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     

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.     

Accurate potential energy curves for the group 12 dimers Zn2, Cd2, and Hg2

Potential energy curves of the electronic ground states of the group 12 dimers Zn₂ and Cd₂ were computed at the CCSD(T) level of theory, including full triple corrections $\Updelta$ T in the coupled-cluster procedure, and spin-orbit (SO) contributions from four-component coupled-cluster calculations, extrapolated to the complete basis set (CBS) limit. For Hg₂, the potential energy curve published recently (Pahl et al. in J Chem Phys 132:114301, 2010] is complemented in this work by non-relativistic calculations to quantify and discuss relativistic effects. We obtain very accurate fits of our CBS/CCSD(T) and CBS/CCSD(T)+ $\Updelta$ T data points to an analytically simple and computationally efficient extended Lennard Jones form. For the CBS/CCSD(T)+ $\Updelta$ T+SO curves, we obtain dissociation energies of D _e?=?226?cm^?1 and D _e?=?319?cm^?1 for Zn₂ and Cd₂ respectively, in very good agreement with recent theoretical calculations and experimental data. We also present equilibrium distances and rotational and vibrational spectroscopic constants to compare with available theoretical and experimental data. The results obtained for non-relativistically treated Hg₂ continue nicely the trends with increasing atom number preset by Zn₂ and Cd₂, confirming that indeed, relativistic effects account for the known peculiarities for the mercury dimer.     

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     

The X˜1A1, a˜3B1, a˜1B˜1, and B˜1A1 electronic states of SiH2

Four electronically low-lying states of silylene (SiH₂) have been studied systematically using high level ab initio electronic structure theory. Self-consistent field (SCF), two-configuration (TC) SCF, complete active space (CAS) SCF, configuration interaction with single and double excitations (CISD), and CASSCF second-order (SO) CI levels of theory were employed with eight distinct basis sets. The zeroth-order wave functions of the ground (X˜ ¹A₁ or 1 ¹A₁) and B˜ ¹A₁ (or 2 ¹A₁) excited states are appropriately described by the first and second eigenvectors of the TCSCF secular equations. The TCSCF-CISD, CASSCF, and CASSCF-SOCI wave functions for the B˜ ¹A₁ (or 2 ¹A₁) state were obtained by following the second root of the CISD, CASSCF, and SOCI Hamiltonian matrices. At the highest level of theory, the CASSCF-SOCI method with the triple zeta plus triple polarization augmented with two sets of higher angular momentum functions and two sets of diffuse functions basis set [TZ3P(2f,2d)+2diff], the energy separation (T₀) between the ground (X˜ ¹A₁) and first excited (a˜ ³B₁) states is determined to be 20.5 kcal/mol (0.890eV,7180cm⁻¹), which is in excellent agreement with the experimental T₀ value of 21.0 kcal/mol (0.910eV,7340cm⁻¹). With the same method the T₀ value for the a˜ ¹B₁−X˜ ¹A₁ separation is predicted to be 45.1 kcal/mol (1.957 eV,15780 cm⁻¹), which is also in fine agreement with the experimental value of 44.4 kcal/mol (1.925 eV,15530 cm⁻¹). The T₀ value for the B˜ ¹A₁−X˜ ¹A₁ separation is determined to be 79.6 kcal/mol (3.452 eV,27 840 cm⁻¹). After comparison of theoretical and experimental T₀ values for the a˜ ³B₁ and a˜ ¹B₁ states and previous studies, error bars for the B˜ ¹A₁ state are estimated to be ±1.5 kcal/mol (±525 cm⁻¹). The predicted geometry of the B˜ ¹A₁ state is r_e(SiH)=1.458 and θ_e=162.3^∘. The physical properties including harmonic vibrational frequencies of the B˜ ¹A₁ state are newly determined. Received: 10 March 1997 / Accepted: 2 April 1997     

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     

Ab initio study of structures and energies of Al2H4 and Al2H 4 −

The low-lying isomers of Al₂H₄ and their anions are investigated with the hybrid density functional B3LYP, the coupled-cluster CCSD and CCSD(T) methods, and the electron propagator theory. The positive adiabatic electron affinities 5,798 and 10,112 cm⁻¹ are predicted for the neutral C_2v and D_2d symmetric isomers, respectively. The D_2h symmetric anion is more stable by 852 cm⁻¹ than the C_2v symmetric anion. The photodetachment spectra for Al₂H₄⁻ anions at the C_2v and D_2h symmetries are simulated on the basis of the Franck–Condon factor calculations, indicating a reasonable way to study the transition state of the intramolecular torsion process     

Oxygen reduction on a Ru x S y (CO) n cluster electrocatalyst in 0.5 M H2SO4

A ruthenium-sulfur carbonyl cluster electrocatalyst, Ru _x S _y (CO) _n , was synthesized by pyrolysis of Ru₃(CO)₁₂ and elemental sulfur in a sealed ampoule at 300 °C. The pyrolyzed compound was characterized by DSC, FT-IR, XRD and SEM (EDX) techniques. The electrocatalytic activity and kinetic parameters for the molecular oxygen reduction were determined by a rotating ring-disk electrode (RRDE) in a 0.5 M H₂SO₄ solution at 25 °C. The cathodic polarization indicates two Tafel slopes: −0.124 ± 0.002 V dec⁻¹ at low and −0.254 ± 0.003 V dec⁻¹ at high overpotentials, and first-order kinetics with respect to O₂ concentration. From the analysis of Levich plots and RRDE results, the oxygen reduction on Ru _x S _y (CO) _n was determined to proceed mostly via a multielectron transfer path (4e⁻) to water formation ( >94%). Received: 4 March 1999 / Accepted: 26 May 1999     

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     

Photocatalytic intercalated material based on HLaNb<Subscript>2</Subscript>O<Subscript>7</Subscript> as host and Cd<Subscript>0.8</Subscript>Zn<Subscript>0.2</Subscript>S as guest

A novel photocatalytic material (Pt,Cd0.8Zn0.2S)/HLaNb2O7 was fabricated by successive intercalation and exchange reactions. The (Pt,Cd0.8Zn0.2S)/HLaNb2O7 possessed a gallery height less than 0.5 nm and showed a broad absorption with wavelength over 370-500 nm. Using (Pt,Cd0.8Zn0.2S)/HLaNb2O7 as catalyst, the photocatalytic H2 evolution was more than 160 cm3·h-1·g-1 in the presence of Na2S as a sacrificial agent under irradiation with wavelength more than 290 nm from a 100-W mercury lamp. Furthermore, the catalyst showed photocatalytic activity even under visible light irradiation.     

Autoionizing rydberg states of. The Li2 molecule: Molecular constants for Li2+

Autoionizing Rydberg series of Li₂ have been observed in the two-step optical cxcitation of a supersonic lithium beam. The series limits are vibrational states of Li₂⁺. In the most probable assignment IP(Li₂) = 41236.4 ± 2.5 cm^?1 and for Li₂⁺ω_e = 263.45 ± 1.3 cm^?1; ω_eχ_e = 1.35 ± O.2 cm^?1; r_e = 3.032 ± 0.01 Å; D_e = 10807 ± 150 cm^?1.     

Solvent effects on the nπ* transition of pyrimidine in aqueous solution

A hybrid quantum mechanical and molecular mechanical potential is used in Monte Carlo simulations to examine the solvent effects on the electronic excitation energy for the n→π* transition of pyrimidine in aqueous solution. In the present study, the pyrimidine molecule is described by the semi-empirical AM1 model, while the solvent molecules are treated classically. Two sets of calculations are performed: the first involves the use of the pairwise three-point charge TIP3P model for water, and the second computation employs a polarizable many-body potential for the solvent. The latter calculation takes into account the effect of solvent polarization following the solute electronic excitation, and makes a correction to the energies determined using pairwise potentials, which neglects such fast polarization effects and overestimates the solute-solvent interactions on the Franck-Condon excited states. Our simulation studies of pyrimidine in water indicate that the solvent charge redistribution following the solute electronic excitation makes modest corrections (about −130␣cm⁻¹) to the energy predicted by using pairwise potentials. Specific hydrogen bonding interactions between pyrimidine and water are important for the prediction of solvatochromic shifts for pyrimidine. The computed n→π* blue shift is 2275±110 cm⁻¹, which may be compared with the experimental value (2700 cm⁻¹) from isooctane to water. Received: 14 January 1997 / Accepted: 21 February 1997     

Benchmark calculations with correlated molecular wave functions XII. Core correlation effects on the homonuclear diatomic molecules B2-F2

Using systematic sequences of the newly developed correlation consistent core-valence basis sets from cc-pCVDZ through cc-pCV6Z, the spectroscopic constants of the homonuclear diatomic molecules containing first row atoms, B–F, are calculated both with and without inclusion of 1s correlation. Internally contracted multireference configuration interaction (IC-MRCI) and singles and doubles coupled cluster (CCSD) theory with a perturbational estimate of connected triple excitations, CCSD(T), have been investigated. By exploiting the convergence of the correlation consistent basis sets, complete basis set (CBS) limits have been estimated for total energies, dissociation energies, equilibrium geometries, and harmonic frequencies. Based on the estimated CBS limits the effects of 1s correlation on D _e (kcal/mol), r _e (?), and ω _e (cm⁻¹) are: +1.1, −0.0070, +10 for B₂; +1.5, −0.0040, +13 for C₂; +0.9, −0.0020, +9 for N₂; +0.3, −0.0020, +6 for O₂; and −0.1, −0.0015, +1 for F₂. Received: 20 January 1997 / Accepted: 6 May 1997     

Pseudopotential study of the ground and excited states of Yb2

The ground state of the van der Waals-type lanthanide dimer Yb₂ has been studied by means of relativistic energy-consistent ab initio pseudopotentials using three different core definitions. Electron correlation was treated by coupled-cluster theory, whereby core-valence correlation effects have been accounted for either explicitly by correlating the energetically highest coreorbitals or implicitly by means of an effective core-polarization potential. Results for the first and second atomic ionization potentials, the atomic dipole polarizability, and the spectroscopic constants of the molecular ground state are reported. Low-lying excited states have been investigated with spin-orbit configuration interaction calculations. It is also demonstrated for the whole lanthanide series that correlation effects due to the atomic-like, possibly open 4f-shell in lanthanides can be modeled effectively by adding a core-polarization potential to pseudopotentials attributing the 4f-shell to the core. Received: 3 April 1998 / Accepted: 27 July 1998 / Published online: 9 October 1998     

Electrochemical redox reactions studied in frozen tetrabutylammonium halide hydrates

The electrochemical redox reactions: Fe(CN)₆ ⁴⁻−e⁻↔ Fe(CN)₆ ³⁻, Ru(NH₃)₆ ³⁺+e⁻↔ Ru (NH₃)₆ ²⁺ and Fc(CH₂OH)₂−e⁻↔ Fc(CH₂OH)₂ ⁺ (Fc–ferrocene) were investigated in tetrabutylammonium halide hydrates at temperatures below and above the electrolyte melting point. They were studied by cyclic voltammetry, potential step chronoamperometry and impedance spectroscopy. Freezing of the electrolyte affects both the shape and position of the cyclic voltammogram on the potential scale. Also the shapes of the current-time relationship and the impedance spectra change at temperatures below the melting point. It has been proposed that this behaviour is caused by slow transport of the reactant and the heterogeneous nature of the electrolyte. The activation energies of reactant transport are about four times larger in frozen electrolytes than those in liquid. It has been concluded that reactant transport is restricted to the intergrain space of the electrolyte. Received: 16 December 1997 / Accepted: 10 February 1998     

The kinetics of chemical reactions in the products of dissociation of the CO2−H2 gas mixture in microwave discharge

The yields of hydrogen atoms, oxygen atoms and molecules, and hydroxyl radicals after a microwave discharge in the mixture of CO₂ and H₂ were measured by ESR spectroscopy in a flow-type system. A mathematical model of the kinetics of chemical reactions downstream the microwave discharge was devised. The concentrations of particles that cannot be detected under our experimental conditions were estimated. Experimental values of the concentration sensitivity for an RE-1306 ESR spectrometer are as follows: for a pressure of 1 Torr and optimized detection conditions, H^., 10¹¹ cm⁻³; O^., 3·10¹⁰ cm⁻³; OH^., 10¹⁰ cm⁻³; O₂, 3·10¹³ cm⁻³ (Ref. 7); for a pressure of 2 Torr, H^., 5·10¹² cm⁻³; O^., 2·10¹² cm⁻³; OH^., 2.5·10¹¹ cm⁻³; O₂, 7.5·10¹⁴ cm^{−3 8} Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 4, pp. 665–669, April, 2000.     

The modes of complexation of benzimidazole with aqueous β-cyclodextrin explored by phase solubility, potentiometric titration, 1H-NMR and molecular modeling studies

The results of rigorous modeling of phase solubility diagrams, pH solubility profiles and potentiometric titrations revealed the following for benzimidazole (BZ) and BZ/β-CD complexation in aqueous solution: (a) the pK _a value of BZ estimated at 5.66 ± 0.08 was reduced to 5.33 ± 0.06 in the presence of 15 mM β-CD at 25 °C, thus indicating inclusion complex formation; (b) BZ forms soluble 1:1 and 2:1 BZ/β-CD complexes with complex formation constants K ₁₁ = 104 ± 8 M⁻¹ and K ₂₁ = 16 ± 6 M⁻¹; (c) protonated BZ forms only 1:1 complex with K ₁₁ = 42 ± 12 M⁻¹; (d) ¹H-NMR studies in D₂O showed significant upfield chemical shift displacements for inner cavity β-CD protons indicating inclusion complex formation, while (e) Molecular modeling of BZ-β-CD interactions in water clearly indicated complete inclusion of one BZ molecule into the β-CD cavity.     

A theoretical study of the acetylide anion, HCC−

The results of various ab initio calculations are reported for the electronic ground state of the acetylide anion. An “Eyring's lake” in the T-shaped configuration is identified with six different methods (SCF, MP2, CCSD, CCSD-T, CCSD(T), and CEPA–1). The equilibrium bond lengths of HCC⁻ are estimated to be r _e (CH)=1.0689(3) ? and R _e (CC)=1.2464(2) ?, and the ground-state rotational constant is predicted to be B ₀=41636(20)MHz. The large permanent dipole moment of μ₀=−3.093D should facilitate detection of the anion by microwave spectroscopy. The band centers are predicted to be 3211.3cm⁻¹(ν₁), 511.1cm⁻¹(ν₂), and 1805.0cm⁻¹(ν₃). A large transition dipole moment of 0.477 D is calculated for the ν₂ band. Rovibrational levels of HCC⁻ up to approximately 20 000 cm⁻¹ above equilibrium are calculated with DVR-DGB and FBR methods on the basis of a previous CEPA–1 potential energy surface. Different energy patterns are found and discussed, for which anharmonic and Coriolis resonances are shown to play an important role. Received: 27 July 1998 Accepted: 12 August 1998 / Published online: 19 October 1998     

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     

Oxygen reduction in acid media by a Ru<Subscript>x</Subscript>Fe<Subscript>y</Subscript>Se<Subscript>z</Subscript>(CO)<Subscript>n</Subscript> cluster catalyst dispersed on a glassy carbon-supported Nafion film

Electrocatalytic oxygen reduction was studied on a Ru_xFe_ySe_z(CO)_n cluster catalyst with Vulcan carbon powder dispersed into a Nafion film coated on a glassy carbon electrode. The synthesis of the electrocatalyst as a mixture of crystallites and amorphous nanoparticles was carried out by refluxing the transition metal carbonyl compounds in an organic solvent. Electrocatalysis by the cluster compound is discussed, based on the results of rotating disc electrode measurements in a 0.5 M H₂SO₄. A Tafel slope of −80.00±4.72 mV dec⁻¹ and an exchange current density of 1.1±0.17×10⁻⁶ mA cm⁻² was calculated from the mass transfer-corrected curve. It was found that the electrochemical reduction reaction follows the kinetics of a multielectronic (n=4e⁻) charge transfer process producing water, i.e. O₂+4H⁺+4e⁻→2H₂O. Electronic Publication