## 2 The Selective Energy Transfer (SET) Theory  
During the past few decades, one of the present authors has developed a new model for catalysis, different from those schemes that have commonly been used to describe the technological aspects of a catalyst and the mechanism of a catalytic reaction.  
The basis of this concept [14; 15] is the selective transfer of energy from a molecular vibrator in the catalyst system towards a vibrating system in the molecule that is involved in the reaction. Because of this view, the new model has been named \"SET\" or the selective energy transfer model.  
The main idea of the SET theory is that energy is transferred from a molecular vibration of the catalyst system to a vibration of similar frequency in the reacting molecule. The condition for such a transfer of energy is that a state of resonance holds between the two systems. The rate of energy transfer from one vibrator to another in a damped, coupled oscillating system was calculated in classical physics [16].  
The classical expression for the rate of energy exchange is  
\[P=P_{res}\times(\omega^{2}/\tau^{2})/[(\upsilon^{2}-\omega^{2})^{2}+\omega^{2 }/\tau^{2}], \tag{1}\]  
where \(P\) is the energy transfer per unit of time;  
\(P_{res}\) is the power absorption at resonance (i.e., when \(\upsilon=\omega\));  
\(\omega\) is the frequency of the catalyst system;  
\(\upsilon\) is the frequency of the reacting molecule;  
\(\tau\) is the relaxation time; and  
\(Q=\tau\times\upsilon\) is the \"quality factor\".  
We take this rate--after integrating over all possible values of the \"quality factor\" Q, and freshening it up to quantum chemistry standards--to equal the rate of the chemical reaction [13; 15]. Further details can be found in [13].  
The SET theory has recently been summarized [15]. One fact, illustrated by the investigated catalytic systems, is that the activation energy (enthalpy) is built up by a certain number of vibrational quanta related to the \(\upsilon\) vibration. This can be expressed [15] as a second-order relation between the activation enthalpy, \(\Delta H^{\#}\), and the vibrational quantum number n:  
\[\Delta H^{\#}=M0+M1~{}\text{n}+M2~{}\text{n}^{2}. \tag{2}\]  
The second-order term corresponds to the anharmonicity of the system, and shall consequently have a negative sign. The M1 coefficient describes the wave number of the \(\upsilon\) vibration. M0 indicates the state of adsorption of the reacting molecule. In most cases reported before [15], M0 is very close to zero, indicating that the activation occurs for only lightly adsorbed species, but close to the catalyst surface (for reaction with another reactant available at the surface). This latter statement is a reasonable one, as the molecule can better keep its state of activation when not in contact with a solid surface. In the concluding remarks on this model [15], it was reported on the decomposition of formic acid (which can react along two different lines), but also on some dehydrochlorination reactions. Recently, the SET model has been applied to the technically important dehydrogenation of propane [17], as well as to the equally important ammonia synthesis from N\({}_{2}\) and H\({}_{2}\)[18]. In all these cases, one can state that the SET model works well [19].