Dihedral bond angles

Elucidation of the stereostructure - configuration and conformation - is the next step in structural analysis. Three main parameters are used to elucidate the stereochemistry. Scalar coupling constants (mainly vicinal couplings) provide informa-hon about dihedral bond angles within a structure. Another way to obtain this information is the use of cross-correlated relaxation (CCR), but this is rarely used for drug or drug-like molecules. 

Theory suggests and experiment confirms that coupling constants can be related to a number of physical parameters. Among the most important are (1) hybridization, (2) dihedral bond angles, and (3) electronegativity of substituents. 

The average of these converged structures is taken as the protein structure, whose precision can be assessed by the deviations of the individual structures from the average. The quality of the final structure can be described in terms of this root mean square deviation, for both the peptide backbone and side chains, and to some extent by the extent to which it conforms to limitations of dihedral bond angles and interatomic contacts anticipated from thousands of previously known structures (the Ramachandran plot ). By all criteria, NMR structures of proteins that are determined in this way are comparable to structures determined by x-ray crystallography. In addition, NMR methods can be applied to evaluate the... 

Vicinal J-coupling constants provide valuable information for the determination of biomacromolecule conformation. The stmctural information is derived from Karplus equations (12) that provide empirical relationships between dihedral bond angles, and the J-coupling. Karplus equations obey the following general formula ... 

Some crystal structures of chelate complexes have been reported. An O-acryloyl-lactate-TiCU complex (Fig. 3) [26,27] has rare out-of-plane (Fig. 4) coordination of the acryloyl carbonyl group to the titanium a further study has been conducted [28]. Diethyl phthalate-TiCU [29], l,2-diketone-TiCl4 [25], and achiral [24] or chiral [30] acyloxazolidinone-TiCU complexes have been reported to involve in-plane coordination as shown in Fig. 5. The /S-alkoxyketone-TiCU complex shown in Fig. 6 [31] is characterized by a rare out-of-plane coordination geometry (dihedral bond angle of... 

Figure 3. General formula for tripeptides of this study. Arrows with accompanying Greek letters indicate dihedral bond angles.

An extensive use of Vrh couplings has been made by Tolonen and coworkers in order to elucidate the dihedral bond angles in 5 -0-caffeoylquinic acid and three isomeric T5 -0-, 3 ,5 -0- and 4 ,5 -0-dicaffeoylquinic acids. 

Similarly, torsional motions can change a dihedral bond angle while leaving the attached bond lengths and angles unchanged, so torsions often have even lower vibrational constants than bends. 

Polymers, which consist of many covalently bonded fragments, are usually modelled with a set of intramolecular potentials describing direct bonds, bond angles and torsional or dihedral bond angles. Common analytical functions are ... 

The reason for the extremely high modulus of oriented polyethylene in comparison to typical specimens ( 1 GPa for injection-molded high density polyethylene [24]) is simple. The tensile deformation of isotropic samples at low strains principally involves the distortion of molecules whose trajectories approximate to a random coil, which is largely accommodated by bond rotation. This requires much less force than the molecular stretching required to extend the all-trans configuration, which involves bond elongation and an increase in the C—C—C dihedral bond angle. 

But the methods have not really changed. The Verlet algorithm to solve Newton s equations, introduced by Verlet in 1967 [7], and it s variants are still the most popular algorithms today, possibly because they are time-reversible and symplectic, but surely because they are simple. The force field description was then, and still is, a combination of Lennard-Jones and Coulombic terms, with (mostly) harmonic bonds and periodic dihedrals. Modern extensions have added many more parameters but only modestly more reliability. The now almost universal use of constraints for bonds (and sometimes bond angles) was already introduced in 1977 [8]. That polarisability would be necessary was realized then [9], but it is still not routinely implemented today. Long-range interactions are still troublesome, but the methods that now become popular date back to Ewald in 1921 [10] and Hockney and Eastwood in 1981 [11]. 

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).

Additional features determine properties such as interatomic distances, bond angles, and dihedral angles from atomic coordinates. Animations of computed vibrational modes from quantum chemistry packages arc also included. http //fiourceforge.nei/projecl /j mol/... 

The Universal Force Field, UFF, is one of the so-called whole periodic table force fields. It was developed by A. Rappe, W Goddard III, and others. It is a set of simple functional forms and parameters used to model the structure, movement, and interaction of molecules containing any combination of elements in the periodic table. The parameters are defined empirically or by combining atomic parameters based on certain rules. Force constants and geometry parameters depend on hybridization considerations rather than individual values for every combination of atoms in a bond, angle, or dihedral. The equilibrium bond lengths were derived from a combination of atomic radii. The parameters [22, 23], including metal ions [24], were published in several papers. 

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. 

The force field ec uations for M.Vf+, AMBER, BlOg and OPES are similar in the types of terms they contain bond, angle, dihedral, van der Waals. and electrostatic. There are som e differences m the form s of the etinations that can al fect your ch oice of force field. 

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. 

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