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Electron dynamic

In circumstances where the electron energy bands arc neither completely full nor completely empty, the behavior of individual electrons in the bands will be of interest. This is not the principal area of concern in this text, but it is important to understand electron dynamics because this provides the link between the band properties and electronic properties of solids. [Pg.36]

Consider a Brillouin Zone, such as that defined for CsCl, and an energy band (k), defined within that zone. F urther, imagine a single electron within that band. If its wave function is an energy eigenstate, the time-dependent Schroedingcr equation, Eq. (1-17), tells us that [Pg.36]

The magnitude of the wave function and therefore also the probability density at any point do not change with time. To discuss electron dynamics we must consider linear combinations of energy eigenstates of different energy. The convenient choice is a trave packet. In particular, we construct a packet, using states with wave numbers near ko and parallel to it in the Brillouin Zone  [Pg.36]

Taking the form of i/ from Eqs. (2-1) and (2-3), and treating k — ko as small, a little algebra shows that at t = 0, Oq. (2-8) corresponds to the slate modulated by a gaussian peak centered at r = 0. Furthermore, writing (k) = (ko) + (d /dk) (k — ko), we may sec that the center of the gaussian moves with a velocity [Pg.37]

Thus it is natural to associate this velocity with an electron in the state Indeed, the relation is consistent with the expectation value of the current operator obtained for that state. [Pg.37]


Petek H and Ogawa S 1997 Femtosecond time-resolved two-photon photoemission studies of electron dynamics in metals Prog. Surf. Sc/. 56 239... [Pg.320]

The discussion in the previous sections assumed that the electron dynamics is adiabatic, i.e. the electronic wavefiinction follows the nuclear dynamics and at every nuclear configuration only the lowest energy (or more generally, for excited states, a single) electronic wavefiinction is relevant. This is the Bom-Oppenlieimer approxunation which allows the separation of nuclear and electronic coordinates in the Schrodinger equation. [Pg.2316]

In this minimal END approximation, the electronic basis functions are centered on the average nuclear positions, which are dynamical variables. In the limit of classical nuclei, these are conventional basis functions used in moleculai electronic structure theoiy, and they follow the dynamically changing nuclear positions. As can be seen from the equations of motion discussed above the evolution of the nuclear positions and momenta is governed by Newton-like equations with Hellman-Feynman forces, while the electronic dynamical variables are complex molecular orbital coefficients that follow equations that look like those of the time-dependent Hartree-Fock (TDHF) approximation [24]. The coupling terms in the dynamical metric are the well-known nonadiabatic terms due to the fact that the basis moves with the dynamically changing nuclear positions. [Pg.228]

In order to make END better suited to the application of low energy events it is important to include an explicitly correlated description of the electron dynamics. Therefore multiconfigurational [25] augmentations of the minimal END are under development. [Pg.234]

To properly describe electronic rearrangement and its dependence on both nuclear positions and velocities, it is necessary to develop a time-dependent theory of the electronic dynamics in molecular systems. A very useful approximation in this regard is the time-dependent Hartree-Fock approximation (34). Its combination with the eikonal treatment has been called the Eik/TDHF approximation, and has been implemented for ion-atom collisions.(21, 35-37) Approximations can be systematically developed from time-dependent variational principles.(38-41) These can be stated for wavefunctions and lead to differential equations for time-dependent parameters present in trial wavefunctions. [Pg.319]

This chapter discusses the apphcation of femtosecond lasers to the study of the dynamics of molecular motion, and attempts to portray how a synergic combination of theory and experiment enables the interaction of matter with extremely short bursts of light, and the ultrafast processes that subsequently occur, to be understood in terms of fundamental quantum theory. This is illustrated through consideration of a hierarchy of laser-induced events in molecules in the gas phase and in clusters. A speculative conclusion forecasts developments in new laser techniques, highlighting how the exploitation of ever shorter laser pulses would permit the study and possible manipulation of the nuclear and electronic dynamics in molecules. [Pg.1]

Bonn M, Denzler DN, Eunk S, Wolf M. 2000. Ultrafast electron dynamics at metal surfaces Competition between electron-phonon coupling and hot-electron transport. Phys Rev B 61 1101-1105. [Pg.404]

In all liquids, the free-ion yield increases with the external electric field E. An important feature of the Onsager (1938) theory is that the slope-to-intercept ratio (S/I) of the linear increase of free-ion yield with the field at small values of E is given by e3/2efeB2T2, where is the dielectric constant of the medium, T is its absolute temperature, and e is the magnitude of electronic charge. Remarkably S/I is independent of the electron thermalization distance distribution or other features of electron dynamics in fact, it is free of adjustable parameters. The theoretical value of S/I can be calculated accurately with a known value of the dielectric constant it has been well verified experimentally in a number of liquids, some at different temperatures (Hummel and Allen, 1967 Dodelet et al, 1972 Terlecki and Fiutak, 1972). [Pg.305]

In this section, we present the first experimental evidence of the destructive interference (DI) and the constructive interference (Cl) in a mixed gas of He and Ne, which prove the validity of the method. The observed interference modulation is, as discussed in Sect. 4.2, attributed to the difference between the phases of the intrinsically chirped harmonic pulses from He and Ne, which leads to the novel method for broadband measurement of the harmonic phases and for observing the underlying attosecond electron dynamics. [Pg.69]

Basic electron transfer theory, summarized eompactly by Sutin [8, see also Bertrand, Chapter 1 in this volume], and reviewed in the biological context by Jortner [9], separates the reaction dynamics into nuclear and electronic dynamics. This basic separation is very central to the simplification of a complex dynamical phenomenon, and a few words about the nuclear factors are in order here, before we proceed to the electronic factors. [Pg.51]

Equation (28) is still exact. To introduce the classical-path approximation, we assume that the nuclear dynamics of the system can be described by classical trajectories that is, the position operator x is approximated by its mean value, namely, the trajectory x t). As a consequence, the quantum-mechanical operators of the nuclear dynamics (e.g., Eh (x)) become classical functions that depend parametrically on x t). In the same way, the nuclear wave functions dk x,t) become complex-valued coefficients dk x t),t). As the electronic dynamics is evaluated along the classical path of the nuclei, the approximation thus accounts for the reaction of the quantum DoE to the dynamics of the classical DoF. [Pg.268]

Figure 6 shows the results for the more challenging model. Model IVb, comprising three strongly coupled vibrational modes. Overall, the MFT method is seen to give only a qualitatively correct picture of the electronic dynamics. While the oscillations of the adiabatic population are reproduced quite well for short time, the MFT method predicts an incorrect long-time limit for both electronic populations and fails to reproduce the pronounced recurrence in the diabatic population. In contrast to the results for the electronic dynamics, the MFT is capable of describing the almost undamped coherent vibrational motion of the vibrational modes. [Pg.271]

To summarize, the results presented for five representative examples of nonadiabatic dynamics demonstrate the ability of the MFT method to account for a qualitative description of the dynamics in case of processes involving two electronic states. The origin of the problems to describe the correct long-time relaxation dynamics as well as multi-state processes will be discussed in more detail in Section VI. Despite these problems, it is surprising how this simplest MQC method can describe complex nonadiabatic dynamics. Other related approximate methods such as the quantum-mechanical TDSCF approximation have been found to completely fail to account for the long-time behavior of the electronic dynamics (see Fig. 10). This is because the standard Hartree ansatz in the TDSCF approach neglects all correlations between the dynamical DoF, whereas the ensemble average performed in the MFT treatment accounts for the static correlation of the problem. [Pg.276]

Electron Dynamic Theory - The Bloch wave method... [Pg.153]

Electron dynamic scattering must be considered for the interpretation of experimental diffraction intensities because of the strong electron interaction with matter for a crystal of more than 10 nm thick. For a perfect crystal with a relatively small unit cell, the Bloch wave method is the preferred way to calculate dynamic electron diffraction intensities and exit-wave functions because of its flexibility and accuracy. The multi-slice method or other similar methods are best in case of diffraction from crystals containing defects. A recent description of the multislice method can be found in [8]. [Pg.153]

Electron attachment to O2 has been investigated in supercritical hydrocarbon fluids at densities up to about 10 molecules/cm using the pulsed electric conductivity technique [110], and the results have been explained in terms of the effect of the change in the electron potential energy and the polarization energy of 2 in the medium fluids. In general, electron attachment to O2 is considered to be a convenient probe to explore electron dynamics in the condensed phase. [Pg.131]

This equation is sufficiently valid that it is considered to be a law of electron dynamics. Exceptions exist only for very high values of /iq (see Chap. 10). [Pg.184]

ULTRAFAST AND EFFICIENT CONTROL OE COHERENT ELECTRON DYNAMICS VIA SPODS... [Pg.235]

In Figure 6.2, the SPODS concept for control of photochemical reactions by the steering of electron dynamics is illustrated taking a fully nonperturbative approach including molecular dynamics into account. Experimental results obtained on charge oscillation-controlled molecular excitation are presented in Section 6.6. [Pg.238]

Figure 6.2 Steering of photochemical reactions by coherent control of ultrafast electron dynamics in molecules by shaped femtosecond laser pulses. Ultrafast excitation of electronic target states in molecules launches distinct nuclear dynamics, which eventually lead to specific outcomes of the photochemical reaction. The ability to switch efficiently between different electronic target channels, optimally achieved by turning only a single control knob on the control field, provides an enhanced flexibility in the triggering of photochemical events, such as fragmentation, excited state vibration, and isomerization. Figure 6.2 Steering of photochemical reactions by coherent control of ultrafast electron dynamics in molecules by shaped femtosecond laser pulses. Ultrafast excitation of electronic target states in molecules launches distinct nuclear dynamics, which eventually lead to specific outcomes of the photochemical reaction. The ability to switch efficiently between different electronic target channels, optimally achieved by turning only a single control knob on the control field, provides an enhanced flexibility in the triggering of photochemical events, such as fragmentation, excited state vibration, and isomerization.

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Accounting for Dynamical Electron Correlation An Important Step Towards Accurate Predictions

Analysis of electron dynamics

Boundary conditions electron nuclear dynamics

By Aron Kuppermann and Ravinder Abrol Electron Nuclear Dynamics

CIDEP (Chemically Induced Dynamic Electron

Chemical Induced Dynamic Electron Polarization,

Chemically Induced Dynamic Electron Polarisation

Chemically induced dynamic electron

Chemically induced dynamic electron polarization

Chemically induced dynamic electron polarization CIDEP)

Chemically induced dynamic electron polarization technique

Chemically induced dynamic electron spin

Chemically induced dynamic electron spin polarization

Chemically induced dynamic nuclear electron transfer

Chemically induced dynamic nuclear polarization electron spin resonance

Classical Electron Dynamics

Complex-valued natural orbitals in electron wavepacket dynamics

Coupled dynamics in electronic excitation

Coupling of electronic and nuclear motion in tautomerization dynamics

Cross Sections in Electron-Nuclear Dynamics

Direct molecular dynamics electronic states

Dynamic electron correlation

Dynamic electron correlation energy

Dynamic electron correlation energy accurate estimation method

Dynamic electron correlation energy orbitals

Dynamic electron microscopy in controlled environments

Dynamic electron polarization

Dynamic electron-pair formation

Dynamic mechanical properties electron microscopy

Dynamical electron correlation

Dynamical electron correlation nondynamical

Dynamical electronic polarizability tensor

Dynamical method Electron Nuclear Double Resonance

Dynamics electron transfer across

Dynamics in the electron-nuclear quantum-classical mixed representation

Dynamics of crystal electrons

Dynamics of electron transfer

Dynamics of electrons

Dynamics, electron transfer pathways

ELECTRON PARAMAGNETIC RESONANCE SPECTROSCOPY AND HEMICALLY INDUCED DYNAMIC NUCLEAR POLARIZATION

Electron Dynamics in Laser Fields

Electron and Energy Transfer Dynamics

Electron and Energy Transfer Dynamics of Adsorbed Monolayers

Electron and nucleus dynamics tracked with pulse train in time-resolved photoelectron spectroscopy

Electron density quantum fluid dynamics

Electron dynamical

Electron dynamical solvent effect

Electron dynamics adsorbate states

Electron dynamics image-potential states

Electron dynamics in dimerization process

Electron dynamics in double proton transfer

Electron dynamics semiconductor surface states

Electron dynamics, at surfaces

Electron dynamics, local control theory

Electron dynamics, photodetachment

Electron medium dynamics controlled

Electron nuclear dynamics

Electron nuclear dynamics , final-state

Electron nuclear dynamics , molecular

Electron nuclear dynamics , molecular function

Electron nuclear dynamics , molecular systems

Electron nuclear dynamics , molecular systems, final-state analysis

Electron nuclear dynamics , molecular systems, reactive collisions

Electron nuclear dynamics , theoretical

Electron nuclear dynamics , theoretical background

Electron nuclear dynamics formalism

Electron nuclear dynamics format

Electron nuclear dynamics general reactions

Electron nuclear dynamics intramolecular transfer

Electron nuclear dynamics permutational symmetry

Electron nuclear dynamics properties

Electron nuclear dynamics structural properties

Electron nuclear dynamics theoretical considerations

Electron nuclear dynamics, research

Electron paramagnetic resonance dynamic susceptibility

Electron paramagnetic resonance dynamical effects

Electron spin dynamics

Electron transfer direct molecular dynamics

Electron transfer polypeptides, dynamics

Electron transfer rates protein dynamics

Electron transfer, nonadiabatic chemical dynamics

Electron transport dynamics

Electron-exchange reactions molecular dynamics

Electron-proton transfer, dynamics

Electron-transfer dynamics

Electron-transfer dynamics absorption spectroscopy

Electron-transfer dynamics fluorescence

Electronic magnetic moments, chemically induced dynamic nuclear polarization

Electronic nonadiabatic dynamics

Electronic states nuclear dynamics

Electronic states triatomic quantum reaction dynamics

Electronic states, quantum reaction dynamics

Electronic structure methods dynamics

Electronic structure theory, electron nuclear dynamics

Electronic structure tight-binding molecular dynamics

Electronically non-adiabatic effects in the adsorption dynamics

Electronics nonlinear dynamics

Electrons hydration dynamics

Englman and A. Yahalom Quantum Reaction Dynamics for Multiple Electronic States

Excited-state dynamics, time-resolved electronic relaxation

Final-state analysis, electron nuclear dynamics

Formalisms for the Explicit Inclusion of Electronic Polarizability in Molecular Modeling and Dynamics Studies

Free electrons, electron nuclear dynamics

Free electrons, electron nuclear dynamics principle

Hartree Fock electron nuclear dynamics

Heterogeneous electron transfer dynamics

Hot electron and hole cooling dynamics in quantum-confined

Hydrated electron relaxation dynamics

Induced Dynamic Electron Spin Polarization (CIDEP)

Intramolecular nuclear and electronic dynamics

Many-body, generally electron dynamics

Many-body, generally electron dynamics methods

Many-body, generally electron dynamics problems

Marcus electron transfer theory dynamics

Marcus theory, electron nuclear dynamics

Minimal electron nuclear dynamics

Modulation of Electron Transfer Dynamics by Electric Fields

Molecular dynamics electronic temperature algorithm

Molecular dynamics multiple states electronic structure

Molecular dynamics with electronic friction

New understanding of defect mechanisms in oxidation catalysis from dynamic electron microscopy

Non dynamic electron correlation

Non-dynamical electron correlation

Nonadiabatic Electron Wavepacket Dynamics in Path-branching Representation

Nonadiabatic dynamics electronic continua

Nonadiabatic dynamics of hydrated electron

Nonadiabatic electron dynamics

Nuclear dynamics electronic wave function

Protein dynamics electron microscopy

Quantities characterizing the electron dynamics

Quantum reaction dynamics, electronic

Quantum reaction dynamics, electronic analysis

Quantum reaction dynamics, electronic states adiabatic representation

Quantum reaction dynamics, electronic states equation

Quantum reaction dynamics, electronic states nuclear motion Schrodinger equation

Radical pair mechanism, chemically induced dynamic electron polarization

Reactive collisions, electron nuclear dynamics

Real-time dynamics of electron migration in a model water cluster anion system

Relaxation time, solvent dynamic effect electron transfer

Rovibrational states, electron nuclear dynamics

Rovibrational states, electron nuclear dynamics analysis

Schrodinger equation electron nuclear dynamics

Solvated electron dynamics

Solvent-controlled electron transfer dynamic

Subject electron dynamics

The Dynamics of Electron Transfer (Kinetics and Thermodynamics)

The Dynamics of Electronically Adiabatic Collisions

Time evolution electron nuclear dynamics

Time-dependent equation electron nuclear dynamics

Time-dependent molecular theory electron nuclear dynamics

Time-resolved chemically induced dynamic electron polarization

Ultrafast dynamics electronic structure

Ultrafast electron dynamics

Wave function electron nuclear dynamics

Wavepacket Dynamics of Hydrogen Bonds in the Electronic Ground State

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