Extension of selected configuration interaction for transcorrelated methods

Area of Science:

• Quantum chemistry
• Computational physics

Background:

• Selected Configuration Interaction (SCI) methods are widely used for electronic structure calculations.
• The Transcorrelated (TC) framework offers a way to incorporate electron correlation.
• Extending SCI to the TC framework can potentially improve computational efficiency and accuracy.

Purpose of the Study:

• To extend popular selected configuration interaction (SCI) algorithms to the Transcorrelated (TC) framework.
• To investigate the impact of the non-Hermitian character of the TC Hamiltonian on SCI convergence.
• To compare the convergence rates of SCI in the TC framework with traditional SCI methods.

Main Methods:

• Formalization of the non-Hermitian TC eigenvalue problem as a search for stationary points.
• Development of a general framework applicable to various correlation factors and selection criteria.
• Numerical investigations on second-row atomic and molecular systems using large basis sets.

Main Results:

• Accounting for the non-Hermitian TC Hamiltonian in the selection criterion is crucial for fast convergence.
• Different selection criteria (first-order coefficient vs. second-order energy) yield distinct convergence rates in the TC-SCI framework.
• The quality of the left-function significantly impacts the accuracy of the second-order perturbation energy.
• The proposed TC-SCI algorithm demonstrates faster convergence than standard SCI regarding basis set size and determinant count.

Conclusions:

• The extension of SCI to the TC framework provides a more efficient approach for electronic structure calculations.
• Careful consideration of the non-Hermitian TC Hamiltonian and left-function choice is essential for optimal performance.
• TC-SCI offers a promising avenue for achieving faster convergence in quantum chemical calculations.