A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Iterative diagonalization is crucial for solving quantum mechanical problems.
• Random-phase approximation (RPA) matrices in time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation are non-Hermitian.
• Standard iterative diagonalization techniques are not directly applicable to non-Hermitian RPA matrices.

Purpose of the Study:

• To present a novel iterative diagonalization technique for non-Hermitian RPA matrices.
• To enable efficient computation of electronic excitation energies.
• To overcome limitations of existing methods for TDDFT and Bethe-Salpeter equation calculations.

Main Methods:

• Introduction of a block variational principle tailored for RPA matrices.
• Development of an algorithm for simultaneous calculation of multiple eigenvalues and eigenvectors.
• Validation of the algorithm on small systems (Na2, Na4) and application to benzene.

Main Results:

• The new algorithm demonstrates convergence and stability comparable to methods for Hermitian matrices.
• Successfully computed multiple low-lying TDDFT excitation energies for the benzene molecule.
• Validated the technique's applicability to complex molecular systems.

Conclusions:

• The presented iterative diagonalization technique offers an efficient and stable approach for handling RPA matrices.
• This method advances the computational capabilities within TDDFT and related electronic structure theories.
• The findings pave the way for more accurate and accessible calculations of molecular properties.