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Electron Methods

The simplest approximation to the Schrodinger equation is an independent-electron approximation, such as the Hiickel method for Jt-electron systems, developed by E. Hiickel. Later, others, principally Roald Hoffmann of Cornell University, extended the Hiickel approximations to arbitrary systems having both n and a electrons—the Extended Hiickel Theory (EHT) approximation. This chapter describes some of the basics of molecular orbital theory with a view to later explaining the specifics of HyperChem EHT calculations. [Pg.219]


The LMTO method is the fastest among the all-electron methods mentioned here due to the small basis size. The accuracy of the general potential teclmique can be high, but LAPW results remain the gold standard . [Pg.2214]

The projector augmented-wave (PAW) DFT method was invented by Blochl to generalize both the pseudopotential and the LAPW DFT teclmiques [M]- PAW, however, provides all-electron one-particle wavefiinctions not accessible with the pseudopotential approach. The central idea of the PAW is to express the all-electron quantities in tenns of a pseudo-wavefiinction (easily expanded in plane waves) tenn that describes mterstitial contributions well, and one-centre corrections expanded in tenns of atom-centred fiinctions, that allow for the recovery of the all-electron quantities. The LAPW method is a special case of the PAW method and the pseudopotential fonnalism is obtained by an approximation. Comparisons of the PAW method to other all-electron methods show an accuracy similar to the FLAPW results and an efficiency comparable to plane wave pseudopotential calculations [, ]. PAW is also fonnulated to carry out DFT dynamics, where the forces on nuclei and wavefiinctions are calculated from the PAW wavefiinctions. (Another all-electron DFT molecular dynamics teclmique using a mixed-basis approach is applied in [84].)... [Pg.2214]

As an indication of the types of infonnation gleaned from all-electron methods, we focus on one recent approach, the FLAPW method. It has been used to detennine the band stmcture and optical properties over a wide energy range for a variety of crystal stmctures and chemical compositions ranging from elementary metals [ ] to complex oxides [M], layered dichalcogenides [, and nanoporous semiconductors The k p fonnulation has also enabled calculation of the complex band stmcture of the A1 (100) surface... [Pg.2214]

Computational solid-state physics and chemistry are vibrant areas of research. The all-electron methods for high-accuracy electronic stnicture calculations mentioned in section B3.2.3.2 are in active development, and with PAW, an efficient new all-electron method has recently been introduced. Ever more powerfiil computers enable more detailed predictions on systems of increasing size. At the same time, new, more complex materials require methods that are able to describe their large unit cells and diverse atomic make-up. Here, the new orbital-free DFT method may lead the way. More powerful teclmiques are also necessary for the accurate treatment of surfaces and their interaction with atoms and, possibly complex, molecules. Combined with recent progress in embedding theory, these developments make possible increasingly sophisticated predictions of the quantum structural properties of solids and solid surfaces. [Pg.2228]

Nemoshkalenko V V and Antonov V N 1998 Computational Methods in Solid State Physics (Amsterdam Gordon and Breach) An explicit introduction to the all-electron methods. [Pg.2239]

The half-electron method can also apply to triplet states. For this calciilatioit. IlyperCheni populates selected molecular orbitals with pairs of half electron s. The final energy is computed by assigning the proper spins. [Pg.47]

Although LHF is often a better theoretical treatment of open-shell systems than the RHF (half-electron) methods, it takes longer to compute. Separate matrices for electrons of each spin roughly double the length of the calculation. ... [Pg.47]

Semiempirical programs often use the half-electron approximation for radical calculations. The half-electron method is a mathematical technique for treating a singly occupied orbital in an RHF calculation. This results in consistent total energy at the expense of having an approximate wave function and orbital energies. Since a single-determinant calculation is used, there is no spin contamination. [Pg.229]

More elaborated treatments have also been applied ab initio methods by Bouscasse (130) and Bernardi et al. (131) then the all-valence-electrons methods, derived from PPP. by Gelus et ai. (132) and by Phan-Tan-Luu et al. (133) and CNDO methods by Bojesen et al. (113) and by Salmona et al. (134). [Pg.26]

In all cases the ir net charge of sulfur is positive, whereas its cr net charge is sometimes positive (133,130) and sometimes negative (122,132). The all-electrons methods, like ab initio, give a positive total net charge with the exception of the CNDO/2 method for which it is negative (134). [Pg.31]

In Table 1-9 we have collected only the 7r-bond orders calculated by allvalence-electrons methods and compared their values with those deduced from experimental bond lengths. Both data are indicative of an aromatic molecule with a large dienic character. The 2-3 and 4-5 bonds especially present a large double-bond character, whereas both C-S bonds are relatively simple. [Pg.39]

The introduction of a methyl substituent into the empirical calculations may be performed according to two main different models the pseudoheteroatomic model and the hyperconjugated model (161-166). Both approximations have been used in rr-electron methods (HMO, w, PPP). On the other hand, in the all-valence-electrons... [Pg.42]

In the true independent-electron methods you only have to obtain the matrix elements Hj y of some quite unspecified effective one-... [Pg.224]

HyperChem currently supports one first-principle method ab initio theory), one independent-electron method (extended Hiickel theory), and eight semi-empirical SCFmethods (CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S). This section gives sufficient details on each method to serve as an introduction to approximate molecular orbital calculations. For further details, the original papers on each method should be consulted, as well as other research literature. References appear in the following sections. [Pg.250]

Since EHT is an independent-electron method, it is defined by giving formulas for each of the Hj y matrix elements of the... [Pg.268]

The need for weU-trained technical service professionals is expected to continue as an essential aspect of the chemical industry, despite the phenomenal growth ia electronic methods of information storage, retrieval, and transmission. Advanced troubleshooting of complex customer processes and accelerated accurate product development and market introductions should continue to be principal elements of technical service personnel duties. Increased levels of integration, perhaps blurring the lines between suppHer and customer, may come to pass. There are already instances of personnel swapping between customers and suppHers for extended periods to allow cross-fertilization of ideas and provide more accurate perspectives for the companies involved in these efforts. Technical service and research personnel have been those persons most directly involved in such efforts. [Pg.381]

Stratifying water systems for selective extraction of thiocyanate complexes of platinum metals have been proposed. The extraction degree of mthenium(III) by ethyl and isopropyl alcohols, acetone, polyethylene glycol in optimum conditions amounts to 95-100%. By the help of electronic methods, IR-spectroscopy, equilibrium shift the extractive mechanism has been proposed and stmctures of extractable compounds, which contain single anddouble-chai-ged acidocomplexes [Rh(SCN)J-, [Ru(SCN)J, [Ru(SCN)J -have been determined. Constants of extraction for associates investigated have been calculated. [Pg.257]

Aj[ the beginning of this chapter, I introduced the notion that the 16 electrons iU ethene could be divided conceptually into two sets, the 14 a and the 2 n electrons. Let me refer to the space and spin variables as xi, Xj, > xi6, and for the minute I will formally label electrons 1 and 2 as the 7r-electrons, with 3 through 16 the cr-electrons. Methods such as Huckel rr-electron theory aim to treat the TT-electrons in an effective field due to the nuclei and the remaining a electrons. To see how this might be done, let s look at the electronic Hamiltonian end see if it can be sensibly partitioned into a rr-electron part (electrons 1 and 2) and a cr part (electrons 3 through 16). We have... [Pg.133]

The complete rules for the application of the ion-electron method may be expressed as follows ... [Pg.849]

There are other methods. For a discussion of the free-electron method, see Streitwieser Jr., A. Molecular Orbital Theory for Organic Chemists Wiley NY, 1961, p. 27. For the nonpairing method, in which benzene is represented as having three electrons between adjacent carbons, see Hirst, D.M. Linnett, J.W. J. Chem. Soc., 1962,1035 Firestone, R.A. J. Org. Chem., 1969, 34, 2621. [Pg.78]

In the approach of Dewar and co-workers (34), termed the half-electron method , a physical model is considered in which an unpaired electron is replaced by two hypothetical half-electrons of opposite spin. For radicals containing one unpaired electron, the eigenvalue problem of this method is, in our opinion, identical with the method of Longuet-Higgins and Pople (27) ... [Pg.336]

For reasons given later, we shall most frequently use in applications the method of Longuet-Higgins and Pople. Recently, the half-electron method was extended to the lowest-energy open-shell states of any given symmetry and multiplicity (57). [Pg.336]

The description of configuration interaction given for rr-electron methods is also valid for all-valence-electron methods. Recently, two papers were published in which the half-electron method was combined with a modified CNDO method (69) and the MINDO/2 method was combined with the Roothaan method (70). Appropriate semiempirical parameters and applications of all-valence-electron methods are most probably the same as those reviewed for closed-shell systems (71). [Pg.342]

Until now, applications of semiempirical all-valence-electron methods have been rare, although the experimental data for a series of alkyl radicals are available (108,109). In Figure 9, we present the theoretical values of ionization potentials calculated (68) for formyl radical by the CNDO version of Del Bene and Jaffe (110), which is superior to the standard CNDO/2 method in estimation of ionization potentials of closed-shell systems (111). The first ionization potential is seen, in Figure 9, to agree fairly well with the experimental value. Similarly, good results were also obtained (113) with some other radicals (Table VII). [Pg.354]


See other pages where Electron Methods is mentioned: [Pg.2206]    [Pg.2210]    [Pg.2210]    [Pg.227]    [Pg.219]    [Pg.72]    [Pg.31]    [Pg.219]    [Pg.233]    [Pg.162]    [Pg.510]    [Pg.512]    [Pg.512]    [Pg.1135]    [Pg.848]    [Pg.866]    [Pg.54]    [Pg.43]    [Pg.345]    [Pg.348]   


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A Testing Ground for Electronic Structure Methods

AIMD simulation method electronic structure calculations

Ab initio electron correlation methods

Ab initio electron propagator methods

All-electron methods

All-valence-electron methods

Analytical methods scanning electron microscope

Applications of electron propagator methods

Atom-superposition electron-delocalization method

Atomic electronic structure methods

Balancing Redox Equations Using the Ion-Electron Method

Basic electronic structure methods

Born-Oppenheimer approximation electronic structure methods

Carbon electron-nuclear relaxation methods

Carlo Quantum Methods for Electronic Structure

Characterization electron methods

Collective electronic oscillators method

Computational methods electronic structure calculations

Configuration-interaction methods electronic structure calculations

Continuous-wave electron spin resonance pulsed methods

Coupled Electron Pair Approximation method

Coupled Electron-Ion Monte Carlo method

Cross-sectional transmission electron microscopy methods

Density functional theory electronic structure methods

Detection methods electron capture detector

Detection methods electron paramagnetic spin resonance

Determination of Bond Dissociation Energies by Electron Impact and Spectroscopic Methods

Diffraction methods single crystal electron density determination

Direct electron correlation methods

Direct electron transfer methods

Discrete variational methods electronic structures

Dynamic electron correlation energy accurate estimation method

Dynamical method Electron Nuclear Double Resonance

Electrochemical methods electron-transfer process

Electrochemical methods electronic

Electron Affinities Determined Using Photon Methods

Electron CISDT-method

Electron Correlation and Post-SCF Methods

Electron Correlation---Post-Hartree-Fock Methods

Electron Density Integrals and Atoms-in-Molecules Methods

Electron Hartree-Fock method

Electron MCSCF-method

Electron Method of Balancing Half-Cell Equations

Electron Microscopy (EM) Methods

Electron Transfer in the Mediatorless Method of Bioelectrocatalysis

Electron beam curing method

Electron beam dosimetry methods

Electron beam irradiation method

Electron beam irradiation method components

Electron beam method

Electron capture method

Electron comparison with other methods

Electron correlation coupled-cluster methods

Electron correlation localized methods

Electron correlation method Density-functional theory Mpller-Plesset

Electron correlation method, Density-functional theory

Electron correlation methods

Electron correlation methods Mpller-Plesset perturbation theory

Electron correlation methods accuracy

Electron correlation methods beryllium atom

Electron correlation methods configuration interaction

Electron correlation methods convergence

Electron correlation methods coupled cluster theory

Electron correlation methods dissociation

Electron correlation methods excited Slater determinants

Electron correlation methods excited states

Electron correlation methods interelectronic distance

Electron correlation methods size consistency

Electron correlation methods size extensivity

Electron correlation methods spin contamination

Electron correlation multiconfiguration-based methods

Electron counting methods

Electron coupled cluster-method

Electron delocalization computational methods

Electron density MEDLA method

Electron density maps anomalous dispersion methods

Electron density method

Electron detectors coincidence methods

Electron diffraction methods

Electron equilibration method

Electron impact methods

Electron ionization method development

Electron lithography scanning methods

Electron microprobe analysis methods

Electron microprobe method

Electron microscopic methods

Electron microscopy methods

Electron microscopy, analytical method

Electron pair method, comparison with molecular

Electron paramagnetic resonance experimental methods

Electron paramagnetic resonance methods

Electron paramagnetic resonance spectroscopic methods

Electron propagator methods

Electron propagator theory methods

Electron spectroscopy, analytical method

Electron spectroscopy, analytical method Applications

Electron spin resonance and other spectral methods

Electron spin resonance pulsed methods

Electron spin transient nutation methods

Electron structure methods

Electron tomography method

Electron transfer initiated cyclization method

Electron-Density Distributions Determined by X-Ray Diffraction Methods

Electron-density distribution methods

Electron-nuclear relaxation methods

Electron-pair Approximation and Related Methods

Electron-spin resonance methods

Electronic assemblies methods, specifications

Electronic characterization techniques experimental methods

Electronic chemical potential, 353 methods

Electronic impact method

Electronic states density functional method

Electronic states self-consistent field method

Electronic structure CNDO method

Electronic structure Green-function methods

Electronic structure Hartree-Fock, restricted, method

Electronic structure Korringa-Kohn-Rostoker method

Electronic structure computations methods

Electronic structure computations wavefunction-based methods

Electronic structure configuration-interaction methods

Electronic structure full-potential methods

Electronic structure methods

Electronic structure methods B3LYP functional

Electronic structure methods Gaussian

Electronic structure methods Hartree-Fock theory

Electronic structure methods Kohn-Sham equations

Electronic structure methods Koopmans’ theorem

Electronic structure methods Moller-Plesset perturbation

Electronic structure methods ONIOM

Electronic structure methods Siesta

Electronic structure methods Slater determinants

Electronic structure methods adiabatic approximation

Electronic structure methods approximation

Electronic structure methods configuration interaction method

Electronic structure methods dynamics

Electronic structure methods exchange-correlation functional

Electronic structure methods for excited states

Electronic structure methods frozen core

Electronic structure methods independent-particle models

Electronic structure methods linear scaling

Electronic structure methods local density approximation

Electronic structure methods parameterization

Electronic structure methods periodic density functional theory

Electronic structure methods periodic systems

Electronic structure methods pseudopotential approximation

Electronic structure methods self-consistent approximation

Electronic structure methods self-consistent field theory

Electronic structure methods variational problem

Electronic structure moments methods

Electronic structure real-space methods

Electronic structure self-consistent field methods

Electronic structure variational methods

Electronic textiles methods

Electronics solder reflow methods

Electrons DVME method

Electrons method and

Equilibrium Methods for Determining Electron Affinities

Exchange integrals electronic structure methods

Excited electron correlation methods

Experimental methods electron spin resonance

Exploring Chemistry with Electronic Structure Methods

Films structure electron diffraction methods

First Principles Electronic Structure Methods

Free-electron method

Free-electron molecular orbital method FEMO)

Free-electron molecular-orbital method

Frontier-electron method

Global methods in the theory of many-electron atoms

Half-electron method

Hamiltonian operators electron correlation methods

Hamiltonian operators electronic structure methods

Hartree-Fock theory electron correlation methods

Heterogeneous Electron Transfer Steady-State Methods

Heterogeneous Electron Transfer Transient Methods

Hybrid force field electronic structure method

Independent-electron method

Ion-electron method

Ion-electron method for balancing

Ion-electron method for balancing equations

Local MP2 Electron-correlation Method for Nonconducting Crystals

Local electron-correlation method

Low-energy electron diffraction methods

Many-body, generally electron dynamics methods

Many-electron methods

Many-electron methods 2-particle density matrix

Material characterization methods electron microscopy

Measurement methods electron microscopy

Measurement methods scanning electron microscopy

Measurement methods transmission electron microscopy

Methode Electronics

Methods of electronic structure calculation

Molecular electron density lego assembler method

Molecular orbital methods electron correlation

Molecular orbital methods electron distribution from

Multi-configuration self-consistent field electron correlation methods

Multi-determinant wave functions electron correlation methods

Multiple electrons ionization methods

One-electron methods

Organic electronic devices using method

Outlook on Electron Correlation Methods for Large Systems

Pi-electron method

Post Dirac-Fock-Methods - Electron Correlation

Potential energy surfaces electronic structure methods

Quantum mechanics electron correlation methods

Quantum mechanics methods electronic structure-based explicit

Reduction electron transfer methods

Restricted Hartree-Fock method electron correlation methods

Restricted Hartree-Fock method, single electronic configuration

Restricted open-shell Hartree-Fock electron correlation methods

SCF Methods and Two-Electron Integral Screening

Scaling electron correlation methods

Scanning Electron Microscopy acid treatment method

Scanning electron microscopy SEM) method

Scanning electron microscopy preparation methods

Scanning electron microscopy specimen preparation methods

Schrodinger equation electron correlation methods

Schrodinger equation electronic structure methods

Self-consistent electron-pair method

Self-consistent field theory electron correlation methods

Semi-empirical electronic structure method

Semi-empirical electronic structure method advantages

Semi-empirical electronic structure method limitations

Semi-empirical electronic structure method parameterization

Semi-empirical electronic structure method performance

Semiempirical methods of electronic

Semiempirical methods of electronic structure calculation

Sensor measurement, electronic methods

Shared-electron number method

Single-molecule methods electron microscopy

Size methods electron microscope

Slater determinants electron correlation methods

Specimen preparation method scanning electron microscop

Specimen preparation method transmission electron

Specimen preparation method transmission electron microscop

Spectroscopic methods Auger-electron-spectroscopy

State-specific many-electron method

Summary of Electron Correlation Methods

Temperature measurement electronic methods

Temperature-dependent electron tunneling. Methods of determining the activation energy

Testing methods electron microscopy

Testing methods electron spin resonance

The Free-Electron MO Method

The Free-Electron Molecular Orbital Method

The Ion-Electron Method for Balancing Equations

The Spin-Free Valence Bond Method Applications to Metallic and Electron Rich Systems

Theoretical methods electronic spectra

Transmission electron microscopy method

Transmission electron microscopy specimen preparation method

Transmission electron staining, methods

Two-component all-electron methods for spin-orbit coupling

Unrestricted Hartree-Fock method electron correlation methods

Valence Shell Electron Pair Repulsion method

Valence bond method, electronic structure

Valence-electron method

Valence-shell electron-pair repulsion VSEPR) method

Wave Function Electronic Structure Methods

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