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,... 

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... 

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. 

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) ... 

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. 

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