Long-range dispersion interactions involving excited atoms; The H(1s)–H(2s) interaction

The dispersion interaction between two nonoverlapping atoms (or molecules) is expressed in terms of single-atom “polarizabilities.” The formulation is valid even if one atom (or both) is in an excited state. To illustrate the procedure, the dispersion interaction between a 1s and a 2s hydrogen atom is computed accurately through order R^?10 (R = internuclear separation).     

Fully relativistic study on electron impact elastic scattering from Nq+ (q = 1–3), Na+, Arq+ (q = 1–3, 7–8), and Xeq+ (q = 2–6, 8)

A study is presented on the elastic scattering of electrons from N^q+ (q = 1–3), Na⁺, Ar^q+ (q = 1–3, 7–8), Xe^q+ (q = 2–6, 8) to understand the available experimental differential cross section results. A model potential approach has been utilized to describe the scattering process. The model potential includes the static, exchange, polarization and absorption potentials. The static potentialis obtained through the charge density calculated by obtaining ionic wave functions using multi-configuration Dirac-Fock (MCDF) approximation. Thereafter, the static potential is added to the suitable exchange, polarisation and absorption potentials to construct the spherically averaged complex optical potential. Using the obtained potential in the Dirac equations,these are solved with the partial wave phase shift analysis method and the differential cross sections are calculated. Results for different ions exhibit prominent interference structures in the energy versus cross section curves and show good agreement on comparison with the experimental results available in the selected energy ranges.     

Molecular beam scattering studies of the reaction D + H2 (v = 0) and D + H2 (v = 1) → HD + H

The reaction D + H₂ → HD + H has been investigated in two molecular beam scattering experiments. Angular and time-of-flight distributions have been measured for the initial vibrational ground state (v = 0) at a most probable collision energy of E_cm = 1.5 eV and for the first vibrational excited state (v = 1) at E_cm = 0.28 eV with the same apparatus. Results for the ground-state experiment are compared with quasiclassical trajectory calculations(QCT) on the LSTH-hypersurface transformed into the laboratory system and averaged over the apparatus distributions. The agreement isquite satisfactory. At this high collision energy the HD products are no longer scattered in a backward direction but in a wide angular region concentrated about θ = 90° in the center-of-mass system. The absolute reactive cross section has been determined and the agreement with the theoretical value from QCT calculations is within the experimental error. The high sensitivity of the experiment to different properties of the doubly differential cross section has also been demonstrated. A preliminary evaluation of the experiment with initial vibrational excitation (v = 1) shows that the HD-product molecules are preferably backward scattered and the change of internal energy is small supporting the concept of a reaction which is adiabatic with respect to the internal degrees of freedom.     

Variationen modulo 4–4+, 4+3–3+4–, 4–5+, 5–4+4–5+4–4+ bei Seltenerdcarbidhalogeniden

The new compounds Pr₈(C₂)₄Cl₅ (1), Pr₁₄(C₂)₇Cl₉ (2), Pr₂₂(C₂)₁₁Cl₁₄ (3), Ce₂(C₂)Cl (4), La₂(C₂)Br (5), Ce₂(C₂)Br (6), Pr₂(C₂)Br (7), Ce₁₈(C₂)₉Cl₁₁ (8), and Ce₂₆(C₂)₁₃Cl₁₆ (9) were prepared by heating mixtures of LnX₃, Ln and carbon or in an alternatively way LnX₃, and “Ln₂C_3–x” in appropriate amounts for several days between 750 and 1200 °C. The crystal structures were investigated by X‐ray powder analysis (5–7) and/or single crystal diffraction (1–4, 8, 9). Pr₈(C₂)₄Cl₅ crystallizes in space group P2₁/c with the lattice parameters a = 7.6169(12), b = 16.689(2), c = 6.7688(2) Å, β = 103.94(1) °, Pr₁₄(C₂)₇Cl₉ in Pc with a = 7.6134(15), b = 29.432(6), c = 6.7705(14) Å, β = 104.00(3) °, Pr₂₂(C₂)₁₁Cl₁₄ in P2₁/c with a = 7.612(2), b = 46.127(9), c = 6.761(1) Å, β = 103.92(3) °, Ce₂(C₂)₂Cl in C2/c with a = 14.573(3), b = 4.129(1), c = 6.696(1) Å, β = 101.37(3) °, La₂(C₂)₂Br in C2/c with a = 15.313(5), b = 4.193(2), c = 6.842(2) Å, β = 100.53(3) °, Ce₂(C₂)₂Br in C2/c with a = 15.120(3), b = 4.179(1), c = 6.743(2) Å, β = 101.09(3) °, Pr₂(C₂)₂Br in C2/c with a = 15.054(5), b = 4.139(1), c = 6.713(3) Å, β = 101.08(3) °, Ce₁₈(C₂)₉Cl₁₁ in P$\bar{1}$ with a = 6.7705(14), b = 7.6573(15), c = 18.980(4) Å,α = 88.90(3) °, β = 80.32(3) °, γ = 76.09(3) °, and Ce₂₆(C₂)₁₃Cl₁₆ in P2₁/c with a = 7.6644(15), b = 54.249(11), c = 6.7956(14) Å, β = 103.98(3) ° The crystal structures are composed of Ln octahedra centered by C₂ dumbbells. Such Ln₆(C₂)‐octahedra are condensed into chains which are joined into undulated sheets. In compounds 1–4 three and four up and down inclined ribbons alternate (4₊4_–, 4₊3_–3₊4_–, 4₊4_–3₊4_–4₊3_–), in compounds 8 and 9 four and five (4₊5_–, 5₊4_–4₊5_–4₊4_–), and in compounds 4–7 one, one ribbons (1₊1_–) are present. The Ln‐(C₂)‐Ln layers are separated by monolayers of X atoms.     

Theoretical Investigation on the Reactions of H with (CH3)4‐nSiHn (n = 1–4)

The abstractions of H with (CH₃)_4‐nSiH_n (n = 1–4) have been investigated at high levels of ab initio molecule orbital theory. Geometries have been optimized at the MP‐2 level with 6–31G(d) basis set, and G2MP2 level has been used for the final energy calculations. Theoretical analysis provided conclusive evidence that the main process occurring in each case is the abstraction of H from the Si? H bond leading to the formation of the H₂ and silyl radicals; the abstraction of H from C? H bond has higher barrier and is difficult to react in each case. The kinetics of the title reactions have been calculated with variational transition state theory over the temperature range 200–1000 K, and the theoretical rate constants match well with the experimental values.     

Linear response theory of the dipole–dipole dispersion interaction between H(1s) atoms

A self-consistent theory of the linear response previously developed by one of us is applied to the dipole–dipole dispersion interaction of two ground state H atoms in the united atom (He) limit, using a Sellmeier representation of the polarizability in terms of pseudostates. Numerical calculations show that a truncated 12-term expansion out of the N = 22 H(1s) dipole pseudospectrum built from STOs with orbital exponent c = 0.985 gives a result exceeding by no more than 5% the variational result for the He dispersion energy.     

Tris[3‐hydroxy‐2(1 H)‐pyridinonato]‐Komplexe von Al3+, Cr3+ und Fe3+ – Kristall‐ und Molekülstrukturen von 3‐Hydroxy‐2(1 H)‐pyridinon und Tris[3‐hydroxy‐2(1 H)‐pyridinonato]chrom(III)

Tris[3‐hydroxy‐2(1 H)‐pyridinonato] Complexes of Al³⁺, Cr³⁺, and Fe³⁺ – Crystal and Molecular Structures of 3‐Hydroxy‐2(1 H)‐pyridinone and Tris[3‐hydroxy‐2(1 H)‐pyridinonato]chromium(III) Tris[3‐hydroxy‐2(1 H)‐pyridinonato] complexes of Al³⁺, Cr³⁺ and Fe³⁺ are obtained by reactions of 3‐hydroxy‐2(1 H)pyridinone with the hydrates of AlCl₃, CrCl₃ or Fe(NO₃) in aqueous alkaline solutions as polycrystalline precipitates. The compounds are isotypic. X‐ray structure determinations were performed on single crystals of the uncoordinated 3‐hydroxy‐2(1 H)‐pyridinone ( 1 ) (orthorhombic, space group P2₁2₁2₁, a = 405.4(1), b = 683.0(1), c = 1770.3(3) pm, Z = 4) and of the chromium compound 3 (rhombohedral with hexagonal setting, space group R3c, a = 978.1(1), c = 2954.0(1) pm, Z = 6).     

Hybrid Slater–Gaussian-type 1s orbitals for the 1∑ ground state of H2 and He

Introduction of noninteger powers of r (or the elliptical coordinate ξ) in the definition of the 1s AO is shown to give better approximate wave-functions for the ground states of H₂ and He than other functions of comparable complexity. This trend is examined for various definitions of hybrid Slater–Gaussian orbitals using a limited CI . The best optimized single-term expansion energy is only 0.000160 a.u. above the “SCF limit” for H₂ at R = 1.4 a.u. and 0.000382 a.u. for He at R = 1.3 a.u.     

Si-H, P-H 和 S-H 键离解能Alfa取代基效应研究

CBS-Q and G3 methods were used to generate a large number of reliable Si--H, P---H and S--H bond dissociation energies （BDEs） for the first time. It was found that the Si--H BDE displayed dramatically different substituent effects compared with the C--H BDE. On the other hand, the P---H and S--H BDE exhibited patterns of substituent effects similar to those of the N--H and O--H BDE. Further analysis indicated that increasing the positive charge on Si of XSiH3 would strengthen the Si--H bond whereas increasing the positive charge on P and S of XPH2 and XSH would weaken the P---H and S--H bonds. Meanwhile, increasing the positive charge on Si of XSiH2^＋ stabilized the silyl radical whereas increasing the positive charge on P and S in XPH＂ and XS＊ destabilized P- and S-centered radicals. These behaviors could be reasonalized by the fact that Si is less electronegative than H while P and S are not. Finally, it was demonstrated that the spin-delocalization effect was valid for the Si-, P- and S-centered radicals.     

Electron correlation effects at Sn/Si(1 1 1)– and Sn/Ge(1 1 1)– reconstructions

Electron correlation effects for the two-dimensional electron gas associated with the surface bands of the Sn/Si(1 1 1)–3×3, , Sn/Ge(1 1 1)–3×3 and reconstructions are analyzed. Unrestricted local-density-approximation (LDA) calculations enable to define a many-body hamiltonian that includes intra- and inter-site electron interactions. From the analysis of this hamiltonian, it can be concluded that the reconstructions present a Mott transition, while the 3×3 surface remains metallic. How these results can be used to to discriminate between conflicting models explaining the phase transition is described. Inverse photoemission data for the Sn/Si(1 1 1) surface suggests that this phase transition can be explained by means of a dynamical fluctuations model.