Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• Time-dependent density functional theory (TDDFT) is crucial for studying electronic properties.
• Current TDDFT methods face challenges with computational cost for large and complex systems.

Purpose of the Study:

• To reformulate TDDFT equations for efficient application to large-scale systems.
• To enable accurate electronic response and excitation calculations in complex molecular structures.

Main Methods:

• Developed a novel TDDFT formulation using non-orthogonal localized molecular orbitals (NOLMOs).
• Utilized the sparsity of NOLMOs in an atomic orbital (AO) representation for simplified time propagation.
• Implemented and tested the method within the self-consistent charge density-functional tight-binding (SCC-DFTB) framework.

Main Results:

• Achieved a simplified form of time propagation equations for TDDFT.
• Demonstrated linear-scaling computational effort for the new method.
• Validated the accuracy of the NOLMO-based TDDFT approach on long-chain saturated and conjugated molecules.

Conclusions:

• The NOLMO reformulation of TDDFT offers a computationally efficient and accurate solution for large systems.
• This advancement paves the way for applying TDDFT to complex biological and nanoscale systems.
• The method provides a new computational tool for investigating excited states and electronic dynamics in extended molecular architectures.