Electronic structure static polarizabilities

This technique has been applied in the analysis of the electronic structure of stoichiometric and non-stoichiometric (111) surfaces of BaFj and CaF2 crystals [85-88] or in the case of AI2O3 crystals by Guo, Ellis and Lam [89-91]. Vg t could also represent an applied static electric field as used for evaluation of static polarizabilities as discussed below. In the latter case, we could evaluate the multipolar moments separately, thus obtaining the static polarizability, induced by a field of the form [92]... 

Apart from primary structural and energetic data, which can be extracted directly from four-component calculations, molecular properties, which connect measured and calculated quantities, are sought and obtained from response theory. In a pilot study, Visscher et al. (1997) used the four-component random-phase approximation for the calculation of frequency-dependent dipole polarizabilities for water, tin tetrahydride and the mercury atom. They demonstrated that for the mercury atom the frequency-dependent polarizability (in contrast with the static polarizability) cannot be well described by methods which treat relativistic effects as a perturbation. Thus, the varia-tionally stable one-component Douglas-Kroll-Hess method (Hess 1986) works better than perturbation theory, but differences to the four-component approach appear close to spin-forbidden transitions, where spin-orbit coupling, which the four-component approach implicitly takes care of, becomes important. Obviously, the random-phase approximation suffers from the lack of higher-order electron correlation. 

The next phase for the theorists in connection with this work lies in predictions of helium atom scattering intensities associated with surface phonon creation and annihilation for each variety of vibrational motion. In trying to understand why certain vibrational modes in these similar materials appear so much more prominently in some salts than others, one is always led back to the guiding principle that the vibrational motion has to perturb the surface electronic structure so that the static atom-surface potential is modulated by the vibration. Although the polarizabilities of the ions may contribute far less to the overall binding energies of alkali halide crystals than the Coulombic forces do, they seem to play a critical role in the vibrational dynamics of these materials. 

Most often, (hyper)polarizabilities of polymers are calculated using a perturbation-theoretical approach based on the formalism of Genkin and Mednis [14]. Thereby, both occupied and unoccupied orbitals have to be included in the calculation and the fact that different electronic-structure methods (most notably, Hartree-Fock- and density-functional-based methods) often yield fairly inaccurate results for the unoeeupied orbitals may be the reason for the fact that the calculated (hyper)polarizabilities often depend strongly on the method (see, e.g.. Refs. [13,15]). Thus, in order to access the accuracy of the different methods or, alternatively, to avoid the problems related to the accuracy of the unoccupied orbitals, one may include a DC field directly in the calculations whereby at least the static (hyper)polarizabilities can be calculated. 

Analyzing the main information-theoretic properties of many-electron systems has been a field widely studied by means of different procedures and quantities, in particular, for atomic and molecular systems in both position and momentum spaces. It is worthy to remark the pioneering works of Gadre et al. [62,63] where the Shannon entropy plays a fundamental role, as well as the more recent ones concerning electronic structural complexity [27, 64], the connection between information measures (e.g., disequilibrium, Fisher information) and experimentally accessible quantities such as the ionization potentials or the static dipole polarizabilities [44], interpretation of chemical phenomena from momentum Shannon entropy [65, 66], applications of the LMC complexity [36, 37] and the quantum similarity measure [47] to the study of neutral atoms, and their extension to the FS and CR complexities [52, 60] as well as to ionized systems [39, 54, 59,67]. 

A precise theoretical and experimental determination of polarizability would provide an important probe of the electronic structure of clusters, as a is very sensitive to the presence of low-energy optical excitations. Accurate experimental data for a wide range of size-selected clusters are available only for sodium, potassium [104] and aluminum [105, 106]. Theoretical predictions based on DFT and realistic models do not cover even this limited sample of experimental data. The reason for this scarcity is that the evaluation of polarizability by the sum rule (46) requires the preliminary computation of S(co), which, with the exception of Ref. [101], is available only for idealized models. Two additional routes exist to the evaluation of a, in close analogy with the computation of vibrational properties static second-order perturbation theory and finite differences [107]. Again, the first approach has been used exclusively for the spherical jellium model. In this case, the equations to be solved are very similar to those introduced in Ref. [108] for the computation of atomic polarizabilities. Applications of this formalism to simple metal clusters are reported, for instance, in Ref. [109]. 

Aluminum clusters have been investigated using a variety of experimental techniques, providing abundance spectra [164, 165], spin multiplicities [166], IPs [164, 167], EAs, and static polarizability [105]. Reactivity studies have been reported for size-selected A1 clusters in contact with a variety of small molecules (see, for instance, [167]), and the presence of different isomers in a population of clusters has been investigated by measuring the mobility of clusters in a buffer gas [168]. Finally, the electronic structure of these clusters has been probed by photoelectron spectroscopy on the anion species Al [169, 170]. As mentioned above, bulk aluminum is remarkably close to a nearly... 

SA(A)1011]. Static dipole polarizabilities were computed up to the MP4(SDQ) level [94MP557]. A study of the electronic structure of the 2 and 3 states of 192 showed that inclusion of dynamic electron correlation effects is very important [98JPC(A)8021]. The multiplicity of the 13.5-triazine dication is predicted to be a high-spin triplet while the trication is most likely a doublet. In hexahydro-... 

This effective interaction Hamiltonian operator is difficult to evaluate as it requires the knowledge of the transition dipole moments between the essential states and all the non-essential states. For a general molecular system, there is an infinity of such states, including bound states but also the various continua. In practice however, one can further approximate the second term of Eq. (6.51) by neglecting the (ro)vibrational structure of the non-essential electronic states. This term can then be expressed as a function of static electronic polarizabilities, that can be computed using standard electronic structure methods available in the major quantum chemistry program packages. 

High polarizability of electrons in Ceo is one of the reasons for which ions and polar molecules are stabilized when trapped in endohedral complexes [3,30]. The dipole polarizability (a) measures the electronic response to a static electric field of a constant strength. Experimental data on polarizability of Ceo or other fullerenes are currently lacking however, a lower bound to a equal to 442.1 au was established by Fowler et al. [31] with the help of ab initio electronic structure calculations carried out at the HF/6-3lG(d) level. Based on this result, one may conclude that, atom for atom, Ceo is at least as polarizable as benzene. A similar (but with a much worse basis set) estimate was obtained for the C70 cluster [32], which was found to be more polarizable than Ceo ... 

Polarizability is a general concept that quantifies the response of an electron cloud of an ion to the apphcation of a time-dependent electromagnetic field resulting in a frequency-dependent polarizability. Our strict concern is with static, or zero-frequency polarizability as variations of an electric field induced by thermal fluctuations of an electrolyte operate at timescales much larger than the timescales of inner dynamics of an electron cloud. Frequency-dependent polarizability leads to other interesting effects, such as the London forces [32], when spontaneous fluctuations of electronic structure of two molecules become correlated at close spacial separations. These interactions, however, play secondary role when compared to induced interactions that arise from static polarizability [33, 34]. 

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