A note on the Pulay force at finite electronic temperatures

Area of Science:

• Computational Chemistry
• Electronic Structure Theory

Background:

• Pulay's force is crucial for Hellmann-Feynman forces in electronic structure theory.
• The original Pulay force expression is invalid at finite electronic temperatures due to fractional state occupation.

Purpose of the Study:

• Derive a generalized Pulay force suitable for finite electronic temperatures.
• Enable accurate large-scale ab initio simulations with nonorthogonal basis sets at elevated temperatures.

Main Methods:

• Developed a generalized Pulay force expression.
• Utilized temperature-dependent density matrices.
• Proposed a recursive Fermi operator expansion algorithm for density matrix construction.

Main Results:

• The generalized Pulay force is computationally efficient and accurate for finite electronic temperatures.
• The recursive Fermi operator expansion algorithm converges to the correct chemical potential.

Conclusions:

• The derived generalized Pulay force overcomes limitations of the conventional expression at finite temperatures.
• This advancement facilitates more accurate large-scale electronic structure calculations in condensed matter physics and materials science.