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The 4 Orbitals

In Table 8 we show the calculated energies of the highest occupied orbitals for a set of isolated atoms together with experimental ionization potentials. The table confirms the conclusion above, i.e., that the Kohn-Sham energies are too high. Furthermore, these tend to have a too weak dependence on the system, [Pg.342]

Politzer and Abu-Aw wad61 studied the calculated single-particle energies for 12 smaller molecules and compared them with experimental ionization potentials. They found that the Kohn-Sham orbital energies were at least 2 eV too high [Pg.342]

Any experimental study of the properties of a given system involves perturbing the system somehow and by measuring the response of the system trying to [Pg.343]

Electronic excitations involve changing the populations of the various orbitals. A special case is that of ionization for which one electron is removed from an occupied orbital and, in principle, brought infinitely far away from the molecule. In the reverse case, one adds an electron to an unoccupied orbital. The excitation of an electron from an occupied to an unoccupied orbital is, in principle, the combination of the two former processes. [Pg.344]

As discussed in Section 2, the density-functional methods are, in principle, capable of describing only the properties of the energetically lowest state for [Pg.344]

Russell-Saunders formalism is simple to use and will be carried through this chapter. Term symbols with the format which summarise the quantum number information, are [Pg.3]

A complete diagram, showing the ground and excited states of all lanthanide ions in the +III oxidation state with corresponding term symbols, is displayed in Fig. 1.2. [Pg.4]


Aufbau principle In building up the electronic configuration of an atom or a molecule in its ground state, the electrons are placed in the orbitals in order of increasing energy. [Pg.46]

To arrive at the electronic configuration of an atom the appropriate number of electrons are placed in the orbitals in order of energy, the orbitals of lower energy being filled first (Aufbau principle ), subject to the proviso that for a set of equivalent orbitals - say the three p orbitals in a set - the electrons are placed one... [Pg.152]

The index for the orbital ( ). (r) can be taken to include the spin of the electron plus any other relevant quantum numbers. The index runs over the number of electrons, each electron being assigned a unique set of quantum... [Pg.89]

Using the orbitals, ct)(r), from a solution of equation Al.3.11, the Hartree many-body wavefunction can be constructed and the total energy detemiined from equation Al.3,3. [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]

The wavevector is a good quantum number e.g., the orbitals of the Kohn-Sham equations [21] can be rigorously labelled by k and spin. In tln-ee dimensions, four quantum numbers are required to characterize an eigenstate. In spherically syimnetric atoms, the numbers correspond to n, /, m., s, the principal, angular momentum, azimuthal and spin quantum numbers, respectively. Bloch s theorem states that the equivalent... [Pg.101]

There are complicating issues in defmmg pseudopotentials, e.g. the pseudopotential in equation Al.3.78 is state dependent, orbitally dependent and the energy and spatial separations between valence and core electrons are sometimes not transparent. These are not insunnoimtable issues. The state dependence is usually weak and can be ignored. The orbital dependence requires different potentials for different angular momentum components. This can be incorporated via non-local operators. The distinction between valence and core states can be addressed by incorporating the core level in question as part of the valence shell. For... [Pg.112]

Initially, we neglect tenns depending on the electron spin and the nuclear spin / in the molecular Hamiltonian //. In this approximation, we can take the total angular momentum to be N(see (equation Al.4.1)) which results from the rotational motion of the nuclei and the orbital motion of the electrons. The components of. m the (X, Y, Z) axis system are given by ... [Pg.168]

Wlien the atom-atom or atom-molecule interaction is spherically symmetric in the chaimel vector R, i.e. V(r, R) = V(/-,R), then the orbital / and rotational j angular momenta are each conserved tln-oughout the collision so that an i-partial wave decomposition of the translational wavefiinctions for each value of j is possible. The translational wave is decomposed according to... [Pg.2044]

The orbit eoinmon to all ehaimels is found by ehoosing the potential governing the relative motion as the average [22]... [Pg.2054]

Notice that the orbitals occupied in the configuration under study appear in the mean-field potential. However, it is that, tln-ough the one-electron Scln-ddinger equation, detennines the orbitals. For these reasons, the solution of these... [Pg.2163]

The HF equations must be solved iteratively beoause the J- and K. operators in F depend on the orbitals ( ). for whioh solutions are sought. Typioal iterative sohemes begin with a guess for those ([). that appear in T", whioh then allows f to be fonned. Solutions to = e.. are then found, and those (j). whioh possess the spaoe and... [Pg.2169]

Cartesian Gaussian-type orbitals (GTOs) Jfa.i.f( ( characterized by the quantum numbers a, b and c, which detail the angular shape and direction of the orbital, and the exponent a which governs the radial size . [Pg.2170]

The orbitals from which electrons are removed can be restricted to focus attention on the correlations among certain orbitals. For example, if the excitations from the core electrons are excluded, one computes the total energy that contains no core correlation energy. The number of CSFs included in the Cl calculation can be far in excess of the number considered in typical MCSCF calculations. Cl wavefimctions including 5000 to 50 000 CSFs are routine, and fimctions with one to several billion CSFs are within the realm of practicality [53]. [Pg.2176]


See other pages where The 4 Orbitals is mentioned: [Pg.152]    [Pg.152]    [Pg.152]    [Pg.264]    [Pg.357]    [Pg.1025]    [Pg.2]    [Pg.32]    [Pg.33]    [Pg.37]    [Pg.112]    [Pg.138]    [Pg.174]    [Pg.296]    [Pg.380]    [Pg.980]    [Pg.994]    [Pg.1124]    [Pg.1314]    [Pg.1321]    [Pg.1553]    [Pg.1554]    [Pg.1608]    [Pg.1855]    [Pg.2045]    [Pg.2048]    [Pg.2049]    [Pg.2077]    [Pg.2163]    [Pg.2163]    [Pg.2168]    [Pg.2168]    [Pg.2171]    [Pg.2172]    [Pg.2173]    [Pg.2174]    [Pg.2176]   


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A Molecular Orbital Model of the Hydrogen Bond

A molecular orbital description of the bonding in organometallic complexes

A tt Molecular Orbital Analysis of the Diels-Alder Reaction

Analysis of the Orbital-Dependent Correlation

And the frontier orbital method

Angular Orbital Momentum and the Impact Parameters

Appendix C Tracking the continuity of molecular orbitals along a nuclear path

Assessing the contribution of d orbitals

Astronomical factors in orbit of the Earth

Atomic Orbitals A Quantum Mechanical Description of Electrons Around the Nucleus

Atomic orbitals, electronic configurations and the Periodic Table

Beyond the Molecular Orbital Approach

Beyond the Orbital Approximation

Bloch Theorem and the Crystal Orbitals

Bonding in H2 The Molecular Orbital Model

Calculation of the photoelectron orbitals

Centring of the atomic orbital

Coefficients of the atomic orbitals

Combining the Localized Electron and Molecular Orbital Models

Comparison of the Resonance and Molecular-Orbital Methods

Computational technique atomic orbitals as building blocks of the molecular wave function

Crystal field splitting patterns of the 4f orbitals

Crystal orbital overlap population the formation of bonds

Dienes and the Allyl System 2p Orbitals in Conjugation

Electron Configurations of the Lanthanides and f Orbitals

Equilibrium-orbit Models the Model of Barth

Equivalence of the molecular orbital and valence bond models

Evaluation of the nuclear derivative coupling matrix elements with canonical molecular orbitals

Explicit construction of the energy density functional within an orbit

Filled orbital of the

Filling the 2p Orbitals

Filling the 3s, 3p, and 4s Orbitals

Fragment orbitals by the valence-bond method

Frontier Orbital Interactions in the Transition States of One-Step -Cycloadditions

Frontier Orbital Interactions in the Transition States of One-Step 1,3-Dipolar Cycloadditions Sustmann Classification

Group Product Functions and the Basis Orbitals

Heavy particle transfer and the Langevin orbiting theory

Hybrid Orbitals and the Structure of Acetylene

Hybrid Orbitals and the Structure of Ethane

Hybrid Orbitals and the Structure of Ethylene

Hybrid Orbitals and the Structure of Methane

Hybrid orbitals the valence bond model

Hybridization sp Orbitals and the Structure of Acetylene

ISOTOPES, ELECTRON ORBITALS, AND THE PERIODIC TABLE

Idiopathic inflammation of the orbit

Improving the Atomic Orbital

Information on the Graph Orbits

Interface with the Orbital Model

Linear H3, HF, and the Three-Orbital Problem

Linear combinations of the atomic orbitals

Localization of molecular orbitals within the RHF method

Molecular Orbital Analysis of the Diels-Alder Reaction

Molecular Orbital Calculations on the

Molecular Orbital Contributions to the Chemical Shift

Molecular Orbitals for the Hydrogen Molecule-ion

Molecular Orbitals for the Water Molecule

Molecular Orbitals of the Allylic System

Molecular orbital theory applied to the polyatomic molecules BH

Molecular orbitals The Fock and Roothaan equations

Molecular orbitals associated with the

Molecular orbitals for the

Molecular orbitals the hydrogen molecule ion

Muffin-Tin Orbitals in the ASA

Multi-Electronic Orbitals in the Crystal Field

Open Shell Atomic Beam Scattering and the Spin Orbit Dependence of Potential Energy Surfaces

Orbit of the Earth

Orbital A representation of the space occupied level

Orbital Blocks in the Periodic Table

Orbital Calculations of the Anomeric Effect

Orbital Contributions at the Strong-Field limit

Orbital Interaction in the Diels-Alder Reaction

Orbital Ordering in the Perovskite Manganates

Orbital Quenching and the Spin-Only Formula

Orbital Symmetry Basis for the Stereospecificity of Electrocyclic Reactions

Orbital Treatment of the Isolated Molecule Method

Orbital functional theory of the -matrix

Orbital picture of the allyl radical

Orbitals and the Non-Interacting Reference System

Orbitals and the Periodic Table

Orbitals and the Secular Equation

Orbitals and the structure

Orbitals of the hydrogen atom

Orbitals. The LCAO Method

Perturbation of the molecular orbitals

Quaternion form of the hybrid orbitals and hybridization tetrahedra

Relative sizes of hydrogenic orbitals and the probability criterion

Response of the Monsoon to Orbital Forcing

Scenario 2—There is a Single Unpaired Electron in One of the Orbitals

Shape and symmetry of the orbitals

Solving for the Molecular Orbitals

Some Connections Between the Representation Table and Molecular Orbitals

Spin Orbitals and the Pauli Principle

Spin and orbital contributions to the magnetic moment

Spin-Orbit Coupling - The Free Ion Case

Spin-Orbit Coupling in the H Atom

Spin-orbit effects and reactivity on the ground state

Spin-orbit interaction and the vector

Spin-orbit interaction in complexes the double group

Splitting of d orbitals in the octahedral crystal field

Splitting of the 3d orbital energies

Stabilization of the d orbitals

Stereoelectronic Effects in Action The Many Doors Opened by Orbital Interactions

Symmetry restrictions in the orbital basis

Symmetry restrictions in the spin-orbital basis

THE SHAPES OF f ORBITALS

The 3d bound orbital and two examples of ef continuum wavefunctions

The 7r orbitals of

The Atomic Orbitals of Hydrogen

The Atomic Orbitals of a Hydrogen Atom

The Basic Ideas of Molecular Orbital Methods

The Bohr Model Atoms with Orbits

The Bonding Contributions of d Orbitals

The Breathing-Orbital Valence Bond Method

The Characteristics of Hydrogen Orbitals

The Chemical Bond Energy from Molecular Orbitals

The Chemical Bond Formation Energy Based on Rigid Atomic Orbitals

The Complete Atomic Orbitals

The Conservation of Orbital Symmetry (Woodward-Hoffmann Rules)

The CpM Fragment Orbitals

The Cyclic Three-Orbital Mixing Problem

The Description of Molecules by Sigma and Pi Orbitals

The Dirac Equation Without Spin-Orbit Coupling

The Direction of Nucleophilic Attack and Orbital Steering

The Effect of Orbital Symmetry on ET Dynamics

The Exact Muffin-Tin Orbital Method

The Free-Electron Molecular Orbital Method

The Generalized Orbital Symmetry Rule

The Goppert-Mayer-Fermi theory of orbital contraction

The Hydrogen Atom and Atomic Orbitals

The Hydrogen Molecule Molecular Orbitals

The Hydrogen Orbitals

The Kohn-Sham Molecular Orbital Model

The LCAO-Molecular Orbital Model

The LiH molecule approximate molecular orbital calculations

The Localized Orbitals of a CH2 Group

The Metallic Orbital

The Molecular Orbital Account of Polarizability

The Molecular Orbital Approach to Colour and Constitution

The Molecular Orbital Energy

The Molecular Orbital Model of Bonding

The Molecular Orbital Picture of Benzene

The Molecular Orbital Picture of Cyclobutadiene

The Molecular Orbital-Valence Bond Theory of Excited States

The Molecular Orbitals of Benzene

The Natural Orbitals

The Nature of Chemical Bonds Molecular Orbital Theory

The Nature of Spin-Orbit Coupling

The Non-bonding Molecular Orbital Method

The One-electron Bond and Non-paired Spatial Orbital Structures

The Orbital Approximation Helium

The Orbital Approximation for Lithium

The Pair Density. Orbital-dependent Exchange-correlation Functionals

The Pariser-Parr-Pople Crystal-Orbital Method

The Phase of Orbitals

The Phase of an Orbital

The Quantistic Approach Molecular Orbital (MO) Theory

The Quantum Mechanical Atom Principal Shells, Subshells, and Orbitals

The Quantum-Mechanical Model Atoms with Orbitals

The Recently Claimed Observation of Atomic Orbitals and

The Relationship between Molecular Orbital and Valence Bond Wave Functions

The Relative Energies of Atomic Orbitals from Electronegativity

The Role of Frontier Orbitals

The Role of d Orbitals

The Shapes of Atomic Orbitals

The Special Crystal Orbital of Glitter

The Spin-Orbit Operator

The Two-Orbital Mixing Problem

The Two-Orbital Problem—Summary

The Use (or Not) of d Orbitals by Nonmetals

The Use of Self-consistent Field Methods to Obtain Atomic Orbitals

The Use of p Orbitals in Pi Bonding

The Uses of Frontier Orbitals

The Walsh Diagram and Group Orbitals

The Wavefunctions of Many-Electron Atoms Can Be Described to a Good Approximation Using Atomic Orbitals

The Woodward-Hoffmann rules and molecular orbitals

The atomic orbital model

The carbon orbitals expanded in GTOs

The carbon orbitals expanded in HO functions

The carbon orbitals expanded in Laguerre functions

The concept of molecular orbitals in other systems

The crystal orbital approach

The d Orbitals in a Tetrahedral Field

The d Orbitals in an Octahedral Field

The d and f Orbitals

The d orbitals

The energies of molecular orbitals in diatomic molecules

The frontier orbital description of cycloadditions

The g-Hartree theory of orbital collapse

The hybridization model and two-center molecular orbitals

The independent functions from an orbital product

The introduction of quantum mechanics atomic orbitals and orbital energies

The localized molecular orbital (LMO) model

The mathematical form of hybrid orbitals

The mechanism of orbital collapse

The molecular orbital Model

The molecular-orbital theory

The nodeless Gaussian-type orbitals

The orbital approximation

The p Orbitals

The s Orbitals

The shapes of d orbitals

The shapes of p orbitals

The shapes of s orbitals

The sp (n 1-3) hybrid orbitals

The spin-orbit interaction

The tt Molecular Orbitals of Ethylene and 1,3-Butadiene

The wave equation and molecular orbitals

Three-orbital interactions stereoelectronic reasons for the preferred trajectories of intermolecular attack at a chemical bond

Tin Orbitals and the Atomic Sphere Approximation

Use and misuse of the hybrid orbital concept

Using the Group Orbitals to Construct Organometallic Complexes

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