## 2 The Selective Energy Transfer (SET) Theory
### COS and Resonance Conditions

Table 2: Collection of a series vibrational frequencies (cm\({}^{-1}\)) from both an amino acid chelate (designated “Cu”) and the COS molecule. The percentage of the differences are calculated based on the data in column 2. We can thus write: \(\omega=2\ v\), or  
\[\omega/v=2\cdot 1. \tag{3}\]  
Relation (3) implies that two vibrational quanta of the \(\omega_{\mathrm{w}}\) (NH\({}_{2}\)) vibration of the amino acid can accept energy from one quantum of the COS molecule. As Table 2 indicates, another combination of vibrations is close to a state of resonance, viz., \(2\times\upsilon_{2}\) of COS agrees quite well with 1058 cm\({}^{-1}\) of the Cu chelate (i.e., \(2\times 527/1058=0.996\)). However, we prefer to concentrate the discussion to the above treatment of \(v\) 3 of COS because this vibration shows a very strong absorption of IR radiation [6], (vide Figure 1), and thus gives a much higher emission than what the \(v\) 2 of the same molecule. In other words, the flow of quanta from 2079 cm\({}^{-1}\) is much stronger than the flow of quanta from 527 cm\({}^{-1}\). The designation of this vibration as \(\omega_{\mathrm{w}}\)(NH\({}_{2}\)) means - as said above - that it is an out-of-plane \"wagging\" movement, in which both H atoms bend away from the plane that they form with nitrogen (cf. Figure 2) [24]. It follows from SET that the vibration found in this supposed molecular reaction is the one that actually activates the reaction [13; 14; 15]. If activation energies had been measured, we would have seen (Equation (1)) that they all had been a sum of the energy of a vibration with a frequency of 1058-1038 cm\({}^{-1}\). Of course, this is an approximate statement, as one must take the anharmonicity into consideration (Equation (2)). In the present case, the NH\({}_{2}\) group is part of an amino acid chelate around the metal ion M. To emphasize the role of the NH\({}_{2}\) group, we display a schematic picture of the nearest atom groups around the tetrahedrally bonded central nitrogen atom (Figure 2). The tetrahedral configuration around the nitrogen atom can be described so that each of the four groups at the corners of the tetrahedron engages with one sp3 orbital, each one originating from  
Figure 1: Schematic representation of the out-of-plane vibrations in relation to the plane formed by three atoms. Figure 2: Environment of the nitrogen atom with sp3 orbital hybridization (cf. Scheme 1). M represents the metal ion that keeps the two amino acid molecules together, C depicts the carbon atom nearest the carboxylate group of the acid under consideration. the nitrogen atom. However, when the two hydrogen atoms move together, in the \(\phi_{\text{w}}\)(NH\({}_{2}\)) vibration, perpendicularly against the N-H-H plane, the type of bonding tends more and more towards an sp2 configuration. In the extreme, the system forms three sp2 orbitals from the central nitrogen atom towards each of three remaining atoms or atomic groups (cf. Figure 3). This implies that one of the two hydrogen atoms must leave the scene. Or rather (vide Scheme 1), this H atom is free to attack the OH- group of the neighboring amino acid, forming water and making possible a combination of the two amino acids to form a peptide bond. Thus, the interference of the catalyst (COS) and the amino acids results in a peptide bond between the two molecules and the formulation of a water molecule. The catalyst COS remains intact, but for a loss of some energy and ready for the next cycle of activation and energy transfer under the hydrothermal vent condition (along with fresh supply of COS coming from the effluent of the vents); before being lost due to dissipation or through hydrolysis or other types of reactions. Figure 3: **(a) The plane of wagging. ** The three atoms, N, H, and H, define a plane in space. When the two hydrogen atoms move perpendicularly against this plane, the vibration is called “wagging”, cf. Figure 2. **(b) The more complete structure around the sp3 nitrogen.