Shedding light on the optical and nonlinear optical properties of superalkali-doped borophene

The present investigation highlights the two-dimensional design of several interesting superalkali-doped borophene derivatives for efficient nonlinear optics (NLO). The combination effects and resulting NLO responses of borophene (B36) and superalkali units (Li3O) were evaluated by orienting superalkali clusters at various sites, such as the hub, rim, and bridge, around an B36 molecule. The charge analysis was characterized by frontier and natural bond orbital analyses, a narrowed HOMO–LUMO bandgap and greater intramolecular charge transfers. Molecular electrostatic potential surfaces demonstrated enhanced optoelectronic features of these complexes that are viable due to Li3O adsorption. Singly doped and doubly doped complexes were considered, and their NLO properties were calculated. Bandgap energy was reduced approximately threefold when doped with two Li3O. As a considerably high figure of merit, first hyperpolarizability (βo) values of up to five digits (including 10,611 au for complex A) prove that these systems can be utilized as promising candidates in various NLO applications.


Introduction
There are several compelling applications of nonlinear optical (NLO) materials in the contemporary and hi-tech science which range from optical data storage, modern computing to telecommunications [1]- [5]. The first hyperpolarizability which is a molecular level NLO response of materials can be enhanced by several molecular designing techniques such as increase in π-conjugation and better use of donor-acceptor molecular configurations [6][7][8]. Among several available examples that were remained quite useful in designing highperformance NLO materials both in theory and experiments are incorporation of π-conjugated bridge between donor and acceptor moieties (D-π-A) [9][10][11][12][13][14][15][16], by approaching an optimal bond length alteration (BLA) [17], by employing multi-decker sandwiching like clusters [18,19], and doping or adsorbing alkali metals, transition metals, or superalkali on different nanoclusters [20][21][22]. Often, boron is used as a p-type dopant in silicon owing to its smaller diffusion coefficient and higher solubility. Boron is also an effective dopant for silicon due to interstitial spaces [23], while, on the other hand, lithium is an n-type dopant that helps to decrease the bandgap of the molecules. Some recent studies showed that the doping of lithium is helpful to increase the optoelectronic properties of the perovskite solar cells [24]. Along the above lines, Solimannejad et al. [25] have studied the interaction of borophene (B 36 ) with the alkali metal (Li) and first-row transition metals by placed metal atoms at different sites of borophene. Such doping strategies were anticipated as an effective approach in designing highperformance optoelectronic materials [26]. Similarly, Kosar et al. [27] calculated the optoelectronic properties of alkali metal-doped boron nitride.
On the other hand, superalkali metals which can donate their valence electrons with larger ability and ease are also interesting dopants [28]. In 1938, the first superalkali cation (Li 3 O + ) has been studied as a sub-unit in Li 3 O + NO 2 crystals [29]. In 1979, the isolated form of neutral Li 3 O was first investigated during mass spectrometric measurements [30]. The incorporation of superalkali and super halogen atoms into various molecular configurations especially with push-pull chromophoric systems [31][32][33], metal-ligand complexes [34,35], borophene (B 40 ) nanocage, and fullerene (C 20 ) [36] has shown several promising results having higher hyperpolarizabilities and lower bandgap. For instance, Khan et al. [37] explored the effect of superhalogen (AlF 4 )-doped boron nitride (B 12 N 12 ) with an enhanced linear and nonlinear optical response. The first hyperpolarizability of boron nitride was found to be 34.51 au that enhanced up to 13 times in the doped compounds. Superhalogen and superalkali (BCl 4 and NLi 4 )-doped graphitic carbon nitride (g-C 3 N 4 ) has been studied for the first hyperpolarizability that increases the response from pure graphitic carbon nitride (95.37 au) to the doped compound (90,733 au) [38]. Shafiq et al. [39] also studied the effect of superalkali metal (OLi 3 ) and superhalogen (MgF 3 ) doped with boron nitride where the first hyperpolarizability increases from pure form (0.003 × 10 −30 esu) to MgF 3 doped boron nitride 73 × 10 −30 esu. Likewise, Ishaq et al. [40] investigated the NLO properties of superhalogens BF 4 and BeF 3 doped borophenes. The first hyperpolarizability was enhanced from 389 to 20,727 au by doping BF 4 into borophene (B 36 ).
Borophene manifests varieties of planar, quasi-planar, cagelike, and other structural configurations which have been confirmed by experimental and computational investigations. The most stable cluster among its different analogs is found to be the borophene containing 36 boron atoms (B 36 ) in umbrellalike fashion having out-of-plane symmetry and exhibiting very fine contrasting orderings of hexagonal and triangular units with a hexagonal hole present in the center [41]. Borophene (B 36 ) contributes little resemblance with other 2-D analogs like fullerene in terms of lattice constants or crystal symmetry [42] but shares the most of its hexagonal two-dimensional layered structure with that of graphene in which the carbon atoms are being successively replaced by boron atoms. Moreover, it is experimentally synthesized and successfully isolated as Al and Au single crystal substrates [43], which illustrated promising electronic and optical characteristics. Its band structure exhibited highly anisotropic behavior [44] and strong bonding interactions among all boron atoms which aided borophene to withstand high mechanical stress [25,45]. Owing to its excellent physical, chemical, and thermal properties, borophene has made its way in countless material applications such as alkali metal ion batteries, Li-S batteries, hydrogen storage, supercapacitors, sensors, catalytic hydrogen evolution, oxygen reduction or evolution, and CO 2 electro reduction [46].
In the light of the above literature, it will be very interesting to investigate the role of the number and position of superalkali clusters (Li 3 O) for tuning the NLO response properties of doped borophenes. In our current design, one unit of the superalkali cluster (Li 3 O) was placed on the (left) corner from the center of the sheet which is called A; two on the lower side of the left and right corners from the center called as B; two on the side-by-side (right and left corners) from the center of the sheet called as C; two at the void region of the sheet about center called as D; one at the void region of the sheet about center called as E; and one at the parallel or side-by-side of the sheet about center called as F (see Fig. 1). Within the framework of the above-designed structures, we will focus mainly on the following aspects: (1) structural investigation for the interaction of bowl-shaped borophene (B 36 ) with superalkali cluster (Li 3 O) as placed at various orientations, (2) role of such structural modifications in tuning their linear and NLO response properties in pure and doped borophene.

Computational methodology
Gaussian 09 suit of programs is applied to do all the quantum chemical calculations in the current study [48]. Borophene and its Li 3 O-doped derivatives were optimized through the density functional theory (DFT) method using B3LYP functional and 6-31G(d,p) basis set [40]. The frequency calculations were also performed on the same level of theory for the sake of inspecting the nature of stationary points, which confirmed that these optimized structures correspond to real minima; i.e., exclusion of any imaginary frequencies was assured. The B3LYP is considered reliable functional found in the study of superalkali-and superhalogen-doped compounds [38,40]. Moreover, the density of states (DOS), natural bond orbital (NBO) charges, and HOMO-LUMO bandgaps also were estimated at the same level of theory. The density of states (DOS) analysis was performed with the help of PyMOlyze software [49]. The charge transfer phenomenon between borophene (B 36 ) and Li 3 O was evaluated by natural bond (NBO) analysis [50]. Interaction energies (E int ) have been calculated by the following equation [51].
Similarly, the following equations were used for the calculation of dipole moment, average linear polarizability (α o ), and first NLO hyperpolarizability [52,53].
where Eqs. 4.1, 4.2, and 4.3 are the 3 × 3 tensor components of the first hyperpolarizability and calculated through Gaussian suite of programs.

Molecular geometries
The top and lateral views of borophene (B 36 ) nanosheet exhibit slight out-of-plane umbrella-like quasi-planar C 6 v symmetry with a hexagonal hole existing in the center. The optimized geometry was obtained utilizing B3LYP/6-31G(d,p) level of theory. The borophene (B 36 ) nanosheets are made-up of intervening of three main types of boron atoms, the first six innermost "hub" boron atoms (B h ) of the central hexagonal ring interlinking eighteen outer "rim" boron atoms (B r ) via twelve "bridged" boron atoms (B b ) lying in the center of those former ones, thus acting as a bridge holding the inner and outer layers of boron atoms in B 36 nano-skeleton [25]. The optimized geometries and the exact position of these three types of boron atoms which are the hub, rim, and bridge have been labeled in Fig. 1a.
Elemental boron being an electron-deficient molecule exhibits peculiar behavior in terms of structure and chemical bonding [54].
In the bowl-shaped borophene, two different kinds of B-B bond lengths were found on outward side, i.e., 1.678 Å and 1.579 Å. The obtained results are quite promising with the previously reported data [41]. Superalkali cluster (Li 3 O) is used to enhance the NLO response of pristine borophene molecules. For this purpose, various sites have been chosen around the quasi-planar B 36 molecule, starting from the superalkali cluster on its top concave face to alternate position around the borophene nanosheet, from near to outer rim-corner atoms of borophene, single-sandwich, and fully sandwiched combinations, by setting superalkali clusters on both concave and convex sides (compacting B 36 nanosheet between two superalkali clusters) and by putting it in the left-right orientations. Their solo and the combined effect has been observed. The top and lateral views of optimized geometries with real-time interaction and vibrational frequencies have been depicted in Fig. 2.

Orbital analysis
The FMO analysis has been carried out to visualize the HOMO-LUMO orbitals and also its DOS plot for pristine borophene molecule as shown in Fig. 1b. The bandgap value for pristine borophene molecule is found to be 1.918 eV, which agrees well with the literature data [40]. The larger bandgap width for pristine B 36 molecules limits its use in optoelectronic implementations. In FMO diagram, redistribution of electronic charge density during excitation confirms charge transference. From Fig. 3, pristine-B 36 has a uniform electronic cloud in the ground state (HOMO) exhibiting the equal distribution of electron density over the atoms which distribute transversely in the excited state orbitals (LUMO). Complexes A, B, C, D, E, and F have electronic density mainly on the Li 3 O along with These charges also indicate the π-conjugation within these molecules, thereby decreasing the bandgap of the molecules. A low value of bandgap increases the chances of low energy transitions from lower to higher orbitals. Therefore, the linear and nonlinear optical response increases.
To support the FMO analysis, the molecular electrostatic potential (MEP) has been performed which refers to the molecular electrostatic potential mapped onto the total The central blue region of the B 36 may arise because of empty p-orbitals associated with the elemental boron; it can be interpreted that the lithium-based superalkali clusters colored blue in the MEP diagrams highlight the transference of their excessive diffused electronic density from Li 3 O cluster to quasi-planar B 36 nanosheet that enhanced the nonlinear optical response (first hyperpolarizability) in the doped compounds as these MEP diagrams assist to predict the reactive sites of the compound [55]. Obvious complexes with lower bandgap energy values encounter greater intramolecular charge transfer (ICT) as compared to pristine-B 36 . This charge transfer process is in absolute agreement with natural bond orbital (NBO) analysis. The total NBO charge that each superalkali cluster carries in its corresponding system is represented by [Q] and the positive value of the NBO charge reaffirming the fact that charge is being transferred from Li 3 O to the borophene sheet.

Optical properties and thermodynamic stability
The distance of interaction between borophene nanosheet and superalkali cluster kept in the range of 2.143-3.125 Å. In this interactive distance, some of the superalkali clusters tend to attach to the borophene sheet, some just alter the bond lengths, and others develop bonding with each other and exert their combined effect on this boron-based nanocluster (see complex E in Fig. 2). All these changes lead to structural abnormalities in sense of bond angles and bond lengths which in turn can affect the NLO properties of the considered systems. Among the different structures (A-F), complexes A, B, and F displayed the narrowest bandgap with notable energy of interaction in comparison with its other single superalkali-doped analog such as A, E, and F. However, the interaction energy of complexes C and D is greater Materials exhibiting larger first hyperpolarizability values are suitable candidates in doubled frequency second harmonic generation (SHG)-based NLO applications [57]. For this purpose, corresponding materials should exhibit transparency under laser light used, besides the fact that it owes a greater NLO response. To confirm this statement, ultraviolet-visible and near infra-red region (UV-Vis-NIR) analysis has also been carried out for all the studied complexes and their maximum absorption values have been provided in Table 2. From Fig. 5, peaks show maximum absorption values in the IR region and very weak absorption in the visible region of the electromagnetic spectrum. Hence, these

Total density of states (TDOS)
To investigate electronic structures more deeply, density of states (DOS) spectra have also been approached. The DOS spectra represent the density of states versus energy intervals available for each energy level to be occupied. Doping of atoms responsible for the formation of new HOMOs mainly contributes to the decreasing bandgap for these considered systems, locating somewhere in between or at higher levels than that of pristine B 36 molecule. The constructed DOS spectra (Fig. 6) showed a significant interaction between superalkali cluster and B 36 nanosheet which implies enhanced HOMOs and lower LUMOs in such a way that leads to narrowed HOMO-LUMO energy gap as compared to pristine B 36 molecule.

Origin of NLO hyperpolarizability
NLO properties for borophene molecule have also been checked by the aid of B3LYP/6-31G(d,p) level of theory and approximate negligible first hyperpolarizability value ensures naught to NLO properties of pristine B 36 molecule.
To be more concerned, a famous two-level model has been considered to describe the fluctuations between excitation energies, dipole moment, and first hyperpolarizability as [51]: whereby Δ , f o , and ΔE 3 refer to change in dipole moment, oscillator strength, and the change in transition energy values due to crucial excitations from the ground state to an influential excited state. As obvious from the equation, a small change in excitation energy can alter the first hyperpolarizability (β o ) value to a remarkable extent, because of its third power reciprocated dependence in the relation. Thus, complexes with higher β o values own smaller excitation energies ( ΔE ) and larger dipole moments ( Δ ) and oscillator strengths ( f o ) that are shown in Fig. 7. For instance, compound A possesses the lowest excitation energy value with the highest "β o " response, whereas compound F holds the lowest hyperpolarizability value with the greatest excitation energy value. The greater the charge transfer, the better will be the NLO responses.

Conclusion
Thus, based on the applied theoretical framework, drastic changes in structural, optical, and NLO properties were observed by the intercalation of superalkali clusters and borophene molecules. The intermolecular interactions between superalkali clusters and borophene led to higher charge transfer properties with narrowed HOMO-LUMO bandgaps, as found in complexes A, B, and F. A lower bandgap energy is suitable for considerably high first hyperpolarizability values. The FMO, MEP, and NBO analyses yielded promising results that assure that the charge is being transferred from superalkali clusters to borophene molecules. Among all complexes, complex A achieved the highest first hyperpolarizability value (approximately 10,611 au), which is about 186% higher than the pristine B 36 molecule. The Author contribution Muhammad Hussnain: the acquisition, analysis, or interpretation of data; drafted the work or revised it critically for important intellectual content. Rao Aqil Shehzad: the acquisition, analysis, or interpretation of data; drafted the work or revised it critically for important intellectual content; approved the version to be published; and agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved. Shabbir Muhammad: made substantial contributions to the conception of the work; acquisition; revised it critically for important  showing reciprocal dependence intellectual content; approved the version to be published; and agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.
Javed Iqbal: made substantial contributions to the conception or design of the work; acquisition; revised it critically for important intellectual content; approved the version to be published; and agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.
Abdullah G. Al-Sehemi: the acquisition, analysis, or interpretation of data; drafted the work or revised it critically for important intellectual content.
Saleh S. Alarfaji: the acquisition, analysis, or interpretation of data; drafted the work or revised it critically for important intellectual content.
Khurshid Ayub: the acquisition, analysis, or interpretation of data; drafted the work or revised it critically for important intellectual content.
Muhammad Yaseen: the acquisition, analysis, or interpretation of data; drafted the work or revised it critically for important intellectual content. Data availability All data generated or analyzed during this study are included in this published article.