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Electronic potentials

The first reliable energy band theories were based on a powerfiil approximation, call the pseudopotential approximation. Within this approximation, the all-electron potential corresponding to interaction of a valence electron with the iimer, core electrons and the nucleus is replaced by a pseudopotential. The pseudopotential reproduces only the properties of the outer electrons. There are rigorous theorems such as the Phillips-Kleinman cancellation theorem that can be used to justify the pseudopotential model [2, 3, 26]. The Phillips-Kleimnan cancellation theorem states that the orthogonality requirement of the valence states to the core states can be described by an effective repulsive... [Pg.108]

Most TB approaches are not charge self-consistent. This means that they do not ensure that the charge derived from the wavefiinctions yields the effective potential assumed in their calculation. Some methods have been developed which yield charge densities consistent with the electronic potential [14, H and 16]. [Pg.2204]

The pseudopotential is derived from an all-electron SIC-LDA atomic potential. The relaxation correction takes into account the relaxation of the electronic system upon the excitation of an electron [44]- The authors speculate that ... the ability of the SIRC potential to produce considerably better band structures than DFT-LDA may reflect an extra nonlocality in the SIRC pseudopotential, related to the nonlocality or orbital dependence in the SIC all-electron potential. In addition, it may mimic some of the energy and the non-local space dependence of the self-energy operator occurring in the GW approximation of the electronic many body problem [45]. [Pg.2209]

In the following, we shall demonstrate techniques for calculating the electronic potential energy terms up to the second order. For simplicity, we shall study the case of H2 molecule, the simplest multi-electron diatomic molecule. [Pg.406]

How is electronic potential energy computed Electrons, which are more than three orders of magnitude lighter than nuclei, are too small for classical mechanics calculations. Electronic energy must... [Pg.32]

The Extended Hiickel method, for example, does not explicitly consider the effects of electron-electron repulsions but incorporates repulsions into a single-electron potential. This simplifies the solution of the Schrodinger equation and allows HyperChem to compute the potential energy as the sum of the energies for each electron. [Pg.34]

Rapid-Scan Corrosion Behavior Diagram (CBD) Basically, all the same equipment used in the conductance of an ASTM G5 slow-scan polarization study is used for rapid-scan CBDs (that is, a standard test cell, potentiostat, voltmeters, log converters, X-Y recorders, and electronic potential scanning devices). The differences... [Pg.2431]

Thus, the effective electron potential at site Ry consists of two terms site-independent average potential V(r) and an addition connected with spin polarization, AV (r). [Pg.140]

The last term in Eq. 11.47 gives apparently the "average one-electron potential we were asking for in Eq. 11.40. The Hartree-Fock equations (Eq. 11.46) are mathematically complicated nonlinear integro-differential equations which are solved by Hartree s iterative self-consistent field (SCF) procedure. [Pg.226]

One basic reason which made the absolute electron potential problem so complicated to solve in aqueous electrochemistry is the experimental difficulty of measuring work functions on metal surfaces covered with liquid films or in contact with liquids and their vapours. [Pg.333]

Trasatti14 16 has done a very thorough and lucid work in clarifying the concept of absolute electrode potentials in aqueous electrochemistry. He has pointed out that at least four different absolute, or single , electron potentials can be defined, depending on the choice of the reference state of electrons. [Pg.334]

Figure 7.1. Definition of absolute electron potential in aqueous electrochemistry according to Trasatti16 in a classical (a) and liquid covered (b) electrode geometry. Point C corresponds to the zero energy level. O0 is the work function of the bare electrode surface and AC>(=eA P) is the work function modification induced by the presence of the electrolyte layer (b). Reprinted with permission from Elsevier Science. Figure 7.1. Definition of absolute electron potential in aqueous electrochemistry according to Trasatti16 in a classical (a) and liquid covered (b) electrode geometry. Point C corresponds to the zero energy level. O0 is the work function of the bare electrode surface and AC>(=eA P) is the work function modification induced by the presence of the electrolyte layer (b). Reprinted with permission from Elsevier Science.
The same conceptional approach used in aqueous electrochemistry to define "absolute electron potentials can be used in solid state electrochemistry. Thus if one chooses as the zero level an electron just outside the solid electrolyte surface, which has been shown14-16 by Trasatti to be the most realistic choice in aqueous electrochemistry, one has ... [Pg.351]

Thus the absolute electron potential Uw(abs) in solid state electrochemistry can indeed be simply defined by the equation ... [Pg.352]

The adiabatic electronic potential energy surfaces (a function of both nuclear geometry and electric field) are obtained by solving the following electronic eigenvalue equation... [Pg.58]

The hrst step in theoretical predictions of pathway branching are electronic structure ab initio) calculations to define at least the lowest Born-Oppenheimer electronic potential energy surface for a system. For a system of N atoms, the PES has (iN — 6) dimensions, and is denoted V Ri,R2, - , RiN-6)- At a minimum, the energy, geometry, and vibrational frequencies of stationary points (i.e., asymptotes, wells, and saddle points where dV/dRi = 0) of the potential surface must be calculated. For the statistical methods described in Section IV.B, information on other areas of the potential are generally not needed. However, it must be stressed that failure to locate relevant stationary points may lead to omission of valid pathways. For this reason, as wide a search as practicable must be made through configuration space to ensure that the PES is sufficiently complete. Furthermore, a search only of stationary points will not treat pathways that avoid transition states. [Pg.225]

As for the theoretical treatment, we could only try to include the eleetrostatie solute-solvent interaetions and, in faet, we corrected the electronic potential energies for the solvation effeets by simply adding as calculated according to the solvaton model [eq. (2)]. The resulting potential curves are to be seen as effective potentials at equilibrium, i.e. refleeting orientational equilibrium distributions of the solvent dipoles around the eharged atoms of the solute molecule. In principle, the use of potentials thus corrected involves the assumption that solvent equilibration is more rapid than internal rotation of the solute molecule. Fig. 4 points out the effects produced on the potential... [Pg.389]

When inserting into (4.5), the term ZeR will be multiplied with the elements of the electric field gradient tensor V. Fortunately, the procedure can be restricted to diagonal elements Vu, because V is symmetric and, consequently, a principal axes system exists in which the nondiagonal elements vanish, = 0. The diagonal elements can be determined by using Poisson s differential equation for the electronic potential at point r = 0 with charge density (0), AV = Anp, which yields... [Pg.76]

Perturbation terms in the Hamiltonian operator up to still lead to the uncoupling of the nuclear and electronic motions, but change the form of the electronic potential energy funetion in the equation for the nuclear motion. Rather than present the details of the Bom-Oppenheimer perturbation expansion, we follow instead the equivalent, but more elegant procedure of M. Bom and K. Huang (1954). [Pg.266]

The electronic potential energy is due to the attraction between the positive nuclei and the negative electrons, which can be expressed as ... [Pg.4]


See other pages where Electronic potentials is mentioned: [Pg.714]    [Pg.109]    [Pg.1179]    [Pg.1210]    [Pg.2181]    [Pg.2293]    [Pg.129]    [Pg.400]    [Pg.32]    [Pg.352]    [Pg.32]    [Pg.357]    [Pg.337]    [Pg.139]    [Pg.212]    [Pg.479]    [Pg.34]    [Pg.218]    [Pg.11]    [Pg.59]    [Pg.60]    [Pg.192]    [Pg.283]    [Pg.101]    [Pg.144]    [Pg.66]    [Pg.390]    [Pg.444]    [Pg.227]   
See also in sourсe #XX -- [ Pg.4 , Pg.2722 ]




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1- -ethanone one-electron reduction potential

AEAPS (Auger electron appearance potential

Adiabatic electron potential

Adiabatic vector potential, electronic

Adiabatic vector potential, electronic geometric phase factors

And one-electron reduction potential

Appearance potential electron impact

Auger electron appearance potential

Auger electron appearance potential spectroscopy

Auger electron appearance potential spectroscopy, AEAPS

Availability of Electron Acceptors with Higher Reduction Potentials

Bond critical point electronic potential energy density

Bonding electrons, ionization potential

Born-Oppenheimer electronic potential energy

Born-Oppenheimer separation, electronic potential

Chemical potential of electron

Chemistry without potential energy surfaces Highly quasi-degenerate electronic states

Corrosion process electronic electrode potential

Coulomb potential between electrons

Coulomb potential, electronic kinetic

Coulomb potential, electronic kinetic energy

Coulomb potentials electron emission

Coulomb potentials electron transfer

Coupled Electron Pair Approximation potential energy surfaces

Current-potential relationship for steady-state electron transfer

Density functional theory electronic chemical potential

Dichlorocarbene, electronic structure electrostatic potential map

Dirac Electron in External Electromagnetic Potentials

Electrochemical potential of electron

Electrode Potential, E, and the Rate Equations for Electron Transfer Reactions

Electrode potential in electron transfer equilibrium

Electrode potential multiple electron transfer

Electrode potentials of mitochondrial electron carriers

Electromagnetic potentials due to a moving electron

Electron Affinities and Half-Wave Reduction Potentials

Electron Affinities and Ionization Potentials of Aromatic Hydrocarbons

Electron Affinities from Reduction Potentials

Electron Affinities from Reduction Potentials and CURES-EC

Electron Affinities of Biological Molecules from Reduction Potentials

Electron Appearance Potential Fine

Electron Appearance Potential Fine Structure

Electron Configurations. Ionization Potentials

Electron Density and the External Potentials

Electron Potential, pe

Electron Transfer Processes Redox Potentials

Electron Transport Creates an Electrochemical Potential Gradient for Protons across the Inner Membrane

Electron acceptors reduction potentials

Electron affinities, standard potentials

Electron affinity potential energy curves

Electron affinity potential energy surfaces

Electron correlation potential energy surfaces

Electron density distributions electrostatic potential calculations

Electron density electrostatic potential

Electron density relativistic effective core potentials

Electron detachment potential

Electron dynamics image-potential states

Electron electrochemical potential

Electron in a Potential Rectangular Box k-Space

Electron ionisation potential

Electron overlap potential, work

Electron potential energy diagram

Electron potential in metals

Electron self-energy potential expansion

Electron spectroscopy potential energy surface

Electron transfer complex reduction potential values

Electron transfer equilibrium potential

Electron transfer potential energy description

Electron transfer proteins reduction potentials

Electron transfer redox potential control

Electron transfer reduction potential values

Electron transport chain observed potential

Electron transport chain potentials

Electron transport chain redox potential

Electron transport chain reduction potentials

Electron transport chain standard redox potential

Electron-ion potential

Electron-neutral species interaction potentials

Electron-nuclear potential

Electron-transfer reactions redox potentials

Electron-transfer standard electrode potentials

Electronic Structure. Ionization Potential. Dipole Moment

Electronic Structure. Potential Energy Functions

Electronic chemical potential

Electronic chemical potential configuration

Electronic chemical potential energy

Electronic chemical potential levels

Electronic chemical potential states

Electronic chemical potential terms

Electronic chemical potential transition

Electronic chemical potential, 353 methods

Electronic conductivity potentials

Electronic electrode potential

Electronic energy potential

Electronic geometric phase factors potential

Electronic ionization potential

Electronic potential barrier

Electronic potential energy diagram

Electronic potential energy, total

Electronic potential energy, total molecule

Electronic potentials hypersurfaces

Electronic state potentials

Electronic structure full-potential methods

Electronic structure molecular potential energy surfaces

Electronic wave functions Electron-repulsion potentials

Electronically excited molecules potential energy diagram

Electrons chemical potential

Electrons in a Central Potential

Electrons in crystal potential

Electrons potential

Electrons scattering potentials

Electrostatic potential, molecular interactive electronic charge distributions

Electrostatic potential, molecular interactive electronic density function

Energy derivatives, electron number chemical potential

Energy derivatives, electron number ionization potential

Equilibrium potential of electron transfer reactions

Excitation energy, ionization potential, and electron affinity (RHF approach)

General Form of One-Electron Orbitals in Periodic Potentials— Blochs Theorem

Grounded electronic state potential energy surface, vibrational

H2 the Electronic Potential Energy

Heterogeneous electron transfer potential-dependent

Hydrated electron, reduction potentials

Interaction between electrons, effective potential

Ionic Binding Energies, Ionization Potentials, and Electron Affinity

Ionisation Potentials, Electron Affinities and Koopmans Theorem

Ionization potential and electron affinity

Ionization potential and electron affinity (Koopmans rule)

Ionization potential electron affinity, relationship between

Ionization potentials electron donors

Ionization potentials valence electron

Ionization potentials, electron affinities and stabilities of oxidation states

Irreversible electron transfer, totally, potential

Local reactivity indexes electronic chemical potential

Many-electron local potential

Many-electron local potential calculation

Mitochondrial electron carriers electrode potentials of, table

Molecules electronic potential energy

Naphthalene electron affinity and ionization potential

Nonlocal charge-density electronic potential energy

One-electron oxidation potential

One-electron redox potentials

One-electron reduction potential

Operator transfer, potential exchange-electron

Oxidation potentials electron donors

Oxidative phosphorylation electron-transfer potential

Oxygen ions, electron affinity ionization potential

Pair potentials free electron

Periodic potential electronic levels

Positron-electron correlation potential

Potential Energy Curves from Electronic Band Spectra

Potential Energy Surfaces for Ground-State Electron Transfer. Relation to Photochemistry Nonadiabatic Chemistry

Potential Relation for Electron Transfer at the Electrode

Potential acting on an electron

Potential acting on an electron in a molecule

Potential and Electron Affinity of Buckminsterfullerene

Potential averaged electron

Potential due to electron transfer reaction

Potential electron energy density

Potential electron transfer

Potential electron transfer, role

Potential energy curves electron transfer

Potential energy curves electronic excitation

Potential energy curves for two electronic states

Potential energy curves in excited electronic states

Potential energy curves, electronic structure

Potential energy diagram electronic transitions

Potential energy electron

Potential energy electron-nuclear

Potential energy many-electron atom

Potential energy of electrons

Potential energy surface electron-transfer

Potential energy surface electronic spectroscopy

Potential energy surface electronic structure, global surfaces

Potential energy surfaces electronic structure methods

Potential energy surfaces electronically adiabatic

Potential energy symmetrical electron transfer

Potential parameters free-electron

Potential, centrifugal electron-nuclear

Potential, one-electron

Potential-energy surface electronic states

Potential-energy surfaces electronic factor

Potential. Electron Affinity

Potential. Electron Affinity. Polarizability

Potentials and Electron Affinities

Quantum free-electron theory, constant-potential

Real potential of electron

Redox coenzymes potential electron transport chain

Redox potential, hydrated electron

Redox potentials of electron transfer

Reduction potentials electron-transfer oxidation

Reduction potentials mitochondrial electron-transfer chain

Relativistic effective core potentials molecular properties, electron density

Relativistic electron in a local, central potential

Scattering potentials, electron spin-0 particle

Solutions, electrochemical potential electrons

Solvated electron standard oxidation potential

Standard electrochemical potential electron

Standard potential hydrated electron

States electron image potential

Surface electron potential

Surface potential electron accumulation layer

Surface potential electron affinity

Surface potentials, scanning electron microscopy

The Electronic Structure-Based Explicit Polarization (X-Pol) Potential

The Hydrated Electron and Absolute Values of Reduction Potentials

The Surface Electron Potential

Two-electron potential

Two-electron potential energy

Vibrational potential energy electron transfer

Vinylic carbocation, electronic electrostatic potential map

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