Analytic gradients for natural orbital functional theory.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Natural Orbital Functional (NOF) theory offers an alternative to traditional electronic structure methods.
• Efficient calculation of energy gradients is crucial for molecular structure optimization.
• Previous NOF gradient calculations were computationally intensive.

Purpose of the Study:

• To derive analytic energy gradients for NOF theory.
• To optimize molecular structures using NOF functionals.
• To assess the accuracy of NOF functionals by comparing with high-level methods and experimental data.

Main Methods:

• Derivation of analytic energy gradients for NOF theory, avoiding linear-response theory.
• Optimization of molecular structures for 15 spin-compensated systems using the conjugate gradient algorithm.
• Application of two Piris NOF (PNOF5 and PNOF6) functionals.

Main Results:

• The derived NOF gradient equations are computationally analogous to Hartree-Fock gradient calculations.
• Optimized equilibrium geometries were obtained for the studied systems.
• PNOF6 equilibrium geometries show good agreement with coupled cluster singles and doubles (CCSD) calculations and empirical data.

Conclusions:

• Analytic energy gradients for NOF theory provide an efficient and accurate method for electronic structure calculations.
• PNOF5 and PNOF6 are viable functionals for geometry optimization of molecular systems.
• The study validates the utility of NOF theory in predicting molecular structures.