Bond angle bend

According to the namre of the empirical potential energy function, described in Chapter 2, different motions can take place on different time scales, e.g., bond stretching and bond angle bending vs. dihedral angle librations and non-bond interactions. Multiple time step (MTS) methods [38-40,42] allow one to use different integration time steps in the same simulation so as to treat the time development of the slow and fast movements most effectively. 

A2) In spite of the high individual frequencies, bond length and bond angle vibrations participate in quasi-classical low frequency collective normal modes. Bond angle bending is necessary for the flexibility of five-membered rings, which plays a key role in the polymorphism of nucleic acids. 

A4) Bond angle bending makes a nonnegligible contribution to conformational entropy and can affect computed equilibrium populations [11]. 

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 ... 

Figure 4. Schematic illustration of force-constant parameters used in Modified Urey-Bradley Force-Field (MUBFF) vibrational modeling (Simanouti (Shimanouchi) 1949). The MUBFF is a simplified empirical force field that has been used to estimate unknown vibrational frequencies of molecules and molecule-like aqueous and crystalline substances. Here, three force constants (K, H, and describe distortions of a tetrahedral XY molecule, [Cr04] due to bond stretching (Cr-O), bond-angle bending (Z O-Cr-O), and repulsion between adjacent non-bonded atoms (0..0). Less symmetric molecules with more than one type of bond or unequal bond angles require more parameters, but they will belong to the same basic types.

Table 1. Block diagonalized G and F matrices for tetrahedral XY4 and octahedral XYn molecules, using the modified Urey-Bradley force field. Adapted from Nakmoto (1997). nix and nij are the masses of atoms ofX and Y, and r is the length of the X-Y bond. K, H, and are force constants for bond stretching, bond-angle bending, and non-bonded repulsion, respectively.

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

The molecular mechanics energy of a molecule is described in terms of a sum of contributions arising from distortions from ideal bond distances ( stretch contributions ), bond angles ( bend contributions ) and torsion angles ( torsion contributions ), together with contributions due to non-bonded (van der Waals and Coulombic) interactions. It is commonly referred to as a strain energy , meaning that it reflects the strain inherent to a real molecule relative to some idealized form. 

Fig. 1 Anisotropy of the principal elastic interactions in a C-C chain. (1) Bond stretching (2) Bond angle bending (3) Bond rotation (4) Inter-segmental attraction...

---