SPA^HM(a,b): Encoding the Density Information from Guess Hamiltonian in Quantum Machine Learning Representations

Area of Science:

• Computational Chemistry
• Machine Learning
• Quantum Chemistry

Background:

• Traditional molecular representations struggle with charged and excited-state systems.
• Lightweight one-electron Hamiltonians offer a promising basis for molecular descriptors.
• Spectrum of approximated Hamiltonian matrices (SPA^HM) was previously introduced using eigenvalues.

Purpose of the Study:

• To expand the SPA^HM framework into local and transferable molecular representations.
• To assess the performance and efficiency of these new representations on diverse chemical datasets.
• To address limitations of existing methods in predicting properties of complex molecular systems.

Main Methods:

• Development of SPA^HM(a,b) using one-electron density matrices.
• Construction of atomic and bond density overlap fingerprints.
• Evaluation on QM7 dataset (organic molecules) and excited-state azoheteroarene dyes.
• Comparison with state-of-the-art molecular representations.

Main Results:

• SPA^HM(a,b) successfully generate local and transferable molecular representations.
• The new representations demonstrate high performance on challenging prediction tasks.
• SPA^HM(a,b) outperform existing methods for charged open-shell species and π-conjugated systems.

Conclusions:

• The expanded SPA^HM(a,b) representations offer significant improvements over traditional methods.
• These novel descriptors are effective for kernel-based regression, particularly for complex molecular properties.
• SPA^HM(a,b) provide a robust and efficient approach for molecular property prediction in computational chemistry.