Polarizability dipole

The dipole polarizability tensor characterizes the lowest-order dipole moment induced by a unifonu field. The a tensor is syimnetric and has no more than six independent components, less if tire molecule has some synnnetry. The scalar or mean dipole polarizability... 

In linear, spherical and synnnetric tops the components of a along and perpendicular to the principal axis of synnnetry are often denoted by a and respectively. In such cases, the anisotropy is simply Aa = tty -If the applied field is oscillating at a frequency w, then the dipole polarizability is frequency dependent as well a(co). The zero frequency limit of the dynamic polarizability a(oi) is the static polarizability described above. 

There are higher multipole polarizabilities tiiat describe higher-order multipole moments induced by non-imifonn fields. For example, the quadnipole polarizability is a fourth-rank tensor C that characterizes the lowest-order quadnipole moment induced by an applied field gradient. There are also mixed polarizabilities such as the third-rank dipole-quadnipole polarizability tensor A that describes the lowest-order response of the dipole moment to a field gradient and of the quadnipole moment to a dipolar field. All polarizabilities of order higher tlian dipole depend on the choice of origin. Experimental values are basically restricted to the dipole polarizability and hyperpolarizability [21, 24 and 21]. Ab initio calculations are an imponant source of both dipole and higher polarizabilities [20] some recent examples include [26, 22] ... 

These moments are related to many physical properties. The Thomas-Kulm-Reiche sum rule says that. S (0) equals the number of electrons in the molecule. Other sum rules [36] relate S(2),, S (1) and. S (-l) to ground state expectation values. The mean static dipole polarizability is md = e-S(-2)/m,.J Q Cauchy expansion... 

Miller T M and Bederson B 1988 Electric dipole polarizability measurements Adv. At. Mol. Phys. 25 37... 

Bonin K D and Kresin V V 1997 Electric-dipole Polarizabilities of Atoms, Molecules and Clusters (Singapore World Scientific)... 

Sohleoht S, Sohafer R, Woenokhaus J and Beoker J A 1995 Eleotrio dipole polarizabilities of isolated gallium arsenide olusters Chem. Phys. Lett. 246 315... 

The molecular quantities can be best understood as a Taylor series expansion. For example, the energy of the molecule E would be the sum of the energy without an electric field present, Eq, and corrections for the dipole, polarizability, hyperpolarizability, and the like ... 

The dipole polarizability, the field gradient and the quadrupole moment are all examples of tensor properties. A detailed treatment of tensors is outside the scope of the text, but you should be aware of the existence of such entities. 

The second-order property, the dipole polarizability, as given by the derivative formula eq. (10.31), is... 

A comparison of MP2/6-31G structural parameters of 1,2-oxazole 19 (isox-azole) and 1,3-oxazole 20 with microwave data is provided by Kassimi et al. (Scheme 16) [96JPC8752]. The general agreement is excellent. The same authors investigated dipole moments, quadrupole moments, octopole moments, and dipole polarizabilities of 19 and 20 together with several oxadiazoles and oxatriazoles [96JPC8752, 99JPC(A) 10009]. For the mean polarizability of these species, they found the approximative formula... 

SA(A)1011]. Static dipole polarizabilities were eomputed up to the MP4(SDQ) level [94MP557]. A study of the eleetronie strueture of the and S" " states of 192 showed that inelusion of dynamie eleetron eorrelation effeets is very important [98JPC(A)8021]. The multiplieity of the 1,3,5-triazine dieation is predieted to be a high-spin triplet while the trieation is most likely a doublet. In hexahydro-... 

The mean dipole polarizability monotonically increases with n and linearly correlates with the molecular volume. 

The static electric dipole polarizability a of the model system investigated is therefore... 

Five large basis sets have been employed in the present study of benzene basis set 1, which has been taken from Sadlej s tables [37], is a ( ()s6pAdl6sAp) contracted to 5s >p2dl >s2p and contains 210 CGTOs. It has been previously adopted by us in a near Hartree-Fock calculation of electric dipole polarizability of benzene molecule [38]. According to our experience, Sadlej s basis sets [37] provide accurate estimates of first-, second-, and third-order electric properties of large molecules [39]. 

The theoretical results provided by the large basis sets II-V are much smaller than those from previous references [15-18] the present findings confirm that the second-hyperpolarizability is largely affected by the basis set characteristics. It is very difficult to assess the accuracy of a given CHF calculation of 2(ap iS, and it may well happen that smaller basis sets provide theoretical values of apparently better quality. Whereas the diagonal eomponents of the eleetrie dipole polarizability are quadratic properties for which the Hartree-Fock limit can be estimated with relative accuracy a posteriori, e.g., via extended calculations [38], it does not seem possible to establish a variational principle for, and/or upper and lower bounds to, either and atris-... 

As a matter of fact, the electric dipole polarizabilities obtained via basis sets II-IV are larger than those reported in Ref. 16 and Ref. 18 from Table 1 of Ref. 39 it can be seen that a from those basis sets ranges from 78.352 to 79.142 a.u., and that 0 ... 

Due to the relativistic 6s contraction in gold, the 6s shell becomes more compact (inert, hence the nobility of gold) and the (static dipole) polarizability an decreases substantially from 9.50 (NR) to 5.20 (R) [99], Table 4.3. The relativistic enhance-... 

Table 4.3 Nonrelativistic (NR) and relativistic (R) static dipole polarizabilities tto (in A ), relativistic effects Af.aD, and relativistic enhancementfactors Yaforthe Croup 11 elements ofthe periodic table.

Saue and Jensen used linear response theory within the random phase approximation (RPA) at the Dirac level to obtain static and dynamic dipole polarizabilities for Cu2, Ag2 and Au2 [167]. The isotropic static dipole polarizability shows a similar anomaly compared with atomic gold, that is, Saue and Jensen obtained (nonrelativ-istic values in parentheses) 14.2 for Cu2 (15.1 A ), 17.3 A for Ag2 (20.5 A ), and 12.1 A for Au2 (20.2 A ). They also pointed out that relativistic and nonrelativistic dispersion curves do not resemble one another for Auz [167]. We briefly mention that Au2 is metastable at 5 eV with respect to 2 Au with a barrier to dissociation of 0.3 eV [168, 169]. 

Schwerdtfeger, P. and Bowmaker, G.A. (1994) Relativistic effects in gold chemistry. V. Group 11 Dipole-Polarizabilities and Weak Bonding in Monocarbonyl Compounds. Journal of Chemical Physics, 100, 4487-4497. 

TOO Schwerdtfeger, P. (2006) Atomic Static Dipole Polarizabilities, in Computational Aspects of Electric Polarizability Calculations Atoms, Molecules and Clusters (ed. G. Maroulis), Imperial College Press, London, pp. 1-32. 

Kello, V., Urban, M. and Sadlej, A.J. (1996) Electric dipole polarizabilities of negative ions of the coinage metal atoms. Chemical Physics Letters, 253, 383-389. 

Saue, T. and Jensen, H.J.Aa. (2003) Linear response at the 4-component relativistic level Application to the frequency-dependent dipole polarizabilities of the coinage metal dimers. Journal of Chemical Physics, 118, 522-536. 

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