Correlation-dependent electronic properties

In Section 2 the general features of the electronic structure of supported metal nanoparticles are reviewed from both experimental and theoretical point of view. Section 3 gives an introduction to sample preparation. In Section 4 the size-dependent electronic properties of silver nanoparticles are presented as an illustrative example, while in Section 5 correlation is sought between the electronic structure and the catalytic properties of gold nanoparticles, with special emphasis on substrate-related issues. 

Homonuclear correlation spectroscopy (COSY) experiments (see Chapter 9) substantiate the theoretical predictions, based on molecular orbital calculation, of the pattern of spin delocalization in the 3e orbitals of low-spin Fe(III) complexes of unsymmetrically substituted tetraphenylporphyrins [46]. Furthermore, the correlations observed show that this n electron spin density distribution is differently modified by the electronic properties of a mono-orf/io-substituted derivative, depending on the distribution of the electronic effect over both sets of pyrrole rings or only over the immediately adjacent pyrrole rings [46]. No NOESY cross peaks are detectable, consistently with expectations of small NOEs for relatively small molecules and effective paramagnetic relaxation [47]. 

Density functional approaches to molecular electronic structure rely on the existence theorem [10] of a universal functional of the electron density. Since this theorem does not provide any direction as to how such a functional should be constructed, the functionals in existence are obtained by relying on various physical models, such as the uniform electron gas and others. In particular, the construction of an exchange-correlation potential that depends on the electron density only locally seems impossible without some approximations. Such approximate exchange-correlation potentials have been derived and applied with some success for the description of molecular electronic ground states and their properties. However, there is no credible evidence that such simple constructions can lead to either systematic approximate treatments, or an exact description of molecular electronic properties. The exact functional that seems to... 

Quantitative structure-activity relationships represent an attempt to correlate activities with structural descriptors of compounds. These physicochemical descriptors, which include hydrophobicity, topology, electronic properties, and steric effects, are determined empirically or, more recently, by computational methods. The success of a QSAR method depends on two factors the training dataset obtained by testing a group of chemicals and the descriptors obtained from some easily measurable or calculable property of the chemicals. 

Many ferromagnets are metals or metallic alloys with delocalized bands and require specialized models that explain the spontaneous magnetization below Tc or the paramagnetic susceptibility for T > Tc. The Stoner-Wohlfarth model,6 for example, explains these observed magnetic parameters of d metals as by a formation of excess spin density as a function of energy reduction due to electron spin correlation and dependent on the density of states at the Fermi level. However, a unified model that combines explanations for both electron spin correlations and electron transport properties as predicted by band theory is still lacking today. 

Calculations of time-dependent electromagnetic properties of molecules at the correlated electronic structure level are conveniently carried out by the utilization of modern response theory [43-51], The transition of modern response theory for gas phase molecular systems to solvated molecules has been established [1-6] and these methods include the use of correlated electronic wavefunctions. These methods, reviewed here, have given rise a large number of computational approaches for calculating electric and magnetic molecular properties of solvated molecules. 

To summarize the discussion in this section, it is fair to state that the Hartree-Fock approximation is adequate in many cases and that the importance of correlation effects is sometimes overestimated. It appears that the basis set effects may be larger than the correlation effects and that the errors in theoretical heats of formation may be mainly due to the limited basis set used30,31. Very instructive discussions on this problem were reported for the inversion barrier in ammonia6,20,32 and the barrier to rotation20 in H2O2. Finally, it should be noted that the Hartree-Fock approximation is also justifiable for the one-electron properties because the latter do not depend explicitly on relative positions of electrons (electron correlation), but rather on the overall distribution of electronic charge. 

It can be mentioned the work of Cerecetto et al. [ 133,134] where the anti-7 cruzi activities of a series of QDO and its vanadyl complexes were correlated with theoretical physicochemical descriptors. On the one hand, a clear two-variable correlation was found between both QDO-antiparasite activity and theoretical lipophilicity and LUMO energy [133]. The equation confirms some previously observed aspects, i.e., that the presence of an electron-withdrawing substituent, like halogen, in 5-8-positions produces more active compounds. On the other hand, it was found that the anti-T. cruzi response of a family of QDO-vanadyl complexes depends on the lipophilic properties and the electronic properties, am, of 6-7-substituents [134], Another QSAR study involving PDO derivatives with selective hypoxic cytotoxicity was performed by these researchers [145]. In this case, electrochemical properties, expressed as pc, together with lipophilicity correlated to the fraction of cell survival in hypoxia finding that when the redox potential of the N-oxidc moiety decreases the hypoxic cytotoxicity increase. 

Increase of the electronic state density in the carbon pore walls with the voltage. Hahn et al. [52] have measured double-layer capacitance and electronic conductance of an activated carbon electrode in an aprotic electrolyte solution, 1 mol/dm3 (C2H5)4NBF4 in acetonitrile. Both quantities show a similar dependency on the electrode potential with distinct minima near the potential of zero charge. This correlation suggests that the capacitance, like the conductance, is governed substantially by the electronic properties of the solid, rather than by the ionic properties of the solution in the interface of the double layer. 

In Chapter 4 the H/D exchange of cyclopentane was measured for Pt catalysts with supports of various acidity. With the earlier developed Monte-Carlo model the contributions of the various possible intermediates in the H/D exchange can directly be measured. It was shown that the activity and the selectivity in the H/D exchange over the supported Pt catalysts strongly depend on the support acid/base properties. The activities of the various catalysts show a compensation effect. The compensation effect can directly be correlated to the contribution of the various exchange mechanisms, which proceed via different intermediates. The contribution of each intermediate depends on the electronic properties of the Pt particles, which in turn depend on the support acidity. This shows that the compensation effect is caused by support induced changes in the adsorption modes of cyclopentane. 

This qualitative picture is taken into account in the unrestricted Hartree-Fock (UHF) approach, but it is found that UHF calculations normally overestimate Ajgo drastically. To obtain reliable results, the interactions between the electrons must be described much more accurately. Furthermore, in difference to most other electronic properties, such as dipole moments etc., a proper treatment of the hfcc s also requires special consideration of the inner valence and the Is core regions, since these electrons possess a large probability density at the position of the nucleus. Because the contributions from various shells are similar in magnitude but differ in sign, a balanced description of the electron correlation effects for all occupied shells is essential. All this explains the strong dependence of A on the atomic orbital basis and on the quality of the wavefunction used for the calculation. 

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