Methods for efficient evaluation of integrals for Gaussian type basis sets

Methods are described that allow for an efficient evaluation of two-electron integrals over contracted Gaussian lobe functions. The improvement in computational speed is achieved by avoiding the computation of integrals that are: 1. sufficiently small on numerical reasons, 2. zero by symmetry, 3. identical to other integrals by symmetry. Examples of the effectiveness of these techniques are included. We also report the timings for a further processing of two-electron integrals in a Hartree Fock and correlation energy computation.     

A fully automated mass spectrometer for the analysis of organic solids

Automation of a mass spectrometer—computer system makes it possible to process up to 30 samples without attention after sample loading. An automatic sample changer introduces the samples successively into the ion source by means of a direct inlet probe. A process control unit determines the operation sequence. Computer programs are available for the hardware support, system supervision and evaluation of the spectrometer signals. The most essential precondition for automation — automatic evaporation of the sample material by electronic control of the total ion current — is confirmed to be satisfactory. The system operates routinely overnight in an industrial laboratory, so that day work can be devoted to difficult analytical problems. The cost of routine analyses is halved.     

Synthesis of 2,3-dimethyltetra-cyclo(5.5.1.04,13.010,13)trideca-2,5-dien-9-one,a new derivative of all-cis-(5.5.5.5)fenestrane

Intramolecular arene-olefin photoreaction of methyl-6-methyl-2-phenylhept-5-enoate (9a) leads to the tetracyclic product 10a, from which the fenestra-dienone, 2, has been obtained. Mechanistic aspects of the photoreaction are discussed.     

Zur Reaktion des Germaniums mit Germaniumtetrachlorid und zur Existenz der Oxidchloride GeOCl2 und GeOCl6 im Gleichgewicht

On the Reaction of Germanium with Germanium Tetrachloride and on the Existence of the Oxidechlorides GeOCl₂ and GeOCl₆ at the Equilibrium The above equilibrium was measured in a Gauge-manometer and the enthalpy of formation and the entropy for GeCl₂,g were derived from these results. From total pressure measurements and transport experiments of GeO₂ with GeCl₄ follows, that the oxidechlorides Ge₂OCl₆ and GeOCl₂ are not present in measurable concentrations, that means the enthalpy of formation of GeOCl₂ must be higher than ?327 kJ · mol^?1.     

Anab initio investigation of Cu2Se and Cu4Se2

Summary Experimentally known copper selenium clusters show extraordinary geometrical features, especially short Cu-Cu distances. We report the first theoretical investigation of Cu₂Se and Cu₄Se₂. Various quantum chemical methods (SCF, MP2, CPF, CCSD, CCSD(T), LDF) are applied to determine the importance of dynamic electron correlation. We find that inclusion of correlation does not essentially change the electronic structure of the clusters but has a strong influence on geometries. To reduce the computational effort we apply effective core potentials (ECPs) in combination with small, but carefully optimized basis sets. The applicability of simple modellings of correlation energies for approximate inclusion of correlation effects in SCF geometry optimizations is tested.     

Asymptotic behaviour of molecular bound state wavefunctions

Upper bounds are derived for |r^μ_i|, μ = 1,2, ·, where ? denotes an exact electronic bound state wavefunction of a molecular system in the Born-Oppenheimer approximation, and r_i is the distance of the ith electron from an appropriately chosen point, e.g., the molecular center. It is further shown that ? decays exponentially if r_i → ∞.     

On the growth of meromorphic functions of infinite order

Letf be a meromorphic function of infinite order,T(r, f) its Nevanlinna (or Ahlfors-Shimizu) characteristic, andM(r, f) its maximum modulus. It is proved that $$\mathop {\lim \inf }\limits_{r \to \infty } \frac{{\log M(r,f)}}{{rT'(r,f)}} \leqslant \pi and\mathop {\lim \inf }\limits_{r \to \infty } \frac{{\log M(r,f)}}{{T(r,f)\psi (log T(r,f))}} = 0$$ . if ? (x)/x is non-decreasing, ?′(x)<-√?(x) and ∝^∞ dx/?(x) < ∞.