Atom centered dipole

Figure 3.12. Different approaches to localization of chaigeused in electrostatic models, (a) Atom-centered monopole (b) atom-centered dipole and (c) atom-centered quadrapole.

In contrast to the point charge model, which needs atom-centered charges from an external source (because of the geometry dependence of the charge distribution they cannot be parameterized and are often pre-calculated by quantum mechanics), the relatively few different bond dipoles are parameterized. An elegant way to calculate charges is by the use of so-called bond increments (Eq. (26)), which are defined as the charge contribution of each atom j bound to atom i. 

The third integral vanishes because the derivative of the dipole operator itself p = Zi e rj + Za Za e Ra with respect to the coordinates of atomic centers, yields an operator that contains only a sum of scalar quantities (the elementary charge e and the... 

The electrostatic energy is calculated using the distributed multipolar expansion introduced by Stone [39,40], with the expansion carried out through octopoles. The expansion centers are taken to be the atom centers and the bond midpoints. So, for water, there are five expansion points (three at the atom centers and two at the O-H bond midpoints), while in benzene there are 24 expansion points. The induction or polarization term is represented by the interaction of the induced dipole on one fragment with the static multipolar field on another fragment, expressed in terms of the distributed localized molecular orbital (LMO) dipole polarizabilities. That is, the number of polarizability points is equal to the number of bonds and lone pairs in the molecule. One can opt to include inner shells as well, but this is usually not useful. The induced dipoles are iterated to self-consistency, so some many body effects are included. 

Inductive effects on dipole moments and the effects of intervening atoms on electrostatic interaction energies are represented by polarizability centers In conjunction with bond centered dipoles. Solvation energies are estimated by means of a continuum dlpole-quadrupole electrostatic model. Calculated energies of a number of conformations of meso and racemic 2,4-dichloropentane and the iso, syndio, and hetero forms of 2,4,6-triehloroheptane give satisfactory representations of isomer and conformer populations. Electrostatic effects are found to be quite important. 

Charges can be obtained at different level of moments such as monopole (s = 1), dipole (s = 3) and quadrupole (s = 9). Torsion energy barriers for the HS-SH molecule calculated by several methods can be seen in Fig. 9 [90]. For the PCM model of this molecule the number of expansion centers is six (c = 6) beside the atomic centers, one center per S-H bond is further included. It can be seen that the PCM result is very close to the CMMM one and the PCM charges can be used for calculating intramolecular electrostatic interactions as well. 

The first water molecule model used here assumed for simplicity that the negative dipole charges are at 0.15 A from the oxygen atom center, in the H-O-H planey ... 

The two-center-two-electron bond is also modified by the presence of heteroatoms. Two important effects concern how electron density is shared between the two atom centers of a two-center bond. First, each bond is now polarized due to the fact that the electronegativities of the two atoms differ. This leads to molecules with net electric dipole... 

The Ce dispersion coefficients for dipole dipole dispersion between pairs of interacting species, the coefficients for terms involving higher multipolar dispersion, and coefficients for three-body dispersion terms can be and have been evaluated by ab initio techniques [114 119] as well as through relations to experimental optical data based on moments of the dipole oscillator strength [120 122]. These are parameters of the interaction, not properties. However, as noted in Section IVA, values for Ce coefficients of like pairs (e.g., A-A), and possibly for other dispersion coefficients, can be used in simple [Eq. (4)] or in more complete forms [Eq. (2)] as an intrinsic property of a molecule. The basis set and correlation requirements for adequate evaluation show, in part, the same requirements for describing polarizabilities however, there are further needs and other than atom-centered functions are seen as being suited [49 52]. 

Charge density analyses can provide experimental information on the concentration of electron density around atoms and in intra- and intermolecular bonds, including the location of lone pairs. Transition metal d-orbital populations can be estimated from the asphericity of the charge distribution around such metal centers. A number of physical properties that depend upon the electron density distribution can also be calculated. These include atomic charges, dipole and higher moments, electric field gradients, electrostatic potentials and interaction... 

Interactions between atoms that are not transmitted through bonds are referred to as nonbonded interactions. Most interactions are between centers of atoms, while some force fields use through-space interactions between points that are not centered on nuclei, such as lone pairs and bond-center dipoles. Interactions between atoms separated by only one or two bonds are normally not calculated, whereas atoms in the 1, 4-position with three intervening bonds interact both via torsional and nonbonded potentials. Thus these interactions become partially dependent. Introduction of scalable parameters for nonbonded 1,4-interactions can reduce this interdependence. 

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