Linear-scaling implementation of molecular response theory in self-consistent field electronic-structure theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Accurate calculation of molecular response properties and excitation energies is crucial in chemistry and materials science.
• Traditional methods often scale poorly with system size, limiting their application to large molecules.
• Self-consistent field (SCF) theories like Hartree-Fock (HF) and Kohn-Sham (KS) are fundamental but computationally intensive.

Purpose of the Study:

• To develop a linear-scaling implementation of HF and KS SCF theories for calculating frequency-dependent molecular response properties and excitation energies.
• To present a novel computational approach that avoids canonical orbitals and utilizes an atomic-orbital subspace method for efficiency.
• To demonstrate the method's performance on large polyalanine peptides.

Main Methods:

• A linear-scaling implementation based on a nonredundant exponential parametrization of the one-electron density matrix in the atomic-orbital basis.
• Iterative solution of response equations using an atomic-orbital subspace method with paired trial vectors, a nondiagonal preconditioner, and good initial guesses.
• Application of sparse-matrix algebra for achieving linear complexity in calculations.

Main Results:

• The iterative subspace method achieves performance comparable to canonical molecular-orbital theory, requiring only 5–10 iterations for convergence.
• Linear complexity is achieved, enabling calculations on large systems.
• Demonstrated successful calculations of excitation energies and frequency-dependent polarizabilities for polyalanine peptides up to 1400 atoms.

Conclusions:

• The developed linear-scaling implementation provides an efficient and robust method for calculating molecular response properties and excitation energies.
• The atomic-orbital subspace approach effectively overcomes the computational bottlenecks of traditional SCF methods for large systems.
• This method significantly advances the capability to study large molecular systems in computational chemistry.