Excited-State Geometry Optimization with the Density Matrix Renormalization Group, as Applied to Polyenes.

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• State-specific analytic density matrix renormalization group (DMRG) energy gradients are crucial for studying molecular excited states.
• Previous methods had limitations in optimizing excited-state wave functions efficiently.

Purpose of the Study:

• To extend the formalism of state-specific analytic DMRG energy gradients.
• To introduce a novel technique for optimizing excited-state wave functions.
• To investigate the electronic and excited-state properties of trans-polyenes.

Main Methods:

• Developed and extended state-specific analytic DMRG energy gradients.
• Introduced a DMRG wave function maximum overlap following technique for excited-state optimization.
• Applied DMRG-configuration interaction (DMRG-CI) gradients to relax low-lying singlet states of trans-polyenes (up to C20H22).

Main Results:

• Successfully relaxed excited-state geometries of trans-polyenes.
• Elucidated the exciton, soliton, and bimagnon character of excited states using relaxed geometries and correlation functions.
• Provided evidence for a planar conical intersection in the excited states.

Conclusions:

• The extended DMRG gradient formalism and optimization technique are effective for studying excited states in extended systems.
• The study reveals complex electronic characters and structural features in the excited states of trans-polyenes.
• Findings contribute to understanding photophysical processes and potential applications in materials science.