The Kernel Energy Method: Construction of 3 & 4 tuple Kernels from a List of Double Kernel Interactions

Area of Science:

• Computational chemistry
• Molecular modeling
• Biophysics

Background:

• Calculating ab-initio energy for large biological molecules is computationally intensive.
• The Kernel Energy Method (KEM) offers a balance between accuracy and reduced computation time.
• Further optimization of KEM is needed to enhance computational efficiency for complex molecular systems.

Purpose of the Study:

• To investigate the use of double kernel interactions for optimizing the Kernel Energy Method (KEM).
• To explore the potential for significant additional reductions in computational effort while preserving ab-initio accuracy.
• To demonstrate the application of the optimized KEM to a large biological molecule, such as the protein insulin.

Main Methods:

• Numerical comparison of indices for known double kernel interactions.
• Identification of higher-order interactions with topological continuity.
• Development of a kernel expansion weighting the relative importance of each kernel for total molecular energy.

Main Results:

• A list of higher-order interactions with topological continuity was identified.
• The kernel expansion effectively weighted the importance of each kernel.
• High accuracy was maintained with a significant reduction in computational effort.

Conclusions:

• Optimizing KEM with double kernel interactions significantly reduces computational cost.
• The enhanced KEM retains ab-initio accuracy for large molecular energy calculations.
• The method is effective, as demonstrated by its application to the protein insulin using the HF/STO3G model.