Bond stretch terms

SISM Treatment of only Bond Stretching Term... 

In addition to these basic term s. force fieldsoften h ave cross term s that combine the above interactions. For example there may be a term which causes ati angle bend to interact with a bond stretch term (opening a bond angle may tend to lengthen the bonds in volved). 

A typical force field model for propane contains ten bond-stretching terms, eighteen angle-bending terms, eighteen torsional terms and 27 non-bonded interactions. 

MOMEC is a force field for describing transition metal coordination compounds. It was originally parameterized to use four valence terms, but not an electrostatic term. The metal-ligand interactions consist of a bond-stretch term only. The coordination sphere is maintained by nonbond interactions between ligands. MOMEC generally works reasonably well for octahedrally coordinated compounds. 

The first step in creating a force field is to decide which energy terms will be used. This determines, to some extent, the ability of the force field to predict various types of chemistry. This also determines how dilficult the parameterization will be. For example, more information is needed to parameterize an-harmonic bond-stretching terms than to parameterize harmonic terms. 

A larger value for the bending force constant K0 leads to a greater tendency for the angle to remain at its equilibrium value 0g. There may be cubic, quartic, etc. terms as with the corresponding bond stretch term in addition to the quadratic term shown here. 

Inclusion of 1,3-nonbonded interactions1285-2871 was achieved in the same way as was used firstly for the modeling of cobalt(III) complexes11481 and more recently for a wide range of transition metal compounds14,5 451. That is, standard models with M-L harmonic bond stretching terms were used, but the L-M-L harmonic terms were deleted and L...L nonbonded interactions were used in their place. In the first of... 

The Bond Stretching Term The increase in the energy of a spring (remember that we are modelling the molecule as a collection of balls held together by springs) when it is stretched (Fig. 3.2) is approximately proportional to the square of the extension ... 

Parameterizing the Bond Stretching Term A forcefield can be parameterized by reference to experiment (empirical parameterization) or by getting the numbers from high-level ab initio or density functional calculations, or by a combination of both approaches. For the bond stretching term of Eq. 3.2 we need stretch ancl 4q-Experimentally, stretch could be obtained from IR spectra, as the stretching frequency of a bond depends on the force constant (and the masses of the atoms involved) [8], and Zeq could be derived from X-ray diffraction, electron diffraction, or microwave spectroscopy [9],... 

The bond-stretching term Vbonds has the following form ... 

The strategies employed by CHARMM and MM3 in the formulations of bond stretch terms are repeated in the formulation of angle bending terms. Thus, CHARMM uses simple harmonic terms, whereas MM3 uses an expansion up to sextic terms. 

For purposes of energy calculations, bonding is described by the Keating potential [27], which is a simple sum of bond-bending and bond-stretching terms ... 

Morse potential A Morse potential is often used for the bond stretching term in a force field. Instead of the quadratic dependence of a harmonic bond stretching... 

We stress that it is specifically the second derivative that extracts the relevant information about the bond-stretching term. As noted above, this is modulated only by derivatives of the nonbonded term and the third-order terms. If, for example, we tried to parameterize v, by, say, changing just one C —H bond length in ethane and fitting the energy profile along this coordinate, then we will find that this profile contains contributions from other coordinates that actually change with the increase in the bond stretch. 

The nonbonded interactions term. This represents the change in potential energy with distance apart of atoms A and B that are not directly bonded (as in A-B) and are not bonded to a common atom (as in A-X-B) these atoms, separated by at least two atoms (A-X-Y-B) or even in different molecules, are said to be nonbonded (with respect to each other). Note that the A-B case is accounted for by the bond stretching term stretch> and the A-X-B term by the angle bending term bend. but the nonbonded term nonbond is, for the A-X-Y-B case, superimposed upon the torsional term torsion we can think of lorsion as representing some factor inherent to resistance to rotation about a (usually single) bond X-Y (MM does not attempt to explain the theoretical, electronic basis of this or any other effect), while for certain atoms attached to X and Y there may also be nonbonded interactions. 

The short-range interaction combines a number of components including non-bonded interactions (electron repulsion and van der Waals attraction), electronic polarizability and, where relevant, covalent interactions, modelled by bond-bending and bond-stretching terms. 

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