Permanent-induced dipole

Even a covalent bond can possess a permanent induced dipole. 

Figure 6. Number of open channels for the interaction between H3 and HC1 (SACM calculations from Ref. IS PST phase-space theory full curves permanent + induced dipole dashed smoothed curves permanent dipole J total angular momentum of H3-HCI complex).

The cavity and the reaction fields are related to the Maxwell field in the medium and to the total (permanent+induced) dipole moment /xa of the molecule at the frequency O by... 

The term van der Waals forces includes three types of intermolecular forces London (dispersion) forces, permanent dipole-dipole forces (sometimes referred to as Keesom forces) and permanent-induced dipole interactions (Debye forces). In 1910, van der Waals was awarded the Nohel Prize for his work on the equation of state for gases and liquids concerned with the reasons for non-ideal behaviour in real gases. His equation introduced compensatory terms to account for the non-zero size of the particles and the inter-particle forces between them. This broader definition of van der Waals forces runs contrary to the use of the term in many current textbooks, but is consistent with its use in the IB syllabus. 

The first term accounts for the average total (permanent- -induced) dipole moment and vanishes in the absence of ideal dipole /r, as for monoatomic ions the second term accounts for fluctuations. For particles of C2v or higher symmetry, the scalar C mf) that contains the electrostatic coupling with the neighbonrhood is defined by the expression... 

Our discussion of elecfronic effects has concentrated so far on permanent features of the cliarge distribution. Electrostatic interactions also arise from changes in the charge distribution of a molecule or atom caused by an external field, a process called polarisation. The primary effect of the external electric field (which in our case will be caused by neighbouring molecules) is to induce a dipole in the molecule. The magnitude of the induced dipole moment ginj is proportional to the electric field E, with the constant of proportionahty being the polarisability a ... 

Dipole/induced dipole attraction (Section 4 6) A force of at traction that results when a species with a permanent dipole induces a complementary dipole in a second species... 

As argued above, this result is found to work best for substances in which both the 1,1 and 2,2 forces are either London or dipole-dipole. Even the case of one molecule with a permanent dipole moment interacting with a molecule which has only polarizability and no permanent dipole moment-such species interact by permanent dipole-induced dipole attraction-is not satisfactorily approximated by Eq. (8.46). In this context the like dissolves like rule means like with respect to the origin of intermolecular forces. 

Now let us examine the molecular origin of Molecular polarity may be the result of either a permanent dipole moment p or an induced dipole moment ind here the latter arises from the distortion of the charge distribution in a molecule due to an electric field. We saw in Chap. 8 that each of these types of polarity are sources of intermolecular attraction. In the present discussion we assume that no permanent dipoles are present and note that the induced dipole moment is proportional to the net field strength at the molecule ... 

A polar molecule can also induce a dipole on a neighbouring molecule that possesses no permanent dipole. The resultant intermolecular attraction between the permanent and the induced dipole is spoken of as the induction force. Its magnitude is small and independent of temperature. 

The induced counter-dipole can act in a similar manner to a permanent dipole and the electric forces between the two dipoles (permanent and induced) result in strong polar interactions. Typically, polarizable compounds are the aromatic hydrocarbons examples of their separation using induced dipole interactions to affect retention and selectivity will be given later. Dipole-induced dipole interaction is depicted in Figure 12. Just as dipole-dipole interactions occur coincidentally with dispersive interactions, so are dipole-induced dipole interactions accompanied by dispersive interactions. It follows that using an n-alkane stationary phase, aromatic... 

Two Molecules Interacting and Held Together by Dispersive Forces and Polar Forces from Permanent and Induced Dipoles... 

There are three types of interactions that contribute to van der Waals forces. These are interactions between freely rotating permanent dipoles (Keesom interactions), dipole-induced dipole interaction (Debye interactions), and instantaneous dip le-induced dipole (London dispersion interactions), with the total van der Waals force arising from the sum. The total van der Waals interaction between materials arise from the sum of all three of these contributions. 

Both the permanent dipole and the applied field are vector quantities, and the direction of the induced dipole need not be the same as the direction of the applied field. Hence, we need a more general property than a vector to describe the polarizability. 

FIGURE 4.7. A schematic description of the different contributions to the PDLD model. The figure considers the energetics of an ion pair inside a protein interior. The upper part describes the protein permanent dipoles, the middle part describes the induced dipoles of the protein, while the lower part describes the surrounding water molecules and the bulk region, which is represented by a macroscopic continuum model. 

Closely related to the London interaction is the dipole-induced-dipole interaction, in which a polar molecule interacts with a nonpolar molecule (for example, when oxygen dissolves in water). Like the London interaction, the dipole—induced-dipole interaction arises from the ability of one molecule to induce a dipole moment in the other. However, in this case, the molecule that induces the dipole moment has a permanent dipole moment. The potential energy of the interaction is... 

Polar forces also arise from electrical charges on the molecule but in this case from permanent or induced dipoles. It must be emphasized... 

Induction forces, the so-called Debye forces ind> occur in the interaction between a permanent dipole of a solute or a polar solvent and an induced dipole in another compound. They are weak and appear during the analysis of the nonpolar polarized compounds, such as those with multiple... 

Eo and E (Afi(i)) are respectively the electric fields generated by the permanent and induced multipoles moments. a(i) represents the polarisability tensor and Afi(i) is the induced dipole at a center i. This computation is performed iteratively, as Epoi generally converges in 5-6 iterations. It is important to note that in order to avoid problems at the short-range, the so-called polarization catastrophe, it is necessary to reduce the polarization energy when two centers are at close contact distance. In SIBFA, the electric fields equations are dressed by a Gaussian function reducing their value to avoid such problems. 

The total electric field, E, is composed of the external electric field from the permanent charges E° and the contribution from other induced dipoles. This is the basis of most polarizable force fields currently being developed for biomolecular simulations. In the present chapter an overview of the formalisms most commonly used for MM force fields will be presented. It should be emphasized that this chapter is not meant to provide a broad overview of the field but rather focuses on the formalisms of the induced dipole, classical Drude oscillator and fluctuating charge models and their development in the context of providing a practical polarization model for molecular simulations of biological macromolecules [12-21], While references to works in which the different methods have been developed and applied are included throughout the text, the major discussion of the implementation of these models focuses... 

The dipole moment, p , induced on a site i is proportional to the electric field at that site, E . The proportionality constant is the polarizability tensor, a,. The dipole feels an electric field both from the permanent charges of the system and from the other induced dipoles. The expression for is... 

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