Accuracy Diagnostics for Natural Orbitals and Their Occupation Numbers from the Contracted Schrödinger Equation

Area of Science:

• Quantum Chemistry
• Computational Physics
• Electronic Structure Theory

Background:

• Calculating electronic properties often involves wave functions from explicitly correlated basis sets.
• Diagonalization of one-electron reduced density matrices to find natural orbitals (NOs) and occupation numbers (ONs) is computationally challenging.
• The accuracy of NOs and ONs depends on the wave function and the projection onto finite basis sets, whose properties are often unknown.

Purpose of the Study:

• To develop and validate new accuracy diagnostics for estimating errors in NOs and ONs.
• To partition errors into contributions from the wave function and the projection basis set.
• To identify whether the combined system exhibits wave function-bound, basis set-bound, or balanced errors.

Main Methods:

• Utilizing diagnostics derived from the contracted Schrödinger equation.
• Projecting density matrices onto finite one-electron basis functions.
• Extensive testing on ground states of few-electron systems.

Main Results:

• The developed diagnostics provide reliable estimation of deviations of NOs and ONs from exact values.
• Errors can be accurately partitioned into wave function and projection contributions.
• The diagnostics successfully classify error types (Ψ-bound, ϕ-bound, balanced).

Conclusions:

• New accuracy diagnostics offer a robust method for evaluating the quality of NOs and ONs in electronic structure calculations.
• These diagnostics are crucial for understanding and controlling errors in quantum chemical computations.
• The approach is validated for ground states of several few-electron systems.