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Slater

Regardless of how many single-particle wavefiinctions i are available, this number is overwhelmed by the number of n-particle wavefiinctions ( ) (Slater detenninants) that can be constructed from them. For example, if a two-electron system is treated within the Flartree-Fock approximation using 100 basis fiinctions, both of the electrons can be assigned to any of the % obtained m the calculation, resulting in 10,000 two-electron wavefimctions. For water, which has ten electrons, the number of electronic wavefiinctions with equal numbers of a and p spin electrons that can be constructed from 100 single-particle wavefimctions is roughly... [Pg.34]

This fomi of the wavefiinction is called a Slater detemiinant. It reflects the proper symmetry of the wavefiinction and... [Pg.90]

If one uses a Slater detemiinant to evaluate the total electronic energy and maintains the orbital nomialization, then the orbitals can be obtained from the following Hartree-Fock equations ... [Pg.90]

For a free electron gas, it is possible to evaluate the Flartree-Fock exchange energy directly [3, 16]. The Slater detemiinant is constructed using ftee electron orbitals. Each orbital is labelled by a k and a spin index. The Coulomb... [Pg.94]

Slater was one of the first to propose that one replace V m equation A 1.3.18 by a tenn that depends only on the cube root of the charge density [T7,18 and 19]. In analogy to equation A1.3.32, he suggested that V be replaced by... [Pg.95]

This expression is not orbitally dependent. As such, a solution of the Hartree-Fock equation (equation (Al.3.18) is much easier to implement. Although Slater exchange was not rigorously justified for non-unifonn electron gases, it was quite successfiil in replicating the essential features of atomic and molecular systems as detennined by Hartree-Fock calculations. [Pg.95]

Comparing this to the fonn chosen by Slater, we note that this fonn, known as Kolm-Sham exchange, differs by a factor of = i.e. = 2 /3- For a number of years, some controversy existed as to whether the... [Pg.96]

Kohn-Sham or Slater exchange was more accurate for realistic systems [H]. Slater suggested that a parameter be introduced that would allow one to vary the exchange between the Slater and Kolm-Sham values [19]. The parameter, a, was often... [Pg.96]

Wlien first proposed, density llinctional theory was not widely accepted in the chemistry conununity. The theory is not rigorous in the sense that it is not clear how to improve the estimates for the ground-state energies. For wavefiinction-based methods, one can include more Slater detenuinants as in a configuration interaction approach. As the wavellmctions improve via the variational theorem, the energy is lowered. In density fiinctional theory, there is no... [Pg.97]

Slater and Kirkwood s idea [121] of an exponential repulsion plus dispersion needs only one concept, damping fiinctions, see section Al.5.3.3. to lead to a working template for contemporary work. Buckingham and Comer [126] suggested such a potential with an empirical damping fiinction more than 50 years ago ... [Pg.206]

Pekeris C L 1934 The rotation-vibration coupling in diatomic molecules Phys. Rev. 45 98 Slater J C and Kirkwood J G 1931 The van der Waals forces in gases Phys. Rev. 37 682... [Pg.216]

Slater N B 1959 Theory of Unimolecular Reactions (Wnaca, NY Cornell University Press)... [Pg.796]

For some systems qiiasiperiodic (or nearly qiiasiperiodic) motion exists above the unimoleciilar tlireshold, and intrinsic non-RRKM lifetime distributions result. This type of behaviour has been found for Hamiltonians with low uninioleciilar tliresholds, widely separated frequencies and/or disparate masses [12,, ]. Thus, classical trajectory simulations perfomied for realistic Hamiltonians predict that, for some molecules, the uninioleciilar rate constant may be strongly sensitive to the modes excited in the molecule, in agreement with the Slater theory. This property is called mode specificity and is discussed in the next section. [Pg.1027]

Slater J C 1951 Quantum Theory of Matter New York McGraw-Hill)... [Pg.1039]

The simplest trial fiinction employed in ab initio quantum chemistry is the single Slater detemiinant fiinction in which N spin orbitals are occupied by N electrons ... [Pg.2167]

To overcome some of the problems inlierent in the UFIF method, it is possible to derive SCF equations based on minimizing the energy of a wavefiinction fomied by spin projecting a single Slater detemiinant starting... [Pg.2168]

A) SLATER-TYPE ORBITALS AND GAUSSIAN-TYPE ORBITALS... [Pg.2170]

The //yj matrices are, in practice, evaluated in temis of one- and two-electron integrals over the MOs using the Slater-Condon mles [M] or their equivalent. Prior to fomiing the Ffjj matrix elements, the one-and two-electron integrals. [Pg.2176]

The so-ealled Slater-Condon rules express the matrix elements of any one-eleetron (F) plus two-eleetron (G) additive operator between pairs of antisymmetrized spin-orbital produets that have been arranged (by permuting spin-orbital ordering) to be in so-ealled maximal eoineidenee. Onee in this order, the matrix elements between two sueh Slater determinants (labelled >and are summarized as follows ... [Pg.2196]

Becke A D 1983 Numerical Flartree-Fock-Slater calculations on diatomic molecules J. Chem. Phys. 76 6037-45... [Pg.2198]

Ziegler T, Rauk A and Baerends E J 1977 On the calculation of multiplet energies by the Hartree-Fock-Slater method Theor. Chim. Acta 43 261-71... [Pg.2199]


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84 Hartree-Fock-Slater Method for Materials Science

Antisymmetrized wave function Slater determinant

Antisymmetry and the Slater Method

Basis Functions Slater-Type

Basis Slater-type orbitals

Basis atomic orbital Slater type

Basis expansion Slater-type functions

Basis function Slater

Basis functions function Slater-type orbitals

Basis sets Slater-type atomic orbital

Basis sets Slater-type functions

Basis sets Slater-type orbitals

Basis sets Slater-type-orbital

Bethe-Slater curve

Bethe-Slater-Pauling relation

Chemical bonding Slater determinant

Comparison of Slater-Type and Contracted Gaussian Basis Sets

Configuration interaction Slater determinants

Coordinate transformations Slater determinants

Crystal Slater integrals

Crystal Slater parameters

Density functional theory Hartree-Fock-Slater exchange

Density functional theory basis Slater determinants

Density functionals Slater-Kohn-Sham-type methods

Density matrices single Slater determinant

Dirac-Fock-Slater

Dirac-Fock-Slater 2503 method

Dirac-Fock-Slater potential

Dirac-Hartree-Fock-Slater method

Dirac-Hartree-Slater

Dirac-Slater

Dirac-Slater calculations

Dirac-Slater discrete-variational

Dirac-Slater discrete-variational method

Double-zeta Slater functions/orbitals

Effective Slater integrals

Eigenvalues calculations using Slater orbitals

Electron correlation Slater determinant

Electron correlation methods excited Slater determinants

Electronic structure methods Slater determinants

Electronic structure representation Slater determinants

Electronic structure single Slater determinant

Energy of a Slater Determinant

Exchange Slater model

Exchange potential Slater

Exchange potential Slater derivation

Excited Slater determinant

Expansion in Slater determinants

Finite basis functions Slater-type orbitals

Gaussian Expansion of Slater-Type Orbitals

Hartree Slater

Hartree-Fock Slater local exchange

Hartree-Fock method Slater determinants

Hartree-Fock method Slater-type orbitals

Hartree-Fock self-consistent field Slater determinant

Hartree-Fock theory. Slater determinant

Hartree-Fock-Slater

Hartree-Fock-Slater LCAO calculations

Hartree-Fock-Slater approximation

Hartree-Fock-Slater calculation

Hartree-Fock-Slater exchange

Hartree-Fock-Slater method

Hartree-Fock-Slater method total energy calculations

Hartree-Fock-Slater simulation

Hartree-Fock-Slater theory

Hartree-Fock-Slater wave function

Hartree-Slater approximation

Hartree—Fock—Slater values

Heitler-London, Pauling-Slater approach

Heitler-London-Slater-Pauling

Heitler-London-Slater-Pauling functions

Hydrogen atom using Slater orbitals

INDEX Slater determinants

INDEX Slater type orbitals

Integral Slater

Jastrow-Slater wave function

Jesse Slater

Koster-Slater equation

Koster-Slater tables

Linear combination of Slater determinants

Many-electron wave functions Slater determinants

Mathematical methods Slater determinants

Models single Slater determinant

NON-VARIATIONAL METHODS WITH SLATER DETERMINANTS

Normalization Slater determinants

Numerical solutions calculations using Slater orbitals

Orbital energy using Slater double-zeta functions

Orthogonalization Slater determinants

Orthonormality Slater determinants

Parameters Slater, definition

Perturbation theory Slater determinant

Plane Waves and Atomic-like Basis Sets. Slater-type Functions

Point of Interest John Clarke Slater

Potentials Slater

Quantum chemistry Slater determinants

Quantum-chemical Dynamics with the Slater-Roothaan Method

Radial integrals, Slater

Radii, covalent Slater

Relativistic Hartree-Fock-Slater calculations

Schrodinger equation Slater determinants

Second quantization formalism Slater determinant

Self-consistent field method Slater determinant orbital function

Self-consistent field theory Slater determinants

Single Slater determinant

Slater Coulomb integrals

Slater Determinants and Fermi Correlation

Slater Determinants and the Pauling 3-Electron Bond

Slater Matrix Element Rules

Slater Theory

Slater Xa method

Slater and Gaussian Type Orbitals

Slater approximation

Slater atomic orbitals

Slater atomic wavefunctions

Slater augmented plane wave

Slater bases

Slater basis set

Slater condition

Slater decomposition

Slater determinant Subject

Slater determinant definition

Slater determinant doubly

Slater determinant energy

Slater determinant function optimization

Slater determinant integrals

Slater determinant linear combination

Slater determinant quadruply

Slater determinant singly

Slater determinant triply

Slater determinant wave function

Slater determinantal

Slater determinantal density matrix

Slater determinantal wave function

Slater determinants

Slater determinants calculation

Slater determinants density functional theory

Slater determinants electron correlation methods

Slater determinants many-body perturbation

Slater determinants optimization techniques

Slater determinants orbital rotations

Slater determinants orbitals

Slater determinants spin projection

Slater determinants total spin

Slater determinants valence bond theory

Slater determinants wave function analysis

Slater determinants, momentum density

Slater determinants, open-shell molecules

Slater determinants, trial wavefunctions

Slater determination

Slater determination of orbitals

Slater diagram

Slater distributions

Slater exchange

Slater exchange approximation

Slater exchange functions

Slater exponent

Slater factor

Slater functions

Slater functions disadvantages

Slater functions orbital energy calculations using

Slater geminal methods

Slater hull

Slater hull necessary conditions

Slater local-exchange approximation

Slater matrix

Slater method

Slater orbital

Slater orbital Exponents

Slater orbitals

Slater orbitals valence state theory

Slater parameters

Slater parameters under pressure

Slater polynomials

Slater potential asymptotic structure

Slater rules

Slater s exchange potential

Slater sum

Slater sum rules

Slater theory applications

Slater theory orthonormality

Slater theory, of unimolecular reactions

Slater transition

Slater transition state

Slater type orbitals complex form

Slater type orbitals description

Slater type orbitals functions

Slater type orbitals radial part

Slater wave functions

Slater wavefunctions

Slater, John

Slater, John Clarke

Slater, coordinate

Slater, coordinate orbitals

Slater-Condon factors

Slater-Condon integrals

Slater-Condon parameters

Slater-Condon parameters, effective

Slater-Condon rules

Slater-Condon-Shortley parameters

Slater-Condon-Shortley rules

Slater-Condor rules

Slater-Dirac exchange potential

Slater-Kirkwood

Slater-Kirkwood approximation

Slater-Kirkwood equation

Slater-Kirkwood expression

Slater-Kirkwood formula

Slater-Kohn-Sham potential

Slater-Koster

Slater-Pauling curve

Slater-Type Orbitals

Slater-type

Slater-type Atomic Orbital (STO)

Slater-type atomic functions

Slater-type atomic orbital

Slater-type atomic orbital , definition

Slater-type atomic orbitals

Slater-type correlation function

Slater-type function

Slater-type functions, spin orbital products

Slater-type orbital

Slater-type orbital approximation

Slater-type orbitals (STO)

Slater-type orbitals Gaussian expansion

Slater-type orbitals STO basis sets

Slater-type orbitals calculations

Slater-type orbitals computation

Slater-type orbitals definition

Slater-type orbitals limitations

Slater-type orbitals minimal valence

Slater-type orbitals orthonormality

Slater-type orbitals overlap integral

Slater-type radial function

Slaters Approximation of Hartree-Fock Exchange

Slaters Bond Functions

Slaters Multiple Scattering Xa Method for Molecules

Slaters Rules for Screening Constants

Slaters Screening Rules Size of Atoms

Slaters Xa Model

Slaters band-theory treatment of Mott-Hubbard insulators

Slater’s rules

Slater’s transition state

Spin Orbitals and Slater Determinants

Spinorbitals, Slater Determinants, and Configuration Interaction

The Condon-Slater Rules

The Energy of a Slater Determinant

The Pauli Principle and Slater determinants

The Slater Theory

The Slater-Roothaan Method

The generalized Slater-Condon rules

Unimolecular reactions Slater theory

Wavefunction Slater

Wavefunctions Slater determinants

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