Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Self-consistent field Koopmans’ theorem

From Figures 8.1(a) and 8.1(b) it would appear that the energy required to eject an electron from an orbital (atomic or molecular) is a direct measure of the orbital energy. This is approximately true and was originally proposed by Koopmans whose theorem can be stated as follows Tor a closed-shell molecule the ionization energy of an electron in a particular orbital is approximately equal to the negative of the orbital energy calculated by a self-consistent field (SCF see Section 7.1.1) method , or, for orbital i,... [Pg.296]

Toroidal forms of carbon were predicted to be stable on the basis of molecular dynamics simulations using a Stillinger-Weber-type potential.To test these predictions, the stability of a C120 torus was compared with that of Ceo using ab initio self-consistent field calculations and ionization potentials determined by Koopman s theorem (Table 4). The C120 structure investigated hadDs symmetry, and appears to... [Pg.291]

Koopmans Theorem. In contrast to many other spectroscopic methods, interpretation of photoelectron spectra requires the support of calculations. According the equation 3 it is in principle necessary to calculate the total energy of both the ground state and the various cationic states of a molecule. In most cases—for exceptions, see Section III—it is sufficient to calculate the electronic structure of the ground state of the molecule within the self-consistent-field (SCF) method. [Pg.154]

Traditionally, Koopman s theorem (KT) has been applied to calculate IPs of molecules. KT for self-consistent field (SCF) wavefunctions provides a simple model for ionization, according to which an electron is removed from an orbital and the ionization energy (IE) is the negative of the orbital energy (e) ... [Pg.1190]

The next five chapters are each devoted to the study of one particular computational model of ab initio electronic-structure theory Chapter 10 is devoted to the Hartree-Fock model. Important topics discussed are the parametrization of the wave function, stationary conditions, the calculation of the electronic gradient, first- and second-order methods of optimization, the self-consistent field method, direct (integral-driven) techniques, canonical orbitals, Koopmans theorem, and size-extensivity. Also discussed is the direct optimization of the one-electron density, in which the construction of molecular orbitals is avoided, as required for calculations whose cost scales linearly with the size of the system. [Pg.546]


See other pages where Self-consistent field Koopmans’ theorem is mentioned: [Pg.296]    [Pg.294]    [Pg.48]    [Pg.30]    [Pg.46]    [Pg.218]    [Pg.132]    [Pg.1013]    [Pg.41]   
See also in sourсe #XX -- [ Pg.358 , Pg.359 ]




SEARCH



Koopman theorem

Koopmans

Self-Consistent Field

Self-consisting fields

© 2024 chempedia.info