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Electron functionalization

The necessary material to perform annual verification of flaw detector is mainly composed of an electronic function generator, an external calibrated attenuator and an oscilloscope. [Pg.703]

Both terms on the right are related to the rate of change of the adiabatic electronic functions with respect to the nuclear coordinates. The first term Gy is given by... [Pg.277]

The diabatic electronic functions are related to the adiabatic functions by unitary transformations at each point in coordinate space... [Pg.280]

Note that, although there is a r esemblance, this ansatz is quite differ ent from the Born representation of Eq. (A.3) due to the time dependence of the electronic functions. By taking a single configuration. [Pg.317]

The basis consisting of the adiabatic electronic functions (we shall call it bent basis ) has a seiious drawback It leads to appearance of the off-diagonal elements that tend to infinity when the molecule reaches linear geometry (i.e., p 0). Thus it is convenient to introduce new electronic basis functions by the transformation... [Pg.487]

T is a rotational angle, which determines the spatial orientation of the adiabatic electronic functions v / and )/ . In triatomic molecules, this orientation follows directly from symmetry considerations. So, for example, in a II state one of the elecbonic wave functions has its maximum in the molecular plane and the other one is perpendicular to it. If a treatment of the R-T effect is carried out employing the space-fixed coordinate system, the angle t appearing in Eqs. (53)... [Pg.520]

This algebra implies that in case of Eq. (111) the only two functions (out of n) that flip sign are and because all in-between functions get their sign flipped twice. In the same way, Eq. (112) implies that all four electronic functions mentioned in the expression, namely, the jth and the (j + 1 )th, the th and the (/c -h 1 )th, all flip sign. In what follows, we give a more detailed explanation based on the mathematical analysis of the Section Vin. [Pg.673]

The simplest many-electron wave function that satisfies the Exclusion Principle is a product of N different one-electron functions that have been antisymmetrized, or written as a determinant. Here, N is the number of electrons (or valence electrons) in the molecule. HyperChem uses this form of the wave function for most semi-empirical and ab initio calculations. Exceptions involve using the Configuration Interaction option (see page 119). HyperChem computes one-electron functions, termed molecular spin orbitals, by relatively simple integration and summation calculations. The many-electron wave function, which has N terms (the number of terms in the determinant), never needs to be evaluated. [Pg.36]

Any set of one-electron functions can be a basis set in the LCAO approximation. However, a well-defined basis set will predict electronic properties using fewer terms than a poorly-defined basis set. So, choosing a proper basis set in ab initio calculations is critical to the reliability and accuracy of the calculated results. [Pg.109]

Du Pont Co. conformal coatings, photoresists, manufacturing aids, electronic functional coating compounds... [Pg.121]

Unilver Table 1. Worldwide 1992 Electronics Industry Value/ x 10 adhesives, dielectric coatings, protective coatings, dielectric interlayers, electronic functional coatings... [Pg.121]

The next approximation involves expressing the jiiolecular orhiiah as linear combinations of a pre-defined set of one-electron functions kjiown as basis functions. These basis functions are usually centered on the atomic nuclei and so bear some resemblance to atomic orbitals. However, the actual mathematical treatment is more general than this, and any set of appropriately defined functions may be u.sed. [Pg.261]

I am assuming that this particular electronic state is the lowest-energy one of that given spatial symmetry, and that the i/f s are orthonormal. The first assumption is a vital one, the second just makes the algebra a little easier. The aim of HF theory is to find the best form of the one-electron functions i/ a,. .., and to do this we minimize the variational energy... [Pg.111]

Without introducing any approximations, the total (exact) wave function can be written as an expansion in the complete set of electronic functions, with the expansion coefficients being functions of the nuclear coordinates. [Pg.54]

As mentioned in Chapter 5, one can think of the expansion of an unknown MO in terms of basis functions as describing the MO function in the coordinate system of the basis functions. The multi-determinant wave function (4.1) can similarly be considered as describing the total wave function in a coordinate system of Slater determinants. The basis set determines the size of the one-electron basis (and thus limits the description of the one-electron functions, the MOs), while the number of determinants included determines the size of the many-electron basis (and thus limits the description of electron correlation). [Pg.99]

Since the exact density matrix is not known, the (approximate) density is written in terms of a set of auxiliary one-electron functions, orbitals, as... [Pg.179]

The variational problem may again be formulated as a secular equation, where the coordinate axes are many-electron functions (Slater determinants), <, which are orthogonal (Section 4.2). [Pg.315]

Before proving this theorem, we will make some general remarks about the nature of the one-electron functions ipk(x) or spin orbitals. For the two values of the spin coordinate f — 1, such a function y)k(r, f) has two space components... [Pg.227]

Let us now consider a system of N electrons, where N+ electrons occupy spin orbitals of a character or plus spin, and N electrons occupy spin orbitals of character or minus spin. By using the separation of the one-electron functions y>k x) into two groups having different spins, we may write the fundamental invariant (Eq. 11.41) in the form... [Pg.228]

The method of superposition of configurations described in the first paper (1928) implies that, after choosing a complete basic set of one-electron functions rpk rx) one can develop the space function in Eq. III. 1 in the form ... [Pg.250]

The method of superposition of configurations as well as the method of different orbitals for different spins belong within the framework of the one-electron scheme, but, as soon as one introduces the interelectronic distance rijt a two-electron element has been accepted in the theory. In treating the covalent chemical bond and other properties related to electron pairs, it may actually seem more natural to consider two-electron functions as the fundamental building stones of the total wave function, and such a two-electron scheme has also been successfully developed (Hurley, Lennard-Jones, and Pople 1953, Schmid 1953). [Pg.258]

Every normalizable antisymmetric wave function can be expressed as the sum of a series of Slater determinants built up from a complete basic set of one-electron functions. [Pg.261]

The results in Table VI are of considerable interest also for atoms with more than two electrons, since they show the possibilities and limitations of the method of superposition of configurations/ when the latter are built up from one-electron functions... [Pg.295]

We note that it is possible to combine the method with correlation factor with the method using superposition of configurations to obtain any accuracy desired by means of comparatively simple wave functions. For a very general class of functions g(r12), one can develop the quotient (r r2)lg(r12) according to Eq. III.2 into products of one-electron functions y>k(r), which leads to the expansion... [Pg.302]

Hurley, A. C., Lennard-Jones, J., and Pople, J. A., Proc. Roy. Soc. [London) A220, 446, The molecular orbital theory of chemical valency XVI. A theory of paired electrons in polyatomic molecules." Use of two-electron functions T fa, x5) as a basis. [Pg.335]

One-electron function, 228, 261 One particle scheme, 210 Ordered configuration, 261 Ortho-iodo-phenol, radiation resistance, 196... [Pg.410]

The total wavefunction, , is an antisymmetrized product of the one-electron functions i/q (a Slater determinant). The i/tj are called one-electron functions since they depend on the coordinates of only one electron this approximation is embedded in all MO methods. The effects that are missing when this approximation is used go under the general name of electron correlation. [Pg.12]


See other pages where Electron functionalization is mentioned: [Pg.157]    [Pg.313]    [Pg.485]    [Pg.486]    [Pg.523]    [Pg.730]    [Pg.351]    [Pg.36]    [Pg.133]    [Pg.146]    [Pg.263]    [Pg.265]    [Pg.274]    [Pg.207]    [Pg.211]    [Pg.58]    [Pg.140]    [Pg.195]    [Pg.213]    [Pg.29]    [Pg.260]    [Pg.279]    [Pg.660]    [Pg.663]   
See also in sourсe #XX -- [ Pg.52 ]




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Adiabatic electron wave function

Adiabatic electronic wave functions

An Introduction to the Electron Localization Function

Antisymmetric many-electron wave function

Antisymmetrized wave function, electronic

Antisymmetrized wave function, electronic structure calculations

Applications, molecular electronics functional materials

Approximations to the Many-Electron Wave Function

Aromaticity electron localization function

Atomic Many-Electron Wave Function and -Coupling

Basis Sets for Electronic Wave Functions

Basis-Set Expansions of Relativistic Electronic Wave Functions

Benzene, charge density- functions electronic states

Benzenes electronic localization function

Biomolecules-nanoparticle systems electronic functions

Calculation of molecular electronic wave functions and energies

Catalytic activity electron work function

Conducting polymers electronic wave functions

Correlation function electronic

Coupled-cluster wave functions, derivatives electronic energy

Definition of Electronic Charges from the Wave Function

Density functional theory electron affinities

Density functional theory electron correlation procedures

Density functional theory electron transfer

Density functional theory electronic chemical potential

Density functional theory electronic circular dichroism

Density functional theory electronic structure calculations

Density functional theory electronic structure methods

Density functional theory electrons

Density functional theory intermolecular interactions, electron

Density functional theory many-electron system energy

Density functional theory-electron spin resonance calculations

Density functionals electronic excitation energy

Density-functional theory electronic problem

Determinantal wave function, electron nuclear

Diabatic electron wave function

Diatomic molecules electronic partition functions

Electron Density and Hole Functions

Electron Pair Functions

Electron Paramagnetic Resonance (EPR) Characterization of Heterogeneously Functionalized Dendrimers

Electron Work Function of the Elements

Electron affinities functions

Electron affinity, relation work function

Electron configurations orbital wave functions

Electron correlation method Density-functional theory Mpller-Plesset

Electron correlation method, Density-functional theory

Electron densities wave function properties

Electron density Wigner correlation energy functional

Electron density function

Electron density function, full

Electron density functionals

Electron density, distribution function

Electron distribution function

Electron distribution function for

Electron energy distribution function

Electron energy distribution function EEDF)

Electron energy distribution function for

Electron free energy function

Electron locahzation function

Electron locahzation function molecules

Electron localisation function

Electron localization function

Electron localization function (ELF

Electron localization function , local

Electron localization function , local nuclear motion

Electron localization function analysis

Electron localization function analysis substituent

Electron localization function bifurcation analysis

Electron localization function density construction

Electron localization function isosurfaces

Electron localization function kinetic energy density

Electron localization function partition

Electron localization function partition based

Electron localization function topological analysis

Electron nuclear dynamics , molecular function

Electron pair localization function

Electron probability density function

Electron radial distribution function

Electron repulsion functional

Electron spectral function

Electron transfer distribution functions

Electron transfer rate constants, function

Electron transfer rate constants, function free-energy change

Electron transmission function

Electron velocity distribution, function

Electron wave function

Electron wave functions for two

Electron work function

Electron work function and

Electron work function, equation

Electron-correlated calculations, nuclear density functional theory

Electron-density difference function

Electron-positron overlap function

Electron-spin spectral density functions

Electronic Hamiltonian function

Electronic Indices from Greens Functions

Electronic Motion Density Functional Theory (DFT)

Electronic Office Functions Management

Electronic States in Solids-The Fermi Distribution Function

Electronic Structure Calculations Via Density Functional Theory

Electronic Structure of Naked, Ligated and Supported Transition Metal Clusters from First Principles Density Functional Calculations

Electronic Structure. Potential Energy Functions

Electronic Work Function and Related Values in Electrochemical Kinetics

Electronic absorption spectroscopy wave functions

Electronic and Nuclear Partition Functions

Electronic coupling, between donor and acceptor wave functions

Electronic density Fukui function

Electronic density function

Electronic density functions first order

Electronic density response function

Electronic distribution electron localization function

Electronic effects of functional groups

Electronic encapsulants, function

Electronic energy coupled-cluster waves functions

Electronic energy levels partition function

Electronic energy wave functions

Electronic excited states basis functions

Electronic function

Electronic localization function

Electronic localization function nodal planes

Electronic options basic functions

Electronic states density functional method

Electronic states time-dependent wave functions

Electronic structure Green-function methods

Electronic structure calculations with Gaussian basis functions

Electronic structure computations density functional tight-binding

Electronic structure density-functional theory

Electronic structure methods B3LYP functional

Electronic structure methods exchange-correlation functional

Electronic structure methods periodic density functional theory

Electronic structure wave function description

Electronic structure wave-function calculations

Electronic wave function

Electronic wave function angular

Electronic wave function anthracene

Electronic wave function butadiene

Electronic wave function determination

Electronic wave function ethylene

Electronic wave function for molecule

Electronic wave function for the

Electronic wave function for the H2 molecule

Electronic wave function fundamental property

Electronic wave function many-electron atoms

Electronic wave function radial

Electronic wave function symmetry properties

Electronic wave function transferring electron

Electronic wave function, permutational

Electronic wave function, permutational symmetry

Electronic wave functions Electron-repulsion potentials

Electronic wave functions electrostatic energy

Electronic wave functions electrostatic interactions

Electronic wave functions of homonuclear diatomic molecules

Electronic wave functions transitions

Electronic wave functions, stationary

Electronic wavefunction and probability density function

Electronic work function

Electronically Conducting Polymers with Built-In or Pendant Redox Functionalities

Electronically functional inorganic

Electrons Lindhard dielectric function

Electrons dielectric function

Electrons envelope function

Electrons radial electron density function

Electrons, locations/functions

Electrophiles electron-rich functionalities

Electrostatic potential, molecular interactive electronic density function

Energy Resolution and Response Function of Electron Detectors

Equivalence of the electronic wave function and electron density

Ethane electron localization function

Fermions electronic wave functions

Force constants from electronic wave functions

Fukui function electron density

Fukui function electronic

Function electron microscopy

Function electron-group

Functional Additives for Polymer Electronics

Functional Electronic Materials

Functional groups electron-withdrawing effects

Functional groups electronic effects

Functional groups electronic properties

Functional groups inductive electron-donating

Functional groups inductive electron-withdrawing

Functional safety of electrical/electronic

Functionalities of Non-Bonding Electrons Size Emergence

Functionals of the electronic density

Gauge-including atomic orbital density functional theory, electron

Gaussian basis functions electron correlation effects

Gaussian basis functions many-electron molecules

Gaussian functions, electronic structure

Gaussian functions, electronic structure calculation

Generation of Many Electron Spin Functions

Geometric phase effect electronic wave function

Gradient corrected density functional theory electronic structure

Ground-state electronic wave function

Ground-state wave function electronic Hamiltonian, spin-orbit

Group , electron functional

Hartree-Fock wave functions multiple electronic states

Highly Conductive Plastics - Custom-formulated Functional Materials for Injection Mouldable Electronic Applications

Homonuclear diatomic molecules electronic wave functions

Homonuclear molecules, permutational electronic wave function

Hybrid electron functions

Hydrogen bonding electron localization function

Hyperpolarizabilities electron-correlated functions

Imaging functional electron transfer

Independent-electron models density functional theory

Independent-electron models orbital functional theory

Irradiation, electron energy distribution function under

Irreducible representations electronic wave function

Jellium Surfaces Electron Spillout, Surface Dipole, and Work Function

Many-electron atoms wave function

Many-electron atoms, radial wave functions

Many-electron basis functions

Many-electron functions

Many-electron molecular wave functions

Many-electron wave functions Slater determinants

Many-electron wave functions atomic orbitals approximation

Many-electron wave functions the Hartree-Fock equation

Many-electron wave functions, electronic structure

Many-electron wave functions, electronic structure calculations

Maxwellian electron energy distribution function

Metabolic functions electron transferring flavoproteins

Molecular function electron transfer, Marcus theory

Molecular one-electron functions

Molecular orbitals , nuclear magnetic density functional theory, electron

Molecular partition functions electronic

Molecules electronic partition functions

Monolayer- and Multilayer-enzyme Assemblies Functionalized with Electron-transfer Mediators

Multi-determinant wave functions electron correlation methods

Multiconfigurational wave function electron correlation

N-electron wave function

Nonlinear molecules electronic wave function

Nuclear dynamics electronic wave function

One-electron density function

One-electron functions

PEDOT layers with electronic functions

Partition function electronic

Point group symmetry electronic wave function

Polarons electronic wave function

Polymers with Electronic Functions

Potassium atom, electron localization function

Projected electron density function

Proper functions 2 electrons)

Quasi-degenerate electronic wave functions

Radial distribution function electron diffraction

Radial electron localization function

Requirements on one-electron basis functions

Semiempirical wave functions electronic states

Separating q Nuclear and Electronic Partition Functions

Shape function electron density

Shape function electron density, variations

Single electron function

Single-electron wave functions

Solvated electron electronic wave function

Spatial function symmetry three-electron

Structure-Function Correlations Electron Transfer Chain

Symmetric properties electronic wave function

Tensor Structure of the Many-Electron Hamiltonian and Wave Function

The Electron Localization Function

The Work Function for Electrons in Metals

The electron pair distribution function

The electronic partition function

The pair function. Electron correlation

Thouless determinantal wave function, electron

Time-dependent density functional interacting electrons

Time-dependent density functional theory electronic excitations

Time-dependent electron localization function

Topic 1.4. Representation of Electron Density by the Laplacian Function

Transition dipole moment functions, electronic

Two-electron density functional

Two-electron integrals over basis functions

Two-electron spin functions

Ubiquinone, electron transfer function

Valence electron wave function

Vosko, Wilk and Nusair electron correlation functional

Wave Function Electronic Structure Methods

Wave Function for Many Electrons

Wave Functions for Many-Electron Systems

Wave function analysis electron density

Wave function determination from electron density

Wave function electron density from

Wave function electron nuclear dynamics

Wave function many-electron

Wave function one-electron

Wave function two electrons

Wave function, electronic excited state

Wave function, electronic total

Wave function, electronic vibrational

Wave functions, factoring into electronic

Work Function and Electron Paramagnetic Resonance

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