The Hartree–Fock ground state of atomic two-electron systems and the Wilson–Silverstone 1s orbital

For the Hartree–Fock ground state of atomic two-electron systems, the variational function of Wilson and Silverstone, ?(r) = (a + kr)^?1 exp(-kr) / (4π)^1/2, can be optimized in two complementary ways. For small values of the atomic number Z, all intergrals have been calculated numerically and optimization can be performed accurately. However, as Z increases, loss of significant figures is increasingly detrimental to the optimization process. For sufficiently large values of Z, the integrals may be replaced by asymptotic expansions in terms of (2a)^?. As a result of optimization, the parameters and expectation values can be given as expansions in terms of (32Z)^?1/2. Both methods yield good results for Z ≈ 25, so that the whole range of Z can be treated accurately. The results have been compared with those derived from other analytical two-parameter functions. It is found that ?(r) is indeed the outstanding two-parameter function, at least for small and intermediate values of Z.     

Two phosphonodehydrotripeptides: Boc0–Gly1–Δ(Z)Phe2–α‐Abu3PO3Me2 and Boc0–Gly1–Δ(Z)Phe2–α‐Nva3PO3Et2

The present paper reports the crystal structures of two short phosphonotripeptides (one in two crystal forms) containing one ΔPhe (dehydrophenylalanine) residue, namely dimethyl (3‐{[tert‐butoxycarbonylglycyl‐α,β‐(Z)‐dehydrophenylalanyl]amino}propyl)phosphonate, Boc⁰–Gly¹–Δ(Z)Phe²–α‐Abu³PO₃Me₂, C₂₁H₃₂N₃O₇P, (I), and diethyl (4‐{[tert‐butoxycarbonylglycyl‐α,β‐(Z)‐dehydrophenylalanyl]amino}butyl)phosphonate, Boc⁰–Gly¹–Δ(Z)Phe²–α‐Nva³PO₃Et₂, as the propan‐2‐ol monosolvate 0.122‐hydrate, C₂₄H₃₈N₃O₇P·C₃H₈O·0.122H₂O, (II), and the ethanol monosolvate 0.076‐hydrate, C₂₄H₃₈N₃O₇P·C₂H₆O·0.076H₂O, (III). The crystals of (II) and (III) are isomorphous but differ in the type of solvent. The phosphono group is linked directly to the last C_α atom in the main chain for all three peptides. All the amino acids are trans linked in the main chains. The crystal structures exhibit no intramolecular hydrogen bonds and are stabilized by intermolecular hydrogen bonds only.     

Quadrupole and octupole polarizabilities for the ground states of lithiumlike systems from Z=3 to 20

The quadrupole and octupole polarizabilities for the ground states of lithiumlike systems from Z=3 to 20 are calculated with the full-core plus correlation method. For the neutral lithium atom, the typical patterns of convergence of the quadrupole and octupole polarizabilities are analyzed. The calculated quadrupole and octupole polarizabilities of the ground state for lithium atom are compared with the previous theoretical results obtained by other methods; our predictions agree with the most accurate reports in the literature very well. For lithiumlike ions, our prediction may provide valuable reference data for other accurate theoretical calculations in future.     

The electronic structure of a diarsaallene –As=C=As– and a phosphaarsaallene –P=C=As–: UV photoelectron spectroscopy and theoretical studies

The electronic properties of a diarsaallene ArAs=C=AsAr and a phosphaarsaallene ArP=C=AsAr (Ar: 2,4,6-tri-tert-butylphenyl) have been investigated by using UV photoelectron spectroscopy and by density functional calculations on model compounds [(CH₃)₂C₆H₃Pn=C=AsC₆H₃(CH₃)₂, Pn: As, P]. Moreover, a comparison of the geometrical and electronic structures of the parent heteroallenes with those of the arsaethene H₂C=AsH and phosphaethene H₂C=PH has also been undertaken in order to determine the magnitude of the interaction between the π bond and the pnictogen lone pair n_Pn.     

Combined CI–HY studies of atomic states. II. Compact wave functions for the be ground state

Combined CI –HY method techniques have been employed in obtaining a 57-term CI –HY wave function with an energy of ?14.66632 a.u. A method due to Brown has been adopted for obtaining this wave function and various shorter expansions. A 44-term expansion with an energy of ?14.66606 a.u. is analyzed in terms of various pair effects, and qualitative arguments are presented for understanding these effects.     

Restricted Hartree-Fock and unrestricted Hartree-Fock as reference states in many-body perturbation theory: a critical comparison of the two approaches

Summary The paper deals with two topics related to the problem which reference state is better for many-body perturbation theory: restricted Hartree-Fock (RHF) or unrestricted Hartree-Fock (UHF)? The first topic concerns the potential surfaces. Several examples are presented to show shortcomings of the two approaches and a simple way is presented which seems to give a useful potential curve in the whole range of interatomic distances by a composition of RHF and UHF potential curves. The second topic concerns the many-body perturbation theory for open-shell systems in the RHF formalism. The method is critically examined and compared with the ordinary many-body perturbation theory using UHF as the reference. This examination of many-body techniques provides also some insight into the problems inherent of the SCF theory: spin contamination from higher multiplets, localization of orbitals, and self-consistency effects.     

Magnetic Ordering in the Solid Solution CePt1–xPdxAl (x = 0.1–0.8)

In order to investigate the magnetic properties of the solid solution CePt_1–xPd_xAl the individual compounds were synthesized from the elements using an arc furnace. From x = 0–0.8 the solid solution crystallizes in the orthorhombic TiNiSi‐type structure (Pnma, no. 62; a = 721–722, b = 448–453 and c = 778–779 pm) and for x = 0.9 both the TiNiSi‐ as well as the hexagonal ZrNiAl‐type structures were observed. The solid solution exhibits an interesting magnetic behavior as for small values of x ferromagnetic ordering can be found. At higher palladium content this changes towards an antiferromagnetic ordering. Furthermore the solid solution exhibits a spin‐reorientation (meta‐magnetic step) for x = 0.2–0.7.     

The valence bond calculations for conjugated hydrocarbons having 24–28 π‐electrons

A novel algorithm is introduced for coding all Slater determinants in the covalent space with conserved S_Z, the z component of total spin S for a classical valence bond (VB) model. It effectively minimizes the search time and the storing space in the central memory of the computer. In cooperation with symmetry reductions based on molecular point group and spin inversion, the VB calculations have been extended to benzenoid hydrocarbons of up to 28 π‐electrons that have 4×10⁷ configurations. The low‐lying states of benzenoids with 24, 26, and 28 π‐electrons have been obtained for 62 species. To rationalize the aromaticity of benzenoids in a VB scheme, the resonance energy per hexagon (REPH) is defined. A linear correlation between the REPH and the energy gap of the ground (singlet) state and the first excited (triplet) state for 89 benzenoids is established. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 856–869, 2000     

Isotopic effects for the ground 1 1S(L=0) states in the light two-electron ions

The total energies and various bound state properties are determined to very high accuracy for the ground 1 (1)S(L=0) states in some light two-electron ions, including the Li(+), Be(2+), B(3+), and C(4+) ions. The corrections due to the finite nuclear masses and lowest order QED corrections ( approximately alpha(3)) are considered/computed for each of these ions. In particular, the specific mass shift is determined for each of the Li(+), Be(2+), B(3+), and C(4+) ions. We also discuss the field shift related to the extended nuclear charge distribution.     

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.     

The α and α parameters for spin polarized Hartree–Fock–Slater calculations

α and α are derived for use in spin polarized Hartree–Fock–Slater programs. They are assumed to depend only on the number of up and down spin electrons in the atom. The calculated eigenvalues show a slight improvement only for carbon, nitrogen, and oxygen.     

Gradual Cerium Valence Change in the Solid Solution CeRu1–xPdxAl (x = 0.1–0.9)

The solid solution CeRu_1–xPd_xAl was synthesized for x = 0.1–0.9 from the elements by arc‐melting and subsequent annealing and characterized by powder X‐ray diffraction. All members crystallize in the orthorhombic LaNiAl type structure, space group Pnma. The lattice parameters range from a = 718–722, b = 412–426, and c = 1588–1620 pm, but no linear change of the lattice parameters was found. Magnetic measurements reveal intermediate cerium valences, which change to more trivalent cerium with increasing Pd content. The susceptibility data was interpreted by either the Inter‐Configuration Fluctuation (ICF) model or the Curie‐Weiss law.     

A theoretical study of alkali metal atomic clusters: From Lin to Csn (n = 2–8)

A theoretical study of the electronic structure of the first members of the alkali metal atomic clusters series Li_n to Cs_n (n = 2–8) has been done. The geometries of some isomers of the neutral, positive, and negative charged clusters have been determined. Some important properties have also been calculated: atomic binding energies, vertical and adiabatic ionization potentials, vertical and adiabatic electron affinities, static dipole polarizabilities, and energy gaps. Whenever possible they have been compared with experimental values yielding a reasonable agreement which supports some new values as reliable predictions. The data have been discussed in light of the periodic table of elements trends. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Four 1‐naphthyl‐substituted tetrahydro‐1,4‐epoxy‐1‐benzazepines: hydrogen‐bonded structures in one,two and three dimensions

(2S*,4R*)‐2‐exo‐(1‐Naphthyl)‐2,3,4,5‐tetrahydro‐1H‐1,4‐epoxy‐1‐benzazepine, C₂₀H₁₇NO, (I), crystallizes with Z′ = 2 in the space group P2₁; the two independent molecules have the same absolute configuration, although this configuration is indeterminate. The molecules of each type are linked by a combination of C—H...O and C—H...π(arene) hydrogen bonds to form two independent sheets, each containing only one type of molecule. (2SR,4RS)‐7‐Methyl‐2‐exo‐(1‐naphthyl)‐2,3,4,5‐tetrahydro‐1H‐1,4‐epoxy‐1‐benzazepine, C₂₁H₁₉NO, (II), crystallizes as a true racemate in the space group P2₁/c, and a combination of C—H...N, C—H...O and C—H...π(arene) hydrogen bonds links the molecules into sheets, each containing equal numbers of the two enantiomorphs. (2S*,4R*)‐2‐exo‐(1‐Naphthyl)‐7‐trifluoromethyl‐2,3,4,5‐tetrahydro‐1H‐1,4‐epoxy‐1‐benzazepine, C₂₁H₁₆F₃NO₂, (III), crystallizes as a single enantiomorph, as for (I), but now with Z′ = 1 in the space group P2₁2₁2₁; again, the absolute configuration is indeterminate. A single C—H...π(arene) hydrogen bond links the molecules of (III) into simple chains. (2S,4R)‐8‐Chloro‐9‐methyl‐2‐exo‐(1‐naphthyl)‐2,3,4,5‐tetrahydro‐1H‐1,4‐epoxy‐1‐benzazepine, C₂₁H₁₈ClNO, (IV), crystallizes as a single enantiomorph of well defined configuration, in the space group P2₁2₁2₁, where two independent C—H...π(arene) hydrogen bonds link the molecules into a single three‐dimensional framework structure.     

Searching for transition states: The line–then–plane (LTP) approach

A procedure for finding transition states ( TS ) that does not require the evaluation of the second derivatives during the search is proposed. The procedure is based on connecting a series of points representing products P _i and reactants R _i and taking conservative steps along the difference vector from P _i toward R _i and from R _i toward P _i until the two points coalesce. Although the points P _o and R _o represent the product and reactant specifically, other P _i and R _i are determined by minimization in hyperplanes perpendicular to P _{i ?1} and R _i?1. We apply this technique to six well-known potential functions and compare these results with those obtained from other well-known procedures. © 1995 John Wiley & Sons, Inc.     

Triphenylsilanol–4,4′‐bipyridyl (4/1): the Z′ = 4 polymorph revisited

A fully ordered structure is reported for the polymorph of triphenylsilanol–4,4′‐bipyridyl (4/1), 4C₁₈H₁₆OSi·C₁₀H₈N₂, having Z′ = 4. The asymmetric unit contains four similar but distinct five‐molecule aggregates, in which the central bipyridyl unit is linked to two molecules of triphenylsilanol via O—H...N hydrogen bonds, with a further pair of triphenylsilanol molecules linked to the first pair via O—H...O hydrogen bonds. An extensive series of C—H...π(arene) hydrogen bonds links these aggregates into complex sheets. This structure is compared with a previously reported structure [Bowes, Ferguson, Lough & Glidewell (2003). Acta Cryst. B 59 , 277–286], which was based on an erroneous disordered structural model arising from a false direct‐methods solution with reference to a strong pseudo‐inversion centre.     

The reactivity of the A-CH=N-NR-CX-B system. 1,3,4-Oxadiazoles and 2,3,4,5-tetrahydro-1,2,4-triazin-3-ones through the 1–5 and 1–6 cyclization reactions of α-thienylglyoxal monosemicarbazones

The factors influencing the reactivity of α-thienylglyoxal monosemicarbazones when treated with cyclizing reagents (bromine/sodium acetate and hydrobromic acid in acetic acid) were investigated. Depending on the experimental conditions, on the position of the substituent on the semicarbazide residue, and on the cyclizing agent, the substrates 1a-e give the semicarbazone bromides 2a-b, 5 , the 1,3,4-oxadiazoles 3a-c , the 1,2,4-triazine 11 and the 2,3,4,5-tetrahydro-1,2,4-triazine-3-ones 6, 8 and 9 . Compound 6 by thermolysis undergoes ring contraction in the Δ²-1,3,4-oxadiazoline 12 , while treatment with base involves the conversion of 6 into 1,2,4-triazol-5-one 13 . Ir, nmr and mass spectra support the reported structures.