*3.4. Modeling Studies*

The thermodynamic parameters of the SMT-BCD or SMT-RAMEB complexes were determined at 298 K as follows: The enthalpy change considered as the energy change calculated by subtracting the total energies of the reactants from the total energies of the products. Similarly, the entropy changes were calculated by subtracting the entropy terms of the reactants from the entropy terms of the products. The entropy terms of the species interacted were calculated applying Boltzmann statistics. The higher contribution to the entropy comes from the vibrational motions. Therefore, after calculating the vibrational frequencies using the harmonic approximation, the entropy was then determined as the following equation implemented in the HyperChem code:

$$S\_{vib} = R \sum\_{i} \left\{ \frac{h\nu\_i/kT}{e^{(h\nu\_i/kT)} - 1} - \ln[1 - e^{(-h\nu\_i/kT)}] \right\} \tag{2}$$

where the ν*<sup>i</sup>* is the frequency of vibration and *T* is the temperature (298.16 K).

The total energies of the species interacted have been calculated at semi-empirical MINDO/3 level using HyperChem 8 code. After the geometry optimization at MINDO/3 level the vibrational-rotational analysis was performed in harmonic approximation using AM1 approximation. Neutral aqueous environment was considered by the TIP3P solvation model implemented in HyperChem code [47]. Considering that in the present studies ionic species are interacted, the ionic strength of the buffer were considered by the additional PO<sup>4</sup> <sup>3</sup>−, K+, Na<sup>+</sup> and H3O<sup>+</sup> ions as described in an earlier study [34]. Accordingly, the final cube for representing solvents has 30 Å × 30 Å × 30 Å sizes and contained water, PO<sup>4</sup> <sup>3</sup>−, HPO<sup>4</sup> <sup>2</sup>−, K+, Na<sup>+</sup> and 9 H3O<sup>+</sup> according to the composition of the buffer solution while the pH varied from 7, 5 and 2. After 10 ps MD simulation to equilibrate the system at room-temperature at MM+ level, the calculations for the complexes and the separated species interacted were performed at MINDO/3 level. To reduce the huge computational time, the random-methylated CD derivative (RAMEB, which have electron-rich cavity) was considered as negatively charged species of the native BCD [48,49].
