Reducing agents with low ionization energies (IEs) play a crucial role in chemical synthesis. As is well-known, alkali metal atoms possess the lowest ionization energies (5.39–3.89 eV) (Lide, 2003) among all the elements in the periodic table. However, it is reported that a class of extraordinary compounds possesses even lower IEs than those of alkali metal atoms. Such species were termed “superalkalis” by Gutsev and Boldyrev (1982). Initially, superalkalis were designed by decorating an electronegative central atom with alkali-metal ligands, such as FLi₂, OLi₃, and NLi₄ following the formula ML _k+1 (L is an alkali-metal atom and M is an electronegative atom of valency k). In ML _k+1, one more alkali metal atom will bring an extra valence electron for the electronic shell of M according to the octet rule. Consequently, such an ML _k+1 complex has a great tendency to lose the extra valence electron and thus possess strong reducibility (Sun and Wu, 2019).

Owing to their excellent reducing ability, superalkalis can be used to synthesize unusual charge-transfer salts (Zintl and Morawietz, 1938; Jansen, 1976) with the counterpart possessing relatively low electron affinity and activate stable CO₂ and N₂ molecules (Park and Meloni, 2017; Zhao et al., 2017; Park and Meloni, 2018; Sun et al., 2019; Sikorska and Gaston, 2020) to produce high-value products (Zhang et al., 2021a; Zhang et al., 2021b). In particular, as a special subset of superatom (Reveles et al., 2009; Luo and Castleman, 2014), superalkalis can behave as alkali metal atoms and maintain their structural and electronic integrities when assembled into extended nanostructures (Reber et al., 2007). Hence, they offer an exciting prospect of serving as building blocks for nanomaterials with highly tunable properties (Jena and Sun 2018), such as supersalts (Giri et al., 2014), hydrogen storage materials (Merino et al., 2012), noble-gas-trapping agents (Pan et al., 2013), superbases (Srivastava and Misra, 2015), and nonlinear optical materials (Sun et al., 2014a; Sun et al., 2014b; Sun et al., 2016b; Sun et al., 2016c; Sun et al., 2018a).

In view of the great importance of superalkalis in chemistry, various superalkalis have been theoretically (Tong et al., 2009; Tong et al., 2011, Tong et al., 2012a,Tong et al., 2012b; Hou et al., 2013; Liu et al., 2014; Sun et al., 2013; Sun et al., 2016a; Giri et al., 2016; Zhao et al., 2017; Sun et al., 2018b; Sun et al., 2019; Park and Meloni, 2018; Sun and Wu, 2019; Tkachenko et al., 2019; Sikorska and Gaston, 2020) and experimentally (Lievens et al., 1999; Yokoyama et al., 2000, 2001; Hou and Wang, 2020) characterized in the past decades. To date, conventional mononuclear ML _k+1 superalkalis have been expanded to dinuclear (Tong et al., 2009; Tong et al., 2011) and polynuclear (Tong et al., 2012a; Tong et al., 2012b; Liu et al., 2014) superalkalis, aromatic superalkalis (Sun et al., 2013), Zintl-ion-based superalkalis (Giri et al., 2016; Sun et al., 2018b), hyperalkalis (Sun et al., 2016a), alkali-metal complexes (Tkachenko et al., 2019), and so on. More importantly, some alkali-metal-free superalkalis (Hou et al., 2014; Liu et al., 2016), particularly nonmetallic superalkalis (Hou et al., 2013; Srivastava, 2019a; Srivastava, 2019b), have been proposed in recent years. For example, Hou et al. (2013) designed a class of M₂H_2n+1 ⁺ (M = F, O, N, C for n = 1, 2, 3, 4, respectively) superalkali cations by using hydrogen atoms as ligands. Following a similar rule, the other two series of nonmetallic superalkali cations, namely, F _n H _n+1 ⁺ (n = 1–10) and C _x H_4x+1 ⁺ (x = 1–5), have been proposed by Srivastava (2019a, 2019b). These achievements demonstrate that the potential of designing superalkalis of new type is limitless and thereby motivate us to create more diverse superalkali species by using different rules and ligands to further enrich the superalkali family.

More recently, Tkachenko et al. (2019) reported the record low ionization potentials (1.70–1.52 eV) of alkali metal complexes with crown ethers and cryptands and defined them as superalkali species. In fact, such alkali metal complexes were previously named as electrides, a special kind of ionic solids with trapped electrons serving as anions (Dye, 2009). Hence, this work first built a bridge between superalkalis and electrides. However, it is known that crown ethers and cryptands are prone to be cleaved at the C-O bonds (Redko et al., 2002). Fortunately, analogous complexants, such as adamanzane (adz) (Redko et al., 2002) and aza-cage (aza222) (Kim et al., 1999) with only C-N linkages and no amine hydrogens are considerably stable to synthesize the crystalline salts, including alkalides (Kim et al., 1999; Redko et al., 2002) and electrides (Redko et al., 2005) at room temperature. Hence, it is highly expected that such complexants could also be used as excellent building blocks to design and synthesize new superalkalis.

To verify this hypothesis, the 3⁶adamanzane (3⁶adz) has been chosen as a representative to design a series of X@3⁶adz (X = H, B, C, N, O, F, and Si) by encapsulating nonmetallic atoms into the cavity of this cage-like complexant in this work (see Figure 1). The 3⁶adz complexant is composed of tricyclic tetra-amines with aliphatic chains (Springborg, 2003), which has been used to synthesize a stable alkalide [H@3⁶adz]⁺Na⁻ (Redko et al., 2002). In this complexant, all the lone pairs of 4 N atoms direct toward the center of the cage (see Supplementary Figure S1). Under the repulsion of the lone pairs of N atoms, the outmost valence electrons of X are destabilized to different degrees, leading to the obvious rise of HOMO level of X@3⁶adz as compared with the isolated 3⁶adz complexant. As a result, these proposed complexes exhibit extraordinarily low AIE values of 0.78–5.28 eV although X atoms possess very high ionization energies (IEs) of 8.15–17.42 eV (Lide, 2003). In particular, the B@3⁶adz complex also has the potential to serve as new nonlinear optical (NLO) molecule with a remarkably large first hyperppolarizability of 1.35 × 10⁶ au because the valence electron of boron atom is pushed out of cage to form diffuse excess electrons. We hope that this work will not only provide new nonmetallic members for the superatom family, but will also open the door to design strong reducing matters by embedding nonmetallic atoms into the various cage-like complexants.

In this work, all the calculations were carried out by using the coulomb-attenuated hybrid exchange-correlation functional (CAM-B3LYP) (Tawada et al., 2004; Yanai et al., 2004), which has been reported to be capable of providing not only the molecular geometries close to the experimentally observed structures but also the (hyper)polarizabilities close to those of the coupled cluster calculations (Limacher et al., 2009). Hence, this method has been widely used to calculate the (hyper)polarizabilities of NLO molecules in the previous works (Sun et al., 2014a; Sun et al., 2014b, Sun et al., 2016c). Also, a method test has also been carried out by sampling B@3⁶adz (see Supplementary Table S1) to verify the reliability of this method in calculating the properties of such systems. From Supplementary Table S1, it is found that CAM-B3LYP gives approximately equal VIE and β ₀ to those obtained by several other functionals, which indicates that this method is reliable for these studied systems. Hence, all the optimized geometric structures of the studied species with real frequencies were obtained under the CAM-B3LYP/6-31+G(d) level. Based on the optimized structures, the single-point energies, nature population analysis (NPA) charges, and static electric properties were calculated at the CAM-B3LYP/6-311++G (d, p) level.

In this work, the vertical ionization energies (VIEs) of X@3⁶adz (X = H, B, C, N, O, F, and Si) were calculated as the energy difference between the optimized neutral complex and the cation in the geometry of the neutral complex, while their adiabatic ionization energies (AIEs) are defined as the energy difference between the neutral and cationic complex at their respective optimized structures. In addition, the TD-M06-2X calculations were performed to obtain the transition energies and oscillator strengths of the crucial excited states as well as the difference of the dipole moments between the ground state and crucial excited state of X@3⁶adz by using the 6-311++G (d, p) basis set. Herein, the dipole moments (µ ₀), polarizabilities (α ₀), and first hyperpolarizabilities (β ₀) are defined as follows, μ 0 = ( μ x 2 + μ y 2 + μ z 2 ) 1 / 2 (1) α 0 = 1 3 ( α xx + α yy + α zz ) (2) β 0 = ( β x 2 + β y 2 + β z 2 ) 1 / 2 (3) where β i = 1 3 ∑ j ( β i j j + β j j i + β j i j ) , i, j = {x, y, z}.

All the above calculations were performed by using the GAUSSIAN 16 program package (Frisch et al., 2016). The dimensional plots of the molecular structures were generated with the GaussView program (Dennington et al., 2016).

Initially, seven X@3⁶adz (X = H, B, C, N, O, F, and Si) compounds have been constructed by encapsulating one X atom into a 3⁶adz cage. After optimization, the geometric structures of X@3⁶adz are illustrated in Figure 2, while the corresponding cations are plotted in Supplementary Figure S2. Moreover, selected structural parameters of these resulting X@3⁶adz compounds are summarized in Table 1.

As shown in Figure 1, 3⁶adz is a cage-like complexant with S ₄ symmetry. From Figure 2, it is observed that the geometric integrity of 3⁶adz cage is well-preserved in these X@3⁶adz compounds. However, the geometric symmetries of these compounds are lowered to C ₁ and C ₂, except for H@3⁶adz, which maintains the S ₄ symmetry of 3⁶adz. To be specific, the encapsulated hydrogen atom located at the central position of 3⁶adz in H@3⁶adz, yields the newly formed N-H bonds of 2.11 Å and ∠N1-H-N2 of 113.5°. As for B@3⁶adz, the boron atom tends to bind with 3 N atoms of the complexant, forming 3 N-B bonds of 1.63 Å ∼ 1.66 Å, while the distance between the uncombined N and B atoms is as long as 3.02 Å. The C@3⁶adz complex possesses a C ₂-symmetric structure, where the introduced carbon atom prefers to bind with 2 N atoms of 3⁶adz by forming two N-C bonds of 1.52 Å. Differently, the more electronegative N, O, and F atoms are linked to only 1 N atom of the cage complexant via N-N, N-O, and N-F bonds of 1.41, 1.34, and 1.87 Å, respectively, generating the very similar structures of X@3⁶adz (X = N, O, and F). Similar to B@3⁶adz, the introduced silicon atom tends to bind with 3 N atoms of complexant via 3 N-Si bonds of 2.06–2.35 Å in Si@3⁶adz.

By turning to the cations of X@3⁶adz, it is found that only the optimized structure of [B@3⁶adz]⁺ cation almost coincides with the geometry of the corresponding neutral one (see Supplementary Figure S2). For instance, the critical geometric parameters of d _B-N1, d _B-N2, and ∠N1-B-N2 are hardly changed after one electron is lost from B@3⁶adz. However, for the rest of X@3⁶adz (X = H, C, N, O, F, and Si), quite different geometries of cationic and neutral complexes were found. For instance, the H⁺ is attached to 1 N atom of the complexant in the resulting [H@3⁶adz]⁺, while the doped N atom turns to combine with 2 N atoms of 3⁶adz in [N@3⁶adz]⁺ and Si atom almost moves to the center of the cage in [Si@3⁶adz]⁺. The geometry of C@3⁶adz is distorted from C ₂ symmetry to C ₁ with the changes of 0.29 Å for the C-N2 bond and 7.3° for ∠N1-C-N2. As for [F@3⁶adz]⁺, the N-F bond is shortened from 1.87 Å to 1.38 Å because the introduced F atom further loses 0.333e (see Supplementary Table S1) and thus tends to bind more tightly with the N atom of the complexant. Also, as shown in Table 2, the difference in the geometry can also be reflected by the difference of 0.29–3.06 eV between the vertical ionization energies (VIEs) and adiabatic ionization energies (AIEs) of these X@3⁶adz (X = H, C, N, O, F, and Si) species.

More interestingly, as shown in Table 2, extraordinarily low AIE values of 0.78–5.28 eV were found for all the studied X@3⁶adz (X = H, B, C, N, O, F, and Si) complexes, although X atoms possess very high ionization energies (IEs) of 8.15–17.42 eV (Lide, 2003). Such low AIE values of X@3⁶adz are not only lower than that of 6.56 eV for the 3⁶adz complexant but also significantly lower than that of 5.39 eV (Lide, 2003) for lithium atom. In particular, the AIE values of H@3⁶adz (0.78 eV), B@3⁶adz (2.16 eV), C@3⁶adz (2.72 eV), N@3⁶adz (3.15 eV), and Si@3⁶adz (1.79 eV) are even lower than the IE of 3.89 eV (Lide, 2003) for Cs atoms. Hence, these compounds should be classified as novel nonmetallic superalkalis.

How to understand the low IE values of such X@3⁶adz complexes? We can find some clues from the frontier molecular orbital analysis. From Figure 3, a clear inverse correlation between the VIE values and HOMO levels of these studied compounds can be observed, that is, the higher the HOMO level is, the lower the VIE is. This is reasonable considering the fact that the valence electrons on the higher HOMOs are easier to be ionized. To be specific, all the HOMO energies (−1.81 ∼ −5.87 eV) of X@3⁶adz are much higher than that of −6.49 eV for 3⁶adz, because of the repulsion between the lone pairs of N atoms and the outmost valence electrons of X, resulting in the lower VIEs (2.18–6.38 eV) than that (6.80 eV) of 3⁶adz. In particular, B@3⁶adz exhibits the highest HOMO level of −1.81 eV, and thus possesses the lowest VIE of 2.18 eV among these X@3⁶adz complexes. This is because that the valence electron of embedded boron atom is pushed out of the cage by the lone pairs of N atoms of the complexant, forming a electride-like molecule [B⁺@3⁶adz](e^‒) with obvious diffuse electrons in the HOMO of B@3⁶adz (see Supplementary Figure S3). Thus, the existence of diffuse excess electrons in its high-lying HOMO level results in the high reducibility of this B@3⁶adz complex.

Differently, as shown in Supplementary Figure S3, the valence electrons are accommodated into the HOMOs mainly composed of the 1s atomic orbital of embedded hydrogen atom in H@3⁶adz, and the np orbitals of C and Si atoms in X@3⁶adz (X = C and Si), which show obvious antibonding character with respect to the central atom-complexant interaction. Such antibonding HOMOs destabilize the neutral structures of X@3⁶adz (X = H, C, and Si) and result in their low VIE values (Gutsev and Boldyrev, 1987; Tkachenko et al., 2019). Hence, these 3 species also have quite low VIE values of 2.73–3.83 eV. However, it should be mentioned that the VIEs of 5.72–6.38 eV for X@3⁶adz (X = N, O, and F) are larger than that of 5.39 eV for Li atom, although their HOMOs also possess obvious antibonding character. This is attributed to the larger elertonegativities of N, O, and F atoms than H, C, and Si atoms, which hinders the ionization of the valence electrons on their np orbitals in the HOMOs of X@3⁶adz (X = N, O, and F).

On the other hand, the difference between the VIE and AIE values are also related to the different electron distribution in the HOMOs of X@3⁶adz. To be specific, the geometric structure of B@3⁶adz is hardly changed after its diffuse excess electron of HOMO is lost, resulting in its nearly equal VIE (2.18 eV) and AIE (2.16 eV) values. However, the destabilization of antibonding HOMOs for the neutral X@3⁶adz (X = H, C, and Si) complexes drives the embedded X atom to lose nearly one valence electron (0.667 e ∼ 0.867 e, as shown in Supplementary Table S1), forming relatively stable [X@3⁶adz]⁺ cations. After losing one electron, the formed X⁺ ion changes its interaction mode with the cage complexant, which leads to the large structural distortion and considerable difference between the VIE and AIE values of X@3⁶adz (X = H, C, and Si). Note that the AIE of H@3⁶adz is as low as 0.78 eV because the formed [H@3⁶adz]⁺ is very stable and has been identified in various synthesized ionic compounds, such as [H@3⁶adz]⁺X^‒ (X = Cl, Br, I, and Na) (Kim et al., 1994; Springborg et al., 1996; Redko et al., 2002).

Finally, considering the diffuse excess electron in the HOMO of B@3⁶adz, it is highly expected that this superalkali also exhibits considerable nonlinear optical (NLO) response. Thus, the static electric properties of these studied X@3⁶adz compounds and 3⁶adz complexant were calculated and listed in Table 3. It is observed that B@3⁶adz has the largest dipole moment (3.326 au) and polarizability (1,599 au) among these X@3⁶adz complexes because of the existence of diffuse electrons in the HOMO of this superalkali. In particular, the first hyperpolarizability (β ₀) of B@3⁶adz is as large as 1.35 × 10⁶ au, which is significantly larger than those of the reported superalkalis and superalkali-based NLO materials, such as the aromatic organometallic superalkali Au₃(Py)₃ (3.74 × 10⁴ au) (Parida et al., 2018), superalkali-based alkalide Li₃O⁺(calix [4]pyrrole)M^‒ (M = Li, Na, and K) (1.18 × 10⁴–3.33 × 10⁴ au) (Sun et al., 2014a), and superalkali-based electride Li₃O@Al₁₂N₁₂ (8.73 × 10⁵ au) (Sun et al., 2016b), indicating that this proposed superalkali species can indeed be considered as a new kind of NLO molecule of high performance.

To understand the eminently large β ₀ value of B@3⁶adz, we focus our attention on the simple two-level model (Oudar, 1977; Oudar and Chemla, 1977), β 0 ∝ Δ μ ⋅ f 0 Δ E 3 (4) where ΔE, f ₀, and Δµ are the transition energy, oscillator strength, and the difference in the dipole moment between the ground state and crucial excited state, respectively. According to this two-level expression, β ₀ is proportional to f ₀ and ∆µ, while is inversely proportional to the cube of ΔE, and therefore, the transition energy is considered to be the decisive factor in the first hyperpolarizability (Sun et al., 2014a,b, 2016b,c). Hence, the ΔE, f ₀, and Δµ values of the crucial excited states with the largest oscillator strength of 3⁶adz and X@3⁶adz are summarized in Table 3. It is noted that B@3⁶adz possesses extremely smaller ΔE and much larger f ₀ and ∆µ values than those of other X@3⁶adz (X = H, C, N, O, F, and Si) compounds, which rationalizes its largest β ₀ value among these studied X@3⁶adz species. In addition, the proposed C@3⁶adz and Si@3⁶adz superalkalis also show considerable β ₀ values of 4.05 × 10³ au and 1.95 × 10⁴ au, respectively, because of their relatively smaller ΔE values and larger Δµ values.

By using 3⁶adamanzane (3⁶adz) as a complexant, a series of X@3⁶adz (X = H, B, C, N, O, F, and Si) compounds were constructed and studied based on the density functional theory. It is interesting to find that the X@3⁶adz (X = H, B, C, N, and Si) complexes possess lower AIE values than the IE of Cs atoms though the X atoms and 3⁶adz possess very high IE values. Thereby, they can be regarded as a new kind of nonmetallic superalkalis. In particular, different from other complexes, the low IE of B@3⁶adz is derived from the diffuse excess electron formed by the repulsion between the valence electron of the embedded boron atom and lone pairs of N atoms of the complexant. Due to the existence of diffuse electrons, this superalkali also possesses a remarkably large β ₀ of 1.35 × 10⁶ au, which can serve as a new kind of NLO molecule. Hence, it is highly hoped that the theoretical design and characterization of these nonmetallic superalkali species could provide meaningful references to further design novel reducing matters or NLO materials by using such cage-like molecules as complexants.