Force constant, bond stretching

Then an increase in antibonding character could rednce the bond strength and the force constant of stretching vibration. It should be emphasized that despite the variety of interpretations, pressure effects are observed clearly and confirm independently the existence of dihydrogen bonds. 

Vibrational frequencies give insight into the nature of the forces responsible for chemical binding. Typical force constants for stretching of chemical bonds are in the range 5 — 20 x 10 newton/Angstrom. 

In these equations, m is the mass of an element (a CHa group), kc is the force constant for stretching of a C—C bond, ka is the force constant for bending of the CCC angle, and

phase difference between the motions of adjacent elements of the chain. Since we are interested only in the factor group modes, i.e those in which the vibrations of corresponding elements in neighboring unit cells are in phase, we require that... 

The force constant is defined as the proportionality constant in the equation force = tx extension (of length or angle), so integrating force with respect to extension to get the energy (= force X extension) needed to stretch the bond gives E = (fc/2)(extension), i.e. = force constant = 2 stretch (or2 bend) ... 

Representative force constants (/) for stretching of chemical bonds are listed in this table. Except where noted, all force constants are derived from values of the harmonic vibrational frequencies cd. Values derived from the observed vibrational fundamentals V, which are noted by a, are lower than the harmonic force constants, typically by 2 to 3% in the case of heavy atoms (often by 5 to 10% if one of the atoms is hydrogen). Values are given in the SI unit newton per centimeter (N/cm), which is identical to the commonly used cgs unit mdyn/A. 

Interaction contributions to a typical force held. Bond stretch vibrations are described by a harmonic potential 1/ , the minimum of which is at the equilibrium distance bo between the two atoms connected by chemical bond / (the indices i,j etc. are not shown in the Figure). Bond angles and out-of-plane (Improper) angles are also described by harmonic potential terms, and V, where 00 and (q denote the respective equilibrium angles. Dihedral twists (torsional angles) are subjected to a periodic potential 1/° the respective force constants are denoted by ft s with appropriate indices. Non-bonded forces are described by Coulomb interactions, 1/ -, and Lennard-Jones potentials, + /Vdw where the latter includes the Pauli repulsion, V and the van der... 

---