Xa-calculations

Parr R G 1983 Density functional theory Ann. Rev. Phys. Chem. 34 631 -56 Salahub D R, Lampson S FI and Messmer R P 1982 Is there correlation in Xa analysis of Flartree-Fock and LCAO Xa calculations for O3 Chem. Phys. Lett. 85 430-3... 

The orbitals and orbital energies produced by an atomic HF-Xa calculation differ in several ways from those produced by standard HF calculations. First of all, the Koopmans theorem is not valid and so the orbital energies do not give a direct estimate of the ionization energy. A key difference between standard HF and HF-Xa theories is the way we eoneeive the occupation number u. In standard HF theory, we deal with doubly oecupied, singly occupied and virtual orbitals for which v = 2, 1 and 0 respectively. In solid-state theory, it is eonventional to think about the oecupation number as a continuous variable that can take any value between 0 and 2. 

The great advantage of sueh HF-Xa calculations over traditional HF ones is that they take account of electron reorganization on ionization, and so the Xa ionization energies were thought to be superior. 

Table 12.2 HF-Xa calculation on H2O ROHF transition state, ionization energies/ h...

In Fig. 5, a similar selection of results for the tran -difluoro-oxrrane molecule is presented, again comparing B-spline and CMS-Xa calculations as before. In this case, the outer two orbitals have a reversed ordering the O lone parr (orbital 9b) is the HOMO-1 while the HOMO (11a) has C—C—O a-bonding characteristics. The 5b level is analogous to the 9a in methyl oxirane. 

Another detailed comparative study of B-spline and CMS-Xa calculations that has been presented [57] addresses core and valence-shell PECD in camphor. For this molecule, a substantial amount of relevant experimental PECD data for the core [56] and valence-shell ionization [36, 56, 64, 65] is now available, allowing a full three-way comparison to be performed. Detailed discussion of the interpretation of the experimental results achieved with these calculations is deferred until Section VI.B, but it is helpful here to summarize the conclusions regarding the computational approaches. 

Figure 17. Camphor PECD from the HOMO (carbonyl oxygen lone-pair) ionization. Experimental data are (S)-camphor, (R)-camphor (both from Ref. [36]) (R)- and (S)-enantiomer data from Ref [64] O data from Ref [65]. Also shown as curves are CMS-Xa calculations (Ref. [36]) and B-spline calculations (Ref [57]).

As a consequence of the smaller covalence of Cu(TPP), the pyrrole proton tensors are nearly axially symmetric and the Cu-H distances calculated with the entire unpaired electron at the Cu(II) ion are in excellent agreement with X-ray data. The difference in covalency of Ag(TPP) and Cu(TPP) is also reflected by the s-spin densities on the pyrrole protons which amount to PH(Ag) = 0.15% and pH(Cu) = 0.093%, respectively. A comparison with the corresponding data of an Xa calculation on Cu(II)-porphine1725 (oh(Cu) = 0.071%) indicates that the state-of-the-art electronic structure calculation underestimates the amount of unpaired spin density on the porphyrin ring. 

Figure 5,2 MO energy levels for the [8104]" cluster based on MS-SCF Xa calculations. Reprinted from Tossell et al. (1973), with permission of Elsevier Science B.V.

Choosing convenient values of Xa, calculating the temperatures from eqn. (38) and using the Arrhenius expression (36) to obtain the rate coefficient corresponding to each value of Xa, allows Table 1 to be drawn up. 

Koopmans s theorem is not valid for Xa calculations, but Slater s transition state concept applies. This approximation allows the interpretation of electronic transitions in terms of 1-electron orbitals and yet includes electronic relaxation effects (208). The virtual (unoccupied) orbitals of Xa theory have a physical significance and can be used to discuss excitations of the electronic system, because the same potential due to the iV - 1 other electrons affects both occupied and unoccupied... 

Table II also shows the calculated ionization energies for ferrocene based on the SCF-SW-A"a procedure. The Xa calculation gives a better quantitative account of the observed photoelectron spectrum than the ab initio calculations of Veillard et al. (58). Whether the Xa technique is generally more reliable remains to be established.

As is discussed earlier for Ni(CO)4, the results of SCF-XQ calculations depend on the nature of the potential employed. The two Xa calculations on... 

X-Ray photoelectron spectroscopy (XPS) has been used129-131 to investigate several dithiolene ligands and complexes. Sano et al. correlated their results with Xa calculations, while Blomquist et a/.131 related theirs to EHT results. 

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