Analytical two-center integrals over Slater geminal functions

We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary differential equation that is obeyed by the master integral, the simplest integral with inverse powers of all interparticle distances. To solve this equation it was necessary to introduce a new family of special functions which are defined through their series expansions around regular singular points of the differential equation. To increase the power of the interparticle distances under the sign of the integral we developed a family of open-ended recursion relations. A handful of special cases of the integrals is also analysed with some remarks on simplifications that occur. Additionally, we present some numerical examples of the master integral that validate the usefulness and correctness of the key equations derived in this paper. In particular, we compare our results with the calculations based on the series expansion of the exp(-\gamma r12) term in the master integral.Comment: 28 pages, 0 figures, 7 table

From functional food to medicinal product: Systematic approach in analysis of polyphenolics from propolis and wine

In the last decade we have been working on standardization of propolis extract and determination of active constituents of wine those are rich in polyphenolics and have nutritional as well as therapeutic value. Here we are summarizing our results and providing overview on systematic approach how to analyse natural products rich in flavonoids and phenolic acids

Ступінь приверженості до лікування та його ефективність у пацієнтів з гіпертонічною хворобою залежно від способу життя

Vitamin C is a widely used vitamin. Here we review the occurrence and properties of aldonolactone oxidoreductases, an important group of flavoenzymes responsible for the ultimate production of vitamin C and its analogs in animals, plants, and single-cell organisms