Ab Initio Study on the Potential Energy Surfaces of B4 Cluster

The singlet and triplet potential energy surfaces (PES) for the isomerization and dissociation reactions of B₄ isomers have been investigated using ab initio methods. Ten B4 isomers have been identified and of these 10 species, 4 have not been reported previously. The singlet rhombic structure ¹1 is found to be the most stable on the B₄ surface, in agreement with the results of previous reports. Several isomerization and dissociation pathways have been found. On the singlet PES, the linear ¹3b can rearrange to rhombus ¹1 directly, while ¹3c rearranges to ¹1 through two‐step reactions involving a cyclic intermediate. On the triplet PES, the capped triangle structure ³2 undergoes ring opening to the linear isomer ³3b with a barrier of 34.8 kcal/mol and 44.9 kcal/mol, and the latter undergoes ring closure to the square structure ³1 with a barrier of 30.4 kcal/mol and 33.0 kcal/mol at the MP4/6–311+G(3df)//MP2/6–311G(d) and CCSD/aug‐cc‐pVTZ//MP2/6–311G(d) levels of theory, respectively. The direct decomposition of singlet B₄ yielding to B₃+B is shown to have a large endothermicity of 87.3 kcal/mol (CCSD), and that producing 2B₂ to have activation energy of 133.4 kcal/mol (CCSD).     

Is the stereomutation of methane possible?

Large basis set ab initio calculations at correlated levels, including MP2, single reference, as well as multireference configuration interaction, carried out on the methane potential energy surface, have located and characterized a transition structure for stereomutation (one imaginary frequency). This structure is best described as a pyramidal complex between singlet methylene and a side-on hydrogen molecule with C_s symmetry. At the single reference CI level, it lies 105 kcal/mol above the methane T_d-ground state but is stable relative to dissociation into CH₂(¹A₁) and H₂ by 13 kcal/mol at 0 K (with harmonic zero point energy (ZPE) corrections for all structures). Dissociation of the transition state into triplet methylene and hydrogen also is endothermic (by 4 kcal/mol), but single bond rupture to give CH and H^. is 3 kcal/mol exothermic. Thus, it does not appear likely that methane can undergo stereomutation classically beneath the dissociation limit. Confirming earlier conclusions, side-on insertion of ¹A₁ CH₂ into H₂ in a perpendicular geometry occurs without activation energy. Planar (D_4h) methane (130.5 kcal/mol) has four imaginary frequencies. Two of these are degenerate and lead to equivalent planar C_2v structures with one three-center, two-electron bond and two two-electron bonds and two imaginary frequencies. The remaining imaginary frequencies of the D_4h form lead to tetrahedral (T_d) and pyramidal (C_4v) methane. The latter has three negative eigenvalues in the force-constant matrix; one of these leads to the T_d global minimum and the other to the C_s (parallel) stereomutation transition structure. Multireference CI calculations with a large atomic natural orbitals basis set produce similar results, with the electronic energy of the C_s stereomutation transition state 0.7 ± 0.5 kcal/mol higher than that of CH + H^. dissociation products, and a ZPE-corrected energy which is 5 ± 1 kcal/mol higher. Also considered are photochemical pathways for stereomutation and the possible effects of nuclear spin, inversion tunneling, and the parity-violating weak nuclear interaction on the possibility of an experimental detection of stereomutation in methane. © 1995 by John Wiley & Sons, Inc.     

Bonding and correlation analysis of various Si2CO isomers on the potential energy surface

At various levels of theory, singlet and triplet potential energy surfaces (PESs) of Si₂CO, which has been studied using matrix isolation infrared spectroscopy, are investigated in detail. A total of 30 isomers and 38 interconversion transition states are obtained at the B3LYP/6‐311G(d) level. At the higher CCSD(T)/6‐311+G(2d)//QCISD/6‐311G(2d)+ZPVE level, the global minimum ¹1 (0.0 kcal/mol) corresponds to a three‐membered ring singlet O‐cCSiSi (¹A′). On the singlet PES, the species ¹2 (0.2 kcal/mol) is a bent SiCSiO structure with a ¹A′ electronic state, followed by a three‐membered ring isomer Si‐cCSiO (¹A′) ¹3 (23.1 kcal/mol) and a linear SiCOSi ¹4 (¹Σ⁺) (38.6 kcal/mol). The isomers ¹1, ¹2, ¹3 , and ¹4 possess not only high thermodynamic stabilities, but also high kinetic stabilities. On the triplet PES, two isomers ³1 (³B₂) (18.8 kcal/mol) and ³7 (³A″) (23.3 kcal/mol) also have high thermodynamic and kinetic stabilities. The bonding natures of the relevant species are analyzed. The similarities and differences between C₃O, C₃S, SiC₂O, and SiC₂S are discussed. The present results are also expected to be useful for understanding the initial growing step of the CO‐doped Si vaporization processes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Bridged structures in multiply bonded silicon compounds: Disilyne,protonated disilyne and disilene

Ab initio SCF and electron correlation calculations are reported for the singlet ground state of the title compounds. These calculations confirm earlier findings that non-planar bridged Si₂H₂ is the most stable structure. For protonated disilyne (Si₂H³⁺) a bridged D_3h structure is the global mimimum. Two bridged structures of C_2v and C_2h symmetry are found in the case of disilene (Si₂H₄) which are only 14–17 kcal/mol above the D_2h structure.     

Ab initio calculations find 2,2-disilylcyclopentane-1,3-diyl is a singlet diradical with a high barrier to ring closure

Ab initio calculations on the lowest singlet and triplet states of 2,2-disilylcyclopentane-1,3-diyl find that the singlet lies well below the triplet. The C ₂ singlet diradical is calculated to be a minimum on the potential energy surface with an enthalpic barrier to ring closure of ΔH ^‡ ₂₉₈ = 13.5 kcal/mol at the CASPT2/6-31G* level of theory. The energy of the 1,3-divinyl-substituted singlet diradical is calculated to be only 0.8 kcal/mol higher than that of 5,5-disilyl-1,3-divinylbicyclo[2.1.0]pentane at this level of theory, but the transition state for their equilibration is computed to be 12.8 kcal/mol above the diradical in energy. Received: 2 July 1998 / Accepted: 4 August 1998 / Published online: 16 November 1998     

Some theoretical studies on hydrogen molecule capture by platinum atoms

Pseudopotential SCF-LCAO-MO and variational and perturbative Cl calculations were carried out for H₂ molecule capture by a single Pt atom with C_2v symmetry. A pseudopotential for the platinum atom including relativistic effects was used. Singlet and triplet states of the Pt-H₂ interaction having different representations of the mentioned C_2v symmetry were studied. The triplet ground state of Pt leads to two A₁ and B₂ states in which the metal atom cannot capture H₂; i.e., both have repulsive interaction energies. The electronic state responsible for the capture of H₂ is the closed-shell, singlet A₁ excited state. The equilibrium geometry of the system is reached with a broken H? H bond at a HPtH angle of about 100°. Additionally another shallower minimum for a singlet A₁ linear structure is observed. Specific predictions for the thermal and photochemical Pt + H₂ reactions that can be carried out under matrix isolation conditions are made.     

Stereodynamics of 1,3,5-tris(trifluoromethylsulfonyl)-1,3,5-triazinane: experimental and theoretical analysis

Dynamic NMR of 1,3,5-tris(trifluoromethylsulfonyl)-1,3,5-triazinane reveals two dynamic processes: ring inversion leading to equilibrium between two degenerate rotamers of C_s symmetry (ΔG^≠ = 13.5 kcal/mol), and rotation about the S-N bond leading to equilibrium between the C_s (more stable) and C_3v (2.12 kcal/mol less stable) rotamers (ΔG^≠ = 13.0 kcal/mol).     

Ab initio SCF studies of the molecular structure of XeF6, IF 6 − , and TeF 6 2− in non-octahedral geometries

All-electron SCF calculations in contracted large Gaussian basis sets were performed for the molecules in the isoelectronic series XeF₆, IF ₆ ^– , and TeF ₆ ^2– . Molecular equilibrium geometry of these molecules was studied first in O _h symmetry. Then, the gradient minimization technique was used to determine molecular structure of the studied systems near the local minima corresponding to C _3v and C _2v geometries involved in the internal motion.In the O _h symmetry, TeF ₆ ^2– and IF ₆ ^– are bound by 172 and 104 kcal/mol, respectively. The total energy of XeF₆ is larger than the sum of total energies of the constituent atoms by 192 kcal/mol. Lowering the symmetry to C _3v and C _2v results in an energy gain of about 20 kcal/mol for all studied systems.     

CEPA Calculations of potential energy surfaces for open-shell systems. II. The reaction of C+ Ions with molecular hydrogen

Ab initio calculations including electron correlation effects (mainly on CEPA-PNO level) have been performed for the potential energy surface (PES) of the reaction of ²P carbon ions with molecular hydrogen. For the collinear abstraction reactions (C_∞v symmetry: ²σ⁺, ²Π-2) the minimum energy paths have been determined. The vertical insertion reaction (C_2v; ²A₁,B₁, ²B₂) has been investigated with particular emphasis (minimum energy path, barrier heights, intersystem crossing). The influence of the size of the orbital basis and of electron correlation has been studied in some detail. The interaction of the ²A₁, and ²B₂ surfaces has been analyzed, leading to the conclusion that close to C_2v symmetry a low energy path exists by which CH₂⁺(²A₁)can be easily formed, with a barrier (²B₂ → ²A₁) ≈ 18 kcal/mol below the asymptote. The analysis of electron correlation effects reveals that it is compulsory to correlate the whole valence shell if one wants to obtain reliable surfaces. The influence of singly excited configurations for getting the correct behaviour of the PES is generally small.     

Cepa calculations of potential energy surfaces for open-shell systems. I. The reaction of O(3P) with H2(1Σg+)

Ab initio calculations including electron correlation effects (mainly on CEPA-PNO level) have been performed for the potential energy surface of the reaction of ³P oxygen atoms with molecular hydrogen. The collinear abstraction reaction (C_∞v symmetry) and the vertical insertion reaction (C_2v) have been investigated with particular emphasis.The influence of the orbital basis size and of electron correlation both on the reaction energy and on the barrier height and location for the abstraction reaction has been studied in some detail. Our extrapolated value for the barrier for this reaction is 13.4 ± 1.0 kcal/mol, in fair agreement with the experimental activation energy, while the insertion reaction has to pass over a barrier of =48 kcal/mol. The analysis of electron correlation effects reveals that it is compulsory to include all singly and doubly substituted configurations, to correct for unlinked cluster contributions and to use fairly large basis sets if one wants to get accurate ab initio potential surfaces for the reactions of triplet oxygen atoms.     

A pseudopotential ab initio molecular orbital study of the copper(I)-ethylene system

The π and σ-coordinated complexes for the copper(I)-ethylene system are studied by a pseudopotential ab initio MO method. It is found that the lowest-energy structure shows a bent C_2v conformation. A C₅ σ-coordinated complex lies only about 2 kcal/mol above the minimal energy one.     

Construction and applications of symmetrized valence bond wave functions

A method constructing symmetry-adapted bonded Young tableau bases is proposed, based on the symmetry properties of bonded tableaus and the projection operator associated with a point group. Several examples including the ground states and π excited states of O₃⁻, O₃, O₃⁺, and C₃⁻ are shown for instruction to construct the symmetrized valence bond (VB) wave function. Excitation energies of transitions from the ground states to π excited states of O₃⁻, C₃H₅, and C₃⁻ are calculated with an optimized symmetrized valence bond wave function in the σ–π separation approximation. Good agreement between the VB and experimental excitation energies is observed. The bonding features of the ground state and the first π excited singlet and triplet states for S₃ are discussed according to bonding populations from VB calculations. Both the singlet-biradical and the dipole structures have significant contributions to the ground state X ¹A₁ of S₃, while the excited state 1 ¹B₂ is essentially composed of the dipole structures, and the 1 ³B₂ excited state is comprised from a triplet-biradical structure. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 1–7, 1998     

Stable Oxindolyl‐Based Analogues of Chichibabin's and Müller's Hydrocarbons

Chichibabin's and Müller's hydrocarbons are classical open‐shell singlet diradicaloids but they are highly reactive. Herein we report the successful synthesis of their respective stable analogues, OxR‐2 and OxR‐3 , based on the newly developed oxindolyl radical. X‐ray crystallographic analysis on OxR‐2 reveals a planar quinoidal backbone similar to Chichibabin's hydrocarbon, in accordance with its small diradical character (y₀=11.1 %) and large singlet–triplet gap (ΔE_S‐T=−10.8 kcal mol⁻¹). Variable‐temperature NMR studies on OxR‐2 disclose a slow cis/trans isomerization process in solution through a diradical transition state, with a moderate energy barrier (ΔG^≠_298K=15–16 kcal mol⁻¹). OxR‐3 exhibits a much larger diradical character (y₀=80.6 %) and a smaller singlet–triplet gap (ΔE_S‐T=−3.5 kcal mol⁻¹), and thus can be easily populated to paramagnetic triplet diradical. Our studies provide a new type of stable carbon‐centered monoradical and diradicaloid.     

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.     

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.     

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     

Excited states and photochemistry of saturated molecules. ab initio calculations on methane

STO 4G calculations are carried out on methane in both tetrahedral and Jahn—Teller distorted C_2v and C_3v symmetries. Large increases in CH bond lengths are predicted in all states, and the ^IB₁ state in C_2v symmetry is predicted to dissociate to ^IB₁ methylene and ¹A₁ H₂ width no energy barrier. THe results are compared with earlier INDO calculations, and the latter are found to qualitatively consistent with the ab initio results.     

CEPA calculations of potential energy surfaces for open-shell systems.: IV. Photodissociation of H2O in the A1B1 state

A three-dimensional potential energy surface for the photodissociation of H₂O in its lowest excited singlet state $\text{A}$¹B₁ in C_2v or $\text{A}$¹A″ in C₃ symmetry, respectively, has been calculated with quantum-chemical ab initio methods including electron correlation. The main features of the surface are discussed and qualitative explanations are given for the experimentally observed vibrational and rotational excitations of the product OH(²Π) radicals. The surface will be used in subsequent investigations of the dynamics of the H₂O photodissociation process.     

The structure and stability of the acetylene dication

The dication C₂H has been investigated by ab initio molecular orbital theory. It is found to have a linear (D_∞h), structure with a triplet (³σ^?_g) ground state. Deprotonation to C₂H⁺ is exothermic by 9.8 kcal/mol, but this process is hindered by a large barrier of 65 kcal/mol.     

Excited states and photochemistry of saturated molecules. extended basics calculations on the 1B1 (1T2) state of methane

The surface of the lowest excited singlet state in methane is analyzed using a basis set composed of 4-31G augmented by a set of one s and three p Rydbergs. The state (1T₂ in T_d symmetry, 1B₁ in C_2v) is found to be dissociative to 1B₁ CH₂ and ground state H₂. Vertically a Rydberg state, 1B₁ rapidly becomes a valence state on distortions from tetrahedral symmetry. Avoided crossings with higher B₁ states are discussed.