International Journal of Quantum Chemistry
International Journal of Quantum Chemistry
4 years ago

Evolutionary algorithm based configuration interaction approach

Evolutionary algorithm based configuration interaction approach
Debashree Ghosh, Rahul Chakraborty, Paulami Ghosh
A new evolutionary algorithm for stochastic configuration interaction (CI) method designed as an affordable approximation to full configuration interaction (FCI) has been described here. The key components of the algorithm are initiation, propagation, and termination steps taking inspiration from the genetic algorithm. The propagation step is performed with cloning (retention of a Slater determinant without change), mutation (single excitation/de-excitation), and crossover (exchange of α and β strings between two Slater determinants) and termination is selection of few Slater determinants based on certain fitness function (measure of importance of a determinant in the CI space) and rejection of the rest. We find that the absolute value of the CI coefficients is a suitable fitness function when combined with a fixed selection scheme. We have tested its accuracy in 1D Hubbard problem and ground state potential energy surface (PES) has also been constructed for symmetric bond breaking of water molecule, where the errors are found to be around 10 mEh with low non-parallelity error, when retaining only a small fraction of the total number of Slater determinants in the final population. This shows that this method has the ability to capture both static and dynamic correlation. Performance and convergence properties of the algorithm are also tested for N2 triple bond breaking problem. The algorithm opens up a promising way for stochastic sampling of the important determinants in the full Hilbert space. An evolutionary algorithm-based method to sample the important part of the Hilbert space in strongly correlated systems is developed as an alternative to stochastic approaches like MCCI, FCI-QMC, DMRG, and ACI. This method has the ability to capture both static and dynamic correlation, with excellent performance and convergence properties, when tested against the N2 triple bond breaking problem. The genetic algorithm accelerates the search of important configurations in the full configuration space.

Publisher URL: http://onlinelibrary.wiley.com/resolve/doi

DOI: 10.1002/qua.25509

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