Unity bond index-Quadratic exponential

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. ... 

Besides using the DFT approach, other high-level theoretical models have also been developed to probe the kinetic parameters, relevant to SOFC operation. For example, the unity bond index-quadratic exponential potential (UBI-QEP) [104,105] was successfully performed to study several elementary reactions on various transition metal surfaces [106]. This approach generated activation barriers and enthalpy changes for forward and reverse reactions for the formation and dissociation of H20 and OH" species. 

UBI-QEP, See Unity bond index-quadratic exponential potential (UBI-QEP) Ubiquitinated proteins, folding of, 271-273 protein degradation, 271-272... 

Unity Bond Index-Quadratic Exponential Potential... 

Thus, it is adequate to determine the energetic characteristics of the elementary reactions based on the Unity Bond Index-Quadratic Exponential Potential (UBI-QEP) method developed by Shustorovich [2], while the pre-exponential factors may be estimated simply from the transition-state theory [4,26]. Here we employ, for illustrative purposes, a simplified version of a microkinetic WGSR model developed by us earlier [14],... 

The second step is to find good estimates of the rate parameters. The rate parameters can be obtained from collision theory, transition state theory, as well as first principles calculations such as DFT Calorimetric measurements of heats of adsorption is possible for the surface intermediates with a gas phase precursor. Otherwise, the surface energetic must be estimated. As we have mentioned earlier, the computational cost of DFT is overriding its utility and accuracy in the present-day capabilities. Eventually, the parameter space must be constructed with two major constraints. The first constraint requires the consistency with the thermodynamics and the second constraint requires that the macroscopic rate data can be reproduced. Unity bond index-quadratic exponential potential (UBI-QEP) method of Shustorovich (1986, 1998) offers a relatively accurate and affordable estimation of the surface energetics. 

The semi-empirical methods referred to as bond-order conserving Morse potential (BOC-MP) or the unity bond index quadratic exponential potential (UBI-QEP) method have been reviewed extensively by Shustorovich and Sellers [145]. The UBI-QEP method is, like some of the empirical methods mentioned above, also based on the use of atom-atom interaction potentials, and here again a Morse form is convenient... 

Elementary rate constants can be estimated also using semi-empirical methods, which are not as accurate as quantum mechanical approaches, being able at the same time to reduce the computational costs of model development. One of such computationally inexpensive semi-empirical approaches appHcable to small molecules, is the bond-order conservation (BOG) or unity bond index—quadratic exponential potential (UBI—QEP) technique of Shustorovich and Sellers. This method ensures thermodynamic consistency... 

Very recently, Shustorovich and coworkers have extended the conceptual framework of this initial BOC-MP model to prove that the quadratic exponential potential (QEP), expressed in terms of a unity bond index (UBI) after normalization, provides a general, accurate description of any two-center, quasi-spherical interaction. As a result, the formalism has been renamed the UBI-QEP method [19-22]. This recent work includes a newly developed formalism to calculate the heat of adsorption of polyatomic molecules, such as ethylene and acetylene, without bond energy partitioning [19,22]. The reader is invited to study these latter papers to learn the most recent and accurate applications of this approach, which will be referred to as the BOC-MP/UBI-QEP method in this chapter. In this section, only an overview of the initial BOC-MP method will be provided, and greater detail is provided in these publications of Shustorovich [16-18]. 

---