Normalization and Fermi–Coulomb and Coulomb hole sum rules for approximate wave functions

For approximate wave functions, we prove the theorem that there is a one‐to‐one correspondence between the constraints of normalization and of the Fermi–Coulomb and Coulomb hole charge sum rules at each electron position. This correspondence is surprising in light of the fact that normalization depends on the probability of finding an electron at some position. In contrast, the Fermi–Coulomb hole sum rule depends on the probability of two electrons staying apart because of correlations due to the Pauli exclusion principle and Coulomb repulsion, while the Coulomb hole sum rule depends on Coulomb repulsion. We demonstrate the theorem for the ground state of the He atom by the use of two different approximate wave functions that are functionals rather than functions. The first of these wave function functionals is constructed to satisfy the constraint of normalization, and the second that of the Coulomb hole sum rule for each electron position. Each is then shown to satisfy the other corresponding sum rule. The significance of the theorem for the construction of approximate “exchange‐correlation” and “correlation” energy functionals of density functional theory is also discussed. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Exact electronic properties in the classically forbidden region of a metal surface

We derive exact properties of the inhomogeneous electron gas in the asymptotic classically forbidden region at a metal–vacuum interface within the framework of local effective potential energy theory. We derive a new expression for the asymptotic structure of the Kohn–Sham density functional theory (KS‐DFT) exchange‐correlation potential energy v_xc(r) in terms of the irreducible electron self‐energy. We also derive the exact asymptotic structure of the orbitals, density, the Dirac density matrix, the kinetic energy density, and KS exchange energy density. We further obtain the exact expression for the Fermi hole and demonstrate its structure in this asymptotic limit. The exchange‐correlation potential energy is derived to be v_xc(z → ∞) = ?α_KS,xc/z, and its exchange and correlation components to be v_x(z → ∞) = ?α_KS,x/z and v_c(z → ∞) = ?α_KS,c/z, respectively. The analytical expressions for the coefficients α_KS,xc and α_KS,x show them to be dependent on the bulk‐metal Wigner–Seitz radius and the barrier height at the surface. The coefficient α_KS,c = 1/4 is determined in the plasmon‐pole approximation and is independent of these metal parameters. Thus, the asymptotic structure of v_xc(z) in the vacuum region is image‐potential‐like but not the commonly accepted one of ?1/4z. Furthermore, this structure depends on the properties of the metal. Additionally, an analysis of these results via quantal density functional theory (Q‐DFT) shows that both the Pauli W_x(z → ∞) and lowest‐order correlation‐kinetic W(z → ∞) components of the exchange potential energy v_x(z → ∞), and the Coulomb W_c(z → ∞) and higher‐order correlation‐kinetic components of the correlation potential energy v_c(z → ∞), all contribute terms of O(1/z) to the structure. Hence correlations attributable to the Pauli exclusion principle, Coulomb repulsion, and correlation‐kinetic effects all contribute to the asymptotic structure of the effective potential energy at a metal surface. The relevance of the results derived to the theory of image states and to KS‐DFT is also discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Heats of solution and neutralization ofLewis acids and bases in acetic anhydride

Heats solution of someLewis acids and bases in acetic anhydride have been determined and the following order of their relative strengths is proposed: SbCl₅>SO₃>SnCl₄>TiCl₄>AsCl₃ and piperidine> n-butylamine>potassium acetate>sodium acetate -picoline>quinoline. Heats neutralization of theseLewis acids and bases in acetic anhydride suggest that the major enthalpy change in these neutralization reactions is due to the combination of a proton and the (CH₂COOCOCH₃)-ion, resulting in the formation of acetic anhydride.

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Lösungs- und Neutralisationswärmen von Lewis-Säuren und-Basen in Essigsäureanhydrid

Zusammenfassung Es wurden die Lösungswärmen einigerLewis-Säuren in Essigsäureanhydrid bestimmt und folgende Reihung nach ihrer relativen Stärke vorgeschlagen: SbCl₅>SO₃>SnCl₄>TiCl₄>AsCl₃ und Piperidin> n-Butylamin>KAc>NaAc-Picolin>Chinolin. Die Neutralisationswärmen dieserLewis-Säuren und-Basen legen nahe, daß der Hauptanteil daran auf die Reaktion eines Protons mit (CH₂–COOCOCH₃)-zurückzuführen ist.

     

Synthesis and characterization of monomers and polymers of acrylated phosphonate esters derived from glycerol,D-mannitol,D-sorbitol,pentaerythritol, and dipentaerythritol

Phosphonic acid ester derivatives of glycerol, D -mannitol, D -sorbitol, pentaerythritol, and dipentaerythritol have been synthesized by transacetalation reactions with diethyl 2,2-diethoxyethylphosphonate. These phosphonated derivatives of polyols and carbohydrates have been esterified to from the corresponding methacrylates. All these compounds have been characterized on the basis of their elemental analysis and spectroscopic (infrared including FT–IR, ¹H-, ¹³C-, ³¹P-NMR, and mass) methods. Transacetalation reactions with dialkyl 2,2-dialkoxyethylphosphonate lead to the synthesis of 1,3-dioxane derivatives in the case of D -mannitol, pentaerythritol, and dipentaerythritol, whereas a mixture of both 1,3-dioxane and 1,3-dioxolane derivatives is obtained with D -sorbitol and glycerol. The methacrylates of phosphonylated polyol derivatives show the capacity to dissolve and interact with metal salts such as bismuth bromide and uranyl nitrate. Some of the polymers obtained from these monomers have been characterized on the basis of their spectral and thermal (differential scanning calorimetry) properties.     

Novel five- and six-coordinate zinc (II), cadmium (II) and mercury(II) complexes of macrocyclic ligands

Summary Complexes of 2,6-dipicolinic acid hydrazide, DPH, with Zn^II, Cd^II and Hg^II have been prepared and characterized by elemental analysis, i.r. and electronic spectra and by electrical conductance measurements. The ligand is terdentate, having coordination sites at two deprotonated amide-nitrogen and pyridine-nitrogen atoms. The Zn^II and Hg^II complexes are pentacoordinate whereas the Cd^II complexes are hexacoordinate and have trigonal bipyramidal and pseudooctahedral stereochemistries, respectively. The Zn, Cd and Hg ions induce cyclization of DPH complexes upon reaction with-diketones. The complexes of macrocyclic ligands so formed have the same stereochemistries as those of DPH.     

Dimeric tetrahedral complexes of manganese(II) and iron(II) with benzoyl hydrazones

Summary Dimeric manganese(II)and iron(II)complexes, (ML)₂, derived from benzoyl hydrazones ofo-hydroxyaryl aldehydes and ketones arc described and characterised by elemental analyses and by conductance, molecular weight, magnetic, electronic and i.r. spectral measurements. The dimeric nature of the complexes is revealed by i.r. spectra which show bands atca. 885 Mn²⁺ and 820 cm^–1 Fe²⁺, characteristic of ring vibrations. The i.r. spectra reveal the terdentate nature of the ligands. The electronic spectra in dimethylformamide are consistent with the tetrahedral nature of the complexes. The appreciable lowering in _eff is attributed to the presence of exchange interactions between two paramagnetic atomsvia oxygen bridges.Reprints of this article are not available.     

Raman study of (NH4)2CuCl4·2H2O—I: Dynamics and structure in low temperature phase

We report the results of a Raman scattering study of (NH₄)₂CuCl₄2H₂O at 300, 205 and 100°K, in order to elucidate the dynamics and phase transition in this double salt. A group theoretical calculation of the symmetry vectors, in the high temperature phase (D_4h¹⁴), is made and the various modes are identified. The deuterated compound (ND₄)₂CuCl₄·2D₂O has also been investigated to help in identifying the modes involving motion of the ammonium ions and water molecules. Through a careful analysis of the spectra at 100°K, the space group in the low temperature phase has been established as D_2d³. The important consequence of this result is that this leads to parallel spatial ordering of ammonium tetrahedra in this compound in the low temperature phase.