Experimental ionization energy correlation

Figure 4. Experimental ionization energy correlation diagram of N2.

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. 

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... 

If experimental data is used to parameterize a semi-empirical model, then the model should not be extended beyond the level at which it has been parameterized. For example, experimental bond energies, excitation energies, and ionization energies may be used to determine molecular orbital energies which, in turn, are summed to compute total energies. In such a parameterization it would be incorrect to subsequently use these mos to form a wavefunction, as in Sections 3 and 6, that goes beyond the simple product of orbitals description. To do so would be inconsistent because the more sophisticated wavefunction would duplicate what using the experimental data (which already contains mother nature s electronic correlations) to determine the parameters had accomplished. 

Other attempts to correlate experimental binding energies with molecular-charge distributions have been made. Kato et al.532 have derived a correlation formula between the chemical shift of the inner-shell electron of a molecule and the charges both on the ionized and other atoms (cf. ref. 529). Very recently Ishida et al.533 reported an... 

Cyanogen Azide. Cyanogen azide (NCN3) has recently been studied experimentally, despite its instability, and a calculation with a (73)- [2,l] GTO basis has been reported.137 The first two IP correlate with the theoretical orbital energies, using Koopmans theorem, but the lone pair orbital ionization energies are in error by 3 eV. 

Table III. Minus the total Si crystal valence electron energy per atom with relaxation energy and pseudopotential corrections included, along with the equilibrium lattice constant, bulk modulus, and cohesive energy calculated with four different exchange-correlation functionals (defined in the caption of Table I) are compared with experimental values. The experimental total energy is the sum of Acoh plus the four-fold ionization energy.

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. 

Photoelectron spectroscopy is a very valuable tool in measuring the different energy levels of a molecule. This is however based on the assumption that the ionization potentials which are determined experimentally are directly correlated with the MO s of a certain molecule, i.e. Koopman s theorem must be valid. The few azo compounds studied so far already allow a clear assignment of the orbitals concerned and a deeper insight into the ordering of the n and -states in azo compounds. 

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