Bond angle energy

Model Symmetry Electronic state Bond lengths (A) Bond angles (°) Energy (a.u.)... 

In contrast to the bond lnd bond angle energies, the dihedral angle energy is a periodic function of the dihedral angle, ... 

Generally, only a small number of scaling constants are needed. For example, ten scaling constants and reference values were derived for hydrocarbons from comparisons of gas phase structures, conformational energies, rotational barriers, and vibrational frequencies measured by experiment and calculated by the QMFF. For the bond and bond angle energy functions in equation (1) the same scale factor is multiplied by the QMFF quadratic, cubic, and quartic force constants. Similarly, the same scale factor is used for the one-, two-, and threefold torsion force constants, and a single scale factor is used for all cross terms. 

Bond-Bond Interactions. Bond angles variability is much more important to structural analysis of polyatomic molecules than the variability of bond lengths, but no theoretical basis for an analytical presentation of bond angle energy potentials has been offered as yet. However, quantum mechanics has given us a comprehensive conceptual insight into the nature of the forces which determine bond... 

The bond angle, A — B — C, between three atoms is defined as the angle between the bonds A — B and B - C (Fig. 14.1). A harmonic potential is typically used to model bond angle energies,... 

In Table 14.3, typical values of bond angle energies are shown. 

Table 14.3 Example equilibrium bond angles and bond angle energies.

Fig. 10. Differences in potential energy components for the blocked alanine model (for bond length, bond angle, dihedral angle, van der Waals, and electrostatic terms, shown top to bottom) before and after the residual corrections in LIN trajectories at timesteps of 2 fs (yellow), 5 fs (red), and 10 fs (blue).

As for bond stretching, the simplest description of the energy necessary for a bond angle to deviate firom the reference value is a harmonic potential following Hooke s law, as shown in Eq. (22). 

The potential energy of a molecular system in a force field is the sum of individnal components of the potential, such as bond, angle, and van der Waals potentials (equation H). The energies of the individual bonding components (bonds, angles, and dihedrals) are function s of th e deviation of a molecule from a h ypo-thetical compound that has bonded in teraction s at minimum val-n es. 

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. 

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