## 2 The Selective Energy Transfer (SET) Theory
### COS and Resonance Conditions  
As mentioned in the Introduction, the basis of SET [13] is that energy is transferred between catalyst and reactants when there is a state of resonance between some vibrations of these species. In turn, this requires that there is a simple relation between the vibrational frequencies of catalyst and of the reactant-to-be. Thus, \(\omega\)/\(\upsilon\) can be 1:1, 2:1, 1:2, 3:1, etc. The important point is that an equal amount of energy is donated from the catalyst as is accepted by the reactant molecule. In Table 1, we have collected vibrational frequencies of the molecule COS [7] as well as of a small amino acid (glycine) bound to a metal atom (in this case Ni\({}^{2+}\) or Cu\({}^{2+}\)) [23]. At first glance one does not note any obvious relation between the wave numbers of COS and those of the metal complexes of the amino acid. However, one clearly notices, vide Table 2, that two times of the 1058 cm\({}^{-1}\) vibration of the (Cu) amino acid complex agrees well with the \(\upsilon\) vibration of COS (2079 cm\({}^{-1}\)). This observation gives \(2\times 1058/2079=1.018\), which is as close to a resonance condition as one might imagine. However, this amino acid vibration at 1058 cm\({}^{-1}\) is not just any vibration. It is the out-of-plane wagging of the amino group (cf. Figure 1), and designated as \(\varrho_{\rm w}\) (NH\({}_{2}\)), [23], Table III -19 (page 236). For the nickel complexes, the similar value for the NH\({}_{2}\) wagging is 1038 cm\({}^{-1}\)[23], which gives \(2\times 1038/2079=0.999\). Thus, taking the mean value of both Cu and Ni data, we get \(\omega\) _(COS)/\(2\)\(\upsilon\) glycinate = \(1.009\pm 0.01\)_. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Assignment**} & \multicolumn{2}{c}{**Cu**} & \multirow{2}{*}{**Ni (Glycinate)\({}_{2}\)**} & \multirow{2}{*}{**Assignment**} & \multirow{2}{*}{**COS**} \\  & **(Glycinate)\({}_{2}\)** & & & \\ \hline \(\upsilon\) (NH\({}_{2}\)) & 3320 & 3340 & & \\ \(\upsilon\) (NH\({}_{2}\)) & 3260 & 3280 & \(\upsilon\) 1 & 850 m \\ \(\upsilon\) (C=O) & 1593 & 1589 & & \\ \(\upsilon\) (NH\({}_{2}\)) & 1608 & 1610 & \(\upsilon\) 2 & 527 m \\ \(\upsilon\) (C-O) & 1392 & 1411 & & \\ \(\varrho_{\rm t}\) (NH\({}_{2}\)) & 1151 & 1095 & \(\upsilon\) 3 & 2079 v s \\ \(\varrho_{\rm w}\) (NH\({}_{2}\)) & 1058 & 1038 & & \\ \(\varrho_{\rm r}\) (NH\({}_{2}\)) & 644 & 630 & & \\ \(\delta\) (C=O) & 736 & 737 & & \\ \(\prod\) (C=O) & 592 & 596 & & \\ \(\upsilon\) (MN) & 439 & 439 & & \\ \(\upsilon\) (MO) & 360 & 290 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Vibrational assignments for Ni and Cu glycinate complexes [23] and for carbonyl sulfide [7]. Assignments are denoted as in these references. Vibration frequencies are given in cm\({}^{-1}\). Data used by copyright according to Sections 107 and 108 of the 1976 United States Copyright Act (relating to research use/“fair use”). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{2}{c}{**Cu**} & \multirow{2}{*}{**Ways of Forming Differences**} & \multirow{2}{*}{**COS**} & \multicolumn{2}{c}{**Diff (Cu -**} & \multirow{2}{*}{**Diff Absolute**} \\  & **(Glycinate)\({}_{2}\)** & & & **COS) cm\({}^{-1}\)** & \\ \hline
1 & 1593 & \(\upsilon\) C - \(\upsilon\)1(COS) & 850 & 743 & 46.6 \\
2 & & \(\upsilon\)Cu - \(2\times\upsilon\)1(COS) & & \(-\)107 & 6.7 \\
3 & 1608 & \(\upsilon\)Cu - \(\upsilon\)1(COS) & 850 & 758 & 47.1 \\
4 & & \(\upsilon\)Cu - \(2\times\upsilon\)1(COS) & & \(-\)92 & 5.7 \\
5 & 1392 & \(\upsilon\)Cu - \(\upsilon\)1(COS) & 850 & 542 & 38.9 \\
6 & & \(\upsilon\)Cu - \(2\times\upsilon\)1(COS) & & \(-\)308 & 22.1 \\
7 & & \(\upsilon\)Cu - \(2\times\upsilon\)2(COS) & 527 & \(-\)338 & 24.3 \\
8 & & \(\upsilon\)Cu - \(3\times\upsilon\)2 (COS) & 1581 & \(-\)189 & 13.6 \\
9 & 1058 & \(\upsilon\)Cu - \(2\times\upsilon\)2 (COS) & \(2\times 527\) & 4 & 0.4 \\
10 & 1058 & \(2\times\upsilon\)Cu - \(\upsilon\)3(COS) & 2079 & 37 & 3.5 \\ \hline \hline \end{tabular}
\end{table}