SCF orbital energy

Figure 9. Determination of the first electron affinity, and the first and higher ionization potentials of formyl radical from the SCF orbital energies and electronic repulsion integrals, and K,j (cf. eqs. (90), (92), and (93)). The experimental value (112), 9.88 eV, for the first ionization potential corresponds to the theoretical value I . All entries are given in eV. With A and I a lower index stands for MO the upper one indicates the state multiplicity after ionization.

Finally, it should be stressed that although the spectroscopic data yield the order of one-electron core energies as 5 Ko ir, these quantities are not synonymous with the corresponding SCF orbital energies. Consequently there is no contradiction involved by the... 

For the moment however it is not clear where the results of X - a calculations can be fitted into the pattern since it is not evident that the calculated electronic energies of the various levels have the same significance viz a viz Koopmans theorem as do the SCF orbital energies. 

Following Hendrickson s (55) treatment of Fe(Cp)2 one may write the SCF orbital energies as... 

For the open-shell d3 V(Cp)2 system, with the 4Z (a S2) ground level, the SCF orbital energies may be similarly expressed without ambiguity, yielding AeSCF =... 

Within an orbital picture of molecular electronic structure, formation of ion states can be described by removal of electrons from occupied orbitals in a molecule (Figure 1). Koopmans put this model on a quantitative footing by relating the ionization energy of a molecule to the negative of the self-consistent field (SCF) orbital energy, -Bj (equation 5) ... 

For a closed-shell molecule, Koopmans approximation identifies an IE with the negative of the SCF orbital energy (equation 5) if this were the case, a PE spectrum would provide an exact mapping of the occupied orbitals of a molecule (Figure 3). 

Electron densities and SCF orbital energies for chromone and some derivatives calculated by the PPP method have been correlated with H shifts and polarographic half-wave potentials (78IJC(A)53l). 

Relativistic contributions to the orbital energies computed by Herman and Skillman added to the nonrelativistic SCF orbital energies of Froese for use as VSIP. 

Using the SCF orbital energies and two-electron integrals given in Problem 2.1, insert numerical values for the requisite integrals and orbital energies to express each of the elements of the 2 x 2 matrix P2(E) as functions of . 

The important conclusion to be drawn from these observations is that the assumption of equivalent bond orbitals 2 as used in an EBO treatment can be validated by the properties of LMOs Aj derived from ab initio calculations. The mathematical formalism for handling LMOs according to equations, 32 and 33 is exactly the same as that of an EBO model, which implies that this Hiickel-type treatment is capable of yielding excellent approximations to the SCF orbital energies Sj and the corresponding CMOs (pj of saturated hydrocarbons. 

The condition (17.38) determining the tt-MO coefficients for benzene was derived solely from symmetry considerations, without use of the Hiickel approximations. Thus the MOs (17.41) are (except for normalization constants) the correct minimal-basis-set SCF TT-electron MOs for benzene. (The Hiickel energies ei,..., e are, however, not the true SCF orbital energies. The Hiickel method ignores electron repulsions and takes the total TT-electron energy as the sum of orbital energies. The SCF MO method takes electron... 

We have extended the application of the OVGF method to the calculation of IPs of radicals as well. The SCF orbital energies were calculated by the half-electron (HE) method, using doublet correction for IPs. The SAMI, AMI. and OVGF(AMl) calculated vertical IPs of 28 organic radicals (see Scheme 3) are collected in Table 7 together with available experimental data. 

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