Orbitals electric moments

We now can get further information on the electronic configuration by studying the magnetism of the compounds. Any electron revolving around a nucleus in a closed orbital is equivalent to a circular electric current, and thus produces a magnetic moment. Usually these orbital magnetic moments are directed in such a way that they just cancel each other, in which case the orbital moments are of no further interest for our present purpose. 

In a naive and incorrect way we can say that the electron with S = lk senses the orbital magnetic moment. Actually, a charged particle cannot sense the orbital magnetic moment due to its own movement. However, the electron moves in the electric potential of the charged nucleus. If we change the system of reference,... 

On the basis of the Bohr theory the orbital magnetic moment may be obtained in the following way. The electron, during rotation about a closed orbit, is equivalent to an electric current, ev, where v is the number of rotations of the electron in the orbit per second and e is the electronic charge. For such a system, the magnetic moment will be equal to the product of the area of the orbit, Trr and the current flowing, i.e. 

ECP (Effective Core Potential) 171 Effective pair potential 68 EHMO (Extended Huckel Molecular Orbital Model) 130 Eigenvalue 17 Eigenvector 17 Einstein relation 253 Electric dipole moment 100, 265, 282 Electric field gradient 278 Electric moments 184 Electric quadrupole moment 268, 269 Electric second moment 268 Electric susceptibility 256 Electron affinity 147 Electron correlation 186, 273 Electron density 100, 218, 222 Electron relaxation 118 Electron spin 91, 95, 99, 277, 305 Electronic Schrodinger equation 74 Electrostatic field 14 Electrostatic field gradient 271... 

It is well known that transferability is an important property for the investigation of related systems. In cases when one can define quantities for molecular parts, which are additive and transferable, certain similarities of different molecules can be simply recognized. One-electron properties, as electric moments or kinetic energy contributions derivable from transferable/localized molecular orbitals, are especially useful for the above purpose. 

It is known, that in the framework of the independent particle model the one-electron properties of the system can be written as the sum of contributions from the individual orbitals. The transferability of the one-electron properties is implied by the transferability of the orbitals. The first and higher order electric moments determined for localized molecular orbitals (LMOs) in different systems can thus be used in comparative studies. 

The multipole expansion has already been used in certain quantum chemical calculations [59-65]. As localized orbitals are concentrated in certain spatial region, they can also be represented by their multipole moments. In the following we investigate whether the Coulomb integrals in terms of localized orbitals can be substituted by the multipole expansion of electric moments. 

We decompose the charge distribution of the whole electron system into sum of contributions from localized orbitals. If the localized orbitals do not overlap and their electric moments can be considered as transferable, than it is expected that the Coulomb integrals can be approached by the sum of interaction energies... 

These calculations are of special interest because Purcell and coworkers have been interested in the structure-activity relationships of this series of compounds for several years and have compared several approaches to structure-activity relationships with the same compounds. Earlier they (27, 28) reported on detailed studies of the effect of partition coefficients (benzene-water), electric moments, and electronic structures on the relative activity of the congeners. Purcell (28) used Huckel molecular orbital theory to calculate the net charges on all the atoms of each compound. The only apparent success was the apparent correlation of the net charge at the amide nitrogen atom with activity. This was later shown to be caused by the statistically significant correlation between the 7T value and the net charge on the nitrogen atom (29). 

If we transform to the rectangular co-ordinates , rj, , where is perpendicular to the orbital plane, we find for the components of the electric moment p expressions of the form... 

It is interesting to see how these electrical moments, and particularly the dipole moment, can be thought of in terms of contributions from different parts of the molecule. The nuclei are, of course, easily treated but it is helpful to think of the electronic contribution, not in terms of symmetry orbitals like (1.2) but rather as localized orbitals which can be pictured as 0-H bonds and lone pairs. This can be done by performing a unitary transformation upon the wave function specified in terms of components... 

Recalling that the dipole moment operator is a one-electron operator (as are aU electric moment operators), the following orbital equations are obtained... 

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