Functions Using Three-Dimensional Atomic Coordinates

7 Functions Using Three-Dimensional Atomic Coordinates 

The previous section shows how molecular structures stored in an RDBMS can be made available to client programs that traditionally read molecular structure files. The advantage of storing molecular structures in an RDBMS is that the information can be used from within the database, as well as by external clients. For example, it would be possible to search a table of molecular structures for three-dimensional overlap, much like it might be searched for substructure match. Of course, such search functions need to be written and installed as extensions to an RDBMS, just like the matches functions was done for substructure searches. This section shows some possible ways this might be accomplished. 

There are many methods to overlap one molecule s three-dimensional coordinates onto another molecule s. Perhaps the simplest method simply finds the center of one molecule and translates the other molecule to that central coordinate. The following functions can be used to do this. The align f unchon takes two arrays of coordinates and returns the difference between the two centers. This difference can be applied to either molecule to align it with the other. The functions center and difference are utility functions. 

Create Or Replace Function align(amol float[][3], float[][3]) Returns float[3] A s  

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Note that the various T and V terms defined in Eqs. (8.3)—(8.5) are functions of the density, while the density itself is a function of three-dimensional spatial coordinates. A function whose argument is also a function is called a functional , and thus the T and V terms are density functionals . The Thomas-Fermi equations, together with an assumed variational principle, represented the first effort to define a density functional theory (DFT) the energy is computed with no reference to a wave function. However, while these equations are of significant historical interest, the underlying assumptions are sufficiently inaccurate that they find no use in modem chemistry (in Thomas-Fermi DFT, all molecules are unstable relative to dissociation into their constituent atoms...)... 

The state of any particle at any instant is given by its position vector q and its linear momentum vector p, and we say that the state of a particle can be described by giving its location in phase space. For a system of N atoms, this space has 6iV dimensions three components of p and the three components of q for each atom. If we use the symbol F to denote a particular point in this six-dimensional phase space (just as we would use the vector r to denote a point in three-dimensional coordinate space) then the value of a particular property A (such as the mutual potential energy, the pressure and so on) will be a function of r and is often written as A(F). As the system evolves in time then F will change and so will A(F). 

In order to form a crystal, molecules must aggregate in an orderly manner. This implies that intermolecular interactions have occurred in specific ways. It therefore follows that the crystal structure per se contains information on preferred modes of binding between the molecules in the crystalline state. In this Chapter we show how information on the most likely stereochemistries of interactions between functional groups in different molecules can be extracted from the three-dimensional coordinates of atoms listed in reports of crystal structure determinations. Three-dimensional structural data on binding stereochemistry may also be obtained from X-ray diffraction studies of the binding of small molecules to crystalline proteins and other macromolecules. These two types of information can be used, for example, to predict how drugs will interact with their biological receptors. 

While atomic coordinates form the fundamental structure of a molecule, many methods prefer to represent a three-dimensional structure as a surface or a shape. Of course, these are ultimately computed from the atomic coordinates and perhaps atomic partial charges. It may be possible to represent these molecular surfaces or shapes as an array of three-dimensional coordinates. These could be stored as a column in the database analogous to the array of atomic coordinates. It might be necessary to create another data type, perhaps a composite data type, to store molecular surfaces or shapes. Once these representations are stored, they can be used in new SQL functions to assist in searching based on molecular surface or shape. 

Molecular Mechanics Model Builder. The three-dimensional molecular model builder routine interfaced to ADAPT (MOLMEC) is used to derive information on the special conformation of molecules. A molecule can be viewed as a collection of particles held together by simple harmonic or elastic forces. These forces can be defined by potential energy functions whose terms are functions of the atomic coordinates of the molecule. This function can then be minimized to obtain a strain-free three-dimensional model of the molecule. In the strain minimization section, the atom coordinates are systematically altered until a mlnlmun is found in the strain or potential energy function. 

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