Localized molecular orbitals electric moments

I is in general no direct relation between such functions and ionization energies or electron excitation this is because they are not eigenfunctions of a hamiltonian, hence they cannot be associated with an energy. For that reason, we kept the usual designation localized molecular orbitals but with [ the last word in inverted commas orbitals . However, for the interpretation of some other molecular properties, the minimized residual interactions i between quasi-localized molecular orbitals are not very importaint and, so, the direct use of a localized bond description is quite justified. That is the [ Case for properties such as bond energies and electric dipole moments, as well as the features of the total electron density distribution with which those properties are directly associated. 

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. 

Considerations similar to those made about electric dipole moments apply to other one-electron properties, for instance the nuclear spin-spin coupling constants between non-bonded hydrogen atoms in molecules like methane. These quantities are approximately equal to zero in the simple molecular orbital theory, as it is easily proved by using equivalent orbitals corresponding to the CH bonds instead of the usual delocalized MO s (34). Actually, the nuclear spins of protons cannot interact wta the electrons, since a localized MO cannot be large on two hydrogens at the same time, and correlation should be primarily responsible for all coupling constants, except perhaps for those observed for directly bonded atoms (see Sec. 4). 

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