Atomic properties definition

Two other atomic properties have been used in the definition of atom type, thereby increasing its fuzziness relative to that in the ap and tt descriptors - atomic log P contribution (yielding hydrophobic pairs, hps, and torsions, hts) and partial atomic charges (charge pairs, cps, and charge torsions, cts). 

This requires a methodology for characterising a large range of metastable solutions and compoimds which, by definition are difficult, if not impossible, to access experimentally. The available methods involve various levels of compromise between simplicity and accuracy and can be categorised by the choice of atomic properties used in the process. 

The concept of electronegativity is easy to visualize but difficult to apply quantitatively. Muffiken s definition, based on free-atomic properties, does not account for the influence of the local atomic environment on the ionic state that is reflected, for example, in the fact that the degree of ionicity... 

When iodine is dissolved in hydriodic acid or a soln. of a metallic iodide, there is much evidence of chemical combination, with the formation of a periodide. A. Baudrimont objected to the polyiodide hypothesis of the increased solubility of iodine in soln. of potassium iodide, because he found that an extraction with carbon disulphide removed the iodine from the soln. but S. M. Jorgensen showed that this solvent failed to remove the iodine from an alcoholic soln. of potassium iodide and iodine in the proportion KI I2, and an alcoholic soln. of potassium iodide decolorized a soln. of iodine in carbon disulphide. The hypothesis seemed more probable when, in 1877, G. S. Johnson isolated cubic crystals of a substance with the empirical formula KI3 by the slow evaporation of an aqueous-alcoholic soln. of iodine and potassium iodide over sulphuric acid. There is also evidence of the formation of analogous compounds with the other halides. The perhalides or poly halides—usually polyiodides—are products of the additive combination of the metal halides, or the halides of other radicles with the halogen, so. that the positive acidic radicle consists of several halogen atoms. The polyiodides have been investigated more than the other polyhalides. The additive products have often a definite physical form, and definite physical properties. J. J. Berzelius appears to have made the first polyiodide—which he called ammonium bin-iodide A. Geuther called these compounds poly-iodides and S. M. Jorgensen, super-iodides. They have been classified 1 as... 

The fact that the co-ordination number for so many elements is six, and is generally independent of the nature of the co-ordinated groups, has made A. Werner suggest that the number is decided by available space rather than affinity, and that six is usually the maximum number which can be fitted about the central atom to form a stable system. Consequently, the co-ordination number represents a property of the atom which enables the constitution of molecular compounds to be referred back to actual linkings between definite atoms. A molecular compound is primarily formed through the agency of secondary valencies and, just as primary valencies determine the number of univalent atoms or their equivalent which can be linked to a central atom, so secondary valencies determine the number of mols. which can be attached to the central atom. The secondary valency is often active only towards definite mol. complexes, and hence the formation of additive compounds with other mol. complexes does not occur. Accordingly, the number of secondary valencies which are active towards different molecules is not always the same. 

You will recall that there are three possible p orbitals for any value of the principal quantum number. You should also recall that p orbitals are not spherical, like s orbitals, but are elongated, and thus possess definite directional properties. The three p orbitals correspond to the three directions of Cartesian space, and are frequently designated px, py, and pz, to indicate the axis along which the orbital is aligned. Of course, in the free atom, where no coordinate system is defined, all direction are equivalent, and so are the p orbitals. But when the atom is near another atom, the electric field due to that other atom acts as a point of reference that defines a set of directions. The line of centers between the two nuclei is conventionally taken as the x axis. If this direction is represented horizontally on a sheet of paper, then the y axis is in the vertical direction and the z axis would be normal to the page. 

Secondary atomic properties as those, which require, in addition to the experimentally determined quantities for the free atoms, theoretical concepts of the quantum mechanical characerisation of the electronic structure of the atoms. These are orbitals, the shell structure of atoms with emphasis of the valence shell as well as concepts like hybridisation, the definition of the valence state and the valence state promotion energy in its relation to the spectroscopic term values of the free atoms. 

A continuing issue of discussion is the precise meaning of a in terms of atomic properties. 3-137 Obviously there is some ambiguity in the way that the radius of the sphere can be related to the various definitions of the radius of an atom or in whetheri36 a shell of solvent should be included. 

TTie definition of a bound atom—an atom in a molecule— must be such that it enables one to define all of its average properties. For reasons of physical continuity, the definition of these properties must reduce to the quantum mechanical definitions of the corresponding properties for an isolated atom. The atomic values for a given property should, when summed over aU the atoms in a molecule, yield the molecular average for that property The atomic properties must be additive in the above sense to account for the observation that, in certain series of molecules, the atoms and their properties are transferable between molecules, leading to what are known as additivity schemes. An additivity scheme requires both that the property be additive over the atoms in a molecule and that the atoms be essentially transferable between molecules. 

We shall use the principle of stationary action to obtain a variational definition of the force acting on an atom in a molecule. This derivation will illustrate the important point that the definition of an atomic property follows directly from the atomic statement of stationary action. To obtain Ehrenfest s second relationship as given in eqn (5.24) for the general time-dependent case, the operator G in eqn (6.3) and hence in eqn (6.2) is set equal to pi, the momentum operator of the electron whose coordinates are integrated over the basin of the subsystem 1. The Hamiltonian in the commutator is taken to be the many-electroii, fixed-nucleus Hamiltonian... 

The result is multiplied by JV, the total number of electrons, in the definition of an atomic property. The reader is reminded that the mode of integration indicated by N dx [l/ ijy as used in this definition of an atomic average is the same as that employed in the definition of the electronic charge density, p r) (eqns (1.3) and (1.4)). From this point on the subscript T will be dropped from the coordinates of the electron whose coordinates are integrated only over 2 and all single-particle, unlabelled coordinates and operators will refer to this electron. 

From the preceding discussion, the mode of integration used in the definition of an atomic property is determined by the atomic variation principle and is the same as that used in the definition of the charge density itself. The atomic average of an observable A is given by... 

From its definition in eqn (6.71) in terms of an integral of an energy density, it is clear that, like other atomic properties (eqn (6.41)), the sum of the energies of the atoms in a system equals the total electronic energy... 

It was emphasized in Chapter 6 that the definition of an atomic stationary state property is determined by the form of the atomic stationary state functional fl]. In precisely the same manner, the definition of an atomic property in the general time-dependent case is determined by the form of the atomic Lagrangian integral 2,t]. In both the stationary-state and... 

The determination of a property density at some point in a molecule by the total distribution of particles in the system is essential to the definition of atomic contributions to the electric and magnetic properties of a system. The densities for properties resulting from the molecule being placed in an external field must describe how the perturbed motion of the electron at r depends upon the field strength everywhere inside the molecule, a point that has been emphasized by others (Maaskant and Oosterhoff 1964). This requirement is met by the definition of an atomic property as determined by the theory of atoms in molecules. Property densities for a molecule in the presence of external electric and magnetic fields have been defined and discussed by Jameson and Buckingham (1980) and the present introduction follows their presentation. 

To put the definition of this property into direct correspondence with the definition of other atomic properties, as one for which the property density at r is determined by the effect of the field over the entire molecule, we express the perturbed density in terms of the first-order corrections to the state function. This is done in a succinct manner by using the concept of a transition density (Longuet-Higgins 1956). The operator whose expectation value yields the total electronic charge density at the position r may be expressed in terms of the Dirac delta function as... 

Atomic properties P are physics and chemical observables characterizing each chemical element. They play a fundamental role in the definition of most of the molecular descriptors, being physico-chemical properties, as well as biological, toxicological, and environmental properties, deeply determined by the chemical elements constituting the molecule itself. 

Th.e refinements of the theory, which have been worked out in particular by Houston, Bloch, Peierls, Nordheim, Fowler and Brillouin, have two main objects. In the first place, the picture of perfectly free electrons at a constant potential is certainly far too rough. There will be binding forces between the residual ions and the conduction electrons we must elaborate the theory sufficiently to make it possible to deduce the number of electrons taking part in the process of conduction, and the change in this number with temperature, from the properties of the atoms of the substance. In principle this involves a very complicated problem in quantum mechanics, since an electron is not in this case bound to a definite atom, but to the totality of the atomic residues, which form a regular crystal lattice. The potential of these residues is a space-periodic function (fig. 10), and the problem comes to this— to solve Schrodinger s wave equation for a periodic poten-tial field of this kind. That can be done by various approximate methods. One thing is clear if an electron... 

While semiempirical models which can be applied to molecules the size of 1 and 2 are necessarily only approximate, we were searching for trends rather than absolute values. In concept, the design of semiempirical quantum mechanical models of molecular electronic structure requires the definition of the electronic wavefunction space by a basis set of atomic orbitals representing the valence shells of the atoms which constitute the molecule. A specification of quantum mechanical operators in this function space is provided by means of parameterized matrices. Specification of the number of electrons in the system completes the information necessary for a calculation of electronic energies and wavefunctions if the molecular geometry is known. The selection of the appropriate functional forms for the parameterization of matrices is based on physical intuition and analogy to exact quantum mechanics. The numerical values of the parameters are obtained by fitting to selected experimental results, typically atomic properties. 

Each nucleus is characterized by a definite atomic number Z and mass number A for clarity, we use the symbol M to denote the atomic mass in kinematic equations. The atomic number Z is the number of protons, and hence the number of electrons, in the neutral atom it reflects the atomic properties of the atom. The mass number gives the number of nucleons (protons and neutrons) isotopes are nuclei (often called nuclides) with the same Z and different A. The current practice is to represent each nucleus by the chemical name with the mass number as a superscript, e.g., 12C. The chemical atomic weight (or atomic mass) of elements as listed in the periodic table gives the average mass, i.e., the average of the stable isotopes weighted by their abundance. Carbon, for example, has an atomic weight of 12.011, which reflects the 1.1% abundance of 13C. 

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