Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Physics

Background:

• Accurate calculation of excitation energies is crucial for understanding molecular properties.
• Traditional methods for excitation energy calculations can be computationally intensive, limiting scalability.
• The random phase approximation (RPA) offers a promising route for such calculations.

Purpose of the Study:

• To develop a computationally efficient and scalable algorithm for excitation energy calculations within the RPA.
• To circumvent the computational bottleneck associated with calculating molecular orbitals.
• To enable large-scale, reduced complexity calculations of time-dependent optical properties and linear response.

Main Methods:

• A nonlinear conjugate gradient optimization scheme was employed to solve the RPA eigenvalue equation.
• A modified Thouless functional, based on an asymmetric Rayleigh quotient, was used for variational characterization.
• The algorithm operates in an orthogonalized atomic orbital representation, avoiding explicit molecular orbital calculations.

Main Results:

• The developed molecular-orbital-free algorithm was found to be robust and computationally efficient.
• The feasibility of a linear scaling RPA implementation was investigated by analyzing convergence behavior.
• The method successfully reduces the variational space to physically relevant transitions via projections.

Conclusions:

• The proposed algorithm represents a significant step towards large-scale, reduced complexity calculations of time-dependent properties.
• The molecular-orbital-free approach demonstrates robustness and efficiency, even for ill-conditioned problems.
• The algorithm is extensible to other time-dependent perturbation theories, including time-dependent density functional theory.