Comparison of many-particle representations for selected-CI I: A tree based approach

The full configuration interaction (FCI) method is only applicable to small molecules with few electrons in moderate size basis sets. One of the main alternatives to obtain approximate FCI energies for bigger molecules and larger basis sets is selected CI. However, due to: (a) the lack of a well-defined structure in a selected CI Hamiltonian, (b) the potentially large number of electrons together with c) potentially large orbital spaces, a computationally and memory efficient algorithm is difficult to construct. In the present series of papers, we describe our attempts to address these issues by exploring tree-based approaches. At the same time, we devote special attention to the issue of obtaining eigenfunctions of the total spin squared operator since this is of particular importance in tackling magnetic properties of complex open shell systems. Dedicated algorithms are designed to tackle the CI problem in terms of determinant, configuration (CFG) and configuration state function many-particle bases by effective use of the tree representation. In this paper we describe the underlying logic of our algorithm design and discuss the advantages and disadvantages of the different many particle bases. We demonstrate by the use of small examples how the use of the tree simplifies many key algorithms required for the design of an efficient selected CI program. Our selected CI algorithm, called the iterative configuration expansion, is presented in the penultimate part. Finally, we discuss the limitations and scaling characteristics of the present approach.

Automated summary

The full configuration interaction method is limited to small molecules, while selected CI is used to approximate FCI energies for larger molecules. Challenges in constructing an efficient algorithm include the lack of structure in the Hamiltonian, large number of electrons, and orbital spaces. Through tree-based methods and focus on total spin squared operator and multi-particle bases, the CI problem is addressed. The paper discusses logic behind algorithm design, advantages of different particle bases, and demonstrates how tree simplifies key algorithms for efficient CI program design.