Carbazochrome carbon nanotube as drug delivery nanocarrier for anti-bleeding drug: quantum chemical study

The interaction between drugs and single-walled carbon nanotubes is proving to be of fundamental interest for drug system of delivery and nano-bio-sensing. In this study, the interaction of pristine CNT with carbazochrome, an anti-hemorrhagic or hemostatic agent, was investigated with M06-2X functional and 6-31G* basis set. All probable positions of related adsorption for these kind drugs were thought-out to find out which one is energetically suitable. Based on the achieved data, the stronger interactions appeared the oxygen atom of C = O group and nitrogen atom of imine groups. The topology analysis of QTAIM (quantum theory of atoms in a molecule) method was accomplished to understand the properties of interactions between the CNT and carbazochrome. Frontier molecular orbital energies of all systems, global index including stiffness, softness, chemical Gibbs energies, and electrophilicity parameters, as well as some other important physical data such as dipole moment, polarizability, anisotropy polarisibility, and hyperpolaribility were calculated, evaluated, and then compared together. The essence of the formed bonding model progress along the reaction roots was further validated using electron localization function (ELF) calculations. The highest values of adsorption energies were determined in the range of 18.24 up to 22.12 kcal mol−1 for these kind systems. The acceptable recovery time of 849 s was obtained for the desorption of carbazochrome from the CNT surface under UV-light. The final results exhibit that carbazochrome can serve as a promising carrier and also as sensitive sensors in any kind of practical application.


Introduction
Spontaneous bleeding control is a concern for surgeons, anesthetists, hematologists, and the patient. The spontaneous cessation of bleeding caused by rupture of blood vessels is called hemostasis. Extravasation would be stopped if any holes can be blocked in the system or if the pressure becomes lower than the pressure outside the bleeding vessel [1]. Carbazochrome, an antihemorrhagic or hemostatic agent, causes blocking of blood flow by forming a platelet plug of platelets in the blood. Due to the unique property of the molecule, the drug can be used to prevent excessive blood flow during surgical operations and to treat hemorrhoids [2]. IUPAC name of carbazochrome is (3,6-dihydroxy-1-methyl-2,3-dihydroindol-5-yl)iminourea. They analyzed thermodynamically stable crystal packs of carbazochrome conformers from the stability and properties of the global minimum carbazochrome produced from lattice energy optimisation applying in the repulsion/attraction or dispersion potential field, hydrogen bond analysis, and second derivative properties [3].
Carbon nanotubes (CNTs) are used in biology and medicine as drug delivery systems due to their unique properties such as high tensile strength, high stacking efficiency, low toxicity, elasticity, ultralightweight, excellent chemical and thermal stability, high surface area and non-immunogenicity [4,5]. Due to their intrinsic properties and high dynamism, they have recently been applied as drug adsorbents in the medical and pharmaceutical industries [6]. Because of their characteristic surface properties and their capsule and needle-like shape, they can encapsulate drugs and a variety of biomolecules such as DNA molecules.
Among the numerous delivery systems currently under investigation, single-walled carbon nanotubes seem to hold a promising option, consisting of carbon atoms arranged and tubularly wound in a series of condensed benzene rings [7]. In particular, single-walled carbon nanotubes, calixarene, as new carriers for drug delivery, application of fulourene, and cytosine properties became feasible soon after the cellular uptake of this new material was demonstrated [8][9][10][11]. It also brings with it the solubility problem, which can be considered as the main obstacle to the applications of fullerene and carbon nanotube molecular systems as sensors and drug carriers. It has been shown that the solubility problem can be overcome by substitution of heteroatoms [12].
They investigated interaction and bond properties of anticancer drug doxorubicin (DOX), armchair singlewalled carbon nanotube (SWCNT), and hydroxyl-and carboxyl-functionalized SWCNT (ƒ-SWCNT) based on DFT theory to design, improve, and expand carbon nanotube (CNT) drug carriers which is applied in biomedical systems such as drug delivery systems [13].
The physical chemistry data and also pharmacological properties of the bioactive product can be affected through the physiological situation [14]. A drug delivery system (DDS) can be used to increase the effectiveness of drugs and prevent them from being deactivated to the target areas [15]. Various categories of carriers have been studied, containing lipids, PEGs, and polypeptides [16,17]. Among the many delivery systems, (n, n) single-walled carbon nanotubes, composed of armchair atom arranging in a tubular form, appear to represent a promising option [18]. Findings regarding the SWNT-(streptavidin protein) of conjugates to human promyelocytic leukemia (HL60) and human T cells, have been reported by this work [19].
It has been reported that useful information about the interaction of nanostructures and drug molecules can be obtained using density functional theory (DFT) calculations [20,21].
They examined the (6,6) single-wallled carbon nanotube-SWCNTs-fluorouracil and p-sulphonato-calix aren [4]-fluorouracil composite with DFT method in view point of drug delivery [11]. They investigated the potentiality of SWCNTs as a carrier for droksidopa by quantum mechanical calculation and also by molecular dynamics simulation in both gas and water phases [22]. With the bibliography searching, we know, there is no earlier report about using CNT as a nano-carrier for carbazochrome drug. Therefore, the goal of this study is to investigate the quantum-chemical aspects of the interaction of this drug with SWCNTs.

Computational details
Through a theoretical quantum calculation, equilibrium geometries optimization, total energies, and electronic densities were accomplished in the DFT framework with M062X functional and 6-31G* basis set were made using the Gaussian 09 program package [23].
The adsorption behavior of carbazochrome on a zigzag (4,0)SWCNTs (40atom) was investigated. The adsorption energies of carbazochrome on SWCNTs via the different active sites were calculated using the following relationship: where E drug : is the energy of the free drug, E CNT : is the energy of the free carbon nanotube. The binding energy has been corrected using the basis set superposition error (BSSE).
Also, the relaxed CNT-drug system strength is defined as the difference between the energy of interaction (E int ) with the energy of the complex and the drug molecule bonded to the SWCNTs in the optimized complexes If E int is negative, it indicates pull between drug and CNT, if E inter is positive, it indicates push between drug and CNT.
E def , can be denoted as the used energy for changing the molecule from its ideal configuration to the relaxed moleculesurface system.
where E def −CNT is the energy of the deformed CNT surface after drug adsorption. E def −drug is the energy of the drug form molecule with deformed geometry after its adsorption on CNT. The counter-poise (CP) method of Boys and Bernardi was used to correct the E ads and E int based on BSSE [24].
The nature of intermolecular energies between drug and CNT surfaces is investigated by using Bader's QTAIM theory using MULTIWFN software [25]. QTAIM theory is used to examine the bond critical points (BCP) between two adjacent atoms: their electron densities and Laplacians [26].
Parameters related to HOMO and LUMO energies such as stiffness, softness, chemical Gibbs energies, electronegativity, chemical potential and electrophility index, nucleofugality, electrofugality, and maximum electron flow were calculated using the following equations [27,28].

Current electron density, ELF, and LOL functions
The current densities can be formulated as follows: That χ, i , and C are the basis function for orbitals, occupation number, and a coefficient matrix. Bader [29,30] illustrated regions of large electron localization have a wide value of Fermi-hole. Becke and coworkers [31] illustrated that spherically average like-spin pair has suitable correlation with the Fermi hole. Consequently, they introduced a new function as "electrons localization functions" [32,14].
where and for closed-shell systems, since (r) = (r) = 1 2 , D and D 0 terms can be simplified as � and Savin et al. [33] showed, D(r) parameter as the excess kinetic energies due to the Pauli repulsion, while D 0 (r) is known as Thomas-Fermi kinetic term. Here the ELF can be interpreted in view point of kinetic energies among Kohn-Sham DFT's wave-functions. And it would be in the range of [0,1], which means for a large ELF value, electrons are strongly localized. Although ELF can be used for the wide varieties of molecules, localized orbital locator (LOL) is the other important function that has been investigated by Becke and coworkers instead of ELF for some special molecules [34]. D 0 (r) is used synonymously with ELF for spin polarized and closed shell systems.
Jacobsen showed that the kinetic energies of LOL can be interpreted much better than ELF, since LOL provides a more precise and clear image than ELF. LOL can also be interpreted in terms of localized orbitals. LOL's range of values is between zero and 1, as with ELF [0, 1].

Result and discussion
Various computational tools can be used, such as DFT, Car-Parrinello MD simulations, and hybrid QM/MM approximations for any further calculations. Quantum molecular calculations has been provided recently as a relatively consistent phenomenon of the interaction forces and geometries about the structure, charge distribution, and energy of these kind interacting molecules. As drug carriers, the administration, absorption, and transportation of CNTs must be considered for obtaining the desired treatment effects. The studied routes of CNT administration include oral and injections such as subcutaneous injection, abdominal injection, and intravenous injection. There are different ways of absorption and transportation when CNTs are administered by different routes. Various interaction orientations considered for the interacting drug molecule (N1, O2, N3, N4, which are the semicarbazide group, and the interactions between the O5, N6, and O7 atoms belonging to the indole group) and the CNT were calculated with DFT method in level M062X/6-31G (d) and given in Fig. 1 that exhibits the optimized compound carbazozchrome, a zigzag CNT (4,0) (40atom), and carbazochrome -CNT(4,0) complexes (complex1-com-plex6). From Fig. 1, it can be concluded that carbazochrome has various sites for interaction.
The calculated equilibrium binding distance between carbazochrome and CNT for the complex1-complex6 are given in Table 1 and the calculated interaction, adsorption, and deformation energies of complex1-complex6 are given in Table 2.
Computing the free energy change of any reaction is a useful approach to assessing its thermodynamic feasibility. A large negative change in free energy as it passes from reagents to products creates a quantitative spontaneous (and exothermic) reaction. SETE in interaction for com-plex1-complex6 are − 2.59, 3.54, − 1.72, 2.33, − 7.99, − 9.84, and − 10.13 kcal mol −1 . It was found that the complex6 gives the strongest spontaneous (and exothermic) reaction in the other configurations. It can be said that the weak intermolecular interference between CNT and carbazochrome is an alternative, and the CNT favors the suitability of the carbazochrome molecule as a drug, resulting in desorption [36,37].
From the thermodynamic quantities calculated in the gas phase, it is seen that the formation of all complexes is exothermic, and all except complex2 and complex3 are thermodynamically applicable under ambient conditions. Charge population analysis using the Mulliken approach shows that there is − 0.02295 ē charge flow from CNT to carbazochroma in complex1, whereas in complex2-complex6, there was a charge flow of 0.004935, 0.007103, 0.029106, 0.002562, and 0.002217 ē from the carbazochrome to the CNT.
According to the Mulliken charge population analysis with the Mulliken approach, the Mulliken charge of the C38 atom in CNT, which was − 0.205 ē, was − 0.196 ē in complex1. The mulliken charge, which was − 0.815 ē in carbazochrome, was − 0.796 ē in complex1 The negative charge densities of the C38 and N1 atoms in the interaction of CNT and carbazochrome show that they decrease to 0.009 ē and 0.019 ē, respectively. However, the fact that there is a charge density flow from CNT to carbazochroma during the interaction indicates that the charge densities are distributed over other atoms.
In complex5, which has the highest adsorption and interaction energy in the studied complexes, the charge transfer from carbazochrome to CNT was 0.002562 ē, and in this interaction, the Mulliken charge density of C38 decreased to 0.027 ē, and the N4 and O2 atoms increased to 0.034 and 0.043 ē. It shows that it is distributed over other atoms. In order to clarify the binding nature in these complexes, we evaluated the total electron density maps of carbazochrome, CNT, and complexes. Regions with high electron density are shown in red and yellow. In the carbazochrome molecule, it is seen that the phenyl group has a negative potential, while in the complexes, it is concentrated in the binding groups, as can be seen in Fig. 2.

Topology analysis
Topology analysis based on Bader's QTAIM method has been employed with MULTIWFN program. It has been applied for the selected complexes with the strong interaction energy and more negative adsorption energy values given in Table 1. Thus, the property of intermolecular interactions between CNT and drug is determined in terms of electron densities at bond critical points (BCPs).
In QTAIM analysis, mostly, laplacian ∇ 2 (r) characteristics and the electron density of (r) are widely used to understand the bonding interactions property. However, the total energy density of H(r) and |V(r)|∕G(r) are more remarkable parameters on bonding characteristics. It has been noted that for weak and medium-strength hydrogen bonding and van der waals interactions due to the ∇ 2 (r) > 0, H(r) > 0, |V(r)|∕G(r) < 1 . The strong hydrogen bonds as the intermediate type of interaction r e l a t e d t o ∇ 2 (r) > 0, H(r) < 0, 1 < |V(r)|∕G(r) < 2 .
All the BCP parameters for the selected two complexes are given in Table 3. The computed molecular topographical map of com-plex1 and complex5 with critical points and atom labels are also illustrated in Fig. 3.
According to Table 3, the highest electron density at BCP between the nitrogen atom (N62) of the drug and the carbon atom (C38) of the CNT, which indicates more accumulation of charge from the computational results presented in Table 2, the all interactions in the both complex structures indicate the typical electrostatic interactions according to QTAIM classification with the topology parameters as ∇ 2 (r) > 0, H(r) > 0, |V(r)|∕G(r) < 1.
QTAIM analysis shows that the majority of the interactions of drug with the surface of CNT can be defined as non-covalent nature. One of the important measurements of chemical stability is the energy gap between HOMO and LUMO, and if a molecule is little or no HOMO-LUMO gap, it can be chemically reactive.
Atomic and bond critical points are presented by atom labels and orange spheres, respectively. The cage and ring critical points are due to green and yellow circles. The lines are bond paths. Tables 4 and 5 summarize HOMO-LUMO energies and the parameters like such as hardness (η), softness (σ), electronegativity (χ), the maximum amount of electronic charge transfer ΔN maks , chemical potential (μ) and electrophilicity index (ω), nucleofugality, electrofugality related to E HOMO and E LUMO , and thermal energy, heat capacity, and entropy values of carbazochrome, CNT, and complex1-complex6 calculated with M062X/6-31 g* level. It is notable, in single-electron excitation process, an electron leaves one space function to the real space functions that can be perfectly described as HOMO → LUMO transition. However, in most practical cases, this single-orbital pair model is not suitable, and the excitations have to be represented as the transition of multiple MO pairs with proper weighting coefficients. Intermolecular orbital overlap integral is important in discussions of intermolecular charge transfer. In this study, we calculate HOMO-HOMO and LUMO-LUMO overlap integrals between carbazochrome, CNT, and complex1-com-plex6 calculated.The wavefunction level we used is M062X functional and 6-31 g (d) basis set correspond to HOMO and LUMO, respectively.Consequently, we examine which transport routes are the most favorable due to the atom with larger contribution to HOMO/LUMO) which is more likely to be the preferential site of electrophilic/nucleophilic) attack, respectively. The concepts of absolute electronegativity ( = (I+A) 2 ) and absolute hardness( = I−A 2 ) , are related as (I = + ),where I and A are the ionization potential and electron affinity of our system ( Table 4). The usefulness of and lies in their ability to help predict chemical behavior. The value of for different systems does correlate with chemical hardness and softness defined empirically. The theoretical basis for the new quantities lies in the density functional formalism. Since molecular orbital (MO) theory is by far the most widely used by chemists, it is important to place and in a MO framework. Within the validity of Koopmans' theorem, the frontier orbital energies are given by − HOMO = I and − LUMO = A . The stability of chemical compounds against deformation in an electric field can be related by its hardness. The hardness of CNT Table 3 The QTAIM parameters of selected complexes at the BCPs. ( (r) ), ( ∇ 2 (r)) , y(G(r)), (V(r)) (H(r)), the ratio |    Table 4).
The isolated carbazochrome has a large HOMO-LUMO energy gap of 5.856 eV, where E HOMO , is − 6.753 eV, and the E LUMO , is − 0.896 eV. The isolated CNT has 3.916 eV HOMO-LUMO energy gap, where the HOMO energy is − 6.220 eV, and the LUMO energy is − 2.304 eV. As can be seen in Table 3, after adsorption of carbazochrome on CNT, the HOMO-LUMO energy gap of system decreases to 3.902, 3.905, 3.875, 3.907, and 3.915 eV, respectively for complex1-complex6 and, however, increases slightly to 3.917 for complex4.
In order to understand the sensing mechanism of the CNT to drug, the variation of ΔE g gap during the adsorption process is taken into account by the following equation.
where ΔE g1 and ΔE g2 are the ΔE g values of CNT and complex, respectively.
Sensors are concerned with the change of their electrical conductivity after drug adsorption due to electron exchange between the drug and the sensor. In this line, the drug sensitivity of CNT is based on the HOMO and LUMO energies.
The percentage change values, of %ΔE g for each complex is given in Table 3. As reported energies of E HOMO and E LUMO and energy gap (E g ) in Table 3, the electronic properties of CNT are affected by the adsorption of carbazochrome drug. The decreasing order of percentage change values are obtained for complex3, complex1, complex2, complex5, and complex6 as 1.05%, 0.36%, 0.28%, 0.22%, and 0.022%, but for complex4, it is about % 0.025 by increasing.
The lower E g values indicate higher electrical conductivity, reactivity, and sensitivity. Therefore, decreased E g through adsorption of carbazochrome drug indicates the CNT can detect the drug. Except complex4, all studied geometries of complex structures can be detected the drug material. The density of states (DOS) diagram of each complex was also calculated in order to better understanding the stability of the system. The change in E g by DOS analysis can be confirmed as shown in Fig. 4.
The DOS diagrams of CNT and selected complexes are calculated in the energy range of − 15 to 0 eV have been shown in Fig. 4. In these plots, we have selected the complexes with the significant %ΔE g values given in Table 3, as complex3 and complex1.
The ionization potential of the system may decrease when carbazochrome is adsorbed (complex2, complex4, and com-plex5) or increase (complex1, complex3, and complex6) depending on the adsorption site; but these variations are not noticeable.
ELF current-densities image obtained from DFT studies of carbazochrome carbon nanotube as drug delivery nanocarrier for anti-bleeding drug are represented in (Fig. 5) and the currents consist of HOMO contributions (Table. 4).
The chemical hardness (η) and chemical potential (µ) for the investigated structures are the parameters used to predict the reactivity of the molecules. Since compounds with lower chemical hardness and higher chemical potential values will be more reactive, the electron transfer required for the implementation of the chemical reaction can be easier [29]. As can be seen in Table 5, in complex2 and complex5, when carbazochrome is adsorbed to CNT surfaces, the hardness decreases, and the chemical potential increases in both configurations, indicating that the reactivity of carbazochrome increases after its adsorption to the CNT surface [42]. The global electrophilicity index measures the total ability to attract electrons. CNT can be accepted as a strong electrophile due to possessing a high electrophilicity index at B3LYP (4.639), and carbazochrome posses a lower electrophilicity index at B3LYP (2.498) ( Table 5). Therefore, in the interaction of the carbazochrome with the CNT, the electron density flows from the carbazochrome to the CNT [43].
The fractional number (ΔN) of the electron transferred between two molecules is determined by Eq. 12. Electron transfer parameter determines the direction of spontaneous electron flow, as well as the fraction of electrons transferred from system A to system B [37,44] where, η A , and η B chemical hardness of the acceptor (A) and donor (B) systems, and µ A is chemical potential of the acceptor (A) and µ B is those of donor (B) systems. If ΔN is positive, the charge transfer occurs spontaneously from B to A, and if negative, the charge transfer occurs in the opposite direction. ΔN value of 0.09 in the equation ΔN = carbazole − CNT carbazole + CNT supports that the charge flow from carbazochrome to CNT supports that CNT treats as electron acceptor and carbazochrome treats as electron donor.
The thermodynamic equilibrium constants of the reaction are also calculated by placing the values of Gibbs free energy changes in the following equation. In this formula, R denotes the ideal gas constant and T the temperature. As can be seen from the Table 4, complex5 has the largest K value among the studied complexes. As seen in Table 5, equilibrium constants order are complex3 < complex2 < complex1 < complex4 < com-plex6 < complex 5. Complex1, complex4-complex6, is exergonic and thus thermodynamically favorable.
The results of the dipole moments (µ), static and dynamic polarizability (α), anisotropic polarisability, and first hyperpolarizability (β) of carbazochrome, CNT, and complexes obtained by the interaction of different functional groups with M062X6-31G (d) are given in Table 6.
A dipole moment is a mathematical calculation dealing with unequal distribution of charge in a compound. In other words, the higher the dipole moment of a compound, the more polar the compound is. On the other hand, polarizability is the tendency of a compound to form a dipole when an external electric field is encountered.
In an applied electric field, the energy of a system is a function of the electric field. The first hyperpolarizability is the third-order tensor with a 3 × 3 × 3 matrix. The 27 components of the 3-dimensional matrix can be decreased to 10 components by means of Kleinman symmetry [47]. The µ of pure model CNT is 0, and the symmetry is very x = xxx + xyy + xzz y = yyy + yzz + yxx z = zzz + zxx + zyy = 2 x + 2 y + 2 z 1∕2 high; therefore, its corresponding β value is very small (0.01 × 10 −30 cm 5 esu −1 ). The value of the dipole moment increases in the adsorbed configurations relative to the free CNT (0.00 Debye), which can be attributed to the the perturbation in the electron density. The dipole moment of complex1 (8.57), complex4 (4.81), and complex5 (5.04) is smaller than that of the single drug and the dipole moment of complex2 (14.02), complex3 (13.67), and complex6 (21.63) is higher than that of the single carbazochrome which shows that adsorption of carbazochromer on the CNT in these three complexes enhances the polarity of the system that is a good feature for drug delivery in biological environments [48]. When carbazochrome is adsorbed to CNT, the symmetry is broken. The µ and β values both increased, and the variation of β value is very apparent. The β values of complex1-complex6 are 16.42, 62.49, 22.96, 15.56, 13.03, and 15.10 × 10 −30 cm 5 esu −1 . When we compare the different interaction ways, the hyperpolarisability value of complex1, which is formed by the interaction of CNT and carbazochrome with the carbonyl group, is the largest of the complexes formed by the interaction of CNT and carbazochrome with the other groups. It has been reported that a large initial hyperpolarizability (4.187944 × 10 −30 esu) value is a prerequisite for it to behave like a good NLO material [49].

Recovery time
We have calculated recovery time of the drug from the studied CNT surfaces. It is known that the recovery time gives an information about the time interval (short or long) of the deformation process. It can be predicted as follows where, υ is the attempt frequency, E ads is the BSSE corrected adsorption energy, k is the Boltzmann constant and T is temperature. If the vacuum UV light ( ∼ 3x10 16 s −1 ) is applied to recover of the drug from the studied surfaces,  can be a proper sensor material for carbazole drug under UV light frequency and room temperature.
In addition under the UV-light frequency ( ∼ 3x10 12 s −1 ), which is used for the drug 12 s −1 desorption from nanosurfaces [50]. Here, the recovery time of 849 s for complex5 was calculated under the UV-light. It is an acceptable value for the desorption process of carbazochrome drug from CNT surfaces.

Conclusions
In this study, we perused the carbazochrome molecule adsorption on the CNT by various functional groups performing DFT calculations and provided valuable information on structural properties, adsorption energy, orientation, and charge transfer between CNT and carbazochrome drug in CNT/carbazochrome complexes.
CNTs have been used because of in several research, it can be exhibited that cell viability decreases significantly in human bronchial epithelial cells. The trend also shows how DNA damage increases considerably with dose concentration of SWCNTs due to the non-functionalised SWCNT. Therefore, using CNTs needs to be studied carefully for any further drug delivery systems. QTAIM analysis shows that drug's interactions with the CNT surface are non covalent. The global electrophilicity index measures the overall ability to attract electrons. Since CNT has a high electrophilic index and carbazochrome has a lower electrophilic index, electron density shifts from carbazochrome to CNT in the interaction of carbazochrome with CNT.
The formation of all gas-phase complexes is exothermic, and all are thermodynamically feasible under ambient conditions except for complex2 and complex3. The results indicated that when carbazochrome adsorbed on CNT, the hyperpolarizability for adsorbed nanotubes increases many times, which indicates that organic chromophore adsorbed to nanotube enhances the nonlinear optical properties. It has been shown that the interaction with different functional groups changes the geometric structure and charge distribution and affects the electrical properties, dipole moment, and polarization. On this line, based on the percentage values of band gap of complexes with respect to the bare CNT, the CNT (4,0) can be used to detect carbazochrome drug as an electrochemical sensor. Furthermore, first-order hyperpolarizability of the complex2 shows that it is an attractive object for future studies of nonlinear optical properties. The nature of the formed bonding mode analysis along the reaction pathways was further approved via electron localization function (ELF) calculations.