Proton polarizability contribution

The result in (6.28) is obtained neglecting the contributions connected with the polarizability of the constituent nucleons in the deuterium atom, and the polarizability contribution of the proton in the hydrogen atom. Meanwhile, as may be seen from (6.21), proton polarizability contributions are comparable to the accuracy of the polarizability contribution in (6.28), and cannot be ignored. The deuteron is a weakly bound system and it is natural to assume that the deuteron polarizability is a sum of the polarizability due to... 

After calculation of these corrections, the uncertainty in the sum of all theoretical contributions except those which are directly proportional to the proton radius squared will be determined by the uncertainty of the proton polarizability contribution of order (Za). This uncertainty of the proton polarizability contribution is currently about 0.002 meV, and it will be difficult to reduce it in the near future. If the experimental error of measurement... 

The proposed experiment on Is hfs will test the accuracy and verify the validity of the PSI experiment on the excited states. With improved accuracy it may yield a result which can be used as a sum rule for the magnetic form factor of the proton. The uncertainty of this is on the same level as the proton polarizability contribution. 

In the case of hydrogen the characteristic excitation energy is about 300 MeV, the logarithm is rather large, and the logarithmic approximation works very well. Using the proton polarizabilities [32] one easily obtains the polarizability contribution for the proton nS state [26, 31, 33, 34]... 

Experimental data on the deuterium-hydrogen isotope shift (see Table 12.4 below) have an accuracy of about 0.1 kHz and, hence, a more accurate theoretical result for the polarizability contribution is required. In order to obtain such a result it is necessary to go beyond the zero range approximation, and take the deuteron structure into account in more detail. Fortunately, there exist a number of phenomenological potentials which describe the properties of the deuteron in all details. Some calculations with realistic proton-neutron potentials were performed [40, 41, 42, 43]. The most precise results were obtained in [43]... 

The contribution of an atomj to the polarizability effect is attenuated by the number of bonds, H , between this atom and the site of protonation, i. 

Radiative corrections to the nuclear polarizability a(Za) m to S -levels are described by the diagrams in Fig. 7.16 and in Fig. 7.17 (compare with the diagrams in Fig. 6.4). As usual for muonic hydrogen the dominant polarization operator contribution is connected with the electron loops, while heavier loops are additionally suppressed. The contribution of the diagrams in Fig. 7.16 was calculated in [52] on the basis of the experimental data on the proton structure functions... 

Hardness and softness as chemical concepts were presaged in the literature as early as 1952, in a paper by Mulliken [138], but did not become widely used till they were popularized by Pearson in 1963 [139]. In the simplest terms, the hardness of a species, atom, ion or molecule, is a qualitative indication of how polarizable it is, i.e. how much its electron cloud is distorted in an electric field. The adjectives hard and soft were said to have been suggested by D.H. Busch [140], but they appear in Mulliken s paper [138], p. 819, where they characterize the response to spatial separation of the energy of acid-base complexes. The analogy with the conventional use of these words to denote resistance to deformation by mechanical force is clear, and independent extension, by more than one chemist, to the concept of electronic resistance, is no surprise. The hard/soft concept proved useful, particularly in rationalizing acid-base chemistry [141]. Thus a proton, which cannot be distorted in an electric field since it has no electron cloud (we ignore the possibility of nuclear distortion) is a very hard acid, and tends to react with hard bases. Examples of soft bases are those in which sulfur electron pairs provide the basicity, since sulfur is a big fluffy atom, and such bases tend to react with soft acids. Perhaps because it was originally qualitative, the hard-soft acid-base (HSAB) idea met with skepticism from at least one quarter Dewar (of semiempirical fame) dismissed it as a mystical distinction between different kinds of acids and bases [142]. For a brief review of Pearson s contributions to the concept, which has been extended beyond strict conventional acid-base reactions, see [143],... 

The total protonation energy, defined as the difference, AE, between the total energy of the non-protonated molecule and that of its conjugated acid was analyzed via theoretical quantum chemical calculations. It was considered that this energy could be split into three additive contributions, electronic (Ae), electrostatic (AZ elst) and polarization (A p0lar). An increase was observed on going from carbon to silicon that was attributed mainly to the difference in the respective polarizabilities of carbon and silicon atoms.34,35... 

The electronic and esr spectra of the CuL complexes are consistent with an octahedral tetragonally distorted structure 101as present in most Cu2+ complex compounds in aqueous solution. The spectroscopic measurements indicate that there are some contribution from the highly polarizable C = 0 groups. On the other hand, the spectra of the Cu2+ complexes with polymers have been found to be almost identical to those of complexes with the corresponding models100 101>. This suggests that for each polymer-model pair, the structure of the complexes is the same. Hence, as in protonation, the difference between the stability constants must be due mainly to entropic effects. 

Yet the attached oxygen atoms cannot be the sole reason for the stability of anions next to sulfur because the sulfide functional group also acidifies an adjacent proton quite significantly. There is some controversy over exactly why this should be, but the usual explanation is that polarization of the sulfur s 3s and 3p electrons (which are more diffuse, and therefore more polarizable, than the 2s and 2p electrons of oxygen) contributes to the stabilization. 

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