Core polarization

The core polarization may be considered to be not particularly large. However, the inner shell electrons are closer to the iron nucleus and, hence, the integrals are much... 

According to the results of [60], the isotropic term was scaled by 1.8 in order to compensate for the intrinsic underestimation of the core polarization by DFT methods... 

Since the core polarization will give a negative spin density at the iron nucleus, it is expected that in the state the isotropic and dipolar contributions partially cancel each other along the Fe-O bond direction while they will reinforce each other along this direction in the state. 

In contrast to the EFG analyzed before, aU of these expectations from ligand field theory are largely confirmed by the DFT calculations. Despite the fact that the S = 2 state has a smaller prefactor for the isotropic Fermi contact term, the core polarization in the presence of four unpaired electrons is much larger and, consequently, the isotropic Fe-HFC is predicted to be roughly a factor of two larger in magnitude for as compared to 2g. Similarly, the dipolar MFCs are comparable for both spin states, which must be due to a considerable contribution from anisotropic covalency in the 5 = 2 species which partially compensates for the smaller prefactor. 

Each of the eight hyperfine resonances is an unresolved quadmpole doublet, due to the quadmpole interaction of Os in the hexagonal Os metal source. The authors have interpreted the hyperfine fields in terms of core polarization, orbital and spin-dipolar contributions. 

Attempts to account for this bending have emphasized two physical effects, (1) d-orbital participation,18 and (2) core polarization,19 but no clear theoretical consensus has been achieved. The calculated bending in BaH2, for example, is found to disappear with removal of either d-orbitals or a polarizable-core, suggesting that both aspects are operative. The adequacy of the core-polarization rationale was questioned, and an alternative rationalization based on differences in atomic softness between metal and ligand was proposed by Szentpaly and Schwerdtfeger.20... 

The magnetic parameters of aquo-Mb obtained from Fig. 44 are collected in Table 15.1. The theoretical A values for the heme and histidine nitrogen, which are about 50% smaller than the observed values, have been determined by Mun et al.242), using an extended Hiickel-type calculation. According to these authors, the agreement between theoretical and experimental values could perhaps be improved further by considering electron core polarization effects. 

It was recently suggested by Nicklass and Peterson [60] that the use of core polarization potentials (CPPs) [61] could be an inexpensive and effective way to account, for the effects of inner shell correlation. The great potential advantage of this indeed rather inexpensive method over the MSFT bond-equivalent model is that it does not depend on... 

The largest basis set, denoted as G3Large [21] includes some core polarization functions as well as multiple sets of valence polarization functions. It should be noted that MP2 calculation with the largest basis set in Eq. (3.4) is carried out at the MP2(fu) level. 

In G3(MP2) theory, the MP2(fu)/G2Large calculation of G3 is replaced with a frozen core calculation with the G3MP2Large basis set [23] that does not contain the core polarization functions of the G3Large basis set. 

Since core polarization effects are not included in the present DSW calculations, no Fermi contribution to the metal hyper-fine interaction arises from the present wavefunction, although its contribution to the experimental tensor is significant. We have discussed such core polarization effects elsewhere.O, )... 

As previously done [11], we have employed two differents forms of the transition operator, Q(r) = r, and a core-polarization corrected expression [12], given by ... 

Abstract. We present a quantum-classieal determination of stable isomers of Na Arii clusters with an electronically excited sodium atom in 3p P states. The excited states of Na perturbed by the argon atoms are obtained as the eigenfunctions of a single-electron operator describing the electron in the field of a Na Arn core, the Na and Ar atoms being substituted by pseudo-potentials. These pseudo-potentials include core-polarization operators to account for polarization and correlation of the inert part with the excited electron . The geometry optimization of the excited states is carried out via the basin-hopping method of Wales et al. The present study confirms the trend for small Na Arn clusters in 3p states to form planar structures, as proposed earlier by Tutein and Mayne within the framework of a first order perturbation theory on a "Diatomics in Molecules" type model. 

The pseudo-potentials also incorporate core polarization operators using a stepwise cut-off adaptation by Foucrault and coworkers of the formulation proposed by Muller and Meyer These operators account for the polarization of the alkali ionic core as well as of the argon atoms considered as a core entities. The core-polarization operator reads... 

Figure 4 Polarization of the cores of Bi111 and Cu1. Oxygen ligands are unable to form strong bonds using the empty Cu 4s or Bi 6p orbitals due to interference of the 3d or 6s cores. Core polarization, d-s, for copper solves this problem and gives two-fold linear coordination for Cu1 and other d10 cations such as Ag1 and Hgn. Core polarization, s-p, for bismuth results in strong bonds on one side of Bi111 and weak bonds on the opposite side.

Among all electron methods, that of CNDO in its variants CNDO/2 and CNDO/S has been most used. Particularly worthy of note is the work of Galasso434 where -electron methods are compared with all valence electron methods for the 3a-azapentalene anion 246 and 3a,6a-diazapentalene 262a. The conclusion drawn from this study was that core polarization plays a fundamental role in determining overall charge distribution in the ground state but is relatively less important in interpreting electronic spectra. 

As we have seen, the basis set requirements for CC and CV correlation axe very stringent. There is therefore considerable attraction in methods that treat these effects semi empirically. One approach is to treat CV correlation effects by an effective operator. The core polarization potential used by Muller et al. for CV correlation in the alkali atoms and alkali dimers is one such approach [101]. This method has been used successfully for other atoms, such as copper [98]. 

---