Dipole classical

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 interaction arises from the coupling between two magnetic dipoles. Classically the energy of two interacting dipoles p,] and p2, a distance r apart, is given by... 

Agarwal et showed, using a point-dipole, classical electrodynamic calculation, that the image can be considerable near a metal sphere (simulating a roughness feature) of about 2-3 nm and with similar molecule-sphere distances. At such distances the approximations are tolerable, so that their results are dependable. The reason for the increase in the interaction is a coupling to the surface plasmon (or shape resonance), which in the sphere can occur at lower frequencies than for a flat surface. 

In order to illustrate some of the basic aspects of the nonlinear optical response of materials, we first discuss the anliannonic oscillator model. This treatment may be viewed as the extension of the classical Lorentz model of the response of an atom or molecule to include nonlinear effects. In such models, the medium is treated as a collection of electrons bound about ion cores. Under the influence of the electric field associated with an optical wave, the ion cores move in the direction of the applied field, while the electrons are displaced in the opposite direction. These motions induce an oscillating dipole moment, which then couples back to the radiation fields. Since the ions are significantly more massive than the electrons, their motion is of secondary importance for optical frequencies and is neglected. 

Selenolopyrylium salts, 4, 1034—1036 Selenolo[2,3-c]pyrylium salts synthesis, 4, 969 Selenolo[3,2-b]pyrylium salts synthesis, 4, 1035 Selenolo[3,2-c]pyrylium salts synthesis, 4, 969 Selenoloseknophenes electrophilic substitution, 4, 1057 NMR, 4, 13 synthesis, 4, 135 UV spectra, 4, 1044 Selenoloselenophenes, alkyl-synthesis, 4, 967 Selenolo[2,3-b]selenophenes ionization potentials, 4, 1046 Selenolo[3,2- bjselenophenes dipole moments, 4, 1049 ionization potentials, 4, 1046 structure, 4, 1038, 1039 Selenolo 3,4-f)]selenophenes H NMR, 4, 1042 synthesis, 4, 1067 Selenolo[3,4-c]selenophenes non-classical reactions, 4, 1062 synthesis, 4, 1076 Selenolothiophenes electrophilic substitution, 4, 1057 H NMR, 4, 1041 UV spectra, 4, 1044 Selenolo[2,3- bjthiophenes... 

HF-LCAO calculations on molecules with small electric dipoles need to be treated with caution. The classic case is CO. Burrus (1958) determined the magnitude of the vector from a Stark experiment as 0.112 0.005 D (0.374 0.017 x 10-30 Cm). 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

In the presence of an external magnetic induction B this dipole Pm has a potential energy given by the laws of classical electromagnetism as... 

There are two terms of interest. First there is a classical electron spin-nuclear spin dipole-dipole interaction... 

We consider first the polarizability of a molecule consisting of two or more polarizable parts which may be atoms, bonds, or other units. When the molecule is placed in an electric field the effective field which induces dipole moments in various parts is not just the external field but rather the local field which is influenced by the induced dipoles of the other parts. The classical theory of this interaction of polarizable units was presented by Silberstein36 and others and is summarized by Stuart in his monograph.40 The writer has examined the problem in quantum theory and finds that the same results are obtained to the order of approximation being considered. 

The charge distribution of neutral polar molecules is characterized by a dipole moment which is defined classically by jx = E, , , where the molecular charge distribution is defined in terms of the residual charges (qt) at the position r,. The observed molecular dipole moment provides useful information about the charge distribution of the ground state and its ionic character. 

In order to compare calculated and observed dipole moments, we should replace the classical expression of the dipole moment by its quantum analogue jx = f F x1Ir dr where /I is the dipole moment operator (given by jx = —eri + . eZ-Blj with i and j running over the electronic and nuclear coordinates, respectively, and — e the electron charge). The actual calculation of a VB dipole moment is described below. 

This equation would enable one to predict the UWR vs t behaviour in galvanostatic transients such as those of Fig. 4.15 if the value of the Na dipole moment on Pt were exactly known. The surface science literature (Chapter 2) suggests pNa=5.2 D for the initial dipole moment of Na on Pt(lll). This value has been used, in conjunction with Eq. (4.25) to draw the lines labeled Eq. (4.25) ] in Fig. 4.15 and in subsequent figures throughout this book. As shown in Fig. 4.15 there is very good qualitative agreement between Eq. (4.25) and the initial Uwr vs t transient. This supports the approach and underlines the similarities between electrochemical and classical promotion. 

N2 - NO+ + N, compared with a theory (7) based on classical trajectories subject to an ion-induced dipole potential. The assumptions involved in calculating the measured cross-sections are noted in the text... 

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