Static dipole

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... 

The dielectric constant is a property of a bulk material, not an individual molecule. It arises from the polarity of molecules (static dipole moment), and the polarizability and orientation of molecules in the bulk medium. Often, it is the relative permitivity 8, that is computed rather than the dielectric constant k, which is the constant of proportionality between the vacuum permitivity so and the relative permitivity. 

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-... 

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]. 

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. 

Fuentalba, P., Simon-Manso, Y., 1997, Static Dipole Polarizabilities Through Density Functional Methods , J. 

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>. 

In an effort to understand the mechanisms involved in formation of complex orientational structures of adsorbed molecules and to describe orientational, vibrational, and electronic excitations in systems of this kind, a new approach to solid surface theory has been developed which treats the properties of two-dimensional dipole systems.61,109,121 In adsorbed layers, dipole forces are the main contributors to lateral interactions both of dynamic dipole moments of vibrational or electronic molecular excitations and of static dipole moments (for polar molecules). In the previous chapter, we demonstrated that all the information on lateral interactions within a system is carried by the Fourier components of the dipole-dipole interaction tensors. In this chapter, we consider basic spectral parameters for two-dimensional lattice systems in which the unit cells contain several inequivalent molecules. As seen from Sec. 2.1, such structures are intrinsic in many systems of adsorbed molecules. For the Fourier components in question, the lattice-sublattice relations will be derived which enable, in particular, various parameters of orientational structures on a complex lattice to be expressed in terms of known characteristics of its Bravais sublattices. In the framework of such a treatment, the ground state of the system concerned as well as the infrared-active spectral frequencies of valence dipole vibrations will be elucidated. 

Now we consider the two principal challenges presented by the systems under study. The first involves determination of the ground state for a lattice system of static dipole moments and implies Ho minimization over all possible orientations of the vectors eR,. Molecules are assumed to have uniform dipole moments, = n with arbitrary orientations, eR> in the absence of dipole-dipole interactions. On... 

The second problem of interest is to find normal vibrational frequencies and integral intensities for spectral lines that are active in infrared absorption spectra. In this instance, we can consider the molecular orientations, to be already specified. Further, it is of no significance whether the orientational structure eRj results from energy minimization for static dipole-dipole interactions or from the competition of any other interactions (e.g. adsorption potentials). For non-polar molecules (iij = 0), the vectors eRy describe dipole moment orientations for dipole transitions. 

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... 

The calculation of polarizabilities is one of the research topics Jens Oddershede is working on since the beginning of his career [1-21], Already in one of his first papers he discussed the dipole polarizability of HF [1] and returned to it several times later [3,6,13,14,18]. Therefore, we decided to contribute to this special issue with a study of static dipole and quadrupole polarizabilities which are still one of the most studied electromagnetic properties. 

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. 

In MCSCF linear response theory [32] and the SOPPA and SOPPA(CCSD) [5,33,36] this leads to the following expression for the static dipole polarizability, e.g.,... 

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

When a charge approaches a molecule without a static dipole moment, all energies considered so far would be zero. Nevertheless, there is an attractive force. Reason The monopole induces a charge shift in the non-polar molecule. An induced dipole moment arises, which interacts with the charge. The Helmholtz free energy is... 

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