Double Aromaticity in Monocyclic Carbon, Boron, and Borocarbon Rings Based on Magnetic Criteria

Silyliumylidene Ion Stabilized by Two σ-Donating Ni(0)- and Pd(0)-Fragments

A silyliumylidene ion 2 stabilized by two σ-donating Ni(0)- and Pd(0)-fragments was successfully synthesized. Due to the σ-donation of M→Si interactions, 2 presents a pyramidalized cationic silicon center with a localized lone pair. The additional coordination of basic Pd(0) fragment to the mono-Ni(0)-stabilized silyliumylidene 1 results in a higher HOMO level and an unchanged HOMO-LUMO gap and thus, 2 remains highly reactive. Interestingly, the coordination mode at the Si center is closely related to the nature of M-ligands. Indeed, the donor/donor-stabilized silyliumylidene ion 2 has been transformed into a donor/acceptor-stabilized ion 13, featuring a trigonal planar Si center with a vacant orbital, just via a ligand exchange reaction from PCy3/NHC toward PMe3.

Exploring the Use of "Honorary Transition Metals" To Push the Boundaries of Planar Hypercoordinate Alkaline-Earth Metals

The quest for planar hypercoordinate atoms (phA) beyond six has predominantly focused on transition metals, with dodecacoordination being the highest reported thus far. Extending this bonding scenario to main-group elements, which typically lack d orbitals despite their larger atomic radius, has posed significant challenges. Intrigued by the potentiality of covalent bonding formation using the d orbitals of the heavier alkaline-earth metals (Ae = Ca, Sr, Ba), the so-called "honorary transition metals", we aim to push the boundaries of planar hypercoordination. By including rings formed by 12-15 atoms of boron-carbon and Ae centers, we propose a design scheme of 180 candidates with a phA. Further systematic screening, structural examination, and stability assessments identified 10 potential clusters with a planar hypercoordinate alkaline-earth metal (phAe) as the lowest-energy form. These unconventional structures embody planar dodeca-, trideca-, tetradeca-, and pentadecacoordinate atoms. Chemical bonding analyses reveal the important role of Ae d orbitals in facilitating covalent interactions between the central Ae atom and the surrounding boron-carbon rings, thereby establishing a new record for coordination numbers in the two-dimensional realm.

Neural network atomistic potentials for global energy minima search in carbon clusters

The global energy optimization problem is an acute and important problem in chemistry. It is crucial to know the geometry of the lowest energy isomer (global minimum, GM) of a given compound for the evaluation of its chemical and physical properties. This problem is especially relevant for atomic clusters. Due to the exponential growth of the number of local minima geometries with the increase of the number of atoms in the cluster, it is important to find a computationally efficient and reliable method to navigate the energy landscape and locate a true global minima structure. Newly developed neural network (NN) atomistic potentials offer a numerically efficient and relatively accurate approach for molecular structure optimization. An important question that needs to be answered is "Can NN potentials, trained on a given set, represent the potential energy surface (PES) of a neighboring domain?". In this work, we tested the applicability of ANI-1ccx and ANI-nr NN atomistic potentials for the global minima optimization of carbon clusters Cn (n = 3-10). We showed that with the introduction of the cluster connectivity restriction and consequent DFT or ab initio calculations, ANI-1ccx and ANI-nr can be considered as robust PES pre-samplers that can capture the GM structure even for large clusters such as C20.

Magnetic Aromaticity of Cycloporphyrin Nanorings

The ascertainment of magnetic aromaticity is not necessarily straightforward, especially for large and bent systems, such as the cycloporphyrin nanorings recently synthesized by the group of Anderson. Six of these cycloporphyrin nanorings were studied here computationally. Indirect methods, based on nuclear shielding and magnetizabilities, and direct methods, based on standard quantum mechanics, were both used effectively to determine their magnetically induced current strength, which mostly confirmed Anderson’s classification. However, in the case of hexanions, and in particular for cyclohexaporphyrin hexacations, a significant cancellation of delocalized diatropic and paratropic flow occurred, showing that the resultant faint aromatic character was a result of competing aromatic and antiaromatic contributions, as also evidenced by the ipsocentric method. A warning is renewed on the use of isotropic shielding to determine the tropicity of the magnetically induced current.

Isolation and Reactivity of an Antiaromatic s-Block Metal Compound

The concepts of aromaticity and antiaromaticity have a long history, and countless demonstrations of these phenomena have been made with molecules based on elements from the p, d, and f blocks of the periodic table. In contrast, the limited oxidation-state flexibility of the s-block metals has long stood in the way of their participation in sophisticated π-bonding arrangements, and truly antiaromatic systems containing s-block metals are altogether absent or remain poorly defined. Using spectroscopic, structural, and computational techniques, we present herein the synthesis and authentication of a heterocyclic compound containing the alkaline earth metal beryllium that exhibits significant antiaromaticity, and detail its chemical reduction and Lewis-base-coordination chemistry.

Aromaticity of Even-Number Cyclo[n]carbons (n = 6-100)

The recently synthesized cyclo[18]carbon molecule has been characterized in a number of studies by calculating electronic, spectroscopic, and mechanical properties. However, cyclo[18]carbon is only one member of the class of cyclo[n]carbons—standalone carbon allotrope representatives. Many of the larger members of this class of molecules have not been thoroughly investigated. In this work, we calculate the magnetically induced current density of cyclo[n]carbons in order to elucidate how electron delocalization and aromatic properties change with the size of the molecular ring (n), where n is an even number between 6 and 100. We find that the Hückel rules for aromaticity (4k + 2) and antiaromaticity (4k) become degenerate for large C_n rings (n > 50), which can be understood as a transition from a delocalized electronic structure to a nonaromatic structure with localized current density fluxes in the triple bonds. Actually, the calculations suggest that cyclo[n]carbons with n > 50 are nonaromatic cyclic polyalkynes. The influence of the amount of nonlocal exchange and the asymptotic behavior of the exchange–correlation potential of the employed density functionals on the strength of the magnetically induced ring current and the aromatic character of the large cyclo[n]carbons is also discussed.

"Bottled" spiro-doubly aromatic trinuclear [Pd2Ru]+ complexes

Following an ongoing interest in the study of transition metal complexes with exotic bonding networks, we report herein the synthesis of a family of heterobimetallic triangular clusters involving Ru and Pd atoms. These are the first examples of trinuclear complexes combining these nuclei. Structural and bonding analyses revealed both analogies and unexpected differences for these [Pd₂Ru]⁺ complexes compared to their parent [Pd₃]⁺ peers. Noticeably, participation of the Ru atom in the π-aromaticity of the coordinated benzene ring makes the synthesized compound the second reported example of ‘bottled’ double aromaticity. This can also be referred to as spiroaromaticity due to the participation of Ru in two aromatic systems at a time. Moreover, the [Pd₂Ru]⁺ kernel exhibits unprecedented orbital overlap of Ru d_z² AO and two Pd d_xy or d_x²−y² AOs. The present findings reveal the possibility of synthesizing stable clusters with delocalized metal–metal bonding from the combination of non-adjacent elements of the periodic table which has not been reported previously.

Synthesis of a triangular [Pd₂Ru]⁺ complex with delocalized metal–metal bonding between non-adjacent elements of the periodic table, double aromaticity and overlap of d-AOs with different angular momentum.

Searching for double σ- and π-aromaticity in borazine derivatives

Inspired by the double-aromatic (σ and π) C6H3 +, C6I6 2+, and C6(SePh)6 2+ ring-shaped compounds, herein we theoretically study their borazine derivative analogues. The systems studied are the cation and dications with formulas B3N3H3 +, B3N3Br6 2+, B3N3I6 2+, B3N3(SeH)6 2+, and B3N3(TeH)6 2+. Our DFT calculations indicate that the ring-shaped planar structures of B3N3H3 +, B3N3I6 2+, and B3N3(TeH)6 2+ are more stable in the singlet state, while those of B3N3Br6 2+ and B3N3(SeH)6 2+ prefer the triplet state. Besides, exploration of the potential energy surface shows that the ring-shaped structure is the putative global minimum only for B3N3I6 2+. According to chemical bonding analysis, B3N3H3 +, B3N3I6 2+, and B3N3(TeH)6 2+ have σ and π delocalized bonds. The number of delocalized σ/π electrons is 2/6 for the first, and 10/6 for the second and third, similar to what their carbon analogs exhibit. Finally, the analysis of the magnetically induced current density allows B3N3H3 +, B3N3I6 2+, and B3N3(TeH)6 2+ to be classified as strongly σ aromatic, and poorly π aromatic compounds.

Induced magnetic field in sp-hybridized carbon rings: analysis of double aromaticity and antiaromaticity in cyclo[2N]carbon allotropes

The induced magnetic field of C2N (N = 3-14) carbon rings was dissected to contributions from out-of-plane and in-plane π orbitals revealing two concurrent long range shielding or deshielding cones as a manifestation of the dual aromatic and antiaromatic character of C4n+2 and of C4n rings respectively. Aromaticity based on the magnetic criterion was evaluated with regard to the bonding pattern and geometrical characteristics that elucidate the influence of bond length and bond angle alteration on out-of-plane and in-plane magnetic responses. Ground state polyynic geometries of C4n+2 rings exhibit comparable shielding cones to annulenes, decreasing the magnetic response with regard to the ring size and similar πout and πin diatropicity. Transition state cumulenic rings display increased aromaticity expressed by a very strong constant magnetic response and augmented πout diatropicity with regard to πin. The variations of the induced magnetic field are explained on the basis of frontier orbital interactions through rotational excitations, which enable further rationalization of the aromatic/antiaromatic behavior.

Unconventional Aromaticity in Organometallics: The Power of Transition Metals

Aromaticity, one of the most fundamental concepts in chemistry, has attracted considerable attention from both theoreticians and experimentalists. Much effort on aromaticity in organometallics has been devoted to metallabenzene and derivatives. In comparison, aromaticity in other organometallics is less developed. This Account describes how our group has performed quantum chemical calculations to examine aromaticity in recently synthesized novel organometallic complexes. By collaborations with experimentalists, we have extended several aromaticity concepts into organometallics to highlight the power of transition metals. In general, the transition metal could participate in delocalization either out of rings or in the rings. We examined the former by probing the possibility of transition metal substituents in hyperconjugative aromaticity, where the metal is out of the rings. Calculations on tetraaurated heteroaryl complexes reveal that incorporation of the aurated substituents at the nitrogen atom can convert nonaromaticity in the parent indolium into aromaticity in the aurated one due to hyperconjugation, thus extending the concept of hyperconjugative aromaticity to heterocycles with transition metal substituents. More importantly, further analysis indicates that the aurated substituents can perform better than traditional main-group substituents. Recently, we also probed the strongest aromatic cyclopentadiene and pyrrolium rings by hyperconjugation of transition metal substituents. Moreover, theoretical calculations suggest that one electropositive substituent is able to induce aromaticity; whereas one electronegative substituent prompts nonaromaticity rather than antiaromaticity. We also probed the possibility of Craig-type Möbius aromaticity in organometallic chemistry, where the position of the transition metals is in the rings. According to the electron count and topology, aromaticity can be classified as Hückel-type and Möbius-type. In comparison with numerous Hückel aromatics containing 4 n+2 π-electrons, Möbius aromatics with 4 n π-electrons, especially the Craig-type species, are particularly limited. We first examined aromaticity in osmapentalynes. Theoretical calculations reveal that incorporation of the osmium center not only reduces the ring strain of the parent pentalyne, but also converts Hückel antiaromaticity in the parent pentalyne into Craig-type Möbius aromaticity in metallapentalynes. Further studies show that the transition metal fragments can also make both 16e and 18e osmapentalenes aromatic, indicating that the Craig-type Möbius aromaticity in osmapentalyne is rooted in osmapentalenes. In addition, Möbius aromaticity is also possible in dimetalla[10]annulenes, where the lithium atoms are not spectator cations but play an important role due to their bonding interaction with the diene moieties. We then examined the possibility of σ-aromaticity in an unsaturated ring. Traditional π-aromaticity is used to describe the π-conjugation in fully unsaturated rings; whereas σ-aromaticity may stabilize fully saturated rings with delocalization caused by σ-electron conjugation. We found that the unsaturated three-membered ring in cyclopropaosmapentalene is σ-aromatic. Very recently, we extended σ-aromaticity into in a fully unsaturated ring. The concepts and examples presented here show the importance of interplay and union between experiment and theory in developing novel aromatic systems and, especially, the indispensable role of computational study in rationalization of unconventional aromaticity. All these findings highlight the strong power of transition metals originating from participation of d orbitals in aromaticity, opening an avenue to the design of unique metalla-aromatics.

Magnetically induced current density in triple-layered beryllium–boron clusters

Magnetically induced current densities reveal the double aromatic character of the examined Be–B clusters.

σ-Aromaticity in a Fully Unsaturated Ring

Aromaticity is one of the most fundamental and fascinating chemical topics, attracting both experimental and theoretical chemists owing to its many manifestations. Both σ- and π-aromaticity can be classified depending on the character of the cyclic electron delocalization. In general, σ-aromaticity stabilizes fully saturated rings with σ-electron delocalization whereas the traditional π-aromaticity describes the π-conjugation in fully unsaturated rings. Here, we demonstrate a strong correlation between nucleus-independent chemical shift (NICS) values and extra cyclic resonance energies (ECREs), which are used to evaluate the σ-aromaticity in an unsaturated three-membered ring (3MR) of cyclopropene, which were computed by molecular orbital (MO) theory and valence bond (VB) theory, respectively. Further study shows that the fully unsaturated ring in methylenecyclopropene and its metallic analogy is σ-aromatic. Our findings revolutionize the fundamental knowledge of the concept of σ-aromaticity, thus opening an avenue to design σ-aromaticity in other fully unsaturated systems, which are traditionally reserved as the domain of π-aromaticity.

Carbon rings: a DFT study on geometry, aromaticity, intermolecular carbon–carbon interactions and stability

Strong complimentary electrostatic interactions lead to large number of C⋯C interactions in doubly antiaromatic C_4N dimers while the delocalized system of π electrons in doubly aromatic C_4N+2 dimers suggest very few intermolecular C⋯C interactions.

Theoretical study of the solvent effect on the aromaticity of benzene: a NICS analysis

Nucleus-independent chemical shift (NICS) quantities for benzene-benzene and benzene-water species were obtained and are discussed in gas phase and in solution. Besides standard polarizable continuum model (PCM) calculations, sequential Monte Carlo/quantum mechanics (S-MC/QM) were also performed. Benzene was shown to be slightly more aromatic in condensate phase when we considered the average solvent configuration (ASEC) approach with explicit molecules.

Calculation of spin-current densities using gauge-including atomic orbitals

The gauge-including magnetically induced current method for calculating the components of the current-density tensor using gauge-including atomic orbitals has been extended to treating open-shell molecules. The applicability of the method is demonstrated by calculations of first-order induced current densities on cyclobutadiene, Al(3), and B(3) at correlated ab initio levels of theory. For comparison, current-density calculations were also performed on the lowest closed-shell singlet state of cyclobutadiene as well on the closed-shell Al(3)(-) and B(3)(-) anions. The ring-current susceptibilities of the open-shell species are computed at the Hartree-Fock self-consistent-field, second-order Møller-Plesset perturbation theory, and coupled-cluster singles and doubles levels, whereas for the closed-shell systems also density functional theory calculations were employed. Explicit values for the current strengths caused by α and β electrons as well as the difference, representing the spin current, were obtained by numerical integration of the current-density contributions passing a plane perpendicular to the molecular ring. Comparisons of the present results to those recently obtained for the lowest triplet state of biphenyl emphasize that electron correlation effects must be considered for obtaining an accurate description of spin-current densities.

Density functional theory study of BnC clusters

B(n)C clusters (n = 3-10) were studied at the density functional theory (DFT) (B3LYP)/6-311G** level of theory. The calculations predicted that the most stable configurations of the B(n) C clusters are the (n + 1)-membered cyclic structures. For boron-carbon clusters, the configurations containing greater numbers of three-membered boron rings are more favorable, except for the B(7)C and B(9)C clusters. Through molecular orbital analysis of these B(n)C clusters, we have concluded that π-electron delocalization plays a crucial role in the stability of n + 1-membered cyclic structures. In this paper, the relative stability of each cluster is discussed based on their single atomic-binding energies. The capability of clusters to obtain or lose an electron was also discussed, based on their vertical electron detachment energies (VDEs), adiabatic electron detachment energies (ADEs), vertical electron affinities (VEAs) and adiabatic electron affinities (AEAs).

Search for structures, potential energy surfaces, and stabilities of planar BnP(n = 1 ∼ 7)

We have systematically explored and investigated the geometrical structures, stability, growth pattern, bonding character, and potential energy surface (PES) of the possible isomers of each cluster for planar B(n)P (n = 1 ∼ 7) at the CCSD(T)/6-311+;G(d)//B3LYP/6-311+G(d) level. A large number of planar structures for the possible isomers of B(n)P (n = 1 ∼ 7) and transition states are located. Isomers 1a ∼ 7a of B(n)P are the lowest-energy structures and 2a, 4a, as well as 6a are more stable than their neighbors. For the lowest-energy structures (1a ∼ 7a) of B(n)P, P atom lies at the apex and tends to form two B-P bonds with boron atoms. They exhibit planar zigzag growth feature or approximately spherical-like growth pattern. Results from molecular orbital analysis demonstrate that the formation of the delocalized π MOs and the σ-radial and σ-tangential MOs plays a critical role in stabilizing the structures of lowest-energy isomers (2a ∼ 7a) of B(n)P. Importantly, isomers 3a, 3c, 3d, 4a, 4b, 5b, and 5c of B(n)P are stable both thermodynamically and kinetically at the CCSD(T)/6-311+G(d)// B3LYP/6-311+G(d) level and detectable in laboratory, which is valuable for further experimental studies of B(n)P.

Investigation of 1H NMR chemical shifts of organic dye with hydrogen bonds and ring currents

The (1)H NMR chemical shifts were theoretically computed for the organic dyes 2-(2,6-dimethyl-4H-pyran-4-ylidene)-malononitrile (1), cyano-(2,6-dimethyl-4H-pyran-4-ylidene)-acetic acid methyl ester (2), 2-(2,6-bis(4-(dimethylamino)styryl)-4H-pyran-4-ylidene)-malononitrile (3), and methyl 2-(2,6-bis(4-(dimethylamino)styryl)-4H-pyran-4-ylidene)-2-cyanoacetate (4) at the GIAO/B3LYP/6-311++G(d,p)//B3LYP/6-311++G(d,p) level of theory. Moreover, the intramolecular rotational barriers of the molecules were calculated to evaluate the internal flexibility with respect to the torsional degrees of freedom, and the nuclear-independent chemical shifts (NICS) were employed to analyze the ring currents. The difference was explained in terms of intramolecular hydrogen bonds and ring currents of the molecules. The (1)H NMR spectra were reproduced by experiments for the comparison with computationally constructed data. Our results suggest a good guideline in interpreting (1)H NMR chemical shifts using computational methods and furthermore a reliable perspective for designing molecular structures.

Diagnosis of magnetoresponsive aromatic and antiaromatic zones in three-membered rings of d- and f-block elements

Magnetoresponsive three-membered rings of d- and f-block elements have been thoroughly investigated with the help of electronic structure calculation methods. The magnetic response of the clusters was evaluated by the Nucleus Independent Chemical Shifts (NICS)(zz)-scan curves, which in conjunction with symmetry-based selection rules for the most significant translationally and rotationally allowed transitions helped rationalize and predict the orbital-type of aromaticity/antiaromaticity of the clusters. The magnetoresponsive early (Groups 3, 4, and 5) transition metal M(3) rings exhibit successive aromatic and antiaromatic zones separated by a nodal plane. The magnetoresponsive late (Groups 11 and 12) transition metal M(3) rings exhibit long-range aromatic zone with the NICS(zz)(R) values decaying rapidly and monotonically with respect to R. The magnetic response of Group 10 transition metal M(3) rings is similar to that of the early transition metal M(3) rings, but it is long-range antiaromatic only for the [c-Ni(3)] cluster. The NICS(zz)-scan curve of the [(H(t)La)(3)(mu(2)-H)(6)] cluster is indicative of weak pure sigma-aromaticity due to the induced diatropic ring current from the translationally allowed a(1)(') --> e' and e' --> a(1)(') transitions. The aromatic-antiaromatic behavior of the [(H(t)Ce)(3)(mu(2)-H)(6)](+) and [(H(t)Tm)(3)(mu(2)-H)(6)](2-) clusters is similar to that of the early d-block elements. The magnetic response of [(H(t)Yb)(3)(mu(2)-H)(6)](3-) is similar to that of [c-Hg(3)](2-). The [(H(t)Lu)(3)(mu(2)-H)(6)] cluster can be considered as a doubly (sigma + pi) aromatic system, with the sigma-aromatic component being much stronger than the pi-aromatic one. Finally, the [(X(t)Re)(3)(mu(2)-X)(6)] and [(X(t)Ru)(3)(mu(2)-X)(6)](+) (X = Cl, Br, I) clusters exhibit significant aromatic character with the greatest contribution to the induced diatropic ring currents coming from pi-type transitions.

The distortivity of pi-electrons in conjugated boron rings

DFT calculations indicate that pi-distortivity in boron rings as manifested via the Kekulé b(2u) stretching mode is greatly reduced compared to carbocyclic annulenes.

Structure and stability of B5C and C5B clusters

Geometry optimizations and vibrational frequencies of B5C and C5B clusters were calculated with the Becke-3LYP method using the 6-311+G(d) basis set and some stable configurations of B5C and C5B clusters have been found. The most stable structure of B5C is a planar six-membered ring. However, for C5B clusters, the most stable structure is linear with a boron atom in position 3. Various configurations of B5C clusters containing three-membered boron rings have predominance in energy, whereas various configurations of C5B clusters containing three-membered carbon rings are disadvantageous in energy. In B5C clusters, isomer2 can be converted into isomer1 by surmounting an energy barrier of 43.83 kJ.mol(-1). In C5B clusters, the conversions of isomer5 into isomer2 and isomer7 into isomer2 have energy barriers of 19.66 and 20.57 kJ.mol(-1), respectively.