Stieltjes orbitals

Brief descriptions are given in the following of needed aspects of cross sections, molecular orbitals, and of the more recently devised Stieltjes orbitals that have proved useful in spectral studies. Examples of the use of the Stieltjes formalism In identifying Mulliken valence orbitals in the cross sections of diatomic and polyatomic compounds are reported next. Also indicated are more general aspects of such intravalence transitions as they relate to electron-impact resonances in selected cases. The Importance of dealing with both discrete and continuous spectral intervals on a common basis is emphasized throughout, particularly with reference to the clarification of the positionings of a-xj and tv-ht excitations in molecular photoabsorption and ionization cross sections. 

Figure 10. Stieltjes orbitals in tenth-order for (5a-+ka)b n ionization of NO in static-exchange approximation (28). Layout as in Figure 7.

Figure 12, Occupied canonical Hartree-Fock and 5th-order Stieltjes orbitals In static-exchange approximation for 5a- -ko ionization of CO (20). Layout as in Figure 7, with the carbon nucleus on the left, the oxygen on the right.

Figure 13. Occupied canonical Hartree-Fock and 5th-order Stieltjes orbitals in static-exchange approximation for 5ai- ka2 ionization of H2CO (20). Results shown refer to orbital values in a molecular plane of dimension 6 by 16 Sq, with the hydrogen nucleii on the left of the figure.

Photoionization of NO. We consider photoionization of the 2n orbital of NO into ka, kn and k5 y continua (29). Our interest in this process stemmed from a desire to resolve the rather large differences between the Stieltjes (44) and SVM calculations (45). The results of our calculations and a comparison of theory ah3 ... 

Because EXAFS spectra are usually recorded in solution they reflect an average structural picture of a system resulting from a thermodynamic averaging across fluctuating metal-ligand configurations. Moreover, these spectra correspond to excitations from core orbitals to the continuum, the inability of the finite basis sets employed in electronic structure calculations to properly describe the continuum wavefunctions leads to a spurious basis set dependences on the calculated spectra unless techniques such as Stieltjes imaging [142,143] are employed. Such methods are currently available to a number of electronic structure approaches in a non-relativistic framework (e.g., [144-147], but not yet for relativistic ones). 

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