Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Electronic models

Arguments based on a free electron model can be made to explain the conductivity of a metal. It can be shown that the k will evolve following a Newtonian law [1] ... [Pg.127]

Another important accomplislnnent of the free electron model concerns tire heat capacity of a metal. At low temperatures, the heat capacity of a metal goes linearly with the temperature and vanishes at absolute zero. This behaviour is in contrast with classical statistical mechanics. According to classical theories, the equipartition theory predicts that a free particle should have a heat capacity of where is the Boltzmann constant. An ideal gas has a heat capacity consistent with tliis value. The electrical conductivity of a metal suggests that the conduction electrons behave like free particles and might also have a heat capacity of 3/fg,... [Pg.128]

The resolution of this issue is based on the application of the Pauli exclusion principle and Femii-Dirac statistics. From the free electron model, the total electronic energy, U, can be written as... [Pg.128]

Simple metals like alkalis, or ones with only s and p valence electrons, can often be described by a free electron gas model, whereas transition metals and rare earth metals which have d and f valence electrons camiot. Transition metal and rare earth metals do not have energy band structures which resemble free electron models. The fonned bonds from d and f states often have some strong covalent character. This character strongly modulates the free-electron-like bands. [Pg.129]

In collaboration with Wavefunction we have created a cross function CD ROM that contains an electronic model building kit and a rich collection of molecular models that reveal the interplay between electronic struc ture and reactivity m organic chemistry... [Pg.1332]

Cl calculations can be used to improve the quality of the wave-function and state energies. Self-consistent field (SCF) level calculations are based on the one-electron model, wherein each electron moves in the average field created by the other n-1 electrons in the molecule. Actually, electrons interact instantaneously and therefore have a natural tendency to avoid each other beyond the requirements of the Exclusion Principle. This correlation results in a lower average interelectronic repulsion and thus a lower state energy. The difference between electronic energies calculated at the SCF level versus the exact nonrelativistic energies is the correlation energy. [Pg.38]

In addition to dielectric property determinations, one also can measure valence electron densities from the low-loss spectrum. Using the simple free electron model one can show that the bulk plasmon energy E is governed by the equation ... [Pg.140]

The physical description of strongly pressure dependent magnetic properties is the object of considerable study. Edwards and Bartel [74E01] have performed the more recent physical evaluation of strong pressure and composition dependence of magnetization in their work on cobalt and manganese substituted invars. Their work contrasts models based on a localized-electron model with a modified Zener model in which both localized- and itinerant-electron effects are incorporated in a unified model. Their work favors the latter model. [Pg.122]

Imagine a model hydrogen molecule with non-interacting electrons, such that their Coulomb repulsion is zero. Each electron in our model still has kinetic energy and is still attracted to both nuclei, but the electron motions are completely independent of each other because the electron-electron interaction term is zero. We would, therefore, expect that the electronic wavefunction for the pair of electrons would be a product of the wavefunctions for two independent electrons in H2+ (Figure 4.1), which I will write X(rO and F(r2). Thus X(ri) and T(r2) are molecular orbitals which describe independently the two electrons in our non-interacting electron model. [Pg.87]

One of the earliest models for treating conjugated molecules is afforded by the Hiickel rr-electron model. This dates from the work of E. Hiickel in 1931. The ideas are simple and appealing, and the model enjoyed many years of successful application to individual molecules, molecular clusters and solids. [Pg.122]

In the Hiickel TT-electron model, ethene is a two-electron problem. 1 have numbered the carbon atoms C and Cj, and X is centred on Ci with X2 on Cj. The HF matrix becomes... [Pg.124]

Notice molecular symmetry at work. The Huckel rr-electron model is in many ways a blunt instrument, because we would get exactly the same answers for either of the following possible conformers of hexatriene (Figure 7.3). [Pg.125]

The Huckel rr-electron model uses information about what is bonded to what (i.e. the connectivity) but does not cater for molecular geometries. [Pg.125]

How does the Hiickel ff-electron model deal with pyridine Nitrogen is more electronegative than carbon, so the N atom ought to have a higher (more negative) T-electron charge than a carbon atom in benzene. It is conventional to write the heteroatom (X and Y are used to denote heteroatoms such as N and O) parameters in terms of the standard ac and yScc... [Pg.128]

The Extended Hiickel model treats all valence electrons within the spirit of the TT-electron model. Each molecular orbital is written as an LCAO expansion of the valence orbitals, which can be thought of as being Slater-type orbitals (to look ahead to Chapter 9). Slater-type orbitals are very similar to hydrogenic ones except that they do not have radial nodes. Once again we can understand the model best by considering the HF-LCAO equations... [Pg.130]

The next step came in the 1950s, with more serious attempts to include formally the effect of electron repulsion between the valence electrons. First came the jT-electron models associated with the name of Pople, and with Pariser and Parr. You might like to read the synopses of their first papers. [Pg.136]

In the TT-electron theories, each first-row atom contributes a single basis function. For the all valence electron models there is now an additional complication in at some of the basis functions could be on the same atomic centre. So how should we treat integrals involving basis functions all on the same atomic centre such as... [Pg.145]

It is traditional to divide quantum-mechanical molecular models into three broad bands depending on their degree of sophistication. There are sublevels within each band, and a great deal of jargon accompanied by acronyms. Many authors speak of the level of theory . The Hiickel independent electron model of Chapter 7 typifies the lowest level of theory, and authors sometimes refer to these models as empirical . The Hamiltonian is not rigorously defined, and neither are the basis functions. Nevertheless, these models have been able to produce impressive predictions and rationalizations. [Pg.173]

Slater s Xa method is now regarded as so much history, but it gave an important stepping stone towards modem density functional theory. In Chapter 12, I discussed the free-electron model of the conduction electrons in a solid. The electrons were assumed to occupy a volume of space that we identified with the dimensions of the metal under smdy, and the electrons were taken to be non-interacting. [Pg.221]

Electrons do of course interact with each other through their mutual Coulomb electrostatic potential, so an alternative step to greater sophistication might be to allow electron repulsion into the free-electron model. We therefore start again from the free-electron model but allow for the Coulomb repulsion between the electrons. We don t worry about the fermion nature of electrons at this point. [Pg.221]

NEW Spartan Model Electronic Modeling Kit, A set of easy-to-use builders allow for the construction and 3-D manipulation of molecules of any size or complexity— from a hydrogen atom to DNA and everything in between. This kit includes the SpartanModel software on CD-ROM, an extensive molecular database, 3-D glasses, and a Tutorial and Users Guide that includes a wealth of activities to help you get the most out of your course. (0-495-01793-0)... [Pg.1340]

The new quantum mechanics contradicts this independent electron model as it is often called. In Heisenberg s formulation of quantum mechanics the fundamental equation is,... [Pg.26]

It is difficult to point to the basic reason why the average-potential model is not better applicable to metallic solutions. Shimoji60 believes that a Lennard-Jones 6-12 potential is not adequate for metals and that a Morse potential would give better results when incorporated in the same kind of model. On the other hand, it is possible that the main trouble is that metal solutions do not obey a theorem of corresponding states. More specifically, the interaction eAB(r) may not be expressible by the same function as for the pure components because the solute is so strongly modified by the solvent. This point of view is supported by considerations of the electronic models of metal solutions.46 The idea that the solvent strongly modifies the solute metal is reached also through a consideration of the quasi-chemical theory applied to dilute solutions. This is the topic that we consider next. [Pg.137]

Araki, G., and Araki, H., Progr. Theoret. Phys. [Kyoto) 11, 20, Interaction between electrons in one-dimensional free-electron model with application to absorption spectra of cyanine dyes. ... [Pg.337]

A Del Electronics, Model ESP-100A, electrostatic precipitator was used for sample collection. Cigarette smoke particles were found to give approx the same particle distribution pattern on the collection filter paper as the gunshot residue, and since the smoke stains the paper, this provided a v rapid technique for optimizing operation conditions. With a flow rate of 15cfm and a corona current of 125 uA, the residue collects primarily on a narrow band across the sample paper. Samples were collected on Whatman No 1541 filter paper which lined the inside of the sample collection tube. The presence of this paper allowed air to flow only thru the center of the tube, so particle collection was made upon the filter paper exclusively. The filter paper samples were pelletized prior to neutron activation analysis... [Pg.376]

The spectrometer was a Physical Electronics Model 548 modified for emplacement in a glovebox so that actinide samples could be examined. Spectra were taken using AIK radiation (1486.6 eV). The overall energy resolution of tne spectrometer was 1.2 eV using an analyzer pass energy of 25 eV. The spectrometer control was interfaced to a Nicolet 1180 minicomputer providing automatic data acquisition and analysis capability. [Pg.149]

The relevant Hamiltonian for the gas-phase solute molecules can be treated by the same three-orbitals four-electron model used in Chapter 2. Since the energy of 3 is much higher than that of , and d>2 (see Table 2.4), we represent the system by its two lowest energy resonance structures, using now the notation fa and fa as is done in eq. (2.40). The energies of these two effective configurations are now written as... [Pg.84]

The Lewis model of the chemical bond assumes that each bonding electron pair is located between the two bonded atoms—it is a localized electron model. However, we know from the wave-particle duality of the electron (Sections 1.5-1.7) that the location of an electron in an atom cannot be described in terms of a precise position, but only in terms of the probability of finding it somewhere in a region of... [Pg.229]


See other pages where Electronic models is mentioned: [Pg.38]    [Pg.1258]    [Pg.286]    [Pg.1258]    [Pg.87]    [Pg.122]    [Pg.136]    [Pg.144]    [Pg.313]    [Pg.362]    [Pg.567]    [Pg.43]    [Pg.332]    [Pg.20]    [Pg.158]    [Pg.184]   
See also in sourсe #XX -- [ Pg.452 , Pg.455 ]

See also in sourсe #XX -- [ Pg.735 ]

See also in sourсe #XX -- [ Pg.283 ]

See also in sourсe #XX -- [ Pg.221 ]

See also in sourсe #XX -- [ Pg.445 ]




SEARCH



A Model for m-LPPP Electronic Structure

A Model for the Electron Transfer Complex

A simple model for electron-transfer reactions

Ammonia localized electron model

Atomic models electron-wave model

Bond energy localized electron model

Bonding in Complex Ions The Localized Electron Model

Bonding localized electron model

Cerium oxide electronic structure models

Charged-particle state electron models

Classical electron analog model

Classical electron analog models, nonadiabatic

Classical electron analog models, nonadiabatic semiclassical mapping

Cluster model electronic structure

Collective electron models

Combining the Localized Electron and Molecular Orbital Models

Completely free electron model

Complex ions localized electron model

Conduction electrons nearly free electron model

Conductivity, electronic Anderson model

Core electron-binding energies modeling

Covalent bonding electron model

Covalent bonds electron model

Covalent bonds localized electron model

Delocalized electrons combined model

Dielectric continuum model, electron-transfer

Dielectric response electron oscillator model

Dissociative electron transfer Morse curve model

Drude free-electron model

Electrical breakdown electronic models

Electrochemical Modeling of Electronic Systems

Electromagnetic theory electron model

Electron Capture Detector kinetic Model

Electron Transfer Mechanisms in Molybdenum and Tungsten Model Compounds

Electron Tunneling Model

Electron classical model

Electron cloud atomic model

Electron correlation expansion, independent particle model

Electron correlation models

Electron correlation, model description

Electron count in a complex the covalent model

Electron covalent models

Electron density Thomas-Fermi statistical model

Electron density maps model building

Electron density maps modeling

Electron density modeling

Electron density modeling Crystallographic

Electron density space-filling model

Electron gas model

Electron hopping diffusion model

Electron hopping model

Electron impact ionization model

Electron lattice models

Electron models

Electron models equilibrium state equations

Electron noncovalent models

Electron orbital models

Electron promotion model

Electron quantum-mechanical model

Electron repulsion model

Electron scattering analytical models

Electron sea model

Electron spherical wave model

Electron spin mechanical model

Electron transfer Marcus model

Electron transfer Marcus-Hush model

Electron transfer classical model

Electron transfer kinetic model, flavocytochrome

Electron transfer model approximation

Electron transfer model systems

Electron transfer models

Electron transfer models for

Electron transfer pathway model

Electron transfer porphyrin-based models

Electron transfer proteins, modeling

Electron transfer quantum mechanical model

Electron transfer rate model rates

Electron transfer semi-classical model

Electron transfer semiclassical model

Electron transfer superexchange model

Electron transfer theoretical models

Electron transfer tunneling pathway model

Electron transport, theoretical models

Electron trapping modelling

Electron-Dot Model of Bonding Lewis Structures

Electron-density model

Electron-dot model of bonding

Electron-in-a-box model

Electron-sea model, of metals

Electron-solid scattering models

Electron-transfer reactions superoxide dismutase models

Electron-wave model

Electronic Distortion Model

Electronic Models of Electrical Breakdown

Electronic Properties of Alloys and Theoretical Models

Electronic band model

Electronic components, process modeling

Electronic conduction theory Drude model

Electronic conductivity model

Electronic configuration quantum mechanical model

Electronic data interchange models

Electronic gas model

Electronic model molecules

Electronic model, matrix elements

Electronic polaron model

Electronic polaron model band narrowing

Electronic process models

Electronic shell model

Electronic state, excited, numerical model

Electronic states oxide glass modeling

Electronic states silicate glass model

Electronic structural model

Electronic structural model analysis

Electronic structural model fragment orbital type

Electronic structural model problems

Electronic structure computations hybrid models

Electronic structure methods independent-particle models

Electronic structure models

Electronic structure qualitative models

Electronic structures, intermolecular interaction models

Electronic tunneling model

Electronically conducting polymer conductivity models

Electrons Bohr model

Electrons Lewis model

Electrons Thomas-Fermi model

Electrons electron-pair repulsion model

Electrons jellium model

Electrons model and

Electrons plum pudding model

Electrons vector model

Electrons, crystalline solid materials energy band model

Embedded cluster model electronic states

Equilibrium state parameters, electron models

Excitation, electronic hopping model

Experimental Test of Bridge-assisted Electron Transfer Models

Experimental Testing of the Electron Transfer Models

Fokker-Planck Modeling of the Electronic Localization

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

Free Electron Gas and the Jellium Model

Free Electron Model in One Dimension

Free electron gas model

Free electron model

Free electron model, Pauli exclusion

Free-electron Modelling

Free-electron model aromatic molecules

Free-electron model highest occupied molecular orbital

Free-electron model lowest unoccupied molecular orbital

Free-electron molecular orbital model

Free-electron molecular orbital model description

Generalized electronic polaron model

Geometrical Model of the Electron

Half-electron Model

Half-electron model, definition

Heterogeneous electron transfer Butler-Volmer model

Hot Electron Model

Huckel model, free-electron

Huckel theory electron densities, model

Hybridization and the Localized Electron Model

Independent-electron models

Independent-electron models Hartree

Independent-electron models Hartree-Fock

Independent-electron models density functional theory

Independent-electron models local-density approximation

Independent-electron models orbital functional theory

Interstitial electron model

Johnsons Interstitial Electron Model for Metals

Lewis electron pair model

Lewis electron pair model electrons probabilities

Lewis electron pair model probability

Localized Electron Model for Molecules

Localized electron model Lewis structures

Localized electron model alkanes

Localized electron model ammonia molecule

Localized electron model hybrid orbitals

Localized electron model limitations

Localized electron model summary

Localized electron model three parts

Localized electron orbital models

Localized-electron model

Lorentz electron model

MO Models of Electronic Excitation

MO model, electronic excitation light absorption

Many-Electron Theoretical Models

Marcus model of electron transfer

Metal clusters electronic model

Metals free electron model

Model Electron system, electronic states

Model electronic Hamiltonian

Modeling electron transfer from

Modeling first electron transfer

Modeling first electron transfer reaction centers

Modelling Molecules Electronic States

Modelling of Electronic Structure in the

Models and theories valence-shell electron-pair repulsion

Models independent particle, electron correlation

Models many-electron molecules

Models of Bond-Breaking Ion and Electron Transfer Reactions

Models of Electron Density in Molecules

Models of electrochemical electron transfer kinetics

Models of electron transport

Models, of electron density

Molecular Geometry The Valence Shell Electron Pair Repulsion Model

Molecular geometry and the valence-shell electron pair repulsion model

Molecular modeling, electronic polarizability

Molecular modelling electronic structure

Molecular orbitals electron model

Nearly free electron model

Nitrogen localized electron model

One-Electron Density Matrix Models

One-Electron MO Models

One-Electron Theoretical Models

One-electron model

Orbitals localized electron model

Outer-sphere electron transfer classical model

Perimeter free electron model

Photoinduced electron transfer reaction center models

Photosynthetic bacteria electron-transfer models

Plane-Wave Expansion - The Free-Electron Models

Polarizable continuum model excited electronic states

Polyhedral skeletal electron pair model

Primary event electron transfer model

Qualitative models, electronic structure calculations

Quantum Model of Bonding Electrons in Crystal

Quantum Model of Free Electrons in Crystal

Quantum Model of Quasi-Free Electrons in Crystals

Quantum Model of Tight-Binding Electrons in Crystal

Quantum mechanical model electron spin

Quasi-Free Electronic Model of Solids

Radical electron model

Reaction center proteins, modeling electron transfer from

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

Rectangular band model electronic energy

Relativistic model Hamiltonians for many-electron systems

Ruthenium electron-transfer protein models

Schrbdinger equations, model electronic

Sea of electrons model

Simple quantum chemical models of electronic excitation

Skill 1.3c-Predict molecular geometries using Lewis dot structures and hybridized atomic orbitals, e.g., valence shell electron pair repulsion model (VSEPR)

Solar cells, modeling electron diffusion length

Solvated electron models

Sommerfeld free-electron model

Spin-boson model, electron-transfer

Substituent-ring interactions, electron density model

Summary of 7r-electron models

Surface electron gas model

The -electron Zero Differential Overlap Models

The All Valence Electron NDO models

The Band Model of Electrons in Solids

The Free Electron Model

The Free Electron Model and Thermionic Emission

The Free Electron Model of Metallic Bonding

The Free Electron Model of a Metal

The Lewis electron-pair model

The Localized Electron Bonding Model

The Marcus-Hush Model of Electron Transfer

The Non-Interacting Electron Model

The One-Electron Model

The Valence Shell Electron Pair Repulsion (VSEPR) model

The Valence Shell Electron Pair Repulsion model

The electrostatic model and non-bonding electron pairs

The independent-electron model as a quantum field theory

Theoretical Model. Electronic Structure

Theoretical Models of Electron Transport

Theoretical Models of the Solvated Electron

Theoretical ionic models—the modified electron-gas approach

Thermodynamics of Electron Trapping and Solvation in the Quasi-ballistic Model

Three center four electron bond model

Topological electron-counting model

Uniform electron gas model

VSEPR model shell electron-pair repulsion

Valence Shell Electron Pair Repulsion model Group 15 elements

Valence Shell Electron-pair Repulsion VSEPR) model

Valence electron models

Valence electrons VSEPR) model application

Valence shell electron pair repulsion bonding models

Valence shell electron pair repulsion model

Valence shell electron pair repulsion model repulsions

Valence shell electron-pair VSEPR model

Valence shell electron-pair repulsion model. See

Valence-shell electron-pair repulsion model lone pairs

Valence-shell electron-pair repulsion model pairs

Wave Model of the Electron

© 2024 chempedia.info