How to calculate the dipole polarizability

The molecular dipole moment can be represented as the sum of the individual atomic dipole moments and the pairwise atomic dipole contributions. 

The is large, when k and / belong to the aioms forming tue chemical bunds (if compared to two non-bonded atoms, see Appendix S, p. 1015), therefore the dipole moments related to pairs of atoms come practical unique fiom chemical bonds. The contribution of the lone pairs of the atom A is hidden in the second term of and may be quite large (cf. Appendix T on p. 1020). 

In several semiempirical methods of quantum chemistry (e.g., in the Hiickel method) we assume the Zero Differential Overlap (ZDO) approximation, i.e. that XkXl (Xk) kl and hence the second terms in as weU as in are equal to zero, and therefore 

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Coordinate System Dependence Hartree-Fock Approximation Atomic and Bond Dipoles Within the ZDO Approximation How to Calculate the Dipole Polarizability (4[Pg.720]

The Non-Homogeneous Electric Field Multipole Polarizabilities and Hyperpolarizabilities How to Calculate the Dipole Momeut ( ( ))... 

The earliest calculations of the dipole and quadrupole contributions to the crystal field used free-ion values for the dipole polarizability, a,-, and for the quadrupole polarizability (Hutchings and Ray, 1963). It is generally recognized today, however, that the polarizability of an ion in a solid is generally much less than the corresponding value for the free ion (Chakrabarti et al., 1976 Bogomolova et al., 1977). How much less, however, is not clear. For this reason, therefore, computations of dipole and quadrupole contributions to the crystal field should be regarded as imprecise, even if they are performed with reduced polarizability values. 

The cavity size in the Bom/Onsager/Kirkwood models strongly influences the calculated stabilization. Unfortunately, there is no consensus on how to choose the cavity radius. In some cases, the molecular volume is calculated from the experimental density of the solvent and the cavity radius is defined by equating the cavity volume to the molecular volume. Alternatively, the cavity size may be derived from the (experimental) dielectric constant and the calculated dipole moment and polarizability. In any case, the underlying assumption of these models is that the molecule is roughly spherical or ellipsoidal, which is only generally true for small compact molecules. 

Let us now demonstrate a simple example of the above process which will show us how the O Eq. 20.4 can be utilized in order to calculate aU the components of the polarizability tensor for a cluster without symmetry (Q point group). For this symmetry group there are three independent components of the dipole moment fix,Fy nd y.z) and the six for the dipole polarizability three principal (axial) components a, Uyy, and (Xzz and three transversal ones... 

This is not an SCRF model, as the dipole moment and stabilization are not calculated in a self-consistent way. When the back-polarization of the medium is taken into account, the dipole moment changes, depending on how polarizable the molecule is. Taking only the first-order effect into account, the stabilization becomes (a is the molecular polarizability, the first-order change in the dipole moment with respect to an electric field, Section 10.1.1). 

The challenges outlined above still await a solution. In this section, we show how some of the theoretical limitations employed in traditional formulations of the band shape analysis can be lifted. We discuss two extensions of the present-day band shape analysis. First, the two-state model of CT transitions is applied to build the Franck-Condon optical envelopes. Second, the restriction of only two electronic states is lifted within the band shape analysis of polarizable chromophores that takes higher lying excited states into account through the solute dipolar polarizability. Finally, we show how a hybrid model incorporating the electronic delocalization and chromophore s polarizability effects can be successfully applied to the calculation of steady-state optical band shapes of the optical dye coumarin 153 (C153). We first start with a general theory and outline the connection between optical intensities and the ET matrix element and transition dipole. 

Our interest is how to treat polarizability of ion in the molecular dynamics calculation. There have been paid a lot of attention up to now and three methods to include the effect of the polarizability are considered a shell model method, a modified potential method, a dipole rod method. 

A much more accurate way to include the induced dipole interactions is to compute them for every configuration and include them in the simulation. Barker [16] showed how to make such calculations using an iterative procedure. For point charge models, together with the assumption that the molecular polarizability can... 

Certain intrinsic molecular properties describe how and in what manner a molecule responds to an applied field. These properties offer a good illustration of what is at stake in a direct calculation of a property. For uniform electric fields, the kind developed between two oppositely charged parallel plates, the first-order energy response is the dipole or first moment. The first-order response to a field gradient is the second moment, the quadrupole, and so on. Polarizabilities correspond to the second-order response, and hyperpolarizabilities to third-order and higher order changes. So, each of these is obtained as a derivative. 

HYNES - You raise an important point that concerns us. Electronic solvent polarization would presumably adjust "instantly to the reactive motion and exert no force to induce recrossing, however we use the "bare" H2O dipole moment in the calculations and not the solvent polarizability enhanced value. At some stage, polarizability should be included in such calculations, but we do not know how to do it. 

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