Big Chemical Encyclopedia

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

Articles Figures Tables About

State quantum

In many crystals there is sufficient overlap of atomic orbitals of adjacent atoms so that each group of a given quantum state can be treated as a crystal orbital or band. Such crystals will be electrically conducting if they have a partly filled band but if the bands are all either full or empty, the conductivity will be small. Metal oxides constitute an example of this type of crystal if exactly stoichiometric, all bands are either full or empty, and there is little electrical conductivity. If, however, some excess metal is present in an oxide, it will furnish electrons to an empty band formed of the 3s or 3p orbitals of the oxygen ions, thus giving electrical conductivity. An example is ZnO, which ordinarily has excess zinc in it. [Pg.717]

The Heisenberg uncertainty principle offers a rigorous treatment of the qualitative picture sketched above. If several measurements of andfi are made for a system in a particular quantum state, then quantitative uncertainties are provided by standard deviations in tlie corresponding measurements. Denoting these as and a, respectively, it can be shown that... [Pg.16]

Alternative descriptions of quantum states based on a knowledge of the electronic charge density equation Al.3.14 have existed since the 1920s. For example, the Thomas-Femii description of atoms based on a knowledge of p (r)... [Pg.92]

Many phenomena in solid-state physics can be understood by resort to energy band calculations. Conductivity trends, photoemission spectra, and optical properties can all be understood by examining the quantum states or energy bands of solids. In addition, electronic structure methods can be used to extract a wide variety of properties such as structural energies, mechanical properties and thennodynamic properties. [Pg.113]

The structure in the reflectivity can be understood in tenns of band structure features i.e. from the quantum states of the crystal. The nonnal incident reflectivity from matter is given by... [Pg.118]

It is possible to make a coimection between the quantum states of a solid and the resulting optical properties of a solid. [Pg.118]

Unlike the solid state, the liquid state cannot be characterized by a static description. In a liquid, bonds break and refomi continuously as a fiinction of time. The quantum states in the liquid are similar to those in amorphous solids in the sense that the system is also disordered. The liquid state can be quantified only by considering some ensemble averaging and using statistical measures. For example, consider an elemental liquid. Just as for amorphous solids, one can ask what is the distribution of atoms at a given distance from a reference atom on average, i.e. the radial distribution function or the pair correlation function can also be defined for a liquid. In scattering experiments on liquids, a structure factor is measured. The radial distribution fiinction, g r), is related to the stnicture factor, S q), by... [Pg.132]

It is possible to use the quantum states to predict the electronic properties of the melt. A typical procedure is to implement molecular dynamics simulations for the liquid, which pemiit the wavefiinctions to be detemiined at each time step of the simulation. As an example, one can use the eigenpairs for a given atomic configuration to calculate the optical conductivity. The real part of tire conductivity can be expressed as... [Pg.133]

Shapiro M and Brumer P 1986 Laser control of product quantum state populations in unimolecular reactions J. Chem. Phys. 84 4103... [Pg.281]

For those who are familiar with the statistical mechanical interpretation of entropy, which asserts that at 0 K substances are nonnally restricted to a single quantum state, and hence have zero entropy, it should be pointed out that the conventional thennodynamic zero of entropy is not quite that, since most elements and compounds are mixtures of isotopic species that in principle should separate at 0 K, but of course do not. The thennodynamic entropies reported in tables ignore the entropy of isotopic mixing, and m some cases ignore other complications as well, e.g. ortho- and para-hydrogen. [Pg.371]

The microcanonical ensemble is a set of systems each having the same number of molecules N, the same volume V and the same energy U. In such an ensemble of isolated systems, any allowed quantum state is equally probable. In classical thennodynamics at equilibrium at constant n (or equivalently, N), V, and U, it is the entropy S that is a maximum. For the microcanonical ensemble, the entropy is directly related to the number of allowed quantum states C1(N,V,U) ... [Pg.375]

The set of microstates of a finite system in quantum statistical mechanics is a finite, discrete denumerable set of quantum states each characterized by an appropriate collection of quantum numbers. In classical statistical mechanics, the set of microstates fonn a continuous (and therefore infinite) set of points in f space (also called phase space). [Pg.382]

For each degree of freedom, classical states within a small volume A/ij Aq- h merge into a single quantum state which cannot be fiirther distinguished on account of the uncertainty principle. For a system with /... [Pg.386]

Actually equation (A3.4.72) for o. is still fomial, as practically observable cross sections, even at the highest quantum state resolution usually available in molecular scattering, correspond to certain sums and averages of... [Pg.773]

In a final, sixth step one may also average (sum) over a thennal (or other) quantum state distribution I (and F) and obtain the usual thennal rate coefficient... [Pg.774]

Simple collision theories neglect the internal quantum state dependence of a. The rate constant as a function of temperature T results as a thennal average over the Maxwell-Boltzmaim velocity distribution p Ef. [Pg.776]

In principle, the reaction cross section not only depends on the relative translational energy, but also on individual reactant and product quantum states. Its sole dependence on E in the simplified effective expression (equation (A3.4.82)) already implies unspecified averages over reactant states and sums over product states. For practical purposes it is therefore appropriate to consider simplified models for tire energy dependence of the effective reaction cross section. They often fonn the basis for the interpretation of the temperature dependence of thennal cross sections. Figure A3.4.5 illustrates several cross section models. [Pg.776]

Figure A3.9.9. Dissociation probability versus incident energy for D2 molecules incident on a Cu(l 11) surface for the initial quantum states indicated (u indicates the mitial vibrational state and J the initial rotational state) [100], For clarity, the saturation values have been scaled to the same value irrespective of the initial state, although in reality die saturation value is higher for the u = 1 state. Figure A3.9.9. Dissociation probability versus incident energy for D2 molecules incident on a Cu(l 11) surface for the initial quantum states indicated (u indicates the mitial vibrational state and J the initial rotational state) [100], For clarity, the saturation values have been scaled to the same value irrespective of the initial state, although in reality die saturation value is higher for the u = 1 state.
The site specificity of reaction can also be a state-dependent site specificity, that is, molecules incident in different quantum states react more readily at different sites. This has recently been demonstrated by Kroes and co-workers for the Fl2/Cu(100) system [66]. Additionally, we can find reactivity dominated by certain sites, while inelastic collisions leading to changes in the rotational or vibrational states of the scattering molecules occur primarily at other sites. This spatial separation of the active site according to the change of state occurring (dissociation, vibrational excitation etc) is a very surface specific phenomenon. [Pg.911]

Conceptually similar studies have since been carried out for the reaction of Ft atoms with Cl/Aii(l 11). More recently, quantum-state distributions have been obtamed for both the Ft + Cl/Aii(l 11)[, and M and Ft(D) + D (Ft)/Cii(l 11) systems. The results of these studies are in good qualitative agreement widi calculations. Even for the Ft(D) + D (Ft)/Cii(l 11) system [89], where we know that the incident atom caimot be significantly accommodated prior to reaction, reaction may not be direct. Detailed calculations yield much smaller cross sections for direct reaction than the overall experimental cross section, indicating that reaction may occur only after trapping of the incident atom [90]. [Pg.914]

Rettner C T, Micheisen H A and Auerbach D J 1993 From quantum-state-specific dynamics to reaction-rates-the dominant roie of transiationai energy in promoting the dissociation of D2on Cu(111) under equiiibrium conditions Faraday D/scuss. 96 17... [Pg.916]

Rettner C T, Miehelsen H A and Auerbaeh D J 1995 Quantum-state-speeifie dynamies of the dissoeiative adsorption and assoeiative desorption of H2 at a Cu(111) surfaee J. Chem. Phys. 102 4625... [Pg.918]

Rettner C T and Auerbach D J 1996 Quantum-state distributions for the HD product of the direct reaction of H(D)/Cu(111) with D(H) incident from the gas phase J. Chem. Phys. 104 2732... [Pg.919]

Note that the sums are restricted to the portion of the frill S matrix that describes reaction (or the specific reactive process that is of interest). It is clear from this definition that the CRP is a highly averaged property where there is no infomiation about individual quantum states, so it is of interest to develop methods that detemiine this probability directly from the Scln-ddinger equation rather than indirectly from the scattering matrix. In this section we first show how the CRP is related to the physically measurable rate constant, and then we discuss some rigorous and approximate methods for directly detennining the CRP. Much of this discussion is adapted from Miller and coworkers [44, 45]. [Pg.990]

Figure A3,12.2(a) illnstrates the lifetime distribution of RRKM theory and shows random transitions among all states at some energy high enongh for eventual reaction (toward the right). In reality, transitions between quantum states (though coupled) are not equally probable some are more likely than others. Therefore, transitions between states mnst be snfficiently rapid and disorderly for the RRKM assumption to be mimicked, as qualitatively depicted in figure A3.12.2(b). The situation depicted in these figures, where a microcanonical ensemble exists at t = 0 and rapid IVR maintains its existence during the decomposition, is called intrinsic RRKM behaviour [9]. Figure A3,12.2(a) illnstrates the lifetime distribution of RRKM theory and shows random transitions among all states at some energy high enongh for eventual reaction (toward the right). In reality, transitions between quantum states (though coupled) are not equally probable some are more likely than others. Therefore, transitions between states mnst be snfficiently rapid and disorderly for the RRKM assumption to be mimicked, as qualitatively depicted in figure A3.12.2(b). The situation depicted in these figures, where a microcanonical ensemble exists at t = 0 and rapid IVR maintains its existence during the decomposition, is called intrinsic RRKM behaviour [9].
RRKM theory allows some modes to be uncoupled and not exchange energy with the remaining modes [16]. In quantum RRKM theory, these uncoupled modes are not active, but are adiabatic and stay in fixed quantum states n during the reaction. For this situation, equation (A3.12.15) becomes... [Pg.1013]

Barnes R J, Dutton G and Sinha A 1997 Unimolecular dissociation of HOCI near threshold quantum state and time-resolved studies J. Phys. Cham. A 101 8374-7... [Pg.1042]

In the case of polarized, but otherwise incoherent statistical radiation, one finds a rate constant for radiative energy transfer between initial molecular quantum states i and final states f... [Pg.1048]

The index J can label quantum states of the same or different chemical species. Equation (A3.13.20) corresponds to a generally stiff initial value problem [42, 43]. In matrix notation one may write ... [Pg.1050]

I i i(q,01 in configuration space, e.g. as defined by the possible values of the position coordinates q. This motion is given by the time evolution of the wave fiinction i(q,t), defined as die projection ( q r(t)) of the time-dependent quantum state i i(t)) on configuration space. Since the quantum state is a complete description of the system, the wave packet defining the probability density can be viewed as the quantum mechanical counterpart of the classical distribution F(q- i t), p - P t)). The time dependence is obtained by solution of the time-dependent Schrodinger equation... [Pg.1057]

In the present section, we concentrate on coherent preparation by irradiation with a properly chosen laser pulse during a given time interval. The quantum state at time t may be chosen to be the vibrational ground... [Pg.1059]

In equation (A3.13.73), 8j is the average angular frequency distance between quantum states within level /... [Pg.1080]

Weston R E and Flynn G W 1992 Relaxation of molecules with chemically significant amounts of vibrational energy the dawn of the quantum state resolved era Ann. Rev. Rhys. Chem. 43 559-89... [Pg.1084]


See other pages where State quantum is mentioned: [Pg.107]    [Pg.275]    [Pg.275]    [Pg.276]    [Pg.379]    [Pg.379]    [Pg.773]    [Pg.999]    [Pg.1018]    [Pg.1047]    [Pg.1047]    [Pg.1055]    [Pg.1079]    [Pg.1080]    [Pg.1080]    [Pg.1181]    [Pg.2059]   
See also in sourсe #XX -- [ Pg.28 ]

See also in sourсe #XX -- [ Pg.178 ]

See also in sourсe #XX -- [ Pg.444 ]

See also in sourсe #XX -- [ Pg.44 ]

See also in sourсe #XX -- [ Pg.109 ]

See also in sourсe #XX -- [ Pg.334 , Pg.367 , Pg.383 ]




SEARCH



A Quantum Chemical Approach to Magnetic Interactions in the Solid State

Ab Initio Quantum Simulation in Solid State Chemistry

Advanced ab initio Methods, Density Functional Theory and Solid-state Quantum Mechanics

Atomic ions trapped, coherent quantum state

Atomic structure, quantum mechanics spectroscopic states

Bound states in quantum mechanics

Bound-state quantum electrodynamics

Coherent states molecular photonics, quantum

Coherent states quantum interference

Coherent states quantum mechanics

Coherent states quantum optics

Corresponding states quantum

Dark transition states quantum interference

Density of quantum states

Detailed quantum transition state theory

Determining rate parameters using quantum chemical calculations and transition state theory

Diffraction quantum state

Displaced number states , quantum optics

Distribution of quantum states

Double-quantum solid state NMR

Electron transfer reactions quantum transition-state theory

Electronic states elements of molecular quantum mechanics

Electronic states triatomic quantum reaction dynamics

Electronic states, quantum reaction dynamics

Electronic states, triatomic quantum reaction

Elementary States of Quantum Mechanical Systems

Energy of quantum states

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

Entangled states nonlinear quantum optics

Exact Ground State of One- and Two-Dimensional Frustrated Quantum Spin Systems

Excited states of dioxins as studied by ab initio quantum chemical computations anomalous luminescence characteristics

External quantum state

Hydrogen, atom, quantum state

Hydrogen, atom, quantum state molecular

Hydrogen, atom, quantum state spectrum

Hydrogen, atom, quantum state stationary states

Internal quantum state

Internal quantum states, measurements

Isolated quantum states

Laser pulses, quantum dynamics coherent states

Laser pulses, quantum dynamics states

Liquid state quantum chemistry

Molecular Rydberg states quantum defects

Motional quantum state

NMR Quantum State Tomography

NMR Quantum State Tomography of quadrupole nuclei

Negative-Energy States and Quantum Electrodynamics

Nonnegative quantum states

Nonpure states, quantum

Optical and quantum density of states in nanostructures Finite-energy conservation

Oscillations Between Quantum States of an Isolated System

Path integral quantum transition state theory

Path-integral quantum transition-state

Polarization moments, quantum ground state

Product distribution quantum states

Pure states, quantum

Quantum Atom on Valence State

Quantum Franck-Condon state

Quantum Mechanical Methods for Studying the Solid State

Quantum Monte Carlo method excited states

Quantum Theory of the Defect Solid State

Quantum Yield of Excited States Larger than One

Quantum and Thermal Corrections to the Ground-State Potential Energy

Quantum beats ground state

Quantum bottleneck states

Quantum confinement of electronic states

Quantum defect theory for bound states

Quantum description of steady-state processes

Quantum discrete states momentum

Quantum distributions steady states

Quantum harmonic oscillator coherent states

Quantum indirect damping state

Quantum many-body state

Quantum mechanical model energy state

Quantum mechanics classical transition state theory

Quantum mechanics excited states

Quantum mechanics ground states

Quantum mechanics multiple states electronic structure

Quantum mechanics of steady states

Quantum mechanics quantal states

Quantum optics state generation

Quantum optics truncated states

Quantum reaction dynamics, electronic states adiabatic representation

Quantum reaction dynamics, electronic states equation

Quantum reaction dynamics, electronic states nuclear motion Schrodinger equation

Quantum relaxation processes initial state

Quantum relaxation processes steady states

Quantum representations slow mode states

Quantum spin liquid state

Quantum spin states

Quantum state function

Quantum state tomography

Quantum state vector

Quantum state-specific detector

Quantum states Schrodinger cats

Quantum states coherence

Quantum states entanglement issues

Quantum states experiment

Quantum states motion

Quantum states recording screens

Quantum states spectroscopy

Quantum states trap types

Quantum states, decay rates

Quantum states, energy

Quantum states, energy levels and wave functions

Quantum states, number

Quantum states, size-dependent

Quantum transition state theory

Quantum transition state theory background

Quantum transition-state theory centroid density

Quantum transition-state theory formalism

Quantum transition-state theory reactions

Quantum transitional state theory

Quantum transitional state theory QTST)

Quantum well states

Quantum well states density functional theory

Quantum well states periodic potential

Quantum yields triplet state energy correlation

Quantum-mechanical states

Quantumness parameter, metastable state

Reconstruction of density matrices in NMR QIP Quantum State Tomography

Reference state quantum field theory

Resonance state quantum mechanical, time-dependent

Ring-puckering quantum states

Rotational quantum state

Rotational quantum state distribution

Rotational-vibrational quantum states

Rydberg states multichannel quantum defect theory

Rydberg states quantum defect functions

Scattered quantum states

Solid state quantum chemistry

Solid state quantum mechanics

Solid-state heteronuclear multiple-quantum

Solid-state heteronuclear multiple-quantum correlation experiment

Solid-state quantum physics (band theory and related approaches)

Solid-state quantum yield

Squeezed states quantum optics

State correlation diagrams quantum chemical calculations

State quantum mechanics applied

State specific rate constant quantum calculations

Steady-state quantum yield

Superposition States and Interference Effects in Quantum Optics

Superposition states quantum interference

Superpositions, of quantum states

The Quantum Mechanical State

The Theorem of Corresponding States in Quantum Mechanics

The quantum states of macroscopic systems

Thin quantum-well states

Transition state quantum

Transitions between the nuclear spin quantum states - NMR technique

Trapping states quantum interference

Triplet state Quantum efficiency

Triplet state quantum yield

Unimolecular reaction rates and products quantum states distribution

© 2024 chempedia.info