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     

A systematic theoretical investigation of the valence excited states of the diatomic molecules B2, C2, N2 and O2

A quantitative survey on the performance of multireference (MR), configuration interaction with all singles and doubles (CISD), MRCISD with the Davidson correction and MR-average quadratic coupled cluster (AQCC) methods for a wide range of excited states of the diatomic molecules B₂, C₂, N₂ and O₂ is presented. The spectroscopic constants r _e, ω_e, T _e and D _e for a total of 60 states have been evaluated and critically compared with available experimental data. Basis set extrapolations and size-extensivity corrections are essential for highly accurate results: MR-AQCC mean-errors of 0.001 ?, 10 cm⁻¹, 300 cm⁻¹ and 300 cm⁻¹ have been obtained for r _e, ω_e, T _e and D _e, respectively. Owing to the very systematic behavior of the results depending on the basis set and the choice of method, shortcomings of the calculations, such as Rydberg state coupling or insufficient configuration spaces, can be identified independently of experimental data. On the other hand, significant discrepancies with experiment for states which indicate no shortcomings whatsoever in the theoretical treatment suggest the re-evaluation of experimental results. The broad variety of states included in our survey and the uniform quality of the results indicate that the observed systematics is a general feature of the methods and, hence, is molecule-independent. Received: 12 June 2000 / Accepted: 1 September 2000 / Published online: 21 December 2000     

Molecular orbital study on the OH stretching frequency of the phenol dimer and its cation

Ab initio calculations were performed to investigate the structure and bonding of the phenol dimer and its cation, especially the OH stretching frequencies. Some stable structures of the phenol dimer and its cation were obtained at the Hartree–Fock level and were found to be in agreement with predictions based on spectroscopic investigations. In these dimers the phenol moieties are bound by a single OH⋯O hydrogen bond. The hydrogen bond is much stronger in the dimer cation than in the neutral dimer. The calculated binding energy of the phenol dimer in the most stable structure was 6.5–9.9 kcal/mol at various levels of calculation, compared with the experimental value of 5 kcal/mol or greater. The binding energy of the phenol dimer cation is more than 3 times (24.1–30.6 kcal/mol) as large as that of the neutral dimer. For the phenol dimer the OH stretching frequency of the proton-accepting phenol (PAP) is 3652 cm⁻¹ and that of the proton-donating phenol (PDP) is 3516 cm⁻¹; these are in agreement with observed values of 3654 and 3530 cm⁻¹, respectively. For the phenol dimer cation the OH stretching frequency of the PAP is 3616–3618 cm⁻¹ in comparison with an observed value of 3620 ± 3 cm⁻¹. That of the PDP in the dimer cation is calculated to be 2434–2447 cm⁻¹, which is 1210–1223 cm⁻¹ lower than that of the bare phenol. The large reduction in the OH stretching frequency of the PDP in the phenol dimer cation is attributed to the formation of a stronger hydrogen bond in the cation than in the neutral dimer. Received: 24 March 2000 / Accepted: 26 April 2000 / Published online: 11 September 2000     

Perspective on “An extended Hückel theory. I. Hydrocarbons”

 The size-consistent self-consistent matrix dressing method has been applied on an open-shell single-configuration reference state. Once the reference state is converged, several low-lying roots can be obtained for the dressed configuration interaction (CI) matrices of appropriate symmetry. The CI matrices were built with a complete-active-space singles and doubles CI method in order to deal properly with multiconfiguration excited states. The vertical ionization and ionization–excitation transitions are obtained from the difference to the closed shell ground-state energy of the neutral molecule. The method has been applied to NH⁺ ₃ and N⁺ ₂ using atomic natural orbital basis sets and state-average adapted molecular orbitals. Two ²A₁ states, very similar and showing great mixing of the (2a _l ⁻¹) and (3a _l ⁻²5a _l ¹) determinants, can be assigned to the broad asymmetric band at 27.6 ± 2 eV in the photoelectron spectrum of NH₃. The possible contribution of a ²Π _g (3σ _g ⁻²1π _g ¹) state to the A shake-up peak of N₂ at 24.6 eV is also discussed. Other states, doublets and quadruplets, are reported for both systems up to 30 eV for NH₃ and 37 eV for N₂. Received: 16 September 1999 / Accepted: 3 February 2000 / Published online: 2 May 2000     

Accurate calculations of dissociation energies of weakly bonded He<Subscript>2</Subscript> and Be<Subscript>2</Subscript> molecules by MRCI method

The He₂ and Be₂ ground state potential curves have been calculated by extrapolating to an infinite basis BSSE corrected MRCI total energies obtained with large Gaussian basis sets, large reference configuration spaces, and pseudo-natural molecular orbitals. The calculated D _e = 11.0031 K and R _e = 5.607 a.u. of He₂ are in an excellent agreement with D _e = 11.006 ± 0.004 K and R _e = 5.608 ± 0.012 a.u. obtained recently by SAPT with SM energy correction. The obtained Be₂ non-relativistic D _e = 822 cm⁻¹ and relativistically corrected D _e = 818 cm⁻¹ are in a good agreement with experimental D _e = 790 ± 30 cm⁻¹ and the value of 829 ± 64 cm⁻¹ obtained recently by a quantum Monte Carlo method.     

Ionic conduction of lithium for Perovskite-type compounds, Li x La(1− x )/3NbO3 and (Li0.25La0.25)1− x Sr0.5 x NbO3

Perovskite-type compounds, Li _x La_{(1− x )/3}NbO₃ and (Li_0.25La_0.25)_{1− x} Sr_{0.5 x} NbO₃ as lithium ionic conductors, were synthesized by a solid-state reaction. From powder X-ray diffraction, the solid solution ranges of the two compounds were determined to be 0≤x≤0.25 and 0≤x≤0.125, respectively. In the Li _x La_{(1− x )/3}NbO₃ system, the ionic conductivity of lithium at room temperature, σ₂₅, exhibited a maximum value of 4.7 × 10⁻⁵ S · cm⁻¹ at x = 0.10. However, because of the decrease in the lattice parameters with increasing Li concentration x˙, σ₂₅ of the samples decreased with increasing x from 0.10 to 0.25. Also, in the (Li_0.25La_0.25)_{1− x} Sr_{0.5 x} NbO₃ system, the lattice parameter increased with the increase of Sr concentration and the σ₂₅ achieved a maximum (7.3 × 10⁻⁵ S · cm⁻¹ at 25 °C) at x = 0.125. Received: 12 September 1997 / Accepted: 15 November 1997     

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     

Physicochemical Properties of Plant Protection Substances: I Polymorphism and Binary Systems of Triadimenol

 The fungicide triadimenol consists of a mixture of two diastereoisomers. Diastereoisomer A (1RS,2SR) could be obtained from the mixture by fractionated crystallization from ethanol/water and toluene, successively, whereas diastereoisomer B (1RS,2RS) could be separated by column chromatography on a silica gel column using ethylacetate as eluent. Four different crystal forms of diastereoisomer A could be derived. The modifications were characterized by means of thermal analysis (thermomicroscopy, DSC), FTIR-spectroscopy, FT-Raman-spectroscopy and powder X-ray diffraction, as well as pycnometry. The thermodynamic relationships are illustrated in a semischematic energy/temperature-diagram which provides information about the relative thermodynamic stabilities and physical properties of the four crystal forms. Mod. II (m.p. 132 °C, ΔH_f 33.1±0.2 kJ mol⁻¹, density 1.271±0.001 g cm⁻³) was obtained from toluene after the separation of diastereoisomer A and is enantiotropically related to mod. I (m.p. 138 °C, ΔH_f 32.0 ± 0.2 kJ mol⁻¹, density 1.243±0.001 g cm⁻³). The transition point of mod. II with mod. I was determined between 30 and 40 °C, which means that mod. II is thermodynamically stable at ambient conditions. Mod. III (m.p. 112 °C, ΔH_f 25.1±0.5 kJ mol⁻¹) and mod. IV were obtained from the melt. Furthermore, the phase diagrams of the binary systems of diastereoisomer B and the four modifications of diastereoisomer A were calculated by means of the experimentally obtained thermodynamical data. Received September 30, 1999. Revision July 30, 2000.     

CEPA calculations on open-shell molecules. II. Singlet-triplet energy splitting in π2 configurations of diatomic molecules

The CEPA-PNO method is used for calculating the energy difference ΔE _ST between the³∑⁻ and the¹Δ states of diatomic molecules in electronic π² configurations. An analysis of the contribution of electron correlation to ΔE _ST is performed in terms of physically understandable effects such as direct correlation, dynamic spin polarization, semiinternal and internal excitations. It is shown that these effects are of completely different importance for the molecules treated in this study: For C₂ the direct correlation between the two singly occupied π-orbitals is the dominant correlation contribution to ΔE _ST; for O₂, S₂, SO the internal excitation π _u ² → π _g ² is predominant, whereas for NH and PH there is a close competition between the direct correlation and the spin polarization of the underlying σ-orbitals. The basis set dependence of these effects is investigated, in particular for NH. Our final results reproduce experimental values of ΔE _ST within 0.05–0.10 eV.     

Impedance studies on the 5-V cathode material,LiCoPO<Subscript>4</Subscript>

Olivine-structured LiCoPO₄ is synthesized by a Pechini-type polymer precursor method. The structure and the morphology of the compounds are studied by the Rietveld-refined X-ray diffraction, scanning electron microscopy, Brunauer, Emmett, and Teller surface area technique, infrared spectroscopy, and Raman spectroscopy techniques, respectively. The ionic conductivity (σ ionic), dielectric, and electric modulus properties of LiCoPO₄ are investigated on sintered pellets by impedance spectroscopy in the temperature range, 27–50 °C. The σ (ionic) values at 27 and 50 °C are 8.8 × 10⁻⁸ and 49 × 10⁻⁸ S cm⁻¹, respectively with an energy of activation (E _a) = 0.43 eV. The electric modulus studies suggest the presence of non-Debye type of relaxation. Preliminary charge–discharge cycling data are presented.     

Toward spectroscopic accuracy of ab initio calculations of vibrational frequencies and related quantities: a case study of the HF molecule

Calculations at various coupled-cluster (CC) levels with and without the inclusion of linear r _{i j} -dependent terms are performed for the HF molecule in its ground state with a systematic variation of basis sets. The main emphasis is on spectroscopic properties such as the equilibrium distance r _e and the harmonic vibration frequency ω_e. Especially with the R12 methods (including linear r _{i j} -dependent terms), convergence to the basis set limit is reached. However, the results (at the basis set limit) are rather sensitive to the level of the treatment of electron correlation. The best results are found for the CCSDT1-R12 and CCSD[T]-R12 methods (CCSD[T] was previously called CCSD+T(CCSD)), while CCSD(T) overestimates ω_e by ≈6 cm⁻¹. The good agreement of conventional CCSD(T) with experiment for basis sets far from saturation (e.g. truncated at g-functions) is probably the result of a compensation of errors. The contribution of core-correlation is non-negligible and must be included (effect on ω_e≈5 cm⁻¹). Relativistic effects are also important (23 cm⁻¹), while adiabatic effects are much smaller (<1cm⁻¹) and non-adiabatic effects on ω_e can be simulated in replacing nuclear by atomic masses; for rotation nuclear masses appear to be the better choice, at least for hydrides. From a potential curve based on calculations with the CCSDT1-R12 method with relativistic corrections, the IR spectrum is computed quantum-mechanically. Both the band heads and the rotational structures of the observed spectra are reproduced with a relative error of ≈10⁻⁴ for the three isotopomers HF, DF, and TF. Received: 3 July 1998 / Accepted: 4 August 1998 / Published online: 28 October 1998     

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     

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     

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     

Spectrophotometric Investigation of the Complexing Reaction between Rutin and Titanyloxalate Anion in 50% Ethanol

Summary.  In the present work, rutin (3,3′ ,4′ ,5,7-pentahydrohyflavone-3-rhamnoglucoside) was determinated via a complexing reaction with a titanyloxalate anion. K₂[TiO(C₂O₄)₂] and rutin react in 50% ethanol forming a 1:2 complex in a pH range from 4.00 to 11.50, in which the TiO(C₂O₄)₂ ²⁻ ion is linked to rutin through the 4-carbonyl and 5-hydroxyl group. The thermodynamic stability constant log β₂ ⁰ of the complex is determined to 10.80 at pH = 6.50. The change of the standard Gibbs free energy Δ G⁰ amounts to −61 kJċ mol⁻¹, indicating that the process of complex formation is spontaneous. The optimal conditions for the spectrophotometric determination of microconcentrations of rutin are at pH=6.40 and λ= 430 nm, where the complex shows an absorption maximum with a molar absorption coefficient a ₄₃₀=(60±2)ċ10³ dm³ċ mol⁻¹ċ cm⁻¹. The method is applied rutin determination from tablets. Received January 4, 2000. Accepted (revised) February 17, 2000     

Development of a highly precise ID-ICP-SFMS method for analysis of low concentrations of lead in rice flour reference materials

Microwave digestion and isotope dilution inductively coupled plasma mass spectrometry (ID-ICP-SFMS) has been applied to the determination of Pb in rice flour. In order to achieve highly precise determination of low concentrations of Pb, the digestion blank for Pb was reduced to 0.21 ng g⁻¹ after optimization of the digestion conditions, in which 20 mL analysis solution was obtained after digestion of 0.5 g rice flour. The observed value of Pb in a non-fat milk powder certified reference material (CRM), NIST SRM 1549, was 16.8 ± 0.8 ng g⁻¹ (mean ± expanded uncertainty, k = 2; n = 5), which agreed with the certified value of 19 ± 3 ng g⁻¹ and indicated the effectiveness of the method. Analytical results for Pb in three brown rice flour CRMs, NIST SRM 1568a, NIES CRM 10-a, and NIES CRM 10-b, were 7.32 ± 0.24 ng g⁻¹ (n = 5), 1010 ± 10 ng g⁻¹ (n = 5), and 1250 ± 20 ng g⁻¹ (n = 5), respectively. The concentration of Pb in a candidate white rice flour reference material (RM) sample prepared by the National Metrology Institute of Japan (NMIJ) was observed to be 4.36 ± 0.28 ng g⁻¹ (n = 10 bottles). Figure Digestion blank of Pb was carefully reduced to approximately 0.2 ng g^-1 which permitted the highly precise determination of Pb at low ng g^-1 level in foodstuff samples by ID-SFMS     

Absolute integrated intensities of vapor-phase hydrogen peroxide (H2O2) in the mid-infrared at atmospheric pressure

We report quantitative infrared spectra of vapor-phase hydrogen peroxide (H₂O₂) with all spectra pressure-broadened to atmospheric pressure. The data were generated by injecting a concentrated solution (83%) of H₂O₂ into a gently heated disseminator and diluting it with pure N₂ carrier gas. The water vapor lines were quantitatively subtracted from the resulting spectra to yield the spectrum of pure H₂O₂. The results for the ν₆ band strength (including hot bands) compare favorably with the results of Klee et al. (J Mol. Spectrosc. 195:154, 1999) as well as with the HITRAN values. The present results are 433 and 467 cm^-2 atm⁻¹ (±8 and ±3% as measured at 298 and 323 K, respectively, and reduced to 296 K) for the band strength, matching well the value reported by Klee et al. (S = 467 cm⁻² atm⁻¹ at 296 K) for the integrated band. The ν₁ + ν₅ near-infrared band between 6,900 and 7,200 cm⁻¹ has an integrated intensity S = 26.3 cm⁻² atm⁻¹, larger than previously reported values. Other infrared and near-infrared bands and their potential for atmospheric monitoring are discussed.     

Ab initio study of bonding trends for f0 actinide oxyfluoride species

 Fully relativistic, four-component Dirac–Fock calculations and quasirelativistic pseudopotential calculations at different ab initio levels are used to study the bonding trends among the naked, triatomic [OAnO] ^q+ groups or the oxyfluorides [AnO _n F _m ] ^q with f ⁰ configurations. The triatomic f ⁰ series is suggested to range from the bent ThO₂ via the linear OPaO⁺ to at least NpO₂ ³⁺, a possible new gas-phase species. The neutral oxyfluoride molecules include the experimentally unknown NpO₂F₃ and PuO₂F₄. The latter is a candidate for the so far unknown oxidation state Pu(VIII), which is found to lie considerably above Pu(VI), but to be locally stable. Their all-oxygen isoelectronic analogues are NpO₅ ³⁻, known in the solid state, and the unknown PuO₆ ⁴⁻. Further possible candidates for Pu(VIII) are PuO₄(D _4h ) and the cube-shaped PuF₈(O _h ). Isoelectronic UF₈ ²⁻ is calculated to be D _4d , in agreement with experiment. Received: 18 May 2001 / Accepted: 21 June 2001 / Published online: 11 October 2001