An MRD-CI study of low-lying electronic states in CaF

Dipole moments and various spectroscopic constants of some low-lying electronic states of the CaF molecule have been calculated using the multireference single· and double-excitation configuration-interaction (MRD-CI) method. The electronic structure of the highly ionic molecule in various excited states can be explained in tenns of different polarisations of the mainly Cacentered valence electron in the field of the F$^-$ anion. Plots of natural orbitals occupied by the valence electron in the different states give a qualitative picture of the charge distribution and provide a visualisation of the different polarisations of the valence electron in the various states. Comparisons with the electrostatic polarisation model ofTörring, Ernstand Kändler (TEK model) are made. The unknown A' $^2 \Delta$ state is predicted to lie about 21200 cm$^{-1}$ above the ground state

Analysis and Depertubation of the C2^2Π and D2^2Σ+^+ states of CaF

No abstract availabl

Symmetrization based completion

We argue that most completion procedures for finitely presented algebras can be simulated by term completion procedures based on a generalized symmetrization process. Therefore we present three different constructive definitions of symmetrization procedures that can take the role of the orientation step in a symmetrization based completion procedure. We investigate confluence and compatibility properties of the symmetrized rules computed by the different symmetrization procedures. Based on semicompatibility properties we can present a generic version of the critical pair theorem that specializes to the critical pair theorems of Knuth-Bendix completion procedures and algebraic completion procedures like Buchberger's algorithm respectively. This critical pair theorem also applies to symmetrization based completion procedures using a normalized reduction relation if the result of the symmetrization is both semi-compatible and semi-stable. We conclude our paper showing how a generic Buchberger algorithm for polynomials over arbitrary finitely presented rings can be formulated as a symmetrization based completion procedure

Equational Prover of Theorema

The equational prover of the Theorema system is described. It is implemented on Mathematica and is designed for unit equalities in the first order or in the applicative higher order form. A (restricted) usage of sequence variables and Mathematica built-in functions is allowed

Deriving Theory Superposition Calculi from Convergent Term Rewriting Systems

We show how to derive refutationally complete ground superposition calculi systematically from convergent term rewriting systems for equational theories, in order to make automated theorem proving in these theories more eective. In particular we consider abelian groups and commutative rings. These are dicult for automated theorem provers, since their axioms of associativity, commutativity, distributivity and the inverse law can generate many variations of the same equation. For these theories ordering restrictions can be strengthened so that inferences apply only to maximal summands, and superpositions into the inverse law that move summands from one side of an equation to the other can be replaced by an isolation rule that isolates the maximal terms on one side. Additional inferences arise from superpositions of extended clauses, but we can show that most of these are redundant. In particular, none are needed in the case of abelian groups, and at most one for any pair of ..