Reduced-Scaling Approach for Configuration Interaction Singles and Time-Dependent Density Functional Theory...

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Configuration Interaction Singles (CIS) and Time-Dependent Density Functional Theory (TDDFT) are crucial for calculating excited states.
• Hybrid functionals in these methods present significant computational challenges, limiting their application to larger systems.

Purpose of the Study:

• To develop an efficient approximation to reduce the computational cost of CIS and TDDFT methods with hybrid functionals.
• To enable accurate excited-state calculations for larger molecules and complex electronic structures.

Main Methods:

• Adaptation of the local density fitting scheme for excited-state calculations.
• Reduction of the quartic scaling of CIS and TDDFT methods to cubic.
• Application to time-dependent Hartree-Fock (TDHF) and Tamm-Dancoff approximation (TDA) TDDFT.

Main Results:

• Achieved average speedups of 2-4 for molecules with 50-100 atoms.
• Negligible errors in calculated excitation energies and oscillator strengths.
• Demonstrated feasibility of excited-state calculations for 1000-atom molecules on a single processor.

Conclusions:

• The local density fitting approximation significantly enhances the efficiency of excited-state calculations.
• This method allows for the study of larger and more complex molecular systems previously inaccessible.
• The approach provides a practical solution for computational chemists dealing with high computational expenses.