Pulay forces from localized orbitals optimized in situ using a psinc basis set.

Area of Science:

• Computational chemistry
• Quantum mechanics
• Materials science

Background:

• Accurate calculation of ionic forces is essential for geometry optimization in electronic structure theory.
• Pulay forces arise from the dependence of the basis set on atomic positions and can be significant, especially with localized orbitals.
• Traditional methods often neglect or approximate Pulay forces, potentially impacting the accuracy of calculated forces.

Purpose of the Study:

• To investigate the necessity and impact of including Pulay forces in geometry optimization calculations.
• To demonstrate that Pulay forces can be non-negligible even with basis sets designed to be atom-position independent.
• To validate a method for calculating Pulay forces and its benefits for convergence in electronic structure calculations.

Main Methods:

• Implementation of Pulay force calculation as a correction to Hellmann-Feynman forces.
• In situ optimization of localized orbitals with respect to a systematically improvable basis set (e.g., psinc functions).
• Validation of the method on various test cases, including a large DNA fragment (1045 atoms).

Main Results:

• Pulay forces were found to be non-negligible under strict localization constraints and small localization regions.
• Including Pulay forces significantly improved the convergence of geometry optimization calculations.
• The method showed benefits for both atom-position independent basis sets and conventional pseudo-atomic orbital multiple-ζ basis sets.

Conclusions:

• Pulay forces must be calculated as a correction to Hellmann-Feynman forces for accurate ground-state ionic forces, even with advanced basis sets.
• The inclusion of Pulay forces enhances the reliability and efficiency of geometry optimization in computational chemistry.
• The validated method is applicable to complex molecular systems, as demonstrated by the DNA fragment calculations.