Introduction

The underlying principles that enable quantum chemistry are captured in the Schrödinger equation. This equation is famously intractable, and is usually introduced as being unsolvable except for the most simple of chemical systems. These statements are formally correct, but numerical approximations to the equation can still be highly useful. Some approximations can even reach “chemical” accuracy, which is usually defined to be within 1 kcal/mol of the accurate, experimental value. The most famous algorithm for solving the Schrödinger equation is called Full Configuration Interaction (FCI), which expresses a wave function in the basis of all possible (full) electron configurations (CI), and is therefore exact within the basis. FCI is intractable in principle, having exponentially growing costs for large system sizes.

Incremental FCI

The Zimmerman group has created a systematic approximation to FCI, using the many-body expansion to break the FCI problem into smaller, more tractable pieces. MBE-FCI–or incremental FCI–is a polynomially scaling technique that has been shown to recover the FCI energy to mHa precision (i.e. chemical accuracy). Tests on several examples, shown in the papers referenced below, demonstrate that iFCI is applicable to molecules with >10 heavy atoms, >100 electrons, and hundreds of AO basis functions. iFCI captures static as well as dynamic correlation, making it useful for studying molecules with diverse characteristics.

 Recent Electronic Structure Publications:

1. B. Kanungo, P. M. Zimmerman, V. Gavini, “Exact exchange-correlation potentials from ground-state electron densities,” Nature Commun. 2019, 10, 4497.

2. P. M. Zimmerman, A. E. Rask, “Evaluation of Full Valence Correlation Energies and Gradients,” J. Chem. Phys. 2019, 150, 244117.

3. M. W. Li, P. M. Zimmerman, “Stepwise Basis Set Selection,” J. Comput. Chem. 2018, 39, 2153-2162.

4. P. M. Zimmerman, “Strong Correlation in Incremental Full Configuration Interaction,” J. Chem. Phys. 2017, 146, 224104.

5. P. M. Zimmerman, “Singlet-Triplet Gaps through Incremental Full Configuration Interaction,” J. Phys. Chem. A 2017, 121, 4712-4720.