Generalized Energy-Based Fragmentation Approach for the Electronic Emission Spectra of Large Systems

The excited-state (ES) geometry optimization and electronic
emission
(fluorescence and phosphorescence) spectra and the ES vibrational
spectra of large systems are great challenges in quantum chemistry.
In this work, we develop a generalized energy-based fragmentation
(GEBF) approach to compute the localized ES structures and vibrational
frequencies of large systems. In this approach, the ES energy derivatives
(gradients or Hessians) for a localized ES of a large system can be
obtained by combining the ES energy derivatives of the corresponding
active subsystems (including local excitation center) and the ground-state
energy derivatives of inactive subsystems. Two strategies are adopted
to overcome two difficulties from state-classification and state-tracking
for treating specific ESs. First, for state-classification, we develop
an improved density-based spatial clustering applied with noise algorithm
with a modified transition orbital projection (TOP) algorithm, which
allow a certain ES energy and energy derivatives of the whole system
to be calculated with different ES energies and energy derivatives
of active subsystems. Furthermore, we also employ the TOP algorithm
for tracking the ESs in their geometry optimizations at the time-dependent
density functional theory (TDDFT) level. Then, the GEBF approach is
applied to investigate the optimized ES geometries or ES vibrational
frequencies for two typical systems. Our results show that the cost-effective
GEBF approach can accurately reproduce the TDDFT fluorescence spectra
of the cytosine derivative and the experimental phosphorescence spectra
of the β-cyclodextrin derivative. The GEBF approach is expected
to be routinely applied to investigate the electronic emission spectra
of very large systems with local chromophores.