Covalent bond-angle interaction

ReaxFF describes the total energy of an atomistic system with three main terms i) covalent (bonds, angles, torsions, etc.), ii) electrostatics with environment-dependent charges, and iii) van der Waals interactions. Covalent interactions are based on the concept of partial bond orders that are calculated solely from atomic positions (no pre-determined connectivities). Once the bond order between every pair of atoms is known, bond energies, angles, and torsions are determined. The second key concept in reactive force fields (also used in the... 

The first summation constrains the conformational torsion angles (and sometimes the covalent bond angles) to lie near to the expected values derived from single crystal and polymer studies the second summation minimizes the differences between the observed and calculated X-ray structure factor amplitudes the third summation relaxes unfavourable non-bonded interactions and the fourth summation contains constraints Hn whose values are zero when residue connectivity and furanose ring closure have been achieved. 

The term representing the covalent bond-angle bending interaction reads... 

XB is a particularly directional interaction, more directional than HB. The angle between the covalent and non-covalent bonds around the halogen in D- X-Y is approximately 180° [48]. As discussed above, the origin of this directionality is in the anisotropic distribution of electron density around the halogen atom. Figure 5 shows the Cambridge Structure Database (CSD, ver-... 

T-shaped Y- E-X 3c-4e interactions occur by the attack of Y at E of polar E-X bonds. Such interactions are usually highly unsymmetric.17,43 However, the N-E-X bonds are close to symmetric in some cases. Singh and co-workers reported such interactions. Table 2 shows the bond distances and the deferences from the sum of covalent radii in 19 (E = Se), together with the angles.44 The N-E-X (E = Se) bonds are rather typical 3c-4e for X of halogens, especially for X = I. The Y-E- -X character shown in 19A contributes to the interactions in substantial amount, although the distances are affected by the nature of the Se-X bonds. Similar interactions are reported.45 48... 

The discussion thus far has focused on the forces between an array of atoms connected together through covalent bonds and their angles. Important interactions occur between atoms not directly bonded together. The theoretical explanation for attractive and repulsive forces for nonbonded atoms i and j is based on electron distributions. The motion of electrons about a nucleus creates instantaneous dipoles. The instantaneous dipoles on atom i induce dipoles of opposite polarity on atom j. The interactions between the instantaneous dipole on atom i with the induced instantaneous dipole on atom j of the two electron clouds of nonbonded atoms are responsible for attractive interactions. The attractive interactions are know as London Dispersion forces,70 which are related to r 6, where r is the distance between nonbonded atoms i and j. As the two electron clouds of nonbonded atoms i and j approach one another, they start to overlap. There is a point where electron-electron and nuclear-nuclear repulsion of like charges overwhelms the London Dispersion forces.33 The repulsive... 

The most critical aspect of atomistic simulations is thus the representation of the interactions between atoms by an algebraic function. If covalency is important, a part of the expression should contain details of how the interaction changes with angle, to mimic directional covalent bonds. In cases where a simulation is used to predict the location of a cluster of atoms within or at the surface of a solid, interactions between the atoms in the cluster, interactions between the atoms in the solid, and interactions between the atoms in the cluster and those in the solid must all be included. 

Chemists use two parameters, bond lengths and bond angles, to describe the 3D structures of covalent compounds. A bond length is the average distance between the nuclei of the atoms that are covalently bonded together. A bond angle is the angle formed by the interaction of two covalent bonds at the atom common to both. 

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