Boron-Based Cluster Modeling and Simulations: Application Point of View

Abstract

Among sub-nanometer clusters, boron-based clusters and their atom-doped counterparts have attracted great attention due to their mechanical, physical, and chemical properties as well as their applications. Molecular dynamics (MDs) simulations and ab initio methods, including density functional theory (DFT) calculations, have been used to understand the physical and chemical properties of different materials. Much research has recently been conducted by using various methods to determine the different properties of boron clusters. In this chapter, we briefly introduce the relevant modeling and simulation methods, then review very recent theoretical researches on the application of small boron clusters, such as gas sensors, electrodes, H2 storage, drug delivery, and catalytic applications.

1. Introduction

In recent years, wonderful molecular features have emerged through the study of pure and atom-doped boron clusters. Boron is a p-element that has three valence electrons and one of them in the p-orbital. Also, this element is located between the metallic and nonmetallic elements of the periodic table and, like carbon, is an exceptional element with a self-catenation character. Boron can form bonds between the same elements leading to the synthesis of the pure hydride of boron compounds. Also, it scarcely obeys the octet rule, and its valence shell typically contains only six electrons.

The main family of boron compounds is classified into two different branches: (i) the boron clusters that can form carboranes, borohydrides, metallacarboranes, and (ii) the organic compounds, in which they structures are different and their characteristics depend on the size. Although the organic compounds contain chains and rings, the boron clusters have a planar or cage-like structures. Also, the boron clusters have various shapes and symmetries that are the result of occupying vertices through different numbers of boron atoms or heteroatoms. The shape of these clusters is widespread, from unstable tetrahedral to more stable icosahedral [1, 2].

According to these intrinsic features, the chemical properties of boron clusters have gained great attention from researchers. To date, 16 polymorphs have been detected for bulk boron. Among them, the B₁₂ icosahedron is a predominant motif [3]. However, it is shown that B₁₂ cluster in isolated form is not stable and tends to form planar or quasi-planar structures. The anionic and cationic forms of the small boron clusters (B_n; $n\le$ 36) usually prefer to have planar and two-dimensional structures, respectively.

The planar structures in the edge consist of two-center two-electron (2c-2e) sigma bonds and between the inner atoms have multicenter two-electron (nc-2e) bonds. Multidimensional aromaticity as a result of delocalized $\sigma$ and $\pi$ bonds is responsible for the stability, planarity, and bioavailability of planar boron-based clusters. Furthermore, energetically favorable 1D boron nanotubes [4] and 2D boron sheets [5, 6, 7] have been produced, and their structure contains planar triangular lattices with hexagonal holes.

By discovering the cage-like structure of B₄₀/${\mathrm{B}}_{40}^{-}$, a new family is introduced to the boron cluster which is called borospherene. These hollow structures are generally interlocking boron chains formed from trigonal fragments and containing holes with hexa, hepta, and other sizes. Also, planar B₃₆ is a pioneer in the borophene concept having a monolayer structure with hexagonal vacancies. The smallest borospherene that has been discovered is ${\mathrm{B}}_{28}^{-}$ and other motifs for borophene are ${\mathrm{B}}_{26}^{-}$, ${\mathrm{B}}_{35}^{-}$, ${\mathrm{B}}_{37}^{-}$, and ${\mathrm{B}}_{38}^{-}$.

Experimental and theoretical studies revealed that 0D boron clusters with ${\mathrm{B}}_n^{-}$ ($n<38$) structure are planar and quasi-planar, and their stability is the result of delocalized multicentric bonding [8, 9, 10, 11]. They also demonstrated that the B_n (31$\le$$n$$\le$50) clusters can have a tubular structure [10]. Series of axially chiral borospherenes structures for ${\mathrm{B}}_{38}^{+}$, ${\mathrm{B}}_{38}^{2+}$, ${\mathrm{B}}_{31}^{+}$, and B₃₂ clusters are also investigated [12, 13]. In a boron cluster of a certain size with a large number of boron atoms, the structures proposed for its ground state are cage-like [14], quasi-planar, and bilayer (i.e. ${\mathrm{B}}_{48}^{-}$) [15, 16, 17]. Moreover, for B_n clusters with $n>$68, the most energetically stable structure is found to be core-shell [18].

Replacing a boron atom with a specific dopant leads to the production of a new subclass that is of particular interest and diverse in structure. For example, transition metal doping of B_n (12$\le$$n$$\le$22) clusters forms metal-centered monocyclic boron rings [19, 20, 21, 22], half-sandwich structures in metal-doped B_n clusters [23, 24], inverse-sandwich structure in La-doped ${\mathrm{B}}_n^{-}$ cluster [25], and endohedral boron cage in NiB₈₀ cluster [26]. However, a new way to achieve intriguing features in boron clusters can be constructed by a specific combination of the number of doped atoms and boron atoms in the boron clusters.

The variety in boron clusters and their atom-doped counterparts has increased the ability of these clusters to be applied in different applications. As such, in this chapter, to generate new insights into the various applications, we review some important applications of boron clusters and their atom-doped counterparts. We will briefly introduce the most relevant computational methods to simulate these clusters and then present examples of their use in different areas, ranging from drug delivery to reaction catalysis. We hope to inspire the general community and research groups to get involved in proposing new applications for boron clusters.

2. Introducing the relevant method for modeling and simulations

The optimum structure of the materials and their corresponding applications can be predicted by modeling and simulation methods. They require analogous levels of precision and control that can also accurately describe the pertinent processes and conditions. As shown in Figure 1, across length and timescales, these methods can equip a wide range of opportunities to shed light on properties and phenomena that are unattainable through experimental effort. Among these methods, ab initio methods (such as density functional theory (DFT) calculations), standard molecular dynamics (MDs) simulations, and ab initio molecular dynamics simulations (AIMD) have been employed, mainly to study the properties of materials including boron clusters at the nanoscale.

Figure 1.

Typical length and timescales in the simulation of the materials.

Ab initio methods refer to those methods derived directly from theoretical principles, and their equations have not contained any empirical or semi-empirical parameters and the inclusion of experimental ones. The Hartree-Fock (HF) method is the simplest type of ab initio electronic structure calculations in which the correlated electron-electron repulsion is not explicitly included, and only its average effect is taken into account in the calculations [27, 28].

In DFT calculations, the ground-state energy is obtained as a function of a set of n one-electron Schrodinger-like equations, which are known as Kohn-Sham orbitals. This equation expresses the ground-state energy as a function of the interactions between the electrons, the nuclei, and themselves, the kinetic energy, and the exchange-correlation energy (see Eq. (1)). In these calculations, functionals (functions of another function) are employed to determine the properties of a many-electron system. There is an approximation in the hamiltonian and the expression for the total electron density in the DFT calculations. However, these type of calculations can be very accurate for little computational cost [29, 30, 31, 32]:

$$E\left[n\right]=E_{\mathit{Kin}}\left[n\right]+E_{\mathit{\text{Coul}}}\left[n\right]+E_{\mathit{xc}}\left[n\right]+E_{\mathit{ext}}\left[n\right],$$E1

Determining the exact functionals for exchange and correlation is the main problem in DFT. Accordingly, a bunch of functionals for DFT calculations is developed which can be classified from the simplest to the most accurate functionals. The exchange-correlation energy term in the functionals is constructed based on some approximation, i.e. local density approximation (LDA, see Eq. (2)), generalized gradient approximations (GGAs, see Eq. (3)), meta-GGA (see Eq. (4)), and hybrid functionals. For example, hybrid functionals are termed based on the density functional exchange functional in combination with the Hartree-Fock exchange term:

$$E_{\mathit{xc}}^{\mathit{LDA}}\left[\rho \right]=\int \rho \left(r\right){\epsilon }_{\mathit{xc}}\left(\rho \left(r\right)\right)\mathit{dr},$$E2

$$E_{\mathit{xc}}^{\mathit{GGA}}\left[\rho \right]=\int \rho \left(r\right){\epsilon }_{\mathit{xc}}\left(\rho \left(r\right),\nabla \rho \left(r\right)\right)\mathit{dr},$$E3

$$E_{\mathit{xc}}^{\mathit{\text{MGGA}}}\left[\rho \right]=\int \rho \left(r\right){\epsilon }_{\mathit{xc}}\left(\rho \left(r\right),\nabla \rho \left(r\right),{\nabla }^2\rho \left(r\right)\right)\mathit{dr},$$E4

where $\rho$ and ${\epsilon }_{\mathit{xc}}$ refer to the electronic density and the exchange-correlation energy per particle of a homogeneous electron gas with the charge density of $\rho$, respectively.

In the standard molecular dynamics (MDs) simulations, by considering classical treatment, Newton’s second law is applied to the atomic coordinates. Then, force fields (FFs) which are a gradient of a prescribed interatomic potential functions are employed to calculate instantaneous force on each atom. FFs are the heart of MDs which are a function of the atomic coordinates and containing parameter sets (see Eq. (5)):

$$\mathit{FF}\left(\overrightarrow{R}\right)=U_{\mathit{\text{bonds}}}+U_{\mathit{\text{angles}}}+U_{\mathit{\text{dihedrals}}}+U_{\mathit{\text{impropers}}}+U_{\mathit{\text{nonbond}}},$$E5

$$U_{\mathit{\text{bonds}}}=\sum _{\mathit{\text{bonds}}}{k}_i^{\mathit{\text{bonds}}}{\left(r_i-r_0\right)}^2,$$

$$U_{\mathit{\text{angles}}}=\sum _{\mathit{\text{angles}}}{k}_i^{\mathit{\text{angles}}}{\left({\theta }_i-{\theta }_0\right)}^2,$$

$$U_{\mathit{\text{dihedrals}}}=\sum _{\mathit{\text{dihedrals}}}{k}_i^{\mathit{\text{dihedrals}}}\left(1+cos\left(n_i{\varphi }_i-{\delta }_i\right)\right),$$

$$U_{\mathit{\text{improper}}}=V_{\mathit{imp}}$$

$$U_{\mathit{\text{nonbond}}}=\sum _{\mathit{ij}}4k{\epsilon }_{\mathit{ij}}\left(\frac{{\sigma }_{\mathit{ij}}^{12}}{r_{\mathit{ij}}^{12}}-\frac{{\sigma }_{\mathit{ij}}^6}{r_{\mathit{ij}}^6}\right)+\sum _{\mathit{\text{elec}}}\frac{q_i{q}_j}{r_{\mathit{ij}}}$$

where the local contributions to the total energy are included in the first four terms, i.e. bond stretching, angle bending, dihedral, and improper torsions. In this case, when considering a 12-6 Lennard-Jones potential, the repulsive, van der Waals, and coulombic interactions are described in the last two terms. The parameters are derived from experiments and quantum mechanics. After that, the position and velocity of the particles can be calculated by numerical integration [33, 34, 35].

In the ab initio MD simulations (AIMDs), at first, the interatomic forces are found at a given time instant. Then, from a quantum-mechanical perspective, the system is parameterized as a function of nuclei and electrons coordinates at a fixed time. Using the Born-Oppenheimer (BO) approximation, the nuclei are considered to be fixed at the instantaneous positions of the atoms. Consequently, the time-independent Schrodinger equation can be invoked to calculate the many-body electron wave function and the energy. In fact, the obtained energy is a function of the nuclei coordinates which were previously considered fixed. This energy can be considered as an interatomic potential to obtain the forces in Newton’s equation of motion. In the other words, the gradients of the DFT energy at this fixed point can be calculated to obtain forces in which the nuclei are moved by this force to reach the next time step. This whole mentioned process is then repeated for these new atomic positions [36, 37].

The calculation way of the interatomic forces and the computational costs are the manifest and the origin of the difference between the standard MDs, AIMDs, and DFT calculations. AIMDs can be applied only for small system sizes, due to its huge computational cost. Also, AIMDs allow determining the dynamics of the systems that have no FFs. Intrinsically, AIMDs can deal with some effects such as polarization, bonding, many-body effects, and charge transfer, whereas in standard MDs these effects are artificially imposed from the data. Moreover, DFT as a quantum mechanical method for calculating energy as well as other properties of the material is a time-consuming technique. However, empirical potentials (FFs) are much faster but less accurate than the ab initio method like DFT. Finaly, the method selection for a specific case should be made based on these factors.

3. The application of the boron-based clusters

3.1 Gas sensor

From life safety point view, the design of sensitive materials to detect toxic gases in the environment is highly demanded. Among these hazardous gases, CO, NH₃, NO, H₂S, SO₂, SO₃, and CO₂ are mainly produced through industrial applications and automobile exhaust, which represent a harmful threat to human life and the natural environment.

Hossain et al. [38] in a theoretical study using DFT calculations investigated the quasi-planar 2D borophene B₃₅ (see Figure 2(a)) as an efficient gas sensor toward NO, NO₂, N₂O, and NH₃ gases. Gases prefer to adsorb on the hexagonal hallow site of B₃₅ where N₂O gas is chemically adsorbed, and the other gases are physically adsorbed on this nanocluster. Also, after gas adsorption, the hardness and stability of all systems increased as a result of the increased highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) energy gap.

Figure 2.

The structure of some small clusters of boron. In the panels, two different views are shown and green balls represent B atoms.

It is also demonstrated that the B₃₆ (see Figure 2(b)) can be applied as a good detector for ammonia gas (NH₃). The minimum energy configuration of this interaction is the adsorption of NH₃ from N-head on a B atom of the B₃₆. During this interaction, the enthalpy changes −90.5 kJ/mol and 0.35 $\mid$e$\mid$ charge is transferred from ammonia to the B₃₆. Also, the electrical conductance of B₃₆ is found to increase after NH₃ adsorption in which the HOMO-LUMO energy gap decreased from 1.55 to 1.35 eV [39].

Ploysongsri and Ruangpornvisuti [40] studied the adsorption of gases containing sulfur on B₃₆ cluster i.e. H₂S, SO₂, and SO₃. SO₂ and SO₃ gases adsorb from the oxygen side to the edge of the cluster that is thermodynamically favorable, while H₂S adsorption is not spontaneous on this cluster. The H₂S, SO₂, and SO₃ gases can be adsorbed on the edge of B₃₆ with an adsorption energy of −5.29, −43.85, and − 80.57 kcal/mol, respectively.

Also, it is shown that metal-decorated B₃₆ and its nitrogen-doped counterparts (M-N_x-${\mathrm{B}}_{36-x}$ (M = Fe, Ni, and Cu; $x$ = 0, 3)) are also sensitive to detect CO, NO, O₂, and N₂ molecules. The substitution of three nitrogen atoms in the central ring of B₃₆ can increase the stability and sensitivity of the B₃₆ cluster. The adsorption energy of CO, NO, O₂, and N₂ gases for the most stable configurations changes in the range of −0.32 to −3.31 eV. Among the studied gases, Fe-N₃-B₃₃ and Ni-N₃-B₃₃ are more sensitive to CO and NO gases, which leads to reducing the energy gap between the highest occupied molecular orbital (HOMO) and the energy of the lowest unoccupied molecular orbital (LUMO) [41].

One of the dangerous gases emitted by industrial application is nitrogen dioxide (NO₂) that puts human health at risk. Hou et al. [42] studied borophene as a highly sensitive and selective material for the NO₂ detection. The borophene-based sensor can detect NO₂ at a low concentration of 200 ppb, which has a fast response time of 30 s. The recovery time of the introduced sensor at room temperature was 200 s. The properties of this sensor were significantly better than those of other 2D materials such as phosphorene, MoS₂, and graphene. For instance, this sensor demonstrates excellent flexibility, long-time stability, and outstanding stability under different bending angles.

Wang et al. [43] using first principles density functional calculations investigated hexagonal Cr-doped borophene (CrB₆) as a potential sensor material for CO, CH₄, and CO₂ gases. The adsorption process of these gases on the CrB₆ surface is different, in which for CO₂ and CH₄ gases it is physisorption while for CO it is chemisorption. CO adsorption remarkably affects the conduction bands of the CrB₆ monolayer, and CH₄ and CO₂ adsorption affects these bands less. Since reversibility is an important property of gas sensors, CrB₆ monolayer is recommended as a good material for CO₂ and CH₄ detection.

3.2 Electrode

One of the efficient anode materials for Li-ion batteries is 2D borophene that is not stable as free standing form. Accordingly, Khan et al. [44] using DFT calculations investigated borophene in conjugation with boron nitride (B/BN) as a good anode for Li-ion battery. Using AIMD simulation, they found that the thermal and mechanical stability of the B/BN structure was dramatically improved compared to that of pristine borophene. Also, the specific charge capacity of B/BN increased compared to the other 2D material, which was 1698 mA h g⁻¹. Moreover, Li can easily diffuses into the B/BN interlayer due to the low energy barrier (ranging from 0.06 to 0.75 eV).

Kolosov and Glukhova [45] using first-principle calculations studied how surface decoration of single-walled carbon nanotubes (CNTs) by B₁₂ icosahedral clusters can affect electronic properties, capacitance, and stability. They found that the B₁₂ clusters (see Figure 2(c)) form a chemical bond with the wall of the CNTs, and the entire system demonstrates metallic behavior. The quantum capacitance and conductivity of the CNTs increased after binding the B₁₂ icosahedral clusters to the inner and outer walls of CNTs. The latter was verified by calculating the transmission function near the Fermi level. They found that increasing boron concentration decreases the heat of formation that strongyle affects the stability of the system. After increasing the boron concentration, the proposed system illustrates attributes such as an asymmetric electrode.

Xie et al. [46] studied the 3D topological porous B₄ cluster (H-boron) as a high ionic and electronic conductivity anode for lithium- and sodium-ion batteries. The electron-deficient boron atoms led to expose different adsorption sites for Li and Na ions that impose a low mass density (0.91 g/cm³) and a high specific capacity (30 mAh/g). Li (Na) can readily migrate through this anode material with a low barrier energy of 0.15 (0.22) eV and small volume changes of 0.6% (9.8%). Suggesting that H-boron based anodes can operate with fast dynamic charge-discharge process and good cyclic life.

3.3 Hydrogen storage

Hydrogen storage as one of the clean energy sources is gaining tremendous attention from computational and experimental scientists. Hydrogen has some specific characteristics compared to gasoline, such as high energy content by weight and low energy content by volume, which offer hydrogen as a suitable fuel to obviate global energy and environmental concerns. However, there is a concern about the storage and safety of hydrogen-based technologies due to its fast burning feature. To resolve this important barrier, hydrogen can be stored on the material through chemisorption and physisorption mechanisms for future demands.

Studies indicated that metal-decorated boron clusters are potential candidates for hydrogen storage. Kumar et al. [47] studied the application of small boron clusters doped with two magnesium atoms (Mg₂B_n; $n$ = 4–14) in hydrogen storage. The DFT results show that all the clusters are stable and H₂ molecules were adsorbed in molecular form on these clusters with an absorbtion energy in the range of 0.13–0.22 eV/H₂. Although, the Mg₂B₆ cluster indicated the maximum storage capacity of H₂, MDs analysis indicates that after 200 fs H₂ molecules are desorbed from the surface of all clusters except one H₂ molecule adsorbed on the Mg₂B₁₁ cluster. Also, Liu et al. [48] predicted that the titanium-decorated B₈ cluster (Ti₂B₈) has a capacity of 6.17 wt% for hydrogen storage with the average hydrogen adsorption energy of 0.247–0.358 eV/H₂.

Kumar et al. [49] using DFT calculations investigated H₂ storage capacity of lithium-doped B₁₄ clusters (Li_nB₁₄; $n$ = 1–5, see Figure 2(d)). These clusters are stable at room temperature and capable of storing hydrogen in molecular form. The Li₅B₁₄ cluster has a maximum H₂ storage capacity of 13.89 wt%. However, based on the AIMDs results, most of the hydrogen molecules desorb from the clusters within 400 fs.

Esrafili and Sadeghi [50] studied hydrogen storage and adsorption of yttrium-decorated B₃₈ fullerene using DFT calculations (see Figure 2(e)). They found that the Y atoms are tightly bound to the hexagonal cavities of the cluster, which makes Y@B₃₈ stable and prevents aggregation of Y atoms. This suggests that Y@B₃₈ is an efficient cluster for hydrogen storage. There are six H₂ molecules per Y atom adsorbed on Y@B₃₈ cluster with the gravimetric density of 4.96 wt% in which both polarization effects and Kubas mechanism play crucial role in the hydrogen adsorption process. They investigated a suitable energy range for hydrogen adsorption on Y@B₃₈ cluster which is −0.180 to −0.249 eV/H₂.

Wang et al. [51] using first-principal calculations investigated the ultrahigh hydrogen storage capacity for sandwich-like beryllium-doped boron clusters B₆Be₂ and B₈Be₂. Each Be atom in these clusters can adsorb seven hydrogen molecules which convert to a hydrogen storage capacity of 25.3 and 21.1 wt% for B₆Be₂ and B₈Be₂ clusters, respectively, which far exceeds the target gravimetric density of hydrogen adsorption (5.5 wt%). Consequently, both clusters are promising for H₂ release and adsorption with adsorption energy in the range of 0.10 (0.11)–0.45 (0.50) eV/H₂ for B₆Be₂ (B₈Be₂) clusters.

3.4 Catalyst

Wang et al. [52] for the first time reported a spherical isomer of boron and phosphorus atoms that have high capability for overall water splitting (see Figure 3(a)). This theoretically introduced isomer has 20 atoms and eight of them are boron, which can bare its spherical structure throughout the water-splitting process. The water molecule can adsorb on each B▬P bond and strongly dissociates to OH + H. This step is the rate-limiting step with an energy barrie of 2.92 eVr.

Figure 3.

The structure of some small clusters of boron that are used as a catalyst. In the figure, light gray, gray, red, green, yellow, plum, mustard, and fuchsia balls represent H, C, O, B, S, P, Fe, and Pt atoms, respectively.

Hamadi et al. [53] investigated the adsorption of iron atom on B₄₀ fullerene (Fe@B₄₀, see Figure 3(b)) and its application as a catalyst for carbon monoxide oxidation by DFT calculations. The iron atom prefers to be adsorb on top of the heptagonal and hexagonal rings of B₄₀ with an adsorption energy of −4.39 and − 3.45 eV, respectively. They found that when both CO and O₂ molecules are injected into the B₄₀, the surface must be covered by CO due to its higher adsorption energy. Also, the preferable mechanism of CO oxidation is predicted to be termolecular Eley-Rideal (TER) with a small energy barrier of 0.26 eV.

The most stable form of boron is $\alpha$-boron which is capable of adsorbing single-metal atoms and storing hydrogen molecules. Dong et al. [54] by using DFT calculation studied the oxidation of methane (CH₄) to form methanol on boron nanosheet/PdO (see Figure 3(c)). Initially, methane prefers to adsorb on the boron layer with the adsorption energy of −0.15 eV. Then, C▬H bond of methane is broken through the interaction with the Pt▬O moiety of the catalyst and leads to the oxidation of CH₄. This catalyst had high stability and offers excellent methanol selectivity.

Metal-free catalysts can be used instead of the toxic metal oxide catalysts. Amorphous boron (A-Boron) exhibited great catalytic merits for peroxymonosulfate (PMS) activation (see Figure 3(d)). The later is carried out by Duan et al. [55] to remove organic contaminants such as benzene, antibiotics, phenolics, and dyes from the water. Their results show that the performance of A-Boron is better than that of nanocarbons, transition metal oxides, and non-carbonaceous materials. They discovered through in situ radical capture analysis that both hydroxyl and sulfate radicals are responsible in the oxidation process of organic contaminants. In addition, a boric acid/hydroxide can form on the surface of A-Boron during heat treatment, which can further deteriorate its catalytic performance. Moreover, DFT calculations revealed that PMC decomposition and peroxide O▬O bond cleavage can occur directly on boron atoms along (1 0 0), (1 0 1), and (1 1 0) faces of A-Boron crystal.

Zhao et al. [56] by using DFT calculations proposed a mechanism for the ethanol decomposition on the surface of nano-boron (0 0 1). They found that (I) the rate-limiting step is the dehydrogenation of CH to form a carbon atom (CH + CO $\to$ C + CO); (II) the oxygen dissociation can easily take place on the surface (0 0 1) of the boron crystal; and (III) the existence of O site on the surface (0 0 1) lowers the dehydrogenation energy barrier of CH₃CH₂O, CHCHO, and CHCH₂O species in the ethanol decomposition pathway. The most favorable reaction pathway for the decomposition of methanol and corresponding species on this pathway is presented in Figure 3(e).

3.5 Drug delivery

Boron neutron capture therapy (BNCT) is a new cancer therapy technique that allows the elimination of tumor cells without harmful side effects for other healthy tissues. Harder-Viddal et al. [57] by using MDs studied the storage of the ortho-carborane cluster (C₂B₁₀H₁₂, see Figure 4(a)) within the right-handed coiled-coil (RHCC) tetrabrachion as a nanotube carrier for BNCT. Their results of binding free energies demonstrated that C₂B₁₀H₁₂ can potentially enter and leave the RHCC-tetrabrachion, which refers to the feasibility of diffusion of C₂B₁₀H₁₂ cluster between solvent and carrier in the drug delivery process. They also found that there are about eight storage cavities along the central channel of the conveyor that lead to some stable configurations for this cluster within the conveyor.

Figure 4.

The structure of some small clusters of boron that are used in drug delivery. The right panel two different views of B₄₀ cluster are shown. In the figure, light gray, gray, red, green, dark blue, orange, and fuchsia balls represent H, C, O, B, N, F, and Pt atoms, respectively.

The small boron-based cluster has also appeared in cancer therapies. Among the boron clusters, B₄₀ (see Figure 4(b)) as the first all-boron fullerene has been investigated as a drug carrier in cancer therapy. For example, Zhang et al. [58] studied the adsorption of 5-fluorouracil (5-Fu) on B₄₀ fullerene and M@B₄₀ (M = Mg, Al, Si, Mn, Cu, Zn). The 5-Fu was adsorbed on the B atom in the corner of the B₄₀ cage, forming the B▬O bond. The adsorption energy of 5-Fu was −11.15 kcal mol⁻¹, which refers to the ease of release of this drug from the surface of B₄₀ cage in an acidic environment of tumor tissues.

Shakerzadeh [59] studied Li- and Na-encapsulated B₄₀ (Li(Na)@B₄₀) fullerenes as carrier for anticancer drug nedaplatin (NdaPt, see Figure 4(b)). The energy gap decreased after drug absorbtion, which refers to the formation of stable complexes. The later is a chemical signal to describe drug adsorption and its effects on the electronic properties of B₄₀ cage. The results demonstrated that in both gas and water phases, the adsorption of NdaPt altered more the electronic properties of Li- and Na-encapsulated B₄₀ fullerenes compared to bare B₄₀ fullerene. The dipole moments of the Li(Na)@B₄₀ complexes in water were high, suggesting that the solubility of these complexes in the polar medium. Moreover, the adsorption energy for NdaPt/Li(Na)@B₄₀ complexes was −28 kcal/mol.

Zhang et al. [60] by using DFT calculations investigated the potential of B₄₀ fullerene as a carrier for drug nitrosourea (NU, see Figure 4(b)). This drug was adsorbed from its N and O atoms on the fullerene surface with an adsorption energy of −25.18 kcal/mol. They showed that newly formed N▬B and O▬B bonds are strong polar covalent bonds. Also, it is investigated that the recovery time of NU drug under body temperature is 52 s due to the easy release of NU in the medium of cancer tissues. They also found that B₄₀ fullerene has a high loading capacity in which it can simultaneously transport five NU drugs.

4. Conclusions

In this chapter, we briefly introduced the application of the boron clusters that can be characterized by using DFT and MD simulations. We show that both methods are useful for simulating different physical and chemical properties of small boron clusters. Based on the intrinsic characteristic of the studied systems, several groups have used MD and/or DFT techniques to model boron clusters. They were employed to model boron cluster structures for a variety of applications including H₂ storage, gas sensor, electrode, catalyst, and drug delivery. In some cases, MD and DFT were used to confirm the results of the experiment. The development of more precise nanoscale systems that can be more comparable to experimental conditions is required.

Conflict of interest

The authors declare no conflict of interest.