Structure and stability of hypervalent NLi n Na2 (n = 1–4) and related species at density functional theory level

A number of configurations of NLi _n Na₂ (n = 1–4) species were optimized using the B3LYP–density functional theory method; the 6-31G^* basis set was used in this calculation. In order to study all possible dissociation energies, some related species such as NLi₂Na, NLi _n (n = 1–4), Li _n (n = 1, 2) and Na _n (n = 1, 2) were also considered. Optimizations of these species were followed by fundamental frequency calculations at the same level. Global minima of these species were shown to adopt C _{2 v} (NLi₄Na₂, NLi₂Na₂), D _{3 h} (NLi₃Na₂) and C _s (NLiNa₂ and NLi₂Na) configurations. All possible dissociation energies were obtained. Received: 30 November 1998 / Accepted: 15 October 1999 / Published online: 14 March 2000     

Improved generator coordinate Hartree–Fock method for molecular systems: application to H2, Li2 and LiH

The improved generator coordinate Hartree–Fock (GCHF) method is extended to molecular systems. The Griffin–Hill–Wheeler–HF equations were solved by an integral discretization technique. The method is then implemented with the use of the GAMESS program and applied to the H₂, Li₂, and LiH molecules. For these molecules, sequences of basis sets of atom-centred Gaussian-type functions are employed to explore the accuracy achieved with our approach. For all systems studied, our ground-state HF total energies are better than those obtained with basis sets generated with the original GCHF method for molecules and larger even-tempered basis sets. For H₂, Li₂, and LiH, the differences between our best energies and the corresponding numerical HF results are about 2 × 10⁻², 1, and 4 × 10⁻¹ μhartree, respectively. The dipole, quadrupole, and octupole moments at the center of mass and electric field, the electric field gradient, the electrostatic potential, and the electron density at the nuclei were evaluated and compared with results reported in the literature. Received: 4 May 1999 / Accepted: 22 July 1999 / Published online: 2 November 1999     

Energetics, structures, bonding, and kinetics of the HSCl–HClS system

The [H,S,Cl] potential-energy surface has been investigated at the self-consistent field (SCF), complete active space self-consistent field (CASSCF), second-order M?ller–Plesset, coupled-cluster single-double and perturbative triple excitation, [CCSD(T)]/6-31G(d,p), 6-31G(2df,2pd), and correlation-consistent polarized valence triple zeta (cc-pVTZ) levels of theory. CCSD(T)/ cc-pVTZ results predict a very stable HSCl species, an isomer HClS, 51.84 kcal/mol higher in energy, and a transition state 57.68 kcal/mol above HSCl. Independent of the level of theory, results with the smaller 6-31G(d,p) basis set turned out to be poor, especially for HClS. Vibrational analysis indicates that both species can be easily differentiated if isolated. Bonding differences between these molecules are illustrated by contour plots of valence orbitals. Viewed classically, bonding in HClS involves a dative bond. Transition-state rate constants, and equilibrium constants for the HSCl ↔ HClS isomerization have been estimated for various temperatures (200–1000 K). At 298.15 K, the forward rate is predicted to be 7.95 × 10⁻²⁹ s⁻¹, and the equilibrium constant to be 2.31 × 10⁻³⁸. Tunneling corrections vary from 1.57 at 298.15 K to 1.05 at 1000 K. Activation energies have been obtained by a two-points linear fit to the Arrhenius equation. Received: 7 May 1999 / Accepted: 22 July 1999 / Published online: 4 October 1999     

Π delocalisation in 1,3-butadiene: a nonempirical molecular orbital study

A value of −0.33 eV or −7.6 kcal mol⁻¹ has been obtained for the vertical delocalisation energy of trans-1,3-butadiene from a nonempirical molecular orbital calculation on the π system. The result agrees well enough with ab initio calculations to suggest that a simplified approach need not be semiempirical. In a basis of orthogonalised atomic orbitals the central bond order is found to be 0.295 (Hückel value 0.447) for the delocalised structure and 0.125 for the localised (Hückel value zero). Core resonance integrals between neighbouring atoms, the analogues of Hückel's β, have theoretical values of −3.9 and −3.2 eV compared with −3.6 eV in benzene. Received: 11 May 1999 / Accepted: 22 July 1999 / Published online: 2 November 1999     

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     

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     

Direct ab initio dynamics calculations on the rate constants for the hydrogen-abstraction reaction of C2H5F with O (3P)

The hydrogen-abstraction reaction C₂H₅F+O → C₂H₄F+OH has been studied by a dual-level direct dynamics method. For the reaction, three reaction channels, one for α-abstraction and two for β-abstraction, have been identified. The potential-energy surface information is obtained at the MP2(full)/6-311G(d,p) and PMP2(full)/6-311G(3df,3pd) (single-point) levels. By canonical variational transition-state theory, rate constants for each reaction channel are calculated with a small-curvature tunneling correction. The total rate constant is calculated from the sum of the individual rate constants and the temperature dependence of the branching ratios is obtained over a wide range of temperatures from 300 to 5,000 K. The agreement of the rate constants with experiment is good in the experimental temperature range from 1,000 to 1,250 K. The calculated results indicate that at low temperatures α-abstraction is most likely to be the major reaction channel, while β-abstraction channels will significantly contribute to the whole reaction rate as the temperature increases. Received: 23 January 2002 / Accepted: 23 June 2002 / Published online: 20 September 2002     

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     

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     

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     

Self-consistent reaction field calculation of solvent reorganization energy in electron transfer: a dipole-reaction field interaction model

Based on the continuum dielectric model, this work has established the relationship between the solvent reorganization energy of electron transfer (ET) and the equilibrium solvation free energy. The dipole-reaction field interaction model has been proposed to describe the electrostatic solute-solvent interaction. The self-consistent reaction field (SCRF) approach has been applied to the calculation of the solvent reorganization energy in self-exchange reactions. A series of redox couples, O₂/O⁻ ₂, NO/NO⁺, O₃/O⁻ ₃, N₃/N⁻ ₃, NO₂/NO⁺ ₂, CO₂/CO⁻ ₂, SO₂/SO⁻ ₂, and ClO₂/ClO⁻ ₂, as well as (CH₂)₂C-(-CH₂-) _n -C(CH₂)₂ (n=1 ∼ 3) model systems have been investigated using ab initio calculation. For these ET systems, solvent reorganization energies have been estimated. Comparisons between our single-sphere approximation and the Marcus two-sphere model have also been made. For the inner reorganization energies of inorganic redox couples, errors are found not larger than 15% when comparing our SCRF results with those obtained from the experimental estimation. While for the (CH₂)₂C–(–CH₂–) _n –C(CH₂)₂ (n=1 ∼ 3) systems, the results reveal that the solvent reorganization energy strongly depends on the bridge length due to the variation of the dipole moment of the ionic solute, and that solvent reorganization energies for different systems lead to slightly different two-sphere radii. Received: 19 April 2000 / Accepted: 6 July 2000 / Published online: 27 September 2000     

Second-order Møller–Plesset perturbation theory with terms linear in the interelectronic coordinates and exact evaluation of three-electron integrals

 The second-order correlation energy of M?ller–Plesset perturbation theory is computed for the neon atom using a wave function that depends explicitly on the interelectronic coordinates (MP2-R12). The resolution-of-identity (RI) approximation, which is invoked in the standard formulation of MP2-R12 theory, is largely avoided by rigorously computing the necessary three-electron integrals. The basis-set limit for the second-order correlation energy is reached to within 0.1 mE _h. A comparison with the conventional RI-based MP2-R12 method shows that only three-electron integrals over s and p orbitals need to be computed exactly, indicating that the RI approximation can be safely used for integrals involving orbitals of higher angular momentum. Received: 9 May 2001 / Accepted: 31 October 2001 / Published online: 9 January 2002     

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     

A theoretical study of photoinduced electron transfer between tetracyanoethylene and arene

 Ab initio calculations have been performed to investigate the state transition in photoinduced electron transfer reactions between tetracyanoethylene and biphenyl as well as naphthalene. Face-to-face conformations of electron donor–acceptor (EDA) complexes were selected for this purpose. The geometries of the EDA complexes were determined by using the isolated optimized geometries of the donor and the acceptor to search for the maximum stabilization energy along the center-to-center distance. The correction of interaction energies for basis set superposition error was considered by using counterpoise methods. The ground and excited states of the EDA complexes were optimized with complete-active-space self-consistent-field calculations. The theoretical study of the ground state and excited states of the EDA complex in this work reveals that the S₁ and S₂ states of the EDA complexes are charge–transfer (CT) excited states, and CT absorption which corresponds to the S₀→S₁ and S₀→S₂ transitions arise from π−π^* excitation. On the basis of an Onsager model, CT absorption in dichloromethane was investigated by considering the solvent reorganization energy. Detailed discussions on the excited state and on the CT absorptions were made. Received: 30 April 2001 / Accepted: 18 October 2001 / Published online: 9 January 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     

Solvent effects on the electronic absorption spectrum of formamide studied by a sequential Monte Carlo/quantum mechanical approach

Sequential Monte Carlo/quantum mechanical calculations are performed to study the solvent effects on the electronic absorption spectrum of formamide (FMA) in aqueous solution, varying from hydrogen bonds to the outer solvation shells. Full quantum-mechanical intermediate neglect of differential overlap/singly excited configuration interaction calculations are performed in the supermolecular structures generated by the Monte Carlo simulation. The largest calculation involves the ensemble average of 75 statistically uncorrelated quantum mechanical results obtained with the FMA solute surrounded by 150 water solvent molecules. We find that the n → π* transition suffers a blueshift of 1,600 cm⁻¹ upon solvation and the π → π* transition undergoes a redshift of 800 cm⁻¹. On average, 1.5 hydrogen bonds are formed between FMA and water and these contribute with about 20% and about 30% of the total solvation shifts of the n → π* and π → π* transitions, respectively. The autocorrelation function of the energy is used to sample configurations from the Monte Carlo simulation, and the solvation shifts are shown to be converged values. Received: 14 March 2002 / Accepted: 3 April 2002 / Published online: 24 June 2002     

Formulas and numerical table for the radial part of overlap integrals with the same screening parameters of Slater-type orbitals

 The numerical properties of the radial part of overlap integrals with the same screening parameters in the form of polynomials in p = ξR over Slater-type orbitals have been studied and obtained by using three different methods. For that purpose, the characteristics of auxiliary functions were used first, then Fourier transform convolution theorem, and recurrence relations for the basic coefficients of A ^s _{n l λ, n ′ l ′λ} were used. The calculations of the radial part of overlap integrals with the same screening parameters were made in the range 1 ≤ n ≤ 75, 1 ≤ n′ ≤ 75, and 10⁻⁶ ≤ p. Received: 18 January 2001 / Accepted: 5 April 2001 / Published online: 27 June 2001     

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     

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