Electric properties atomic dipoles

Table 2.1 List of molecules studied with four-component methods. The fourth column lists quantities, which have been investigated primary data P = (total electronic energies (E), orbital energies e,-, population analyses PA), ionization energies IE, election affinities EA, atomization energies A, spectroscopic data S = (equilibrium distance re, dissociation energy De, frequencies/wave numbers coe, bond angles 0), electric properties E = (dipole moment fx, quadrupole moment 0, dipole polarizability a, infrared intensities I, excited states ES, electric field gradients EFG, energetics of reaction R.

General properties and definitions of polarizabilities can be introduced without invoking the complete DFT formalism by considering first an elementary model the dipole of an isolated, spherical atom induced by a uniform electric field. The variation of the electronic density is represented by a simple scalar the induced atomic dipole moment. This coarse-grained (CG) model of the electronic density permits to derive a useful explicit energy functional where the functional derivatives are formulated in terms of polarizabilities and dipole hardnesses. 

An infrared spectrum thus represents the attenuation of the incident radiation as a function of frequency each absorption band corresponding to a jump between two vibrational levels and a specific vibrational movement. Moreover, the activity (a mode is said to be active when the corresponding absorption band can be detected) of the vibrational mode depends on the variation in an electrical property of the molecule, namely its dipole moment. In the case of a homonuclear molecule, such as N2 for example, the electrical symmetry is maintained during the elongation movement along the axis which connects the two nitrogen atoms and the corresponding absorption transition is prohibited. 

As an example, explicit expressions of /3 can be given in the case of the dipole polarizability of the H atom and for a few simple VdW interactions which depend on the electrical properties of the molecules such as electric dipole moments and polarizabilities (Stone, 1996). As we have already said, these dipole moments, and the higher ones known generally as multipole moments, can be permanent (when they persist in absence of any external field) or induced (when due, temporarily, to the action of an external field and disappear when the field is removed). 

Figure 1 Variation with intermolecular separation of calculated energy and electric properties of the complex HsN- -Bra. The plots (a) to (d) show the results of rigid-monomer SCF supermolecule calculations as described in the text. The properties are (a) the energy (E) in millihartree, (b) dipole moment enhancement (A/z) in ea0, electric field gradients at (c) nitrogen ( V(iV) ) and (d) bromine ( V(Br) ) in atomic units, all displayed as functions of the distance R (in bohr) between N and the nearer Br atom. In (d), the top curve represents the electric field gradient at the inner bromine and the bottom curve the gradient at the outer the middle curve is the mean of the two.

Recently, xenon has been used as a nonreactive probe of surface structure. As long as the surface can be cooled to a low enough temperature to adsorb this inert gas atom, its local interaction with surface sites of different structure yields large enough variations in its heat of adsorption to be used as a probe of the surface structure. As we shall see in the chapter on electrical properties of surfaces, the surface electric dipole varies from site to site, depending on the structure of the site. This electric dipole influences the polarizability and thus the bonding of adsorbed atoms or molecules at that site. 

In practice, the electric and magnetic dipole transition moments are usually expressed as summations of atomic properties, namely the atomic polar tensor (APT), Pgp, and atomic axial tensor (AAT), respectively. In the... 

The description of dipole moments of molecular complexes is significantly sophisticated as the number of atoms in the interacting molecules increases. The electrical properties of molecular van der Waals complexes are now studied not fully enough. Below, we concentrate our attention only on two relatively large molecular complexes CH4-N2 and C2H2-C2H2 (Sect. 3.2.4) which have, on the one hand, the astrophysical interest and on the other hand, they illustrate effectively the theory discussed above. 

Maroulis calculated the interaction-induced dipole polarizability and hyperpolarizability of the He2, Ne2, Ar2 and Kr2 homodiatoms relying on finite-field Moller-Plesset perturbation theory and coupled cluster calculations. Special attention was paid to the design of flexible basis sets, suitable for interaction-induced electric property calculations. Atom-specific, prepared basis sets were used on all atoms. The construction is completed in four steps ... 

The interaction-induced dipole polarizability and second hyperpolarizability of two neon atoms was reported by Hattig et al They subsequently used the calculated values along with an accurate potential for Nc2 to estimate the refractivity and hyperpolarizability second virial coefficients of gaseous neon. The calculation of ctint, Aai t and yjnt was performed at the CCSD level of theory with a d-aug-cc-pVQZ-33211 basis set. The R-dependence of the interaction-induced electric properties was obtained at a range of internuclear separations defined by 3 < R/ao < 20. 

If the changes of the molecular dipole moment are thought to be linear with the atomic displacements during a vibration, the integrated intensity of the i-th normal mode is related to the electrical properties of the molecule by the relation [47] ... 

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