Electronic distribution dipole moments

In most molecules, it is possible to describe the a—n interaction by simple electrostatic considerations and to explain in this way physical properties depending on them like dipole moments. Electron correlation seems to play no role, except for molecules with a very small polarity, like carbon monoxide 119>. The matter is more complicated for excitation phenomena, because it is necessary to take into account possible changes in the charge distribution, even if the electronic structure... 

Further, we have considered the equilibrium configuration or distribution of the electrons within the molecule (dipole moments, electron density maps, and, for simple molecules, the spectroscopic description of the ground electronic states of molecules). We now have left a consideration of the displaceability of these electrons from their equilibrium configurations in their ground states. We have already encountered a term which is in effect a measure of this displaceability, namely the polarizability (see section 18). Since the molecule as a whole and especially its electrons must be subject to the quantum restrictions, the electrons cannot be considered as continuously displaceable but rather as capable of existing only in a... 

It became of interest to study the chemical properties of these compounds to gain some insights into how they may interact with the H2 histamine receptor. The analysis was simplified by concentrating on a series of antagonists depicted in Fig. 1 whose structures were closely related to cimetidine. The stodies emphasized the importance of such physicochemical properties as geometry, acidity (pX ), hydrophilicity (octanol-water partition, P) and dipole moment (electron density distribution). 

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... 

The long-range interactions between a pair of molecules are detemiined by electric multipole moments and polarizabilities of the individual molecules. MuJtipoJe moments are measures that describe the non-sphericity of the charge distribution of a molecule. The zeroth-order moment is the total charge of the molecule Q = Yfi- where q- is the charge of particle and the sum is over all electrons and nuclei in tlie molecule. The first-order moment is the dipole moment vector with Cartesian components given by... 

Also produced in electronic structure sunulations are the electronic waveftmctions and energies F ] of each of the electronic states. The separation m energies can be used to make predictions on the spectroscopy of the system. The waveftmctions can be used to evaluate the properties of the system that depend on the spatial distribution of the electrons. For example, the z component of the dipole moment [10] of a molecule can be computed by integrating... 

The calculated electronic distribution leads to an evaluation of the dipole moment of thiazole. Some values are collected in Table 1-7 that can be compared to the experimental value of 1.61 D (158). 

The molecular dipole moment is perhaps the simplest experimental measure of charge density in a molecule. The accuracy of the overall distribution of electrons in a molecule is hard to quantify, since it involves all of the multipole moments. Experimental measures of accuracy are necessary to evaluate results. The values for the magnitudes of dipole moments from AMI calculations for a small sample of molecules (Table 4) indicate the accuracy you may... 

A variety of methodologies have been implemented for the reaction field. The basic equation for the dielectric continuum model is the Poisson-Laplace equation, by which the electrostatic field in a cavity with an arbitrary shape and size is calculated, although some methods do not satisfy the equation. Because the solute s electronic strucmre and the reaction field depend on each other, a nonlinear equation (modified Schrddinger equation) has to be solved in an iterative manner. In practice this is achieved by modifying the electronic Hamiltonian or Fock operator, which is defined through the shape and size of the cavity and the description of the solute s electronic distribution. If one takes a dipole moment approximation for the solute s electronic distribution and a spherical cavity (Onsager s reaction field), the interaction can be derived rather easily and an analytical expression of theFock operator is obtained. However, such an expression is not feasible for an arbitrary electronic distribution in an arbitrary cavity fitted to the molecular shape. In this case the Fock operator is very complicated and has to be prepared by a numerical procedure. 

The unequal distribution of electron density in covalent bonds produces a bond dipole, the magnitude of which is expressed by the dipole moment, having the units of charge times distance. Bonds with significant bond dipoles are described as being polar. The bond and group dipole moments of some typical substituents are shown in Table 1.7. 

The dispersion (London) force is a quantum mechanieal phenomenon. At any instant the electronic distribution in molecule 1 may result in an instantaneous dipole moment, even if 1 is a spherieal nonpolar moleeule. This instantaneous dipole induces a moment in 2, which interacts with the moment in 1. For nonpolar spheres the induced dipole-induced dipole dispersion energy function is... 

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

In Section 2.12, we saw that a polar covalent bond in which electrons are not evenly distributed has a nonzero dipole moment. A polar molecule is a molecule with a nonzero dipole moment. All diatomic molecules are polar if their bonds are polar. An HC1 molecule, with its polar covalent bond (8+H—Clfi ), is a polar molecule. Its dipole moment of 1.1 D is typical of polar diatomic molecules (Table 3.1). All diatomic molecules that are composed of atoms of different elements are at least slightly polar. A nonpolar molecule is a molecule that has no electric dipole moment. All homonuclear diatomic molecules, diatomic molecules containing atoms of only one element, such as 02, N2, and Cl2, are nonpolar, because their bonds are nonpolar. 

FIGURE 5.5 The rapid fluctuations in the electron distribution in two neighboring molecules result in two instantaneous electric dipole moments that attract each other. The fluctuations flicker into different positions, but each new arrangement in one molecule induces an arrangement in the other that results in mutual attraction. 

This implies that Br2 is the electrophile. But how does Br2 function as an electrophile The bond between the two bromine atoms is a covalent bond, and we therefore expect the electron density to be equally distributed over both Br atoms. However, an interesting thing happens when a Br2 molecule approaches an alkene. The electron density of the pi bond repels the electron density in the Br2 molecule, creating a temporary dipole moment in Br2. 

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