Efficient computation of two-electron integrals in a mixed Gaussian/B-spline basis


Key Personnel

PI/Co-I: Jimena Gorfinkiel, The Open University; Jonathan Tennyson - UCL

Technical: Zdenek Masin - The Open University

Project summary

The aim of this project was to develop efficient parallel routines to calculate two-particle integrals in a mixed basis of Gaussian Type Orbitals (GTOs) and B-spline orbitals.

Many computational tools to study atomic and molecular processes, chemical properties of molecules, etc. require the calculation of integrals involving basis functions and 1 or 2 particles. In the vast majority of software these basis functions are Gaussian Type Orbitals (GTOs) and many algorithms exist to calculate the corresponding integrals efficiently. However, these algorithms are usually embedded in large software packages and cannot be adapted for use in other suites. In addition, some very interesting and challenging current research questions (for example, understanding how a molecule behaves when it interacts with a very short, very intense laser pulse) cannot be answered using software based on GTOs only. The aim of our project was to develop an object-oriented library for the efficient calculation of these integrals both using GTOs and using a mixed basis of GTOs and B-splines (BTOs).

This library is being used to significantly improve the capability of another suite of codes, the UKRmol+ suite, designed to study electron and positron collisions with molecules. Electron-molecule scattering is a process that occurs in many environments. Understanding and quantifying it is important in a number of technological areas; for example, when plasmas are involved, or when radiation interacts with matter, in particular biological matter. The work performed under this project will enable us to study scattering process of applied relevance. For example, we will be able to study electron interaction with bigger molecules than ever before, and with these molecules surrounded by a few water molecules. We hope that this will help us better understand how radiation damages cell constituents, in particular DNA.

Use of the library and the UKRmol+ suite will also enable the investigation of new phenomena that take place when a molecule is subjected to the action of intense laser light, allowing us to provide a theoretical counterpart to very exciting experiments currently being performed.

Finally, the newly developed library, once fully optimized, could be of use to many researchers working in a number of areas of atomic and molecular physics. The software has specifically been designed so that developers will find it easy to use.

Summary of the software

All the software developed during this project is freely available under GPL licence and can be downloaded from:


This includes both the integral library and the UKRmol+ suite (inner region; the outer region and scripts to run the code are also available, from different projects in CCPForge).

The software is available on ARCHER where it is currently being used to perform electron-­molecule and electron-molecular cluster scattering calculations. The software is also being used at The Open University (both on Linux desktops and a Linux cluster, http://impact.open.ac.uk) and at MIB (Berlin, Germany) where it is run on an Intel Cluster platform.

In the near future we plan to release the object-oriented library separately and make it freely available from the CCPForge website. In addition, we plan to publish a detailed paper in Computer Physics Communication. We hope to disseminate the availability and characteristics of the library as much as possible, to ensure uptake from other researchers and communities.