Molecular integrals an introduction

There are many books that describe relational database management systems (RDBMS) and the structured query language (SQL) used to manipulate the data. Understanding SQL is important, and this book contains an introduction to SQL. However, the focus is on the concepts of relational data. One goal is to show how a proper integration of a new molecular structure data type yields a powerful, extended relational database for use in chemistry. For those of you new to relational databases, it is expected that the SQL introduction will suffice for your understanding of the concepts in this book. For those of you already familiar with SQL, it is hoped that you will see how the extensions described here provide a powerful, integrated way to handle molecular structures within the database. In either case, there are plenty of practical SQL examples contained in this book. 

As an introduction to the integration over GTOs, let us consider the simplest of all multicentre molecular integrals - namely, the integral over a spherical Gaussian charge distribution... 

V. R. Saunders, An introduction to molecular integral evaluation, in G. H. F. Diercksen, B. T. Sutcliffe and A. Veillard (eds). Computational Techniques in Quantum Chemistry and Molecular Physics, Reidel. 1974. p. 347. 

Ab initio methods are characterized by the introduction of an arbitrary basis set for expanding the molecular orbitals and then the explicit calculation of all required integrals involving this basis set. 

The Laplace-Young equation refers to a spherical phase boundary known as the surface of tension which is located a distance from the center of the drop. Here the surface tension is a minimum and additional, curvature dependent, terms vanish (j ). The molecular origin of the difficulties, discussed in the introduction, associated with R can be seen in the definition of the local pressure. The pressure tensor of a spherically symmetric inhomogeneous fluid may be computed through an integration of the one and two particle density distributions. 

---