**2. Methodology**

In this section, a brief discussion is presented on the various features of the biosensors and drug delivery systems, that can be predicted using quantum chemical methods. Density functional theory (DFT) ranks as the most widely used quantum mechanical method and plays an increasingly larger role in a number of disciplines besides chemistry, such as physics, materials, biology, and pharmacy [94–103]. While DFT computations have long been used to complement experimental investigations, the approach has emerged as an indispensable and powerful tool for predictions of different fields.

A general theoretical approach to this topic boils down to an assessment of the interactions between the materials and the biomolecules or drugs considered. It simply leads to an examination of the structures and properties of the interacting complexes. This requires a determination of all possible configurations of the complexes by carrying out systematic geometry optimizations and making use of appropriate DFT methods. The nature of local energy minima corresponding to various configurations needs to be verified through an analysis of their vibrational frequencies. In order to assess the capability of a boron cluster for detection of a biomolecule or drug delivery system, the structural, energetic, and electronic properties can simply be computed for the relaxed favorable geometries. These properties can provide us with valuable information for biomedical applications. All the mentioned calculations can be performed in both vacuum and aqueous media. It is essential to evaluate these parameters in aqueous medium since these systems are anticipated to act in human body. The polarizable continuum model (PCM) and the conductor-like screening model (COSMO) are common continuum models for the treatment of the solvent effects. The key factors of the properties mentioned above are described as follows.

### **2.1 Structural parameters**

From an optimized geometry, the bond lengths and bond angles between the constituent atoms in the complexes can be determined. These are simple but essential parameters determining the nature of the interaction between the drug molecules and respective adsorbents.

#### **2.2 Energetic properties**

The interaction energy (*E*int) of a biomolecule or drug with a boron cluster is the key parameter that should be determined in order to emphasize the nature of the interaction. The interaction energy is usually computed as in Eq. (1):

$$E\_{\text{Int}} = E\_{\text{BC-adsorbent}} - E\_{\text{BC}} - E\_{\text{adsorbent}} \tag{1}$$

where *E*BC–adsorbent denotes the total energy of the adduct formed upon interaction between the boron cluster with the corresponding drug or biomolecule. The *E*BC and *E*adsorbent terms correspond to the total energies of the isolated boron cluster and the drug or biomolecule, respectively. These energies are usually calculated using DFT methods. The efficiency of DFT methods, namely the functionals, for evaluating interaction energies was documented previously. The reported results show a good performance with the root-mean-square deviation of 0.05 kcal/mol and the mean absolute deviation of 0.07–0.13 kcal/mol against the benchmark energies of N-methylacetamide-water complex obtained at the CCSD (T)/CBS-aTQ complete basis set limit level [104]. N-methylacetamide is the simplest model for the peptide linkage in peptides and proteins.

As for a convention, a negative interaction energy indicates that the obtained complex is thermodynamically stable, while a positive adsorption energy refers to a local minimum where the interaction is prevented by an energy barrier connecting it with the global minimum. The interaction energy can provide us with meaningful insights to distinguish between a chemisorption and a physisorption process.

The recovery time (τ) is one of the important factors for biomedical applications. It can be used for estimation of the drug desorption from the cluster surface or the sensor refreshing, which can be occurred by exposing to light. Based on the conventional transition state theory, the recovery time can be computed using the Arrhenius-type Eq. (2):

$$
\tau = \nu\_0^{-1} \exp\left(\frac{-E\_{\text{int}}}{kT}\right) \tag{2}
$$

where ν <sup>0</sup> , *T*, and *k* terms stand for the attempt frequency, the temperature of the system, and the Boltzmann constant, respectively. A larger interaction energy inherently leads to a longer recovery time, which is not a good factor for drug release or for a biosensor refreshing. Thus, the adsorption process energy should be neither chemisorption nor physisorption; it should be in a semi-chemisorption to provide an efficient recovery time. Accordingly, an interaction characterized by *a large interaction energy is not always favorable for biomedical applications.*

It is possible to investigate the thermodynamical nature of the interaction, through the change in the Gibbs energy using Eq. (3):

$$\begin{array}{l} \Delta \mathbf{G} = \mathbf{G}\_{\text{BC\text{-}adardent}} - \mathbf{G}\_{\text{BC}} - \mathbf{G}\_{\text{adardate}}\\ = \left(\mathbf{H}\_{\text{BC\text{-}adardent}} - \mathbf{H}\_{\text{BC}} - \mathbf{H}\_{\text{adardate}}\right) - T\left(\mathbf{S}\_{\text{BC\text{-}adardent}} - \mathbf{S}\_{\text{BC}} - \mathbf{S}\_{\text{adardate}}\right) \end{array} \tag{3}$$

where *G* represents the sum of electronic and thermal free energies. *H* stands for the sum of electronic and thermal enthalpies. S and T refer to entropy and temperature, respectively. Computations of the *S* and *G* quantities are carried out using the electronic, rotational, and vibrational parameters associated with the equilibrium structures according to the well-known thermochemical equations. A negative change in the Gibbs energy (free energy) represents a spontaneous interaction between the adsorbate molecule and adsorbent, which is desired in both drug delivery and drug sensor devices.

It is worth mentioning that a drug release from a carrier in the target cell is the most vital step in a drug delivery process. Owing to the excessive lactic production, a cancer cell is generally more acidic than normal cells (*p*H < 7) [105]. Thus, it is crucial to examine the performance of anticancer drug delivery systems in a low *p*H cancerous cell region for a better evaluation of the drug release performance of the nanostructure in the targeted region. This is well-known as the *p*H-dependent drug release mechanism [106].

Furthermore, the photochemical mechanism of light-triggered release from nanocarriers is also well known. Distinct wavelengths including ultraviolet (UV, 200–400 nm), visible (400–750 nm), and near-infrared (NIR, 780–1700 nm) lights, can be utilized to activate the light responsiveness [107]. Although the UV light is a relatively poor candidate due to its limited tissue penetration capacities and potentially carcinogenic effects under prolonged exposure, the NIR light has the advantages of lower phototoxicity, improved penetration depth in biological tissues, and reduced background signal. Thus, it is more suitable for biological applications. The NIR light is regarded as a transparent therapeutic window for light-activated delivery system in vivo due to its deep tissue penetration and minimum cellular damage [108]. The recovery time (Eq. (2)) could provide a theoretical estimation for light controlled release mechanism.

#### **2.3 Electronic properties**

The electronic properties investigation is usually performed using the HOMO-LUMO gap as a quantum descriptor, to establish correlation in various chemical and biochemical systems. The HOMO-LUMO gap *E*g values are considered to explore the electronic properties and reactivities of the complexes formed upon interaction. This parameter is simply calculated by the following operational Eq. (4):

$$E\_{\rm g} = \varepsilon\_{\rm LUMO} - \varepsilon\_{\rm HMOO} \tag{4}$$

where *ε*HOMO and *ε*LUMO are the energies of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), respectively.

The electrical conductivity is exponentially related to the energy gap in a semiconductor material as follows (5):

$$
\sigma = AT \frac{\mathfrak{Z}}{2} \mathbf{e} \left( -\frac{E\_{\mathfrak{g}}}{2kT} \right) \tag{5}
$$

where *A* (electrons/m3 K3/2) is a pre-factor constant, *k* is the Boltzmann's constant, and *T* is the absolute temperature. This equation has frequently been used and

#### *Boron Clusters in Biomedical Applications: A Theoretical Viewpoint DOI: http://dx.doi.org/10.5772/intechopen.106215*

previously demonstrated to yield results in agreement with experiment. The change in energy gap is a proper pointer for identification of the presence and attachment of a drug or biomolecule to a substrate.

Furthermore, the charge transfer between the adsorbate molecules and the adsorbent is generally performed through the natural bond orbital (NBO) or Hirshfeld population analyses. The amount of charge transfer plays an essential role in the development of a biosensor device. It helps determine the capability of a boron cluster in generating a detectable electrochemical signal on the presence of a biomolecule or a drug.

The electronic dipole moment is also an important issue for design of nanocarriers. The dissolvability of a nanostructure into a polar medium, such as an aqueous solution, can be explored using the dipole moment (*μ*). It plays a vital part in the design of a drug delivery device. A dipole moment enhancement is necessary for their solubility in a polar solvent. An increase in the hydrophilicity upon formation of the complex is a valuable factor for the efficient drug delivery system.

In summary, the structural, energetic, and electronic parameters necessary for the design of relevant materials are the basic molecular properties that can easily be determined using simple quantum chemical computations.
