Efficient Method for the Computation of Frozen-Core Nuclear Gradients within the Random Phase Approximation

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• The frozen-core approximation simplifies electronic structure calculations by excluding core electrons.
• Evaluating the response of active electron density is crucial but challenging.
• Standard Kohn-Sham density response is also a key component.

Purpose of the Study:

• To develop an efficient method for evaluating analytical frozen-core gradients within the random phase approximation (RPA).
• To address the computational difficulties associated with the frozen-core approximation in density response calculations.
• To extend the methodology to other electron correlation methods.

Main Methods:

• Development of a procedure to efficiently evaluate the response of active electron density under the frozen-core approximation.
• Integration with the response of the standard Kohn-Sham density.
• Utilizing Cholesky decomposed densities to reintroduce occupied index in time-determining steps.

Main Results:

• Achieved speedups of 20-30% using the frozen-core approximation with Cholesky decomposed densities.
• Observed computational efficiency comparable to molecular orbital formulations.
• Demonstrated that errors introduced by the frozen-core approximation are negligible for molecular geometries.

Conclusions:

• The presented method offers an efficient way to compute analytical frozen-core gradients in RPA.
• The approach is generalizable to various electron correlation methods.
• The frozen-core approximation is reliable for geometry calculations in terms of accuracy.