1 Introduction

Floxuridine (FUDR) with pyrimidine structure has attracted much attention due to its great applications such as inhibitory, antimetabolites, advanced colon, kidney, hepatic arterial infusion, and stomach cancer treatment [1]. How to transfer FUDR drug into target cells is an important point due to its side effects such as decreasing white and red blood cells and levels of platelets [2]. Some research groups were proposed endogenous serum albumin to transfer and delivery of FUDR drug [2, 3]. In another study, the self-assemblies of the FUDR-containing DNA and RNA nano-gels were introduced as drug delivery systems [4]. Therefore, selection of favorable carrier is an important challenge in cancer therapy due to decrease in side effects [5, 6].

In recent years, nano-materials were introduced as reliable carriers to transfer drug molecules into target cells such as boron nitride (BN) and carbon (C) nanotubes. Combining both types of nanotubes results in producing a novel nanotube with more and better applications. Many research groups experimentally have been synthesized this novel nanotube as ternary B–C–N nanotube (Cx(BN)y or BC2N or BCNNT) [7,8,9,10,11,12,13,14,15]. In addition, there have been several theoretical studies on optical, electronic, and elastic properties of the BC2N nanotubes [16,17,18,19,20,21,22,23,24]. For example, both zigzag and armchair nanotubes were studied in order to investigate energetics and electronic properties [25]. In another studies, adsorption of amino acids was investigated with the aim of biotechnological applications and nano-devices [26, 27]. In fact, the BC2N nanotubes with high polarity and surface-to-volume ratio, magnetic behavior, and low-chemical potential are suggested for drug delivery applications [19, 28]. That’s why, single-wall BC2N nanotube (SWBCNNT) is considered as building block in current study.

Doping of metal in SWBCNNTs can change its behavior in interaction with other molecules due to change of electrostatic potentials in the inner/outer surface [28, 29]. For instance, Si-doping in SWBCNNTs leads to sensing of the presence H2CO molecule due to increase in the electric conductivity of nanotube [30]. In another report, this doping decreases formation energy of SWBCNNTs in comparison with CNT and BNNTs [31]. In current study, we have doped the Fe-metal into the SWBCNNT structure because this metal maybe helps to solve the problem of anemia in cancer patients after drug delivery. However, serious side effect has not been reported for this doping on FUDR anticancer drug delivery. So, the aim of this study is to assess geometric and electronic candidate structures of Fe doped and un-doped SWBCNNTs. After this assay, influence of metal doping into FUDR adsorption will investigate by means of density functional theory (DFT).

2 Computational methods

Ground state structures have been investigated in the framework of density functional theory (DFT) implemented to Gaussian 09 program package [32]. M06-2X hybrid functional with all electron basis sets, 6–31 + G (d), is used in the optimization process after DFT calibration method [33,34,35]. In this method, selected exchange–correlation (xc) functional and basis set in comparison with the other xc functional (Table S1) calculates more exact bond length and frequency for studied molecules, more negative energy of ground state, and low spin contamination. Geometry optimization of structures is carried out without any symmetry constrains (C1 symmetry). With vibrational frequency test, it can be found that the optimized geometries stand in the local minima.

The propensity of boron, carbon, and nitrogen atoms to segregate and the formation of SWBCNNTs are calculated by mixing energy [36]. The more negative (less positive) values of the mixing energy indicate favorable mixing among the compositions and thus more stable nanotube [36]. Mixing (excess) energy, \(E_{{{\text{mix}}}}\) [36], is used in order to assess stability of SWBCNNTs with respect to their composition:

$$E_{{{\text{mix}}}} = E_{{B_{m} C_{n} N_{O} }} - \frac{m + O}{N}E_{{B_{m} N_{O} C_{0} }} - \frac{n}{N}E_{{B_{0} N_{0} C_{n} }}$$
(1)

where \(E_{{{\text{mix}}}}\) is mixing energy, and \(E_{{B_{m} C_{n} N_{O} }}\), \(E_{{B_{m} N_{O} C_{0} }}\), and \(E_{{B_{0} N_{0} C_{n} }}\) are total energy of SWBCNNTs, pure SWBNNTs and SWCNTs. The N, n, m, O are number of total atoms in SWBCNNTs, number of carbon, boron, and nitrogen atoms, respectively.

Chemical reactivity of un-doped and doped SWBCNNTs with FUDR was calculated based on global and local reactivity descriptors. Global reactivity descriptors are electronic chemical potential (µ = − (IP + EA)/2), chemical hardness (η = (IP − EA)/2), softness (S = 1/η), and electrophilicity (ω = µ2/2η), respectively [37]. The μ is the escaping tendency of electrons; the η is a resistance to charge transfer; and the ω is floating of electron between nucleophile and electrophile. Local reactivity descriptors were only calculated to the most active site in favorable Fe-doped SWBCNNT and FUDR anticancer. Local Fukui function (\(f^{ + }\)), local softness (\(s^{ + }\)), and local philicity (\(\omega^{ - }\)) are clear-cut examples. The \(f^{ + }\), \(s^{ + }\), and the \(\omega^{ - }\) show active center to nucleophilic attacks.

Using three approach point methods, adiabatic ionization potential (IP) and electron affinity (EA) in above equations were calculated [38]:

$$IP_{{{\text{ad}}}} = E_{{{\text{total}}}} \left( {{\text{compound}}^{ + } } \right) - E_{{{\text{total}}}} \left( {{\text{compound}}} \right)$$
(2)
$$EA = E_{{{\text{total}}}} \left( {{\text{compound}}^{ - } } \right) - E_{{{\text{total}}}} \left( {{\text{compound}}} \right)$$
(3)

where \(E_{{{\text{total}}}} \left( {{\text{compound}}} \right)\), \(E_{{{\text{total}}}} \left( {{\text{compound}}^{ + } } \right)\), and \(E_{{{\text{total}}}} \left( {{\text{compound}}^{ - } } \right)\) are total energy of natural, cationic, and anionic compound (SWBCNNT or FUDR), respectively.

Stability of the complexes is evaluated by binding energy factor in the following form:

$$E_{{{\text{bind}}}} = E_{{{\text{complex}}}} - \left( {E_{{{\text{Fe - C}}\left\{ {{\text{SWBCNNT}}} \right\}}} + E_{{{\text{FUDR}}}} } \right)$$
(4)

In this equation, \(E_{{{\text{complex}}}}\), \(E_{{Fe - C\left\{ {{\text{SWBCNNT}}} \right\}}}\), and \(E_{{{\text{FUDR}}}}\) are the total energy of complex, the Fe–C{SWBCNNT}, and floxuridine.

Depletion of occupancies, percent of Lewis and non-Lewis and stabilization energies (E2ij) [39, 40] as complementation of geometric information are obtained by natural bond orbital (NBO) analysis:

$$E_{ij}^{2} = \frac{{\left| {i\left| {\hat{H}} \right|j} \right|^{2} }}{{E_{j} - E_{i} }}$$
(5)

where \(\hat{H}\) is interaction Hamiltonian, \(E_{j}\) and \(E_{i}\) are orbital energies, and \(\langle \left| {\hat{H}} \right|\rangle\) is the matrix element.

3 Results and discussion

3.1 Geometric and electronic analysis

Low-lying structures of FUDR and possible SWBCNNTs geometries were investigated using M06-2X/6–31G* level of theory, as shown in Fig. 1. Geometry optimization shows that the B–N, B–C, C–C, and C–N bond lengths in open end SWBNNTs are 1.438, 1.498, 1.400, and 1.409 Å, respectively; this result is in good agreement with other reports [41,42,43,44,45]. Performance and reactivity of SWBCNNTs can be tuned by controlling their structures, composition, and size. For instance, L(BN) R(C)3 geometry has less positive value of mixing energy in comparative to two structure of nanotubes, see Table 1. In addition, the least relative energy is belonging to this nanotube. Therefore, this nanotube has more stability than two BC2N nanotubes. So, we consider this geometry as favorable candidate structure in order to doping of Fe-metal and interaction with FUDR anticancer in current study.

Fig. 1
figure 1

Optimized geometry structures of un-doped and doped SWBCNNTs and floxuridine anticancer in M06-2X/6–31G* level of theory

Full size image
Table 1 Calculated stability of local minimum (ΔE) and mixing energy (Emixing) in kcal mol−1, dipole moment (Debye), and bond length (Å) of possible structures of un-doped SWBCNNTs
Full size table

For improvement of FUDR anticancer adsorption and better drug delivery, one Fe-metal was doped on L(BN) R(C)3 nanotube. There are three possible centers for Fe-metal doping in this nanotube, see Fig. 1. Fe-doping instead carbon (Fe–C) and boron or nitrogen atoms (Fe–B and Fe–N) causes high and low localization of electrons in closed- and open-shell systems. In fact, metal doping results in changing in energetic, geometric, and electronic parameters in SWBCNNTs. For example, negative relative energy of the Fe–N- and Fe–B-doped nanotubes than Fe–C structure indicates more stability of them, see Table 2. Besides, changing in the X–Fe (X = B, C, and N) bond lengths leads to changing of dipole moments and creation conditions for effective interaction with anticancer molecule. The least changing of dipole moments was seen in the Fe–N- and Fe-B-doped nanotubes in comparative to selected un-doped nanotube, see Table 2. So, these structures are probably high stability than Fe–C-doped nanotube and low tendency for interaction with FUDR anticancer. Furthermore, global and local reactivity descriptors were calculated to confirm above results.

Table 2 Hartree–Fock energy, relative local minimum energy, bond length (Å), dipole moment, and difference dipole moment with un-doped nanotube (Debye) of favorable Fe-doped SWBCNNTs (Fe–X{L(BN) R(C)3}, x = B, C, and N)
Full size table

Reactivity descriptors investigate role of molecules and active sites in their reaction; these indices were calculated for un-doped, doped SWBCNNTs, and FUDR molecules, see Table 3. With regard to this table, both L(BN) R(C)3 and Fe–C{L(BN) R(C)3} structures have more negative chemical potential than others; so, they rarely loss electron and play the electrophile role in the reaction. Among doped and un-doped nanotubes, the least chemical hardness (0.08 eV) and the most softness (12.50 eV) values belong to Fe–C{L(BN) R(C)3} structure; so, this doped nanotube has high tendency for interaction with nucleophile. On the other hand, FUDR as ligand with the most chemical hardness (3.94 eV) plays the nucleophile role in reaction with selected Fe-doled nanotube. Finally, the most (123.77 eV) and least (1.91 eV) values of electrophilicity belong to Fe–C{L(BN) R(C)3} (as electrophile) and ligand (as nucleophile); this issue confirms that the floating of electron is between these compounds.

Table 3 Global reactivity descriptors of un-doped and doped L(BN) R(C)3 and floxuridine, HOMO–LUMO gaps in eV
Full size table

Local reactivity descriptors of Fe–C{L(BN) R(C)3} and FUDR structures are used to find active sites and better understanding interaction, as given in Table 4. With regard to this table, the highest local Fukui function (\(f^{ + }\)) and local philicity (\(\omega^{ + }\)) descriptors belong to the Fe center in Fe–C{L(BN) R(C)3} nanotube. So, this atom is active center in the nucleophilic attacks. On the other hand, more positive value of \({\text{s}}^{ + }\) and ∆s in metal center of Fe–C{L(BN) R(C)3} nanotube shows existence suitable condition for nucleophile attacks of FUDR. In fact, nucleophile attacks are mainly due to high local softness and dual softness in the oxygen (O5 and O6) and nitrogen (N7) centers in FUDR anticancer molecule. Herein, we have considered these atoms as nucleophile centers in interactions with Fe–C{L(BN) R(C)3} nanotube.

Table 4 Local reactivity descriptors of un-doped and doped Fe–C{L(BN) R(C)3} and floxuridine for heteroatoms in eV
Full size table

Molecular electrostatic potential (MEP) maps can help to confirm reactivity results and investigate interactions. Fe–X{SWBCNNTs, X = B, C, and N} and FUDR anticancer maps are plotted in Fig. 2. High and low electron densities are related to negative and positive regions, respectively. The yellow, blue, and green colors elucidate the most negative, positive, and zero electrostatic potential, respectively. According to Fig. 2, there are only two positive (blue color) and zero (green color) electrostatic potential regions in Fe–C{SWBCNNT} system. Positive point is belonging to Fe-metal site and shows electrophilic property of this atom; this issue confirms that Fe-doping instead carbon atom leads to increasing localization of electrons and electrophilic property in Fe center of Fe–C{SWBCNNT} system. So, adsorption and delivery of the FUDR anticancer by the Fe–C{L(BN) R(C)3} nanotube are probably carried out better than the Fe-B and Fe–N doped and un-doped nanotubes; this issue is due to being reliable of global reactivity descriptors and the MEP maps, see Table 3 and Fig. 2.

Fig. 2
figure 2

Plotted molecular electrostatic potential (MEP) maps of floxuridine anticancer and Fe–X{SWBCNNTs, X = B, C, and N} in selected theoretical method

Full size image

Highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) gap is other reactivity parameter to show stability of nanotubes. Fe-doping partly results in decrease in the HOMO–LUMO gap in comparison with pure nanotube, especially Fe–C{L(BN) R(C)3}, see Table 3. According to this table and Fig. 3, decrease in HOMOFUDR-LUMOFe-C{L(BN)R(C)3} gap is mainly followed by better charge transfer between anticancer and nanotube. So, adsorption and delivery of FUDR anticancer are probably carried out better than other Fe-doped nanotubes, where this issue is in good agreement with previous results.

Fig. 3
figure 3

Highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) gap of un-doped and doped of L(BN) R(C)3 and floxuridine anticancer. All presented energies are in eV

Full size image

3.2 Adsorption of floxuridine anticancer on doped SWBCNNTs

Fe doped and un-doped BC2N nanotubes were interacted with FUDR anticancer at parallel and perpendicular orientations in order to confirm previous results. Besides, introduced active sites in FUDR structure such as the O5 and O6 and N7 atoms are considered as the most possible interaction sites at perpendicular orientations, see Fig. 4 and Figure S1 (S means supplementary file). According to Table 5, the X–Fe (X = O, and N atoms of FUDR) distance at parallel orientations is longer than perpendicular orientations in FUDR-[Fe-SWBCNNTs] complexes. On the other words, long distance in parallel than perpendicular orientations is reflection of low adsorption energies. This issue is confirmed with more negative adsorption energy (Eads) in perpendicular orientations, see Table 5. Furthermore, the most negative Eads was shown in perpendicular orientations of FUDR-Fe–C{L(BN) R(C)3} complexes. So, according to this issue previous result can guess that the Fe–C{L(BN) R(C)3} nanotube will be probably favorable career for drug delivery.

Fig. 4
figure 4

Interactions of floxuridine and Fe–C L(BN) R(C)3 in parallel (A) and perpendicular (B) orientations, respectively

Full size image
Table 5 Adsorption (binding) energy in different methods (kcal mol−1), distances (D, Å), and bond angles (degree, °) in parallel and perpendicular orientations (O and N sites)
Full size table

On the other hand, repulsive interaction between anticancer and surface of nanotube in parallel orientation is greater than other. Therefore, binding of anticancer in the perpendicular orientations is stronger than other. The Fe–O–Ph bond angle is larger than Fe–N–Ph bond angle in perpendicular orientation of FUDR-BC2N complexes; this issue can be reflecting of their stability and better drug delivery. More negative adsorption (binding) energies show the best orientation of their adsorptions, see Table 5. With regard to this table, less binding energy and more stability belongs to FUDR-Fe–C{L(BN) R(C)3} complex in perpendicular orientations (especially in O5 active site). This result is in good agreement with reactivity results.

Density of state (DOS) has been applied to analysis of the HOMO–LUMO gap of chemical structures for better understanding of FUDR anticancer adsorption on Fe–C{L(BN) R(C)3} nanotube. Total DOS of FUDR-Fe–C{L(BN) R(C)3} complex in perpendicular orientation is plotted in Fig. 5 and for other complexes is plotted in Figure S2. In fact, decrease in HOMO–LUMO gaps mainly results from low modification and reliable adsorption of drug molecule on BC2N complexes. According to these figures, the most decreasing is belonging to FUDR-Fe–C{L(BN) R(C)3} complex. So, charge transfers between FUDR and Fe–C{L(BN) R(C)3} nanotube are conveniently carried out.

Fig. 5
figure 5

Total density of state (DOS) of FUDR- Fe–C L(BN) R(C)3 complexes in parallel (A) and perpendicular (B) orientations

Full size image

NBO-based calculation shows that there are significant charge transfers in perpendicular interaction; there is no any significant donor–acceptor interaction in parallel orientation. Total donor acceptors at the O5, O6, and N7 atoms of perpendicular orientations with delocalization energy based on second-order perturbation theory are 17.0, 19.8, and 21.1 kcal mol−1. Total Lewis electron densities for the FUDR-[Fe–C{L(BN) R(C)3}] complexes are 97.22%, 97.12%, and 97.19%, of the idealized structure, respectively. Therefore, existence of significant charge transfers, low Lewis localization, and low occupancies confirms reliable interactions in perpendicular orientations.

4 Conclusion

In this study, after optimization processing of the un-doped BC2N nanotubes, L(BN) R(C)3 was selected as candidate structure for Fe-doping due to more negative mixing energy value. After Fe-doping instead carbon, nitrogen, and boron nanotube atoms, Fe–C{L(BN) R(C)3} was selected as candidate structure for interaction with drug molecule due to positive mixing energy (low stability) and high changing of dipole moment. In addition, global chemical reactivity indices imply that Fe–C{L(BN) R(C)3} structure has high tendency to interact with FUDR anticancer; this issue results from low chemical hardness, high chemical softness, and fast floating of electrons between these compounds. More importantly, high localization of electrons and low HOMOFUDR-LUMOFe-C{SWBCNNT} gap result in improvement in adsorption energies about 80% than un-doped nanotube. Besides, existence of several significant charge transfers with high stabilization energy causes introducing of this nanotube as favorable carrier to transfer anticancer molecule.