Drug delivery of carvedilol (cardiovascular drug) using phosphorene as a drug carrier: a DFT study

2D nanomaterial phosphorene is a chemistically stable, biocompatible, and biodegradable drug delivery platform. This study investigates the drug loading efficiency of phosphorene for the cardiovascular drug carvedilol using density-functional theory (DFT). In the gas phase, carvedilol prefers to interact with phosphorene via P-H bonding with an adsorption energy of 0.59 eV (0.45 eV in water). The complex HOMO–LUMO energy gap has been calculated in gas and solvent media to assess phosphorene-carvedilol reactivity. As compared to free carvedilol and phosphorene, the phosphorene-carvedilol complex has increased solubility. The NCI analysis visualises non-covalent interactions within complexes. The low Van der Waals interactions between carvedilol and phosphorene allow for easy drug offloading. The phosphorene-carvedilol complex is more soluble in water than previously thought. Phosphorene's electron density changes significantly after complex formation, as revealed by charge decomposition plots and electron-localization function plots. PET (photo-induced electron transfer) analysis explains quenching. GRAPHICAL ABSTRACT


Introduction
Globally, cardiovascular diseases (CVDs) become a massive economical and medical burden, so these should not be left untreated as they lead to heart failure [1]. According to the World Heart Federation report, CVDs are responsible for 17.3 million deaths per year, and this figure is anticipated to rise in upcoming years [2,3]. In 2017, approximately 17.8 million individuals have died worldwide due to CVDs, and it is expected that 23.6 million people will die by 2030 due to CVDs [4,5]. Various chemical entities or therapeutic formulations have been formulated to face these pressing issues to give timely treatment. However, several new drugs failed in their therapeutic potential due to their low water solubility, poor systemic bioavailability, cytotoxicity, lack of specificity, low permeability, poor shelf half-life, and poor biopharmaceutical properties [6]. These issues emerged particularly when drug exposure and medical science moved from wet science to combinatorial science.
Conventional drug delivery approaches pose several issues, including low precision, potential toxicity, and drug resistance [7]. In the realm of biomedicine, drug delivery is empowered by nanotechnology [8]. In the present scenario, "Nanotechnology", a rapidly developing science, offers multiple benefits by introducing nanocarriers. These nano-sized particles have shown great excellence indrug delivery, bio-imaging, gene therapy, bio-sensing, and tissue engineering. Furthermore, their physio-chemical properties can be tailored by varying their sizes, shapes, compositions, and surface properties [9]. They exhibit remarkable structural [10], chemical [11], mechanical [12], magnetic [13], electrical [14], and biological characteristics due to large surface areas [15]. Nanocarriers deliver with immense success at the targeted location, while improving therapeutic index and minimizing adverse effects [16]. This revolutionary development of nano-vehicles improves the pharmacokinetic profiles of drugs.
Various low-dimensional nanomaterials have been reported in the literature which serve as excellent drug delivery vehicles [17,18]. Hossain et al. theoretically scrutinized the adsorption potential of an active anti-protozoal medication "Metronidazole" on various nanocomposite surfaces (i.e. graphene, (BN) boron nitride and (BC) boron carbide) employing DFT and QTAIM approaches, and claimed that boron nitride nanosheet could be a promising platform for the delivery of metronidazole drug and minimalize the side effects associated with the drug [19]. The same group of researchers reported the suitability of functionalizedboron nitride (BN)-based drug delivery system as viable candidate for favipiravir delivery engaging DFT calculations [20]. Quantum mechanical studies were conducted by different research groups to explore theoretical aspects of fullerene-like nanocages i.e. C 24 , C 60 , C 48, and boron nanocluster i.e. B 35 , B 12 N 12, and B 12 C 6 N 6 as efficient nano-vehicles for different anticancer drugs and in gas-sensing applications [21][22][23][24][25][26]. Recently, Shahabi and coworkers studied the effectiveness of graphyne-3 (GY-3) and graphdiyne (GDY) as drug delivery systems for Idarubicin drug, implementing MD (molecular dynamics) simulation in conjunction with DFT approaches [27]. Their findings revealed that Graphyne's family members could deliver Idarubicin drug at intended sites without altering the bio-activity of this drug and exhibit a great promise in cancer treatment.
In corresponding to the usage of new advances, colossal information has been gathered on natural variables, such as carriers, processing chemicals, and efflux frameworks. Next-generation nanostructures, 2D nanomaterials, such as graphene [28], molybdenum disulphide [29], tungsten disulphide [30], and graphdiyne [31,32] stand out as ideal candidates, depicting highly directional physio-chemical characteristics. The success of these 2D nanomaterials has driven material scientists to investigate other 2Dlayered materials. In that line of 2D nanomaterials, "phosphorene" (black phosphorous), a stable allotropic form of phosphorus, has revolutionized the landscape of many scientific and technological research areas due to its extraordinary properties [33,34]. Although phosphorene was experimentally fabricated in 1914 by P.W Bridgman from red phosphorous under high temperature and pressure conditions, it remained unnoticed for almost a century [35]. Phosphorene got recognition in 2014 when it was rediscovered by mechanical exfoliation from bulk black phosphorus (BP) into BP nanosheets and nanoribbons in the same way graphene was synthesized from bulk graphite by the scotch-tape method [36]. Phosphorene is a new graphene due to the state-of-the-art in many fields. Unlike graphene, it possesses a layer-dependent energy gap. The experimentally predicted band-gap ranging from 0.3 eV value in bulk crystal to 2.05 eV in case of few layers [37,38].
The prime impetus to choose phosphorene as a drug carrier in the present review is its unique combination of properties, such as ultra-high surface area, absence of toxic metal element, adjustable bandgap, biocompatibility, excellent biosafety, and a wide-range absorption in UV (ultraviolet)-visible and (NIR) near infra-red region [39][40][41]. The ultra-high surface area of this metal-free nanomaterial is due to its honeycomb (wrinkled) structure, which ensures efficient drug-loading capacity [42]. Moreover, higher electron mobility and anisotropic behaviour make phosphorene a promising material in optoelectronic fields, water purification, field-effective transistors, and sensing applications [43][44][45][46][47][48]. Black phosphorous (BP) also demonstrates excellent photothermal conversion behaviour and broad absorption within UV-Vis-NIR region [49]. Phosphorous is extremely harmful in its elemental form and can damage tissue cells; however, phosphorene (BP nanosheets) releases non-toxic intermediates, such as phosphate and phosphonate upon biodegradation. These substances are physiologically friendly, causing no damage to kidneys [41,50]. Hence, phosphorene is innocuous and a safer biomedical material for disease diagnosis and biosensing [51,52]. Phosphorene, being biocompatible and biodegradable, exhibits intriguing potential in numerous fields, such as drug delivery, tissue engineering, bone regeneration, gene therapy, and cell imaging [53][54][55][56]. Phosphorene captures drug molecules by loading chemical entities into nanocavities by the weak force of attraction. These weak forces enable easy offloading of drugs at targeted locations.
Cardiovascular drugs or medications are among the most extensively used drugs in the medical field. In cardiovascular drugs, a third-generation non-cardio selective β-blocker; "Carvedilol drug", has become a favourable lead in the treatment of IHD (ischaemic heart disease), arrhythmias, hypertension and congestive heart failure [57][58][59]. The drug fits in BCS (biopharmaceutical classification system) class II (low solubility and high permeability) system [60]. A major vault for this drug to achieve therapeutic excellence is its poor solubility (6-8 μg/ml), and poor bioavailability (25%) as its active ingredients are unable to dissociate properly. Hence, the activity of the drug is unelaborated at the intended site [61]. A drug should have better aqueous solubility at the absorption site in order to gain better access to circulation channels. Erratic drug absorption leads to poor bioavailability because of undergoing hepatic first-pass metabolism [62]. If we overcome this hurdle of carvedilol, it will be a huge success in the medical field. In this regard, considerable efforts are being made to introduce nanoscale carriers to enhance the clinical potential of carvedilol and minimize adverse effects associated with its delivery [63]. To explore therapeutic efficacy of phosphorene as drug-delivery carrier for carvedilol, DFT (density-functional theory) and TD (time-dependent)-DFT computations were performed comprehensively.

Computational details
All the required theoretical computations are done applying the DFT (density functional theory) approach [64] in Gaussian 09 package [65]. Ground-state molecular geometry optimizations of carvedilol drug and phosphorene carrier are accomplished using B3LYP hybrid functional with 6-31G * * level of DFT. B3LYP/6-31G * * theory level provides reliable results and has a low computational cost [57,66]. Moreover, it is an excellent choice for accurately estimating electronic properties and molecular geometries. Previous reports suggested that it performs reasonably well for molecular adsorption studies [67][68][69]. Different attainable orientations of the drug on phosphorene carriers are optimized to procure the most stable structure of carvedilol on phosphorene. TD-DFT (Time dependent-DFT), along with TD-B3LYP/6-31G * * basis set, is applied for excited-state calculations [70]. Adsorption energy is forecasted to realize interactions between different complex-forming components (i.e. carrier and drug). The strength of adsorption energies (E ads ) is calculated using the following mathematical equation [71,72]: where E Phosphorene−Carvedilol indicates calculated DFT energy of complex. E Phosphorene and E Carvedilol are the energies of carvedilol and phosphorene, respectively. The term E BSSE represents the basis-set superposition error calculated to exclude the basis-function overlap effect. The standard counterpoise method [73] is used to calculate BSSE energy. Furthermore, the structural stability of phosphorene carrier is evaluated by estimating formation energy (E formation ) using the following equation [74][75][76]: where E formation reperesents the total energy of formation, E Phosphorene represents the total energy of phosphorene. The terms E(P) and E(H) signify the energy of solitary hydrogen and phosphorous atom, respectively. "n" denotes the total number of atoms in complex, while "x" and "y" stand for total count of phosphorous and hydrogen atoms in phosphorene sheet.
To explicitly treat the effect of solvent on phosphorene-carvedilol interactions, IEFPCM (Integral equation formalism-PCM model has been applied [77]. Being an essential part of the living system, water has been chosen as a solvent to study the solubility and stability of the complex. The stability and solubility of the phosphorene carvedilol complex can be computed using the following expression [78]: E Solvation denotes system's total solvation energy, while E gas and E Sol stand for energy in gas and solvent media, respectively. Some important factors, like dipole moment (μ), quantum reactivity parameters and HOMO-LUMO energies are considered in solvent as well as in gas media for carvedilol, phosphorene, and complex, which provide information about their preferences for reactivity in both phases [79]. Electron localization function (ELF) is performed to visualize electron-density changes within carrier (phosphorene) prior to and after complex formation [80,81]. CDA analysis is performed to map out the donor-acceptor interactions and splitting the ligand field for the complex. Mechanisms, such as charge donation and charge separation within the complex molecule, are also investigated by the CDA analysis [82,83]. The natural bond orbital [84] investigation is done by using NBO calculations. The NBO analysis accounts for the inter and intramolecular interactions in complex molecules and redistribution of electrons within various orbitals. The charge transfer from carvedilol to phosphorene molecule and from phosphorene to carvedilol molecule and electronic transitions within phosphorene itself is ensured through NBO calculations [85,86]. The UV-Visible spectra of drug, carrier and complex are plotted using theTD-DFT approach, and are analyzed via Swizard program [87]. The strength of non-covalent interactions between carrier and drug are envisaged throuhg NCI analysis in three-dimensional space. The Photo-induced electron transfer and charge analysis is performed using aforementioned functional of DFT.

Molecular geometry optimization
Firstly, ground-state geometries of drug (carvedilol), carrier (phosphorene), and complex (phosphorenecarvedilol) are optimized applying B3LYP/6-31G(d.p) functional as depicted in Figure 1. The optimized structure of the complex illustrates the P-H interaction between the carvedilol drug and the phosphorene carrier. This non-bonding interaction demonstrates that drug moleculeserves as a contributor to hydrogen bonding, when adsorbed onto the surface of the carrier. One P-H interaction appears during complex formation. One proton from an aromatic drug ring interacts with the phosphorous atom of phosphorene with an interaction distance of 2.79 Å. The dipole moment calculated for optimized phosphorene carrier is insignificant. The increment in dipole moment of 1.38 Debye after complex formation (phosphorene-carvedilol) improves the solubility of phosphorene-carvedilol complex in polar sovents, facilitating active drug movements through the systemic circulation.
The adsorption energy is computed using Eq. (1) to gain insight about adsorption mechanism. In gas phase, BSSE counterpoise-corrected adsorpyion energy (E ads ) for phosphorene-carvedilol complex is computed to be −0.59 eV (−0.45 eV in water). The negative E ads value for phosphorene-carvedilol complex signifies that complex formation is an exothermic and thermo-dynamically favoured process. It also indicates the stability of complex and spontaneous adsorption of carvedilol on the phosphorene surface. The more the negative value of the E ads , the stronger the adsorption between the drug and carrier molecule. However, in this case, the adsorption is not so strong as the drug develops non-covalent interactions with the phosphorene molecule (i.e. P-H bond), which facilitates drug desorption at the targeted site. The formation energy (E formation ) of phosphorene is -3.36 eV/atom, the negative value of E formation indicates the sufficient stability of the phosphorene carrier (Table 1). Table 1. Calculated HOMO/LUMO energies, E g (band gap) along with λ max wavelength of maximum absorption of phosphorene carrier, carvedilol drug, and the phosphorenecarvedilol complex in gaseous phase using B3LYP/6-31G * * basic set.

Frontier molecular orbital (HOMO and LUMO) analysis
FMO (frontier molecular orbitals) analysis provides valuable information about UV-visible spectrum, optoelectronic properties, and reactivity parameters of the molecule [88]. The HOMO (highest-occupied molecular orbital) behaves as an electron contributor or nucleophile, while LUMO (lowest-unoccupied molecular orbital) has electrin-accepting ability or electrophilic nature. The HOMO and LUMO characterize charge distribution within the molecule. The charge transfer from HOMO to LUMO corresponds to the change in energy gap (E g ) that enables to compute chemical reactivity, polarizability, and reaction stability [89,90]. A molecule with a small energy band gap has high polarizability, which increases chemical reactivity and reduces kinetic stability. These characteristics make the molecule soft. [91]. Figure 2 represents the HOMO and LUMO of carvedilol, phosphorene, and phosphorene-carvedilol complex. In carvedilol, LUMO is mainly distributed at the carbazole end of the molecule, whereas the electron density of HOMO is concentrated not only at the carbazole end but also on the nitrogen and hydroxyl group of molecules. The electron density of HOMO and LUMO of phosphorene, is uniformly distributed on the entire structure. An inclusive density separation is observed in phosphorene-carvedilol complex with charge density distribution of HOMO on carvedilol and LUMO on phodphorene. This density distribution map represents the transfer of charge between the carrier and drug. Moreover, it also confirms that carvedilol acts as an electron-donating group, while phosphorene contributes as an electron acceptor in the phosphorene-carvedilol complex (i.e. charge transition occurs from carvedilol towards phosphorene). Table  1 summarizes HOMO/LUMO energies (E HOMO , E LOMO ), band gaps (E g ), along with maximum absorption wavelengths in gas phase.
The E HOMO /E LUMO of carvedilol are found to be −5.32 eV and −0.54 eV, respectively, with E g of 4.78 eV. The E g value for phosphorene is 3.28 eV with E HOMO and E LUMO of −6.01 eV and −2.73 eV, respectively. The phosphorene-carvedilol complex has an energy gap of 2.78 eV, a much lower value than that of carvedilol (4.78 eV) and phosphorene (3.28 eV) which implys that the complex (phosphorene-carvedilol) requires less energy for excitation. The value of E HOMO of the phosphorene-carvedilol complex molecule (−5.41 eV) is nearly equal to E HOMO of carvedilol (−5.32 eV), whereas E LUMO (−2.63 eV) resembles E LUMO of phosphorene (−2.73 eV). Remarkably, this pattern is in good agreement with FMOs' densities (i.e. highest occupied MO is confined on carvedilol, while the lowest unoccupied MO is situated on phosphorene in the complex). The phosphorene shows λ max at 438 nm, whereas the phosphorene-carvedilol complex shows an absorption peak at 440 nm (red-shifted by 2 nm). This red-shift in excita-tion wavelength (λ max ) for the carvedilol-phosphorene complex is due to a smaller energy gap between LUMO and HOMO.

Non-covalent interaction and iso-surface analysis
The NCI analysis provides real-space visualization of non-covalent interactions within a complex structure. NCI scatter diagram can be used to characterize molecular regions with weak interactions and strong directional attractions. In the NCI plot, the type of interactions within the complex structure can be identified based on spikes that occur at low densities of RDG (reduced density gradient). The visual interpretation of the NCI scatter plot is shown in Figure 3. The scatter diagram has schemed between RDG and the sign of the second Hessian Eigenvalue (sin λ 2 ρ), which gives a stiletto-heel shape.
The sin of λ 2 (ρ) describes the nature and strength of chemical bonding and parameters related to local bonding in the complex. In the NCI plot, the value of λ 2 ρ > 0 signifies repulsive/steric hindrance, λ 2 ρ < 0 indicates hydrogen bonding and λ 2 ρ ≈ 0 signifies vander Waals' interactions between component fragments of complex [92]. Interestingly, the scatter graph shows all types of NCIs within the phosphorene-carvedilol complex system. The weak van-der Waals' interactions, hydrogen bonding, and steric interactions are distinguished by green, blue, and red colour codes. These weak interactions are very important in the case of drug delivery as they allow easy drug detachment from the carrier at the desired location. The 3D colour-filled   iso-surface of phosphorene-carvedilol implemented in visual molecular dynamics (VMD) [93] is depicted in Figure 4, where green patches show weak van-der Waals' interactions between the carrier and drug.

Charge decomposition analysis and density of state spectrum
CDA (charge decomposition analysis) helps explain the charge transfer in molecular orbital (MO) energy levels and investigate donor-acceptor interactions [82]. The intermixing of MOs of individual fragments generates new MO energy levels in a complex molecule. This addition results in the lowering of bandgap of the complex structure. The molecular orbital contribution from each fragment is confirmed by plotting the orbital interaction diagram for the phosphorenecarvedilol complex, as represented in Figure 5(b). The mixing of MO energy levels from each fragment (phosphorene and carvedilol) generates new MO energy levels in the phosphorene-carvedilol complex, contributing to an increase in E HOMO (−5.41 eV) and a decrease in E LUMO value (−2.63 eV) of the complex. Thus the gap between H-L of phosphorene-carvedilol complex is reduced (2.78 eV). The smaller band-gap of the complex enables intra-molecular charge transfer within the complex.The density of state (DOS) spectrum is plotted using PyMOlyze 1.1 software (Figure 5(a)). The DOS spectrum shows a good agreement with CDA results. The DOS spectrum revealed that the bandgap of the complex has been reduced (E g = 2.78 eV) due to the intermixing of individual fragments' orbitals. It is found from CDA and DOS results that the charge transfer process occurs between carvedilol and phosphorene.

Chemical reactivity parameters
Chemical reactivity parameters can explain molecular stability, reactivity, and other electronic properties, like charge transfer and drug-carrier interactions. The chemical reactivity descriptors based on E HOMO and E LUMO values i.e. chemical potential, electrophilicity index, global hardness, and chemical softness were calculated for carvedilol (drug), phosphorene and phosphorene-carvedilol (complex) in gas phase In Eqs. (4) and (5) Table 2).
Many interesting properties of the complex are reported. The chemical stability of a molecule correlates with hardness (η). The higher values of chemical hardness correspond to better stability, whereas Table 2. Calculated reactivity parameters such as chemical potential (μ), chemical hardness (η), softness (s), electrophilicity (ω) of phosphorene carrier, carvedilol drug, and the phosphorene-carvedilol complex in the gaseous phase.  molecules with low chemical hardness are more reactive. The η value of the complex is 1.39 eV, which is lower than that of carvedilol (η = 2.44 eV) and phosphorene carrier (η = 1.64 eV), which suggested that the complex has more reactivity. The higher chemical softness (0.72 eV −1 ) and lower chemical hardness (1.39 eV) values for the phosphorene-carvedilol complex revealed that the complex is softer than carvedilol and phosphorene. The electrophilicity index explains the ability of the molecular system to gain electrons [101]. Complex (phosphorene-carvedilol) has high electrophilicity index (5.81 eV), indicating that it is a good electrophile. A comparatively low value of η (1.39 eV) with a high negative value of μ (−4.02 eV) means that the complex has high polarizability. The stability of the phosphorenecarvedilol complex is predicted by negative chemical potential.

ELF and NBO (natural bond orbital) analysis
The electron density changes in the carrier after phosphorene-carvedilol complex formation can be interpreted by ELF plot. Figure 6(a) and 6(b) illustrates ELF (Electron localization function) plots for phosphorene carrier and phosphorene-carvedilol complex, respectively. The electron density of phosphorene has been considerably changed after forming a complex with carvedilol drug and can be seen in Figure 6. The ELF values based on kinetic energy density ranges from 0.0 to 1.0. ELF values ranging from 0.5 to 1.0 show regions in position space-occupying localized electrons (bonding and anti-bonding). The low range of ELF (0.0-0.5) represents regions containing delocalized electrons [102]. From these ELF plots, we can also investigate transitions from carvedilol to phosphorene and vice versa in NBO analysis. Moreover, density changes in phosphorene after complex formation are also studied. NBO (natural bond orbital) analysis based on secondorder perturbation is used to evaluate inter-molecular interactions from donor to acceptor and provides an appropriate basis for investigating intramolecular charge transfer (ICT) within the molecular system. NBO analysis gives reliable information about interactions taking place in virtual as well as in filled orbital space [103]. Higher the charge delocalization from donor NBO to acceptor NBO, higher will be the degree of conjugation which ensures complex stability.
The highest values of Perturbation energy for the carrier (phosphorene) and the phosphorene-carvedilol complex are depicted in Tables 4 and 5, respectively, where the term E(j)-E(i) indicates energy dfference between donor (i) and acceptor (j) NBO orbitals and F i,j is the off-diagonal Fock matrix element. NBO analysis disclosed that the interactions: π * C 101 -N 102 → π * C 99 -N 100 and π * C 101 -C 102 → π * C 97 -C 98 provide high stabilization to the complex system by 284.63 and 249.20 kJmol −1 , respectively ( Table 5). The overlapping between π (bonding) and π * orbitals (anti-bonding) causes charge transfer (ICT), making the molecular system more polarized. A slight change has been observed in E 2 values of the carrier before and after the complex formation process, and these energy changes resulting from internal transitions (charge delocalization) are listed in Table 6. The energy sustainability E 2 ( Table 6) represents stabilizing interactions between the donor and acceptor.
From the NBO analysis, the charge transfers from the phosphorene to carvedilol, carvedilol to phosphorene, and from the phosphorene to phosphorene itself can be predicted and comprehended with the aid of the ELF electron-density plots.

Solvent effect
The solvent effect is investigated to explain the solubility and stability of the complex. Water is the solvent of choice as it mimics a real biological environment. IEF-PCM solvent model is applied to study the interactions between carvedilol drug and phosphorene carrier in the water phase [77]. The adsorption energy (E ads ) computed for complex water media is −0.45 eV. The adsorption energy with negative sign shows that adsorption is vigorously favourable and exothermic. When E ads of complex is compared in the water and gas phase, it has been found that the E ads value of complex in the water phase is less (−0.45 eV) than its corresponding value in the gaseous phase (−0.59 eV). However, this difference is insignificant, indicating the chemical stabilization of the complex in both phases. The solvation energies of carvedilol, phosphorene, and complex are also determined using Eq. (3). Solvation energy for carvedilol, phosphorene and phosphorene-carvedilol system are −0.45 eV, −0.86 eV, and −1.17 eV, respectively. All the Figure 6. Electron density changes in electron localization function plot (a) phosphorene (b) phosphorene-carvedilol complex.
negative solvation energies indicate a spontaneous solvation. It is inferred from the above data that the smaller value of solvation energy results in improved solubility of the complex in the aqueous phase in contrast to free carvedilol and phosphorene. Solvation studies also revealed that the solvent media i.e. water stabilizes the complex by decreasing its solvation energy.
The E HOMO , E LUMO , their energy band gaps (E g ), and chemical stability descriptors of phosphorene, the carvedilol drug, and the phosphorene-carvedilol complex are also calculated in the solvent (water) phase and are depicted in Tables 3 and 7. The solvent phase analysis shows that HOMO-LUMO energies and E g values of carvedilol, phosphorene, and the phosphorenecarvedilol complex are slightly changed in the presens of water. The increase in band-gap (2.83 eV) of phosphorene-carvedilol complex suggests that phosphorene-carvedilol complex is somewhat more reactive in water phase. It is also observed that by switching from the gas to the aqueous phase, the dipole moment of the complex (phosphorene-carvedilol) has been increased significantly. Dipole moment value observed in aqueous phase for the phosphorene-carvedilol complex is 2.04 D, while in gas phase, its value is 1.95 D. Greater dipole moment suggests more solubility of complex in water phase, which is useful for drug delivery in the biological environment. The negative chemical potential given in Tables 2 and 3, indicates stabilization of phosphorene-carvedilol in both phases. The increment in hardness value of phosphorene-carvedilol complex (1.41 eV) and lower softness (0.70 eV) indicates that complex has more stability in water phase as compared to gas phase.

UV-Visible spectral analysis
TD-DFT method is employed to simulate UV-Visible spectra of phosphorene, carvedilol, and phosphorene-carvedilol complex within gas and solvent phase Table 7. HOMO and LUMO energies, E g (band gap) along with λ max (maximun absorption wavelenth) of carvedilol drug, phosphorene carrier, and the phosphorene-carvedilol complex in the water (solvent) phase using B3LYP/6-31G * * basic set. to investigate excited-state properties. The carvedilolphosphorene system shows λ max at 440 nm providing broad absorption within UV-visible region when compared to carvedilol (λ max = 231 nm) as demonstrated in Figure 7(a). The maximum absorption peak for phosphorene is 438 nm ( Table 1). The solvent effect on the UV-Visible spectra of the complex, carvedilol drug, and phosphorene carrier is also investigated. λ max of phosphorene, carvedilol, and the phosphorene-carvedilol complex is listed in Table 7.

Surface charge analysis
The effect of surface charge has been studied for the carrier and complex as it provides information about molecular and biological components [104]. The optimized structures e.g. phosphorene and phosphorenecarvedilol in their cationic (+1) and anionic (−1) states, are analyzed. The variations in bond length associated wirth surface charge (+1/−1) of phosphorene (phosphorene +1/−1 ) and its corresponding complex with carvedilol (phosphorene +1 -carvedilol and phosphorene −1 -carvedilol) are shown in Figure 8. For bond length analysis, graphs are plotted between the bond index (number of bonds) and bond length. Bond length evaluation of phosphorene +1 (phosphorene with +1 charge state) showed that the bond lengths of P-P bonds are in the range of 2.22 Å-2.31 Å, and the P-H bond displays a range from 1.41 Å to 1.42 Å (Figure  8(a)). Similarly, phosphorene −1 (phosphorene with −1 charge state) shows P-P and P-H bonds with bond lengths from 2.21-2.30 Å and 1.41 Å-1.43 Å, respectively (Figure 8(b)). After the adsorption of carvedilol on the surface of phosphorene +1/−1 , the subsequent phosphorene +1/−1 -carvedilol complex showed less bond length dispersion respecting to phosphorene +1/−1 carrier, as demonstrated in Figure 8(c and d).
The bond-length analysis of complex in its cationic state (phosphorene +1 -carvedilol) reveals that the bond lengths of P-P and P-H bonds are in the range of 2.23-2. The spreading of charges has been analyzed by means of ADCH population method (Atomic-dipole moment-corrected Hirshfeld) [105] to figure out problems accompanying poor dipole-moment reproducibility of Hirshfeld-charge. To realize the ADCH analysis, a graphical demonstration is shown in Figure  9 for phosphorene +1/−1 -carvedilol complexes with ADCH charge and atomic-index on the x and y-axis, respectively.

PET analysis
PET (photo-induced electron transfer) based on electron/hole theory provides a better understanding of fluorescence quenching. Fluorescence quenching is useful to considerate drug-protein interaction nature and the accessibility of drug molecules to bind with protein. Electron/charge shift from chelator to fluorophore induces fluorescence quenching [107]. This excitation occurs in the visible region as UV light poses potential damage to human body. The PET process is of great importance in biological systems as it can alter the dynamics of the photo-luminescence process (phosphorescence and fluorescence). The photo-induced electron transfer analysis helps in drug detection and monitoring [108,109]. PET phenomenon is observed for the phosphorene-carvedilol complex at different absorption wavelengths via the TD-DFT method. Figure 10 shows electron-hole orbital diagrams for 1-5 excited states of the phosphorene-carvedilol complex. The distance between electron-hole orbitals (D), overlap integral (S), the wavelength of absorption (λ max ), oscillator strength (F), and excitation energy for each state (1-5) is given in Table 8. The schematic illustration  of energy-level diagrams for 1-5 excited states is also presented in Figure 10 for the phosphorene-carvedilol complex.
The energy-level diagrams for the first two excited states show two electronic transitions, ground state to LUMO+0 and LUMO+1 state. In 3rd excited state, only one transition occurs from the ground state to LUMO+2. Two electronic excitations are observed in 4th excited state from ground state to LUMO+0 state, while in 5th state, only one excitation (towards LUMO+3) is seen.
The absorption wavelengths observed for 1-5 states are 515, 513, 469, 460 and 459 nm, respectively. In Figure 9, MOs located on carvedilol drug and phosphorene carrier are characterized by blue and red colours, respectively. The D index is related to charge-transfer length, while S represents the charge-transfer rate between the hole and electron. The distances between  In PET charge transfer has taken place from carvedilol which acts as a chelator to phosphorene, which functions as a fluorophore. This charge separation interprets that quenching takes place between electron-hole orbital within the fluorescence emission spectrum. For example, For LP (1) P 3 → σ * P 7 -P 9 excitation energy is increased after adsorption of carvedilol on phodphorene (2.93 kcal mol −1 to 2.96 kcal mol −1 ). Similarly, an increase in excitation energy is observed from 1.93 kcal mol −1 to 2.26 kcal mol −1 for σ * P 21 -P 27 → σ * P 27 -P 30 .

Drug delivery to the target cell
The Eads of about −1.30 eV (−30 kcal mol −1 ) is found to be opt for carvedilol adsorption and its successful release at the target cell/tissue [110], and our calculated Eads for the complex molecule is found to be less than 1 eV. The calculated adsorption energy value for the phosphorene-carvedilol complex (−0.59 eV) is moderate, which signifies the physisorption of the carvedilol drug onto the phosphorene sheet. The Eads indicate that the carvedilol drug molecule can be absorbed well by phosphorene, however, it is not strong enough to avoid offloading or desorption of carvedilol at targeted arena. Furthermore, the physio-sorption based on Van der Waal interactions gives rise to weak forces of the carvedilol molecule on the phosphorene surface. This physisorption of the carvedilol drug facilitates the drugoffloading at the target site.

Conclusion
The drug delivery capability of phosphorene for carvedilol (cardiovascular drug) has been evaluated by the DFT approach. Some important parameters of the carvedilol, phosphorene, and the phosphorenecarvedilol complex are investigated at the ground and the excited state configuration to explore the use of phosphorene in medicine (particularly in drug delivery). Adsorption properties showed that carvedilol is adsorbed to the phosphorene surface through the P-H interaction, where carvedilol acts as a donor for hydrogen bonding. The adsorption energy (E ads ) calculated for the phosphorene-carvedilol complex is −0.59 eV, which suggests the spontaneous adsorption of carvedilol on phosphorene. The estimated formation energy for the phosphorene carrier with a negative sign, verifying sufficient structural stability of the considered phosphorene molecule. A significant increase in dipole moment (μ = 1.95 D) of the phosphorenecarvedilol complex compared to phosphorene carrier (μ = 0.57 D) indicates an increased solubility of the complex within polar solvents (water), which facilitates drug movement through the systemic circulation. Moreover, the decrease in solvation energy of the phosphorene-carvedilol complex in contrast to free carvedilol and phosphorene also reveals that the solubility of the complex is improved in the aqueous environment. The FMO analysis revealed that the HOMO of the phosphorene-carvedilol is located on carvedilol drug, while LUMO is localized entirely on the phosphorene molecule, which ensures charge transfer from carvedilol towards phosphorene. The non-covalent interactions between carvedilol and phosphorene are responsible for favourable drug release and help in targeted drug delivery. The charge decomposition analysis results explain that the HOMO-LUMO gap of complex decreases due to the maximum overlapping between fragments i.e. carvedilol and phosphorene orbitals resulting in intra-molecular charge shifting within the complex. The NBO analysis results ensure that internal transitions take place from carvedilol to phosphorene, from phosphorene to carvedilol, and within the carrier. The photo-induced electron-transfer analysis at different excited states suggests that fluorescence quenching phenomena occur. Surface charge analysis shows that phosphorene +1/−1 makes a stable complex with carvedilol. Our findings show that phosphorene holds considerable potential as a drug carrier, and it can be used as a favourable platform for carvedilol delivery. It is believed that this theoretical study will encourage researchers to explore other 2-D nanomaterials and investigate their potential in drug-delivery applications.