ΔNO and the complexities of electron correlation in simple hydrogen clusters

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of electron correlation is crucial for predicting molecular properties.
• Multideterminantal wave functions are necessary for describing complex electronic systems.
• Existing methods often face challenges in balancing accuracy and computational cost.

Purpose of the Study:

• To derive and implement a Δ natural orbital (ΔNO) two-electron density matrix (2-RDM) and energy expression.
• To develop and test a trust-region Newton's method optimization algorithm for ΔNO orbitals and occupancies.
• To assess the performance of ΔNO combined with on-top density functionals against established quantum chemistry methods.

Main Methods:

• Derivation of ΔNO 2-RDM and energy expression from multideterminantal wave functions.
• Combination of approximate ΔNO 2-RDM with on-top density functionals and double-counting corrections.
• Implementation of a trust-region Newton's method for orbital and occupancy optimization.
• Assessment on small hydrogen clusters, comparing with Density Functional Theory (DFT), Coupled-Cluster (CC), and Multireference Møller-Plesset Perturbation Theory (MRMP2).

Main Results:

• The ΔNO-Colle-Salvetti (CS) and ΔNO-Opposite-spin exponential cusp and Fermi-hole correction (OF) methods demonstrate improved accuracy.
• These ΔNO-based methods outperform single-reference quantum chemical approaches.
• ΔNO-CS and ΔNO-OF show results comparable to the more computationally intensive MRMP2 method.
• A qualitative error was identified in the ΔNO potential energy surface for H₄ compared to exact calculations.

Conclusions:

• The developed ΔNO methods, particularly with CS and OF functionals, offer a promising avenue for capturing electron correlation.
• These methods provide a competitive alternative to traditional quantum chemistry techniques for certain systems.
• Further analysis is needed to address the observed discrepancies in the ΔNO potential energy surface for specific cases like H₄.