Polarizations of atomic and molecular charge distributions

1969 ◽  
Vol 47 (12) ◽  
pp. 2308-2311 ◽  
Author(s):  
R. F. W. Bader ◽  
I. Keaveny ◽  
G. Runtz
Keyword(s):  
Electric Field ◽  
Charge Distribution ◽  
Primary Response ◽  
Fundamental Nature ◽  
Charge Distributions ◽  
Molecular Charge ◽  
A Charge

It is shown that the dominant polarization of a molecular charge distribution in the region of a nucleus of an atom which employs p orbitals in its bonding (Be → F, Mg → Cl) is quadrupolar in nature, and dipolar for an atom which employs s orbitals (H, He, Li, Na). That these polarizations are of a fundamental nature is demonstrated by showing that they represent the primary response of a charge distribution to an electric field, whether it be internal or external, static or dynamic.

On the Cherenkov radiation from extended charge distributions

2000 ◽  
Vol 77 (10) ◽  
pp. 775-784 ◽  
Author(s):  
M Villavicencio ◽  
J L Jiménez ◽  
JAE Roa-Neri
Keyword(s):  
Explicit Expression ◽  
Charge Distribution ◽  
Constant Velocity ◽  
Cherenkov Radiation ◽  
Poynting Vector ◽  
Time Dependent ◽  
Spherically Symmetric ◽  
Charge Distributions ◽  
Extended Charge ◽  
A Charge

In this work the Cherenkov effect for extended charge distributions is analyzed using two different methods. In the first method, the Poynting vector is employed to determine the energy radiated, whereas in the second one, we apply the idea of generating time-dependent elemental dipoles, induced by a charge distribution moving with constant velocity, inside a material medium. An explicit expression for the Cherenkov radiation generated by some different kinds of spherically symmetric charge, travelling inside a medium, is obtained.PACS Nos.: 03.50.De, 41.20.Bt, 41.60.-m, 41.60.Bq

A view of bond formation in terms of molecular charge distributions

1968 ◽  
Vol 46 (6) ◽  
pp. 953-966 ◽  
Author(s):  
R. F. W. Bader ◽  
A. K. Chandra
Keyword(s):  
Charge Distribution ◽  
Bond Formation ◽  
Atomic Charge ◽  
Maximum Error ◽  
Calculated Density ◽  
Hartree Fock ◽  
Charge Distributions ◽  
Molecular Charge ◽  
Nuclear Separation ◽  
Order Of Magnitude

The process of bond formation as a function of internuclear separation for H2 and Li2 is interpreted in terms of the changes in the charge distributions and the forces which they exert on the nuclei. The charge distributions are calculated from extended Hartree–Fock wave functions which reduce to the Hartree–Fock atomic functions for infinite nuclear separation. The results for H2 indicate that at separations greater than 5 a.u. the net attractive force exerted on the approaching nuclei arises from a simultaneous inwards polarization of the atomic charge distributions. For separations less than 5 a.u. the nuclei are bound by the force exerted by the delocalized component of the charge distribution. The density distributions and forces for He2 over a range of internuclear separations are compared with those for H2 to contrast the formation of stable and unstable molecular species in terms of their respective charge distributions.The final section of the paper examines in detail the changes in the Hartree–Fock molecular charge distribution which arise from the inclusion of electron correlation in the wave function. The maximum error in the Hartree–Fock charge distribution for H2 is found to be in the region between the nuclei, where it overestimates the charge density by approximately 1%. The errors in the Hartree–Fock charge distribution for Li2 are found to be of the same order of magnitude as the uncertainty in the calculated density distribution itself.

The vibration of electrified water drops

1971 ◽  
Vol 322 (1551) ◽  
pp. 523-534 ◽  
Keyword(s):  
Electric Field ◽  
Electric Fields ◽  
Axial Ratio ◽  
Uniform Electric Field ◽  
Interferometric Technique ◽  
Photographic Analysis ◽  
Wide Range ◽  
Water Drops ◽  
Strength And Deformation ◽  
A Charge

Pressure has been used as the principal parameter in calculations of the fundamental vibrational frequencies of spherical drops of radius R , density ρ, and surface tension T carrying a charge Q or uncharged spheroidal drops of axial ratio a / b situated in a uniform electric field of strength E . Freely vibrating charged drops have a frequency f = f 0 ( 1 - Q 2 /16π R 3 T ) ½ , as shown previously by Rayleigh (1882) using energy considerations; f 0 is the vibrational frequency of non-electrified drops (Rayleigh 1879). The fundamental frequency of an uncharged drop in an electric field will decrease with increasing field strength and deformation a / b and will equal zero when E ( R )/ T ) ½ = 1.625 and a / b = 1.86; these critical values correspond to the disintegration conditions derived by Taylor (1964). An interferometric technique involving a laser confirmed the accuracy of the calculations concerned with charged drops. The vibration of water drops of radius around 2 mm was studied over a wide range of temperatures as they fell through electric fields either by suspending them in a vertical wind tunnel or allowing them to fall between a pair of vertical electrodes. Photographic analysis of the vibrations revealed good agreement between theory and experiment over the entire range of conditions studied even though the larger drops were not accurately spheroidal and the amplitude of the vibrations was large.

scholarly journals Electrostriction Effects During Defibrillation

2007 ◽  
Vol 6 (2) ◽  
Author(s):  
Michelle Fritz ◽  
Phil Prior ◽  
Bradley Roth
Keyword(s):  
Electric Field ◽  
Cardiac Tissue ◽  
Imaging Techniques ◽  
Stress And Strain ◽  
Mechanical Forces ◽  
Physical Origin ◽  
Anisotropic Cylinder ◽  
Simple Geometry ◽  
Complicated Manner ◽  
A Charge

Background—The electric field applied to the heart during defibrillation causes mechanical forces (electrostriction), and as a result the heart deforms. This paper analyses the physical origin of the deformation, and how significant it is. Methods—We represent the heart as an anisotropic cylinder. This simple geometry allows us to obtain analytical solutions for the potential, current density, charge, stress, and strain. Results—Charge induced on the heart surface in the presence of the electric field results in forces that deform the heart. In addition, the anisotropy of cardiac tissue creates a charge density throughout the tissue volume, leading to body forces. These two forces cause the tissue to deform in a complicated manner, with the anisotropy suppressing radial displacements in favor of tangential ones. Quantitatively, the deformation of the tissue is small, although it may be significant when using some imaging techniques that require the measurement of small displacements. Conclusions—The anisotropy of cardiac tissue produces qualitatively new mechanical behavior during a strong, defibrillation-strength electric shock.

Electric Field of a Charge Moving in a Medium

1963 ◽  
Vol 31 (8) ◽  
pp. 601-605 ◽  
Author(s):  
G. M. Volkoff
Keyword(s):  
Electric Field ◽  
A Charge
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