Electronic charge distribution second moment

The second group of semiempirical MO LCAO methods is constituted by zero-differential overlap methods (9). Two subgroups can be specified here which somewhat conventionally may be called physical and chemical. The former involves CNDO/2, INDO, and some of their modifications, for example, CNDO/S. These methods are directed to the calculations of the electron characteristics charge distributions, dipole moments, polarizabili-... 

Using ab initio wave functions and the full operators, dipole and second moments (cf. Section 4.11.3.2.2) as well as electronic charge distributions have been calculated for... 

The diamagnetic susceptibility anisotropies and molecular second moments of the electronic charge distributions for COCIF have been calculated by Maksic and Mikac [1303a], and these authors suggested that their calculated values showed that the experimentally derived second moments (calculated from the Zeeman effect in the Stark-modulated microwave... 

The anisotropies in the second moment of the electronic charge distributions are also available from the above information and the molecular structure ... 

The individual second moments of the electronic charge distributions can also be determined by... 

TABLE 5 Calculated Molecular Dipole Moments, Molecular Quadrupole Moments, Second Moments of the Electronic Charge Distribution, and Diamagnetic Susceptibilities ... 

These are the equations which have been used in Section II in order to extract ground state properties such as the second moments of the electron charge distribution, the molecular electric quadrupole moments and the sign of the electric dipole moment from the Zeeman data. 

Ab initio SCF-MO calculations have been performed on BFg, and alterations in predicted geometries with different gaussian-orbital basis sets noted. Further non-empirical SCF calculations on this molecule have been reported by Rothenberg and Schaeffer. Values of the dipole moment, quadrupole moment, octupole moment, second and third moments of the electronic charge distribution, diamagnetic susceptibility, and electric field gradient were calculated. 

Second, the polarizability of a medium can arise from the polarizabilities of the atoms or molecules composing it, even if they have no permanent dipole moment. Atoms or molecules that lack permanent dipoles have electronic polarizability, a tendency of nuclear or electronic charge distributions to shift slightly within the atom, in response to an electric field (see Chapter 24). The electronic polarizabilities of hydrocarbons and other nonpolar substances are the main contributors to their dielectric constants (D 2). 

Individual second-moment electronic charge distributions , (or < >, are listed in... 

From the total molecular quadrupole moment the arusotropy of the second moment of the electronic charge distribution can be calculated using... 

Individual second-moment electronic charge distributions , , (or < >, bulk susceptibility information was available to the authors and they could be obtained from the anisotropies, - , — (or

— spectroscopical information alone. 

First-order properties for ground states dipole and quadrupole moments, second moments of the electronic charge distribution and electric field gradients at the nuclei, as well as scalar-relativistic one-electron corrections (Darwin and mass velocity). 

Dipole Moments.— Electronic charge distribution dipole and second moments have been calculated for thiophen using ab initio wavefunctions and the full operators. The structure of thiophen-2-aldehyde in the gas phase has been calculated from dipole-moment data and principal moments of... 

These nuclei (and they form by far the majority of the NMR-active nuclei ) are subject to relaxation mechanisms which involve interactions with the quadrupole moment. The relaxation times Tj and T2 (T2 is a second relaxation variable called the spin-spin relaxation time) of such nuclei are very short, so that very broad NMR lines are normally observed. The relaxation times, and the linewidths, depend on the symmetry of the electronic environment. If the charge distribution is spherically symmetrical the lines are sharp, but if it is ellipsoidal they are broad. 

Most of the potential energy surfaces reviewed so far have been based on effective pair potentials. It is assumed that the parameterization is such as to account for nonadditive interactions, but in a nonexplicit way. A simple example is the use of a charge distribution with a dipole moment of 2.ID in the ST2 model. However, it is well known that there are significant non-pairwise additive interactions in liquid water and several attempts have been made to include them explicitly in simulations. Nonadditivity can arise in several ways. We have already discussed induced dipole interactions, which are a consequence of the permanent diple moment and polarizability of the molecules. A second type of nonadditive interaction arises from the deformation of the molecules in a condensed phase. Some contributions from such terms are implicitly included in calculations based on flexible molecule potentials. Other contributions arises from electron correlation, exchange, and similar effects. A good example is the Axilrod-Teller three-body dispersion interaction ... 

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