Atomic orbitals with angularly dependent Z eff to be used in molecular orbitals calculations

A new type of atomic orbital is proposed for use in molecular problems of quantum mechanics. This orbital is formally similar to Slater's orbitals but is characterized by an effective nuclear charge Z _eff which is an explicit function of the angles ? and φ. The fundamental state of the molecule H₂ ⁺ is studied using such an orbital.     

Pseudo-Kähler metrics on six-dimensional nilpotent Lie algebras

It is well known that any symplectic manifold (M,Ω) has an almost complex structure J which is compatible with Ω. In this paper, we deal with the existence of compatible pairs (J,Ω) on nilpotent Lie algebras of dimension ≤6, J being an integrable almost complex structure. We prove that if such a pair exists, J must satisfy some extra conditions, namely J must be nilpotent in the sense of [Trans. Am. Math. Soc. 352 (2000) 5405]. Associated to any such a compatible pair, there is a pseudo-Kähler metric g which cannot be positive definite unless be abelian. All these metrics are Ricci flat, although many of them are nonflat, and we study the behaviour of its curvature tensor under deformation.     

X-ray photoelectron spectra of nickel halides: multiplet structure and multi-electron excitations in Ni2+ 3p and 2p shells

The satellite structure in the X-ray photoelectron spectra of nickel halides has been measured. The satellites found in the photoelectron spectra of Ni²⁺ 3p and 2p subshells have two common sources: multiples splitting and multi-electron excitations. The experimental spectra are compared with theoretical results on multiples splitting and with calculations of band structure.     

Formality of Donaldson submanifolds

We introduce the concept of s–formal minimal model as an extension of formality. We prove that any orientable compact manifold M, of dimension 2n or (2n−1), is formal if and only if M is (n−1)–formal. The formality and the hard Lefschetz property are studied for the Donaldson submanifolds of symplectic manifolds constructed in [13]. This study permits us to show an example of a Donaldson symplectic submanifold of dimension eight which is formal simply connected and does not satisfy the hard Lefschetz theorem. An erratum to this article is available at .