Morse potential definition

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. ... 

In a stochastic approach the frequency-depiendent friction appears in the definition of the energy dependence of the relaxation rate P(E), defined by Eq. (4.12), and is evaluated for a Morse potential by Eq. (4.14). In this section the applicability of these relationships and the friction kernel B(d)( )) of Eq. (3.27) is tested in a variety of approaches for the case of u = 1, a diatomic. The use of frequency-dependent friction in the evaluation of D(E) for a system with many degrees of freedom is an area of ongoing activity. While many of the features of a stochastic approach to vibrational relaxation are found in inelastic scattering theories or master equation kernels, it is the characteristic of... 

There is no theoretical basis for a Morse potential energy curve. Its form is empirical (that is, based on observation), but it is useful. First, it shows a dissociation limit, just as real diatomic molecules experience. The dissociation energy, D, appears in two places in the form of the Morse potential, as a premultiplicative term and as part of the definition of the constant a. It accurately predicts the observed trend of closer-spaced vibrational levels as the vibrational quantum number increases. Although diatomic molecules (and larger molecules also) do not behave as perfect Morse oscillators, the Morse potential is usually a better fit to the real vibrational behavior of molecules. 

For K 2kT and /Km, the collinear result of Eq. (5.13) differs from the three-dimensional model of this work by a factor of 3. This difference is interpreted in terms of the projection of forces along the internuclear axis. The slightly different kinematic factors arise, in part, from the definition of the collision frequency that is used to derive, Eq. (5.11). The hard-sphere model gave excellent agreement with simulations for a very steep exponential repulsive potential with exponent 2a = 256h, where b is that of the Morse oscillator. It is to be remembered that Eq. (5.12) was derived from a stochastic model with three major assumptions ... 

The usual definition of the "activated complex rests on conditions (112,111) which are not always realized simultaneously, as is the case of a Morse-type potential function V(x) which has no peak. According to (110,111), however, the free energy F(x,T) may posses a maximum in such a case, too. Therefore, the activated complex can be defined in the framework of the adiabatic approximation, using the conditions (110.Ill), also for reactions for which a potential energy barrier does nor exist. 

The position of the mercury meniscus in the capillary depends on the surface tension between the mercury and the sulphuric acid and this, in turn, depends on the electrical potential between the mercury and the acid. If this potential is altered, as, for example, by connecting the two mercury electrodes with a cell or with two points of a circuit between which there is a difference of potential, the meniscus will movej and for small differences of potential, the amount of movement is proportional to the difierence of potential. In order, however, that the meniscus shall take up a definite position, the two electrodes must be connected together except when making a measurement This is efiected by means of a triple contact Morse key, shown in Fig. 72. The electrical connections between the terminals a, b, c and the contacts d, V, d are indicated by means of the dotted lines. The electrodes of the electrometer are connected with the terminals b and c, so that they are connected together when the key is in its normal position. The terminals a and c are connected with the rest of the circuit, so... 

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