Angles, dihedral angle

Fig. 1. The time evolution (top) and average cumulative difference (bottom) associated with the central dihedral angle of butane r (defined by the four carbon atoms), for trajectories differing initially in 10 , 10 , and 10 Angstoms of the Cartesian coordinates from a reference trajectory. The leap-frog/Verlet scheme at the timestep At = 1 fs is used in all cases, with an all-atom model comprised of bond-stretch, bond-angle, dihedral-angle, van der Waals, and electrostatic components, a.s specified by the AMBER force field within the INSIGHT/Discover program.

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).

All properties (energy dipole moment atomic charges) and geometry parame ters (distance angle dihedral angle) can be animated or stepped through... 

Molecule Interatomic di,stance/pm Bond angle Dihedral angle... 

We refer to models where we write the total potential energy in terms of chemical endties such as bond lengths, bond angles, dihedral angles and so on as valence force field models. 

Suppose that our potential function U is now a function of many p) variables. They could be bond lengths, bond angles, dihedral angles or the Cartesian coordinates of each atom in a molecule. I will write these variables x, X2, , Xp and so... 

The hypothetical enantiophore queries are constructed from the CSP receptor interaction sites as listed above. They are defined in terms of geometric objects (points, lines, planes, centroids, normal vectors) and constraints (distances, angles, dihedral angles, exclusion sphere) which are directly inferred from projected CSP receptor-site points. For instance, the enantiophore in Fig. 4-7 contains three point attachments obtained by ... 

Atom Bond Length Bond Angle Dihedral Angle Atom Number ... 

Let US first examine current practice in nomenclature of the phenom-menon of internal rotation. Standard textbooks on conformational analysis on the one hand and those on spectroscopy on the other hand deal differently with the basic definitions. Internal rotation is measured by one or more torsion angles (dihedral angles, azimuthal angles). In the simple cases of e.g. a 1,2-disubstituted ethane the potential energy associated with the internal rotation may be written in a formal sense as a truncated Fourier expansion ... 

Compound Method" X-X distance (A) X-Y distance (A) Bond angle ( ) Dihedral angle (°) Reference... 

Figure 2. Schematic representation of the partitioning of an aspartate amino acid residue into QM and MM regions. The side chain (which may be involved in e.g. chemical reaction or binding) is treated QM (up to and including C(3). To account for the bond between Ca and C(3, a link atom (typically hydrogen) may be added toCp. Alternatively, a localized hybrid orbital on CP can be employed. Consideration must also be given as to which MM interactions to include between the MM and QM atoms, e.g. which bonded terms (for bonds, bond angles, dihedral angles, etc.) between the two regions. In the implementation of Fielder al. [41], all MM bonded terms involving at least one MM atom are retained.

Interpolation. - The simplest approach (that still often is used) is to define some fictitious reaction coordinate <5 that equals 0 (1) for the initial (final) structure and then let all internal coordinates (i.e., bond lengths, bond angles, dihedral angles, etc.) vary linearly between the two end values. It is very unlikely that this approach indeed will pass through a saddle point and, therefore, it will usually lead to an upper bound for the transition energy. 

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