Polarization term

Bamford, Jenkins and coworkers131157 concluded that many of the limitations of the Q-e scheme stemmed from its empirical nature and proposed a new scheme containing a radical reactivity term, based on experimentally measured values of the rate constant for abstraction of benzylic hydrogen from toluene (Ay i), a polar term (the Hammett o value) and two constants a and J which are specific for a given monomer or substrate (eq. 57) 146... 

The five second-moment spherical tensor components can also be calculated and are defined as the quadrupolar polarization terms. They can be seen as the ELF basin equivalents to the atomic quadrupole moments introduced by Popelier [32] in the case of an AIM analysis ... 

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. 

The charge-transfer and polarization terms, Eq. 1, CT and P, can be understood be referring to Fig. 2. These configurations may make a contribution to the perturbation energy of the composite state if one... 

It is interesting to compare the parameters exhibited by the cavitands with and without the functional group improving hydrogen bonding. The effect of the functionalization is expected to increase the parameter a this effectively happens for 1 and 2. The stronger effect of polarization is instead observed for the polarization term. This explains the... 

Slater developed an approach (the "determinantal method") that offers a way of choosing among linear combinations (essentially sums and differences) of the polar and nonpolar terms in the Hund-Mulliken equations to bring their method into better harmony with the nonpolar emphasis characteristic of the Heitler-London-Pauling approach in which polar terms do not figure in the wave equation. 72... 

A satisfactory feature of (116) is that the first-order term, which describes the interaction between the external charge and the unperturbed molecule, continues to disappear if the electron distribution is highly uniform as in an alternant hydrocarbon in such cases the propensities for reaction are still dominated by the polarization term, but this now has a less simple form, depending upon all atom-atom polarizabilities and on the position of the attacking ion with respect to all conjugated centres. 

Subtracting a charge in a given lattice position also contributes to the defect energy with an induced polarization term whose significance was described in section 1.19 ... 

Polarity term, mainly related to hydrogen bonding capability of a solute Logarithm of the partition coefficient (P) of neutral species Logarithm of the distribution coefficient (D) at a selected pH, usually assumed to be measured in octanol/water... 

The superscripts h and p refer to group contributions due to hydrocarbon and polar groups, respectively. The polar term is often found to be small while the shape of the cavity occupied by the solute molecule is irregular and requires a shape factor. Equation (4.9) then becomes ... 

The energy of the 5 f electrons consists of their band-energy Ef and of a spin polarization term Asp. Ajp has an atomic origin, and tends to localize the itinerant 5f... 

Conversely, Brooks and Johansson have calculated the spin-polarization term Ajp from a spin-polarized local-density approximation in atoms. These values can also be used in Eq. (3). The two evaluations, though not identical, do not differ greatly. 

Spin-polarization sets up in the second part of the series, as in the case of metals, and, correspondingly, Eq. (22) should be modified with the use of spin-polarized terms. This explains the onset of an actinide contraction trend in heavier actinide NaCl compounds, as shown in Fig. 5 of Chap. A for the AnN system. 

As compared to conventional organic solvents, ILs are much more complex solvents, capable of undergoing many types of interactions. Therefore, a single polarity term fails to describe the type and magnitude of individual interactions that they make. 

In this way the mass polarization term may be removed from the Hamiltonian. However, the resulting electronic wave functions which are obtained are then dependent upon the nuclear masses as well as the nuclear charges and such wave functions are an inconvenient basis from which to investigate nonadiabatic processes. 

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