Adaptive Density Partitioning Research Articles

Chemical bonding analysis of excited states using the adaptive natural density partitioning method.

A novel approach to chemical bond analysis for excited states has been developed. Using an extended adaptive natural density partitioning method (AdNDP) as implemented in AdNDP 2.0 code, we obtained chemically intuitive bonding patterns for the excited states of H2O, B5+, and C2H4+ molecules. The deformation pathway in the excited states could be easily predicted based on the analysis of the chemical bond pattern. We expect that this new method of chemical bonding analysis would be very helpful for photochemistry, photoelectron spectroscopy, electron spectroscopy and other chemical applications that involved excited states.

Chemical Bonding in Transition Metal Nitride Os3N3 + Cluster: 6π Inorganic Benzene and δ2δ*1δ*1 Aromaticity.

Inorganic benzene-like clusters with a planar hexagonal ring are of interest in chemistry, as are new types of aromaticity, multifold aromaticity, and in particular δ aromaticity beyond carbon-based organic systems. Here we report on a computational study of chemical bonding in a binary Os3N3+D3h (7A2″) cluster. This transition metal nitride cluster assumes a perfectly planar, heteroatomic, hexagonal geometry. An array of quantum chemistry tools is exploited to elucidate the electronic, structural, and bonding properties of D3h Os3N3+ cluster, which include canonical molecular orbitals, adaptive natural density partitioning, natural bond orbital analysis, orbital composition calculations, and nucleus-independent chemical shifts. The computational data collectively support the bonding picture of 2-fold π/δ aromaticity: 6π electrons delocalized over all Os/N centers versus an Os-based 4δ framework in the unique δ2δ*1δ*1 configuration. The π sextet renders this heteroatomic cluster an inorganic analog of benzene. Transition metal-based inorganic benzenes are unknown in the literature, to our knowledge. The triplet 4δ electron-counting is a rare case of d-orbital aromaticity and δ-aromaticity, following the reversed 4n Hückel rule for aromaticity in a triplet system. This bonding picture is concrete, differing fundamentally from a recent study on the relevant system.

On the Nature of Bonding in Synthetic Charged Molecular Alloy [P7ZnP7]4- Cluster and Its Relevant [P7]3- Zintl Ion.

Charged molecular alloys and Zintl ions are of interest in synthetic chemistry. However, their chemical bonding has seldom been elucidated using modern quantum chemistry tools. Herein, we report on in-depth chemical bonding analyses for a charged molecular alloy C2 [P7ZnP7]4– cluster and its relevant Zintl ion C3v [P7]3– ligand, making use of electronic structure calculations at PBE0/def2-TZVP level, natural bond orbital and orbital composition analyses, canonical molecular orbitals, and adaptive natural density partitioning (AdNDP). The computational data show that C3v [P7]3– Zintl ion has three isolated, negatively charged, bridging P sites. Such charges are largely P 3p lone-pairs in nature, but they also participate in secondary P–P bonding along the bridging sites. C2 [P7ZnP7]4– cluster is formulated as [P7]2–[Zn]0[P7]2–, in which [P7]2– ligands maintain the structural and bonding integrity of [P7]3– Zintl ion despite their difference in charge state. Two [P7]2– ligands collectively bind with Zn center via four bridging P sites, resulting in a quasi-tetrahedral ZnP4 core with the eight-electron counting. This bonding picture can alternatively be rationalized using the superatom concept. The Zn–P bonds are weak with a bond order of around 0.5, because the P centers have partial nonbonding 3p character, akin to 3p2 lone-pairs albeit with a lower occupation number.

Analyzing torquoselectivity in a series of unusual ring‐opening reactions through bond reactivity indices and the adaptive natural density partitioning method

AbstractIn this study, a theoretical analysis of the torquoselectivity in a set of unusual ring‐opening reactions (R1‐R5) is presented. To describe the mechanism of the reactions, a recent methodology has been used to estimate the electrophilicities of the natural bond orbitals of the reagents and has been complemented with a second‐order perturbation theory analysis. The adaptive natural density partitioning method has also been used to verify the results and conclusions of the analysis. The concordant results of the three methodologies provide us with a better understanding of the reaction mechanism involving the torquoselectivity. We also carried out the analysis in both directions of the reaction to verify the conclusions obtained.

A Robust Distributed Big Data Clustering-based on Adaptive Density Partitioning using Apache Spark

Unsupervised machine learning and knowledge discovery from large-scale datasets have recently attracted a lot of research interest. The present paper proposes a distributed big data clustering approach-based on adaptive density estimation. The proposed method is developed-based on Apache Spark framework and tested on some of the prevalent datasets. In the first step of this algorithm, the input data is divided into partitions using a Bayesian type of Locality Sensitive Hashing (LSH). Partitioning makes the processing fully parallel and much simpler by avoiding unneeded calculations. Each of the proposed algorithm steps is completely independent of the others and no serial bottleneck exists all over the clustering procedure. Locality preservation also filters out the outliers and enhances the robustness of the proposed approach. Density is defined on the basis of Ordered Weighted Averaging (OWA) distance which makes clusters more homogenous. According to the density of each node, the local density peaks will be detected adaptively. By merging the local peaks, final cluster centers will be obtained and other data points will be a member of the cluster with the nearest center. The proposed method has been implemented and compared with similar recently published researches. Cluster validity indexes achieved from the proposed method shows its superiorities in precision and noise robustness in comparison with recent researches. Comparison with similar approaches also shows superiorities of the proposed method in scalability, high performance, and low computation cost. The proposed method is a general clustering approach and it has been used in gene expression clustering as a sample of its application.

Multicenter Bonding Effects in Oxygen Vacancy in the Bulk and on the Surface of MgO

We have studied the electronic structure of F-centers in the bulk and on the (100) surface of the MgO crystal. Chemical bonding analysis was performed using the natural bond orbital (NBO) analysis with periodic boundary conditions and the solid state adaptive natural density partitioning (SSAdNDP) method. The bonding in the pristine MgO was found to be very ionic, i.e., there are four lone pairs (s-, px-, py-, and pz-type) on every oxygen atom with the occupation numbers (ONs) in the range of 1.76–1.86 |e|. Within the O vacancy (Ov) located in the bulk of MgO we found a pair of electrons in the place of the missing oxygen atom that is revealed by SSAdNDP as a six-center two-electron (6c–2e) σ bond delocalized over six Mg atoms with ON = 1.87 |e|. In the other defected MgO system featuring the Ov on the (100) surface we also found a pair of electrons in the place of the missing oxygen atom that is revealed as a 5c–2e σ bond with ON = 1.84 |e|. Inclusion of the four closest Mg atoms of the second layer incr...

Nature of Bonding in Bowl‐Like B36 Cluster Revisited: Concentric (6π+18π) Double Aromaticity and Reason for the Preference of a Hexagonal Hole in a Central Location

The bowl-shaped C6v B36 cluster with a central hexagon hole is considered an ideal molecular model for low-dimensional boron-based nanosystems. Owing to the electron deficiency of boron, chemical bonding in the B36 cluster is intriguing, complicated, and has remained elusive despite a couple of papers in the literature. Herein, a bonding analysis is given through canonical molecular orbitals (CMOs) and adaptive natural density partitioning (AdNDP), further aided by natural bond orbital (NBO) analysis and orbital composition calculations. The concerted computational data establish the idea of concentric double π aromaticity for the B36 cluster, with inner 6π and outer 18π electron counting, which both conform to the (4n+2) Hückel rule. The updated bonding picture differs from existing knowledge of the system. A refined bonding model is also proposed for coronene, of which the B36 cluster is an inorganic analogue. It is further shown that concentric double π aromaticity in the B36 cluster is retained and spatially fixed, irrespective of the migration of the hexagonal hole; the latter process changes the system energetically. The hexagonal hole is a destabilizing factor for σ/π CMOs. The central hexagon hole affects substantially fewer CMOs, thus making the bowl-shaped C6v B36 cluster the global minimum.

Tug-of-war between classical and multicenter bonds in H-(Be)n-H species

Quantum chemical calculations were performed for beryllium homocatenated compounds [H-(Be)n-H]. Global minimum structures were found using machine searches (Coalescence Kick method) with density functional theory. Chemical bonding analysis was performed with the Adaptive Natural Density Partitioning method. It was found that H-(Be)2-H and H-(Be)3-H clusters are linear with classical two-center two-electron bonds, while for n > 3, three-dimensional structures are more stable with multicenter bonding. Thus, at n = 4, multicenter bonding wins the tug-of-war vs. the classical bonding.

Boron Nanowheels with Axles Containing Noble Gas Atoms: Viable Noble Gas Bound M©B10- Clusters (M=Nb, Ta).

The viability of noble gas axled boron nanowheels Ngn M©B10- (Ng=Ar-Rn; M=Nb, Ta; n=1, 2) is explored by ab initio computations. In the resulting Ng2 -M complexes, the Ng-M-Ng nanorod passes through the center of the B10- ring, providing them with an inverse sandwich-like structure. While in the singly Ng bound analogue, the Ng binding enthalpy Hb at 298 K ranges from 2.5 to 10.6 kcal mol-1 , in doubly Ng bound cases it becomes very low for the Ng2 M©B10- →Ng+NgM©B10- dissociation channel, except for the case of Rn, for which the corresponding Hb values are 3.4 (Nb) and 4.0 kcal mol-1 (Ta). For a given Ng, Ta has slightly higher Ng-binding ability than Nb. The corresponding free-energy changes indicate that these systems, particularly the Xe and Rn complexes, are good candidates for experimental realization in a low-temperature matrix. The Ng-M bonds were found to be covalent in nature, as reflected in their large Wiberg bond indices, formation of a 2c-2e σ orbital between Ng and M centers in natural bond orbital and adaptive natural density partitioning (AdNDP) analyses, and the short Ng-M distances. Energy decomposition analysis and a study on the natural orbitals for chemical valence show that the Ng-M contact is supported mainly by the orbital and electrostatic interactions, with almost equal contributions. Although both the Ng→M σ donation and Ng←M π backdonation play roles in the origin of orbital interaction, the former is significantly dominant over the latter. Further, AdNDP analysis indicates that the doubly aromatic character (both σ and π) in MB10- clusters is not perturbed by the interaction with Ng atoms.

Stable NCNgNSi (Ng=Kr, Xe, Rn) Compounds with Covalently Bound C-Ng-N Unit: Possible Isomerization of NCNSi through the Release of the Noble Gas Atom.

Although the noble gas (Ng) compounds with either Ng-C or Ng-N bonds have been reported in the literature, compounds containing both bonds are not known. The first set of systems having a C-Ng-N bonding unit is predicted herein through the analysis of stability and bonding in the NCNgNSi (Ng=Kr-Rn) family. While the Xe and Rn inserted analogues are thermochemically stable with respect to all dissociation channels, but for the one producing CNSiN and free Ng, NCKrNSi has another additional three-body dissociation channel, NCKrNSi→CN+Kr+NSi, which is exergonic by -9.8 kcal mol-1 at 298 K. This latter dissociation can be hindered by lowering the temperature. Moreover, the NCNgNSi→Ng+CNSiN dissociation is also kinetically prohibited by a quite high free energy barrier ranging from 25.2 to 39.3 kcal mol-1 , with a gradual increase in going from Kr to Rn. Therefore, these compounds are appropriate candidates for experimental realization. A detailed bonding analysis by employing natural bond orbital, electron density, energy decomposition, and adaptive natural density partitioning analyses indicates that both Ng-N and C-Ng bonds in the title compounds are covalent in nature. In fact, the latter analysis indicates the presence of delocalized 3c-3e σ-bond within the C-Ng-N moiety and a totally delocalized 5c-2e σ-bond in these compounds. This is an unprecedented bonding characteristic in the sense that the bonding pattern in Ng inserted compounds is generally represented as the presence of covalent bond in one side of Ng, and the ionic interaction in the other side. Further, the dissociation of Ng from NCNgNSi facilitates the formation of a higher energy isomer of NCNSi, CNSiN, which cannot be formed from bare NCNSi as such, because of the very high free energy barrier associated with the isomeric transformation. Therefore, in the presence of Ng atoms it might be possible to detect the high energy isomer.

Probing the structural and electronic properties of zirconium doped boron clusters: Zr distorted B12 ligand framework.

As an extension of boron based materials, transition-metal doped boron clusters deserve interest in controlling size-dependent structural and electronic properties. Herein, using the Crystal structure AnaLYsis by Particle Swarm Optimization (CALYPSO) method and density functional theory (DFT) calculations, we have performed a global search for the lowest-energy structures of ZrBQn (Q = 0, -1) clusters with n = 10-20. The results show that the ground-state structures of the obtained clusters feature a distinctive structural evolution pattern, from half-sandwich bowl to distorted drum-like and then to Zr-centered distorted tubular motifs. For the sake of validating the current ground-state structures, photoelectron spectra are predicted from time-dependent DFT calculations. More interestingly, the neutral and anionic ZrB12 clusters are found to possess enhanced stability in the size regime studied here. The stability of the closed shell half-sandwich ZrB12 cluster is analyzed by intrinsic bond orbital (IBO) and Adaptive Natural Density Partitioning (AdNDP) methods, which indicates that the stability mechanism is caused by the dopant Zr atom breaking the boron bowl's triangle B3 unit to form a quasi-linear B3 unit in B12 and strengthen both the interaction of the B-B σ-bonds and the Zr-B π-bonds.

A photoelectron spectroscopy and quantum chemical study on ternary Al-B-O clusters: AlnBO2- and AlnBO2 (n = 2, 3).

Both B and Al have high oxygen affinity and their oxidation processes are highly exothermic, hinting at intriguing physical chemistry in ternary Al-B-O clusters. We report a combined photoelectron spectroscopy and density-functional study on the structural, electronic, and bonding properties of AlnBO2- and AlnBO2 (n = 2, 3) clusters. Ground-state vertical detachment energies (VDEs) are measured to be 2.83 and 2.24 eV for Al2BO2- and Al3BO2-, respectively. A weak isomer is also observed for Al3BO2- with a VDE of 1.31 eV. Coalescence-kick global searches allow the identification of candidate structures, confirmed via comparisons with experiment. The Al2BO2- anion is V-shaped in geometry, Cs (1A'), with an Al center connecting to OB and OAl terminals. It can be viewed alternatively as the fusion of BOAl and AlOAl by sharing an Al atom. Al3BO2- has a Cs (2A'') global minimum in which an Al2 dimer interacts with bridging boronyl (BO) and an OAl unit, as well as a low-lying C2v (2B2) isomer consisting of boronyl and OAl that are doubly bridged by two Al atoms. The BO2 block (linear O[double bond, length as m-dash]B[double bond, length as m-dash]O chain) is nonexistent in any of the anion and neutral species. Chemical bonding in these Al-B-O clusters is elucidated via canonical molecular orbitals and adaptive natural density partitioning. The cluster structures are also rationalized using the concept of sequential and competitive oxidation of B versus Al centers in AlnB. The first O atom prefers to oxidize B and form BO, whereas the second O atom has options to interact with a fresh Al/Aln/AlnB unit or a BO group. The former route wins thermodynamically, leading to the observed geometries.

Cyanide-isocyanide isomerization: stability and bonding in noble gas inserted metal cyanides (metal = Cu, Ag, Au).

The internal isomerization, MNC ↔ MCN (M = Cu, Ag, Au), is investigated through quantum chemical computations. CuNC and AgNC are shown to be neither thermochemically nor kinetically stable against transformation to MCN. The free energy barrier (ΔG‡) for AuNC is somewhat considerable (7.1 kcal mol-1), indicating its viability, particularly at low temperature. Further, the Ng inserted analogues, MNgCN (M = Cu, Ag, Au; Ng = Xe, Rn) turn out to be thermochemically stable with respect to all possible dissociation channels but for two two-body dissociation channels, viz., MNgCN → Ng + MCN and MNgCN → Ng + MNC, which are connected to the internal isomerization processes, MNgCN → NgMCN and MNgCN → NgMNC, respectively. However, they are kinetically protected by substantial ΔG‡ values (11.8-15.4 kcal mol-1 for Cu, 9.8-13.6 kcal mol-1 for Ag, and 19.7-24.7 kcal mol-1 for Au). The pathways for such internal conversion are explored in detail. A thorough inspection of the bonding situation of the studied molecules, employing natural bond order, electron density, adaptive natural density partitioning, and energy decomposition analyses indicates that the M-Ng bonds in MNgCN and Ng-C bonds in AuNgCN can be represented as an electron-shared covalent bond. For the other Ng-C bonds, although an ionic description is better suited, the degree of covalent character is also substantial therein.

From quantum fragments to Lewis structures: electron counting in position space.

An electron counting technique that easily provides Lewis structures from real space analyses of general wavefunctions is proposed. We base our approach on reformulating the adaptive natural density partitioning (AdNDP) algorithm proposed by Zubarev and Boldyrev (Phys. Chem. Chem. Phys., 2008, 10, 5207) in position space through the use of domain-averaged cumulant densities, which take into account many-electron correlations. Averages are performed over the basins provided by the quantum theory of atoms in molecules. The decomposition gives rise to a set of n-center, two-electron orbitals which describe the dominant Lewis structures of a molecular system, and is available both for single- and multi-determinant wavefunctions. As shown through several examples, chemically intuitive Lewis descriptions are now available from fully orbital invariant position space descriptors. In this sense, real space methods are now in a position to compete with natural bond order (NBO) orbital procedures without the many biases of the latter.

Structural Stability and Evolution of Medium-Sized Tantalum-Doped Boron Clusters: A Half-Sandwich-Structured TaB12- Cluster.

Transition-metal (TM)-doped boron clusters have received considerable attention in recent years, in part, because of their remarkable size-dependent structural and electronic properties. However, the structures of medium-sized boron clusters doped with TM atoms are still not well-known because of the much increased complexity of the potential surface as well as the rapid increase in the number of low-energy isomers, which are the challenges in cluster structural searches. Here, by means of an unbiased structure search, we systematically investigated the structural evolution of medium-sized tantalum-doped boron clusters, TaBn0/- (n = 10-20). The results revealed that TaBn0/- (n = 10-15) clusters adopt half-sandwich molecular geometries, with the notable exception of TaB10-, while for n = 16-18 and 19-20, the lowest-energy clusters are characterized by drum-type geometries and tubular molecules with two B atoms on the top, respectively. Good agreement between the calculated and experimental photoelectron spectra strongly support the validity of our global minimum structures. Molecular orbital and adaptive natural density partitioning analyses indicate that the enhanced stability of half-sandwich TaB12- is due to the strong interaction of the Ta atom (5d orbitals) with surrounding B atoms (2p orbitals) and σ B-B bonds in the B12 moiety.

(Rg = He ∼ Rn, n = 1–4): In quest of the potential trapping ability of the aromatic ring

AbstractA new series of divalent boron‐rare gas cations (Rg = He ∼ Rn, n = 1–4) have been predicted theoretically at the B3LYP, MP2, and CCSD(T) levels to present the structures, stability, charge distributions, bond natures, and aromaticity. The RgB bond energies are quite large for heavy rare gases and increase with the size of the Rg atom. Because of steric hindrance new Rg atoms introduced to the B4 ring will weaken the RgB bond. Thus in the RgB bond has the largest binding energy 90–100 kcal/mol. p‐ has a slightly shorter RgB bond length and a larger bond energy than o‐ . NBO and AIM analyses indicate that for the heavy Rg atoms Ar ∼ Rn the BRg bonds have character of typical covalent bonds. The energy decomposition analysis shows that the σ‐donation from rare gases to the boron ring is the major contribution to the RgB bonding. Adaptive natural density partitioning and nuclear‐independent chemical shift analyses suggest that both and have obvious aromaticity.

Ab initio investigation of structure, spectrum, aromaticity and electronic properties of C10 carbon cluster

The predicted lower energy structures of neutral carbon cluster C10 are presented by using the particle swarm optimization method in combination with quantum chemistry calculation. Our results describe a wonderful diversity of C10 configuration with the DFT and MP2 methods. For linear and cyclic clusters, the energy of most stable monocyclic structure with D5h symmetry is lower by 1.38kcal/mol than the transition isomers with D10h symmetry at CCSD(T)/cc-pVTZ level, which is consistent with the previous theoretical results by others. All linear structures of C10 cluster have been certified as the metastable states at different calculation methods in this work. Simulated infrared spectra reveals that the extensive electron localization exists in the D10h configuration leading to the decreasing of the number of vibration modes compared with D5h configuration. The nucleus independent chemical shift (NICS) calculations indicate that planar C10 system is a stable aromatic compound and the position used to calculate the aromatic indices can be affected by the most shielding or deshielded location that we employed. The contribution of the delocalized electrons to the π-aromaticity is identical in C1a and C1b. By the adaptive natural density partitioning (AdNDP) and canonical molecular orbital (CMO) analysis, we know that the highly symmetric structures have more energy degenerate CMOs and 2 center-2 electron bond connection, and monocyclic C10 cluster is a globally doubly (σ- and π-) aromatic compound. Topological analysis and natural bond orbital (NBO) analysis show that there isn’t any electrostatic type of interactions in C10 structures, and much of negative natural valence electron configuration comes from high angular momentum orbitals. According to the electron configurations, the natural hybrid orbital is mainly composed of sp hybrid in the systems. It is worth mentioning that the competition of complicated many-body effects plays a significant role in stabilizing the distorted configuration of C10 cluster. We expect our work can provide more information for further experimental studies.

Theoretical Designs for Organoaluminum C2Al4R4 with Well-Separated Al(I) and Al(III).

It is well-known that the chemistry of aluminum is dominated by Al(III) in the +3 oxidation state. Only during the past 2 decades has the chemistry of Al(I) and Al(II) been rapidly developed. However, if Al(I) and Al(III) are combined, the inherently high reactivities of Al(I) and Al(III) mostly result in their coupling with each other or interacting with surrounding elements, which easily results in significant deactivation or quenching of the desired oxidation states, as in the case of reported mixed valent Al-compounds. In this article, we report an unprecedented type of organoaluminum system, C2Al4R4 (R = H, SiH3, Si(C6H5)3, SiiPrDis2, SiMe(SitBu3)2), whose lowest-energy structure, C2Al4R4-01, contains two Al(I) and two Al(III) atoms. The global nature and bonding motif of the parent C2Al4R4-01 (R = H) were supported by an extensive global isomeric search, CBS-QB3 energy calculations, adaptive natural density partitioning, and bond order analysis. Interestingly and in sharp contrast to most organoaluminum species, C2Al4R4-01 is associated with little multicenter bonding. C2Al4R4-01 has a high feasibility of being observed either in the gas or condensed phases (with suitable substitutents). With well-separated Al(I) and Al(III), C2Al4R4-01 (with suitable substitutents) could serve as the first Al/Al frustrated Lewis pair.

Chemical Bonding and \u03c3-Aromaticity in Charged Molecular Alloys: [Pd2As14]4\u2212 and [Au2Sb14]4\u2212 Clusters

We report a computational study on the structures and bonding of a charged molecular alloy D2h [Pd2As14]4− (1), as well as a model D2h [Au2Sb14]4− (2) cluster. Our effort makes use of an array of quantum chemistry tools: canonical molecular orbital analysis, adaptive natural density partitioning, natural bond orbital analysis, orbital composition analysis, and nucleus independent chemical shift calculations. Both clusters consist of two X7 (X = As, Sb) cages, which are interconnected via a M2 (M = Pd, Au) dumbbell, featuring two distorted square-planar MX4 units. Excluding the Pd/As or Au/Sb lone-pairs, clusters 1 and 2 are 50- and 44-electron systems, respectively, of which 32 electrons are for two-center two-electron (2c-2e) As-As or Sb-Sb σ bonds and an additional 16 electrons in 1 for 2c-2e Pd-As σ bonds. No covalent Pd-Pd or Au-Au bond is present in the systems. Cluster 1 is shown to possess two globally delocalized σ electrons, whereas 2 has two σ sextets (each associated with an AuSb4 fragment). Thus, 1 and 2 conform to the (4n + 2) Hückel rule, for n = 0 and 1, respectively, rendering them σ-aromaticity.

Ligand-Supported E3 Clusters (E=Si-Sn).

The interaction among E3 (E=Si, Ge, Sn) clusters and different ligands (L) encompassing five carbon-based donors (cyclic (alkyl)(amino)carbene (cAAC), N-heterocyclic carbene (NHC), saturated NHC (SNHC), mesoionic carbenes (MIC1, and MIC2)), two nitrogen-based donors (trimethylamine and pyridine), and two phosphorous-based donors (phosphinine and trimethylphosphine) in E3 (L)3 complexes is explored through DFT computations. Although all carbenes form very strong bonds with E3 clusters, cAAC makes the strongest bond with Si3 and Ge3 clusters, and MIC1 with the Sn3 cluster. Nevertheless, other ligand-bound complexes are also viable at room temperature. This finding indicates that experimentalists may make use of them to synthesize the desired clusters based on precursor availability. The nature of the interaction in E-L bonds is analyzed through natural bond orbital analysis; energy decomposition analysis, in combination with the natural orbital for chemical valence; and adaptive natural density partitioning analysis. The L→E σ-donation and L←E π-back-donation play important roles in making contacts between L and E3 clusters favorable; where the former is significantly more dominant over the latter.