Singlet-triplet splitting of divalent five-membered fused rings C<Subscript>12</Subscript>H<Subscript>8</Subscript>M (M = C,Si, Ge,Sn, and Pb): Application in nanocomplex synthesis

Energy differences, ΔX _s−t (X = E, H, and G) (ΔX _s−t = X(singlet) − X(triplet)) between singlet (s) and triplet (t) states of C₁₂H₈M were calculated at B3LYP/6-311+G*. The DFT calculations indicated that the ΔG _s−t between singlet (s) and triplet (t) states of C₁₂H₈M were increased from M = C to M = Pb. The ΔG _s−t of C₁₂H₈M was compared with its analogue C₄H₄M through replacement of heavy atoms from M = C to M = Pb. Configurations of the electrons in orbitals (σ² or π²) for the singlet state of C₁₂H₈M were discussed.     

Singlet–triplet splitting and stability of divalent five‐membered ring C4H4M,C4H6M,and C4H8M (M = C,Si, Ge,Sn, and Pb)

The sum of electronic and thermal free energy differences between singlet and triplet states (Δ G_t‐s) is calculated for C₄H₄M, C₄H₆M, and C₄H₈M (M = C, Si, Ge, Sn, and Pb) at B3LYP/6‐311++G (3df,2p) level. Singlet–triplet splitting (Δ G_t‐s) is compared for three analogs C₄H₄M, C₄H₆M, and C₄H₈M. The change order of Δ G_t‐s is (except for M = C) C₄H₆M > C₄H₈M > C₄H₄M. The results of homodesmotic reaction energies show the most stability for singlet state of C₄H₆M with respect to C₄H₄M and C₄H₈M. In contrast, the triplet state of C₄H₄M (except for M = C) is the most stable with respect to C₄H₆M and C₄H₈M. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:245–251, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20428     

通过核独立化学位移(NICS)计算研究二价三、五、七元环C2H2M, C4H4M and C6H6M(M=C, Si, Ge, Sn and Pb)的芳香族特性

The aromatic character of divalent three, five and seven-membered rings C₂H₂M, C₄H₄M and C₆H₆M(M=C, Si, Ge, Sn and Pb) is investigated through magnetic and geometric criteria by Density Functional Theory (DFT)method using 6^-311++G(3df,2p) basis set of the GAUSSIAN 98 program. The result of Nucleus-independent Chemical Shifts (NICS)(0.5) calculations show an aromatic character for singlet state of C₂H₂M(M=C, Si, Ge, Sn and Sn) and nonaromatic character for triplet states of C₂H₂M(except M=Ge and Pb). NICS (0.5) calculations show nonaromatic character for the singlet state of C₄H₄C and antiaromatic character for C₄H₄M(M=Si, Ge, Sn and Pb). In contrast, NICS (0.5) calculations indicate antiaromatic character for the triplet state of C₄H₄C and nonaromatic character to C₄H₄M(M=Si, Ge, Sn and Pb). NICS (0.5) calculations show a slightly homoaromatic character for the singlet state of C₆H₆M and anti-aromatic character for triplet state of C₆H₆M.     

Isomerization Mechanisms of C_5H_2 on the Triplet and Singlet Potential Energy Surfaces

Density functional theory calculations with the B3LYP functional are used to study the structure and stabilities of C5H2 isomers and possible isomerization mechanisms on the triplet and singlet potential energy surfaces.Calculated results show that isomerization of C5H2 is likely to occur on the triplet potential energy surface while direct conversions of the singlet C5H2 isoers via 1,3-hydrogen migration transitions of the singlet C5H2 isomers via 1,3-hydrogen migration transition states are extremely difficult dynamically.In such isomerization processes,the hydrogen transfer processes in carbon chains are the rate-determining steps.The triplet species except the linear ground state X^3∑g^- are rather less stable than their singlet forms,although the singlet and triplet species haver similar geometries.     

Theoretical studies of cyclopropylsilylenes: The structures and stability of cyclopropylsilylene C3H5SiH

Ab initio molecular orbital calculations at the G2(MP2) level have been carried out on cyclopropylsilylene C₃H₅SiH. Four equilibrium structures were located. Like H₂Si, the ground state of C₃H₅SiH is singlet and the triplet is the low‐lying excited state. The singlet–triplet separation energy is 127.9 kJ/mol. The cis‐trans isomerization path of singlet cyclopropylsilylene was investigated by intrinsic reaction coordinate (IRC) calculations. The calculations show that no gauche conformers exist along the potential energy curve of the cis‐trans isomerization and the isomerization happens with a barrier of 30.1 kJ/mol. Changes (ΔH and ΔG) in thermodynamic functions, equilibrium constant K(T), and A factor and reaction rate constant k(T) in Eyring transition state theory of the cis‐trans isomerization were also calculated. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

C3H4: Theoretical study of structures and stabilities of isomers

The various isomers including stable structures, carbenes, and diradicals on the C₃H₄ surface have been investigated. The two carbenes propenylidene and cyclopropylidene have been found to have singlet ground states. Vinylmethylene is predicted to have a triplet ground state with a planar diradical type of structure. The syn and anti forms of this state are degenerate. This is in agreement with the observation of two triplet states in the electron spin resonance (ESR ) spectra. The π electrons are found to be delocalized over the three carbons. The singlet diradical structures are found to be more stable than the carbene structures, which retain the CH₂ (DOUBLE BOND) CH allylic structures. The orbital compositions of the frontier orbitals of all systems have been determined to examine the nature of these orbitals. © 1996 John Wiley & Sons, Inc.     

Structure and stability of X4Y4H4 (XY=CC,BN)

Ab initio calculations have been carried out to study the structures and relative stabilities of the planar eight‐membered ring B₄N₄H₄ and its isoelectronic species C₈H₄ at the HF/6‐31G*, MP2/6‐31G*, MP2/6‐311G**, and MP4SDQ/6‐31G* levels. The analyses of Milliken population, vibration frequencies, π‐molecular orbital components, and orbital energy levels were used to evaluate the relative stabilities of these two similar systems. The homodesmotic reactions were also taken to be a useful index of relative stability for X₄Y₄H₄ (XY=CC, BN) and gave the resonance energies with MP4SDQ/6‐31G* of C₈H₄ (?37.2 kcal/mol) < B₄N₄H₄ (?29.2 kcal/mol). Furthermore, we calculated the thermodynamic functions of these reactions to discuss the influence of temperature. It is concluded that B₄N₄H₄ may exist in theory and could be a little more stable than C₈H₄. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 293–298, 2001     

The DFT study on mechanisms for NCO with C2H5 reaction

A detailed investigation has been performed at the QCISD(T)/6‐311++G(d,p)//B3LYP/6‐311+G(d,p) level for the reaction of NCO with C₂H₅ by constructing singlet and triplet potential energy surfaces (PES). The results show that the title reaction is more favorable on the singlet PES than on the triplet PES. On the singlet PES, the initial addition processes are barrierless and release lots of energy. The dominant channel occurs via the fragmentations of the initial adduct C₂H₅NCO and C₂H₅OCN to form C₂H₄ + HNCO and HOCN, respectively. With higher barrier heights, other products such as CH₄ + HNC + CO, CH₃CHNH + CO, CH₃CH + HNCO, and CH₃CN + H₂ + CO are less competitive. On the triplet PES, the entrance reactions surpass significant barriers; therefore, it could be negligible at the normal atmospheric condition. However, the most feasible channel on the triplet PES is the direct hydrogen abstraction channel to form CH₂CH₂ + HNCO. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Heteroatom effects on allenic seven-membered ring X2C4H4C (X = CH,N, P,and As)

Stable configurations of seven-membered rings X₂C₄H₄C (1 _X , X = CH, N, P, and As) in the singlet (s) and triplet (t) states are found at B3LYB/6-311++G** level of theory. Thermal energy gaps, ΔE _s-t; enthalpy gaps, ΔH _s-t; Gibbs free energy gaps, ΔG _s-t, between the singlet and triplet states of 1 _X were estimated at the same level of theory. The ΔG _s-t gap between the singlet and triplet states of 1 _X changes in the order: 1 _P > 1 _As > 1 _N , respectively.     

Beryllepin,C6H6Be,and “Beryllium‐Inserted Benzenes,” C6H6Ben,n = 2–6: A Density Functional Computational Investigation

The seven‐membered beryllium‐containing heterocycle beryllepin, C₆H₆Be, has been examined computationally at the B3LYP/6‐311++G** density functional level of theory. Beryllepin is best described as a planar singlet heterocyclic conjugated triene with marginal aromatic character containing a C–Be–C moiety forced to be nonlinear (∠C‐Be‐C = 146.25°) by the cyclic constraints of the seven‐membered ring. The molecule can be considered to be derived from a benzene‐like system in which a neutral beryllium atom has been inserted between two adjacent carbon atoms. The 11 other possible “beryllium‐inserted benzenes,” C₆H₆Be_n, n = 2–6, have also been investigated. Only two of these heterocyclic systems, the eight‐membered 1,4‐diberyllocin and the nine‐membered 1,4,7‐triberyllonin, were found to be stable, singlet‐ground‐state systems, albeit with little aromatic character. Of the remaining nine beryllium‐inserted benzenes, with the exception of the 11‐membered ring containing five beryllium atoms and the 12‐membered ring containing six beryllium atoms, which were calculated to exist as a ground state pentet and septet, respectively, all were calculated to be ground state triplet systems.     

Ab initio study of C4H3 potential energy surface and reaction of ground‐state carbon atom with propargyl radical

The potential energy surface for the reaction of the ground‐state carbon atom [C(³P_j)] with the propargyl radical [HCCCH₂(X²B₁)] is investigated using the G2M(RCC,MP2) method. Numerous local minima and transition states for various isomerization and dissociation pathways of doublet C₄H₃ are studied. The results show that C(³P_j) attacks the π system of the propargyl radical at the acetylenic carbon atom and yields the n‐C₄H₃(²A′) isomer i3 after an 1,2‐H atom shift. This intermediate either splits a hydrogen atom and produces singlet diacetylene, [HCCCCH ( p1 )+H] or undergoes (to a minor amount) a 1,2‐H migration to i‐C₄H₃(²A′) i5 , which in turn dissociates to p1 plus an H atom. Alternatively, atomic carbon adds to the triple C?C bond of the propargyl radical to form a three‐member ring C₄H₃ isomer i1 , which ring opens to i3 . Diacetylene is concluded to be a nearly exclusive product of the C(³P_j)+HCCCH₂ reaction. At the internal energy of 10.0 kcal/mol above the reactant level, Rice–Ramsperger–Kassel–Marcus calculations show about 91.7% of HCCCCH comes from fragmentation of i3 and 8.3% from i5 . The other possible minor channels are identified as HCCCC+H₂ and C₂H+HCCH. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1522–1535, 2001     

Azulenylcarbenes: Rearrangements on the C11H8 Potential Energy Surface

Four isomeric azulenylcarbenes were synthesized in argon matrices by photolysis of the corresponding diazo precursors, and the photochemistry of these carbenes was studied. The carbenes and their rearranged products were characterized by IR, UV/Vis, and EPR spectroscopy, and the experimental data were compared to results from DFT calculations. While 2‐, 5‐ and 6‐azulenylcarbene show triplet ground states, 1‐azulenylcarbene exhibits a singlet ground state, in accord with theoretical predictions. The rearrangements of the azulenylcarbenes give access to a number of unusual C₁₁H₈ isomers, such as other carbenes and strained allenes.     

Gas‐Phase Synthesis of the Benzyl Radical (C6H5CH2)

Dicarbon (C₂), the simplest bare carbon molecule, is ubiquitous in the interstellar medium and in combustion flames. A gas‐phase synthesis is presented of the benzyl radical (C₆H₅CH₂) by the crossed molecular beam reaction of dicarbon, C₂(X¹Σ_g⁺, a³Π_u), with 2‐methyl‐1,3‐butadiene (isoprene; C₅H₈; X¹A′) accessing the triplet and singlet C₇H₈ potential energy surfaces (PESs) under single collision conditions. The experimental data combined with ab initio and statistical calculations reveal the underlying reaction mechanism and chemical dynamics. On the singlet and triplet surfaces, the reactions involve indirect scattering dynamics and are initiated by the barrierless addition of dicarbon to the carbon–carbon double bond of the 2‐methyl‐1,3‐butadiene molecule. These initial addition complexes rearrange via multiple isomerization steps, leading eventually to the formation of C₇H₇ radical species through atomic hydrogen elimination. The benzyl radical (C₆H₅CH₂), the thermodynamically most stable C₇H₇ isomer, is determined as the major product.     

Potential energy surfaces for the molecular and free radical dissociations of H2CS,F2CS and Cl2CS: An ab initio SCF MO study

Energies along the planar symmetric (C_2v) and planar assymetric (C_s paths to molecular dissociation of the ground state thiocarbonyl halides, F₂CS and Cl₂CS, together with their transition state geometries, have been calculated by ab initio SCF MO methods using the STO-3G and 4-31G basis sets. For comparison, results on H₂CS at similar levels of calculation are also included in this report. In addition, the 4-31G^** basis set has been employed to predict the geometries of the ground state species and the endothermicities of their free radical dissociations. The results of experiments in which the lowest excited singlet states of these molecules have been photoexcited are interpreted in light of these calculations. Thermodynamic data for both molecular and free radical dissociations are evaluated and discussed.     

Halogen switching of azacarbenes C2NH ground states at ab initio and DFT levels

Relative stabilities and singlet–triplet energy differences are calculated for 24 C₂NX azacarbenes (where X is H, F, Cl, and Br). Three skeletal arrangements are employed including azacyclopropenylidene, [(imino)methylene]carbene, and cyanocarbene. Halogens appear to alternate the electronic ground states of C₂NH azacarbenes, from triplet to singlet states, at MP3/6‐311++G**, B1LYP/6‐311++G**, B3LYP/6‐311++G**, MP2/6‐311++G**, MP4(SDTQ)/6‐311++G**, QCISD(T)/6‐311++G**, CCSD(T)/6‐311++G**, CCSD(T)/cc‐pVTZ, G1, and G2 levels of theory. The aromatic characters of singlet cyclic azacyclopropenylidenes are measured using GIAO–NICS calculations. Linear correlations are found between the B3LYP/6‐311++G** calculated LUMO–HOMO energy gaps (ΔE_{HOMO ‐ LUMO}) of the singlet carbenes versus their corresponding singlet–triplet energy separations (ΔE). Electrophilic characters are found for all singlet azacarbenes in their addition reactions to alkenes with the highest electrophilicity being exhibited for X = F. © 2008 Wiley Periodicals, Inc. Heteroatom Chem 19:377–388, 2008; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/hc.20442     

Theoretical studies on structures and electronic spectra of linear carbon chains C2nH+ (n = 1−5)

The density functional theory (DFT) and the complete active space self‐consistent‐field (CASSCF) method have been used for full geometry optimization of carbon chains C_2nH⁺ (n = 1–5) in their ground states and selected excited states, respectively. Calculations show that C_2nH⁺ (n = 1–5) have stable linear structures with the ground state of X³Π for C₂H⁺ or X³Σ^? for other species. The excited‐state properties of C_2nH⁺ have been investigated by the multiconfigurational second‐order perturbation theory (CASPT2), and predicted vertical excitation energies show good agreement with the available experimental values. On the basis of our calculations, the unsolved observed bands in previous experiments have been interpreted. CASSCF/CASPT2 calculations also have been used to explore the vertical emission energy of selected low‐lying states in C_2nH⁺ (n = 1–5). Present results indicate that the predicted vertical excitation and emission energies of C_2nH⁺ have similar size dependences, and they gradually decrease as the chain size increases. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Crossover Sorption of C2H2/CO2 and C2H6/C2H4 in Soft Porous Coordination Networks

Porous sorbents are materials that are used for various applications, including storage and separation. Typically, the uptake of a single gas by a sorbent decreases with temperature, but the relative affinity for two similar gases does not change. However, in this study, we report a rare example of “crossover sorption,” in which the uptake capacity and apparent affinity for two similar gases reverse at different temperatures. We synthesized two soft porous coordination polymers (PCPs), [Zn₂(L1)(L2)₂]_n (PCP-1) and [Zn₂(L1)(L3)₂]_n (PCP-2) (L1= 1,4-bis(4-pyridyl)benzene, L2=5-methyl-1,3-di(4-carboxyphenyl)benzene, and L3=5-methoxy-1,3-di(4-carboxyphenyl)benzene). These PCPs exhibits structural changes upon gas sorption and show the crossover sorption for both C₂H₂/CO₂ and C₂H₆/C₂H₄, in which the apparent affinity reverse with temperature. We used in situ gas-loading single-crystal X-ray diffraction (SCXRD) analysis to reveal the guest inclusion structures of PCP-1 for C₂H₂, CO₂, C₂H₆, and C₂H₄ gases at various temperatures. Interestingly, we observed three-step single-crystal to single-crystal (sc-sc) transformations with the different loading phases under these gases, providing insight into guest binding positions, nature of host–guest or guest-guest interactions, and their phase transformations upon exposure to these gases. Combining with theoretical investigation, we have fully elucidated the crossover sorption in the flexible coordination networks, which involves a reversal of apparent affinity and uptake of similar gases at different temperatures. We discovered that this behaviour can be explained by the delicate balance between guest binding and host–guest and guest-guest interactions.     

Theoretical study of [Si,O,C,O] species: Prediction of new species on triplet potential energy surface

The intermediates [Si,O,C,O] of the Si + CO₂ reaction have been studied in detail using high level ab iniitio methods. Both singlet and triplet [Si,O,C,O] species are characterized structurally and energetically. On the singlet potential energy surface (PES), the vdw‐OSi–CO isomer and in the triplet PES, the bent‐SiOCO isomer is found to be thermodynamically as well as kinetically most stable species. All possible isomerization transition states (TS) are located on both singlet and triplet potential surfaces. On the triplet surface, the stability of the trans‐OSiCO isomer is comparable with that of the bent‐SiOCO isomer. A non‐planar cis‐SiOCO isomer is located on the triplet PES, which is predicted for the first time. Heats of formation at 0 K (Δ_fH°, 0 K) for all singlet and triplet species are computed using G3B3, G3MP2, and CBS‐Q theories. The discrepancy between G3B3 and the other two methods for the heat of formation value for triplet trans‐OSiCO is discussed. The PESs for singlet as well as triplet species with their dissociation asymptotes are explored at the CCSD(T)/6‐311G(d,p)//MP2/6‐311G(d,p) level of theory. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical study of fullerene derivatives: C40H4 and C40X4 cluster molecules

Herein we demonstrate that the C₄₀ cluster molecule is easily formed to T_d symmetry structure and its ground state is ⁵A₂ open shell with four unpaired electrons. These four unpaired electrons are located at the tip points of the T_d symmetry structure. This work also indicates that these four unpaired electrons can easily react with a single valence atom, such as hydrogen or halogen atoms, to form a stable carbon hydrogen cluster molecule, C₄₀H₄, and carbon halogen cluster molecules, C₄₀X₄ (X=F, Cl, Br, I), respectively. The PM3 semiempirical molecular orbital method from Gaussian 94W computer program package was applied very well to these cluster molecules. According to the results in this study, the structures of geometrical optimization, ionization potential, energy gap, heat of formation, atomization energy, vibration frequency, and the remaining data of C₄₀H₄ and C₄₀X₄ cluster molecules. The above-calculated data prove that these unknown cluster molecules are stable and have a stable capacity similar to 1,3,5,7-tetrahaloadamantane molecules. They can be possibly synthesized experimentally in the near future. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 273–284, 1998     

Theoretical study of fullerene derivatives: C28H4 and C28X4 cluster molecules

Based on the basic theory of C₂₈ cluster molecule proven by H. W. Kroto and the research findings of C₂₈'s derivative such as Ti@C₂₈* and Mg@C₂₈, proven by T. Guo, B. I. Dunlap, O. D. Haberlen, and others, we examine the two series fullerene derivatives, C₂₈H₄ and C₂₈X₄ cluster molecules, which are formed by the skeleton of C₂₈ cluster molecule. In this work, we not only prove that C₂₈ cluster molecule belongs to the T_d symmetry structure and its ground state is ⁵A₂ open-shell with four unpaired electrons, but also find that C₂₈ can easily react with single valence electron atoms, like hydrogen atom and halogen atoms, to be formed to stable fullerene derivatives, C₂₈H₄ and C₂₈X₄ cluster molecules (X=F, Cl, Br, I). The PM3 semiempirical molecular orbital method from G94W and Hyperchem program packages were applied very well in these fullerene derivatives. According to the results presented herein, we obtain the structures of geometrical optimization, ionization potential energy gap, heat of formation, atomization energy, and vibration frequency data of the C₂₈H₄ and C₂₈X₄ cluster molecules. The above calculation data confirm that these unknown fullerene derivatives are stable molecules; the stable behavior resembles the 1,3,5,7-tetrahaloadamantane molecules. It is quite possible that they can be synthesized experimentally in the near future. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 187–197, 1998