Atomic properties polarizability

The chirality code of a molecule is based on atomic properties and on the 3D structure. Examples of atomic properties arc partial atomic charges and polarizabilities, which are easily accessible by fast empirical methods contained in the PETRA package. Other atomic properties, calculated by other methods, can in principle be used. It is convenient, however, if the chosen atomic property discriminates as much as possible between non-equivalent atoms. 3D molecular structures are easily generated by the GORINA software package (see Section 2.13), but other sources of 3D structures can be used as well. 

This coding is performed in three steps (cf Chapter 8) First the 3D coordinates of the atoms arc calculated using the structure generator CORINA (COoRdlNAtes). Subsequently the program PETRA (Parameter Estimation for the Treatment of Reactivity Applications) is applied for calculating physicochemical properties such as charge distribution and polarizability. The 3D information and the physicochemical atomic properties are then used to code the molecule. 

All the elements in a main group have in common a characteristic valence electron configuration. The electron configuration controls the valence of the element (the number of bonds that it can form) and affects its chemical and physical properties. Five atomic properties are principally responsible for the characteristic properties of each element atomic radius, ionization energy, electron affinity, electronegativity, and polarizability. All five properties are related to trends in the effective nuclear charge experienced by the valence electrons and their distance from the nucleus. 

The atomic properties satisfy the necessary physical requirement of paralleling the transferability of their charge distributions - atoms that look the same in two molecules contribute identical amounts to all properties in both molecules, including field-induced properties. Thus the atoms of theory recover the experimentally measurable contributions to the volume, heats of formation, electric polarizability, and magnetic susceptibility in those cases where the group contributions are found to be transferable, as well as additive additive [4], The additivity of the atomic properties coupled with the observation that their transferability parallels the transferability of the atom s physical form are unique to QTAIM and are essential for a theory of atoms in molecules that purports to explain the observations of experimental chemistry. 

These are three examples of the use of atomic properties to obtain quantitative structure-activity relationships (QSAR) or structure-function relationships. One should bear in mind that all properties have an atomic basis, making a multitude of new relationships possible. The atomic contribution to the polarizability, for example, is definable and shown to be transferable [26-28], offering the possibility of improving the use of an electrostatic potential map from zero- to first-order estimates of energies of interaction. 

The average polarizability a, defined by equation 9, is a global property, which pertains to a molecule as a whole. It is a measure, to the first order, of the overall effect of an external electric field upon the charge distribution of the molecule. We are unaware of any experimentally determined a for the molecules that are included in this chapter. However, they can be estimated using equation 12 and the atomic hybrid polarizabilities, and corresponding group values, that were derived empirically by Miller. These were found to reproduce experimental molecular a with an average error of 2.8%. The relevant data, taken from his work, are in Table 7. 

Recent work improved earlier results and considered the effects of electron correlation and vibrational averaging [278], Especially the effects of intra-atomic correlation, which were seen to be significant for rare-gas pairs, have been studied for H2-He pairs and compared with interatomic electron correlation the contributions due to intra- and interatomic correlation are of opposite sign. Localized SCF orbitals were used again to reduce the basis set superposition error. Special care was taken to assure that the supermolecular wavefunctions separate correctly for R —> oo into a product of correlated H2 wavefunctions, and a correlated as well as polarized He wavefunction. At the Cl level, all atomic and molecular properties (polarizability, quadrupole moment) were found to be in agreement with the accurate values to within 1%. Various extensions of the basis set have resulted in variations of the induced dipole moment of less than 1% [279], Table 4.5 shows the computed dipole components, px, pz, as functions of separation, R, orientation (0°, 90°, 45° relative to the internuclear axis), and three vibrational spacings r, in 10-6 a.u. of dipole strength [279]. 

Figure 1. Graphic display of atomic properties of metastable noble gases. Solid lines correspond to metastables, dashed to analogous alkali atom (He corresponds to Li, etc.) -o-, excitation energies ionization potentials -A-, polarizabilities, with angular momentum substates of metastables shown separately (see Table I for values).

Primary atomic properties as those, which can be determined experimentally. These are nuclear charges and atomic masses, ionisation potentials and electron affinities and the spectroscopic term values of the atoms and corresponding ions. Also atomic polarizabilities and in principle the electronic charge distributions of the atoms would correspond to this class. 

To obtain spatial autocorrelation molecular descriptors, function /(x,) is any physico-chemical property calculated for each atom of the molecule, such as atomic mass, polarizability, etc., and - local vertex invariants such as - vertex degree. Therefore, the molecule atoms represent the set of discrete points in space and the atomic property the function evaluated at those points. 

The atomic properties considered are partial charges, electron densities and polarizabilities, calculated by - computational chemistry methods moreover, bond properties have been proposed as the difference between the property values of the atoms forming the bond. The range of each property is determined by the maximum and minimum values for all the atoms in all the molecules, thus obtaining uniform spectrum length for all the molecules in the data set. 

The weights w can be any chemical or topological atomic properties. Examples of chemical -> atomic properties are - van der Waals volume, atomic mass, - polarizability examples of -> local vertex invariants are - vertex degree, - path degree, - walk degree. 

The atomic properties constitute the weights used to characterize molecule atoms the most common atomic properties are atomic mass, - atomic charge, -> van der Waals radius, -> atomic polarizability, and hydrophobic atomic constants. Atomic properties can also be defined by the - local vertex invariants (LOVIs) derived from graph therory. 

Both indices can be extended to any other atomic property different from atomic mass, such as -+ atomic polarizability, atomic - van der Waals volume, etc. 

Veldhuizen and de Leeuw (1996) used the OPLS parameters for methanol and both a nonpolarizable and a polarizable model for carbon tetrachloride for MD simulations over a wide range of compositions. The polarization contribution was found to be very important for the proper description of mixture properties, such as the heat of mixing. A recent study by Gonzalez et at (1999) of ethanol with MD simulations using the OPLS potential concluded that a nonpolarizable model for ethanol is sufficient to describe most static and dynamic properties of liquid ethanol. They also suggested that polarizabilities be introduced as atomic properties instead of the commonly approach of using a single molecular polarizability. 

One of the major advantages of dynamic atomic properties in this context is that they account for valuable molecular information beyond the raw 3D data of atoms. Dynamic atomic properties depend on the chemical enviromnent of the atoms. Typical examples are atom polarizability, molecular polarizability, residual electronegativity, partial atomic charges, ring-strain energies, and aromatic stabilization energies. 

Dynamic Atomic Properties depend on the chemical environment of the atom and are characteristic for the molecule. Examples are partial atomic charge, atom polarizability, and partial electronegativity. 

The empirical hydration free energy density is expressed by a linear combination of some physical properties calculated around the molecule with net atomic charges, polarizabilities, dispersion coefficients of the atoms in the molecule, and solvent accessible surface [Son, Han et al, 1999]. These physical properties are the result of the interaction of the molecule with its environment. To calculate the H F E D of a molecule a grid model was proposed a shell of critical thickness rc was defined around the solvent-accessible surface with a number of grid points inside (e.g., 8 points/A ). 

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