Incremental full configuration interaction.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Electronic Structure Theory

Background:

• Accurate computation of electronic correlation energies is crucial for understanding molecular properties.
• Full Configuration Interaction (FCI) provides exact energies but is computationally intractable for most systems due to its exponential scaling.
• Developing methods with polynomial scaling that approach FCI accuracy is a major goal in computational chemistry.

Purpose of the Study:

• To introduce and detail a novel algorithm and implementation for the incremental expansion of FCI (iFCI).
• To demonstrate the capability of iFCI to recover accurate correlation energies at low n-body orders.
• To enable FCI-quality energy calculations for larger and more complex molecular systems.

Main Methods:

• The iFCI method divides the FCI problem into n-body interaction terms for parallel computation.
• Approximations are achieved by solving for incremental energies within specified thresholds.
• A select-CI (heat-bath CI) approach is incorporated to further reduce computational cost.

Main Results:

• iFCI achieves polynomial scaling for computing electronic correlation energies.
• Systematic tests confirm that FCI-quality energies can be reached for both dynamic and static correlation regimes.
• The first FCI energy estimate for hexatriene using a polarized double zeta basis set (32 electrons, 118 orbitals) was obtained.

Conclusions:

• iFCI offers a highly parallelizable and accurate method for obtaining FCI-quality correlation energies.
• The incorporation of select-CI extends the applicability of iFCI to larger chemical systems.
• iFCI represents a significant advancement in computational methods for electronic structure calculations.