Calculation of three-center electric and magnetic multipole moment integrals using translation formulas for Slater-type orbitals

 By the use of translation formulas for the expansion of Slater-type orbitals (STOs) in terms of STOs at a new origin, three-center electric and magnetic multipole moment integrals are expressed in terms of two-center multipole moment integrals for the evaluation of which closed analytical formulas are used. The convergence of the series is tested by calculating concrete cases. Computer results with an accuracy of 10⁻⁷ are obtained for 2^ν– pole electric and magnetic multipole moment integrals for 1≤ν≤5 and for arbitrary values of screening constants of atomic orbitals and internuclear distances. Received: 28 October 1999 / Accepted: 15 February 2000 / Published online: 5 June 2000     

Analytical evaluation of molecular electric and magnetic multipole moment integrals over Slater-type orbitals

The analytical expressions are derived for the magnetic multipole moment integrals in terms of electric multipole moment integrals for which the closed formulas through the overlap integrals are obtained. By the use of the derived expressions in terms of overlap integrals, the electric and magnetic multipole moment integrals, the electric and magnetic properties of molecules can be evaluated most efficiently and accurately. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 145–150, 1998     

Convergence of multipole expanded intermolecular interaction energies for Gaussian-type-function and Slater-type-function basis sets

 It is shown that the multipole expansion of each order of the polarization series converges for large enough intermolecular distances when finite basis sets of Gaussian or Slater-type functions are used to approximate molecular response properties. Convergence of the multipole expansion for each order of the polarization series does not imply convergence of the polarization series itself. A corresponding convergence condition is extracted from the general perturbation theory in a finite-dimensional space and is applied to the H + H⁺ problem. Received: 29 September 1999 / Accepted: 22 May 2000 / Published online: 18 August 2000     

RISM-SCF study of the free-energy profile of the Menshutkin-type reaction NH3+CH3Cl→NH3CH3++Cl− in aqueous solution

The free-energy profile for the Menshutkin-type reaction NH₃ + CH₃Cl → NH₃CH₃ ⁺ + Cl⁻ in aqueous solution is studied using the RISM-SCF method. The effect of electron correlation on the free-energy profile is estimated by the RISM-MP2 method at the HF optimized geometries along the reaction coordinate. Solvation was found to have a large influence on the vibrational frequencies at the reactant, transition state and product; these vibrational frequencies are utilized to calculate the zero-point energy correction of the free-energy profile. The computed barrier height and reaction exothermicity are in reasonable agreement with those of experiment and previous calculations. The change of solvation structure along the reaction path is represented by radial distribution functions between solute-solvent atomic sites. The mechanisms of the reaction are discussed from the view points of solute electronic and solvation structures. Received: 26 June 1998/Accepted: 28 August 1998 / Published online: 2 November 1998     

Theoretical studies of the potential energy surface and wavepacket dynamics of the Li3 system

The three-dimensional (3D) potential energy surface of the ground state of Li₃ was determined by the multireference configuration interaction method. The vibrational motions and pseudorotation were investigated by a 3D time-dependent wavepacket formalism. The analytical expression of the 3D surface is given and the results of vibrational analyses at several critical points are presented. The low-lying excited states of Li₃ were examined for the C _{2 v} structure and the vertical and adiabatic excitation energies were calculated. The ground and singlet excited states of Li₂ were calculated and their spectroscopic constants compare well with the experimental values. A 3D wavepacket calculation was performed for simulations of the stimulated emission pumping spectrum in which the A state was taken as an intermediate. The recurrences of the autocorrelation functions were characterized by classical trajectory calculations. The autocorrelation functions obtained by wavepacket propagation are reproduced well by the accumulation of the classical trajectories in the short-time region. Received: 2 July 1998 / Accepted: 3 September 1998 / Published online: 8 February 1999     

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     

Efficient boundary basis functions for time-independent quantum scattering calculations

Novel parametrically energy-dependent boundary functions, F, combined with a finite L ² basis set, permit accurate and efficient calculation of scattering wavefunctions for many energies. Both accuracy and efficiency are achieved simultaneously because all the necessary integrals are energy-independent and also certain functionals, (H−E)|F>, in the Schr?dinger equation are allowed to satisfy desirable boundary conditions. In addition, slight modification of the Schr?dinger equation in the boundary region is shown to be useful for improving the numerical accuracy when a cutoff-radius-truncated basis set is used. The advantages of the present approaches are demonstrated for the one-dimensional Eckart barrier problem. Received: 17 June 1998 / Accepted: 13 July 1998 / Published online: 18 September 1998     

The structure and energetics of cryolite melts

A method of solvation energy computation is proposed for ions and molecules in the environment of an ionic melt, based on the approximation of the ionic melt as an ideal conductor. The method is used to compute equilibrium constants of some equilibria in cryolite melt. Theoretically obtained results predict that aluminium is bound in tetrafluorocomplexes AlF₄ ⁻. Received: 16 March 1998 / Accepted: 19 June 1998 / Published online: 7 October 1998     

Analytic UHF-CCSD(T) second derivatives: implementation and application to the calculation of the vibration-rotation interaction constants of NCO and NCS

An implementation of analytic open-shell UHF-CCSD(T) second derivatives is presented. To demonstrate applicability and test the accuracy of the UHF-CCSD(T) approach for the determination of spectroscopical parameters, vibration-rotation interaction constants were calculated for the ground (1²Π) and first electronically excited (1²Σ) states of the NCO and NCS radicals. In addition, harmonic vibrational frequencies for both states, the Renner-Teller parameter for the ground state, as well as the 1²Π→1²Σ excitation energy are reported. While the computed values are in good agreement with reliable experimental information for NCO, most of the data presented for NCS are predictions of quantities not well known from experiment. Received: 4 May 1998 / Accepted: 27 July 1998 / Published online: 12 October 1998     

Variational solution of the single-particle Dirac equation in the field of two nuclei using relativistically adapted Slater basis functions

A variational method for solving the time-independent single-particle Dirac equation in the Coulomb field of two nuclei is described. A minimax variational principle and basis functions that have the proper analytic behavior, i.e. behave like r ^γ,γ non-integer, in the neighborhood of a nucleus, are used. A momentum space integration scheme for computing the necessary two-center integrals is described. Results are given for a standard test problem on two nuclei with Z=90 with an internuclear separation of 2.0/Z. The results confirm those of a previous calculation [F.A. Parpia and A.K. Mohanty, Chem Phys Lett 238: 209 (1995)]. Received: 13 May 1998 / Accepted: 22 June 1998 / Published online: 28 August 1998     

Argon-matrix-isolation Raman spectra and density functional study of 1,3-butadiene conformers

s-trans, s-cis and gauche conformers of 1,3-butadiene have been studied using density functional theory and the coupled-cluster method using double substitutions (CCD). Matrix isolation Raman and IR data for the minor conformer were obtained and are used in combination with the theoretical results to resolve earlier ambiguities in vibrational assignments. Based on high-quality Hessians, new harmonic stretching force constants are reported for the carbon backbone of s-trans-1,3-butadiene. For the minor conformer the best unscaled root mean square error of the calculated frequencies for the s-cis and gauche geometries are 17.5 cm⁻¹ and 7.4 cm⁻¹, respectively, primarily due to a better agreement of the gauche results for the vibrations at 983 cm⁻¹, 596 cm⁻¹ and 470 cm⁻¹ which depend strongly on the torsional angle. Although this points towards the gauche form rather than the s-cis form, the calculated transition dipole moment directions at the CCD/6-311G(d,p) level confirm the earlier conclusion that the minor conformer has C _{2 v} symmetry in the matrix. It is concluded that either the better agreement between the frequencies calculated for the gauche form and the observed values is coincidental, or that the molecule is indeed nonplanar in the matrix and tunnels very rapidly between the two mirror-image forms (or its lowest vibrational level lies above the barrier). Received: 1 July 1998 / Accepted: 26 October 1998 / Published online: 15 February 1999     

The saddle point of the nucleophilic substitution reaction Cl− + CH3Cl: results of large-scale coupled cluster calculations

On the basis of large-scale coupled cluster calculations including connectedz triple substitutions in a perturbative way, the geometrical parameters of the D _{3 h} saddle point of the Walden inversion reaction Cl⁻ + CH₃Cl′→ ClCH₃ + Cl′⁻ are predicted to be R _s (C—Cl) = 2.301 ? and r _s (C—H) = 1.069 ?. The barrier height with respect to the reactants is recommended to be 11.5 ± 1.0 kJ mol⁻¹. Connected triple substitutions lower the barrier height by almost a factor of 2, but have very little influence on the geometric structure of the saddle point. Received: 26 June 1998 / Accepted: 15 July 1998 / Published online: 28 September 1998     

Dissociative recombination of HeH+. I. Rovibrational spectrum of HeH Rydberg states

The repulsive ground electronic state X²Σ⁺ of HeH is strongly coupled to the Rydberg states at small interatomic distances. Such large couplings also occur between some of the Rydberg states. HeH⁺ ions that capture an electron in a Rydberg state end up in separated He and H atoms by indirect predissociation. This paper presents a study of potential functions and pertinent matrix elements involving the lowest electronic states: the ²Σ⁺ states, X, A, C, and D, and the ²Π states B and E. Individual transition rates as well as total radiative and non-radiative lifetimes have been computed for the lowest vibrational and rotational levels. Received: 22 June 1998 / Accepted: 21 August 1998 / Published online: 12 October 1998     

FAD-modified SiO2/ZrO2/C ceramic electrode for electrocatalytic reduction of bromate and iodate

SiO₂/ZrO₂/C carbon ceramic material with composition (in wt%) SiO₂ = 50, ZrO₂ = 20, and C = 30 was prepared by the sol–gel-processing method. A high-resolution transmission electron microscopy image showed that ZrO₂ and the graphite particles are well dispersed inside the matrix. The electrical conductivity obtained for the pressed disks of the material was 18 S cm⁻¹, indicating that C particles are also well interconnected inside the solid. An electrode modified with flavin adenine dinucleotide (FAD) prepared by immersing the solid SiO₂/ZrO₂/C, molded as a pressed disk, inside a FAD solution (1.0 × 10⁻³ mol L⁻¹) was used to investigate the electrocatalytic reduction of bromate and iodate. The reduction of both ions occurred at a peak potential of −0.41 V vs. the saturated calomel reference electrode. The linear response range (lrr) and detection limit (dl) were: BrO₃ ⁻, lrr = 4.98 × 10⁻⁵–1.23 × 10⁻³ mol L⁻¹ and dl = 2.33 μmol L⁻¹; IO₃ ⁻, lrr = 4.98 × 10⁻⁵ up to 2.42 × 10⁻³ and dl = 1.46 μmol L⁻¹ for iodate.     

Anodic oxidation of 2-aminofluorene in CH2Cl2 + 0.2 M Bu4NBF4: electrochemical behaviour of the derived oxidation products

The physicochemical properties and electrochemical behaviour of products obtained by anodic oxidation of 2-aminofluorene in CH₂Cl₂ + 0.2 M Bu₄NBF₄ are presented together with the oxidation conditions. Received: 8 January 1998 / Accepted: 21 September 1998     

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     

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     

Possible long-lived quartet resonance states of CO−

Two states of CO⁻ which are expected to live longer than the well-known ²Π shape resonance are examined and the results obtained are compared with the analogous states of the isoelectronic N₂ ⁻ system. The ⁴Σ⁻ and ⁴Π states are found to be stable with respect to dissociation. The latter state is also stable with respect to single-electron loss to its parent neutral state. The lifetime of this state is supposed to be long, but not necessarily long enough to allow detection in a mass spectrometer. Received: 28 May 1998 / Accepted: 23 July 1998 / Published online: 9 October 1998     

The influence of monovalent cations on the stability of electrochemically formed nickel fluoride films

The stability of electrochemically formed NiF₂ film in 1.0 M perchloric acid containing monovalent fluorides namely, NH₄F, HF, NaF, KF and LiF, is investigated using cyclic voltammetry, chronoamperometry, atomic absorption spectroscopy and scanning electron microscopy. In addition to direct dissolution of nickel and dissolution through the oxide layer, a new mode of dissolution of NiF₂ film as NiF₃ ⁻ and NiF₄ ²⁻ through complex formation is proposed. This process is significantly influenced by the alkali metal fluorides. On a comparative basis the stability of NiF₂ decreases in the order NH₄F > HF > KF > LiF. Received: 29 July 1998 / Accepted: 3 November 1998     

Nafion-based solid-state gas sensors: Pt / Nafion electrodes prepared by an impregnation-reduction method in sensing oxygen

The influences of the reductant concentration of NaBH₄ and the quantity of Pt loading on the active surface area and the sensitivity of the Pt/Nafion electrodes prepared by an impregnation-reduction method in detecting oxygen were investigated in this study. The Pt/Nafion electrodes with a Pt loading of 4.99 mg/cm², obtained at 0.0107 M Pt(NH₃)₄Cl₂ and 0.06 M NaBH₄, show maximum sensitivities of 0.0528 A/ppm and 0.0538 A/ppm obtained in O₂ concentration regions of 0–5000 and 5000–50 000 ppm, respectively. A sensing model was also proposed to illustrate the sensing phenomenon. Received: 21 January 1998 / Accepted: 10 March 1998