Geometry Optimization for Nonlocal Excited State Using the Divide-and-Conquer Method

Area of Science:

• Computational Chemistry
• Quantum Chemistry
• Theoretical Chemistry

Background:

• Excited-state calculations are crucial for understanding molecular properties and reactions.
• Geometry optimization of large molecular systems with delocalized or charge-transfer excitations is computationally demanding.
• Existing methods like time-dependent Hartree-Fock/density functional theory face scalability challenges.

Purpose of the Study:

• To develop an efficient and scalable analytic gradient method for excited-state geometry optimization.
• To enable the study of large molecular systems with complex electronic excitations.
• To reduce the computational cost associated with excited-state calculations.

Main Methods:

• Implementation of a divide-and-conquer (DC) based analytic gradient method.
• Extraction of transition density matrices from response densities near polarizability poles.
• Independent solution of subsystem Z-vector equations for computational efficiency.

Main Results:

• Reduced computational scaling from O(N^3.55) to O(N^1.60) for excited-state calculations.
• Accurate reproduction of excited-state structural relaxation in push-pull polyenes and [9]cycloparaphenylene ([9]CPP).
• Demonstrated convergence of DC-based gradients with increasing buffer size.

Conclusions:

• The developed DC-based analytic gradient method is a practical and scalable approach for excited-state geometry optimization.
• The method accurately captures structural relaxations, including quinoid distortion and large Stokes shifts.
• This technique extends the feasibility of excited-state calculations to systems previously beyond conventional methods.