Analytic gradients for spin multiplets in natural orbital functional theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of molecular properties is crucial for understanding chemical reactions.
• Deriving analytic energy gradients is essential for geometry optimization in computational chemistry.
• Existing methods for non-singlet systems can be computationally intensive.

Purpose of the Study:

• To derive analytic energy gradients for non-singlet compounds within natural orbital functional theory.
• To develop a computationally efficient method applicable to various many-electron systems.
• To provide accurate theoretical equilibrium geometries for molecules with multiple spin states.

Main Methods:

• Exploitation of multiplet formulation for a general formula.
• Avoidance of linear response theory and iterative procedures.
• On-the-fly computation of integral derivatives using Schwarz inequality for screening.

Main Results:

• A simple and general formula for analytic energy gradients was obtained.
• The method requires only a single evaluation, enhancing computational efficiency.
• Accurate equilibrium geometries were computed for small- and medium-sized molecules with diverse spin multiplicities.

Conclusions:

• The developed method provides an efficient and accurate way to compute analytic energy gradients for non-singlet systems.
• This advancement facilitates more precise geometry optimizations and property predictions in theoretical chemistry.
• The findings are validated by comparison with experimental data and other high-accuracy theoretical methods.