Holomorphic Hartree-Fock Theory and Configuration Interaction.

Area of Science:

• Quantum chemistry
• Computational physics
• Theoretical chemistry

Background:

• Standard Hartree-Fock (HF) methods can encounter issues with solution stability, particularly for molecular systems like H2 across varying geometries.
• The disappearance of HF solutions with changes in molecular geometry poses a challenge for accurate electronic structure calculations.

Purpose of the Study:

• To investigate the behavior and limitations of Hartree-Fock solutions for the H2 molecule in a minimal basis set.
• To propose and validate a novel theoretical framework, Holomorphic Hartree-Fock (HHF) theory, to overcome the solution disappearance problem.
• To generate a smooth and accurate binding curve for H2 across all internuclear distances.

Main Methods:

• Analysis of Hartree-Fock solutions for H2 in a minimal basis set.
• Modification of the self-consistent field (SCF) equations within the HHF framework to ensure solution stability.
• Application of HHF solutions as a basis for nonorthogonal configuration interaction (CI) calculations.

Main Results:

• Observed properties and geometric dependence of standard HF solutions for H2.
• Successful implementation of HHF theory to maintain stable SCF solutions across a wide range of H2 geometries.
• Generation of a continuous and smooth binding energy curve for H2 using HHF-based nonorthogonal CI.

Conclusions:

• Holomorphic Hartree-Fock theory provides a robust alternative to standard HF methods for systems exhibiting solution instabilities.
• The HHF approach enables reliable electronic structure calculations and accurate potential energy surface generation for molecules like H2.
• This work offers a pathway to more stable and accurate quantum chemical computations across diverse molecular geometries.