simplefci

Introduction

A simple FCI (full configuration interaction) implementation in Python.

• Slater-Condon rule to evaluate the Hamiltonian matrix within the Slater determinant basis ( $\hat{S}_z$ eigen states), and diagonalize the Hamiltonian matrix with the condense eigensolver in scipy.
• The “string-based” determinant-CI (or direct-CI) algorithm to generate the matrix multiplication of the Hamiltonian matrix and use the sparse eigensolver in scipy to diagonalize the Hamiltonian matrix.

In the tests, MOs and integrals are generated from pyscf.

TODO:

• Davidson algorithm for matrix diagonalization and implement it for any symmetric matrix.

As the programs are completely written in Python, it should be able to solve problem with a maximum system size of ∼ 12 orbitals with 12 electrons.

Acknowledgements

Thanks to Qiming Sun's tutorial and the guidance of Garnet Chan. And the invaluable advice from Drs. Zhen Luo and Yihan Shao, and the discussions with Rui Li, Bo Li and Zhihao Cui.

References

[1] Szabo and Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory, Dover Publications, New York, 1996

[2] https://github.com/pyscf/pyscf