature and difficult preparation, so it is urgent to develop a low-dimensional ferromagnetic material with higher Curie temperature and lower production difficulty. Recently, a series of studies on the preparation of two-dimensional crystals with abnormal stoichiometry at room temperature and pressure, especially the discovery of two-dimensional ferromagnetic material CaCl at room temperature, have provided a new idea for the study of low-dimensional ferromagnetic materials^[11]. Further experiments show that two-dimensional CaCl crystal has good conductivity and can form heterojunction, which makes it have great potential in the application of magnetic materials.

In this paper, we will review the two-dimensional crystals with abnormal stoichiometry based on hydrated ion-π interaction and their exotic properties, including Na₂Cl, Na₃Cl and CaCl at room temperature and pressure, which are called "inverse crystals" with abnormal stoichiometry. Anomalous stoichiometric crystals have different anion-cation ratios and unique electronic structures from conventional three-dimensional crystals, so they should have completely different physical and chemical properties from conventional three-dimensional crystals. The study of anomalous stoichiometric crystals will greatly expand the research fields of magnetic effects and magnetic medicine in biological systems, and provide new ideas for the design of low-dimensional magnetic materials.

Classical molecular dynamics simulation can effectively characterize the van der Waals interaction, hydrogen bonding, hydrophobic interaction and other interactions between ions, water molecules, graphene and other components at the graphene-solution interface, but it can not accurately characterize the hydrated ion-π interaction between ions and aromatic ring structures. In order to accurately characterize this effect in classical molecular dynamics calculations, force field parameters were generated based on quantum mechanics calculations, and related software was developed based on this (software copyright C161003C-C (ZQH)). With such software, the classical molecular dynamics simulation of ion motion and distribution on graphene sheets in NaCl solution can be carried out. Considering that the hydrated ion-π interaction between Cl^- ions and graphene surface is less than 1/10 of that of cations such as Na⁺, the hydrated anion-π interaction is ignored in the simulation^[13]. The simulation results show (Fig. 2) that Na⁺, Cl^- ions in unsaturated NaCl solution (3.0 mol/L) will be enriched on the surface of graphene sheet.

Fig. 3 shows the probability density distribution variation of the two ions of Na⁺, Cl^- with height (Z) in the direction perpendicular to the graphene surface. It is worth noting that there are two sharp probability density distribution peaks near the height of 3. 7 and 6. 5 nm. The position and sharp shape of the two peaks indicate that the Na/Cl ions in this region are highly enriched and form a two-layer structure, and the distance between the two layers is stable. This ion enrichment caused by hydrated ion-π interaction has been observed on the surface and in the interior of reduced graphene oxide (rGO) films^[19]. So far, the importance of hydrated ion-π interaction has been recognized by the international academic community.

At normal temperature, the thermal disturbance is not negligible. Based on the idea of thermodynamic statistical physics, a large number of ions adsorbed on the surface are likely to form an ordered structure under the action of thermal disturbance. So why do these possible structures represent forms? Ordered structures generally appear in the form of crystals, while crystals formed by anions and cations have direct contact between ions and direct overlap of electron orbitals. Obviously, classical molecular dynamics simulation is not suitable for calculating this system, and further analysis needs to be carried out through first-principles quantitative calculation.

Several Na-Cl configurations, including two-dimensional NaCl on graphene, Na₂Cl, and two-dimensional Na₃Cl crystal configurations between graphene layers, can be obtained by the quantum calculation software CP2K based on density functional theory (DFT). The stoichiometric ratios of Na and Cl in these three two-dimensional structures are 1:1, 2:1 and 3:1, respectively, as shown in fig. 4. In particular, it should be pointed out that in the previous general understanding of nature, crystals composed of Na and Cl elements only have a stoichiometric ratio of 1:1 at normal temperature and pressure, while the two-dimensional Na₂Cl and Na₃Cl crystals obtained by theoretical calculation break this thinking pattern. Fig. 5 shows the Na-Cl mean spacing of these two-dimensional structures as 2.81, 2.78, and 2.7575 Å, respectively. Among them, the simulated Na-Cl spacing of two-dimensional NaCl crystal is consistent with that of conventional three-dimensional NaCl crystal, while the Na-Cl spacing of Na₂Cl and Na₃Cl crystals is smaller than that of conventional three-dimensional NaCl crystal. At the same time, comparing the difference between the total energy of the three configurations calculated by DFT and the total energy of each atom of the crystal when it is free, namely Cohesive energy, it is found that the two-dimensional Na₂Cl and Na₃Cl crystal structure on the surface of graphene may be more stable than the two-dimensional NaCl crystal structure.

Since the Na-Cl two-dimensional crystal is prepared by soaking the rGO film in an unsaturated NaCl solution, the direct characterization of this crystal needs to be carried out in the solution, so the sample preparation must be carried out according to the following process. First, the rGO membrane was placed on a glass slide and put into a self-made PE (Polyethylene) bag. Condly, adding a certain amount of NaCl solution with different concentrations into the bag; After the rGO membrane was fully soaked by NaCl solution, the glass slide was tilted at a certain angle, and most of the solution was transferred to one side of the PE bag to minimize the solution attached to the membrane surface. After that, the glass slide was placed on the sample stage of XRD, and the rGO film was taken as the center for XRD test. The XRD test results shown in fig. 6 show that crystal peaks are observed near the 32 ° position (red box area) of the rGO film samples immersed in both saturated and unsaturated NaCl solutions, indicating the presence of Na-Cl crystals, and these crystal peaks are located close to the (200) plane of the conventional three-dimensional NaCl crystal. At the same time, it can be judged that the sample soaked in the unsaturated solution does not have the (400) peak similar to the conventional three-dimensional NaCl crystal, indicating that the unsaturated crystal is very thin. The XRD results are consistent with the prediction of theoretical calculation, that is, the thickness of the obtained Na-Cl crystal in the direction perpendicular to the graphene is only 2 ~ 3 layers. It should be emphasized that compared with the (200) peak of the conventional three-dimensional NaCl crystal, the peak of the Na-Cl crystal measured in the unsaturated solution has a shift to the right (Fig. 6B), which means that the structure of the Na-Cl crystal measured in the unsaturated NaCl solution is different from that of the conventional three-dimensional NaCl crystal with a stoichiometric ratio of Na: Cl of 1:1 precipitated from the saturated solution.

The rGO film was immersed in an unsaturated NaCl solution and then dried to obtain a sample, which was characterized by energy dispersive spectroscopy (EDS) of TEM to analyze the elemental composition of the crystals precipitated on the rGO film. As a result, it was confirmed that these crystals were composed of Na and Cl, and the ratio of these two elements was in the range of 0.6 to 4 except for one case, and the ratio of a large number of samples was between 2 and 3, as shown in fig. 7. This result is consistent with the theoretical results of the element ratio of 2 ∶ 1 and 3 ∶ 1 for the two configurations. It should be noted that because EDS and TEM experiments must use dry samples, the saturated crystallization of excess solution attached to a large number of samples during the drying process will lead to the appearance of conventional three-dimensional NaCl crystals, so there will be a situation where the ratio of Na to Cl is close to 1 in the EDS results. Fig. 8 shows the results of five repeated EDS measurements on the same area of the rGO film. During the continuous bombardment of the electron beam generated by the energy spectrometer, the sample maintained a fairly close elemental content and ratio. This result shows that these crystals with abnormal stoichiometry have good stability.

Fig. 9 is a comparison of the TEM detection results of Na-Cl crystals on rGO film (Na-Cl @ rGO film) and the fitting points of the theoretical calculation results. The white points are the electron diffraction spots observed by TEM, and the colored points are the fitting results of the Na-Cl position relationship corresponding to different Na-Cl structures in the reciprocal lattice space calculated by theory. It can be seen that the experimental diffraction spots are most close to the fitting results of the two-dimensional Na₂Cl and Na₃Cl crystal structures obtained by theoretical calculation, while there is a big gap between the experimental diffraction spots and the conventional three-dimensional NaCl structure. It was further confirmed that two-dimensional crystals with anomalous stoichiometry were obtained in the experiment.

Two-dimensional crystals of Na₂Cl and Na₃Cl with anomalous stoichiometry can be obtained by immersing rGO films in unsaturated NaCl solution, but the fine structure of these crystals in liquid phase can not be directly obtained by in-situ detection because conventional TEM equipment can only detect dry samples. In addition, the crystal structure may be changed or destroyed during the drying process; At the same time, the attached excess solution will crystallize and interfere with the detection results. It is clear that cryo-EM techniques are the most suitable means to carry out in situ studies. However, the ion-π interaction between monovalent Na ions and the surface of the multi-aromatic ring structure is relatively weak, and the electron beam can easily destroy the crystal structure of the multi-aromatic ring structure during the TEM characterization experiment. Because the ion-π interaction of divalent ions is much stronger than that of monovalent ions, another more stable two-dimensional inverse crystal composed of calcium ions, CaCl inverse crystal, was prepared by a method similar to that of Na₂Cl inverse crystal, and was studied in depth^[11,13].

Fig. 10 shows the experimental process and results of in situ characterization of the structure of Ca-Cl crystals on rGO films by cryo-TEM. Fig. 10a shows the experimental flow chart: the ultrathin rGO film was immersed in an unsaturated CaCl₂ salt solution (5.0 mol/L) and prepared into a frozen sample, which was then observed directly on the rGO film by cryo-electron microscopy. Fig. 11 b-ii shows the diffraction spot distribution of a stable single crystal on an ultrathin rGO film. High-resolution images of cryo-EM show that the lattice spacing of this crystal is 4.29 ± 0.1414 Å, and the length of one side in the honeycomb lattice in the corresponding graphene phase is 2.86 ± 0.0909 Å. The results show that the crystal is a regular hexagonal two-dimensional crystal with twice the lattice constant of graphene and has P3m1 symmetry (space group: 156). The insets of Fig. 10 b-i are the enlarged high-resolution images and the corresponding theoretical models. Through experimental observation and theoretical analysis, it is found that the thickness of these Ca-Cl crystals is less than 1 nm, and the spreading area of the single crystal is very large, which can fill the field of view of the electron microscope, and it is a typical two-dimensional crystal material. The surface of the sample is deeply etched by an argon ion gun equipped with an X-ray absorption spectrometer, and the appropriate etching intensity and etching time are controlled, so that the substances at different depths of the sample are exposed, and then the spectrum analysis is carried out, so that the proportion of different substances at the corresponding depths can be given. As shown in fig. 10c, that Ca: Cl ratio is less than 0. 6:1 at the upper surface of the film, while the Ca: Cl ratio is stable at 1. 2:1 within the film.

Fig. 11 show that theoretical configurations of five relatively low cohesive energy (relatively most stable) two-dimensional Ca-Cl crystal obtained by density functional theory and the crystal prediction algorithm CALYPSO on the basis of the experimental results already obtained^[20]. Among them, the carbon substrates of CaCl @ graphene structures 1 and 2 are both graphene standard structures, and the positions of Ca and Cl in these two structures are different, that is, the positions of CaCl crystals relative to graphene are different, but they have the same CaCl lattice constant (a=4.92Å,b=4.92Å,α_ab=60.0°). First-principles molecular dynamics (AIMD) simulations show that the crystal configuration of structure 2 can be easily transformed into the crystal configuration of structure 1 by thermal perturbation at room temperature and pressure. Structure 1 is the structure with the lowest cohesive energy, and this crystal structure has the same lattice parameters as the Ca-Cl crystal structure observed by TEM.

At present, the emerging Internet technology and traditional industrial manufacturing, medical and biological research, have put forward new requirements for magnetic materials, and constantly produced a variety of new low-dimensional magnetic composite materials. However, it must be pointed out that although these low-dimensional ferromagnetic materials have shown great potential for application, there are still some problems to be overcome in practical applications in various industries. In particular, it has the disadvantages of low Curie temperature, difficult preparation, large resistance and easy to be affected by external environment, so it is difficult to be applied to conventional commercial devices^[13,14]. In this chapter, the experimental results will show that Ca-Cl two-dimensional crystal not only has room temperature ferromagnetism, but also has advantages in the application of magnetic materials, including low resistivity, piezoelectricity, heterojunction and so on, which has great potential for application. In order to experimentally test the various physical properties of this structure, it is necessary to prepare dry and thick Ca-Cl @ rGO film samples (thickness much larger than 100 μm). The main steps were as follows: firstly, the rGO membrane was immersed in 5. 0 mol/L calcium chloride solution at room temperature for 12 H, and then the rGO membrane was taken out and the solution attached to the surface was removed, and dried at 70 ℃ in vacuum. Subsequently, the ferromagnetism and related application properties of the prepared samples were studied.

A) Experimental measurement

The room temperature magnetic properties of dry samples of Ca-Cl @ rGO films were measured by a magnetic property measurement system (MPMS-SQUID VSM-094). As shown in fig. 12, the dry sample of Ca-Cl @ rGO film has an obvious closed magnetization curve when the magnetic field intensity changes periodically, indicating that it is ferromagnetic. The dry sample saturation magnetic moment (Ms) of the Ca-Cl @ rGO film at 300 K is 2.1 emu/G. Under the same conditions, the saturation magnetic moment (Ms) of the dry rGO film sample is about 0.4 emu/G. Considering that the weight fraction of Ca in the dry sample of Ca-Cl @ rGO film is only 4.7%, and the average saturation magnetic moment of each Ca atom is 0.24 μB, the CaCl crystal greatly enhances the ferromagnetism of the whole two-dimensional structure. Otherwise, similar measurements were performed on dry samples of Cu-Cl @ rGO films prepared by unsaturated CuCl₂ solution, which also have similar room temperature ferromagnetism.

In order to eliminate the interference of impurities in the sample on the magnetic detection, the sample was subjected to elemental analysis by inductively coupled plasma optical emission spectrometer (ICP-OES) (Fig. 13). The dry sample of Ca-Cl @ rGO membrane contains 0. 16% Fe, while the content of Ni is basically lower than the detection value. By conversion, the saturation magnetization of the dry sample of Ca-Cl @ rGO film (2.1 emu/G at 300 K) is much stronger than the saturation magnetization (about 0.4 emu/G) provided by the current Fe content of 0.16%, reaching the intensity equivalent to the Fe content of 0.95%. Therefore, the main source of ferromagnetism of the sample is not Fe impurity. Interestingly, the saturation magnetization (Ms) of the rGO film at the same temperature is about 0. 4 emu/G corresponding to 0. 18% Fe, which is close to the mass percentage of Fe in the pure rGO film, which is consistent with the results of ICP-OES for the iron content of the two samples, so it can be determined that the ferromagnetism in the control rGO sample is mainly due to the Fe element.

B) Analysis of magnetic theory

Fig. 14 and Table 1 demonstrate the results of the theoretical calculation of the magnetic properties of Ca-Cl clusters on the graphene sheet, and the Ca-Cl crystal clusters adsorbed on the graphene substrate indeed show relatively strong magnetism, with an average magnetic moment of 0.1553~0.7677μ_B per crystal cluster.

A) Resistivity test of two-dimensional Ca-Cl crystal

As mentioned in the introduction of this chapter, when ferromagnetic materials are used in highly integrated and low-power electronic devices such as magnetic storage and spintronic devices, relatively small resistance is more conducive to the performance and stability of the devices. Fig. 15 shows the conductivity measurement results of Ca-Cl @ graphene oxide (GO) film and Ca-Cl @ rGO film samples in comparison with the corresponding rGO and GO films. It should be noted that in this experiment, the Ca-Cl @ GO membrane sample and the control GO membrane were prepared from the same membrane; The Ca-Cl @ rGO membrane sample and the control rGO membrane are also derived from the same membrane, so that the conductivity of the sample can be reasonably compared. It can be seen from the figure that the conductivity of Ca-Cl @ rGO is slightly improved compared with that of rGO film; The conductivity of Ca-Cl @ GO film is improved by one order of magnitude compared with GO film. Considering that the rGO film itself has good conductivity, these results show that the Ca-Cl @ GO film and the two-dimensional Ca-Cl crystal in the Ca-Cl @ rGO film have good conductivity, which establishes a great advantage for the application of two-dimensional Ca-C1 crystal as a ferromagnetic material in the field of electronic devices.

The conductivity of Ca-Cl crystal on graphene sheet (Ca-Cl @ graphene) was measured by conductive atomic force microscopy^[21]. Fig. 16 shows the resistance of graphene sheets with different thicknesses and Ca-Cl @ graphene samples with corresponding thicknesses. The resistance of the Ca-Cl @ graphene samples containing Ca-Cl crystals is reduced by at least 2 ∼ 6 times compared to pure graphene lamellar sheets with similar thickness, indicating better conductivity. This also indicates that the Ca-Cl @ graphene composite structure has a metallic nature.

B) Theoretical analysis of the conduction properties of two-dimensional Ca-Cl crystal

Fig. 17 (a, B) presents the band projection and electronic density of States maps of each element in the two-dimensional Ca-Cl crystal without graphene substrate in the CaCl @ graphene structure 1 in Fig. 11 and the complete structure, respectively. It is clear that the graphene substrate, the two-dimensional Ca-Cl crystal, and the composite of both are strongly metallic, with Ca and Cl together accounting for 37.7% of the total electronic States near the Fermi level.

Fig. 18 shows the electronic density of States (DOS) near the Fermi level of the three configurations of single graphene sheet, CaCl @ graphene structure 1 and two-dimensional Ca-Cl crystal obtained by theoretical calculation. It can be seen from the figure that the two-dimensional Ca-Cl crystal has stronger metallic property than graphene; The CaCl @ graphene structure 1 is more metallic than the 2D Ca-Cl crystal part alone.

Two-dimensional materials with piezoelectric properties can effectively reduce the size of devices. Materials with both piezoelectricity and ferromagnetism have great application value in the field of energy conversion sensors through magnetoelectric coupling effect^[23]. Since the two-dimensional metallic Ca-Cl crystal has two elements (Ca, Cl) arranged alternately (as shown in Structure 1 of Fig. 12), the Ca-Cl @ rGO film containing these two-dimensional Ca-Cl crystals is very likely to have piezoelectric properties. Fig. 19 shows the open-circuit voltage of a dry sample of Ca-Cl @ rGO film bent at an angle of 90 °, with a maximum output voltage of about 4 mV when the film is bent. After removing the bending force from the membrane, the output voltage can be reduced to zero or even overshoot to a negative value.

Since the dry sample of Ca-Cl @ rGO film has obvious metallicity (Fig. 16, 17), now the experimental data also show that the sample has piezoelectric-like properties. Metallic materials generally do not have piezoelectricity, as mentioned in the literature: "Piezoelectricity is only possible in materials with non-centrosymmetric structure and band gap, that is," non-metallic "^[22]; And "existing two-dimensional materials are piezoelectric only if they satisfy both of the following conditions: they must have an asymmetric crystal structure and must be non-metallic (i.e., have a band gap)". Metallicity and piezoelectricity coexist in the Ca-Cl @ rGO film composite structure, which may have applications in related fields.

The coexistence of metallicity and piezoelectricity is the result of the unique structure of two-dimensional CaCl, which is metallic on the one hand due to the univalent behavior of Ca ions (discussed in detail later); On the other hand, the structure has two elements (Ca, Cl), which produce different electrical effects under compressive or tensile strain.

"Graphene-CaCl" is a typical heterojunction structure with superior compatibility. This compatibility makes the two-dimensional Ca-Cl crystal very advantageous in some fields of magnetic materials, such as magnetoelectric materials, magneto-optical artificial heterojunction devices and so on^[24]. In order to further study the heterojunction properties of two-dimensional Ca-Cl @ rGO film structure, we carried out relevant experimental detection. As shown in fig. 20, the current-voltage curves of the Ca-Cl @ rGO film sample are nonlinear and asymmetric at positive and negative gate voltages, indicating typical rectifying behavior. As a control, the current-voltage curve of the rGO membrane sample showed a clear symmetry. This result confirms the heterojunction characteristics of the two-dimensional Ca-Cl @ rGO film structure, and lays the foundation for the further development of this room temperature ferromagnetic material in the field of heterojunction devices.

The anomalous stoichiometry, ferromagnetism and other physical properties of Ca-Cl crystal on rGO film indicate that the crystal orbital and electronic structure of two-dimensional Ca-Cl crystal are different from those of conventional three-dimensional CaCl₂ crystal. A possible inference is that the calcium ion in the crystal is probably monovalent, rather than divalent as we usually understand. To confirm this, dry samples of Ca-Cl @ rGO films were characterized by near edge X-ray absorption fine structure (NEXAFS) spectroscopy and compared with the NEXAFS results of metal Ca and conventional three-dimensional CaCl₂. As shown in fig. 21, the peaks at the Ca L₃ and L₂ edges in the Ca-Cl crystal in the dry sample of Ca-Cl @ rGO film are shifted, and are obviously different from the peak at the Ca⁰ in metal Ca and the peak at the Ca²⁺ in the conventional three-dimensional CaCl₂ crystal. The energy of the shifted L₃ edge is 348.02 eV, which is larger than 347.92 eV for metallic Ca and 347.82 eV for conventional three-dimensional CaCl₂ crystal. This indicates that the Ca peak from the sample cannot be any combination of peaks from normal Ca⁰ and Ca²⁺, so the Ca in the sample should have a new valence state different from zero and 2.

Fig. 21 shows the Ca-Cl crystal in the rGO film, and the Minor peaks (Minor peak in fig. 20) in the L-edge NEXAFS spectrum of Ca are at 346.92 and 350.22 eV, respectively, while the minor peaks in the spectrum of Ca-Ca bond in metallic calcium are at 346.62 and 349.92 eV, respectively. There are obvious differences in the relative intensities and energies of the secondary peaks between the two kinds of Ca, and the secondary peaks are related to the coordination number and symmetry of the Ca-Cl system^[25]. This indicates that the coordination number of Ca in Ca-Cl crystal in rGO film is different from that in metallic calcium of Ca-Ca bond, that is, Ca in Ca-Cl @ rGO has a unique electronic state.

Since the monovalent chemical state of Ca has never been reported, there is no standard map of monovalent Ca to compare with, which makes it impossible to determine whether the Ca ion of Ca-Cl crystal on graphene is monovalent. Considering that Cu ion has not only divalent Cu²⁺ but also monovalent Cu⁺ in nature. Therefore, based on the previous method of studying Ca-Cl crystals in graphene films, the valence state of Cu ions in Cu-Cl in graphene films was studied. The NEXAFS spectra of the Cu L₃ and L₂ edges are shown in Fig. 22. The L₃ and L₂ side peaks of Cu in the dry sample of Cu-Cl @ rGO film are at 925.39 and 945.19 eV (red-dashed positions), which are consistent with the positions of the L₃ and L₂ side peaks of Cu of the standard CuCl crystal, indicating that there is Cu with + 1 valence in the Cu-Cl crystal in the rGO film.

X-ray photoelectron spectroscopy (XPS) was used to characterize the stability of the Cu⁺ in rGO films. The 2p_3/2 peak of Cu in the Cu-Cl @ rGO sample after soaking in CuCl₂ solution and drying treatment is at 932.0 eV, which is the same as CuCl (932.0 eV), but different from CuCl₂(934.7 eV). Shows that the valence electron of Cu ions in these crystals changes from + 2 to + 1, which is consistent with the results of NEXAFS experiments. In addition, the peak of Cu⁺ could be clearly observed after the rGO film was soaked in CuCl₂ solution and left for 3 and 10 days, indicating that Cu⁺ could exist stably within rGO for at least 10 days (Fig. 23). Considering that the + 1 copper ion is unstable in the natural environment, this will help to solve the difficulties caused by the lack of stability of the + 1 copper ion in the field of catalyst application^[26][27].

Under the interaction of hydrated ion-π, ions will be adsorbed on the surface of polyaromatic ring structure rich in π electrons. Under the action of thermal perturbation, these adsorbed anions and cations will form an ordered structure, forming a two-dimensional crystal with an abnormal stoichiometric ratio, which is called "anti-crystal". Because the adsorption energy intensity of π electrons is different from that of anions and cations, the surface of multi-aromatic ring structure will regulate the proportion of anions and cations adsorbed on the surface. In this paper, we summarize the progress in the study of two-dimensional crystals of Na₂Cl/Na₃Cl and CaCl with anomalous stoichiometry at room temperature and pressure. It is obvious that the anomalous stoichiometric crystal has a unique electronic structure and thus has physicochemical properties completely different from those of the general crystal. For example, CaCl two-dimensional crystal shows the coexistence of conductivity, ferromagnetism and piezoelectricity. These properties indicate that the calcium ion in CaCl shows the characteristics of monovalence, and the NEXAFS experiment also confirms that the spectral characteristics of calcium ion are different from those of metal calcium and divalent calcium ions, and can not be formed by the linear superposition of the spectral characteristics of metal calcium and divalent calcium ions, which again indicates that the calcium ion in CaCl two-dimensional crystal has a new valence that has never been reported.

The ferromagnetism of CaCl two-dimensional crystal with abnormal stoichiometry breaks through the traditional understanding that only ferromagnetic substances have ferromagnetism. Considering the universality of this mechanism, it can be speculated that Na₂Cl crystals and other inverse crystals will also have ferromagnetism. In recent years, more and more attention has been paid to the magnetic effects of organisms and the corresponding magnetic medical technology, but people have been arguing whether these magnetic effects are caused by traditional ferromagnetic substances or free radicals. If calcium and sodium ions can induce ferromagnetism or superstrong paramagnetism through ion-π interaction, it will provide a new idea for the study of biomagnetic effect and magnetic medicine. At the same time, as a low-dimensional magnetic material at room temperature which is easy to produce, the discovery of CaCl two-dimensional crystal with abnormal stoichiometry not only expands the types of low-dimensional ferromagnetic materials,It also overcomes the shortcomings of low Curie temperature, difficult preparation and difficult large-scale production of this type of materials, and provides a new idea for the research of this type of materials.

It should be noted that the interaction potential that can adsorb ions on the surface is not only the ion-π interaction, but also these interactions are different for different anions and cations, so the two-dimensional crystal adsorbed on the surface is generally different from the conventional three-dimensional crystal. Considering these, we may think that "normal" (conventional three-dimensional NaCl, CaCl₂ crystals) is a small probability event, abnormal is a large probability, "abnormal is normal".

Finally, it is worth noting that ion-π interaction was considered a chemical concept, but was first discovered by biologists. However, the interaction between hydrated ions and π electrons has been underestimated for a long time, because the study of this interaction is limited to the consideration of a single hydrated ion and an aromatic ring structure system, which is limited by the weak interaction between the two and the short residence time of the ion. However, when the idea of physical statistics is introduced to consider the interaction between a large number of hydrated ions and aromatic ring structures on a long time scale, there is a dynamic equilibrium of continuous adsorption-desorption of ions on the surface of aromatic ring structures. The average number of hydrated ions adsorbed on an aromatic ring is determined by the competition between the energy of the hydrated ion-π interaction (leading to adsorption) and the energy of the thermal perturbation (leading to desorption). When the concentration of ions is high enough, the interaction between hydrated ions and aromatic rings becomes very important, which further illustrates the importance of physical, chemical and biological integration.