Linear Response Equations Revisited: A Simple and Efficient Iterative Algorithm.

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Physics

Background:

• Linear response theory is crucial for calculating molecular properties.
• Existing methods for solving linear response equations can be computationally intensive.
• Hartree-Fock (HF), Density Functional Theory (DFT), and Multiconfigurational Self-Consistent Field (MCSCF) are widely used quantum chemistry methods.

Purpose of the Study:

• To present a novel, simple, and efficient algorithm for solving linear response equations.
• To improve the computational efficiency of calculating properties using HF, DFT, and MCSCF methods.
• To offer a robust and stable numerical solution for quantum chemistry calculations.

Main Methods:

• The algorithm utilizes symmetric and antisymmetric combinations of trial vectors.
• It orthogonalizes these vectors with respect to the response matrix scalar product.
• This transforms the problem into a standard, symmetric block eigenvalue problem.

Main Results:

• The method reduces the eigenvalue problem to diagonalizing a matrix half the size of the expansion space.
• Numerical tests confirm the algorithm's robustness and stability.
• The approach offers a significant simplification for linear response calculations.

Conclusions:

• The presented algorithm provides an efficient and straightforward way to solve linear response equations.
• It enhances the practicality of using advanced quantum chemistry methods for property calculations.
• The robustness and stability make it a reliable tool for computational chemists.