Following the evolution of excited states along photochemical reaction pathways

Abstract

Analyzing the behavior of potential energy surfaces (PESs) of diabatic excited states (ESs) becomes of crucial importance for a complete understanding of complex photochemical reactions. Since the definition of a compact representation for the transition density matrix, the use of the natural transition orbitals (NTOs) has become a routine practice in time‐dependent density functional theory calculations. Their popularity has remarkably grown due to its simple orbital description of electronic excitations. Indeed, very recently, we have presented a new formalism used for the optimization of ESs by tracking the state of interest computing the NTO's overlap between consecutive steps of the procedure. In this new contribution, we generalize the use of this NTO's overlap‐based state‐tracking formalism for the analysis of all the desired diabatic states along any chemical reaction pathway. Determining the PES of the different diabatic states has been automatized by developing an extension of our recently presented algorithm, the so‐called SDNTO: “Steepest Descent minimization using NTOs.” This automatized overlap‐based procedure allows an agile and convenient analysis of the evolution of the ESs avoiding the intrinsic ambiguity of visualizing orbitals or comparing physical observables. The analysis of two photochemical reactions of the same nature with different PES landscapes perfectly illustrates the utility of this new tool.

Bioluminescent Nanoluciferase–Furimamide Complex: A Theoretical Study on Different Protonation States

“…Then, the system relaxes to the ground state by fluorescence, emitting photons with the energy of about 3.5 eV. It is worth noting that also in the gas phase and in water (PCM), a crossing point between states S1 and S2 is found near the Franck–Condon geometry using three different methods: (i) the standard optimization algorithm used by Gaussian, (ii) a steepest descent optimization as implemented in Gaussian, and (iii) a steepest descent minimization using NTOs (SDNTO) , (Figures S9 and S10). Moreover, we find here that the results are consistent with the Kasha’s rule, which states that the photon emission (fluorescence or phosphorescence) occurs in an appreciable yield only from the lowest excited state of a given multiplicity (the first singlet excited state in Figure ).…”

pysisyphus: Exploring potential energy surfaces in ground and excited states

“…To overcome this problem, robust algorithms for ES tracking are of vital importance. Until now, many different techniques for state tracking have been proposed, that is, comparison of attachment and detachment densities, [ 33 ] quantified natural transition orbital (NTO) analysis, [ 34,35 ] overlaps between transition density matrices on the molecular orbital (MO) basis [ 36 ] and the NTO basis, [ 14,37 ] overlaps between wavefunctions comprised of an arbitrarily excited Slater determinant (SDs), [ 38 ] and overlaps between wavefunctions constructed from singly excited SDs. [ 39 ] As the latter two methods calculate overlaps between SDs, they are computationally much more demanding in comparison to the former methods.…”

“…N NTO is determined from the number of singular values of T I above a prescribed threshold (default 0.3). A full derivation of the NTO overlap algorithm is presented in Reference 37.…”

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

“… If the target ES is incorrectly tracked, the PES will follow a totally different state. To tackle this state-tracking problem, a series of strategies have been proposed based on CI vectors, NTOs, and so on. ,, However, these methods do not contain the phase information of transition orbitals; thus, fail to cope with some transition-metal complexes . The steepest descent minimization using NTOs (SDNTO) , is applied to the state-tracking of several transition-metal complexes but still have difficulty for systems with more degenerate orbitals.…”