Atomic polarizabilities Bohr

Fig. 1. Relationship between polarizability, in bohr , and I(r,), in eV, for all of the atoms in the first four rows of the periodic table (Li-Xe) the correlation coeflScient in 0.96. Experimental atomic polarizabilities are taken from Ref. [61]...

The atomic unit (AU) of dipole moment is that of a proton and electron separated by a distance equal to the first Bohr orbit, oq. Similarly, the au of polarizability is Oq [125]. Express and o for NH3 using both the cgs/esu and SI approach. 

The dimensions of the polarizability a are those of volume. The polarizability of a metallic Bphere is equal to the volume of the sphere, and we may anticipate that the polarizabilities of atoms and ions will be roughly equal to the atomic or molecular volumes. The polarizability of the normal hydrogen atom is found by an accurate quantum-mechanical calculation to be 4.5 ao that is, very nearly the volume of a sphere with radius equal to the Bohr-orbit radius a0 (4.19 a ). 

All molecules are polarizable. When a non-polar molecule is subjected to an electric field, the electrons in the molecule are displaced from their ordinary positions so that the electron clouds and nuclei are attracted in opposite directions. The charges inside the molecules shift, a dipole is induced, and the molecule has a temporarily induced dipole moment, p. One would expect that the molecular polarizability, a should increase with the molecular size because in larger molecules the electrons can be displaced over longer distances. In fact, a is proportional to the volume of the molecule. As a simplified example, a one-electron Bohr atom is shown in Figure 2.5 a in which an electron (q = e ) moves around a nucleus (q = e+) with a circularly symmetrical orbit having a radius, r, in the absence of an external field. When this non-polar atom is subjected to an external electric field, E, the electron orbit is shifted by a distance, l, from the nucleus as shown in Figure 2.5 b. The external force, F, on the electron due to the field E can be calculated from Equation (5) so that... 

The original PCM method uses atomic spheres with radii 1.2 times the van der Waals radii to define the molecular cavity. The isodensity polarizable continuum model (IPCM) is a modification of the PCM that defines the surface of the molecular cavity as a contour surface of constant electron probability density of the solute molecule M [J. B. Foresman et al.,/. Phys Chem., 100,16098 (19%)]. iscxlensity value of 0.0004 electrons/bohr is reconunended, since it gives molecular volumes that agree with experimental values of where is the molar volume of the liquid solute... 

K.L.C. Hunt, B.A. Zilles, J.E. Bohr, Effect of van der Waals interactions on the polarizability of atoms, oscillators, and dipolar rotors at long range. J. Chem. Phys. 75(6), 3079-3086 (1981)... 

Unlike the homonuclear diatomic F2, which has a symmetrical distribution of radial electron density, the het-eronuclear diatomic GIF has an asymmetric distribntion as predicted due to the unequal sharing of electron density. When Cl (at y = 0 bohr) and F (at y = 3.050 bohr) combine to form CIF, the single core shell in the F atom and both core shells in the Cl atom remain mostly nnchanged in the bonded molecule as shown in Fig. 2b. This hgnre also shows that the RBCP is skewed toward the flnorine nucleus. This feature makes sense because F is more electronegative than chlorine, and Cl is fairly polarizable. In Fig. 2d, the cross section of the GIF molecnle depicts the two core shells for Cl and the single core shell for F. 

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