Molecular geometry coordinate space

The molecular geometry of a complex depends on the coordination number, which is the number of ligand atoms bonded to the metal. The most common coordination number is 6, and almost all metal complexes with coordination number 6 adopt octahedral geometry. This preferred geometry can be traced to the valence shell electron pair repulsion (VSEPR) model Introduced In Chapter 9. The ligands space themselves around the metal as far apart as possible, to minimize electron-electron repulsion. 

The molecular geometry of Sr(OC6H2-f-Bu3)2(THF)3 can best be described as distorted trigonal bipyramidal. The large aryl oxide groups occupy two of the equatorial sites, which allows the f-Bu groups to better extend into space without causing serious repulsive contacts. The metal center in this compound has an unusually low coordination number of five.132... 

Autocorrelation descriptors can also be calculated for 3D-spatial molecular geometry. In this case, the distribution of a molecular property can be a mathematical function /(x, y, z), x, y, and z being the spatial coordinates, defined either for each point of molecular space (i.e. a continuous property such as electronic density or molecular interaction energy) or only for points occupied by atoms (i.e. atomic properties). An example of 3D autocorrelation descriptors are the - spectral weighted invariant molecular descriptors defined by - SWM signals. 

To begin with, we may not have to calculate the PES throughout the whole of the 3N - 6)-dimensional coordinate space. Suppose that we only want to study the chemical reaction when the reactants have less than some maximum amount of energy available to them call it Then to study the reaction dynamics using classical mechanics would only require us to know the PES, E(R), at those molecular geometries, R, for which... 

Notation. We shall use the ideas of an n-dimensional vector space—Section 5.2. Let q be the (3N — 6)-dimensional vector whose components are the nuclear coordinates that define the molecular geometry. [If Cartesian coordinates are used in the optimization, we deal with a 3iV-dimensional vector if internal coordinates are used. 

For a secure account to be given in terms of the separation (O Eq. 2.43), which is what is really required if one is to use the clamped nuclei electronic Hamiltonian, it would be necessary to consider more than one coordinate space. On the manifold at least two coordinate spaces are required to span the whole manifold. The internal coordinates within any coordinate space are such that it is possible to construct two distinct molecular geometries at the same internal coordinate specification, so that a potential expressed in the internal coordinates cannot be analytic everywhere (CoUins and Parsons 1993). It would therefore seem to be a very tricky job. But even if it were to be accomplished it seems very unlikely that a multiple minima argument could be constructed to account for point group symmetry in this context It is possible to show (see Section IV of Sutcliffe (2000)) that in the usual Eckart form of the Hamiltonian for nudear motion, permutations can be such as to cause the body-fixed frame definition to fail completely. 

To support 3D query formulation beyond the spartan specification of relative atomic coordinates in space, a large contingent of 3D features have been devised which encourage the rich description of inter- and intra-molecular geometries and interactions. These additional 3D features and constraints are not simply a minor syntactic extension, but a critical and important capability of any 3D CIR system. 

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