Experimental ionization correlation

Figure 2. Experimental ionization correlation diagram for CI2, HCl and NaCl.

Similarly, as the case with response properties discussed in the previous section, imposing the correct asymptotic behavior of vxc improves the agreement between the numerical values of —sH0M0 and the experimental ionization potentials.85,90,91,94 For these reasons, the ionization potentials and electron affinities are usually obtained as energy differences (ASCF) in calculations using common approximations to the exchange-correlation functional. The discussed hereafter numerical values were obtained in this way. 

Since all of the above calculations are strongly dependent on orbital energies, it is worthwhile to close with a short comparison of orbital energies, as calculated by HF and by DFT, and as measured experimentally by ESCA and photoelectron spectroscopy. These are shown in Table 2.8. Both the HF and KS orbital energies are quite close to the experimental ionization potentials. In principle, the KS energy for the outermost orbital should equal the first ionization potential, but this has not yet happened. It will be recalled that the KS results depend on how well the exchange-correlation potential is represented. " ... 

In other analytical work, Shevchenko et al. [80] found excellent agreement between theoretical and experimental ionization potentials. Semenov and Khodyreva (81) compare photoelectron spectra with CNDO/S3 calculations and found good resnlts. Semiempirical calculations, on a number of lignin model compounds have also been nsed as an aid in the interpretation of ESR spectroscopy [34]. In more general research on substituted aromatic systems [82] correlated experimental p/f valnes to semiempirical heats of formation and HOMO energies, with correlations in the 0.7-0.9 range. 

The formal relationship between experimental ionization energies and theoretically calculated orbital eigenvalues is given by Koopmans theorem.(26) Koopmans theorem shows that the additional theoretical contributions of electron relaxation and electron correlation that appear as terms in ab initio orbital approximations are neglected in equating orbital eigenvalues to ionization energies. 

The parameters used in Eqs. 64 - 68 have to be adjusted either to experimental data or ab initio data from highly correlated calculations for the one valence electron atoms or ions. Similarly, the core dipole polarizability may be taken from experiment or could be calculated by ab initio methods. Although the experimental ionization potentials (and excitation energies) for not too small cores... 

Figure 4. Experimental ionization energy correlation diagram of N2.

Density functional calculations in which the exchange-correlation effects are treated beyond the LDA give the hope that Eq. (21) will be fulfilled better. This has been achieved to a large extent by the so called non-local weighted-density-approximation (WDA) [24, 29]. The results are also given in Table 2. IchomoI is very close to the experimental ionization potential and also rather close to the WDA ionization potential calculated from Eq. (20). The original paper [30] should be consulted for details. 

They were interested in the performance of different density-functional approaches. In all cases they used the ALDA for the exchange-correlation kernel, but for the response function Xs of Eq. (96) they used different density functionals. Since most of the current density functionals give a wrong ionization threshold (cf. the discussion of the preceding section), they rigidly shifted the single-particle energies so that the experimental ionization potential was obtained. 

The second and most important point of Table 3.16 is that the correct Hartree-Fock results are in qualitative disagreement with experiment. In the molecular orbital Hartree-Fock model, the l7r orbital is the highest occupied orbital, yet the lowest experimental ionization potential corresponds to the production of an ion with symmetry. This implies a breakdown of the simple orbital picture of ionization. The Hartree-Fock picture is an approximation. For the case of N2 this approximation is not sufficiently accurate for even a qualitative understanding of the ionization phenomena. As we shall see in Chapters 4 and 7, when the single determinant Hartree-Fock model is replaced by a multideterminantal model, with its associated inclusion of correlation effects, theoretical calculations and experiment ultimately agree on the ionization spectra of N2. 

Rotational constants and centrifugal distortion constants of the upper vibrational state 2 vg of H2B-NH2 have also been determined by microwave spectroscopy for details, see [3]. Also, the He(I) photoelectron spectrum of H2B-NH2 (produced by controlled thermal decomposition of H3N-BH3) has been measured [4]. The five ionization potentials observed up to 21.2 eV have been correlated with those of ethene. A good correspondence of the observed values was obtained with data from Koopmans theorem calculations for the ground state molecule (semiempirical MNDO and SCF ab initio calculations with 3-21G and 6-31G bases). Experimental ionization potentials (IP) and calculated orbital energies are given in Table 4/24, p. 222 [4]. A correlation of the IP data of H2B-NH2 and H2CCH2 is given for the five uppermost filled levels in Fig. 4-47, p. 222. 

March and Wind [17] took as starting point the correlation energies Ec of neutral atoms extracted in the early work of dementi [18] from experimental ionization energies (see Fig. 1) and modified appropriately for relativistic corrections which are needed essentially in the K shell. Writing the correlation energy density per electron as Sc r) then the total correlation energy Ec is evidently... 

Table 3.7. Comparison of LDA [18], Cl (estimated from non-relativistic CI-calculations for the three innermost electrons and the experimental ionization potentials of all other electrons [25]) and MBPT2 [26] correlation energies for neutral atoms - non-relativistic correlation energy, AE - relativistic contribution...

The ultraviolet spectra of crowded olefins and substituted butadienes have been studied the sign of the Cotton effect has been related to the chirality of a series of w-molecular complexes of olefins with tetracyanoethylene the sign of the chiral-optical effects of non-planar heteroannular cisoid dienes is opposite to that predicted from the diene rule. Studies of linear and circular dichroism in mono-olefins and magnetic circular dichroism of conjugated olefins have been made, and the experimental ionization potentials of fourteen alkenes have been correlated with the inductive effects of substituents. ... 

It was seen in Section 5.3 that to determine the QP band structures of a polymeric chain one must use a size-consistent method to determine the major part of the correlation [many-body perturbation theory (MBPT) in the Moller-Plesset partitioning, coupled-cluster theory, etc.]. Suhai, in his QP band-structure calculation on polyacetylenes and polydiace-tylenes, used second-order (MP/2) Moller-Plesset MBPT. For polydiacetylenes he obtained 5.7 eV as first ionization potential (using the generalized Koopmans theorem) for the PTS structure (see Figure 8.1), in reasonable agreement with experiment (A = 5.5 0.1 while the HF value (the simple Koopmans theorem) is 6.8 eV.< > For the TCDU diacetylene structure the theoretical value is 5.0 eV (HF value, 6.2 eV). Unfortunately, there is no reliable experimental ionization-potential value available for the TCDU structure of polydiacetylene. 

A comparison of the experimental ionization potentials for N2, P2, and Asa. The dashed lines correlate the experimental state averaged ionization potentials from the atoms (from 2.9). 

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