Softmax parameterization of the occupation numbers for natural orbital functionals based on electron pairing...

Area of Science:

• Quantum Chemistry
• Computational Physics
• Theoretical Chemistry

Background:

• Efficient computation in natural orbital functional theory relies on accurate representation of occupation numbers and orbitals.
• Existing methods may face challenges in computational performance and adherence to N-representability principles.

Purpose of the Study:

• To introduce an innovative parameterization of occupation numbers for natural orbital functional theory.
• To enhance the computational efficiency and N-representability of first-order reduced density matrix (1RDM) calculations.

Main Methods:

• Utilized the electron-pairing approach from Piris natural orbital functionals.
• Adopted the softmax function, a key component in deep learning models, for parameterization.
• Assessed the method using the W4-17-MR molecular set.

Main Results:

• The proposed parameterization ensures N-representability of the 1RDM.
• Achieved significant enhancements in computational efficiency for 1RDM functional theory.
• Demonstrated faster and more robust convergence compared to previous implementations.

Conclusions:

• The novel parameterization using softmax function offers a computationally efficient and N-representable approach for natural orbital functional theory.
• This method represents a significant advancement in the field of quantum chemistry calculations.