Morse potential, bond distance

The Morse function rises more steeply ihan ihe harmonic potential at short bonding distances. This difference can be important especially during molecular dynamics simulations, where thermal energy takes a molecule away from a potential minimum. ... 

In 1936, de Boer formulated his theory of a stressed bond which, despite its simplicity, still constitutes the basis for most models of chemical reactivity under stress [92], In order to fracture an unstressed bond which, in the absence of any vibration, is approximated by the Morse potential of Fig. 18, an energy D must be supplied. If, however, the bond is under tension due to a constant force feitt pulling on either end, the bond rupture activation energy will be decreased by an amount equivalent to the work performed by the mechanical force over the stretching distance from the equilibrium position. The bond potential energy in the presence of stress is given by ... 

It is not necessary to restrict ourselves to bonds that are described by Morse potentials. We can regard eqn. (56) as a quadratic equation in x, use any form of the potential energy V(R) with the usual shape (i.e., a minimum, a repulsive barrier at short distances, and a monotonical increase at large distances), and determine x to get another definition of the bond order. This is called the unity bond index quadratic exponential potential (UBI QEP) method by Shustor-ovich and Sellers. ... 

Equation 2 is not a poor representation of the energy function because it can be shown that a Morse potential in real distances assumes a simple quadratic form if one uses a dimensionless bond order coordinate.1263 In any event, minimization of this function leads to the conclusion that the minimum energy is attained when all bonds have the same length. Furthermore, a bond alternating distortion that lengthens and shortens a pair of adjacent bonds by Ar can be shown to raise the cr-energy as in eq 3a. 

Moments of inertia at fixed geometries are calculated by changing only the bond distance in the reaction coordinate. The potential energy surface along the reaction coordinate is modeled by a Morse function including the centrifugal barrier [48]... 

Price and Parker (1984), who found that simulations with full ionic charges could satisfactorily reproduce either the structure or the elastic properties of olivines but not both. They presented a simulation with fractional charges and a semiempirical Morse potential for the Si-0 bond and found that both structural and elastic properties could be adequately modeled (see Chapter 7 for further discussion). Their calculated Si-O distances, shown in Table 5.2, are in quite good agreement with experiment. The atomic charges used in this simulation are also in reasonable agreement with the effective charges inferred from x-ray diffraction studies (Fujino et al., 1981). 

Aside from the assumptions not open to direct test [e.g., equations (1) and (2)], there is a serious we2ikness in the assumption of constant A—H distance. Experiment shows that a H bond of over-all length 2.5 A would have an O—H bond length near 1.07 A (see Fig. 9-1). Because equation (2) is extremely sensitive to a change in r(A—H), this raises the estimate of the amount of covalent character to 22 percent, double the value obtained by Coulson and Danielsson. Since this is in fair agreement with a second estimate (based on a Morse potential curve) by Coulson and Danielsson, it would seem that the appropriate conclusion of this paper should not be that the H bond is essentially ionic but rather that the covalent contribution is quite important for... 

The ground state vibrational constants are from the compilation of Rosen (J ). The adopted value of r estimated by Margrave (3) and is also the bond distance in Bal Cg) (7). B is calculated from the adopted assuming a Morse potential function. 

Van der Waals (vdW) interactions are also computed between all pairs of atoms (including bonded ones). As in electrostatics, a shielded Morse potential is used [13] this avoids extremely large repulsions at normal bonding distances that would be obtained with the usual vdW interactions. 

In MM3, this problem of trying to compute as efficiently as possible has been corrected by adding a quartic term. In this way, the possibility of having the potential energy curve invert is eliminated. Moreover, the new curve is a better approximation to a Morse potential over a longer distance. Accordingly, MM3 has one additional term to describe bond stretching as shown in Eq. [4]. 

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