Mindless Chemistry

Exploring the Structural and Electronic Properties of Niobium Carbide Clusters: A Density Functional Theory Study

This paper systematically investigates the structure, stability, and electronic properties of niobium carbide clusters, NbmCn (m = 5, 6; n = 1-7), using density functional theory. Nb5C2 and Nb5C6 possess higher dissociation energies and second-order difference energies, indicating that they have higher thermodynamic stability. Moreover, ab initio molecular dynamics (AIMD) simulations are used to demonstrate the thermal stability of these structures. The analysis of the density of states indicates that the molecular orbitals of NbmCn (m = 5, 6; n = 1-7) are primarily contributed by niobium atoms, with carbon atoms having a smaller contribution. The composition of the frontier molecular orbitals reveals that niobium atoms contribute approximately 73.1% to 99.8% to NbmCn clusters, while carbon atoms contribute about 0.2% to 26.9%.

Investigation of Structures, Stabilities, and Electronic and Magnetic Properties of Niobium Carbon Clusters Nb7Cn (n = 1-7)

The geometrical structures, relative stabilities, and electronic and magnetic properties of niobium carbon clusters, Nb7Cn (n = 1-7), are investigated in this study. Density functional theory (DFT) calculations, coupled with the Saunders Kick global search, are conducted to explore the structural properties of Nb7Cn (n = 1-7). The results regarding the average binding energy, second-order difference energy, dissociation energy, HOMO-LUMO gap, and chemical hardness highlight the robust stability of Nb7C3. Analysis of the density of states suggests that the molecular orbitals of Nb7Cn primarily consist of orbitals from the transition metal Nb, with minimal involvement of C atoms. Spin density and natural population analysis reveal that the total magnetic moment of Nb7Cn predominantly resides on the Nb atoms. The contribution of Nb atoms to the total magnetic moment stems mainly from the 4d orbital, followed by the 5p, 5s, and 6s orbitals.

CBe4H6: a molecular rotor with a built-in on-off switch

It is highly challenging to control (stop and resume as needed) molecular rotors because their intramolecular rotations are electronically enabled by delocalized σ bonding, and the desired control needs to be able to destroy and restore such σ bonding, which usually means difficult chemical manipulation (substitution or doping atom). In this work, we report CBe4H6, a molecular rotor that can be controlled independently of chemical manipulation. This molecule exhibited the uninterrupted free rotation of Be and H atoms around the central carbon in first-principles molecular dynamics simulations at high temperatures (600 and 1000 K), but the rotation cannot be witnessed in the simulation at room temperature (298 K). Specifically, when a C-H bond in the CBe4H6 molecule adopts the equatorial configuration at 298 K, it destroys the central delocalized σ bonding and blocks the intramolecular rotation (the rotor is turned "OFF"); when it can adopt the axial configuration at 600 and 1000 K, the central delocalized σ bonding can be restored and the intramolecular rotation can be resumed (the rotor is turned "ON"). Neutral CBe4H6 is thermodynamically favorable and electronically stable, as reflected by a wide HOMO-LUMO gap of 7.99 eV, a high vertical detachment energy of 9.79 eV, and a positive electron affinity of 0.24 eV, so it may be stable enough for the synthesis, not only in the gas phase, but also in the condensed phase.

Tetracoordinate or tricoordinate? Planar tetracoordinate nitrogen in the NBe4H4- cluster stabilized by multicenter bonds

Realization of planar tetracoordinate arrangements of nitrogen atoms is challenging because their preference for localized bonding (caused by its high electronegativity) makes them typically tricoordinate. This is especially true for the more electronegative oxygen atoms. Herein, we computationally designed two clusters NBe4H4- and OBe4H4; they contain a planar tetracoordinate nitrogen (ptN) and planar tetracoordinate oxygen (ptO) atom, respectively. Remarkably, the former is a dynamically stable global minimum, while the latter is not. The bonding analysis proves that planar tetracoordination in NBe4H4- favors over tricoordination because of the presence of multicenter delocalized bonds. In contrast, the planar tricoordination dominates due to its weak delocalized bonding ability of oxygen in the OBe4H4 cluster. Moreover, the 6σ/2π double aromaticity due to multicenter delocalized bonds allows the NBe4H4- cluster to obtain additional stability. This cluster is a promising synthetic due its dynamic and thermodynamic stability.

Breaking the Hoff/Le Bel rule by an electron-compensation strategy: the global energy minimum of NGa4S4. Phys Chem Chem Phys 2024;26:3907-3911. [PMID: 38230710 DOI: 10.1039/d3cp05290g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

In tetracoordinate chemistry, there is an attractive scientific problem of how to make the planar configuration more stable than the tetrahedral configuration. For tetracoordinate nitrogen, the abundant studies indicate that the planar tetracoordinate nitrogen (ptN) is far less stable than the tetrahedral tetracoordinate nitrogen (ttN). Herein, we introduced four S atoms to the unstable ptN-NGa4+ and stable ttN-NGa4+ by following an electron-compensation strategy. Surprisingly, ptN-NGa4S4+ is more stable than ttN-NGa4S4+. Thermodynamically, ptN-NGa4S4+ is the global energy minimum, which is 46.7 kcal mol-1 lower in energy than ttN-NGa4S4+. Dynamically, the BOMD simulations indicated that ptN-NGa4S4+ has excellent dynamic stability at 4, 298, 500 and 1000 K, but the ttN-NGa4S4+ is isomerized at 1000 K. Electronically, the HOMO-LUMO gap of ptN-NGa4S4+ (6.91 eV) is much wider than that of ttN-NGa4S4+ (5.25 eV). Moreover, AdNDP analyses showed that the eight 2c-2e Ga-S σ-bonds eliminated the 4s2 lone pair/4s2 lone pair repulsion between the four Ga atoms and provided a strong spatial protection for ptN-NGa4S4+; and that the four 3c-2e Ga-S-Ga π back-bonds could compensate electrons for Ga, weakening the electron-deficiency of Ga. Simultaneously, the double 6σ/2π aromaticity further enhanced the stability of ptN-NGa4S4+. Thus, as the dynamically stable global energy minimum displaying double aromaticity, ptN-NGa4S4+ will be more promising than ttN-NGa4S4+ in gas phase generation.

A Vision for the Future of Astrochemistry in the Interstellar Medium by 2050

By 2050, many, but not nearly all, unattributed astronomical spectral features will be conclusively linked to molecular carriers (as opposed to nearly none today in the visible and IR); amino acids will have been observed remotely beyond our solar system; the largest observatories ever constructed on the surface of the Earth or launched beyond it will be operational; high-throughput computation either from brute force or machine learning will provide unprecedented amounts of reference spectral and chemical reaction data; and the chemical fingerprints of the universe delivered by those of us who call ourselves astrochemists will provide astrophysicists with unprecedented resolution for determining how the stars evolve, planets form, and molecules that lead to life originate. Astrochemistry is a relatively young field, but with the entire universe as its playground, the discipline promises to persist as long as telescopic observations are made that require reference data and complementary chemical modeling. While the recent commissionings of the James Webb Space Telescope and Atacama Large Millimeter Array are ushering in the second "golden age" of astrochemistry (with the first being the radio telescopic boom period of the 1970s), this current period of discovery should facilitate unprecedented advances within the next 25 years. Astrochemistry forces the asking of hard questions beyond the physical conditions of our "pale blue dot", and such questions require creative solutions that are influential beyond astrophysics. By 2050, more creative solutions will have been provided, but even more will be needed to answer the continuing question of our astrochemical ignorance.

CBe2 H5 - : Unprecedented 2σ/2π Double Aromaticity and Dynamic Structural Fluxionality in a Planar Tetracoordinate Carbon Cluster

A 14-electron ternary anionic CBe2 H5 - cluster containing a planar tetracoordinate carbon (ptC) atom is designed herein. Remarkably, it can be stabilized by only two beryllium atoms with both π-acceptor/σ-donor properties and two hydrogen atoms, which means that the conversion from planar methane (transition state) to ptC species (global minimum) requires the substitution of only two hydrogen atoms. Moreover, two ligand H atoms exhibit alternate rotation, giving rise to interesting dynamic fluxionality in this cluster. The electronic structure analysis reveals the flexible bonding positions of ligand H atoms due to C-H localized bonds, highlighting the rotational fluxionality in the cluster, and two CBe2 3c-2e delocalized bonds endow its rare 2σ/2π double aromaticity. Unprecedentedly, the fluxional process exhibits a conversion in the type of bonding (σ bond↔π bond), which is an uncommon fluxional mechanism. The cluster can be seen as an attempt to apply planar hypercoordinate carbon species to molecular motors.

Planar Hexacoordinate Beryllium: Covalent Bonding Between s-block Metals

Achieving a planar hypercoordinate arrangement of s-block metals through covalent bonding with ligands is challenging due to the strong ionicity involved. Herein, we report the first case of a neutral binary global minimum containing a planar hexacoordinate beryllium atom. The central Be atom is coordinated by six active Be atoms, the latter in turn are enclosed by an equal number of more electronegative chlorine atoms in the periphery, forming a star-like phBe cluster (Be©Be6 Cl6 ). Importantly, the cluster exhibits dynamically stabilized stemming geometrically from the appropriate matching of metal-ligand size and electronically from adherence to the octet rule as well as possessing a 6σ/2π double aromaticity. Remarkably, energy decomposition analysis-natural orbitals for chemical valence (EDA-NOCV) analysis reveals a significant covalent interaction between the ligand and the central metal beryllium atoms, a fact further supported by a large Wiberg bond index. This cluster is a promising synthetic as its excellent electronic, dynamic and thermodynamic stability.

Boron-based Pd3B26 alloy cluster as a nanoscale antifriction bearing system: tubular core-shell structure, double π/σ aromaticity, and dynamic structural fluxionality

Boron-based nanoclusters show unique geometric structures, nonclassical chemical bonding, and dynamic structural fluxionality. We report here on the theoretical prediction of a binary Pd3B26 cluster, which is composed of a triangular Pd3 core and a tubular double-ring B26 unit in a coaxial fashion, as identified through global structural searches and electronic structure calculations. Molecular dynamics simulations indicate that in the core-shell alloy cluster, the B26 double-ring unit can rotate freely around its Pd3 core at room temperature and beyond. The intramolecular rotation is virtually barrier free, thus giving rise to an antifriction bearing system (or ball bearing) at the nanoscale. The dimension of the dynamic system is only 0.66 nm. Chemical bonding analysis reveals that Pd3B26 cluster possesses double 14π/14σ aromaticity, following the (4n + 2) Hückel rule. Among 54 pairs of valence electrons in the cluster, the overwhelming majority are spatially isolated from each other and situated on either the B26 tube or the Pd3 core. Only one pair of electrons are primarily responsible for chemical bonding between the tube and the core, which greatly weaken the bonding within the Pd3 core and offers structural flexibility. This is a key mechanism that effectively diminishes the intramolecular rotation barrier and facilitates dynamic structural fluxionality of the system. The current work enriches the field of nanorotors and nanomachines.

Boron-Based Inverse Sandwich V2B7- Cluster: Double π/σ Aromaticity, Metal-Metal Bonding, and Chemical Analogy to Planar Hypercoordinate Molecular Wheels

Inverse sandwich clusters composed of a monocyclic boron ring and two capping transition metal atoms are interesting alloy cluster systems, yet their chemical bonding nature has not been sufficiently elucidated to date. We report herein on the theoretical prediction of a new example of boron-based inverse sandwich alloy clusters, V₂B₇^-, through computational global-minimum structure searches and quantum chemical calculations. This alloy cluster has a heptatomic boron ring as well as a perpendicular V₂ dimer unit that penetrates through the ring. Chemical bonding analysis suggests that the inverse sandwich cluster is governed by globally delocalized 6π and 6σ frameworks, that is, double 6π/6σ aromaticity following the (4n + 2) Hückel rule. The skeleton B-B σ bonding in the cluster is shown not to be strictly Lewis-type two-center two-electron (2c-2e) σ bonds. Rather, these are quasi-Lewis-type, roof-like 4c-2e V-B₂-V σ bonds, which amount to seven in total and cover the whole surface of inverse sandwich in a truly three-dimensional manner. Theoretical evidence is revealed for a 2c-2e Lewis σ single bond within the V₂ dimer. Direct metal-metal bonding is scarce in inverse sandwich alloy clusters. The present inverse sandwich alloy cluster also offers a new type of electronic transmutation in physical chemistry, which helps establish an intriguing chemical analogy between inverse sandwich clusters and planar hypercoordinate molecular wheels.

Chemical Bonding and Dynamic Structural Fluxionality of a Boron-Based Na5B7 Sandwich Cluster

Doping alkali metals into boron clusters can effectively compensate for the intrinsic electron deficiency of boron and lead to interesting boron-based binary clusters, owing to the small electronegativity of the former elements. We report on the computational design of a three-layered sandwich cluster, Na5B7, on the basis of global-minimum (GM) searches and electronic structure calculations. It is shown that the Na5B7 cluster can be described as a charge-transfer complex: [Na4]2+[B7]3-[Na]+. In this sandwich cluster, the [B7]3- core assumes a molecular wheel in shape and features in-plane hexagonal coordination. The magic 6π/6σ double aromaticity underlies the stability of the [B7]3- molecular wheel, following the (4n + 2) Hückel rule. The tetrahedral Na4 ligand in the sandwich has a [Na4]2+ charge-state, which is the simplest example of three-dimensional aromaticity, spherical aromaticity, or superatom. Its 2σ electron counting renders σ aromaticity for the ligand. Overall, the sandwich cluster has three-fold 6π/6σ/2σ aromaticity. Molecular dynamics simulation shows that the sandwich cluster is dynamically fluxional even at room temperature, with a negligible energy barrier for intramolecular twisting between the B7 wheel and the Na4 ligand. The Na5B7 cluster offers a new example for dynamic structural fluxionality in molecular systems.

CAl4X4 (X = Te, Po): Double Aromatic Molecular Stars Containing Planar Tetracoordinate Carbon Atoms

Planar tetracoordinate carbon (ptC) species are scarce and exotic. Introducing four peripheral Te/Po auxiliary atoms is an effective strategy to flatten the tetrahedral structure of CAl₄ (T_d, ¹A₁). Neutral CAl₄X₄ (X = Te, Po) clusters possess quadrangular star structures containing perfect ptC centers. Unbiased density functional theory (DFT) searches and high-level CCSD(T) calculations suggest that these ptC species are the global minima on the potential energy surfaces. Bonding analyses indicate that 40 valence-electron (VE) is ideal for the ptC CAl₄X₄ (X = Te, Po): one delocalized π and three σ bonds for the CAl₄ core; four lone pairs (LPs) of four X atoms, eight localized Al-X σ bonds, and four delocalized Al-X-Al π bonds for the periphery. Thus, the ptC CAl₄X₄ (X = Te, Po) clusters possess the stable eight electron structures and 2π + 6σ double aromaticity. Born-Oppenheimer molecular dynamics (BOMD) simulations indicate that neutral ptC CAl₄X₄ (X = Te, Po) clusters are robust.

3-D molecular stars with covalent axial bonding

In designing three-dimensional (3-D) molecular stars, it is very difficult to enhance the molecular rigidity through forming the covalent bonds between the axial and equatorial groups because corresponding axial groups will generally break the delocalized π bond over equatorial frameworks and thus break their star-like arrangement. In this work, exemplified by designing the 3-D stars Be₂ ©Be₅ E₅ ⁺ (E = Au, Cl, Br, I) with three delocalized σ bonds and delocalized π bond over the central Be₂ ©Be₅ moiety, we propose that the desired covalent bonding can be achieved by forming the delocalized σ bond(s) and delocalized π bond(s) simultaneously between the axial groups and equatorial framework. The covalency and rigidity of axial bonding can be demonstrated by the total Wiberg bond indices of 1.46-1.65 for axial Be atoms and ultrashort Be-Be distances of 1.834-1.841 Å, respectively. Beneficial also from the σ and π double aromaticity, these mono-cationic 3-D molecular stars are dynamically viable global energy minima with well-defined electronic structures, as reflected by wide HOMO-LUMO gaps (4.68-5.06 eV) and low electron affinities (4.70-4.82 eV), so they are the promising targets in the gas phase generation, mass-separation, and spectroscopic characterization.

18-valence-electron rule lighted planar tetracoordinate carbon and nitrogen: the global energy minima of CAl4Zn and NAl4Zn. Phys Chem Chem Phys 2023;25:4211-4215. [PMID: 36655923 DOI: 10.1039/d2cp04743h]

The exploration of planar hypercoordinate carbon (phC) is challenging and significant. It is often puzzling to chemists whether the designed phC species should satisfy the 18-valence-electron rule, an authoritative rule in the phC field. In this study, we introduced a zinc atom into the extremely unstable 16-valence-electron planar tetracoordinate carbon (ptC) species CAl₄ and its isoelectronic structure NAl₄⁺ with a planar tetracoordinate nitrogen (ptN), and designed the 18-valence-electron CAl₄Zn and NAl₄Zn⁺ possessing a ptC and ptN, respectively. The thermodynamic results indicate that the ptC/N species CAl₄Zn and NAl₄Zn⁺ are the global energy minima, and also showed that the 18-valence-electron rule is more appropriate in designing ptC/N species having the CAl₄ and NAl₄⁺ skeletons, compared with the 16-valence-electron rule. Simultaneously, the BOMD simulations found that CAl₄Zn is dynamically stable. Although NAl₄Zn⁺ was isomerized at 298 and 500 K, it is dynamically viable. The excellent stability may be explained by the perfect electronic structure. First, the HOMO-LUMO gaps became much wider after the introduction of the Zn atom. Second, AdNDP analysis indicated that the introduction of the Zn atom promoted the formation of peripheral Al-Al and Al-Zn covalent bonds, providing a stable and comfortable bonding environment for ptC/N. In addition, the σ and π double aromaticity further stabilized the ptC/N species. Hence, as dynamic global energy minima display σ and π double aromaticity, the ptC/N species CAl₄Zn and NAl₄Zn⁺ are promising in gas phase generation.

Be3B11- cluster: a dynamically fluxional beryllo-borospherene

The beryllium-doped Be₃B₁₁^- cluster has two nearly isoenergetic isomers, adopting the smallest trihedral spherical geometries with a boron single-chain skeleton. The B₁₁ skeleton in the global minimum (C_2v, ¹A₁) comprises three conjoined boron rings (one B₈/two B₇) on the waist, sharing two B₃ equilateral triangles at the top and bottom, respectively. However, the local minimum (C_s, ¹A') has one deformed B₄ pyramid at the top. The drastic structural transformation of B₁₁ skeletons from perfectly planar B₁₁ clusters mainly profited from robust electrostatic interaction between Be atoms and B₁₁ skeletons. The dynamic simulations suggest that two species can interconvert via a novel mechanism, that is "triangle-pyramid-triangle", which facilitates the free migration of boron atoms in the B₁₁ skeleton, thereby showing the fascinating dynamic fluxionality. The chemical bonding analyses reveal that the B₁₁ skeleton is covered by two types of delocalized π bonds in an orthogonal direction, which leads to its spherical aromaticity.

The dodeca-coordinated La©B8C4 +/0/- molecular wheels: conflicting aromaticity versus double aromaticity

The transition-metal centered boron molecular wheels have attracted the attention of chemists. The highest deca-coordination number for central metal atoms was observed in D _10h Ta©B₁₀ ^- and Nb©B₁₀ ^- molecular wheels. Here, we report a theoretical study of La©B₈C₄ ^q (q = +1, 0, -1) clusters with the dodeca-coordinated La atom. The La©B₈C₄ ^q clusters adopt fascinating molecular wheel structures, showing a La atom enclosed by a perfect B₈C₄ monocyclic ring. The cationic La©B₈C₄ ⁺ cluster has a C _4v symmetry with the distinctly out-of-plane distortion of the La atom (0.70 Å), which is gradually flattened by the sequential reduction reaction. The distortion of the La atom from the plane in the neutral La©B₈C₄ cluster decreases to 0.46 Å. The La©B₈C₄ ^- species turns out to be perfectly planar. Chemical bonding analyses indicate that the neutral La©B₈C₄ and anionic La©B₈C₄ ^- possess 10σ and 9π/10π double aromaticity, respectively, obeying the principle of double aromaticity. However, the cationic La©B₈C₄ ⁺ has 10σ and 8π conflicting aromaticity, representing a counterexample in planar hyper-coordinated molecular wheels. The dodeca-coordination number in La©B₈C₄ ^q (q = +1, 0, -1) clusters is unprecedented, which provides a new idea and concept for searching planar hyper-coordinated systems.

Chemical bonding and dynamic structural fluxionality of a boron-based Al2B8 binary cluster: the robustness of a doubly 6π/6σ aromatic [B8]2- molecular wheel

Despite the isovalency between Al and B elements, Al-doping in boron clusters can deviate substantially from an isoelectronic substitution process. We report herein on a unique sandwich di-Al-doped boron cluster, Al₂B₈, using global structural searches and quantum chemical calculations. The cluster features a perfectly planar B₈ molecular wheel, with two isolated Al atoms symmetrically floating above and below it. The two Al atoms are offset from the center of the molecular wheel, resulting in a C _2v symmetry for the cluster. The Al₂B₈ cluster is shown to be dynamically fluxional even at far below room temperature (100 K), in which a vertical Al₂ rod slides or rotates freely within a circular rail on the B₈ plate, although there is no direct Al-Al interaction. The energy barrier for intramolecular rotation is only 0.01 kcal mol^-1 at the single-point CCSD(T) level. Chemical bonding analysis shows that the cluster is a charge-transfer complex and can be formulated as [Al]⁺[B₈]^2-[Al]⁺. The [B₈]^2- molecular wheel in sandwich cluster has magic 6π/6σ double aromaticity, which underlies the dynamic fluxionality, despite strong electrostatic interactions between the [Al]⁺, [B₈]^2-, and [Al]⁺ layers.

A plier-shaped binary molecular wheel B7Mg4+ cluster: hybrid in-plane heptacoordination, double π/σ aromaticity, and electronic transmutation

A plier-shaped charge-transfer [Mg2]2+[Mg2B7]− complex cluster exhibits double 6π/6σ aromaticity, whose hybrid molecular wheel structure is rationalized using the concept of electronic transmutation.

Ternary CE2Ba2 (E = As, Sb) Clusters: New Pentaatomic Planar Tetracoordinate Carbon Species with 18 Valence Electrons

18-valence-electron (ve) rule is one important guide for us to design planar tetracoordinate carbon (ptC) species. Using the "polarization of ligands" strategy, the new pentaatomic ptC species CE₂Ba₂ (E = As, Sb) with 18 ve are designed in this work. Computer structural searches and high-level calculations reveal that the ptC CE₂Ba₂ (E = As, Sb) species are global minima (GMs) on the potential energy surfaces, whose C center is coordinated by the interspaced E and Ba atoms. CE₂Ba₂ (E = As, Sb) are also kinetically stable. Chemical bonding analyses reveal that the ptC core is stabilized by two localized C-E σ bonds, one delocalized five-center two-electron (5c-2e) σ bond and one delocalized 5c-2e π bond. One π and three σ bonds collectively conform to the 8-electron counting, which determines the stability of ptC CE₂Ba₂ (E = As, Sb) species. Interestingly, the delocalized 2π and 2σ electrons render the ptC systems π/σ double aromaticity. Additional 10 electrons contribute to peripheral lone pairs of E and E-Ba bonding.

Binary mono-anions with unprecedented anti-aromatic planar tetracoordinate carbon and nitrogen atoms

Global minima (CBe₄^- and NBe₄^-) with planar tetracoordinate carbon and nitrogen atoms are stabilized by multicentric bonds. Their unusual anti-aromaticity is due to the strong localized Be-Be bonds preventing the full delocalization of the electrons in the CBe₄/NBe₄ skeleton. These binary mono-anions are expected to be experimentally realized in the gas phase.

Why an integrated approach between search algorithms and chemical intuition is necessary?

Though search algorithms are appropriate tools for identifying low-energy isomers, fixing several constraints seems to be a fundamental prerequisite to successfully running any structural search program. This causes some potential setbacks as far as identifying all possible isomers, close to the lowest-energy isomer, for any elemental composition. The number of explored candidates, the choice of method, basis set, and availability of CPU time needed to analyze the various initial test structures become necessary restrictions in resolving the issues of structural isomerism reasonably. While one could arrive at new structures through chemical intuition, reproducing or achieving those exact same structures requires increasing the number of variables in any given program, which causes further constraints in exploring the potential energy surface in a reasonable amount of time. Thus, it is emphasized here that an integrated approach between search algorithms and chemical intuition is necessary by taking the C₁₂O₂Mg₂ system as an example. Our initial search through the AUTOMATON program yielded 1450 different geometries. However, through chemical intuition, we found eighteen new geometries within 40.0 kcal mol^-1 at the PBE0-D3/def2-TZVP level. These results indirectly emphasize that an integrated approach between search algorithms and chemical intuition is necessary to further our knowledge in chemical space for any given elemental composition.

Structures and chemical bonding of boron-based B12O and B11Au clusters. A counterexample in boronyl chemistry

Boron oxide clusters have structural diversity and unique chemical bonding, and recent literature has shown that boronyl complexes dominate boron-rich oxide clusters. A counterexample in boronyl chemistry is presented in this work. Using global structural searches, electronic structure calculations, and chemical bonding analyses, we shall report on the computational design of two boron-based quasi-planar or planar clusters: B₁₂O and B₁₁Au. Contrary to expectation, the B₁₂O cluster has a circular quasi-planar shape with a peripheral B-O-B bridge, which resembles bare B₁₂ cluster. It does not contain a boronyl ligand. The isomeric boronyl complex turns out to be 10.32 kcal mol^-1 higher in energy at the single-point CCSD(T) level. In contrast, B₁₁Au cluster behaves normally with an elongated B₁₁ moiety and a terminal Au ligand. Chemical bonding analyses reveal three-fold π/σ aromaticity in circular B₁₂O cluster, including global 6π aromaticity, as well as spatially isolated inner 2σ aromaticity and outer 10σ aromaticity. The three-fold 6π/2σ/10σ aromaticity underlies the stability of B₁₂O cluster. This bonding picture is unknown for bare B₁₂ cluster and its derivatives. The elongated B₁₁Au cluster has conflicting π/σ aromaticity (with 6π versus 8σ electron-counting). The B₁₂O cluster is actually isoelectronic with bare B₁₂ cluster in terms of delocalized π/σ bonding, which inherits the structural and electronic robustness of the latter.

Ternary 14-electron XB2Be2 (X = Si, Ge, Sn, Pb) clusters: a planar tetracoordinate silicon (ptSi) system and its ptGe/Sn/Pb congeners

A class of ternary 14-electron clusters, XB₂Be₂ (X = Si, Ge, Sn, Pb), have been computationally predicted with a planar tetracoordinate silicon (ptSi) unit, as well as its heavier ptGe/Sn/Pb congeners. These pentaatomic ptSi/Ge/Sn/Pb species are established as global-minimum structures via computer global searches, followed by electronic structure calculations at the PBE0-D3, B3LYP-D3, and single-point CCSD(T) levels. Molecular dynamics simulations indicate that they are also kinetically stable against isomerization or decomposition. Chemical bonding analyses show that the clusters have double 2π/2σ aromaticity. The latter concept underlies the stability of ptSi/Ge/Sn/Pb clusters, overriding the 14-electron count or its variants, such as the 18-electron rule. No sp³ hybridization occurs in these species, which naturally explains why they are ptSi/Ge/Sn/Pb (rather than traditional tetrahedral) systems.

The unique sandwich K6Be2B6H6 cluster with a real borozene B6H6 core

Theoretical evidence is reported for a boron-based K₆Be₂B₆H₆ sandwich cluster, showing a perfectly D _6h B₆H₆ ring, being capped by two tetrahedral K₃Be ligands. Due to the comfortable charge transfer, the sandwich is viable in [K₃Be]³⁺[B₆H₆]^6-[BeK₃]³⁺ ionic complex in nature. The [B₆H₆]^6- core with 6π aromaticity vividly imitates the benzene (C₆H₆), occurring as a real borozene. In contrast, the tetrahedral [K₃Be]³⁺ ligand is 2σ three-dimensional aromatic, acting as the simple superatom. Thus, this complex possesses a collectively three-fold 2σ/6π/2σ aromaticity. The interlaminar interaction is governed by the robust electrostatic attraction. The unique chemical bonding gives rise to interesting dynamic fluxionality.

Planar pentacoordinate carbon in a sulphur-surrounded boron wheel: the global minimum of CB5S5. Chem Commun (Camb) 2022;58:2552-2555. [PMID: 35103735 DOI: 10.1039/d1cc07313c]

We report a σ + π double aromatic CB₅S₅⁺ cluster, the first global minimum unusually having a planar hypercoordinate carbon inside a boron wheel. Five peripheral sulfur atoms stabilize the carbon-centered boron wheel by weakening the electron deficiency of the boron atoms through strong S → B π back-bonding.

Prediction of heptagonal bipyramidal nonacoordination in highly viable [OB-M©B7O7-BO]- (M = Fe, Ru, Os) complexes

Non-spherical distributions of ligand atoms in coordination complexes are generally unfavorable due to higher repulsion than for spherical distributions. To the best of our knowledge, non-spherical heptagonal bipyramidal nonacoordination is hitherto unreported, because of extremely high repulsion among seven equatorial ligand atoms. Herein, we report the computational prediction of such nonacoordination, which is constructed by the synergetic coordination of an equatorial hepta-dentate centripetal ligand (B₇O₇) and two axial mono-dentate ligands (-BO) in the gear-like mono-anionic complexes [OB-M©B₇O₇-BO]^- (M = Fe, Ru, Os). The high repulsion among seven equatorial ligand B atoms has been compensated by the strong B-O bonding. These complexes are the dynamically stable (up to 1500 K) global energy minima with the HOMO-LUMO gaps of 7.15 to 7.42 eV and first vertical detachment energies of 6.14 to 6.66 eV (being very high for anions), suggesting their high probability for experimental realization in both gas-phase and condensed phases. The high stability stems geometrically from the surrounded outer-shell oxygen atoms and electronically from meeting the 18e rule as well as possessing the σ + π + δ triple aromaticity. Remarkably, the ligand-metal interactions are governed not by the familiar donation and backdonation interactions, but by the electrostatic interactions and electron-sharing bonding.

Six Low-Lying Isomers of C11H8 Are Unidentified in the Laboratory-A Theoretical Study

Isomers of C₁₁H₈ have been theoretically examined using density functional theory and coupled-cluster methods. The current investigation reveals that 2aH-cyclopenta[cd]indene (2), 7-ethynyl-1H-indene (6), 4-ethynyl-1H-indene (7), 6-ethynyl-1H-indene (8), 5-ethynyl-1H-indene (9), and 7bH-cyclopenta[cd]indene (10) remain elusive till date in the laboratory. The puckered low-lying isomer 2 lies at 9 kJ mol^-1 below the experimentally known molecule, cyclobuta[de]naphthalene (3), at the fc-CCSD(T)/cc-pVTZ//fc-CCSD(T)/cc-pVDZ level of theory. 2 lies at 36 kJ mol^-1 above the thermodynamically most stable and experimentally known isomer, 1H-cyclopenta[cd]indene (1), at the same level. It is identified that 1,2-H transfer from 1 yields 2H-cyclopenta[cd]indene (14) and subsequent 1,2-H shift from 14 yields 2. Appropriate transition states have been identified, and intrinsic reaction coordinate calculations have been carried out at the B3LYP/6-311+G(d,p) level of theory. Recently, 1-ethynyl-1H-indene (11) has been detected using synchrotron-based vacuum ultraviolet ionization mass spectrometry. 2-Ethynyl-1H-indene (4) and 3-ethynyl-1H-indene (5) have been synthetically characterized in the past. While the derivatives of 7bH-cyclopenta[cd]indene (10) have been isolated elsewhere, the parent compound remains unidentified till date in the laboratory. Although C₁₁H₈ is a key elemental composition of astronomical interest for the formation of polycyclic aromatic hydrocarbons in the interstellar medium, none of its low-lying isomers have been characterized by rotational spectroscopy though they are having a permanent dipole moment (μ ≠ 0). Therefore, energetic and spectroscopic properties have been computed, and the present investigation necessitates new synthetic studies on C₁₁H₈, in particular 2, 6-10, and also rotational spectroscopic studies on all low-lying isomers.

Boron-based Be2B5+/0/− alloy clusters: inverse sandwiches with pentagonal boron ring and reduction-induced structural transformation to molecular wheel structure

Boron-based Be₂B₅^+/0/− alloy clusters feature inverse sandwich versus molecular wheel structures, which sensitively depend on their charge states and show distinct π/σ aromaticity.

Nitrogen versus carbon in planar pentacoordinate environments supported by Be5Hn rings

Nitrogen is a better fit for Be₅H_n rings, both geometrically and electronically, than carbon, leading to the viable planar pentacoordinate nitrogen species.

Systematic cluster growth: a structure search method for transition metal clusters

The systematic cluster growth (SCG) method is a biased structure search strategy based on a seeding process for investigating the structural evolution and growth pattern of transition metal clusters.

Kinetic Stability of Si2C5H2 Isomer with a Planar Tetracoordinate Carbon Atom

Dissociation pathways of the global minimum geometry of Si2C5H2 with a planar tetracoordinate carbon (ptC) atom, 2,7-disilatricyclo[4.1.0.01,3]hept-2,4,6-trien-2,7-diyl (1), have been theoretically investigated using density functional theory and coupled-cluster (CC) methods. Dissociation of Si-C bond connected to the ptC atom leads to the formation of 4,7-disilabicyclo[4.1.0]hept-1(6),4(5)-dien-2-yn-7-ylidene (4) through a single transition state. Dissociation of C-C bond connected to the ptC atom leads to an intermediate with two identical transition states and leads back to 1 itself. Simultaneous breaking of both Si-C and C-C bonds leads to an acyclic transition state, which forms an acyclic product, cis-1,7-disilahept-1,2,3,5,6-pentaen-1,7-diylidene (19). Overall, two different products, four transition states, and an intermediate have been identified at the B3LYP/6-311++G(2d,2p) level of theory. Intrinsic reaction coordinate calculations have also been done at the latter level to confirm the isomerization pathways. CC calculations have been done at the CCSD(T)/cc-pVTZ level of theory for all minima. Importantly, all reaction profiles for 1 are found be endothermic in Si2C5H2. These results are in stark contrast compared to the structurally similar and isovalent lowest-energy isomer of C7H2 with a ptC atom as the overall reaction profiles there have been found to be exothermic. The activation energies for Si-C, C-C, and Si-C/C-C breaking are found to be 30.51, 64.05, and 61.85 kcal mol−1, respectively. Thus, it is emphasized here that 1 is a kinetically stable molecule. However, it remains elusive in the laboratory to date. Therefore, energetic and spectroscopic parameters have been documented here, which may be of relevance to molecular spectroscopists in identifying this key anti-van’t-Hoff-Le Bel molecule.

Anchoring a bow-shaped boron single chain in binary Be6B7- cluster: hybrid octagonal ring, multifold π/σ aromaticity, and dual electronic transmutation

Elemental boron clusters do not form linear chain or monocyclic ring structures, which is in contrast to carbon. Based on computer global searches and quantum chemical calculations, we report on the viability of a curved boron single chain in binary Be6B7- cluster. The boron motif assumes a bow shape, being anchored on a Be6 prism. Such a motif, which appears to be highly strained in its free-standing form, is exotic in boron-based clusters and nanostructures. Chemically, the cluster is analogous to a "clam-and-pearl-chain" system at the nanoscale (about 1 nm in size), in which a Be6 clam moderately opens its mouth, except that a B7 pearl chain is too large to be encapsulated inside. The picture differs from a three-layered sandwich. This cluster features a hybrid Be2B7 monocyclic ring, which is octagonal in nature and supports double 10π/6σ aromaticity. The number of π bonds substantially surpasses that in bare boron clusters of similar sizes. Two Be3 rings in the prism are also σ aromatic, albeit with effective 1σ/1σ electron-counting only. The unique multifold 1σ/10π/6σ/1σ aromaticity governs the geometry of the Be6B7- cluster, which can also be rationalized using the concept of dual electronic transmutation.

MgC6H2 Isomers: Potential Candidates for Laboratory and Radioastronomical Studies

Eighty three stationary points of MgC₆H₂ isomers spanning from 0 to 215 kcal mol^-1 have been theoretically identified using density functional theory at the B3LYP/6-311++G(2d,2p) level of theory. Among them, four low-lying isomers lying within 23.06 kcal mol^-1 (1 eV) have been further characterized in detail using high-level coupled-cluster (CC) methods. The thermodynamically most stable isomer turns out to be 1-magnesacyclohepta-4-en-2,6-diyne (1). The other three isomers, 3-magnesahepta-1,4,6-triyne (2), 1-magnesacyclohepta-2,3,4-trien-6-yne (3), and 1-magnesahepta-2,4,6-triyne (4) lie 8.24, 19.76, and 21.36 kcal mol^-1, respectively, above 1 at the ae-CCSD(T)/cc-pCVTZ level of theory. All the four isomers are polar with a permanent electric dipole moment (μ ≠ 0). Hence, they are potential candidates for rotational spectroscopic studies. Considering the recent identification of magnesium-bearing hydrocarbons such as, MgC₂H and MgC₄H in IRC+10216, it is believed that the current theoretical data may be of relevance to laboratory molecular spectroscopic and radioastronomical studies on MgC₆H₂ isomers. The energetic and spectroscopic information gathered in this study would aid the detection of low-lying MgC₆H₂ isomers in the laboratory, which are indispensable for radioastronomical studies. It is also noted here that neither the National Institute of Standards and Technology Chemistry WebBook nor the Kinetic Database for Astrochemistry lists any isomer of MgC₆H₂ at the moment. Therefore, these isomers are studied here theoretically for the very first time.

Dibridged, Monobridged, Vinylidene-Like, and Linear Structures for the Alkaline Earth Dihydrides Be2H2, Mg2H2, Ca2H2, Sr2H2, and Ba2H2. Proposals for Observations

This research reports a search for peculiar monobridged structures of the E₂H₂ molecules (E = Be, Mg, Ca, Sr, Ba). For Be₂H₂ and Mg₂H₂, the monobridged geometry is not an equilibrium but rather a transition state between the vinylidene-like structure and the global minimum HE-EH linear geometry. However, for Ca₂H₂, Sr₂H₂, and Ba₂H₂, this situation changes significantly; the linear structure is no longer the global minimum but lies higher in energy than two other equilibria, the dibridged and monobridged structures. The planar dibridged structures of both Sr₂H₂ and Ba₂H₂ should be observable via IR spectroscopy. Although the remarkable monobridged structures lie 8.3 (Sr) and 7.6 kcal/mol (Ba) higher, the large IR intensities of the terminal E-H stretching frequencies may make the monobridged structures observable. The monobridged structures have sizable permanent dipole moments (3.07 and 3.06 D for Sr and Ba, respectively) and also should be observable via microwave spectroscopy.

Planar or tetrahedral? A ternary 17-electron CBe5H4+ cluster with planar pentacoordinate carbon

A 17-electron CBe₅H₄⁺ cluster features planar pentacoordinate carbon, owing to the 2π/6σ double aromaticity. The neutral CBe₅H₄ cluster has a tetrahedral configuration despite its 18-electron counting. The latter species is governed by σ conjugation.

Influence of stepwise oxidation on the structure, stability, and properties of planar pentacoordinate carbon species CAl5. Phys Chem Chem Phys 2020;22:17062-17067. [PMID: 32568316 DOI: 10.1039/d0cp01106a]

Computational design has played an important role in planar hyper-coordinate carbon (phC) chemistry. However, none of numerous computationally predicted phC species were subsequently successfully synthesized in the condensed phase, perhaps due to the frustrating issue of oxidation. In the present work, we studied the influence of stepwise oxidation on the structure, stability, and properties of phC species using the milestone planar pentacoordinate carbon (ppC) species CAl₅⁺ as an example. Our results indicated that the ppC structure of CAl₅⁺ would be directly destroyed with one, two, or six O atom(s) per molecule present and indirectly with three or four O atoms, but maintained with five O atoms due to the ppC isomer of CAl₅O₅⁺ being a kinetically stable global energy minimum displaying σ and π double aromaticity. Moreover, the magnitudes of the first to fifth vertical oxygen affinities (VOAs) for CAl₅⁺ were determined to be very high (-85.5 to -116.3 kcal mol^-1), probably due to the existence of peripheral diffuse Al-Al bond(s). However, the sixth VOA was reduced significantly to -50.2 kcal mol^-1, consistent with the absence of any diffuse Al-Al bond in the corresponding CAl₅O₅⁺ species. So CAl₅O₅⁺ may be insensitive to oxidation. Therefore, the ppC species D_5h CAl₅O₅⁺ might be resistant to being degraded under a delicate control of oxidation level (producing five O atoms per CAl₅⁺ molecule).

Si2C5H2 isomers - search algorithms versus chemical intuition

The pros and cons of using search algorithms alone in identifying new geometries have been discussed by using the Si₂C₅H₂ elemental composition as an example. Within 30 kcal mol^-1 at the CCSD(T)/def2-TZVP//PBE0/def2-TZVP level of theory, the coalescence kick and cuckoo methods postulate merely four isomers (1, 3, 6, and 7) for Si₂C₅H₂ (O. Yañez et. al., Chem. Commun., 2017, 53, 12112). On the contrary, chemical intuition yields fourteen (2, 4, 5, and 8-18) new isomers within the same energy range at the B3LYP/6-311++G(2d,2p) level of theory. Based on the relative energies of the first eleven isomers of Si₂C₅H₂ (1, C_2v, 0.00; 2, C_s, 21.39; 3, C_s, 21.95; 4, C_s, 22.76; 5, C_s, 24.74; 6, C_s, 25.34; 7, C_s, 25.64; 8, C_s, 25.79; 9, C_s, 27.20; 10, C_2v, 28.59; and 11, C_2v, 29.16 kcal mol^-1) calculated at the CCSD(T)/cc-pVTZ level of theory, it is evident that the search algorithms had missed at least seven isomers in the same energy range. The relative energy gaps of isomers 12-18 fall in the range of 30-40 kcal mol^-1 at the latter level of theory. Consequentially, this scenario triggers a speculation going forward with search algorithms alone in the search of all new isomers. While one cannot underestimate the power of these algorithms, the role of chemical intuition may not be completely neglected. Retrospectively, the fourteen new isomers found by chemical intuition may help in writing better search algorithms. All eighteen isomers - including the most stable isomer with a planar tetracoordinate carbon atom 1- remain elusive in the laboratory to date. Thus, structural and spectroscopic parameters have been presented here, which may possibly aid the future experimental studies.

Boron-based ternary Rb6Be2B6 cluster featuring unique sandwich geometry and a naked hexagonal boron ring

Boron-based ternary Rb₆Be₂B₆ cluster features a naked hexagonal boron ring and unique “Big Mac” sandwich shape, being stabilized collectively by four-fold 2σ/6π/6σ/2σ aromaticity.

Planar tetracoordinate carbon molecules with 14 valence electrons: examples of CBe4Mnn−2 (M = Li, Au; n = 1–3) clusters

Planar tetracoordinate carbon species are viable with 14 valence electrons, which violate the 18-electron rule. Chemical bonding around the C center is governed by double 2π/6σ aromaticity.

The structure and chemical bonding in inverse sandwich B6Ca2 and B8Ca2 clusters: conflicting aromaticity vs. double aromaticity

Boron-based B₆Ca₂ and B₈Ca₂ clusters adopt unique inverse sandwich architectures, which are stabilized by interesting conflicting aromaticity and double aromaticity, respectively.

CLiAl2E and CLi2AlE (E = P, As, Sb, Bi): Planar Tetracoordinate Carbon Clusters with 16 and 14 Valence Electrons

The strategy to remove the lone pairs of ligands combined with the bonding similarity between Li and Al have been utilized to design new planar tetracoordinate carbon (ptC) species C 2v CLiAl2E and CLi2AlE based on ptC global minima CAl3E (E = P, As, Sb, Bi) clusters. The explorations of potential energy surfaces and high-level CCSD(T) calculations indicate that these planar tetracoordinate carbon (ptC) species with 16 and 14 valence electrons (ve) are the global minima except for CLiAl2P. Bonding analyses reveal that there is one π and three σ bonds between C and ligands, one delocalized σ bond between the peripheral ligands, and three/two lone pairs for CLiAl2E and CLi2AlE (E = P, As, Sb, Bi). Especially, the C=E double bonds are crucial for the stabilities of these ptC clusters. The ptC core is governed by 2π + 6σ bonding, which conforms to the 8-electron counting. Born-Oppenheimer molecular dynamics (BOMD) simulations reveal that CLiAl2E and CLi2AlE (E = P, As, Sb, Bi) clusters are robust against isomerization and decomposition. The results obtained in this work complete the series of ptC CLi n Al3-n E (E = P, As, Sb, Bi; n = 0-3) systems and 18ve, 16ve, 14ve, and 12ve counting.

Ternary 12-electron CBe3X3+ (X = H, Li, Na, Cu, Ag) clusters: planar tetracoordinate carbons and superalkali cations

Molecules with planar tetracoordinate carbons (ptCs) are exotic in chemical bonding, and they are normally designed according to the 18-electron rule. Here we report on the viability of ptC clusters with as few as 12 valence electrons, which represent the lower limit in terms of electron counting. Specifically, we have computationally designed a class of ternary 12-electron ptC clusters, CBe3X3+ (X = H, Li, Na, Cu, Ag), based on a rhombic CBe32- unit. Computer structural searches reveal that the ptC species are global minima, whose C center is coordinated in-plane by three Be atoms and a terminal X atom via robust C-Be/C-X bonding, either covalent or ionic. The other two X atoms are on the periphery and each bridge two Be atoms. Bonding analyses show that the ptC core is governed by delocalized 2π/6σ bonding, that is, double π/σ aromaticity, which collectively conforms to the 8-electron counting. Additional 4 electrons contribute to peripheral Be-X-Be and Be-Be σ bonding. The delocalized 2π/6σ frameworks appear to be universal for all ptC clusters, ranging from 18-electron down to 12-electron systems. In other words, the ptC species are dictated entirely by the 8-electron counting. Predicted vertical electron affinities of these ptC clusters range from 3.13 to 5.48 eV, indicative of superalkali or pseudoalkali cations.

Recent Progress on the Design, Characterization, and Application of Superalkalis

Superalkalis are clusters or molecules featuring lower ionization energies (IEs) than that of cesium atoms, and thus exhibit excellent reducing properties. Such special species have great potential to be used in the synthesis of unusual charge-transfer salts and cluster-assembled nanomaterials with tailored properties, in the reduction of carbon dioxide, or as hydrogen storage materials and noble-gas-trapping agents, etc. In this regard, ongoing efforts have been devoted to designing and characterizing superalkalis of new types. The recent progress on the study of superalkalis in terms of theoretical design, characterization, and potential application is summarized in this minireview. We hope this review will not only provide a broad overview of this research field, but also highlight the prospect of further extending the experimental synthesis and practical application of superalkalis.

Starting a subnanoscale tank tread: dynamic fluxionality of boron-based B10Ca alloy cluster

Alloying an elongated B₁₀ cluster with Ca is shown to give rise to a dynamically fluxional B₁₀Ca cluster, the latter behaving like a tank tread at the subnanoscale. Computer global search identifies the B₁₀Ca C ₂ (¹A) global-minimum structure, which is chiral in nature and retains the quasi-planar moiety of bare B₁₀ cluster with Ca capped at one side, forming a half-sandwich. The rotation barrier of B₁₀Ca cluster is reduced with respect to B₁₀ by one order of magnitude, down to 1 kcal mol^-1 at the PBE0/6-311+G* level, which demonstrates structural fluxionality at 600 K and beyond via molecular dynamics simulations. Structurewise, the Ca alloying in B₁₀Ca cluster generates rhombic defect holes, preactivating the species and making it flexible against deformation. Chemical bonding analyses indicate that the B₁₀Ca cluster is a charge-transfer [B₁₀]^2-[Ca]²⁺ complex, being doubly π/σ aromatic with the 6π and 10σ electron-counting. Such a pattern offers ideal π/σ delocalization and facilitates fluxionality. In contrast, bare B₁₀ cluster has conflicting aromaticity with 6π and 8σ electrons, which is nonfluxional with a barrier of 12 kcal mol^-1. Double π/σ aromaticity versus conflicting aromaticity is a key mechanism that distinguishes between fluxional B₁₀Ca and nonfluxional B₁₀ clusters, offering a compelling example that the concept of aromaticity (and double aromaticity) can be exploited to design dynamically fluxional nanosystems.

Computational design of species with ultrashort Be–Be distances using planar hexacoordinate carbon structures as the templates

Replacing the planar hexacoordinate carbon in CX₃M₃⁺ species with the Be₂ moiety leads to isoelectronic species with ultrashort Be–Be distances.

Be2B6 and Be2B7+: two double aromatic inverse sandwich complexes with spin-triplet ground state

Be₂B₆ and Be₂B₇⁺ clusters adopt interesting inverse sandwich structures with double σ/π aromaticity, and the former possesses the smallest monocyclic boron ring motif.