Simulation Of Electron Dynamics Research Articles

Gas-phase preparation of silylacetylene (SiH3CCH) through a counterintuitive ethynyl radical (C2H) insertion.

Elementary reaction mechanisms constitute a fundamental infrastructure for chemical processes as a whole. However, while these mechanisms are well understood for second-period elements, involving those of the third period and beyond can introduce unorthodox reactivity. Combining crossed molecular beam experiments with electronic structure calculations and molecular dynamics simulations, we provide compelling evidence on an exotic insertion of an unsaturated sigma doublet radical into a silicon-hydrogen bond as observed in the barrierless gas-phase reaction of the D1-ethynyl radical (C2D) with silane (SiH4). This pathway, which leads to the D1-silylacetylene (SiH3CCD) product via atomic hydrogen loss, challenges the prerequisite and fundamental concept that two reactive electrons and an empty orbital are required for the open shell, unsaturated radical reactant to insert into a single bond.

Simulating Real-Time Molecular Electron Dynamics Efficiently Using the Time-Dependent Density Matrix Renormalization Group.

Compared to ground-state electronic structure optimizations, accurate simulations of molecular real-time electron dynamics are usually much more difficult to perform. To simulate electron dynamics, the time-dependent density matrix renormalization group (TDDMRG) has been shown to offer an attractive compromise between accuracy and cost. However, many simulation parameters significantly affect the quality and efficiency of a TDDMRG simulation. So far, it is unclear whether common wisdom from ground-state DMRG carries over to the TDDMRG, and a guideline on how to choose these parameters is missing. Here, in order to establish such a guideline, we investigate the convergence behavior of the main TDDMRG simulation parameters, such as time integrator, the choice of orbitals, and the choice of matrix-product-state representation for complex-valued nonsinglet states. In addition, we propose a method to select orbitals that are tailored to optimize the dynamics. Lastly, we showcase the TDDMRG by applying it to charge migration ionization dynamics in furfural, where we reveal a rapid conversion from an ionized state with a σ character to one with a π character within less than a femtosecond.

Conformational and Solvent Effects on the Photoinduced Electron Transfer Dynamics of a Zinc Phthalocyanine-Benzoperylenetriimide Conjugate: A Nonadiabatic Dynamics Simulation.

Herein, we employed a combination of static electronic structure calculations and nonadiabatic dynamics simulations at linear-response time dependent density functional theory (LR-TDDFT) level with the optimally tuned range-separated hybrid (OT-RSH) functional to explore the ultrafast photoinduced dynamics of a zinc phthalocyanine-benzoperylenetriimide (ZnPc-BPTI) conjugate. Due to the flexibility of the linker, we identified two major conformations: the stacked conformation (ZnPc-BPTI-1) and the extended conformation (ZnPc-BPTI-2). Since the charge transfer states are much lower than the lowest local excitation in ZnPc-BPTI-1, which is contrary to ZnPc-BPTI-2, the ultrafast electron transfer (~3.6 ps) is only observed in the nonadiabatic simulations of ZnPc-BPTI-1 upon local excitation around the absorption maximum of ZnPc. However, when considering the solvent effects in benzonitrile: the lowest S1 states are both charge transfer states from ZnPc to BPTI for different conformers. Subsequent nonadiabatic dynamics simulations indicate that both conformers experience ultrafast electron transfer in benzonitrile with two time constants of 90 [100] fs and 1.40 [1.43] ps. Our present work not only agrees well with previous experimental study, but also points out the important role of conformational changes and solvent effects in regulating the photodynamics of organic donor-acceptor conjugates.

Photocarrier Dynamics of Two-Dimensional Aza-Fused Covalent Organic Frameworks as Bifunctional Photocatalysts toward Overall Water Splitting.

Designing high-efficiency bifunctional photocatalysts toward photoinduced overall water splitting is one of the most promising and challenging research directions for clean energy generation. By employing static electronic structure calculation and nonadiabatic molecular dynamics (NAMD) simulation, we herein established a recently synthesized two-dimensional (2D) aza-fused covalent organic framework (aza-COF) as a potential bifunctional photocatalyst toward overall water splitting reactions. Our calculated results reveal that the overpotentials for hydrogen evolution reaction and oxygen evolution reaction are only 0.06 and 0.31 V, respectively, at pH = 4. The dynamics of photoexcited charge carriers studied through NAMD simulation predicts the electron-hole recombination time (25.15 ns), and this confirms that the photogenerated electron and hole carriers migrate to the active sites for the occurrence of reaction before they recombine. Therefore, our results suggest that the 2D aza-COFs exhibit great potential as metal-free and single-material photocatalysts toward overall water splitting under visible light.

Photoinduced Nonadiabatic Dynamics of a Single-Walled Carbon Nanotube-Porphyrin Complex.

Single-walled carbon nanotubes (SWCNTs) have gained a lot of attention in the past few decades due to their promising optoelectronic properties. In addition, SWCNTs can form complexes that have good chemical stability and transport properties with other optical functional materials through noncovalent interactions. Elucidating the detailed mechanism of these complexes is of great significance for improving their optoelectronic properties. Nevertheless, simulating the photoinduced dynamics of these complexes accurately is rather challenging since they usually contain hundreds of atoms. To save computational efforts, most of the previous works have ignored the excitonic effects by employing nonadiabatic carrier (electron and hole) dynamics simulations. To properly consider the influence of excitonic effects on the photoinduced ultrafast processes of the SWCNT-tetraphenyl porphyrin (H2TPP) complex and to further improve the computational efficiency, we developed the nonadiabatic molecular dynamics (NAMD) method based on the extended tight binding-based simplified Tamm-Dancoff approximation (sTDA-xTB), which is applied to study the ultrafast photoinduced dynamics of the noncovalent SWCNT-porphyrin complex. In combination with statically electronic structure calculations, the present work successfully reveals the detailed microscopic mechanism of the ultrafast excitation energy transfer process of the complex. Upon local excitation on the H2TPP molecule, an ultrafast energy transfer process occurs from H2TPP (SWCNT-H2TPP*) to SWCNT (SWCNT*-H2TPP) within 10 fs. Then, two slower processes corresponding to the energy transfer from H2TPP to SWCNT and hole transfer from H2TPP to SWCNT take place in the 1 ps time scale. The sTDA-xTB-based electronic structure calculation and NAMD simulation results not only match the previous experimental observations from static and transient spectra but also provide more insights into the detailed information on the complex's photoinduced dynamics. Therefore, the sTDA-xTB-based NAMD method is a powerful theoretical tool for studying the ultrafast photoinduced dynamics in large extended systems with a large number of electronically excited states, which could be helpful for the subsequent design of SWCNT-based functional materials.

"On-the-Fly" Nonadiabatic Dynamics Simulation on the Ultrafast Photoisomerization of a Molecular Photoswitch Iminothioindoxyl: An RMS-CASPT2 Investigation.

Iminothioindoxyl (ITI) is a new class of photoswitch that exhibits many excellent properties including well-separated absorption bands in the visible region for both conformers, ultrafast Z to E photoisomerization as well as the millisecond reisomerization at room temperature for the E isomer, and switchable ability in both solids and various solvents. However, the underlying ultrafast photoisomerization mechanism at the atomic level remains unclear. In this work, we have employed a combination of high-level RMS-CASPT2-based static electronic structure calculations and nonadiabatic dynamics simulations to investigate the ultrafast photoisomerization dynamics of ITI. Based on the minimum-energy structures, minimum-energy conical intersections, linear interpolation internal coordinate paths, and nonadiabatic dynamics simulations, the overall photoisomerization scenario of ITI upon excitation is established. Upon excitation around 416 nm, the molecule will be excited to the S2 state considering its close energy to the experimentally measured absorption maximum and larger oscillator strength, from which ultrafast decay of S2 to S1 state can take place efficiently with a time constant of 62 fs. However, the photoisomerization is not likely to complete in the S2 state since the dihedral associated with the Z to E isomerization changes little during the relaxation. Upon relaxing to the S1 state, the molecule will decay to the S0 state ultrafast with a time constant of 232 fs. In contrast, the decay of the S1 state is important for the isomerization considering that the dihedral related to the isomerization of the hopping structures is close to 90°. Therefore, the S1/S0 intersection region should be important for the isomerization of ITI. Arriving at the S0 state, the molecule can either go back to the original Z reactant or isomerize to the E products. At the end of the 500 fs simulation time, the E configuration accounts for nearly 37% of the final structures. Moreover, the photoisomerization mechanism is different from the isomerization mechanism in the ground state; i.e., instead of the inversion mechanism in the ground state, the photoisomerization prefers the rotation mechanism. Our results not only agree well with previous experimental studies but also provide some novel insights that could be helpful for future improvements in the performance of the ITI photoswitches.

Perspective on Theoretical and Experimental Advances in Atmospheric Photochemistry.

Research that explores the chemistry of Earth's atmosphere is central to the current understanding of global challenges such as climate change, stratospheric ozone depletion, and poor air quality in urban areas. This research is a synergistic combination of three established domains: earth observation, for example, using satellites, and in situ field measurements; computer modeling of the atmosphere and its chemistry; and laboratory measurements of the properties and reactivity of gas-phase molecules and aerosol particles. The complexity of the interconnected chemical and photochemical reactions which determine the composition of the atmosphere challenges the capacity of laboratory studies to provide the spectroscopic, photochemical, and kinetic data required for computer models. Here, we consider whether predictions from computational chemistry using modern electronic structure theory and nonadiabatic dynamics simulations are becoming sufficiently accurate to supplement quantitative laboratory data for wavelength-dependent absorption cross-sections, photochemical quantum yields, and reaction rate coefficients. Drawing on presentations and discussions from the CECAM workshop on Theoretical and Experimental Advances in Atmospheric Photochemistry held in March 2024, we describe key concepts in the theory of photochemistry, survey the state-of-the-art in computational photochemistry methods, and compare their capabilities with modern experimental laboratory techniques. From such considerations, we offer a perspective on the scope of computational (photo)chemistry methods based on rigorous electronic structure theory to become a fourth core domain of research in atmospheric chemistry.

Consideration of the effect of nanoscale porosity on mass transport phenomena in PECVD coatings

Here we show a novel approach to characterize the gas transfer behavior of silicon-oxide (SiO x ) coatings and explain the underlying dynamics. For this, we investigate the coating on a nm-scale both by measurement and simulation. Positron annihilation spectroscopy (PAS) and quantum mechanical electronic structure-based molecular dynamics simulations are combined to characterize the porous landscape of SiO x coatings. This approach analyses the influence of micropores smaller than 2 nm in diameter on gas permeation which are difficult to study with conventional methods. We lay out the main pore diameter ranges and their associated porosity estimates. An influence of layer growth on pore size and porosity was found, with an increased energy input during layer deposition leading to smaller pore sizes and a reduced porosity. The molecular dynamics simulations quantify the self-diffusion of oxygen and water vapor through those PAS deducted micropore ranges for hydrophilic and hydrophobic systems. The theoretical pore size ranges are fitting to our PAS results and complete them by giving diffusion coefficients. This approach enables detailed analysis of pore morphology on mass transport through thin film coatings and characterization of their barrier or membrane performance. This is a crucial prerequisite for the development of an exhaustive model of pore dominated mass transports in PECVD coatings.

Non-adiabatic dynamics of photoexcited cyclobutanone: Predicting structural measurements from trajectory surface hopping with XMS-CASPT2 simulations.

Over the years, theoretical calculations and scalable computer simulations have complemented ultrafast experiments, as they offer the advantage of overcoming experimental restrictions and having access to the whole dynamics. This synergy between theory and experiment promises to yield a deeper understanding of photochemical processes, offering valuable insights into the behavior of complex systems at the molecular level. However, the ability of theoretical models to predict ultrafast experimental outcomes has remained largely unexplored. In this work, we aim to predict the electron diffraction signals of an upcoming ultrafast photochemical experiment using high-level electronic structure calculations and non-adiabatic dynamics simulations. In particular, we perform trajectory surface hopping with extended multi-state complete active space with second order perturbation simulations for understanding the photodissociation of cyclobutanone (CB) upon excitation at 200nm. Spin-orbit couplings are considered for investigating the role of triplet states. Our simulations capture the bond cleavage after ultrafast relaxation from the 3s Rydberg state, leading to the formation of the previously observed primary photoproducts: CO + cyclopropane/propene (C3 products), ketene, and ethene (C2 products). The ratio of the C3:C2 products is found to be about 1:1. Within 700fs, the majority of trajectories transition to their electronic ground state, with a small fraction conserving the initial cyclobutanone ring structure. We found a minimal influence of triplet states during the early stages of the dynamics, with their significance increasing at later times. We simulate MeV-ultrafast electron diffraction (UED) patterns from our trajectory results, linking the observed features with specific photoproducts and the underlying structural dynamics. Our analysis reveals highly intense features in the UED signals corresponding to the photochemical processes of CB. These features offer valuable insights into the experimental monitoring of ring opening dynamics and the formation of C3 and C2 photoproducts.

A different photochromic mechanism of spirooxadiazine: Electronic structure calculations and nonadiabatic dynamics simulations

Previously, we conducted electronic structure calculations and surface hopping dynamics to investigate the photochromic mechanism of spirooxazine (SO). Herein, a very similar calculation strategy was employed to simulate the excited-state ring-opening, relaxation, and subsequent isomerization of spirooxadiazine (SOD). Interestingly, we discovered a significantly different photochromic behavior compared to SO. Firstly, the bright state of SOD is the S2(ππ*) state, while the S1 state is a weakly absorbing state with a nπ* character. This is in stark contrast to SO, of which the S1 state is a ππ* state. Secondly, we identified a new excited-state decay channel along the C2N3 dissociation within the benzoxadiazine ring, in addition to the closed-loop and C2O7 cleavage relaxation pathways. Thirdly, the out-of-plane hydrogen (HOOP) oscillations were no longer operative in the relaxation processes, as the CH group was replaced by the N atom in SOD. Finally, several nonadiabatic trajectories will lead to the ‘N2 release’ product in the ground state, which might result in deactivation of SOD and affect the light fatigue resistance.

Light-induced electron dynamics of molecules in cavities: comparison of model Hamiltonians

The rapidly expanding field of polaritonic chemistry requires accurate theoretical simulations to understand new phenomena at the atomic scale. Computing the optoelectronic properties of molecules using established electronic structure methods is a careful balance of accuracy and computational expense, and expanding these methods to quantum electrodynamics to describe coupled cavity-molecule systems is an active topic of development. Key to these methods are the Hamiltonian operators representing the photon cavity modes. The recently introduced quantum electrodynamics time-dependent configuration interaction (QED-TDCI) method allows for the combination of electron dynamics simulations with quantum electrodynamics, enabling the simulation of time-dependent optoelectronic properties of cavity-molecule systems. Using this method, a comparison of two many-state QED Hamiltonians—the Pauli-Fierz and quantum Rabi model Hamiltonians—is presented, with a particular focus on time-dependent properties in applied electric fields.

Mechanistic Insights into the Excited-State Intramolecular Proton Transfer (ESIPT) Process of 2-(2-Aminophenyl)naphthalene.

The 2-(2-aminophenyl)naphthalene molecule attracted much attention due to excited-state intramolecular proton transfer (ESIPT) from an amino NH2 group to a carbon atom of an adjacent aromatic ring. The ESIPT mechanisms of 2-(2-aminophenyl)naphthalene are still unclear. Herein, the decay pathways of this molecule in vacuum were investigated by combining static electronic structure calculations and nonadiabatic dynamics simulations. The calculations indicated the existence of two stable structures (S0-1 and S0-2) in the S0 and S1 states. For the S0-1 isomer, upon excitation to the Franck-Condon point, the system relaxed to the S1 minimum quickly, and then there exist four decay pathways (two ESIPT ones and two decay channels with C atom pyramidalization). In the ESIPT decay pathways, the system encounters the S1S0-PT-1 or S1S0-PT-2 conical intersection, which funnels the system rapidly to the S0 state. In the other two pathways, the system de-excited from the S1 to the S0 state via the S1S0-1 or S1S0-2 conical intersection. For the S0-2 structure, the decay pathways were similar to those of S0-1. The dynamics simulations showed that 75 and 69% of trajectories experienced the two ESIPT conical intersections for the S0-1 and S0-2 structures, respectively. Our simulations showed that the lifetime of the S1 state of S0-1 (S0-2) is estimated to be 358 (400) fs. Notably, we not only found the detailed reaction mechanism of the system but also found that the different ground-state configurations of this system have little effect on the reaction mechanism in vacuum.

Photochemical Mechanisms of Hydroxyquinoline Benzimidazole: Insights from Electronic Structure Calculations and Nonadiabatic Dynamics Simulations.

Excited-state intramolecular double proton transfer (ESIDPT) has received much attention because of its widespread existence in the life reactions of living organisms, and materials with this property are significant for their special luminescent properties. In this work, the complete active space self-consistent field (CASSCF) and OM2/multireference configuration interaction (OM2/MRCI) methods have been employed to study the static electronic structure calculations of the photochemistry and the possibility of ESIDPT process of hydroxyquinoline benzimidazole (HQB) molecule, along with the nonadiabatic dynamics simulations. The computational results show that the HQB molecule is relaxed to the S1-ENOL minimum after being excited to the Franck-Condon point in the S1 state. Subsequently, during the nonadiabatic deactivation process, the OH···N proton transfer and the twisting of benzimidazole occur before arriving at the single proton transfer conical intersection S1S0-KETO. Finally, the system can either return to the initial ground-state structure S0-ENOL or to the single proton transfer ground-state structure S0-KETO, both of which have almost the same probability. The dynamics simulations also show that no double proton transfer occurs. The excited-state lifetime of HQB is fitted to 1.1 ps, and only 64% of the dynamic trajectories return to the ground state within the 2.0 ps simulation time. We hope the detailed reaction mechanism of the HQB molecule will provide new insights into similar systems.

Deciphering the Internal Conversion Processes Involved in the Photochemical Ring-Opening of 1,3-Cyclohexadiene by Symmetric sp2-Carbon Substitutions.

Chemical substituents hold the potential to markedly influence the photochemical behavior in molecular systems and assist in gaining a comprehensive understanding of nonadiabatic phenomena. In this study, we have conducted a comparative analysis of the influence of chemical substituents on the photochemical ring-opening of 1,3-cyclohexadiene (CHD), considering four systems: CHD, 2,3-dimethylcyclohexadiene (CHD-Me2-1), 1,4-dimethylcyclohexadiene (CHD-Me2-2), and 1,2,3,4-tetramethylcyclohexadiene (CHD-Me4), using electronic structure theory calculations and nonadiabatic molecular dynamics simulations. Employing extended multistate complete active space second-order perturbation (XMS-CASPT2) theory, we optimized reactants, S1 states, conical intersections (CIns), and products, revealing structural and energetic variations consistent with prior research. Nonadiabatic molecular dynamics simulation was used to gain insights into photochemical dynamics at state-averaged complete active space self-consistent field (SA-CASSCF) theory. CHD-Me4 exhibited reduced carbon-carbon single bond rupture rates, responsible for ring-opening, due to substituent proximity. Further, CHD-Me2-2 and CHD-Me4 displayed prolonged excited-state relaxation times, highlighting notable substituents' impact. Analysis of kinetic energy profiles of specific carbon atoms also revealed restrained atomic displacements, particularly in CHD-Me2-2 and CHD-Me4. These findings advance our understanding of how substituents modulate photochemical reactions in cyclohexadiene derivatives, guiding new molecular design and future research.

Ab initio electron-lattice downfolding: Potential energy landscapes, anharmonicity, and molecular dynamics in charge density wave materials

The interplay of electronic and nuclear degrees of freedom presents an outstanding problem in condensed matter physics and chemistry. Computational challenges arise especially for large systems, long time scales, in nonequilibrium, or in systems with strong correlations. In this work, we show how downfolding approaches facilitate complexity reduction on the electronic side and thereby boost the simulation of electronic properties and nuclear motion-in particular molecular dynamics (MD) simulations. Three different downfolding strategies based on constraining, unscreening, and combinations thereof are benchmarked against full density functional calculations for selected charge density wave (CDW) systems, namely 1H-TaS_22, 1T-TiSe_22, 1H-NbS_22, and a one-dimensional carbon chain. We find that the downfolded models can reproduce potential energy surfaces on supercells accurately and facilitate computational speedup in MD simulations by about five orders of magnitude in comparison to purely ab initio calculations. For monolayer 1H-TaS_22 we report classical and path integral replica exchange MD simulations, revealing the impact of thermal and quantum fluctuations on the CDW transition.

Time propagation of electronic wavefunctions using nonorthogonal determinant expansions.

The use of truncated configuration interaction in real-time time-dependent simulations of electron dynamics provides a balance of computational cost and accuracy, while avoiding some of the failures associated with real-time time-dependent density functional theory. However, low-order truncated configuration interaction also has limitations, such as overestimation of polarizability in configuration interaction singles, even when perturbative doubles are included. Increasing the size of the determinant expansion may not be computationally feasible, and so, in this work, we investigate the use of nonorthogonality in the determinant expansion to establish the extent to which higher-order substitutions can be recovered, providing an improved description of electron dynamics. Model systems are investigated to quantify the extent to which different methods accurately reproduce the (hyper)polarizability, including the high-harmonic generation spectrum of H2, water, and butadiene.

Two-dimensional trilayer heterostructures with cascade dual Z-schemes to achieve efficient hydrogen evolution reaction

Electronic properties and diabatic molecular dynamics simulations reveal that the maximum solar-to-hydrogen efficiency of photocatalytic cascade dual Z-schemes with Bi(InAs3)/HfSeTe/ZrSe2 heterostructures can reach 41.04%.

Molecular Simulation Study of Surface-Enhanced Raman Scattering of Liquid Water.

We developed in our previous study [J. Chem. Phys., 2021, 155, 174118, J. Phys. Chem. A, 2022, 126, 4762] a classical electronic and molecular dynamics simulation method to describe the optical response of metal material in solution based on an atomistic model by incorporating the classical equation of motion for free electrons under an applied electric field. To show further usefulness of the method, in the present study, we apply it to surface-enhanced Raman scattering of liquid water to examine the signal enhancement of the solution system caused by plasmon resonance effects of a silver nanoparticle.

Jellyfish: A modular code for wave function‐based electron dynamics simulations and visualizations on traditional and quantum compute architectures

AbstractUltrafast electron dynamics have made rapid progress in the last few years. With Jellyfish, we now introduce a program suite that enables to perform the entire workflow of an electron‐dynamics simulation. The modular program architecture offers a flexible combination of different propagators, Hamiltonians, basis sets, and more. Jellyfish can be operated by a graphical user interface, which makes it easy to get started for nonspecialist users and gives experienced users a clear overview of the entire functionality. The temporal evolution of a wave function can currently be executed in the time‐dependent configuration interaction method (TDCI) formalism, however, a plugin system facilitates the expansion to other methods and tools without requiring in‐depth knowledge of the program. Currently developed plugins allow to include results from conventional electronic structure calculations as well as the usage and extension of quantum‐compute algorithms for electron dynamics. We present the capabilities of Jellyfish on three examples to showcase the simulation and analysis of light‐driven correlated electron dynamics. The implemented visualization of various densities enables an efficient and detailed analysis for the long‐standing quest of the electron–hole pair formation.This article is categorized under: Theoretical and Physical Chemistry > Spectroscopy Software > Simulation Methods

Multistate Reaction Coordinate Model for Charge and Energy Transfer Dynamics in the Condensed Phase.

Constructing multistate model Hamiltonians from all-atom electronic structure calculations and molecular dynamics simulations is crucial for understanding charge and energy transfer dynamics in complex condensed phases. The most popular two-level system model is the spin-boson Hamiltonian, where the nuclear degrees of freedom are represented as shifted normal modes. Recently, we proposed the general multistate nontrivial extension of the spin-boson model, i.e., the multistate harmonic (MSH) model, which is constructed by extending the spatial dimensions of each nuclear mode so as to satisfy the all-atom reorganization energy restrictions for all pairs of electronic states. In this work, we propose the multistate reaction coordinate (MRC) model with a primary reaction coordinate and secondary bath modes as in the Caldeira-Leggett form but in extended spatial dimensions. The MRC model is proven to be equivalent to the MSH model and offers an intuitive physical picture of the nuclear-electronic feedback in nonadiabatic processes such as the inherent trajectory of the reaction coordinate. The reaction coordinate is represented in extended dimensions, carrying the entire reorganization energies and bilinearly coupled to the secondary bath modes. We demonstrate the MRC model construction for photoinduced charge transfer in an organic photovoltaic caroteniod-porphyrin-C60 molecular triad dissolved in tetrahydrofuran as well as excitation energy transfer in a photosynthetic light-harvesting Fenna-Matthews-Olson complex. The MRC model provides an effective and robust platform for investigating quantum dissipative dynamics in complex condensed-phase systems since it allows a consistent description of realistic spectral density, state-dependent system-bath couplings, and heterogeneous environments due to static disorder in reorganization energies.