Stabilization Studies on Divalent Five‐Membered Rings C4H4C,C4H4Si,C4H4Ge,C4H4Sn,and C4H4Pb

Energy differences, ΔX_S‐t (X = E, H and G) (ΔX_S‐t = X_(singlet)‐X_(triplet)) between singlet (s) and triplet (t) states are calculated at B3LYP/6‐311++G (3df,2p). The DFT calculations show that the triplet state of C₄H₄C is a ground state with planar conformer respect to its corresponding nonplanar singlet state. Both singlet and triplet states of C₄H₄M (M = Si, Ge, Sn and Pb) have a planar conformer with the singlet ground state. Four isodesmic reactions are presented for determining the stability energies, SE. NICS calculations are carried out for C₄H₄M to determine the aromatic character.     

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.     

Electronic and Vibrational Coherence Dynamics in a Cyanine Dye Studied Using a Few‐Cycle Pulsed Laser

We report the relaxation times of electronic and vibrational coherence in the cyanine dye 1,1′,3,3,3′,3′‐hexamethyl‐4,4′,5,5′‐dibenzo‐2,2′‐indotricarbocyanine, measured using a 7.1 fs pulsed laser. The vibrational phase relaxation times are found to be between 380 and 680 fs in the ground and lowest excited singlet states. The vibrational dephasing times of the 294, 446, and 736 cm^?1 modes are relatively long among the six modes associated with excited‐state wave packets. The slower relaxations are explained in terms of a coupled triplet of vibrational modes, which preserves coherence by forming a tightly bound group to satisfy the condition of circa conservation of vibrational energy. Using data from the negative‐time range (i.e., when the probe pulse precedes the pump pulse), the electronic phase relaxation time is found to be 31±1 fs. The dynamic vibrational mode in the excited state (1171 cm^?1), detected in the positive‐time range, is also studied from the negative‐time traces under the same experimental conditions.     

A theoretical comparison of the lowest-lying singlet and triplet states of H2CBe and of HCBeH

The low-lying singlet and triplet states of H₂CBe and HCBeH are examined using ab inito molecular orbital theory. In agreement with earlier results, the lowest-lying structure of H₂CBe has C_2v symmetry and is a triplet with one π electron (³ B₁). The results presented here suggest that the lowest-energy singlet structure is the (¹B₁) open-shell singlet, also with C_2v symmetry, at least 2.5 kcal/mol higher in energy. The singlet C_2v structure with two π electrons (¹A₁) is 15.9 kcal/mol higher than ³B₁. All of these structures are bound with respect to the ground state of methylene and the beryllium atom. In HCBeH, linear equilibrium geometries are found for the triplet (³Σ) and singlet (¹Δ) states. The triplet is more stable than the singlet (¹Δ) by 35.4 kcal/mol, and is only 2.9 kcal/mol higher in energy than triplet H₂ CBe. Since the transition structure connecting these two triplet molecules is found to be 50.2 kcal/mol higher in energy than H₂ CBe, both triplet equilibrium species might exist independently. The harmonic vibrational frequencies of all structures are also reported.     

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.     

Nitrogen Analogues of Thiele’s Hydrocarbon

A series of bis[N,N‐di‐(4‐methoxylphenyl)amino]arene dications 1 ²⁺– 3 ²⁺ have been synthesized and characterized. Their electronic structures were investigated by various experiments assisted by theoretical calculations. It was found that they are singlets in the ground state and that their diradical character is dependent on the bridging moiety. 3 ²⁺ has a smaller singlet–triplet energy gap and its excited triplet state is thermally readily accessible. The work provides a nitrogen analogue of Thiele’s hydrocarbon with considerable diradical character.     

A Thermally Populated,Perpendicularly Twisted Alkene Triplet Diradical

Variable‐temperature NMR and ESR spectroscopic studies reveal that bis(dibenzo[a,i]fluorenylidene) 1 possesses a singlet ground state, 1 (S₀), while the 90° twisted triplet 1 (T₁) is populated to a small extent already at room temperature. Analysis of the increasing amount of paramagnetic 1 (T₁) at temperatures between 300 and 500 K yields the exchange interaction J_ex/h c=3351 cm^?1 and a singlet–triplet energy splitting of 9.6 kcal mol^?1, which is in excellent agreement with calculations (9.3 kcal mol^?1 at the UKS BP86/B3LYP/revPBE level of theory). In contrast, the zero‐field splitting parameter D is very small (calculated value ?0.018 cm^?1) and unmeasurable.     

A Thermally Populated,Perpendicularly Twisted Alkene Triplet Diradical

Variable‐temperature NMR and ESR spectroscopic studies reveal that bis(dibenzo[a,i]fluorenylidene) 1 possesses a singlet ground state, 1 (S₀), while the 90° twisted triplet 1 (T₁) is populated to a small extent already at room temperature. Analysis of the increasing amount of paramagnetic 1 (T₁) at temperatures between 300 and 500 K yields the exchange interaction J_ex/h c=3351 cm⁻¹ and a singlet–triplet energy splitting of 9.6 kcal mol⁻¹, which is in excellent agreement with calculations (9.3 kcal mol⁻¹ at the UKS BP86/B3LYP/revPBE level of theory). In contrast, the zero‐field splitting parameter D is very small (calculated value −0.018 cm⁻¹) and unmeasurable.     

Evidence for long-lived excited states of [CnH2]2+ carbodications

The energetics, structures, stabilities and reactivities of[C_nH₂]²⁺ ions have been investigated using computational methods and experimental mass spectrometric techniques. Spontaneous decompositions of [C_nH₂]²⁺ into [C_nH]⁺ + H⁺ products, observed for ions with odd-n values, have been explained by invoking the formation of excited triplet states. Even-n [C_nH]⁺ ions possess triplet ground states with low-lying excited states, whereas odd-n ions have triplet states with energies several eV above ground singlet states. Radiationless transitions of vibrationally excited long-lived triplet state ions into singlet state continua are suggested as possible mechanisms for spontaneous deprotonation processes of odd-n [C_nH₂]²⁺ ions. Evidence for these long-lived excited states has been obtained in bimolecular single electron transfer reactions.     

Beryllium Atom Mediated Dinitrogen Activation via Coupling with Carbon Monoxide

The reactions of laser‐ablated beryllium atoms with dinitrogen and carbon monoxide mixtures form the end‐on bonded NNBeCO and side‐on bonded (η²‐N₂)BeCO isomers in solid argon, which are predicted by quantum chemical calculations to be almost isoenergetic. The end‐on bonded complex has a triplet ground state while the side‐on bonded isomer has a singlet electronic ground state. The complexes rearrange to the energetically lowest lying NBeNCO isomer upon visible light excitation, which is characterized to be an isocyanate complex of a nitrene derivative with a triplet electronic ground state. A bonding analysis using a charge‐ and energy decomposition procedure reveals that the electronic reference state of Be in the NNBeCO isomers has an 2s⁰2p² excited configuration and that the metal‐ligand bonds can be described in terms of N₂→Be←CO σ donation and concomitant N₂←Be→CO π backdonation. The results demonstrate that the activation of N₂ with the N?N bond being completely cleaved can be achieved via coupling with carbon monoxide mediated by a main group atom.     

C-Br Bond Dissociation Mechanisms of 2-Bromothiophene and 3-Bromothiophene at 267 nm

C-Br bond dissociation mechanisms of 2-bromothiophene and 3-bromothiophene at 267 nm were investigated using ion velocity imaging technique. Translational energy distributions and angular distributions of the photoproducts, Br(²P_3/2) and Br^*(²P_½), were obtained and the possible dissociation channels were analyzed. For these two bromothiophenes, the Br fragments were produced via three channels: (i) the fast predissociation following the intersystem crossing from the excited singlet state to repulsive triplet state; (ii) the hot dissociation on highly vibrational ground state following the internal conversion of the excited singlet state; and (iii) the dissociation following the multiphoton ionization of the parent molecules. Similar channels are involved for photoproduct Br^* of the 2-bromothiophene dissociation at 267 nm; whereas for the photoproduct Br^* of 3-bromothiophene, the dissociation channel via internal conversion from the excited singlet state to highly vibrational ground state became dominating and the fast predissociation channel via the excited triplet state almost disappeared. Informations about the relative contribution, energy disposal, and the anisotropy of each channel were quantitatively given. It was found that with the position of Br atom in thienyl being far from S atom, the relative ratios of products from channels (i) and (ii) decreased obviously and the anisotropies corresponding to each channel became weaker.     

Singlet and Triplet Excited States and Intersystem Crossing in Free‐Base Porphyrin: TDDFT and DFT/MRCI Study

Extensive time-dependent DFT (TDDFT) and DFT/multireference configuration interaction (MRCI) calculations are performed on the singlet and triplet excited states of free-base porphyrin, with emphasis on intersystem crossing processes. The equilibrium geometries, as well as the vertical and adiabatic excitation energies of the lowest singlet and triplet excited states are determined. Single and double proton-transfer reactions in the first excited singlet state are explored. Harmonic vibrational frequencies are calculated at the equilibrium geometries of the ground state and of the lowest singlet and triplet excited states. Furthermore, spin–orbit coupling matrix elements of the lowest singlet and triplet states and their numerical derivatives with respect to nuclear displacements are computed. It is shown that opening of an unprotonated pyrrole ring as well as excited-state single and double proton transfer inside the porphyrin cavity lead to crossings of the potential energy curves of the lowest singlet and triplet excited states. It is also found that displacements along out-of-plane normal modes of the first excited singlet state cause a significant increase of the 2|H_so|S₁>, 1|H_so|S₁>, and 1|H_so|S₀> spin–orbit coupling matrix elements. These phenomena lead to efficient radiationless deactivation of the lowest excited states of free-base porphyrin via intercombination conversion. In particular, the S₁→T₁ population transfer is found to proceed at a rate of ≈10⁷ s⁻¹ in the isolated molecule.     

Electronic structure and the hydrogen-shift isomerization of hydrogen nitryl HNO2

Summary Electronic structure of hydrogen nitryl HNO₂, a yet not identified entity, and the path of its possible isomerization totrans-HONO have been investigated byab initio SCF and MRD-CI computations using the 6-31G** basis set. HNO₂ isC _2v -symmetric and its ground state (¹ A ₁) is less stable thantrans-HONO by 66 kJ/mol (with the SCF vibrational zero-point energy correction). The lowest two excited singlet states (¹ A ₂ and¹ B ₁) are nearly degenerate, their vertical excitation energies being predicted to be 4.8 eV. The isomerization path is traced by the CASSCF procedure and the activation barrier height is evaluated by the CI treatment. HNO₂ in its ground state isomerizes totrans-HONO by maintaining the planar (C _s-symmetric) structure. The activation energy is calculated to be 171 kJ/mol, which is clearly lower than the calculated H-N bond energy (253 kJ/mol). The transition state seems to be more adequately described as an interacting system of proton and the nitrite anion rather than as a pair of two fragment radicals.     

An ab initio study of the structures and energetics of the planar ground and 90°‐twisted excited states of substituted ethylenes

Ab initio molecular orbital calculations are performed on the planar ground states (S₀), the 90°‐twisted triplet (T₁), and pyramidalized singlet (S₁) excited states of ethylene, methaniminium cation (MC), monocyano‐ (MCE), 1,1‐dicyano‐ (DCE), 1,1‐dihydroxy‐ (DHE), and 1,1‐dicyano‐2,2‐dihydroxy (DCHE) ethylenes. Equilibrium geometries are optimized at the Hartree–Fock (HF) level with the 6‐31G* basis set. Electron correlation corrections are estimated by optimizing the HF/6‐31G* geometries at the (U)MP2/6‐31G* level and then by carrying out single‐point calculations at the fourth‐order Møller–Plesset perturbation theory ((U)MP4/6‐311G**//MP2/6‐31G*). The effects of various types of perturbations on the structures, energetics, dipole moments, and state ordering of S₀, S₁, and T₁ are carefully investigated. “Positive” S₁–T₁ splittings are estimated at the HF level for all studied molecules, while “negative” S₁–T₁ splittings are obtained at the MP2 level for MC, DHE, and DCHE. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 242–254, 2001     

Observation of a Thermally Accessible Triplet State Resulting from Rotation around a Main‐Group π Bond

We report the first direct spectroscopic observation by electron paramagnetic resonance (EPR) spectroscopy of a triplet diradical that is formed in a thermally induced rotation around a main‐group π bond, that is, the Si?Si double bond of tetrakis(di‐tert‐butylmethylsilyl)disilene ( 1 ). The highly twisted ground‐state geometry of singlet 1 allows access to the perpendicular triplet diradical 2 at moderate temperatures of 350–410 K. DFT‐calculated zero‐field splitting (ZFS) parameters of 2 accurately reproduce the experimentally observed half‐field transition. Experiment and theory suggest a thermal equilibrium between 1 and 2 with a very low singlet–triplet energy gap of only 7.3 kcal mol^?1.     

An ab initio study of the electronic structure of diimide

Ab initio calculations on the structure and geometry of the three isomers of N₂H₂ (trans-diimide, cis-diimide, and 1,1-dihydrodiazine) were performed both on HF and CI level using gaussian basis sets with polarization functions. The trans and cis isomers have singlet ground states; the trans isomer is found to be lower in energy than the cis isomer by 6.9 kcal/mol (HF) and 5.8 kcal/mol (CI), respectively. The barrier for the trans-cis isomerization is predicted to be 56 (HF) and 55 (CI) kcal/mol. H₂ N=N has a triplet ground state with a non-planar equilibrium geometry and a rather long NN bond of 1.34 Å. Its lowest singlet state, however, is planar with an NN double bond of 1.22 Å; it is found to lie about 3 kcal/mol above the triplet and 26 kcal/mol above the singlet ground state of trans-diimide.     

Spiro[4.4]nonatetraene and its Positive and Negative Radical Ions: Molectronic Structure Investigations

The electronic structure of spiro[4.4]nonatetraene 1 as well as that of its radical anion and cation were studied by different spectroscopies. The electron‐energy‐loss spectrum in the gas phase revealed the lowest triplet state at 2.98 eV and a group of three overlapping triplet states in the 4.5 – 5.0 eV range, as well as a number of valence and Rydberg singlet excited states. Electron‐impact excitation functions of pure vibrational and triplet states identified various states of the negative ion, in particular the ground state with an attachment energy of 0.8 eV, an excited state corresponding to a temporary electron attachment to the 2b₁ MO at an attachment energy of 2.7 eV, and a core excited state at 4.0 eV. Electronic‐absorption spectroscopy in cryogenic matrices revealed several states of the positive ion, in particular a richly structured first band at 1.27 eV, and the first electronic transition of the radical anion. Vibrations of the ground state of the cation were probed by IR spectroscopy in a cryogenic matrix. The results are discussed on the basis of density‐functional and CASSCF/CASPT2 quantum‐chemical calculations. In their various forms, the calculations successfully rationalized the triplet and the singlet (valence and Rydberg) excitation energies of the neutral molecule, the excitation energies of the radical cation, its IR spectrum, the vibrations excited in the first electronic absorption band, and the energies of the ground and the first excited states of the anion. The difference of the anion excitation energies in the gas and condensed phases was rationalized by a calculation of the Jahn‐Teller distortion of the anion ground state. Contrary to expectations based on a single‐configuration model for the electronic states of 1 , it is found that the gap between the first two excited states is different in the singlet and the triplet manifold. This finding can be traced to the different importance of configuration interaction in the two multiplicity manifolds.     

Perylene Bisimide Radicals and Biradicals: Synthesis and Molecular Properties

Unprecedented neutral perylene‐3,4:9,10‐tetracarboxylic acid bisimide (PBI) radicals and biradicals were synthesized by facile chemical oxidation of 4‐hydroxyaryl‐substituted PBIs. Subsequent characterization by optical and magnetic spectroscopic techniques, as well as quantum chemical calculations, revealed an open‐shell singlet biradical ground state for the PBI biradical OS ‐ 2^.. (〈s²〉=1.2191) with a relatively small singlet–triplet energy gap of 0.041 eV and a large singlet biradical character of y=0.72.     

Photoinduced Triplet–Triplet Energy Transfer in a 2‐Ureido‐4(1H)‐Pyrimidinone‐Bridged,Quadruply Hydrogen‐Bonded Ferrocene–Fullerene Assembly

2‐Ureido‐4(1H)‐pyrimidinone‐bridged ferrocene–fullerene assembly I is designed and synthesized for elaborating the photoinduced electron‐transfer processes in self‐complementary quadruply hydrogen‐bonded modules. Unexpectedly, steady‐state and time‐resolved spectroscopy reveal an inefficient electron‐transfer process from the ferrocene to the singlet or triplet excited state of the fullerene, although the electron‐transfer reactions are thermodynamically feasible. Instead, an effective intra‐assembly triplet–triplet energy‐transfer process is found to be operative in assembly I with a rate constant of 9.2×10⁵ s^?1 and an efficiency of 73 % in CH₂Cl₂ at room temperature.     

Aromaticity Effects on the Profiles of the Lowest Triplet‐State Potential‐Energy Surfaces for Rotation about the CC Bonds of Olefins with Five‐Membered Ring Substituents: An Example of the Impact of Baird’s Rule

A density functional theory study on olefins with five‐membered monocyclic 4n and 4n+2 π‐electron substituents (C₄H₃X; X=CH⁺, SiH⁺, BH, AlH, CH₂, SiH₂, O, S, NH, and CH^?) was performed to assess the connection between the degree of substituent (anti)aromaticity and the profile of the lowest triplet‐state (T₁) potential‐energy surface (PES) for twisting about olefinic C?C bonds. It exploited both Hückel’s rule on aromaticity in the closed‐shell singlet ground state (S₀) and Baird’s rule on aromaticity in the lowest ππ* excited triplet state. The compounds CH₂?CH(C₄H₃X) were categorized as set A and set B olefins depending on which carbon atom (C2 or C3) of the C₄H₃X ring is bonded to the olefin. The degree of substituent (anti)aromaticity goes from strongly S₀‐antiaromatic/T₁‐aromatic (C₅H₄⁺) to strongly S₀‐aromatic/T₁‐ antiaromatic (C₅H₄^?). Our hypothesis is that the shapes of the T₁ PESs, as given by the energy differences between planar and perpendicularly twisted olefin structures in T₁ [ΔE(T₁)], smoothly follow the changes in substituent (anti)aromaticity. Indeed, correlations between ΔE(T₁) and the (anti)aromaticity changes of the C₄H₃X groups, as measured by the zz‐tensor component of the nucleus‐independent chemical shift ΔNICS(T₁;1)_zz, are found both for sets A and B separately (linear fits; r²=0.949 and 0.851, respectively) and for the two sets combined (linear fit; r²=0.851). For sets A and B combined, strong correlations are also found between ΔE(T₁) and the degree of S₀ (anti)aromaticity as determined by NICS(S₀,1)_zz (sigmoidal fit; r²=0.963), as well as between the T₁ energies of the planar olefins and NICS(S₀,1)_zz (linear fit; r²=0.939). Thus, careful tuning of substituent (anti)aromaticity allows for design of small olefins with T₁ PESs suitable for adiabatic Z/E photoisomerization.