Localized Orbitals Research Articles

Exploring the Physical Properties of LiBeX (X = Sb, Bi) Compounds via Ab Initio Approach

In the current study, it is aimed to scrutinize the physical properties of LiBeX (X = Sb, Bi) compounds in detail. Density‐functional‐theory‐based WIEN2k and the Vienna Ab initio Simulation Package, employing the generalized gradient approximation of Perdew–Burke–Ernzerhof, Wu–Cohen, and Tran–Blaha‐modified Becke–Johnson (TB‐mBJ) exchange‐correlation schemes, are utilized to better validate the outcomes. The compounds exhibit energetic, lattice dynamic, and mechanical stability. Electronic structure calculations using the TB‐mBJ functional reveal indirect bandgaps of 1.007 eV for LiBeSb and 0.789 eV for LiBeBi compounds, respectively. The partial charge distribution in the highest occupied molecular orbital and the lowest unoccupied molecular orbital discloses maximum charge localization around the X site. The examination of the crystal orbital Hamilton population reveals the strongest BeX bonding interactions among the bonding pairs. The physio‐mechanical properties indicate brittle and mechanically anisotropic behavior of both compounds, with covalent bonding characteristics. The comparative analysis suggests that the TB‐mBJ potential is suitable for bandgap calculations due to its close alignment with experimental results. Additionally, the optimized results for these compounds indicate their potential for use in optoelectronic devices, such as visible to ultraviolet sensors and photovoltaics. The determined properties are consistent with previous theoretical findings.

The Trifluorooxygenate Anion [OF3]-: Spectroscopic Evidence for a Binary, Hypervalent Oxygen Species.

Experimental evidence for hypervalent compounds of second-row elements is still scarce in literature. Here, we present the first report of the long-sought binary hypervalent trifluorooxygenate anion [OF3]-. It was isolated in solid Ne matrices under cryogenic conditions after reacting oxygen difluoride with free fluoride ions from laser ablation of alkali metal fluorides MF (M = Li-Cs). As predicted by VSEPR theory and calculations at the CCSD(T) level, and confirmed by FTIR spectroscopy as well as isotopic labeling, [OF3]- exhibits a C2v-symmetric T-shaped structure with one short and two long O-F bond distances. Analysis of the natural local molecular orbitals shows the presence of 2c-2e bond and one 3c-4e bond. Natural resonance theory indicates the importance of the stability of [OF2]•- for the stability of [OF3]-. Although free [OF2]•- was not detected, the species MOF2 (M = Na-Cs) could be observed in the same experiments, which are best described as contact ion pairs of M+[OF2]•-.

The Trifluorooxygenate Anion [OF3]−: Spectroscopic Evidence for a Binary, Hypervalent Oxygen Species

Experimental evidence for hypervalent compounds of second‐row elements is still scarce in literature. Here, we present the first report of the long‐sought binary hypervalent trifluorooxygenate anion [OF3]−. It was isolated in solid Ne matrices under cryogenic conditions after reacting oxygen difluoride with free fluoride ions from laser ablation of alkali metal fluorides MF (M = Li–Cs). As predicted by VSEPR theory and calculations at the CCSD(T) level, and confirmed by FTIR spectroscopy as well as isotopic labeling, [OF3]− exhibits a C2v‐symmetric T‐shaped structure with one short and two long O‐F bond distances. Analysis of the natural local molecular orbitals shows the presence of 2c‐2e bond and one 3c‐4e bond. Natural resonance theory indicates the importance of the stability of [OF2]•− for the stability of [OF3]−. Although free [OF2]•− was not detected, the species MOF2 (M = Na–Cs) could be observed in the same experiments, which are best described as contact ion pairs of M+[OF2]•−.

The aromatic amino acid phenylalanine: a versatile tool for binding transition metal ions.

The human body contains many different types of transition metal ions, such as Zn2+, Cu2+, which are involved in many physiological processes. An excess or deficiency of these ions can cause diseases, such as Alzheimer's disease, which is closely related to the levels of these ions in the body. In-depth understanding of various physiological and pathological mechanisms related to metal ions requires understanding the interaction between metal ions and nearby amino acids at the atomic level. This article selected four transition metal ions: Zn2+, Cu2+, Fe2+, and Mn2+ and the aromatic amino acid Phe, known for its strong coordination capability, as study subjects, comprehensively examining their binding situations. The results show that there are multiple binding modes between them and Phe, and most of the binding modes involve benzene ring coordination. The coordination strength order of the four metal ions with benzene ring, carbonyl O, hydroxyl O and amino N is different. For the lowest energy structure formed by each ion with Phe, all four ions are bound to N, carbonyl O, and benzene ring. Zn2+ is combined with two C's of the benzene ring, Cu2+ with four C's of the benzene ring, and Fe2+ and Mn2+ with the benzene ring as a whole. Part of the reason for this phenomenon may be derived from the tendency of transition metal ions to reach 18e stable structures when bound to ligands. There is a strong binding force between the four ions and Phe, and the binding trend is Cu2+(-294.9kcal/mol) > Zn2+(-261.3kcal/mol) > Fe2+(-247.5kcal/mol) > Mn2+(-220.2kcal/mol). Mayer bond order analysis and molecular orbital localization analysis found that there are very strong chemical interactions between transition metal ions and surrounding atoms, especially with N and carbonyl O. Several initial structures with different coordination modes to Phe were created according to chemical intuition for each divalent cation. Then semiempirical MD simulations at GFN2 level were run on these structures. The numerous generated structures were classified according to some criteria, then representative geometries were preliminarily optimized by TPSSh/6-31G*/LanL2DZ. To get more accurate electronic energies, high-precision quantum chemistry calculations at the level of TPSSh/def2TZVPP//TPSSh/def2QZVPP were carried out on the selected low-lying structures. All the optimized structures were confirmed to be minima without imaginary frequency by performing frequency analyses. Further electronic structure analyses such as IRI, Mayer bond order, IBSI etc. were performed to get more insights into the binding between the transition metal ions and Phe.

Periodic Local Coupled-Cluster Theory for Insulators and Metals.

We describe the implementation details of periodic local coupled-cluster theory with single and double excitations (CCSD) and perturbative triple excitations [CCSD(T)] using local natural orbitals (LNOs) and k-point symmetry. We discuss and compare several choices for orbital localization, fragmentation, and LNO construction. By studying diamond and lithium, we demonstrate that periodic LNO-CC theory can be applied with equal success to both insulators and metals, achieving speedups of 2 to 3 orders of magnitude even for moderately sized k-point meshes. Our final predictions of the equilibrium cohesive energy, lattice constant, and bulk modulus for diamond and lithium are in good agreement with previous theoretical predictions and experimental results.

Improving Predictions of Spin-Crossover Complex Properties through DFT Calculations with a Local Hybrid Functional.

We conducted a study on the performance of the local hybrid exchange-correlation functional PBE0r for a set of 95 experimentally characterized iron spin-crossover (SCO) complexes [Vennelakanti, V.; J. Chem. Phys. 2023, 159, 024120]. The PBE0r functional is a variant of PBE0 where the exchange correction is restricted to on-site terms formulated on the basis of local orbitals. We determine the free parameters of the PBE0r functional against the experimental data and other hybrid functionals. With a Hartree-Fock (HF) exchange factor of 4%, the PBE0r functional accurately reproduces the electronic and free-energy trends predicted in prior DFT studies for these 95 complexes by using the B3LYP functional. Larger values of HF exchange stabilize high-spin states. The PBE0r-predicted bond lengths tend to exceed the experimental bond lengths, although bond lengths are less sensitive to HF exchange than in global hybrids. The predicted SCO transition temperatures T1/2 from PBE0r correlate moderately with the experimental transition temperatures, showing a slight improvement compared to the previous modB3LYP-predicted T1/2. This study suggests that the PBE0r functional is computationally cost-effective and offers the possibility of simulating larger complexes with accuracy comparable to global hybrid functionals, provided the HF-exchange parameter is carefully optimized.

Electric Field Dependence of EPR Hyperfine Coupling Constants.

In this article, we introduce a simple but reliable method to calculate the electric field dependence of the isotropic hyperfine coupling tensor Aiso for free radicals. This dependence, also referred to as the Bloembergen effect, can be of interest in analyzing EPR experiments for solid-state materials but is rarely studied for isolated radicals in the gaseous phase. The proposed method uses the numerical differentiation of the field-perturbed A tensor and, consequently, as a purely numerical method, does not depend on a quantum chemical method used to determine the hyperfine tensor A. To test the performance of the proposed method, we used a set of 28 systems, including seven organic radicals, the majority of which were taken from a recent benchmark study by Bartlett's group. We employed the well-tested and robust density functional theory (DFT) functional, namely CAM-B3LYP, and the variant of the CCSD method based on local pair natural orbitals, namely DLPNO-CCSD to calculate the Aiso tensor itself, and all first derivatives or Bloembergen effect constants ai(1).

Exploiting Non-Abelian Point-Group Symmetry to Estimate the Exact Ground-State Correlation Energy of Benzene in a Polarized Split-Valence Triple-Zeta Basis Set.

Local electronic-structure methods in quantum chemistry operate on the ability to compress electron correlations more efficiently in a basis of spatially localized molecular orbitals than in a parent set of canonical orbitals. However, many typical choices of localized orbitals tend to be related by selected, near-exact symmetry operations whenever a molecule belongs to a point group, a feature which remains largely unexploited in most local correlation methods. The present Letter demonstrates how to leverage a recent unitary protocol for enforcing symmetry properties among localized orbitals to yield a high-accuracy estimate of the exact ground-state correlation energy of benzene (D6h) in correlation-consistent polarized basis sets of both double- and triple-ζ quality. Through an initial application to many-body expanded full configuration interaction (MBE-FCI) theory, we show how molecular point-group symmetry can lead to computational savings that are inversely proportional to the order of the point group in a manner generally applicable to the acceleration of modern local correlation methods.

Wannier Function Localization Using Bloch Intrinsic Atomic Orbitals.

We extend the intrinsic atomic orbital (IAO) method for the localization of molecular orbitals to calculate well-localized generalized Wannier functions in crystals in the spirit of the Pipek-Mezey method. We furthermore present a one-shot diabatic Wannierization procedure that aligns the phases of the Bloch functions, providing immediate Wannier localization, which serves as an excellent initial guess for optimization. We test our Wannier localization implementation on a number of solid-state systems, highlighting the effectiveness of the diabatic preparation, especially for localizing core bands. Partial charges of Wannier functions generated using Bloch IAOs align well with chemical intuition, which we demonstrate through the example of the adsorption of CO on a MgO surface.

A detailed TD-DFT and intermolecular interaction study of vitamin K in soluble, poorly soluble and insoluble solvents, as well as an ADME and molecular docking study

Vitamin K is one of the most important fat-soluble vitamins and while there are two main types of vitamin K in nature, known as K1 (phylloquinone) and K2 (menaquinones), there is also a synthetic type of vitamin K known as K3 (menadione). Recent studies have shown that it is crucial to know the non-covalent interactions, ADME and molecular docking of molecules in different solvent media. Therefore, we have performed some quantum chemical calculations, ADME and intra-and intermolecular interaction calculations of a number of K1, K2 and K3 such as K1-water (K1 + W), K1-methanol (K1 + M), K1-triacetin (K1 + T), K2-water (K2 + W), K2-methanol (K2 + M), K2-triacetin (K2 + T), K3-water (K3 + W), K3-methanol (K3 + M), K3-triacetin (K3 + T) performed by Density Functional Theory (DFT) and Multiwfn: A multifunctional wavefunction analyzer. Molecular structures, HOMO-LUMO energies, MEP and electronic properties have been calculated and described using DFT at the level of B3LYP/6-311G (d,p) level. The nature of the molecular interactions between vitamin K and solvents such as water, methanol and triacetin were also investigated using topological analyses such as atoms in molecule (AIM), non-covalent interaction index (NCI), reduced density gradient (RDG), Localized orbital locator (LOL) and electron localization function (ELF). In addition, FMO for electronic transitions, MEP for electrophilic and nucleophilic attack, ADME to investigate how a chemical is processed by a living organism, and Fukui functions to determine electron density are explained. Finally, molecular docking was used to determine the biological activity of the vitamin K.

Closest Wannier functions to a given set of localized orbitals

Closest Wannier functions to a given set of localized orbitals

Theoretical Investigation of the Effects of Aldehyde Substitution with Pyran Groups in D-π-A Dye on Performance of DSSCs.

This work investigated the substitution of the aldehyde with a pyran functional group in D-π-aldehyde dye to improve cell performance. This strategy was suggested by recent work that synthesized D-π-aldehyde dye, which achieved a maximum absorption wavelength that was only slightly off the threshold for an ideal sensitizer. Therefore, DFT and TD-DFT were used to investigate the effect of different pyran substituents to replace the aldehyde group. The pyran groups reduced the dye energy gap better than other known anchoring groups. The proposed dyes showed facile intermolecular charge transfer through the localization of HOMO and LUMO orbitals on the donor and acceptor parts, which promoted orbital overlap with the TiO2 surface. The studied dyes have HOMO and LOMO energy levels that could regenerate electrons from redox potential electrodes and inject electrons into the TiO2 conduction band. The lone pairs of oxygen atoms in pyran components act as nucleophile centers, facilitating adsorption on the TiO2 surface through their electrophile atoms. Pyrans increased the efficacy of dye sensitizers by extending their absorbance range and causing the maximum peak to redshift deeper into the visible region. The effects of the pyran groups on photovoltaic properties such as light harvesting efficiency (LHE), free energy change of electron injection, and dye regeneration were investigated and discussed. The adsorption behaviors of the proposed dyes on the TiO2 (1 1 0) surface were investigated by means of Monte Carlo simulations. The calculated adsorption energies indicates that pyran fragments, compared to the aldehyde in the main dye, had a greater ability to induce the adsorption onto the TiO2 substrate.

Crystal structures, NCI-RDG, Hirshfeld surface and energy framework analysis of tetra aryl substitute bispidine and oxaquinuclidine core containing derivatives: A potential COVID-19 drug candidate

Two of the title compounds are crystallized in P21/c and monoclinic face groups. Each crystal unit cell has four molecules. There are two piperidine rings: one in the chair conformation and another one in the boat conformation. The piperidine nitrogen in the boat conformation is joined to the oxygen-containing chair conformation piperidine ring to produce the oxaquinuclidine ring (-N-CH2O-). Furthermore, because of the steric barrier between rings, all aryl groups are oriented in an equatorial position. The crystal network is maintained through several interactions, including C—H⋯O/N/Cl/π. The crystal void and interaction energy studies gave additional evidence of the strength of the crystal packing and intermolecular linkage. Crystal 3b has less cavity than crystal 3c, indicating that it is densely packed. The dispersion energy contribution dominates the stability, according to the analysis of the electrostatic, dispersion, and total energy frameworks. Reduced density gradient (RDG), electron localization function (ELF), and localized orbital locator (LOL) analysis were used to determine the molecular interaction, electron pair density, and maximally localized orbitals overlapping sites, respectively. This approach reveals that oxaquinuclidine ring steric hindrance and the electron densities throughout the molecules. Density function theory (DFT) provides more evidence for the ring's orientation and the molecules' reactivity. A molecular docking investigation of four essential COVID-19 proteins was carried out using these theoretical ideas. This investigation demonstrates that each protein's reactivity varies; certain proteins have more interaction with high electron density molecules (electron-donating substituent), while others have more interaction with low electron density molecules (electron-withdrawing substituent). The ADMET and drug-likeness investigations reveal that methoxy group substituted molecules perfectly correlate with the required pharmacological characteristics. The cytotoxicity of the five compounds was assessed using the HEK293T cell.

Investigation of spectroscopic characterization, crystal structure, and antitumor activity of a novel 2ATP molecule

In this section, the spectroscopic characteristics of 2-amino-toysl-pyridine (2ATP) are fully examined, using both experimental and computational investigations guided by density functional theory (DFT). It will facilitate our computational research using the B3LYP approach to use the basis set 6–311++G(d,p). Comprehensive assignments of vibrational modes were obtained from the vibrational spectra, which comprised FT-Raman and FT-IR spectroscopy and were recorded in the region of 3500–400 cm−1 and 4000–500 cm-1, respectively, using the Vibrational Energy Distribution Analysis (VEDA) approach. The net atomic charges inside the molecule were ascertained by using Mulliken population analysis, natural atomic charges, and electrostatic potentials (CHELPG). The structural conformations of 2ATP were determined using NMR spectroscopy in a CDCl3 solvent. The donor-acceptor interactions of the 2ATP molecule at the 6–311++G(d,p) level were studied by means of a Natural Bond Orbital (NBO) study. Studies of the ultraviolet (UV) spectrum in ethanol were used to assess the effects of the solvent. An assessment was made of the energy difference between the lowest unoccupied molecular orbital (LUMO) and the highest occupied molecular orbital (HOMO) in order to understand charge transfer processes that suggest the molecule may have biological activity. Molecular electrostatic potential (MEP) surfaces were used to predict the nucleophilic and electrophilic sites in molecules. The non-covalent interactions were evaluated using the reduced density gradient (RDG) approach. The Multiwfn software was used to analyze the topological properties of the 2ATP, including the Localized Orbital Locator (LOL) and Electron Localization Function (ELF). Further attention was drawn to the compound's exceptional pharmacological potential when its ADMET (Absorption, Distribution, Metabolism, Excretion, and Toxicity) characteristics were evaluated. Not to add, molecular docking experiments were carried out to evaluate the feasibility of 2ATP as a bioactive material with possible uses in the pharmaceutical business.

DFT study of electron energy loss spectra of sulfur in Janus MoSSe, MoSTe, WSSe and WSTe monolayers

In this paper, electronic properties of Janus MSX monolayers (M = Mo, W; X = Se or Te), including electron energy loss near edge structures (ELNES), as K and [Formula: see text] edge spectra of sulfur atoms, have been calculated using a full potential scheme and the augmented plane wave plus local orbitals (APW+lo) method in the framework of density functional theory (DFT). Due to the lack of experimental results, the obtained spectra are compared with the corresponding spectra of MoS2 monolayer. The band structure analysis shows that the Janus MoSSe and WSSe monolayers are direct bandgap semiconductors, while the Janus MoSTe and WSTe monolayers are indirect bandgap semiconductors. In comparison to MoS2, the main structures of the K edge ELNES spectra of sulfur atoms in Janus monolayers occur at lower energies, due to the structural change and increased bond length. The relative reduction of intensities in the main structures predicts the possibility of reducing the number of partial densities of states (PDOS), that is, the reduced p PDOS for the K edge in the corresponding energy range. In the K ([Formula: see text] edge ELNES spectra of the sulfur atom in Janus monolayers and MoS2 monolayers, the main structures are due to the electron transfer to the unoccupied [Formula: see text] and [Formula: see text] states (3s of sulfur and 4d states of the transition metal).

Basis-Set Limit CCSD(T) Energies for Large Molecules with Local Natural Orbitals and Reduced-Scaling Basis-Set Corrections.

The calculation of density-based basis-set correction (DBBSC), which remedies the basis-set incompleteness (BSI) error of the correlation energy, is combined with local approximations. Aiming at large-scale applications, the procedure is implemented in our efficient local natural orbital-based coupled-cluster singles and doubles with perturbative triples [LNO-CCSD(T)] scheme. To this end, the range-separation function, which characterizes the one-electron BSI in space, is decomposed into the sum of contributions from individual localized molecular orbitals (LMOs). A compact domain is constructed around each LMO, and the corresponding contributions are evaluated only within these restricted domains. Furthermore, for the calculation of the complementary auxiliary basis set (CABS) correction, which significantly improves the Hartree-Fock (HF) energy, the local density fitting approximation is utilized. The errors arising from the local approximations are examined in detail, efficient prescreening techniques are introduced to compress the numerical quadrature used for DBBSC, and conservative default thresholds are selected for the truncation parameters. The efficiency of the DBBSC-LNO-CCSD(T) method is demonstrated through representative examples of up to 1000 atoms. Based on the numerical results, we conclude that the corrections drastically reduce the BSI error using double-ζ basis sets, often to below 1 kcal/mol compared to the reliable LNO-CCSD(T) complete basis set references, while significant improvements are also achieved with triple-ζ basis sets. Considering that the calculation of the DBBSC and CABS corrections only moderately increases the wall-clock time required for the post-HF steps in practical applications, the proposed DBBSC-LNO-CCSD(T) method offers a highly efficient and robust tool for large-scale calculations.

Self-assembled belt[12]pyridine nanotube for the adsorption and removal of anti-TB drugs from wastewater

Environmental safety is a major concern of today's world, and it has attracted the attention of the scientific research community. The environment gets contaminated due to various toxic drugs and pharmaceutical toxins coming from different sources. Therefore, removing these toxins is necessary for making the environment greener and safer. Nanomaterials are excellent candidates for adsorption and removal of harmful materials due to their unique properties. Herein we have studied self-assembled nanotube based on belt[12]pyridine (2-(12BPy)) as an adsorbent for the removal of antituberculosis drugs i.e. isoniazid (INZ) and pyrazinamide (PZA). The adsorption ability is studied by considering the adsorption energy (Eads), non-covalent interaction index analysis (NCI), quantum theory of atoms in molecules (QTAIM), energy decomposition analysis (EDA), charge transfer via natural bond orbital analysis (NBO) and electron localization function (ELF), and dipole moment. The results indicate strong adsorption of selected drugs with self-assembled nanotube without altering the electronic properties. Recovery time of the complexes is also calculated to understand the regeneration of the nanotube. Results also demonstrate that van der Waals forces are major contributor in the adsorption of drug molecules within the nanotube. Our results indicate that belt[12]pyridine (2-(12BPy)) nanotube can be used as an adsorbent for the removal of toxic drug molecules from the environment. This research will benefit the scientists working in the field of new sensors for biological components and materials.

Accurate and efficient open-source implementation of domain-based local pair natural orbital (DLPNO) coupled-cluster theory using a t1-transformed Hamiltonian.

We present an efficient, open-source formulation for coupled-cluster theory through perturbative triples with domain-based local pair natural orbitals [DLPNO-CCSD(T)]. Similar to the implementation of the DLPNO-CCSD(T) method found in the ORCA package, the most expensive integral generation and contraction steps associated with the CCSD(T) method are linear-scaling. In this work, we show that the t1-transformed Hamiltonian allows for a less complex algorithm when evaluating the local CCSD(T) energy without compromising efficiency or accuracy. Our algorithm yields sub-kJ mol-1 deviations for relative energies when compared with canonical CCSD(T), with typical errors being on the order of 0.1kcal mol-1, using our TightPNO parameters. We extensively tested and optimized our algorithm and parameters for non-covalent interactions, which have been the most difficult interaction to model for orbital (PNO)-based methods historically. To highlight the capabilities of our code, we tested it on large water clusters, as well as insulin (787 atoms).

Predictive Guidelines for Electrocyclization of Dithienylethenes.

Molecular photoswitches undergo a structural transformation upon photoexcitation to interconvert between two or more stable forms. In some cases, the structural rearrangement involves the transition between ring-open and ring-closed forms. In this work, we develop simple guidelines for the design of organic molecules able to undergo photochemical electrocyclization, using electronic structure calculations on dithienylethene (DTE)-based compounds. We conclude that the ability to photocyclize can be predicted from the localization and symmetry of frontier molecular orbitals. These ideas are based on the Woodward-Hoffmann rules but go beyond them, allowing us to address a more general family of chromophores. Our methodology has been experimentally validated in a novel series of quinoline-based DTEs, where the ability for photocyclization depends on specific chemical modifications. We use the DTE scaffold as the workhorse model in our study; however, these simple yet powerful guidelines are expected to be generally valid to guide the design of other diarylethenes.

Metal-Induced Enhancement of Tetrel Bonding. The Case of C⋅⋅⋅X-IrIII (X=Cl, Br) Tetrel Bond Involving a Methyl Group.

In X-ray structures of the isomorphic mer-[IrX3(THT)(CNXyl)2] (X=Cl 1, Br 2; THT=tetrahydrothiophene; Xyl=2,6-Me2C6H3-) complexes, we revealed short intermolecular contacts between the C-atom of an isocyanide methyl group and halide ligands of another molecule. Geometrical consideration of the X-ray data and analysis of appropriate DFT studies allowed the attribution of these contacts to CMe⋅⋅⋅X-IrIII (X=Cl, Br) tetrel bond. Specifically, through the application of DFT calculations and various theoretical models, the presence of tetrel bonding interactions was validated, and the contribution of the CMe⋅⋅⋅X-IrIII interaction was assessed. The reinforcement of the tetrel bond upon the isocyanide coordination to iridium(III) is substantiated by molecular electrostatic potential (MEP) surface calculations. To distinguish the tetrel bonding characteristics of CMe⋅⋅⋅X-IrIII (X=Cl, Br) interactions from conventional hydrogen bonding, we employed multiple computational methodologies, including Natural Bond Orbital (NBO) analysis and Electron Localization Function (ELF) analysis. Additionally, Energy Decomposition Analysis (EDA) was applied to selected model systems to explore the underlying physical nature of these interactions.