Inverse-power dependence

A+B L -fl/2) have also been used. The theoretical assumption underlying an inverse power dependence is that the basis set is saturated in the radial part (e.g. the cc-pVTZ ba.sis is complete in the s-, p-, d- and f-function spaces). This is not the case for the correlation consistent basis sets, even for the cc-pV6Z basis the errors due to insuficient numbers of s- to i-functions is comparable to that from neglect of functions with angular moment higher than i-functions. 

The correlation energy is expected to have an inverse power dependence once the basis set reaches a sufficient (large) size. Extrapolating the correlation contribution for n = 3-5(6) with a function of the type A + B n + I) yields the cc-pVooZ values in Table 11.8. The extrapolated CCSD(T) energy is —76.376 a.u., yielding a valence correlation energy of —0.308 a.u. 

From the high inverse power dependence of CTe on v as seen from Eq. (3.5), it is clear that capture probability increases very rapidly with slowing down. The equilibrium ionic charge can be estimated at a given velocity from Eqs. (3.4) and (3.5). Since charge exchange is a nonequilibrium phenomenon,... 

This is a Dunham-like expansion but done around the anharmonic solution. It converges very quickly to the exact solution if the potential is not too different from that of a Morse oscillator (Figure 2.3). This will not, however, be the case for the highest-lying vibrational states just below the dissociation threshold. The inverse power dependence of the potential suggests that fractional powers of n must be included (LeRoy and Bernstein, 1970). 

The inverse power dependence of Lennard-Jones terms... 

Our primary interest in this section is to discuss the functional form that relates potential energy to the distance of separation for various types of interactions. For many interactions an inverse power dependence on the separation describes the potential energy. Several examples of this are shown in Table 10.1. The main point to be observed now is that the value of the exponent in the inverse power dependence on the separation differs widely for the various types of interactions. An immediate consequence of this is that the range of the interactions is quite different also. 

In a study of the decay kinetics for annealed dimethyloctoxy, methoxy-PPV (dMOM-PPV), the form of the decay was found to gradually change from stretched-exponential (Act = Acr(0)exp[-(t/T) ]) at 150°C to an inverse power-dependence (Acr = Act(0)[1 - (f/r) ]) at -50°C. A similar effect has been found in a more thorough analysis of the decay kinetics for regio-regular... 

The correlation energy is expected to have an inverse power dependence once the basis set reaches a sufficient (large) size. Extrapolating the correlation contribution for... 

Table 1 contains a short overview over the dominant contributions to the interaction between a molecule and an oxide surface. It is useful to make the distinction between physical and chemical contributions. Contrary to most experimentalists who use the numerical value of the adsorption energy as criterion to discriminate between physisorption and chemisorption (e.g., physisorption only for adsorption energies below about 0.30 eV [4]) we prefer to employ the distance dependence of the interaction potential for this purpose. We will speak of a physical contribution if the interaction potential decays with an inverse power dependence on the distance R between adsorbate and surface while a chemical interaction shows an exponential behavior. 

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