Static Dipole Polarizabilities a

In the presence of a uniform static electric field (F) the energy of an atom may be expressed by the Taylor series[ 14] 

There are both numerical and analytical ways of carrying out this procedure. The first is the easiest to understand and was first applied to the Hartree-Fock (HF) method by Cohen and Roothaan[23]. One simply takes various values of F (usually of the order of 0.001 au), finds the corresponding EF and makes a fit to Eq. (9). This is called the finite field method and it may be applied within the framework of any of the standard methods which determine energies, e.g., HF, MP2, MP4, coupled cluster (CC), MCSCF. 

Alternatively, analytical methods can be used such as coupled Hartree-Fock (CHF), where the perturbed HF equations are solved directly. Using standard perturbation theory one can also develop a sum-over-states (SOS) formalism and write 

Though numerical wavefunctions have been used for polarizability calculations, see Refs. [22] and [24], it is much more common to use analytical basis functions such as Gaussians. In this case, the proper optimization of the nonlinear parameters (exponents), in the context of the a and y computations is crucial. Two recent papers address this problem[25],[26], 

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Soldan, P., Fee, E.P.F., and Wright, T.G. (2001) Static dipole polarizabilities (a) and static second hyperpolarizabilities (y) of the rare gas atoms. Phys. Chem. Chem. Phys., 3, 4661-4666. 

The polarizability (a) of an atom or a molecule means the lowest order response of its electron cloud to an external weak electric field [277, 278]. The static dipole polarizability (a), a linear response property, is defined as the second derivative of the total electronic energy ( ) with respect to the external homogeneous electric field as... 

In general, the expansion sites are the (heavy) atoms of the dimer, using a simpler formulation due to London. The London formulation uses the averaged (isotropic) value of the static dipole polarizabilities, a j, of the atoms and their first ionization potentials Ij and Ij ... 

At the same time, a London-type formula for the dispersion interactions in the endohedral A B systems (where one subsystem A is inside another subsystem B) has been derived by Pyykko et al. [45]. It involves the static dipole polarizability, a(A) of the inner system. A, and a new type of dipole polarizability, a (B) with an radial operator, for the outer system, B. The second-order correction energy is... 

As a byproduct of the computation of photoabsorption spectra, it is possible to compute the static dipole polarizability a, given by the well-known sum rule... 

Static dipole polarizabilities (a) were calculated most accurately at the DC CC level of theory for elements Cn through FI, elements 118 through 120 [119, 125-127, 131, 132]. For elements 115 through 117, a were determined via a correlation with Rmux of the outermost valence AOs in the chemical groups [130], Results are given in Table 4 and Fig. 17 in comparison with experimental polarizabilities of the homologs in the 6th period. 

The properties that are routinely computed and discussed are the mean (or average) static dipole polarizability (a), the anisotropy (Act) of the polarizability tensor, the vector component of the first hyperpolarizabUity tensor in the direction of the ground state permanent dipole moment (/3 ), the total first-order hyperpolarizabUity tot, and the scalar component of the second hyperpolarizability tensor y. Those quantities are related to the experiment and in terms of the Cartesian components are defined as... 

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

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]. 

Ab initio electron correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities were reported for oxadiazoles <1996JPC8752>. The various measures of delocalization in the five-membered heteroaromatic compounds were obtained from MO calculations at the HF/6-31G level and the application of natural bond orbital analysis and natural resonance theory. The hydrogen transfer and aromatic energies of these compounds were also calculated. These were compared to the relative ranking of aromaticity reported by J. P. Bean from a principal component analysis of other measures of aromaticity <1998JOC2497>. 

Vela, A. and Gazquez, J. L. 1990. A relationship between the static dipole polarizability, the global softness, and the Fukui function. J. Am. Chem. Soc. 112 1490-92. 

The static dipole polarizability is the linear response of an atomic or molecular system to the application of a weak static electric field [1], It relates to a great variety of physical properties and phenomena [2-5]. Because of its importance, there have been numerous ab initio calculations of isolated atomic and molecular polarizabilities [6-14]. Particular theoretical attention has been dedicated to the polarizability of free atomic anions [15-21] because of its fragility and difficulty in obtaining direct experimental results. In recent years theoretical studies have... 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

Spackman, M.A. (1989) Accurate prediction of static dipole polarizabilities with moderately sized basis sets. J. Phys. Chem., 93 (22), 7594-7603. 

Fuentalba, P., Simon-Manso, Y., 1997, Static Dipole Polarizabilities Through Density Functional Methods , J. Phys. Chem. A, 101, 4231. 

This polarization has two components the induced polarization P (due to movement of the centers of charge, or to the static electric dipole polarizability a of molecules) and the dipole polarization Pjt (due to the orientation of the permanent dipoles m in the applied electric field E) ... 

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