Probing the Reactions of Thiourea (CH4N2S) with Metals (X = Au, Hf, Hg, Ir, Os, W, Pt, and Re) Anchored on Fullerene Surfaces (C59X)

Upon various investigations conducted in search for a nanosensor material with the best sensing performance, the need to explore these materials cannot be overemphasized as materials associated with best sensing attributes are of vast interest to researchers. Hence, there is a need to investigate the adsorption performances of various metal-doped fullerene surfaces: C59Au, C59Hf, C59Hg, C59Ir, C59Os, C59Pt, C59Re, and C59W on thiourea [SC(NH2)2] molecule using first-principles density functional theory computation. Comparative adsorption study has been carried out on various adsorption models of four functionals, M06-2X, M062X-D3, PBE0-D3, and ωB97XD, and two double-hybrid (DH) functionals, DSDPBEP86 and PBE0DH, as reference at Gen/def2svp/LanL2DZ. The visual study of weak interactions such as quantum theory of atoms in molecule analysis and noncovalent interaction analysis has been invoked to ascertain these results, and hence we arrived at a conclusive scientific report. In all cases, the weak adsorption observed is best described as physisorption phenomena, and CH4N2S@C59Pt complex exhibits better sensing attributes than its studied counterparts in the interactions between thiourea molecule and transition metal-doped fullerene surfaces. Also, in the comparative adsorption study, DH density functionals show better performance in estimating the adsorption energies due to their reduced mean absolute deviation (MAD) and root-mean-square deviation (RMSD) values of (MAD = 1.0305, RMSD = 1.6277) and (MAD = 0.9965, RMSD = 1.6101) in DSDPBEP86 and PBE0DH, respectively.


INTRODUCTION
Thiourea also known as thiocarbamide is classified as an organosulfur compound with the molecular formula SC-(NH 2 ) 2 . 1 Thiourea is structurally similar to urea, except that the oxygen atom in urea is replaced with the sulfur atom in thiourea, and they also have significant differences in their chemical properties. Due to its poisonous characteristics, it is a contributor to pollution, thereby causing sustainability issue to the environment. Exposure to this poisonous substance can bring about various health consequences. 2 It can be taken into the body system through inhalation of its aerosol, and ingestion when in solid state can lead to poisoning of the body system, as a consequence causing damages to the human cells. 3 On exposure repeatedly for a longer period of time, it causes skin irritations and a whole lot of thyroid problems, 4 which has the potency of causing death. It can lead to acute toxicity, skin irritation, 5 eye irritation, and cancer hazards, genotoxicity and cytotoxicity. 5 hiourea has been observed as the cause of thyroid and liver cancers in animals. 6 Hence, it may exist as a carcinogen in the human body. Thiourea is applied in little amounts in various fields such as photography, used as a fixing or repairing agent, 7 in the industry for the production of thermosetting resin, as an insecticide, in the treatment of textiles, 8 and as a starting ingredient for some colors and pharmaceuticals. 9 Thiourea is also used as a reagent in organic synthesis due to its bitter taste and color (it is a white crystalline chemical substance). 10 Above all, thiourea is soluble in water. However, thiourea tends to form colorless crystals at the temperature of 182°C (860°F). It is industrially produced by inducing a chemically similar substance like ammonium thiocyanate (NH 4 SCN) to undergo rearrangement. 11 It can also be produced by the reaction between hydrogen sulfide and calcium cyanamide (CaCN) in the presence of carbon dioxide (CO 2 ). 12 Despite the poisonous characteristics of thiourea, its derivatives prove to be useful in drug delivery. 13 Research has shown that thiourea derivatives are used for the treatment of HIV and as antioxidants, and they also act as antibacterial substances. Thiourea derivatives are used as antithyroid, antiepileptic, and antihypertensive drugs 14 and most impor-tantly as anticancer drugs for the treatment of cancer. Thiourea, therefore, is the direct opposite of its derivatives.
Nanomaterials have been of wide interest to scientific researchers due to their unique electrical, magnetic, optical, mechanical, and structural properties. 15 Hence, they have versatile applications in electronics, medicine, 16 aviation, chemical industry, and so forth. Nanomaterials have also been applied as sensors over the years for the adsorption of prominent poisonous gases and also for drug delivery. 15 Fekri et al. in 2020 conducted a density functional theory (DFT) study on the adsorption of metranidazole drugs on the surface of fullerene (C 60 ) doped with Si, B, and Al atoms employing the DFT/B3YLP/6-31G(d,p) level of theory. The conclusion from this study indicates that doping of C 60 nanocages with silicon, boron, and aluminum atoms improves the sensing performance of C 60 as a nanocarrier in drug-delivery systems. 17 Sanaz et al. in 2021 carried out a DFT investigation on metaloxide adsorption on fullerene C 60 and its potentials for the adsorption of pollutant gases using the DFT/B97D/6-311G(d,p) level of theory. Sanaz et al. concluded from the study that the adsorbents containing C 60 are much softer than the metal oxide (MOx) adsorbents, and it is predicted that they exhibit higher conductivity and reactivity. The MOx/C 60 complexes are more potent in the selectivity of adsorption of different gases, such as CO and NO 2 , and they may require lower operating temperatures than the metal oxides. 18 Hassani et al. in 2014 conducted a theoretical study on S-doped fullerene, reporting that it can be a potential sensor for the detection of iodine via DFT/CAM-B3LYP/6-311G(d,p) level of theory. DFT calculations and atoms in molecule (AIM) and natural bond orbital (NBO) analyses showed that the SFs surface can be used as a sensor for the adsorption of I 2 molecule. 19 Li et al. in 2019 conducted a DFT theoretical study on the following metal-doped fullerene: Al, Si, and pristine doped C70 fullerene as a nanosensor for the detection of isoniazid drug using DFT/B3LYP/6-311++G(d, p) level of theory. It was observed that the isoniazid drug was adsorbed on the surface of pristine C70 showing that pristine C 70 is a better sensor for the detection of isoniazid. 20 Also, engineering of carbide nanoparticles coated with noble metal monolayers for catalysis has offered a new direction for improved catalyst design by enhancing the reactivity and stability while reducing the overall noble metal (platinum, osmium, gold, silver, iridium, rhodium, and ruthenium) loadings. 21 These DFT investigations conducted have shown that nanomaterials are good sensor materials for the adsorption of pollutant gases and also for drug delivery. In the investigation of vertical excitation energies, 13 BODIPY-based dye sensitizers benchmarked using TD-BLYP and DSD-PBEP86 were calculated with the smallest mean absolute error (MAE) values of 0.083 and 0.106 eV, respectively. It was concluded in the investigation that these two double hybrids (DHs) show excellent consistency and quality. 22 Another comparative studied carried out in the comparative study of xDH-PBE0 and DSD-PBEPBE-D3BJ DH density functionals demonstrated the superiority of the DH functionals over the conventional functionals. 23 Hence, we extend our comparative studies using another two DHs as reference and four other hybrids as training sets.
This present study is aimed at (i) devising a potential nanosensor material for the adsorption of thiourea molecule in the environment and (ii) comparative adsorption study using six models of adsorption energy designed from six functionals (four hybrids and two DHs): DSDPBEP86, PBE0DH, M06-2X, M062X-D3, PBE0-D3, and ωB97XD. Ab intio, we  investigated which surfaces show better sensing performance;  however, this comparative study aimed at investigating which  adsorption model is best suitable for the adsorption of  CH 4 N 2 S molecule on different metal-doped fullerene surfaces:  C 59 Au, C 59 Hf, C 59 Hg, C 59 Ir, C 59 Os, C 59 Pr, C 59 Re, and C 59 W. The choice of the third-row transition metals (lanthanides series) in the doped surface is due to their unique chemical properties such as softness, magnetic properties, and different reaction tendencies. In addition, thorough literature reviews show that doping of transition metals increases the conductivity and sensitivity of a nanomaterial. 24,25 The pure fullerene surface under study has been doped by the sixth row transition metals, Au, Hf, Hg, Ir, Os, W, Pt, and Re, to enhance the performance of the fullerene surface. DFT was used to carry out all geometric calculations, optimizations, and theoretical investigations within the framework of M062X functional with Gen/def2svp/LanL2DZ basis set. Information about the intermolecular and intramolecular interactions, the mechanism of sensing, and the nature of interactions were accomplished by the various parameters from NBOs and the frontier molecular orbital (FMO), the highest occupied molecular orbital−lowest unoccupied molecular orbital (HOMO−LUMO) analysis. Quantum theory of atoms in molecule (QTAIM) analysis was carried out to study the noncovalent interactions (NCIs) in the complexes formed after interacting the metal-doped fullerene surface (C 59 X) with the thiourea molecule.
2. Computational Details. To find the minimum energy configurations, DFT has been employed in optimization using meta-generalized gradient approximation (GGA) functional exchange (M06-2x) assigning the Gen/def2svp/LanL2DZ basis set level of theory. 26 Initial structural equilibration was carried out using def2svp basic set. At first, pure fullerene was optimized before and after interaction with the thiourea molecule. Then, it was further optimized after substituting a carbon atom of the fullerene surface with X metals (X = Au, Hf, Hg, Ir, Os, Pt, Re, and W). With these, we ascertain stable structures in the resulted doped geometries. All computational calculations were accomplished using Gaussian 16 software with its embedded GaussView 6.0.16 interphase. 27,28 Last, all files generated from Gaussian software were analyzed with the Chemcraft program v1.6. Adsorption energies for the various complexes were calculated with eq 1. Also, this equation provides the basis for the adsorption models used in the comparative adsorption. For the comparative adsorption studies, the thiourea molecule, the metal-doped surfaces, and the resulted complexes were optimized separately in six different functionals, namely, DSDPBEP86, PBE0DH, M06-2X, M062XD3, PBE0D3, and ωB97XD, of which the first two are DHs and the latter are hybrids. Adsorption energy can be mathematically expressed as NBO analysis has been used putting into consideration the second-order perturbation energies to arrive at various conclusions pertaining to stability and charge-transfer mechanism. Insights were gained into the overall reactivity of the studied molecules via quantum descriptors which are the energy of the HOMO, the energy of the LUMO, the energy gaps, and the global reactivity descriptors as postulated by generalized Koopmans' hypothesis. 29 The study of weak interactions was accomplished using the AIM hypothesis postulated and developed by Professor Richard Bader and his research group. QTAIM analysis employ topological parameters such as the Hamiltonian kinetic energy K(r), the electronic charge density V(r), the energy density H(r), the density of all electrons ρ(r), the Laplacian of electron density ∇ 2 ρ(r), and the Lagrangian kinetic energy G(r) at critical points (CPs) to gain more insights into the noncovalent nature of interactions. 30 The visual extension of AIM analysis, the NCI, visualizes and classifies the nature of interactions into three, namely, noncovalent, steric, and van der Waal interactions using the isosurface color range from blue to red.

Optimization and Molecular Geometry.
Geometric equilibration and energy minimization have been initially administered as a medium of ensuring stability and sensitivity of the designed systems. In order to calculate the adsorption energies of the various systems obtained after interactions, optimization of the gas molecule and the metal-doped fullerene nanocages are also necessary. 31 The thiourea (CH 4 N 2 S) gas molecule was optimized separately, and also, each of the surfaces, including the pure and doped fullerene surfaces, was geometrically optimized. The bond lengths of the optimized gas molecule and the pure fullerene surface were computed and are depicted in Figure 1.
The essence of Figure 1 is to provide easy glance into the molecular structure of the thiourea gas molecule studied in this present paper. This enables easy visualization of the bond lengths between two atoms in the molecule. The visual representation of the optimized gas molecule and the pure surface in Figure 1 enhances easy grasp into the geometries of the adsorbent and the adsorbate. Bonds between two atoms in the thiourea gas molecule and those within the rings of the surface can be clearly visualized. The bond lengths for the bonds C1−S2, C1−N3, and C1−N4 were computed as 1.668, 1.353, and 1.353 Å, respectively. Last, the carbon−carbon bond length of bond C 49 −C 50 of the surface was computed as 1.453 Å. The bond lengths computed in this present study are similar to those in the previous computational studies carried out on thiourea and pure fullerene.
To increase the sensing performance of fullerene on this gas, the nanocage was doped with gold (Au), hafnium (Hf), mercury (Hg), iridium (Ir), osmium (Os), platinum (Pt), rhenium (Re), and tungsten (W). The doping of the nanocage was achieved by substituting the carbon atom in the fullerene for the metals, namely, Au, Hf, Hg, Ir, Os, Pt, Re, and W.
Afterward, reoptimization was carried out to obtain the doped nanocages which are presented in Figure 2. The following surfaces, namely, C 59 Au, C 59 Hf, C 59 Hg, C 59 Ir, C 59 Os, C 59 Pr, C 59 Re, and C 59 W, are the results of the metal-doped surfaces. In Figure 2, different doped nanocages are shown along with the bond lengths before interactions. In addition, both pure fullerene and doped fullerene contain 60 atoms in the following distributions: pure fullerene (60 carbon atoms) and doped fullerene (59 carbon atoms, 1 metal atom). Table 1 provides the computed bond lengths between atoms of the same element (C−C) and those of different elements (metal-S or metal-C) before and after interactions. Figure 2 visualizes the optimized structures of the doped fullerene surfaces before interactions. In Table 1, geometry such as bond lengths were provided before interactions to gain insight into the effects of bond lengths on interactions. 29 Figure 3 also depicts the optimized structures of pure fullerene before and after interactions, and one can observe that interaction has no effect on the bond length of the C 49 −C 50 bond. Bond lengths were calculated for four bonds and five bonds before and after interactions. Before interactions, three bonds around the doped metal of the surface and a bond within the surface were computed, while a bond between the S atom of the thiourea and the doped metal of the surface was calculated for the surface after interactions.
The computed bond lengths before and after interactions for the complexes in Table 1 show that interaction has slight or no effect on the bond length of the C 49 −C 50 bond within the pure fullerene nanocage (1.456 Å), while that between intermolecular interaction resulting in the bond C 48 −S 68 is 5.260 Å which is observed as the greatest bond length computed. Greater bond lengths are often associated with weaker interactions. Hence, we perform further investigations on the doped surfaces as many studies have highlighted the contributions of doped surface on increased reactivity and sensitivity. In most cases, increase in bond lengths is observed in the three bonds around the doped fullerene nanocage. These increased bond lengths are an indication that reactions have taken place, thus leading to stretches in bond lengths. The ranges of values of these bond lengths in CH 4 N 2 S@C 59 Au (A1), CH 4  . From this pattern, the least and highest bond lengths can be observed in P1 and H1 complexes. Thus, the weakest and strongest interactions were observed in P1 and H1 complexes, respectively. From Figure 4, the optimized structures of the complexes formed after interactions, along with their respective bond lengths, are visualized.

Adsorption Study.
Stable adsorption configuration was ascertained between the interactions of the thiourea molecule and metal-doped fullerene. The doped fullerene surface has been optimized to find the minimum energy configurations. 32 DFT has been employed in optimization using meta-GGA functional exchange (M06-2x) assigning the Gen/def2svp/LanL2DZ basis set level of theory. Initial structural equilibration was carried out using the def2svp basic set on Cluster. For the purpose of comparative adsorption study which is discussed in the later section of this study, each system was optimized in six different functionals. DHs and hybrids are contained within these functional. Six adsorption models corresponding to each functional were investigated. However, this section focuses on the effects of the adsorption energies on the interactions between the adsorbents and the adsorbate. In Table 2a, the calculated values of the adsorption energies for various interactions (systems) are presented. As observed in Table  2a, it is apparent that the thiourea molecule is weakly adsorbed by the metal-doped fullerene. This occurrence is justified by the positive values of adsorption energies in the complexes. The adsorption energies follow an increasing pattern of H2 (4.4142) < W1 (5.1155) < H1 (5.8390) < R1 (5.9764) < O1 (6.0995) < A1 (6.3129) < I1 (6.3797) < P1 (10.6648), and all are in electron volt (eV). Our deduction from this pattern shows that the least and greatest adsorption energy values are in the H2 and P1 complexes, respectively. The adsorption phenomena observed here are described as physisorption, 33 which is characterized by weak adsorption. These claimed physisorption phenomena have been reported in previous DFT studies and are shown in Table 2b. 3.3. HOMO−LUMO Analysis. Quantum descriptors are carried out employing the FMO analysis. The HOMO and the LUMO are collectively called the FMO as they are the primary parameters on which others rely. 39 Based on the generalized Koopmans's theorem, the mathematical expressions for the global indices of reactivity such as electron potential (EA), ionization potential (IP), electrophilicity index (ω), chemical potential (μ), chemical softness (S), and chemical hardness (η) were derived. 40 The HOMO−LUMO analysis provides information on the change in the electronic structural properties of the studied surfaces which is majorly influenced by the differences in the energy of the HOMO and LUMO. 41 The difference in energy between the two FMOs can be used to predict the energy, strength, and stability of the surfaces and the complex after adsorption. 42 This reveals the change in electronic structural properties during interaction of thiourea with the transition metal-doped fullerene. It is observed as reviewed in other literature that an increase in the energy difference is a function of the decrease in the charge flow or conductivity and increased stability of the transition metaldoped fullerene. 43 The energy of the HOMO and LUMO of the transition metal-doped fullerene (C 59 Au, C 59 Hf, C 59 Hg, C 59 Ir, C 59 Os, C 59 Pt, C 59 Re, C 59 W), C 60 fullerene, and the resulting complexes (A1, H1, H2, I1, O1, P1, R1, and W1) are shown in Table 3, while the electronic density distributions are depicted in Figure 5. As obtained from Table 3, the energy gap of the HOMO−LUMO is observed to be in relative ascending order of C 59 Ir < C 59 W < C 59 Pt < C 59 Hf < C 59 Os < C 59 Re < C 60 . This pattern has shown that pure fullerene possesses the highest energy gap of 4.4929 eV, while the C 59 Hg surface is observed to have the lowest energy gap of 2.8504 eV. Since the energy gap value in pure fullerene is significantly more than that for the doped surface, we then carried out our investigations within the scope of the metal-doped surfaces. The relative decrease in the HOMO−LUMO energy gap shows that the C 59 Hg surface offers higher stability for the adsorption of thiourea. 44 This implies that pure C 60 surface with a relative higher energy gap is less reactive and less suitable for adsorption of thiourea, while C 59 Hg with the least energy gap tends to be more reactive and more suitable for the adsorption of thiourea. After adsorption, it was observed that the complexes have energy gaps of the order O1 > R1 > W1 > H1 > H2 > A1 > I1 > P1. This explains that the O1 complex has the highest energy gap with a value of 3.9729 eV and P1 complex has the least energy gap with a value of 1.8996 eV. This further entails that the surface with the least energy gap  has the greatest potential for the nanosensor for the adsorption of the thiourea molecule. The pattern summarizes the order of reactivity and stability, and clearly P1, I1, and A1 complexes are relatively the three most stable complexes. Insights into the behavior of the surface to resist charge particle in its environment can be gained from chemical hardness. 45 Higher values of electron potential and chemical hardness are often associated with higher stability and lower reactivity. For chemical softness, higher chemical softness brings about higher stability and lower reactivity. 46 From Table 3, we observed complexes. This result is an indication of higher stability and lower reactivity in P1, H1, and I1 complexes.

Perturbation Energy Analysis.
A useful DFT approach developed by Weinhold et al. that gives insight into the pattern in which charges are transferred within studied molecules is known as NBO analysis. 47 It is possible to gain useful knowledge about the stability of molecules by electron delocalization and density charge transfer. In the NBO analysis, all focuses point at the second-order perturbation energies of the Lewis and non-Lewis donor−acceptor interactions of the molecules within the studied systems. 48 It is of great importance because it gives information on the intermolecular and intramolecular interactions (charge transfer). The secondorder perturbation energy is evaluated using the mathematical representation given in eq 2 49  In eq 2, q represents the donor occupancy, E i and E j represent the diagonal elements, and F(i,j) represent the element in the Fock matrix. The second-order perturbation energy (E (2) ) of the donor and acceptor interacting NBOs within the studied complexes is depicted in Table 4. The analysis in this present study is characterized by the secondorder perturbation energies corresponding to the contributions from each excited-type transition from the donor (i) to the acceptor (j). The observed transitions follow thus: π* π*, π* LP*, LP* LP*, σ σ, σ LP*, σ* LP*, σ* σ*, σ π*, and LP LP*. The NBO intermolecular interactions within A1, H1, H2, I1, O1, P1, R1, and W1, showing their intramolecular charge transfer, can also influence the stability of the studied complexes. 50 The charge transfers of the charge delocalization from the bonding natural orbital of sigma (σ) type to the same σ type is of the highest perturbation energy value of 691.11 kcal/mol and is observed in H1. It can be observed that the metal-doped surfaces having greater perturbation energies before interaction are C 59 Ir, C 59 Pt, C 59 W, and C 59 Re with values of 972.93, 972.02, 997.45, and 814.61 kcal/mol, respectively. It is also observed that the complexes having high second-order perturbation energies are in H1, P1, H2, and W1 with their energy values of 691.11, 572.76, 280.31, and 257.07 kcal/mol, respectively. Before interaction, C 59 W has the highest second-order perturbation energy; after interaction, the H1 complex has the highest second-order perturbation energy, and I1 has the least perturbation energy as shown in Table 4. The higher the perturbation energy, the more stable the interactions between the adsorbate and the adsorbent. 51 Hence, the surface with the highest perturbation energy is regarded as the potential surface for the adsorption of thiourea. 52 3.5. Visual Study of Weak Interactions. 3.5.1. QTAIM Analysis. Structural and microelectronic investigations may not be sufficient to gain complete insights into the intermolecular interaction of a complex system as atoms exhibit characteristic sets of features which differ between relatively small bound, and this reason invokes the AIM hypothesis. The QTAIM by Richard F. W Bader et al. 53 makes provision for exploring various kinds of interactions in the molecule with the propensity to seek the position of the bond between any two atoms at the bond CPs. By CP, it means a point where the first derivative of the charge density [ρ(r)] vanishes. 54 The position of extrema (maxima, minima, and saddle points) in the charge density can also be determined by the CPs. 54 Diverse useful properties in relation to their orientation in space can be determined on the basis of localization of specified bond CPs. 55 AIM hypothesis is one of the most valuable approaches to gain more insights into hydrogen and non-hydrogen bonding interactions. 56 The     Figure 6. NCI visualization using color-filled isosurface graphs was generated from the grid points using VMD software.   electrophilicity index of electron density (ε), the electron localization function (ELF), and the Eigen values 1 to 3 (λ 1 , λ 2 , and λ 3 ) are required to further inquire into the nature of interactions, G(r)/V(r) and λ 1 /λ 3 . From Table 5, it can be observed that all Laplacian of electron density ∇ 2 ρ(r) values are less than 1 for the studied complexes. This implies accumulation of electron density between two bounded atoms. 57 The studied system can be classified into noncovalent, partially covalent, and strongly covalent by putting into use the coupling ∇ 2 ρ(r) and H(r). The following couples ∇ 2 ρ(r) > 0 and H(r) > 0, ∇ 2 ρ(r) > 0 and H(r) < 0, and ∇ 2 ρ(r) < 0 and H(r) < 0 identifying the noncovalent, partially covalent, and covalent, 58 Table 5.

ACS
From Tables 5 and 6, one can infer into the nature of intermolecular interactions of the studied systems. The λ 1 /λ 3 values are observed to be less than 1, and this attribute was accounted for, 59 which is an indication of the strong presence of intermolecular interactions. The ellipticity of electron density (ε) is often invoked to gain more insights into the regions of charge density accumulation and the stability of the bond. The ε values in the table show that hydrogen bonds in the different systems are significantly stable as lower ellipticity index denotes greater stability and vice versa. 60 The least and greatest ellipticity index are found in H2 (ε = 0.078 a.u) and W1 (ε = 0.786 a.u) among the studied complexes obtained by doping the pure fullerene nanocage. This result indicates that the H2 complex is the most stable, while the W1 complex is the least stable. Other complexes such as O1 and P1 show relatively greater stability with ellipticity index values of 0.091 and 0.096 a.u, respectively.
3.5.2. NCI Analysis. Using the electron density and its derivatives, NCI analysis aids in the discovery of NCIs in real space. 61 Eight doped encapsulated surfaces, including the surface (CH 4 N 2 S@C60), were subjected to NCI studies in the current work. These complexes (A1, W1, R1, P1, O1, I1, H1, and H2) demonstrated a significant number of weak interactions between the molecules, elucidating a number of interaction features, including electrostatic attractions, the π effect, van der Waals forces, and hydrophobic effects. Using the Multiwfn program, 62 which produced high-quality grid data for two real space functions in the same spatial range, all examined complexes were computationally predicted. Reduced density gradient (RDG) clusters, RDG spikes, and λ2 all provide some insight about the type of bond and the degree of interaction in the RDG analysis. Figure 6 shows the NCI visualization using color-filled isosurface graphs generated from the grid points. The hydrogen interactions show large negative values of λ2 with high values of density (ρ > 0; λ2 < 0), while the van der Waals interactions show values of 2 and density that are close to zero (ρ > 0; λ2 > 0). In contrast, the strong repulsive interaction regions are known to have large positive values of λ2 and high densities (ρ > 0; λ2 > 0). The color-filled isosurface graphs were generated from the grid points using visual molecular dynamics (VMD) software. 63 It is therefore fascinating to note that the intermolecular and intramolecular interactions caused almost all of the nine complexes to appear to be under the influence of a relatively significant force of attraction. The rich blue color visible in P1 and A1 suggests the presence of a very strong force of attraction caused by the hydrogen bond interaction, which promotes the adsorption between the surfaces and the gases. Peaks appearing in the extremely very negative zone of the eigen values serve as concurrent confirmation that the aforementioned complexes have a significant electrostatic force of attraction. Due to lack of chemical bonds, these identical complexes were seen to exhibit physisorption. Contacts at the real positive zones of R1, I1, W1, and O1�which shimmer red�substantially prove the existence of extremely strong steric repulsion by increasing the instability of the interactions. It is crucial to show that there is stronger repulsion within the doped enclosed surfaces in contrast to the minimal force of attraction and van der Waals interactions between these complexes. This is caused by the way the atoms are arranged spatially, which raises the energy in the surfaces. Yet, the geometry and reactivity of ions are impacted by the presence of nonbonding interactions. Less repulsive interactions were observed on the doped encapsulating surfaces. The structural groups of the surfaces' surfaces have overlapping electrons, which are kept in place by the way that like charges attract and opposite charges repel. A loss of equilibrium and an increase in the energy of adsorption between the molecules are also suggested by the modest amount of van der Waals form of interaction that occurs in the (CH 4 N 2 S@C60), H1, and H2 complexes. The green color of the 3D RDG maps, however, indicates that practically all complexes have low van der Waals interactions.
3.6. Density of States. The density of states (DOS) plot describes the energy difference between the HOMO and the LUMO of the complex under study. 64 The DOS plot displays the atomic orbital or molecular orbital contribution to the interaction. The DOS plot shows the most permissible energy for the transition and also explains the electronic pattern of the HOMO−LUMO of the transition metal-doped fullerene before and after interaction with thiourea. The DOS plot is in accordance with the energy gap and the physical geometry property results we obtained from the FMO analysis and geometric optimization. As visualized in Figure 7, there is an increase and decrease in the HOMO−LUMO energy gap, which also gives information regarding the conductivity of the surface. The changes in the electronic properties of the surfaces after adsorption of thiourea were made comprehensible from the total density of states (TDOS). The changes in the intensity and the shift observed in the TDOS peak show the variations in the conductivity of nanosensors upon adsorption of thiourea. The complex with the highest energy gap is O1, and the complex with the least energy is the P1 complex. The change in the energy gap causes a change in the electrical conductivity of the surface, hence determining the sensitivity of the nanosensor. DOS plot also provides the visualization of the changes that occurs in the complexes as a result of the interaction of the transition metal-doped fullerene and thiourea. The increase in the energy gap of O1 indicates weak sensitivity within the interaction, and the decrease in the energy gap of P1 shows strong sensitivity within the interaction (Figure 7).

Comparative Adsorption Studies.
Currently, DH density functionals are the most accurate density functionals for electronic excitation and ground-state properties, especially ACS Omega http://pubs.acs.org/journal/acsodf Article that with long-range correctional schemes. 65 For this reason, they have been designed and positioned at the top of the rungs (fifth rung) of the Jacobi's ladder. In this study, we demonstrate the excellence performance of the two DH density functionals (DSDPBEP86 and PBE0DH), using these two as the reference or standard for this adsorption study. According to the reasoning from Schwabe and Goerigk, the use of initial high-level data as the standard enables one to directly compare with other wave function approaches and without accompanying any erroneous data that may influence the expected results. 66 Hybrids such as M06-2X, M062XD3, Pbe0D3, and ωb97XD are the testing hybrid functionals used for the comparative study. 3.7.1. Definition of DSDPBEP86 and PBE0DH. Literature review has shown that DHs such as DSDPBEP86 and PBE0DH yield best performance for transition metals and are associated with weak interaction energies and vibrational energies. 67 DH functionals are generated from Kohn−Sham (GGA) orbitals and eigen values. It is the combination or mixing of standard generalized gradient exchange and correction with perturbative second-order correlation part (PT2) and Hartree-Fock (HF) exchange. 68 The general equation for representing the DH functional is given in eq 3 as Variables and components are very useful tools used in maximizing the accuracy of DHs. 69 The selection of exchange and correction functionals, addition of ad-hoc dispersion correction, and the coefficients of each component such as exact exchange DFT, and perturbative correlation in both equal and opposite spins are components that enhance the functionality and accuracy of DHs. 70 The dispersion-corrected, spin component-scaled, double-hybrid DFT (DSD-DFT) encompasses various deterministic parameters of functionals. At least, part of the dispersion effects has been recovered by the DGs. 71 However, their performance has been improved by the use of dispersion correction such as D2 and D3 methods. 72 The MP2 like term can handle dispersion forces, which enables the provision of some bindings in DHs, which has failed in other DFT methods. 73 Despite this reason, the use of wellparameterized dispersion method is of great use to DHs as a result of the relatively small amount of perturbation correction. 74 Moreover, subladder within the fifth rung of the Jacobi's Ladder can be attained by applying GGA, meta-GGA, or local density approxiamtion functional on the DH functional

ACS Omega
http://pubs.acs.org/journal/acsodf Article design. 75 The hierarchy used in the dispersion correction is described as "stairway to Heaven" in the "Jacobi's Ladder" of John P. Perdew. From this, accuracy-approaching wave function methods can be achieved by empirical DH functionals with dispersion corrections. 70 In the M06 family of functional, aside from pseudopotential approaches, one could find implicit treatment by parametrization of the semilocal functional as also done in the BMK, PW6B95, and M06 functionals. PBE0-DH (Perdew−Burke−Ernzerhof−double hybrid) functional is an exchange correlation functional with no empirical parameters. The PBE0-DH can be defined with the mathematical expression in eq 4: 76 Table 7, and the results show that these MAD values reduced in functionals as compared to the reference dataset. The MAD values in M06-2X and M062Xd3 are calculated to be 1.0860 and 1.1060 eV, respectively, and 1.9373 and 1.0373 eV for PBE0D3 and ωB97XD, respectively. Clearly, the DH density functionals show better performance in estimating the adsorption energies due to their reduced MAD values (DSDPBEP86 = 1.0305 eV and PBE0DH = 0.9965 eV). Since the standard functionals were confirmed to better perform than M06-2X (MAD = 1.0860 eV), M062Xd3 (MAD = 1.1060 eV), PBE0D3 (MAD = 1.9373 eV), and ωB97XD (MAD = 1.0373 eV), and then within the training dataset, we ranked as follows: ωB97XD (first rank), M06-2X (second rank), M062Xd3 (third rank), and last the PBE0D3 (fourth rank). The chart in Figure 8 shows the six adsorption models with their statistical values. This enables easy capture of the patterns in the different models.
To strengthen our findings on the forecasting errors of various models of adsorption energy in the single dataset which arises as a result of errors associated with theoretical computations, we further employed the RMSD analysis. It is true that the smaller the RMSD value, the less the deviation in the dataset. 78 Hence, our basis on various conclusions is established. The RMSD values for various models are presented in Table 7, and the results are discussed as follows: It can be observed that DSDPBEP86 (RMSD = 1.6277) and PBE0DH (RMSD = 1.6101) outperformed the following training dataset. Meanwhile, within the frame of DHs, PBE0DH outperformed DSDPBEP86. Considering the training dataset, ωB97XD emergence as the first rank is due to its least RMSD value of 1.6387 eV, while M06-2X ranks second, M062Xd3 ranks third, and PBE0D3 ranks fourth in the overall performance within the training dataset. The MAE values are presented in Tables 8 and 9. The MAE values are calculated for each training dataset with respect to the individual standard dataset (DSDPBEP86 or PBE0DH). This error calculation provides the proximity or variability of the training dataset from the standard dataset. The MAE values indicate that PBE0D3 ranks fourth with the greatest MAE Dsdpbep86-Pbe0d3 of 1.1701 eV. In this comparative study, we affirmed that DSDPBEP86 and PBE0DH are superior to the training dataset, namely, ωB97XD, PBE0D3, M06-2X, and M062Xd3, and provide the rank to which errors are minimized. Our results show that DSDPBEP86 and PBE0DH offer a significant level of accuracy in the adsorption of thiourea molecule on the transition metal-doped fullerene surfaces.

CONCLUSIONS
Adsorption of thiourea molecule on the X-doped fullerene surfaces (X = Au, Hf, Hg, Ir, Os, Pt, Re, and W) has been investigated using the first-principle DFT. To find the minimum energy configurations, DFT has been employed in optimization using meta-GGA functional exchange (M06-2x) assigning the Gen/def2svp/LanL2DZ basis set level of theory. To gain more insights into the sensing performance of the various metal-doped fullerene surfaces, NBO analysis, quantum descriptors (FMO analysis), and the DOS plots have been explored. Also, visual study of weak interactions such as QTAIM analysis and NCIs was also explored to gain more knowledge into the nature of interactions within these studied systems. Our deduction from the adsorption patterns in the different surfaces show the following: The bond lengths between sulfur atom and doped metals in the complexes follow an increasing trend of: P1 (2.112) < W1(2.442) < O1(2.501) < A1(2.516) < R1(2.519) < I1(2.523) < H2(2.602) < H1(2.707). From this trend, the least and highest bond lengths can be observed in P1 and H1 complexes. Thus, the weakest and strongest interactions were observed in P1 and H1 complexes, respectively. ii. The least and greatest adsorption energy values are in the H2 and P1 complexes with adsorption energy values of 4.4142 and 10.6648 eV, respectively. The adsorption phenomena observed here are described as physisorption, which are characterized by weak adsorption. iii. Each complex follows energy gap of the order: O1 > R1 > W1 > H1 > H2 > A1 > I1 > P1. This explains that the O1 complex has the highest energy gap with the value of 3.9729 eV and P1 complex has the least energy gap with value of 1.8996 eV. The pattern summarizes the order of reactivity and stability, and clearly P1, I1, and A1 complexes are relatively the three most stable and less reactive complexes. Also, increment in the values of the chemical softness (σ) was observed from 0.2966, 0.2653, and 0.3081 eV before adsorptions to 0.5264, 0.2671, and 0.3258 eV after adsorption in P1, H1, and I1 complexes. This result affirms the higher stability and lower reactivity in P1, H1, and I1 complexes. iv. The charge transfers of the charge delocalization from bonding natural orbital of sigma (σ) type to the same σ type and the localization from the lone pair of platinum to the antibonding character of lone pair of sulfur (LP*S) possess the greatest perturbation energy values Also, Laplacian of electron density ∇ 2 ρ(r) values are less than 1 for the studied complexes. This implies accumulation of electron density between two bounded atoms. Complexes such as O1 and P1 show relatively greater stability with the electrophilicity index of 0.091 and 0.096 a.u, respectively. vi. The NCI analysis shows that P1 and A1 possess rich blue color signifying the presence of a very strong force of attraction as a result of hydrogen bond interaction. The green color of the 3D RDG maps, however, indicates that practically all complexes have low van der Waals interactions. In all cases, P1 complex shows better sensing attributes than its studied counterparts. vii. In the comparative adsorption study, DH density functionals show better performance in estimating the adsorption energies due to their reduced MAD values (SDPBEP86 = 1.0305 eV and PBE0DH = 0.9965 eV) and RMSD values (DSDPBEP86 = 1.6277 and PBE0DH = 1.6101). Finally, within the training dataset, we ranked the models in the order of performance as follows: ωB97XD (first rank), M06-2X (second rank), M062Xd3 (third rank), and last PBE0D3 (fourth rank).
■ ASSOCIATED CONTENT

* sı Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.2c04044. Detailed information on the NBO analysis (PDF)