Internal coordinate mechanics

ICM (Internal Coordinate Mechanics) software, MolSoft LLC, http //www. molsoft.com/icm pro.html. 

Internal coordinated mechanics (ICM) uses global MC minimization docking procedure, describes... 

Abagyan, R., Batalov, S., Cardozo, T., Totrov, M., Webber, J., and Zhou, Y. (1997) Homology modeling with internal coordinate mechanics deformation zone mapping and improvements of models via conformational search. Proteins Suppl 1, 29-37. 

Z-matriccs arc commonly used as input to quantum mechanical ab initio and serai-empirical) calculations as they properly describe the spatial arrangement of the atoms of a molecule. Note that there is no explicit information on the connectivity present in the Z-matrix, as there is, c.g., in a connection table, but quantum mechanics derives the bonding and non-bonding intramolecular interactions from the molecular electronic wavefunction, starting from atomic wavefiinctions and a crude 3D structure. In contrast to that, most of the molecular mechanics packages require the initial molecular geometry as 3D Cartesian coordinates plus the connection table, as they have to assign appropriate force constants and potentials to each atom and each bond in order to relax and optimi-/e the molecular structure. Furthermore, Cartesian coordinates are preferable to internal coordinates if the spatial situations of ensembles of different molecules have to be compared. Of course, both representations are interconvertible. 

It is always possible to convert internal to Cartesian coordinates and vice versa. However, one coordinate system is usually preferred for a given application. Internal coordinates can usefully describe the relationship between the atoms in a single molecule, but Cartesian coordinates may be more appropriate when describing a collection of discrete molecules. Internal coordinates are commonly used as input to quantum mechanics programs, whereas calculations using molecular mechanics are usually done in Cartesian coordinates. The total number of coordinates that must be specified in the internal coordinate system is six fewer... 

The traditional way to provide the nuclear coordinates to a quantum mechanical program is via a Z-matrix, in which the positions of the nuclei are defined in terms of a set of intei ii.il coordinates (see Section 1.2). Some programs also accept coordinates in Cartesian formal, which can be more convenient for large systems. It can sometimes be important to choow an appropriate set of internal coordinates, especially when locating rninima or transitinn points or when following reaction pathways. This is discussed in more detail in Section 5.7. 

The final step in the molecular-mechanics calculation of molecular conformation involves the minimization of the energy Approximations are involved whose importance is not always clear. Usually, all first derivatives with respect to the various internal coordinates are set equal to zero - although these coordinates are often not independent (see Section 10.6). Furthermore, the final conformation obtained depends on the assumed initial structure. Therefore, (he method must be applied with care and a certain amount of chemical intuition. In spite of these uncertainties the molecular mechanics method has been employed with considerable success, particularly in the conformational analysis of branched alkanes. For molecules containing hetero-atoms, it can be applied, but with somewhat less confidence. 

All schemes presented are similar and conventional to a great extent. It is characteristic that the epoxidation catalysis also results in the heterolytic decomposition of hydroperoxides (see Section 10.1.4) during which heterolysis of the O—O bond also occurs. Thus, there are no serious doubts that it occurs in the internal coordination sphere of the metal catalyst. However, its specific mechanism and the structure of the unstable catalyst complexes that formed are unclear. The activation energy of epoxidation is lower than that of the catalytic decomposition of hydroperoxides therefore, the yield of oxide per consumed hydroperoxide decreases with the increase in temperature. 

As is well known, the vibrational Hamiltonian defined in internal coordinates may be written as the sum of three different terms the kinetic energy operator, the Potential Energy Surface and the V pseudopotential [1-3]. V is a kinetic energy term that arises when the classic vibrational Hamiltonian in non-Cartesian coordinates is transformed into the quantum-mechanical operator using the Podolsky trick [4]. The determination of V is a long process which requires the calculation of the molecular geometry and the derivatives of various structural parameters. 

By using internal coordinates, the quantum-mechanical operator may be obtained by the application of the Podolsky trick [4]. For this purpose, the kinetic energy has to be multiplied by the determinant g of the G matrix. The classical kinetic energy operator is ... 

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