Computing molecular correlation energies with guaranteed precision.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate computation of electron correlation energies is crucial for understanding molecular properties.
• Traditional methods often face challenges with basis set limitations and computational scaling.
• Multiresolution analysis (MRA) offers a potential framework for more efficient and accurate calculations.

Purpose of the Study:

• To develop and present an MRA-based approach for computing accurate correlation energies in atoms and molecules.
• To generalize existing methods to handle general many-electron systems at the MP2 level.
• To demonstrate the feasibility and accuracy of the method for representative systems.

Main Methods:

• Utilizing an adaptive discontinuous multiresolution spectral-element representation for the six-dimensional pair function.
• Employing low-rank tensor approximations for functions and operators.
• Analytically eliminating operator singularities via explicit correlation, building on prior work.
• Generalizing equations for non-symmetric many-electron systems at the MP2 level.

Main Results:

• Accurate correlation energies were computed for the beryllium atom and the water molecule.
• Results were reproduced to within tens of microhartrees of basis set limit literature data.
• The method demonstrated high accuracy and low scaling with system size.

Conclusions:

• The developed molecular MRA-MP2 approach provides accurate correlation energies.
• Key advantages include the absence of basis set bias and arbitrariness.
• The method exhibits favorable scaling, making it suitable for larger systems.