Energy Relaxation Research Articles

Nonadiabatic Molecular Dynamics in Momentum Space Beyond Harmonic Approximation: Hot Electron Relaxation in Photoexcited Black Phosphorus.

We simulated hot-electron relaxation in black phosphorus using the nonadiabatic molecular dynamics (NA-MD) approach with a non-Condon effect in momentum space beyond the harmonic approximation. By comparing simulations at the Γ point in a large supercell with those using a few k-points in a smaller supercell─while maintaining the same number of electronic states within the same energy range, we demonstrate that both setups yield remarkably consistent energy relaxation times, regardless of the initial state energy. This consistency arises from the complementary effects of supercell size in real space and the number of k-points in the reciprocal space. This finding confirms that simulations at a single k-point in large size supercells are an effective approximation for NA-MD with a non-Condon effect. This approach offers significant advantages for complex photophysics, such as intervalley scattering and indirect bandgap charge recombination, and is particularly suitable for large systems without the need for a harmonic approximation.

Relaxed Energy Preserving Hashing for Image Retrieval

Relaxed Energy Preserving Hashing for Image Retrieval

Interplay between photoinduced charge and energy transfer in manganese doped perovskite quantum dots.

A comprehensive study on the photo-excited relaxation dynamics in semiconducting perovskite quantum dots (PQDs) is pivotal in realizing their extensive potential for optoelectronics applications. Among different competing photoinduced relaxation kinetics, energy transfer and charge transfer (CT) in PQDs need special attention, as they often influence the device efficacy, particularly with the donor-acceptor hybrid architecture. In this work, we explore a detailed investigation into photoinduced CT dynamics in mixed halide undoped CsPb(Br/Cl)3 and Mn2+ doped CsPb(Br/Cl)3 PQDs with a quinone molecule, p-benzoquinone (BQ). The energy level alignment of undoped PQDs with BQ allows an efficient CT, whereas Mn2+ doping reduces the CT efficiency, experiencing a competition between energy transfer from host to dopant and CT to BQ. The conductive atomic force microscopy measurements unveil a direct correlation with the spectroscopic studies by showing a significant improvement in the conductance of undoped PQDs in the presence of BQ, while an inappreciable change is observed for doped PQDs. A much-reduced transition voltage and barrier height in the presence of BQ further validate faster CT for undoped PQD than the doped one. Furthermore, Mn2+ doping in PQDs is observed to enhance their stability, showing better air and thermal stability compared to their undoped counterparts. These results reveal that doping strategy can regulate the CT dynamics in these PQDs and increase their stability, which will be beneficial for the development of desired optoelectronic devices with long-term stability.

Nonadiabatic molecular dynamics with subsystem density functional theory: application to crystalline pentacene

In this work, we report the development and assessment of the nonadiabatic molecular dynamics approach with the electronic structure calculations based on the linearly scaling subsystem density functional method. The approach is implemented in an open-source embedded Quantum Espresso/Libra software specially designed for nonadiabatic dynamics simulations in extended systems. As proof of the applicability of this method to large condensed-matter systems, we examine the dynamics of nonradiative relaxation of excess excitation energy in pentacene crystals with the simulation supercells containing more than 600 atoms. We find that increased structural disorder observed in larger supercell models induces larger nonadiabatic couplings of electronic states and accelerates the relaxation dynamics of excited states. We conduct a comparative analysis of several quantum-classical trajectory surface hopping schemes, including two new methods proposed in this work (revised decoherence-induced surface hopping and instantaneous decoherence at frustrated hops). Most of the tested schemes suggest fast energy relaxation occurring with the timescales in the 0.7–2.0 ps range, but they significantly overestimate the ground state recovery rates. Only the modified simplified decay of mixing approach yields a notably slower relaxation timescales of 8–14 ps, with a significantly inhibited ground state recovery.

Light harvesting in purple bacteria does not rely on resonance fine-tuning in peripheral antenna complexes

The ring-like peripheral light-harvesting complex 2 (LH2) expressed by many phototrophic purple bacteria is a popular model system in biological light-harvesting research due to its robustness, small size, and known crystal structure. Furthermore, the availability of structural variants with distinct electronic structures and optical properties has made this group of light harvesters an attractive testing ground for studies of structure–function relationships in biological systems. LH2 is one of several pigment-protein complexes for which a link between functionality and effects such as excitonic coherence and vibronic coupling has been proposed. While a direct connection has not yet been demonstrated, many such interactions are highly sensitive to resonance conditions, and a dependence of intra-complex dynamics on detailed electronic structure might be expected. To gauge the sensitivity of energy-level structure and relaxation dynamics to naturally occurring structural changes, we compare the photo-induced dynamics in two structurally distinct LH2 variants. Using polarization-controlled 2D electronic spectroscopy at cryogenic temperatures, we directly access information on dynamic and static disorder in the complexes. The simultaneous optimal spectral and temporal resolution of these experiments further allows us to characterize the ultrafast energy relaxation, including exciton transport within the complexes. Despite the variations in PPC molecular structure manifesting as clear differences in electronic structure and disorder, the energy-transport and—relaxation dynamics remain remarkably similar. This indicates that the light-harvesting functionality of purple bacteria within a single LH2 complex is highly robust to structural perturbations and likely does not rely on finely tuned electronic- or electron-vibrational resonance conditions.

The electronic and optical properties of Al interstitial defects in KH2PO4 crystal: First principles study

KH2PO4 (KDP) crystals are widely used as frequency multipliers in inertial confinement controlled fusion ignition devices. The electronic and optical properties of KDP crystals with Al interstitial defects based on first principles are investigated. The results show that neutral and +3 charged Al interstitial can exist stably in the crystal. The +3 charged defect produces a larger lattice distortion. Bond length varies from −18.78 % to 43.71 % in the paraelectric phase(P-KDP) and from −25.57 % to 66.09 % in the ferroelectric phase (F-KDP). At the same time, +3 charged Al interstitial may also cause HO bond to break, resulting in the generation of H interstitials, which may compensate for the H vacancies in as-grown KDP. This may make the laser damage threshold slightly increase when KDP crystal is doped with +3 charged Al ion at low concentration. The optical spectra of Al interstitial are calculated, and the results show that in the paraelectric and ferroelectric phases, the optical transition of Al ions generally produces a large lattice relaxation energy, such as the lattice relaxation energy of up to 4.00 eV in the +2 to +3 charged defect transition in the paraelectric phase. This shows that the optical transition of Al interstitial will cause serious damage to the crystal. In the paraelectric phase, the absorption peaks of optical transitions found in the ultraviolet and visible regions are consistent with experiments. The absorption peak of the +1 to +2 charged defect transition is at 260 nm, which is very close to the absorption peak at 270 nm measured by experiments. The analysis of the Huang-Rys factors and transition displacement further confirms the conclusion that the optical transition of the defect charged state will cause serious crystal damage.

Slow energy relaxation in anharmonic chains with and without on-site potentials: Roles of distinct types of discrete breathers

Slow energy relaxation has been observed in one-dimensional lattices with and without a nonlinear on-site potential; however, a comprehensive understanding of the detailed relaxation process remains elusive. Here we revisit this issue by introducing damping conditions at the free-end boundary of a thermalized lattice. We reveal that, in the long-cooling-time regime considered, for systems with a nonlinear on-site potential, energy relaxation exhibits a strong temperature-dependent behavior and with the increase of temperature, there is a crossover between decaying and non-decaying behaviors, around a crossover temperature point of Tc≃4.2. This non-decaying behavior at higher temperature is attributed to the presence of standing multi Sievers–Takeno discrete breather (DB) states. Conversely, for systems without on-site potentials, relaxation is nearly independent of temperature but dependent on interparticle potential. Notably, we observe that the cubic anharmonicity can generate moving single Page DB states that contribute to the unusual slow energy relaxation within a specific time regime. Our results provide enhanced insights into the mechanisms governing slow energy relaxation during lattice cooling.

Vibrational energy relaxation in shock-heated CO/N2/Ar mixtures.

Experimental and numerical studies were performed on the vibrational energy relaxation in shock-heated CO/N2/Ar mixtures. A laser absorption technique was applied to the time-dependent rovibrational temperature time-history measurements. The vibrational relaxation data of reflected-shock-heated CO were summarized at 1720-3230K. In shock-tube experiments, the rotational temperature of CO quickly reached equilibrium, whereas a relaxation process was found in the time-dependent vibrational temperature. For the mixture with 1.0% CO and 10.0% N2, the vibrational excitation caused a decrease in the macroscopic thermodynamic temperature of the test gas. In the simulations, the state-to-state (StS) approach was employed, where the vibrational energy levels of CO and N2 are treated as pseudo-species. The vibrational state-specific inelastic rate coefficients of N2-Ar collisions were calculated using the mixed quantum-classical method based on a newly developed three-dimensional potential energy surface. The StS predictions agreed well with the measurements, whereas deviations were found between the Schwartz-Slawsky-Herzfeld formula predictions and the measurements. The Millikan-White vibrational relaxation data of the N2-Ar system were found to have the most significant impact on the model predictions via sensitivity analysis. The vibrational relaxation data of the N2-Ar system were then modified according to the experimental data and StS results, providing an indirect way to optimize the vibrational relaxation data of a specific system. Moreover, the vibrational distribution functions of CO and N2 and the effects of the vibration-vibration-translation energy transfer path on the thermal nonequilibrium behaviors were highlighted.

Spontaneous resolution and magnetic properties of lanthanide metal organic frameworks based on oxydiacetate

Chiral lanthanide metal organic frameworks (Ln-MOFs) have become a kind of promising platform for developing various chiral functional materials. However, their members are still scarce up to now, especially those obtained from spontaneous resolution. In this work, two pairs of enantiomers of chiral Ln-MOFs, namely, [Ln2(oda)3(H2O)4]·2H2O [Ln = Dy (Λ-1 and Δ-1), Gd (Λ-2 and Δ-2); oda = oxydiacetate], have been prepared from an achiral H2oda ligand by spontaneous resolution. They display homochiral Λ- or Δ-configurational 2D grid-like frameworks in the absence of any chiral source, where four carboxylate groups of oda2− ligands within each [LnIII(oda)3]3− module link to adjacent four Ln ions either in a left- or right-handed fashions. Their homochirality was further confirmed by solid-state circular dichroism (CD) spectrum. Magnetic measurements revealed that Λ-1 exhibits field-induced dual-relaxation behavior of single-molecule magnet (SMM). The effective energy barrier (Ueff) and relaxation time (τ0) of slow relaxation (SR) process are 92.63 K and 1.49 × 10−12 s, respectively. Furthermore, Λ-2 was found to show magnetocaloric effect (MCE), with the maximum magnetic entropy change (−ΔSm) of 10.02 J kg−1 K−1 at 7.0 T and 2.0 K.

Impact on activation energy with elevating calcination temperature of barium bismuth ferrite nanocomposite

Barium Bismuth Ferrite nanoparticles having the general formula Ba1-xBixFeO3 were successfully made by the sol-gel system, using nitrates as the fundamental material. Tartaric acid and polyvinyl alcohol were used as chelating agents. The synthesized nanoparticle powder was sintered at 650 ̊C and 750 ̊C for 3 h. Filtering with dilute nitric acid and distilled water is used to remove the impurities. The structural, optical, and dielectric properties were determined at room temperature. Using X-ray diffraction (XRD) analysis, structure, lattice parameter, microstrain, and dislocation density were calculated. Using the Scherrer equation, the peak's crystalline size was ascertained. In FTIR, the vibrational modes of the octahedral and tetrahedral metal complexes in the sample have been studied using the wavenumber in this range. The synthesized nanocomposite contains morphological features, such as interconnecting agglomerates with spherical, irregular, or non-uniform elongated shapes, as demonstrated by SEM images. The activation energy for relaxation and activation energy for conduction was measured from the Cole-Cole plot and the AC conductivity versus frequency plot respectively. The determined activation energies from the two investigations were relatively close to one another. The Barium Bismuth Ferrite nanoparticles samples at room temperature indicate that the samples have implicit candidates for information storage devices for spintronic devices. In the high frequency range, all samples depending upon the temperature demonstrate excellent dielectric behaviour and small dielectric loss, and with stable dielectric constant, these samples make their prospective for the practical application in spintronic devices the main goal of this work.

Understanding the coupling of non-metallic heteroatoms to CO2 from a Conceptual DFT perspective

ContextA Conceptual DFT (CDFT) study has been carry out to analyse the coupling reactions of the simplest amine (CH3NH2), alcohol (CH3OH), and thiol (CH3SH) compounds with CO2 to form the corresponding adducts CH3NHCO2H, CH3OCO2H, and CH3SCO2H. The reaction mechanism takes place in a single step comprising two chemical events: nucleophilic attack of the non-metallic heteroatoms to CO2 followed by hydrogen atom transfer (HAT). According to our calculations, the participation of an additional nucleophilic molecule as HAT assistant entails important decreases in activation electronic energies. In such cases, the formation of a six-membered ring in the transition state (TS) reduces the angular stress with respect to the non-assisted paths, characterised by four-membered ring TSs. Through the analysis of the energy and reaction force profiles along the intrinsic reaction coordinate (IRC), the ratio of structural reorganisation and electronic rearrangement for both activation and relaxation energies has been computed. In addition, the analysis of the electronic chemical potential and reaction electronic flux profiles confirms that the highest electronic activity as well as their changes take place in the TS region. Finally, the distortion/interaction model using an energy decomposition scheme based on the electron density along the reaction coordinate has been carried out and the relative energy gradient (REG) method has been applied to identify the most important components associated to the barriers.MethodsThe theoretical calculation were performed with Gaussian-16 scientific program. The B3LYP-D3(BJ)/aug-cc-pVDZ level was used for optimization of the minima and TSs. IRC calculations has also been carried out connecting the TS with the associated minima. Conceptual-DFT (CDFT) calculations have been carried out with the Eyringpy program and in-house code. The distortion/interaction model along the reaction coordinate have used the decomposition scheme of Mandado et al. and the analysis of the importance of each components have been done with the relative energy gradient (REG) method.

Perspectives on fatigue management among veterans living with multiple sclerosis

BackgroundChronic fatigue is one of the most common, disabling, and least understood symptoms of many chronic health conditions including multiple sclerosis (MS). A multidisciplinary rehabilitative treatment approach is recommended for MS-related fatigue, but few people with MS have access to such treatment. In-person and telehealth cognitive behavioral therapy (CBT) for fatigue is an emerging acceptable and effective treatment for MS-related fatigue in civilians that has not been studied in Veterans with MS, a population that is more likely to be older, male, unemployed, and disabled. The present study aimed to understand how Veterans with MS (1) describe their fatigue and (2) manage their fatigue, and (3) perceive telehealth CBT for MS-related fatigue. MethodTwenty-four Veterans with MS completed semi-structured interviews and a brief survey. For descriptive purposes, the survey included questionnaires on demographics, fatigue, psychosocial functioning, depression, and pain. Thematic analysis with a combined deductive and inductive approach was used to analyze interview transcripts. ResultsThree themes emerged. First, “experience of MS fatigue as ‘one big tapestry’” described fatigue as deficits in physical and mental energy that were fluctuating and complex in their interaction with biological factors. Veterans described that MS fatigue negatively impacted daily activities of living, emotions, and cognitive functioning. Second, “managing MS fatigue through trial and error” revealed that Veterans expend significant time and effort learning and trialing fatigue management strategies based on their personal beliefs, military training/experiences, provider recommendations, and iterative learning. Most Veterans described energy management, relaxation, exercise, and adaptive thinking as helpful for managing fatigue. Interestingly, the helpfulness of medication for fatigue was highly variable, and none of the Veterans described medication as a standalone fatigue treatment. The third theme, “practicing flexibility with telehealth CBT for MS fatigue” revealed Veteran's enthusiasm about telehealth CBT for MS-related fatigue and highlighted the importance of flexible delivery to meet individual needs. ConclusionVeteran participants shared their experience of MS-related fatigue as well as management strategies that are consistent with previous research in civilians with MS fatigue. Notably, Veterans’ preference for flexible nonpharmacological intervention can inform adaptation of telehealth CBT for Veterans with MS fatigue.

Low-temperature growth of narrow optical gap highly conducting nc-Ge thin films with superior crystallinity involving dominant orientation

The nc-Ge thin films are grown at a moderately low temperature (∼220 °C) in rf PECVD via optimizing the GeH4 plasma with H2-dilution, within 97.5 ≤ D(H2)(%) ≤ 99.5. At elevated D(H2), while the bonded H-content in the matrix reduces, the film's crystallinity and dc conductivity increase. However, the optical band gap widens for 97.5 ≤ D(H2)(%) ≤ 98.5, via the elevated quantum confinement effect from the increased number of Ge-ncs of dimension below Bohr radius. Conversely, for D(H2) ≥ 98.5%, switching in the quantum effect in larger-sized Ge-ncs induces the band gap narrowing. Significantly reduced ultra-nanocrystalline-Ge (unc-Ge) component occupying the grain boundary zone, minimizes the contribution of grain-boundary defects. However, the persistent amorphous Ge matrix becomes highly defective and less dense, and those induce enhanced O-absorption from the ambient in the dominant Ge-Ox (x < 2) configuration. On increased crystallinity, the activation energies of dipole relaxation (ΔEτ) and resistance (ΔE) in the impedance data reduce dominantly in the a-Ge component than its nc-Ge counterpart, which occurs identically for the dc conductivity when the amorphous component in the matrix sharply disappears at increased D(H2) > 98.5%. A narrow band gap (∼0.90 eV), conducting (σd ∼3.0 ×10−2 S cm−1), and photosensitive nc-Ge network, involving dominant <111>-oriented Ge-ncs (∼35.2 nm) of enriched volume fraction (XC ∼90.2%), obtained at D(H2) ∼99.5%, seems extremely useful for need-based applications as a narrow band gap absorber layer in the bottom sub-cell of flexible high-efficiency cost-effective multijunction thin film solar cells.

Structural regulation strategy for Dy-MOFs based on [Qn+][Dy(β-diketonate)4-]n (Qn+ = Et3NH+, Et4N+, R-H2MPPA2+)

In this study, [Qn+][Dy(β-diketonate)4-]n (β-diketonate = Hfac, Hbtfa, Hdbm; n = 1, Q+ = Et3NH+, Et4N+; n = 2, Q2+= R-H2MPPA2+) was used to regulate the hydrolysis process of DyIII ions to generate different secondary building units (SBUs). The SBUs were further connected with fumaric acid ligands, exhibiting diverse coordination modes. Five dysprosium-based metal–organic frameworks (Dy-MOFs; 1–5) with various structural connections and topologies were synthesized. When cations in [Qn+][Dy(β-diketonate)4-]n were Et3NH+ and the anions changed from [Dy(fac)4]- to [Dy(dbm)4]- and [Dy(btfa)4]-, three SBUs (C2v Dy1O8, D2d Dy2O8 in 1; C2v Dy1O8 in 2; C4v Dy1O9 in 3) were formed. When anions in [Qn+][Dy(β-diketonate)4-]n were [Dy(btfa)4]- and the cations changed from Et3NH+ to Et4N+ and R-H2MPPA2+, four SBUs (C4v Dy1O9 in 3; Cs Dy1O9, D3h Dy2O9 in 4; D4d Dy1O8 in 5) were formed. Further magnetic characterization indicated that 2, 3, and 4 exhibited antiferromagnetic behavior, while 1 and 5 exhibited ferromagnetic properties. The alternating-current magnetic susceptibilities of 1 and 5 exhibited significant frequency and temperature dependence. The Cole–Cole plot of 1 and 5 displayed a semicircular shape, and the effective energy barrier and relaxation time were 77.54 K and 3.20 × 10–8 s and 6.8 K and 7.50 × 10–5 s for 1 and 5, respectively.

The relaxed energy of fractional Sobolev maps with values into the circle

We deal with the weak sequential density of smooth maps in the fractional Sobolev classes of Ws,p maps in high dimension domains and with values into the circle. When s is lower than one, using interpolation theory we introduce a natural energy in terms of optimal extensions on suitable weighted Sobolev spaces. The relaxation problem is then discussed in terms of Cartesian currents. When sp=1, the energy gap of the relaxed functional is always finite and is given by the minimal connection of the singularities times an energy weight, obtained through a minimum problem for one dimensional W1/p,p maps with degree one. When sp>1, instead, concentration on codimension one sets needs unbounded energy. We finally treat the case where s is greater than one, obtaining an almost complete picture.

Direct-write printed controllable concave surface for fabricating flexible metal electrode

Structured surface of flexible substrate could generate a positive impact on flexibility of metal electrode due to the surface free energy relaxation, which could make the flexibility of metal electrode meet the performance requirement of flexible electronics. However, the preparation of controllable structured surface of flexible substrate is still a tough and challenge process. In this research work, controllable concave surface of flexible substrate was prepared by direct-write print with a viscoelastic substrate. When the controllable concave surface of flexible substrate was evaporated with a nanoscale metal layer, various metal electrodes could be obtained with a controllable morphology of concave surface. The direct-write printed concave surface efficiently enhanced the flexibility of metal electrodes. When the prepared concave surface generated a continuous connected structure with a 0.1 mm printing space, an excellently enhanced flexibility of metal electrode was achieved with an internal bending flexibility of 93.72%, external bending flexibility of 93.67%, stretchability of 85% and number of stable cyclic bending times over 12,000. Meanwhile, the direct-write printed concave surface generated a reversed convex surface, which could be used for pressure sensing as a flexible pressure sensor. Therefore, this research work provides an efficient method for fabricating flexible electrode, which has important research and application value in the area of high-performance flexible electronics.

Designing Advanced Amorphous/Nanocrystalline Alloys by Controlling the Energy State.

Amorphous alloys, also known as metallic glasses, exhibit many advanced mechanical, physical, and chemical properties. Owing to the nonequilibrium nature, their energy states can vary over a wide range. However, the energy relaxation kinetics are very complex and composed of various types that are coupled with each other. This makes it challenging to control the energy state precisely and to study the energy-properties relationship. This brief review introduces the recent progresses on studying the enthalpy relaxation kinetics during isothermal annealing, for example, the observation of two-step relaxation phenomenon, the detection of relaxation unit (relaxun), the key role of large activation entropy in triggering memory effect, the influence of glass energy state on nanocrystallization. Based on the above knowledge, a new strategy is proposed to design a series of amorphous alloys and their composites consisting of nanocrystals and glass matrix with superior functional properties by precisely controlling the nonequilibrium energy states. As the typical examples, Fe-based amorphous alloys with both advanced soft magnetism and good plasticity, Gd-based amorphous/nanocrystalline composites with large magnetocaloric effect, and Fe-based amorphous alloys with high catalytic performance are specifically described.

Anisotropic relaxation of nuclear spins dipolar energy of water molecules in two-dimensional nanopores - A single crystal NMR study

Energy transfer from Zeeman to dipolar order discovered by Jeener et al. is usually observed in solids with a strong dipole-dipole interaction of nuclear spins. It is not observed in liquids, where fast molecular motion completely averages this interaction. The intermediate case, when the dipole-dipole interaction of nuclear spins is only partially averaged, has been poorly studied. We report on the first measurement of an angular-dependent proton spin relaxation of a dipolar reservoir in mobile water molecules confined in the interlayer pores of a vermiculite single crystal. In this layered crystal, the intramolecular dipole-dipole interactions of nuclear spins are only partially averaged due to the restricted anisotropic molecular motion in nanopores. We show that this allows the formation of dipolar echo. We measured the spin-lattice relaxation times of the dipolar order T1D at different angles between the normal to the crystal surface and the applied magnetic field and obtained a distinct angular dependence of T1D. The minimum relaxation rate R1D was found around the magic angle of 54.74°.

Efficiently linear and unconditionally energy-stable time-marching schemes with energy relaxation for the phase-field surfactant model

In this article, we consider consistent, efficient, and accurate numerical approximations for a recently developed Cahn–Hilliard type phase-field surfactant model enjoying the bounded-from-below condition of total energy. The phase-field surfactant model naturally satisfies the energy dissipation property in time. Based on this feature, we construct linearly decoupled and unconditionally energy-stable time-marching schemes based on an efficient variant of scalar auxiliary variable approach. To enhance the consistency of discrete modified energy and discrete original energy, a practical energy relaxation technique is adopted. We analytically proved the unique solvability and unconditional energy stability of the proposed schemes. In each time step, only two linear elliptic type equations with constants coefficients need to be solved and several algebraic operations need to be performed. Therefore, the proposed schemes are highly efficient and easy to implement. The space is discretized by the finite difference method and the linear multigrid algorithm is used to accelerate the convergence. The numerical results indicate that the proposed method not only has desired accuracy in time but also satisfies the energy dissipation law even if larger time steps are used. Furthermore, the surfactant laden spinodal decompositions and surfactant absorptions can be well simulated.

A Thorough Examination of the Variables Affecting the Quantum Efficiency of Radiative Decay of Trichlorotriphenylmethyl Radicals.

Fluorescence quantum efficiency is determined by the competition between radiation and nonradiation processes of the excited states. Understanding the factors affecting the radiation and nonradiative decay rates is of great significance for the design of luminescent materials. The excitation state deactivation mechanisms of singlet and triplet states have been extensively studied, providing a comprehensive understanding of the processes involved in the relaxation of these states. However, research on free radical systems involving doublet states is relatively scarce. Therefore, in this study, radiation and nonradiative decay rates and the mechanism of a series of trichlorotriphenylmethyl-based radicals were investigated theoretically. The results indicate that the relative rotations of electron donor and acceptor, as well as the internal rotations of trichlorotriphenylmethyl moiety, play important roles in energy dissipation through nonradiative channels. The effect of a solid-state environment on the radiation and nonradiative decay rates of radicals was investigated using a combination of quantum mechanics and molecular mechanics methods. The results indicate that the solid-state environment restricts the expansion of the conjugated system in the excited state of radicals, leading to a slight decrease in radiative decay rate. In addition, the solid-state environment reduces the reorganization energy and also affects the adiabatic excitation energy of radicals. The reduction in reorganization energy results in a decrease in nonradiative rate, while the opposite effect is observed for adiabatic excitation energy. The nonradiative rate of radicals in a solid-state environment is thus inflected by a combination of molecular geometric structure relaxation and ground-excited state energy gap.