Bis-periazulene: a simple Kekulé biradical with a triplet ground state

B3LYP/6-31G* calculations on bis-periazulene (cyclohepta[def]-fluorene) predict a triplet ground state for this molecule. The singlet has an aromatic 14π-electron periphery but is 2 kcal/mol higher in energy. The results agree with earlier predictions by Heilbronner. Received: 19 August 1998 / Accepted: 6 October 1998 / Published online: 23 February 1999     

The spin-forbidden reaction CH(2∏) + N2→ HCN + N(4S) revisited I. Ab initio study of the potential energy surfaces

High-level ab initio electronic structure theories have been applied to investigate the detailed reaction mechanism of the spin-forbidden reaction CH(²∏) + N₂ → HCN + N(⁴S). The G2M(RCC) calculations provide accurate energies for the intermediates and transition states involved in the reaction, whereas the B3LYP/6-311G(d,p) method overestimates the stability of some intermediates by as much as about 10 kcal/mol. A few new structures have been found for both the doublet and quartet electronic states, which are mainly involved in the dative pathways. However, due to the higher energies of these structures, the dominant mechanism remains the one involving the C ₂ intersystem-crossing step. The C ₂ minima on the seam of crossing (MSX) structures and the spin-orbit coupling between the doublet and quartet electronic states are rather close to those found in previous studies. Vibrational frequencies orthogonal to the normal of the seam which have been applied in a separate publication to calculate the rate of the CH(²∏) + N₂ → HCN + N(⁴S) reaction with a newly proposed nonadiabatic transition-state theory for spin-forbidden reactions have been calculated at the MSX from first principles. Received: 23 June 1998 / Accepted: 21 September 1998 / Published online: 8 February 1999     

The singlet and triplet states of phenyl cation. A hybrid approach for locating minimum energy crossing points between non-interacting potential energy surfaces

The phenyl cation is known to have two low-energy minima, corresponding to ¹ A ₁ and ³ B ₁ states, the first of which is more stable by ca. 25 kcal/mol. The minimum energy crossing point between these two surfaces, located at various levels including a hybrid method first described here, lies just above the minimum of the triplet, 0.12 kcal/mol at the CCSD(T)/cc-pVDZ//B3LYP/SV level, and there is significant spin-orbit coupling between the surfaces at this point. On the basis of these results, the lifetime of the triplet is expected to be very short. Received: 24 October 1997 / Accepted: 25 November 1997     

Spectroscopic Observation of the Triplet Diradical State of a Cyclobutadiene

Tetrakis(trimethylsilyl)cyclobuta‐1,3‐diene ( 1 ) was subjected to a temperature‐dependent EPR study to allow the first spectroscopic observation of a triplet diradical state of a cyclobutadiene ( 2 ). From the temperature dependent EPR absorption area we derive a singlet→triplet ( 1 → 2 ) energy gap, E _ST, of 13.9 kcal mol⁻¹, in agreement with calculated values. The zero‐field splitting parameters D =0.171 cm⁻¹, E =0 cm⁻¹ are accurately reproduced by DFT calculations. The triplet diradical 2 is thermally accessible at moderate temperatures. It is not an intermediate in the thermal cycloreversion of cyclobutadiene to two acetylene molecules.     

Density functional study of ethylene oxidation on an Ag(111) surface

The mechanism of ethylene epoxidation on Ag surfaces has been investigated using the density functional method and Ag _n clusters (n = 3 to 10) modeling the Ag(111) surface. The adsorption energy of O₂ to the Ag clusters was strongly dependent on the HOMO level of the cluster, and the clusters with higher HOMO levels afforded larger O₂ adsorption energies. The energetics was investigated for both the molecular and atomic oxygen epoxidation mechanisms. For the atomic oxygen mechanism, epoxidation was found to proceed without an activation energy, whereas a small amount of activation energy (about 5 kcal/mol) was calculated for the molecular oxygen mechanism. Received: 2 July 1998 / Accepted: 9 September 1998 / Published online: 8 February 1999     

Transition structures and exo/endo stereoselectivities of concerted [6 + 4] cycloadditions with density functional theory

Density functional theory transition structures were located for three concerted [6 + 4] cycloaddition reactions involving cis-hexatriene and butadiene, cyclopentadiene and cycloheptatriene, and cyclopentadiene and tropone. Geometries, energies, and entropies were computed at the Becke3LYP/6-31G* level. The activation energy of the concerted [6 + 4] cycloaddition of hexatriene and butadiene is 33.3 kcal/mol, about 8 kcal/mol above the activation energy of the butadiene plus ethylene [4 + 2] cycloaddition. The endo concerted [6 + 4] transition state is 1.1 kcal/mol higher than the exo. The [6 + 4] reaction of cyclopentadiene and cycloheptatriene has a barrier of 25.9 kcal/mol, while the cyclopentadiene–tropone barrier drops to 20.7 kcal/mol. Received: 3 December 1998 / Accepted: 18 February 1999 / Published online: 7 June 1999     

Conformational free energy surface of the linear DPDPE peptide: cost of pre-organization for disulfide bond formation

We have calculated the free energy differences between four conformers of the linear form of the opioid pentapeptide DPDPE in aqueous solution. The conformers are Cyc, representing the structure adopted by the linear peptide prior to disulfide bond formation, β _C and β _E , two slightly different β-turns previously identified in unconstrained molecular dynamics simulations, and Ext, an extended structure. Our simulations indicate that β _E is the most stable of the studied conformers of linear DPDPE in aqueous solution, with β _C , Cyc and Ext having free energies higher by 2.3, 6.3, and 28.2 kcal/mol, respectively. The free energy differences of 4.0 kcal/mol between β _C and Cyc, and 6.3 kcal/mol between β _E and Cyc, reflect the cost of pre-organizing the linear peptide into a conformation conducive for disulfide bond formation. Such a conformational change is a pre-requisite for the chemical reaction of S–S bond formation to proceed. The relatively low population of the cyclic-like structure agrees qualitatively with observed lower potency and different receptor specificity of the linear form relative to the cyclic peptide, and with previous unconstrained simulation results. Free energy component analysis indicates that the moderate stability difference of 4.0–6.3 kcal/mol between the β-turns and the cyclic-like structure results from cancellation of two large opposing effects. In accord with intuition, the relaxed β-turns have conformational strain 43–45 kcal/mol lower than the Cyc structure. However, the cyclic-like conformer interacts with water about 39 kcal/mol strongly than the open β-turns. Our simulations are the first application of the recently developed multidimensional conformational free energy thermodynamic integration (CFTI) protocol to a solvated system, with fast convergence of the free energy obtained by fixing all flexible dihedrals. Additionally, the availability of the CFTI multidimensional free energy gradient leads to a new decomposition scheme, giving the contribution of each fixed dihedral to the overall free energy change and providing additional insight into the microscopic mechanisms of the studied processes. Received: 20 April 1998 / Accepted: 9 September 1998 / Published online: 7 December 1998     

Ab initio calculations for the potential curves and spin–orbit coupling of Mg2

 The ground state and several low-lying excited states of the Mg₂ dimer have been studied by means of a combination of the complete-active-space multiconfiguration self-consistent-field (CASSCF)/CAS multireference second-order perturbation theory (CASPT2) method and coupled-cluster with single and double excitations and perturbative contribution of connected triple excitations [CCSD(T)] scheme. Reasonably good agreement with experiment has been obtained for the CCSD(T) ground-state potential curve but the dissociation energy of the only experimentally known A¹Σ _u ⁺ excited state of Mg₂ is somewhat overestimated at the CASSCF/CASPT2 level. The spectroscopic constants D _e, R _e and ω_e deduced from the calculated potential curves for other states are also reported. In addition, some spin–orbit matrix elements between the excited singlet and triplet states of Mg₂ have been evaluated as a function of internuclear separation. Received: 10 May 2001 / Accepted: 15 August 2001 / Published online: 30 October 2001     

Core-valence correlation effects for molecules containing first-row atoms. Accurate results using effective core polarization potentials

The accuracy of employing effective core polarization potentials (CPPs) to account for the effects of core-valence correlation on the spectroscopic constants and dissociation energies of the molecules B₂, C₂, N₂, O₂, F₂, CO, CN, CH, HF, and C₂H₂ has been investigated by comparison to accurate all-electron benchmark calculations. The results obtained from the calculations employing CPPs were surprisingly accurate in every case studied, reducing the errors in the calculated valence D _e values from a maximum of nearly 2.5 kcal/mol to just 0.3 kcal/mol. The effects of enlarging the basis set and using higher-order valence electron correlation treatments were found to have only a small influence on the core-valence correlation effect predicted by the CPPs. Thus, to accurately recover the effects of intershell correlation, effective core polarization potentials such as the ones used in the present work provide an attractive alternative to carrying out computationally demanding calculations where the core electrons are explicitly included in the correlation treatment. Received: 11 May 1998 / Accepted: 27 July 1998 / Published online: 28 October 1998     

Photoelectron spectroscopy of the trimethylenemethane negative ion

The photoelectron spectrum of the trimethylenemethane (TMM) negative ion is described. The electron affinity of TMM is found from the spectrum to be 0. 431±0.006 eV, and the energy difference between the [(X)\tilde]³ A￠₂\tilde X^3 A'_2 ³A′₂ and [(b)\tilde]¹ A₁\tilde b^1 A_1 ¹A₁ states of TMM is determined to be 16.1±0.2 kcal/mol. The energy difference between the lowest energy triplet and singlet states is estimated to be 13–16 kcal/mol. The enthalpy of formation of TMM is measured to be 70±3 kcal/mol, and the C-H bond enthalpy in 2-methylallyl radical is 90±2 kcal/mol. Previously unobserved vibrational frequencies of 425, 915, and 1310 cm⁻¹ are found for the triplet state of TMM, whereas a frequency of 325 cm⁻¹ is found for the singlet state. In addition, an overtone peak is observed for the triplet state at 1455 cm⁻¹, and both states contain peaks that are assigned to bands arising from excited vibrational levels of the ion.     

Structure and stabilities of (HA1NH)n (n = 2–4)

Ab initio molecular electronic structure methods have been used to study the relative stability of the planar inorganic ring (HAlNH)_n (n = 2–4) during homodesmotic and monomer polymerization reactions. Optimized geometries, frequencies and energies through restricted Hartree-Fock/6-31G* are reported, and energies at the self-consistent field optimized geometries including M?ller-Plesset fourth perturbation theory with single, double and quadruple excitation (MP4SDQ) corrections are also reported for both reactions. Homodesmotic reactions with MP4SDQ −28.5 kcal/mol for (AlN)₂, 1.9 kcal/mol for (AlN)₃ and −0.97 kcal/mol for (AlN)₄. On analysing a π-molecular orbitals diagram, only one, three and three strongly bonding π-molecular orbitals exist for the planar four-, six- and eight-membered AlN rings, respectively. Received: 9 March 1998 / Accepted: 19 March 1998 / Published online: 23 June 1998     

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.     

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.     

Acetylene-insertion reactions into Pt(II)–H and Pt(II)–SiH3 bonds. An ab initio MO study and analysis based on the vibronic coupling model

Acetylene insertion into Pt(II)–H and Pt(II)SiH₃ bonds of PtH(SiH₃)(PH₃) was investigated using ab initio molecular orbital and M?ller-Plesset perturbation theory methods. The insertion into PtH was predicted to proceed with a smaller activation energy (E _a =12.8 kcal/mol) than that into PtSiH₃ (E _a =20.9 kcal/mol). The reaction energy (ΔE) of the insertion into PtH is 10 kcal/mol smaller than that for the insertion into PtSiH₃, which reflects differences in bond energies between CH and CSi and between PtH and PtSiH₃. A comparison with ethylene insertion revealed that the acetylene insertion occurs more easily, and the latter reaction is more exothermic. A simple vibronic coupling model combined with Toyozawa's interaction mode analysis was used to examine interesting differences in E _a and ΔE between insertions into PtH and PtSiH₃, and between acetylene and ethylene insertions. This analysis suggests that the factors determining E _a are the stiffness of the PtH and PtSiH₃ bonds and the vibronic coupling strength of acetylene and ethylene. Received: 13 August 1998 / Accepted: 2 September 1998 / Published online: 15 February 1999     

Ab initio MO study of ethylene insertion into the Sm–C bond of H2SiCp2SmCH3

Ethylene insertion into the Sm–C bond of H₂SiCp₂SmCH₃, a model reaction of an olefin polymerization propagation step, has been studied by ab initio molecular orbital methods. The small electronegativity of the Sm atom makes the Sm–C bond ionic, the methyl group being negatively charged by −0.75. The reaction passes through a loose ethylene complex with a binding energy of 15 kcal/mol and then a tight four-centered transition state with an agostic interaction between the Sm atom and one of the methyl CH bonds. A small activation energy of 14 kcal/mol is required to pass through this transition state, indicating that this is an easy reaction. Compared with the reactions with group 4 cationic silylene-bridged metallocenes the activation energy is higher and the reaction is less exothermic. The origin of these differences is discussed. The results of molecular mechanics calculations on regio- and stereoselectivities in the insertion reaction of propylene are also reported. Received: 13 July 1998 / Accepted: 28 August 1998 / Published online: 2 November 1998     

Theoretical study of the valence π → π* excited states of polyacenes: anthracene and naphthacene

The valence π → π ^* excited states of anthracene and naphthacene are studied with multireference perturbation theory with complete active space self-consistent field reference functions. The predicted spectra provide a consistent assignment of all one- and two-photon spectra and T-T spectra of low-lying valence π → π ^* excited states of anthracene and naphthacene. The present theory predicts the valence π → π ^* excitation energies with an accuracy of 0.15 eV for anthracene and of 0.25 eV or better for naphthacene. The excited states of anthracene and naphthacene are compared with those of benzene and naphthalene studied previously. The present calculations predict that, going from anthracene to naphthacene, there is a symmetry reversal of the two lowest singlet state transitions, but not for the triplet, just as indicated by the experimental data. Some general trends of polyacene excited states are discussed based on the calculated results for benzene to naphthacene. Conclusive results obtained for anthracene and naphthacene can be used as a model for understanding the excited states of larger polyacenes. Received: 22 April 1998 / Accepted: 6 July 1998 / Published online: 28 September 1998     

Ab initio quantum chemical study of the formation, decomposition and isomerization of the formaldiminoxy radical (CH2NO): comparison of the Gaussian-2 and CASPT2 techniques in the calculation of potential energy surfaces

The reaction between triplet methylene and nitric oxide, producing the formaldiminoxy (CH₂NO) radical, and the subsequent decomposition and isomerization reactions of CH₂NO have been studied using ab␣initio quantum chemical techniques that include the Gaussian-2 (G2), CASSCF and CASPT2 methods. Stationary points on the potential energy surfaces were located at MP2/6-31G(d) and CASSCF/cc-pVDZ levels of theory, while the electronic energies were determined using G2, G2(MP2), QCISD(T)/cc-pVTZ, RCCSD(T)/cc-pVTZ and CASPT2/cc-pVTZ approaches. G2 is believed to be reliable at equilibrium geometries, but the determination of certain transition state geometries and energies requires a MCSCF-based approach. The calculations suggest that CH₂NO (²A^′) forms in a barrierless reaction and could readily decompose to H+HCNO. A subsequent abstraction reaction then results in H₂+CNO. No molecular elimination channel was found. An alternative pathway is the formation of CH₂ON, which readily isomerizes to CH₂NO. Received: 8 May 1998 / Accepted: 11 August / Published online: 9 October 1998     

2-Silyl group effect on the reactivity of cyclopentane-1,3-diyls. Intramolecular ring-closure versus silyl migration

Generation of singlet and triplet 2-silylcyclopentane-1,3-diyls and their reactivity have been investigated in the thermal and photochemical denitrogenation of 2,3-diaza-7-silylbicyclo[2.2.1]hept-2-ene. 5-Silylcyclopentene (silyl migration product) is quantitatively obtained, while 5-silylbicyclo[2.1.0]pentane (intramolecular ring-closure product) is not detected in the denitrogenation reactions. Deuterium labeling studies clarify that 5-silylcyclopentene is formed by a suprafacial [1,2] silyl migration in singlet 2-silylcyclopentane-1,3-diyl. UDFT calculations closely reproduce the observed reactivity of the singlet diradical: The enthalpic barriers of the intramolecular ring-closure are calculated to be DeltaH++exo468 = 5.8 kcal/mol and DeltaH++endo468 = 6.7 kcal/mol, which are much higher than the energy barrier for the [1,2] silyl migration, DeltaH++468 = 2.7 kcal/mol. The notable effect of the silyl group on raising the energy barrier of the intramolecular cyclization is rationalized by an electronic configuration of the lowest singlet state of 2-silylcyclopentane-1,3-diyls.     

Geometry optimization of the ring-opened oxirane diradical: mechanism of the addition reaction of the triplet oxygen atom to olefins

Geometry optimizations of several low-lying diradical states of the ring-opened oxirane (·CH₂CH₂O·) were performed by using the energy gradients of the UHF MINDO/3, STO-3G and 4-31G solutions. Both the STO-3G and 4-3 IG methods predict that the most stable form is the triplet state of the non-twisted σπ conformation in which the unpaired spins localized on the terminal carbon and oxygen atoms are oriented perpendicularly to each other. The singlet σσ diradical state in which both the radical-site p orbitals are coplanar with the molecular framework is only 2.3 (STO-3G) and 1.2 (4-31G) kcal/mol less stable than the triplet σπ diradical state. It is found that the geometry of the singlet σσ diradical is unique in that the C-C-O angle is noticeably small as compared with various other diradical states. Implications of these results to the mechanism of the oxirane-forming O(³P) + C₂H₄ reaction are discussed.     

Theoretical analysis of the internal rotation in aminoborane and borylphosphine

Using a recently proposed orbital deletion procedure and the block-localized wavefunction method, the rotational barriers in H₂BNH₂ and H₂BPH₂ are analyzed in terms of conjugation, hyperconjugation, steric effect and pyramidalization. With the zero-point energy corrections, the π-binding strengths in the planar H₂BNH₂ and H₂BPH₂ are both around 20 kcal/mol at the HF level using the 6-311+G** basis set. With the deactivation of the π atomic orbitals on the boron atom and the evolution from a planar structure to a 90°-twisted structure, the steric repulsion between the B‐H and the N‐H or P‐H is relieved and moreover, the negative hyperconjugation from the lone electron pair or pairs on the nitrogen or phosphorus atoms to the antibonding orbital ^χ* _B H ₂ of the BH₂ group stabilizes the twisted structure by 7.4(8.8) or 4.0(5.0) kcal/mol at the HF/6-31G*(6-311+G**) level. However, the repulsive interaction between the lone pair(s) and the two BH σ bonds is so prominent that the overall steric effect contributes 20.3(22.9) and 19.3(19.8) kcal/mol to the rotational barriers in H₂BNH₂ and H₂BPH₂ with the 6-31G*(6-311+G**) basis set. The present techniques and analyses may also give some clues to justify the parameterization in the empirical molecular mechanics methods. Received: 17 April 1998 / Accepted: 17 September 1998 / Published online: 1 February 1999