Electron Dynamics Research Articles

Constrained Hamiltonian dynamics for electrons in magnetic field and additional forces besides the Lorentz force acting on electrons

Abstract We consider the forces acting on electrons in magnetic field including the constraints and a condition arising from quantum mechanics. The force is calculated as the electron mass, m e , multiplied by the total time-derivative of the velocity field evaluated using the quantum mechanical many-electron wave function. The velocity field includes a term of the Berry connection from the many-body wave function; thereby, quantum mechanical effects are included. It is shown that additional important forces besides the Lorentz force exist; they include the gradient of the electron velocity field kinetic energy, the gradient of the chemical potential, and the ‘force’ for producing topologically protected loop currents. These additional forces are shown to be important in superconductivity, electric current in metallic wires, and charging of capacitors.

Abnormal Relaxation Behavior of Excited Electrons in the Flat Band of Kagome Compound Nb3Cl8.

Carrier dynamics is crucial in semiconductors, and it determines their conductivity, response time, and overall functionality. In flat bands (FBs), carriers with high effective masses are predicted to host unconventional transport properties. The FBs usually overlap with other trivial energy bands, however, making it difficult to accurately distinguish their carrier dynamics. In this paper, we have investigated the flat-band carrier dynamics of excited electrons in Nb3Cl8, which hosts ideal nonoverlapping FBs near the Fermi level. The optical transition between Hubbard bands is abnormally weakened, exhibiting weak interband absorption and its related slow photoresponse with a time constant of ∼120 s, which are associated with flat-band Mottness-induced large electron effective mass and parity-forbidden transitions. Besides, the localized states created by chlorine vacancies also act as trapping centers for carriers with a time constant of ∼600 s, which are similar to those of the compact localized states of the FB, making the relaxation behavior even more extraordinary. The presence and impacts of atomic defects are confirmed experimentally and theoretically. This work has revealed the abnormal flat-band carrier dynamics of Nb3Cl8, which is essential for understanding the optical, electrical, and thermal transport properties of flat-band materials.

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.

Atomic-scale imaging of laser-driven electron dynamics in solids

Resolving laser-driven electron dynamics on their natural time and length scales is essential for understanding and controlling light-induced phenomena. Capabilities to reveal these dynamics are limited by challenges in interpreting wave mixing of a driving and a probe pulse, low energy resolution at ultrashort time scales and a lack of atomic-scale resolution by standard spectroscopic techniques. Here, we demonstrate how ultrafast x-ray diffraction can access fundamental information on laser-driven electronic motion in solids. We propose a method based on subcycle-resolved x-ray-optical wave mixing that allows for a straightforward reconstruction of key properties of strong-field-induced electron dynamics with atomic spatial resolution. Namely, this technique provides both phases and amplitudes of the spatial Fourier transform of optically-induced charge distributions, their temporal behavior, and the direction of the instantaneous microscopic optically-induced electron current flow. It captures the rich microscopic structures and symmetry features of laser-driven electronic charge and current density distributions.

Dynamical channel coupling in strong-field ionization of CO2

We present a theoretical study employing the time-dependent density functional theory (TDDFT) to explore the effects of angle-resolved channel coupling in strong field ionization of carbon dioxide (CO2) molecules. Our results reveal significant angular sensitivity of both the channel-resolved ionization probabilities and the effects of laser-induced channel couplings. By applying a linearly polarized two-color field scheme, we demonstrate the ability to significantly modify the strength of the laser-induced coupling, evidenced by the changes in the population distributions among the ionic states induced by the strong-field ionization. Importantly, the two-color field optimally modulates the coupling strength at the alignment angle where ionization of the highest occupied molecular orbital (HOMO) electrons is most efficient. This optimization is attributed to the reduction of the electron shielding effect. Our research provides valuable insights into the coherent manipulation of electron distribution within the cation, paving the way for the precise control of ultrafast electron dynamics during strong-field ionization processes.

Local and nonlocal conditions for electron runaway in a gas gap with a conical cathode with a variable opening angle

The conditions for the generation of runaway electrons in an air gap are compared at different degrees of inhomogeneity of the electric field distribution provided by varying the opening angle of the conical cathode: in the range 40°–120° in experiments and 0°–180° in calculations. It is demonstrated that, in a weakly inhomogeneous electric field (according to the proposed classification, this corresponds to cones with angles greater than the Taylor angle of 98.6°), the runaway condition has a local character. The transition of free electrons into the runaway mode is determined by the local distribution of the electric field near their starting point—the tip of the cone. The local electric field strength must exceed a threshold value comparable to the strength critical for the runaway of electrons in a uniform field. In a strongly inhomogeneous field (cones with angles less than 98.6°), this condition is not sufficient for electrons to run away throughout the gap. Electrons accelerating in the near-cathode region may begin to slow down in a weak field at a distance from the cathode. In this case, the runaway condition becomes nonlocal. It is determined by the dynamics of electrons in the entire gap, primarily in the near-anode region, and reduces to the requirement that the potential difference applied to the gap exceeds a certain threshold value.

Spontaneous asymmetry effect induced by uniform magnetic fields in capacitively coupled plasmas under perfectly symmetric conditions

Abstract Introducing asymmetry in capacitively coupled plasmas (CCPs) is a common strategy for achieving independent control of ion mean energy and flux. Our 1d3v particle-in-cell/Monte Carlo collision simulations reveal that a uniform magnetic field within a specific range can induce spatial asymmetry in low-pressure CCPs, even under perfectly symmetric conditions. This asymmetry, characterized by a shift in the plasma density distribution and significant differences in electron kinetics between the two sides of the plasma, leads to strong ionization and most electron losses on the low-density side, while the high-density side experiences weak ionization and minimal electron losses. The underlying mechanism triggering this spontaneous asymmetry is the differential influence of the magnetic field on low-energy (local) and high-energy (relatively nonlocal) electrons. Under conditions of low pressure and an appropriate magnetic field, this disparity in electron kinetic behavior leads to a spontaneous amplification of the asymmetry induced by random fluctuations until a steady state is reached, culminating in a spontaneous asymmetric effect.

Electron kinetics near the minimum of Paschen's curves of pulsed breakdown

The main objective of the present paper is the detailed analysis of the electron kinetics near the Paschen's curve minimum of pulsed breakdown of nitrogen gas. Three main questions are to be answered. First, whether the breakdown curve minimum corresponds to the threshold electric field necessary for the runaway electron generation. Second, what is the role of these electrons in the vicinity of the Paschen's curve minimum. Third, what is the ionization cost near the minimum. To answer these questions, the one-dimensional model is used in which electrons are modeled using the Particle-in-Cell approach, while ions are modeled in the drift-diffusion approximation.

Verification of the kinetic electron role in the microinstabilities in a negative triangularity model equilibrium

Effect of kinetic electrons on negative triangularity plasmas has been investigated and compared against the corresponding positive triangularity plasmas, using the global gyrokinetic code X-point Gyrokinetic Code with scale-separated delta-f option without Coulomb collisions. Our model magnetic equilibria have strong positive and negative triangularities and weak magnetic shear. However, unusually large ρi/a and low density plasmas are chosen to maximize the nonlocal effect to investigate the finite ρi effect and to be clearly away from kinetic ballooning modes. Similar conclusions to previous flux tube and global simulations have been obtained in this highly nonlocal model plasma: it is essential to include kinetic electrons in the micro-instability study of negative triangularity plasmas. Most physics findings agree with existing reports, with some disagreement. We offer a new “effective trapping fraction” concept that can add to the explanation of the growth rate difference between NT and PT plasmas, pointing to the significant variation in trapped particle fractions that have turning points in the mode growth regions.

Flare-accelerated Electrons in the Kappa Distribution from X-Ray Spectra with the Warm-target Model

Abstract X-ray observations provide important and valuable insights into the acceleration and propagation of nonthermal electrons during solar flares. Improved X-ray spectral analysis requires a deeper understanding of the dynamics of energetic electrons. Previous studies have demonstrated that the dynamics of accelerated electrons with a few thermal speeds are more complex than those with significantly higher speeds. To better describe the energetic electrons after injection, a model considering energy diffusion and thermalization effects in flare conditions (the warm-target model) has recently been developed for spectral analysis of hard X-rays. This model has demonstrated how the low-energy cutoff, which can hardly be constrained in cold-target modeling, can be determined. However, the power-law form may not be the most suitable representation of injected electrons. The kappa distribution, which is proposed as a physical consequence of electron acceleration, has been applied successfully in RHESSI spectral analysis. In this study, we employ the kappa-form injected electrons in the warm-target model to analyze two M-class flares, observed by RHESSI and the Spectrometer/Telescope for Imaging X-rays, respectively. The best-fit results show that the kappa-form energetic electron spectrum generates lower nonthermal energy than the power-law form when producing a similar photon spectrum in the fit range. We also demonstrated that the fit parameters associated with the kappa-form electron spectrum can be well determined with small uncertainty. Further, the kappa distribution, which covers the entire electron energy range, enables the determination of key electron properties such as total electron number density and average energy at the flare site, providing valuable information on electron acceleration processes.

Rugged magneto-hydrodynamic invariants in weakly collisional plasma turbulence: Two-dimensional hybrid simulation results

Aims. We investigated plasma turbulence in the context of solar wind. We concentrated on properties of ideal second-order magneto-hydrodynamic (MHD) and Hall MHD invariants. Methods. We studied the results of a two-dimensional hybrid simulation of decaying plasma turbulence with an initial large cross helicity and a negligible magnetic helicity. We investigated the evolution of the combined energy and the cross, kinetic, mixed, and magnetic helicities. For the combined (kinetic plus magnetic) energy and the cross, kinetic, and mixed helicities, we analysed the corresponding Kármán-Howarth-Monin (KHM) equation in the hybrid (kinetic proton and fluid electron) approximation. Results. The KHM analysis shows that the combined energy decays at large scales. At intermediate scales, this energy cascades (from large to small scales) via the MHD non-linearity and this cascade partly continues via Hall coupling to sub-ion scales. The cascading combined energy is transferred (dissipated) to the internal energy at small scales via the resistive dissipation and the pressure-strain effect. The Hall term couples the cross helicity with the kinetic one, suggesting that the coupled invariant, referred to here as the mixed helicity, is a relevant turbulence quantity. However, when analysed using the KHM equations, the kinetic and mixed helicities exhibit very dissimilar behaviours to that of the combined energy. On the other hand, the cross helicity, in analogy to the energy, decays at large scales, cascades from large to small scales via the MHD+Hall non-linearity, and is dissipated at small scales via the resistive dissipation and the cross-helicity equivalent of the pressure-strain effect. In contrast to the combined energy, the Hall term is important for the cross helicity over a wide range of scales (even well above ion scales). In contrast, the magnetic helicity is scantily generated through the resistive term and does not exhibit any cascade.

MCEND: an open-source program for quantum electron-nuclear dynamics

The software MCEND (Multi-Configuration Electron-Nuclear Dynamics) is a free open-source program package which simulates the quantum dynamics of electron-nuclei simultaneously for diatomic molecules. Its formulation, implementation, and usage are described in detail. MCEND uses a grid-based basis representation for the nuclei, and the electronic basis is derived from standard electronic structure basis sets on the nuclear grid. The wave function is represented as a sum over products of electronic and nuclear wave functions, thus capturing correlation effects between electrons, nuclei, and electrons and nuclei. The LiH molecule was used as an example for simulating the molecular properties such as the dipole moment and absorption spectrum. Program summaryProgram Title: MCEND, v.2.6.0CPC Library link to program files:https://doi.org/10.17632/tkb9dwf85t.1Developer's repository link:https://github.com/MCEND-hub/MCEND (https://github.com/MCEND-hub/MCEND-library and https://github.com/MCEND-hub/MCEND-tools are git submodules of MCEND)Licensing provisions: MITProgramming language: Fortran 90 and Python 3External routines/libraries: FFTW, OpenMP, BLAS, LAPACK, PSI4, Matplotlib, mendeleev, NumPy, Pandas, SciPy, PyTablesNature of problem: MCEND is to simulate the quantum dynamics of electrons and nuclei simultaneously at multiconfiguration levels.Solution method: The presented program package solves the time-dependent Schrödinger equation with the wave function represented as sum over configuration products using an 8th-order adaptive step size Runge-Kutta ordinary differential equation (ODE) solver. The software can be extended by supplementing modules on the existing infrastructure.

Improved Lifetime Model of Energetic Electrons Due to Their Interactions With Chorus Waves

AbstractChorus waves induce both electron acceleration and loss. In this letter, we provide significantly improved models of electron lifetime due to interactions with chorus waves. The new models fill the gap that previous models have on some magnetic local time (MLT) sectors of the Earth's magnetosphere. This improvement is critical for modeling studies. The lifetime models developed using two different methods are valid for electrons with an energy range from 1 keV to 2 MeV. To facilitate the integration of these new models into different ring current and radiation belt codes, we parameterize the electron lifetime as a function of ‐shell and electron kinetic energy at each MLT and geomagnetic activity (Kp). The parameterized electron lifetimes exhibit strong dependencies on ‐shell, MLT, and energy. Simulations using these new models demonstrate improved agreement with satellite observations compared to simulations using previous models, advancing our understanding of electron dynamics in the magnetosphere.

Electron Pitch Angle Distributions in Magnetotail Tailward Flows

AbstractElectron pitch angle distributions (PADs) are crucial to revealing electron acceleration and heating in geospace. The electron PADs in the Earth's magnetotail have been widely studied by statistical or case analysis. However, the statistical features of electron PADs in tailward flows are still unclear. We survey data from the Magnetospheric Multiscale (MMS) satellite to statistically investigate electron PADs in tailward flows in the Earth's magnetotail for the first time. We find that for most (66.3%) tailward flows, electrons with energy from 0.1 to 30 keV are mainly field‐aligned. The PADs of suprathermal (>2 keV) electrons in a part of tailward flows (26.3%) are mostly isotropic. Additionally, the perpendicular‐dominated PADs of suprathermal electrons only exist in a few (7.4%) tailward flows. According to the different dominant PADs of suprathermal electrons, the tailward flows are classified into three types: field‐aligned‐dominated type, isotropic‐dominated type and perpendicular‐dominated type flows. The dependence of electron PADs on plasma environmental parameters is investigated in these three types of flows. For field‐aligned‐dominated type flows, the field‐aligned anisotropy decreases toward the central plasma sheet (CPS) and with the increase of the energy. In addition, it is found that the field‐aligned anisotropy in the field‐aligned‐dominated tailward flows reduces noticeably when the |Vix| exceeds 800 km/s. In isotropic‐dominated type flows, the field‐aligned anisotropy of electrons with energy ≥10 keV also shows a slight decreasing trend toward the CPS. For perpendicular‐dominated type flows, the perpendicular anisotropy exhibits two non‐monotonic processes, initially increasing and then decreasing with the increase of distance from the CPS; while becomes more evident for higher energy electrons. Our statistical results indicate that in tailward flows, electron anisotropy depends on the distance from the CPS, energy and plasma flow velocity. Tailward flows are associated with the transport of plasma toward the distant tail, and the statistical analysis of electron PADs in these flows can improve our understanding of the related electron dynamics in the magnetotail.

One-step hydrothermal synthesis of ternary heterostructure stannic sulfide - bismuth sulfide - bismuth oxychloride (SnS2-Bi2S3-BiOCl) composite loaded on carbon felt for highly efficient piezocatalytic degradation of organic dyes and antibiotics

The piezoelectric catalysis technique harnesses naturally occurring vibrational energy to remove organic pollutants from water in an environmentally friendly manner. In this study, a ternary heterostructure SnS2-Bi2S3-BiOCl (S-B-B) composite was successfully synthesized via a one-step hydrothermal method and simultaneously deposited on the surface of carbon felt. The S-B-B heterojunction exhibits significantly enhanced piezoelectric catalytic activity compared to SnS2, Bi2S3, and BiOCl, achieving a k value of 2.26 × 10⁻² min⁻¹ and a degradation efficiency of 89.9 % towards methyl orange (MO) dye after 100 min of ultrasonic degradation. This performance is markedly superior to the individual components, with k values of 3.80 × 10⁻⁴ min⁻¹ for SnS2, 1.16 × 10⁻² min⁻¹ for BiOCl, and 1.31 × 10⁻² min⁻¹ for Bi2S3. Moreover, in addition to levofloxacin (LV), it demonstrates high removal efficiency for Congo red (CR), methylene blue (MB), tetracycline hydrochloride (TC-HCl), and sulfanilamide (SN). Furthermore, it can be loaded onto carbon felt for use in piezoelectric catalytic degradation of dyeing wastewater, highlighting its potential for practical applications. Trapping experiments suggest that singlet oxygen non-radicals and hydroxyl radicals play a critical role in the piezocatalytic degradation of organic contaminants. Based on LC-MS results, a possible degradation pathway for MO dye is proposed. Furthermore, DFT calculations confirm electron transfer from Bi2S3 to SnS2 and BiOCl at the interfaces between SnS2/Bi2S3 and BiOCl/Bi2S3. The piezoelectric mechanism of the S-B-B composite is also elucidated, highlighting the interaction and electron dynamics within the heterostructure.

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.

Nonadiabatic Photodynamics of Amantadine and 1-Cyanoadamantane Cations.

Cations of diamondoids and derivatives thereof have recently become the subject of experimental, spectroscopic studies due to their potential role in astrochemistry. In particular, their electronic spectra and photoinduced dynamics trigger great interest. Here, we report on computational investigations of two nitrogen-containing derivatives of the adamantane cation (Ada+, ), the amantadine cation (Ama+, ) and the 1-cyanoadamantane cation (Ada-CN+, C10H15CN+). Specifically, we study electronic (vibrationally resolved) spectra and nonadiabatic molecular dynamics (modeled using the surface hopping approach based on semiempirical electronic structure theory) of these radical cations. The internal conversion time constants as well as reactive relaxation outcomes (cage-opening and hydrogen loss) are compared for the two derivatives and also with the case of Ada+.[29] Remarkably, we find a longer ground-state recovery time for Ada-CN+ than for Ama+ (for the same excitation energy window), despite a smaller excitation energy for the former. Thus, a static energy gap law cannot be used to rationalize nonadiabatic dynamics and excited state lifetimes in this case: Dynamics and details of the couplings between several states play a decisive role.

Effects of Superthermal Plasmas on Hiss Wave‐Driven Scattering Loss of Radiation Belt Electrons

AbstractPlasmaspheric hiss plays an important role in the loss of radiation belt electrons via cyclotron resonant interactions. The cold plasma approximation is widely used in the evaluation of hiss‐driven electron losses, which however can break down during disturbed periods of geomagnetic storms and substorms. The kappa particle velocity distribution, characterized by a pronounced high‐energy tail, is well‐established to model the profile of superthermal plasma under disturbed geomagnetic conditions. In the present study, by calculating the electron bounce‐averaged pitch angle diffusion coefficients with kappa plasma dispersion relations, we investigate the sensitivity of hiss‐induced cyclotron‐resonant electron scattering loss to the spectral index κ under a variety of superthermal plasma conditions. Our results demonstrate that, with increasing κ, the diffusion coefficients of ∼20–100 keV radiation belt electrons significantly decrease at lower pitch angles and increase at higher pitch angles. In contrast, for electrons at higher energies, the diffusion coefficients tend to increase at lower pitch angles and decrease at relatively higher pitch angles. We also find that decrease of L‐shell and increase of α* and temperature anisotropy tend to weaken the hiss‐driven pitch angle scattering efficiency of electrons at energies from tens to hundreds of keV with a dip at ∼30–50 keV, while the scattering of higher energy electrons can be enhanced. This study confirms the important role of superthermal plasmas in the hiss‐driven electron loss processes and should be carefully incorporated in future modeling of radiation belt electron dynamics.

Enhanced Carrier Lifetime and Mobility in Monolayer NbOI2.

The lifetime and mobility of hot carriers are critical parameters for assessing the performance of optoelectronic materials, as they directly impact the response speed and operational efficiency of devices. Combining first-principles calculations with nonadiabatic molecular dynamics (NAMD) simulations, we systematically investigated the electronic properties and carrier dynamics of monolayer NbOI2. Our findings indicate that, at room temperature, this material demonstrates a carrier lifetime of up to ∼13 ns and an electron mobility reaching as high as ∼9 × 103 cm2 V-1 s-1. The low Young's modulus makes it susceptible to deformation under external stress, and we found that the carrier lifetime extends to ∼40 ns under a 4% tensile strain, along with a significant increase in hole mobility. This study elucidates the carrier dynamics in monolayer NbOI2, facilitating its potential application in future flexible optoelectronic devices.

Investigation on the vibrational relaxation and ultrafast electronic dynamics of S1 state in 2,4-difluoroanisole.

Intramolecular vibrational energy redistribution (IVR) has a profound impact on dynamic processes. We have studied two types of IVR processes, restricted and dissipative, and ultrafast dynamics of the S1 state of 2,4-difluoroanisole using time-resolved photoelectron spectroscopy and time-of-flight mass spectroscopy. The restricted IVR occurs in the intermediate regime of 219cm-1 vibrational level, and the dissipative IVR occurs in the statistical regime of 1200cm-1. The lifetimes of IVR processes are measured to be 90 and 11ps, respectively, depending on the internal energies of the S1 state and differ by a factor of eight. Similar subsequent dynamics were observed at two vibrational levels in the S1 state. The population undergoes IVR following the initial excitation and subsequently leaks into a triplet state, accompanied by intersystem crossing within ∼400ps followed by a slower nonradiative relaxation of the triplet state on the nanosecond time scale. Furthermore, the values of 3s and 3px Rydberg states of 2,4-difluoroanisole were experimentally determined to be 5.02 and 6.28eV.