Coupled-Cluster in Real Space. 1. CC2 Ground State Energies Using Multiresolution Analysis.

Area of Science:

• Quantum chemistry
• Computational physics

Background:

• Coupled-cluster theory is essential for accurate electronic structure calculations.
• Existing methods often face challenges with basis set convergence and computational scaling.
• Real-space methods offer an alternative to traditional basis set approaches.

Purpose of the Study:

• To develop and implement a novel framework for calculating coupled-cluster, singles, doubles, and triples (CC2) approximated ground state correlation energies.
• To adapt CC2 calculations for use with multiresolution bases and real-space methods.
• To address singularities in quantum mechanical potentials within the CC2 framework.

Main Methods:

• Derivation of CC2 working equations in first quantization for real-space suitability.
• Implementation within the MADNESS (Multiresolution Adaptive Near-neighbor Difference Equation System Solver) library.
• Regularization of nuclear and electronic potential singularities using cusp analysis.
• Representation of cluster functions on adaptive grids.
• Development of adjusted diagrammatic interpretation rules for first-quantized equations.

Main Results:

• Successful implementation of a CC2 framework in a multiresolution basis.
• Generation of singularity-free and virtual orbital-free equations with low intrinsic scaling.
• Computation of correlation energies approaching the basis set limit for small molecules.
• Demonstration of the framework's suitability for real-space quantum chemistry methods.

Conclusions:

• The developed framework provides an efficient and accurate method for calculating CC2 correlation energies.
• This work represents a significant step towards enabling CC2 excitation energy calculations in multiresolution bases.
• The approach overcomes limitations of traditional methods, offering a promising direction for future electronic structure studies.