Highly Efficient Algorithms for CIS Type Excited State Wave Function Overlaps.

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• Calculating overlaps between excited state wave functions is crucial for quantum dynamics simulations.
• Existing methods can be computationally expensive, limiting the size of systems studied.

Purpose of the Study:

• To develop and present novel, efficient algorithms for computing excited state wave function overlaps.
• To assess the performance and applicability of these new algorithms.

Main Methods:

• Developed two algorithms: one based on overlap determinants into level 2 minors (OL2M) and another using natural transition orbitals (ONTO).
• Evaluated computational speed and scalability for varying system sizes.
• Tested the accuracy of approximate overlaps derived from truncated wave functions.

Main Results:

• Both OL2M and ONTO algorithms demonstrate significant speed improvements over previous methods.
• The ONTO algorithm offers substantial computational savings, particularly for large systems.
• Truncation of wave functions can introduce significant errors in overlap calculations.
• The OL2M algorithm is advantageous for calculating overlaps between a large number of states.

Conclusions:

• The new algorithms, especially ONTO, enhance the feasibility of large-scale time-dependent density functional theory (TDDFT) nonadiabatic dynamics simulations.
• Accurate overlap calculations are essential, as approximations like truncation can be unreliable.
• These methods open avenues for broader applications of wave function overlaps beyond nonadiabatic dynamics.