Obviously the n ionization energy is a function of the type, number and position of the substituents. The IP( n) values of 4-substituted quinuclidines correlate linearly with Taft s a values51 (Figure 3). [Pg.169]

It should be noted that the IP s and EA s of valenee-state orbitals are not identieal to the experimentally measured IP s and EA s of the eorresponding atom, but ean be obtained from sueh information. For example, the 2p valenee-state IP (VSIP) for a Carbon atom is the energy differenee assoeiated with the hypothetieal proeess [Pg.196]

We have m x m equations because each of the m spatial MO s i// we used (recall that there is one HF equation for each ip, Eqs. 5.47) is expanded with m basis functions. The Roothaan-Hall equations connect the basis functions (p (contained in the integrals F and S, Eqs. 5.55, above), the coefficients c, and the MO energy levels . Given a basis set

It is noted that if ei = e2 the anti-symmetric wave function vanishes, ipa = 0. Two identical particles with half-spin can hence not be in the same non-degenerate energy state. This conclusion reflects Pauli s principle. Particles with integral spin are not subject to the exclusion principle (ips 0) and two or more particles may occur in the same energy state. [Pg.467]

Xrx is a parameter characterizing the homologous series RX. The values of /j,r are direct measures of the polar inductive effects of alkyl groups relative to that of methyl and correlate well with Taft s a values. Substituent-induced IP shifts can thus be handled by linear free energy relationships (LFER) of the Hammett pcr-type. [Pg.169]

The ionization potential and electron affinity of naphthalene were determined experimentally as IP = 8.2 eV and EA 0.0 eV. According to Koopmans theorem it is possible to equate minus the orbital energies of the occupied or unoccupied MOs with molecular ionization potentials and electron affinities, respectively (IP, = - s, and EA = - ). Thus, in the simple one-electron model, the excitation energy of the HOMO->LUMO transition in naphthalene may be written according to Equation (1.22) as [Pg.14]

From Table 19 it can be derived that AIP is small for all helicenes, so that the a-band is expected to precede the p-band. (This is observed experimentally for [6], [7] and [8].) From the study of planar aromatic compounds 124) it was also found that the p-band correlates linearly with the first IP, whereas for the a- and P-band energies a linear correlation with the mean of the first two IP s was established. [Pg.103]

This behaviour of GF theory at the level of the second-order self-energy is more striking for the lowest ionization potentials of the ten-electron series shown in Table 7.4. At the level of 6-31G both the Koopmans and GF results appear to have converged. For all four molecules, Koopmans theorem overestimates the IP s, and in all cases the GF treatment lowers the IP too far, so that the Koopmans result actually agrees better with experiment. [Pg.406]

We assume that we have a solid metal M which reacts with a diatomic, gaseous nonmetal X2 (e.g., CI2, F2, 02). Similar cycles can be written for solid elements such as sulfur as the nonmetal. In either case, before we can connect U with AHf we must form gaseous ions of M and X. We need not only the relevant ionization potentials (IP) and electron affinities (EA), but also the heats of atomization of solid M and gaseous X2. These atomization energies are traditionally referred to as heats of sublimation AHsuh of M(s) and of dissociation AHd ss of X2. For NaCl itself, we have [Pg.90]

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