MOF-inspired porphyrinic single sites as promising platforms for stable immobilization of 2-thiouracil: a DFT study

Abstract

The potential of MOF‑inspired porphyrinic Fe–N₄ and Mg–N₄ single sites as platforms for the stable immobilization of 2‑thiouracil (2TU) was examined using density functional theory (DFT) and time‑dependent DFT (TD‑DFT). Adsorption energies revealed strong chemisorption through both O‑ and S‑anchoring groups, with Fe–N₄ sites exhibiting significantly higher affinity than Mg–N₄ counterparts. Atoms‑in‑Molecules (AIM) and natural bond orbital (NBO) analyses indicated partially covalent Fe–O/S interactions, whereas Mg–O/S contacts remained predominantly electrostatic. Electronic‑structure descriptors and TD‑DFT spectra showed only minor perturbations upon adsorption, suggesting limited sensing capability. The data also show that 2TU adsorption is weaker in an aqueous solution than gas phase. Based on these results, the Mg–N₄NC can release the 2TU drug more easily at its target site than Fe–N₄NC, making it more suitable as a drug delivery vehicle. Conversely, Fe–N₄NC may be used as proper adsorbent for removing unwanted 2TU drugs emitted to water environments.

Introduction

Porphyrinic metal–nitrogen single sites supported on carbon‑based nanostructures have emerged as promising components in advanced functional materials, due to their structural robustness, tunable electronic properties, and well‑defined coordination environments^1–5. These MOF‑inspired M–N₄ motifs are known to interact selectively with heteroatom‑containing molecules and have been successfully integrated into platforms for photodynamic therapy, nanocarrier development, and molecular recognition systems^6–8. Their ability to establish directional interactions suggests strong potential for application in the immobilization and controlled handling of biologically relevant compounds^9–13.

Unlike extended MOFs, single‑site porphyrinic systems provide molecular‑level precision, allowing direct insight into host–guest interactions while avoiding complications arising from framework flexibility or pore heterogeneity^14,15. The choice of the central metal ion (M) in porphyrinic platforms is a decisive factor governing the nature and strength of guest immobilization^16–18. In this study, Fe and Mg are deliberately selected to represent two fundamentally distinct yet complementary coordination regimes. Iron (Fe), a redox‑active transition metal, offers strong coordination affinity toward sulfur- and nitrogen-containing ligands, making it particularly suitable for stabilizing 2TU through directional metal–ligand interactions and potential electronic coupling^19,20. Moreover, Fe‑porphyrins are ubiquitous in biological systems, lending additional relevance to Fe‑based platforms for bio‑inspired and catalytic applications^21–23.

In contrast, magnesium (Mg) represents a closed‑shell, redox‑inactive metal center with predominantly electrostatic and Lewis‑acidic character. Mg‑porphyrins provide a valuable reference system to disentangle pure coordination and hydrogen‑bonding effects from redox or strong covalent interactions. The comparison between Fe‑ and Mg‑centered porphyrinic sites thus enables a systematic evaluation of how metal identity modulates adsorption strength, stability, and electronic structure of immobilized 2TU^24–26.

Among heterocyclic therapeutic molecules, 2TU is notable for its clinical relevance, including antithyroid activity and emerging biomedical importance^27–30. However, its strong tendency to coordinate through oxygen and sulfur donor sites poses challenges for environmental persistence and controlled manipulation. Developing stable and selective immobilization platforms is therefore essential for applications involving drug stabilization, storage, or incorporation into functional nanocarrier architectures. Previous studies have evaluated the interaction of 2TU with various nanostructured materials, including doped nanocones, noble‑metal surfaces, and metal complexes^31–35.

The mechanistic details of 2TU adsorption on porphyrinic single‑site systems remain insufficiently understood. MOF‑inspired porphyrinic Fe–N₄ and Mg–N₄ centers therefore present a valuable opportunity to elucidate these mechanisms. Transition‑metal Fe–N₄ sites, in particular, may enable stronger and more directional chemisorption than their main‑group Mg–N₄ counterparts, due to differences in electronic structure and metal–ligand interaction character. Identifying the relative binding strengths, preferred anchoring pathways, and electronic consequences of 2TU adsorption on these single sites is essential for assessing their suitability as immobilization platforms, which offers the way for the design of next‑generation functional materials for biomedical, catalytic, and sensing applications^36–40.

This work introduces a novel approach in the immobilization of heterocyclic molecules on solid platforms. While the stability and catalytic activity of intact porphyrin complexes are well-studied, the strategic design of these porphyrin units to mimic the single-atom confinement characteristic of modern single-atom catalysts (SACs) represents a less explored frontier. The challenge of developing stable, recyclable heterogeneous catalysts and functional materials hinges on effectively anchoring active sites onto robust scaffolds. MOFs and their analogues offer immense potential due to their tunable porosity and high surface area. However, designing sites that retain high activity upon immobilization remains a significant hurdle, particularly for complex biomolecules or pharmaceutical precursors. By confirming the robust and electronically favorable immobilization of 2TU onto this engineered single-site platform, this study paves the way for developing a new class of highly stable, reusable functional materials.

Computational approaches, particularly DFT and TD‑DFT, enable atomistic evaluation of adsorption energetics, bonding characteristics, hydrogen‑bonding contributions, and the resulting electronic perturbations. Such insights are crucial for assessing whether porphyrinic M–N₄ architectures can provide the robustness and orientation‑specific binding required for the stable immobilization of 2TU within functional nanocarrier systems.

Computational details

All calculations were performed using the Gaussian 09 package⁴¹, employing the M06-2X functional⁴² in conjunction with the 6-31G(d) basis set. Geometry optimizations were carried out using tight convergence criteria, with the self-consistent field (SCF) convergence threshold set to 10^− 8 Hartree. The determination of the binding orientation of 2TU on M-N₄NC involved analysis of the electrostatic potential (ESP) maps of both 2TU and M-N₄NC. For this purpose, the Multiwfn 3.7 program was used⁴³, and the maps were visualized using VMD 1.9.3 software⁴⁴. The adsorption energy (E_ads) of 2TU on M-N₄NC is defined as follows:

1

In this formula, E_2TU@M–N4NC, E_2TU, and E_M−N4NC denote the energies corresponding to the nanocone with the adsorbed drug, the free 2TU molecule, and the isolated M–N₄NC, respectively. To ensure accurate calculation of the adsorption energy, the basis set superposition error (BSSE) was evaluated using the counterpoise method⁴⁵. It is important to note that the adsorption energy comprises both the interaction energy (E_int) and the deformation energy (E_def) generated during the adsorption process. Therefore, the following equations were employed to assess the contributions of these energy components:

2

3

4

5

6

Here, E_{M−N4NC in com} and E_{2TU in com} denote the energies of M–N₄NC and 2TU within the relaxed complexes, respectively. Additionally, E_{def (2TU)}, E_{def (M−N4NC)}, and E_{def (total)} represent the deformation energies of 2TU, M–N₄NC, and the total system, respectively.

To determine the bonding characteristics, an AIM analysis⁴⁶ was performed using the AIMAll software⁴⁷. The NBO analysis⁴⁸ was employed to evaluate the stabilization energies and bond orders of the investigated systems. To compute the quantum chemical parameters, including global hardness (η)⁴⁹, electronic chemical potential (µ)⁵⁰, and electronegativity (χ)⁵¹, the energies of the frontier molecular orbitals (FMOs) were analyzed, focusing on the highest occupied molecular orbital (HOMO), the lowest unoccupied molecular orbital (LUMO), and their energy gap (E_g). Moreover, the total density of states (TDOS) and partial density of states (PDOS) spectra were obtained using the Multiwfn 3.7 program⁴³. Finally, to depict the UV–visible spectra of M–N₄NC and its complexes, the TD‑DFT method was employed to compute 30 singlet excited states.

Results and discussion

Geometry and electronic structure of 2TU, N₄NC, and M-N₄NC

To determine the optimal orientation of the target molecule around the nanocones, the ESP plots of 2TU and M–N₄NC were generated using the Multiwfn program⁴³. Figure 1 shows the optimized structure of 2TU and its ESP map, displaying regions of positive and negative potential, designated as V_max and V_min, respectively. In 2TU, the global surface minimum (–33.94 kcal/mol) is located near the oxygen atom, indicating the most favorable site for interaction with positively charged species. Conversely, the global surface maximum (+ 59.44 kcal/mol) occurs near the hydrogen atom, corresponding to its stronger ability to attract negatively charged species (see Fig. 1b).

Fig. 1.

The optimized geometry (a) and molecular electrostatic potential (b) mapped on corresponding 0.001 au electron density isosurface of 2TU molecule along with the observed V_max and V_min values in kcal/mol.

The selected model system consists of a nanocone with a cone angle of 83.6° and a length of 8.46 Å, composed of 81 carbon atoms and 20 hydrogen atoms. To introduce a defect into the carbon nanocone, a porphyrin ring containing four nitrogen and twenty carbon atoms was inserted at the tip of the cone to form M–N₄NC. The optimized configurations of N₄NC and Fe–N₄NC are shown in Fig. 2a and b. Optimization calculations for M–N₄NC indicate that the resulting hole size is sufficient to accommodate various ions. Consequently, it is expected that the coordination of metal ions with the nitrogen atoms in the cavity prevents their aggregation. The positioning of the ions within the cavity depends on its dimensions. This study focuses on two model systems, Fe–N₄NC (a transition‑metal center) and Mg–N₄NC (an alkaline‑earth‑metal center).

Fig. 2.

The optimized geometries of N₄NC, (a) and Fe-N₄NC (b) along with its electrostatic potential map (c).

The ESP map of Fe–N₄NC is shown in Fig. 2c. As observed, the V_min value of − 17.33 kcal/mol represents the global minimum on the surface, and its relatively large negative value is due to the lone electron pairs on the nitrogen atoms. The V_max value of + 151.80 kcal/mol corresponds to the global maximum, which arises from the positively charged region. The ESP at this point is significantly higher than in other areas due to the presence of four neighboring nitrogen atoms with high electronegativity. This observation clearly indicates that the cationic sites are ideal locations for electrophilic reactions.

Molecular geometry and adsorption energy

This study investigates the interaction between the 2TU drug and M–N₄NC. To determine the most favorable adsorption configuration, the 2TU molecule was allowed to interact with the cationic sites of M–N₄NC from different orientations. Based on the ESP analysis of both 2TU and M–N₄NC, two stable configuration models for the 2TU@M-N₄NC complexes were identified. The optimized structures of 2TU@Fe–N₄NC are presented in Fig. 3.

Fig. 3.

Optimized structures of the 2TU adsorption on the outer surface of Fe-N₄NC.

The results summarized in Table 1 show that the adsorption energies of 2TU interacting through its oxygen and sulfur sites on Fe–N₄NC, denoted as 2TU/O@Fe–N₄NC and 2TU/S@Fe–N₄NC, are − 27.78 and − 27.32 kcal/mol, respectively. Similarly, the adsorption energies of 2TU on Mg–N₄NC, represented as 2TU/O@Mg–N₄NC and 2TU/S@Mg–N₄NC, are − 22.75 and − 20.02 kcal/mol, respectively. The negative adsorption energy values (E_ads) indicate that functionalization of the M–N₄NC systems with 2TU is energetically favorable. Moreover, the adsorption energies of 2TU on M–N₄NC exceed the physisorption–chemisorption threshold of 11.5 kcal/mol^21,52,53, confirming that the interaction between 2TU and M–N₄NC is predominantly governed by a chemisorption mechanism.

Table 1.

Adsorption (E_ads), interaction (E_int), and deformation (E_def) energies (in kcal/mol) of 2TU adsorption on M-N₄NCs.

	Eads	Eint	Edef (2TU)	Edef (M−PCNC)	Edef (total)
2TU/O@Fe-N4NC	−27.78	−36.71	1.29	1.24	2.53
2TU/S@Fe-N4NC	−27.32	−32.91	0.78	1.62	2.39
2TU/O@Mg-N4NC	−22.75	−31.75	1.37	3.15	4.52
2TU/S@Mg-N4NC	−20.02	−26.49	0.96	3.16	4.12

Evaluation of the E_ads values also reveals a stronger interaction between 2TU and Fe–N₄NC compared with Mg–N₄NC, indicating that 2TU has a higher tendency to adsorb on Fe–N₄NC than on Mg–N₄NC (see Table 1). In addition, the results show that 2TU interacting through its O site (2TU/O) is more strongly adsorbed on M–N₄NC than when interacting through its S site (2TU/S). This trend may be attributed to the higher electronegativity of the O atom compared with that of the S atom.

Table 2 indicates that the interatomic distances (M···X, where X represents O or S) in the 2TU@Fe–N₄NC systems are shorter than those observed in the 2TU@Mg–N₄NC configurations. These observations are consistent with the results obtained from the adsorption energy calculations. Within the 2TU@M–N₄NC structures, hydrogen bonding (HB) is also identified, specifically between the hydrogen atom of 2TU and the nitrogen atom of the nanocone (H_2TU∙∙∙N_M−N4NC). As shown in Table 2, the shortest interaction distances (H···N) are found in the 2TU@Fe–N₄NC complexes, in contrast to the 2TU@Mg–N₄NC systems. This indicates that the interactions among the reactants are significantly stronger in the former case than in the latter. Overall, the formation of hydrogen bonds between 2TU and M–N₄NC contributes to the enhanced stability of the studied complexes.

Table 2.

Bond lengths obtained for the M-N before and after 2TU adsorption on M-N₄NCs, along with M⋯X (X = O and S) bonds and H⋯N contacts of HBs.

	M-N1	M-N2	M-N3	M-N4	M∙∙∙X	H∙∙∙N
Fe-N4NC	2.034	2.034	2.034	2.034	‒	‒
2TU/O@Fe-N4NC	2.040	2.072	2.051	2.051	1.989	1.909
2TU/S@Fe-N4NC	2.051	2.051	2.041	2.076	2.416	1.872
Mg-N4NC	2.092	2.092	2.092	2.092	‒	‒
2TU/O@Mg-N4NC	2.112	2.168	2.130	2.130	2.045	1.938
2TU/S@Mg-N4NC	2.165	2.113	2.127	2.127	2.600	1.877

To investigate the effect of 2TU adsorption on the nanocones, the M–N bond lengths of M–N₄NC were measured both before and after interaction with the target molecule (see Table 2). The data presented in this table reveal a noticeable increase in the M–N bond lengths of M–N₄NC in the adsorbed states compared with the pristine M–N₄NC, indicating a weakening of the M–N bonds upon adsorption. Consequently, these interactions suggest that M–N₄NC nanocones may be effectively utilized for the detection and removal of unwanted 2TU molecules from the environment.

Electronic properties

TDOS and PDOS analyses were conducted to enable an in‑depth investigation of the electronic structure and adsorption characteristics of the studied species. In the TDOS plot, each vertical line corresponds to a distinct molecular orbital (MO), while the dashed line denotes the position of the highest occupied molecular orbital (HOMO), as shown in Fig. 4. This curve represents the TDOS derived from the distribution of MO energy levels. In addition, PDOS calculations are essential for elucidating the orbital contributions of individual atoms or fragments. The configurations examined in this study were analyzed using the Hirshfeld method^43,54,55. Figure 4 illustrates the electronic structure of Fe–N₄NC and its associated complexes. The PDOS curves in these figures are predominantly distributed in higher energy regions, indicating that the π‑MOs in these systems have higher energy levels than the σ‑MOs.

Fig. 4.

The TDOS and PDOS diagrams of atoms in the Fe-N₄NC (a) (the C atoms as fragment 1, the H atoms as fragment 2, the N atoms as fragment 3, and the Fe atom as fragment 4) and complexes of 2TU/O@Fe-N₄NC (b) and 2TU/S@Fe-N₄NC (c) (Fe-N₄NC as fragment 1 and 2TU as fragment 2).

The DOS diagrams shown in Fig. 4 indicate that the adsorption of 2TU modifies the electronic properties of Fe–N₄NC to some extent. According to Table 3, the band‑gap energy (E_g) of pristine Fe–N₄NC is 3.204 eV, classifying it as a semiconductor. The results show that the E_g value of Fe–N₄NC upon 2TU/O adsorption shifts to lower energy, whereas the E_g value for 2TU/S‑adsorbed Fe–N₄NC shifts to a slightly higher value, which is negligible. This observation suggests that the DOS profiles of these complexes closely resemble that of pristine Fe–N₄NC. In addition, the prominent peak observed in the PDOS of Fe–N₄NC highlights its significant role in facilitating interactions among the involved species.

Table 3.

HOMO and LUMO energies (E_HOMO and E_LUMO), Fermi level energy (E_FL), energy gap (E_g) and work function (Φ) in terms of eV, change of E_g and Φ upon adsorption of 2TU (ΔE_g (%) and ΔΦ (%)).

	EHOMO	EFL	ELUMO	Eg	ΔEg (%)	Φ (eV)	ΔΦ (%)
2TU	−7.690	−4.116	−0.543	7.148	‒	4.116	‒
Fe-N4NC	−5.726	−4.124	−2.522	3.204	‒	4.124	‒
2TU/O@Fe-N4NC	−5.539	−3.944	−2.349	3.190	−0.425	3.944	−4.366
2TU/S@Fe-N4NC	−5.716	−4.113	−2.510	3.206	0.076	4.113	−0.254
Mg-N4NC	−5.726	−4.147	−2.568	3.158	‒	4.147	‒
2TU/O@Mg-N4NC	−5.501	−3.934	−2.366	3.136	−0.706	3.934	−5.155
2TU/S@Mg-N4NC	−5.708	−4.133	−2.558	3.151	−0.224	4.133	−0.348

The results presented in Table 3 indicate that, after the adsorption of 2TU on M–N₄NC, both the E_HOMO and E_LUMO values increase for all systems. These changes are more pronounced in the 2TU/O@M–N₄NC complexes than in the 2TU/S@M–N₄NC counterparts. Accordingly, for the most stable configurations, the Fermi level energy (E_FL, defined as the midpoint of E_g at 0 K) increases from − 4.124 eV for pristine Fe–N₄NC to − 3.944 eV for 2TU/O@Fe–N₄NC and − 4.113 eV for 2TU/S@Fe–N₄NC. This indicates that Fe–N₄NC is more sensitive to 2TU adsorption through its O site than through its S site.

The sensitivity of M–N₄NC toward 2TU is also evaluated through the relationship between electronic conductivity (σ) and the band‑gap energy (E_g), as expressed by the following equation^56–58:

7

In this context, k denotes the Boltzmann constant, while T represents the temperature. Equation (7) illustrates the exponential relationship between E_g and σ, indicating that a lower E_g value corresponds to higher electrical conductivity. According to the DFT calculations, the percentage change in the band gap (%ΔE_g) of M–N₄NC remains relatively small compared with that of the corresponding monomer systems. Consequently, the sensitivity of M–N₄NC toward 2TU is low, rendering these materials unsuitable for use as electronic conductivity‑based sensors for 2TU.

Another crucial parameter in assessing sensing capability is the work function (Φ). Variations in the work function are associated with charge transfer between the adsorbent (M–N₄NC) and the adsorbate (2TU). The calculated values of Φ are given below:

8

Here, E_inf denotes the electrostatic potential at an infinite distance, which is assumed to be zero, while E_FL represents the Fermi‑level energy. The results indicate that the calculated Φ values of M–N₄NC do not change significantly after 2TU adsorption (see Table 3). Therefore, it can be concluded that M–N₄NC is not suitable for use as a Φ-type sensor for the 2TU drug.

The electron emission current density in a vacuum (J) is a critical parameter that can be determined from the work function. The following equation presents the standard approach used to calculate this quantity:

9

The parameters are defined as follows: A represents the Richardson constant (m²), T denotes the temperature (K), Φ signifies the work function (eV), and k refers to the Boltzmann constant. Our results demonstrate that the variation in the work‑function value (%ΔΦ) is negligible, indicating that the current density changes only slightly upon adsorption of 2TU onto M–N₄NC. This observation implies that the adsorbents exhibit minimal sensitivity toward the presence of 2TU.

Analysis of boundary orbitals

The electronic configuration of M–N₄NC was examined to assess its reactivity toward the selected pharmaceutical compound. The diagrams illustrating the HOMO and LUMO for 2TU, pristine Fe–N₄NC, and their corresponding most stable complexes are presented in Figs. 5 and 6. In the case of 2TU, the HOMO exhibits a greater spatial distribution over the oxygen, sulfur, and nitrogen atoms, indicating that these sites are more reactive than other regions of the molecule. In contrast, the LUMO is distributed over the entire molecular structure. As shown in Fig. 5, the orbital distribution of pristine Fe–N₄NC reveals that the HOMO is predominantly located in the central and terminal regions of the nanocone. Notably, the largest contributions to the HOMO originate from carbon atoms terminated with hydrogen atoms, whereas the LUMO is mainly localized around the iron ion at the center of the cavity. For the complexes, the HOMOs are more widely delocalized over the surface of the nanocone, while the LUMOs are primarily concentrated on the iron atom and its adjacent rings, as illustrated in Fig. 6.

Fig. 5.

The schemas of HOMO and LUMO of the 2TU and Fe-N₄NC monomers.

Fig. 6.

The schemas of HOMO and LUMO of the 2TU adsorption on Fe-N₄NC.

Density functional theory provides valuable insights into quantum chemical concepts. The global hardness (η), electronic chemical potential (µ), and electronegativity (χ) were calculated using the following equations:

10

11

The ionization potential is defined as I = − E_HOMO, while the electron affinity is expressed as A = − E_LUMO. Table 4 presents the electronic properties of M–N₄NC after adsorption of 2TU. It is observed that the chemical potential is defined as the negative of electronegativity (µ = -χ). Consequently, during the adsorption process, electrons are transferred from regions of higher chemical potential (lower electronegativity) to regions of lower chemical potential (higher electronegativity)^59,60. According to the results reported in Table 4, electrons transfer spontaneously from 2TU to M–N₄NC. In addition, the data in this table indicate that, in most cases, the global hardness values decrease, suggesting reduced chemical stability of the complexes and enhanced reactivity.

Table 4.

The quantum molecular descriptors including electronegativity (χ), chemical hardness (η), electronic chemical potential (μ), charge transfer (ΔN), and dipole moment (μ°, in Debye).

	χ (eV)	η (eV)	µ (eV)	ΔN	µ° (D)
2TU	4.116	3.574	−4.116	‒	4.670
Fe-N4NC	4.124	1.602	−4.124	‒	7.813
2TU/O@Fe-N4NC	3.944	1.595	−3.944	−0.0014	0.680
2TU/S@Fe-N4NC	4.113	1.603	−4.113	‒	8.635
Mg-N4NC	4.147	1.579	−4.147	‒	7.908
2TU/O@Mg-N4NC	3.934	1.568	−3.934	−0.0060	0.598
2TU/S@Mg-N4NC	4.133	1.575	−4.133	‒	8.696

To further confirm the direction of electron transfer between the interacting species, the fractional number of electrons transferred (ΔN) was also calculated as follows:

12

In this context, µ_2TU and µ_{M−N4NC ‎}, as well as η_2TU and η_M−N4NC represent the chemical potential and global hardness of the 2TU and M–N₄NC systems, respectively. A positive ΔN value indicates charge transfer from M–N₄NC to 2TU, implying that 2TU acts as an electron acceptor. Conversely, a negative ΔN value signifies electron transfer from 2TU to M–N₄NC, with 2TU functioning as an electron donor. The magnitude of charge transfer between the interacting species is reported in Table 4. The observed negative ΔN values confirm the spontaneous transfer of electrons from 2TU to M–N₄NC. Furthermore, a larger value of ΔN corresponds to stronger interactions between the species.

A notable electronic property of the investigated complexes is the dipole moment (µ°)^61,62. Table 4 provides a comprehensive overview of the dipole moments of M–N₄NC and their corresponding complexes. The dipole moment of N₄NC is approximately 11.78 Debye, whereas those of Fe–N₄NC and Mg–N₄NC are about 7.81 and 7.91 Debye, respectively. These values indicate that the dipole moments of the metal‑embedded systems are significantly lower than that of pristine N₄NC. The introduction of defects and nitrogen atoms into the N₄NC structure leads to enhanced charge separation. As a result, the dipole‑moment vector is oriented toward the highly electronegative nitrogen atoms within the N₄NC framework. In contrast, the incorporation of metal cations, which possess lower electronegativity than nitrogen, into the central cavity reduces the overall dipole moment, thereby balancing the polarity of the systems. As shown in Table 4, the effect of 2TU adsorption on the dipole moment of M–N₄NC is more pronounced when 2TU is adsorbed at the S site than at the O site. This variation in dipole moment among the systems can be attributed to differences in the orientation of the drug relative to the nanocone.

AIM analysis

Table 5 summarizes the parameters obtained from AIM analysis, including the electron density (ρ), the Laplacian of the electron density (∇²ρ) at the bond critical point (BCP), and energetic quantities such as G(r), V(r), and H(r). The molecular graphs of the 2TU@Fe–N₄NC complexes are presented in Fig. 7, where the identified critical points and bond paths are clearly illustrated. The nature of the interactions can be determined from the values of H(r) and ∇²ρ at the BCPs⁴⁶. Specifically, negative values of both H(r) and ∇²ρ indicate covalent interactions, whereas positive values correspond to electrostatic interactions. In contrast, opposite signs of H(r) and ∇²ρ suggest interactions with partial covalent character.

Table 5.

AIM analyses of 2TU adsorption on M-N4NCs (in a.u.) along with the hydrogen bond energies of H⋯N contacts (EHB, in kJ/mol).

	Interaction path	ρ(r)	σ2ρ(r)	G(r)*	V(r)*	H(r)*	G(r)/ǀVǀ(r)	EHB
2TU/O@Fe-N4NC	Fe⋯O	0.0677	0.3286	0.0923	−0.1025	−0.0102	0.9005	‒
	H⋯N	0.0340	0.0936	0.0287	−0.0340	−0.0053	0.8441	−37.17
2TU/S@Fe-N4NC	Fe⋯S	0.0510	0.0747	0.0271	−0.0356	−0.0085	0.7612	‒
	H⋯N	0.0366	0.0941	0.0302	−0.0368	−0.0067	0.8207	−40.75
2TU/O@Mg-N4NC	Mg⋯O	0.0337	0.3529	0.0723	−0.0563	0.0160	1.2842	‒
	H⋯N	0.0307	0.0892	0.0260	−0.0298	−0.0037	0.8725	−32.44
2TU/S@Mg-N4NC	Mg⋯S	0.0194	0.1263	0.0233	−0.0150	0.0083	1.5533	‒
	H⋯N	0.0351	0.0929	0.0290	−0.0347	−0.0058	0.8357	−38.56

* The total energy density of electrons (H), and its two components, the kinetic (G) and potential (V) electron, energy densities.

Fig. 7.

The different configurations of 2TU adsorption on Fe-N₄NC (the bond critical points have been exhibited by red points).

The findings presented in Table 5 demonstrate that, for the Fe–N₄NC complexes, the positive ∇²ρ values and negative H values at the BCPs associated with the Fe⋯X interactions (where X denotes O or S) indicate the presence of partially covalent interactions. In contrast, the Mg–N₄NC complexes exhibit positive ∇²ρ and H values at the BCPs corresponding to the Mg⋯X interactions, suggesting that these interactions are dominated by van der Waals forces.

Notably, for all complexes analyzed, the H values at the H⋯N BCPs are negative, indicating that these interactions possess at least a partially covalent character (as detailed in Table 5). A comparative assessment of the electron‑density values across the models further reveals that the intermolecular bonds in the 2TU@Fe–N₄NC systems are stronger than those in the 2TU@Mg–N₄NC systems. These observations are consistent with the higher adsorption energies obtained for the former relative to the latter (see Tables 1 and 5).

The theoretical parameters derived from AIM analysis were also employed to evaluate the hydrogen‑bond energy (E_HB) using the Espinosa approach (E_HB = 1/2 V_BCP)⁶³. As shown in Table 5, the electron density at the BCPs of the H⋯N contacts directly correlates with the E_HB. Accordingly, higher electron‑density values correspond to stronger hydrogen bonds, whereas lower values are associated with weaker interactions. The results in Table 5 indicate that the 2TU@Fe–N₄NC configurations exhibit the highest hydrogen‑bond energies. Furthermore, our data show that 2TU interacting through its S site forms stronger hydrogen bonds than when interacting through the O site. Notably, the 2TU/S@Fe–N₄NC complex, which has the highest electron density at the BCP (0.0366 a.u.) and the shortest hydrogen‑bond distance (1.872 Å), exhibits the largest hydrogen‑bond energy (–40.75 kJ mol^− 1). Overall, a strong correlation is observed between electron density and interatomic distance, clearly demonstrating that an increase in ρ is accompanied by a decrease in the hydrogen‑bond length.

The − G/V ratio can also be used as a criterion to characterize the nature of non‑covalent interactions^64–67. Specifically, when − G/V ≥ 1, the interaction is predominantly electrostatic, whereas values in the range 0.5 < − G/V < 1 indicate partially covalent character. Our results show that the − G/V values for the Fe⋯X bonds in the 2TU@Fe–N₄NC complexes indicate at least partially covalent interactions. In contrast, the corresponding values confirm that the Mg⋯X bonds in the 2TU@Mg–N₄NC complexes are predominantly electrostatic in nature (see Table 5). For both 2TU@M–N₄NC systems, the H⋯N contacts also exhibit partially covalent character, which is consistent with the findings obtained from other AIM parameters. Overall, these results contribute to a deeper understanding of drug–receptor interactions in biological systems.

Reduced density gradient (RDG) analysis was also employed to identify interaction regions and evaluate their nature. The plots of the RDG versus signλ₂(r)ρ(r) allowed for the identification of the types of non-covalent interactions present in the adsorbed complexes. The RDG was defined as follows⁶⁸:

13

In these plots, points corresponding to strong interactions appeared in the region where signλ₂(r)ρ(r) < 0. Relatively weaker van der Waals interactions were observed around signλ₂(r)ρ(r) ≈ 0, while repulsive interactions were primarily found where signλ₂(r)ρ(r) > 0. It was noteworthy that bond strength (and consequently bond order) was closely related to both the electron density ρ(r) and the sign of λ₂.

The RDG plots were generated using the Multiwfn program²⁷. Figure 8 presented the RDG versus signλ₂(r)ρ(r) plots for 2TU adsorbed on the Fe–N₄NC surface. Using the RDG = 0.5 isosurface as a reference, many points corresponding to 2TU adsorption on Fe–N₄NC appeared near signλ₂(r)ρ(r) ≈ 0 (green regions), indicating that the interaction was primarily weak and of van der Waals type, consistent with previous observations. In contrast, a relatively small concentration of points was observed in the region where signλ₂(r)ρ(r) < 0 (blue regions), suggesting stronger non-covalent interactions in the system (HB interactions). The RDG analysis also revealed broad red regions (signλ₂(r)ρ(r) > 0), which were attributed to intramolecular steric effects inherent to the selected nanocone structure.

Fig. 8.

The RDG analysis of the 2TU adsorption on Fe-N₄NC as the most stable configurations.

NBO analysis

Further investigation was necessary to attain a more profound understanding of the intermolecular interactions present in the examined complexes. Table 6 presents the second‑order perturbation energies (E⁽²⁾) for pristine Fe–N₄NC and its complexes in their most stable configurations. The elevated E⁽²⁾ values indicate strong interactions between the species, suggesting an increased likelihood of electron transfer from donor to acceptor orbitals.

Table 6.

The second-order perturbation energies (E⁽²⁾, in kcal/mol) calculated for the donor-acceptor natural orbitals in the most stable configuration (2TU@Fe-N₄NC).

	Donor NBO	Acceptor NBO	E(2)
Fe-N4NC	LPN (1)	LP*Fe	38.85
	LPN (2)	LP*Fe	38.85
	LPN (3)	LP*Fe	38.65
	LPN (4)	LP*Fe	38.66
2TU/O@Fe-N4NC	LPN (1)	LP*Fe	66.26
	LPN (2)	LP*Fe	52.41
	LPN (3)	LP*Fe	62.18
	LPN (4)	LP*Fe	62.22
	LPO	LP*Fe	57.89
	LPN	LP*H	5.98
2TU/S@Fe-N4NC	LPN (1)	LP*Fe	48.49
	LPN (2)	LP*Fe	48.49
	LPN (3)	LP*Fe	36.99
	LPN (4)	LP*Fe	16.41
	LPS	LP*Fe	53.58
	LPN	LP*H	7.66

The findings suggest that the most pronounced stabilization energies are associated with the transitions LP(O/S) → LP*Fe (non‑covalent interactions) and LP(N) → LP*H (hydrogen‑bonding interactions) for 2TU adsorbed on Fe–N₄NC. In this context, charge transfer occurs from the lone‑pair electrons of the O (or S) and N atoms to the antibonding lone‑pair orbitals of the Fe and H atoms, respectively. Data presented in Table 6 indicate that the E⁽²⁾ values associated with 2TU/O@Fe–N₄NC are greater than those observed for 2TU/S@Fe–N₄NC. This trend is consistent with the corresponding electron‑density values. Additionally, the results demonstrate that the interactions LP(N1) → LP*Fe for 2TU/O@Fe–N₄NC, as well as LP(N1) → LP*Fe and LP(N2) → LP*Fe for 2TU/S@Fe–N₄NC, exhibit the highest stabilization energies. This observation signifies a considerable delocalization of electron density from the nitrogen atoms toward the metal ions.

The NBO method was also employed to evaluate bond orders. The most commonly used approaches include the Mulliken⁶⁹, Mayer⁷⁰, and Wiberg bond indices (WBI) based on the Löwdin orthogonalized basis⁷¹. The calculated bond‑order values are reported in Table 7. According to the obtained results, the 2TU@Fe–N₄NC adsorbent is more active in drug adsorption than 2TU@Mg–N₄NC. Furthermore, analysis of the bond‑order values indicates that the 2TU/S@M–N₄NC systems exhibit stronger hydrogen bonding than the corresponding 2TU/O@M–N₄NC systems. These findings are directly correlated with the E⁽²⁾ values, electron densities, and the corresponding hydrogen‑bond energies (E_HB). Among the different bond‑order schemes, the Mulliken results show good agreement with the adsorption energies reported in Table 1, while the Wiberg indices are consistent with the hydrogen‑bond energies (Tables 5 and 7).

Table 7.

Wiberg bond orders, Mulliken, and Mayer determined by the interaction of 2TU with M-N₄NCs.

	Interaction path	Wiberg	Mulliken	Mayer
2TU/O@Fe-N4NC	Fe⋯O	0.304 (0.075)	0.407 (0.079)	0.616 (0.081)
2TU/S@Fe-N4NC	Fe⋯S	0.474 (0.086)	0.365 (0.089)	0.897 (0.090)
2TU/O@Mg-N4NC	Mg⋯O	0.087 (0.050)	0.307 (0.082)	0.373 (0.083)
2TU/S@Mg-N4NC	Mg⋯S	0.148 (0.064)	0.190 (0.099)	0.319 (0.097)

* Values in parentheses refer to the bond orders obtained for H⋯N contacts of HBs.

TD-DFT analysis

To simulate the UV–visible spectra of pristine Fe–N₄NC and its most stable complexes with 2TU, the TD‑DFT approach at the M06‑2X/6‑31G(d) level of theory was employed (see Fig. 9). The pristine Fe–N₄NC and its complexes exhibit a moderate peak in the UV region, along with two peaks of different intensities, one weak and the other intense, in the visible region. Compared with the bare nanocone, the UV–visible spectra of the complexes show a slight decrease in the maximum absorption wavelength (λ_max) of Fe–N₄NC after 2TU adsorption (Fig. 9). The peak intensity in the visible region also decreases slightly upon 2TU adsorption on the nanocone surface. These observations indicate that the spectral changes induced by adsorption are relatively small.

Fig. 9.

The UV-vis spectra of Fe-N₄NC monomer and complexes of 2TU/O@Fe-N₄NC (b) and 2TU/S@Fe-N₄NC (c) as the most stable configuration.

We also calculated the contributions of electronic transitions for all intense absorption peaks. For pristine Fe–N₄NC, the dominant contribution to the main peak is 64%, corresponding to the HOMO‑1 → LUMO transition. In comparison, the main peak contribution is 63% for 2TU/O@Fe–N₄NC, arising from the HOMO‑1 → LUMO + 1 transition, and 61% for 2TU/S@Fe–N₄NC, also associated with the HOMO‑1 → LUMO + 1 transition. The strongest absorption bands in the visible spectra of Fe–N₄NC upon 2TU/O adsorption are governed by electron excitation from the lone‑pair (LP) orbital of the O atom to the antibonding lone‑pair (LP*) orbital of the Fe atom. Similarly, electron excitation from the LP orbital of the S atom to the LP* orbital of the Fe atom is responsible for the intense absorption bands observed for 2TU/S adsorbed on Fe–N₄NC. Based on these results, Fe–N₄NC can be inferred to exhibit limited sensitivity for 2TU detection using UV‑based methods.

Aqueous solution impact

To investigate the drug delivery behavior of M-N₄NCs toward 2TU, the impact of aqueous solution on the 2TU adsorption was studied by employing the polarizable continuum model (PCM)⁷². The adsorption energies of 2TU on the considered M-N₄NCs in aqueous solution were calculated at the M06-2X/6-31G(d) level of theory, yielding values of − 28.40 and − 21.38 kcal/mol for Fe–N₄NC as well as − 21.31 and − 12.98 kcal/mol for Mg–N₄NC (without BSSE correction). Since BSSE is not technically possible to evaluate in solution, the 2TU adsorption energies in solution should be compared to the corresponding BSSE uncorrected adsorption energies in the gas phase (−34.18, −30.52, and − 27.23, −22.37 kcal/mol, respectively). The adsorption energies in solution can be compared with those in the gas phase, indicating that 2TU adsorption is weaker in an aqueous solution than gas phase, consistent with previous studies^73–77. Due to non-covalent interactions and weaker adsorption, the Mg–N₄NC can release the 2TU drug more easily at its corresponding biological target site than Fe–N₄NC, making it more suitable as a drug delivery vehicle. Conversely, Fe–N₄NC may be used as proper adsorbent for removing unwanted 2TU drugs emitted to water environments.

Conclusions

This computational investigation elucidates how MOF‑inspired porphyrinic Fe–N₄ and Mg–N₄ single sites interact with 2TU and evaluates their potential as platforms for stable drug immobilization. The strong, orientation‑specific adsorption energies, together with AIM and NBO evidence for partially covalent Fe–O/S bonding, highlight the superior anchoring capability of Fe–N4 sites relative to Mg–N4. Additional hydrogen bonding with the nanocone framework further enhances the stability of the complexes. Only minor changes in electronic descriptors and TD‑DFT spectra are observed upon adsorption, indicating that these systems are not suitable for sensing applications but are well suited for robust and persistent drug binding. Overall, the results identify porphyrinic Fe–N₄ single sites as potential applicants for the immobilization and controlled handling of thiouracil‑based therapeutics within carbon‑supported single‑site architectures.

Author contributions

All authors contributed significantly to the conception, execution, and preparation of this study. S. Soleimani-Amiri designed the computational framework, performed the DFT and TD-DFT ‎calculations, analyzed the electronic-structure data, and drafted the initial version of the ‎manuscript. H.A. Imanov contributed to the theoretical methodology, interpretation of adsorption and ‎bonding analyses, and refinement of computational models. S.V. Menon assisted in data curation, validation of quantum-chemical outputs, and preparation ‎of figures and tables. A. Khanmohammadi supervised the project, contributed to conceptual development, provided ‎critical revisions, and ensured the overall scientific coherence of the manuscript. R. Yilmaz Saber contributed to methodological validation, AIM/NBO interpretation, and ‎scientific editing of the manuscript. S. Ray supported the discussion of physicochemical relevance, contributed to the interpretation ‎of interaction mechanisms, and reviewed the manuscript for clarity and accuracy. K. Jayabalan participated in analyzing TDOS/PDOS results, assisted in visualization, and ‎contributed to the discussion of sensing characteristics. A. Sinha contributed to computational data verification and the preparation of supplementary ‎analyses. R. Sharma assisted in reviewing the theoretical framework, editing the manuscript, and ‎ensuring alignment with journal standards.‎All authors reviewed and approved the final version of the manuscript and agree to be ‎accountable for all aspects of the work.‎.

Data availability

The computational datasets generated and analysed during the current study are available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.