CEBE, calculated

The most promising approaches for efficient electronic structure calculations on large molecules are generally based on density functional theory with Kohn-Sham orbitals [32-35]. The most efficient such method for CE-BEs is based on Koopmans theorem, but this approach has quite limited accuracy [36-39]. Better accuracy can be obtained from calculations based on an effective core potential [40-45], an equivalent core approximation [46-48], a fractionally occupied transition state [49-52], or with a ASCF approach [29, 31, 53-57]. Time-dependent density functional theory is also widely used for CEBE calculation [58-62], wherein the best results are usually given with functionals having a long-range correction [63, 64]. 

In an effort to better understand the differences observed upon substitution in carvone possible changes in valence electron density produced by inductive effects, and so on, were investigated [38, 52]. A particularly pertinent way to probe for this in the case of core ionizations is by examining shifts in the core electron-binding energies (CEBEs). These respond directly to increase or decrease in valence electron density at the relevant site. The CEBEs were therefore calculated for the C=0 C 1 orbital, and also the asymmetric carbon atom, using Chong s AEa s method [75-77] with a relativistic correction [78]. 

The computations, however, were quite expensive, and a need for a cost-effective method enabling the accurate calculation of the CEBEs was still present. Recently, Chong has proposed a method called uGTS using Density Functional (DFT) calculations [14], based on the ideas of Slater s transition-state (TS) [15] later generalized by... 

In order to compare the calculated CEBEs with experiment, we need an evaluation of relativistic effects (which we do not take into account explicitly in the quantum mechanical treatment). A crude estimate of relativistic corrections can be made by adding to the thoeretical values the quantity [29] ... 

Table 2 Theoretical vs experimental CIs and OIs CEBEs (in eV) for CO adsorbed on Pd(IOO) and Pd(llO). The values in parenthesis indicate the absolute deviation (in eV) with respect to the experimental values. All calculated values are corrected for relativistic effects and referenced to the vacuum...

The core ionization potentials, more frequently called core electron binding energies (CEBEs) when molecular systems are studied, have been also recently calculated for the tautomeric structures of thio- and seleno-cytosine [35]. The role of relativistic effects in ly ionization have been studied for selenocytosine by the comparison of the nonrelativistic and relativistic SCE and MP2 results of the calculations. 

Shim et al. used the MCPs in the calibration of the AMP2 method for calculating core electron binding energies (CEBE) [263]. In that method, MCPs are used for aU atoms except for the one from which the Is electron is removed (that atom is treated... 

In the present study, we use the ASCF approach with Hartree-Fock and a wide variety of pure and hybrid density functional approaches to study CEBEs in glycine, methane, ammonia, and water. Each approach is evaluated for its accuracy in reproducing experimental values for the absolute CEBEs in all four molecules, as well as for the intramolecular and intermolecular chemical shifts between like nuclei in the same or different molecules. Several promising candidates are found that can be recommended for future testing to establish accurate and efficient methods for calculations of CEBEs and their chemical shifts in large biomolecules. 

Separate initial state and final core-hole state calculations provided ASCF values of the CEBEs. The maximum overlap method [67, 68] was used to prevent variational collapse of the final hole state. This simply replaces the usual aufbau criterion for occupying orbitals in each iteration with a criterion that the occupied orbitals be selected to overlap as much as possible with those of the previous iteration. The Ahhichs VTZ basis set [69] was used, based on the very good results it provided in a recent MCSCF-... 

MRPT study of CEBEs in simple hydrides [39]. All calculations were performed with the Q-Chem 4.0 program [70, 71]. 

Unsurprisingly, we can conclude that a functional s good performance in the calculation of CEBEs almost necessarily means a good description of chemical shifts, but the converse is not true. 

Fig. 21. Overlay of CeBe fllO) spectrum with CePtj (001) spectrum after subtracting backgrounds (fiom Andrews et al. 1995a). Except for a slight shift of the f peak die spectra are nearly identical in ite of a factor of 40 difference in The calculated...

OS ctrum approximates the parameters for CeBe i.e., rK=400K, r=0.116, JF=10eV, 4so = 280meV, no CF s, 6f=-2.5e ( t/ r = 14eV It was normalized to the data by using equal areas of the / peaks. Note the laige discrepancy in the/" peak width between experiment and calculation. 

The thin lined spectrum in fig. 21 is a GS calculation with parameters approximately matching CeBen (i.e., W= 0eV, C/ff = 14e ( rK=400K), smoothed to match the instrument resolution, and normalized in such a way that the total area of the calculated Lorentzian/ peak matches the total area of the measured Ciaussian/ peak in CeBeu. The mismatch is obvious. While better fits can be obtained with different parameters such as a smaller W, these are not justified. The width of the conduction band used above (10 eV) may in fact be even conservative since experimentally it peaks at about -8 eV Also, there are no Ce nearest neighbors in CeBe so that the 4f electron can only hybridize with the Be conduction band. 

Calculated CEBEs for several open-shell molecules are summarized in Table 13. We see that the scaled cc-pVTZ basis set provides CEBEs that are as accurate as those from the cc-pV5Z basis set and the estimated complete basis set limit. The AAD of the computed CEBEs of open-shell molecules is somewhat larger than that of closed-shell molecules, 0.29 eV, partly because the experimental values have larger uncertainties. 

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