Reorganization Energy Research Articles

A computational study on the effect of structural isomerism on the excited state lifetime and redox energetics of archetype iridium photoredox catalyst platforms [Ir(ppy)2(bpy)]+ and Ir(ppy)3.

This study investigates the impact of structural isomerism on the excited state lifetime and redox energetics of heteroleptic [Ir(ppy)2(bpy)]+ and homoleptic Ir(ppy)3 photoredox catalysts using ground-state and time-dependent density functional theory methods. While the ground- and excited-state reduction potentials differ only slightly among the isomers of these complexes, our findings reveal significant variations in the radiative and non-radiative decay rates of the reactivity-controlling triplet 3MLCT states of these closely related species. The observed differences in radiative decay rates could be traced back to variations in the transition dipole moment, vertical energy gaps, and spin-orbit coupling of the isomers. In [Ir(ppy)2(bpy)]+, transition dipole moment differences play a significant role in controlling the relative lifetime of the triplet states, which we rationalized by a vectorial analysis of permanent dipole moments of the ground and excited states. Regarding the two isomers of Ir(ppy)3, changes in radiative decay rates were primarily attributed to variations in vertical energy gaps and intensity borrowing from other singlet-singlet transitions driven by spin-orbit coupling. Non-radiative decay variations were assessed in terms of differences in reorganization energies, adiabatic energy gap, and spin-orbit coupling. For both complexes, reorganization energies associated with low-energy molecular vibrations and metal-ligand bond length changes following the de-excitation process were major contributors. These insights provide a deeper understanding of how molecular design can be leveraged to optimize the performance of iridium-based photoredox catalysts, potentially guiding the development of more efficient catalytic systems for future applications.

Viologen-Radical-Driven Hydrogen Evolution from Water Catalyzed by Co-NHC Catalysts: Radical Scavenging by Nitrate and Volmer-Heyrovsky-like CPET Pathway.

The factors controlling the catalytic activity in photochemical hydrogen evolution reaction (HER) are studied in detail for two macrocyclic cobalt compounds bearing two N-heterocyclic carbenes and two pyridyl donors (Co-NHC1 and Co-NHC2, where Co-NHC2 has a methoxy substituent on each pyridyl ligand). The present study adopts an aqueous photosystem consisting of EDTA, [Ru(bpy)3]2+ (bpy = 2,2'-bipyridine), and MV2+ (MV2+ = methylviologen) at pH = 5. Both catalysts are shown to promote HER in a similar efficiency (TON = 12-13 in 6 h), revealing a minor contribution of the electron-donating methoxy substituents. The catalyst degradation is shown to proceed during the photocatalysis, leading to afford [Co(edta)]- (EDTA = H4edta) as a dead-end species. The lack of any heterogeneous species was evidenced by DLS (dynamic light scattering). It was also found that nitrate involved as a counteranion in the photocatalysis components substantially inhibits the photocatalytic HER, giving rise to a large diminishment in TON from 12.7 to 7.2. The Griess test was used to confirm that NO3- serves as a scavenger deactivating the reduced form of MV2+ (i.e., MV+·). The detailed spectroscopic study reveals that the radical dimer (MV+·)2 plays a key role in promoting the one-step two-electron process: (MV+·)2 + NO3- + 2H+ → 2MV2+ + NO2- + H2O. Experimental and DFT results also reveal that a unique double CPET (concerted proton-electron transfer) pathway is taken to evolve H2 by the Co-NHC catalysts with substantially minimized reorganization energies: Co(II)-NHC Co(III)(H)-NHC Co(II)-NHC + H2. This pathway can be viewed as related to the so-called Volmer-Heyrovsky mechanism adopted by some metals and is quite unique to the Co-NHC catalysts.

Fusion of Heterocyclic Aromatic Hydrocarbons With Multiple Resonance: Balancing Spectral Redshifts and Broadening

AbstractEfforts to fabricate ideal narrowband, long‐wavelength (>520 nm) multiple resonance (MR) emitters are often hampered by the mutual obstacles of effective spectral redshift and maintaining a small full width at half maximum (FWHM). This review focuses on a sophisticated molecular design methodology called “fusing heterocyclic aromatic hydrocarbons (HAHs) with MR” to overcome the aforementioned challenges. Here, HAH serves as a rigid structural fragment with a modest reorganization energy, which mainly plays the role of reducing ground‐excited state structural displacement and spectral redshift, while the MR fragment mainly plays the role of restricting low‐frequency vibrational coupling and narrowband emission. The synergy of these two advantages theoretically allows the significant redshift of the emission peak while further narrowing the spectrum. Utilizing the ingeniously designed emitters, the corresponding MR devices can achieve superior external quantum efficiencies of over 20% while maintaining remarkably small FWHMs of <25 nm in the green to red regions. These discoveries will spur the development of narrowband, full‐color, high‐efficiency MR emitters and usher in a transformative shift in the organic light‐emitting diode industry.

Leveraging Intramolecular π-Stacking to Access an Exceptionally Long-Lived 3MC Excited State in an Fe(II) Carbene Complex.

The ability to manipulate excited-state decay cascades using molecular structure is essential to the application of abundant-metal photosensitizers and chromophores. Ligand design has yielded some spectacular results elongating charge-transfer excited state lifetimes of Fe(II) coordination complexes, but triplet metal-centered (3MC) excited states─recently demonstrated to be critical to the photoactivity of isoelectronic Co(III) polypyridyls─have to date remained elusive, with temporally isolable examples limited to the picosecond regime. With this report, we show how strong-field donors and intramolecular π-stacking can conspire to stabilize a long-lived 3MC excited state for a remarkable 4.1 ± 0.3 ns in fluid solution at ambient temperature. Analysis of variable-temperature time-resolved absorption data using theoretical models ranging from Arrhenius to semiclassical Marcus theory, combined with computational modeling and X-ray crystallography, reveal a Jahn-Teller stabilized excited state with a high activation barrier for ground-state recovery. The net result is a chromophore with a 3MC excited-state lifetime that is orders of magnitude longer than anything yet observed for an Fe(II) complex.

Intramolecular Repulsive Interactions Enable High Efficiency of NIR-II Aggregation-Induced Emission Luminogens for High-Contrast Glioblastoma Imaging.

Strategies to acquire high-efficiency luminogens that emit in the second near-infrared (NIR-II, 1000-1700 nm) range are still rare due to the impediment of the energy gap law. Herein, a feasible strategy is pioneered by installing large-volume encumbrances in a confined space to intensify the repulsive interactions arising from overlapping electron densities. The experimental results, including smaller coordinate displacement, reduced reorganization energy, and suppressed internal conversion, demonstrate that the repulsive interactions assist in the inhibition of radiationless deactivation. Meanwhile, the configuration and hybridization form of the donor units are transformed along with the repulsive interactions, bringing about improved oscillator strength. A 3.8-fold higher luminescence efficiency is realized via the synergistic effect. Furthermore, the repulsive interactions endow the NIR-II fluorophores with a highly twisted conformation, superior AIE activity, and cascaded improvement of fluorescence emission from isolated molecules to aggregates. By utilizing a brain-targeting peptide to functionalize the NIR-II nanoparticles, accurate detection and high-contrast imaging of orthotopic glioblastoma are realized. This work not only explores a fundamental principle to handle the intractable energy gap law but also provides potential applications of NIR-II luminogens in high-contrast bioimaging and glioblastoma detection.

Enhancement of photoinduced reactive oxygen species generation in open-cage fullerenes.

Photodynamic therapy is an important tool in modern medicine due to its effectiveness, safety, and the ability to provide targeted treatment for a range of diseases. Photodynamic therapy utilizes photosensitizers to generate reactive oxygen species (ROS). Fullerenes can be used as photosensitizers to produce ROS in high quantum yields. Open-cage fullerenes are a subclass of fullerenes characterized by a partially open structure, with one or more openings or apertures. The promising electrochemical properties of open-cage fullerenes motivated us to investigate their use for DNA-cleavage and ROS generation under visible light irradiation through type I electron transfer and type II energy transfer reactions. Our results show that open-cage C60 fullerenes are more efficient for photoinduced cleavage of DNA and ROS generation via both the type I electron transfer and type II energy transfer pathways than pristine C60 or a C60 pyrrolidine derivative without open-cage. The greater efficiency of ROS generation by open-cage C60 fullerene in type I and type II reactions can be attributed to the increased rate of the initial intersystem crossing process, resulting from larger total reorganization energies, as indicated by computationally calculated relative rates using the Marcus equation, and the lower reduction potential of the open-cage derivative 3, as determined by CV, which facilitates a more efficient generation of the corresponding radical anion (C60˙-).

Optoelectronic analysis of designed semi-circular shaped thiophene-based bridged Y-series NFAs for organic solar cell applications.

The highly adaptable optoelectronic and morphological properties of non-fullerene acceptors (NFAs) have made them a prominent research topic in the organic solar cell (OSC) field. This work describes the design of new molecules and investigates the potential optoelectronic aspects of remodified Y-series NFAs endowing with five new semi-circular shaped derivatives (BTPB1-BTPB5) based on the DFT-based quantum simulations. The designed molecules possess higher-lying LUMO energy levels with narrowed bandgaps and excellent coherence between the acceptor and core via inserted bridges. The molecules demonstrate a significant red shift and a wide-ranging absorption spectrum extending from 400nm to 1500nm, with the most extensive absorption occurring in the near-infrared (NIR) region. Effective π-π stacking and drastically lower binding energy certify facile charge dissociation and transmission rate. Thiophene-based bridge modification decreased reorganization energy by 47% which results in facile charge transmission and high current density. Theoretically, simulated PCE is achieved as high as 31.49% owing to the higher-lying LUMOs. The results demonstrate the value of designing systems and exploring new possibilities for developing effective Y-series NFAs-based high-performance organic solar cells.

Ultrafast dynamics of mCP and Br-mCP: Insights from transient absorption spectroscopy

Heavy atom activated organic room-temperature phosphorescence (RTP) has attracted considerable interest due to its high phosphorescence quantum yield and prolonged lifetime. This research provides a detailed analysis of the transient absorption spectroscopy of 1,3-Bis(N-carbazolyl)benzene (mCP) and 9,9'-(5-Bromo-1,3-phenylene)bis(9H-carbazole) (Br-mCP) in toluene solution. In the femtosecond transient absorption (fs-TA) spectroscopy of mCP, the excited state absorption (ESA) signal decreases at 630 nm while the triplet-triplet absorption (TTA) signal increases at 420 nm. Meanwhile, the isosbestic point observed at 455 nm indicates an intersystem crossing (ISC) lifetime of 15.4 ns. Moving on to the nanosecond transient absorption (ns-TA) spectroscopy, the TTA signal reaches its peak at 27.3 ns before decreasing, with the triplet lifetime of mCP measured at 2.8 μs. Br-mCP exhibits a similar dynamic evolution to mCP, but with a quicker ISC process (9.4 ns) and a longer triplet lifetime (3.9 μs). The quicker ISC process in Br-mCP is ascribed to the presence of heavy atom in the molecular structure, leading to an enhanced spin-orbit coupling constant (ξ(S1, T3)Br-mCP = 1.371 cm-1 > ξ(S1, T4)mCP = 0.060 cm-1). The prolonged triplet lifetime of Br-mCP (3.9 μs > 2.8 μs) results from its lower reorganization energy, effectively reducing non-radiative vibrational energy losses within the molecule. This work significantly enhances our understanding of RTP materials incorporating heavy atoms.

Hydrogen Bond "Double-Edged Sword Effect" on Organic Room-Temperature Phosphorescence Properties: A Theoretical Perspective.

The strategy of designing efficient room-temperature phosphorescence (RTP) emitters based on hydrogen bond interactions has attracted great attention in recent years. However, the regulation mechanism of the hydrogen bond on the RTP property remains unclear, and corresponding theoretical investigations are highly desired. Herein, the structure-property relationship and the internal mechanism of the hydrogen bond effect in regulating the RTP property are studied through the combination of quantum mechanics and molecular mechanics methods (QM/MM) coupled with the thermal vibration correlation function method. Intermolecular interactions, excited-state transition properties, reorganization energies, radiative and nonradiative decay rates, and the intersystem crossing rates are analyzed in detail. Results show that intermolecular hydrogen bonds can effectively delocalize molecular orbitals, enhance spin-orbit coupling (SOC) effect, and thus accelerate intersystem crossing (ISC) processes. In addition, an intermolecular hydrogen bond can also suppress nonradiative transition by restricting molecular motion, thereby promoting generation of phosphorescence. However, an excessively enhanced intermolecular hydrogen bond effect promotes molecular vibrations, leading to increased reorganization energies and thus facilitating nonradiative energy consumption process. The hydrogen bond "double-edged sword" effect on RTP properties and nonradiative decay process is theoretically revealed. Therefore, reasonable control of the hydrogen bond strength is beneficial for the development of efficient RTP emitters. Our research provides rational explanations for previous measurements and highlights the hydrogen bond effect in constructing efficient RTP emitters.

Tunneling barriers in an extended Marcus theory of electron transfer: Incorporating effects of the bridging medium.

The Marcus semi-classical and quantum theories of electron transfer (ET) have been extensively used to understand and predict tunneling ET reaction rates in the condensed phase. Previously, the traditional Marcus two-state model has been extended to a three-state model, which assumes a harmonic dependence of donor (D), bridge (B), and acceptor (A) free energies on the reaction (e.g., solvent polarization) coordinate. Here, we generalize the previously proposed three-state extended Marcus model (EMM) to an (N + 2)-state model for N bridge sites separating the D from the A. Using the EMM, an analytic expression for the electron tunneling barrier is derived. The EMM model predicts that both the relative thermodynamics of the D-A states and B state reorganization energies can influence the D-A electronic coupling. We discuss signatures of bridge state thermal fluctuations using the EMM on the driving force and distance dependence of ET rates, which can be tested experimentally.

Unraveling the competition between charge and energy transfer in 0D/2D nanographene-graphene heterojunctions

The charge and energy transfer processes in photoexcited 0D/2D donor/graphene heterojunctions occur through multiple different pathways. A donor deexcitation event occurring in the most prevalent Förster energy transfer mechanism (strongly favored over Dexter transfer in van der Waals heterojunctions) prevents charge transfer from taking place, thus creating a competition between the two processes. By applying a robust computational approach, we describe the two processes from first principles and quantify their rates using Förster and Marcus theories. We consider nanojunctions where the donor are nanographenes with varying size and symmetry, and discern important trends, e.g., the symmetry-induced quenching, or the enhancement due to increased size. We observe that heterojunctions where nanographenes do not have a center of symmetry show decreased photoinduced hole and energy transfer rates, which can then be recovered by increasing the delocalization length, whereas for centrosymmetric nanographenes both hole and energy transfer processes are enhanced. Nevertheless, the hole transfer rate dominates over the energy transfer process, providing a new computation-driven design principle for obtaining a high-charge transfer junction with minimized contribution of the competing energy transfer.

FULLY ANALYTICAL SOLUTION FOR THE FIRST SPECTRAL MOMENT OF A FLUOROPHORE IN SOLUTION

One of the common methods for assessing the solvation dynamics of a fluorescent system in a polar medium is the analysis of the first spectral moment behavior. So there is a need to build a model that takes into account important physical processes and at the same time is not demanding in terms of calculations. In this paper, an approach is proposed that considers the parameters of the exciting laser pulse and intramolecular vibrational relaxation for constructing the solvation dynamics. A method for building an analytical solution for the dynamics of the first spectral moment is presented. This model is free of numerical methods using, and it is a simple construction built by basics functions and an additional error function. The influence of all key parameters on the system relaxation is illustrated. It is shown that delocalization in time of the pump pulse suppresses the oscillatory behavior of the first moment and hides information about the damped intramolecular mode. The similar effect is also observed with the diffusion and inertial processes contribution insreasion to the reorganization energy at early stages of relaxation. The presented model can be generalized to take into account quantum transitions between vibrational sublevels of high-frequency intramolecular vibrations.

BN-Acene Ladder with Enhanced Charge Transport for Organic Field-Effect Transistors.

The in-depth research on the charge transport properties of BN-embedded polycyclic aromatic hydrocarbons (BN-PAHs) still lags far behind studies of their emitting properties. Herein, we report the successfully synthesis of novel ladder-type BN-PAHs (BCNL1 and BCNL2) featuring a highly ordered BC3N2 acene unit, achieved via a nitrogen-directed tandem C-H borylation. Single-crystal X-ray diffraction analysis unambiguously revealed their unique and compact herringbone packing structures. Micro-sized single-crystalline organic field-effect transistors (OFETs) demonstrated that an enhanced charge transport capability, with BCNL2 achieving a hole mobility of up to 0.62 cm2 V-1 s-1-three orders of magnitude higher than that of BCNL1 (μhmax = 6 × 10-4 cm2 V-1 s-1), ranking among the highest values for BN-PAHs-based OFETs. Detailed calculations attribute this significant enhancement in the hole mobility to the marked reduction in reorganization energy (λ) of BCNL2, resulting from the five-membered pyrrole ring annulation and molecular skeleton elongation. This work provides insight into molecular design principles for potential BN-PAHs in optoelectronic applications.

BN‐Acene Ladder with Enhanced Charge Transport for Organic Field‐Effect Transistors

The in‐depth research on the charge transport properties of BN‐embedded polycyclic aromatic hydrocarbons (BN‐PAHs) still lags far behind studies of their emitting properties. Herein, we report the successfully synthesis of novel ladder‐type BN‐PAHs (BCNL1 and BCNL2) featuring a highly ordered BC3N2 acene unit, achieved via a nitrogen‐directed tandem C‐H borylation. Single‐crystal X‐ray diffraction analysis unambiguously revealed their unique and compact herringbone packing structures. Micro‐sized single‐crystalline organic field‐effect transistors (OFETs) demonstrated that an enhanced charge transport capability, with BCNL2 achieving a hole mobility of up to 0.62 cm2 V‐1 s‐1—three orders of magnitude higher than that of BCNL1 (μhmax = 6 × 10‐4 cm2 V‐1 s‐1), ranking among the highest values for BN‐PAHs‐based OFETs. Detailed calculations attribute this significant enhancement in the hole mobility to the marked reduction in reorganization energy (λ) of BCNL2, resulting from the five‐membered pyrrole ring annulation and molecular skeleton elongation. This work provides insight into molecular design principles for potential BN‐PAHs in optoelectronic applications.

Design and analysis of diisobutoxybenzodithiophene based donor for application in organic solar cell: DFT and TD-DFT Study

The newly designed chromophores (BT1-BT7) of the highly unsaturated donor-acceptor (D-A) were theoretically analyzed and recommended for applications in organic solar cells (OSCs). Conjugated A-groups have been replaced in the reference (BTR) during its design. The structural and optoelectronic properties of designed molecules were calculated using density functional theory (DFT) and Time-dependent DFT (TD-DFT) techniques. The frontier molecular orbitals (FMO) study revealed that BT7 has the lowest energy gap of 2.01 eV, which has significantly less than BTR (2.34 eV), and a significant amount of charge transfer (CT) between HOMO and LUMO has been observed. Out of all the newly designed chromophores in chloroform, the highest absorption spectra were found in the visible region with a bathochromic shift up to 768 nm. The dipole moment values of all the new chromophores (BT1-BT7) were significantly higher than the BTR (5.46 D), which resulted in good solvation. ESP analysis revealed electron distribution on various parts of the molecules by colored maps that are found to be effective for better ICT. The electron transition density resulting from light absorption at different chemical sites was shown using TDM plots. The electron and hole reorganization energy (RE) values were proved as highly efficient in promoting charge mobility and hindered charge recombination for new compounds. By scaling our designed donor to the recognized acceptor Y6, which has demonstrated the creation of OSCs, the open circuit voltage of each molecule was ascertained. The designed molecules exhibited higher open circuit voltages than the reference, indicating improved and fine-tuned optoelectronic properties that would aid in the development of solar cell devices in the future.

Tuning optical and electronic properties of indanthrene derivatives with electron-withdrawing groups (-Cl, -NO₂ and -C≡N) for enhanced organic solar cell performance: a DFT approach

Abstract In this study, we focused on improving the electronic and optical properties of the reference compound indanthrene (R) by introducing electron-withdrawing groups (−Cl, −C≡N, −NO₂). density functional theory and time-dependent density functional theory calculations were performed using Gaussian 16 software to study indanthrene derivatives as electron acceptor materials. The electronic and optical properties of the designed molecules (M1-M8) were investigated through frontier molecular orbital analysis, UV-visible absorption spectra, density of states, and transition density matrix analysis, utilizing GaussView 6.0 and Multiwfn 3.8 software. The designed molecules exhibit absorption across the entire visible spectrum, with maxima extending up to ~737 nm. Their electron affinity values range from 3.0 to 4.0 eV, surpassing the fullerene-based acceptor material. Among the designed molecules, M5 stands out with superior photovoltaic parameters, including a narrow optical band gap (~1.68 eV), exciton binding energy (0.25 eV), higher electron affinity (3.35 eV), an extended excited state lifetime (17.0 ns) owing to its low electron and hole reorganization energies (λe ~ 0.190 eV, and λh ~ 0.134 eV), and improved short-circuit current density of ~ 15.7 mA/cm². The photovoltaic parameters and power conversion efficiency were assessed using the Scharber and Alharbi models. The calculated device parameters, including light harvesting energy and photovoltaic characteristics (Voc, FF, Jsc, and PCE), suggest that these molecules, with electron-withdrawing groups, show great potential for use as acceptors in organic solar cells, particularly in terms of stability and power conversion efficiency. Notably, M2 and M5, with their PCE values exceeding 16%, emerge as outstanding candidates for device performance, impressively outperforming the other designed molecules.

Fundamental understanding of quantum confinement effect on gate oxide reliability for gate-all around field-effect transistor

Gate oxide reliability has become a significant concern for emerging technology nodes, particularly as transistors continue to scale down. Quantum confinement effects in nano-scaled devices complicate the trapping dynamics near the interface. Although these behaviors can be modeled using density-functional theory (DFT) and Marcus theory, a more efficient method is essential for characterizing critical reliability issues at the nano-device level. This paper presents a pioneering numerical study that employs a Bohm potential and Marcus theory, examining carrier concentration decay near the channel/oxide interface to evaluate the charge-trapping process using density-gradient coupled Poisson equations. This approach incorporates vital quantum corrections to classical studies. Key physics-based parameters are initially derived from DFT calculations and subsequently calibrated against experimental data. Our findings indicate that charge trap rates decrease with carrier density at the interface, ultimately affecting the device's threshold voltage shift.

Enhancing Interlayer Charge Transport of Two-Dimensional Perovskites by Structural Stabilization via Fluorine Substitution.

Two-dimensional lead-halide perovskites provide a more robust alternative to three-dimensional perovskites in solar energy and optoelectronic applications due to increased chemical stability afforded by interlayer ligands. At the same time, the ligands create barriers for interlayer charge transport, reducing device performance. Using a recently developed ab initio simulation methodology, we demonstrate that ligand fluorination can enhance both hole and electron mobility by 1-2 orders of magnitude. The simulations show that the enhancement arises primarily from improved structural order and reduced thermal atomic fluctuations in the system rather than increased interlayer electronic coupling. Arising from stronger hydrogen bonding and dipolar interactions, the higher structural stability decreases the reorganization energy that enters the Marcus formula and increases the charge transfer rate. The detailed atomistic insights into the electron and hole transfer in layered perovskites indicate that the use of interlayer ligands that make the overall structure more robust is beneficial simultaneously for chemical stability and charge transport, providing an important guideline for the design of new, efficient materials.

Effect of Alkyl- vs Alkoxy-Arene Substituents on the Deactivation Processes and Fluorescence Quantum Yields of Exciplexes.

Decay processes of exciplexes of cyanoanthracenes with alkylbenzene donors were compared to those with alkoxybenzenes. For the three decay processes of exciplexes, the radiative rate constant (kf) of alkoxy derivatives is slightly lower than those of alkylbenzenes at the same average exciplex energy. However, the corresponding deactivation rate constants, intersystem crossing (kisc) and nonradiative decay (knr), are considerably higher. Consequently, the fluorescence quantum yields of the alkoxybenzene exciplexes are one-half to one-fifth of the corresponding alkylbenzenes at comparable emission energies. This trend is solvent-independent. The results can be rationalized in terms of the differing electronic character of the donor radical cation moieties in the alkoxy- vs alkylbenzene exciplexes and differences in their reorganization energies. The impact of these results for the design of exciplexes that emit more efficiently is discussed.

Complementing Adiabatic and Nonadiabatic Methods To Understand Internal Conversion Dynamics in Porphyrin Derivatives.

We analyze the internal conversion dynamics within the Qy and Qx excited states of both bare and functionalized porphyrins, which are known to exhibit significantly different time constants experimentally. Through the integration of two complementary approaches, static calculation of per-mode reorganization energies and nonadiabatic molecular dynamics, we achieve a comprehensive understanding of the factors determining the different behavior of the two molecules. We identify the key normal and essential modes responsible for the population transfer between excited states and discuss the efficacy of different statistical and nonstatistical analyses in providing a full physics-based description of the phenomenon.