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Hartree theory

In the framework of a Hartree theory, the effective atomic orbital energies j defined as the diagonal matrix elements of the self consistent Hartree operator H on the atomic orbital basis set, read ... [Pg.64]

A MINDO/3 method has been used to calculate the electronic structure of polyethylene,127 and comparison has been made with the photoelectron spectrum. Extended Huckel calculations on six fluorinated compounds derived from linear polyethylene have been carried out with the same objective.128 The circular dichroism of unordered polymers has been treated on the basis of time-dependent Hartree theory,129 130 131 and high-resolution inelastic tunnelling spectroscopy of macromolecules has been reported.180... [Pg.519]

Chapter 3 is devoted to atoms. One-electron atom and multi-electron atoms of chemical elements are considered. The probability density functions (orbitals) for electrons are illustrated. The Hartree theory is presented as a first method of approximation that has been proposed in order to calculate wave functions and energies of electrons in atoms. The covalently bonded diatomic molecules are subject of the consequent consideration. [Pg.3]

D.R. Hartree and V.A. Fock made an important contribution to the science of systems consisting of a large number of electrons and nuclei. We review the Hartree theory, which gives an approximation method for the determination of the ground-state eigenfunction and the corresponding eigenvalue of a many-body quantum system. [Pg.21]

The Hartree theory involves solving (3.28) for a system of Z electrons moving independently in the atom. The total potential of the atom can be written as a sum of a set of Z identical potentials V( rj), each depending on the radial coordinate r of one electron only. Consequently, the equation can be separated into a set of Z time-... [Pg.34]

Here we consider the results of the Hartree theory of multi-electron atoms given in [2]. [Pg.35]

Figure 3.10 presents the radial behavior of the multi-electron atom eigenfunctions for an argon atom, 2 = 18. The innermost electron shell Is has a much smaller radius than the hydrogen shell because the ratio of their nuclei charges is 18 1. For argon, the radius of the innermost shell (n = 1) is 0.07 ao- The Hartree theory predicts that the radius of the n = 1 shell for multi-electron atoms is smaller than that of the n = 1 shell for the one-electron atoms by the factor 1/(2 — 2). In multi-electron atoms, the inner shells of n = 1, n = 2 have relatively small radii because for these shells there is little shielding, and the electrons feel the full Coulomb attraction. [Pg.36]

The basis of the Kohn-Sham functional is an approximation to exchange-correlation energy of electrons. The approximations should include all many-body contributions to energy that is beyond the Hartree theory. The most common choices for the exchangeenergy functionals are local density approximation and generalized density approximation (Section 8.6). However, application of these functionals reveals a poor fitness for treatment systems that are bonded by the van der Waals forces. [Pg.244]

We can estimate the repulsion between molecules using the general exponential decay seen in the atomic orbitals (Table 3.2) and a rough application of Hartree theory (Eq. 4.26) ... [Pg.423]

Combining Hartree theory (which takes care of electron correlation by ignoring it) and Fock theory (which provides an exact account of electron exchange) gives Hartree-Fock (HF) theory. For a many-electron system, Schrodinger s equation has now been replaced with N x 1-electron Hartree-Fock equations. It works... [Pg.47]

When fxc is set to zero in Eq. [42], physicists call it the random-phase approximation (RPA). The inclusion of fxc is an exactification of RPA, in the same way that the inclusion of fxcCr) in ground-state DFT was an exactification of Hartree theory. [Pg.109]

Hartree theory embodies the self-consistent nature of the type of theories that one deals with in modern electron theory, but the many-electron wave functions of Hartree theory,... [Pg.165]

Thus, when expressing matrix elements of the many-body wavefunction in the position representation, the set of variables appearing as arguments in the single-particle states of the bra and the ket must be in exactly the same order for example, in the Hartree theory, Eq. (2.10), the Coulomb repulsion term is represented by... [Pg.538]

Thus within the Hartree theory we get the same energies as in the zero potential case. The Hartree-Fock case can now be treated by adding the exchange term to... [Pg.145]


See other pages where Hartree theory is mentioned: [Pg.145]    [Pg.479]    [Pg.589]    [Pg.169]    [Pg.169]    [Pg.37]    [Pg.119]    [Pg.120]    [Pg.120]    [Pg.33]    [Pg.33]    [Pg.35]    [Pg.37]    [Pg.37]    [Pg.114]    [Pg.112]    [Pg.47]    [Pg.73]    [Pg.145]    [Pg.146]    [Pg.201]   
See also in sourсe #XX -- [ Pg.45 , Pg.111 ]

See also in sourсe #XX -- [ Pg.34 , Pg.35 , Pg.37 , Pg.113 ]

See also in sourсe #XX -- [ Pg.47 ]

See also in sourсe #XX -- [ Pg.112 , Pg.145 , Pg.199 ]




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Approximations of MO theory Hartree-Fock

Bond breaking Hartree-Fock theory

Bond dissociation Hartree-Fock theory

Coulomb potential Hartree-Fock theory

Coupled Hartree-Fock perturbation theory

Coupled Hartree-Fock theory

Coupled perturbed Hartree-Fock theory

Coupled-perturbed Hartree-Fock orbital theory

DERIVATION OF HARTREE-FOCK THEORY

Density functional theory Hartree-Fock exchange

Density functional theory Hartree-Fock-Slater exchange

Density-based Hartree-Fock theory

Density-based Hartree-Fock theory matrix

Density-based Hartree-Fock theory self-consistent field method

Derivative Hartree-Fock theory

Differentiation, derivative Hartree-Fock theory

Dirac-Hartree-Fock theory

Direct Hartree-Fock theory

Electronic Hessian Hartree-Fock theory

Electronic structure Hartree-Fock theory

Electronic structure methods Hartree-Fock theory

Electronically excited states Hartree-Fock theory

Exchange-correlation potential Hartree-Fock theory

Excitation energy Hartree-Fock theory

Hamiltonian equation derivative Hartree-Fock theory

Hartree Fock coupled-cluster theory

Hartree-Fock crystal field theory

Hartree-Fock crystal-orbital theory

Hartree-Fock crystal-orbital theory periodic polymers

Hartree-Fock equations/theory

Hartree-Fock equations/theory application

Hartree-Fock equations/theory closed-shell

Hartree-Fock equations/theory configuration interaction

Hartree-Fock equations/theory many-body perturbation

Hartree-Fock method band structures, theory

Hartree-Fock method perturbation theory based

Hartree-Fock method theory applications

Hartree-Fock model perturbation theory

Hartree-Fock molecular orbital theory

Hartree-Fock theory

Hartree-Fock theory 592 INDEX

Hartree-Fock theory Brillouin theorem

Hartree-Fock theory Koopmans’ theorem

Hartree-Fock theory approach

Hartree-Fock theory approximation

Hartree-Fock theory basis sets

Hartree-Fock theory canonical orbitals

Hartree-Fock theory classical mechanics

Hartree-Fock theory correlation problem

Hartree-Fock theory dissociation

Hartree-Fock theory dissociation curves

Hartree-Fock theory electron correlation methods

Hartree-Fock theory electronic gradient

Hartree-Fock theory energy

Hartree-Fock theory exchange potential

Hartree-Fock theory fluctuation potential

Hartree-Fock theory force field methods

Hartree-Fock theory ground state

Hartree-Fock theory half-electron

Hartree-Fock theory instability

Hartree-Fock theory interaction energy

Hartree-Fock theory introduction

Hartree-Fock theory limit

Hartree-Fock theory mathematical methods

Hartree-Fock theory methods

Hartree-Fock theory molecular properties

Hartree-Fock theory multiple solutions

Hartree-Fock theory numerical

Hartree-Fock theory of free electrons

Hartree-Fock theory optimization techniques

Hartree-Fock theory orbital energies

Hartree-Fock theory periodic

Hartree-Fock theory post-theories

Hartree-Fock theory predictions from

Hartree-Fock theory projected

Hartree-Fock theory qualitative theories

Hartree-Fock theory redundant parameters

Hartree-Fock theory relativistic methods

Hartree-Fock theory restricted

Hartree-Fock theory restricted open-shell

Hartree-Fock theory second-order optimization

Hartree-Fock theory semiempirical

Hartree-Fock theory single-reference methods

Hartree-Fock theory size-extensivity

Hartree-Fock theory solid-state materials

Hartree-Fock theory states

Hartree-Fock theory structure optimization

Hartree-Fock theory symmetry

Hartree-Fock theory theor

Hartree-Fock theory unrestricted

Hartree-Fock theory variational conditions

Hartree-Fock theory wave function

Hartree-Fock theory, description

Hartree-Fock theory, early work

Hartree-Fock theory, localized

Hartree-Fock theory, solution

Hartree-Fock theory, time-dependent coupled-perturbed

Hartree-Fock theory, total energy

Hartree-Fock theory, total energy computations

Hartree-Fock theory. Slater determinant

Hartree-Fock theory. The independent-particle model

Hartree-Fock, density functional/perturbation theory

Hartree-Fock-Slater theory

Hartree—Fock/density-functional theory

Hyperpolarizabilities Hartree-Fock theory

Hyperpolarizabilities derivative Hartree-Fock theory

Integral-direct Hartree-Fock theory

Key Technical and Practical Points of Hartree-Fock Theory

Molecular orbital theory Hartree-Fock self-consistent field approximation

Moller-Plesset perturbation theory coupled perturbed Hartree-Fock

ORBITAL INTERACTION THEORY Relationship to Hartree-Fock Equations

Open-shell Hartree-Fock theory (RHF)

Post-Hartree-Fock theories

Quantum Hartree-Fock theory

Quantum Mechanics Hartree-Fock theory

Reaction mechanisms Hartree-Fock theory

Restricted Hartree-Fock theory energy

Restricted Hartree-Fock theory operator

Restricted and unrestricted Hartree-Fock theory

Results of the Hartree Theory

Self-consistent field theory Hartree-Fock electronic structure calculations

Successes and Failures of Hartree-Fock Theory

Symmetry in Hartree-Fock Theory

The Hartree Theory

The g-Hartree theory of orbital collapse

Time-dependent Hartree-Fock TDHF) theory

Time-dependent Hartree-Fock theory

Variational methods. Coupled Hartree-Fock theory

Wave-function calculations Hartree-Fock theory

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