Lone Pair Research Articles

The sulfur lone-pair⋯π interaction: The subtle dispersion features of the sulfur interactions in model complexes of disulfides with the heteroaromatic benzofuran.

A direct observation of the non-covalent interactions between sulfur lone pairs and electron-rich aromatic rings (SLP⋯π) has not been achieved in the gas phase, even though these interactions are crucial for the stability and function of biomacromolecules. Herein, we characterized the SLP⋯π interactions in the dimers of benzofuran with diethyl disulfide and dimethyl disulfide using high-resolution rotational spectroscopy and quantum chemical calculations. The observation of two isomers for each dimer confirmed the leading role of the SLP⋯π interactions, along with cooperative effects from C-H⋯π and C-H⋯O weak hydrogen bonds. The molecular structures, electronic properties, and non-covalent interactions were accurately determined using density functional theory [B3LYP-D3(BJ)] and domain-based local pair natural orbital coupled-cluster theory [DLPNO-CCSD(T)]. The determined atomic distances between sulfur and the benzofuran ring are within the range of 3.465(4)-3.621(5) Å, resembling bonding patterns commonly observed in proteins. Dispersion energy is found to play a significant role in these sulfur interactions, accounting for 67%-71% of the total attractive interactions in the dimers. This study thus offers insights into the structural and energetic properties of SLP⋯π interactions that can serve as a benchmark for future theoretical explorations and molecular design based on disulfide patterns.

Electronic Manifestations of Scandide Contraction: Theoretical Photoelectron Spectroscopy of Monovalent Group 13 Compounds.

A wide-ranging density functional theory (DFT) survey of monovalent Group 13 complexes (trielylenes) has afforded detailed insights into periodic trends in these compounds. Five classes of neutral complexes were examined, based on β-diketiminate, bis(imino)carbazolate (pincer), hydrotrispyrazolylborate, cyclopentadienide, and monocoordinate aryl ligands. Also examined was a set of N,N'-diaryl-1,4-diazabutadiene dianion-coordinated triel(I) anions. In general, the ionization potential of the Ga-based lone pairs was found to be nearly 1 eV or more higher than that of Al-based lone pairs in similar species; the corresponding IPs for In were found to hover around the values calculated for Ga. This general trend may be thought of as an electronic manifestation of scandide contraction, which results in stabilization of the 4s and 4p subshells due to poor screening by the filled 3d subshell. Only for the aryl series was this effect found to be quite muted, apparently because these complexes do not harbor a genuine metal-based lone pair. Instead, the highest occupied molecular orbital (HOMO) consists of a metal-carbon σ-antibonding orbital, spread over multiple atoms. The calculations also underscore the major role of the supporting ligand in modulating the electronic properties of trielylenes and help explain why certain species such as Al(I) bis(imino)carbazolates might not be stable enough to permit isolation.

How does the conformational landscape change on replacement in tetralin? A computational investigation with oxygen, sulfur, and selenium.

The oxygen, sulfur, and selenium derivatives of tetralin termed as isochroman (IC), isothiochroman (ITC), and isoselenochroman (ISC) showed interesting conformational patterns. In particular, ITC and IC have immense pharmacological significance. The twisted conformer is the global minimum in IC, where the bent is a transition state (TS) and remains 1100 ± 100cm-1 higher. The bent form in ITC and ISC possesses the lowest energy. But, the twisted conformer lies higher by about 80 ± 20cm-1 in ITC and 700 ± 50cm-1 in ISC. The potential energy surfaces (PES) locate all the conformations and TSs. Molecular electrostatic potentials indicate the sites of electrophilic interactions, and the small energy difference between the minima in ITC predicts an interesting interplay of intermolecular interactions in suitable environments. The validity of the maximum hardness principle and minimum electrophilicity principles is checked. Frontier molecular orbitals show the change in electron densities on excitation, which are mostly π → π* in nature. Hyperconjugative interactions involving different σ and lone pair orbitals explain the change in conformational patterns in these molecules. We suggest some experiments to corroborate our findings. Computations are performed with different functionals (B3LYP, M06-2X, and ωB97X-D) in DFT as well as ab initio methods (MP2 and CCSD) with 6-311G + + (2d, 3p) and augmented cc-pVDZ as basis sets. Gaussian 09 is used for the above computations. PED analyses were performed by Veda 4 software. For viewing and plotting purposes, Gaussview 5.0 and Origin 8.5 are used.

Interplay Between Lone Pair Stereochemical Activity and Structural Anisotropy Drives Ultralow Thermal Conductivity in Layered AGeS3 (A = Pb, Sn) Metal Sulfides.

Metal sulfides have recently drawn significant interest from the scientific community due to their nontoxicity and abundance, making them suitable for a wide range of applications, including thermoelectric and optoelectronic technologies. Although numerous ternary metal sulfides have been reported in the literature, their crystal structures and physical properties remain largely unexplored. In the present work, we have synthesized bulk polycrystalline samples of AGeS3 (A = Pb/Sn) using mechanical alloying followed by spark plasma sintering and studied their crystal structures, microstructures, and thermal and vibrational properties in relation to computational modeling. The low lattice thermal conductivity in this class of compounds is mainly attributed to the weak interlayer bonding (2D character) due to the stereochemical activity of the lone pairs of Sn2+ in SnGeS3 and Pb2+ in PbGeS3. Importantly, we examine the nature of the chemical bonds in AGeS3 and elucidate the origin of distinct thermal conductivities in these two compounds despite having similar crystal structures. We show that the enhanced stereochemical activity of Sn2+ in SnGeS3, compared to Pb2+ in PbGeS3, leads to a more distinct two-dimensional character. This is demonstrated by stronger intralayer bonding, weaker interlayer interactions, and more prominent interlayer Sn-S antibonding states near the Fermi level. Anisotropic grain growth, observed in our TEM data, further supports this interpretation. Consequently, glass-like lattice thermal conductivity is observed in SnGeS3 while PbGeS3 exhibits crystalline-like thermal conductivity. These findings enrich the fundamental knowledge of crystal chemistry and thermal conduction relationships in metal sulfides and encourage further investigations into the design of materials for thermal management applications.

Dual-Sided Multidentate Coordination Strategy Enables Record Birefringence in UV-Transparent Antimony-Based Hybrid Crystals.

Achieving ultrahigh birefringence in UV-transparent materials remains fundamentally constrained by the trade-off between strong optical anisotropy and wide bandgap transparency. Herein, we report a dual-sided multidentate coordination (DMC) strategy to construct two butterfly-shaped UV organic-inorganic hybrid crystals-(C6H4NO2)2SbF (PCSF) and (C10H6NO2)2SbF (QCSF)-in which planar π-conjugated bidentate ligands symmetrically chelate stereochemically active lone pair (SCALP) Sb3+ centers. This coordination architecture enforces coplanar alignment of optical functional units and promotes dense π-π stacking, thereby significantly enhancing macroscopic birefringence. Notably, QCSF achieves a record-high birefringence of Δn = 0.87 at 546 nm, surpassing all previously reported lone-pair-containing halide crystals with UV transparency. The exceptional optical performance is attributed to the unique [SbN2O2F] coordination geometry, near-planar molecular configuration, and extended π-electron delocalization. First-principles calculations reveal that the observed anisotropy stems from synergistic orbital coupling between the Sb centers and the π-conjugated organic ligands. This work introduces a broadly applicable molecular design paradigm for next-generation birefringent crystals that simultaneously offer high optical anisotropy and UV transparency.

Chlorobenzene sensing with transition metals decorated magnesium oxide nanostructures: a promising approach for environmental monitoring

We studied how decorating magnesium oxide (MgO) nanocages with nickel (Ni), palladium (Pd), and platinum (Pt) affects their ability to detect chlorobenzene (CB), a polluting organic compound. Using the DFT method, we examined how well these decorated structures bind to CB molecules and how close they get. The results showed that the bare MgO nanocage exhibits a HOMO of −8.49 eV and a LUMO of −0.92 eV, resulting in a wide HOMO-LUMO energy gap of 7.57 eV, which limits its chemical reactivity. To enhance the binding affinity toward CB, various adsorption sites for TM-decorated MgO were explored. Optimised configurations and vibrational frequency calculations confirm the stability of the TM-decorated systems. Pristine MgO shows weak interaction with CB (−10.2 kcal.mol−1), but TMs significantly improve stability, with Pt-MgO displaying the strongest interaction (E ads = −21.1 kcal.mol−1) and the closest contact distance of 2.43 Å. Natural bond orbital (NBO) analysis reveals minimal charge transfer between CB and the nanocages, and the interactions are particularly dependent on lone pair electrons from Cl interacting with Mg orbitals. Notably, Pt-MgO shows a significant decrease in energy gap (∼19.1%) upon CB adsorption, indicating enhanced electrical conductivity. Ni-decorated MgO might be suitable for designing and developing a different type of CB sensor design, i.e. Φ-type sensor. We also evaluated the recovery times for desorption using transition state theory in UV light, highlighting that Pt-MgO offers a favourable recovery time of 2.8 × 10−1 s. This research identifies Pt-MgO as a promising candidate for selective CB detection, demonstrating the potential of TM decoration in enhancing the reactivity of MgO nanocages. The selectivity of the Pt-MgO nanocage for CB detection was evaluated in the presence of interfering pollutants, including toluene (TL), phenol (PH), benzene (BZ), bromobenzene (BB), and fluorobenzene (FB) and it was revealed that the studied species do not significantly interfere with CB detection using the Pt-MgO nanocage.

Strain-driven lone pair electron expression for thermal transport in BiCuSeO

The stereochemical activity of lone-pair electrons critically influences lattice anharmonicity and thermal transport in crystals. However, traditional chemical substitution methods lack continuity and reversibility. We propose a strain-engineered bond angle distortion strategy in layered BiCuSeO to continuously modulate lone-pair electrons. Theoretically, tensile strain reduces the O-Bi-O bond angle, expands lone-pair electron spatial distribution, and decreases Bi-O bond charge overlap, intensifying Bi atom anharmonic vibrations. Furthermore, tensile strain induces reverse O atom vibrations and strong lattice dynamic disorder, lowering the phonon band gap and enhancing anharmonic phonon-phonon interactions and Umklapp scattering. Importantly, strain modulates lone-pair electron distribution and interaction strength without uniformly weakening long-range interatomic forces. As a result, 4% tensile strain reduces lattice thermal conductivity of BiCuSeO to 0.53 W/mK (54% decrease) at 300 K. This work establishes a multiscale framework linking strain, lone-pair electron behavior, and phonon dynamics, enabling robust and continuous control of thermal transport properties.

Four Ounces Can Move a Thousand Pounds: A Nitrogen Atom Greatly Influences Phosphorescence and Photochromism

Abstract How to precisely regulate ultralong phosphorescence and photochromism in a single molecule is a current technical challenge that needs to be solved. Herein, a simple atom‐level modification method is developed to tune both ultralong phosphorescence and photochromism of organic molecules. A series of nitrogen‐modified dinaphthylamine‐structured molecules is designed and synthesized by altering the number and position of the N atom. All these molecules demonstrate colorful ultralong phosphorescence and tunable photochromism due to the subtle structural change. The changing position of the N atom greatly influences the T1 energy level, intersystem crossing (ISC) efficiency, Singlet‐Triplet Energy Gap (ΔEST), and the electron density (Mulliken charge) of the ‐NH‐ group. The lone electron pair of ‐NH‐ will shift to the nitrogen‐modified aromatic ring due to its strengthened electron‐drawing ability. Photo‐induced generation of cation radicals is involved in the photochromic process, and these molecules show a controllable recovery rate due to the different electron density of the ‐NH‐ group. In this case, phosphorescence and photochromism are two competitive pathways for excitons. This work realizes the effect of minor modifications from the atomic level to tune the UORTP properties, as well as photochromism to a large extent.

A Spatially Separated Germylene-Carbene Compound for Site-Selective Small-Molecule Activation.

We report the synthesis and characterization of a spatially separated germylene-carbene compound (1) via a salt elimination strategy between an (amidinato)chlorogermylene and a deprotonated N-heterocyclic carbene. Compound 1 exhibits excellent site-selective reactivity, engaging in small-molecule activation at either germylene or the carbene center, depending on the nature of the reactant. Isocyanates, isothiocyanates, BH3·SMe2, and GeCl2·dioxane undergo preferential activation at the carbene site, yielding novel addition and coordination products. Reactions with two equiv of S8 and BH3·SMe2 also led to 2-fold addition products, both on germylene and on the carbene center. However, the reaction with one equivalent of mesitylazide selectively occurs on germylene instead of carbene, forming an imidogermane compound. Addition of the second equivalent of mesitylazide resulted in formation of an imidogermane-triazene compound via azide addition to carbene without N2 loss. DFT calculations reveal that HOMO and HOMO-2 are primarily associated with carbene carbon and the σ-type lone pairs on the Ge atom, respectively, separated by a small energy gap. Natural population analysis indicates a more negative charge on the carbene carbon, consistent with its higher nucleophilicity toward electrophiles. The LUMO, localized on the Ge 4p orbital, supports the observed germylene reactivity with azides through nucleophilic addition pathways.

Energetic Origins of the Hydrogen-Bond Redshift: IQA Partitioning of Normal Mode Force Constants.

The redshift of the D-H (where D represents the H donor group containing F, O, N) bond stretch normal coordinate is notable evidence of a hydrogen-bonded system. Upon the formation of the hydrogen bond, electron density is transferred from the acceptor moiety of the complex to the hydrogen atom donor, causing an elongation of the D-H bond and a reduction of the force constant. Within the orbital paradigm of chemistry, the redshift of the D-H stretch frequency is caused by the donation of electrons from the base lone pair to the antibonding, σ*, orbital of the D-H bond. The increased electron population of the antibonding orbital is, therefore, responsible for the decrease in the force constant and, consequently, for the redshift. In this work, we present a description of the H-bond redshift in terms of the electron density, substituting the molecular orbital theory interpretation with the Quantum Theory of Atoms in Molecules with the Interacting Quantum Atoms (IQA) energy decomposition scheme. The results herein suggest that the energetic origin of the redshift depends on the acid structure. When H2O acts as a H donor, the redshift is mostly determined by the intratomic and exchange-correlation, whereas the redshift of the HF stretch is caused primarily by the Coulomb contribution. The H acceptor molecule modulates the amount of variation in the above-mentioned cases. The better the acceptor, the greater the variation in the IQA contribution to the force constant.

Ho2[As4O9]: The First Ternary catena‐Oxotetraarsenate(III) of the Lanthanoids

The pale yellow holmium(III) catena‐oxotetraarsenate(III) Ho2[As4O9] crystallizes needle‐shaped from a CsBr‐flux‐assisted metallothermic reaction between As2O3 and elemental holmium at 875 °C in the monoclinic space group P21/c with the lattice parameters a = 802.98(6) pm, b = 548.83(4) pm, c = 1101.62(9) pm and β = 107.519(3)° for Z = 2. The singular Ho3+ cation is surrounded by seven oxygen atoms in the shape of a capped distorted octahedron [HoO7]11−. These polyhedra link with each other twice via edge and twice via corner to form layers described by the Niggli formula , which spread out parallel to the (100) plane. Both distinct As3+ cations form ψ1‐tetrahedral [AsO3]3− units with three oxygen atoms, which are vertex‐condensed to a catena‐oxotetraarsenate(III) anion [As4O9]6−. All [As4O9]6− groups serve as linkers between the layers, while the stereochemically active free electron pairs at the As3+ cations arrange themselves to create lone‐pair channels along the [010] direction. Furthermore, Raman‐spectroscopic investigations, which frequently show Ho3+ luminescence, and effective coordination number calculations are carried out for the new crystal structure of Ho2[As4O9].

Bonding Evolution Theory Study of the [3+2] Cycloaddition Reaction Between Benzonitrile Oxide and Ethylenic Derivatives.

Using the framework of the bonding evolution theory (BET), we investigated the molecular mechanism of the [3+2] cycloaddition reaction of benzonitrile oxide (1) with five ethylenic derivatives (2a-e). The global mechanism consists in the concerted attack of one of the O lone pairs of 1 on one of the atoms of the C-X double or triple bond of 2 (X = C, O, N), the attack of the C-X double or triple bond of 2 on the C of the C-N triple bond of 1, and the conversion of C-N triple bond of 1 into a double bond and the creation of a lone pair on N. The reaction proceeds through a one-step mechanism, the creation and modification of the electron basins occur at different places along the intrinsic reaction coordinate, as unraveled by the BET study. In the cases of dipolarophiles (2a-c), first the C-N triple bond of 1 is converted into a double bond with the creation of a lone pair on N. Then, a C-C single bond between the C-N triple bond of 1 and one of the C atoms of the C-C double or triple bond of 2 is created. Finally, the O-C single bond is formed. Concerning 2e, the meta-path follows the same reaction mechanism as 2a-c, while for the ortho-path, the formation of C-N and C-O bonds are synchronous and mediated by the N4 lone pair. A similar observation (but for the two C-O bonds) is found for 2d ortho-path while the mechanism for the meta-path is quite different to the other ones due to the formation of an O-O bond. The present work represents a new example showing how the use of BET can provide curly arrows and electron flow representation to unravel molecular mechanisms.

Differences and regulation of self-trapped luminescence in one-dimensional Pb-based and Sn-based perovskites.

One-dimensional (1D) perovskites have garnered significant interest due to their structural stability and self-trapped emission, with Sn-based and Pb-based perovskites being the primary focus. However, the reasons underlying the similarities and differences in the luminescent properties of these two types of perovskites remain unexplored in a systematic manner. Moreover, their properties can be influenced by external factors such as humidity, temperature, and illumination, which may induce subtle lattice expansions or contractions. In this study, we employ density functional theory (DFT) calculations to systematically investigate the similarities and differences in the optical properties and structural stability of 1D perovskites (C4N2H14)PbBr4 and (C4N2H14)SnBr4, as well as the effects of strain on these materials. Our results reveal that the molecular dissociation energy is higher for Pb-based perovskites than for their Sn-based counterparts, and both systems show increasing dissociation energies under greater lattice size. Under strain conditions, both the absorption and emission energies show a regular variation. This trend is more pronounced in Sn-based perovskites, whose optical characteristics are more sensitive to strain, indicating a higher degree of tunability. This enhanced sensitivity is attributed to the more active lone-pair electrons in Sn-based perovskites, inducing stronger lattice distortions and electron-phonon coupling. Furthermore, strain engineering can effectively modify the carrier mobility, optical absorption, and transition dipole moment of 1D perovskite materials, enabling improvements in both phosphor-based luminescence and electroluminescent applications.

Geometric and Electronic Structure Evolution of Gallium Hydrides: Group 13 Perspective.

This article systematically investigates the structural evolution of gallium (Ga) hydrides using a combination of density functional theory and ab initio calculations. The global minimum energy structures are determined for each cluster in the Ga2Hx (x = 0-6) and Ga3Hy (y = 0-9) series. The chemical bonding characteristics are analyzed through orbital- and electron-density-based methods, providing insights into the properties of Ga hydrides within the broader context of Group 13 hydrides. The examined Ga hydride clusters exhibit structural and electronic similarities to their aluminum (Al) counterparts, positioning them as a bridge between the lighter boron (B) hydrides and the heavier indium (In) and thallium (Tl) hydrides. While B hydrides tend to share electrons through two-center and three-center bonding, the heavier congeners often retain unpaired electrons or lone pairs and exhibit thermodynamic instability toward dehydrogenation of their saturated hydrides.

The Nature and Stability of Transition Metal-Anchored Nitrogen-Doped Graphene Single-Atom Catalysts.

Transition metal-anchored nitrogen-doped graphene single-atom catalysts represent an emerging class of catalysts that combine the advantages of homogeneous and heterogeneous catalysis. To prevent demetallation and ensure catalyst stability, sufficiently strong bonds between the transition metal and support are essential. We have quantum chemically analyzed the trend in bonding interaction between period 4 transition metals (TM = Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn) and the four-nitrogen-doped graphene support. We find that the metal-support interactions strengthen from Ti to Ni but weaken from Ni to Zn. Activation strain and Kohn-Sham molecular orbital analyses reveal that this trend stems from changes in the interaction between the metal's 3dxyatomic orbital and the nitrogen lone pair orbitals of the support. As we move along period 4, the bonding mechanism changes froman increasingly more stabilizing HOMO-LUMO interaction (TM = Ti-Ni), due to the higher effective nuclear charge of the metal, to a less favorable HOMO-SOMO (TM = Cu) and unfavorable HOMO-HOMO (TM = Zn) interaction, as a result of the filling of the metal's 3dxyatomic orbital. This results in the observed strengthening, followed by weakening, of the metal-support interaction. These insights could guide the rational design of future single-atom catalysts.

Theoretical Study on the Influence of Building Blocks in Benzotrithiophene-Based Covalent Organic Frameworks for Optoelectronic Properties

Covalent organic frameworks (COFs) have emerged as unique catalysts for photocatalysis; however, the relationship between their building block units and optoelectronic properties remains elusive. Herein, we explored the influence of building blocks on the optoelectronic properties of benzotrithiophene-based COFs (BTT-COFs) using density functional theory (DFT) and time-dependent DFT (TD-DFT) calculations. The calculation results suggested that three critical factors—the conjugated structure, planarity, and the introduction of nitrogen heteroatoms—significantly influenced charge separation and transfer within BTT-COFs. Structure–property relationships were established through several critical quantitative parameters, such as Sr, t, and CT. Among seven BTT-COFs, BTT-Tpa (Tpa: 4,4′,4″-triaminotriphenylamine) exhibited the most efficient charge separation and the highest charge transfer capability due to the electronegativity of triphenylamine, the delocalization of its lone pair electrons, and its unique star-shaped configuration. These theoretical results will provide an essential foundation for selecting donor–acceptor units in the design of novel COF materials for photocatalytic reaction applications.

Colossal Room-Temperature Magnetoelectric Coupling in Anion-Deficient Layered Perovskite Films with Ordered Cation Distribution.

The anion-deficient layered perovskite Pb2Fe2O5, featuring a polarizable active Pb cation with lone pair electrons and a magnetically active transition metal Fe cation, presents a promising candidate for multiferroic applications. Nonetheless, the exploration of multiferroic properties and magnetoelectric coupling in Pb2Fe2O5 is extremely rare due to its complex structure. Herein, a colossal magnetoelectric coupling coefficient (5.19 × 105 mV cm-1 Oe-1), high ferroelectric polarization (2 μC/cm2), and magnetic moment (25 emu/cc) at room temperature have been discovered in an epitaxial Pb2+0.48Fe2O5 film. The findings of this study demonstrate that the introduction of excessive Pb ions can disrupt the disordered arrangement of the mixed layer and convert it to an ordered distribution to improve ferroelectric properties. This research not only enriches the magnetoelectric coupling material system but also offers a viable strategy for achieving strong room-temperature magnetoelectric coupling and multiferroicity in layered oxide materials.

Unlocking Tellurium‐Centered Radicals: From Intermediates in Total Organic Syntheses to Stable Organotellurides and Catalysts

Abstract In this perspective, organotellurium compounds will be examined across three key areas: the synthesis of organic substrates bearing tellurium (Section 2), their use as carbon‐centered radical precursors (Section 3), and their role as organocatalysts (Section 4). All these areas will include the tellurium radical as an intermediate. A noteworthy property of tellurium is its so‐called chalcogen bonding (ChB) capacity, a non‐covalent interaction in which chalcogen atoms function as Lewis acid sites, interacting with atoms or groups capable of acting as Lewis bases through their lone pairs or π electrons, in a manner akin to halogen bonding. This salient property of tellurium outperforms that of its lighter sulfur and selenium counterparts and drives the use of tellurium compounds as catalysts in organic transformations and other numerous reactions.

Anisotropic chemical bonding of lanthanide-OH molecules

We present a theoretical study of the low lying adiabatic relativistic electronic states of lanthanide monohydroxide (Ln-OH) molecules near their linear equilibrium geometries. In particular, we focus on heavy, magnetic DyOH and ErOH relevant to fundamental symmetry tests. We use a restricted-active-space self-consistent field method combined with spin-orbit coupling as well as a relativistic coupled-cluster method to determine ground and excited electronic states. In addition, electric and magnetic dipole moments are computed with the self-consistent field method. Analysis of the results from both methods shows that the dominant molecular configuration of the ground state is one where an electron from the partially filled and anisotropic 4f orbital of the lanthanide atom moves to the hydroxyl group, leaving the closed outer-most lone electron pair of the lanthanide atom intact in sharp contrast to the bonding in alkaline-earth monohydroxides and YbOH, where an electron from the outer-most s shell moves to the hydroxyl group. For linear molecules the projection of the total electron angular momentum on the symmetry axis is a conserved quantity with quantum number and we study the polynomial dependence of the energies of the ground states as well as their electric and magnetic moments. We find that for both molecules lies between and , where the degenerate states with the lowest energy have and 1/2 for DyOH and ErOH, respectively. The zero field splittings among these states is approximately , where h is the Planck constant and c is the speed of light in vacuum. We find that the permanent dipole moments for both triatomics are fairly small at 0.23 atomic units and are mostly independent of . The magnetic moments are closely related to that of the corresponding atomic ion in an excited electronic state. From the polynomial dependences, we also realize that the total electron angular momentum is to good approximation conserved and has a quantum number of 15/2 for both triatomic molecules. We describe how this observation can be used to construct effective Hamiltonians containing spin–spin operators.

DFT Study of PVA Biocomposite/Oyster Shell (CaCO3) for the Removal of Heavy Metals from Wastewater

The persistent contamination of aquatic environments by heavy metals, particularly Pb2+, Cd2+, and Cu2+, poses a serious global threat due to their toxicity, persistence, and bioaccumulative behavior. In response, low-cost and eco-friendly adsorbents are being explored, among which CaCO3-based biocomposites derived from mollusk shells have shown exceptional performance. In this study, a hybrid biocomposite composed of poly(vinyl alcohol) (PVA) and oyster shell-derived CaCO3 was computationally investigated using Density Functional Theory (DFT) to elucidate the electronic and structural basis for its high metal-removal efficiency. Calculations were performed at the B3LYP/6-311++G(d,p), M05-2X/6-311+G(d,p), and M06-2X/6-311++G(d,p) levels using GAUSSIAN 16. Among them, B3LYP was identified as the most balanced in terms of accuracy and computational cost. The hybridization with CaCO3 reduced the HOMO-LUMO gap by 20% and doubled the dipole moment (7.65 Debye), increasing the composite’s polarity and reactivity. Upon chelation with metal ions, the gap further dropped to as low as 0.029 eV (Cd2+), while the dipole moment rose to 17.06 Debye (Pb2+), signaling enhanced charge separation and stronger electrostatic interactions. Electrostatic potential maps revealed high nucleophilicity at carbonate oxygens and reinforced electrophilic fields around the hydrated metal centers, correlating with the affinity trend Cu2+ > Cd2+ > Pb2+. Fukui function analysis indicated a redistribution of reactive sites, with carbonate oxygens acting as ambiphilic centers suitable for multidentate coordination. Natural Bond Orbital (NBO) analysis confirmed the presence of highly nucleophilic lone pairs and weakened bonding orbitals, enabling flexible adsorption dynamics. Furthermore, NCI/RDG analysis highlighted attractive noncovalent interactions with Cu2+ and Pb2+, while FT-IR simulations demonstrated the formation of hydrogen bonding (O–H···O=C) and Ca2+···O coordination bridges between phases.