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

Abstract

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.

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

“…Although larger fragments have sometimes been used for proteins, 37 we are able to achieve our target accuracy of 1 kcal/mol using mostly singleresidue fragments, except for the substrate whose treatment is discussed below. Alternatively, overlapping fragments have sometimes been used for polypeptides and proteins, [24][25][26][27][28][37][38][39][40][41][42] which can be rationalized in terms of a generalized (G)MBE. 1,6,43,44 To date, most overlappingfragment applications use a one-body approach that captures through-bond interactions but not through-space interactions.…”

Fragment-Based Calculations of Enzymatic Thermochemistry Require Dielectric Boundary Conditions

“…(The treatment of the substrate is discussed below.) Alternatively, overlapping fragments have sometimes been used for polypeptides and proteins. − ,− This can be motivated in terms of a generalized (G)MBE, ,,, but most overlapping fragment applications to date have used a one-body approach that captures through-bond interactions but not through-space interactions . A two-body GMBE can capture both, but is relatively expensive in terms of the number of subsystems that are generated. , As such, we stick to the simple MBE­( n ) approach in this work.…”