Self-atom polarizabilities

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

The self-atom polarizability TZaa is analogously defined as... 

An index for total self-atom polarizability is obtained as... 

Historically, multiple theoretical descriptor-based approaches to H-bond strength ranking were proposed. That includes approaches based on group contribution method [46], electrostatic potentials [47], electrophilic superdelocalizability and self-atom polarizability [48], Quantum Theory of Atoms In Molecules (QTAIM) descriptors [49-51], the two-center shared electron number a and the product of ionization potential [45, 52], and local quantum mechanical molecular parameters, which quantify electrostatic, polarizability, and charge transfer contributions to H-bonding [53, 54],... 

Using data from Example 12-6, calculate the self-atom polarizability, jri.i for carbon 1 in naphthalene. 

The molecular descriptors used are as follows CMR (Calculated molar refractivity), pZ (Z component of the dipole moment), HOMO (Energy of the highest occupied molecular orbital), FZ (9), FY (6) and FY (11) (Z and Y are the components of the electric field at specified grid points), VDWE (4) (The van der Waal s energy of the interaction of a carbon atom at a specified grid point), ALP (3) (The self atom polarizability of the specified atom). 

The self-atom and atom-atom polarizabilities (nAA,nAB) defined using perturbation theory have been also employed to describe chemical reactivity [44], These quantities represent the effect of an electric field perturbation at one atom on the electronic charge at the same (nAA) or another atom (nAB), respectively. 

In this section we briefly outline the parametrization protocol for determining the partial atomic charges, atomic polarizabilities, and the atom-based Thole damping factors, as well as the optimization procedure of the force field parameters not dependent of the Drude oscillator positions, namely the bonded and Lennard-Jones terms. While the overall parameter optimization is described linearly in the text, it is important to bear in mind that the bonded and nonbonded parameters are strongly interdependent, such that in practice, an iterative procedure is adopted, with the electrostatic and LJ nonbonded and bonded parameters optimized in turn until a self-consistent solution is reached, offering optimal agreement with all sets of target data. 

An alternative way of including polarization is by using the ideas developed by Applequist and coworkers.By modifying the dipole operator and assigning point polarizabilities to all atoms, it is possible to generate a self-consistent set of atom polarizabilities for a large number of small molecules. With this approach, the atom polarizabilities are transferable and molecular polarization can be constructed for arbitrary molecules. 

Lastly, as shown in eqn (7.17), the energies contributed from atomic polarizability are the dipole self-energy, the dipole-charge interaction, and the dipole-dipole interaction, respectively. 

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 Drude oscillators are typically treated as isotropic on the atomic level. However, it is possible to extend the model to include atom-based anisotropic polarizability. When anisotropy is included, the harmonic self-energy of the Drude oscillators becomes... 

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