Local dipole moment density

Dipole moment density occurs as a result of very small translational displacements of the electronic cloud with respect to the nucleus, whether in single atoms or in molecules. Displacement of electrons is very fast (picosecond), and the dispersion is in the gigahertz region. Induced dipoles will have the direction of the local E-field and undergo no rotation. 

Jasien, P. G., and G. Fitzgerald. 1990. Molecular dipole moments and polarizabilities from local density functional calculations Applications to DNA base pairs. J. Chem. Phys. 93, 2554. 

As discussed earlier, VCD depends on both the electric and magnetic dipole moment derivatives in a molecule. The simpler descriptions of VCD focus only on local electric dipole moment derivatives that have an overall chiral disposition. More advanced descriptions of VCD allow for induced electronic currents or charge flows in molecules, which give rise to additional magnetic dipole moment intensity. Such additional contributions are likely whenever delocaliz-able electron density is present in a molecule. 

The Hirshfeld functions give an excellent fit to the density, as illustrated for tetrafluoroterephthalonitrile in chapter 5 (see Fig. 5.12). But, because they are less localized than the spherical harmonic functions, net atomic charges are less well defined. A comparison of the two formalisms has been made in the refinement of pyridinium dicyanomethylide (Baert et al. 1982). While both models fit the data equally well, the Hirshfeld model leads to a much larger value of the molecular dipole moment obtained by summation over the atomic functions using the equations described in chapter 7. The multipole results appear in better agreement with other experimental and theoretical values, which suggests that the latter are preferable when electrostatic properties are to be evaluated directly from the least-squares results. When the evaluation is based on the density predicted by the model, both formalisms should perform well. 

As seen from comparison of data in Tables AlO-l and AlO-2, local density models parallel the behavior of the corresponding Hartree-Fock models. Except for highly polar ( ionic ) lithium and sodium compounds, dipole moments are generally larger than experimental values. Recall that local density models typically (but not always) exhibit the same systematic errors in bond lengths (too short) and stretching frequencies (too large) as Hartree-Fock models. 

Hartree-Fock, local density, density functional and MP2 models provide a credible account of dipole moments in hydrocarbons. Even STO-3G and 3-2IG (Hartree-Fock) models appear to be suitable. Not only is the mean absolute error very low (0.1 debye or less), but all models properly account for a variety of subtle trends in the experimental data, for example, the increase in dipole moment in cyclopropene in response to methyl substitution on the double bond. Finally, note that there is very little difference in the performance of any of the models with 6-3IG and 6-311+G basis sets. 

Dipole moments from 6-31G and 6-311+G calculations are nearly identical both for the amines (Table 10-3) and for the full set of molecules found in Appendix AlO. Comparison of Figures 10-3 and 10-4 further drives home the point. It is difficult to justify use of the larger basis set for this purpose. On the other hand, dipole moments resulting from all density functional models (including local density models) and from MP2 models, display some sensitivity to basis set. In most (but not all) cases, agreement with experiment improves, as generally reflected by the mean absolute errors in Table 10-4, and by... 

Table AlO-2 Dipole Moments in Diatomic and Small Polyatomic Molecules. Local Density Models... 

Table AlO-lO Dipole Moments in Density Models Molecules Containing Heteroatoms. Local... 

In most simple aldehydes and ketnoes, including benzophenone, the longest wavelength absorption is a low intensity n - iz transition. The promotion of a n-electron, localized on O-atom to a n-orbital, leaves behind a positive hole on this atom. The charge density on C-atom is increased creating a bipolar state. The dipole moment of >C = O bond is reduced. Three primary processes are commonly encountered for this electrophilic centre ... 

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