Atomic dipole model

Finally, in the third section of this paper, we describe a semiempirical atom dipole model that allows a reliable prediction of molecular electric dipole and quadrupole moments, diamagnetic susceptibilities, and diamagnetic nuclear shieldings. A set of localized bond and atom values are developed for the individual diagonal elements in the total molecular magnetic susceptibility tensor. 

Surprisingly, the atomic dipole model (D) is nearly as good as the atomic charge (M) model. If only dipoles are used, it may be better to locate them in the bonds. The table shows that the bond dipole model (BD) gives a better representation of the electric potential for most of the molecules considered. Of course, at least one monopole is needed if the molecule is an ion and therefore has a net charge. 

The local diamagnetic term i.e., shielding restricted only to the electrons of the N atom, and the difference Aafoc with respect to N2 were calculated semiempirically for small N-containing molecules including N2F4 using Pople s model [15] and the atom-dipole model... 

Pulsed source techniques have been used to study thermal energy ion-molecule reactions. For most of the proton and H atom transfer reactions studied k thermal) /k 10.5 volts /cm.) is approximately unity in apparent agreement with predictions from the simple ion-induced dipole model. However, the rate constants calculated on this basis are considerably higher than the experimental rate constants indicating reaction channels other than the atom transfer process. Thus, in some cases at least, the relationship of k thermal) to k 10.5 volts/cm.) may be determined by the variation of the relative importance of the atom transfer process with ion energy rather than by the interaction potential between the ion and the neutral. For most of the condensation ion-molecule reactions studied k thermal) is considerably greater than k 10.5 volts/cm.). 

When the Drude particles are treated adiabatically, a SCF method must be used to solve for the displacements of the Drude particle, d, similarly to the dipoles Jtj in the induced dipole model. The implementation of the SCF condition corresponding to the Born-Oppenheimer approximation is straightforward and the real forces acting on the nuclei must be determined after the Drude particles have attained the energy minimum for a particular nuclear configuration. In the case of N polarizable atoms with positions r, the relaxed Drude particle positions r + d5CF are found by solving... 

An important alternative to SCF is to extend the Lagrangian of the system to consider dipoles as additional dynamical degrees of freedom as discussed above for the induced dipole model. In the Drude model the additional degrees of freedom are the positions of the moving Drude particles. All Drude particles are assigned a small mass mo,i, taken from the atomic masses, m, of their parent atoms and both the motions of atoms and Drude particles (at positions r, and rdj = r, + d, ) are propagated... 

An important addition to the model was the inclusion of virtual particles representative of lone pairs on hydrogen bond acceptors [60], Their inclusion was motivated by the inability of the atom-based electrostatic model to treat interactions with water as a function of orientation. By distributing the atomic charges on to lone pairs it was possible to reproduce QM interaction energies as a function of orientation. The addition of lone pairs may be considered analogous to the use of atomic dipoles on such atoms. In the model, the polarizability is still maintained on the parent atom. In addition, anisotropic atomic polarizability, as described in Eq. (9-28), is included on hydrogen bond acceptors [65], Its inclusion allows for reproduction of QM polarization response as a function of orientation around S, O and N atoms and it facilitates reproduction of QM interaction energies with ions as a function of orientation. 

Applequist J, Carl JR, Fung K-K (1972) Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities. J Am Chem Soc... 

As its name implies, AIM enables us to calculate such properties of atoms in a molecule as atomic charge, atomic volume, and atomic dipole. Indeed it shows us that the classical picture of a bond as an entity that is apparently independent of the atoms, like a Lewis bond line or a stick in a ball-and-stick model, is misleading. There are no bonds in molecules that are independent of the atoms. AIM identifies a bond as the line between two nuclei. 

Williams, D. E. 1988. Representation of the Molecular Electrostatic Potential by Atomic Multipole and Bond Dipole Models. J. Comp. Chem. 9, 745. 

General properties and definitions of polarizabilities can be introduced without invoking the complete DFT formalism by considering first an elementary model the dipole of an isolated, spherical atom induced by a uniform electric field. The variation of the electronic density is represented by a simple scalar the induced atomic dipole moment. This coarse-grained (CG) model of the electronic density permits to derive a useful explicit energy functional where the functional derivatives are formulated in terms of polarizabilities and dipole hardnesses. 

A large number of dipole models have been developed in the past to predict the molecular polarizabilities [46,47], In these models, two atoms interact via Coulomb... 

Since the unpaired electron in transition metal complexes is generally localized near the central ion and the ligand atoms in the first coordination sphere, summation in (5.5) over these nuclei is often sufficient. In this approximated form, the point-dipole model has frequently been applied in ENDOR studies of transition metal complexes to determine the proton positions from their hfs tensors (Sect. 6). In some cases the accuracy of this method has turned out to be significantly higher than that of an X-ray diffraction analysis62,130 131). 

From Eq, (1) it is clear that a model of crystal polarization that is adequate for the description of the piezoelectric and pyroelectric properties of the P-phase of PVDF must include an accurate description of both the dipole moment of the repeat unit and the unit cell volume as functions of temperature and applied mechanical stress or strain. The dipole moment of the repeat unit includes contributions from the intrinsic polarity of chemical bonds (primarily carbon-fluorine) owing to differences in electron affinity, induced dipole moments owing to atomic and electronic polarizability, and attenuation owing to the thermal oscillations of the dipole. Previous modeling efforts have emphasized the importance of one more of these effects electronic polarizability based on continuum dielectric theory" or Lorentz field sums of dipole lattices" static, atomic level modeling of the intrinsic bond polarity" atomic level modeling of bond polarity and electronic and atomic polarizability in the absence of thermal motion. " The unit cell volume is responsive to the effects of temperature and stress and therefore requires a model based on an expression of the free energy of the crystal. 

Molecular gases. In the case of molecular gases, or of mixtures involving a molecular gas, one must in general account for several induced dipole components, as the asymptotic expressions of Section 4.7 suggest. Besides these multipole-induced terms, one or more overlap-induced terms are usually necessary, especially if induction in species of low polarizability is considered (He atoms). While for certain systems just one or two dipole components need to be accounted for, for other systems elaborate sets had to be assumed for a satisfactory fit of the spectra. Moreover, for the molecular systems, we have to consider a number of different dipole models for the different bands (rototranslational, rotovibrational and overtones). It is, therefore, impractical to repeat here even the most important measurements. Table 4.2 quotes some sources where such information may be found. Examples of what is expected for a few representative systems are given below. These are based on first principles. 

As noted above, the asymptotic formulae given here, Eqs. 4.47 through 4.86, are valid for two interacting diatomic molecules, i = 1 and 2. For symmetric molecules like H2, only even 2, occur. In that case, for example, no octopoles exist. If one of the interacting partners is an atom, the associated 2, can assume the value 0 only this reduces the amount of computations needed significantly. Empirical dipole model components have been proposed in the past that were consistent with the asymptotic expressions above, sometimes with exponential overlap terms of the form of Eq. 4.1 added. 

Other quantum line shape computations of absorption by dissimilar atomic pairs based on empirical or ab initio dipole models have been known for some time [39, 44, 76, 251, 330, 332, 361, 365, 386], Such studies are of interest for the analysis of measurements, for predicting... 

Exercise 16-1 Draw valence-bond structures and an atomic-orbital model for carbon monoxide. Why can the bond energy of this molecule be expected to be higher than for other carbonyl compounds (see Table 16-1) Explain why the dipole moment of CO is very small (0.13 debye).,... 

The transition dipole moment lies in the plane of the molecule rather than perpendicular to this plane. A model was developed in which charge transfer occurs in the excited (SnCl2) molecule, resulting from photoexcitation between the nonbonding p orbital on the Cl atom and the px orbital on the Sn atom. This model... 

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