Ab initio study of rate constants of the reaction: HCN + OH → CN + H2O

A method applying ab initio direct dynamics has been utilized in studying the hydrogen abstraction reaction HCN + OH → CN + H₂O. The geometries of the reactants, products, and the transition state have been optimized at the QCISD/6-311G(d, p) level. Single-point energies were further evaluated at the QCISD(T)/6-311+G(2df, 2p)//QCISD/6-311G(d, p) level. The barrier heights for the forward and reverse reactions were predicted to be 15.95 and 7.51 kcal mol⁻¹ at the QCISD(T)/6-311 + G(2df, 2p)//QCISD/6-311G(d, p) level, respectively. The reaction rate constants were calculated in the temperature range from 298 to 4,000 K using the canonical variational transition-state theory with a small-curvature tunneling correction. The results of the calculation show that the theoretical rate constants are in good agreement with experimental data over the measured temperature range of 400–2,600 K. Received: 18 August 2002 / Accepted: 30 August 2002 / Published online: 20 November 2002 Acknowledgements. Our thanks are due to D.G. Truhlar for providing the POLYRATE 8.2 program. This work was supported by the National Science Foundation of China. We also thank D.C. Fang and Y. M. Xie for their valuable help, and P.R. Yan for reading our paper. Correspondence to: Q. S. Li e-mail: qsli@mh.bit.edu.cn     

Theoretical predictions of the structure, gas-phase acidity and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid

Results of ab initio self-consistent-field (SCF) and density functional theory (DFT) calculations of the gas-phase structure, acidity (free energy of deprotonation, ΔG^o), and aromaticity of 1,2-diseleno-3,4-dithiosquaric acid (3,4-dithiohydroxy-3-cyclobutene-1,2-diselenone, H₂C₄Se₂S₂) are reported. The global minimum found on the potential energy surface of 1,2-diseleno-3,4-dithiosquaric acid presents a planar conformation. The ZZ isomer was found to have the lowest energy among the three planar conformers and the ZZ and ZE isomers are very close in energy. The optimized geometric parameters exhibit a bond length equalization relative to reference compounds, cyclobutanediselenone, and cyclobutenedithiol. The computed aromatic stabilization energy (ASE) by homodesmotic reaction (Eq 1) is −20.1 kcal/mol (MP2(fu)/6-311+G** //RHF/6-311+G**) and −14.9 kcal/mol (B3LYP//6-311+G**//B3LYP/6-311+G**). The aromaticity of 1,2-diseleno-3,4-dithiosquaric acid is indicated by the calculated diamagnetic susceptibility exaltation (Λ) −17.91 (CSGT(IGAIM)-RHF/6-311+G**//RHF/6-311+G**) and −31.01 (CSGT(IGAIM)-B3LYP/6-311+G**//B3LYP/6-311+G**). Thus, 1,2-diseleno-3,4-dithiosquaric acid fulfils the geometric, energetic and magnetic criteria of aromaticity. The calculated theoretical gas-phase acidity is ΔG^o _1(298K)=302.7 kcal/mol and ΔG^o _2(298K)=388.4 kcal/mol. Hence, 1,2-diseleno-3,4-dithiosquaric acid is a stronger acid than squaric acid(3,4-dihydroxy-3-cyclobutene-1,2-dione, H₂C₄O₄). Received: 11 April 2000 / Accepted: 7 July 2000 / Published online: 27 September 2000     

Theoretical study of the potential-energy surface of C2NP

 The B3LYP/6-311G(d) and CCSD(T)/6-311G(2df) (single-point) methods have been used to investigate the singlet potential energy surface of C₂NP, in which seven stationary isomers and seventeen interconversion transition states are involved. At the final CCSD(T)/6-311G(2df)//B3LYP6-311G(d) level with zero-point vibrational energy correction the lowest-lying isomer is a linear NCCP followed by two linear CNCP isomers at 23.9  and CCNP at 65.8 kcal mol⁻¹, respectively. The three isomers are kinetically very stable towards both isomerization and dissociation, and CCNP is even more kinetically stable than CNCP – by 14.3 kcal mol⁻¹ despite its high energy. Further comparative calculations were performed at the QCISD and QCISD(T) levels with the 6-311G(d) and 6-311G(2d) basis sets to obtain more reliable structures and spectroscopy for the three isomers. The calculated bond lengths, rotational constant, and dipole moment for NCCP were in close agreement with the experimentally determined values. Finally, similarities and discrepancies between the potential energy surface of C₂NP and those of the analogous species C₂N₂ and C₂P₂ were compared. The results presented in this paper might be helpful for future identification of the two still unknown yet kinetically very stable isomers CNCP and CCNP, both in the laboratory and in interstellar space. Received: 3 January 2001 / Accepted: 6 June 2001 / Published online: 30 October 2001     

Theoretical study on the gas phase reaction of dimethyl sulfoxide with atomic chlorine in the presence of water

We have investigated theoretically the gas phase reactions of dimethyl sulfoxide (DMSO) with atom Cl in the absence and presence of a single water molecule. The calculations of the potential energy surfaces in the water-free and water-assisted along the different channels are performed at the CCSD(T)/6-311++G(2df,2p)//MP2/6-31G(d) level. The calculated results show that energy barriers of the H_c-abstraction reaction are reduced due to one water molecule added. The computed rate constants of H_c-abstraction reaction indicate that the reaction with water is faster than the value of the naked reaction. However, H_a-abstraction reaction, path2, path3, and path4 are slower without water than hydrous channels.     

Use of addition theorems in evaluation of multicenter nuclear-attraction and electron-repulsion integrals with integer and noninteger n Slater-type orbitals

Multicenter integrals appearing in the Hartree–Fock–Roothaan equations for molecules are calculated using different kinds of series expansion formulas obtained from the expansions of integer and noninteger n Slater-type orbitals, in terms of Ψ ^α -exponential-type orbitals (where α=1, 0, –1, –2,...) at a displaced center, that form complete orthonormal sets and are represented by linear combinations of integer n Slater-type orbitals. The convergence of these series is tested by calculating concrete cases. The accuracy of the results is quite high for quantum numbers, screening constants, and location of orbitals. Received: 13 February 2002 / Accepted: 11 March 2002 / Published online: 4 July 2002     

Theoretical study of the structural character of weakly bonding silicon carbonyl complexes

The structures, properties and the bonding character for sub-carbonyl Si, SiCO and Si(CO)₂, in singlet and triplet states have been investigated using complete-active-space self-consistent field (CASSCF), density functional theory and second-order M?ller–Plesset methods with a 6-311+G* basis set. The results indicate that the SiCO species possesses a ³∑⁻ ground state, and the singlet ¹Δ excited state is higher in energy than the ³∑⁻ state by 17.3 kcalmol⁻¹ at the CASSCF–MP2/6-311+G* level and by 16.4 kcalmol⁻¹ at the CCSD(T)/6-311+G* level. The SiCO ground state may be classified as silene (carbonylsilene), and its CO^δ− moiety possesses CO⁻ property. The formation of SiCO causes the weakening of CO bonds. The Si–C bond consists of a weak σ bond and two weak π bonds. Although the Si–C bond length is similar to that of typical Si–C bonds, the bond strength is weaker than the Si–C bonds in Si-containing alkanes; the calculated dissociation energy is 26.2 kcalmol⁻¹ at the CCSD(T)/6-311+G* level. The corresponding bending potential-energy surface is flat; therefore, the SiCO molecule is facile. For the bicarbonyl Si systems, Si(CO)₂, there exist two V-type structures for both states. The stablest state is the singlet state (¹A₁), and may be referred to the ground state. The triplet state (³B₁) is energetically higher in energy than the ¹A₁ state by about 40 kcalmol⁻¹ at the CCSD(T)/6-311 + G* level. The bond lengths in the ¹A₁ state are very close to those of the SiCO species, but the SiCO moieties are bent by about 10°, and the CSiC angles are only about 78°. The corresponding ³B₁ state has a CSiC angle of about 54° and a SiCO angle of about 165°, but its Si–C and C–O bonds are longer than those in the ¹A₁ state by about 0.07 and 0.03 ?, respectively. This Si(CO)₂ (¹A₁) has essentially silene character and should be referred to as a bicarbonyl silene. Comparison of the CO dissociation energies of SiCO and Si(CO)₂ in their ground states indicates that the first CO dissociation energy of Si(CO)₂ is smaller by about 7 kcalmol⁻¹ than that of SiCO; the average one over both CO groups is also smaller than that of SiCO. A detailed bonding analysis shows that the possibility is small for the existence of polycarbonyl Si with more than three CO. This prediction may also be true for similar carbonyl complexes containing other nonmetal and non-transition-metal atoms or clusters. Received: 17 April 2002 / Accepted: 11 August 2002 / Published online: 4 November 2002 Acknowledgements. This work was supported by the National Natural Science Foundation of China (29973022) and the Foundation for Key Teachers in University of the State Ministry of Education of China. Correspondence to: Y. Bu e-mail: byx@sdu.edu.ch     

Ab initio and density functional theory studies on the mechanism of nucleophilic vinylic substitution of 4<Emphasis Type="Italic">H</Emphasis>-pyran-4-one and 2-methyl-4<Emphasis Type="Italic">H</Emphasis>-pyran-4-one with ammonia

 Nucleophilic vinylic substitutions of 4H-pyran-4-one and 2-methyl-4H-pyran-4-one with ammonia were calculated by the B3LYP method using the 6-31G(d,p) basis set. Bulk solvent effects of aqueous solution were estimated by the polarized continuum and Poisson–Boltzmann self-consistent reaction field models using the 6-311+G(d,p) basis set. In the gas phase different mechanisms were found for the two reaction systems calculated. The reaction of 4H-pyran-4-one proceeds through enol, whereas a feasible path for the less reactive 2-methyl-4H-pyran-4-one is the mechanism through a keto intermediate. Addition of ammonia in concert with proton transfer is the rate-determining step ofthe reaction. The mechanism proceeding either by a bimolecular nucleophilic substitution (S_N2) or by one involving a tetrahedral zwitterionic intermediate is shown to be unlikely in the gas phase or nonpolar solution. The effects of bulk solvent not only consist in a reduction of the various activation barriers by about 25–40 kJ mol⁻¹ but also in a change in the reaction mechanism. Received 26 May 2002 / Accepted 26 July 2002 / Published online: 14 February 2003     

Monte Carlo simulation of 2-ethoxyethanol in continuum configurational biased procedure: conformational analysis and association in aqueous and non-aqueous media

 Monte Carlo simulations have been carried out for 2-ethoxyethanol (C₂E₁) in isothermal-isobaric ensemble (NPT) at different temperatures and 1 atm pressure with a continuum configurational biased procedure in water and chloroform media. Hydrogen bond bridges were formed between adjacent oxygen atoms in C₂E₁ (CH₃CH₂OCH₂CH₂OH) through water molecules. We also found that the stable conformers of C₂E₁ in water and CHCl₃ are different and the effect of temperature on solute-solvent interaction energies is considerable. The self-association of C₂E₁ in aqueous and nonaqueous media has been studied by statistical perturbation theory, and the relative free energy has been obtained at different reaction coordinates by double-wide sampling method. Two minima were found in water solvent in the potential of mean force (PMF), corresponding to the contact and solvent-separated pairs, but only one minimum was found in CHCl₃ solvent corresponding to a contact pair complex. Received: 18 January 2001 / Accepted: 22 October 2001 / Published online: 21 January 2002     

Mechanism and kinetics properties for the reaction: Chloroethane with atomic O (P)

In this paper, we present direct dynamics calculations for the multiple-channel reaction of CH₃CH₂Cl with atomic O (³P) in a wide temperature range (200–3000 K), based on canonical variational transition state theory including small curvature corrections. Four distinct saddle points, one for α-abstraction and three for β-abstraction, have been located for this reaction. The potential energy surface information has been calculated at the MP2/6-311G(d,p) level. The energies along the minimum energy path have been further improved by single-point energy calculations at the G3MP2 level. In the β-abstraction channel, Jahn–Teller effect has been found. Changes of geometries, generalized normal-mode vibrational frequencies, and potential energies along the reaction paths for all channels have been discussed and compared. The calculated total rate constants match the available experimental values reasonable well over the measured temperature range. The results show the variational effect can be negligible and the small curvature tunneling contribution plays an important role for the calculation of the rate constant. At low temperature α-abstraction may be the major reaction channel, while β-abstraction will have more contribution to the whole reaction rate as the temperature increase.     

A thermodynamic and kinetic study of the formation of C<Subscript>20</Subscript> compounds encapsulating H,He and Ne atoms

 Binding energies of helium, neon and atomic hydrogen encapsulated inside a C₂₀ cage were calculated using an ab initio method at the B3LYP/6-31+G⋆ level of theory. The standard equilibrium constants for the reactions of noble-gas atoms going into the C₂₀ molecular cage have also been studied. The transition states for the reactions of C₂₀ with hydrogen and helium were further obtained with an ab initio method at the B3LYP/6-31+G⋆ level and the rate constants were estimated by using conventional transition-state theory. It was found that the hydrogen and helium atoms are extremely difficult to put into the C₂₀ cage. Once inside the cage, a helium atom can hardly get out, while a hydrogen atom can easily escape from the cage. The results are expected to enrich fullerene science and be helpful for fullerene applications such as storage. Received: 2 November 2002 / Accepted: 19 December 2002 / Published online: 30 April 2003 Correspondence to: R. Q. Zhang, e-mail: aprqz@cityu.edu.hk Acknowledgements. The work described in this paper was jointly supported by a grant from the City University of Hong Kong (project no. 7001222) and a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. 9040633/CityU, 1011/01P].     

Recombination of tert-butyl radicals: the role of weak van der Waals interactions

A mechanism for the recombination of tert-butyl radicals is postulated to involve the loosely bonded intermediates tert-C₄H₉⋯tert-C₄H₉. Three processes contribute to the overall recombination rate constant: tert-C₄H₉+ tert-C₄H ⇆ tert-C₄H₉⋯tert-C₄H₉ characterized by the equilibrium constant K ₁ and tert-C₄H₉⋯tert-C₄H₉ → C₈H₁₈* characterized by the rate constant k ₂, k _rec,∞(T) ≈ K ₁ k ₂. This recombination rate constant exhibits a negative temperature dependence and is proportional to T ^−3/2. The agreement with experiment is very good. Received: 2 October 2000 / Accepted: 2 May 2002 / Published online: 7 August 2002     

Dual-level direct dynamics calculations of deuterium kinetic isotope effects for the Cl(2P)+C2H6 abstraction reaction

 Kinetic isotope effects, KIEs, for hydrogen abstraction from C₂H₆ and C₂D₆ by chlorine atom have been studied by the dual-level direct dynamics approach. A low-level potential energy surface is obtained with the MNDO-SRP method. High-level structural properties of the reactants, transition state, and products were obtained at the MP2 level with the cc-pVDZ, aug-cc-pVDZ, and the cc-pVTZ basis sets. Using the variational transition state theory with microcanonical optimized multidimensional tunneling, the values of deuterium KIE, at 300 K, range from 2.28 to 3.27, in good agreement with the experimental values (2.69–5.88). Received: 6 June 2001 / Accepted: 12 July 2001 / Published online: 19 November 2001     

Structures and stability of N7+ and N7− clusters

Ab initio molecular orbital theory and density functional theory have been used to study nine isomers of N₇ ionic clusters with low spin at the HF/6-31G*, MP2/6-31G*, B3LYP/6-31G*, and B3LYP/6-311(+)G* levels of theory. All stationary points are examined with harmonic vibrational frequency analyses. Four N₇ ⁺ isomers and five N₇ ⁻ isomers are determined to be local minima or very close to the minima on their potential-energy hypersurfaces, respectively. For N₇ ⁺ and N₇ ⁻, the energetically low lying isomers are open-chain structures (C _{2 v} and C _{2 v} or C₂). The results are very similar to those of other known odd-number nitrogen ions, such as N₅ ⁺, N₉ ⁺, and N₉ ⁻, for which the open-chain structures are also the global minima. This research suggests that the N₇ ionic clusters are likely to be stable and to be potential high-energy-density materials if they could be synthesized. Received: 16 July 2001 / Accepted: 8 October 2001 / Published online: 21 January 2002     

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     

Theoretical study on structures and stability of HC2P isomers

 The structures and isomerization pathways of various HC₂P isomers in both singlet and triplet states are investigated at the B3LYP/6-311G(d,p), QCISD/6-311G(d,p) (for isomers only) and single-point CCSD(T)/6-311G(d,p)//B3LYP/6-311G(d,p) levels. At the CCSD(T)/6-311G(d,p)//B3LYP/6-311G(d,p) level, the lowest-lying isomer is a linear HCCP structure ³ 1 in the ³∑⁻ state. The second low-lying isomer has a CPC ring with exocyclic CH bonding ¹ 5 in a singlet state at 10.5 kcal/mol. The following third and fourth low-lying isomers are a singlet bent HCCP structure ¹ 1 at 20.9 kcal/mol and a bent singlet HPCC structure ¹ 3 at 35.8 kcal/mol, respectively. Investigation of the HC₂P potential-energy surface indicates that in addition to the experimentally known isomer ³ 1, the other isomers ¹ 1, ¹ 3 and ¹ 5 also have considerable kinetic stability and may thus be observable. However, the singlet and triplet bent isomers HCPC ¹ 2 and ³ 2 as well as the triplet bent isomer HPCC ³ 3 are not only high-lying but are also kinetically unstable, in sharp contrast to the situation of the analogous HCNC and HNCC species that are both kinetically stable and that have been observed experimentally. Furthermore, the reactivity of various HC₂P isomers towards oxygen atoms is briefly discussed. The results presented here may be useful for future identification of the completely unknown yet kinetically stable HC₂P isomers ¹ 1, ¹ 3 and ¹ 5 either in the laboratory or in interstellar space. Received: 5 November 2000 / Accepted: 25 November 2001 / Published online: 8 April 2002     

Theoretical investigation into structures and magnetic properties of smaller fullerenes and their heteroanalogues

The smaller fullerenes, C₂₀, C₂₄, C₂₈, C₃₂, C_36, C₄₀ and C₅₀, their hydrogenation products and selected B-, N- and P-doped analogues have been investigated systematically at the B3LYP/6-31G* density functional level of theory. The degree of spherical electron delocalization is evaluated by using the computed nucleus-independent chemical shifts ( NICS) at the cage center and the individual ring centers of interest. The calculated NMR chemical shifts and the NICS values at the cage center, which can be accessed by endohedral ³He chemical shifts, should provide a basis for further experimental characterization of these compounds. Received: 26 March 2001 / Accepted: 10 May 2001 / Published online: 11 October 2001     

Calculations of the geometries, electronic structures and nonlinear second-order optical susceptibilities of spiroannelated quinone-type methanofullerenes

 The equilibrium geometries, electronic structures and UV–vis spectra of a series of spiroannelated quinone-type methanofullerenes have been determined by using Zerner's intermediate neglect of differential overlap method. The results show that between fullerene and the addend there exists a special interaction, “periconjugation”, which results in through-space orbital interactions. The calculated UV–vis spectra are in good agreement with experiments. On the basis of the electronic spectra, the β values are calculated. The results show that spiroannelated quinone-type methanofullerenes have quite large β values. We attribute the large β values to both the charge transfer from C₆₀ to benzoquinone and on the C₆₀ three-dimensional conjugated sphere. Received: 17 December 2000 / Accepted: 16 March 2001 / Published online: 13 June 2001     

Endohedral chemical shifts in higher fullerenes with 72–86 carbon atoms

For all isolated pentagon isomers of the fullerenes C₆₀–C₈₆ with nonzero HOMO–LUMO gap and for one nonclassical C₇₂ isomer (C_{2 v} ), endohedral chemical shifts have been computed at the GIAO-SCF/3-21G level using B3LYP/6-31G* optimized structures. The experimental ³He NMR signals are reproduced reasonably well in cases where assignments are unambiguous (e.g. C₆₀, C₇₀ and C₇₆). On the basis of the calculated thermodynamic stability order and the comparison between the computed and experimental ³He chemical shifts, the assignments of the observed ³He NMR spectra are discussed for all higher fullerenes, and new assignments are proposed for one C₈₂ and one C₈₆ isomer (C₈₂:3 and C₈₆:17). The calculated helium chemical shifts also suggest the reassignment of the δ(³He) resonances of two C₇₈ isomers. Received: 26 March 2001 / Accepted: 10 May 2001 / Published online: 11 October 2001     

Pseudopotential study of lanthanum and lutetium dimers

Relativistic energy-consistent small-core lanthanide pseudopotentials of the Stuttgart–Bonn variety and extended valence basis sets have been used for the investigation of the dimers La₂ and Lu₂. It was found that the ground states for La₂ and Lu₂ are most likely ¹∑ _g ⁺ (σ _g ²π _u ⁴) and ³∑ _g ⁻ (4f ¹⁴4f ¹⁴σ _g ²σ _u ²π_u ²), respectively. The molecular constants including error bars were derived from multireference configuration interaction as well as coupled-cluster calculations, taking into account corrections for atomic spin–orbit splitting as well as possible basis set superposition errors. The theoretical values for La₂ (R _e=2.70±0.03 ?, D _e=2.31±0.13 eV, ω_e=186±13 cm⁻¹) show good agreement with the experimental binding energy (D _e=2.52±0.22 eV), but the experimental vibrational constant in an Ar matrix (ω_e=236±0.8 cm⁻¹) is significantly higher. For Lu₂ the theoretical values (R _e=3.07±0.03 ?, D _e=1.40±0.12 eV, ω_e=123±1 cm⁻¹) are in overall excellent agreement with experimental data (D _e=1.43±0.34 eV, ω_e=122± 1 cm⁻¹). The electronic structures of La₂ and Lu₂ are compared to those other lanthanide dimers and trends in the series are discussed. Received: 25 March 2002 / Accepted: 2 June 2002 / Published online: 21 August 2002     

A proposed modification of CBS-4M model chemistry for application to molecules of increasing molecular size

 In order to calculate more accurately the enthalpies of formation, ΔH _f°(298 K), for large molecules using the CBS-4M method, a new formulation of the empirical higher-level correction to the energy is proposed: ΔE=a|S|² _{i i} I _{i i} +b(n _α+n _β)+cΔ<S ²>+Σn _i d _{i .} The new methodology (CBS-4MB) applied to a set of 114 molecules of different size significantly decreases the mean absolute deviation from 3.78 to 2.06 kcal/mol. Received: 7 February 2001 / Accepted: 5 April 2001 / Published online: 13 June 2001