Definition of atomic properties

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 

An atomic property is therefore, determined by the integration of a corresponding property density Px(r) over the basin of the atom where 

The quantity f e(fl) equals the repulsion energy of the electrons in ( 1, 2) and one-half the repulsion of the electrons in 2 with that of those in the remainder of the system 2, ( 2, 2 ). Since the average value of the 

The electron population of an atom in a molecule, its average number of electrons N ( 2), is obtained by setting the operator A equal to 1 in which case p (r) reduces to the electronic charge density p(r). 

Setting A equal to the radial distance of an electron from the nucleus of the atom, or some power n of this distance yields the corresponding average over the charge density of the atom. 

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The partitioning of the space into separate non-overlapping atomic basins, exhausting all three-dimensional space, entails the definition of atomic properties that add-up to yield the corresponding molecular counterparts. Such atomic properties are obtained by integrating each corresponding property density over the bounded region of real space occupied by the atomic basin. 

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). 

Population Analyses Population analyses are used to gain a detailed understanding of the electronic properties of a molecule. A common feature of most of these analytic tools is the definition of atomic charges. Because there is no... 

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. 

Topological Definition of Atoms, Bonds, and Structure.—The definitions of an isolated atom, of an atom in a molecule, of a chemical bond, and of molecular structure derive from the properties of critical points of the charge density. 

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. 

The subsystem or atomic Lagrangian integral is defined by the standard mode of integration used in the definition of the subsystem functional [ F, iJ] for a stationary state and for the definition of subsystem properties. 

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... 

It is the use of zero-flux surfaces for the topological definition of atoms or functional grouping of atoms in molecules that maximizes the extent of transferability of their properties between systems. 

Many of the rigorous definitions of atomic and bond properties that are described in this article invoke the concepts of the quantum-mechanical theory of atoms in molecules (AIMs) (see Atoms in Molecules). The AIMs consist of nuclei and disjoint portions of Cartesian space called atomic basins. Direct integration of property densities over those basins yields the first-order properties of AIMs, whereas the calculations of the second-order properties and quantities such as atomic electronegativities and similarities are somewhat more involved. Topological analysis of the electron density p r) that accompanies the construction of AIMs yields a wealth of other information, including the location of major interactions within molecules. ... 

The definition of the term bond concludes the presentation of the ROSDAL syntax. The bond symbols represent a single, double, triple, and any bond the bond modification list contains further terms to allow for a precise representation of stereochemical properties of the respective bond. The term chain allows for a detailed encoding of atomic properties via the atom attributes and further enables a specification of the connection table of a compound through the atom bond atom construction. 

Clearly, the next step is the handling of a molecule as a real object with a spatial extension in 3D space. Quite often this is also a mandatory step, because in most cases the 3D structure of a molecule is closely related to a large variety of physical, chemical, and biological properties. In addition, the fundamental importance of an unambiguous definition of stereochemistry becomes obvious, if the 3D structure of a molecule needs to be derived from its chemical graph. The moleofles of stereoisomeric compounds differ in their spatial features and often exhibit quite different properties. Therefore, stereochemical information should always be taken into ac-count if chiral atom centers are present in a chemical structure. 

The explicit definition of water molecules seems to be the best way to represent the bulk properties of the solvent correctly. If only a thin layer of explicitly defined solvent molecules is used (due to hmited computational resources), difficulties may rise to reproduce the bulk behavior of water, especially near the border with the vacuum. Even with the definition of a full solvent environment the results depend on the model used for this purpose. In the relative simple case of TIP3P and SPC, which are widely and successfully used, the atoms of the water molecule have fixed charges and fixed relative orientation. Even without internal motions and the charge polarization ability, TIP3P reproduces the bulk properties of water quite well. For a further discussion of other available solvent models, readers are referred to Chapter VII, Section 1.3.2 of the Handbook. Unfortunately, the more sophisticated the water models are (to reproduce the physical properties and thermodynamics of this outstanding solvent correctly), the more impractical they are for being used within molecular dynamics simulations. 

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