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A theoretical study of the interaction between melamine and CO was carried out using density functional theory (DFT) with the B3LYP-D3(BJ)/aug-cc-pVTZ level of theory. The presence of anions interacting with melamine transforms the weakly bonded tetrel complexes into adducts. Thus, melamine acts as an FLP (frustrated Lewis pair) with acid groups (NHs as hydrogen bond donors) and a base group (N of the triazine ring). The application of the relative energy gradient formalism (REG) along the reaction coordinate has demonstrated that the ability of the melamine-anion systems to capture CO is linked to its capacity to polarize the CO molecule. These results have been confirmed by placing the melamine:CO complex in a uniform electric field with different strengths.

The isolated (pyridin-2-ylmethyl)triel derivatives (triel=B, Al and Ga) show an intramolecular N⋅⋅⋅Tr triel bond as shown by compounds found in the Cambridge Structural Database and DFT calculations. The possibility to use them as masked frustrated Lewis pairs (mFLP) has been explored theoretically concerning their reaction with CO2 . The adduct formation proceeds in two steps. In the first one, the (pyridin-2-ylmethyl)triel derivatives break the intramolecular N⋅⋅⋅Tr bond assisted by CO2 and in the second step the adduct is formed with Tr-O and N-C covalent bonds. The corresponding energy minima and transition states (TS) of the reaction have been characterized and analyzed. The distortion/interaction model analysis of the stationary points indicates that the whole process can be divided in two parts: reorganization of the mFLP in the first steps of the reaction while the reaction with CO2 (associated to the distortion of this molecule) is more important in the formation of the final adduct. In all cases studied, the final products are more stable than the starting molecules that combine with reasonable TS energies indicating that these reactions can occur.

A theoretical study of the reaction between several borataacenes (1-methylboratabenzene, 9-methyl-9-borataanthracene and cis and trans diboratapentacene) and CO2 has been carried out at the M06-2X computational level. The influence of a counterion (potassium cation), the cation complexation by 18-crown-6-ether and solvent effects have been explored. The computational results predict anti/syn selectivity as found experimentally in the cis- and trans-diboratapentacene reaction with CO2 (Baker et al., J. Am. Chem. Soc., 2023, 145, 2028).

The reaction of seventeen borane derivatives of five-membered N-heterocyclic rings (BNHRs) with CO has been studied by means of DFT calculations. Several non-covalent complexes between the BNHRs and CO which evolve through a TS in a single adduct for each BNHR have been identified. The calculated IRC of the TS has allowed to identify the non-covalent complex involved in the reaction in each case. The stationary points of the reactions have been analyzed with the distortion/interaction partition model. In addition, empirical models have been attempted to correlate the acid (fluoride ion affinity) and basic (proton affinity) properties of the isolated BNHR with the TS barriers and adduct energies. The energetics of the reactions are influenced by the number of nitrogen atoms in the ring.

Mössbauer and X-ray photoelectron spectroscopies (XPS) are complemented with high-level quantum-chemical computations in the study of the geometric and electronic structure of the paramagnetic salt of the metallacarborane sandwich complex [Fe(1,2-CBH)]Cs = FeSanCs. Experimental Fe isomer shifts and quadrupole splitting parameters are compared with the theoretical prediction, with good agreement. The appearance of two sets of Cs(3d) doublets in the XPS spectrum, separated by 2 eV, indicates that Cs has two different chemical environments due to ease of the Cs cation moving around the sandwich complex with low-energy barriers, as confirmed by quantum-chemical computations. Several minimum-energy geometries of the FeSanCs structure with the corresponding energies and Mössbauer parameters are discussed, in particular the atomic charges and spin population and the surroundings of the Fe atom in the complex. The Mössbauer spectra were taken at different temperatures showing the presence of a low-spin Fe atom with S = 1/2 and thus confirming a paramagnetic Fe species.

The one-to-one structural correspondence between any conjugated hydrocarbon CnHm and the borane BnHm+n is extended here to pure conjugated carbon systems. We study the closo-borane B60H60 system, isoelectronic with the Buckminsterfullerene C60, and the fluorine substituted systems B60F30H30 and B60F60, all of them with icosahedral Ih symmetry. All these systems, except B60(F30)in(H30)out, correspond to energy minima in the potential energy hypersurface. Selected electronic structure methods are used to characterize these molecules: molecular electrostatic potentials (MEP), atomic charges, bond orders, and topological properties of the electron density within the quantum theory of atoms-in-molecules (QTAIM) and electron localization function (ELF) theory. In the particular case of B60H60 we use the recently developed Hückeloid model for planar boranes. The stability of the energy minimum of the B60F60 icosahedral structure could have its origin in F···F attractive interactions of the inner fluorine atoms of the cage.

The reactivity of 5,10-disubstituted dibenzoazaborines and dibenzophosphaborines towards carbon dioxide was studied by DFT, M06-2X/def2-TZVP, computational methods. The reaction comprises three stationay points: a pre-reactive complex minima, an adduct and the TS linking both minima. The initial results show that the dibenzoazaborines derivatives are less suitable to form adducts with CO 2 than the dibenzophosphaborine ones. The influence of the basicity on the P atom and the acidity on the B of the dibenzophosphaborine towards it reaction with CO 2 has been explored. An equation has been developed that relates the properties (acidity, basicity and boron hybridization) of the isolated dibenzophosphaborine derivatives with the adduct energy. The modulation of the boron acidity allows to obtain adducts more stable than the pre-reactive complexes and isolated monomers.

The complexes formed between three molecules where the diboryl units (HBHBH) replace the CH moiety in benzene (BH, CBH, and CBH) and 10 anions (H, F, Cl, Br, OH, CCH, CH, CN, N, and CNO) have been studied using MP2 computational methods with the complete basis set (CBS) extrapolation scheme. The stability of the complexes for a given anion increases with the number of diborane units in the molecules, and these energy values are correlated with the presence of different anions and number of diborane units. The electron density of the complexes has been characterized and analyzed using the quantum theory of atoms in molecules (QTAIM) and electron density shift (EDS) models.

Malignancies such as lung, breast and pancreatic carcinomas are associated with increased expression of the epidermal growth factor receptor, EGFR, and its role in the pathogenesis and progression of tumors has made this receptor a prime target in the development of antitumor therapies. In therapies targeting EGFR, the development of resistance owing to mutations and single nucleotide polymorphisms, and the expression of the receptor ligands themselves are very serious issues. In this work, both the ligand neuregulin and a bispecific antibody fragment to EGFR are conjugated separately or together to the same drug-delivery system to find the most promising candidate. Camptothecin is used as a model chemotherapeutic drug and superparamagnetic iron oxide nanoparticles as a delivery system. Results show that the lowest LD50 is achieved by formulations conjugated to both the antibody and the ligand, demonstrating a synergy. Additionally, the ligand location in the nucleus favors the antitumor activity of Camptothecin. The high loading capacity and efficiency convert these systems into a good alternative for administering Camptothecin, a drug whose use is otherwise severely limited by its chemical instability and poor solubility. Our choice of targeting agents allows treating tumors that express ErbB2 (Her2+ tumors) as well as Her2- tumors expressing EGFR.

By following the intrinsic reaction coordinate connecting transition states with energy minima on the potential energy surface, we have determined the reaction steps connecting three-dimensional hexaborane(12) with unknown planar two-dimensional hexaborane(12). In an effort to predict the potential synthesis of finite planar borane molecules, we found that the reaction limiting factor stems from the breaking of the central boron-boron bond perpendicular to the C2 axis of rotation in three-dimensional hexaborane(12).

The gas phase acidities (GA) of 5,5-alkylbarbituric acids have been experimentally determined by electrospray ionization-triple quadrupole (ESI-TQ) mass spectrometry and by using the extended kinetic Cooks method (EKCM). The GAs of C-H (1330.9 ± 10.0 kJ mol-1) and N-H (1361.5 ± 10.5 kJ mol-1) deprotonated sites of bifunctional barbituric acid were determined from the selective production of their corresponding heterodimers. The GA value in the N-H site was confirmed by measuring the GAs of 5,5-dimethyl- and 5,5-diethyl barbituric acids (∼1368 kJ mol-1). The experimental results have been rationalized and discussed with the support of quantum chemical calculations with Gaussian-n (G3 and G4) composite methods, which confirmed the excellent consistency of the results.

High-level quantum-chemical computations (G4MP2) are carried out in the study of complexes featuring tetrel bonding between the carbon atom in the carbenoid CBH-obtained by hydride removal in the C-H bond of the known closo-monocarbadodecaborate anion CBH (-) and acting as Lewis acid (LA)-and Lewis bases (LB) of different type; the electron donor groups in the tetrel bond feature carbon, nitrogen, oxygen, fluorine, silicon, phosphorus, sulfur, and chlorine atomic centres in neutral molecules as well as anions H, OH, and F. The empty radial 2pr vacant orbital on the carbon centre in CBH, which corresponds to the LUMO, acts as a Lewis acid or electron attractor, as shown by the molecular electrostatic potential (MEP) and electron localization function (ELF). The thermochemistry and topological analysis of the complexes {CBH:LB} are comprehensively analysed and classified according to shared or closed-shell interactions. ELF analysis shows that the tetrel C…X bond ranges from very polarised bonds, as in H11B11C:F to very weak interactions as in HBC…FH and HBC…O=C=O.

In order to explore the angular strain role on the ability of Be to form strong beryllium bonds, a theoretical study of the complexes of four beryllium derivatives of orthocloso-carboranes with eight molecules (CO, N2, NCH, CNH, OH2, SH2, NH3, and PH3) acting as Lewis bases has been carried out at the G4 computational level. The results for these complexes, which contain besides Be other electron-deficient elements, such as B, have been compared with the analogous ones formed by three beryllium salts (BeCl2, CO3Be and SO4Be) with the same set of Lewis bases. The results show the presence of large and positive values of the electrostatic potential associated to the beryllium atoms in the isolated four beryllium derivatives of ortho-carboranes, evidencing an intrinsically strong acidic nature. In addition, the LUMO orbital in these systems is also associated to the beryllium atom. These features led to short intermolecular distances and large dissociation energies in the complexes of the beryllium derivatives of ortho-carboranes with the Lewis bases. Notably, as a consequence of the special framework provided by the ortho-carboranes, some of these dissociation energies are larger than the corresponding beryllium bonds in the already strongly bound SO4Be complexes, in particular for N2 and CO bases. The localized molecular orbital energy decomposition analysis (LMOEDA) shows that among the attractive terms associated with the dissociation energy, the electrostatic term is the most important one, except for the complexes with the two previously mentioned weakest bases (N2 and CO), where the polarization term dominates. Hence, these results contribute to further confirm the importance of bending on the beryllium environment leading to strong interactions through the formation of beryllium bonds.

Diborane has long been realized to be analogous to ethylene in terms of its bonding MOs, both as to symmetries and splitting patterns. This naturally suggests an investigation to see whether other similar conjugated hydrocarbons manifest a similar boron-substituted and H supplemented borane. That is, for a conjugated hydrocarbon structure with a neighbor-paired resonance pattern, we propose to look at boranes where each carbon atom is replaced by a boron atom, and an H-atom pair is added to each double bond of the resonance structure, with one H above the molecular plane and one below. This construction of concatenated diboranes is uniformly different than that for the previously known stable boranes of 4 or more B atoms. We find from quantum-chemical computations that our so constructed polyboranes are stable. All this suggests a possible novel new chapter in borane chemistry – a chapter with some promise of understandings related to that for (alternant) conjugated hydrocarbons.

The recently proved one-to-one structural equivalence between a conjugated hydrocarbon CnHm and the corresponding borane BnHm+n is applied here to hybrid systems, where each C=C double bond in the hydrocarbon is consecutively substituted by planar B(H2)B moieties from diborane(6). Quantum chemical computations with the B3LYP/cc-pVTZ method show that the structural equivalences are maintained along the substitutions, even for non-planar systems. We use as benchmark aromatic and antiaromatic (poly)cyclic conjugated hydrocarbons: cyclobutadiene, benzene, cyclooctatetraene, pentalene, benzocyclobutadiene, naphthalene and azulene. The transformation of these conjugated hydrocarbons to the corresponding boranes is analyzed from the viewpoint of geometry and electronic structure.

By means of the isolobality concept between a hydrogen atom and the radical dianion [BH ] derived from an extraction of a hydrogen atom in the dianion [BH], forming part of the K(BH) structure, we rationalize the 3D boron skeleton architecture in the solids CaB and KB. The above statement is supported by electronic structure computations based on the Electron Localisation Function (ELF) in the dianion [BH] and radical anion [BH ]. Valence-Bond (VB) theory is also used in the study of the B–B sigma bond connecting the octahedra in the CaB structure, with the model dimer [(HB)B–B(BH)]. Quantum-chemical geometry optimizations of clusters extracted from the CaB solid structure show the analogies between molecular chemistry and solid-state chemistry: In the same way as benzene is the building block of graphene and graphite, the anion [BH] is the building block of CaB provided every hydrogen atom in [BH] is connected to a further [(B)] octahedron in the three directions of the 3D space, and every void at the Ca positions is embedded with two electrons.

A theoretical study of the hydrogen bond (HB) and halogen bond (XB) complexes between 1-halo-closo-carboranes and hydrogen cyanide (NCH) as HB and XB probe has been carried out at the MP2 computational level. The energy results show that the HB complexes are more stable than the XBs for the same system, with the exception of the isoenergetic iodine derivatives. The analysis of the electron density with the quantum theory of atoms in molecules (QTAIM) shows the presence of a unique intermolecular bond critical point with the typical features of weak noncovalent interactions (small values of the electron density and positive Laplacian and total energy density). The natural energy decomposition analysis (NEDA) of the complexes shows that the HB and XB complexes are dominated by the charge-transfer and polarization terms, respectively. The work has been complemented with a search in the CSD database of analogous complexes and the comparison of the results, with those of the 1-halobenzene:NCH complexes showing smaller binding energies and larger intermolecular distances as compared to the 1-halo-closo-carboranes:NCH complexes

In this work, we study the interactions between adamantane-like structures B4X6 with X = {CH2, NH, O ; SiH2, PH, S} and dihydrogen molecules above the Boron atom, with ab initio methods based on perturbation theory (MP2/aug-cc-pVDZ). Molecular electrostatic potentials (MESP) for optimized B4X6 systems, optimized geometries, and binding energies are reported for all B4X6:nH2 (n = 1–4) complexes. All B4X6:nH2 (n = 1–4) complexes show attractive patterns, with B4O6:nH2 systems showing remarkable behavior with larger binding energies and smaller B···H2 distances as compared to the other structures with different X

We present a detailed computational analysis of a newly proposed family of Co(II) single-ion complexes with large magnetic anisotropy. Starting from previously proposed structures based on oxy- and thio-bridged 1,2-dicarba-closo-dodecaborane and 1,2-dicarba-closo-hexaborane, we explore the substitution of O and S bridging atoms by Se and Te atoms. Our calculations, based on CASSCF/NEVPT2 methods, show that these substitutions also lead to some large magnetic anisotropy complexes. Particularly, one of the proposed single-ion Se-bridged Co(II) chelated by 1,2-dicarba-closo-dodecaborane has a calculated anisotropy parameter D=-144 cm, and a single-ion Se-bridged Co(II) chelated by 1,2-dicarba-closo-hexaborane gives a calculated D=-133 cm. These large D values can be attributed in part to geometric distortion from T symmetry at the Co(II) ion caused by the ligand structure, and in part to the electric effect of the Se atoms. Our results suggest that this strategy could be a feasible alternative to increase the magnetic anisotropy of single-ion transition metal complexes.

In this work we present a computational analysis of a new family of magnetic Co(II) single-ion complexes with large magnetic anisotropy based on icosahedral and octahedral carborane ligands. In particular, we extend our previous computational work on mononuclear Co(II) complexes with 1,2-(HS)2-1,2-C2B10H10 and 9,12-(HS)2-1,2-C2B10H10 icosahedral o-carborane ligands to a larger set of complexes where the Co(II) ion is doubly chelated by those ligands and by other two positional isomers belonging to the 1,2-dicarba-closo-dodecaborane family. We also describe Co(II) complexes with octahedral ligands derived from 1,2-dicarba-closo-hexaborane and study the effects of replacing a thiol group by a hydroxy group in both polyhedral geometries, as well as the influence of the position of the carbon atoms. On analysis of the results for a total of 20 complexes, our results show that carborane-based Co(II) single-ion compounds present a distorted-tetrahedral geometry, high-spin ground states, and high values for the magnetic anisotropy parameters. We point out which of these would be suitable candidates to be synthesized and used as molecular magnets.

Photoswitchable molecules have attracted wide interest for many applications in chemistry, physics, and materials science. In this work, we revisit the reversible photochemical and thermal rearrangements of the two BH isomers reported by Hawthorne and Pilling in 1966, whose mechanism had not been understood so far. We investigate the rearrangements by means of a joint experimental and computational study with the outcome that BH represents the first boron-based photochromic system ever reported. Both photochemical and thermal isomerizations occur through the same intermediate and involve a diamond-square-diamond (DSD) mechanism. Given the absence within boron chemistry of named chemical reactions as opposed to organic chemistry, we propose to label the BH photo- A nd thermal isomerization processes as the Hawthorne rearrangement.

We study the effect of introducing Heq = {0, + 1, + 2}, into icosahedral molecules—XZH , with X = {C, Si}, Z = {B, Al} and n = {0, 1}—to see the effect of charge and spin on the stability and potential existence for these endohedral complexes. For q = 0 and q = +1, all endohedral systems correspond to energy minima with the He atom/ion remaining inside the cage. However, when the charge of the He ion is q = +2, the He atom/ion is ejected from the He@BH and He@CBH cages, but this is not the case for the AlH and SiAlH cages, which retain what is nominally the He ion inside. These results could be helpful for designing quantum bits with atoms encapsulated inside heteroatomic molecular icosahedral cages since the s, p and d atomic levels do not split under an icosahedral field.

Progress in the field of biocompatible SERS nanoparticles has promising prospects for biomedical applications. In this work, we have developed a biocompatible Raman probe by combining anisotropic silver nanoparticles with the dye rhodamine 6G followed by subsequent coating with bovine serum albumin. This nanosystem presents strong SERS capabilities in the near infrared (NIR) with a very high (2.7 × 107) analytical enhancement factor. Theoretical calculations reveal the effects of the electromagnetic and chemical mechanisms in the observed SERS effect for this nanosystem. Finite element method (FEM) calculations showed a considerable near field enhancement in NIR. Using density functional quantum chemical calculations, the chemical enhancement mechanism of rhodamine 6G by interaction with the nanoparticles was probed, allowing us to calculate spectra that closely reproduce the experimental results. The nanosystem was tested in cell culture experiments, showing cell internalization and also proving to be completely biocompatible, as no cell death was observed. Using a NIR laser, SERS signals could be detected even from inside cells, proving the applicability of this nanosystem as a biocompatible SERS probe.

This work encompasses a comprehensive study of host···guest interactions between cyclic trimer metal‐carborane [Au3(1,2‐C2B10H10)3]3−, and several guest species as cations (H+, Li+, Be2+, Hg2+), anions (F−, H−, Cl−, Br−, I−, HCC−), and neutral molecules (H2, CO2, I2, HCCH, N2). A computational study has been carried out in order to evaluate energetic profiles and determine the contribution for attractive or repulsive interactions between guest and host. Several cases call our attention as a function of the energy minima. For instance, all above cations form stable minima as guest complexes with the three gold atoms of the host. Unexpectedly, pyramidal H− or F− species are obtained as energy minima, while other anions give completely repulsive interactions. Finally, the CO2 molecule is also trapped inside the trinuclear ring.

Anthropogenic mercury (Hg(0)) emissions oxidize to gaseous Hg(II) compounds, before deposition to Earth surface ecosystems. Atmospheric reduction of Hg(II) competes with deposition, thereby modifying the magnitude and pattern of Hg deposition. Global Hg models have postulated that Hg(II) reduction in the atmosphere occurs through aqueous-phase photoreduction that may take place in clouds. Here we report that experimental rainfall Hg(II) photoreduction rates are much slower than modelled rates. We compute absorption cross sections of Hg(II) compounds and show that fast gas-phase Hg(II) photolysis can dominate atmospheric mercury reduction and lead to a substantial increase in the modelled, global atmospheric Hg lifetime by a factor two. Models with Hg(II) photolysis show enhanced Hg(0) deposition to land, which may prolong recovery of aquatic ecosystems long after Hg emissions are lowered, due to the longer residence time of Hg in soils compared with the ocean. Fast Hg(II) photolysis substantially changes atmospheric Hg dynamics and requires further assessment at regional and local scales.

By means of MP2 and DFT computations we predict gas-phase acidities and liquid-phase (MeCN) acidities of (di)carboxylic acids derived from icosahedral ortho, meta, and para-carboranes. For comparative purpose, we include the benzoic and phthalic acids. Substitution of benzene by a carborane cage – cage effect – strikingly increases the gas-phase acidity (lower GA) for the (di)carboxylic acids, being the ortho isomers always the most acidic, following the order ortho ≫ meta > para. The computed GA of the dicarboxylic acid derived from ortho-carborane is far lower than sulphuric acid, due to an enhanced stabilization of the carboxylate through an intramolecular OHO bridge connection, also taking place in phthalic acid. The change of GA relative to ortho, meta and para positions of the carboxylic groups - isomer effect - is larger for carboranes. As regards to liquid-phase (MeCN), the computations show that carborane (di)carboxylic acids also show a larger acidity (lower pK) as compared to the phthalic acids and that the dicarboxylic ortho-carborane is also a superacid in the liquid phase (MeCN), due to the OHO bridge connection in the carboxylate, as in the gas phase. Additional computations show how much of this isomeric effect is to be attributed to the electronic delocalization.

Silver nanoparticles offer a huge potential for biomedical applications owing to their exceptional properties and small size. Specifically, cysteamine-capped silver nanoparticles could form the basis for new anticancer therapies combining the cytotoxic effect of the silver core with the inherent antitumor activity of cysteamine, which inhibit cancer cell proliferation and suppress invasion and metastasis. In addition, the capability of the cysteamine coating monolayer to couple a variety of active principles and targeting (bio)molecules of interest proves key to the tailoring of this platform in order to exploit the pathophysiology of specific tumor types. Nevertheless, the chain length and conformational flexibility of cysteamine, together with its ability to attach to the surface of silver nanoparticles via both the thiol and the amine group, have made the in situ synthesis of these particles an especially challenging task. Herein we report a solvent-assisted in situ synthesis method that solves this problem. The obtained nanoparticles have been fully characterized by UV–visible absorption spectroscopy, Fourier transform infrared spectroscopy, transmission electron microscopy, electron diffraction measurement, high resolution transmission electron microscopy, scanning transmission electron microscopy, energy dispersive x-ray spectroscopy nanoanalysis, and dynamic light scattering measurement. Our synthesis method achieves extremely high yield and surface coating ratio, and colloidal stability over a wide range of pH values including physiological pH. Additionally, we have demonstrated that cysteamine-capped nanoparticles obtained by this method can be conjugated to an antibody for active targeting of the epidermal growth factor receptor, which plays an important role in the pathogenesis and progression of a wide variety of tumors, and induce cell death in human squamous carcinoma cells. We believe this method can be readily extended to combinations of noble metals

BH(NCH) is a rare example of two conjoined boron hydride subclusters of nido and arachno geometrical character. At room temperature, solutions of BH(NCH) emit a 690 nm fluorescence. In the solid state, this emission is shifted to 620 nm and intensifies due to restriction of the rotation of the pyridine ligands. In addition, there is a thermochromicity to the fluorescence of BH(NCH). Cooling to 8 K engenders a further shift in the emission wavelength to 585 nm and a twofold increase in intensity. Immobilization in a polystyrene thin-film matrix results in an efficient absorption of pumping excitation energy at 414 nm and a 609 nm photostable fluorescence. Such fluorescence from polystyrene thin films containing BH(NCH) can also be stimulated by emission from the highly fluorescent borane anti-BH via energy transfer mechanisms. Polystyrene thin-film membranes doped with 1:1 mixtures of anti-BH and BH(NCH) thus emit a 609 nm fluorescence and absorb light across more than 300 nm (250–550 nm); this is a significant spectral coverage possibly useful for luminescent solar concentrators. BH(NCH) is fully structurally characterized using NMR spectroscopy, mass spectrometry, and single-crystal X-ray diffraction analysis, and its ground-state and excited-state photophysics are investigated with UV–vis spectroscopy and quantum-chemistry computational methods.

This work extends the previously reported studies (Oliva et al. in Theor Chem Acc 132:1329, 2013, Theor Chem Acc 134:9, 2015) on electronic structures of simple polyhedral polyradicals constructed from s = ¿ closo-carborane CBH structural units. Linear polyradical structures obtained from these units connected by means of –CH– bridges are described in terms of their energies and local spins. The resulting spin states of these chains have been mapped onto a phenomenological Heisenberg spin Hamiltonian, providing the evaluation of spin exchange coupling constants and performing an analysis of their transferability. The eigenvalues of this Hamiltonian allow one to determine the ground spin state and the suitable combinations of spin orientations of the magnetic sites. We prove that the minimal energy in all these systems corresponds to the highest-spin state.

While geometries of 12- and 13-vertex dicarbaborane (carborane) radicals with rare 2n+3 skeletal electrons (SEs) have been determined elsewhere, the geometries of the 11-vertex dicarbaborane monoanion radicals with 2n+3 SEs are established here for the first time by computations in agreement with observed electrochemical and electron paramagnetic resonance (EPR) spectroscopy data.