A New Strategy of bi-Alkali Metal Doping to Design Boron Phosphide Nanocages of High Nonlinear Optical Response with Better Thermodynamic Stability

Nonlinear optical materials have gained immense scientific interest in the recent times owing to their vast applications in various fields. Continuous strides are made to design and synthesize materials with large nonlinear optical response and high thermodynamic stability. In this regard, we present here bi-alkali metal doping on boron phosphide nanocage as a new strategy to design thermodynamically stable materials with large nonlinear optical response. The geometric, thermodynamic, electronic, optical and nonlinear optical properties of complexes are explored through density functional theory (DFT) simulations. The doping of alkali metal atoms introduces excess of electrons in the host (B12P12) nanocage. These electrons contribute towards the formation of new HOMOs, which reduce the HOMO–LUMO gaps of the designed complexes. The HOMO–LUMO gaps of the designed complexes range from 0.63 eV to 3.69 eV. The diffused excess electrons also induce large hyperpolarizability values in the complexes i.e. up to 4.0 × 104au. TD-DFT calculations have been performed for crucial transition states and UV–VIS analysis. Non-covalent interaction (NCI) along with quantum theory of the atoms in molecules (QTAIM) analyses are carried out to understand the bonding interactions between alkali metal atoms and B12P12 nanocage. All the obtained results suggest that bi-alkali metal doped nanocages are exceptionally stable materials with improved NLO response.

Among these materials, inorganic fullerenes (XY) n have recently appeared as excellent materials for applications in optoelectronic devices due to their unique properties. The studies reveal that various III-V fullerenes (XY) n have been synthesized experimentally [26]. These experimental techniques include carbothermal reduction, chemical vapor deposition, direct nitridation [27] and solution growth [28] methods. Molecular simulations show that hetero-fullerenes of type (XY) n [X = Al, B; Y = N, P; n = 12] are the most stable structures. Most of these fullerenes are semiconductors with wide HOMO-LUMO gap [29,30]. Moreover, these fullerenes have negligible NLO response due to centrosymmetry. Various strategies have been employed to induce NLO response in these materials. These strategies include doping of alkali metals [31], alkaline earth metals [32,33], transition metal doping [34], superalkalis [35,36] consideration of diradical character of materials [37] and substitution of different organic and inorganic systems [38,39].
Recently, Li et al. reported an effective strategy where diffuse excess electrons are introduced to increase the NLO response [40,41]. Fullerenes hold centrosymmetric structure, therefore they have negligible dipole moment and hyperpolarizability (β o ). The introduction of diffuse excess electrons causes remarkable increase in hyperpolarizability. Moreover, HOMO-LUMO gaps are significantly narrowed down under the influence of excess electrons [42]. Certainly, doping of foreign metals is an efficient strategy to induce excess electrons in materials. Alkali metals have low ionization potential, therefore valence electrons from these metal atoms are easily diffused out to act as excess electrons in these materials. This technique is frequently used to design high performance NLO materials [43]. Literature reveals that lithium doping on B 10 H 14 framework leads to considerable increase in hyperpolarizability (2.31 × 10 4 au) because of diffuse excess electrons [44]. Huang et al. have studied alkali metal doped AlN nanocages, and proved that hyperpolarizability of the resultant complex (Li@b 66 -Al 12 N 12 ) is increased up to 8.89 × 10 5 au [26]. A related study on B 12 N 12 revealed that alkali metals as substitutional dopants also increased the hyperpolarizability manifold [31] In addition, alkali metal atom doped complexes, Li + ( calix [4] pyrrole)M − ; [M = Li, Na, and K] have shown remarkable increment in hyperpolarizability value up to 7.3 × 10 3 au [45]. Likewise, alkali metal doped aromatic rings (indole, thiophene, and benzene) show enhanced electronic properties and exhibit large hyperpolarizability values ranging from 6.7 × 10 3 to 9.3 × 10 3 au [46]. Muhammad et al. have reported that decoration of Si 12 C 12 with alkali metals tunes up the first hyperpolarizability up to 5.7 × 10 3 au [47]. A remarkable nonlinear optical response of 7.9 × 10 5 au for K@P top -B 12 P 12 has been reported by Maria et al. [48]. Literature reveals a number of studies on single and multi-atom doping but no study is found on bi-metal doping of nanocages. Consequently, there is still a need to explore bi-metal doping strategy to design novel NLO materials. B 12 P 12 is a refractory semiconducting structure. Boron phosphide has been synthesized by molten nickel or nickel phosphide reactions [49], solid state metathesis reaction [50], Sn flux synthesis [51] and high temperature reactions of elements [52]. It holds extreme binding affinity for a number of surfaces that makes it an excellent material for various practical applications [53]. To date, boron phosphide nanocages have been explored for their applications as NLO materials [34,35], hydrogen storage media [54,55], chemical sensors for SO 2 [56] and phenol [57], and as catalytic materials [58]. Doping single alkali metal atom is a popular and the most used strategy to introduce excess electrons. In this study, we are specifically interested to study the considerable impacts of bi-alkali metal atoms doping on B 12 P 12 nanocage and subsequently its NLO response. Geometries, NBO charge, dipole moment, polarizability, hyperpolarizability, NCI and QTAIM analyses are performed to get deep insight of NLO response generated after bi-alkali metal doping. Moreover, UV-Vis, IR spectra have been analyzed to examine the effects of bi-metal doping on the absorption properties of B 12 P 12 . Undoubtedly, this study will provide a new approach to design highly stable bi-metal doped B 12 P 12 based NLO materials.

Computational Details
All calculations for this study are performed using the Gaussian 16 software package [59] and structures have been visualized by using GaussView 6.0 [60]. The reported structures in this work are optimized at (Becke's threeparameter hybrid functional (B3) in relation to the gradient corrected correlation functional of Lee-Yang-Parr (LYP) with 6-31G(d,p) basis set. True minima for all the structures are characterized by frequency calculations at B3LYP/6-31G(d,p) level of theory. To confirm the extent of stability for designed structures, adsorption energies are analyzed by using the following equation: where E complex is the energy of doped nanocage, E cage is the energy of pristine B 12 P 12 nanocage while E M2 stands for the sum energy of doped bi-metal atoms only. The reported energies are corrected for zero-point vibrational correction. NBO (natural bond orbital) and infra-red analysis are also executed using the same level of theory.
Polarizability, first hyperpolarizability and dipole moment are calculated by the following equations: Polarizability

Dipole moment
Polarizability and first hyperpolarizability are calculated at CAM-B3LYP/6-311 + G(d) level of theory as the earlier reported data have disclosed it a well-established method for computing hyperpolarizability of inorganic nanocages [33]. TD-DFT (time-dependent density functional theory) calculations are performed using CAM-B3LYP/6-311 + G(d) level of theory for absorption spectra and crucial excited states of all complexes. Partial density of states (PDOS) were generated through MultiWfn software [61].
To get deeper understanding of bonding patterns, quantum theory of atoms in molecule (QTAIM) topological analysis was performed and the corresponding wave functions were produced. The attributes of the bond critical points (BCP) with reference to electron density (ρ) and its laplacian (∇ 2 ρ), the potential electron energy density (V (r) ), Lagragian kinetic energy (G (r) ), and the total density of electron energy (H (r) ) were obtained and analyzed.
Noncovalent interaction-reduced density gradient (NCI-RDG) strategy has been employed to identify the nature of bonding interactions between dopants and nanocage. The NCI implication depends on the reduced density gradient (s) and electron density (ρ). The said relation is as following: By operating the three parameters along the three foremost axis of maximal variation, the Laplacian can be narrated as NCI isosurfaces are represented by green, red and blue color codes to describe weak van der Waals forces, destabilizing steric interactions and hydrogen bonding interaction in molecules, respectively. Moreover, NCI-RDG and AIM analysis were performed using MultiWfn software program in combination with visual molecular dynamic (VMD) software [62].

Results and Discussion
First of all, pristine boron phosphide nanocage was optimized and the computed results are found comparable with the already reported data [48] [35]. Pristine B 12 P 12 has a C 2V symmetry. It contains six four-membered rings and eight six-membered rings of B-P bonds. The B-P bond length is 1.92 Å in four-membered rings and 1.90 Å for six-membered rings. The geometrical and electronic properties of nanocage are completely changed when decorated with alkali metal atoms. A detailed study on bi-alkali metal atoms (Li, Na, and K) interaction with boron phosphide nanocage is carried out by considering all possible doping positions in a trans-manner. All designed complexes are optimized to true minima as confirmed from all real frequencies. There are total six positions where alkali metals can be decorated at trans-positions. These positions are the top of boron atom (M 2 @B), phosphorus atom (M 2 @P), B-P bond fused between two six-membered rings (M 2 @b 66 ), B-P bond fused between a four and a six-membered ring (M 2 @b 64 ), over the center of six-membered ring (M 2 @r 6 ) and over the center of four membered ring (M 2 @r 4 ). We scanned all these possible positions and five structures for Li (M 2 @b 64 , M 2 @ b 66 , M 2 @r 6 , M 2 @B, and M 2 @P), four structures for sodium (M 2 @b 66 , M 2 @r 6 , M 2 @r 4 , M 2 @P) and three structures for potassium (M 2 @b 64 , M 2 @b 66 , M 2 @r 6 ) have been successfully obtained. The optimized structures discussed are given in Fig. 1 while rest of the structures are given in Fig.S1 of supporting information.

Geometrical Parameters
We have computed interaction distances of decorated alkali metal atoms with the neighboring boron and phosphorus atoms. The distance of both alkali metal atoms with neighboring atoms is almost same, as can be seen from   26 ) than any other alkali metal atoms . Each doped metal in Na 2 @ r 6 has 0.91 charge. The amount of charge depends on the type of metal and its orientation on nanocage. In case of Li 2 @b 66 , the M 25 carries 0.92 NBO charge whereas M 26 carries 0.85 charge. In the case of sodium complexes Na 2 @ r 6 , 0.91 charge is observed for both metal atoms. On the other hand, the potassium metal in K 2 @r 6 has a maximum positive charge of 0.94. Each lithium atom in Li 2 @P shows 0.71 charge. For potassium doped complexes, the highest charge on metal atoms (0.94) is observed for K 2 @r 6 whereas the lowest charge (0.91) is seen for K 2 @b 64 complex. In a nutshell, the positive charges on alkali metal atoms in doped  Table 1.
Dipole moments of all the optimized complexes are given in Table 2. Pristine boron phosphide nanocage has zero dipole moment because of its centrosymmetry. However, dipole moments are observed for doped complexes. The dipole moments increase with increase in the size of alkali metal atoms. The complex, K 2 @b 64 , has the highest charge separation among all complexes therefore, it exhibits the highest dipole moment (11.17D) followed by 7.33D for Li 2 @b 64 . The structure with bi-metallic elements doped on boron site (Li 2 @B) exhibits the dipole moment of 3.85D. These results also reveal high polarity for most of the designed B 12 P 12 complexes.
Adsorption energies of all considered complexes are given in Table 2. All these structures are fully relaxed to true minima. To confirm the stability of complexes, the adsorption energies have been calculated for all complexes. The obtained negative adsorption energies of complexes confirm that doping of bi-alkali metal atoms is a feasible process.
Lithium doped nanocages have higher adsorption energies than sodium and potassium doped complexes. Li 2 @ b 66 , Na 2 @b 66 , and K 2 @b 66 have adsorption energies of − 49.3 kcal/mol, − 20.4 kcal/mol and − 31.9 kcal/mol, respectively. Adsorption energies of Li 2 @r 6 , Na 2 @r 6 and K 2 @r 6 are − 43.3 kcal/mol, − 22.6 kcal/mol and − 34.6 kcal/ mol, respectively. For Na 2 @r 4 complex, the interaction energy value is − 18.5 kcal/mole. Meanwhile, complexes M 2 @b 64 (M = Li, K) have adsorption energies of − 43.2 kcal/ mol and − 31.7 kcal/mol for lithium and potassium doped systems, respectively. The complex, Li 2 @B, has adsorption energy of − 49.3 kcal/mole, while Li 2 @P, and Na 2 @P have adsorption energies of − 22.5 kcal/mol and − 31.9 kcal/mol, respectively. As concluded from the above discussion, Li 2 @ b 66 has the highest adsorption energy among all complexes. Moreover, boron site doped complexes have higher thermodynamic stabilities than those of phosphorus site doped complexes. The bi-metal doped complexes have interaction energies more than twice of the interaction energies of single metal doped B 12 P 12 cage [48]. For example, single lithium atom doped complex Li@b 66 has adsorption energy of − 21.77 kcal/mol while Li 2 @b 66 has − 49.3 kcal/mol interaction energy. Similarly, sodium doped complex Na@P has adsorption energy of − 12.34 kcal/mol while Na 2 @P has − 31.9 kcal//mol interaction energy. These examples confirm that bi-metal doped complexes are thermodynamically more stable structures than single metal doped complexes.

Electronic Properties
Boron phosphide (B 12 P 12 ) is a semiconducting material that has a wide H-L gap of 3.7 eV. H-L gaps are significantly reduced for bi-metal doped complexes. Energies of HOMO, LUMO and the respective H-L gaps are given in Table 3. This reduction in H-L gaps is remarkable in sodium doped structures i.e. H-L gaps for Na 2 @r 4 , Na 2 @r 6 and Na 2 @r 66 complexes are 0.95 eV, 1.58 eV and 1.16 eV, respectively. The H-L gap of Na 2 @P complex is 0.56 eV. The H-L gaps are significantly decreased for lithium doped structures. The H-L gaps of Li 2 @b 64 and Li 2 @r 6 are 1.53 eV and 1.58 eV, respectively. These results (Table 3) illustrate that the H-L gaps are reduced by more than 50% in bi-metal doped nanocages. The H-L gaps in potassium doped structures range from 1.17 eV to 1.09 eV. It is illustrated that the effect of dopant on the energy of HOMO is more pronounced than that of LUMO. This is attributed to the interaction between metal atoms and nanocage, and the excess electrons of alkali metals which are transferred towards the cage. This phenomenon increases the energy of HOMO and reduces the energy gap. The lowest H-L gap of 0.56 eV is observed for Na 2 @P. The charge transfer from metal atoms to fullerene affects the Fermi levels of the doped systems. The transfer of charge from metal to nanocage has been confirmed by NBO analysis. The positive charges on metal atoms indicate transfer of electrons from alkali metal atoms to B 12 P 12 nanocage. This transfer of charges and formation of new high energy HOMO levels contribute towards increased Fermi levels. Fermi levels for all doped complexes have increased and are given in Table 3. The complex K 2 @r 6 has the highest charge transfer and it shows the highest Fermi level value of − 2.37 eV. Fermi levels for Li 2 @b 64 and K 2 @b 64 are present at − 3.29 eV and − 2.42 eV, respectively as greater charge transfer of |0.91| from each K atom has been observed for the later complex. On the other hand, Li 2 @P shows the higher value (− 2.83 eV) of Fermi level than Na 2 @P (− 2.90 eV), consistent with NBO charges of |0.71| and |0.56|, respectively. For the b 66 doped complexes, the Fermi levels follow the order of Li 2 @b 66 < Na 2 @b 66 < K 2 @b 66. The trend is consistent with the trends of NBO charges as the maximum average NBO charge transfer is observed for K 2 @b 66 while minimum is observed for Li 2 @b 66 .These results indicate that doping of bi-alkali metals has substantially decreased the HOMO-LUMO gaps which make them excellent materials for use in many conducting and optoelectronic devices. The densities of the HOMO and LUMO orbitals are presented in Fig. 2. To further elaborate the effect of bi-metal doping, TDOS (total density of states) and PDOS (partial density of states) for pristine and doped cages are plotted. By comparing with bare nanocage, it is evident that high energy HOMO orbitals are generated in doped complexes between the original HOMO and LUMO of B 12

Polarizability and First Hyperpolarizability Analysis
It has been reported that the nonlinear optical response is enhanced efficiently when excess electrons are introduced into a system. These electrons create new (high energy) HOMOs and enhance the polarizability and first hyperpolarizability of the systems. Polarizabilities, first hyperpolarizabilities, and crucial excited states of all designed complexes are given in Table 4  Pristine boron phosphide nanocage has zero hyperpolarizability due to symmetry of the cage. The results reveal that hyperpolarizabilities of doped nanocage are increased significantly as compared to bare boron phosphide nanocage. The highest β o value of 4.06 × 10 4 au is calculated for K 2 @ b 64 , followed by 1.4 × 10 4 au (Li 2 @b 64 ), and 1.4 × 10 3 au (Li 2 @b 66 ). For Na 2 @b 66 and Na 2 @r 4 , the hyperpolarizability values are 6.1 × 10 2 au and 3.2 × 10 2 au, respectively. The hyperpolarizability values for Li 2 @B is 1.64 × 10 3 au..

UV-Visible Exploration
To examine UV-visible spectral properties of the bare and doped nanocage, TD-DFT calculations have been performed. The results obtained by these calculations are summarized in Table 5.
The UV-visible analysis reveals that all doped complexes show bathochromic shifts in the absorption spectra as compared to bare B 12 P 12 nanocage. The UV-visible spectra of doped nanocages show absorbance from visible to the infrared region while bare nanocage showed absorption peak in the ultraviolet region. For M 2 @b 64 (M = Li, K), the maximum absorptions are at 984 nm and 1122 nm, respectively. For M 2 @b 66 , the highest absorption of maximum wavelength is calculated for Na 2 @b 66 (1384 nm) followed by K 2 @b 66 (1272 nm). Li 2 @b 66 shows the lowest value for maximum absorption in the series (532 nm) For M 2 @r 6 complexes, the absorption wavelength follows an increasing trend. The absorption of maximum wavelength for Li 2 @r 6 is 710 nm and it increases to 712 nm and 720 nm for Na 2 @ r 6 and K 2 @r 6 , respectively. The maximum absorbance of 1980 nm is shown by Na 2 @P which may be attributed to the smallest HOMO-LUMO gap of this system. All the UV-visible graphs are shown in Fig. 4.

FTIR Analysis
Pristine boron phosphide nanocage and doped complexes are studied to assess changes in its infra-red spectral properties upon doping. The IR spectra are shown in Fig. 5. From previous studies, it is evident that doping of alkali metal atom reduces the vibrational frequency of host nanocage [53]. Boron phosphide nanocage has vibrational frequencies at 761 cm −1 and 894 cm −1 . All designed complexes show new peaks that appear mainly in the region of 50-400 cm −1 . The appearance of new peaks in this region is due to alkali metal atoms.

NCI-RDG Analysis
The non-covalent interaction analysis is capable of differentiating the regions of hydrogen bonds, repulsive steric interactions and van der Waals interactions [63,64]. Basically, this analysis was introduced for better understanding of types and nature of intermolecular bonding interactions.
The 3D NCI images for some prominent doped complexes are shown in Fig. 6, while rest of isosurfaces are added in supporting information (Fig.S4). On 3D NCI images (isosurfaces), red color represents steric repulsion, while yellow and green patches signify van der Waals interactions.

3
Blue patches denote strong attractive bonding interactions. In Fig. 6, red patches in isosurfaces of complexes reveal steric repulsions between the atoms of nanocage (B&P). In case of lithium doped complexes, each complex shows van der Waals interactions (green spots) except Li 2 @ 64 and Li 2 @P as these complexes show covalent interactions (blue patches). Na 2 @r 6, Na 2 @r 4 and potassium doped complexes show weak van der Waals interaction (green patches) whereas Na 2 @P and Na 2 @b 66 show blue patches which are indicative of strong covalent interaction. The NCI analysis is presented in the form of 2D reduced density gradient (RDG) and 3D isosurfaces [65]. The NCI graphs are evoked with the plots of RDGs against (sign λ 2 ) ρ. For attractive interactions, the values of (sign λ 2 )ρ should be less than zero whereas, for repulsive interaction, (sign λ 2 ) ρ is greater than zero.
NCI plots for B 12 P 12 complexes are given in Fig. 6 along with NCI images. In NCI graphs, dispersion attractions (at higher density values). For bi-metal doped complexes with green patches in isosurfaces, high density green peaks appear in the region of − 0.01 to − 0.03 au. which illustrates that van der Waals interactions are the key features of alkali metal adsorption. High density blue spikes for some lithium and sodium doped structures clearly indicate strong covalent bond interactions which are in accordance with the bonding information obtained from NCI isosurfaces.

QTAIM Analysis
Quantum theory of atoms in molecule (QTAIM) analysis is a robust tool to examine the type and nature of bonding interactions at bond critical points (BCPs) of inter or intra-molecular interactions. QTAIM variables (BCPs) of all complexes generated between alkali metals and nanocage are depicted in Table 6. The topological investigation of electron density reveals the occurrence of one or more BCPs between the doped metals and nanocage. The strength of bond is described by the electron density (ρ); the larger the value of electron density, the stronger will be the bonding interaction. The values of electron density are in range of 0.1059-0.2395 au. The total electron energy density (Hr) and Laplacian of electron density ( ∇ 2 ρ ) are important to ascertain the strength of bonds. The bonding interactions are of covalent type when ∇ 2 ρ < 0 and Hr < 0; while the values are: ∇ 2 ρ > 0 and Hr < 0 for weak bonding (electrostatic).
In case of average strength of ( ∇ 2 ρ) > 0 and Hr < 0, a partial covalent bond is established. In addition to this, a ratio -Gr/Vr > 1 specifies non covalent bonding and -Gr/Vr < 1 depicts covalent interactions. In case of B 12 P 12 decorated with bi-alkali metals, ∇ 2 ρ > 0 and the ratio -Gr/Vr greater than 1 for all examined complexes indicates noncovalent bonding as a major mode of adsorption. The pictorial representation of QTAIM analysis is given in Fig. 7.

Conclusion
In this study, a new strategy of bi-alkali metal doping has been proposed to increase stability and opto-electronic characteristics of B 12 P 12 nanocage. Adsorption energies have been calculated to evaluate the thermodynamic stability of the doped nanocages. Our results reveal that adsorption energies for bi-alkali metal doped nanocages are more than twice of the corresponding interaction energies of single metal doped nanocages reported earlier. Li 2 @b 66 shows the highest adsorption energy (− 49.3 kcal/mole) while Na 2 @P has the lowest adsorption energy (− 12.4 kcal/mole). NBO analysis indicates the charge transfer from doped metals to nanocage. Certainly, this strategy serves as an advantage to resolve the issue of high H-L gap of pristine B 12 P 12 . K 2 @ b 64 shows the highest hyperpolarizability value of 4.06 × 10 4 au. Bi-metal doping has remarkably altered the geometrical and electronic properties of nanocage. HOMO-LUMO gaps for most complexes are reduced to more than 50% of bare nanocage while hyperpolarizability values are increased manifold. NCI and QTAIM analyses reveal noncovalent bonding interaction as a major mode of adsorption between cage and dopants. This study introduces a novel scenario of bi-metal doping for the fabrication of NLO materials.