Representation independent algorithms for molecular response calculations in time-dependent self-consistent field...

Area of Science:

• Computational Chemistry
• Theoretical Physics
• Quantum Mechanics

Background:

• Time-dependent Hartree-Fock (TDHF) and Kohn-Sham (KS) theories are crucial for electronic structure calculations.
• Linear scaling algorithms are needed to handle large molecular systems.
• Efficient computation of electronic excitations is vital in various scientific fields.

Purpose of the Study:

• To evaluate four numerical algorithms for linear scaling implementation of TDHF and KS theories.
• To compare the performance of modified Lanczos, Arooldi, Davidson, and Rayleigh quotient iterative procedures.
• To identify the most suitable algorithms for large-scale electronic excitation calculations.

Main Methods:

• Implementation of four numerical algorithms: modified Lanczos, Arooldi, Davidson, and Rayleigh quotient iterative procedures.
• Solving random-phase approximation (non-Hermitian) and Tamm-Dancoff approximation (Hermitian) eigenvalue equations.
• Benchmarking using semiempirical Hamiltonian models for conjugated polymers and carbon nanotubes.
• Testing convergence and stability under simulated linear scaling conditions.

Main Results:

• The modified Lanczos and Davidson algorithms demonstrated superior performance and stability.
• Arooldi and Rayleigh quotient iterative methods showed limitations in convergence and stability for large systems.
• The study identified specific algorithms best suited for linear scaling calculations of electronic excitations.

Conclusions:

• Modified Lanczos and Davidson algorithms are recommended for efficient linear scaling calculations of electronic excitations.
• These findings facilitate large-scale computational studies in theoretical chemistry and physics.
• The research provides valuable insights for developing advanced computational methods for molecular systems.