Multipole Electric

It has been assumed16 27 that the neon atom and other atoms with an s2p outer shell also may be described as tetrahedral. However, the four spa electrons with positive spin are independent of the four with negaiive spin, and the two corresponding tetrahedra are free to assume arbitrary relative orientation.28 Correlation requires that the most stable relative orientation be the inverse one hence the neon atom and the other s2p6 atoms can be described as cubic. Their polarizability in a cubic multipole electric field is large and that in a tetrahedral field small.29... 

Table 8 Natural permanent) multipole electric moments of simple molecules...

S. Kielich. Nonlinear refractive index and light scattering due to fluctuations of molecular multipole electric fields. Optics Communic., 34 367-374 (1980). 

Taking into account the physical meanings of the atomic operators (41) and (66) and the integrals of motion (64), we can consider the field operators (63) and (69) as the nonnormalized exponential operators of the radiation phase, which, by construction, is the SU(2) phase of the multipole (electric dipole) radiation. By performing a similar analysis to that described in Section III.B, we can define the cosine and sine operators of the radiation phase as follows [36]... 

The charge distribution of a quantum mechanical system can be expanded in terms of its multipole electric moments. The zeroth order moment is the total charge Z... 

In this case the multipole electrical moments of the rank n for any molecule B can be defined in the form (see, for example, [1-6])... 

Sometimes it is useful to represent the multipole electrical moments in a spherical form. The spherical form of these moments allows us to apply effectively the theory of irreducible spherical tensor formalism. For this aim these 2 -pole moments may be written in terms of the regular spherical harmonics using their both complex Rlm r) and real (Rimc r) and Rims r)) forms defined, for m > 0, as... 

It is evident from (2.3.3)-(2.3.5) taking into account (2.2.5) and (2.2.10) that in the presence of an external field the multipole electric moments and polarizabilities of a molecule can be determined as the correspondent derivatives of the energy... 

Yu.N. Kalugina, V.N. Cherepanov, Multipole electric moments and higher polarizabilities of molecules the methodology and some results of ab initio calculations. Atmos. Oceanic Opt 28(5), 406 14 (2015)... 

S. P6rez-Casas, J. Hem idez-Trujillo, M. Costas, "Experimental and theoretical study of aromatic-aromatic interactions. Association enthalpies and central and distributed multipole electric moments analysis", J. Phys. Chem. B, 2003,107,4167-4174. 

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