Force fields angle bending

Now we consider the valence angle bending force field as it appears from the DMM picture. For this end the geometry variation given by the vectors eq. (3.139) must be inserted in eq. (3.72) and the required elasticity constant can be obtained by extracting the second order contribution in vectors 6[Pg.260]

Fractionation factors are calculated using measured vibrational spectra supplemented by simplified empirical force-field modeling (bond-stretching and bond-angle bending force constants only). 

Typically, in the MM framework, the increment from the bending is considered a quadratic function of valence angles. The formula for bending eq. (3.151) can be rewritten in this form. This is obtained by substituting eq. (3.140) to the second order expansion eq. (3.151) and significant simplifications based on vector algebra. After that we see that the bending force field constant can be written as ... 

In principle, the resulting angle bending force constants are generic parameters (Table 12.2). However, in the light of the discussions on the relationship between force field parameters and physical reality presented in Section 3.5, the generic... 

Intensive use of cross-terms is important in force fields designed to predict vibrational spectra, whereas for the calculation of molecular structure only a limited set of cross-terms was found to be necessary. For the above-mentioned example, the coupling of bond-stretching (f and / and angle-bending (B) within a water molecule (see Figure 7-1.3, top left) can be calculated according to Eq. (30). 

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

In a Urey-Bradley force field, angle bending is achieved using 1,3 non-bonded interaction rather than an explicit angle-bending potential. The stretch-bond term in such a forci field would be modelled by a harmonic function of the distance between the 1,3 atoms ... 

Three-body and higher terms are sometimes incorporated into solid-state potentials. The Axilrod-Teller term is the most obvious way to achieve this. For systems such as the alkali halides this makes a small contribution to the total energy. Other approaches involve the use of terms equivalent to the harmonic angle-bending terms in valence force fields these have the advantage of simplicity but, as we have already discussed, are only really appropriate for small deviations from the equilibrium bond angle. Nevertheless, it can make a significant difference to the quality of the results in some cases. 

The force-field model for ethanol contains C-O and O—H bond-stretching contributions in ethane thiol these are replaced by C—S and S—H parameters. Similarly, in ethanol there will be angle-bending terms due to C—O—H, C—C—O and H—C—O angles in ethane thiol these will be C—S—H, C—C—S and H—C—S. The torsional contribution will be modified appropriately, as will the van der Waals and electrostatic interactions (both those within the... 

Terms in the energy expression that describe a single aspect of the molecular shape, such as bond stretching, angle bending, ring inversion, or torsional motion, are called valence terms. All force fields have at least one valence term and most have three or more. 

Terms in the energy expression that describe how one motion of the molecule affects another are called cross terms. A cross term commonly used is a stretch-bend term, which describes how equilibrium bond lengths tend to shift as bond angles are changed. Some force fields have no cross terms and may compensate for this by having sophisticated electrostatic functions. The MM4 force field is at the opposite extreme with nine different types of cross terms. 

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