The prism algorithm for two-electron integrals

A new approach to the evaluation of two-electron repulsion integrals over contracted Gaussian basis functions is developed. The new scheme encompasses 20 distinct, but interrelated, paths from simple shell-quartet parameters to the target integrals, and, for any given integral class, the path requiring the fewest floating-point operations (FLOPS ) is that used. Both theoretical (FLOP counting) and practical (CPU timing) measures indicate that the method represents a substantial improvement over the HGP algorithm.     

Zur Kenntnis von Natrium-hexafluoromanganat(III)

Sodium hexafluoromanganate(III) has been synthesized by heating equimolecular quantities of Na₂MnF₅ and NaF in argon atmosphere. The compound is monoclinic witha=5.56 (1) Å,b=5.84 (1) Å,c=8.10 (2) Å, =90.7 (2) andZ=2. It is a high spin complex with _eff and the deformation of the octahedra is evident from its IR-spectra. Two enantiotropic transitions (at 562 and 653°C) and the melting point at 800°C have been observed.

---

---

8. Mitt.: Mh. Chem.106, 483 (1975).     

Pyrolysis of homoadamant-3-ene

Pyrolysis of homoadamant-3-ene ($\text{5}$), generated from 1-adamantylcarbene ($\text{7}$), leads to the same three olefins ($\text{2}$, $\text{3}$, and $\text{4}$) that are produced from pyrolysis of 3-homoadamantyl acetate ($\text{1}$).     

Some estimates of theH ∞-uniform distribution

The sequences (y _n )=(a+blogn+ _n ) are uniformly distributed in the sense of the summation methodH . In the present paper the speed of convergence of this procedure is estimated for these, sequences and for some other sequences. For the sequences (a+blogn) theH -means converge considerably faster than logarithmic means.     

On the structure of a random sum-free set

Summary There is a natural probability measure on the set of all sum-free sets of natural numbers. If we represent such a set by its characteristic functions, then the zero-one random variabless(i) are far from independent, and we cannot expect a law of large numbers to hold for them. In this paper I conjecture a decomposition of into countably many more tractible pieces (up to a null set). I prove that each piece has positive measure, and show that, within each piece, a random set almost surely has a density which is a fixed rational number depending only on the piece. For example, the first such piece is made up of sets consisting entirely of odd numbers; it has probability 0.218 ..., and its members almost surely have density 1/4.     

On quadratic and sesquilinear functionals

LetX be a leftA-module, whereA is either a complex Banach *-algebra with an identity element or the field of quaternions. The main result of this note is that forQ, anA-quadratic functional defined onX, there exists a sesquilinear functionalB such thatB(x,x)=Q(x) holds for allxX.     

Local limits and harmonic functions for nonisotropic random walks on free groups

Summary Nearest neighbour random walks on the homogeneous tree representing a free group withs generators (2s) are investigated. By use of generating functions and their analytic properties a local limit theorem is derived. A study of the harmonic functions corresponding to the random walk leads to properties that characterize ther-harmonic function connected with the local limits.     

Coloring of universal graphs

LetG be a graph andr a cardinal number. Extending the theorem of J. Folkman we show that if eitherr or clG are finite then there existsH with clH = clG andH (G) _r ¹ . Answering a question of A. Hajnal we show that countably universal graphU ₃ satisfiesU ₃ (U₃) _r ¹ for every finiter.     

Sets of tiles with a prescribed number of tilings

Summary For every k2 and r1 there exists a set of k prototiles that admits exactly r distinct tilings. All the tilings obtained are periodic.     

Investigation of the electronic structure of the TCNQ-TTF system. I. TCNQ and TTF monomers and dimers in the all-valence-electron approximation

Closed-shell and DODS CNDO/2 calculations have been performed for neutral and charged TCNQ and TTF monomers and different dimers. For the sake of comparison the calculation have also performed for the corresponding TCNE molecules.The most important result obtained indicates a large splitting of the lowest unfilled level of TCNQ in going from the monomer to the stacked (TCNQ)₂ dimer. The same holds true for the HOMO level of the (TTF)₂ dimer. This indicates that one should expect a broad conduction band for the neutral poly (TCNQ) chain and a broad valence band for the neutral poly (TTF) chain. In order to test the quality of the CNDO/2 approximation scheme a comparison is attempted with existing experimental findings as well as with some MINDO results and available theoretical predictions within different approximation schemes.