From High-Energy C7H2 Isomers with A Planar Tetracoordinate Carbon Atom to An Experimentally Known Carbene

Energetic and Spectroscopic Properties of Astrophysically Relevant MgC4H Radicals Using High-Level Ab Initio Calculations

Considering the importance of magnesium-bearing hydrocarbon molecules (MgCnH; n = 2, 4, and 6) in the carbon-rich circumstellar envelopes (e.g., IRC+10216), a total of 28 constitutional isomers of MgC4H have been theoretically investigated using density functional theory (DFT) and coupled-cluster methods. The zero-point vibrational energy corrected relative energies at the ROCCSD(T)/cc-pCVTZ level of theory reveal that the linear isomer, 1-magnesapent-2,4-diyn-1-yl (1, 2Σ+), is the global minimum geometry on the MgC4H potential energy surface. The latter has been detected both in the laboratory and in the evolved carbon star, IRC+10216. The calculated spectroscopic data for 1 match well with the experimental observations (error ∼ 0.78%) which validates our theoretical methodology. Plausible isomerization processes happening among different isomers are examined using DFT and coupled-cluster methods. CASPT2 calculations have been performed for a few isomers exhibiting multireference characteristics. The second most stable isomer, 1-ethynyl-1λ3-magnesacycloprop-2-ene-2,3-diyl (2, 2A1, μ = 2.54 D), is 146 kJ mol-1 higher in energy than 1 and possibly the next promising candidate to be detected in the laboratory or in the interstellar medium in future.

CCSD(T) Rotational Constants for Highly Challenging C5H2 Isomers-A Comparison between Theory and Experiment

We evaluate the accuracy of CCSD(T) and density functional theory (DFT) methods for the calculation of equilibrium rotational constants (Ae, Be, and Ce) for four experimentally detected low-lying C5H2 isomers (ethynylcyclopropenylidene (2), pentatetraenylidene (3), ethynylpropadienylidene (5), and 2-cyclopropen-1-ylidenethenylidene (8)). The calculated rotational constants are compared to semi-experimental rotational constants obtained by converting the vibrationally averaged experimental rotational constants (A0, B0, and C0) to equilibrium values by subtracting the vibrational contributions (calculated at the B3LYP/jun-cc-pVTZ level of the theory). The considered isomers are closed-shell carbenes, with cumulene, acetylene, or strained cyclopropene moieties, and are therefore highly challenging from an electronic structure point of view. We consider both frozen-core and all-electron CCSD(T) calculations, as well as a range of DFT methods. We find that calculating the equilibrium rotational constants of these C5H2 isomers is a difficult task, even at the CCSD(T) level. For example, at the all-electron CCSD(T)/cc-pwCVTZ level of the theory, we obtain percentage errors ≤0.4% (Ce of isomer 3, Be and Ce of isomer 5, and Be of isomer 8) and 0.9-1.5% (Be and Ce of isomer 2, Ae of isomer 5, and Ce of isomer 8), whereas for the Ae rotational constant of isomers 2 and 8 and Be rotational constant of isomer 3, high percentage errors above 3% are obtained. These results highlight the challenges associated with calculating accurate rotational constants for isomers with highly challenging electronic structures, which is further complicated by the need to convert vibrationally averaged experimental rotational constants to equilibrium values. We use our best CCSD(T) rotational constants (namely, ae-CCSD(T)/cc-pwCVTZ for isomers 2 and 5, and ae-CCSD(T)/cc-pCVQZ for isomers 3 and 8) to evaluate the performance of DFT methods across the rungs of Jacob's Ladder. We find that the considered pure functionals (BLYP-D3BJ, PBE-D3BJ, and TPSS-D3BJ) perform significantly better than the global and range-separated hybrid functionals. The double-hybrid DSD-PBEP86-D3BJ method shows the best overall performance, with percentage errors below 0.5% in nearly all cases.

Pentacoordinate Carbon Atoms in a Ferrocene Dication Derivative—[Fe(Si2-η5-C5H2)2]2+

Pentacoordinate carbon atoms are theoretically predicted here in a ferrocene dication derivative in the eclipsed-(1; C2v), gauche-(2; C2) and staggered-[Fe(Si2-η5-C5H2)2]2+(3; C2h) forms for the first time. Energetically, the relative energy gaps for 2 and 3 range from −3.06 to 16.74 and −2.78 to 40.34 kJ mol−1, respectively, when compared to the singlet electronic state of 1 at different levels. The planar tetracoordinate carbon (ptC) atom in the ligand Si2C5H2 becomes a pentacoordinate carbon upon complexation. The ligand with a ptC atom was predicted to be both a thermodynamically and kinetically stable molecule by some of us in our earlier theoretical works. Natural bond orbital and adaptive natural density partitioning analyses confirm the pentacoordinate nature of carbon in these three complexes (1–3). Although they are hypothetical at the moment, they support the idea of “hypercoordinate metallocenes” within organometallic chemistry. Moreover, ab initio molecular dynamics simulations carried out at 298 K temperature for 2000 fs suggest that these molecules are kinetically stable.

New Carbenes and Cyclic Allenes Energetically Comparable to Experimentally Known 1-Azulenylcarbene

1-Azulenylcarbene (18; 0 kJ mol^-1) is experimentally known as the key reactive intermediate for the rearrangement reactions of aryl carbenes in the laboratory. Here, using coupled-cluster methods up to the fc-CCSD(T)/cc-pVTZ//fc-CCSD(T)/cc-pVDZ level, thirteen new carbenes and one new cyclic allene are theoretically identified within the C₁₁H₈ elemental composition that either energetically lie below or very close to 18. While the cyclic allene, bicyclo[5.4.0]undeca-2,3,5,7,9,11-hexene (1; -166 kJ mol^-1), is the experimentally known lowest energy isomer, three other cyclic allenes, bicyclo[5.4.0]undeca-1,2,4,6,8,10-hexene (2; -100 kJ mol^-1), bicyclo[5.4.0]undeca-1,3,4,6,8,10-hexene (3; -97 kJ mol^-1), and bicyclo[6.3.0]undeca-1,2,4,6,8,10-hexene (13; -42 kJ mol^-1), demand new experimental studies. In total, thirty-one isomers are studied in this work (within -166 to +15 kJ mol^-1 from 18) and all are found to be polar (μ ≠ 0). Among these, 1H-benzo[7]annulen-1-ylidene (17; -4 kJ mol^-1; μ = 5.24 D), bicyclo[5.4.0]undeca-2,4,6,8,11-pentaene-10-ylidene (24; 13 kJ mol^-1; μ = 7.59 D), 5-methylene-naphthalen-1-ylidene (26; 15 kJ mol^-1; μ = 5.32 D), 6-methylene-naphthalen-2-ylidene (27; -43 kJ mol^-1; μ = 6.60 D), and 8-methylene-naphthalen-2-ylidene (28; -39 kJ mol^-1; μ = 5.55 D) are competitively polar compared to 18 (μ = 5.39 D). Therefore, these carbene molecules are potential targets for rotational spectroscopists and radioastronomers. Considering the importance of naphthyl and azulenylcarbenes in reactive intermediate chemistry, mechanisms of different rearrangement reactions and plausible formation pathways of some of these new carbenes are studied in this work using density functional theory.

Why Are MgC3H Isomers Missing in the Interstellar Medium?

Considering the recent findings of linear doublet (²Σ⁺) MgC_nH isomers (n = 2, 4, and 6) in the evolved carbon star IRC+10216, various structural isomers of MgC₃H and MgC₃H⁺ are theoretically investigated here. For MgC₃H, 11 doublet and 8 quartet stationary points ranging from 0.0 to 71.8 and 0.0 to 110.1 kcal mol^-1, respectively, have been identified initially at the UωB97XD/6-311++G(2d,2p) level. To get accurate relative energies, further energy evaluations are carried out for all isomers with coupled cluster methods and thermochemical modules such as G3//B3LYP, G4MP2, and CBS-QB3 methods. Unlike the even series, where the global minima are linear molecules with a Mg atom at one end, in the case of MgC₃H, the global minimum geometry turns out to be a cyclic isomer, 2-magnesabicyclo[1.1.0]but-1,3,4-triyl (1, C_2v, ²A₁). In addition, five low-lying isomers, magnesium-substituted cyclopropenylidene (2, C_s, ²A'), 1-magnesabut-2,3-dien-1-yl-4-ylidene (3, C_s, ²A″), 1-magnesabut-2-yn-1-yl-4-ylidene (4, C_s, ²A″), 2λ³-magnesabicyclo[1.1.0]but-1,3-diyl-4-ylidene (5, C_2v;, ²A₁), and 1-magnesabut-2,3-dien-2-yl-4-ylidene (6, C_∞v, ²Σ⁺), were also identified. The doublet linear isomer of MgC₃H, 1-magnesabutatrienyl (10, C_∞v, ²Σ⁺) turns out to be a minimum but lies 54.1 kcal mol^-1 above 1 at the ROCCSD(T)/cc-pVTZ level. The quartet (⁴Σ⁺) electronic state of 10 was also found to be a minimum, but it lies 8.0 kcal mol^-1 above 1 at the same level. Among quartets, isomer 10 is the most stable molecule. The next quartet electronic state (of isomer 11) is 34.4 kcal mol^-1 above 10, and all other quartet electronic states of other isomers are not energetically close to low-lying doublet isomers 2 to 6. Overall, the chemical space of MgC₃H contains more cyclic isomers (1, 2, and 3) on the low-energy side unlike their even-numbered MgC_nH counterparts (n = 2, 4, and 6). Though the quartet electronic state of 10 is linear, it is not the global minimum geometry on the MgC₃H potential energy surface. Isomerization pathways among the low-lying isomers (doublets of 1-4 and a quartet of 10) reveal that these molecules are kinetically stable. For the cation, MgC₃H⁺, the cyclic isomers (1⁺, 2⁺, and 3⁺) are on the low-energy side. The singlet linear isomer, 10⁺, is a fourth-order saddle point. The low-lying cations are quite polar, with dipole moment values of >7.00 D. The current theoretical data would be helpful to both laboratory astrophysicists and radioastronomers for further studies on the MgC₃H^0/+ isomers.

CSinGe4-n2+ (n = 1-3): prospective systems containing planar tetracoordinate carbon (ptC)

Density functional theory (DFT) based calculations have been carried out to explore the potential energy surface (PES) of CSi_nGe_4-n^2+/+/0 (n = 1-3) systems. The global minimum structures in the di-cationic states (1a, 1b, and 1c) contain a planar tetracoordinate carbon (ptC). For the CSi₂Ge₂²⁺ system, the second stable isomer (2b) also contains a ptC with 0.67 kcal mol^-1 higher energy than that of the 1b ptC isomer. The global minima of the neutral and mono-cationic states of the designed systems are not planar. The 1a, 1b, and 1c structures follow the 18 valence electron rule. The relative energies of the low-lying isomers of CSiGe₃²⁺, CSi₂Ge₂²⁺, and CSi₃Ge²⁺ systems with respect to the global minima were calculated using the CCSD(T)/aug-cc-pVTZ method. Ab initio molecular dynamics simulations for 50 ps time indicate that all the global minimum structures (1a, 1b, and 1c) are kinetically stable at 300 K and 500 K temperatures. The natural bond orbital (NBO) analysis suggests strong σ-acceptance of the ptC from the four surrounding atoms and simultaneously π-donation occurs from the ptC center. The nucleus independent chemical shift (NICS) showed σ/π-dual aromaticity. We hope that the designed di-cationic systems may be viable 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.

From Molecules with a Planar Tetracoordinate Carbon to an Astronomically Known C5H2 Carbene

Ethynylcyclopropenylidene (2), an isomer of C₅H₂, is a known molecule in the laboratory and has recently been identified in Taurus Molecular Cloud-1 (TMC-1). Using high-level coupled-cluster methods up to the CCSDT(Q)/CBS level of theory, it is shown that two isomers of C₅H₂ with a planar tetracoordinate carbon (ptC) atom, (SP-4)-spiro[2.2]pent-1,4-dien-1,4-diyl (11) and (SP-4)-spiro[2.2]pent-1,4-dien-1,5-diyl (13), serve as the reactive intermediates for the formation of 2. Here, a theoretical connection has been established between molecules containing ptC atoms (11 and 13) and a molecule (2) that is present nearly 430 light years away, thus providing evidence for the existence of ptC species in the interstellar medium. The reaction pathways connecting the transition states and the reactants and products have been confirmed by intrinsic reaction coordinate calculations at the CCSDT(Q)/CBS//B3LYP-D3BJ/cc-pVTZ level. While isomer 11 is non-polar (μ = 0), isomers 2 and 13 are polar, with dipole moment values of 3.52 and 5.17 Debye at the CCSD(T)/cc-pVTZ level. Therefore, 13 is also a suitable candidate for both laboratory and radioastronomical studies.

CSiGaAl2 -/0 and CGeGaAl2 -/0 having planar tetracoordinate carbon atoms in their global minimum energy structures

Density functional theory (DFT) is used to explore the structure, stability, and bonding in CSiGaAl₂ ^-/0 and CGeGaAl₂ ^-/0 systems having planar tetracoordinate carbon (ptC). The neutral systems have 17 valence electrons and the mono-anionic systems have 18 valence electrons. The ab initio molecular dynamics simulations for 2000 fs time at two different temperatures (300 and 500 K) supported the kinetic stability of the systems. From the natural bond orbital (NBO) analysis it is shown that there is a strong electron donation from the ligand atoms to the ptC atom. We have used Li⁺ ion for the neutralization of the mono-anionic systems and more interestingly it does not disrupt the planar structure. The most preferable site for binding of Li⁺ ion is along the AlAl bond in both of the mono-anionic systems. All the systems in this work have both σ and π aromaticity which is predicted from the computations of nucleus independent chemical shift (NICS). Although the anionic species obey the 18 valence electronic rule, the neutral systems break the rule with 17 valence electrons. However, both sets of systems are stable in the planar form. The bonding analysis of the systems includes molecular orbital, adaptive natural density partitioning (AdNDP), quantum theory of atoms in molecules (QTAIM), electron localization function (ELF) basin, and aromaticity analyses. The energy decomposition analysis (EDA) determines the interaction of Li⁺ ion with CSiGaAl₂ ^- and CGeGaAl₂ ^- in Li@SiGaAl₂ and Li@GeGaAl₂ , respectively.

BAl4Mg−/0/+: Global Minima with a Planar Tetracoordinate or Hypercoordinate Boron Atom

We have explored the chemical space of BAl4Mg−/0/+ for the first time and theoretically characterized several isomers with interesting bonding patterns. We have used chemical intuition and a cluster building method based on the tabu-search algorithm implemented in the Python program for aggregation and reaction (PyAR) to obtain the maximum number of possible stationary points. The global minimum geometries for the anion (1a) and cation (1c) contain a planar tetracoordinate boron (ptB) atom, whereas the global minimum geometry for the neutral (1n) exhibits a planar pentacoordinate boron (ppB) atom. The low-lying isomers of the anion (2a) and cation (3c) also contain a ppB atom. The low-lying isomer of the neutral (2n) exhibits a ptB atom. Ab initio molecular dynamics simulations carried out at 298 K for 2000 fs suggest that all isomers are kinetically stable, except the cation 3c. Simulations carried out at low temperatures (100 and 200 K) for 2000 fs predict that even 3c is kinetically stable, which contains a ppB atom. Various bonding analyses (NBO, AdNDP, AIM, etc.) are carried out for these six different geometries of BAl4Mg−/0/+ to understand the bonding patterns. Based on these results, we conclude that ptB/ppB scenarios are prevalent in these systems. Compared to the carbon counter-part, CAl4Mg−, here the anion (BAl4Mg−) obeys the 18 valence electron rule, as B has one electron fewer than C. However, the neutral and cation species break the rule with 17 and 16 valence electrons, respectively. The electron affinity (EA) of BAl4Mg is slightly higher (2.15 eV) than the electron affinity of CAl4Mg (2.05 eV). Based on the EA value, it is believed that these molecules can be identified in the gas phase. All the ptB/ppB isomers exhibit π/σ double aromaticity. Energy decomposition analysis predicts that the interaction between BAl4−/0/+ and Mg is ionic in all these six systems.

Stereomutation in Tetracoordinate Centers via Stabilization of Planar Tetracoordinated Systems

The quest for stabilizing planar forms of tetracoordinate carbon started five decades ago and intends to achieve interconversion between [R]- and [S]-stereoisomers without breaking covalent bonds. Several strategies are successful in making the planar tetracoordinate form a minimum on its potential energy surface. However, the first examples of systems where stereomutation is possible were reported only recently. In this study, the possibility of neutral and dications of simple hydrocarbons (cyclopentane, cyclopentene, spiropentane, and spiropentadiene) and their counterparts with the central carbon atom replaced by elements from groups 13, 14, and 15 are explored using ab initio MP2 calculations. The energy difference between the tetrahedral and planar forms decreases from row II to row III or IV substituents. Additionally, aromaticity involving the delocalization of the lone pair on the central atom appears to help in further stabilizing the planar form compared to the tetrahedral form, especially for the row II substituents. We identified 11 systems where the tetrahedral state is a minimum on the potential energy surface, and the planar form is a transition state corresponding to stereomutation. Interestingly, the planar structures of three systems were found to be minimum, and the corresponding tetrahedral states were transition states. The energy profiles corresponding to such transitions involving both planar and tetrahedral states without the breaking of covalent bonds were examined. The systems showcased in this study and research in this direction are expected to realize molecules that experimentally exhibit stereomutation.

In Silico Studies on Selected Neutral Molecules, CGa2Ge2, CAlGaGe2, and CSiGa2Ge Containing Planar Tetracoordinate Carbon

Density functional theory (DFT) was used to study the structure, stability, and bonding in some selected neutral pentaatomic systems, viz., CGa2Ge2, CAlGaGe2, and CSiGa2Ge containing planar tetracoordinate carbon. The systems are kinetically stable, as predicted from the ab initio molecular dynamics simulations. The natural bond orbital (NBO) analysis showed that strong electron donation occurs to the central planar carbon atom by the peripheral atoms in all the studied systems. From the nucleus independent chemical shift (NICS) analysis, it is shown that the systems possess both σ- and π- aromaticity. The presence of 18 valence electrons in these systems, in their neutral form, appears to be important for their stability with planar geometries rather than tetrahedral structures. The nature of bonding is understood through the adaptive natural density partitioning analysis (AdNDP), quantum theory of atoms in molecules (QTAIM) analysis, and also via Wiberg bond index (WBI) and electron localization function (ELF).

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.

CAl4Mg0/−: Global Minima with a Planar Tetracoordinate Carbon Atom

Isomers of CAl4Mg and CAl4Mg− have been theoretically characterized for the first time. The most stable isomer for both the neutral and anion contain a planar tetracoordinate carbon (ptC) atom. Unlike the isovalent CAl4Be case, which contains a planar pentacoordinate carbon atom as the global minimum geometry, replacing beryllium with magnesium makes the ptC isomer the global minimum due to increased ionic radii of magnesium. However, it is relatively easier to conduct experimental studies for CAl4Mg0/− as beryllium is toxic. While the neutral molecule containing the ptC atom follows the 18 valence electron rule, the anion breaks the rule with 19 valence electrons. The electron affinity of CAl4Mg is in the range of 1.96–2.05 eV. Both the global minima exhibit π/σ double aromaticity. Ab initio molecular dynamics simulations were carried out for both the global minima at 298 K for 10 ps to confirm their kinetic stability.

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.

How to Accomplish a Square C(N)4 Substructure of the Planar Tetracoordinate Carbon

Nitrogen-based groups are usually not used as ligands to coordinate to the ptC atom. However, here we reported only nitrogen-based ligands to accomplish a theoretically successful square planar C(N)4 substructure. The first difficulty in accomplishing a square ptC(N)4 substructure is to conquer the tremendous strain from the planar to tetrahedral arrangements, and the second is to restrict it in a suitable system with the right symmetry. We designed several neutral molecules with the square ptC(N)4 substructures, and the molecules were studied using the density functional theory method at the B3LYP/6-311++G(3df,3pd) and TPSSh/6-311++G(3df,3pd) level of theory. The results of this work show that the molecules are all real minima on the potential energy surface and successfully achieved the square ptC(N)4 substructure in the theoretical method. The group orbitals among the square ptC(N)4 arrangement in the D 2d symmetry have been discussed and used to investigate the bonding interactions among all atoms in the square ptC(N)4 substructure. Usually, the ptC systems have 18 valence electrons, but the present ptC systems mentioned in this work have 24 valence electrons, which is unusual for ptC.

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.

Transition between [R]- and [S]-stereoisomers without bond breaking

The fifty-year old proposal of a nondissociative racemization reaction of a tetracoordinated tetrahedral center from one enantiomer to another via a planar transition state by Hoffmann and coworkers has been explored by many research groups over the past five decades. A number of stable molecules with planar tetracoordinated and higher-coordinated centers have been designed and experimentally realized; however, there has not been a single example of a molecular system that can possibly undergo such racemization. Here we show examples of molecular species that undergo inversion of stereochemistry around tetrahedral centers (Si, Al- and P+) either via a planar transition state or an intermediate state using quantum mechanical, ab initio quasi-classical dynamics calculations, and Born-Oppenheimer molecular dynamics (BOMD) simulations. This work is expected to provide potential leads for future studies on this fundamental phenomenon in chemistry.

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.

Theoretical Studies of SiC4H2 Isomers Delineate Three Low-Lying Silylidenes Are Missing in the Laboratory

Eleven isomers of SiC₄H₂ lying within 50 kcal mol^-1 have been theoretically investigated using density functional theory and high-level coupled-cluster methods. Among them, four isomers, 1-ethynyl-3-silacycloprop-1(2)-en-3-ylidene (1), diethynylsilylidene (2), 1-sila-1,2,3,4-pentatetraenylidene (4), and 1,3-butadiynylsilylidene (5), have already been identified in the laboratory. The current investigation reports three low-lying (<1 eV) silylidenes [2-methylenesilabicyclo[1.1.0]but-1(3)-en-4-ylidene (3), 4-sila-2-methylenebicyclo[1.1.0]but-1(3)-en-4-ylidene (6), and 3-ethynyl-1-silapropadienylidene (7)] and three high-lying (>1 eV) silylidenes [2-sila-(didehydrovinylidene)cyclopropene (8), an isomer with a planar tetracoordinate carbon (ptC) atom (10), and 1-ethynyl-1-silapropadienylidene (11)], which remain elusive in the laboratory to date. Isomer 9 also contains a ptC atom, which turned out to be a transition state at all levels. Though all isomers are polar (μ ≠ 0), rotational spectrum is available only for 4. Using matrix isolation, three isomers (1, 2, and 5) have been trapped in the laboratory at 10 K. Considering the astrochemical relevance of silicon-carbide clusters in the interstellar medium, the current theoretical data demand new molecular spectroscopic studies on SiC₄H₂. Surprisingly, unlike the isovalent C₅H₂ isomers, where the bent carbenes are yet to be identified in the laboratory, the bent silylidenes (2 and 5) have been trapped in the case of SiC₄H₂. In both the cases, molecules with transannular C-C and/or Si-C bonds remain elusive, though they lie in the low-lying region. Using suitable precursors, whether these peculiar geometries (especially 3 and 6) would be identified or not in the laboratory needs to be addressed by molecular spectroscopists. The present investigation documents structural and spectroscopic information of SiC₄H₂ isomers, which may compliment future molecular spectroscopic observations including radioastronomical searches.

Embedding a Planar Hypercoordinate Carbon Atom into a [4n+2] π-System

Through delicate tuning of the electronic structure, we report herein a rational design of seventeen new putative global minimum energy structures containing a planar tetra- or pentacoordinate carbon atom embedded in an aromatic hydrocarbon. These structures are the result of replacing three consecutive hydrogen atoms of an aromatic hydrocarbon by less electronegative groups, forming a multicenter σ-bond with the planar hypercoordinate carbon atom and participating in the π-electron delocalization. This strategy that maximizes both mechanical and electronic effects through aromatic architectures can be extended to several molecular combinations to achieve new and diverse compounds containing planar hypercoordinate carbon centers.

Theoretical Studies of Two Key Low-Lying Carbenes of C5H2 Missing in the Laboratory

The equilibrium geometries and spectroscopic properties of two key singlet carbenes, buta-1,3-diynylcarbene (6) and 2-methylenebicyclo[1.1.0]but-1(3)-en-4-ylidene (9), which have not been experimentally observed to date, are investigated using high-level coupled-cluster (CC) methods. The current theoretical study necessitates new experimental data on C₅H₂ isomers considering the relevance of these molecules to interstellar chemistry. Bent-pentadiynylidene (4) has been missing in the laboratory and the prime focus of our earlier theoretical work. The present theoretical study indicates that isomers 6 and 9 are also viable experimental targets. Apart from ethynylcyclopropenylidene (2), pentatetraenylidene (3), ethynylpropadienylidene (5), and 3-(didehydrovinylidene)cyclopropene (8), which are identified by Fourier transform microwave spectroscopy, the dipole moments of elusive 4, 6, and 9 are also nonzero (μ ≠ 0). The relative energies of these isomers, calculated at the CCSDT(Q)/CBS level of theory, with respect to linear triplet pentadiynylidene (1) reveal that they all lie within 25.1 kcal mol^-1. Therefore, geometric, energetic, aromatic, and spectroscopic parameters are reported here, which may assist the efforts of molecular spectroscopists in the future. Anharmonic vibrational calculations on isomers 6 and 9 indicate that the former is loosely bound and would be challenging to be detected experimentally. Among the undetected carbenes, 9 may be considered as a potential target molecule considering its higher polarity and aromatic nature.

Reply to the ‘Comment on “Exploiting electronic strategies to stabilize a planar tetracoordinate carbon in cyclic aromatic hydrocarbons”’ by V. S. Thimmakondu, Chem. Commun., 2019, DOI: 10.1039/c9cc04639a

The authors respond to the Comment by Thimmakondu, showing that the effectiveness of their approach to stabilize a planar tetracoordinate (ptC) carbon in cyclic aromatic hydrocarbons is unquestionable, since their results are reproducible and reliable.