Model, minimal of a molecule

The minimal model of a molecule may explain most of the chemical reactions, if besides the closed-shell configuration (double occupancy of the molecular orbitals, including HOMO), we consider excited configurations corresponding to electron transfers) from the HOMO to LUMO orbital (see Chapter 14). 

Mendeleev periodic table (p. 446) minimal model of a molecule (p. 489) molecular spinorbital (p. 394) molecular orbital (p. 420) occupied orbital (p. 409) open shell (p. 411) orbital centering (p. 422) orbital localization (p. 467) orbital size (p. 424) penetration energy (p. 454)... 

The forces in a protein molecule are modeled by the gradient of the potential energy V(s, x) in dependence on a vector s encoding the amino acid sequence of the molecule and a vector x containing the Cartesian coordinates of all essential atoms of a molecule. In an equilibrium state x, the forces (s, x) vanish, so x is stationary and for stability reasons we must have a local minimizer. The most stable equilibrium state of a molecule is usually the... 

A realistic model of a solution requires at least several hundred solvent molecules. To prevent the outer solvent molecules from boiling off into space, and minimizing surface effects, periodic boundary conditions are normally employed. The solvent molecules are placed in a suitable box, often (but not necessarily) having a cubic geometry (it has been shown that simulation results using any of the five types of space filling polyhedra are equivalent ). This box is then duplicated in all directions, i.e. the central box is suiTounded by 26 identical cubes, which again is surrounded by 98 boxes etc. If a... 

In the valence-shell electron-pair repulsion model, or VSEPR model, we focus attention on the central atom of a molecule, such as the B atom in BF3 or the C atom in C02. We then imagine that all the electrons involved in bonds to the central atom and the electrons of lone pairs belonging to that atom lie on the surface of an invisible sphere that surrounds it (Fig. 3.3). These bonding electrons and lone pairs are regions of high electron concentration, and they repel one another. To minimize their repulsions, these regions move as far apart as possible on the surface of the sphere. Once we have identified the most distant ... 

Two types of information are obtained from any molecular mechanics study, the minimum value of the strain energy and the structure associated with that minimum. Agreement between the energy-minimized and experimental (crystallographic) structures has often been used as the primary check on the validity of the force field and to refine the force field further, but often little predictive use has been made of the structures obtained. As force fields become more reliable, the potential value of structure predictions increases. More importantly, when no unequivocal determination of a structure is available by experimental methods then structure prediction may be the only means of obtaining a three-dimensional model of the molecule. This is often the case, for instance, in metal-macromolecule adducts, and structures obtained by molecular mechanics can be a genuine aid in the visualization of these interactions. In this chapter we consider the ways in which structure prediction by molecular mechanics calcluations has been used, and point to future directions. 

Either MM or QM can be used to carry out energy minimization. For example, a molecule can be drawn and its crude coordinates can be submitted for geometry optimization. The modeling software would systematically shift the atoms until the calculated energy was minimized. However, there is no way to know that this local minimum is the lowest possible (global) minimum. The method of conformational analysis systematically puts the molecule into all possible shapes and, in recent times, minimizes the energy at each increment of change. 

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