Computational quantum chemistry: A primer

Limitations of Hartree-Fock with quantum resources

The Hartree-Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the Hartree-Fock method, central to many other numerical approaches, is a natural target for quantum enhanced algorithms. While quantum computers and quantum simulation offer many prospects for the future of modern chemistry, the non-deterministic polynomial-complete Hartree-Fock problem is not a likely candidate. We highlight this fact from a number of perspectives including computational complexity, practical examples, and the full characterization of energy landscapes for simple systems.

The Quixote project: Collaborative and Open Quantum Chemistry data management in the Internet age

Computational Quantum Chemistry has developed into a powerful, efficient, reliable and increasingly routine tool for exploring the structure and properties of small to medium sized molecules. Many thousands of calculations are performed every day, some offering results which approach experimental accuracy. However, in contrast to other disciplines, such as crystallography, or bioinformatics, where standard formats and well-known, unified databases exist, this QC data is generally destined to remain locally held in files which are not designed to be machine-readable. Only a very small subset of these results will become accessible to the wider community through publication.

In this paper we describe how the Quixote Project is developing the infrastructure required to convert output from a number of different molecular quantum chemistry packages to a common semantically rich, machine-readable format and to build respositories of QC results. Such an infrastructure offers benefits at many levels. The standardised representation of the results will facilitate software interoperability, for example making it easier for analysis tools to take data from different QC packages, and will also help with archival and deposition of results. The repository infrastructure, which is lightweight and built using Open software components, can be implemented at individual researcher, project, organisation or community level, offering the exciting possibility that in future many of these QC results can be made publically available, to be searched and interpreted just as crystallography and bioinformatics results are today.

Although we believe that quantum chemists will appreciate the contribution the Quixote infrastructure can make to the organisation and and exchange of their results, we anticipate that greater rewards will come from enabling their results to be consumed by a wider community. As the respositories grow they will become a valuable source of chemical data for use by other disciplines in both research and education.

The Quixote project is unconventional in that the infrastructure is being implemented in advance of a full definition of the data model which will eventually underpin it. We believe that a working system which offers real value to researchers based on tools and shared, searchable repositories will encourage early participation from a broader community, including both producers and consumers of data. In the early stages, searching and indexing can be performed on the chemical subject of the calculations, and well defined calculation meta-data. The process of defining more specific quantum chemical definitions, adding them to dictionaries and extracting them consistently from the results of the various software packages can then proceed in an incremental manner, adding additional value at each stage.

Not only will these results help to change the data management model in the field of Quantum Chemistry, but the methodology can be applied to other pressing problems related to data in computational and experimental science.

Projected gradient algorithms for Hartree-Fock and density matrix functional theory calculations

We present projected gradient algorithms designed for optimizing various functionals defined on the set of N-representable one-electron reduced density matrices. We show that projected gradient algorithms are efficient in minimizing the Hartree-Fock or the Muller-Buijse-Baerends functional. On the other hand, they converge very slowly when applied to the recently proposed BBk (k=1,2,3) functionals [O. Gritsenko et al., J. Chem. Phys. 122, 204102 (2005)]. This is due to the fact that the BBk functionals are not proper functionals of the density matrix.