Molecular mechanics bond stretching

In molecular mechanics bond stretching is sometimes modeled using a Morse function (Eq. 3.13)[7() where a describes the curvature and D the depth of the potential function (Fig. 3.6). 

FIGURE 6.2 Hannonic, cubic, and Morse potential curves used to describe the energy due to bond stretching in molecular mechanics force fields. 

The technique most often used (i.e., for an atom transfer) is to hrst plot the energy curve due to stretching a bond that is to be broken (without the new bond present) and then plot the energy curve due to stretching a bond that is to be formed (without the old bond present). The transition structure is next dehned as the point at which these two curves cross. Since most molecular mechanics methods were not designed to describe bond breaking and other reaction mechanisms, these methods are most reliable when a class of reactions has been tested against experimental data to determine its applicability and perhaps a suitable correction factor. 

Molecular mechanical force fields use the equations of classical mechanics to describe the potential energy surfaces and physical properties of molecules. A molecule is described as a collection of atoms that interact with each other by simple analytical functions. This description is called a force field. One component of a force field is the energy arising from compression and stretching a bond. 

As the most notable contribution of ab initio studies, it was revealed that the different modes of molecular deformation (i.e. bond stretching, valence angle bending and internal rotation) are excited simultaneously and not sequentially at different levels of stress. Intuitive arguments, implied by molecular mechanics and other semi-empirical procedures, lead to the erroneous assumption that the relative extent of deformation under stress of covalent bonds, valence angles and internal rotation angles (Ar A0 AO) should be inversely proportional to the relative stiffness of the deformation modes which, for a typical polyolefin, are 100 10 1 [15]. A completly different picture emerged from the Hartree-Fock calculations where the determined values of Ar A0 AO actually vary in the ratio of 1 2.4 9 [91]. 

Molecular mechanics calculations use an empirically devised set of equations for the potential energy of molecules. These include terms for vibrational bond stretching, bond angle bending, and other interactions between atoms in a molecule. All of these are summed up as follows ... 

Theoretical models include those based on classical (Newtonian) mechanical methods—force field methods known as molecular mechanical methods. These include MM2, MM3, Amber, Sybyl, UFF, and others described in the following paragraphs. These methods are based on Hook s law describing the parabolic potential for the stretching of a chemical bond, van der Waal s interactions, electrostatics, and other forces described more fully below. The combination assembled into the force field is parameterized based on fitting to experimental data. One can treat 1500-2500 atom systems by molecular mechanical methods. Only this method is treated in detail in this text. Other theoretical models are based on quantum mechanical methods. These include ... 

In an attempt to aid interpretation of the IR spectrum of MbCO we decided to model the full protein by use of a hybrid quantum mechanics/molecular mechanics approach (QM/MM), to evaluate changes in the CO stretching frequency for different protein conformations. The QM/MM method used [44] combines a first-principles description of the active center with a force-field treatment (using the CHARMM force field) of the rest of the protein. The QM-MM boundary is modeled by use of link atoms (four in the heme vinyl and propionate substituents and one on the His64 residue). Our QM region will include the CO ligand, the porphyrin, and the axial imidazole (Fig. 3.13). The vinyl and propionate porphyrin substituents were not included, because we had previously found they did not affect the properties of the Fe-ligand bonds (Section 3.3.1). It was, on the other hand, crucial to include the imidazole of the proximal His (directly bonded to the... 

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