Double Asymptotic Expansion of Three-Center Electron Repulsion Integrals 2nd Derivatives

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Calculating skeleton Hessians in auxiliary density functional theory (ADFT) requires computing second derivatives of three-center electron repulsion integrals (ERIs).
• Evaluating ERIs and their derivatives involves nonanalytic Boys functions, posing a computational bottleneck for large molecular systems.

Purpose of the Study:

• To extend the double asymptotic expansion method to analytic second derivatives of three-center ERIs.
• To implement these new working equations within the ADFT framework of the deMon2k software.

Main Methods:

• Derivation of working equations for the double asymptotic expansion of three-center ERI second derivatives.
• Implementation of these equations in the analytic second energy derivative calculation module of deMon2k.
• Benchmark calculations of skeleton Hessian matrices for various molecular systems.

Main Results:

• Successful extension of the double asymptotic expansion to analytic second derivatives of three-center ERIs.
• Implementation within deMon2k enables efficient calculations for large systems.
• Benchmark calculations demonstrate the computational performance on diverse molecular structures.

Conclusions:

• The developed method effectively addresses the computational bottleneck associated with ERI second derivatives in ADFT.
• This advancement facilitates more accurate and efficient calculations for complex molecular systems.
• The implementation in deMon2k provides a practical tool for theoretical chemistry research.